LMFDB - Embedded newform 558.2.q.a.185.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [558,2,Mod(185,558)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("558.185"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(558, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.q (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.45565243279$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.15
Character	$\chi$	$=$	558.185
Dual form			558.2.q.a.371.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(1.71705 - 0.227499i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.92707 + 1.11259i) q^{5} +(-1.37326 + 1.05554i) q^{6} +(0.556441 + 0.963784i) q^{7} +1.00000i q^{8} +(2.89649 - 0.781251i) q^{9} -2.22519 q^{10} +(-0.510234 - 0.883751i) q^{11} +(0.661503 - 1.60075i) q^{12} +(2.77056 + 1.59958i) q^{13} +(-0.963784 - 0.556441i) q^{14} +(3.56198 + 1.47197i) q^{15} +(-0.500000 - 0.866025i) q^{16} -4.61929 q^{17} +(-2.11781 + 2.12483i) q^{18} +2.48701 q^{19} +(1.92707 - 1.11259i) q^{20} +(1.17469 + 1.52827i) q^{21} +(0.883751 + 0.510234i) q^{22} +(-1.93084 + 3.34431i) q^{23} +(0.227499 + 1.71705i) q^{24} +(-0.0242726 - 0.0420413i) q^{25} -3.19916 q^{26} +(4.79567 - 2.00039i) q^{27} +1.11288 q^{28} +(-2.06180 - 3.57113i) q^{29} +(-3.82075 + 0.506227i) q^{30} +(-4.17770 + 3.68060i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.07715 - 1.40136i) q^{33} +(4.00043 - 2.30965i) q^{34} +2.47637i q^{35} +(0.771661 - 2.89906i) q^{36} -9.83752i q^{37} +(-2.15382 + 1.24351i) q^{38} +(5.12107 + 2.11626i) q^{39} +(-1.11259 + 1.92707i) q^{40} +(9.95860 + 5.74960i) q^{41} +(-1.78145 - 0.736175i) q^{42} +(5.89094 - 3.40113i) q^{43} -1.02047 q^{44} +(6.45095 + 1.71709i) q^{45} -3.86168i q^{46} +(-8.88791 + 5.13144i) q^{47} +(-1.05554 - 1.37326i) q^{48} +(2.88075 - 4.98960i) q^{49} +(0.0420413 + 0.0242726i) q^{50} +(-7.93154 + 1.05088i) q^{51} +(2.77056 - 1.59958i) q^{52} -9.85277 q^{53} +(-3.15298 + 4.13022i) q^{54} -2.27073i q^{55} +(-0.963784 + 0.556441i) q^{56} +(4.27031 - 0.565792i) q^{57} +(3.57113 + 2.06180i) q^{58} +(5.10909 + 2.94973i) q^{59} +(3.05575 - 2.34878i) q^{60} +(1.55017 - 0.894989i) q^{61} +(1.77769 - 5.27635i) q^{62} +(2.36468 + 2.35687i) q^{63} -1.00000 q^{64} +(3.55937 + 6.16501i) q^{65} +(1.63352 + 0.675042i) q^{66} +(-1.63010 + 2.82341i) q^{67} +(-2.30965 + 4.00043i) q^{68} +(-2.55451 + 6.18160i) q^{69} +(-1.23818 - 2.14460i) q^{70} +1.19637i q^{71} +(0.781251 + 2.89649i) q^{72} +6.14833i q^{73} +(4.91876 + 8.51955i) q^{74} +(-0.0512414 - 