LMFDB - Embedded newform 120.4.m.b.59.16

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			59.16
Character	$\chi$	$=$	120.59
Dual form			120.4.m.b.59.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.12434 + 1.86740i) q^{2} +(0.659128 + 5.15418i) q^{3} +(1.02565 - 7.93398i) q^{4} +(10.6502 + 3.40199i) q^{5} +(-11.0251 - 9.71838i) q^{6} -28.2468 q^{7} +(12.6371 + 18.7698i) q^{8} +(-26.1311 + 6.79452i) q^{9} +O(q^{10})$	\(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} +(-11.0251 - 9.71838i) 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} +(41.5692 + 0.0568831i) 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} +(42.8233 - 63.2310i) 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} +(-88.4133 + 77.5054i) 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} +(-84.3577 - 141.010i) 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} +(27.1062 + 214.292i) 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} +(311.424 + 274.513i) 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} +(43.0868 - 329.751i) 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} +(354.130 + 179.042i) 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} +(442.526 + 142.024i) 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} +(375.114 - 425.552i) 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} +(-457.752 - 404.612i) 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} +(-398.979 - 351.690i) 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} +(-1174.20 - 1.60677i) 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} +(671.187 - 527.738i) 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} +(524.245 + 780.963i) 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}+O(q^{10}) $ 64 * q - 32 * q^4 - 72 * q^6 - 112 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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
$6$	−11.0251	−	9.71838i	−0.750164	−	0.661252i
$7$	−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	$0.822569\pi$
$12$	41.5692	+	0.0568831i	0.999999	+	0.00136839i
$13$	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
$15$	−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	$0.679626\pi$
$18$	42.8233	−	63.2310i	0.560753	−	0.827983i
$19$	−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	$-0.173896\pi$
$24$	−88.4133	+	77.5054i	−0.751971	+	0.659196i
$25$	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	$-0.386173\pi$
$29$	109.327			0.700050			0.350025	+	0.936740i	$0.386173\pi$
$30$	−84.3577	−	141.010i	−0.513385	−	0.858159i
$31$			57.1138i			0.330901i	0.986218	+	0.165451i	$0.0529079\pi$
$31$			57.1138i			0.330901i	−0.986218	+	0.165451i	$0.947092\pi$
$32$	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
$36$	27.1062	+	214.292i	0.125492	+	0.992095i
$37$	−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	$0.892496\pi$
$42$	311.424	+	274.513i	1.14414	+	1.00853i
$43$			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	$0.121377\pi$
$47$			239.821i			0.744286i	−0.928175	+	0.372143i	$0.878623\pi$
$48$	43.0868	−	329.751i	0.129563	−	0.991571i
$49$	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	$0.787935\pi$
$54$	354.130	+	179.042i	0.892426	+	0.451194i
$55$	−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	$0.681953\pi$
$60$	442.526	+	142.024i	0.952164	+	0.305586i
$61$		−	614.842i		−	1.29053i	−0.763958	−	0.645266i	$-0.776747\pi$
$61$		−	614.842i		−	1.29053i	0.763958	−	0.645266i	$-0.223253\pi$
$62$	−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
$66$	375.114	−	425.552i	0.699597	−	0.793665i
$67$			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
$70$	818.522	−	357.637i	1.39760	−	0.610655i
$71$	124.611			0.208291			0.104145	−	0.994562i	$-0.466789\pi$
$71$	124.611			0.208291			0.104145	+	0.994562i	$0.466789\pi$
$72$	−457.752	−	404.612i	−0.749258	−	0.662278i
$73$		−	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
$78$	−398.979	−	351.690i	−0.579172	−	0.510527i
$79$			586.207i			0.834854i	0.908710	+	0.417427i	$0.137068\pi$
$79$			586.207i			0.834854i	−0.908710	+	0.417427i	$0.862932\pi$
