LMFDB - Embedded newform 120.4.w.c.53.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(53,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("120.53");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	120.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.7
Character	$\chi$	$=$	120.53
Dual form			120.4.w.c.77.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.70249 + 0.834608i) q^{2} +(4.97128 + 1.51207i) q^{3} +(6.60686 - 4.51103i) q^{4} +(2.32852 + 10.9352i) q^{5} +(-14.6968 + 0.0627124i) q^{6} +(-7.15720 + 7.15720i) q^{7} +(-14.0900 + 17.7051i) q^{8} +(22.4273 + 15.0339i) q^{9} +(-15.4194 - 27.6087i) q^{10} -4.70815 q^{11} +(39.6656 - 12.4356i) q^{12} +(-1.08192 + 1.08192i) q^{13} +(13.3688 - 25.3157i) q^{14} +(-4.95906 + 57.8827i) q^{15} +(23.3011 - 59.6075i) q^{16} +(11.4144 + 11.4144i) q^{17} +(-73.1568 - 21.9109i) q^{18} +43.0984 q^{19} +(64.7131 + 61.7431i) q^{20} +(-46.4026 + 24.7582i) q^{21} +(12.7237 - 3.92946i) q^{22} +(-135.015 + 135.015i) q^{23} +(-96.8168 + 66.7121i) q^{24} +(-114.156 + 50.9256i) q^{25} +(2.02090 - 3.82687i) q^{26} +(88.7598 + 108.649i) q^{27} +(-15.0002 + 79.5729i) q^{28} +129.508i q^{29} +(-34.9076 - 160.566i) q^{30} +65.4714 q^{31} +(-13.2221 + 180.536i) q^{32} +(-23.4055 - 7.11908i) q^{33} +(-40.3739 - 21.3208i) q^{34} +(-94.9308 - 61.5995i) q^{35} +(215.992 - 1.84334i) q^{36} +(134.768 + 134.768i) q^{37} +(-116.473 + 35.9703i) q^{38} +(-7.01450 + 3.74260i) q^{39} +(-226.418 - 112.850i) q^{40} -418.900i q^{41} +(104.739 - 105.637i) q^{42} +(321.156 - 321.156i) q^{43} +(-31.1061 + 21.2386i) q^{44} +(-112.176 + 280.253i) q^{45} +(252.191 - 477.560i) q^{46} +(-227.893 - 227.893i) q^{47} +(205.968 - 261.093i) q^{48} +240.549i q^{49} +(266.002 - 232.901i) q^{50} +(39.4849 + 74.0038i) q^{51} +(-2.26752 + 12.0287i) q^{52} +(525.792 + 525.792i) q^{53} +(-330.552 - 219.544i) q^{54} +(-10.9630 - 51.4844i) q^{55} +(-25.8744 - 227.564i) q^{56} +(214.254 + 65.1680i) q^{57} +(-108.088 - 349.993i) q^{58} -648.089i q^{59} +(228.347 + 404.793i) q^{60} -440.190i q^{61} +(-176.936 + 54.6430i) q^{62} +(-268.117 + 52.9158i) q^{63} +(-114.944 - 498.931i) q^{64} +(-14.3503 - 9.31175i) q^{65} +(69.1948 - 0.295259i) q^{66} +(150.241 + 150.241i) q^{67} +(126.904 + 23.9226i) q^{68} +(-875.349 + 467.044i) q^{69} +(307.961 + 87.2417i) q^{70} -712.516i q^{71} +(-582.177 + 185.250i) q^{72} +(485.828 + 485.828i) q^{73} +(-476.686 - 251.729i) q^{74} +(-644.505 + 80.5529i) q^{75} +(284.745 - 194.418i) q^{76} +(33.6972 - 33.6972i) q^{77} +(15.8330 - 15.9687i) q^{78} -460.682i q^{79} +(706.076 + 116.005i) q^{80} +(276.964 + 674.338i) q^{81} +(349.617 + 1132.07i) q^{82} +(-369.206 - 369.206i) q^{83} +(-194.891 + 372.898i) q^{84} +(-98.2400 + 151.398i) q^{85} +(-599.880 + 1135.96i) q^{86} +(-195.825 + 643.819i) q^{87} +(66.3378 - 83.3585i) q^{88} +917.147 q^{89} +(69.2524 - 851.002i) q^{90} -15.4871i q^{91} +(-282.967 + 1501.08i) q^{92} +(325.477 + 98.9976i) q^{93} +(806.080 + 425.677i) q^{94} +(100.356 + 471.289i) q^{95} +(-338.714 + 877.501i) q^{96} +(306.578 - 306.578i) q^{97} +(-200.764 - 650.080i) q^{98} +(-105.591 - 70.7819i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 4 q^{6} - 144 q^{7} - 156 q^{10} - 56 q^{12} + 212 q^{15} + 636 q^{16} + 220 q^{18} - 188 q^{22} - 8 q^{25} + 908 q^{28} + 328 q^{30} - 544 q^{31} - 1624 q^{33} - 1268 q^{36} - 136 q^{40} + 328 q^{42}+ \cdots - 3792 q^{97}+O(q^{100}) $ 128 * q - 4 * q^6 - 144 * q^7 - 156 * q^10 - 56 * q^12 + 212 * q^15 + 636 * q^16 + 220 * q^18 - 188 * q^22 - 8 * q^25 + 908 * q^28 + 328 * q^30 - 544 * q^31 - 1624 * q^33 - 1268 * q^36 - 136 * q^40 + 328 * q^42 + 568 * q^46 - 148 * q^48 + 616 * q^52 + 728 * q^55 - 112 * q^57 + 2196 * q^58 - 424 * q^60 - 2304 * q^63 + 304 * q^66 - 4740 * q^70 + 224 * q^72 + 1280 * q^73 - 1624 * q^76 - 1448 * q^78 + 7056 * q^81 - 1472 * q^82 - 5720 * q^87 + 1516 * q^88 - 996 * q^90 + 2732 * q^96 - 3792 * q^97

Character values

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

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−2.70249	+	0.834608i	−0.955473	+	0.295079i
$2$	−2.70249	+	0.834608i	−0.955473	+	0.295079i
$3$	4.97128	+	1.51207i	0.956723	+	0.290999i
$3$	4.97128	+	1.51207i	0.956723	+	0.290999i
$4$	6.60686	−	4.51103i	0.825857	−	0.563879i
$5$	2.32852	+	10.9352i	0.208269	+	0.978072i
$5$	2.32852	+	10.9352i	0.208269	+	0.978072i
$6$	−14.6968	+	0.0627124i	−0.999991	+	0.00426704i
$7$	−7.15720	+	7.15720i	−0.386452	+	0.386452i	−0.873420	−	0.486968i	$-0.838103\pi$
$7$	−7.15720	+	7.15720i	−0.386452	+	0.386452i	0.486968	+	0.873420i	$0.338103\pi$
$8$	−14.0900	+	17.7051i	−0.622696	+	0.782464i
$9$	22.4273	+	15.0339i	0.830639	+	0.556811i
$10$	−15.4194	−	27.6087i	−0.487604	−	0.873065i
$11$	−4.70815			−0.129051			−0.0645255	−	0.997916i	$-0.520553\pi$
$11$	−4.70815			−0.129051			−0.0645255	+	0.997916i	$0.520553\pi$
$12$	39.6656	−	12.4356i	0.954205	−	0.299153i
$13$	−1.08192	+	1.08192i	−0.0230825	+	0.0230825i	−0.718554	−	0.695471i	$-0.755196\pi$
$13$	−1.08192	+	1.08192i	−0.0230825	+	0.0230825i	0.695471	+	0.718554i	$0.255196\pi$
$14$	13.3688	−	25.3157i	0.255211	−	0.483278i
$15$	−4.95906	+	57.8827i	−0.0853616	+	0.996350i
$16$	23.3011	−	59.6075i	0.364080	−	0.931368i
$17$	11.4144	+	11.4144i	0.162847	+	0.162847i	0.783827	−	0.620979i	$-0.213265\pi$
$17$	11.4144	+	11.4144i	0.162847	+	0.162847i	−0.620979	+	0.783827i	$0.713265\pi$
$18$	−73.1568	−	21.9109i	−0.957956	−	0.286914i
$19$	43.0984			0.520392			0.260196	−	0.965556i	$-0.416213\pi$
$19$	43.0984			0.520392			0.260196	+	0.965556i	$0.416213\pi$
$20$	64.7131	+	61.7431i	0.723515	+	0.690309i
$21$	−46.4026	+	24.7582i	−0.482185	+	0.257271i
$22$	12.7237	−	3.92946i	0.123305	−	0.0380802i
$23$	−135.015	+	135.015i	−1.22402	+	1.22402i	−0.257834	+	0.966189i	$0.583009\pi$
$23$	−135.015	+	135.015i	−1.22402	+	1.22402i	−0.966189	+	0.257834i	$0.916991\pi$
$24$	−96.8168	+	66.7121i	−0.823444	+	0.567398i
$25$	−114.156	+	50.9256i	−0.913248	+	0.407404i
$26$	2.02090	−	3.82687i	0.0152435	−	0.0288658i
$27$	88.7598	+	108.649i	0.632661	+	0.774429i
$28$	−15.0002	+	79.5729i	−0.101242	+	0.537067i
$29$			129.508i			0.829275i	0.909987	+	0.414638i	$0.136092\pi$
$29$			129.508i			0.829275i	−0.909987	+	0.414638i	$0.863908\pi$
$30$	−34.9076	−	160.566i	−0.212441	−	0.977174i
$31$	65.4714			0.379323			0.189661	−	0.981850i	$-0.439261\pi$
$31$	65.4714			0.379323			0.189661	+	0.981850i	$0.439261\pi$
$32$	−13.2221	+	180.536i	−0.0730423	+	0.997329i
$33$	−23.4055	−	7.11908i	−0.123466	−	0.0375537i
$34$	−40.3739	−	21.3208i	−0.203649	−	0.107544i
$35$	−94.9308	−	61.5995i	−0.458464	−	0.297492i
$36$	215.992	−	1.84334i	0.999964	−	0.00853399i
$37$	134.768	+	134.768i	0.598801	+	0.598801i	0.939994	−	0.341192i	$-0.110831\pi$
$37$	134.768	+	134.768i	0.598801	+	0.598801i	−0.341192	+	0.939994i	$0.610831\pi$
$38$	−116.473	+	35.9703i	−0.497221	+	0.153557i
$39$	−7.01450	+	3.74260i	−0.0288005	+	0.0153666i
$40$	−226.418	−	112.850i	−0.894994	−	0.446078i
$41$		−	418.900i		−	1.59564i	−0.602897	−	0.797819i	$-0.705987\pi$
$41$		−	418.900i		−	1.59564i	0.602897	−	0.797819i	$-0.294013\pi$
$42$	104.739	−	105.637i	0.384800	−	0.388098i
$43$	321.156	−	321.156i	1.13897	−	1.13897i	0.150338	−	0.988635i	$-0.451964\pi$
$43$	321.156	−	321.156i	1.13897	−	1.13897i	0.988635	−	0.150338i	$-0.0480363\pi$
$44$	−31.1061	+	21.2386i	−0.106578	+	0.0727692i
$45$	−112.176	+	280.253i	−0.371604	+	0.928391i
$46$	252.191	−	477.560i	0.808338	−	1.53070i
$47$	−227.893	−	227.893i	−0.707270	−	0.707270i	0.258691	−	0.965960i	$-0.416709\pi$
$47$	−227.893	−	227.893i	−0.707270	−	0.707270i	−0.965960	+	0.258691i	$0.916709\pi$
$48$	205.968	−	261.093i	0.619351	−	0.785114i
$49$			240.549i			0.701309i
$50$	266.002	−	232.901i	0.752367	−	0.658744i
$51$	39.4849	+	74.0038i	0.108412	+	0.203188i
$52$	−2.26752	+	12.0287i	−0.00604709	+	0.0320785i
$53$	525.792	+	525.792i	1.36270	+	1.36270i	0.870458	+	0.492243i	$0.163823\pi$
$53$	525.792	+	525.792i	1.36270	+	1.36270i	0.492243	+	0.870458i	$0.336177\pi$
$54$	−330.552	−	219.544i	−0.833008	−	0.553261i
$55$	−10.9630	−	51.4844i	−0.0268774	−	0.126221i
$56$	−25.8744	−	227.564i	−0.0617430	−	0.543027i
$57$	214.254	+	65.1680i	0.497872	+	0.151434i
$58$	−108.088	−	349.993i	−0.244701	−	0.792350i
$59$		−	648.089i		−	1.43007i	−0.699089	−	0.715034i	$-0.746411\pi$
$59$		−	648.089i		−	1.43007i	0.699089	−	0.715034i	$-0.253589\pi$
$60$	228.347	+	404.793i	0.491325	+	0.870977i
$61$		−	440.190i		−	0.923944i	−0.886894	−	0.461972i	$-0.847142\pi$
$61$		−	440.190i		−	0.923944i	0.886894	−	0.461972i	$-0.152858\pi$
$62$	−176.936	+	54.6430i	−0.362433	+	0.111930i
$63$	−268.117	+	52.9158i	−0.536183	+	0.105822i
$64$	−114.944	−	498.931i	−0.224500	−	0.974474i
$65$	−14.3503	−	9.31175i	−0.0273837	−	0.0177689i
$66$	69.1948	−	0.295259i	0.129050	−	0.000550665i
$67$	150.241	+	150.241i	0.273953	+	0.273953i	0.830689	−	0.556736i	$-0.187947\pi$
$67$	150.241	+	150.241i	0.273953	+	0.273953i	−0.556736	+	0.830689i	$0.687947\pi$
$68$	126.904	+	23.9226i	0.226315	+	0.0426624i
$69$	−875.349	+	467.044i	−1.52724	+	0.814862i