0.0666648i) q^{75} +(1.24351 - 2.15382i) q^{76} +(0.567830 - 0.983510i) q^{77} +(-5.49311 + 0.727805i) q^{78} +(2.18886 - 1.26374i) q^{79} -2.22519i q^{80} +(7.77929 - 4.52577i) q^{81} -11.4992 q^{82} +(-1.01481 - 1.75771i) q^{83} +(1.91087 - 0.253179i) q^{84} +(-8.90169 - 5.13940i) q^{85} +(-3.40113 + 5.89094i) q^{86} +(-4.35262 - 5.66274i) q^{87} +(0.883751 - 0.510234i) q^{88} -5.33213 q^{89} +(-6.44523 + 1.73843i) q^{90} +3.56029i q^{91} +(1.93084 + 3.34431i) q^{92} +(-6.33596 + 7.27018i) q^{93} +(5.13144 - 8.88791i) q^{94} +(4.79264 + 2.76703i) q^{95} +(1.60075 + 0.661503i) q^{96} +(1.06005 + 1.83605i) q^{97} +5.76149i q^{98} +(-2.16832 - 2.16115i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} + 12 q^{5} - 4 q^{7} - 4 q^{9} - 32 q^{16} + 8 q^{18} - 8 q^{19} + 12 q^{20} + 44 q^{25} - 8 q^{28} + 8 q^{31} - 36 q^{33} - 8 q^{36} + 36 q^{38} - 8 q^{39} + 24 q^{41} - 8 q^{45} - 48 q^{47}+ \cdots - 16 q^{97}+O(q^{100}) $ 64 * q + 32 * q^4 + 12 * q^5 - 4 * q^7 - 4 * q^9 - 32 * q^16 + 8 * q^18 - 8 * q^19 + 12 * q^20 + 44 * q^25 - 8 * q^28 + 8 * q^31 - 36 * q^33 - 8 * q^36 + 36 * q^38 - 8 * q^39 + 24 * q^41 - 8 * q^45 - 48 * q^47 - 36 * q^49 - 32 * q^51 - 12 * q^59 - 52 * q^63 - 64 * q^64 - 16 * q^66 + 16 * q^67 + 112 * q^69 - 12 * q^70 - 8 * q^72 - 4 * q^76 - 28 * q^78 + 60 * q^81 + 44 * q^87 + 56 * q^90 - 64 * q^93 - 180 * q^95 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	1.71705	−	0.227499i	0.991337	−	0.131346i
$3$	1.71705	−	0.227499i	0.991337	−	0.131346i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.92707	+	1.11259i	0.861811	+	0.497567i	0.864618	−	0.502429i	$-0.167560\pi$
$5$	1.92707	+	1.11259i	0.861811	+	0.497567i	−0.00280731	+	0.999996i	$0.500894\pi$
$6$	−1.37326	+	1.05554i	−0.560629	+	0.430923i
$7$	0.556441	+	0.963784i	0.210315	+	0.364276i	0.951813	−	0.306679i	$-0.0992178\pi$
$7$	0.556441	+	0.963784i	0.210315	+	0.364276i	−0.741498	+	0.670955i	$0.765884\pi$
$8$			1.00000i			0.353553i
$9$	2.89649	−	0.781251i	0.965496	−	0.260417i
$10$	−2.22519			−0.703666
$11$	−0.510234	−	0.883751i	−0.153841	−	0.266461i	0.778795	−	0.627278i	$-0.215831\pi$
$11$	−0.510234	−	0.883751i	−0.153841	−	0.266461i	−0.932636	+	0.360817i	$0.882498\pi$
$12$	0.661503	−	1.60075i	0.190959	−	0.462098i
$13$	2.77056	+	1.59958i	0.768414	+	0.443644i	0.832309	−	0.554313i	$-0.187019\pi$
$13$	2.77056	+	1.59958i	0.768414	+	0.443644i	−0.0638944	+	0.997957i	$0.520352\pi$
$14$	−0.963784	−	0.556441i	−0.257582	−	0.148715i
