LMFDB - Embedded newform 120.4.m.b.59.51

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			59.51
Character	$\chi$	$=$	120.59
Dual form			120.4.m.b.59.50

$q$-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} +(-28.9775 - 12.6612i) q^{10} +38.5985i q^{11} +(40.2171 - 10.5159i) q^{12} +36.1882 q^{13} +(-60.0059 - 52.7480i) q^{14} +(24.5543 + 52.6506i) q^{15} +(-61.8961 + 16.2750i) q^{16} +74.9762 q^{17} +(-68.1995 - 34.3633i) q^{18} -136.377 q^{19} +(-37.9147 - 81.0091i) 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} +(-46.1580 + 157.700i) 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} +(70.7326 - 242.893i) q^{40} +173.978i q^{41} +(-232.321 + 344.049i) q^{42} -86.0147i q^{43} +(-306.239 + 39.5886i) q^{44} +(255.186 - 161.261i) q^{45} +(214.030 - 243.480i) q^{46} +239.821i q^{47} +(124.682 + 308.296i) q^{48} +454.882 q^{49} +(351.689 + 36.2627i) 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} +(-392.545 + 248.814i) 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} +(818.522 + 357.637i) q^{70} -124.611 q^{71} +(202.689 - 576.338i) q^{72} +267.766i q^{73} +(-213.342 - 187.538i) q^{74} +(-440.624 - 477.206i) q^{75} +(-139.876 - 1082.01i) q^{76} -1090.28i q^{77} +(297.636 - 440.775i) q^{78} -586.207i q^{79} +(603.838 - 383.901i) 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} +(843.240 + 133.962i) 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	$-0.776074\pi$
$7$	−28.2468			−1.52518			−0.762592	+	0.646880i	$0.776074\pi$
$8$	−12.6371	+	18.7698i	−0.558485	+	0.829515i
$9$	−26.1311	+	6.79452i	−0.967819	+	0.251649i
$10$	−28.9775	−	12.6612i	−0.916349	−	0.400381i
$11$			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	$-0.373846\pi$
$13$	36.1882			0.772061			0.386031	+	0.922486i	$0.373846\pi$
$14$	−60.0059	−	52.7480i	−1.14552	−	1.00696i
$15$	24.5543	+	52.6506i	0.422659	+	0.906289i
$16$	−61.8961	+	16.2750i	−0.967126	+	0.254297i
$17$	74.9762			1.06967			0.534835	−	0.844957i	$-0.320374\pi$
$17$	74.9762			1.06967			0.534835	+	0.844957i	$0.320374\pi$
$18$	−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	$0.807895\pi$
$20$	−37.9147	−	81.0091i	−0.423899	−	0.905710i
$21$	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	$-0.826104\pi$
$23$		−	114.614i		−	1.03908i	0.854448	−	0.519538i	$-0.173896\pi$
$24$	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	$0.613827\pi$
$30$	−46.1580	+	157.700i	−0.280909	+	0.959735i
$31$		−	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	$-0.571621\pi$
$37$	−100.427			−0.446221			−0.223110	+	0.974793i	$0.571621\pi$
$38$	−289.712	−	254.671i	−1.23678	−	1.08719i
$39$	−23.8526	−	186.520i	−0.0979353	−	0.765824i
$40$	70.7326	−	242.893i	0.279595	−	0.960118i
$41$			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	$-0.951260\pi$
$43$		−	86.0147i		−	0.305049i	0.988300	−	0.152525i	$-0.0487403\pi$
$44$	−306.239	+	39.5886i	−1.04926	+	0.135641i
$45$	255.186	−	161.261i	0.845354	−	0.534207i
$46$	214.030	−	243.480i	0.686023	−	0.780416i
$47$			239.821i			0.744286i	0.928175	+	0.372143i	$0.121377\pi$
$47$			239.821i			0.744286i	−0.928175	+	0.372143i	$0.878623\pi$
$48$	124.682	+	308.296i	0.374922	+	0.927056i
$49$	454.882			1.32619
$50$	351.689	+	36.2627i	0.994726	+	0.102566i
$51$	−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	$0.212065\pi$
$53$			476.921i			1.23604i	−0.786162	+	0.618021i	$0.787935\pi$
$54$	−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	$0.681953\pi$
$60$	−392.545	+	248.814i	−0.844622	+	0.535363i
$61$			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	$-0.886642\pi$
$67$		−	382.405i		−	0.697287i	0.937256	−	0.348643i	$-0.113358\pi$
$68$	76.8994	+	594.859i	0.137139	+	1.06084i
$69$	−590.742	+	75.5455i	−1.03068	+	0.131806i
$70$	818.522	+	357.637i	1.39760	+	0.610655i
$71$	−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	$0.0688627\pi$
$73$			267.766i			0.429310i	−0.976690	+	0.214655i	$0.931137\pi$
$74$	−213.342	−	187.538i	−0.335142	−	0.294606i
$75$	−440.624	−	477.206i	−0.678385	−	0.734706i
$76$	−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	$-0.137068\pi$
