LMFDB - Embedded newform 192.2.r.a.85.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(13,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("192.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.r (of order $16$, degree $8$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			85.12
Character	$\chi$	$=$	192.85
Dual form			192.2.r.a.61.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.846436 + 1.13294i) q^{2} +(0.195090 + 0.980785i) q^{3} +(-0.567094 + 1.91792i) q^{4} +(-1.21887 + 0.814423i) q^{5} +(-0.946037 + 1.05120i) q^{6} +(-1.20411 - 0.498758i) q^{7} +(-2.65289 + 0.980911i) q^{8} +(-0.923880 + 0.382683i) q^{9} +O(q^{10})$	\(q+(0.846436 + 1.13294i) q^{2} +(0.195090 + 0.980785i) q^{3} +(-0.567094 + 1.91792i) q^{4} +(-1.21887 + 0.814423i) q^{5} +(-0.946037 + 1.05120i) q^{6} +(-1.20411 - 0.498758i) q^{7} +(-2.65289 + 0.980911i) q^{8} +(-0.923880 + 0.382683i) q^{9} +(-1.95438 - 0.691547i) q^{10} +(5.35111 + 1.06440i) q^{11} +(-1.99170 - 0.182030i) q^{12} +(0.678439 + 0.453319i) q^{13} +(-0.454138 - 1.78635i) q^{14} +(-1.03656 - 1.03656i) q^{15} +(-3.35681 - 2.17528i) q^{16} +(0.0838862 - 0.0838862i) q^{17} +(-1.21556 - 0.722781i) q^{18} +(4.63254 - 6.93308i) q^{19} +(-0.870782 - 2.79954i) q^{20} +(0.254265 - 1.27827i) q^{21} +(3.32347 + 6.96342i) q^{22} +(2.90494 + 7.01314i) q^{23} +(-1.47962 - 2.41055i) q^{24} +(-1.09106 + 2.63405i) q^{25} +(0.0606735 + 1.15233i) q^{26} +(-0.555570 - 0.831470i) q^{27} +(1.63942 - 2.02654i) q^{28} +(-0.541143 + 0.107640i) q^{29} +(0.296977 - 2.05175i) q^{30} -4.09443i q^{31} +(-0.376870 - 5.64429i) q^{32} +5.45595i q^{33} +(0.166042 + 0.0240335i) q^{34} +(1.87385 - 0.372732i) q^{35} +(-0.210029 - 1.98894i) q^{36} +(-3.88386 - 5.81261i) q^{37} +(11.7759 - 0.620033i) q^{38} +(-0.312251 + 0.753841i) q^{39} +(2.43465 - 3.35618i) q^{40} +(1.43034 + 3.45314i) q^{41} +(1.66342 - 0.793911i) q^{42} +(0.346777 - 1.74336i) q^{43} +(-5.07602 + 9.65937i) q^{44} +(0.814423 - 1.21887i) q^{45} +(-5.48661 + 9.22729i) q^{46} +(4.78442 - 4.78442i) q^{47} +(1.47860 - 3.71668i) q^{48} +(-3.74863 - 3.74863i) q^{49} +(-3.90772 + 0.993451i) q^{50} +(0.0986398 + 0.0659090i) q^{51} +(-1.25417 + 1.04412i) q^{52} +(-2.91095 - 0.579023i) q^{53} +(0.471749 - 1.33321i) q^{54} +(-7.38918 + 3.06070i) q^{55} +(3.68360 + 0.142025i) q^{56} +(7.70363 + 3.19095i) q^{57} +(-0.579992 - 0.521971i) q^{58} +(8.27418 - 5.52863i) q^{59} +(2.57587 - 1.40021i) q^{60} +(1.64548 + 8.27240i) q^{61} +(4.63873 - 3.46567i) q^{62} +1.30332 q^{63} +(6.07563 - 5.20450i) q^{64} -1.19612 q^{65} +(-6.18124 + 4.61811i) q^{66} +(-0.993605 - 4.99519i) q^{67} +(0.113315 + 0.208458i) q^{68} +(-6.31166 + 4.21732i) q^{69} +(2.00838 + 1.80746i) q^{70} +(-11.5446 - 4.78192i) q^{71} +(2.07557 - 1.92146i) q^{72} +(-3.75189 + 1.55409i) q^{73} +(3.29788 - 9.32018i) q^{74} +(-2.79629 - 0.556217i) q^{75} +(10.6700 + 12.8165i) q^{76} +(-5.91244 - 3.95056i) q^{77} +(-1.11836 + 0.284317i) q^{78} +(-0.583888 - 0.583888i) q^{79} +(5.86311 - 0.0824825i) q^{80} +(0.707107 - 0.707107i) q^{81} +(-2.70150 + 4.54335i) q^{82} +(-3.90846 + 5.84943i) q^{83} +(2.30743 + 1.21256i) q^{84} +(-0.0339275 + 0.170565i) q^{85} +(2.26865 - 1.08277i) q^{86} +(-0.211144 - 0.509746i) q^{87} +(-15.2400 + 2.42523i) q^{88} +(-2.07094 + 4.99970i) q^{89} +(2.07026 - 0.109005i) q^{90} +(-0.590818 - 0.884221i) q^{91} +(-15.0980 + 1.59432i) q^{92} +(4.01576 - 0.798784i) q^{93} +(9.47015 + 1.37074i) q^{94} +12.2234i q^{95} +(5.46231 - 1.47077i) q^{96} -5.39692i q^{97} +(1.07399 - 7.41994i) q^{98} +(-5.35111 + 1.06440i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) $ 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{16}\right)$

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 $

$2$	0.846436	+	1.13294i	0.598520	+	0.801108i
$2$	0.846436	+	1.13294i	0.598520	+	0.801108i
$3$	0.195090	+	0.980785i	0.112635	+	0.566257i
$3$	0.195090	+	0.980785i	0.112635	+	0.566257i
$4$	−0.567094	+	1.91792i	−0.283547	+	0.958958i
$5$	−1.21887	+	0.814423i	−0.545095	+	0.364221i	−0.797423	−	0.603421i	$-0.793804\pi$
$5$	−1.21887	+	0.814423i	−0.545095	+	0.364221i	0.252328	+	0.967642i	$0.418804\pi$
$6$	−0.946037	+	1.05120i	−0.386218	+	0.429149i
$7$	−1.20411	−	0.498758i	−0.455110	−	0.188513i	0.143339	−	0.989674i	$-0.454216\pi$
$7$	−1.20411	−	0.498758i	−0.455110	−	0.188513i	−0.598449	+	0.801161i	$0.704216\pi$
$8$	−2.65289	+	0.980911i	−0.937937	+	0.346805i
$9$	−0.923880	+	0.382683i	−0.307960	+	0.127561i
$10$	−1.95438	−	0.691547i	−0.618031	−	0.218686i
$11$	5.35111	+	1.06440i	1.61342	+	0.320929i	0.917667	−	0.397351i	$-0.130070\pi$
$11$	5.35111	+	1.06440i	1.61342	+	0.320929i	0.695754	+	0.718280i	$0.255070\pi$
$12$	−1.99170	−	0.182030i	−0.574954	−	0.0525476i
$13$	0.678439	+	0.453319i	0.188165	+	0.125728i	0.646085	−	0.763266i	$-0.276405\pi$
$13$	0.678439	+	0.453319i	0.188165	+	0.125728i	−0.457920	+	0.888994i	$0.651405\pi$
$14$	−0.454138	−	1.78635i	−0.121374	−	0.477421i
$15$	−1.03656	−	1.03656i	−0.267640	−	0.267640i
$16$	−3.35681	−	2.17528i	−0.839202	−	0.543819i
$17$	0.0838862	−	0.0838862i	0.0203454	−	0.0203454i	−0.696861	−	0.717206i	$-0.745421\pi$
$17$	0.0838862	−	0.0838862i	0.0203454	−	0.0203454i	0.717206	+	0.696861i	$0.245421\pi$
$18$	−1.21556	−	0.722781i	−0.286510	−	0.170361i
$19$	4.63254	−	6.93308i	1.06278	−	1.59056i	0.288751	−	0.957404i	$-0.406760\pi$
$19$	4.63254	−	6.93308i	1.06278	−	1.59056i	0.774026	−	0.633154i	$-0.218240\pi$
$20$	−0.870782	−	2.79954i	−0.194713	−	0.625997i
$21$	0.254265	−	1.27827i	0.0554851	−	0.278942i
$22$	3.32347	+	6.96342i	0.708566	+	1.48461i
$23$	2.90494	+	7.01314i	0.605722	+	1.46234i	0.867611	+	0.497244i	$0.165654\pi$
$23$	2.90494	+	7.01314i	0.605722	+	1.46234i	−0.261889	+	0.965098i	$0.584346\pi$
$24$	−1.47962	−	2.41055i	−0.302025	−	0.492051i
$25$	−1.09106	+	2.63405i	−0.218212	+	0.526809i
$26$	0.0606735	+	1.15233i	0.0118991	+	0.225991i
$27$	−0.555570	−	0.831470i	−0.106920	−	0.160016i
$28$	1.63942	−	2.02654i	0.309821	−	0.382979i
$29$	−0.541143	+	0.107640i	−0.100488	+	0.0199883i	−0.245078	−	0.969503i	$-0.578814\pi$
$29$	−0.541143	+	0.107640i	−0.100488	+	0.0199883i	0.144590	+	0.989492i	$0.453814\pi$
$30$	0.296977	−	2.05175i	0.0542204	−	0.374596i
$31$		−	4.09443i		−	0.735382i	−0.929948	−	0.367691i	$-0.880148\pi$
$31$		−	4.09443i		−	0.735382i	0.929948	−	0.367691i	$-0.119852\pi$
$32$	−0.376870	−	5.64429i	−0.0666219	−	0.997778i
$33$			5.45595i			0.949758i
$34$	0.166042	+	0.0240335i	0.0284760	+	0.00412172i
$35$	1.87385	−	0.372732i	0.316739	−	0.0630032i
$36$	−0.210029	−	1.98894i	−0.0350048	−	0.331490i
$37$	−3.88386	−	5.81261i	−0.638503	−	0.955588i	−0.999733	−	0.0231107i	$-0.992643\pi$
$37$	−3.88386	−	5.81261i	−0.638503	−	0.955588i	0.361230	−	0.932477i	$-0.382357\pi$
$38$	11.7759	−	0.620033i	1.91030	−	0.100583i
$39$	−0.312251	+	0.753841i	−0.0500002	+	0.120711i
$40$	2.43465	−	3.35618i	0.384952	−	0.530658i
$41$	1.43034	+	3.45314i	0.223381	+	0.539290i	0.995345	−	0.0963765i	$-0.0307253\pi$
$41$	1.43034	+	3.45314i	0.223381	+	0.539290i	−0.771964	+	0.635667i	$0.780725\pi$
$42$	1.66342	−	0.793911i	0.256672	−	0.122503i
$43$	0.346777	−	1.74336i	0.0528830	−	0.265861i	−0.945294	−	0.326220i	$-0.894225\pi$
$43$	0.346777	−	1.74336i	0.0528830	−	0.265861i	0.998177	+	0.0603599i	$0.0192248\pi$
$44$	−5.07602	+	9.65937i	−0.765238	+	1.45620i
$45$	0.814423	−	1.21887i	0.121407	−	0.181698i
$46$	−5.48661	+	9.22729i	−0.808956	+	1.36049i
$47$	4.78442	−	4.78442i	0.697879	−	0.697879i	−0.266073	−	0.963953i	$-0.585726\pi$
$47$	4.78442	−	4.78442i	0.697879	−	0.697879i	0.963953	+	0.266073i	$0.0857264\pi$
$48$	1.47860	−	3.71668i	0.213417	−	0.536457i
$49$	−3.74863	−	3.74863i	−0.535519	−	0.535519i
$50$	−3.90772	+	0.993451i	−0.552635	+	0.140495i
$51$	0.0986398	+	0.0659090i	0.0138123	+	0.00922910i
$52$	−1.25417	+	1.04412i	−0.173922	+	0.144793i
$53$	−2.91095	−	0.579023i	−0.399849	−	0.0795350i	−0.00893042	−	0.999960i	$-0.502843\pi$
$53$	−2.91095	−	0.579023i	−0.399849	−	0.0795350i	−0.390919	+	0.920425i	$0.627843\pi$
$54$	0.471749	−	1.33321i	0.0641968	−	0.181427i
$55$	−7.38918	+	3.06070i	−0.996357	+	0.412705i
$56$	3.68360	+	0.142025i	0.492242	+	0.0189789i
$57$	7.70363	+	3.19095i	1.02037	+	0.422651i
$58$	−0.579992	−	0.521971i	−0.0761567	−	0.0685381i
$59$	8.27418	−	5.52863i	1.07721	−	0.719766i	0.115351	−	0.993325i	$-0.463201\pi$
$59$	8.27418	−	5.52863i	1.07721	−	0.719766i	0.961855	+	0.273558i	$0.0882006\pi$
$60$	2.57587	−	1.40021i	0.332544	−	0.180767i
$61$	1.64548	+	8.27240i	0.210682	+	1.05917i	0.930858	+	0.365380i	$0.119061\pi$
$61$	1.64548	+	8.27240i	0.210682	+	1.05917i	−0.720176	+	0.693791i	$0.755939\pi$
$62$	4.63873	−	3.46567i	0.589120	−	0.440141i
$63$	1.30332			0.164203
$64$	6.07563	−	5.20450i	0.759453	−	0.650562i
$65$	−1.19612			−0.148361
$66$	−6.18124	+	4.61811i	−0.760859	+	0.568450i
$67$	−0.993605	−	4.99519i	−0.121388	−	0.610260i	−0.992808	−	0.119721i	$-0.961800\pi$
$67$	−0.993605	−	4.99519i	−0.121388	−	0.610260i	0.871419	−	0.490539i	$-0.163200\pi$
$68$	0.113315	+	0.208458i	0.0137415	+	0.0252793i
$69$	−6.31166	+	4.21732i	−0.759835	+	0.507705i
$70$	2.00838	+	1.80746i	0.240047	+	0.216033i
$71$	−11.5446	−	4.78192i	−1.37009	−	0.567510i	−0.428277	−	0.903647i	$-0.640879\pi$
$71$	−11.5446	−	4.78192i	−1.37009	−	0.567510i	−0.941813	+	0.336137i	$0.890879\pi$
$72$	2.07557	−	1.92146i	0.244608	−	0.226446i
