LMFDB - Embedded newform 120.4.m.b.59.1

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			59.1
Character	$\chi$	$=$	120.59
Dual form			120.4.m.b.59.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.80496 - 0.363625i) q^{2} +(3.73183 - 3.61572i) q^{3} +(7.73555 + 2.03990i) q^{4} +(2.66357 - 10.8584i) q^{5} +(-11.7824 + 8.78495i) q^{6} +26.3409 q^{7} +(-20.9561 - 8.53468i) q^{8} +(0.853113 - 26.9865i) q^{9} +O(q^{10})$	\(q+(-2.80496 - 0.363625i) q^{2} +(3.73183 - 3.61572i) q^{3} +(7.73555 + 2.03990i) q^{4} +(2.66357 - 10.8584i) q^{5} +(-11.7824 + 8.78495i) q^{6} +26.3409 q^{7} +(-20.9561 - 8.53468i) q^{8} +(0.853113 - 26.9865i) q^{9} +(-11.4196 + 29.4889i) q^{10} +37.4262i q^{11} +(36.2435 - 20.3570i) q^{12} +30.8736 q^{13} +(-73.8850 - 9.57820i) q^{14} +(-29.3211 - 50.1525i) q^{15} +(55.6776 + 31.5596i) q^{16} -54.0168 q^{17} +(-12.2059 + 75.3858i) q^{18} -4.70847 q^{19} +(42.7543 - 78.5625i) q^{20} +(98.2997 - 95.2413i) q^{21} +(13.6091 - 104.979i) q^{22} -129.048i q^{23} +(-109.064 + 43.9215i) q^{24} +(-110.811 - 57.8443i) q^{25} +(-86.5990 - 11.2264i) q^{26} +(-94.3921 - 103.794i) q^{27} +(203.761 + 53.7329i) q^{28} +230.566 q^{29} +(64.0076 + 151.337i) q^{30} -123.860i q^{31} +(-144.697 - 108.769i) q^{32} +(135.323 + 139.668i) q^{33} +(151.515 + 19.6419i) q^{34} +(70.1608 - 286.021i) q^{35} +(61.6492 - 207.015i) q^{36} -349.557 q^{37} +(13.2070 + 1.71212i) q^{38} +(115.215 - 111.630i) q^{39} +(-148.491 + 204.818i) q^{40} +74.8414i q^{41} +(-310.358 + 231.403i) q^{42} +364.853i q^{43} +(-76.3458 + 289.512i) q^{44} +(-290.759 - 81.1439i) q^{45} +(-46.9252 + 361.975i) q^{46} +45.7642i q^{47} +(321.890 - 83.5397i) q^{48} +350.842 q^{49} +(289.786 + 202.544i) q^{50} +(-201.582 + 195.310i) q^{51} +(238.824 + 62.9791i) q^{52} +682.936i q^{53} +(227.024 + 325.460i) q^{54} +(406.390 + 99.6872i) q^{55} +(-552.003 - 224.811i) q^{56} +(-17.5712 + 17.0245i) q^{57} +(-646.728 - 83.8397i) q^{58} +256.129i q^{59} +(-124.508 - 447.770i) q^{60} +435.099i q^{61} +(-45.0386 + 347.422i) q^{62} +(22.4718 - 710.849i) q^{63} +(366.318 + 357.708i) q^{64} +(82.2339 - 335.238i) q^{65} +(-328.787 - 440.970i) q^{66} -862.064i q^{67} +(-417.850 - 110.189i) q^{68} +(-466.603 - 481.586i) q^{69} +(-300.802 + 776.763i) q^{70} +366.537 q^{71} +(-248.199 + 558.252i) q^{72} -215.240i q^{73} +(980.492 + 127.108i) q^{74} +(-622.676 + 184.796i) q^{75} +(-36.4226 - 9.60482i) q^{76} +985.839i q^{77} +(-363.764 + 271.223i) q^{78} -340.273i q^{79} +(490.988 - 520.510i) q^{80} +(-727.544 - 46.0451i) q^{81} +(27.2142 - 209.927i) q^{82} +605.094 q^{83} +(954.686 - 536.222i) q^{84} +(-143.878 + 586.538i) q^{85} +(132.670 - 1023.40i) q^{86} +(860.434 - 833.664i) q^{87} +(319.421 - 784.308i) q^{88} +517.431i q^{89} +(786.060 + 333.332i) q^{90} +813.237 q^{91} +(263.246 - 998.260i) q^{92} +(-447.843 - 462.225i) q^{93} +(16.6410 - 128.367i) q^{94} +(-12.5413 + 51.1265i) q^{95} +(-933.264 + 117.278i) q^{96} +1441.60i q^{97} +(-984.097 - 127.575i) q^{98} +(1010.00 + 31.9288i) 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 $

$2$	−2.80496	−	0.363625i	−0.991702	−	0.128561i
$2$	−2.80496	−	0.363625i	−0.991702	−	0.128561i
$3$	3.73183	−	3.61572i	0.718191	−	0.695846i
$3$	3.73183	−	3.61572i	0.718191	−	0.695846i
$4$	7.73555	+	2.03990i	0.966944	+	0.254988i
$5$	2.66357	−	10.8584i	0.238237	−	0.971207i
$5$	2.66357	−	10.8584i	0.238237	−	0.971207i
$6$	−11.7824	+	8.78495i	−0.801690	+	0.597740i
$7$	26.3409			1.42227			0.711137	−	0.703053i	$-0.248181\pi$
$7$	26.3409			1.42227			0.711137	+	0.703053i	$0.248181\pi$
$8$	−20.9561	−	8.53468i	−0.926139	−	0.377183i
$9$	0.853113	−	26.9865i	0.0315968	−	0.999501i
$10$	−11.4196	+	29.4889i	−0.361119	+	0.932520i
$11$			37.4262i			1.02586i	0.858431	+	0.512928i	$0.171439\pi$
$11$			37.4262i			1.02586i	−0.858431	+	0.512928i	$0.828561\pi$
$12$	36.2435	−	20.3570i	0.871883	−	0.489714i
$13$	30.8736			0.658676			0.329338	−	0.944212i	$-0.393174\pi$
$13$	30.8736			0.658676			0.329338	+	0.944212i	$0.393174\pi$
$14$	−73.8850	−	9.57820i	−1.41047	−	0.182849i
$15$	−29.3211	−	50.1525i	−0.504711	−	0.863288i
$16$	55.6776	+	31.5596i	0.869962	+	0.493118i
$17$	−54.0168			−0.770648			−0.385324	−	0.922781i	$-0.625910\pi$
$17$	−54.0168			−0.770648			−0.385324	+	0.922781i	$0.625910\pi$
$18$	−12.2059	+	75.3858i	−0.159831	+	0.987144i
$19$	−4.70847			−0.0568524			−0.0284262	−	0.999596i	$-0.509050\pi$
$19$	−4.70847			−0.0568524			−0.0284262	+	0.999596i	$0.509050\pi$
$20$	42.7543	−	78.5625i	0.478008	−	0.878356i
$21$	98.2997	−	95.2413i	1.02146	−	0.989684i
$22$	13.6091	−	104.979i	0.131885	−	1.01734i
$23$		−	129.048i		−	1.16993i	−0.811058	−	0.584966i	$-0.801108\pi$
$23$		−	129.048i		−	1.16993i	0.811058	−	0.584966i	$-0.198892\pi$
$24$	−109.064	+	43.9215i	−0.927606	+	0.373560i
$25$	−110.811	−	57.8443i	−0.886486	−	0.462755i
$26$	−86.5990	−	11.2264i	−0.653210	−	0.0846799i
$27$	−94.3921	−	103.794i	−0.672806	−	0.739819i
$28$	203.761	+	53.7329i	1.37526	+	0.362663i
$29$	230.566			1.47638			0.738191	−	0.674591i	$-0.235680\pi$
$29$	230.566			1.47638			0.738191	+	0.674591i	$0.235680\pi$
$30$	64.0076	+	151.337i	0.389538	+	0.921011i
$31$		−	123.860i		−	0.717610i	−0.933413	−	0.358805i	$-0.883184\pi$
$31$		−	123.860i		−	0.717610i	0.933413	−	0.358805i	$-0.116816\pi$
$32$	−144.697	−	108.769i	−0.799347	−	0.600869i
$33$	135.323	+	139.668i	0.713838	+	0.736761i
$34$	151.515	+	19.6419i	0.764253	+	0.0990751i
$35$	70.1608	−	286.021i	0.338838	−	1.38132i
$36$	61.6492	−	207.015i	0.285413	−	0.958405i
$37$	−349.557			−1.55316			−0.776579	−	0.630020i	$-0.783047\pi$
$37$	−349.557			−1.55316			−0.776579	+	0.630020i	$0.783047\pi$
$38$	13.2070	+	1.71212i	0.0563807	+	0.00730900i
$39$	115.215	−	111.630i	0.473055	−	0.458337i
$40$	−148.491	+	204.818i	−0.586963	+	0.809614i
$41$			74.8414i			0.285080i	0.989789	+	0.142540i	$0.0455269\pi$
$41$			74.8414i			0.285080i	−0.989789	+	0.142540i	$0.954473\pi$
$42$	−310.358	+	231.403i	−1.14022	+	0.850151i
$43$			364.853i			1.29394i	0.762515	+	0.646971i	$0.223965\pi$
$43$			364.853i			1.29394i	−0.762515	+	0.646971i	$0.776035\pi$
$44$	−76.3458	+	289.512i	−0.261581	+	0.991946i
$45$	−290.759	−	81.1439i	−0.963195	−	0.268805i
$46$	−46.9252	+	361.975i	−0.150407	+	1.16022i
$47$			45.7642i			0.142030i	0.997475	+	0.0710148i	$0.0226238\pi$
$47$			45.7642i			0.142030i	−0.997475	+	0.0710148i	$0.977376\pi$
$48$	321.890	−	83.5397i	0.967933	−	0.251207i
$49$	350.842			1.02286
$50$	289.786	+	202.544i	0.819638	+	0.572882i
$51$	−201.582	+	195.310i	−0.553472	+	0.536252i
$52$	238.824	+	62.9791i	0.636903	+	0.167954i