$70$	307.961	+	87.2417i	0.525833	+	0.148962i
$71$		−	712.516i		−	1.19099i	−0.803360	−	0.595494i	$-0.796957\pi$
$71$		−	712.516i		−	1.19099i	0.803360	−	0.595494i	$-0.203043\pi$
$72$	−582.177	+	185.250i	−0.952920	+	0.303222i
$73$	485.828	+	485.828i	0.778929	+	0.778929i	0.979649	−	0.200720i	$-0.0643280\pi$
$73$	485.828	+	485.828i	0.778929	+	0.778929i	−0.200720	+	0.979649i	$0.564328\pi$
$74$	−476.686	−	251.729i	−0.748832	−	0.395445i
$75$	−644.505	+	80.5529i	−0.992280	+	0.124019i
$76$	284.745	−	194.418i	0.429770	−	0.293439i
$77$	33.6972	−	33.6972i	0.0498721	−	0.0498721i
$78$	15.8330	−	15.9687i	0.0229837	−	0.0231807i
$79$		−	460.682i		−	0.656086i	−0.944663	−	0.328043i	$-0.893611\pi$
$79$		−	460.682i		−	0.656086i	0.944663	−	0.328043i	$-0.106389\pi$
$80$	706.076	+	116.005i	0.986771	+	0.162121i
$81$	276.964	+	674.338i	0.379923	+	0.925018i
$82$	349.617	+	1132.07i	0.470838	+	1.52459i
$83$	−369.206	−	369.206i	−0.488261	−	0.488261i	0.419496	−	0.907757i	$-0.362207\pi$
$83$	−369.206	−	369.206i	−0.488261	−	0.488261i	−0.907757	+	0.419496i	$0.862207\pi$
$84$	−194.891	+	372.898i	−0.253146	+	0.484363i
$85$	−98.2400	+	151.398i	−0.125360	+	0.193193i
$86$	−599.880	+	1135.96i	−0.752171	+	1.42434i
$87$	−195.825	+	643.819i	−0.241318	+	0.793387i
$88$	66.3378	−	83.3585i	0.0803595	−	0.100978i
$89$	917.147			1.09233			0.546165	−	0.837678i	$-0.316087\pi$
$89$	917.147			1.09233			0.546165	+	0.837678i	$0.316087\pi$
$90$	69.2524	−	851.002i	0.0811094	−	0.996705i
$91$		−	15.4871i		−	0.0178405i
$92$	−282.967	+	1501.08i	−0.320667	+	1.70107i
$93$	325.477	+	98.9976i	0.362907	+	0.110383i
$94$	806.080	+	425.677i	0.884477	+	0.467077i
$95$	100.356	+	471.289i	0.108382	+	0.508981i
$96$	−338.714	+	877.501i	−0.360103	+	0.932913i
$97$	306.578	−	306.578i	0.320911	−	0.320911i	−0.528206	−	0.849116i	$-0.677135\pi$
$97$	306.578	−	306.578i	0.320911	−	0.320911i	0.849116	+	0.528206i	$0.177135\pi$
$98$	−200.764	−	650.080i	−0.206941	−	0.670082i
$99$	−105.591	−	70.7819i	−0.107195	−	0.0718570i
$100$	−524.485	+	851.419i	−0.524485	+	0.851419i
$101$	787.111			0.775450			0.387725	−	0.921775i	$-0.373261\pi$
$101$	787.111			0.775450			0.387725	+	0.921775i	$0.373261\pi$
$102$	−168.472	−	167.040i	−0.163541	−	0.162151i
$103$	−699.355	−	699.355i	−0.669024	−	0.669024i	0.288466	−	0.957490i	$-0.406855\pi$
$103$	−699.355	−	699.355i	−0.669024	−	0.669024i	−0.957490	+	0.288466i	$0.906855\pi$
$104$	−3.91132	−	34.3999i	−0.00368785	−	0.0324345i
$105$	−378.785	−	449.771i	−0.352054	−	0.418030i
$106$	−1859.78	−	982.116i	−1.70413	−	0.899920i
$107$	512.085	−	512.085i	0.462665	−	0.462665i	−0.436863	−	0.899528i	$-0.643911\pi$
$107$	512.085	−	512.085i	0.462665	−	0.462665i	0.899528	+	0.436863i	$0.143911\pi$
$108$	1076.54	+	317.432i	0.959172	+	0.282824i
$109$	−999.865			−0.878621			−0.439311	−	0.898335i	$-0.644777\pi$
$109$	−999.865			−0.878621			−0.439311	+	0.898335i	$0.644777\pi$
$110$	72.5968	+	129.986i	0.0629257	+	0.112670i
$111$	466.189	+	873.746i	0.398637	+	0.747138i
$112$	259.852	+	593.394i	0.219229	+	0.500629i
$113$	−193.028	+	193.028i	−0.160695	+	0.160695i	−0.782874	−	0.622180i	$-0.786247\pi$
$113$	−193.028	+	193.028i	−0.160695	+	0.160695i	0.622180	+	0.782874i	$0.286247\pi$
$114$	−633.409	+	2.70280i	−0.520388	+	0.00222053i
$115$	−1790.79	−	1162.03i	−1.45211	−	0.942256i
$116$	584.214	+	855.639i	0.467611	+	0.684863i
$117$	−40.5301	+	7.99907i	−0.0320258	+	0.00632063i
$118$	540.901	+	1751.45i	0.421983	+	1.36639i
$119$	−163.391			−0.125866
$120$	−954.948	−	903.368i	−0.726454	−	0.687215i
$121$	−1308.83			−0.983346
$122$	367.387	+	1189.61i	0.272636	+	0.882804i
$123$	633.408	−	2082.47i	0.464329	−	1.52658i
$124$	432.560	−	295.344i	0.313267	−	0.213892i
$125$	−822.694	−	1129.73i	−0.588672	−	0.808372i
$126$	680.418	−	366.777i	0.481083	−	0.259326i
$127$	1044.72	−	1044.72i	0.729953	−	0.729953i	−0.240657	−	0.970610i	$-0.577363\pi$
$127$	1044.72	−	1044.72i	0.729953	−	0.729953i	0.970610	+	0.240657i	$0.0773631\pi$
$128$	727.047	+	1252.42i	0.502051	+	0.864838i
$129$	2082.17	−	1110.94i	1.42112	−	0.758242i
$130$	46.5532	+	13.1880i	0.0314076	+	0.00889740i
$131$	2122.46			1.41557			0.707786	−	0.706427i	$-0.249694\pi$
$131$	2122.46			1.41557			0.707786	+	0.706427i	$0.249694\pi$
$132$	−186.751	+	58.5485i	−0.123141	+	0.0386060i
$133$	−308.464	+	308.464i	−0.201107	+	0.201107i
$134$	−531.417	−	280.632i	−0.342593	−	0.180917i
$135$	−981.421	+	1223.60i	−0.625683	+	0.780077i
$136$	−362.923	+	41.2649i	−0.228827	+	0.0260179i
$137$	−1296.56	−	1296.56i	−0.808558	−	0.808558i	0.175858	−	0.984416i	$-0.443730\pi$
$137$	−1296.56	−	1296.56i	−0.808558	−	0.808558i	−0.984416	+	0.175858i	$0.943730\pi$
$138$	1975.82	−	1992.75i	1.21879	−	1.22923i
$139$	657.301			0.401091			0.200545	−	0.979684i	$-0.435729\pi$
$139$	657.301			0.401091			0.200545	+	0.979684i	$0.435729\pi$
$140$	−905.072	+	21.2573i	−0.546375	+	0.0128326i
$141$	−788.330	−	1477.51i	−0.470847	−	0.882476i
$142$	594.672	+	1925.56i	0.351435	+	1.13796i
$143$	5.09386	−	5.09386i	0.00297881	−	0.00297881i
$144$	1418.71	−	986.527i	0.821015	−	0.570907i
$145$	−1416.19	+	301.562i	−0.811091	+	0.172713i
$146$	−1718.42	−	907.466i	−0.974091	−	0.514400i
$147$	−363.728	+	1195.84i	−0.204080	+	0.670959i
$148$	1498.33	+	282.449i	0.832176	+	0.156873i
$149$			646.750i			0.355596i	0.984067	+	0.177798i	$0.0568974\pi$
$149$			646.750i			0.355596i	−0.984067	+	0.177798i	$0.943103\pi$
$150$	1674.53	−	755.602i	0.911501	−	0.411298i
$151$	2105.73			1.13485			0.567424	−	0.823426i	$-0.307940\pi$
$151$	2105.73			1.13485			0.567424	+	0.823426i	$0.307940\pi$
$152$	−607.256	+	763.064i	−0.324046	+	0.407188i
$153$	84.3911	+	427.598i	0.0445923	+	0.225943i
$154$	−62.9422	+	119.190i	−0.0329352	+	0.0623676i
$155$	152.452	+	715.941i	0.0790013	+	0.371005i
$156$	−29.4608	+	56.3695i	−0.0151202	+	0.0289306i
$157$	1526.33	+	1526.33i	0.775887	+	0.775887i	0.979129	−	0.203242i	$-0.0651477\pi$
$157$	1526.33	+	1526.33i	0.775887	+	0.775887i	−0.203242	+	0.979129i	$0.565148\pi$
$158$	384.489	+	1244.99i	0.193597	+	0.626873i
$159$	1818.82	+	3408.90i	0.907183	+	1.70027i
$160$	−2004.98	+	275.796i	−0.990671	+	0.136272i
$161$		−	1932.65i		−	0.946053i
$162$	−1311.30	−	1591.23i	−0.635959	−	0.771722i
$163$	−2245.11	+	2245.11i	−1.07884	+	1.07884i	−0.0822248	+	0.996614i	$0.526203\pi$
$163$	−2245.11	+	2245.11i	−1.07884	+	1.07884i	−0.996614	+	0.0822248i	$0.973797\pi$
$164$	−1889.67	−	2767.61i	−0.899747	−	1.31777i
$165$	23.3480	−	272.521i	0.0110160	−	0.128580i
$166$	1305.92	+	689.632i	0.610596	+	0.322445i
$167$	−1454.62	−	1454.62i	−0.674024	−	0.674024i	0.284618	−	0.958641i	$-0.408133\pi$
$167$	−1454.62	−	1454.62i	−0.674024	−	0.674024i	−0.958641	+	0.284618i	$0.908133\pi$
$168$	215.465	−	1170.41i	0.0989494	−	0.537494i
$169$			2194.66i			0.998934i
$170$	139.135	−	491.142i	0.0627714	−	0.221581i
$171$	966.580	+	647.937i	0.432258	+	0.289760i
$172$	673.086	−	3570.58i	0.298386	−	1.58287i
$173$	−1196.58	−	1196.58i	−0.525861	−	0.525861i	0.393475	−	0.919335i	$-0.371273\pi$
$173$	−1196.58	−	1196.58i	−0.525861	−	0.525861i	−0.919335	+	0.393475i	$0.871273\pi$
$174$	−8.12174	−	1903.35i	−0.00353855	−	0.829268i
$175$	452.552	−	1181.52i	0.195484	−	0.510369i
$176$	−109.705	+	280.641i	−0.0469849	+	0.120194i
$177$	979.959	−	3221.83i	0.416148	−	1.36818i
$178$	−2478.58	+	765.458i	−1.04369	+	0.322323i
$179$			4093.63i			1.70934i	0.519169	+	0.854672i	$0.326242\pi$
$179$			4093.63i			1.70934i	−0.519169	+	0.854672i	$0.673758\pi$
$180$	523.100	+	2357.62i	0.216609	+	0.976259i
$181$			1675.77i			0.688172i	0.938938	+	0.344086i	$0.111811\pi$
$181$			1675.77i			0.688172i	−0.938938	+	0.344086i	$0.888189\pi$
$182$	12.9257	+	41.8536i	0.00526436	+	0.0170461i
$183$	665.601	−	2188.31i	0.268867	−	0.883959i
$184$	−488.099	−	4292.81i	−0.195561	−	1.71995i
$185$	−1159.90	+	1787.52i	−0.460959	+	0.710383i
$186$	−962.220	+	4.10587i	−0.379319	+	0.00161858i
$187$	−53.7409	−	53.7409i	−0.0210156	−	0.0210156i
$188$	−2533.69	−	477.624i	−0.982918	−	0.185289i
$189$	−1412.90	−	142.353i	−0.543773	−	0.0547867i
$190$	−664.551	−	1189.89i	−0.253745	−	0.454336i
$191$		−	2483.22i		−	0.940730i	−0.882472	−	0.470365i	$-0.844122\pi$
$191$		−	2483.22i		−	0.940730i	0.882472	−	0.470365i	$-0.155878\pi$
$192$	183.000	−	2654.13i	0.0687860	−	0.997631i
$193$	1123.16	+	1123.16i	0.418896	+	0.418896i	0.884823	−	0.465927i	$-0.154279\pi$
$193$	1123.16	+	1123.16i	0.418896	+	0.418896i	−0.465927	+	0.884823i	$0.654279\pi$
$194$	−572.651	+	1084.40i	−0.211928	+	0.401315i
$195$	−57.2594	−	67.9901i	−0.0210278	−	0.0249686i
$196$	1085.13	+	1589.27i	0.395454	+	0.579181i
$197$	1688.32	−	1688.32i	0.610598	−	0.610598i	−0.332504	−	0.943102i	$-0.607893\pi$
$197$	1688.32	−	1688.32i	0.610598	−	0.610598i	0.943102	+	0.332504i	$0.107893\pi$
$198$	344.433	+	103.160i	0.123625	+	0.0370265i
$199$			2588.54i			0.922094i	0.887376	+	0.461047i	$0.152526\pi$
$199$			2588.54i			0.922094i	−0.887376	+	0.461047i	$0.847474\pi$
$200$	706.812	−	2738.69i	0.249896	−	0.968273i
$201$	519.715	+	974.067i	0.182378	+	0.341818i
$202$	−2127.16	+	656.929i	−0.740921	+	0.228819i
$203$	−926.912	−	926.912i	−0.320475	−	0.320475i