$80$	603.838	−	383.901i	0.843889	−	0.536518i
$81$	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	$-0.559789\pi$
$83$	−282.399			−0.373462			−0.186731	+	0.982411i	$0.559789\pi$
$84$	−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	$0.882725\pi$
$90$	843.240	+	133.962i	0.987615	+	0.156898i
$91$	−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	$-0.816563\pi$
$97$		−	1041.15i		−	1.08982i	0.838494	−	0.544911i	$-0.183437\pi$
$98$	966.325	+	849.446i	0.996057	+	0.875581i
$99$	−262.258	−	1008.62i	−0.266242	−	1.02394i
$100$	679.390	+	733.777i	0.679390	+	0.733777i
$101$	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	$-0.409152\pi$
$103$	588.625			0.563097			0.281548	+	0.959547i	$0.409152\pi$
$104$	−457.312	+	679.244i	−0.431184	+	0.640436i
$105$	−693.580	−	1487.21i	−0.644633	−	1.38226i
$106$	−890.602	+	1013.14i	−0.816065	+	0.928351i
$107$	−1877.68			−1.69647			−0.848233	−	0.529624i	$-0.822333\pi$
$107$	−1877.68			−1.69647			−0.848233	+	0.529624i	$0.822333\pi$
$108$	−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	$0.880638\pi$
$110$	488.701	−	1118.49i	0.423598	−	0.969486i
$111$	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	$-0.635271\pi$
$113$	−990.495			−0.824583			−0.412292	+	0.911052i	$0.635271\pi$
$114$	−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
$120$	−1298.53	−	204.471i	−0.987829	−	0.155546i
$121$	−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	$-0.677799\pi$
$127$	−1517.02			−1.05995			−0.529976	+	0.848013i	$0.677799\pi$
$128$	476.707	−	1367.44i	0.329182	−	0.944266i
$129$	−443.335	+	56.6946i	−0.302585	+	0.0386952i
$130$	−1048.64	−	458.184i	−0.707477	−	0.309119i
$131$		−	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
$135$	−999.366	−	1208.98i	−0.637124	−	0.770761i
$136$	−947.478	+	1407.29i	−0.597394	+	0.887307i
$137$	508.245			0.316951			0.158476	−	0.987363i	$-0.449342\pi$
$137$	508.245			0.316951			0.158476	+	0.987363i	$0.449342\pi$
$138$	−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	$0.513258\pi$
$140$	1070.97	+	2288.25i	0.646524	+	1.38137i
$141$	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	$0.501529\pi$
$150$	−44.9034	−	1836.57i	−0.0244423	−	0.999701i
$151$		−	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	$-0.402618\pi$
$157$	1184.99			0.602372			0.301186	+	0.953565i	$0.402618\pi$
$158$	1094.68	−	1245.30i	0.551191	−	0.627032i
$159$	2458.14	−	314.352i	1.22606	−	0.156791i
$160$	1999.65	+	312.068i	0.988041	+	0.154194i
$161$			3237.49i			1.58478i
$162$	2015.61	+	434.567i	0.977538	+	0.210758i
$163$			2466.08i			1.18502i	0.805564	+	0.592509i	$0.201863\pi$
$163$			2466.08i			1.18502i	−0.805564	+	0.592509i	$0.798137\pi$
$164$	−1380.33	+	178.440i	−0.657232	+	0.0849625i
$165$	−2032.23	+	947.757i	−0.958843	+	0.447168i
$166$	−599.913	−	527.352i	−0.280495	−	0.246569i
$167$		−	1316.99i		−	0.610249i	−0.952312	−	0.305125i	$-0.901302\pi$
$167$		−	1316.99i		−	0.610249i	0.952312	−	0.305125i	$-0.0986981\pi$
$168$	−2967.95	−	1490.36i	−1.36299	−	0.684426i
$169$	−887.416			−0.403922
$170$	−2172.62	−	949.285i	−0.980191	−	0.428275i
$171$	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	$-0.877025\pi$
$173$		−	1714.78i		−	0.753598i	0.926295	−	0.376799i	$-0.122975\pi$
$174$	−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	$0.771586\pi$
$180$	1541.17	+	1859.25i	0.638178	+	0.769889i
$181$		−	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
$190$	3951.87	+	1726.69i	1.50894	+	0.659303i
$191$	−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	$-0.894484\pi$
$193$		−	1745.22i		−	0.650901i	0.945559	−	0.325450i	$-0.105516\pi$
$194$	1944.24	−	2211.76i	0.719528	−	0.818531i
$195$	888.574	+	1905.33i	0.326319	+	0.699710i
$196$	466.550	+	3609.03i	0.170026	+	1.31524i
$197$			3.00587i			0.00108710i	1.00000		0.000543552i	$0.000173018\pi$
$197$			3.00587i			0.00108710i	−1.00000		0.000543552i	$0.999827\pi$
$198$	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	$0.635864\pi$
$200$	73.0025	+	2827.48i	0.0258103	+	0.999667i
$201$	−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