$53$			682.936i			1.76997i	0.465619	+	0.884985i	$0.345832\pi$
$53$			682.936i			1.76997i	−0.465619	+	0.884985i	$0.654168\pi$
$54$	227.024	+	325.460i	0.572111	+	0.820176i
$55$	406.390	+	99.6872i	0.996319	+	0.244397i
$56$	−552.003	−	224.811i	−1.31722	−	0.536458i
$57$	−17.5712	+	17.0245i	−0.0408309	+	0.0395605i
$58$	−646.728	−	83.8397i	−1.46413	−	0.189805i
$59$			256.129i			0.565172i	0.959242	+	0.282586i	$0.0911923\pi$
$59$			256.129i			0.565172i	−0.959242	+	0.282586i	$0.908808\pi$
$60$	−124.508	−	447.770i	−0.267899	−	0.963447i
$61$			435.099i			0.913259i	0.889657	+	0.456629i	$0.150943\pi$
$61$			435.099i			0.913259i	−0.889657	+	0.456629i	$0.849057\pi$
$62$	−45.0386	+	347.422i	−0.0922566	+	0.711655i
$63$	22.4718	−	710.849i	0.0449393	−	1.42156i
$64$	366.318	+	357.708i	0.715466	+	0.698648i
$65$	82.2339	−	335.238i	0.156921	−	0.639711i
$66$	−328.787	−	440.970i	−0.613196	−	0.822419i
$67$		−	862.064i		−	1.57191i	−0.618285	−	0.785954i	$-0.712172\pi$
$67$		−	862.064i		−	1.57191i	0.618285	−	0.785954i	$-0.287828\pi$
$68$	−417.850	−	110.189i	−0.745173	−	0.196506i
$69$	−466.603	−	481.586i	−0.814092	−	0.840235i
$70$	−300.802	+	776.763i	−0.513610	+	1.32630i
$71$	366.537			0.612675			0.306338	−	0.951923i	$-0.400896\pi$
$71$	366.537			0.612675			0.306338	+	0.951923i	$0.400896\pi$
$72$	−248.199	+	558.252i	−0.406258	+	0.913759i
$73$		−	215.240i		−	0.345095i	−0.985001	−	0.172547i	$-0.944800\pi$
$73$		−	215.240i		−	0.345095i	0.985001	−	0.172547i	$-0.0551998\pi$
$74$	980.492	+	127.108i	1.54027	+	0.199675i
$75$	−622.676	+	184.796i	−0.958673	+	0.284512i
$76$	−36.4226	−	9.60482i	−0.0549731	−	0.0144967i
$77$			985.839i			1.45905i
$78$	−363.764	+	271.223i	−0.528054	+	0.393717i
$79$		−	340.273i		−	0.484604i	−0.970201	−	0.242302i	$-0.922097\pi$
$79$		−	340.273i		−	0.484604i	0.970201	−	0.242302i	$-0.0779026\pi$
$80$	490.988	−	520.510i	0.686177	−	0.727435i
$81$	−727.544	−	46.0451i	−0.998003	−	0.0631620i
$82$	27.2142	−	209.927i	0.0366501	−	0.282714i
$83$	605.094			0.800214			0.400107	−	0.916469i	$-0.368973\pi$
$83$	605.094			0.800214			0.400107	+	0.916469i	$0.368973\pi$
$84$	954.686	−	536.222i	1.24006	−	0.696508i
$85$	−143.878	+	586.538i	−0.183597	+	0.748458i
$86$	132.670	−	1023.40i	0.166350	−	1.28320i
$87$	860.434	−	833.664i	1.06032	−	1.02733i
$88$	319.421	−	784.308i	0.386936	−	0.950086i
$89$			517.431i			0.616265i	0.951343	+	0.308132i	$0.0997040\pi$
$89$			517.431i			0.616265i	−0.951343	+	0.308132i	$0.900296\pi$
$90$	786.060	+	333.332i	0.920644	+	0.390403i
$91$	813.237			0.936818
$92$	263.246	−	998.260i	0.298319	−	1.13126i
$93$	−447.843	−	462.225i	−0.499346	−	0.515381i
$94$	16.6410	−	128.367i	0.0182595	−	0.140851i
$95$	−12.5413	+	51.1265i	−0.0135443	+	0.0552155i
$96$	−933.264	+	117.278i	−0.992197	+	0.124684i
$97$			1441.60i			1.50900i	0.656302	+	0.754498i	$0.272120\pi$
$97$			1441.60i			1.50900i	−0.656302	+	0.754498i	$0.727880\pi$
$98$	−984.097	−	127.575i	−1.01438	−	0.131500i
$99$	1010.00	+	31.9288i	1.02534	+	0.0324138i
$100$	−739.186	−	673.501i	−0.739186	−	0.673501i
$101$	−422.189			−0.415934			−0.207967	−	0.978136i	$-0.566685\pi$
$101$	−422.189			−0.415934			−0.207967	+	0.978136i	$0.566685\pi$
$102$	636.447	−	474.535i	0.617820	−	0.460647i
$103$	1058.99			1.01307			0.506533	−	0.862221i	$-0.330927\pi$
$103$	1058.99			1.01307			0.506533	+	0.862221i	$0.330927\pi$
$104$	−646.990	−	263.496i	−0.610025	−	0.248441i
$105$	−772.343	−	1321.06i	−0.717837	−	1.22783i
$106$	248.332	−	1915.60i	0.227549	−	1.75528i
$107$	−819.034			−0.739991			−0.369995	−	0.929034i	$-0.620641\pi$
$107$	−819.034			−0.739991			−0.369995	+	0.929034i	$0.620641\pi$
$108$	−518.446	−	995.453i	−0.461921	−	0.886921i
$109$			1139.42i			1.00125i	0.865663	+	0.500627i	$0.166897\pi$
$109$			1139.42i			1.00125i	−0.865663	+	0.500627i	$0.833103\pi$
$110$	−1103.66	−	427.392i	−0.956632	−	0.370456i
$111$	−1304.49	+	1263.90i	−1.11546	+	1.08076i
$112$	1466.60	+	831.307i	1.23732	+	0.701349i
$113$	1448.12			1.20555			0.602776	−	0.797911i	$-0.294061\pi$
$113$	1448.12			1.20555			0.602776	+	0.797911i	$0.294061\pi$
$114$	55.4770	−	41.3637i	0.0455780	−	0.0339830i
$115$	−1401.26	−	343.729i	−1.13625	−	0.278721i
$116$	1783.56	+	470.333i	1.42758	+	0.376460i
$117$	26.3387	−	833.170i	0.0208120	−	0.658347i
$118$	93.1349	−	718.430i	0.0726590	−	0.560482i
$119$	−1422.85			−1.09607
$120$	186.420	+	1301.25i	0.141815	+	0.989893i
$121$	−69.7203			−0.0523819
$122$	158.213	−	1220.43i	0.117409	−	0.905680i
$123$	270.606	+	279.295i	0.198372	+	0.204742i
$124$	252.662	−	958.126i	0.182982	−	0.693889i
$125$	−923.250	+	1049.16i	−0.660624	+	0.750717i
$126$	−321.515	+	1985.73i	−0.227324	+	1.40399i
$127$	−1075.20			−0.751245			−0.375623	−	0.926773i	$-0.622571\pi$
$127$	−1075.20			−0.751245			−0.375623	+	0.926773i	$0.622571\pi$
$128$	−897.436	−	1136.56i	−0.619710	−	0.784831i
$129$	1319.21	+	1361.57i	0.900384	+	0.929298i
$130$	−352.563	+	910.426i	−0.237860	+	0.614228i
$131$			729.865i			0.486784i	0.969928	+	0.243392i	$0.0782601\pi$
$131$			729.865i			0.486784i	−0.969928	+	0.243392i	$0.921740\pi$
$132$	761.886	+	1356.46i	0.502377	+	0.894427i
$133$	−124.025			−0.0808598
$134$	−313.468	+	2418.05i	−0.202086	+	1.55886i
$135$	−1378.46	+	748.488i	−0.878805	+	0.477182i
$136$	1131.98	+	461.016i	0.713727	+	0.290675i
$137$	−505.557			−0.315275			−0.157637	−	0.987497i	$-0.550388\pi$
$137$	−505.557			−0.315275			−0.157637	+	0.987497i	$0.550388\pi$
$138$	1133.68	+	1520.50i	0.699316	+	0.937922i
$139$	−677.815			−0.413608			−0.206804	−	0.978382i	$-0.566306\pi$
$139$	−677.815			−0.413608			−0.206804	+	0.978382i	$0.566306\pi$
$140$	1126.19	−	2069.41i	0.679858	−	1.24926i
$141$	165.471	+	170.784i	0.0988308	+	0.102004i
$142$	−1028.12	−	133.282i	−0.607591	−	0.0787660i
$143$			1155.48i			0.675707i
$144$	899.182	−	1475.62i	0.520360	−	0.853947i
$145$	614.129	−	2503.59i	0.351729	−	1.43387i
$146$	−78.2666	+	603.739i	−0.0443657	+	0.342231i
$147$	1309.28	−	1268.55i	0.734612	−	0.711756i
$148$	−2704.02	−	713.063i	−1.50182	−	0.396037i
$149$	2640.39			1.45174			0.725869	−	0.687833i	$-0.241438\pi$
$149$	2640.39			1.45174			0.725869	+	0.687833i	$0.241438\pi$
$150$	1813.78	−	291.924i	0.987294	−	0.158903i
$151$		−	2466.32i		−	1.32918i	−0.747207	−	0.664591i	$-0.768606\pi$
$151$		−	2466.32i		−	1.32918i	0.747207	−	0.664591i	$-0.231394\pi$
$152$	98.6712	+	40.1853i	0.0526532	+	0.0214438i
$153$	−46.0825	+	1457.73i	−0.0243500	+	0.770263i
$154$	358.476	−	2765.24i	0.187577	−	1.44694i
$155$	−1344.92	−	329.910i	−0.696948	−	0.170961i
$156$	1118.97	−	628.494i	0.574288	−	0.322563i
$157$	1553.13			0.789512			0.394756	−	0.918786i	$-0.370829\pi$