$15$	3.56198	+	1.47197i	0.919698	+	0.380060i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.61929			−1.12034			−0.560172	−	0.828377i	$-0.689265\pi$
$17$	−4.61929			−1.12034			−0.560172	+	0.828377i	$0.689265\pi$
$18$	−2.11781	+	2.12483i	−0.499172	+	0.500827i
$19$	2.48701			0.570560			0.285280	−	0.958444i	$-0.407913\pi$
$19$	2.48701			0.570560			0.285280	+	0.958444i	$0.407913\pi$
$20$	1.92707	−	1.11259i	0.430906	−	0.248783i
$21$	1.17469	+	1.52827i	0.256339	+	0.333496i
$22$	0.883751	+	0.510234i	0.188416	+	0.108782i
$23$	−1.93084	+	3.34431i	−0.402608	+	0.697338i	−0.994040	−	0.109017i	$-0.965230\pi$
$23$	−1.93084	+	3.34431i	−0.402608	+	0.697338i	0.591432	+	0.806355i	$0.298563\pi$
$24$	0.227499	+	1.71705i	0.0464380	+	0.350490i
$25$	−0.0242726	−	0.0420413i	−0.00485451	−	0.00840826i
$26$	−3.19916			−0.627408
$27$	4.79567	−	2.00039i	0.922927	−	0.384975i
$28$	1.11288			0.210315
$29$	−2.06180	−	3.57113i	−0.382866	−	0.663143i	0.608605	−	0.793473i	$-0.291730\pi$
$29$	−2.06180	−	3.57113i	−0.382866	−	0.663143i	−0.991471	+	0.130330i	$0.958396\pi$
$30$	−3.82075	+	0.506227i	−0.697570	+	0.0924239i
$31$	−4.17770	+	3.68060i	−0.750337	+	0.661056i
$31$	−4.17770	+	3.68060i	−0.750337	+	0.661056i
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−1.07715	−	1.40136i	−0.187507	−	0.243946i
$34$	4.00043	−	2.30965i	0.686067	−	0.396101i
$35$			2.47637i			0.418583i
$36$	0.771661	−	2.89906i	0.128610	−	0.483176i
$37$		−	9.83752i		−	1.61728i	−0.588304	−	0.808640i	$-0.700204\pi$
$37$		−	9.83752i		−	1.61728i	0.588304	−	0.808640i	$-0.299796\pi$
$38$	−2.15382	+	1.24351i	−0.349395	+	0.201723i
$39$	5.12107	+	2.11626i	0.820028	+	0.338872i
$40$	−1.11259	+	1.92707i	−0.175916	+	0.304696i
$41$	9.95860	+	5.74960i	1.55527	+	0.897937i	0.997698	+	0.0678092i	$0.0216009\pi$
$41$	9.95860	+	5.74960i	1.55527	+	0.897937i	0.557574	+	0.830127i	$0.311732\pi$
$42$	−1.78145	−	0.736175i	−0.274884	−	0.113594i
$43$	5.89094	−	3.40113i	0.898360	−	0.518668i	0.0216919	−	0.999765i	$-0.493095\pi$
$43$	5.89094	−	3.40113i	0.898360	−	0.518668i	0.876668	+	0.481097i	$0.159761\pi$
$44$	−1.02047			−0.153841
$45$	6.45095	+	1.71709i	0.961650	+	0.255969i
$46$		−	3.86168i		−	0.569374i
$47$	−8.88791	+	5.13144i	−1.29644	+	0.748497i	−0.979787	−	0.200046i	$-0.935891\pi$
$47$	−8.88791	+	5.13144i	−1.29644	+	0.748497i	−0.316649	+	0.948543i	$0.602558\pi$
$48$	−1.05554	−	1.37326i	−0.152354	−	0.198212i
$49$	2.88075	−	4.98960i	0.411535	−	0.712800i
$50$	0.0420413	+	0.0242726i	0.00594554	+	0.00343266i
$51$	−7.93154	+	1.05088i	−1.11064	+	0.147153i
$52$	2.77056	−	1.59958i	0.384207	−	0.221822i