$204$	594.705	+	310.815i	0.204106	+	0.106674i
$205$	4580.74	−	975.417i	1.56065	−	0.332322i
$206$	2473.68	+	1306.31i	0.836649	+	0.441820i
$207$	−5057.81	+	998.214i	−1.69827	+	0.335172i
$208$	39.2808	+	89.7009i	0.0130944	+	0.0299021i
$209$	−202.914			−0.0671572
$210$	1399.04	+	899.362i	0.459729	+	0.295533i
$211$			1866.62i			0.609020i	0.952509	+	0.304510i	$0.0984928\pi$
$211$			1866.62i			0.609020i	−0.952509	+	0.304510i	$0.901507\pi$
$212$	5845.70	+	1101.97i	1.89379	+	0.356998i
$213$	1077.38	−	3542.12i	0.346576	−	1.13945i
$214$	−956.512	+	1811.29i	−0.305541	+	0.578586i
$215$	4259.72	+	2764.08i	1.35121	+	0.876784i
$216$	−3174.28	+	40.6366i	−0.999918	+	0.0128008i
$217$	−468.592	+	468.592i	−0.146590	+	0.146590i
$218$	2702.12	−	834.496i	0.839499	−	0.259262i
$219$	1680.58	+	3149.79i	0.518552	+	0.971887i
$220$	−304.679	−	290.696i	−0.0933703	−	0.0890850i
$221$	−24.6991			−0.00751784
$222$	−1989.10	−	1972.20i	−0.601351	−	0.596241i
$223$	−3600.27	−	3600.27i	−1.08113	−	1.08113i	−0.996404	−	0.0847250i	$-0.972999\pi$
$223$	−3600.27	−	3600.27i	−1.08113	−	1.08113i	−0.0847250	−	0.996404i	$-0.527001\pi$
$224$	−1197.50	−	1386.76i	−0.357193	−	0.413647i
$225$	−3325.82	−	574.088i	−0.985427	−	0.170100i
$226$	360.552	−	682.756i	0.106122	−	0.200957i
$227$	−1341.65	+	1341.65i	−0.392283	+	0.392283i	−0.875500	−	0.483217i	$-0.839468\pi$
$227$	−1341.65	+	1341.65i	−0.392283	+	0.392283i	0.483217	+	0.875500i	$0.339468\pi$
$228$	1709.52	−	535.953i	0.496561	−	0.155677i
$229$	4595.87			1.32622			0.663109	−	0.748523i	$-0.269237\pi$
$229$	4595.87			1.32622			0.663109	+	0.748523i	$0.269237\pi$
$230$	5809.43	+	1645.74i	1.66549	+	0.471814i
$231$	218.471	−	116.565i	0.0622265	−	0.0332010i
$232$	−2292.95	−	1824.76i	−0.648878	−	0.516386i
$233$	−4048.34	+	4048.34i	−1.13826	+	1.13826i	−0.149502	+	0.988761i	$0.547767\pi$
$233$	−4048.34	+	4048.34i	−1.13826	+	1.13826i	−0.988761	+	0.149502i	$0.952233\pi$
$234$	102.856	−	55.4442i	0.0287347	−	0.0154893i
$235$	1961.40	−	3022.71i	0.544458	−	0.839063i
$236$	−2923.55	−	4281.83i	−0.806386	−	1.18103i
$237$	696.586	−	2290.18i	0.190920	−	0.627693i
$238$	441.561	−	136.367i	0.120261	−	0.0371402i
$239$	−164.357			−0.0444827			−0.0222414	−	0.999753i	$-0.507080\pi$
$239$	−164.357			−0.0444827			−0.0222414	+	0.999753i	$0.507080\pi$
$240$	3334.69	+	1644.33i	0.896890	+	0.442255i
$241$	−1373.16			−0.367026			−0.183513	−	0.983017i	$-0.558747\pi$
$241$	−1373.16			−0.367026			−0.183513	+	0.983017i	$0.558747\pi$
$242$	3537.10	−	1092.36i	0.939560	−	0.290164i
$243$	357.217	+	3771.11i	0.0943023	+	0.995544i
$244$	−1985.71	−	2908.27i	−0.520993	−	0.763046i
$245$	−2630.45	+	560.124i	−0.685931	+	0.146061i
$246$	26.2702	+	6156.49i	0.00680864	+	1.59562i
$247$	−46.6292	+	46.6292i	−0.0120119	+	0.0120119i
$248$	−922.491	+	1159.18i	−0.236203	+	0.296807i
$249$	−1277.16	−	2393.70i	−0.325047	−	0.609214i
$250$	3166.21	+	2366.46i	0.800994	+	0.598673i
$251$	−2107.74			−0.530038			−0.265019	−	0.964243i	$-0.585378\pi$
$251$	−2107.74			−0.530038			−0.265019	+	0.964243i	$0.585378\pi$
$252$	−1532.70	+	1559.09i	−0.383140	+	0.389736i
$253$	635.670	−	635.670i	0.157961	−	0.157961i
$254$	−1951.41	+	3695.28i	−0.482057	+	0.912843i
$255$	−717.303	+	604.093i	−0.176154	+	0.148352i
$256$	−3010.11	−	2777.85i	−0.734891	−	0.678185i
$257$	4333.10	+	4333.10i	1.05172	+	1.05172i	0.998588	+	0.0531288i	$0.0169194\pi$
$257$	4333.10	+	4333.10i	1.05172	+	1.05172i	0.0531288	+	0.998588i	$0.483081\pi$
$258$	−4699.83	+	4740.11i	−1.13410	+	1.14382i
$259$	−1929.12			−0.462816
$260$	−136.816	+	3.21337i	−0.0326345	+	0.000766481i
$261$	−1947.01	+	2904.50i	−0.461750	+	0.688829i
$262$	−5735.91	+	1771.42i	−1.35254	+	0.417705i
$263$	−127.265	+	127.265i	−0.0298383	+	0.0298383i	−0.721869	−	0.692030i	$-0.756716\pi$
$263$	−127.265	+	127.265i	−0.0298383	+	0.0298383i	0.692030	+	0.721869i	$0.256716\pi$
$264$	455.828	−	314.091i	0.106266	−	0.0732233i
$265$	−4525.31	+	6973.95i	−1.04901	+	1.61663i
$266$	576.173	−	1091.07i	0.132810	−	0.251494i
$267$	4559.39	+	1386.79i	1.04506	+	0.317867i
$268$	1670.37	+	314.879i	0.380723	+	0.0717698i
$269$			973.773i			0.220714i	0.993892	+	0.110357i	$0.0351994\pi$
$269$			973.773i			0.220714i	−0.993892	+	0.110357i	$0.964801\pi$
$270$	1631.05	−	4125.85i	0.367639	−	0.929968i
$271$	1716.66			0.384795			0.192398	−	0.981317i	$-0.438374\pi$
$271$	1716.66			0.384795			0.192398	+	0.981317i	$0.438374\pi$
$272$	946.355	−	414.417i	0.210960	−	0.0923813i
$273$	23.4176	−	76.9907i	0.00519157	−	0.0170685i
$274$	4586.05	+	2421.81i	1.01114	+	0.533967i
$275$	537.464	−	239.765i	0.117856	−	0.0525760i
$276$	−3676.45	+	7034.42i	−0.801799	+	1.53414i
$277$	−4805.10	−	4805.10i	−1.04228	−	1.04228i	−0.999066	−	0.0432102i	$-0.986241\pi$
$277$	−4805.10	−	4805.10i	−1.04228	−	1.04228i	−0.0432102	−	0.999066i	$-0.513759\pi$
$278$	−1776.35	+	548.589i	−0.383231	+	0.118353i
$279$	1468.34	+	984.290i	0.315080	+	0.211211i
$280$	2428.20	−	812.828i	0.518260	−	0.173485i
$281$		−	6223.57i		−	1.32123i	−0.750723	−	0.660617i	$-0.770295\pi$
$281$		−	6223.57i		−	1.32123i	0.750723	−	0.660617i	$-0.229705\pi$
$282$	3363.60	+	3335.01i	0.710281	+	0.704245i
$283$	−3021.81	+	3021.81i	−0.634729	+	0.634729i	−0.949250	−	0.314522i	$-0.898156\pi$
$283$	−3021.81	+	3021.81i	−0.634729	+	0.634729i	0.314522	+	0.949250i	$0.398156\pi$
$284$	−3214.18	−	4707.49i	−0.671573	−	0.983585i
$285$	−213.728	+	2494.65i	−0.0444216	+	0.518493i
$286$	−9.51471	+	18.0175i	−0.00196719	+	0.00372516i
$287$	2998.15	+	2998.15i	0.616638	+	0.616638i
$288$	−3010.69	+	3850.14i	−0.615995	+	0.787750i
$289$		−	4652.42i		−	0.946961i
$290$	3575.55	−	1996.93i	0.724011	−	0.404358i
$291$	1987.66	−	1060.52i	0.400407	−	0.213638i
$292$	5401.38	+	1018.21i	1.08251	+	0.204062i
$293$	−1152.74	−	1152.74i	−0.229842	−	0.229842i	0.582784	−	0.812627i	$-0.301963\pi$
$293$	−1152.74	−	1152.74i	−0.229842	−	0.229842i	−0.812627	+	0.582784i	$0.801963\pi$
$294$	−15.0854	−	3535.30i	−0.00299251	−	0.701303i
$295$	7086.97	−	1509.09i	1.39871	−	0.297839i
$296$	−4284.95	+	487.205i	−0.841412	+	0.0956697i
$297$	−417.895	−	511.538i	−0.0816455	−	0.0999409i
$298$	−539.783	−	1747.83i	−0.104929	−	0.339762i
$299$		−	292.152i		−	0.0565069i
$300$	−3894.77	+	3439.58i	−0.749550	+	0.661948i
$301$			4597.15i			0.880317i
$302$	−5690.71	+	1757.46i	−1.08432	+	0.334869i
$303$	3912.95	+	1190.17i	0.741891	+	0.225655i
$304$	1004.24	−	2568.99i	0.189465	−	0.484677i
$305$	4813.56	−	1024.99i	0.903683	−	0.192429i
$306$	−584.942	−	1085.14i	−0.109278	−	0.202724i
$307$	−5762.15	−	5762.15i	−1.07122	−	1.07122i	−0.997262	−	0.0739549i	$-0.976438\pi$
$307$	−5762.15	−	5762.15i	−1.07122	−	1.07122i	−0.0739549	−	0.997262i	$-0.523562\pi$
$308$	70.6233	−	374.641i	0.0130654	−	0.0693090i
$309$	−2419.21	−	4534.17i	−0.445386	−	0.834756i
$310$	−1009.53	−	1807.58i	−0.184959	−	0.331174i
$311$			3222.19i			0.587503i	0.955882	+	0.293752i	$0.0949039\pi$
$311$			3222.19i			0.587503i	−0.955882	+	0.293752i	$0.905096\pi$
$312$	32.5710	−	176.926i	0.00591016	−	0.0321040i
$313$	2700.78	+	2700.78i	0.487723	+	0.487723i	0.907587	−	0.419864i	$-0.137922\pi$
$313$	2700.78	+	2700.78i	0.487723	+	0.487723i	−0.419864	+	0.907587i	$0.637922\pi$
$314$	−5398.77	−	2850.99i	−0.970287	−	0.512391i
$315$	−1202.96	−	2808.69i	−0.215172	−	0.502386i
$316$	−2078.15	−	3043.66i	−0.369954	−	0.541834i
$317$	1849.32	−	1849.32i	0.327660	−	0.327660i	−0.524036	−	0.851696i	$-0.675574\pi$
$317$	1849.32	−	1849.32i	0.327660	−	0.327660i	0.851696	+	0.524036i	$0.175574\pi$
$318$	−7760.44	−	7694.49i	−1.36850	−	1.35687i
$319$		−	609.742i		−	0.107019i
$320$	5188.24	−	2418.71i	0.906349	−	0.422531i
$321$	3320.03	−	1771.41i	0.577277	−	0.308007i
$322$	1613.01	+	5222.97i	0.279160	+	0.903928i
$323$	491.944	+	491.944i	0.0847446	+	0.0847446i
$324$	4871.82	+	3205.86i	0.835361	+	0.549702i
$325$	68.4105	−	178.606i	0.0116761	−	0.0304839i
$326$	4193.59	−	7941.17i	0.712459	−	1.34914i
$327$	−4970.61	−	1511.87i	−0.840598	−	0.255678i
$328$	7416.68	+	5902.29i	1.24853	+	0.993596i
$329$	3262.16			0.546652
$330$	164.350	+	755.969i	0.0274157	+	0.126105i
$331$		−	4623.28i		−	0.767729i	−0.923389	−	0.383864i	$-0.874593\pi$
$331$		−	4623.28i		−	0.767729i	0.923389	−	0.383864i	$-0.125407\pi$
$332$	−4104.80	−	773.791i	−0.678554	−	0.127914i
$333$	996.386	+	5048.55i	0.163969	+	0.830807i
$334$	5145.13	+	2717.05i	0.842901	+	0.445121i
$335$	−1293.07	+	1992.75i	−0.210890	+	0.325002i
$336$	394.541	+	3342.84i	0.0640595	+	0.542759i
$337$	7174.30	−	7174.30i	1.15967	−	1.15967i	0.175124	−	0.984546i	$-0.443967\pi$
$337$	7174.30	−	7174.30i	1.15967	−	1.15967i	0.984546	−	0.175124i	$-0.0560327\pi$
$338$	−1831.68	−	5931.03i	−0.294764	−	0.954455i
$339$	−1251.47	+	667.722i	−0.200502	+	0.106978i
$340$	33.9015	+	1443.43i	0.00540755	+	0.230238i
$341$	−308.249			−0.0489520
$342$	−3152.94	−	944.325i	−0.498513	−	0.149308i
$343$	−4176.58	−	4176.58i	−0.657475	−	0.657475i
$344$	1161.03	+	10211.2i	0.181972	+	1.60044i
$345$	−7145.47	−	8484.57i	−1.11507	−	1.32404i
$346$	4232.40	+	2235.06i	0.657616	+	0.347276i
$347$	1816.22	−	1816.22i	0.280979	−	0.280979i	−0.552520	−	0.833500i	$-0.686334\pi$