$73$	−3.75189	+	1.55409i	−0.439126	+	0.181892i	−0.591283	−	0.806464i	$-0.701378\pi$
$73$	−3.75189	+	1.55409i	−0.439126	+	0.181892i	0.152157	+	0.988356i	$0.451378\pi$
$74$	3.29788	−	9.32018i	0.383371	−	1.08345i
$75$	−2.79629	−	0.556217i	−0.322888	−	0.0642264i
$76$	10.6700	+	12.8165i	1.22393	+	1.47016i
$77$	−5.91244	−	3.95056i	−0.673785	−	0.450209i
$78$	−1.11836	+	0.284317i	−0.126629	+	0.0321926i
$79$	−0.583888	−	0.583888i	−0.0656925	−	0.0656925i	0.673497	−	0.739190i	$-0.264791\pi$
$79$	−0.583888	−	0.583888i	−0.0656925	−	0.0656925i	−0.739190	+	0.673497i	$0.764791\pi$
$80$	5.86311	−	0.0824825i	0.655515	−	0.00922182i
$81$	0.707107	−	0.707107i	0.0785674	−	0.0785674i
$82$	−2.70150	+	4.54335i	−0.298331	+	0.501729i
$83$	−3.90846	+	5.84943i	−0.429010	+	0.642058i	−0.981500	−	0.191461i	$-0.938678\pi$
$83$	−3.90846	+	5.84943i	−0.429010	+	0.642058i	0.552491	+	0.833519i	$0.313678\pi$
$84$	2.30743	+	1.21256i	0.251761	+	0.132301i
$85$	−0.0339275	+	0.170565i	−0.00367996	+	0.0185004i
$86$	2.26865	−	1.08277i	0.244634	−	0.116758i
$87$	−0.211144	−	0.509746i	−0.0226370	−	0.0546505i
$88$	−15.2400	+	2.42523i	−1.62459	+	0.258530i
$89$	−2.07094	+	4.99970i	−0.219520	+	0.529967i	−0.994823	−	0.101622i	$-0.967597\pi$
$89$	−2.07094	+	4.99970i	−0.219520	+	0.529967i	0.775303	+	0.631589i	$0.217597\pi$
$90$	2.07026	−	0.109005i	0.218224	−	0.0114901i
$91$	−0.590818	−	0.884221i	−0.0619345	−	0.0926916i
$92$	−15.0980	+	1.59432i	−1.57408	+	0.166220i
$93$	4.01576	−	0.798784i	0.416415	−	0.0828300i
$94$	9.47015	+	1.37074i	0.976771	+	0.141381i
$95$			12.2234i			1.25409i
$96$	5.46231	−	1.47077i	0.557495	−	0.150110i
$97$		−	5.39692i		−	0.547975i	−0.961733	−	0.273987i	$-0.911657\pi$
$97$		−	5.39692i		−	0.547975i	0.961733	−	0.273987i	$-0.0883426\pi$
$98$	1.07399	−	7.41994i	0.108489	−	0.749527i
$99$	−5.35111	+	1.06440i	−0.537807	+	0.106976i
$100$	−4.43315	−	3.58631i	−0.443315	−	0.358631i
$101$	−8.57465	−	12.8329i	−0.853209	−	1.27692i	−0.959251	−	0.282556i	$-0.908818\pi$
$101$	−8.57465	−	12.8329i	−0.853209	−	1.27692i	0.106041	−	0.994362i	$-0.466182\pi$
$102$	0.00882146	+	0.167540i	0.000873455	+	0.0165890i
$103$	−3.64351	+	8.79621i	−0.359006	+	0.866716i	0.636435	+	0.771331i	$0.280408\pi$
$103$	−3.64351	+	8.79621i	−0.359006	+	0.866716i	−0.995440	+	0.0953857i	$0.969592\pi$
$104$	−2.24449	−	0.537115i	−0.220090	−	0.0526684i
$105$	0.731140	+	1.76513i	0.0713520	+	0.172259i
$106$	−1.80793	−	3.78803i	−0.175602	−	0.367926i
$107$	−3.20020	+	16.0885i	−0.309375	+	1.55533i	0.442955	+	0.896544i	$0.353930\pi$
$107$	−3.20020	+	16.0885i	−0.309375	+	1.55533i	−0.752330	+	0.658787i	$0.771070\pi$
$108$	1.90975	−	0.594016i	0.183766	−	0.0571592i
$109$	5.06023	−	7.57318i	0.484683	−	0.725379i	−0.505855	−	0.862618i	$-0.668823\pi$
$109$	5.06023	−	7.57318i	0.484683	−	0.725379i	0.990538	+	0.137240i	$0.0438230\pi$
$110$	−9.72205	−	5.78079i	−0.926961	−	0.551177i
$111$	4.94322	−	4.94322i	0.469190	−	0.469190i
$112$	2.95702	+	4.29350i	0.279413	+	0.405698i
$113$	2.20089	+	2.20089i	0.207042	+	0.207042i	0.803009	−	0.595967i	$-0.203231\pi$
$113$	2.20089	+	2.20089i	0.207042	+	0.207042i	−0.595967	+	0.803009i	$0.703231\pi$
$114$	2.90548	+	11.4287i	0.272123	+	1.07039i
$115$	−9.25241	−	6.18226i	−0.862791	−	0.576499i
$116$	0.100434	−	1.09891i	0.00932508	−	0.102031i
$117$	−0.800274	−	0.159184i	−0.0739853	−	0.0147166i
$118$	13.2672	+	4.69450i	1.22134	+	0.432164i
$119$	−0.142847	+	0.0591692i	−0.0130948	+	0.00542403i
$120$	3.76666	+	1.73311i	0.343848	+	0.158211i
$121$	17.3388	+	7.18195i	1.57625	+	0.652905i
$122$	−7.97931	+	8.86628i	−0.722413	+	0.802715i
$123$	−3.10775	+	2.07653i	−0.280216	+	0.187234i
$124$	7.85278	+	2.32193i	0.705200	+	0.208515i
$125$	−2.24531	−	11.2879i	−0.200826	−	1.00962i
$126$	1.10317	+	1.47658i	0.0982785	+	0.131544i
$127$	−17.0174			−1.51005			−0.755024	−	0.655698i	$-0.772375\pi$
$127$	−17.0174			−1.51005			−0.755024	+	0.655698i	$0.772375\pi$
$128$	11.0390	+	2.47803i	0.975718	+	0.219029i
$129$	1.77752			0.156502
$130$	−1.01244	−	1.35513i	−0.0887969	−	0.118853i
$131$	−0.156693	−	0.787749i	−0.0136903	−	0.0688260i	0.973336	−	0.229383i	$-0.0736709\pi$
$131$	−0.156693	−	0.787749i	−0.0136903	−	0.0688260i	−0.987027	+	0.160557i	$0.948671\pi$
$132$	−10.4641	−	3.09403i	−0.910779	−	0.269301i
$133$	−9.03600	+	6.03766i	−0.783521	+	0.523532i
$134$	4.81822	−	5.35380i	0.416230	−	0.462498i
$135$	1.35434	+	0.560984i	0.116563	+	0.0482818i
$136$	−0.140256	+	0.304826i	−0.0120268	+	0.0261386i
$137$	−15.2249	+	6.30637i	−1.30075	+	0.538789i	−0.922172	−	0.386779i	$-0.873588\pi$
$137$	−15.2249	+	6.30637i	−1.30075	+	0.538789i	−0.378580	+	0.925568i	$0.623588\pi$
$138$	−10.1204	−	3.58103i	−0.861503	−	0.304837i
$139$	13.8277	+	2.75051i	1.17285	+	0.233295i	0.742803	−	0.669510i	$-0.233496\pi$
$139$	13.8277	+	2.75051i	1.17285	+	0.233295i	0.430050	+	0.902805i	$0.358496\pi$
$140$	−0.347780	+	3.80526i	−0.0293928	+	0.321603i
$141$	5.62588	+	3.75909i	0.473785	+	0.316573i
$142$	−4.35413	−	17.1269i	−0.365390	−	1.43726i
$143$	3.14789	+	3.14789i	0.263240	+	0.263240i
$144$	3.93373	+	0.725099i	0.327811	+	0.0604249i
$145$	0.571919	−	0.571919i	0.0474953	−	0.0474953i
$146$	−4.93642	−	2.93523i	−0.408541	−	0.242921i
$147$	2.94528	−	4.40792i	0.242923	−	0.363559i
$148$	13.3506	−	4.15263i	1.09741	−	0.341344i
$149$	−0.930244	+	4.67665i	−0.0762085	+	0.383126i	0.923791	+	0.382896i	$0.125073\pi$
$149$	−0.930244	+	4.67665i	−0.0762085	+	0.383126i	−1.00000		0.000230114i	$0.999927\pi$
$150$	−1.73672	−	3.63882i	−0.141803	−	0.297109i
$151$	6.38801	+	15.4220i	0.519849	+	1.25503i	0.937996	+	0.346647i	$0.112680\pi$
$151$	6.38801	+	15.4220i	0.519849	+	1.25503i	−0.418147	+	0.908380i	$0.637320\pi$
$152$	−5.48886	+	22.9368i	−0.445206	+	1.86042i
$153$	−0.0453989	+	0.109603i	−0.00367028	+	0.00886085i
$154$	−0.528756	−	10.0423i	−0.0426083	−	0.809233i
$155$	3.33460	+	4.99058i	0.267841	+	0.400853i
$156$	−1.26873	−	1.02637i	−0.101580	−	0.0821754i
$157$	23.1862	−	4.61202i	1.85046	−	0.368079i	0.860501	−	0.509449i	$-0.170151\pi$
$157$	23.1862	−	4.61202i	1.85046	−	0.368079i	0.989957	+	0.141370i	$0.0451508\pi$
$158$	0.167285	−	1.15573i	0.0133085	−	0.0919451i
$159$		−	2.96798i		−	0.235376i
$160$	5.05619	+	6.57272i	0.399727	+	0.519619i
$161$		−	9.89344i		−	0.779712i
$162$	1.39963	+	0.202587i	0.109965	+	0.0159168i
$163$	23.0695	−	4.58881i	1.80694	−	0.359423i	0.827550	−	0.561392i	$-0.189734\pi$
$163$	23.0695	−	4.58881i	1.80694	−	0.359423i	0.979392	+	0.201968i	$0.0647338\pi$
$164$	−7.43398	+	0.785015i	−0.580496	+	0.0612993i
$165$	−4.44345	−	6.65009i	−0.345922	−	0.517709i
$166$	−9.93530	+	0.523121i	−0.771129	+	0.0406021i
$167$	4.39817	−	10.6181i	0.340340	−	0.821654i	−0.657341	−	0.753593i	$-0.728319\pi$
$167$	4.39817	−	10.6181i	0.340340	−	0.821654i	0.997681	−	0.0680607i	$-0.0216812\pi$
$168$	0.579338	+	3.64053i	0.0446969	+	0.280873i
$169$	−4.72010	−	11.3953i	−0.363085	−	0.876564i
$170$	−0.221957	+	0.105935i	−0.0170233	+	0.00812482i
$171$	−1.62673	+	8.17813i	−0.124399	+	0.625397i
$172$	3.14697	+	1.65374i	0.239954	+	0.126096i
$173$	6.09151	−	9.11658i	0.463129	−	0.693121i	−0.524238	−	0.851572i	$-0.675650\pi$
$173$	6.09151	−	9.11658i	0.463129	−	0.693121i	0.987367	+	0.158451i	$0.0506499\pi$
$174$	0.398790	−	0.670679i	0.0302322	−	0.0508441i
$175$	2.62750	−	2.62750i	0.198621	−	0.198621i
$176$	−15.6473	−	15.2131i	−1.17946	−	1.14673i
$177$	7.03661	+	7.03661i	0.528904	+	0.528904i
$178$	−7.41727	+	1.88568i	−0.555948	+	0.141337i
$179$	−17.8857	−	11.9509i	−1.33684	−	0.893249i	−0.337989	−	0.941150i	$-0.609747\pi$
$179$	−17.8857	−	11.9509i	−1.33684	−	0.893249i	−0.998852	+	0.0479013i	$0.984747\pi$
$180$	1.87584	+	2.25321i	0.139817	+	0.167944i
$181$	15.7627	+	3.13539i	1.17163	+	0.233051i	0.742282	−	0.670088i	$-0.233744\pi$
$181$	15.7627	+	3.13539i	1.17163	+	0.233051i	0.429347	+	0.903140i	$0.358744\pi$
$182$	0.501678	−	1.41780i	0.0371869	−	0.105094i
$183$	−7.79243	+	3.22773i	−0.576033	+	0.238601i
$184$	−14.5857	−	15.7556i	−1.07528	−	1.16152i
$185$	9.46785	+	3.92171i	0.696090	+	0.288330i
$186$	4.30405	+	3.87348i	0.315588	+	0.284018i
$187$	0.538173	−	0.359596i	0.0393551	−	0.0262963i
$188$	6.46290	+	11.8893i	0.471356	+	0.867119i
$189$	0.254265	+	1.27827i	0.0184950	+	0.0929808i
$190$	−13.8483	+	10.3463i	−1.00466	+	0.750599i
$191$	20.3723			1.47409			0.737043	−	0.675846i	$-0.236221\pi$
$191$	20.3723			1.47409			0.737043	+	0.675846i	$0.236221\pi$
$192$	6.28979	+	4.94354i	0.453926	+	0.356769i
$193$	−4.28011			−0.308089			−0.154045	−	0.988064i	$-0.549230\pi$
$193$	−4.28011			−0.308089			−0.154045	+	0.988064i	$0.549230\pi$
$194$	6.11438	−	4.56815i	0.438987	−	0.327974i
$195$	−0.233352	−	1.17314i	−0.0167107	−	0.0840102i
$196$	9.31539	−	5.06374i	0.665385	−	0.361696i
$197$	−2.57679	+	1.72175i	−0.183589	+	0.122670i	−0.643968	−	0.765052i	$-0.722713\pi$
$197$	−2.57679	+	1.72175i	−0.183589	+	0.122670i	0.460380	+	0.887722i	$0.347713\pi$
$198$	−5.73527	−	5.16153i	−0.407588	−	0.366814i
$199$	−18.0964	−	7.49576i	−1.28282	−	0.531360i	−0.365980	−	0.930623i	$-0.619266\pi$
$199$	−18.0964	−	7.49576i	−1.28282	−	0.531360i	−0.916837	+	0.399263i	$0.869266\pi$
$200$	0.310688	−	8.05806i	0.0219689	−	0.569791i
$201$	4.70537	−	1.94903i	0.331891	−	0.137474i
$202$	7.28095	−	20.5767i	0.512286	−	1.44777i
$203$	0.705281	+	0.140289i	0.0495010	+	0.00984637i
$204$	−0.182346	+	0.151806i	−0.0127668	+	0.0106286i
$205$	−4.55571	−	3.04403i	−0.318185	−	0.212604i
$206$	−13.0495	+	3.31756i	−0.909205	+	0.231145i