$53$	−9.85277			−1.35338			−0.676691	−	0.736267i	$-0.736587\pi$
$53$	−9.85277			−1.35338			−0.676691	+	0.736267i	$0.736587\pi$
$54$	−3.15298	+	4.13022i	−0.429066	+	0.562052i
$55$		−	2.27073i		−	0.306185i
$56$	−0.963784	+	0.556441i	−0.128791	+	0.0743575i
$57$	4.27031	−	0.565792i	0.565617	−	0.0749410i
$58$	3.57113	+	2.06180i	0.468913	+	0.270727i
$59$	5.10909	+	2.94973i	0.665146	+	0.384022i	0.794235	−	0.607611i	$-0.207872\pi$
$59$	5.10909	+	2.94973i	0.665146	+	0.384022i	−0.129089	+	0.991633i	$0.541205\pi$
$60$	3.05575	−	2.34878i	0.394496	−	0.303226i
$61$	1.55017	−	0.894989i	0.198478	−	0.114592i	−0.397467	−	0.917616i	$-0.630111\pi$
$61$	1.55017	−	0.894989i	0.198478	−	0.114592i	0.595946	+	0.803025i	$0.296777\pi$
$62$	1.77769	−	5.27635i	0.225767	−	0.670096i
$63$	2.36468	+	2.35687i	0.297922	+	0.296938i
$64$	−1.00000			−0.125000
$65$	3.55937	+	6.16501i	0.441485	+	0.764675i
$66$	1.63352	+	0.675042i	0.201072	+	0.0830919i
$67$	−1.63010	+	2.82341i	−0.199148	+	0.344935i	−0.948252	−	0.317517i	$-0.897151\pi$
$67$	−1.63010	+	2.82341i	−0.199148	+	0.344935i	0.749104	+	0.662452i	$0.230484\pi$
$68$	−2.30965	+	4.00043i	−0.280086	+	0.485123i
$69$	−2.55451	+	6.18160i	−0.307527	+	0.744178i
$70$	−1.23818	−	2.14460i	−0.147991	−	0.256329i
$71$			1.19637i			0.141983i	0.997477	+	0.0709913i	$0.0226163\pi$
$71$			1.19637i			0.141983i	−0.997477	+	0.0709913i	$0.977384\pi$
$72$	0.781251	+	2.89649i	0.0920713	+	0.341354i
$73$			6.14833i			0.719608i	0.933028	+	0.359804i	$0.117156\pi$
$73$			6.14833i			0.719608i	−0.933028	+	0.359804i	$0.882844\pi$
$74$	4.91876	+	8.51955i	0.571795	+	0.990377i
$75$	−0.0512414	−	0.0666648i	−0.00591685	−	0.00769779i
$76$	1.24351	−	2.15382i	0.142640	−	0.247060i
$77$	0.567830	−	0.983510i	0.0647102	−	0.112081i
$78$	−5.49311	+	0.727805i	−0.621972	+	0.0824077i
$79$	2.18886	−	1.26374i	0.246266	−	0.142182i	−0.371787	−	0.928318i	$-0.621255\pi$
$79$	2.18886	−	1.26374i	0.246266	−	0.142182i	0.618053	+	0.786136i	$0.287922\pi$
$80$		−	2.22519i		−	0.248783i
$81$	7.77929	−	4.52577i	0.864366	−	0.502863i
$82$	−11.4992			−1.26987
$83$	−1.01481	−	1.75771i	−0.111390	−	0.192933i	0.804941	−	0.593355i	$-0.202197\pi$
$83$	−1.01481	−	1.75771i	−0.111390	−	0.192933i	−0.916331	+	0.400422i	$0.868864\pi$
$84$	1.91087	−	0.253179i	0.208493	−	0.0276241i
$85$	−8.90169	−	5.13940i	−0.965524	−	0.557446i
$86$	−3.40113	+	5.89094i	−0.366754	+	0.635236i
$87$	−4.35262	−	5.66274i	−0.466650	−	0.607110i
$88$	0.883751	−	0.510234i	0.0942081	−	0.0543911i
$89$	−5.33213			−0.565204			−0.282602	−	0.959237i	$-0.591198\pi$