$157$	1553.13			0.789512			0.394756	+	0.918786i	$0.370829\pi$
$158$	−123.732	+	954.452i	−0.0623011	+	0.480583i
$159$	2469.31	+	2548.60i	1.23163	+	1.27118i
$160$	−1566.47	+	1281.47i	−0.774002	+	0.633183i
$161$		−	3399.25i		−	1.66396i
$162$	2023.99	+	393.708i	0.981601	+	0.190942i
$163$			3936.58i			1.89164i	0.324694	+	0.945819i	$0.394739\pi$
$163$			3936.58i			1.89164i	−0.324694	+	0.945819i	$0.605261\pi$
$164$	−152.669	+	578.940i	−0.0726919	+	0.275656i
$165$	1877.02	−	1097.38i	0.885610	−	0.517761i
$166$	−1697.26	−	220.027i	−0.793573	−	0.102876i
$167$			1998.86i			0.926208i	0.886304	+	0.463104i	$0.153264\pi$
$167$			1998.86i			0.926208i	−0.886304	+	0.463104i	$0.846736\pi$
$168$	−2872.84	+	1156.93i	−1.31931	+	0.531305i
$169$	−1243.82			−0.566146
$170$	616.850	−	1592.90i	0.278295	−	0.718644i
$171$	−4.01686	+	127.065i	−0.00179635	+	0.0568241i
$172$	−744.264	+	2822.34i	−0.329940	+	1.25117i
$173$		−	2816.75i		−	1.23788i	−0.785438	−	0.618940i	$-0.787562\pi$
$173$		−	2816.75i		−	1.23788i	0.785438	−	0.618940i	$-0.212438\pi$
$174$	−2716.62	+	2025.51i	−1.18360	+	0.882493i
$175$	−2918.85	−	1523.67i	−1.26083	−	0.658164i
$176$	−1181.15	+	2083.80i	−0.505869	+	0.892457i
$177$	926.091	+	955.830i	0.393273	+	0.405901i
$178$	188.151	−	1451.37i	0.0792275	−	0.611151i
$179$		−	905.857i		−	0.378251i	−0.981953	−	0.189125i	$-0.939435\pi$
$179$		−	905.857i		−	0.378251i	0.981953	−	0.189125i	$-0.0605653\pi$
$180$	−2083.65	−	1220.81i	−0.862814	−	0.505522i
$181$		−	174.804i		−	0.0717851i	−0.999356	−	0.0358925i	$-0.988573\pi$
$181$		−	174.804i		−	0.0717851i	0.999356	−	0.0358925i	$-0.0114274\pi$
$182$	−2281.09	−	295.713i	−0.929044	−	0.120438i
$183$	1573.20	+	1623.72i	0.635487	+	0.655894i
$184$	−1101.39	+	2704.35i	−0.441279	+	1.08352i
$185$	−931.069	+	3795.64i	−0.370019	+	1.50844i
$186$	1088.10	+	1459.37i	0.428945	+	0.575301i
$187$		−	2021.65i		−	0.790574i
$188$	−93.3546	+	354.011i	−0.0362159	+	0.137335i
$189$	−2486.37	−	2734.02i	−0.956915	−	1.05223i
$190$	53.7687	−	138.847i	0.0205305	−	0.0530160i
$191$	1267.32			0.480107			0.240053	−	0.970760i	$-0.422835\pi$
$191$	1267.32			0.480107			0.240053	+	0.970760i	$0.422835\pi$
$192$	2660.41	+	10.3984i	0.999992	+	0.00390856i
$193$			2265.21i			0.844838i	0.906401	+	0.422419i	$0.138819\pi$
$193$			2265.21i			0.844838i	−0.906401	+	0.422419i	$0.861181\pi$
$194$	524.203	−	4043.63i	0.193998	−	1.49647i
$195$	−905.246	−	1548.39i	−0.332441	−	0.568627i
$196$	2713.96	+	715.684i	0.989052	+	0.260818i
$197$		−	630.779i		−	0.228128i	−0.993473	−	0.114064i	$-0.963613\pi$
$197$		−	630.779i		−	0.228128i	0.993473	−	0.114064i	$-0.0363868\pi$
$198$	−2821.40	−	456.821i	−1.01267	−	0.163964i
$199$		−	3357.04i		−	1.19585i	−0.801551	−	0.597926i	$-0.795992\pi$
$199$		−	3357.04i		−	1.19585i	0.801551	−	0.597926i	$-0.204008\pi$
$200$	1828.48	+	2157.93i	0.646466	+	0.762943i
$201$	−3116.98	−	3217.08i	−1.09381	−	1.12893i
$202$	1184.22	+	153.518i	0.412482	+	0.0534728i
$203$	6073.32			2.09982
$204$	−1957.76	+	1099.62i	−0.671915	+	0.377397i
$205$	812.660	+	199.345i	0.276871	+	0.0679165i
$206$	−2970.43	−	385.077i	−1.00466	−	0.130241i
$207$	−3482.56	−	110.093i	−1.16935	−	0.0369661i
$208$	1718.97	+	974.356i	0.573023	+	0.324805i
$209$		−	176.220i		−	0.0583225i
$210$	1686.02	+	3986.36i	0.554029	+	1.30993i
$211$	3809.37			1.24288			0.621440	−	0.783462i	$-0.286548\pi$
$211$	3809.37			1.24288			0.621440	+	0.783462i	$0.286548\pi$
$212$	−1393.12	+	5282.89i	−0.451321	+	1.71146i
$213$	1367.85	−	1325.30i	0.440018	−	0.426327i
$214$	2297.35	+	297.821i	0.733850	+	0.0951338i
$215$	3961.73	+	971.810i	1.25669	+	0.308265i
$216$	1092.25	+	2980.72i	0.344064	+	0.938946i
$217$		−	3262.58i		−	1.02064i
$218$	414.322	−	3196.03i	0.128722	−	0.992946i
$219$	−778.248	−	803.239i	−0.240133	−	0.247844i
$220$	2940.30	+	1600.13i	0.901067	+	0.490367i
$221$	−1667.69			−0.507607
$222$	4118.62	−	3070.84i	1.24515	−	0.928385i
$223$	−4261.82			−1.27979			−0.639894	−	0.768463i	$-0.721022\pi$
$223$	−4261.82			−1.27979			−0.639894	+	0.768463i	$0.721022\pi$
$224$	−3811.46	−	2865.07i	−1.13689	−	0.854601i
$225$	−1655.55	+	2941.05i	−0.490534	+	0.871422i
$226$	−4061.90	−	526.571i	−1.19555	−	0.154987i
$227$	−4481.95			−1.31047			−0.655236	−	0.755424i	$-0.727431\pi$
$227$	−4481.95			−1.31047			−0.655236	+	0.755424i	$0.727431\pi$
$228$	−170.651	+	95.8504i	−0.0495687	+	0.0278414i
$229$			1157.74i			0.334085i	0.985950	+	0.167042i	$0.0534216\pi$
$229$			1157.74i			0.334085i	−0.985950	+	0.167042i	$0.946578\pi$
$230$	3805.49	+	1473.68i	1.09098	+	0.422485i
$231$	3564.52	+	3678.98i	1.01527	+	1.04788i
$232$	−4831.78	−	1967.81i	−1.36733	−	0.556867i
$233$	2549.55			0.716852			0.358426	−	0.933558i	$-0.383314\pi$
$233$	2549.55			0.716852			0.358426	+	0.933558i	$0.383314\pi$
$234$	−376.840	+	2327.43i	−0.105277	+	0.650208i
$235$	496.927	+	121.896i	0.137940	+	0.0338367i
$236$	−522.478	+	1981.30i	−0.144112	+	0.546490i
$237$	−1230.33	−	1269.84i	−0.337210	−	0.348039i
$238$	3991.04	+	517.384i	1.08698	+	0.140912i
$239$	714.592			0.193402			0.0967010	−	0.995313i	$-0.469171\pi$
$239$	714.592			0.193402			0.0967010	+	0.995313i	$0.469171\pi$
$240$	−49.7339	−	3717.73i	−0.0133763	−	0.999911i
$241$	−2330.00			−0.622774			−0.311387	−	0.950283i	$-0.600794\pi$
$241$	−2330.00			−0.622774			−0.311387	+	0.950283i	$0.600794\pi$
$242$	195.562	+	25.3520i	0.0519472	+	0.00673426i
$243$	−2881.56	+	2458.77i	−0.760708	+	0.649094i
$244$	−887.561	+	3365.74i	−0.232870	+	0.883070i
$245$	934.492	−	3809.60i	0.243684	−	0.993413i
$246$	−657.478	−	881.810i	−0.170404	−	0.228545i
$247$	−145.367			−0.0374473
$248$	−1057.11	+	2595.63i	−0.270670	+	0.664607i
$249$	2258.11	−	2187.85i	0.574706	−	0.556825i
$250$	2971.18	−	2607.13i	0.751655	−	0.659557i
$251$			3006.17i			0.755966i	0.925812	+	0.377983i	$0.123382\pi$
$251$			3006.17i			0.755966i	−0.925812	+	0.377983i	$0.876618\pi$
$252$	1623.89	−	5452.97i	0.405935	−	1.36311i
$253$	4829.79			1.20018
$254$	3015.88	+	390.968i	0.745011	+	0.0965807i
$255$	1583.83	+	2709.08i	0.388954	+	0.665291i
$256$	2103.99	+	3514.32i	0.513669	+	0.857989i
$257$	−7814.60			−1.89674			−0.948369	−	0.317170i	$-0.897267\pi$
$257$	−7814.60			−1.89674			−0.948369	+	0.317170i	$0.897267\pi$
$258$	−3205.21	−	4298.83i	−0.773441	−	1.03734i
$259$	−9207.64			−2.20902
$260$	1319.98	−	2425.51i	0.314852	−	0.578552i
$261$	196.699	−	6222.18i	0.0466490	−	1.47565i
$262$	265.397	−	2047.24i	0.0625813	−	0.482744i
$263$		−	4366.70i		−	1.02381i	−0.859042	−	0.511905i	$-0.828940\pi$
$263$		−	4366.70i		−	1.02381i	0.859042	−	0.511905i	$-0.171060\pi$
$264$	−1643.82	−	4081.84i	−0.383219	−	0.951591i