$207$	−5.36763	−	5.36763i	−0.373076	−	0.373076i
$208$	−1.29130	−	2.99750i	−0.0895354	−	0.207839i
$209$	32.1688	−	32.1688i	2.22516	−	2.22516i
$210$	−1.38092	+	2.32240i	−0.0952923	+	0.160261i
$211$	−6.78123	+	10.1488i	−0.466839	+	0.698674i	−0.987943	−	0.154819i	$-0.950520\pi$
$211$	−6.78123	+	10.1488i	−0.466839	+	0.698674i	0.521104	+	0.853493i	$0.325520\pi$
$212$	2.76130	−	5.25459i	0.189647	−	0.360887i
$213$	2.43780	−	12.2557i	0.167036	−	0.839744i
$214$	−20.9360	+	9.99223i	−1.43115	+	0.683055i
$215$	0.997160	+	2.40736i	0.0680057	+	0.164180i
$216$	2.28946	+	1.66083i	0.155778	+	0.113005i
$217$	−2.04213	+	4.93014i	−0.138629	+	0.334679i
$218$	12.8631	−	0.677277i	0.871199	−	0.0458710i
$219$	−2.25618	−	3.37661i	−0.152459	−	0.228170i
$220$	−1.67981	−	15.9075i	−0.113253	−	1.07249i
$221$	0.0949389	−	0.0188845i	0.00638628	−	0.00127031i
$222$	9.78448	+	1.41624i	0.656691	+	0.0950519i
$223$			2.22590i			0.149057i	0.997219	+	0.0745287i	$0.0237452\pi$
$223$			2.22590i			0.149057i	−0.997219	+	0.0745287i	$0.976255\pi$
$224$	−2.36134	+	6.98430i	−0.157774	+	0.466658i
$225$		−	2.85107i		−	0.190071i
$226$	−0.630558	+	4.35638i	−0.0419441	+	0.289782i
$227$	−16.3771	+	3.25762i	−1.08699	+	0.216216i	−0.705892	−	0.708320i	$-0.749454\pi$
$227$	−16.3771	+	3.25762i	−1.08699	+	0.216216i	−0.381097	+	0.924535i	$0.624454\pi$
$228$	−10.4887	+	12.9654i	−0.694628	+	0.858651i
$229$	10.0039	+	14.9719i	0.661078	+	0.989373i	0.998841	+	0.0481415i	$0.0153299\pi$
$229$	10.0039	+	14.9719i	0.661078	+	0.989373i	−0.337763	+	0.941231i	$0.609670\pi$
$230$	−0.827453	−	15.7153i	−0.0545606	−	1.03623i
$231$	2.72120	−	6.56955i	0.179042	−	0.432244i
$232$	1.33001	−	0.816370i	0.0873192	−	0.0535973i
$233$	3.34376	+	8.07256i	0.219057	+	0.528851i	0.994759	−	0.102249i	$-0.0326038\pi$
$233$	3.34376	+	8.07256i	0.219057	+	0.528851i	−0.775702	+	0.631100i	$0.782604\pi$
$234$	−0.497034	−	1.04140i	−0.0324921	−	0.0680784i
$235$	−1.93504	+	9.72812i	−0.126228	+	0.634593i
$236$	5.91122	+	19.0044i	0.384788	+	1.23708i
$237$	0.458758	−	0.686580i	0.0297995	−	0.0445981i
$238$	−0.187946	−	0.111754i	−0.0121827	−	0.00724392i
$239$	1.66691	−	1.66691i	0.107823	−	0.107823i	−0.651137	−	0.758960i	$-0.725708\pi$
$239$	1.66691	−	1.66691i	0.107823	−	0.107823i	0.758960	+	0.651137i	$0.225708\pi$
$240$	1.22473	+	5.73436i	0.0790562	+	0.370151i
$241$	−15.9006	−	15.9006i	−1.02425	−	1.02425i	−0.999699	−	0.0245466i	$-0.992186\pi$
$241$	−15.9006	−	15.9006i	−1.02425	−	1.02425i	−0.0245466	−	0.999699i	$-0.507814\pi$
$242$	6.53945	+	25.7228i	0.420372	+	1.65352i
$243$	0.831470	+	0.555570i	0.0533388	+	0.0356398i
$244$	−16.7989	−	1.53533i	−1.07544	−	0.0982892i
$245$	7.62206	+	1.51612i	0.486956	+	0.0968615i
$246$	−4.98308	−	1.76323i	−0.317710	−	0.112420i
$247$	6.28579	−	2.60366i	0.399955	−	0.165667i
$248$	4.01627	+	10.8621i	0.255034	+	0.689742i
$249$	−6.49954	−	2.69220i	−0.411892	−	0.170611i
$250$	10.8880	−	12.0983i	0.688617	−	0.765163i
$251$	13.8714	−	9.26854i	0.875552	−	0.585025i	−0.0345530	−	0.999403i	$-0.511001\pi$
$251$	13.8714	−	9.26854i	0.875552	−	0.585025i	0.910105	+	0.414378i	$0.136001\pi$
$252$	−0.739103	+	2.49965i	−0.0465591	+	0.157463i
$253$	8.07985	+	40.6201i	0.507976	+	2.55377i
$254$	−14.4041	−	19.2796i	−0.903794	−	1.20971i
$255$	−0.173907			−0.0108905
$256$	6.53634	+	14.6040i	0.408521	+	0.912749i
$257$	−12.1283			−0.756546			−0.378273	−	0.925694i	$-0.623482\pi$
$257$	−12.1283			−0.756546			−0.378273	+	0.925694i	$0.623482\pi$
$258$	1.50456	+	2.01382i	0.0936695	+	0.125375i
$259$	1.77750	+	8.93612i	0.110449	+	0.555263i
$260$	0.678313	−	2.29406i	0.0420672	−	0.142272i
$261$	0.458759	−	0.306533i	0.0283965	−	0.0189739i
$262$	0.759840	−	0.844303i	0.0469431	−	0.0521612i
$263$	3.11157	+	1.28885i	0.191868	+	0.0794742i	0.476549	−	0.879148i	$-0.341888\pi$
$263$	3.11157	+	1.28885i	0.191868	+	0.0794742i	−0.284681	+	0.958622i	$0.591888\pi$
$264$	−5.35180	−	14.4740i	−0.329380	−	0.890814i
$265$	4.01963	−	1.66499i	0.246924	−	0.102279i
$266$	−14.4887	−	5.12673i	−0.888359	−	0.314340i
$267$	−5.30766	−	1.05576i	−0.324823	−	0.0646114i
$268$	10.1438	+	0.927089i	0.619633	+	0.0566310i
$269$	−13.9645	−	9.33076i	−0.851429	−	0.568907i	0.0515113	−	0.998672i	$-0.483596\pi$
$269$	−13.9645	−	9.33076i	−0.851429	−	0.568907i	−0.902940	+	0.429766i	$0.858596\pi$
$270$	0.510798	+	2.00921i	0.0310862	+	0.122277i
$271$	5.50370	+	5.50370i	0.334326	+	0.334326i	0.854227	−	0.519901i	$-0.174031\pi$
$271$	5.50370	+	5.50370i	0.334326	+	0.334326i	−0.519901	+	0.854227i	$0.674031\pi$
$272$	−0.464066	+	0.0991143i	−0.0281381	+	0.00600969i
$273$	0.751968	−	0.751968i	0.0455112	−	0.0455112i
$274$	−20.0316	−	11.9109i	−1.21016	−	0.719567i
$275$	−8.64206	+	12.9338i	−0.521136	+	0.779935i
$276$	−4.50916	−	14.4969i	−0.271420	−	0.872608i
$277$	−2.11530	+	10.6343i	−0.127096	+	0.638955i	0.863746	+	0.503928i	$0.168112\pi$
$277$	−2.11530	+	10.6343i	−0.127096	+	0.638955i	−0.990842	+	0.135027i	$0.956888\pi$
$278$	8.58813	+	17.9941i	0.515082	+	1.07921i
$279$	1.56687	+	3.78276i	0.0938061	+	0.226468i
$280$	−4.60550	+	2.82690i	−0.275231	+	0.168939i
$281$	−4.69197	+	11.3274i	−0.279900	+	0.675738i	−0.999832	−	0.0183061i	$-0.994173\pi$
$281$	−4.69197	+	11.3274i	−0.279900	+	0.675738i	0.719933	+	0.694044i	$0.244173\pi$
$282$	0.503129	+	9.55560i	0.0299609	+	0.569028i
$283$	−6.79065	−	10.1629i	−0.403662	−	0.604123i	0.572831	−	0.819674i	$-0.305845\pi$
$283$	−6.79065	−	10.1629i	−0.403662	−	0.604123i	−0.976493	+	0.215551i	$0.930845\pi$
$284$	15.7182	−	19.4298i	0.932703	−	1.15294i
$285$	−11.9885	+	2.38466i	−0.710137	+	0.141255i
$286$	−0.901876	+	6.23085i	−0.0533291	+	0.368438i
$287$		−	4.87135i		−	0.287547i
$288$	2.50816	+	5.07042i	0.147795	+	0.298777i
$289$			16.9859i			0.999172i
$290$	1.13204	+	0.163856i	0.0664757	+	0.00962193i
$291$	5.29322	−	1.05289i	0.310294	−	0.0617214i
$292$	−0.852931	−	8.07713i	−0.0499140	−	0.472678i
$293$	17.6107	+	26.3562i	1.02883	+	1.53975i	0.828476	+	0.560024i	$0.189208\pi$
$293$	17.6107	+	26.3562i	1.02883	+	1.53975i	0.200351	+	0.979724i	$0.435792\pi$
$294$	7.48689	−	0.394205i	0.436644	−	0.0229905i
$295$	−5.58251	+	13.4774i	−0.325026	+	0.784682i
$296$	16.0051	+	11.6105i	0.930278	+	0.674846i
$297$	−2.08790	−	5.04064i	−0.121152	−	0.292487i
$298$	−6.08574	+	2.90458i	−0.352538	+	0.168258i
$299$	−1.20836	+	6.07485i	−0.0698815	+	0.351318i
$300$	2.65254	−	5.04762i	0.153144	−	0.291425i
$301$	−1.28707	+	1.92624i	−0.0741857	+	0.111027i
$302$	−12.0651	+	20.2910i	−0.694271	+	1.16761i
$303$	10.9135	−	10.9135i	0.626962	−	0.626962i
$304$	−30.6319	+	13.1960i	−1.75686	+	0.756842i
$305$	−8.74286	−	8.74286i	−0.500614	−	0.500614i
$306$	−0.162600	+	0.0413375i	−0.00929523	+	0.00236311i
$307$	−20.5068	−	13.7022i	−1.17038	−	0.782026i	−0.190519	−	0.981684i	$-0.561017\pi$
$307$	−20.5068	−	13.7022i	−1.17038	−	0.782026i	−0.979866	+	0.199658i	$0.936017\pi$
$308$	10.9298	−	9.09922i	0.622781	−	0.518476i
$309$	−9.33801	−	1.85744i	−0.531221	−	0.105666i
$310$	−2.83149	+	8.00209i	−0.160818	+	0.454488i
$311$	2.93477	−	1.21562i	0.166415	−	0.0689315i	−0.297921	−	0.954591i	$-0.596293\pi$
$311$	2.93477	−	1.21562i	0.166415	−	0.0689315i	0.464336	+	0.885659i	$0.346293\pi$
$312$	0.0889161	−	2.30615i	0.00503388	−	0.130560i
$313$	−20.3429	−	8.42632i	−1.14985	−	0.476284i	−0.275367	−	0.961339i	$-0.588799\pi$
$313$	−20.3429	−	8.42632i	−1.14985	−	0.476284i	−0.874483	+	0.485055i	$0.838799\pi$
$314$	24.8507	+	22.3647i	1.40241	+	1.26211i
$315$	−1.58857	+	1.06145i	−0.0895060	+	0.0598060i
$316$	1.45097	−	0.788729i	0.0816233	−	0.0443695i
$317$	4.58977	+	23.0743i	0.257787	+	1.29598i	0.865132	+	0.501545i	$0.167235\pi$
$317$	4.58977	+	23.0743i	0.257787	+	1.29598i	−0.607345	+	0.794438i	$0.707765\pi$
$318$	3.36253	−	2.51220i	0.188561	−	0.140877i
$319$	−3.01029			−0.168544
$320$	−3.16674	+	11.2917i	−0.177026	+	0.631227i
$321$	−16.4037			−0.915563
$322$	11.2086	−	8.37416i	0.624634	−	0.466674i
$323$	−0.192984	−	0.970196i	−0.0107379	−	0.0539832i
$324$	0.955176	+	1.75717i	0.0530653	+	0.0976204i
$325$	−1.93428	+	1.29244i	−0.107295	+	0.0716919i
$326$	24.7257	+	22.2522i	1.36943	+	1.23243i
$327$	8.41486	+	3.48555i	0.465343	+	0.192751i
$328$	−7.18175	−	7.75776i	−0.396546	−	0.428351i
$329$	−8.14722	+	3.37469i	−0.449171	+	0.186053i
$330$	3.77304	−	10.6630i	0.207699	−	0.586980i
$331$	−2.02225	−	0.402250i	−0.111153	−	0.0221097i	0.139200	−	0.990264i	$-0.455547\pi$
$331$	−2.02225	−	0.402250i	−0.111153	−	0.0221097i	−0.250353	+	0.968155i	$0.580547\pi$
$332$	−9.00226	−	10.8133i	−0.494063	−	0.593456i
$333$	5.81261	+	3.88386i	0.318529	+	0.212834i
$334$	15.7524	−	4.00470i	0.861934	−	0.219127i
$335$	5.27927	+	5.27927i	0.288438	+	0.288438i
$336$	−3.63412	+	3.73783i	−0.198257	+	0.203915i
$337$	0.249824	−	0.249824i	0.0136088	−	0.0136088i	−0.700270	−	0.713878i	$-0.746937\pi$
$337$	0.249824	−	0.249824i	0.0136088	−	0.0136088i	0.713878	+	0.700270i	$0.246937\pi$
$338$	8.91494	−	14.9930i	0.484909	−	0.815512i
$339$	−1.72923	+	2.58797i	−0.0939187	+	0.140559i
$340$	−0.307890	−	0.161797i	−0.0166977	−	0.00877466i
$341$	4.35812	−	21.9098i	0.236006	−	1.18648i
$342$	−10.6422	+	5.07927i	−0.575466	+	0.274656i
$343$	6.13540	+	14.8122i	0.331281	+	0.799782i
$344$	0.790126	+	4.96511i	0.0426007	+	0.267701i
$345$	4.25841	−	10.2807i	0.229265	−	0.553496i
$346$	15.4846	−	0.815306i	0.832456	−	0.0438311i
$347$	−1.91049	−	2.85925i	−0.102560	−	0.153493i	0.776640	−	0.629945i	$-0.216922\pi$