$347$	1816.22	−	1816.22i	0.280979	−	0.280979i	0.833500	+	0.552520i	$0.186334\pi$
$348$	1610.50	+	5137.00i	0.248080	+	0.791299i
$349$	−5080.12			−0.779177			−0.389588	−	0.920989i	$-0.627383\pi$
$349$	−5080.12			−0.779177			−0.389588	+	0.920989i	$0.627383\pi$
$350$	−236.909	+	3570.75i	−0.0361810	+	0.545327i
$351$	−213.582	−	21.5190i	−0.0324791	−	0.00327236i
$352$	62.2515	−	849.990i	0.00942618	−	0.128706i
$353$	−4367.96	+	4367.96i	−0.658592	+	0.658592i	−0.955047	−	0.296455i	$-0.904195\pi$
$353$	−4367.96	+	4367.96i	−0.658592	+	0.658592i	0.296455	+	0.955047i	$0.404195\pi$
$354$	40.6432	+	9524.84i	0.00610215	+	1.43006i
$355$	7791.49	−	1659.11i	1.16487	−	0.248046i
$356$	6059.46	−	4137.28i	0.902109	−	0.615942i
$357$	−812.261	−	247.059i	−0.120418	−	0.0366267i
$358$	−3416.58	−	11063.0i	−0.504391	−	1.63323i
$359$	−5052.47			−0.742783			−0.371391	−	0.928476i	$-0.621119\pi$
$359$	−5052.47			−0.742783			−0.371391	+	0.928476i	$0.621119\pi$
$360$	−3381.36	−	5934.85i	−0.495037	−	0.868872i
$361$	−5001.53			−0.729192
$362$	−1398.61	−	4528.75i	−0.203065	−	0.657529i
$363$	−6506.58	−	1979.05i	−0.940790	−	0.286153i
$364$	−69.8628	−	102.321i	−0.0100599	−	0.0147337i
$365$	−4181.35	+	6443.87i	−0.599621	+	0.924075i
$366$	27.6054	+	6469.39i	0.00394250	+	0.923936i
$367$	3089.84	−	3089.84i	0.439477	−	0.439477i	−0.452359	−	0.891836i	$-0.649417\pi$
$367$	3089.84	−	3089.84i	0.439477	−	0.439477i	0.891836	+	0.452359i	$0.149417\pi$
$368$	4901.90	+	11193.9i	0.694373	+	1.58566i
$369$	6297.69	−	9394.77i	0.888468	−	1.32540i
$370$	1642.73	−	5798.80i	0.230815	−	0.814770i
$371$	−7526.40			−1.05324
$372$	2596.96	−	814.173i	0.361952	−	0.113476i
$373$	6748.26	−	6748.26i	0.936760	−	0.936760i	−0.0613555	−	0.998116i	$-0.519542\pi$
$373$	6748.26	−	6748.26i	0.936760	−	0.936760i	0.998116	+	0.0613555i	$0.0195424\pi$
$374$	190.087	+	100.381i	0.0262811	+	0.0138786i
$375$	−2381.60	−	6860.20i	−0.327961	−	0.944691i
$376$	7245.90	−	823.869i	0.993827	−	0.113000i
$377$	−140.118	−	140.118i	−0.0191417	−	0.0191417i
$378$	3937.14	−	794.507i	0.535727	−	0.108109i
$379$	2408.79			0.326468			0.163234	−	0.986587i	$-0.447807\pi$
$379$	2408.79			0.326468			0.163234	+	0.986587i	$0.447807\pi$
$380$	2789.03	+	2661.03i	0.376512	+	0.359231i
$381$	6773.30	−	3613.90i	0.910778	−	0.485947i
$382$	2072.51	+	6710.86i	0.277589	+	0.898842i
$383$	−1.58379	+	1.58379i	−0.000211301	+	0.000211301i	−0.707212	−	0.707001i	$-0.750048\pi$
$383$	−1.58379	+	1.58379i	−0.000211301	+	0.000211301i	0.707001	+	0.707212i	$0.250048\pi$
$384$	1720.60	+	7325.48i	0.228657	+	0.973507i
$385$	446.949	+	290.020i	0.0591653	+	0.0383916i
$386$	−3972.72	−	2097.93i	−0.523851	−	0.276636i
$387$	12030.9	−	2374.42i	1.58027	−	0.311883i
$388$	642.534	−	3408.51i	0.0840715	−	0.445981i
$389$		−	2113.51i		−	0.275474i	−0.990469	−	0.137737i	$-0.956017\pi$
$389$		−	2113.51i		−	0.275474i	0.990469	−	0.137737i	$-0.0439829\pi$
$390$	211.488	+	135.953i	0.0274592	+	0.0176519i
$391$	−3082.23			−0.398658
$392$	−4258.96	−	3389.33i	−0.548749	−	0.436702i
$393$	10551.3	+	3209.31i	1.35431	+	0.411930i
$394$	−3153.57	+	5971.75i	−0.403236	+	0.763584i
$395$	5037.64	−	1072.71i	0.641699	−	0.136643i
$396$	−1016.92	+	8.67874i	−0.129046	+	0.00110132i
$397$	−9094.35	−	9094.35i	−1.14970	−	1.14970i	−0.986611	−	0.163093i	$-0.947853\pi$
$397$	−9094.35	−	9094.35i	−1.14970	−	1.14970i	−0.163093	−	0.986611i	$-0.552147\pi$
$398$	−2160.42	−	6995.49i	−0.272090	−	0.881036i
$399$	−1999.88	+	1067.04i	−0.250925	+	0.133882i
$400$	375.582	+	7991.18i	0.0469477	+	0.998897i
$401$			5643.32i			0.702777i	0.936230	+	0.351389i	$0.114290\pi$
$401$			5643.32i			0.702777i	−0.936230	+	0.351389i	$0.885710\pi$
$402$	−2217.49	−	2198.64i	−0.275120	−	0.272782i
$403$	−70.8351	+	70.8351i	−0.00875570	+	0.00875570i
$404$	5200.33	−	3550.68i	0.640411	−	0.437260i
$405$	−6729.09	+	4598.86i	−0.825607	+	0.564245i
$406$	3278.58	+	1731.36i	0.400771	+	0.211640i
$407$	−634.506	−	634.506i	−0.0772759	−	0.0772759i
$408$	−1866.59	−	343.628i	−0.226495	−	0.0416964i
$409$			4592.79i			0.555254i	0.960689	+	0.277627i	$0.0895480\pi$
$409$			4592.79i			0.555254i	−0.960689	+	0.277627i	$0.910452\pi$
$410$	−11565.3	+	6459.17i	−1.39310	+	0.778039i
$411$	−4485.06	−	8406.04i	−0.538277	−	1.00886i
$412$	−7775.35	−	1465.72i	−0.929767	−	0.175270i
$413$	4638.50	+	4638.50i	0.552653	+	0.552653i
$414$	12835.5	−	6918.95i	1.52375	−	0.821371i
$415$	3177.63	−	4897.04i	0.375864	−	0.579244i
$416$	−181.021	−	209.631i	−0.0213348	−	0.0247068i
$417$	3267.63	+	993.889i	0.383733	+	0.116717i
$418$	548.372	−	169.354i	0.0641669	−	0.0198166i
$419$		−	14710.7i		−	1.71519i	−0.514326	−	0.857595i	$-0.671958\pi$
$419$		−	14710.7i		−	1.71519i	0.514326	−	0.857595i	$-0.328042\pi$
$420$	−4531.51	−	1262.86i	−0.526464	−	0.146717i
$421$			13522.1i			1.56539i	0.622405	+	0.782695i	$0.286156\pi$
$421$			13522.1i			1.56539i	−0.622405	+	0.782695i	$0.713844\pi$
$422$	−1557.90	−	5044.51i	−0.179709	−	0.581902i
$423$	−1684.90	−	8537.15i	−0.193671	−	0.981301i
$424$	−16717.6	+	1900.82i	−1.91481	+	0.217717i
$425$	−1884.31	−	721.739i	−0.215065	−	0.0823753i
$426$	44.6836	+	10471.7i	0.00508198	+	1.19098i
$427$	3150.53	+	3150.53i	0.357060	+	0.357060i
$428$	1073.24	−	5693.31i	0.121208	−	0.642982i
$429$	33.0253	−	17.6207i	0.00371673	−	0.00198307i
$430$	−13818.7	−	3914.69i	−1.54976	−	0.439030i
$431$			4574.30i			0.511221i	0.966780	+	0.255610i	$0.0822764\pi$
$431$			4574.30i			0.511221i	−0.966780	+	0.255610i	$0.917724\pi$
$432$	8544.53	−	2759.10i	0.951617	−	0.307285i
$433$	2262.91	+	2262.91i	0.251152	+	0.251152i	0.821443	−	0.570291i	$-0.193170\pi$
$433$	2262.91	+	2262.91i	0.251152	+	0.251152i	−0.570291	+	0.821443i	$0.693170\pi$
$434$	875.272	−	1657.45i	0.0968073	−	0.183319i
$435$	−7496.26	−	642.237i	−0.826248	−	0.0707883i
$436$	−6605.97	+	4510.43i	−0.725616	+	0.495436i
$437$	−5818.92	+	5818.92i	−0.636972	+	0.636972i
$438$	−7170.58	−	7109.65i	−0.782246	−	0.775598i
$439$			13262.1i			1.44183i	0.693024	+	0.720915i	$0.256278\pi$
$439$			13262.1i			1.44183i	−0.693024	+	0.720915i	$0.743722\pi$
$440$	1066.01	+	531.313i	0.115500	+	0.0575668i
$441$	−3616.39	+	5394.86i	−0.390497	+	0.582535i
$442$	66.7490	−	20.6141i	0.00718309	−	0.00221835i
$443$	585.642	+	585.642i	0.0628097	+	0.0628097i	0.737814	−	0.675004i	$-0.235858\pi$
$443$	585.642	+	585.642i	0.0628097	+	0.0628097i	−0.675004	+	0.737814i	$0.735858\pi$
$444$	7021.54	+	3669.72i	0.750513	+	0.392246i
$445$	2135.60	+	10029.2i	0.227499	+	1.06838i
$446$	12734.5	+	6724.86i	1.35201	+	0.713972i
$447$	−977.934	+	3215.18i	−0.103478	+	0.340207i
$448$	4393.62	+	2748.27i	0.463346	+	0.289829i
$449$	7131.93			0.749614			0.374807	−	0.927103i	$-0.377709\pi$
$449$	7131.93			0.749614			0.374807	+	0.927103i	$0.377709\pi$
$450$	9467.11	−	1224.29i	0.991742	−	0.128252i
$451$			1972.24i			0.205919i
$452$	−404.552	+	2146.06i	−0.0420985	+	0.223323i
$453$	10468.2	+	3184.03i	1.08574	+	0.330240i
$454$	2506.03	−	4745.53i	0.259062	−	0.490570i
$455$	169.354	−	36.0620i	0.0174493	−	0.00371563i
$456$	−4172.65	+	2875.19i	−0.428514	+	0.295270i
$457$	−6208.54	+	6208.54i	−0.635499	+	0.635499i	−0.949442	−	0.313943i	$-0.898350\pi$
$457$	−6208.54	+	6208.54i	−0.635499	+	0.635499i	0.313943	+	0.949442i	$0.398350\pi$
$458$	−12420.3	+	3835.75i	−1.26716	+	0.391338i
$459$	−227.028	+	2253.31i	−0.0230866	+	0.229141i
$460$	−17073.5	+	401.001i	−1.73055	+	0.0406452i
$461$	1860.70			0.187986			0.0939930	−	0.995573i	$-0.470037\pi$
$461$	1860.70			0.187986			0.0939930	+	0.995573i	$0.470037\pi$
$462$	−493.127	+	497.354i	−0.0496588	+	0.0500844i
$463$	−3175.82	−	3175.82i	−0.318775	−	0.318775i	0.529522	−	0.848296i	$-0.322371\pi$
$463$	−3175.82	−	3175.82i	−0.318775	−	0.318775i	−0.848296	+	0.529522i	$0.822371\pi$
$464$	7719.64	+	3017.68i	0.772360	+	0.301923i
$465$	−324.677	+	3789.66i	−0.0323796	+	0.377938i
$466$	7561.80	−	14319.3i	0.751703	−	1.42346i
$467$	−12707.0	+	12707.0i	−1.25912	+	1.25912i	−0.307602	+	0.951515i	$0.599527\pi$
$467$	−12707.0	+	12707.0i	−1.25912	+	1.25912i	−0.951515	+	0.307602i	$0.900473\pi$
$468$	−231.693	+	235.682i	−0.0228846	+	0.0232786i
$469$	−2150.61			−0.211740
$470$	−2777.88	+	9805.83i	−0.272625	+	0.962360i
$471$	5279.88	+	9895.73i	0.516527	+	0.968091i
$472$	11474.5	+	9131.57i	1.11898	+	0.890497i
$473$	−1512.05	+	1512.05i	−0.146986	+	0.146986i
$474$	28.8905	+	6770.56i	0.00279954	+	0.656080i
$475$	−4919.94	+	2194.81i	−0.475247	+	0.212010i
$476$	−1079.50	+	737.061i	−0.103947	+	0.0709730i
$477$	3887.38	+	19696.8i	0.373146	+	1.89068i
$478$	444.172	−	137.174i	0.0425020	−	0.0131259i
$479$	−8837.40			−0.842988			−0.421494	−	0.906831i	$-0.638494\pi$
$479$	−8837.40			−0.842988			−0.421494	+	0.906831i	$0.638494\pi$
$480$	−10384.3	−	1660.62i	−0.987454	−	0.157909i
$481$	−291.617			−0.0276436
$482$	3710.95	−	1146.05i	0.350683	−	0.108301i
$483$	2922.32	−	9607.77i	0.275300	−	0.905111i
$484$	−8647.28	+	5904.19i	−0.812103	+	0.554488i
$485$	4066.36	+	2638.61i	0.380709	+	0.247038i
$486$	−4112.78	−	9893.25i	−0.383867	−	0.923388i
$487$	−8996.32	+	8996.32i	−0.837089	+	0.837089i	−0.988475	−	0.151386i	$-0.951626\pi$