$89$	−5.33213			−0.565204			−0.282602	+	0.959237i	$0.591198\pi$
$90$	−6.44523	+	1.73843i	−0.679387	+	0.183246i
$91$			3.56029i			0.373220i
$92$	1.93084	+	3.34431i	0.201304	+	0.348669i
$93$	−6.33596	+	7.27018i	−0.657009	+	0.753883i
$94$	5.13144	−	8.88791i	0.529267	−	0.916718i
$95$	4.79264	+	2.76703i	0.491715	+	0.283892i
$96$	1.60075	+	0.661503i	0.163376	+	0.0675144i
$97$	1.06005	+	1.83605i	0.107631	+	0.186423i	0.914810	−	0.403884i	$-0.132340\pi$
$97$	1.06005	+	1.83605i	0.107631	+	0.186423i	−0.807179	+	0.590307i	$0.799007\pi$
$98$			5.76149i			0.581999i
$99$	−2.16832	−	2.16115i	−0.217924	−	0.217204i
$100$	−0.0485451			−0.00485451
$101$	1.98249	−	1.14459i	0.197265	−	0.113891i	−0.398114	−	0.917336i	$-0.630335\pi$
$101$	1.98249	−	1.14459i	0.197265	−	0.113891i	0.595379	+	0.803445i	$0.297002\pi$
$102$	6.34347	−	4.87586i	0.628097	−	0.482782i
$103$	−0.608600	+	1.05413i	−0.0599671	+	0.103866i	−0.894450	−	0.447167i	$-0.852433\pi$
$103$	−0.608600	+	1.05413i	−0.0599671	+	0.103866i	0.834483	+	0.551033i	$0.185766\pi$
$104$	−1.59958	+	2.77056i	−0.156852	+	0.271675i
$105$	0.563370	+	4.25204i	0.0549793	+	0.414956i
$106$	8.53275	−	4.92639i	0.828774	−	0.478493i
$107$		−	10.3952i		−	1.00494i	−0.864594	−	0.502472i	$-0.832424\pi$
$107$		−	10.3952i		−	1.00494i	0.864594	−	0.502472i	$-0.167576\pi$
$108$	0.665446	−	5.15337i	0.0640326	−	0.495883i
$109$	−11.6174			−1.11275			−0.556373	−	0.830933i	$-0.687807\pi$
$109$	−11.6174			−1.11275			−0.556373	+	0.830933i	$0.687807\pi$
$110$	1.13536	+	1.96651i	0.108253	+	0.187499i
$111$	−2.23802	−	16.8915i	−0.212424	−	1.60327i
$112$	0.556441	−	0.963784i	0.0525787	−	0.0910690i
$113$	−14.5565	−	8.40422i	−1.36936	−	0.790602i	−0.378517	−	0.925595i	$-0.623566\pi$
$113$	−14.5565	−	8.40422i	−1.36936	−	0.790602i	−0.990847	+	0.134992i	$0.956899\pi$
$114$	−3.41530	+	2.62515i	−0.319873	+	0.245868i
$115$	−7.44172	+	4.29648i	−0.693944	+	0.400649i
$116$	−4.12359			−0.382866
$117$	9.27456	+	2.46867i	0.857433	+	0.228229i
$118$	−5.89947			−0.543090
$119$	−2.57036	−	4.45200i	−0.235625	−	0.408114i
$120$	−1.47197	+	3.56198i	−0.134372	+	0.325162i
$121$	4.97932	−	8.62444i	0.452666	−	0.784040i
$122$	−0.894989	+	1.55017i	−0.0810285	+	0.140345i
$123$	18.4074	+	7.60676i	1.65974	+	0.685878i
$124$	1.09865	+	5.45829i	0.0986615	+	0.490169i
$125$		−	11.2340i		−	1.00480i
$126$	−3.22631	−	0.858768i	−0.287422	−	0.0765051i
$127$			2.30229i			0.204295i	0.994769	+	0.102147i	$0.0325713\pi$
$127$			2.30229i			0.204295i	−0.994769	+	0.102147i	$0.967429\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	9.34125	−	7.18008i	0.822451	−	0.632171i