$347$	−1.91049	−	2.85925i	−0.102560	−	0.153493i	−0.879200	+	0.476452i	$0.841922\pi$
$348$	1.09739	−	0.115882i	0.0588262	−	0.00621194i
$349$	−9.98046	+	1.98524i	−0.534242	+	0.106267i	−0.454836	−	0.890575i	$-0.650302\pi$
$349$	−9.98046	+	1.98524i	−0.534242	+	0.106267i	−0.0794055	+	0.996842i	$0.525302\pi$
$350$	5.20081	+	0.752784i	0.277995	+	0.0402380i
$351$		−	0.815952i		−	0.0435523i
$352$	3.99112	−	30.6043i	0.212727	−	1.63122i
$353$			17.8622i			0.950710i	0.879794	+	0.475355i	$0.157680\pi$
$353$			17.8622i			0.950710i	−0.879794	+	0.475355i	$0.842320\pi$
$354$	−2.01600	+	13.9281i	−0.107149	+	0.740269i
$355$	17.9659	−	3.57363i	0.953529	−	0.189669i
$356$	−8.41459	−	6.80720i	−0.445973	−	0.360781i
$357$	−0.0859003	−	0.128559i	−0.00454633	−	0.00680406i
$358$	−1.59954	−	30.3790i	−0.0845382	−	1.60558i
$359$	13.7751	−	33.2560i	0.727021	−	1.75518i	0.0747447	−	0.997203i	$-0.476186\pi$
$359$	13.7751	−	33.2560i	0.727021	−	1.75518i	0.652276	−	0.757981i	$-0.273814\pi$
$360$	−0.964969	+	4.03240i	−0.0508583	+	0.212526i
$361$	−19.3362	−	46.6818i	−1.01770	−	2.45694i
$362$	9.78987	+	20.5120i	0.514544	+	1.07809i
$363$	−3.66133	+	18.4067i	−0.192170	+	0.966103i
$364$	2.03091	−	0.631703i	0.106449	−	0.0331102i
$365$	3.30739	−	4.94985i	0.173117	−	0.259087i
$366$	−10.2526	−	6.09627i	−0.535912	−	0.318657i
$367$	13.1778	−	13.1778i	0.687876	−	0.687876i	−0.273886	−	0.961762i	$-0.588309\pi$
$367$	13.1778	−	13.1778i	0.687876	−	0.687876i	0.961762	+	0.273886i	$0.0883091\pi$
$368$	5.50420	−	29.8608i	0.286926	−	1.55660i
$369$	−2.64292	−	2.64292i	−0.137585	−	0.137585i
$370$	3.57087	+	14.0460i	0.185641	+	0.730214i
$371$	3.21630	+	2.14906i	0.166982	+	0.111574i
$372$	−0.745310	+	8.15487i	−0.0386425	+	0.422811i
$373$	−28.1773	−	5.60480i	−1.45896	−	0.290206i	−0.599077	−	0.800692i	$-0.704466\pi$
$373$	−28.1773	−	5.60480i	−1.45896	−	0.290206i	−0.859886	+	0.510486i	$0.829466\pi$
$374$	0.862929	+	0.305342i	0.0446210	+	0.0157888i
$375$	10.6330	−	4.40433i	0.549085	−	0.227438i
$376$	−7.99944	+	17.3856i	−0.412539	+	0.896595i
$377$	−0.415928	−	0.172283i	−0.0214214	−	0.00887303i
$378$	−1.23299	+	1.37004i	−0.0634179	+	0.0704674i
$379$	2.75031	−	1.83770i	0.141274	−	0.0943961i	−0.482925	−	0.875662i	$-0.660426\pi$
$379$	2.75031	−	1.83770i	0.141274	−	0.0943961i	0.624199	+	0.781266i	$0.285426\pi$
$380$	−23.4434	−	6.93180i	−1.20262	−	0.355594i
$381$	−3.31992	−	16.6904i	−0.170085	−	0.855074i
$382$	17.2438	+	23.0805i	0.882270	+	1.18090i
$383$	−25.5380			−1.30493			−0.652465	−	0.757819i	$-0.726265\pi$
$383$	−25.5380			−1.30493			−0.652465	+	0.757819i	$0.726265\pi$
$384$	−0.276818	+	11.3103i	−0.0141263	+	0.577177i
$385$	10.4239			0.531252
$386$	−3.62284	−	4.84910i	−0.184398	−	0.246813i
$387$	0.346777	+	1.74336i	0.0176277	+	0.0886202i
$388$	10.3508	+	3.06056i	0.525485	+	0.155376i
$389$	−28.1544	+	18.8122i	−1.42749	+	0.953816i	−0.428758	+	0.903420i	$0.641049\pi$
$389$	−28.1544	+	18.8122i	−1.42749	+	0.953816i	−0.998729	+	0.0503966i	$0.983951\pi$
$390$	1.13158	−	1.25736i	0.0572996	−	0.0636689i
$391$	0.831991	+	0.344622i	0.0420756	+	0.0174283i
$392$	13.6218	+	6.26762i	0.688003	+	0.316563i
$393$	0.742044	−	0.307365i	0.0374312	−	0.0155045i
$394$	−4.13172	−	1.46198i	−0.208153	−	0.0736537i
$395$	1.18721	+	0.236152i	0.0597353	+	0.0118821i
$396$	0.993147	−	10.8666i	0.0499075	−	0.546067i
$397$	14.0428	+	9.38309i	0.704787	+	0.470924i	0.855599	−	0.517639i	$-0.173189\pi$
$397$	14.0428	+	9.38309i	0.704787	+	0.470924i	−0.150812	+	0.988562i	$0.548189\pi$
$398$	−6.82518	−	26.8467i	−0.342115	−	1.34570i
$399$	−7.68449	−	7.68449i	−0.384706	−	0.384706i
$400$	9.39226	−	6.46864i	0.469613	−	0.323432i
$401$	−0.633912	+	0.633912i	−0.0316561	+	0.0316561i	−0.722758	−	0.691102i	$-0.757126\pi$
$401$	−0.633912	+	0.633912i	−0.0316561	+	0.0316561i	0.691102	+	0.722758i	$0.257126\pi$
$402$	6.19092	+	3.68116i	0.308775	+	0.183600i
$403$	1.85608	−	2.77782i	0.0924580	−	0.138373i
$404$	29.4750	−	9.16802i	1.46644	−	0.456126i
$405$	−0.285987	+	1.43775i	−0.0142108	+	0.0714426i
$406$	0.438036	+	0.917785i	0.0217394	+	0.0455489i
$407$	−14.5960	−	35.2379i	−0.723498	−	1.74668i
$408$	−0.326331	−	0.0780923i	−0.0161558	−	0.00386614i
$409$	−2.49109	+	6.01403i	−0.123177	+	0.297375i	−0.973425	−	0.229008i	$-0.926452\pi$
$409$	−2.49109	+	6.01403i	−0.123177	+	0.297375i	0.850248	+	0.526382i	$0.176452\pi$
$410$	−0.407422	−	7.73791i	−0.0201212	−	0.382148i
$411$	−9.15543	−	13.7021i	−0.451604	−	0.675873i
$412$	−14.8042	−	11.9762i	−0.729350	−	0.590026i
$413$	−12.7205	+	2.53026i	−0.625933	+	0.124506i
$414$	1.53783	−	10.6245i	0.0755804	−	0.522167i
$415$		−	10.3128i		−	0.506237i
$416$	2.30298	−	4.00015i	0.112913	−	0.196123i
$417$			14.0986i			0.690413i
$418$	63.6741	+	9.21642i	3.11440	+	0.450790i
$419$	−10.6679	+	2.12197i	−0.521160	+	0.103665i	−0.448659	−	0.893703i	$-0.648098\pi$
$419$	−10.6679	+	2.12197i	−0.521160	+	0.103665i	−0.0725012	+	0.997368i	$0.523098\pi$
$420$	−3.79999	+	0.401273i	−0.185421	+	0.0195801i
$421$	−15.1389	−	22.6569i	−0.737824	−	1.10423i	−0.990611	−	0.136710i	$-0.956347\pi$
$421$	−15.1389	−	22.6569i	−0.737824	−	1.10423i	0.252787	−	0.967522i	$-0.418653\pi$
$422$	−17.2379	+	0.907620i	−0.839126	+	0.0441823i
$423$	−2.58931	+	6.25114i	−0.125897	+	0.303941i
$424$	8.29038	−	1.31930i	0.402617	−	0.0640707i
$425$	0.129436	+	0.312485i	0.00627855	+	0.0151578i
$426$	15.9483	−	7.61175i	0.772700	−	0.368791i
$427$	2.14458	−	10.7816i	0.103784	−	0.521756i
$428$	−29.0415	−	15.2614i	−1.40378	−	0.737686i
$429$	−2.47328	+	3.70153i	−0.119411	+	0.178711i
$430$	−1.88335	+	3.16739i	−0.0908233	+	0.152745i
$431$	0.321337	−	0.321337i	0.0154783	−	0.0154783i	−0.699325	−	0.714804i	$-0.746516\pi$
$431$	0.321337	−	0.321337i	0.0154783	−	0.0154783i	0.714804	+	0.699325i	$0.246516\pi$
$432$	0.0562666	+	3.99960i	0.00270713	+	0.192431i
$433$	2.52340	+	2.52340i	0.121267	+	0.121267i	0.765136	−	0.643869i	$-0.222672\pi$
$433$	2.52340	+	2.52340i	0.121267	+	0.121267i	−0.643869	+	0.765136i	$0.722672\pi$
$434$	−7.31407	+	1.85944i	−0.351086	+	0.0892559i
$435$	0.672505	+	0.449354i	0.0322441	+	0.0215449i
$436$	11.6551	+	13.9998i	0.558178	+	0.670469i
$437$	62.0799	+	12.3485i	2.96969	+	0.590707i
$438$	1.91578	−	5.41420i	0.0915395	−	0.258700i
$439$	27.2316	−	11.2797i	1.29969	−	0.538351i	0.377833	−	0.925874i	$-0.376669\pi$
$439$	27.2316	−	11.2797i	1.29969	−	0.538351i	0.921860	+	0.387523i	$0.126669\pi$
$440$	16.6004	−	15.3678i	0.791393	−	0.732632i
$441$	4.89782	+	2.02874i	0.233230	+	0.0966069i
$442$	0.101755	+	0.0915753i	0.00483997	+	0.00435579i
$443$	−3.60567	+	2.40923i	−0.171311	+	0.114466i	−0.638270	−	0.769813i	$-0.720350\pi$
$443$	−3.60567	+	2.40923i	−0.171311	+	0.114466i	0.466959	+	0.884279i	$0.345350\pi$
$444$	6.67742	+	12.2840i	0.316896	+	0.582971i
$445$	−1.54766	−	7.78061i	−0.0733661	−	0.368836i
$446$	−2.52181	+	1.88408i	−0.119411	+	0.0892138i
$447$	−4.76827			−0.225532
$448$	−9.91149	+	3.23651i	−0.468274	+	0.152911i
$449$	−5.19543			−0.245188			−0.122594	−	0.992457i	$-0.539121\pi$
$449$	−5.19543			−0.245188			−0.122594	+	0.992457i	$0.539121\pi$
$450$	3.23009	−	2.41325i	0.152268	−	0.113762i
$451$	3.97837	+	20.0006i	0.187334	+	0.941792i
$452$	−5.46923	+	2.97301i	−0.257251	+	0.139839i
$453$	−13.8795	+	9.27395i	−0.652114	+	0.435728i
$454$	−17.5529	−	15.7969i	−0.823797	−	0.741386i
$455$	1.44026	+	0.596575i	0.0675204	+	0.0279679i
$456$	−23.5669	−	0.908649i	−1.10362	−	0.0425514i
$457$	−4.82455	+	1.99840i	−0.225683	+	0.0934810i	−0.492660	−	0.870222i	$-0.663975\pi$
$457$	−4.82455	+	1.99840i	−0.225683	+	0.0934810i	0.266977	+	0.963703i	$0.413975\pi$
$458$	−8.49458	+	24.0066i	−0.396926	+	1.12175i
$459$	−0.116354	−	0.0231442i	−0.00543092	−	0.00108028i
$460$	17.1040	−	14.2394i	0.797480	−	0.663917i
$461$	−14.1377	−	9.44653i	−0.658460	−	0.439969i	0.180932	−	0.983496i	$-0.442089\pi$
$461$	−14.1377	−	9.44653i	−0.658460	−	0.439969i	−0.839392	+	0.543527i	$0.817089\pi$
$462$	9.74620	−	2.47775i	0.453434	−	0.115276i
$463$	19.4280	+	19.4280i	0.902894	+	0.902894i	0.995686	−	0.0927914i	$-0.0295790\pi$
$463$	19.4280	+	19.4280i	0.902894	+	0.902894i	−0.0927914	+	0.995686i	$0.529579\pi$
$464$	2.05066	+	0.815809i	0.0951996	+	0.0378730i
$465$	−4.24414	+	4.24414i	−0.196817	+	0.196817i
$466$	−6.31542	+	10.6212i	−0.292556	+	0.492016i
$467$	0.891747	−	1.33459i	0.0412651	−	0.0617577i	−0.810263	−	0.586066i	$-0.800676\pi$
$467$	0.891747	−	1.33459i	0.0412651	−	0.0617577i	0.851529	+	0.524308i	$0.175676\pi$
$468$	0.759132	−	1.44459i	0.0350909	−	0.0667760i
$469$	−1.29498	+	6.51032i	−0.0597968	+	0.300619i
$470$	−12.6592	+	6.04195i	−0.583927	+	0.278694i
$471$	9.04679	+	21.8409i	0.416854	+	1.00638i
$472$	−16.5274	+	22.7831i	−0.760734	+	1.04868i
$473$	3.71128	−	8.95983i	0.170645	−	0.411973i
$474$	1.16616	−	0.0614015i	0.0535635	−	0.00282027i
$475$	13.2077	+	19.7667i	0.606011	+	0.906959i
$476$	−0.0324739	−	0.307523i	−0.00148844	−	0.0140953i
$477$	2.91095	−	0.579023i	0.133283	−	0.0265117i
$478$	3.29943	+	0.477571i	0.150912	+	0.0218436i
$479$			20.2808i			0.926653i	0.886188	+	0.463327i	$0.153344\pi$
$479$			20.2808i			0.926653i	−0.886188	+	0.463327i	$0.846656\pi$
$480$	−5.46001	+	6.24131i	−0.249214	+	0.284876i
$481$		−	5.70413i		−	0.260086i
$482$	4.55554	−	31.4731i	0.207499	−	1.43356i
$483$	9.70334	−	1.93011i	0.441517	−	0.0878233i
$484$	−23.6071	+	29.1815i	−1.07305	+	1.32643i
$485$	4.39538	+	6.57815i	0.199584	+	0.298698i