$487$	−8996.32	+	8996.32i	−0.837089	+	0.837089i	0.151386	+	0.988475i	$0.451626\pi$
$488$	7793.63	+	6202.28i	0.722953	+	0.575336i
$489$	−14555.9	+	7766.30i	−1.34609	+	0.718209i
$490$	6641.26	−	3709.12i	0.612289	−	0.341961i
$491$	3320.36			0.305185			0.152592	−	0.988289i	$-0.451238\pi$
$491$	3320.36			0.305185			0.152592	+	0.988289i	$0.451238\pi$
$492$	−5209.25	−	16615.9i	−0.477340	−	1.52257i
$493$	−1478.26	+	1478.26i	−0.135045	+	0.135045i
$494$	87.0977	−	164.932i	0.00793261	−	0.0150215i
$495$	528.141	−	1319.47i	0.0479559	−	0.119810i
$496$	1525.56	−	3902.59i	0.138104	−	0.353289i
$497$	5099.62	+	5099.62i	0.460260	+	0.460260i
$498$	5449.31	+	5403.00i	0.490340	+	0.486173i
$499$	16063.0			1.44104			0.720518	−	0.693437i	$-0.243904\pi$
$499$	16063.0			1.44104			0.720518	+	0.693437i	$0.243904\pi$
$500$	−10531.7	−	3752.79i	−0.941983	−	0.335660i
$501$	−5031.83	−	9430.82i	−0.448714	−	0.840994i
$502$	5696.14	−	1759.14i	0.506437	−	0.156403i
$503$	12463.8	−	12463.8i	1.10483	−	1.10483i	0.111015	−	0.993819i	$-0.464590\pi$
$503$	12463.8	−	12463.8i	1.10483	−	1.10483i	0.993819	−	0.111015i	$-0.0354103\pi$
$504$	2840.88	−	5492.63i	0.251077	−	0.485439i
$505$	1832.80	+	8607.19i	0.161502	+	0.758445i
$506$	−1187.35	+	2248.42i	−0.104317	+	0.197539i
$507$	−3318.49	+	10910.3i	−0.290689	+	0.955704i
$508$	2189.55	−	11615.1i	0.191231	−	1.01444i
$509$			5914.49i			0.515040i	0.966273	+	0.257520i	$0.0829053\pi$
$509$			5914.49i			0.515040i	−0.966273	+	0.257520i	$0.917095\pi$
$510$	1434.32	−	2231.22i	0.124535	−	0.193726i
$511$	−6954.33			−0.602038
$512$	10453.2	+	4994.82i	0.902286	+	0.431137i
$513$	3825.41	+	4682.62i	0.329232	+	0.403007i
$514$	−15326.6	−	8093.69i	−1.31523	−	0.694548i
$515$	6019.10	−	9276.03i	0.515016	−	0.793691i
$516$	8745.08	−	16732.6i	0.746087	−	1.42754i
$517$	1072.96	+	1072.96i	0.0912739	+	0.0912739i
$518$	5213.41	−	1610.06i	0.442209	−	0.136567i
$519$	−4139.20	−	7757.82i	−0.350079	−	0.656128i
$520$	367.062	−	122.872i	0.0309552	−	0.0103621i
$521$		−	8361.56i		−	0.703122i	−0.936165	−	0.351561i	$-0.885651\pi$
$521$		−	8361.56i		−	0.703122i	0.936165	−	0.351561i	$-0.114349\pi$
$522$	2837.63	−	9474.37i	0.237931	−	0.794410i
$523$	−5672.40	+	5672.40i	−0.474257	+	0.474257i	−0.903289	−	0.429032i	$-0.858855\pi$
$523$	−5672.40	+	5672.40i	−0.474257	+	0.474257i	0.429032	+	0.903289i	$0.358855\pi$
$524$	14022.8	−	9574.48i	1.16906	−	0.798212i
$525$	4036.31	−	5189.38i	0.335541	−	0.431396i
$526$	237.715	−	450.147i	0.0197050	−	0.0373143i
$527$	747.319	+	747.319i	0.0617718	+	0.0617718i
$528$	−969.726	+	1229.26i	−0.0799279	+	0.101320i
$529$		−	24291.0i		−	1.99646i
$530$	6409.07	−	22623.9i	0.525269	−	1.85418i
$531$	9743.31	−	14534.9i	0.796278	−	1.18787i
$532$	−646.486	+	3429.47i	−0.0526856	+	0.279485i
$533$	453.218	+	453.218i	0.0368312	+	0.0368312i
$534$	−13479.1	+	57.5164i	−1.09232	+	0.00466101i
$535$	6792.14	+	4407.34i	0.548878	+	0.356160i
$536$	−4776.94	+	543.145i	−0.384948	+	0.0437692i
$537$	−6189.88	+	20350.6i	−0.497417	+	1.63537i
$538$	−812.719	−	2631.61i	−0.0651279	−	0.210886i
$539$		−	1132.54i		−	0.0905047i
$540$	−964.421	+	12511.4i	−0.0768557	+	0.997042i
$541$		−	5378.77i		−	0.427452i	−0.976894	−	0.213726i	$-0.931440\pi$
$541$		−	5378.77i		−	0.427452i	0.976894	−	0.213726i	$-0.0685600\pi$
$542$	−4639.24	+	1432.74i	−0.367661	+	0.113545i
$543$	−2533.89	+	8330.73i	−0.200257	+	0.658390i
$544$	−2211.64	+	1909.79i	−0.174307	+	0.150518i
$545$	−2328.21	−	10933.7i	−0.182990	−	0.859355i
$546$	0.971232	+	227.611i	7.61262e−5	+	0.0178404i
$547$	7404.82	+	7404.82i	0.578807	+	0.578807i	0.934574	−	0.355768i	$-0.115781\pi$
$547$	7404.82	+	7404.82i	0.578807	+	0.578807i	−0.355768	+	0.934574i	$0.615781\pi$
$548$	−14415.0	−	2717.36i	−1.12368	−	0.211824i
$549$	6617.77	−	9872.26i	0.514462	−	0.767464i
$550$	−1252.38	+	1096.53i	−0.0970938	+	0.0850116i
$551$			5581.58i			0.431549i
$552$	4064.58	−	22078.8i	0.313406	−	1.70242i
$553$	3297.19	+	3297.19i	0.253546	+	0.253546i
$554$	16996.1	+	8975.34i	1.30342	+	0.688313i
$555$	−8469.03	+	7132.39i	−0.647731	+	0.545501i
$556$	4342.70	−	2965.11i	0.331243	−	0.226167i
$557$	6259.40	−	6259.40i	0.476157	−	0.476157i	−0.427744	−	0.903900i	$-0.640691\pi$
$557$	6259.40	−	6259.40i	0.476157	−	0.476157i	0.903900	+	0.427744i	$0.140691\pi$
$558$	−4789.68	−	1434.54i	−0.363375	−	0.108833i
$559$			694.933i			0.0525806i
$560$	−5883.79	+	4223.25i	−0.443992	+	0.318688i
$561$	−185.901	−	348.421i	−0.0139906	−	0.0262217i
$562$	5194.24	+	16819.1i	0.389868	+	1.26240i
$563$	643.985	+	643.985i	0.0482073	+	0.0482073i	0.730800	−	0.682592i	$-0.239147\pi$
$563$	643.985	+	643.985i	0.0482073	+	0.0482073i	−0.682592	+	0.730800i	$0.739147\pi$
$564$	−11873.5	−	6205.54i	−0.886462	−	0.463299i
$565$	−2560.26	−	1661.32i	−0.190639	−	0.123703i
$566$	5644.38	−	10688.4i	0.419171	−	0.793761i
$567$	−6808.66	−	2844.08i	−0.504297	−	0.210653i
$568$	12615.2	+	10039.3i	0.931905	+	0.741622i
$569$	−14957.4			−1.10202			−0.551008	−	0.834500i	$-0.685757\pi$
$569$	−14957.4			−1.10202			−0.551008	+	0.834500i	$0.685757\pi$
$570$	−1504.46	−	6920.14i	−0.110553	−	0.508514i
$571$			9803.54i			0.718503i	0.933241	+	0.359252i	$0.116968\pi$
$571$			9803.54i			0.718503i	−0.933241	+	0.359252i	$0.883032\pi$
$572$	10.6758	−	56.6330i	0.000780384	−	0.00413977i
$573$	3754.81	−	12344.8i	0.273751	−	0.900018i
$574$	−10604.7	−	5600.17i	−0.771137	−	0.407224i
$575$	8537.04	−	22288.4i	0.619164	−	1.61651i
$576$	4922.99	−	12917.7i	0.356119	−	0.934441i
$577$	18165.5	−	18165.5i	1.31064	−	1.31064i	0.389693	−	0.920945i	$-0.372581\pi$
$577$	18165.5	−	18165.5i	1.31064	−	1.31064i	0.920945	−	0.389693i	$-0.127419\pi$
$578$	3882.95	+	12573.1i	0.279428	+	0.904796i
$579$	3885.24	+	7281.85i	0.278869	+	0.522665i
$580$	−7996.21	+	8380.85i	−0.572456	+	0.599993i
$581$	5284.96			0.377379
$582$	−4486.50	+	4524.95i	−0.319538	+	0.322277i
$583$	−2475.51	−	2475.51i	−0.175858	−	0.175858i
$584$	−15447.0	+	1756.34i	−1.09452	+	0.124448i
$585$	−181.846	−	424.578i	−0.0128520	−	0.0300071i
$586$	4077.35	+	2153.18i	0.287430	+	0.151787i
$587$	−2923.92	+	2923.92i	−0.205593	+	0.205593i	−0.802391	−	0.596798i	$-0.796439\pi$
$587$	−2923.92	+	2923.92i	−0.205593	+	0.205593i	0.596798	+	0.802391i	$0.296439\pi$
$588$	2991.36	+	9541.52i	0.209799	+	0.669193i
$589$	2821.71			0.197397
$590$	−17892.9	+	9993.14i	−1.24854	+	0.697307i
$591$	10946.0	−	5840.25i	0.761857	−	0.406490i
$592$	11173.4	−	4892.92i	0.775716	−	0.339692i
$593$	14916.3	−	14916.3i	1.03295	−	1.03295i	0.0335146	−	0.999438i	$-0.489330\pi$
$593$	14916.3	−	14916.3i	1.03295	−	1.03295i	0.999438	−	0.0335146i	$-0.0106700\pi$
$594$	1556.29	+	1033.65i	0.107500	+	0.0713989i
$595$	−380.459	−	1786.71i	−0.0262139	−	0.123105i
$596$	2917.51	+	4272.98i	0.200513	+	0.293672i
$597$	−3914.07	+	12868.4i	−0.268328	+	0.882189i
$598$	243.832	+	789.536i	0.0166740	+	0.0539908i
$599$	−27797.2			−1.89610			−0.948049	−	0.318125i	$-0.896947\pi$
$599$	−27797.2			−1.89610			−0.948049	+	0.318125i	$0.896947\pi$
$600$	7654.86	−	12546.0i	0.520848	−	0.853650i
$601$	−11766.2			−0.798588			−0.399294	−	0.916823i	$-0.630745\pi$
$601$	−11766.2			−0.798588			−0.399294	+	0.916823i	$0.630745\pi$
$602$	−3836.82	−	12423.7i	−0.259763	−	0.841119i
$603$	1110.79	+	5628.21i	0.0750162	+	0.380097i
$604$	13912.3	−	9499.03i	0.937223	−	0.639918i
$605$	−3047.65	−	14312.3i	−0.204801	−	0.961783i
$606$	−11568.0	+	49.3616i	−0.775443	+	0.00330887i
$607$	−7246.84	+	7246.84i	−0.484580	+	0.484580i	−0.906591	−	0.422011i	$-0.861324\pi$
$607$	−7246.84	+	7246.84i	−0.484580	+	0.484580i	0.422011	+	0.906591i	$0.361324\pi$
$608$	−569.850	+	7780.81i	−0.0380106	+	0.519002i
$609$	−3206.38	−	6009.50i	−0.213348	−	0.399864i
$610$	−12153.1	+	6787.46i	−0.806663	+	0.450519i
$611$	493.127			0.0326510
$612$	2486.47	+	2444.39i	0.164231	+	0.161452i
$613$	−15206.8	+	15206.8i	−1.00195	+	1.00195i	−0.00195668	+	0.999998i	$0.500623\pi$
$613$	−15206.8	+	15206.8i	−1.00195	+	1.00195i	−0.999998	+	0.00195668i	$0.999377\pi$
$614$	20381.3	+	10763.0i	1.33961	+	0.707425i
$615$	24247.0	+	2077.35i	1.58981	+	0.136206i
$616$	121.820	+	1071.41i	0.00796799	+	0.0700782i
$617$	−12084.9	−	12084.9i	−0.788523	−	0.788523i	0.192729	−	0.981252i	$-0.438266\pi$
$617$	−12084.9	−	12084.9i	−0.788523	−	0.788523i	−0.981252	+	0.192729i	$0.938266\pi$
$618$	10322.1	+	10234.4i	0.671873	+	0.666163i
$619$	−3051.79			−0.198161			−0.0990805	−	0.995079i	$-0.531590\pi$
$619$	−3051.79			−0.198161			−0.0990805	+	0.995079i	$0.531590\pi$
$620$	4236.86	+	4042.41i	0.274446	+	0.261850i
$621$	−26653.2	−	2685.38i	−1.72231	−	0.173528i
$622$	−2689.27	−	8707.92i	−0.173360	−	0.561344i
$623$	−6564.20	+	6564.20i	−0.422133	+	0.422133i
$624$	59.6412	+	505.324i	0.00382622	+	0.0324185i
$625$	10438.2	−	11626.9i	0.668043	−	0.744123i
$626$	−9552.92	−	5044.73i	−0.609922	−	0.322089i
$627$	−1008.74	−	306.821i	−0.0642508	−	0.0195427i
$628$	16969.6	+	3198.91i	1.07828	+	0.203265i
$629$			3076.59i			0.195027i
$630$	5595.13	+	6586.44i	0.353834	+	0.416524i
$631$	2493.74			0.157328			0.0786642	−	0.996901i	$-0.474935\pi$
$631$	2493.74			0.157328			0.0786642	+	0.996901i	$0.474935\pi$
$632$	8156.45	+	6491.01i	0.513364	+	0.408542i