$130$	−6.16501	−	3.55937i	−0.540707	−	0.312177i
$131$	−4.64203	−	2.68008i	−0.405576	−	0.234159i	0.283311	−	0.959028i	$-0.408567\pi$
$131$	−4.64203	−	2.68008i	−0.405576	−	0.234159i	−0.688887	+	0.724869i	$0.741900\pi$
$132$	−1.75219	+	0.232155i	−0.152508	+	0.0202065i
$133$	1.38388	+	2.39694i	0.119997	+	0.207841i
$134$		−	3.26020i		−	0.281638i
$135$	11.4672	+	1.48074i	0.986939	+	0.127442i
$136$		−	4.61929i		−	0.396101i
$137$	−6.98169	−	12.0926i	−0.596486	−	1.03314i	−0.993335	−	0.115260i	$-0.963230\pi$
$137$	−6.98169	−	12.0926i	−0.596486	−	1.03314i	0.396849	−	0.917884i	$-0.370104\pi$
$138$	−0.878527	−	6.63068i	−0.0747852	−	0.564441i
$139$	−6.56075	−	3.78785i	−0.556476	−	0.321281i	0.195254	−	0.980753i	$-0.437447\pi$
$139$	−6.56075	−	3.78785i	−0.556476	−	0.321281i	−0.751730	+	0.659471i	$0.770780\pi$
$140$	2.14460	+	1.23818i	0.181252	+	0.104646i
$141$	−14.0936	+	10.8329i	−1.18689	+	0.912295i
$142$	−0.598183	−	1.03608i	−0.0501984	−	0.0869462i
$143$		−	3.26464i		−	0.273003i
$144$	−2.12483	−	2.11781i	−0.177069	−	0.176484i
$145$		−	9.17576i		−	0.762005i
$146$	−3.07417	−	5.32461i	−0.254420	−	0.440668i
$147$	3.81125	−	9.22274i	0.314346	−	0.760678i
$148$	−8.51955	−	4.91876i	−0.700302	−	0.404320i
$149$	4.53497	+	2.61827i	0.371519	+	0.214497i	0.674122	−	0.738620i	$-0.264522\pi$
$149$	4.53497	+	2.61827i	0.371519	+	0.214497i	−0.302603	+	0.953117i	$0.597856\pi$
$150$	0.0777088	+	0.0321127i	0.00634490	+	0.00262199i
$151$	−8.53103	+	4.92539i	−0.694245	+	0.400823i	−0.805200	−	0.593003i	$-0.797942\pi$
$151$	−8.53103	+	4.92539i	−0.694245	+	0.400823i	0.110955	+	0.993825i	$0.464609\pi$
$152$			2.48701i			0.201723i
$153$	−13.3797	+	3.60883i	−1.08169	+	0.291756i
$154$			1.13566i			0.0915140i
$155$	−12.1457	+	2.44470i	−0.975568	+	0.196363i
$156$	4.39327	−	3.37685i	0.351743	−	0.270365i
$157$	6.67621	−	11.5635i	0.532819	−	0.922870i	−0.466446	−	0.884550i	$-0.654466\pi$
$157$	6.67621	−	11.5635i	0.532819	−	0.922870i	0.999265	−	0.0383206i	$-0.0122008\pi$
$158$	−1.26374	+	2.18886i	−0.100538	+	0.174136i
$159$	−16.9177	+	2.24149i	−1.34166	+	0.177762i
$160$	1.11259	+	1.92707i	0.0879582	+	0.152348i
$161$	−4.29760			−0.338698
$162$	−4.47418	+	7.80908i	−0.351525	+	0.613539i
$163$	−13.6554			−1.06957			−0.534787	−	0.844987i	$-0.679608\pi$
$163$	−13.6554			−1.06957			−0.534787	+	0.844987i	$0.679608\pi$
$164$	9.95860	−	5.74960i	0.777636	−	0.448968i
$165$	−0.516588	−	3.89895i	−0.0402163	−	0.303533i
$166$	1.75771	+	1.01481i	0.136424	+	0.0787647i