$80$	−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	$-0.440211\pi$
$83$	282.399			0.373462			0.186731	+	0.982411i	$0.440211\pi$
$84$	−1174.20	−	1.60677i	−1.52518	−	0.00208705i
$85$	−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	$0.882725\pi$
$90$	671.187	−	527.738i	0.786104	−	0.618094i
$91$	−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
$96$	524.245	+	780.963i	0.557349	+	0.830278i
$97$			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
$100$	679.390	−	733.777i	0.679390	−	0.733777i
$101$	−512.592			−0.504998			−0.252499	−	0.967597i	$-0.581252\pi$
$101$	−512.592			−0.504998			−0.252499	+	0.967597i	$0.581252\pi$
$102$	826.620	+	728.647i	0.802428	+	0.707321i
$103$	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
$105$	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	$0.177667\pi$
$108$	−1086.63	+	280.956i	−0.968162	+	0.250324i
$109$		−	833.606i		−	0.732523i	−0.930512	−	0.366261i	$-0.880638\pi$
$109$		−	833.606i		−	0.732523i	0.930512	−	0.366261i	$-0.119362\pi$
$110$	−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	$-0.364729\pi$
$113$	990.495			0.824583			0.412292	+	0.911052i	$0.364729\pi$
$114$	1503.58	+	1325.37i	1.23529	+	1.08888i
$115$	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
$120$	−1205.29	+	524.666i	−0.916896	+	0.399127i
$121$	−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
$126$	−1209.62	+	1786.08i	−0.855251	+	1.26283i
$127$	−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	$-0.104639\pi$
$132$	−2.19560	+	1604.51i	−0.00144774	+	1.05799i
$133$	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	$0.550658\pi$
$138$	−1113.87	+	1263.64i	−0.687091	+	0.779477i
$139$	−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
$144$	1727.99	+	4.72917i	0.999996	+	0.00273679i
$145$	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	$-0.498471\pi$
$149$	17.4717			0.00960627			0.00480314	+	0.999988i	$0.498471\pi$
$150$	−418.712	−	1788.76i	−0.227918	−	0.973680i
$151$			2010.13i			1.08332i	0.840596	+	0.541662i	$0.182205\pi$
$151$			2010.13i			1.08332i	−0.840596	+	0.541662i	$0.817795\pi$
$152$	−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
$156$	1504.31	+	2.05849i	0.772060	+	0.00105648i
$157$	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
$162$	−689.395	+	1943.26i	−0.334346	+	0.942451i
$163$		−	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	$-0.901302\pi$
$167$		−	1316.99i		−	0.610249i	0.952312	−	0.305125i	$-0.0986981\pi$
$168$	2497.39	−	2189.28i	1.14689	−	1.00540i
$169$	−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	$-0.122975\pi$
$174$	−1205.34	−	1062.48i	−0.525152	−	0.462909i
$175$	−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	$0.771586\pi$
$180$	−440.334	+	2374.47i	−0.182336	+	0.983236i
$181$			3071.89i			1.26150i	0.775985	+	0.630752i	$0.217253\pi$
$181$			3071.89i			1.26150i	−0.775985	+	0.630752i	$0.782747\pi$
$182$	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
$186$	555.053	−	629.686i	0.218809	−	0.248230i
$187$		−	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	$-0.410668\pi$
$191$	1462.25			0.553953			0.276977	+	0.960877i	$0.410668\pi$
$192$	−2572.04	−	680.059i	−0.966777	−	0.255620i
$193$			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	$0.000173018\pi$
$197$			3.00587i			0.00108710i	−1.00000		0.000543552i	$0.999827\pi$
$198$	2440.62	+	1652.91i	0.875997	+	0.593270i
$199$		−	5110.77i		−	1.82057i	−0.413986	−	0.910283i	$-0.635864\pi$
$199$		−	5110.77i		−	1.82057i	0.413986	−	0.910283i	$-0.364136\pi$
$200$	−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
$204$	−3116.70	−	4.26487i	−1.06967	−	0.00146373i
$205$	−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
$210$	2382.84	+	3983.08i	0.783006	+	1.30885i
$211$	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
$216$	1783.73	−	2626.03i	0.561885	−	0.827215i
$217$		−	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
$222$	1107.22	+	975.992i	0.334739	+	0.295064i
$223$	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
$225$	−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	$0.580078\pi$