$486$	0.0743592	+	1.41226i	0.00337300	+	0.0640613i
$487$	−0.686440	+	1.65721i	−0.0311056	+	0.0750955i	−0.938669	−	0.344820i	$-0.887940\pi$
$487$	−0.686440	+	1.65721i	−0.0311056	+	0.0750955i	0.907563	+	0.419915i	$0.137940\pi$
$488$	−12.4798	−	20.3317i	−0.564932	−	0.920371i
$489$	9.00127	+	21.7310i	0.407052	+	0.982709i
$490$	4.73391	+	9.91862i	0.213856	+	0.448078i
$491$	2.30637	−	11.5949i	0.104085	−	0.523270i	−0.893202	−	0.449656i	$-0.851547\pi$
$491$	2.30637	−	11.5949i	0.104085	−	0.523270i	0.997287	−	0.0736143i	$-0.0234534\pi$
$492$	−2.22023	−	7.13799i	−0.100096	−	0.321805i
$493$	−0.0363649	+	0.0544240i	−0.00163779	+	0.00245113i
$494$	8.27030	+	4.91758i	0.372098	+	0.221252i
$495$	5.65543	−	5.65543i	0.254193	−	0.254193i
$496$	−8.90652	+	13.7442i	−0.399915	+	0.617134i
$497$	11.5159	+	11.5159i	0.516559	+	0.516559i
$498$	−2.45135	−	9.64234i	−0.109848	−	0.432084i
$499$	3.10589	+	2.07529i	0.139039	+	0.0929026i	0.623144	−	0.782107i	$-0.285855\pi$
$499$	3.10589	+	2.07529i	0.139039	+	0.0929026i	−0.484106	+	0.875010i	$0.660855\pi$
$500$	22.9226	+	2.09500i	1.02513	+	0.0936911i
$501$	11.2721	+	2.24217i	0.503601	+	0.100173i
$502$	22.2419	+	7.87015i	0.992704	+	0.351262i
$503$	2.14108	−	0.886863i	0.0954659	−	0.0395433i	−0.334439	−	0.942417i	$-0.608547\pi$
$503$	2.14108	−	0.886863i	0.0954659	−	0.0395433i	0.429905	+	0.902874i	$0.358547\pi$
$504$	−3.45755	+	1.27844i	−0.154012	+	0.0569462i
$505$	20.9028	+	8.65821i	0.930160	+	0.385285i
$506$	−39.1810	+	43.5363i	−1.74181	+	1.93542i
$507$	10.2555	−	6.85253i	0.455464	−	0.304331i
$508$	9.65044	−	32.6379i	0.428169	−	1.44807i
$509$	−0.803882	−	4.04139i	−0.0356314	−	0.179131i	0.958871	−	0.283841i	$-0.0916087\pi$
$509$	−0.803882	−	4.04139i	−0.0356314	−	0.179131i	−0.994503	+	0.104710i	$0.966609\pi$
$510$	−0.147201	−	0.197026i	−0.00651817	−	0.00872444i
$511$	5.29280			0.234140
$512$	−11.0128	+	19.7666i	−0.486702	+	0.873568i
$513$	−8.33835			−0.368147
$514$	−10.2659	−	13.7407i	−0.452808	−	0.606074i
$515$	−2.72287	−	13.6888i	−0.119984	−	0.603200i
$516$	−1.00802	+	3.40913i	−0.0443756	+	0.150079i
$517$	30.6945	−	20.5094i	1.34994	−	0.902003i
$518$	−8.61952	+	9.57765i	−0.378720	+	0.420818i
$519$	10.1298	+	4.19590i	0.444649	+	0.184180i
$520$	3.17318	−	1.17329i	0.139153	−	0.0514522i
$521$	−14.5735	+	6.03654i	−0.638477	+	0.264466i	−0.678350	−	0.734739i	$-0.737305\pi$
$521$	−14.5735	+	6.03654i	−0.638477	+	0.264466i	0.0398732	+	0.999205i	$0.487305\pi$
$522$	0.735593	+	0.260285i	0.0321960	+	0.0113924i
$523$	−39.0960	−	7.77669i	−1.70955	−	0.340051i	−0.759111	−	0.650961i	$-0.774366\pi$
$523$	−39.0960	−	7.77669i	−1.70955	−	0.340051i	−0.950439	+	0.310910i	$0.899366\pi$
$524$	1.59970	+	0.146203i	0.0698831	+	0.00638693i
$525$	3.08962	+	2.06442i	0.134842	+	0.0900985i
$526$	1.17355	+	4.61615i	0.0511693	+	0.201274i
$527$	−0.343466	−	0.343466i	−0.0149616	−	0.0149616i
$528$	11.8682	−	18.3146i	0.516497	−	0.797039i
$529$	−24.4821	+	24.4821i	−1.06444	+	1.06444i
$530$	5.28869	+	3.14469i	0.229726	+	0.136597i
$531$	−5.52863	+	8.27418i	−0.239922	+	0.359069i
$532$	−6.45548	−	20.7542i	−0.279880	−	0.899810i
$533$	−0.594976	+	2.99115i	−0.0257713	+	0.129561i
$534$	−3.29648	−	6.90687i	−0.142653	−	0.298890i
$535$	−9.20219	−	22.2161i	−0.397845	−	0.960484i
$536$	7.53576	+	12.2770i	0.325495	+	0.530288i
$537$	8.23189	−	19.8735i	0.355232	−	0.857607i
$538$	−1.24886	−	23.7188i	−0.0538421	−	1.02259i
$539$	−16.0693	−	24.0494i	−0.692153	−	1.03588i
$540$	−1.84396	+	2.27937i	−0.0793512	+	0.0980886i
$541$	20.2828	−	4.03449i	0.872024	−	0.173456i	0.261260	−	0.965269i	$-0.415862\pi$
$541$	20.2828	−	4.03449i	0.872024	−	0.173456i	0.610765	+	0.791812i	$0.290862\pi$
$542$	−1.57682	+	10.8939i	−0.0677302	+	0.467932i
$543$			16.0715i			0.689692i
$544$	−0.505092	−	0.441864i	−0.0216556	−	0.0189447i
$545$			13.3519i			0.571932i
$546$	1.48843	+	0.215440i	0.0636988	+	0.00921999i
$547$	32.3921	−	6.44318i	1.38498	−	0.275490i	0.554338	−	0.832292i	$-0.312971\pi$
$547$	32.3921	−	6.44318i	1.38498	−	0.275490i	0.830646	+	0.556801i	$0.187971\pi$
$548$	−3.46113	−	32.7764i	−0.147852	−	1.40014i
$549$	−4.68594	−	7.01300i	−0.199991	−	0.299307i
$550$	−21.9681	+	1.15668i	−0.936722	+	0.0493210i
$551$	−1.76059	+	4.25044i	−0.0750036	+	0.181075i
$552$	12.6073	−	17.3793i	0.536603	−	0.739710i
$553$	0.411845	+	0.994283i	0.0175134	+	0.0422812i
$554$	−13.8385	+	6.60477i	−0.587941	+	0.280610i
$555$	−1.99927	+	10.0510i	−0.0848643	+	0.426642i
$556$	−13.1169	+	24.9606i	−0.556279	+	1.05857i
$557$	−12.4462	+	18.6271i	−0.527364	+	0.789256i	−0.995536	−	0.0943813i	$-0.969913\pi$
$557$	−12.4462	+	18.6271i	−0.527364	+	0.789256i	0.468172	+	0.883637i	$0.344913\pi$
$558$	−2.95938	+	4.97703i	−0.125280	+	0.210694i
$559$	1.02557	−	1.02557i	0.0433768	−	0.0433768i
$560$	−7.10095	−	2.82495i	−0.300070	−	0.119376i
$561$	0.457679	+	0.457679i	0.0193232	+	0.0193232i
$562$	−16.8047	+	4.27223i	−0.708864	+	0.180213i
$563$	11.8739	+	7.93391i	0.500427	+	0.334375i	0.780031	−	0.625741i	$-0.215203\pi$
$563$	11.8739	+	7.93391i	0.500427	+	0.334375i	−0.279604	+	0.960115i	$0.590203\pi$
$564$	−10.4000	+	8.65821i	−0.437920	+	0.364577i
$565$	−4.47505	−	0.890143i	−0.188267	−	0.0374486i
$566$	5.76611	−	16.2956i	0.242368	−	0.684957i
$567$	−1.20411	+	0.498758i	−0.0505678	+	0.0209459i
$568$	35.3171	+	1.36169i	1.48187	+	0.0571353i
$569$	13.2860	+	5.50325i	0.556979	+	0.230708i	0.643373	−	0.765553i	$-0.277534\pi$
$569$	13.2860	+	5.50325i	0.556979	+	0.230708i	−0.0863943	+	0.996261i	$0.527534\pi$
$570$	−12.8492	−	11.5638i	−0.538192	−	0.484352i
$571$	−26.4868	+	17.6979i	−1.10844	+	0.740635i	−0.968373	−	0.249507i	$-0.919731\pi$
$571$	−26.4868	+	17.6979i	−1.10844	+	0.740635i	−0.140066	+	0.990142i	$0.544731\pi$
$572$	−7.82254	+	4.25224i	−0.327077	+	0.177795i
$573$	3.97443	+	19.9808i	0.166034	+	0.834711i
$574$	5.51893	−	4.12328i	0.230356	−	0.172102i
$575$	−21.6424			−0.902551
$576$	−3.62147	+	7.13337i	−0.150895	+	0.297224i
$577$	−14.6968			−0.611836			−0.305918	−	0.952058i	$-0.598963\pi$
$577$	−14.6968			−0.611836			−0.305918	+	0.952058i	$0.598963\pi$
$578$	−19.2440	+	14.3775i	−0.800444	+	0.598025i
$579$	−0.835008	−	4.19787i	−0.0347018	−	0.174458i
$580$	0.772561	+	1.42122i	0.0320788	+	0.0590131i
$581$	7.62366	−	5.09397i	0.316283	−	0.211333i
$582$	5.67323	+	5.10569i	0.235163	+	0.211638i
$583$	−14.9605	−	6.19684i	−0.619600	−	0.256647i
$584$	8.42893	−	7.80309i	0.348792	−	0.322894i
$585$	1.10507	−	0.457736i	0.0456891	−	0.0189251i
$586$	−14.9537	+	42.2607i	−0.617730	+	1.74577i
$587$	−13.1483	−	2.61536i	−0.542688	−	0.107947i	−0.0838687	−	0.996477i	$-0.526728\pi$
$587$	−13.1483	−	2.61536i	−0.542688	−	0.107947i	−0.458820	+	0.888529i	$0.651728\pi$
$588$	6.78378	+	8.14851i	0.279758	+	0.336039i
$589$	−28.3870	−	18.9676i	−1.16967	−	0.781547i
$590$	−19.9942	+	5.08309i	−0.823150	+	0.209267i
$591$	−2.19138	−	2.19138i	−0.0901412	−	0.0901412i
$592$	0.393347	+	27.9603i	0.0161665	+	1.14916i
$593$	12.6239	−	12.6239i	0.518402	−	0.518402i	−0.398686	−	0.917088i	$-0.630534\pi$
$593$	12.6239	−	12.6239i	0.518402	−	0.518402i	0.917088	+	0.398686i	$0.130534\pi$
$594$	3.94345	−	6.63203i	0.161802	−	0.272116i
$595$	0.125923	−	0.188457i	0.00516235	−	0.00772600i
$596$	−8.44189	−	4.43623i	−0.345793	−	0.181715i
$597$	3.82130	−	19.2110i	0.156396	−	0.786254i
$598$	−7.90523	+	3.77297i	−0.323269	+	0.154288i
$599$	5.86526	+	14.1600i	0.239648	+	0.578562i	0.997246	−	0.0741593i	$-0.0236273\pi$
$599$	5.86526	+	14.1600i	0.239648	+	0.578562i	−0.757598	+	0.652721i	$0.773627\pi$
$600$	7.96384	−	1.26733i	0.325122	−	0.0517386i
$601$	3.46949	−	8.37608i	0.141523	−	0.341668i	−0.837186	−	0.546918i	$-0.815801\pi$
$601$	3.46949	−	8.37608i	0.141523	−	0.341668i	0.978709	+	0.205250i	$0.0658009\pi$
$602$	−3.27174	+	0.172266i	−0.133346	+	0.00702103i
$603$	2.82955	+	4.23472i	0.115228	+	0.172451i
$604$	−33.2008	+	3.50594i	−1.35092	+	0.142655i
$605$	−26.9828	+	5.36722i	−1.09701	+	0.218209i
$606$	21.6018	+	3.12672i	0.877513	+	0.127014i
$607$		−	17.3111i		−	0.702638i	−0.936256	−	0.351319i	$-0.885733\pi$
$607$		−	17.3111i		−	0.702638i	0.936256	−	0.351319i	$-0.114267\pi$
$608$	−40.8782	−	23.5345i	−1.65783	−	0.954450i
$609$			0.719098i			0.0291393i
$610$	2.50484	−	17.3054i	0.101418	−	0.700674i
$611$	5.41480	−	1.07707i	0.219060	−	0.0435736i
$612$	−0.184463	−	0.149226i	−0.00745649	−	0.00603212i
$613$	−10.9075	−	16.3242i	−0.440550	−	0.659330i	0.543048	−	0.839702i	$-0.317270\pi$
$613$	−10.9075	−	16.3242i	−0.440550	−	0.659330i	−0.983599	+	0.180371i	$0.942270\pi$
$614$	−1.83394	−	34.8309i	−0.0740120	−	1.40566i
$615$	2.09676	−	5.06204i	0.0845497	−	0.204121i
$616$	19.5602	+	4.68083i	0.788102	+	0.188596i
$617$	3.03136	+	7.31836i	0.122038	+	0.294626i	0.973078	−	0.230474i	$-0.0740278\pi$
$617$	3.03136	+	7.31836i	0.122038	+	0.294626i	−0.851040	+	0.525100i	$0.824028\pi$
$618$	−5.79965	−	12.1516i	−0.233296	−	0.488808i
$619$	6.62448	−	33.3035i	0.266260	−	1.33858i	−0.583801	−	0.811897i	$-0.698435\pi$
$619$	6.62448	−	33.3035i	0.266260	−	1.33858i	0.850061	−	0.526684i	$-0.176565\pi$
$620$	−11.4625	+	3.56536i	−0.460347	+	0.143188i
$621$	4.21732	−	6.31166i	0.169235	−	0.253278i
$622$	3.86131	+	2.29596i	0.154825	+	0.0920597i
$623$	4.98728	−	4.98728i	0.199811	−	0.199811i
$624$	2.68798	−	1.85127i	0.107605	−	0.0741101i
$625$	1.84981	+	1.84981i	0.0739924	+	0.0739924i
$626$	−7.67249	−	30.1796i	−0.306654	−	1.20622i
$627$	37.8265	+	25.2749i	1.51065	+	1.00938i