$265$	7415.61	+	1819.05i	1.71901	+	0.421672i
$266$	347.885	+	45.0987i	0.0801888	+	0.0103954i
$267$	1870.89	+	1930.96i	0.428825	+	0.442596i
$268$	1758.53	−	6668.54i	0.400818	−	1.51995i
$269$	−4336.63			−0.982933			−0.491467	−	0.870896i	$-0.663539\pi$
$269$	−4336.63			−0.982933			−0.491467	+	0.870896i	$0.663539\pi$
$270$	4138.68	−	1598.23i	0.932859	−	0.360242i
$271$		−	4429.78i		−	0.992952i	−0.868050	−	0.496476i	$-0.834627\pi$
$271$		−	4429.78i		−	0.992952i	0.868050	−	0.496476i	$-0.165373\pi$
$272$	−3007.53	−	1704.75i	−0.670434	−	0.380020i
$273$	3034.86	−	2940.44i	0.672814	−	0.651881i
$274$	1418.07	+	183.833i	0.312659	+	0.0405320i
$275$	2164.89	−	4147.23i	0.474720	−	0.909408i
$276$	−2627.04	−	4677.16i	−0.572932	−	1.02004i
$277$	3024.43			0.656030			0.328015	−	0.944673i	$-0.393620\pi$
$277$	3024.43			0.656030			0.328015	+	0.944673i	$0.393620\pi$
$278$	1901.24	+	246.470i	0.410176	+	0.0531738i
$279$	−3342.55	−	105.667i	−0.717252	−	0.0226742i
$280$	−3911.39	+	5395.08i	−0.834823	+	1.15149i
$281$		−	330.776i		−	0.0702223i	−0.999383	−	0.0351112i	$-0.988821\pi$
$281$		−	330.776i		−	0.0702223i	0.999383	−	0.0351112i	$-0.0111785\pi$
$282$	−402.036	−	539.211i	−0.0848969	−	0.113864i
$283$		−	5051.97i		−	1.06116i	−0.847635	−	0.530580i	$-0.821974\pi$
$283$		−	5051.97i		−	1.06116i	0.847635	−	0.530580i	$-0.178026\pi$
$284$	2835.37	+	747.700i	0.592423	+	0.156225i
$285$	138.057	+	236.141i	0.0286941	+	0.0490801i
$286$	420.161	−	3241.07i	0.0868695	−	0.670100i
$287$			1971.39i			0.405461i
$288$	−3058.74	+	3812.08i	−0.625826	+	0.779963i
$289$	−1995.18			−0.406102
$290$	−2632.97	+	6799.14i	−0.533150	+	1.37676i
$291$	5212.44	+	5379.82i	1.05003	+	1.08375i
$292$	439.069	−	1665.00i	0.0879950	−	0.333688i
$293$		−	1269.80i		−	0.253182i	−0.991955	−	0.126591i	$-0.959596\pi$
$293$		−	1269.80i		−	0.253182i	0.991955	−	0.126591i	$-0.0404036\pi$
$294$	−4133.76	+	3082.13i	−0.820020	+	0.611407i
$295$	2781.16	+	682.217i	0.548899	+	0.134645i
$296$	7325.36	+	2983.36i	1.43844	+	0.585825i
$297$	3884.60	−	3532.74i	0.758948	−	0.690203i
$298$	−7406.17	−	960.111i	−1.43969	−	0.186637i
$299$		−	3984.18i		−	0.770606i
$300$	−5193.71	+	159.299i	−0.999530	+	0.0306572i
$301$			9610.54i			1.84034i
$302$	−896.817	+	6917.93i	−0.170881	+	1.31815i
$303$	−1575.54	+	1526.52i	−0.298720	+	0.289426i
$304$	−262.156	−	148.597i	−0.0494595	−	0.0280350i
$305$	4724.50	+	1158.92i	0.886963	+	0.217572i
$306$	659.325	−	4072.10i	0.123174	−	0.760740i
$307$			5056.64i			0.940057i	0.882651	+	0.470029i	$0.155756\pi$
$307$			5056.64i			0.940057i	−0.882651	+	0.470029i	$0.844244\pi$
$308$	−2011.02	+	7626.01i	−0.372040	+	1.41082i
$309$	3951.99	−	3829.03i	0.727575	−	0.704938i
$310$	3652.49	+	1414.43i	0.669186	+	0.259143i
$311$	−2886.68			−0.526329			−0.263165	−	0.964751i	$-0.584766\pi$
$311$	−2886.68			−0.526329			−0.263165	+	0.964751i	$0.584766\pi$
$312$	−3367.19	+	1356.01i	−0.610992	+	0.246055i
$313$			5771.03i			1.04217i	0.853506	+	0.521083i	$0.174472\pi$
$313$			5771.03i			1.04217i	−0.853506	+	0.521083i	$0.825528\pi$
$314$	−4356.47	−	564.758i	−0.782961	−	0.101500i
$315$	−7658.84	−	2137.40i	−1.36993	−	0.382314i
$316$	694.125	−	2632.20i	0.123568	−	0.468585i
$317$		−	1124.02i		−	0.199153i	−0.995030	−	0.0995765i	$-0.968251\pi$
$317$		−	1124.02i		−	0.199153i	0.995030	−	0.0995765i	$-0.0317488\pi$
$318$	−5999.56	−	8046.61i	−1.05798	−	1.41897i
$319$			8629.22i			1.51456i
$320$	4859.86	−	3024.86i	0.848982	−	0.528422i
$321$	−3056.50	+	2961.40i	−0.531455	+	0.514920i
$322$	−1236.05	+	9534.74i	−0.213921	+	1.65016i
$323$	254.337			0.0438132
$324$	−5534.03	−	1840.30i	−0.948908	−	0.315553i
$325$	−3421.12	−	1785.86i	−0.583907	−	0.304805i
$326$	1431.44	−	11041.9i	0.243191	−	1.87594i
$327$	4119.83	+	4252.13i	0.696719	+	0.719092i
$328$	638.747	−	1568.39i	0.107527	−	0.264023i
$329$			1205.47i			0.202005i
$330$	−5663.99	+	2395.56i	−0.944825	+	0.399610i
$331$	10427.1			1.73150			0.865752	−	0.500474i	$-0.166841\pi$
$331$	10427.1			1.73150			0.865752	+	0.500474i	$0.166841\pi$
$332$	4680.74	+	1234.33i	0.773762	+	0.204045i
$333$	−298.212	+	9433.33i	−0.0490748	+	1.55238i
$334$	726.836	−	5606.72i	0.119074	−	0.918522i
$335$	−9360.65	−	2296.17i	−1.52665	−	0.374486i
$336$	8478.87	−	2200.51i	1.37667	−	0.357285i
$337$		−	4932.89i		−	0.797364i	−0.917089	−	0.398682i	$-0.869468\pi$
$337$		−	4932.89i		−	0.797364i	0.917089	−	0.398682i	$-0.130532\pi$
$338$	3488.87	+	452.285i	0.561448	+	0.0727842i
$339$	5404.12	−	5235.99i	0.865816	−	0.838878i
$340$	−2309.45	+	4243.70i	−0.368376	+	0.676903i
$341$	4635.61			0.736165
$342$	57.4712	−	354.951i	0.00908680	−	0.0561216i
$343$	206.574			0.0325187
$344$	3113.90	−	7645.90i	0.488053	−	1.19837i
$345$	−6472.10	+	3783.83i	−1.00999	+	0.590478i
$346$	−1024.24	+	7900.85i	−0.159143	+	1.22761i
$347$	−3247.36			−0.502385			−0.251192	−	0.967937i	$-0.580823\pi$
$347$	−3247.36			−0.502385			−0.251192	+	0.967937i	$0.580823\pi$
$348$	8356.53	−	4693.65i	1.28723	−	0.723005i
$349$			11995.6i			1.83986i	0.392086	+	0.919929i	$0.371754\pi$
$349$			11995.6i			1.83986i	−0.392086	+	0.919929i	$0.628246\pi$
$350$	7633.21	+	5335.20i	1.16575	+	0.814795i
$351$	−2914.22	−	3204.48i	−0.443161	−	0.487301i
$352$	4070.81	−	5415.47i	0.616406	−	0.820016i
$353$	−6654.12			−1.00330			−0.501648	−	0.865072i	$-0.667273\pi$
$353$	−6654.12			−1.00330			−0.501648	+	0.865072i	$0.667273\pi$
$354$	−2250.08	−	3017.81i	−0.337826	−	0.453093i
$355$	976.296	−	3980.01i	0.145962	−	0.595034i
$356$	−1055.51	+	4002.61i	−0.157140	+	0.595894i
$357$	−5309.84	+	5144.64i	−0.787189	+	0.762697i
$358$	−329.392	+	2540.89i	−0.0486283	+	0.375112i
$359$	−5238.10			−0.770073			−0.385037	−	0.922901i	$-0.625811\pi$
$359$	−5238.10			−0.770073			−0.385037	+	0.922901i	$0.625811\pi$
$360$	5400.64	+	4181.99i	0.790663	+	0.612251i
$361$	−6836.83			−0.996768
$362$	−63.5632	+	490.318i	−0.00922875	+	0.0711894i
$363$	−260.184	+	252.089i	−0.0376202	+	0.0364497i
$364$	6290.84	+	1658.93i	0.905851	+	0.238877i
$365$	−2337.17	−	573.306i	−0.335159	−	0.0822143i
$366$	−3822.33	−	5126.51i	−0.545892	−	0.732150i
$367$	3524.68			0.501326			0.250663	−	0.968074i	$-0.419351\pi$
$367$	3524.68			0.501326			0.250663	+	0.968074i	$0.419351\pi$
$368$	4072.71	−	7185.10i	0.576915	−	1.01780i
$369$	2019.71	+	63.8482i	0.284937	+	0.00900760i
$370$	3991.80	−	10308.0i	0.560875	−	1.44835i
$371$			17989.1i			2.51738i
$372$	−2521.42	−	4489.12i	−0.351424	−	0.625672i
$373$	−3078.40			−0.427328			−0.213664	−	0.976907i	$-0.568540\pi$
$373$	−3078.40			−0.427328			−0.213664	+	0.976907i	$0.568540\pi$
$374$	−735.121	+	5670.63i	−0.101637	+	0.784014i