$633$	−2822.47	+	9279.48i	−0.177224	+	0.582664i
$634$	−3454.31	+	6541.23i	−0.216385	+	0.409756i
$635$	13856.9	+	8991.55i	0.865973	+	0.561919i
$636$	27394.4	+	14317.3i	1.70795	+	0.892640i
$637$	−260.256	−	260.256i	−0.0161879	−	0.0161879i
$638$	508.896	+	1647.82i	0.0315790	+	0.102254i
$639$	10711.9	−	15979.8i	0.663155	−	0.989281i
$640$	−12002.5	+	10866.7i	−0.741312	+	0.671161i
$641$			8717.14i			0.537139i	0.963260	+	0.268570i	$0.0865509\pi$
$641$			8717.14i			0.537139i	−0.963260	+	0.268570i	$0.913449\pi$
$642$	−7493.90	+	7558.13i	−0.460686	+	0.464635i
$643$	−971.938	+	971.938i	−0.0596104	+	0.0596104i	−0.736284	−	0.676673i	$-0.763421\pi$
$643$	−971.938	+	971.938i	−0.0596104	+	0.0596104i	0.676673	+	0.736284i	$0.263421\pi$
$644$	−8718.27	−	12768.8i	−0.533460	−	0.781305i
$645$	16996.7	+	20182.0i	1.03759	+	1.23204i
$646$	−1740.05	−	918.891i	−0.105977	−	0.0559648i
$647$	5723.05	+	5723.05i	0.347753	+	0.347753i	0.859272	−	0.511519i	$-0.170917\pi$
$647$	5723.05	+	5723.05i	0.347753	+	0.347753i	−0.511519	+	0.859272i	$0.670917\pi$
$648$	−15841.7	−	4597.73i	−0.960370	−	0.278728i
$649$			3051.30i			0.184552i
$650$	−35.8126	+	539.776i	−0.00216106	+	0.0325719i
$651$	−3038.05	+	1620.95i	−0.182904	+	0.0975887i
$652$	−4705.36	+	24960.9i	−0.282632	+	1.49930i
$653$	−11589.7	−	11589.7i	−0.694546	−	0.694546i	0.268682	−	0.963229i	$-0.413412\pi$
$653$	−11589.7	−	11589.7i	−0.694546	−	0.694546i	−0.963229	+	0.268682i	$0.913412\pi$
$654$	14694.8	−	62.7039i	0.878613	−	0.00374911i
$655$	4942.19	+	23209.4i	0.294820	+	1.38453i
$656$	−24969.6	−	9760.84i	−1.48612	−	0.580940i
$657$	3591.90	+	18199.7i	0.213293	+	1.08073i
$658$	−8815.93	+	2722.62i	−0.522311	+	0.161305i
$659$		−	7883.21i		−	0.465988i	−0.972478	−	0.232994i	$-0.925148\pi$
$659$		−	7883.21i		−	0.465988i	0.972478	−	0.232994i	$-0.0748523\pi$
$660$	−1075.09	−	1905.83i	−0.0634059	−	0.112400i
$661$		−	25979.6i		−	1.52873i	−0.644783	−	0.764365i	$-0.723052\pi$
$661$		−	25979.6i		−	1.52873i	0.644783	−	0.764365i	$-0.276948\pi$
$662$	3858.62	+	12494.3i	0.226540	+	0.733544i
$663$	−122.786	−	37.3469i	−0.00719249	−	0.00218768i
$664$	11739.0	−	1334.74i	0.686085	−	0.0780088i
$665$	−4091.37	−	2654.84i	−0.238581	−	0.154812i
$666$	−6906.28	−	12812.0i	−0.401821	−	0.745430i
$667$	−17485.5	−	17485.5i	−1.01505	−	1.01505i
$668$	−16172.3	−	3048.63i	−0.936715	−	0.176579i
$669$	−12454.1	−	23341.8i	−0.719734	−	1.34895i
$670$	1831.34	−	6464.60i	0.105599	−	0.372760i
$671$			2072.48i			0.119236i
$672$	−3856.21	−	8704.69i	−0.221364	−	0.499689i
$673$	−14048.3	−	14048.3i	−0.804641	−	0.804641i	0.179176	−	0.983817i	$-0.442657\pi$
$673$	−14048.3	−	14048.3i	−0.804641	−	0.804641i	−0.983817	+	0.179176i	$0.942657\pi$
$674$	−13400.7	+	25376.2i	−0.765840	+	1.45023i
$675$	−15665.5	−	7882.83i	−0.893282	−	0.449497i
$676$	9900.18	+	14499.8i	0.563278	+	0.824977i
$677$	14570.6	−	14570.6i	0.827167	−	0.827167i	−0.159957	−	0.987124i	$-0.551136\pi$
$677$	14570.6	−	14570.6i	0.827167	−	0.827167i	0.987124	+	0.159957i	$0.0511356\pi$
$678$	2824.78	−	2848.99i	0.160008	−	0.161379i
$679$			4388.48i			0.248033i
$680$	−1296.31	−	3872.54i	−0.0731049	−	0.218390i
$681$	−8698.38	+	4641.03i	−0.489460	+	0.261152i
$682$	833.039	−	257.267i	0.0467723	−	0.0144447i
$683$	14821.6	+	14821.6i	0.830354	+	0.830354i	0.987565	−	0.157211i	$-0.0502504\pi$
$683$	14821.6	+	14821.6i	0.830354	+	0.830354i	−0.157211	+	0.987565i	$0.550250\pi$
$684$	9308.92	−	79.4452i	0.520373	−	0.00444103i
$685$	11159.0	−	17197.1i	0.622430	−	0.959225i
$686$	14772.9	+	7801.33i	0.822206	+	0.434193i
$687$	22847.4	+	6949.30i	1.26882	+	0.385928i
$688$	−11660.0	−	26626.6i	−0.646125	−	1.47548i
$689$	−1137.74			−0.0629089
$690$	26391.8	+	16965.8i	1.45612	+	0.936051i
$691$		−	3110.59i		−	0.171248i	−0.996328	−	0.0856241i	$-0.972712\pi$
$691$		−	3110.59i		−	0.171248i	0.996328	−	0.0856241i	$-0.0272884\pi$
$692$	−13303.4	−	2507.81i	−0.730808	−	0.137764i
$693$	1262.33	−	249.136i	0.0691950	−	0.0136564i
$694$	−3392.48	+	6424.14i	−0.185557	+	0.351379i
$695$	1530.54	+	7187.70i	0.0835348	+	0.392295i
$696$	−8639.74	−	12538.5i	−0.470529	−	0.682861i
$697$	4781.50	−	4781.50i	0.259845	−	0.259845i
$698$	13729.0	−	4239.91i	0.744482	−	0.229918i
$699$	−26246.8	+	14004.0i	−1.42024	+	0.757770i
$700$	−2339.93	−	9847.62i	−0.126344	−	0.531722i
$701$	4134.46			0.222762			0.111381	−	0.993778i	$-0.464473\pi$
$701$	4134.46			0.222762			0.111381	+	0.993778i	$0.464473\pi$
$702$	595.162	−	120.102i	0.0319985	−	0.00645723i
$703$	5808.27	+	5808.27i	0.311612	+	0.311612i
$704$	541.175	+	2349.04i	0.0289720	+	0.125757i
$705$	14321.2	−	12061.0i	0.765062	−	0.644314i
$706$	8158.81	−	15449.9i	0.434930	−	0.823603i
$707$	−5633.50	+	5633.50i	−0.299674	+	0.299674i
$708$	−8059.35	−	25706.8i	−0.427809	−	1.36458i
$709$	−378.073			−0.0200266			−0.0100133	−	0.999950i	$-0.503187\pi$
$709$	−378.073			−0.0200266			−0.0100133	+	0.999950i	$0.503187\pi$
$710$	−19671.7	+	10986.6i	−1.03981	+	0.580730i
$711$	6925.85	−	10331.8i	0.365316	−	0.544971i
$712$	−12922.6	+	16238.2i	−0.680189	+	0.854709i
$713$	−8839.61	+	8839.61i	−0.464300	+	0.464300i
$714$	2401.32	−	10.2466i	0.125864	−	0.000537073i
$715$	67.5635	+	43.8411i	0.00353389	+	0.00229310i
$716$	18466.5	+	27046.1i	0.963863	+	1.41167i
$717$	−817.064	−	248.520i	−0.0425576	−	0.0129444i
$718$	13654.2	−	4216.83i	0.709709	−	0.219179i
$719$	25165.0			1.30528			0.652641	−	0.757668i	$-0.273661\pi$
$719$	25165.0			1.30528			0.652641	+	0.757668i	$0.273661\pi$
$720$	14091.3	+	13216.7i	0.729380	+	0.684109i
$721$	10010.8			0.517092
$722$	13516.6	−	4174.32i	0.696723	−	0.215169i
$723$	−6826.38	−	2076.33i	−0.351142	−	0.106804i
$724$	7559.46	+	11071.6i	0.388046	+	0.568331i
$725$	−6595.25	−	14784.1i	−0.337850	−	0.757334i
$726$	19235.7	−	82.0800i	0.983337	−	0.00419597i
$727$	2235.69	−	2235.69i	0.114054	−	0.114054i	−0.647777	−	0.761830i	$-0.724301\pi$
$727$	2235.69	−	2235.69i	0.114054	−	0.114054i	0.761830	+	0.647777i	$0.224301\pi$
$728$	274.201	+	218.213i	0.0139596	+	0.0111092i
$729$	−3926.38	+	19287.4i	−0.199481	+	0.979902i
$730$	5921.93	−	20904.3i	0.300247	−	1.05986i
$731$	7331.63			0.370958
$732$	−5474.01	−	17460.4i	−0.276401	−	0.881632i
$733$	−823.302	+	823.302i	−0.0414862	+	0.0414862i	−0.727546	−	0.686059i	$-0.759339\pi$
$733$	−823.302	+	823.302i	−0.0414862	+	0.0414862i	0.686059	+	0.727546i	$0.259339\pi$
$734$	−5771.44	+	10929.0i	−0.290228	+	0.549589i
$735$	−13923.6	−	1192.90i	−0.698750	−	0.0598649i
$736$	−22589.8	−	26160.2i	−1.13135	−	1.31016i
$737$	−707.358	−	707.358i	−0.0353540	−	0.0353540i
$738$	−9178.47	+	30645.3i	−0.457811	+	1.52855i
$739$	5902.04			0.293789			0.146895	−	0.989152i	$-0.453072\pi$
$739$	5902.04			0.293789			0.146895	+	0.989152i	$0.453072\pi$
$740$	400.267	+	17042.2i	0.0198839	+	0.846600i
$741$	−302.314	+	161.300i	−0.0149876	+	0.00799664i
$742$	20340.0	−	6281.59i	1.00634	−	0.310788i
$743$	22846.8	−	22846.8i	1.12809	−	1.12809i	0.137597	−	0.990488i	$-0.456062\pi$
$743$	22846.8	−	22846.8i	1.12809	−	1.12809i	0.990488	−	0.137597i	$-0.0439379\pi$
$744$	−6338.73	+	4367.74i	−0.312351	+	0.215227i
$745$	−7072.32	+	1505.97i	−0.347798	+	0.0740597i
$746$	−12604.9	+	23869.2i	−0.618631	+	1.17147i
$747$	−2729.68	−	13830.9i	−0.133700	−	0.677438i
$748$	−597.485	−	112.631i	−0.0292062	−	0.00550563i
$749$			7330.18i			0.357596i
$750$	12161.8	+	16551.9i	0.592116	+	0.805853i
$751$	−7941.78			−0.385885			−0.192942	−	0.981210i	$-0.561803\pi$
$751$	−7941.78			−0.385885			−0.192942	+	0.981210i	$0.561803\pi$
$752$	−18894.3	+	8273.99i	−0.916231	+	0.401225i
$753$	−10478.2	−	3187.06i	−0.507099	−	0.154240i
$754$	495.609	+	261.722i	0.0239377	+	0.0126411i
$755$	4903.24	+	23026.6i	0.236354	+	1.10996i
$756$	−9976.97	+	5433.12i	−0.479972	+	0.261376i
$757$	−13847.3	−	13847.3i	−0.664848	−	0.664848i	0.291671	−	0.956519i	$-0.405789\pi$
$757$	−13847.3	−	13847.3i	−0.664848	−	0.664848i	−0.956519	+	0.291671i	$0.905789\pi$
$758$	−6509.73	+	2010.40i	−0.311932	+	0.0963338i
$759$	4121.27	−	2198.91i	0.197092	−	0.105159i
$760$	−9758.24	−	4863.64i	−0.465748	−	0.232135i
$761$			12838.5i			0.611560i	0.952102	+	0.305780i	$0.0989172\pi$
$761$			12838.5i			0.611560i	−0.952102	+	0.305780i	$0.901083\pi$
$762$	−15288.5	+	15419.6i	−0.726831	+	0.733061i
$763$	7156.23	−	7156.23i	0.339545	−	0.339545i
$764$	−11201.9	−	16406.3i	−0.530458	−	0.776908i
$765$	−4479.35	+	1918.50i	−0.211701	+	0.0906713i
$766$	2.95833	−	5.60203i	0.000139542	−	0.000264242i
$767$	701.184	+	701.184i	0.0330095	+	0.0330095i
$768$	−10763.8	−	18361.0i	−0.505736	−	0.862688i
$769$		−	249.488i		−	0.0116993i	−0.999983	−	0.00584964i	$-0.998138\pi$
$769$		−	249.488i		−	0.0116993i	0.999983	−	0.00584964i	$-0.00186201\pi$
$770$	−1449.93	−	410.747i	−0.0678593	−	0.0192238i
$771$	14989.1	+	28093.0i	0.700153	+	1.31225i
$772$	12487.2	+	2353.95i	0.582154	+	0.109741i
$773$	7520.75	+	7520.75i	0.349939	+	0.349939i	0.860087	−	0.510148i	$-0.170409\pi$
$773$	7520.75	+	7520.75i	0.349939	+	0.349939i	−0.510148	+	0.860087i	$0.670409\pi$
$774$	−30531.6	+	16457.9i	−1.41787	+	0.764299i
$775$	−7473.95	+	3334.17i	−0.346416	+	0.154538i
$776$	1108.33	+	9747.70i	0.0512714	+	0.450931i