$167$	3.02979	−	5.24776i	0.234453	−	0.406084i	−0.724661	−	0.689106i	$-0.758004\pi$
$167$	3.02979	−	5.24776i	0.234453	−	0.406084i	0.959113	+	0.283022i	$0.0913369\pi$
$168$	−1.52827	+	1.17469i	−0.117909	+	0.0906296i
$169$	−1.38268	−	2.39487i	−0.106360	−	0.184221i
$170$	10.2788			0.788347
$171$	7.20361	−	1.94298i	0.550873	−	0.148583i
$172$		−	6.80227i		−	0.518668i
$173$	−12.7432	+	7.35730i	−0.968849	+	0.559365i	−0.898885	−	0.438184i	$-0.855622\pi$
$173$	−12.7432	+	7.35730i	−0.968849	+	0.559365i	−0.0699640	+	0.997550i	$0.522288\pi$
$174$	6.60085	+	2.72777i	0.500410	+	0.206792i
$175$	0.0270125	−	0.0467870i	0.00204195	−	0.00353676i
$176$	−0.510234	+	0.883751i	−0.0384603	+	0.0666152i
$177$	9.44359	+	3.90251i	0.709824	+	0.293331i
$178$	4.61776	−	2.66606i	0.346116	−	0.199830i
$179$	−13.1686			−0.984269			−0.492135	−	0.870519i	$-0.663783\pi$
$179$	−13.1686			−0.984269			−0.492135	+	0.870519i	$0.663783\pi$
$180$	4.71252	−	4.72814i	0.351250	−	0.352415i
$181$		−	0.183146i		−	0.0136132i	−0.999977	−	0.00680658i	$-0.997833\pi$
$181$		−	0.183146i		−	0.0136132i	0.999977	−	0.00680658i	$-0.00216662\pi$
$182$	−1.78014	−	3.08330i	−0.131953	−	0.228550i
$183$	2.45810	−	1.88940i	0.181708	−	0.139668i
$184$	−3.34431	−	1.93084i	−0.246546	−	0.142343i
$185$	10.9452	−	18.9576i	0.804704	−	1.39379i
$186$	1.85201	−	9.46415i	0.135796	−	0.693945i
$187$	2.35692	+	4.08230i	0.172355	+	0.298528i
$188$			10.2629i			0.748497i
$189$	4.59645	+	3.50889i	0.334342	+	0.255234i
$190$	−5.53407			−0.401483
$191$	0.0556007	−	0.0321011i	0.00402313	−	0.00232275i	−0.497987	−	0.867184i	$-0.665927\pi$
$191$	0.0556007	−	0.0321011i	0.00402313	−	0.00232275i	0.502010	+	0.864862i	$0.332594\pi$
$192$	−1.71705	+	0.227499i	−0.123917	+	0.0164183i
$193$	−1.25910	+	2.18083i	−0.0906320	+	0.156979i	−0.907777	−	0.419453i	$-0.862222\pi$
$193$	−1.25910	+	2.18083i	−0.0906320	+	0.156979i	0.817145	+	0.576432i	$0.195555\pi$
$194$	−1.83605	−	1.06005i	−0.131821	−	0.0761068i
$195$	7.51412	+	9.77584i	0.538098	+	0.700063i
$196$	−2.88075	−	4.98960i	−0.205768	−	0.356400i
$197$	18.4548			1.31485			0.657426	−	0.753519i	$-0.271645\pi$
$197$	18.4548			1.31485			0.657426	+	0.753519i	$0.271645\pi$
$198$	2.95839	+	0.787455i	0.210244	+	0.0559620i
$199$			26.1593i			1.85439i	0.374583	+	0.927194i	$0.377786\pi$
$199$			26.1593i			1.85439i	−0.374583	+	0.927194i	$0.622214\pi$
$200$	0.0420413	−	0.0242726i	0.00297277	−	0.00171633i
$201$	−2.15663	+	5.21877i	−0.152117	+	0.368104i
$202$	−1.14459	+	1.98249i	−0.0805333	+	0.139488i
$203$	2.29453	−	3.97425i	0.161045	−	0.278938i
$204$	−3.05568	+	7.39435i	−0.213940	+	0.517708i