$210$	1303.82	−	4454.53i	0.428437	−	1.46377i
$211$	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
$220$	3126.83	−	1463.45i	0.958230	−	0.448480i
$221$	2713.25			0.825851
$222$	−825.985	+	1223.22i	−0.249714	+	0.369806i
$223$	2027.95			0.608974			0.304487	−	0.952516i	$-0.401515\pi$
$223$	2027.95			0.608974			0.304487	+	0.952516i	$0.401515\pi$
$224$	4572.60	+	2288.30i	1.36393	+	0.682560i
$225$	−2169.18	+	2585.60i	−0.642719	+	0.766102i
$226$	−2104.15	−	1849.65i	−0.619318	−	0.544410i
$227$	1702.71			0.497853			0.248926	−	0.968522i	$-0.419922\pi$
$227$	1702.71			0.497853			0.248926	+	0.968522i	$0.419922\pi$
$228$	−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	$0.930003\pi$
$230$	−1451.15	+	3321.23i	−0.416026	+	0.952155i
$231$	−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	$-0.244761\pi$
$233$	5111.87			1.43730			0.718648	+	0.695374i	$0.244761\pi$
$234$	−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	$0.269860\pi$
$240$	−2376.70	−	2859.25i	−0.639231	−	0.769015i
$241$	−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
$250$	−3868.92	+	810.236i	−0.978767	+	0.204975i
$251$		−	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
$255$	1840.98	+	3947.54i	0.452106	+	0.969430i
$256$	3566.25	−	2014.72i	0.870666	−	0.491874i
$257$	−4939.16			−1.19882			−0.599410	−	0.800442i	$-0.704598\pi$
$257$	−4939.16			−1.19882			−0.599410	+	0.800442i	$0.704598\pi$
$258$	−1047.67	−	707.444i	−0.252809	−	0.170711i
$259$	2836.76			0.680569
$260$	−1372.06	−	2931.57i	−0.327276	−	0.699263i
$261$	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	$0.0118944\pi$
$263$			318.680i			0.0747174i	−0.999302	+	0.0373587i	$0.988106\pi$
$264$	−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	$0.349988\pi$
$270$	134.660	−	4434.51i	0.0303523	−	0.999539i
$271$			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	$-0.528532\pi$
$277$	−825.382			−0.179034			−0.0895170	+	0.995985i	$0.528532\pi$
$278$	−289.911	−	254.845i	−0.0625456	−	0.0549806i
$279$	388.061	+	1492.45i	0.0832710	+	0.320252i
$280$	−1997.97	+	6860.95i	−0.426434	+	1.46436i
$281$			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	$0.0355019\pi$
$283$			1059.77i			0.222603i	−0.993787	+	0.111301i	$0.964498\pi$
$284$	−127.808	−	988.665i	−0.0267042	−	0.206572i
$285$	−3348.65	−	7180.35i	−0.695988	−	1.49238i
$286$	−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
$290$	3168.01	+	1384.20i	0.641490	+	0.280287i
$291$	−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	$0.320285\pi$
$293$			8474.01i			1.68961i	−0.535072	+	0.844807i	$0.679715\pi$
$294$	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
$300$	3334.21	−	3985.35i	0.641670	−	0.766981i
$301$			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	$0.138131\pi$
$307$			4523.38i			0.840921i	−0.907311	+	0.420461i	$0.861869\pi$
$308$	8650.28	−	1118.25i	1.60031	−	0.206877i
$309$	−387.979	−	3033.88i	−0.0714284	−	0.558548i
$310$	−723.127	+	1655.01i	−0.132487	+	0.303221i
$311$	−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	$-0.819590\pi$
$313$		−	5946.35i		−	1.07383i	0.843637	−	0.536913i	$-0.180410\pi$
$314$	2517.32	+	2212.84i	0.452422	+	0.397701i
$315$	−7208.20	+	4555.10i	−1.28932	+	0.814764i
$316$	4650.96	−	601.244i	0.827964	−	0.107034i
$317$		−	5914.79i		−	1.04797i	−0.851726	−	0.523987i	$-0.824444\pi$
$317$		−	5914.79i		−	1.04797i	0.851726	−	0.523987i	$-0.175556\pi$
$318$	5808.95	+	3922.53i	1.02437	+	0.691713i
$319$		−	4219.84i		−	0.740644i
$320$	3665.19	+	4397.09i	0.640283	+	0.768139i
$321$	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
$330$	−6086.99	−	1781.63i	−1.01539	−	0.297198i
$331$	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	$-0.828914\pi$
$337$		−	6334.65i		−	1.02395i	0.859001	−	0.511974i	$-0.171086\pi$
$338$	−1885.17	−	1657.16i	−0.303373	−	0.266679i
$339$	652.862	+	5105.19i	0.104598	+	0.817922i
$340$	−2842.70	−	6073.75i	−0.453432	−	0.968810i
$341$	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
$345$	6034.51	−	2814.27i	0.941702	−	0.439175i