$375$	348.052	+	7253.50i	0.0479289	+	0.998851i
$376$	390.583	−	959.040i	0.0535712	−	0.131539i
$377$	7118.41			0.972458
$378$	5980.00	+	8572.91i	0.813699	+	1.16652i
$379$	−3244.44			−0.439725			−0.219863	−	0.975531i	$-0.570561\pi$
$379$	−3244.44			−0.439725			−0.219863	+	0.975531i	$0.570561\pi$
$380$	−201.307	+	369.909i	−0.0271759	+	0.0499367i
$381$	−4012.45	+	3887.61i	−0.539538	+	0.522751i
$382$	−3554.79	−	460.831i	−0.476123	−	0.0617229i
$383$		−	5023.39i		−	0.670191i	−0.942184	−	0.335096i	$-0.891231\pi$
$383$		−	5023.39i		−	0.670191i	0.942184	−	0.335096i	$-0.108769\pi$
$384$	−7458.55	−	996.558i	−0.991192	−	0.132436i
$385$	10704.7	+	2625.85i	1.41704	+	0.347599i
$386$	823.688	−	6353.83i	0.108613	−	0.837827i
$387$	9846.10	+	311.261i	1.29330	+	0.0408844i
$388$	−2940.73	+	11151.6i	−0.384776	+	1.45912i
$389$	289.283			0.0377049			0.0188525	−	0.999822i	$-0.493999\pi$
$389$	289.283			0.0377049			0.0188525	+	0.999822i	$0.493999\pi$
$390$	1976.14	+	4672.33i	0.256579	+	0.606647i
$391$			6970.78i			0.901605i
$392$	−7352.30	−	2994.33i	−0.947314	−	0.385807i
$393$	2638.99	+	2723.73i	0.338726	+	0.349604i
$394$	−229.367	+	1769.31i	−0.0293283	+	0.226235i
$395$	−3694.83	−	906.342i	−0.470651	−	0.115451i
$396$	7747.80	+	2307.30i	0.983186	+	0.292793i
$397$	−10915.5			−1.37993			−0.689964	−	0.723843i	$-0.742374\pi$
$397$	−10915.5			−1.37993			−0.689964	+	0.723843i	$0.742374\pi$
$398$	−1220.71	+	9416.36i	−0.153740	+	1.18593i
$399$	−462.841	+	448.441i	−0.0580728	+	0.0562659i
$400$	−4344.14	−	6717.77i	−0.543017	−	0.839722i
$401$		−	9711.60i		−	1.20941i	−0.796449	−	0.604706i	$-0.793291\pi$
$401$		−	9711.60i		−	1.20941i	0.796449	−	0.604706i	$-0.206709\pi$
$402$	7573.19	+	10157.2i	0.939593	+	1.26018i
$403$		−	3824.00i		−	0.472673i
$404$	−3265.86	−	861.224i	−0.402185	−	0.106058i
$405$	−2437.84	+	7777.34i	−0.299105	+	0.954220i
$406$	−17035.4	−	2208.41i	−2.08240	−	0.269955i
$407$		−	13082.6i		−	1.59332i
$408$	5891.28	−	2372.50i	0.714857	−	0.287883i
$409$	611.519			0.0739307			0.0369653	−	0.999317i	$-0.488231\pi$
$409$	611.519			0.0739307			0.0369653	+	0.999317i	$0.488231\pi$
$410$	−2206.99	−	854.658i	−0.265842	−	0.102948i
$411$	−1886.65	+	1827.95i	−0.226428	+	0.219383i
$412$	8191.91	+	2160.25i	0.979578	+	0.258320i
$413$			6746.66i			0.803830i
$414$	9728.41	+	1575.15i	1.15489	+	0.186992i
$415$	1611.71	−	6570.37i	0.190640	−	0.777173i
$416$	−4467.32	−	3358.09i	−0.526511	−	0.395778i
$417$	−2529.49	+	2450.79i	−0.297050	+	0.287807i
$418$	−64.0780	+	494.289i	−0.00749798	+	0.0578385i
$419$		−	5936.35i		−	0.692147i	−0.938207	−	0.346073i	$-0.887515\pi$
$419$		−	5936.35i		−	0.692147i	0.938207	−	0.346073i	$-0.112485\pi$
$420$	−3279.66	−	11794.7i	−0.381026	−	1.37029i
$421$		−	7758.48i		−	0.898159i	−0.893492	−	0.449080i	$-0.851752\pi$
$421$		−	7758.48i		−	0.898159i	0.893492	−	0.449080i	$-0.148248\pi$
$422$	−10685.1	−	1385.18i	−1.23257	−	0.159786i
$423$	1235.02	+	39.0421i	0.141959	+	0.00448768i
$424$	5828.64	−	14311.7i	0.667603	−	1.63924i
$425$	5985.65	+	3124.57i	0.683169	+	0.356621i
$426$	−4318.68	+	3220.01i	−0.491175	+	0.366221i
$427$			11460.9i			1.29890i
$428$	−6335.68	−	1670.75i	−0.715530	−	0.188689i
$429$	4177.89	+	4312.06i	0.470188	+	0.485287i
$430$	−10759.1	−	4166.47i	−1.20663	−	0.467267i
$431$	3682.13			0.411513			0.205756	−	0.978603i	$-0.434035\pi$
$431$	3682.13			0.411513			0.205756	+	0.978603i	$0.434035\pi$
$432$	−1979.84	−	8757.96i	−0.220498	−	0.975388i
$433$		−	9874.56i		−	1.09594i	−0.836499	−	0.547969i	$-0.815401\pi$
$433$		−	9874.56i		−	1.09594i	0.836499	−	0.547969i	$-0.184599\pi$
$434$	−1186.36	+	9151.40i	−0.131214	+	1.01217i
$435$	−6760.45	−	11563.5i	−0.745146	−	1.27454i
$436$	−2324.31	+	8814.06i	−0.255308	+	0.968158i
$437$			607.620i			0.0665135i
$438$	1890.87	+	2536.04i	0.206277	+	0.276659i
$439$		−	12519.6i		−	1.36111i	−0.732698	−	0.680554i	$-0.761739\pi$
$439$		−	12519.6i		−	1.36111i	0.732698	−	0.680554i	$-0.238261\pi$
$440$	−7665.55	−	5557.46i	−0.830547	−	0.602140i
$441$	299.308	−	9468.01i	0.0323192	−	1.02235i
$442$	4677.80	+	606.415i	0.503395	+	0.0652584i
$443$	−7308.73			−0.783856			−0.391928	−	0.919996i	$-0.628192\pi$
$443$	−7308.73			−0.783856			−0.391928	+	0.919996i	$0.628192\pi$
$444$	−12669.2	+	7115.95i	−1.35417	+	0.760603i
$445$	5618.48	+	1378.21i	0.598521	+	0.146817i
$446$	11954.2	+	1549.71i	1.26917	+	0.164531i
$447$	9853.48	−	9546.91i	1.04263	−	1.01019i
$448$	9649.15	+	9422.34i	1.01759	+	0.993669i
$449$			7884.95i			0.828761i	0.910104	+	0.414380i	$0.136002\pi$
$449$			7884.95i			0.828761i	−0.910104	+	0.414380i	$0.863998\pi$
$450$	5713.19	−	7647.52i	0.598494	−	0.801127i
$451$	−2801.03			−0.292451
$452$	11202.0	+	2954.02i	1.16570	+	0.307401i
$453$	−8917.54	−	9203.90i	−0.924906	−	0.954607i
$454$	12571.7	+	1629.75i	1.29960	+	0.168475i
$455$	2166.11	−	8830.47i	0.223184	−	0.909844i
$456$	513.523	−	206.803i	0.0527367	−	0.0212378i
$457$			197.196i			0.0201847i	0.999949	+	0.0100924i	$0.00321256\pi$
$457$			197.196i			0.0201847i	−0.999949	+	0.0100924i	$0.996787\pi$
$458$	420.982	−	3247.40i	0.0429502	−	0.331312i
$459$	5098.76	+	5606.61i	0.518496	+	0.570140i
$460$	−10138.4	−	5517.37i	−1.02762	−	0.559237i
$461$	−8936.49			−0.902850			−0.451425	−	0.892309i	$-0.649084\pi$
$461$	−8936.49			−0.902850			−0.451425	+	0.892309i	$0.649084\pi$
$462$	−8660.55	−	11615.5i	−0.872133	−	1.16971i
$463$	18183.1			1.82514			0.912571	−	0.408919i	$-0.134094\pi$
$463$	18183.1			1.82514			0.912571	+	0.408919i	$0.134094\pi$
$464$	12837.4	+	7276.57i	1.28440	+	0.728031i
$465$	−6211.89	+	3631.71i	−0.619505	+	0.362186i
$466$	−7151.37	−	927.079i	−0.710903	−	0.0921590i
$467$	81.4817			0.00807393			0.00403696	−	0.999992i	$-0.498715\pi$
$467$	81.4817			0.00807393			0.00403696	+	0.999992i	$0.498715\pi$
$468$	1903.33	−	6391.30i	0.187995	−	0.631278i
$469$		−	22707.5i		−	2.23568i
$470$	−1349.53	−	522.608i	−0.132445	−	0.0512896i
$471$	5796.03	−	5615.69i	0.567021	−	0.549379i
$472$	2185.98	−	5367.47i	0.213173	−	0.523428i
$473$	−13655.0			−1.32740
$474$	2989.29	+	4009.23i	0.289668	+	0.388502i
$475$	521.749	+	272.358i	0.0503989	+	0.0263087i
$476$	−11006.5	−	2902.48i	−1.05984	−	0.279485i
$477$	18430.1	+	582.622i	1.76909	+	0.0559254i
$478$	−2004.40	−	259.843i	−0.191797	−	0.0248639i
$479$	19196.4			1.83112			0.915559	−	0.402183i	$-0.131748\pi$
$479$	19196.4			1.83112			0.915559	+	0.402183i	$0.131748\pi$
$480$	−1212.36	+	10446.2i	−0.115284	+	0.993333i
$481$	−10792.1			−1.02303
$482$	6535.55	+	847.246i	0.617606	+	0.0800643i
$483$	−12290.7	−	12685.4i	−1.15786	−	1.19504i
$484$	−539.325	−	142.223i	−0.0506504	−	0.0133567i
$485$	15653.5	+	3839.81i	1.46555	+	0.359498i