$628$	−4.30327	+	47.0846i	−0.171719	+	1.87888i
$629$	−0.813401	−	0.161795i	−0.0324324	−	0.00645121i
$630$	−2.54718	−	0.901304i	−0.101482	−	0.0359088i
$631$	10.9031	−	4.51622i	0.434046	−	0.179788i	−0.154952	−	0.987922i	$-0.549522\pi$
$631$	10.9031	−	4.51622i	0.434046	−	0.179788i	0.588999	+	0.808134i	$0.299522\pi$
$632$	2.12173	+	0.976247i	0.0843979	+	0.0388330i
$633$	−11.2768	−	4.67099i	−0.448211	−	0.185655i
$634$	−22.2568	+	24.7308i	−0.883931	+	0.982187i
$635$	20.7420	−	13.8593i	0.823119	−	0.549991i
$636$	5.69233	+	1.68312i	0.225716	+	0.0667401i
$637$	−0.843894	−	4.24254i	−0.0334363	−	0.168096i
$638$	−2.54802	−	3.41047i	−0.100877	−	0.135022i
$639$	12.4958			0.494325
$640$	−15.4733	+	5.97001i	−0.611634	+	0.235985i
$641$	30.7880			1.21605			0.608027	−	0.793917i	$-0.291961\pi$
$641$	30.7880			1.21605			0.608027	+	0.793917i	$0.291961\pi$
$642$	−13.8846	−	18.5843i	−0.547983	−	0.733464i
$643$	1.48213	+	7.45119i	0.0584496	+	0.293846i	0.998943	−	0.0459659i	$-0.0146365\pi$
$643$	1.48213	+	7.45119i	0.0584496	+	0.293846i	−0.940493	+	0.339812i	$0.889637\pi$
$644$	18.9748	+	5.61051i	0.747712	+	0.221085i
$645$	−2.16656	+	1.44765i	−0.0853084	+	0.0570012i
$646$	0.935823	−	1.03985i	0.0368195	−	0.0409123i
$647$	−5.77856	−	2.39356i	−0.227179	−	0.0941005i	0.266191	−	0.963920i	$-0.414235\pi$
$647$	−5.77856	−	2.39356i	−0.227179	−	0.0941005i	−0.493369	+	0.869820i	$0.664235\pi$
$648$	−1.18227	+	2.56948i	−0.0464438	+	0.100939i
$649$	50.1608	−	20.7773i	1.96898	−	0.815579i
$650$	−3.10150	−	1.09745i	−0.121651	−	0.0430454i
$651$	−5.23380	−	1.04107i	−0.205129	−	0.0408027i
$652$	−4.28161	+	46.8477i	−0.167681	+	1.83470i
$653$	29.7678	+	19.8902i	1.16490	+	0.778363i	0.978931	−	0.204192i	$-0.0654566\pi$
$653$	29.7678	+	19.8902i	1.16490	+	0.778363i	0.185972	+	0.982555i	$0.440457\pi$
$654$	3.17373	+	12.4838i	0.124103	+	0.488155i
$655$	0.832550	+	0.832550i	0.0325304	+	0.0325304i
$656$	2.71017	−	14.7029i	0.105814	−	0.574053i
$657$	2.87157	−	2.87157i	0.112031	−	0.112031i
$658$	−10.7194	−	6.37383i	−0.417886	−	0.248478i
$659$	−11.8597	+	17.7493i	−0.461988	+	0.691415i	−0.987187	−	0.159565i	$-0.948991\pi$
$659$	−11.8597	+	17.7493i	−0.461988	+	0.691415i	0.525199	+	0.850979i	$0.323991\pi$
$660$	15.2742	−	4.75094i	0.594546	−	0.184930i
$661$	−2.52463	+	12.6922i	−0.0981969	+	0.493669i	0.900118	+	0.435646i	$0.143480\pi$
$661$	−2.52463	+	12.6922i	−0.0981969	+	0.493669i	−0.998315	+	0.0580236i	$0.981520\pi$
$662$	−1.25598	−	2.63156i	−0.0488150	−	0.102279i
$663$	0.0370433	+	0.0894305i	0.00143864	+	0.00347319i
$664$	4.63094	−	19.3517i	0.179716	−	0.750993i
$665$	6.09650	−	14.7183i	0.236412	−	0.570749i
$666$	0.519828	+	9.87276i	0.0201429	+	0.382562i
$667$	−2.32688	−	3.48243i	−0.0900973	−	0.134840i
$668$	17.8705	+	14.4568i	0.691430	+	0.559350i
$669$	−2.18313	+	0.434252i	−0.0844047	+	0.0167891i
$670$	−1.51252	+	10.4497i	−0.0584338	+	0.403705i
$671$			46.0180i			1.77650i
$672$	−7.31077	−	0.953398i	−0.282019	−	0.0367781i
$673$			36.4147i			1.40368i	0.712334	+	0.701841i	$0.247638\pi$
$673$			36.4147i			1.40368i	−0.712334	+	0.701841i	$0.752362\pi$
$674$	0.494494	+	0.0715749i	0.0190472	+	0.00275696i
$675$	2.79629	−	0.556217i	0.107629	−	0.0214088i
$676$	24.5320	−	2.59054i	0.943540	−	0.0996362i
$677$	11.6282	+	17.4028i	0.446908	+	0.668845i	0.984705	−	0.174229i	$-0.0557435\pi$
$677$	11.6282	+	17.4028i	0.446908	+	0.668845i	−0.537797	+	0.843074i	$0.680743\pi$
$678$	−4.39569	+	0.231445i	−0.168815	+	0.00888859i
$679$	−2.69176	+	6.49848i	−0.103300	+	0.249389i
$680$	−0.0773034	−	0.485770i	−0.00296445	−	0.0186284i
$681$	−6.39004	−	15.4269i	−0.244867	−	0.591161i
$682$	28.5112	−	13.6077i	1.09175	−	0.521066i
$683$	−0.00824084	+	0.0414295i	−0.000315327	+	0.00158526i	−0.980943	−	0.194298i	$-0.937757\pi$
$683$	−0.00824084	+	0.0414295i	−0.000315327	+	0.00158526i	0.980627	+	0.195883i	$0.0627572\pi$
$684$	−14.7625	−	7.75770i	−0.564457	−	0.296623i
$685$	13.4211	−	20.0862i	0.512796	−	0.767453i
$686$	−11.5880	+	19.4886i	−0.442433	+	0.744077i
$687$	−12.7326	+	12.7326i	−0.485778	+	0.485778i
$688$	−4.95636	+	5.09781i	−0.188960	+	0.194352i
$689$	−1.71242	−	1.71242i	−0.0652379	−	0.0652379i
$690$	15.2519	−	3.87745i	0.580629	−	0.147612i
$691$	24.1778	+	16.1551i	0.919767	+	0.614569i	0.922738	−	0.385427i	$-0.125946\pi$
$691$	24.1778	+	16.1551i	0.919767	+	0.614569i	−0.00297122	+	0.999996i	$0.500946\pi$
$692$	14.0304	+	16.8530i	0.533355	+	0.640653i
$693$	6.97419	+	1.38725i	0.264928	+	0.0526974i
$694$	1.62224	−	4.58463i	0.0615795	−	0.174030i
$695$	−19.0943	+	7.90911i	−0.724287	+	0.300010i
$696$	1.06016	+	1.14519i	0.0401851	+	0.0434081i
$697$	0.409657	+	0.169685i	0.0155169	+	0.00642729i
$698$	−10.6970	−	9.62686i	−0.404886	−	0.364382i
$699$	−7.26511	+	4.85439i	−0.274792	+	0.183610i
$700$	3.54929	+	6.52937i	0.134151	+	0.246787i
$701$	−5.30350	−	26.6625i	−0.200310	−	1.00703i	−0.941828	−	0.336095i	$-0.890894\pi$
$701$	−5.30350	−	26.6625i	−0.200310	−	1.00703i	0.741518	−	0.670933i	$-0.234106\pi$
$702$	0.924422	−	0.690651i	0.0348901	−	0.0260669i
$703$	−58.2915			−2.19850
$704$	38.0510	−	21.3829i	1.43410	−	0.805899i
$705$	−9.91871			−0.373560
$706$	−20.2368	+	15.1192i	−0.761621	+	0.569019i
$707$	3.92431	+	19.7288i	0.147589	+	0.741979i
$708$	−17.4861	+	9.50522i	−0.657166	+	0.357228i
$709$	21.1208	−	14.1125i	0.793209	−	0.530006i	−0.0916902	−	0.995788i	$-0.529227\pi$
$709$	21.1208	−	14.1125i	0.793209	−	0.530006i	0.884899	+	0.465782i	$0.154227\pi$
$710$	19.2556	+	17.3293i	0.722651	+	0.650358i
$711$	0.762886	+	0.315998i	0.0286105	+	0.0118508i
$712$	0.589718	−	15.2951i	0.0221006	−	0.573207i
$713$	28.7148	−	11.8941i	1.07538	−	0.445437i
$714$	0.0729401	−	0.206136i	0.00272971	−	0.00771446i
$715$	−6.40058	−	1.27316i	−0.239368	−	0.0476133i
$716$	33.0636	−	27.5261i	1.23565	−	1.02870i
$717$	1.96007	+	1.30968i	0.0732003	+	0.0489109i
$718$	49.3367	−	12.5427i	1.84123	−	0.468091i
$719$	−17.7440	−	17.7440i	−0.661738	−	0.661738i	0.294052	−	0.955789i	$-0.404996\pi$
$719$	−17.7440	−	17.7440i	−0.661738	−	0.661738i	−0.955789	+	0.294052i	$0.904996\pi$
$720$	−5.38524	+	2.31992i	−0.200696	+	0.0864583i
$721$	8.77436	−	8.77436i	0.326774	−	0.326774i
$722$	36.5207	−	61.4199i	1.35916	−	2.28581i
$723$	12.4930	−	18.6971i	0.464619	−	0.695352i
$724$	−14.9523	+	28.4534i	−0.555698	+	1.05746i
$725$	0.306890	−	1.54284i	0.0113976	−	0.0572996i
$726$	−23.9528	+	11.4321i	−0.888970	+	0.424284i
$727$	0.754099	+	1.82056i	0.0279680	+	0.0675207i	0.937246	−	0.348668i	$-0.113366\pi$
$727$	0.754099	+	1.82056i	0.0279680	+	0.0675207i	−0.909279	+	0.416188i	$0.863366\pi$
$728$	2.43472	+	1.76620i	0.0902366	+	0.0654597i
$729$	−0.382683	+	0.923880i	−0.0141735	+	0.0342178i
$730$	8.40736	−	0.442671i	0.311171	−	0.0163840i
$731$	−0.117154	−	0.175334i	−0.00433312	−	0.00648496i
$732$	−1.77148	−	16.7756i	−0.0654757	−	0.620046i
$733$	−28.5802	+	5.68496i	−1.05564	+	0.209979i	−0.692248	−	0.721659i	$-0.743380\pi$
$733$	−28.5802	+	5.68496i	−1.05564	+	0.209979i	−0.363387	+	0.931638i	$0.618380\pi$
$734$	26.0838	+	3.77547i	0.962771	+	0.139355i
$735$			7.77139i			0.286652i
$736$	38.4894	−	19.0394i	1.41874	−	0.701800i
$737$		−	27.7874i		−	1.02356i
$738$	0.757201	−	5.23133i	0.0278730	−	0.192568i
$739$	2.12447	−	0.422584i	0.0781500	−	0.0155450i	−0.155860	−	0.987779i	$-0.549815\pi$
$739$	2.12447	−	0.422584i	0.0781500	−	0.0155450i	0.234010	+	0.972234i	$0.424815\pi$
$740$	−12.8907	+	15.9346i	−0.473870	+	0.585766i
$741$	3.77993	+	5.65706i	0.138859	+	0.207817i
$742$	0.287637	+	5.46291i	0.0105595	+	0.200550i
$743$	−1.20520	+	2.90961i	−0.0442145	+	0.106743i	−0.944444	−	0.328673i	$-0.893399\pi$
$743$	−1.20520	+	2.90961i	−0.0442145	+	0.106743i	0.900229	+	0.435416i	$0.143399\pi$
$744$	−9.86982	+	6.05819i	−0.361845	+	0.222104i
$745$	−2.67492	−	6.45784i	−0.0980017	−	0.236597i
$746$	−17.5003	−	36.6672i	−0.640733	−	1.34248i
$747$	1.37247	−	6.89987i	0.0502161	−	0.252453i
$748$	0.384480	+	1.23610i	0.0140580	+	0.0451961i
$749$	11.8776	−	17.7761i	0.433999	−	0.649526i
$750$	13.9900	+	8.31853i	0.510841	+	0.303750i
$751$	−33.9762	+	33.9762i	−1.23981	+	1.23981i	−0.279733	+	0.960078i	$0.590246\pi$
$751$	−33.9762	+	33.9762i	−1.23981	+	1.23981i	−0.960078	+	0.279733i	$0.909754\pi$
$752$	−26.4678	+	5.65295i	−0.965182	+	0.206142i
$753$	11.7966	+	11.7966i	0.429893	+	0.429893i
$754$	−0.156870	−	0.617047i	−0.00571288	−	0.0224715i
$755$	−20.3462	−	13.5949i	−0.740474	−	0.494769i
$756$	−2.59582	−	0.237243i	−0.0944089	−	0.00862844i
$757$	−9.29355	−	1.84860i	−0.337780	−	0.0671886i	0.0232862	−	0.999729i	$-0.492587\pi$
$757$	−9.29355	−	1.84860i	−0.337780	−	0.0671886i	−0.361066	+	0.932540i	$0.617587\pi$
$758$	4.40995	+	1.56043i	0.160177	+	0.0566775i
$759$	−38.2633	+	15.8492i	−1.38887	+	0.575289i
$760$	−11.9900	−	32.4272i	−0.434924	−	1.17626i
$761$	−30.7972	−	12.7566i	−1.11640	−	0.462427i	−0.253262	−	0.967398i	$-0.581503\pi$
$761$	−30.7972	−	12.7566i	−1.11640	−	0.462427i	−0.863137	+	0.504971i	$0.831503\pi$
$762$	16.0991	−	17.8886i	0.583207	−	0.648036i
$763$	−9.87025	+	6.59509i	−0.357327	+	0.238758i
$764$	−11.5530	+	39.0723i	−0.417972	+	1.41359i
$765$	−0.0339275	−	0.170565i	−0.00122665	−	0.00616680i
$766$	−21.6162	−	28.9329i	−0.781027	−	1.04539i
$767$	8.11976			0.293188
$768$	−13.0482	+	9.25984i	−0.470836	+	0.334136i
$769$	45.6166			1.64498			0.822488	−	0.568783i	$-0.192586\pi$
$769$	45.6166			1.64498			0.822488	+	0.568783i	$0.192586\pi$