$346$	3202.18	−	3642.78i	0.497544	−	0.566003i
$347$	−1191.58			−0.184344			−0.0921722	−	0.995743i	$-0.529381\pi$
$347$	−1191.58			−0.184344			−0.0921722	+	0.995743i	$0.529381\pi$
$348$	−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	$0.879539\pi$
$350$	−9934.09	−	1024.31i	−1.51714	−	0.156433i
$351$	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	$-0.471358\pi$
$353$	1191.94			0.179718			0.0898592	+	0.995954i	$0.471358\pi$
$354$	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	$0.323229\pi$
$360$	−197.980	+	6827.65i	−0.0289845	+	0.999580i
$361$	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	$-0.456650\pi$
$367$	1909.09			0.271536			0.135768	+	0.990741i	$0.456650\pi$
$368$	1865.35	+	7094.17i	0.264233	+	1.00492i
$369$	−1182.09	−	4546.23i	−0.166768	−	0.641374i
$370$	2910.14	+	1271.53i	0.408894	+	0.178658i
$371$		−	13471.5i		−	1.88519i
$372$	−600.603	−	2296.95i	−0.0837091	−	0.320138i
$373$	−9250.82			−1.28415			−0.642077	−	0.766640i	$-0.721927\pi$
$373$	−9250.82			−1.28415			−0.642077	+	0.766640i	$0.721927\pi$
$374$	−5404.18	+	6147.77i	−0.747175	+	0.849982i
$375$	6316.18	+	3583.33i	0.869776	+	0.493447i
$376$	−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	$0.874108\pi$
$380$	5170.70	+	11047.8i	0.698030	+	1.49142i
$381$	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	$0.0901934\pi$
$383$			4191.08i			0.559149i	−0.960124	+	0.279575i	$0.909807\pi$
$384$	−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	$0.701442\pi$
$390$	−1670.37	+	5706.89i	−0.216879	+	0.740974i
$391$		−	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	$-0.416038\pi$
$397$	4124.77			0.521451			0.260726	+	0.965413i	$0.416038\pi$
$398$	−9543.84	+	10857.0i	−1.20198	+	1.36737i
$399$	−2539.11	−	19855.0i	−0.318582	−	2.49122i
$400$	−5124.96	+	6142.87i	−0.640620	+	0.767858i
$401$		−	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
$405$	−5572.61	+	5947.79i	−0.683717	+	0.729748i
$406$	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	$0.447391\pi$
$410$	2202.76	−	5041.43i	0.265333	−	0.607265i
$411$	−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	$-0.101129\pi$
$420$	11088.1	−	7028.21i	1.28820	−	0.816527i
$421$			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
$430$	−1089.05	+	2492.49i	−0.122136	+	0.279531i
$431$	−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	$0.168766\pi$
$433$			9112.89i			1.01140i	−0.862709	+	0.505701i	$0.831234\pi$
$434$	−3012.64	+	3427.16i	−0.333206	+	0.379053i
$435$	−2684.43	−	5756.11i	−0.295882	−	0.634447i
$436$	−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	$0.622536\pi$
$440$	9375.29	+	2730.17i	1.01579	+	0.295808i
$441$	−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	$-0.476863\pi$
$443$	1354.27			0.145245			0.0726224	+	0.997360i	$0.476863\pi$
$444$	−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	$0.540911\pi$
$450$	−9436.40	+	1441.97i	−0.988525	+	0.151056i
$451$	−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	$0.0108720\pi$
$457$			667.236i			0.0682976i	−0.999417	+	0.0341488i	$0.989128\pi$
$458$	−2823.21	+	3211.67i	−0.288035	+	0.327667i
$459$	3917.05	+	9762.34i	0.398327	+	0.992738i
$460$	−9284.80	+	4345.56i	−0.941100	+	0.440463i
$461$	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	$-0.554451\pi$
$463$	−3391.85			−0.340460			−0.170230	+	0.985404i	$0.554451\pi$
$464$	6766.89	−	1779.29i	0.677036	−	0.178020i
$465$	3007.08	−	1402.39i	0.299892	−	0.139858i
$466$	10859.4	+	9545.90i	1.07951	+	0.948938i
$467$	11937.5			1.18287			0.591437	−	0.806351i	$-0.298561\pi$
$467$	11937.5			1.18287			0.591437	+	0.806351i	$0.298561\pi$
$468$	−2920.71	−	7250.48i	−0.288483	−	0.716140i
$469$			10801.7i			1.06349i
$470$	3036.41	−	6949.41i	0.297998	−	0.682026i
$471$	−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	$0.601670\pi$
$480$	290.425	−	10512.3i	0.0276167	−	0.999619i
$481$	−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	$-0.134867\pi$
$487$	19593.7			1.82315			0.911576	+	0.411133i	$0.134867\pi$
$488$	−11540.4	−	7769.79i	−1.07051	−	0.720742i
$489$	12710.6	−	1625.46i	1.17545	−	0.150319i