$228$	−5669.09	−	7.75756i	−1.64669	−	0.00225332i
$229$		−	1511.84i		−	0.436268i	−0.975919	−	0.218134i	$-0.930003\pi$
$229$		−	1511.84i		−	0.436268i	0.975919	−	0.218134i	$-0.0699970\pi$
$230$	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	$-0.755239\pi$
$233$	−5111.87			−1.43730			−0.718648	+	0.695374i	$0.755239\pi$
$234$	1549.70	−	2288.22i	0.432935	−	0.639254i
$235$	−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	$-0.730140\pi$
$239$	−4889.33			−1.32328			−0.661641	+	0.749820i	$0.730140\pi$
$240$	1580.69	−	3365.33i	0.425138	−	0.905129i
$241$	−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
$246$	1690.78	−	1918.12i	0.438212	−	0.497134i
$247$	−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	$-0.243279\pi$
$252$	−765.664	−	6053.08i	−0.191398	−	1.51313i
$253$	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	$0.295402\pi$
$258$	835.923	−	948.321i	0.201714	−	0.228837i
$259$	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	$0.988106\pi$
$264$	−2991.59	−	3412.62i	−0.697422	−	0.795576i
$265$	−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	$-0.650012\pi$
$269$	−4006.24			−0.908048			−0.454024	+	0.890990i	$0.650012\pi$
$270$	3162.46	+	3111.57i	0.712818	+	0.701349i
$271$		−	2562.23i		−	0.574333i	−0.957881	−	0.287166i	$-0.907287\pi$
$271$		−	2562.23i		−	0.574333i	0.957881	−	0.287166i	$-0.0927132\pi$
$272$	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
$276$	6.51961	−	4764.42i	0.00142186	−	1.03907i
$277$	−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	$0.808579\pi$
$282$	2330.67	−	2644.05i	0.492161	−	0.558337i
$283$		−	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
$288$	−3679.68	+	3216.80i	−0.752872	+	0.658167i
$289$	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	$0.679715\pi$
$294$	−5015.13	−	4420.72i	−0.994858	−	0.876944i
$295$	−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
$300$	4229.82	+	3018.04i	0.814030	+	0.580823i
$301$		−	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
$306$	−3210.73	+	4740.82i	−0.599820	+	0.885669i
$307$		−	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
$310$	−723.127	−	1655.01i	−0.132487	−	0.303221i
$311$	6896.96			1.25753			0.628763	−	0.777597i	$-0.283562\pi$
$311$	6896.96			1.25753			0.628763	+	0.777597i	$0.283562\pi$
$312$	−3199.52	+	2804.78i	−0.580567	+	0.508940i
$313$			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	$-0.824444\pi$
$317$		−	5914.79i		−	1.04797i	0.851726	−	0.523987i	$-0.175556\pi$
$318$	4634.90	−	5258.11i	0.817335	−	0.927234i
$319$			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
$324$	−2164.33	−	5415.52i	−0.371113	−	0.928588i
$325$	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
$330$	5442.76	−	3256.08i	0.907922	−	0.543155i
$331$	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
$336$	−1217.06	+	9314.40i	−0.197608	+	1.51233i
$337$			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
$340$	−2842.70	+	6073.75i	−0.453432	+	0.968810i
$341$	−2204.50			−0.350090
$342$	−5840.13	+	8623.28i	−0.923386	+	1.36343i
$343$	−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	$0.470619\pi$
$348$	4544.62	+	6.21883i	0.700049	+	0.000957944i
$349$		−	4817.79i		−	0.738941i	−0.929242	−	0.369471i	$-0.879539\pi$
$349$		−	4817.79i		−	0.738941i	0.929242	−	0.369471i	$-0.120461\pi$
$350$	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	$-0.528642\pi$
$353$	−1191.94			−0.179718			−0.0898592	+	0.995954i	$0.528642\pi$
$354$	7408.16	−	8404.26i	1.11226	−	1.26181i
$355$	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	$-0.676771\pi$
$359$	−7172.59			−1.05447			−0.527235	+	0.849719i	$0.676771\pi$
$360$	−3498.66	−	5866.46i	−0.512210	−	0.858860i
$361$	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
$366$	−5975.26	+	6778.70i	−0.853366	+	0.968110i
$367$	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
$372$	−3.24881	+	2374.17i	−0.000452803	+	0.330901i
$373$	−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
$375$	−5211.17	+	5057.48i	−0.717610	+	0.696445i
$376$	−4501.38	+	3030.63i	−0.617397	+	0.415672i
$377$	3956.33			0.540481
$378$	−10003.0	−	5057.35i	−1.36111	−	0.688154i