$777$	−9590.18	−	2916.97i	−0.442787	−	0.134679i
$778$	1763.96	+	5711.74i	0.0812865	+	0.263208i
$779$		−	18053.9i		−	0.830358i
$780$	−685.010	−	190.902i	−0.0314453	−	0.00876330i
$781$			3354.63i			0.153698i
$782$	8329.69	−	2572.46i	0.380907	−	0.117635i
$783$	−14070.9	+	11495.1i	−0.642215	+	0.524650i
$784$	14338.5	+	5605.07i	0.653177	+	0.255333i
$785$	−13136.6	+	20244.7i	−0.597280	+	0.920466i
$786$	−31193.3	+	133.104i	−1.41556	+	0.00604030i
$787$	−7054.47	−	7054.47i	−0.319523	−	0.319523i	0.529061	−	0.848584i	$-0.322544\pi$
$787$	−7054.47	−	7054.47i	−0.319523	−	0.319523i	−0.848584	+	0.529061i	$0.822544\pi$
$788$	3538.42	−	18770.6i	0.159963	−	0.848570i
$789$	−825.102	+	440.235i	−0.0372299	+	0.0198641i
$790$	−12718.9	+	7103.44i	−0.572806	+	0.319910i
$791$		−	2763.07i		−	0.124202i
$792$	2740.98	−	872.187i	0.122975	−	0.0391311i
$793$	476.253	+	476.253i	0.0213269	+	0.0213269i
$794$	32167.6	+	16987.1i	1.43776	+	0.759258i
$795$	−33041.7	+	27826.8i	−1.47405	+	1.24140i
$796$	11677.0	+	17102.1i	0.519950	+	0.761518i
$797$	12248.6	−	12248.6i	0.544374	−	0.544374i	−0.380434	−	0.924808i	$-0.624225\pi$
$797$	12248.6	−	12248.6i	0.544374	−	0.544374i	0.924808	+	0.380434i	$0.124225\pi$
$798$	4514.09	−	4552.78i	0.200247	−	0.201963i
$799$		−	5202.55i		−	0.230354i
$800$	−7684.51	−	21282.6i	−0.339611	−	0.940566i
$801$	20569.1	+	13788.3i	0.907332	+	0.608221i
$802$	−4709.96	−	15251.0i	−0.207375	−	0.671485i
$803$	−2287.35	−	2287.35i	−0.100522	−	0.100522i
$804$	7827.73	+	4091.07i	0.343362	+	0.179454i
$805$	21133.9	−	4500.23i	0.925307	−	0.197034i
$806$	132.311	−	250.550i	0.00578222	−	0.0109495i
$807$	−1472.42	+	4840.90i	−0.0642274	+	0.211162i
$808$	−11090.4	+	13935.9i	−0.482869	+	0.606762i
$809$	21242.4			0.923166			0.461583	−	0.887097i	$-0.347282\pi$
$809$	21242.4			0.923166			0.461583	+	0.887097i	$0.347282\pi$
$810$	14347.0	−	18044.5i	0.622349	−	0.782740i
$811$			28917.9i			1.25209i	0.779787	+	0.626045i	$0.215327\pi$
$811$			28917.9i			1.25209i	−0.779787	+	0.626045i	$0.784673\pi$
$812$	−10305.3	−	1942.64i	−0.445376	−	0.0839575i
$813$	8533.98	+	2595.71i	0.368142	+	0.111975i
$814$	2244.31	+	1185.18i	0.0966375	+	0.0510326i
$815$	−29778.5	−	19322.9i	−1.27987	−	0.830492i
$816$	5331.23	−	629.222i	0.228714	−	0.0269941i
$817$	13841.3	−	13841.3i	0.592713	−	0.592713i
$818$	−3833.18	−	12412.0i	−0.163844	−	0.530530i
$819$	232.831	−	347.333i	0.00993380	−	0.0148190i
$820$	25864.2	−	27108.3i	1.10148	−	1.15447i
$821$	−16329.9			−0.694173			−0.347087	−	0.937833i	$-0.612829\pi$
$821$	−16329.9			−0.694173			−0.347087	+	0.937833i	$0.612829\pi$
$822$	19136.6	+	18973.9i	0.812000	+	0.805100i
$823$	−5519.09	−	5519.09i	−0.233759	−	0.233759i	0.580501	−	0.814260i	$-0.302857\pi$
$823$	−5519.09	−	5519.09i	−0.233759	−	0.233759i	−0.814260	+	0.580501i	$0.802857\pi$
$824$	22236.1	−	2528.27i	0.940086	−	0.106889i
$825$	3034.43	−	379.255i	0.128055	−	0.0160048i
$826$	−16406.8	−	8664.15i	−0.691121	−	0.364969i
$827$	7880.89	−	7880.89i	0.331373	−	0.331373i	−0.521735	−	0.853108i	$-0.674715\pi$
$827$	7880.89	−	7880.89i	0.331373	−	0.331373i	0.853108	+	0.521735i	$0.174715\pi$
$828$	−28913.3	+	29411.0i	−1.21353	+	1.23442i
$829$	17418.0			0.729736			0.364868	−	0.931059i	$-0.381114\pi$
$829$	17418.0			0.729736			0.364868	+	0.931059i	$0.381114\pi$
$830$	−4500.39	+	15886.3i	−0.188206	+	0.664361i
$831$	−16621.8	−	31153.2i	−0.693869	−	1.30047i
$832$	664.166	+	415.444i	0.0276753	+	0.0173112i
$833$	−2745.73	+	2745.73i	−0.114206	+	0.114206i
$834$	−9660.23	+	41.2209i	−0.401087	+	0.00171147i
$835$	12519.4	−	19293.6i	0.518865	−	0.799622i
$836$	−1340.62	+	915.352i	−0.0554622	+	0.0378685i
$837$	5811.23	+	7113.43i	0.239983	+	0.293759i
$838$	12277.7	+	39755.4i	0.506116	+	1.63882i
$839$	9460.36			0.389283			0.194641	−	0.980874i	$-0.437646\pi$
$839$	9460.36			0.389283			0.194641	+	0.980874i	$0.437646\pi$
$840$	13300.3	−	369.173i	0.546316	−	0.0151639i
$841$	7616.74			0.312302
$842$	−11285.7	−	36543.4i	−0.461913	−	1.49569i
$843$	9410.50	−	30939.1i	0.384478	−	1.26406i
$844$	8420.38	+	12332.5i	0.343414	+	0.502964i
$845$	−23999.0	+	5110.31i	−0.977029	+	0.208047i
$846$	11678.6	+	21665.3i	0.474608	+	0.880459i
$847$	9367.58	−	9367.58i	0.380016	−	0.380016i
$848$	43592.7	−	19089.6i	1.76531	−	0.773043i
$849$	−19591.5	+	10453.1i	−0.791965	+	0.422554i
$850$	5694.70	+	377.828i	0.229796	+	0.0152463i
$851$	−36391.2			−1.46589
$852$	−8860.53	−	28262.3i	−0.356287	−	1.13645i
$853$	−14483.4	+	14483.4i	−0.581362	+	0.581362i	−0.935278	−	0.353915i	$-0.884850\pi$
$853$	−14483.4	+	14483.4i	−0.581362	+	0.581362i	0.353915	+	0.935278i	$0.384850\pi$
$854$	−11143.7	−	5884.80i	−0.446522	−	0.235801i
$855$	−4834.60	+	12078.4i	−0.193380	+	0.483128i
$856$	1851.26	+	16281.8i	0.0739193	+	0.650118i
$857$	−17674.4	−	17674.4i	−0.704489	−	0.704489i	0.260882	−	0.965371i	$-0.415987\pi$
$857$	−17674.4	−	17674.4i	−0.704489	−	0.704489i	−0.965371	+	0.260882i	$0.915987\pi$
$858$	−74.5441	+	75.1830i	−0.00296608	+	0.00299150i
$859$	17409.9			0.691525			0.345762	−	0.938322i	$-0.387620\pi$
$859$	17409.9			0.691525			0.345762	+	0.938322i	$0.387620\pi$
$860$	40612.2	−	953.851i	1.61031	−	0.0378210i
$861$	10371.2	+	19438.1i	0.410511	+	0.769393i
$862$	−3817.75	−	12362.0i	−0.150850	−	0.488458i
$863$	−7473.18	+	7473.18i	−0.294774	+	0.294774i	−0.838963	−	0.544189i	$-0.816837\pi$
$863$	−7473.18	+	7473.18i	−0.294774	+	0.294774i	0.544189	+	0.838963i	$0.316837\pi$
$864$	−20788.7	+	14587.8i	−0.818571	+	0.574405i
$865$	10298.5	−	15871.0i	0.404809	−	0.623850i
$866$	−8004.14	−	4226.85i	−0.314078	−	0.165859i
$867$	7034.81	−	23128.5i	0.275565	−	0.905980i
$868$	−982.085	+	5209.75i	−0.0384034	+	0.203722i
$869$			2168.96i			0.0846686i
$870$	20794.5	−	4520.80i	0.810346	−	0.176172i
$871$	−325.099			−0.0126470
$872$	14088.1	−	17702.8i	0.547114	−	0.687490i
$873$	11484.8	−	2266.65i	0.445247	−	0.0878744i
$874$	10869.0	−	20582.1i	0.420653	−	0.796567i
$875$	13973.9	+	2197.54i	0.539891	+	0.0849034i
$876$	25312.2	+	13229.1i	0.976277	+	0.510239i
$877$	−3295.09	−	3295.09i	−0.126873	−	0.126873i	0.640819	−	0.767692i	$-0.278595\pi$
$877$	−3295.09	−	3295.09i	−0.126873	−	0.126873i	−0.767692	+	0.640819i	$0.778595\pi$
$878$	−11068.6	−	35840.5i	−0.425453	−	1.37763i
$879$	−3987.57	−	7473.63i	−0.153012	−	0.286780i
$880$	−3324.31	−	546.167i	−0.127344	−	0.0209219i
$881$		−	5084.50i		−	0.194439i	−0.995263	−	0.0972196i	$-0.969005\pi$
$881$		−	5084.50i		−	0.194439i	0.995263	−	0.0972196i	$-0.0309949\pi$
$882$	5270.65	−	17597.8i	0.201215	−	0.671824i
$883$	−11589.3	+	11589.3i	−0.441688	+	0.441688i	−0.892579	−	0.450891i	$-0.851106\pi$
$883$	−11589.3	+	11589.3i	−0.441688	+	0.441688i	0.450891	+	0.892579i	$0.351106\pi$
$884$	−163.184	+	111.419i	−0.00620866	+	0.00423915i
$885$	37513.2	+	3213.92i	1.42485	+	0.122073i
$886$	−2071.47	−	1093.91i	−0.0785468	−	0.0414792i
$887$	−7749.88	−	7749.88i	−0.293366	−	0.293366i	0.545042	−	0.838408i	$-0.316514\pi$
$887$	−7749.88	−	7749.88i	−0.293366	−	0.293366i	−0.838408	+	0.545042i	$0.816514\pi$
$888$	−22038.4	−	4057.14i	−0.832838	−	0.153320i
$889$			14954.5i			0.564184i
$890$	−14141.8	−	25321.3i	−0.532624	−	0.953675i
$891$	−1303.99	−	3174.89i	−0.0490295	−	0.119375i
$892$	−40027.4	−	7545.53i	−1.50248	−	0.283232i
$893$	−9821.85	−	9821.85i	−0.368058	−	0.368058i
$894$	−40.5592	−	9505.16i	−0.00151734	−	0.355593i
$895$	−44764.6	+	9532.11i	−1.67186	+	0.356004i
$896$	−14167.4	−	3760.20i	−0.528237	−	0.140200i
$897$	441.755	−	1452.37i	0.0164434	−	0.0540615i
$898$	−19274.0	+	5952.37i	−0.716236	+	0.221195i
$899$			8479.05i			0.314563i
$900$	−24562.9	+	11209.9i	−0.909738	+	0.415183i
$901$			12003.2i			0.443825i
$902$	−1646.05	−	5329.96i	−0.0607622	−	0.196750i
$903$	−6951.24	+	22853.7i	−0.256171	+	0.842220i
$904$	−697.824	−	6137.34i	−0.0256740	−	0.225802i
$905$	−18324.8	+	3902.07i	−0.673081	+	0.143325i
$906$	−30947.5	+	132.055i	−1.13484	+	0.00484244i
$907$	3698.12	+	3698.12i	0.135385	+	0.135385i	0.771552	−	0.636167i	$-0.219481\pi$
$907$	3698.12	+	3698.12i	0.135385	+	0.135385i	−0.636167	+	0.771552i	$0.719481\pi$
$908$	−2811.86	+	14916.3i	−0.102770	+	0.545170i
$909$	17652.7	+	11833.3i	0.644119	+	0.431779i
$910$	−427.579	+	238.801i	−0.0155759	+	0.00869911i
$911$			12726.4i			0.462838i	0.972854	+	0.231419i	$0.0743369\pi$
$911$			12726.4i			0.462838i	−0.972854	+	0.231419i	$0.925663\pi$
$912$	8876.88	−	11252.7i	0.322306	−	0.408567i
$913$	1738.28	+	1738.28i	0.0630106	+	0.0630106i
$914$	11596.8	−	21960.2i	0.419680	−	0.794725i
$915$	25479.4	+	2182.93i	0.920572	+	0.0788694i
$916$	30364.3	−	20732.1i	1.09527	−	0.747826i
$917$	−15190.8	+	15190.8i	−0.547051	+	0.547051i
$918$	−1267.10	−	6279.03i	−0.0455560	−	0.225750i
$919$		−	7910.72i		−	0.283951i	−0.989870	−	0.141975i	$-0.954655\pi$
$919$		−	7910.72i		−	0.283951i	0.989870	−	0.141975i	$-0.0453453\pi$
$920$	45806.1	−	15333.4i	1.64150	−	0.549484i
$921$	−19932.5	−	37358.1i	−0.713135	−	1.33658i
$922$	−5028.52	+	1552.96i	−0.179615	+	0.0554706i
$923$	770.889	+	770.889i	0.0274909	+	0.0274909i
$924$	917.574	−	1755.66i	0.0326688	−	0.0625075i
$925$	−22247.6	−	8521.41i	−0.790809	−	0.302900i