$486$	8976.71	−	5848.92i	0.837844	−	0.545910i
$487$	−2061.46			−0.191814			−0.0959072	−	0.995390i	$-0.530575\pi$
$487$	−2061.46			−0.191814			−0.0959072	+	0.995390i	$0.530575\pi$
$488$	3713.43	−	9118.00i	0.344466	−	0.845804i
$489$	14233.6	+	14690.7i	1.31629	+	1.35856i
$490$	−4006.47	+	10345.9i	−0.369376	+	0.953841i
$491$		−	10688.0i		−	0.982371i	−0.871055	−	0.491186i	$-0.836564\pi$
$491$		−	10688.0i		−	0.982371i	0.871055	−	0.491186i	$-0.163436\pi$
$492$	1523.55	+	2712.51i	0.139608	+	0.248556i
$493$	−12454.5			−1.13777
$494$	407.748	+	52.8591i	0.0371366	+	0.00481426i
$495$	3036.91	−	10882.0i	0.275755	−	0.988100i
$496$	3908.97	−	6896.23i	0.353867	−	0.624294i
$497$	9654.91			0.871392
$498$	−7129.45	+	5315.73i	−0.641523	+	0.478320i
$499$	−5962.49			−0.534906			−0.267453	−	0.963571i	$-0.586182\pi$
$499$	−5962.49			−0.534906			−0.267453	+	0.963571i	$0.586182\pi$
$500$	−9282.04	+	6232.48i	−0.830210	+	0.557450i
$501$	7227.33	+	7459.42i	0.644498	+	0.665194i
$502$	1093.12	−	8432.16i	0.0971876	−	0.749693i
$503$			9237.66i			0.818861i	0.912341	+	0.409430i	$0.134273\pi$
$503$			9237.66i			0.818861i	−0.912341	+	0.409430i	$0.865727\pi$
$504$	−6537.79	+	14704.8i	−0.577810	+	1.29962i
$505$	−1124.53	+	4584.30i	−0.0990908	+	0.403958i
$506$	−13547.3	−	1756.23i	−1.19022	−	0.154296i
$507$	−4641.74	+	4497.32i	−0.406601	+	0.393950i
$508$	−8317.23	−	2193.29i	−0.726412	−	0.191559i
$509$	−9365.55			−0.815561			−0.407781	−	0.913080i	$-0.633697\pi$
$509$	−9365.55			−0.815561			−0.407781	+	0.913080i	$0.633697\pi$
$510$	−3457.49	−	8174.77i	−0.300196	−	0.709775i
$511$		−	5669.61i		−	0.490820i
$512$	−4623.70	−	10622.6i	−0.399102	−	0.916906i
$513$	444.442	+	488.709i	0.0382507	+	0.0420605i
$514$	21919.6	+	2841.58i	1.88100	+	0.243846i
$515$	2820.70	−	11499.0i	0.241350	−	0.983897i
$516$	7427.32	+	13223.5i	0.633662	+	1.12817i
$517$	−1712.78			−0.145702
$518$	25827.0	+	3348.13i	2.19068	+	0.283993i
$519$	−10184.6	−	10511.6i	−0.861374	−	0.889035i
$520$	−4584.45	+	6323.46i	−0.386619	+	0.533273i
$521$		−	10927.3i		−	0.918874i	−0.888210	−	0.459437i	$-0.848051\pi$
$521$		−	10927.3i		−	0.918874i	0.888210	−	0.459437i	$-0.151949\pi$
$522$	−2814.27	+	17381.4i	−0.235972	+	1.45740i
$523$		−	5024.90i		−	0.420122i	−0.977688	−	0.210061i	$-0.932634\pi$
$523$		−	5024.90i		−	0.420122i	0.977688	−	0.210061i	$-0.0673662\pi$
$524$	−1488.86	+	5645.91i	−0.124124	+	0.470693i
$525$	−16401.8	+	4867.69i	−1.36350	+	0.404654i
$526$	−1587.84	+	12248.4i	−0.131622	+	1.01531i
$527$			6690.53i			0.553025i
$528$	3126.57	+	12047.1i	0.257702	+	0.992961i
$529$	−4486.47			−0.368741
$530$	−20139.0	−	7798.84i	−1.65053	−	0.639170i
$531$	6912.03	+	218.507i	0.564890	+	0.0178576i
$532$	−959.404	−	252.999i	−0.0781869	−	0.0206183i
$533$			2310.62i			0.187775i
$534$	−4545.61	−	6096.57i	−0.368366	−	0.494053i
$535$	−2181.55	+	8893.42i	−0.176293	+	0.718684i
$536$	−7357.44	+	18065.5i	−0.592897	+	1.45580i
$537$	−3275.33	−	3380.50i	−0.263204	−	0.271656i
$538$	12164.1	+	1576.91i	0.974776	+	0.126367i
$539$			13130.7i			1.04931i
$540$	−12190.0	+	2978.05i	−0.971431	+	0.237324i
$541$		−	4558.22i		−	0.362243i	−0.983461	−	0.181121i	$-0.942027\pi$
$541$		−	4558.22i		−	0.362243i	0.983461	−	0.181121i	$-0.0579727\pi$
$542$	−1610.78	+	12425.3i	−0.127655	+	0.984712i
$543$	−632.044	−	652.340i	−0.0499514	−	0.0515554i
$544$	7816.09	+	5875.36i	0.616015	+	0.463058i
$545$	12372.3	+	3034.93i	0.972426	+	0.238536i
$546$	−9581.87	+	7144.25i	−0.751037	+	0.559974i
$547$		−	6925.96i		−	0.541376i	−0.962667	−	0.270688i	$-0.912749\pi$
$547$		−	6925.96i		−	0.541376i	0.962667	−	0.270688i	$-0.0872512\pi$
$548$	−3910.76	−	1031.29i	−0.304853	−	0.0803913i
$549$	11741.8	+	371.189i	0.912803	+	0.0288560i
$550$	−7580.46	+	10845.6i	−0.587695	+	0.840831i
$551$	−1085.61			−0.0839360
$552$	5668.00	+	14074.5i	0.437040	+	1.08524i
$553$		−	8963.10i		−	0.689240i
$554$	−8483.38	−	1099.76i	−0.650586	−	0.0843397i
$555$	10249.4	+	17531.2i	0.783896	+	1.34082i
$556$	−5243.27	−	1382.68i	−0.399936	−	0.105465i
$557$			13278.5i			1.01010i	0.863089	+	0.505052i	$0.168527\pi$
$557$			13278.5i			1.01010i	−0.863089	+	0.505052i	$0.831473\pi$
$558$	9337.28	+	1511.82i	0.708385	+	0.114697i
$559$			11264.3i			0.852288i
$560$	12933.1	−	13710.7i	0.975932	−	1.03461i
$561$	−7309.71	−	7544.44i	−0.550118	−	0.567783i
$562$	−120.279	+	927.813i	−0.00902784	+	0.0696396i
$563$	14521.4			1.08704			0.543520	−	0.839396i	$-0.317091\pi$
$563$	14521.4			1.08704			0.543520	+	0.839396i	$0.317091\pi$
$564$	931.623	+	1658.65i	0.0695539	+	0.123833i
$565$	3857.16	−	15724.3i	0.287207	−	1.17084i
$566$	−1837.02	+	14170.5i	−0.136424	+	1.05235i
$567$	−19164.2	−	1212.87i	−1.41943	−	0.0898337i
$568$	−7681.19	−	3128.28i	−0.567422	−	0.231091i
$569$		−	1852.91i		−	0.136517i	−0.997668	−	0.0682583i	$-0.978256\pi$
$569$		−	1852.91i		−	0.136517i	0.997668	−	0.0682583i	$-0.0217442\pi$
$570$	−301.378	−	712.568i	−0.0221462	−	0.0523617i
$571$	10888.0			0.797980			0.398990	−	0.916955i	$-0.369361\pi$
$571$	10888.0			0.797980			0.398990	+	0.916955i	$0.369361\pi$
$572$	−2357.07	+	8938.28i	−0.172297	+	0.653371i
$573$	4729.44	−	4582.29i	0.344808	−	0.334080i
$574$	716.846	−	5529.66i	0.0521265	−	0.402097i
$575$	−7464.71	+	14299.9i	−0.541391	+	1.03713i
$576$	9965.80	−	9580.50i	0.720905	−	0.693034i
$577$			23942.9i			1.72748i	0.503941	+	0.863738i	$0.331883\pi$
$577$			23942.9i			1.72748i	−0.503941	+	0.863738i	$0.668117\pi$
$578$	5596.39	+	725.497i	0.402732	+	0.0522088i
$579$	8190.38	+	8453.39i	0.587877	+	0.606755i
$580$	9857.71	−	18113.9i	0.705722	−	1.29679i
$581$	15938.7			1.13812
$582$	−12664.4	−	16985.5i	−0.901988	−	1.20975i
$583$	−25559.7			−1.81574
$584$	−1837.00	+	4510.60i	−0.130164	+	0.319606i
$585$	−8976.76	−	2505.20i	−0.634433	−	0.177055i
$586$	−461.730	+	3561.72i	−0.0325493	+	0.251081i
$587$	10172.0			0.715239			0.357620	−	0.933867i	$-0.383588\pi$
$587$	10172.0			0.715239			0.357620	+	0.933867i	$0.383588\pi$
$588$	12715.8	−	7142.11i	0.891818	−	0.500911i
$589$			583.191i			0.0407979i
$590$	−7552.95	−	2924.89i	−0.527034	−	0.204094i
$591$	−2280.72	−	2353.96i	−0.158742	−	0.163839i
$592$	−19462.5	−	11031.9i	−1.35119	−	0.765890i
$593$	−17454.1			−1.20869			−0.604346	−	0.796722i	$-0.706565\pi$
$593$	−17454.1			−1.20869			−0.604346	+	0.796722i	$0.706565\pi$
$594$	−12180.7	+	8496.63i	−0.841383	+	0.586904i
$595$	−3789.86	+	15449.9i	−0.261125	+	1.06451i
$596$	20424.9	+	5386.14i	1.40375	+	0.370176i
$597$	−12138.1	−	12527.9i	−0.832129	−	0.858850i
$598$	−1448.75	+	11175.5i	−0.0990697	+	0.764211i
$599$	−239.830			−0.0163592			−0.00817961	−	0.999967i	$-0.502604\pi$