$490$	−13181.3	−	5759.33i	−1.21525	−	0.530980i
$491$			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
$495$	6224.41	+	9849.79i	0.565185	+	0.894374i
$496$	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	$0.442269\pi$
$500$	−9731.93	−	5503.59i	−0.870450	−	0.492256i
$501$	−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	$0.288774\pi$
$503$			17774.3i			1.57558i	−0.615946	+	0.787788i	$0.711226\pi$
$504$	−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	$0.852494\pi$
$510$	−3460.75	+	11823.8i	−0.300479	+	1.02660i
$511$		−	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
$520$	2559.68	−	8789.85i	0.215864	−	0.741270i
$521$			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	$-0.962271\pi$
$523$		−	2828.70i		−	0.236502i	0.992984	−	0.118251i	$-0.0377287\pi$
$524$	7681.06	−	992.956i	0.640360	−	0.0827814i
$525$	12446.2	+	13479.5i	1.03466	+	1.12056i
$526$	−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
$530$	6038.38	−	13820.0i	0.494888	−	1.13265i
$531$	−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
$540$	8567.05	−	9168.95i	0.682717	−	0.730683i
$541$		−	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	$0.121359\pi$
$547$			9520.53i			0.744184i	−0.928196	+	0.372092i	$0.878641\pi$
$548$	521.282	+	4032.41i	0.0406352	+	0.314336i
$549$	−4177.56	−	16066.5i	−0.324761	−	1.24900i
$550$	−1399.68	+	13574.6i	−0.108514	+	1.05241i
$551$	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
$555$	−2465.92	−	5287.57i	−0.188599	−	0.404405i
$556$	−139.971	−	1082.76i	−0.0106765	−	0.0825883i
$557$		−	7627.12i		−	0.580200i	−0.956996	−	0.290100i	$-0.906311\pi$
$557$		−	7627.12i		−	0.580200i	0.956996	−	0.290100i	$-0.0936885\pi$
$558$	−1962.62	+	3895.13i	−0.148896	+	0.295509i
$559$		−	3112.71i		−	0.235517i
$560$	−17056.5	+	10844.0i	−1.28709	+	0.818289i
$561$	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	$-0.448808\pi$
$563$	4278.28			0.320263			0.160131	+	0.987096i	$0.448808\pi$
$564$	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	$-0.126646\pi$
$570$	6294.90	−	21506.8i	0.462569	−	1.58038i
$571$	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	$0.129901\pi$
$577$			11001.0i			0.793725i	−0.917878	+	0.396862i	$0.870099\pi$
$578$	1504.93	+	1322.91i	0.108299	+	0.0952002i
$579$	−8995.19	+	1150.32i	−0.645643	+	0.0825663i
$580$	4145.08	+	8856.45i	0.296750	+	0.634042i
$581$	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
$585$	9234.73	−	5835.73i	0.652665	−	0.412440i
$586$	−15824.3	+	18001.7i	−1.11552	+	1.26901i
$587$	−4095.31			−0.287958			−0.143979	−	0.989581i	$-0.545990\pi$
$587$	−4095.31			−0.287958			−0.143979	+	0.989581i	$0.545990\pi$
$588$	18294.0	−	4783.49i	1.28305	−	0.335490i
$589$			7789.03i			0.544892i
$590$	9651.39	−	22089.1i	0.673460	−	1.54134i
$591$	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	$-0.363871\pi$
$593$	11978.2			0.829490			0.414745	+	0.909938i	$0.363871\pi$
$594$	−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	$0.349272\pi$
$600$	14525.2	−	2239.94i	0.988318	−	0.152409i
$601$	−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	$-0.502918\pi$
$607$	−274.138			−0.0183310			−0.00916549	+	0.999958i	$0.502918\pi$
$608$	22076.8	+	11048.1i	1.47259	+	0.736937i
$609$	−2035.47	−	15916.8i	−0.135437	−	1.05908i
$610$	7784.61	−	17816.6i	0.516704	−	1.18258i
$611$			8678.68i			0.574635i
$612$	−6051.25	−	15021.8i	−0.399685	−	0.992192i
$613$	−9402.87			−0.619541			−0.309770	−	0.950811i	$-0.600252\pi$
$613$	−9402.87			−0.619541			−0.309770	+	0.950811i	$0.600252\pi$
$614$	−8446.94	+	9609.20i	−0.555197	+	0.631589i
$615$	−9160.03	+	4271.89i	−0.600598	+	0.280097i
$616$	20464.4	+	13778.0i	1.33853	+	0.901186i
$617$	−11725.6			−0.765082			−0.382541	−	0.923938i	$-0.624951\pi$
$617$	−11725.6			−0.765082			−0.382541	+	0.923938i	$0.624951\pi$
$618$	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	$0.424712\pi$
$620$	−4626.74	+	2165.45i	−0.299700	+	0.140269i
$621$	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
$630$	−23818.8	−	3783.99i	−1.50629	−	0.239298i