$379$	−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	$0.909807\pi$
$384$	6733.84	−	3358.35i	0.894882	−	0.446302i
$385$	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	$-0.298558\pi$
$389$	9075.46			1.18289			0.591445	+	0.806346i	$0.298558\pi$
$390$	−3052.75	−	5102.89i	−0.396364	−	0.662551i
$391$			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
$396$	−8271.36	+	1046.26i	−1.04962	+	0.132769i
$397$	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	$-0.0741314\pi$
$402$	3716.36	−	4216.06i	0.461082	−	0.523079i
$403$			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
$408$	6628.89	−	5811.05i	0.804360	−	0.705123i
$409$	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
$414$	−7247.18	−	4908.16i	−0.860337	−	0.582664i
$415$	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	$-0.101129\pi$
$420$	−12499.9	−	4011.71i	−1.45223	−	0.466075i
$421$		−	9513.73i		−	1.10136i	−0.834718	−	0.550678i	$-0.814369\pi$
$421$		−	9513.73i		−	1.10136i	0.834718	−	0.550678i	$-0.185631\pi$
$422$	−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
$426$	−1373.86	−	1211.02i	−0.156252	−	0.137733i
$427$			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	$-0.233854\pi$
$431$	13279.4			1.48410			0.742049	+	0.670345i	$0.233854\pi$
$432$	1114.59	+	8909.50i	0.124134	+	0.992265i
$433$		−	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
$438$	−2602.25	+	2952.15i	−0.283882	+	0.322053i
$439$		−	17049.8i		−	1.85363i	−0.375519	−	0.926815i	$-0.622536\pi$
$439$		−	17049.8i		−	1.85363i	0.375519	−	0.926815i	$-0.377464\pi$
$440$	−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	$-0.523137\pi$
$443$	−1354.27			−0.145245			−0.0726224	+	0.997360i	$0.523137\pi$
$444$	−4174.69	−	5.71262i	−0.446221	−	0.000610606i
$445$	−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	$0.540911\pi$
$450$	8943.63	−	3337.14i	0.936904	−	0.349588i
$451$	−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
$456$	12057.6	−	10570.0i	1.23826	−	1.08549i
$457$		−	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
$460$	−9284.80	−	4345.56i	−0.941100	−	0.440463i
$461$	−18594.5			−1.87860			−0.939300	−	0.343097i	$-0.888524\pi$
$461$	−18594.5			−1.87860			−0.939300	+	0.343097i	$0.888524\pi$
$462$	−10595.8	+	12020.5i	−1.06701	+	1.21048i
$463$	−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
$465$	−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	$0.701439\pi$
$468$	980.924	+	7754.85i	0.0968873	+	0.765958i
$469$		−	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
$474$	5696.98	−	6463.00i	0.552049	−	0.626277i
$475$	−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	$-0.398330\pi$
$479$	6583.62			0.628003			0.314001	+	0.949423i	$0.398330\pi$
$480$	2926.48	+	10100.9i	0.278281	+	0.960500i
$481$	−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
$486$	−10470.3	−	2272.41i	−0.977249	−	0.212096i
$487$	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	$0.919169\pi$
$492$	−9.89638	+	7232.11i	−0.000906836	+	0.662700i
$493$	−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
$498$	−3113.48	−	2744.46i	−0.280158	−	0.246953i
$499$	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	$0.711226\pi$
$504$	12930.0	+	11429.0i	1.14276	+	1.01010i
$505$	−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	$-0.147506\pi$
$509$	20544.9			1.78907			0.894537	+	0.446995i	$0.147506\pi$
$510$	6324.82	+	10572.4i	0.549152	+	0.917946i
$511$			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
$516$	−4.89278	+	3575.56i	−0.000417427	+	0.305049i
$517$	−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	$0.710486\pi$
$522$	4681.72	−	6912.83i	0.392555	−	0.579629i
$523$			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
$528$	12727.9	+	1663.08i	1.04907	+	0.137077i
$529$	−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
$534$	5877.50	−	6667.79i	0.476300	−	0.540344i
$535$	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
$540$	−12528.7	−	704.479i	−0.998423	−	0.0561406i
$541$			16230.2i			1.28982i	0.764260	+	0.644908i	$0.223104\pi$
$541$			16230.2i			1.28982i	−0.764260	+	0.644908i	$0.776896\pi$