$599$	−239.830			−0.0163592			−0.00817961	+	0.999967i	$0.502604\pi$
$600$	14626.1	+	1441.73i	0.995177	+	0.0980976i
$601$	387.340			0.0262894			0.0131447	−	0.999914i	$-0.495816\pi$
$601$	387.340			0.0262894			0.0131447	+	0.999914i	$0.495816\pi$
$602$	3494.63	−	26957.1i	0.236596	−	1.82507i
$603$	−23264.1	−	735.438i	−1.57112	−	0.0496673i
$604$	5031.06	−	19078.4i	0.338926	−	1.28525i
$605$	−185.705	+	757.053i	−0.0124793	+	0.0508737i
$606$	4974.39	−	3708.91i	0.333450	−	0.248621i
$607$	−3054.14			−0.204223			−0.102112	−	0.994773i	$-0.532560\pi$
$607$	−3054.14			−0.204223			−0.102112	+	0.994773i	$0.532560\pi$
$608$	681.303	+	512.135i	0.0454448	+	0.0341609i
$609$	22664.6	−	21959.4i	1.50807	−	1.46115i
$610$	−12830.6	−	4968.66i	−0.851632	−	0.329795i
$611$			1412.90i			0.0935515i
$612$	−3330.10	+	11182.3i	−0.219953	+	0.738592i
$613$	−1899.37			−0.125146			−0.0625732	−	0.998040i	$-0.519931\pi$
$613$	−1899.37			−0.125146			−0.0625732	+	0.998040i	$0.519931\pi$
$614$	1838.72	−	14183.6i	0.120855	−	0.932256i
$615$	3753.49	−	2194.43i	0.246106	−	0.143883i
$616$	8413.82	−	20659.4i	0.550329	−	1.35128i
$617$	−5098.97			−0.332701			−0.166351	−	0.986067i	$-0.553198\pi$
$617$	−5098.97			−0.332701			−0.166351	+	0.986067i	$0.553198\pi$
$618$	−12477.5	+	9303.21i	−0.812165	+	0.605550i
$619$	−11519.4			−0.747988			−0.373994	−	0.927431i	$-0.622012\pi$
$619$	−11519.4			−0.747988			−0.373994	+	0.927431i	$0.622012\pi$
$620$	−9730.75	−	5295.55i	−0.630317	−	0.343023i
$621$	−13394.4	+	12181.1i	−0.865538	+	0.787137i
$622$	8097.00	+	1049.67i	0.521962	+	0.0676653i
$623$			13629.6i			0.876498i
$624$	9937.89	−	2579.17i	0.637554	−	0.165464i
$625$	8933.07	+	12819.6i	0.571716	+	0.820451i
$626$	2098.49	−	16187.5i	0.133982	−	1.03352i
$627$	−637.163	−	657.623i	−0.0405834	−	0.0418867i
$628$	12014.3	+	3168.24i	0.763414	+	0.201316i
$629$	18882.0			1.19694
$630$	20705.5	+	8780.27i	1.30941	+	0.555261i
$631$			11392.7i			0.718757i	0.933192	+	0.359379i	$0.117011\pi$
$631$			11392.7i			0.718757i	−0.933192	+	0.359379i	$0.882989\pi$
$632$	−2904.12	+	7130.81i	−0.182785	+	0.448811i
$633$	14215.9	−	13773.6i	0.892625	−	0.864853i
$634$	−408.723	+	3152.84i	−0.0256033	+	0.197500i
$635$	−2863.86	+	11674.9i	−0.178974	+	0.729615i
$636$	13902.5	+	24752.0i	0.866780	+	1.54321i
$637$	10831.8			0.673736
$638$	3137.80	−	24204.6i	0.194713	−	1.50199i
$639$	312.698	−	9891.56i	0.0193586	−	0.612369i
$640$	−14731.6	+	6717.44i	−0.909871	+	0.414891i
$641$			2495.47i			0.153768i	0.997040	+	0.0768838i	$0.0244970\pi$
$641$			2495.47i			0.153768i	−0.997040	+	0.0768838i	$0.975503\pi$
$642$	9650.17	−	7195.18i	0.593243	−	0.442322i
$643$		−	1618.30i		−	0.0992527i	−0.998768	−	0.0496263i	$-0.984197\pi$
$643$		−	1618.30i		−	0.0992527i	0.998768	−	0.0496263i	$-0.0158030\pi$
$644$	6934.14	−	26295.1i	0.424291	−	1.60896i
$645$	18298.3	−	10697.9i	1.11705	−	0.653067i
$646$	−713.403	−	92.4831i	−0.0434496	−	0.00563266i
$647$			21039.5i			1.27844i	0.769025	+	0.639219i	$0.220742\pi$
$647$			21039.5i			1.27844i	−0.769025	+	0.639219i	$0.779258\pi$
$648$	14853.5	+	7174.29i	0.900466	+	0.434927i
$649$	−9585.93			−0.579785
$650$	8946.72	+	6253.27i	0.539876	+	0.377343i
$651$	−11796.6	−	12175.4i	−0.710207	−	0.733013i
$652$	−8030.25	+	30451.7i	−0.482345	+	1.82911i
$653$		−	3169.58i		−	0.189947i	−0.995480	−	0.0949735i	$-0.969723\pi$
$653$		−	3169.58i		−	0.189947i	0.995480	−	0.0949735i	$-0.0302766\pi$
$654$	−10009.8	−	13425.1i	−0.598490	−	0.802696i
$655$	7925.19	+	1944.05i	0.472768	+	0.115970i
$656$	−2361.96	+	4166.99i	−0.140578	+	0.248009i
$657$	−5808.58	−	183.624i	−0.344923	−	0.0109039i
$658$	438.339	−	3381.29i	0.0259699	−	0.200329i
$659$		−	3243.75i		−	0.191743i	−0.995394	−	0.0958714i	$-0.969436\pi$
$659$		−	3243.75i		−	0.191743i	0.995394	−	0.0958714i	$-0.0305638\pi$
$660$	16758.3	−	4659.87i	0.988358	−	0.274826i
$661$		−	18084.9i		−	1.06418i	−0.846689	−	0.532088i	$-0.821408\pi$
$661$		−	18084.9i		−	1.06418i	0.846689	−	0.532088i	$-0.178592\pi$
$662$	−29247.7	−	3791.57i	−1.71713	−	0.222603i
$663$	−6223.55	+	6029.91i	−0.364559	+	0.353216i
$664$	−12680.4	−	5164.29i	−0.741109	−	0.301827i
$665$	−330.350	+	1346.72i	−0.0192638	+	0.0785316i
$666$	4266.66	−	26351.6i	0.248243	−	1.53319i
$667$		−	29754.2i		−	1.72727i
$668$	−4077.49	+	15462.3i	−0.236172	+	0.895591i
$669$	−15904.4	+	15409.6i	−0.919133	+	0.890536i
$670$	25421.3	+	9844.41i	1.46584	+	0.567646i
$671$	−16284.1			−0.936873
$672$	−24583.0	+	3089.21i	−1.41118	+	0.177334i
$673$		−	19706.8i		−	1.12874i	−0.825523	−	0.564368i	$-0.809120\pi$
$673$		−	19706.8i		−	1.12874i	0.825523	−	0.564368i	$-0.190880\pi$
$674$	−1793.72	+	13836.5i	−0.102510	+	0.790747i
$675$	4455.78	+	16961.5i	0.254079	+	0.967184i
$676$	−9621.66	−	2537.28i	−0.547432	−	0.144360i
$677$		−	22320.7i		−	1.26714i	−0.773686	−	0.633569i	$-0.781589\pi$
$677$		−	22320.7i		−	1.26714i	0.773686	−	0.633569i	$-0.218411\pi$
$678$	−17062.3	+	12721.6i	−0.966478	+	0.720607i
$679$			37973.1i			2.14621i
$680$	8021.03	−	11063.6i	0.452342	−	0.623927i
$681$	−16725.9	+	16205.5i	−0.941170	+	0.911887i
$682$	−13002.7	−	1685.62i	−0.730056	−	0.0946420i
$683$	12949.2			0.725458			0.362729	−	0.931895i	$-0.381845\pi$
$683$	12949.2			0.725458			0.362729	+	0.931895i	$0.381845\pi$
$684$	−290.273	+	974.725i	−0.0162264	+	0.0544876i
$685$	−1346.59	+	5489.55i	−0.0751101	+	0.306197i
$686$	−579.430	−	75.1153i	−0.0322489	−	0.00418063i
$687$	4186.05	+	4320.48i	0.232471	+	0.239937i
$688$	−11514.6	+	20314.1i	−0.638066	+	1.12568i
$689$			21084.7i			1.16584i
$690$	19529.8	−	8260.07i	1.07752	−	0.455733i
$691$	14104.3			0.776489			0.388244	−	0.921556i	$-0.373082\pi$
$691$	14104.3			0.776489			0.388244	+	0.921556i	$0.373082\pi$
$692$	5745.89	−	21789.1i	0.315645	−	1.19696i
$693$	26604.4	+	841.033i	1.45832	+	0.0461013i
$694$	9108.70	+	1180.82i	0.498216	+	0.0645870i
$695$	−1805.41	+	7360.00i	−0.0985366	+	0.401699i
$696$	−25146.4	+	10126.8i	−1.36950	+	0.551518i
$697$		−	4042.70i		−	0.219696i
$698$	4361.90	−	33647.2i	0.236534	−	1.82459i
$699$	9514.48	−	9218.46i	0.514836	−	0.498818i
$700$	−19470.8	−	17740.6i	−1.05133	−	0.957903i
$701$	−26508.0			−1.42823			−0.714117	−	0.700026i	$-0.753172\pi$
$701$	−26508.0			−1.42823			−0.714117	+	0.700026i	$0.753172\pi$
$702$	7009.03	+	10048.1i	0.376836	+	0.540230i
$703$	1645.88			0.0883008
$704$	−13387.6	+	13709.9i	−0.716712	+	0.733965i
$705$	2295.19	−	1341.85i	0.122613	−	0.0716839i
$706$	18664.5	+	2419.60i	0.994970	+	0.128984i
$707$	−11120.8			−0.591572
$708$	5214.03	+	9283.01i	0.276773	+	0.492764i
$709$			5707.61i			0.302333i	0.988508	+	0.151166i	$0.0483029\pi$