$926$	11233.2	+	5932.03i	0.398644	+	0.210517i
$927$	−5170.59	−	26198.6i	−0.183198	−	0.928238i
$928$	−23380.8	−	1712.36i	−0.827060	−	0.0605722i
$929$	48771.3			1.72243			0.861213	−	0.508243i	$-0.169705\pi$
$929$	48771.3			1.72243			0.861213	+	0.508243i	$0.169705\pi$
$930$	−2285.45	−	10512.5i	−0.0805837	−	0.370664i
$931$			10367.3i			0.364956i
$932$	−8484.60	+	45009.0i	−0.298200	+	1.58189i
$933$	−4872.19	+	16018.4i	−0.170963	+	0.562078i
$934$	23735.0	−	44945.7i	0.831514	−	1.57459i
$935$	462.529	−	712.803i	0.0161779	−	0.0249317i
$936$	429.445	−	830.299i	0.0149966	−	0.0289948i
$937$	−32876.6	+	32876.6i	−1.14625	+	1.14625i	−0.158960	+	0.987285i	$0.550814\pi$
$937$	−32876.6	+	32876.6i	−1.14625	+	1.14625i	−0.987285	+	0.158960i	$0.949186\pi$
$938$	5812.00	−	1794.92i	0.202312	−	0.0624799i
$939$	9342.56	+	17510.1i	0.324689	+	0.608542i
$940$	−676.856	−	28818.5i	−0.0234858	−	0.999955i
$941$	34853.4			1.20743			0.603714	−	0.797201i	$-0.293687\pi$
$941$	34853.4			1.20743			0.603714	+	0.797201i	$0.293687\pi$
$942$	−22527.9	−	22336.4i	−0.779191	−	0.772569i
$943$	56557.6	+	56557.6i	1.95310	+	1.95310i
$944$	−38631.0	−	15101.2i	−1.33192	−	0.520660i
$945$	−1733.30	−	15781.7i	−0.0596659	−	0.543259i
$946$	2824.33	−	5348.27i	0.0970685	−	0.183813i
$947$	1840.86	−	1840.86i	0.0631679	−	0.0631679i	−0.674817	−	0.737985i	$-0.735777\pi$
$947$	1840.86	−	1840.86i	0.0631679	−	0.0631679i	0.737985	+	0.674817i	$0.235777\pi$
$948$	−5728.84	−	18273.2i	−0.196270	−	0.626041i
$949$	−1051.26			−0.0359592
$950$	11464.3	−	10037.7i	0.391526	−	0.342805i
$951$	11989.8	−	6397.19i	0.408829	−	0.218131i
$952$	2302.17	−	2892.86i	0.0783759	−	0.0984853i
$953$	30431.5	−	30431.5i	1.03439	−	1.03439i	0.0350033	−	0.999387i	$-0.488856\pi$
$953$	30431.5	−	30431.5i	1.03439	−	1.03439i	0.999387	−	0.0350033i	$-0.0111442\pi$
$954$	−26944.7	−	49985.9i	−0.914430	−	1.69639i
$955$	27154.4	−	5782.23i	0.920101	−	0.195925i
$956$	−1085.88	+	741.420i	−0.0367364	+	0.0250829i
$957$	921.975	−	3031.20i	0.0311424	−	0.102387i
$958$	23883.0	−	7375.77i	0.805452	−	0.248748i
$959$	18559.4			0.624938
$960$	29449.5	−	4179.06i	0.990081	−	0.140498i
$961$	−25504.5			−0.856114
$962$	788.090	−	243.386i	0.0264127	−	0.00815704i
$963$	19183.3	−	3786.03i	0.641924	−	0.126691i
$964$	−9072.30	+	6194.39i	−0.303111	+	0.206958i
$965$	−9666.65	+	14897.3i	−0.322467	+	0.496953i
$966$	121.201	+	28403.8i	0.00403684	+	0.946044i
$967$	20711.3	−	20711.3i	0.688759	−	0.688759i	−0.273199	−	0.961958i	$-0.588082\pi$
$967$	20711.3	−	20711.3i	0.688759	−	0.688759i	0.961958	+	0.273199i	$0.0880817\pi$
$968$	18441.5	−	23173.1i	0.612325	−	0.769433i
$969$	1701.74	+	3189.45i	0.0564165	+	0.105738i
$970$	−13191.5	−	3737.00i	−0.436653	−	0.123699i
$971$	−6046.87			−0.199849			−0.0999244	−	0.994995i	$-0.531860\pi$
$971$	−6046.87			−0.199849			−0.0999244	+	0.994995i	$0.531860\pi$
$972$	19371.7	+	23303.8i	0.639247	+	0.769002i
$973$	−4704.44	+	4704.44i	−0.155002	+	0.155002i
$974$	16804.0	−	31820.8i	0.552809	−	1.04682i
$975$	610.153	−	784.458i	0.0200416	−	0.0257669i
$976$	−26238.7	−	10256.9i	−0.860532	−	0.336390i
$977$	−6989.68	−	6989.68i	−0.228884	−	0.228884i	0.583342	−	0.812226i	$-0.301745\pi$
$977$	−6989.68	−	6989.68i	−0.228884	−	0.228884i	−0.812226	+	0.583342i	$0.801745\pi$
$978$	32855.2	−	33136.8i	1.07423	−	1.08343i
$979$	−4318.07			−0.140966
$980$	−14852.2	+	15566.7i	−0.484120	+	0.507408i
$981$	−22424.2	−	15031.9i	−0.729818	−	0.489226i
$982$	−8973.22	+	2771.20i	−0.291596	+	0.0900534i
$983$	−31952.3	+	31952.3i	−1.03675	+	1.03675i	−0.0374471	+	0.999299i	$0.511923\pi$
$983$	−31952.3	+	31952.3i	−1.03675	+	1.03675i	−0.999299	+	0.0374471i	$0.988077\pi$
$984$	27945.7	+	40556.5i	0.905362	+	1.31392i
$985$	22393.4	+	14530.8i	0.724377	+	0.470040i
$986$	2761.20	−	5228.74i	0.0891832	−	0.168881i
$987$	16217.1	+	4932.62i	0.522995	+	0.159075i
$988$	−97.7267	+	518.419i	−0.00314686	+	0.0166934i
$989$			86721.6i			2.78826i
$990$	−326.051	+	4006.65i	−0.0104673	+	0.128626i
$991$	−29405.8			−0.942589			−0.471294	−	0.881976i	$-0.656213\pi$
$991$	−29405.8			−0.942589			−0.471294	+	0.881976i	$0.656213\pi$
$992$	−865.667	+	11819.9i	−0.0277066	+	0.378310i
$993$	6990.74	−	22983.6i	0.223408	−	0.734504i
$994$	−18037.8	−	9525.46i	−0.575578	−	0.303953i
$995$	−28306.1	+	6027.47i	−0.901874	+	0.192044i
$996$	−19236.1	−	10053.5i	−0.611966	−	0.319836i
$997$	23604.5	+	23604.5i	0.749810	+	0.749810i	0.974443	−	0.224633i	$-0.0721184\pi$
$997$	23604.5	+	23604.5i	0.749810	+	0.749810i	−0.224633	+	0.974443i	$0.572118\pi$
$998$	−43409.9	+	13406.3i	−1.37687	+	0.425219i
$999$	−2680.47	+	26604.4i	−0.0848911	+	0.842567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.w.c.53.7	✓	128
3.2	odd	2	inner	120.4.w.c.53.58	yes	128
5.2	odd	4	inner	120.4.w.c.77.26	yes	128
8.5	even	2	inner	120.4.w.c.53.39	yes	128
15.2	even	4	inner	120.4.w.c.77.39	yes	128
24.5	odd	2	inner	120.4.w.c.53.26	yes	128
40.37	odd	4	inner	120.4.w.c.77.58	yes	128
120.77	even	4	inner	120.4.w.c.77.7	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.w.c.53.7	✓	128	1.1	even	1	trivial
120.4.w.c.53.26	yes	128	24.5	odd	2	inner
120.4.w.c.53.39	yes	128	8.5	even	2	inner
120.4.w.c.53.58	yes	128	3.2	odd	2	inner
120.4.w.c.77.7	yes	128	120.77	even	4	inner
120.4.w.c.77.26	yes	128	5.2	odd	4	inner
120.4.w.c.77.39	yes	128	15.2	even	4	inner
120.4.w.c.77.58	yes	128	40.37	odd	4	inner

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

\(f(q)\)	\(=\)	\(q+(-2.70249 + 0.834608i) q^{2} +(4.97128 + 1.51207i) q^{3} +(6.60686 - 4.51103i) q^{4} +(2.32852 + 10.9352i) q^{5} +(-14.6968 + 0.0627124i) q^{6} +(-7.15720 + 7.15720i) q^{7} +(-14.0900 + 17.7051i) q^{8} +(22.4273 + 15.0339i) q^{9} +(-15.4194 - 27.6087i) q^{10} -4.70815 q^{11} +(39.6656 - 12.4356i) q^{12} +(-1.08192 + 1.08192i) q^{13} +(13.3688 - 25.3157i) q^{14} +(-4.95906 + 57.8827i) q^{15} +(23.3011 - 59.6075i) q^{16} +(11.4144 + 11.4144i) q^{17} +(-73.1568 - 21.9109i) q^{18} +43.0984 q^{19} +(64.7131 + 61.7431i) q^{20} +(-46.4026 + 24.7582i) q^{21} +(12.7237 - 3.92946i) q^{22} +(-135.015 + 135.015i) q^{23} +(-96.8168 + 66.7121i) q^{24} +(-114.156 + 50.9256i) q^{25} +(2.02090 - 3.82687i) q^{26} +(88.7598 + 108.649i) q^{27} +(-15.0002 + 79.5729i) q^{28} +129.508i q^{29} +(-34.9076 - 160.566i) q^{30} +65.4714 q^{31} +(-13.2221 + 180.536i) q^{32} +(-23.4055 - 7.11908i) q^{33} +(-40.3739 - 21.3208i) q^{34} +(-94.9308 - 61.5995i) q^{35} +(215.992 - 1.84334i) q^{36} +(134.768 + 134.768i) q^{37} +(-116.473 + 35.9703i) q^{38} +(-7.01450 + 3.74260i) q^{39} +(-226.418 - 112.850i) q^{40} -418.900i q^{41} +(104.739 - 105.637i) q^{42} +(321.156 - 321.156i) q^{43} +(-31.1061 + 21.2386i) q^{44} +(-112.176 + 280.253i) q^{45} +(252.191 - 477.560i) q^{46} +(-227.893 - 227.893i) q^{47} +(205.968 - 261.093i) q^{48} +240.549i q^{49} +(266.002 - 232.901i) q^{50} +(39.4849 + 74.0038i) q^{51} +(-2.26752 + 12.0287i) q^{52} +(525.792 + 525.792i) q^{53} +(-330.552 - 219.544i) q^{54} +(-10.9630 - 51.4844i) q^{55} +(-25.8744 - 227.564i) q^{56} +(214.254 + 65.1680i) q^{57} +(-108.088 - 349.993i) q^{58} -648.089i q^{59} +(228.347 + 404.793i) q^{60} -440.190i q^{61} +(-176.936 + 54.6430i) q^{62} +(-268.117 + 52.9158i) q^{63} +(-114.944 - 498.931i) q^{64} +(-14.3503 - 9.31175i) q^{65} +(69.1948 - 0.295259i) q^{66} +(150.241 + 150.241i) q^{67} +(126.904 + 23.9226i) q^{68} +(-875.349 + 467.044i) q^{69} +(307.961 + 87.2417i) q^{70} -712.516i q^{71} +(-582.177 + 185.250i) q^{72} +(485.828 + 485.828i) q^{73} +(-476.686 - 251.729i) q^{74} +(-644.505 + 80.5529i) q^{75} +(284.745 - 194.418i) q^{76} +(33.6972 - 33.6972i) q^{77} +(15.8330 - 15.9687i) q^{78} -460.682i q^{79} +(706.076 + 116.005i) q^{80} +(276.964 + 674.338i) q^{81} +(349.617 + 1132.07i) q^{82} +(-369.206 - 369.206i) q^{83} +(-194.891 + 372.898i) q^{84} +(-98.2400 + 151.398i) q^{85} +(-599.880 + 1135.96i) q^{86} +(-195.825 + 643.819i) q^{87} +(66.3378 - 83.3585i) q^{88} +917.147 q^{89} +(69.2524 - 851.002i) q^{90} -15.4871i q^{91} +(-282.967 + 1501.08i) q^{92} +(325.477 + 98.9976i) q^{93} +(806.080 + 425.677i) q^{94} +(100.356 + 471.289i) q^{95} +(-338.714 + 877.501i) q^{96} +(306.578 - 306.578i) q^{97} +(-200.764 - 650.080i) q^{98} +(-105.591 - 70.7819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 4 q^{6} - 144 q^{7} - 156 q^{10} - 56 q^{12} + 212 q^{15} + 636 q^{16} + 220 q^{18} - 188 q^{22} - 8 q^{25} + 908 q^{28} + 328 q^{30} - 544 q^{31} - 1624 q^{33} - 1268 q^{36} - 136 q^{40} + 328 q^{42}+ \cdots - 3792 q^{97}+O(q^{100}) \) 128 * q - 4 * q^6 - 144 * q^7 - 156 * q^10 - 56 * q^12 + 212 * q^15 + 636 * q^16 + 220 * q^18 - 188 * q^22 - 8 * q^25 + 908 * q^28 + 328 * q^30 - 544 * q^31 - 1624 * q^33 - 1268 * q^36 - 136 * q^40 + 328 * q^42 + 568 * q^46 - 148 * q^48 + 616 * q^52 + 728 * q^55 - 112 * q^57 + 2196 * q^58 - 424 * q^60 - 2304 * q^63 + 304 * q^66 - 4740 * q^70 + 224 * q^72 + 1280 * q^73 - 1624 * q^76 - 1448 * q^78 + 7056 * q^81 - 1472 * q^82 - 5720 * q^87 + 1516 * q^88 - 996 * q^90 + 2732 * q^96 - 3792 * q^97

Introduction

L-functions

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