$631$			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
$640$	−424.991	+	16185.3i	−0.0262488	+	0.999655i
$641$		−	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	$-0.906186\pi$
$643$		−	9472.41i		−	0.580957i	0.956882	−	0.290478i	$-0.0938145\pi$
$644$	−25686.2	+	3320.53i	−1.57170	+	0.203179i
$645$	4528.72	−	2112.03i	0.276463	−	0.128932i
$646$	−21721.5	−	19094.2i	−1.32294	−	1.16293i
$647$			10796.3i			0.656024i	0.944674	+	0.328012i	$0.106379\pi$
$647$			10796.3i			0.656024i	−0.944674	+	0.328012i	$0.893621\pi$
$648$	−1380.54	+	16437.5i	−0.0836923	+	0.996492i
$649$	−29423.0			−1.77959
$650$	12727.0	+	1312.28i	0.767989	+	0.0791875i
$651$	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	$-0.803471\pi$
$653$		−	19320.8i		−	1.15786i	0.815378	−	0.578929i	$-0.196529\pi$
$654$	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	$0.916765\pi$
$660$	−9603.85	−	15151.6i	−0.566408	−	0.893600i
$661$		−	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
$670$	−4841.69	+	11081.1i	−0.279180	+	0.638958i
$671$	−23731.9			−1.36537
$672$	8780.38	−	25076.3i	0.504034	−	1.43949i
$673$		−	28415.4i		−	1.62754i	−0.581188	−	0.813769i	$-0.697412\pi$
$673$		−	28415.4i		−	1.62754i	0.581188	−	0.813769i	$-0.302588\pi$
$674$	11829.3	−	13457.0i	0.676036	−	0.769055i
$675$	14756.4	+	9476.08i	0.841442	+	0.540347i
$676$	−910.179	−	7040.74i	−0.0517853	−	0.400588i
$677$			13799.2i			0.783377i	0.920098	+	0.391689i	$0.128109\pi$
$677$			13799.2i			0.783377i	−0.920098	+	0.391689i	$0.871891\pi$
$678$	−8146.51	+	12064.3i	−0.461452	+	0.683373i
$679$			29409.2i			1.66218i
$680$	5303.26	−	18211.2i	0.299074	−	1.02701i
$681$	−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	$-0.927808\pi$
$683$	−34785.2			−1.94878			−0.974392	+	0.224858i	$0.927808\pi$
$684$	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
$690$	18074.7	+	5290.37i	0.997236	+	0.291885i
$691$	−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
$700$	−19190.6	−	20726.9i	−1.03620	−	1.11915i
$701$	−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
$705$	−12626.7	+	5888.63i	−0.674538	+	0.314579i
$706$	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	$-0.0411590\pi$
$710$	3610.93	+	1577.73i	0.190867	+	0.0833957i
$711$	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	$0.676027\pi$
$720$	−13170.5	+	14134.6i	−0.681717	+	0.731616i
$721$	−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	$-0.568570\pi$
$727$	−8380.16			−0.427515			−0.213757	+	0.976887i	$0.568570\pi$
$728$	12917.6	−	19186.5i	0.657635	−	0.976783i
$729$	−14224.1	+	13604.9i	−0.722662	+	0.691202i
$730$	3390.23	−	7759.19i	0.171888	−	0.393398i
$731$		−	6449.05i		−	0.326302i
$732$	6465.61	+	24727.2i	0.326470	+	1.24855i
$733$	−26525.6			−1.33662			−0.668311	−	0.743882i	$-0.732982\pi$
$733$	−26525.6			−1.33662			−0.668311	+	0.743882i	$0.732982\pi$
$734$	4055.57	+	3565.04i	0.203942	+	0.179275i
$735$	11169.3	+	23949.8i	0.560525	+	1.20191i
$736$	−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	$0.365671\pi$
$740$	3807.67	+	8135.54i	0.189153	+	0.404147i
$741$	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	$-0.909813\pi$
$743$		−	11323.5i		−	0.559112i	0.960129	−	0.279556i	$-0.0901873\pi$
$744$	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
$750$	6726.21	+	19407.0i	0.327475	+	0.944860i
$751$			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	$-0.790462\pi$
$757$	−32951.4			−1.58209			−0.791044	+	0.611759i	$0.790462\pi$
$758$	−28928.2	−	25429.3i	−1.38618	−	1.21852i
$759$	−2915.94	−	22801.7i	−0.139449	−	1.09045i
$760$	−9646.32	+	33125.1i	−0.460406	+	1.58102i
$761$		−	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
$765$	19132.9	−	12090.7i	0.904249	−	0.571425i
$766$	−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	$0.390577\pi$
$770$	−13804.2	+	31593.7i	−0.646066	+	1.47865i
$771$	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	$0.0819420\pi$
$773$			10943.3i			0.509189i	−0.967048	+	0.254595i	$0.918058\pi$
$774$	−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
$780$	−14205.5	+	9004.14i	−0.652100	+	0.413333i