$709$			5707.61i			0.302333i	−0.988508	+	0.151166i	$0.951697\pi$
$710$	−4185.70	+	10808.8i	−0.221249	+	0.571332i
$711$	−9182.80	−	290.292i	−0.484362	−	0.0153119i
$712$	4416.11	−	10843.3i	0.232445	−	0.570747i
$713$	−15983.9			−0.839555
$714$	16764.6	−	12499.7i	0.878710	−	0.655167i
$715$	12546.7	+	3077.70i	0.656252	+	0.160978i
$716$	1847.86	−	7007.30i	0.0964494	−	0.365748i
$717$	2666.73	−	2583.76i	0.138900	−	0.134578i
$718$	14692.6	+	1904.70i	0.763683	+	0.0990012i
$719$	−6320.76			−0.327851			−0.163925	−	0.986473i	$-0.552416\pi$
$719$	−6320.76			−0.327851			−0.163925	+	0.986473i	$0.552416\pi$
$720$	−13627.9	−	13694.1i	−0.705390	−	0.708819i
$721$	27894.8			1.44086
$722$	19177.0	+	2486.04i	0.988496	+	0.128145i
$723$	−8695.17	+	8424.63i	−0.447271	+	0.433355i
$724$	356.584	−	1352.21i	0.0183043	−	0.0694122i
$725$	−25549.2	−	13337.0i	−1.30879	−	0.683203i
$726$	821.471	−	612.489i	0.0419940	−	0.0313108i
$727$	7788.82			0.397347			0.198674	−	0.980066i	$-0.436337\pi$
$727$	7788.82			0.397347			0.198674	+	0.980066i	$0.436337\pi$
$728$	−17042.3	−	6940.72i	−0.867623	−	0.353352i
$729$	−1863.28	+	19594.6i	−0.0946642	+	0.995509i
$730$	6347.18	+	2457.95i	0.321808	+	0.124620i
$731$		−	19708.2i		−	0.997173i
$732$	8857.34	+	15769.5i	0.447236	+	0.796255i
$733$	37009.1			1.86489			0.932443	−	0.361317i	$-0.117673\pi$
$733$	37009.1			1.86489			0.932443	+	0.361317i	$0.117673\pi$
$734$	−9886.57	−	1281.66i	−0.497166	−	0.0644509i
$735$	−10287.1	−	17595.6i	−0.516251	−	0.883027i
$736$	−14036.4	+	18672.9i	−0.702976	+	0.935182i
$737$	32263.8			1.61255
$738$	−5641.98	−	913.508i	−0.281415	−	0.0455646i
$739$	8679.66			0.432052			0.216026	−	0.976388i	$-0.430690\pi$
$739$	8679.66			0.432052			0.216026	+	0.976388i	$0.430690\pi$
$740$	−14945.1	+	27462.1i	−0.742422	+	1.36422i
$741$	−542.486	+	525.607i	−0.0268943	+	0.0260576i
$742$	6541.30	−	50458.7i	0.323637	−	2.49649i
$743$		−	18604.8i		−	0.918634i	−0.888272	−	0.459317i	$-0.848094\pi$
$743$		−	18604.8i		−	0.918634i	0.888272	−	0.459317i	$-0.151906\pi$
$744$	5440.12	+	13508.6i	0.268071	+	0.665659i
$745$	7032.85	−	28670.5i	0.345857	−	1.40994i
$746$	8634.77	+	1119.38i	0.423782	+	0.0549377i
$747$	516.214	−	16329.4i	0.0252842	−	0.799814i
$748$	4123.96	−	15638.5i	0.201587	−	0.764441i
$749$	−21574.1			−1.05247
$750$	1661.28	−	20472.3i	0.0808819	−	0.996724i
$751$			23589.9i			1.14621i	0.819481	+	0.573107i	$0.194262\pi$
$751$			23589.9i			1.14621i	−0.819481	+	0.573107i	$0.805738\pi$
$752$	−1444.30	+	2548.04i	−0.0700374	+	0.123560i
$753$	10869.5	+	11218.5i	0.526036	+	0.542928i
$754$	−19966.8	−	2588.43i	−0.964388	−	0.125020i
$755$	−26780.4	−	6569.22i	−1.29091	−	0.316660i
$756$	−13656.3	−	26221.1i	−0.656978	−	1.26144i
$757$	28338.1			1.36059			0.680294	−	0.732939i	$-0.261852\pi$
$757$	28338.1			1.36059			0.680294	+	0.732939i	$0.261852\pi$
$758$	9100.52	+	1179.76i	0.436076	+	0.0565314i
$759$	18023.9	−	17463.2i	0.861960	−	0.835142i
$760$	699.166	−	964.378i	0.0333703	−	0.0460285i
$761$			9122.56i			0.434550i	0.976110	+	0.217275i	$0.0697168\pi$
$761$			9122.56i			0.434550i	−0.976110	+	0.217275i	$0.930283\pi$
$762$	12668.4	−	9445.54i	0.602266	−	0.449050i
$763$			30013.4i			1.42406i
$764$	9803.46	+	2585.22i	0.464236	+	0.122421i
$765$	15705.9	+	4383.14i	0.742284	+	0.207154i
$766$	−1826.63	+	14090.4i	−0.0861603	+	0.664630i
$767$			7907.61i			0.372265i
$768$	20558.5	+	5507.42i	0.965940	+	0.258765i
$769$	−28401.1			−1.33182			−0.665910	−	0.746032i	$-0.731956\pi$
$769$	−28401.1			−1.33182			−0.665910	+	0.746032i	$0.731956\pi$
$770$	−29071.3	−	11257.9i	−1.36059	−	0.526890i

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)

\(f(q)\)	\(=\)	\(q+(-2.80496 - 0.363625i) q^{2} +(3.73183 - 3.61572i) q^{3} +(7.73555 + 2.03990i) q^{4} +(2.66357 - 10.8584i) q^{5} +(-11.7824 + 8.78495i) q^{6} +26.3409 q^{7} +(-20.9561 - 8.53468i) q^{8} +(0.853113 - 26.9865i) q^{9} +O(q^{10})\)	\(q+(-2.80496 - 0.363625i) q^{2} +(3.73183 - 3.61572i) q^{3} +(7.73555 + 2.03990i) q^{4} +(2.66357 - 10.8584i) q^{5} +(-11.7824 + 8.78495i) q^{6} +26.3409 q^{7} +(-20.9561 - 8.53468i) q^{8} +(0.853113 - 26.9865i) q^{9} +(-11.4196 + 29.4889i) q^{10} +37.4262i q^{11} +(36.2435 - 20.3570i) q^{12} +30.8736 q^{13} +(-73.8850 - 9.57820i) q^{14} +(-29.3211 - 50.1525i) q^{15} +(55.6776 + 31.5596i) q^{16} -54.0168 q^{17} +(-12.2059 + 75.3858i) q^{18} -4.70847 q^{19} +(42.7543 - 78.5625i) q^{20} +(98.2997 - 95.2413i) q^{21} +(13.6091 - 104.979i) q^{22} -129.048i q^{23} +(-109.064 + 43.9215i) q^{24} +(-110.811 - 57.8443i) q^{25} +(-86.5990 - 11.2264i) q^{26} +(-94.3921 - 103.794i) q^{27} +(203.761 + 53.7329i) q^{28} +230.566 q^{29} +(64.0076 + 151.337i) q^{30} -123.860i q^{31} +(-144.697 - 108.769i) q^{32} +(135.323 + 139.668i) q^{33} +(151.515 + 19.6419i) q^{34} +(70.1608 - 286.021i) q^{35} +(61.6492 - 207.015i) q^{36} -349.557 q^{37} +(13.2070 + 1.71212i) q^{38} +(115.215 - 111.630i) q^{39} +(-148.491 + 204.818i) q^{40} +74.8414i q^{41} +(-310.358 + 231.403i) q^{42} +364.853i q^{43} +(-76.3458 + 289.512i) q^{44} +(-290.759 - 81.1439i) q^{45} +(-46.9252 + 361.975i) q^{46} +45.7642i q^{47} +(321.890 - 83.5397i) q^{48} +350.842 q^{49} +(289.786 + 202.544i) q^{50} +(-201.582 + 195.310i) q^{51} +(238.824 + 62.9791i) q^{52} +682.936i q^{53} +(227.024 + 325.460i) q^{54} +(406.390 + 99.6872i) q^{55} +(-552.003 - 224.811i) q^{56} +(-17.5712 + 17.0245i) q^{57} +(-646.728 - 83.8397i) q^{58} +256.129i q^{59} +(-124.508 - 447.770i) q^{60} +435.099i q^{61} +(-45.0386 + 347.422i) q^{62} +(22.4718 - 710.849i) q^{63} +(366.318 + 357.708i) q^{64} +(82.2339 - 335.238i) q^{65} +(-328.787 - 440.970i) q^{66} -862.064i q^{67} +(-417.850 - 110.189i) q^{68} +(-466.603 - 481.586i) q^{69} +(-300.802 + 776.763i) q^{70} +366.537 q^{71} +(-248.199 + 558.252i) q^{72} -215.240i q^{73} +(980.492 + 127.108i) q^{74} +(-622.676 + 184.796i) q^{75} +(-36.4226 - 9.60482i) q^{76} +985.839i q^{77} +(-363.764 + 271.223i) q^{78} -340.273i q^{79} +(490.988 - 520.510i) q^{80} +(-727.544 - 46.0451i) q^{81} +(27.2142 - 209.927i) q^{82} +605.094 q^{83} +(954.686 - 536.222i) q^{84} +(-143.878 + 586.538i) q^{85} +(132.670 - 1023.40i) q^{86} +(860.434 - 833.664i) q^{87} +(319.421 - 784.308i) q^{88} +517.431i q^{89} +(786.060 + 333.332i) q^{90} +813.237 q^{91} +(263.246 - 998.260i) q^{92} +(-447.843 - 462.225i) q^{93} +(16.6410 - 128.367i) q^{94} +(-12.5413 + 51.1265i) q^{95} +(-933.264 + 117.278i) q^{96} +1441.60i q^{97} +(-984.097 - 127.575i) q^{98} +(1010.00 + 31.9288i) 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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