$770$	8.82318	+	11.8096i	0.317965	+	0.425590i
$771$	−2.36612	−	11.8953i	−0.0852139	−	0.428399i
$772$	2.42722	−	8.20890i	0.0873577	−	0.295445i
$773$	31.6714	−	21.1621i	1.13914	−	0.761149i	0.164822	−	0.986323i	$-0.447295\pi$
$773$	31.6714	−	21.1621i	1.13914	−	0.761149i	0.974319	+	0.225174i	$0.0722951\pi$
$774$	−1.68160	+	1.86852i	−0.0604438	+	0.0671626i
$775$	10.7849	+	4.46726i	0.387406	+	0.160469i
$776$	5.29390	+	14.3174i	0.190040	+	0.513966i
$777$	−8.41764	+	3.48670i	−0.301981	+	0.125085i
$778$	−45.1440	−	15.9739i	−1.61849	−	0.572692i
$779$	30.5670	+	6.08016i	1.09518	+	0.217844i
$780$	2.38232	+	0.217730i	0.0853006	+	0.00779600i
$781$	−56.6865	−	37.8767i	−2.02840	−	1.35533i
$782$	0.313792	+	1.23429i	0.0112212	+	0.0441382i
$783$	0.390142	+	0.390142i	0.0139426	+	0.0139426i
$784$	4.42913	+	20.7378i	0.158183	+	0.740634i
$785$	−24.5048	+	24.5048i	−0.874613	+	0.874613i
$786$	0.976317	+	0.580525i	0.0348241	+	0.0207066i
$787$	−0.653027	+	0.977324i	−0.0232779	+	0.0348378i	−0.842926	−	0.538029i	$-0.819169\pi$
$787$	−0.653027	+	0.977324i	−0.0232779	+	0.0348378i	0.819648	+	0.572867i	$0.194169\pi$
$788$	−1.84090	−	5.91846i	−0.0655794	−	0.210836i
$789$	−0.657053	+	3.30323i	−0.0233917	+	0.117598i
$790$	0.737356	+	1.54493i	0.0262339	+	0.0549660i
$791$	−1.55240	−	3.74782i	−0.0551969	−	0.133257i
$792$	13.1518	−	8.07271i	0.467329	−	0.286851i
$793$	−2.63367	+	6.35825i	−0.0935244	+	0.225788i
$794$	1.25586	+	23.8518i	0.0445689	+	0.846468i
$795$	2.41719	+	3.61758i	0.0857288	+	0.128302i
$796$	24.6386	−	30.4565i	0.873291	−	1.07950i
$797$	−28.1834	+	5.60603i	−0.998308	+	0.198576i	−0.667089	−	0.744978i	$-0.732460\pi$
$797$	−28.1834	+	5.60603i	−0.998308	+	0.198576i	−0.331219	+	0.943554i	$0.607460\pi$
$798$	2.20162	−	15.2105i	0.0779365	−	0.538445i
$799$		−	0.802694i		−	0.0283973i
$800$	15.2785	+	5.16555i	0.540177	+	0.182630i
$801$		−	5.41164i		−	0.191211i
$802$	−1.25475	−	0.181617i	−0.0443067	−	0.00641312i
$803$	−21.7310	+	4.32256i	−0.766869	+	0.152540i
$804$	1.06969	+	10.1298i	0.0377250	+	0.357250i
$805$	8.05744	+	12.0588i	0.283988	+	0.425017i
$806$	4.71815	−	0.248424i	0.166190	−	0.00875035i
$807$	6.42714	−	15.5165i	0.226246	−	0.546206i
$808$	35.3355	+	25.6332i	1.24310	+	0.901772i
$809$	4.15544	+	10.0321i	0.146098	+	0.352711i	0.979940	−	0.199291i	$-0.0638640\pi$
$809$	4.15544	+	10.0321i	0.146098	+	0.352711i	−0.833843	+	0.552002i	$0.813864\pi$
$810$	−1.87096	+	0.892961i	−0.0657387	+	0.0313755i
$811$	4.20943	−	21.1622i	0.147813	−	0.743107i	−0.833776	−	0.552103i	$-0.813826\pi$
$811$	4.20943	−	21.1622i	0.147813	−	0.743107i	0.981589	−	0.191004i	$-0.0611744\pi$
$812$	−0.669023	+	1.27311i	−0.0234781	+	0.0446775i
$813$	−4.32423	+	6.47166i	−0.151657	+	0.226971i
$814$	27.5678	−	46.3630i	0.966250	−	1.62502i
$815$	−24.3815	+	24.3815i	−0.854046	+	0.854046i
$816$	−0.187745	−	0.435813i	−0.00657238	−	0.0152565i
$817$	−10.4804	−	10.4804i	−0.366664	−	0.366664i
$818$	−8.92207	+	2.26824i	−0.311953	+	0.0793071i
$819$	0.884221	+	0.590818i	0.0308972	+	0.0206448i
$820$	8.42171	−	7.01123i	0.294099	−	0.244843i
$821$	−2.61206	−	0.519570i	−0.0911614	−	0.0181331i	0.149299	−	0.988792i	$-0.452298\pi$
$821$	−2.61206	−	0.519570i	−0.0911614	−	0.0181331i	−0.240460	+	0.970659i	$0.577298\pi$
$822$	7.77410	−	21.9704i	0.271153	−	0.766307i
$823$	44.6852	−	18.5092i	1.55763	−	0.645191i	0.572954	−	0.819588i	$-0.305797\pi$
$823$	44.6852	−	18.5092i	1.55763	−	0.645191i	0.984676	+	0.174396i	$0.0557974\pi$
$824$	1.03752	−	26.9093i	0.0361437	−	0.937430i
$825$	−14.3712	−	5.95275i	−0.500342	−	0.207248i
$826$	−13.6337	−	12.2698i	−0.474376	−	0.426920i
$827$	−1.48819	+	0.994379i	−0.0517496	+	0.0345780i	−0.581176	−	0.813778i	$-0.697407\pi$
$827$	−1.48819	+	0.994379i	−0.0517496	+	0.0345780i	0.529426	+	0.848356i	$0.322407\pi$
$828$	13.3386	−	7.25072i	0.463549	−	0.251980i
$829$	0.519579	+	2.61210i	0.0180457	+	0.0907220i	0.988759	−	0.149521i	$-0.0477730\pi$
$829$	0.519579	+	2.61210i	0.0180457	+	0.0907220i	−0.970713	+	0.240243i	$0.922773\pi$
$830$	11.6838	−	8.72915i	0.405551	−	0.302993i
$831$	−10.8427			−0.376128
$832$	6.48124	−	0.776739i	0.224696	−	0.0269286i
$833$	−0.628917			−0.0217907
$834$	−15.9729	+	11.9336i	−0.553095	+	0.413226i
$835$	3.28684	+	16.5241i	0.113746	+	0.571839i
$836$	43.4544	+	79.9398i	1.50290	+	2.76478i
$837$	−3.40439	+	2.27474i	−0.117673	+	0.0786267i
$838$	−11.4337	−	10.2899i	−0.394972	−	0.355459i
$839$	−7.55103	−	3.12774i	−0.260690	−	0.107982i	0.248510	−	0.968629i	$-0.420059\pi$
$839$	−7.55103	−	3.12774i	−0.260690	−	0.107982i	−0.509201	+	0.860648i	$0.670059\pi$
$840$	−3.67107	−	3.96550i	−0.126664	−	0.136823i
$841$	−26.5113	+	10.9813i	−0.914181	+	0.378666i
$842$	12.8548	−	36.3291i	0.443006	−	1.25198i
$843$	−12.0251	−	2.39195i	−0.414168	−	0.0823831i
$844$	−15.6190	−	18.7612i	−0.537629	−	0.645786i
$845$	15.0338	+	10.0453i	0.517179	+	0.345568i
$846$	−9.27384	+	2.35767i	−0.318841	+	0.0810582i
$847$	−17.2957	−	17.2957i	−0.594287	−	0.594287i
$848$	8.51196	+	8.27579i	0.292302	+	0.284192i
$849$	8.64286	−	8.64286i	0.296622	−	0.296622i
$850$	−0.244467	+	0.411141i	−0.00838515	+	0.0141020i
$851$	29.4823	−	44.1234i	1.01064	−	1.51253i
$852$	22.1229	+	11.6256i	0.757918	+	0.398287i
$853$	6.97767	−	35.0791i	0.238911	−	1.20109i	−0.655972	−	0.754785i	$-0.727741\pi$
$853$	6.97767	−	35.0791i	0.238911	−	1.20109i	0.894883	−	0.446301i	$-0.147259\pi$
$854$	14.0301	−	6.69621i	0.480099	−	0.229140i
$855$	−4.67768	−	11.2929i	−0.159973	−	0.386210i
$856$	−7.29160	−	45.8200i	−0.249222	−	1.56610i
$857$	−7.91166	+	19.1004i	−0.270257	+	0.652459i	−0.999494	−	0.0318025i	$-0.989875\pi$
$857$	−7.91166	+	19.1004i	−0.270257	+	0.652459i	0.729237	+	0.684261i	$0.239875\pi$
$858$	−6.28707	+	0.331032i	−0.214637	+	0.0113012i
$859$	−1.76234	−	2.63753i	−0.0601302	−	0.0899913i	0.800186	−	0.599752i	$-0.204734\pi$
$859$	−1.76234	−	2.63753i	−0.0601302	−	0.0899913i	−0.860316	+	0.509761i	$0.829734\pi$
$860$	−5.18259	+	0.547273i	−0.176725	+	0.0186618i
$861$	4.77775	−	0.950353i	0.162825	−	0.0323879i
$862$	0.636046	+	0.0920636i	0.0216638	+	0.00313570i
$863$			14.9862i			0.510136i	0.966923	+	0.255068i	$0.0820979\pi$
$863$			14.9862i			0.510136i	−0.966923	+	0.255068i	$0.917902\pi$
$864$	−4.48367	+	3.44915i	−0.152538	+	0.117343i
$865$			16.0730i			0.546498i
$866$	−0.722958	+	4.99474i	−0.0245671	+	0.169728i
$867$	−16.6595	+	3.31379i	−0.565788	+	0.112542i
$868$	−8.29751	−	6.71248i	−0.281636	−	0.227837i
$869$	−2.50296	−	3.74594i	−0.0849070	−	0.127072i
$870$	0.0601428	+	1.14225i	0.00203903	+	0.0387261i
$871$	1.59031	−	3.83935i	0.0538857	−	0.130092i
$872$	−5.99562	+	25.0544i	−0.203037	+	0.848450i
$873$	2.06531	+	4.98611i	0.0699003	+	0.168754i
$874$	38.5566	+	80.7849i	1.30420	+	2.73259i
$875$	−2.92635	+	14.7117i	−0.0989285	+	0.497347i
$876$	7.75553	−	2.41231i	0.262035	−	0.0815045i
$877$	−5.58255	+	8.35488i	−0.188509	+	0.282124i	−0.913671	−	0.406454i	$-0.866765\pi$
$877$	−5.58255	+	8.35488i	−0.188509	+	0.282124i	0.725162	+	0.688579i	$0.241765\pi$
$878$	35.8290	+	21.3042i	1.20917	+	0.718981i
$879$	−22.4141	+	22.4141i	−0.756010	+	0.756010i
$880$	31.4619	+	5.79933i	1.06058	+	0.195495i
$881$	32.0053	+	32.0053i	1.07829	+	1.07829i	0.996663	+	0.0816240i	$0.0260107\pi$
$881$	32.0053	+	32.0053i	1.07829	+	1.07829i	0.0816240	+	0.996663i	$0.473989\pi$
$882$	1.84725	+	7.26613i	0.0622002	+	0.244663i
$883$	−33.2572	−	22.2217i	−1.11919	−	0.747821i	−0.148684	−	0.988885i	$-0.547504\pi$
$883$	−33.2572	−	22.2217i	−1.11919	−	0.747821i	−0.970509	+	0.241064i	$0.922504\pi$
$884$	−0.0176203	+	0.192794i	−0.000592635	+	0.00648437i
$885$	−14.3075	−	2.84594i	−0.480941	−	0.0956651i
$886$	−5.78148	−	2.04574i	−0.194233	−	0.0687280i
$887$	−11.8789	+	4.92041i	−0.398855	+	0.165211i	−0.573089	−	0.819493i	$-0.694255\pi$
$887$	−11.8789	+	4.92041i	−0.398855	+	0.165211i	0.174234	+	0.984704i	$0.444255\pi$
$888$	−8.26495	+	17.9627i	−0.277353	+	0.602788i
$889$	20.4907	+	8.48754i	0.687238	+	0.284663i
$890$	7.50495	−	8.33919i	0.251566	−	0.279530i
$891$	4.53645	−	3.03116i	0.151977	−	0.101548i
$892$	−4.26909	−	1.26229i	−0.142940	−	0.0422647i
$893$	−11.0068	−	55.3348i	−0.368328	−	1.85171i
$894$	−4.03603	−	5.40215i	−0.134985	−	0.180675i
$895$	31.5334			1.05405
$896$	−12.0562	−	8.48960i	−0.402769	−	0.283618i
$897$	−6.19387			−0.206807
$898$	−4.39760	−	5.88610i	−0.146750	−	0.196422i
$899$	0.440725	+	2.21567i	0.0146990	+	0.0738968i
$900$	5.46812	+	1.61683i	0.182271	+	0.0538942i
$901$	−0.292760	+	0.195616i	−0.00975326	+	0.00651692i
$902$	−19.2920	+	21.4365i	−0.642353	+	0.713756i
$903$	−2.14032	−	0.886551i	−0.0712255	−	0.0295026i
$904$	−7.99758	−	3.67983i	−0.265996	−	0.122389i
$905$	−21.7662	+	9.01584i	−0.723531	+	0.299697i
$906$	−22.2549	−	7.87475i	−0.739369	−	0.261621i
$907$	39.1560	+	7.78861i	1.30015	+	0.258616i	0.796157	−	0.605090i	$-0.206863\pi$
$907$	39.1560	+	7.78861i	1.30015	+	0.258616i	0.503995	+	0.863706i	$0.331863\pi$
$908$	3.03954	−	33.2574i	0.100871	−	1.10368i
$909$	12.8329	+	8.57465i	0.425639	+	0.284403i
$910$	0.543205	+	2.13669i	0.0180071	+	0.0708305i
$911$	−1.20486	−	1.20486i	−0.0399188	−	0.0399188i	0.686866	−	0.726784i	$-0.258986\pi$
$911$	−1.20486	−	1.20486i	−0.0399188	−	0.0399188i	−0.726784	+	0.686866i	$0.758986\pi$
$912$	−18.9184	−	27.4689i	−0.626451	−	0.909587i
$913$	−27.1408	+	27.1408i	−0.898229	+	0.898229i
$914$	−6.34773	−	3.77440i	−0.209964	−	0.124846i
$915$	6.86922	−	10.2805i	0.227089	−	0.339863i