$781$		−	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	$-0.640160\pi$
$787$		−	39944.3i		−	1.80922i	0.426235	−	0.904612i	$-0.359840\pi$
$788$	−23.8485	+	3.08297i	−0.00107813	+	0.000139374i
$789$	1642.54	−	210.051i	0.0741138	−	0.00947784i
$790$	−7422.06	+	16986.8i	−0.334260	+	0.765017i
$791$	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
$795$	−25110.2	+	11710.5i	−1.12021	+	0.522424i
$796$	−40548.7	+	5241.87i	−1.80554	+	0.233408i
$797$		−	18167.9i		−	0.807452i	−0.914880	−	0.403726i	$-0.867715\pi$
$797$		−	18167.9i		−	0.807452i	0.914880	−	0.403726i	$-0.132285\pi$
$798$	31683.3	−	46920.4i	1.40549	−	2.08141i
$799$			17980.8i			0.796141i
$800$	−22358.3	+	3479.21i	−0.988108	+	0.153761i
$801$	−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	$-0.0671045\pi$
$810$	−22945.0	+	2228.85i	−0.995315	+	0.0966836i
$811$	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
$820$	14093.8	−	6596.30i	0.600215	−	0.280918i
$821$	−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	$-0.394113\pi$
$823$	15420.0			0.653106			0.326553	+	0.945179i	$0.394113\pi$
$824$	−7438.50	+	11048.4i	−0.314481	+	0.467097i
$825$	18419.4	−	17007.4i	0.777311	−	0.717724i
$826$	40208.9	−	45741.5i	1.69376	−	1.92682i
$827$	4715.44			0.198273			0.0991367	−	0.995074i	$-0.468392\pi$
$827$	4715.44			0.198273			0.0991367	+	0.995074i	$0.468392\pi$
$828$	−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	$-0.0131595\pi$
$830$	8183.22	+	3575.50i	0.342222	+	0.149527i
$831$	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	$0.480088\pi$
$840$	36679.5	+	5775.65i	1.50662	+	0.237237i
$841$	−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
$850$	26368.3	+	2718.84i	1.06403	+	0.109712i
$851$			11510.4i			0.463657i
$852$	−5011.51	+	1310.40i	−0.201516	+	0.0526920i
$853$	36888.5			1.48070			0.740350	−	0.672221i	$-0.234660\pi$
$853$	36888.5			1.48070			0.740350	+	0.672221i	$0.234660\pi$
$854$	32431.7	−	36894.1i	1.29952	−	1.47833i
$855$	−34801.6	+	21992.3i	−1.39204	+	0.879673i
$856$	23728.3	−	35243.6i	0.947450	−	1.40724i
$857$	31671.9			1.26242			0.631209	−	0.775613i	$-0.282559\pi$
$857$	31671.9			1.26242			0.631209	+	0.775613i	$0.282559\pi$
$858$	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	$0.534014\pi$
$860$	−6967.97	+	3261.22i	−0.276286	+	0.129310i
$861$	−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	$0.206304\pi$
$863$			30609.9i			1.20738i	−0.797218	+	0.603692i	$0.793696\pi$
$864$	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
$870$	5046.30	−	17240.9i	0.196650	−	0.671862i
$871$		−	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	$-0.355628\pi$
$877$	22759.7			0.876331			0.438165	+	0.898894i	$0.355628\pi$
$878$	−31838.8	+	36219.6i	−1.22381	+	1.39220i
$879$	43676.5	−	5585.45i	1.67596	−	0.214326i
$880$	14818.0	+	23307.2i	0.567630	+	0.892824i
$881$			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	$0.107351\pi$
$883$			17364.5i			0.661790i	−0.943668	+	0.330895i	$0.892649\pi$
$884$	2782.85	+	21526.9i	0.105879	+	0.819035i
$885$	−40134.7	+	18717.3i	−1.52442	+	0.710933i
$886$	2876.94	+	2528.96i	0.109089	+	0.0958942i
$887$			19856.5i			0.751654i	0.926690	+	0.375827i	$0.122641\pi$
$887$			19856.5i			0.751654i	−0.926690	+	0.375827i	$0.877359\pi$
$888$	−10552.1	−	5298.75i	−0.398769	−	0.200242i
$889$	42851.0			1.61662
$890$	7657.24	−	17525.1i	0.288395	−	0.660047i
$891$	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
$900$	−22738.9	−	14558.3i	−0.842181	−	0.539195i
$901$			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	$0.145483\pi$
$907$			24108.8i			0.882601i	−0.897359	+	0.441300i	$0.854517\pi$
$908$	1746.38	+	13509.2i	0.0638279	+	0.493744i
$909$	−13394.6	+	3482.82i	−0.488746	+	0.127082i
$910$	29620.8	+	12942.2i	1.07903	+	0.471463i
$911$	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
$915$	−32371.8	+	15097.0i	−1.16959	+	0.545455i
$916$	−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	$-0.219666\pi$
$920$	−27839.0	−	8106.96i	−0.997635	−	0.290520i
$921$	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	$-0.251893\pi$