$542$	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
$546$	11269.9	+	9934.13i	0.883345	+	0.778648i
$547$		−	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
$550$	−1399.68	−	13574.6i	−0.108514	−	1.05241i
$551$	−14909.7			−1.15276
$552$	8883.22	+	10133.4i	0.684955	+	0.781354i
$553$		−	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	$-0.906311\pi$
$557$		−	7627.12i		−	0.580200i	0.956996	−	0.290100i	$-0.0936885\pi$
$558$	3611.36	+	2445.80i	0.273981	+	0.185554i
$559$			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	$-0.551192\pi$
$563$	−4278.28			−0.320263			−0.160131	+	0.987096i	$0.551192\pi$
$564$	−13.6417	+	9969.15i	−0.00101848	+	0.744286i
$565$	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	$-0.126646\pi$
$570$	11504.5	+	19230.5i	0.845385	+	1.41312i
$571$	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
$576$	1809.84	−	13705.0i	0.130920	−	0.991393i
$577$		−	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
$580$	4145.08	−	8856.45i	0.296750	−	0.634042i
$581$	−7976.88			−0.569599
$582$	10118.3	−	11478.8i	0.720647	−	0.817545i
$583$	−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	$0.454010\pi$
$588$	18909.1	+	25.8751i	1.32619	+	0.00181475i
$589$		−	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	$-0.636129\pi$
$593$	−11978.2			−0.829490			−0.414745	+	0.909938i	$0.636129\pi$
$594$	−6910.73	+	13668.9i	−0.477358	+	0.944176i
$595$	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	$-0.650728\pi$
$599$	−13370.9			−0.912056			−0.456028	+	0.889965i	$0.650728\pi$
$600$	−14621.5	+	1487.41i	−0.994866	+	0.101205i
$601$	−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
$606$	5651.38	+	4981.56i	0.378831	+	0.333931i
$607$	−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
$612$	−2032.32	−	16066.8i	−0.134235	−	1.06121i
$613$	−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
$615$	−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	$0.375049\pi$
$618$	−6489.66	−	5720.48i	−0.422415	−	0.372349i
$619$	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
$624$	1559.23	−	11933.1i	0.100031	−	0.765554i
$625$	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
$630$	−18958.9	+	14906.9i	−1.19895	+	0.942708i
$631$		−	7589.28i		−	0.478803i	−0.970921	−	0.239401i	$-0.923049\pi$
$631$		−	7589.28i		−	0.478803i	0.970921	−	0.239401i	$-0.0769511\pi$
$632$	−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
$636$	−27.1288	+	19825.2i	−0.00169139	+	1.23604i
$637$	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	$-0.00797099\pi$
$642$	−20701.6	−	18248.0i	−1.27263	−	1.12179i
$643$			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	$0.106379\pi$
$647$			10796.3i			0.656024i	−0.944674	+	0.328012i	$0.893621\pi$
$648$	14710.7	+	7462.76i	0.891808	+	0.452415i
$649$	−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	$-0.196529\pi$
$654$	−8101.30	+	9190.60i	−0.484382	+	0.549512i
$655$	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	$0.916765\pi$
$660$	−5481.89	+	17080.8i	−0.323306	+	1.00738i
$661$			24966.4i			1.46911i	0.678552	+	0.734553i	$0.262608\pi$
$661$			24966.4i			1.46911i	−0.678552	+	0.734553i	$0.737392\pi$
$662$	−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
$666$	−4300.64	+	6350.13i	−0.250220	+	0.369464i
$667$		−	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
$672$	−14808.2	−	22059.7i	−0.850060	−	1.26633i
$673$			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	$0.128109\pi$
$677$			13799.2i			0.783377i	−0.920098	+	0.391689i	$0.871891\pi$
$678$	−10920.3	−	9626.00i	−0.618572	−	0.545257i
$679$		−	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	$-0.0721917\pi$
$683$	34785.2			1.94878			0.974392	+	0.224858i	$0.0721917\pi$
$684$	−3696.67	−	29224.6i	−0.206646	−	1.63367i
$685$	−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
$690$	−16161.7	+	9668.60i	−0.891691	+	0.533445i
$691$	−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
$696$	−9665.93	+	8473.40i	−0.526417	+	0.461470i
$697$		−	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	$-0.306881\pi$
$701$	21164.3			1.14032			0.570160	+	0.821534i	$0.306881\pi$