$916$	−34.3881	+	10.6962i	−1.13621	+	0.353413i
$917$	−0.204221	+	1.02669i	−0.00674396	+	0.0339042i
$918$	−0.0722649	−	0.151411i	−0.00238510	−	0.00499732i
$919$	19.1032	+	46.1191i	0.630156	+	1.52133i	0.839427	+	0.543472i	$0.182891\pi$
$919$	19.1032	+	46.1191i	0.630156	+	1.52133i	−0.209271	+	0.977858i	$0.567109\pi$
$920$	30.6098	+	7.32505i	1.00918	+	0.241500i
$921$	9.43824	−	22.7859i	0.311001	−	0.750822i
$922$	−1.26435	−	24.0130i	−0.0416392	−	0.790827i
$923$	−5.66457	−	8.47762i	−0.186451	−	0.279044i
$924$	11.0567	+	8.94458i	0.363738	+	0.294255i
$925$	19.5482	−	3.88838i	0.642741	−	0.127849i
$926$	−5.56615	+	38.4552i	−0.182915	+	1.26372i
$927$		−	9.52095i		−	0.312709i
$928$	0.811492	+	3.01380i	0.0266385	+	0.0989329i
$929$			18.9464i			0.621611i	0.950473	+	0.310806i	$0.100599\pi$
$929$			18.9464i			0.621611i	−0.950473	+	0.310806i	$0.899401\pi$
$930$	−8.40073	−	1.21595i	−0.275471	−	0.0398727i
$931$	−43.3552	+	8.62389i	−1.42091	+	0.282637i
$932$	−17.3787	+	1.83516i	−0.569259	+	0.0601127i
$933$	1.76481	+	2.64122i	0.0577772	+	0.0864697i
$934$	2.26682	−	0.119354i	0.0741726	−	0.00390539i
$935$	−0.363100	+	0.876601i	−0.0118746	+	0.0286679i
$936$	2.27918	−	0.362699i	0.0744974	−	0.0118552i
$937$	2.92566	+	7.06317i	0.0955772	+	0.230744i	0.964436	−	0.264316i	$-0.0851462\pi$
$937$	2.92566	+	7.06317i	0.0955772	+	0.230744i	−0.868859	+	0.495060i	$0.835146\pi$
$938$	−8.47190	+	4.04343i	−0.276617	+	0.132023i
$939$	4.29570	−	21.5959i	0.140185	−	0.704757i
$940$	−17.5604	−	9.22801i	−0.572756	−	0.300985i
$941$	−9.35894	+	14.0066i	−0.305093	+	0.456604i	−0.952059	−	0.305915i	$-0.901038\pi$
$941$	−9.35894	+	14.0066i	−0.305093	+	0.456604i	0.646966	+	0.762519i	$0.276038\pi$
$942$	−17.0868	+	28.7364i	−0.556719	+	0.936281i
$943$	−20.0623	+	20.0623i	−0.653320	+	0.653320i
$944$	−39.8012	+	0.559924i	−1.29542	+	0.0182240i
$945$	−1.35097	−	1.35097i	−0.0439471	−	0.0439471i
$946$	13.2923	−	3.37927i	0.432169	−	0.109869i
$947$	48.8983	+	32.6728i	1.58898	+	1.06172i	0.958333	+	0.285654i	$0.0922110\pi$
$947$	48.8983	+	32.6728i	1.58898	+	1.06172i	0.630648	+	0.776069i	$0.282789\pi$
$948$	1.05664	+	1.26921i	0.0343182	+	0.0412222i
$949$	−3.24993	−	0.646451i	−0.105497	−	0.0209847i
$950$	−11.2150	+	31.6947i	−0.363862	+	1.02831i
$951$	−21.7355	+	9.00315i	−0.704823	+	0.291947i
$952$	0.320917	−	0.297089i	0.0104010	−	0.00962872i
$953$	−24.5087	−	10.1518i	−0.793914	−	0.328850i	−0.0513978	−	0.998678i	$-0.516368\pi$
$953$	−24.5087	−	10.1518i	−0.793914	−	0.328850i	−0.742516	+	0.669828i	$0.766368\pi$
$954$	3.11993	+	2.80781i	0.101011	+	0.0909063i
$955$	−24.8311	+	16.5916i	−0.803517	+	0.536893i
$956$	2.25169	+	4.14228i	0.0728250	+	0.133971i
$957$	−0.587278	−	2.95245i	−0.0189840	−	0.0954391i
$958$	−22.9769	+	17.1664i	−0.742349	+	0.554621i
$959$	21.4778			0.693554
$960$	−11.6926	−	0.902982i	−0.377376	−	0.0291436i
$961$	14.2356			0.459214
$962$	6.46242	−	4.82818i	0.208357	−	0.155667i
$963$	−3.20020	−	16.0885i	−0.103125	−	0.518444i
$964$	39.5131	−	21.4788i	1.27263	−	0.691787i
$965$	5.21690	−	3.48582i	0.167938	−	0.112213i
$966$	10.4000	+	9.35956i	0.334613	+	0.301139i
$967$	−29.1186	−	12.0613i	−0.936391	−	0.387866i	−0.138291	−	0.990392i	$-0.544161\pi$
$967$	−29.1186	−	12.0613i	−0.936391	−	0.387866i	−0.798099	+	0.602526i	$0.794161\pi$
$968$	−53.0427	−	2.04512i	−1.70486	−	0.0657327i
$969$	0.913905	−	0.378552i	0.0293589	−	0.0121608i
$970$	−3.73222	+	10.5477i	−0.119834	+	0.338665i
$971$	28.0520	+	5.57988i	0.900230	+	0.179067i	0.623447	−	0.781865i	$-0.285732\pi$
$971$	28.0520	+	5.57988i	0.900230	+	0.179067i	0.276783	+	0.960932i	$0.410732\pi$
$972$	−1.53706	+	1.27963i	−0.0493012	+	0.0410441i
$973$	−15.2782	−	10.2086i	−0.489798	−	0.327273i
$974$	−2.45855	+	0.625030i	−0.0787769	+	0.0200273i
$975$	−1.64497	−	1.64497i	−0.0526812	−	0.0526812i
$976$	12.4712	−	31.3482i	0.399193	−	1.00343i
$977$	−14.9572	+	14.9572i	−0.478524	+	0.478524i	−0.904659	−	0.426136i	$-0.859875\pi$
$977$	−14.9572	+	14.9572i	−0.478524	+	0.478524i	0.426136	+	0.904659i	$0.359875\pi$
$978$	−17.0009	+	28.5918i	−0.543627	+	0.914264i
$979$	−16.4035	+	24.5496i	−0.524260	+	0.784610i
$980$	−7.23022	+	13.7587i	−0.230961	+	0.439506i
$981$	−1.77692	+	8.93317i	−0.0567326	+	0.285214i
$982$	15.0885	−	7.20136i	0.481493	−	0.229805i
$983$	−9.89352	−	23.8851i	−0.315554	−	0.761815i	−0.999479	−	0.0322631i	$-0.989729\pi$
$983$	−9.89352	−	23.8851i	−0.315554	−	0.761815i	0.683925	−	0.729552i	$-0.260271\pi$
$984$	6.20761	−	8.55722i	0.197891	−	0.272794i
$985$	1.73853	−	4.19719i	0.0553943	−	0.133734i
$986$	−0.0924395	+	0.00486719i	−0.00294387	+	0.000155003i
$987$	−4.89929	−	7.33231i	−0.155946	−	0.233390i
$988$	1.42897	+	13.5321i	0.0454616	+	0.430515i
$989$	13.2338	−	2.63237i	0.420811	−	0.0837046i
$990$	11.1942	+	1.62029i	0.355775	+	0.0514963i
$991$		−	57.7326i		−	1.83394i	−0.398959	−	0.916969i	$-0.630628\pi$
$991$		−	57.7326i		−	1.83394i	0.398959	−	0.916969i	$-0.369372\pi$
$992$	−23.1101	+	1.54307i	−0.733748	+	0.0489925i
$993$		−	2.06187i		−	0.0654314i
$994$	−3.29933	+	22.7943i	−0.104648	+	0.722990i
$995$	28.1618	−	5.60173i	0.892790	−	0.177587i
$996$	8.84926	−	10.9388i	0.280399	−	0.346611i
$997$	−6.42316	−	9.61294i	−0.203424	−	0.304445i	0.715705	−	0.698403i	$-0.246106\pi$
$997$	−6.42316	−	9.61294i	−0.203424	−	0.304445i	−0.919128	+	0.393958i	$0.871106\pi$
$998$	0.277763	+	5.27537i	0.00879243	+	0.166989i
$999$	−2.67525	+	6.45863i	−0.0846412	+	0.204342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.r.a.85.12	yes	128
3.2	odd	2		576.2.bd.b.469.5		128
4.3	odd	2		768.2.r.a.433.4		128
64.3	odd	16		768.2.r.a.337.4		128
64.61	even	16	inner	192.2.r.a.61.12	✓	128
192.125	odd	16		576.2.bd.b.253.5		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.61.12	✓	128	64.61	even	16	inner
192.2.r.a.85.12	yes	128	1.1	even	1	trivial
576.2.bd.b.253.5		128	192.125	odd	16
576.2.bd.b.469.5		128	3.2	odd	2
768.2.r.a.337.4		128	64.3	odd	16
768.2.r.a.433.4		128	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.r (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.846436 + 1.13294i) q^{2} +(0.195090 + 0.980785i) q^{3} +(-0.567094 + 1.91792i) q^{4} +(-1.21887 + 0.814423i) q^{5} +(-0.946037 + 1.05120i) q^{6} +(-1.20411 - 0.498758i) q^{7} +(-2.65289 + 0.980911i) q^{8} +(-0.923880 + 0.382683i) q^{9} +O(q^{10})\)	\(q+(0.846436 + 1.13294i) q^{2} +(0.195090 + 0.980785i) q^{3} +(-0.567094 + 1.91792i) q^{4} +(-1.21887 + 0.814423i) q^{5} +(-0.946037 + 1.05120i) q^{6} +(-1.20411 - 0.498758i) q^{7} +(-2.65289 + 0.980911i) q^{8} +(-0.923880 + 0.382683i) q^{9} +(-1.95438 - 0.691547i) q^{10} +(5.35111 + 1.06440i) q^{11} +(-1.99170 - 0.182030i) q^{12} +(0.678439 + 0.453319i) q^{13} +(-0.454138 - 1.78635i) q^{14} +(-1.03656 - 1.03656i) q^{15} +(-3.35681 - 2.17528i) q^{16} +(0.0838862 - 0.0838862i) q^{17} +(-1.21556 - 0.722781i) q^{18} +(4.63254 - 6.93308i) q^{19} +(-0.870782 - 2.79954i) q^{20} +(0.254265 - 1.27827i) q^{21} +(3.32347 + 6.96342i) q^{22} +(2.90494 + 7.01314i) q^{23} +(-1.47962 - 2.41055i) q^{24} +(-1.09106 + 2.63405i) q^{25} +(0.0606735 + 1.15233i) q^{26} +(-0.555570 - 0.831470i) q^{27} +(1.63942 - 2.02654i) q^{28} +(-0.541143 + 0.107640i) q^{29} +(0.296977 - 2.05175i) q^{30} -4.09443i q^{31} +(-0.376870 - 5.64429i) q^{32} +5.45595i q^{33} +(0.166042 + 0.0240335i) q^{34} +(1.87385 - 0.372732i) q^{35} +(-0.210029 - 1.98894i) q^{36} +(-3.88386 - 5.81261i) q^{37} +(11.7759 - 0.620033i) q^{38} +(-0.312251 + 0.753841i) q^{39} +(2.43465 - 3.35618i) q^{40} +(1.43034 + 3.45314i) q^{41} +(1.66342 - 0.793911i) q^{42} +(0.346777 - 1.74336i) q^{43} +(-5.07602 + 9.65937i) q^{44} +(0.814423 - 1.21887i) q^{45} +(-5.48661 + 9.22729i) q^{46} +(4.78442 - 4.78442i) q^{47} +(1.47860 - 3.71668i) q^{48} +(-3.74863 - 3.74863i) q^{49} +(-3.90772 + 0.993451i) q^{50} +(0.0986398 + 0.0659090i) q^{51} +(-1.25417 + 1.04412i) q^{52} +(-2.91095 - 0.579023i) q^{53} +(0.471749 - 1.33321i) q^{54} +(-7.38918 + 3.06070i) q^{55} +(3.68360 + 0.142025i) q^{56} +(7.70363 + 3.19095i) q^{57} +(-0.579992 - 0.521971i) q^{58} +(8.27418 - 5.52863i) q^{59} +(2.57587 - 1.40021i) q^{60} +(1.64548 + 8.27240i) q^{61} +(4.63873 - 3.46567i) q^{62} +1.30332 q^{63} +(6.07563 - 5.20450i) q^{64} -1.19612 q^{65} +(-6.18124 + 4.61811i) q^{66} +(-0.993605 - 4.99519i) q^{67} +(0.113315 + 0.208458i) q^{68} +(-6.31166 + 4.21732i) q^{69} +(2.00838 + 1.80746i) q^{70} +(-11.5446 - 4.78192i) q^{71} +(2.07557 - 1.92146i) q^{72} +(-3.75189 + 1.55409i) q^{73} +(3.29788 - 9.32018i) q^{74} +(-2.79629 - 0.556217i) q^{75} +(10.6700 + 12.8165i) q^{76} +(-5.91244 - 3.95056i) q^{77} +(-1.11836 + 0.284317i) q^{78} +(-0.583888 - 0.583888i) q^{79} +(5.86311 - 0.0824825i) q^{80} +(0.707107 - 0.707107i) q^{81} +(-2.70150 + 4.54335i) q^{82} +(-3.90846 + 5.84943i) q^{83} +(2.30743 + 1.21256i) q^{84} +(-0.0339275 + 0.170565i) q^{85} +(2.26865 - 1.08277i) q^{86} +(-0.211144 - 0.509746i) q^{87} +(-15.2400 + 2.42523i) q^{88} +(-2.07094 + 4.99970i) q^{89} +(2.07026 - 0.109005i) q^{90} +(-0.590818 - 0.884221i) q^{91} +(-15.0980 + 1.59432i) q^{92} +(4.01576 - 0.798784i) q^{93} +(9.47015 + 1.37074i) q^{94} +12.2234i q^{95} +(5.46231 - 1.47077i) q^{96} -5.39692i q^{97} +(1.07399 - 7.41994i) q^{98} +(-5.35111 + 1.06440i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) \) 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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