$930$	9006.87	+	2636.26i	0.317577	+	0.0929530i
$931$	−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	$-0.667691\pi$
$937$		−	49586.1i		−	1.72882i	0.502784	−	0.864412i	$-0.332309\pi$
$938$	−20171.1	+	22946.5i	−0.702143	+	0.798754i
$939$	−30648.6	+	3919.41i	−1.06515	+	0.136214i
$940$	19427.7	−	9092.73i	0.674107	−	0.315502i
$941$	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
$945$	28228.9	+	34149.9i	0.971731	+	1.17555i
$946$	7052.88	+	6199.82i	0.242398	+	0.213080i
$947$	49832.8			1.70998			0.854989	−	0.518646i	$-0.173564\pi$
$947$	49832.8			1.70998			0.854989	+	0.518646i	$0.173564\pi$
$948$	−6164.49	−	23575.6i	−0.211196	−	0.807699i
$949$			9689.96i			0.331454i
$950$	−47962.4	−	4945.41i	−1.63801	−	0.168895i
$951$	−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	$-0.533862\pi$
$953$	−6247.53			−0.212358			−0.106179	+	0.994347i	$0.533862\pi$
$954$	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
$960$	20247.5	−	21789.3i	0.680715	−	0.732548i
$961$	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	$-0.487930\pi$
$967$	2279.95			0.0758204			0.0379102	+	0.999281i	$0.487930\pi$
$968$	2007.28	−	2981.40i	0.0666491	−	0.0989936i
$969$	6739.61	+	52701.7i	0.223434	+	1.74719i
$970$	−13182.2	+	30169.9i	−0.436344	+	0.998657i
$971$			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
$975$	−15945.4	−	17269.2i	−0.523755	−	0.567238i
$976$	−10006.5	−	38056.3i	−0.328178	−	1.24811i
$977$	−9928.15			−0.325107			−0.162554	−	0.986700i	$-0.551973\pi$
$977$	−9928.15			−0.325107			−0.162554	+	0.986700i	$0.551973\pi$
$978$	30037.0	+	20282.7i	0.982084	+	0.663159i
$979$	−23343.7			−0.762070
$980$	−17246.7	−	36849.6i	−0.562169	−	1.20114i
$981$	−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	$0.286446\pi$
$983$			48280.0i			1.56652i	−0.621692	+	0.783262i	$0.713554\pi$
$984$	−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
$990$	−5170.72	+	32547.8i	−0.165996	+	1.04488i
$991$		−	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	$-0.597163\pi$
$997$	−18921.6			−0.601056			−0.300528	+	0.953773i	$0.597163\pi$
$998$	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.59.51	yes	64
3.2	odd	2	inner	120.4.m.b.59.13	✓	64
4.3	odd	2		480.4.m.b.239.35		64
5.4	even	2	inner	120.4.m.b.59.14	yes	64
8.3	odd	2	inner	120.4.m.b.59.49	yes	64
8.5	even	2		480.4.m.b.239.36		64
12.11	even	2		480.4.m.b.239.32		64
15.14	odd	2	inner	120.4.m.b.59.52	yes	64
20.19	odd	2		480.4.m.b.239.29		64
24.5	odd	2		480.4.m.b.239.31		64
24.11	even	2	inner	120.4.m.b.59.15	yes	64
40.19	odd	2	inner	120.4.m.b.59.16	yes	64
40.29	even	2		480.4.m.b.239.30		64
60.59	even	2		480.4.m.b.239.34		64
120.29	odd	2		480.4.m.b.239.33		64
120.59	even	2	inner	120.4.m.b.59.50	yes	64

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
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} +(-28.9775 - 12.6612i) q^{10} +38.5985i q^{11} +(40.2171 - 10.5159i) q^{12} +36.1882 q^{13} +(-60.0059 - 52.7480i) q^{14} +(24.5543 + 52.6506i) q^{15} +(-61.8961 + 16.2750i) q^{16} +74.9762 q^{17} +(-68.1995 - 34.3633i) q^{18} -136.377 q^{19} +(-37.9147 - 81.0091i) 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} +(-46.1580 + 157.700i) 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} +(70.7326 - 242.893i) q^{40} +173.978i q^{41} +(-232.321 + 344.049i) q^{42} -86.0147i q^{43} +(-306.239 + 39.5886i) q^{44} +(255.186 - 161.261i) q^{45} +(214.030 - 243.480i) q^{46} +239.821i q^{47} +(124.682 + 308.296i) q^{48} +454.882 q^{49} +(351.689 + 36.2627i) 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} +(-392.545 + 248.814i) 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} +(818.522 + 357.637i) q^{70} -124.611 q^{71} +(202.689 - 576.338i) q^{72} +267.766i q^{73} +(-213.342 - 187.538i) q^{74} +(-440.624 - 477.206i) q^{75} +(-139.876 - 1082.01i) q^{76} -1090.28i q^{77} +(297.636 - 440.775i) q^{78} -586.207i q^{79} +(603.838 - 383.901i) 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} +(843.240 + 133.962i) 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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