$702$	12815.3	+	6479.19i	0.689007	+	0.348349i
$703$	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
$708$	−43.3610	+	31687.5i	−0.00230171	+	1.68205i
$709$			4868.59i			0.257890i	0.991652	+	0.128945i	$0.0411590\pi$
$709$			4868.59i			0.257890i	−0.991652	+	0.128945i	$0.958841\pi$
$710$	−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
$714$	−23349.4	−	20581.9i	−1.22385	−	1.07880i
$715$	−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	$-0.323973\pi$
$719$	20252.9			1.05049			0.525246	+	0.850950i	$0.323973\pi$
$720$	18387.4	+	5928.98i	0.951745	+	0.306889i
$721$	−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
$726$	1751.23	+	1543.67i	0.0895239	+	0.0789133i
$727$	−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
$732$	34.9741	−	25558.5i	0.00176596	−	1.29053i
$733$	−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
$735$	−4782.91	+	25989.8i	−0.240027	+	1.30428i
$736$	−9285.01	−	18553.8i	−0.465014	−	0.929214i
$737$	−14760.2			−0.737721
$738$	11000.8	+	7450.30i	0.548705	+	0.371611i
$739$	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	$-0.0901873\pi$
$744$	−4426.62	−	5049.62i	−0.218129	−	0.248828i
$745$	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
$750$	1625.99	−	20475.1i	0.0791636	−	0.996862i
$751$		−	17017.6i		−	0.826872i	−0.910533	−	0.413436i	$-0.864328\pi$
$751$		−	17017.6i		−	0.826872i	0.910533	−	0.413436i	$-0.135672\pi$
$752$	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
$756$	30694.0	−	7936.12i	1.47663	−	0.381791i
$757$	−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	$-0.214100\pi$
$762$	16725.3	+	14743.0i	0.795138	+	0.700895i
$763$			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
$768$	−8033.59	+	19709.0i	−0.377457	+	0.926027i
$769$	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

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)

\(f(q)\)	\(=\)	\(q+(-2.12434 + 1.86740i) q^{2} +(0.659128 + 5.15418i) q^{3} +(1.02565 - 7.93398i) q^{4} +(10.6502 + 3.40199i) q^{5} +(-11.0251 - 9.71838i) q^{6} -28.2468 q^{7} +(12.6371 + 18.7698i) q^{8} +(-26.1311 + 6.79452i) q^{9} +O(q^{10})\)	\(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} +(-11.0251 - 9.71838i) 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} +(41.5692 + 0.0568831i) 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} +(42.8233 - 63.2310i) 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} +(-88.4133 + 77.5054i) 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} +(-84.3577 - 141.010i) 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} +(27.1062 + 214.292i) 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} +(311.424 + 274.513i) 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} +(43.0868 - 329.751i) 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} +(354.130 + 179.042i) 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} +(442.526 + 142.024i) 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} +(375.114 - 425.552i) 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} +(-457.752 - 404.612i) 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} +(-398.979 - 351.690i) 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} +(-1174.20 - 1.60677i) 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} +(671.187 - 527.738i) 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} +(524.245 + 780.963i) q^{96} +1041.15i q^{97} +(-966.325 + 849.446i) q^{98} +(-262.258 - 1008.62i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9}+O(q^{10}) \) 64 * q - 32 * q^4 - 72 * q^6 - 112 * q^9	\( 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9} - 72 q^{10} - 128 q^{16} + 672 q^{19} - 416 q^{24} + 496 q^{25} - 248 q^{30} + 240 q^{34} - 608 q^{36} - 1344 q^{40} + 336 q^{46} + 3520 q^{49} - 544 q^{51} - 952 q^{54} - 2064 q^{60} + 2176 q^{64} - 176 q^{66} + 672 q^{70} - 1600 q^{75} + 2304 q^{76} - 2304 q^{81} - 736 q^{84} - 1432 q^{90} - 2752 q^{91} + 4496 q^{94} + 640 q^{96} + 256 q^{99}+O(q^{100}) \) 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

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