$205$	12.7939	+	22.1597i	0.893567	+	1.54770i
$206$		−	1.21720i		−	0.0848063i
$207$	−2.97991	+	11.1952i	−0.207118	+	0.778123i
$208$		−	3.19916i		−	0.221822i
$209$	−1.26896	−	2.19790i	−0.0877756	−	0.152032i
$210$	−2.61391	−	3.40069i	−0.180377	−	0.234670i
$211$	7.05862	−	12.2259i	0.485936	−	0.841665i	−0.513934	−	0.857830i	$-0.671812\pi$
$211$	7.05862	−	12.2259i	0.485936	−	0.841665i	0.999869	+	0.0161647i	$0.00514561\pi$
$212$	−4.92639	+	8.53275i	−0.338346	+	0.586032i
$213$	0.272172	+	2.05422i	0.0186489	+	0.140753i
$214$	5.19761	+	9.00252i	0.355301	+	0.615400i
$215$	15.1363			1.03229
$216$	2.00039	+	4.79567i	0.136109	+	0.326304i
$217$	−5.87195	−	1.97836i	−0.398614	−	0.134300i
$218$	10.0610	−	5.80870i	0.681415	−	0.393415i
$219$	1.39874	+	10.5570i	0.0945179	+	0.713374i
$220$	−1.96651	−	1.13536i	−0.132582	−	0.0765463i
$221$	−12.7980	−	7.38894i	−0.860888	−	0.497034i
$222$	10.3839	+	13.5094i	0.696923	+	0.906694i
$223$	−24.9380	+	14.3979i	−1.66997	+	0.964158i	−0.702320	+	0.711861i	$0.747853\pi$
$223$	−24.9380	+	14.3979i	−1.66997	+	0.964158i	−0.967650	+	0.252297i	$0.918814\pi$
$224$			1.11288i			0.0743575i
$225$	−0.103150	−	0.102809i	−0.00687667	−	0.00685395i
$226$	16.8084			1.11808
$227$	−12.7248	+	7.34666i	−0.844573	+	0.487615i	−0.858816	−	0.512284i	$-0.828800\pi$
$227$	−12.7248	+	7.34666i	−0.844573	+	0.487615i	0.0142427	+	0.999899i	$0.495466\pi$
$228$	1.64517	−	3.98110i	0.108954	−	0.263655i
$229$	6.07989	+	3.51023i	0.401771	+	0.231962i	0.687248	−	0.726423i	$-0.258819\pi$
$229$	6.07989	+	3.51023i	0.401771	+	0.231962i	−0.285477	+	0.958386i	$0.592152\pi$
$230$	4.29648	−	7.44172i	0.283302	−	0.490693i
$231$	0.751242	−	1.81791i	0.0494281	−	0.119610i
$232$	3.57113	−	2.06180i	0.234456	−	0.135364i
$233$			2.04882i			0.134223i	0.997745	+	0.0671113i	$0.0213783\pi$
$233$			2.04882i			0.134223i	−0.997745	+	0.0671113i	$0.978622\pi$
$234$	−9.26634	+	2.49935i	−0.605760	+	0.163388i
$235$	−22.8368			−1.48971
$236$	5.10909	−	2.94973i	0.332573	−	0.192011i
$237$	3.47087	−	2.66786i	0.225457	−	0.173296i
$238$	4.45200	+	2.57036i	0.288580	+	0.166612i
$239$	7.43679	−	12.8809i	0.481046	−	0.833196i	−0.518718	−	0.854946i	$-0.673590\pi$
$239$	7.43679	−	12.8809i	0.481046	−	0.833196i	0.999763	+	0.0217497i	$0.00692370\pi$
$240$	−0.506227	−	3.82075i	−0.0326768	−	0.246628i
$241$	11.0795	−	6.39675i	0.713693	−	0.412051i	−0.0987341	−	0.995114i	$-0.531479\pi$
$241$	11.0795	−	6.39675i	0.713693	−	0.412051i	0.812427	+	0.583063i	$0.198146\pi$
$242$			9.95865i			0.640166i
$243$	12.3278	−	9.54073i	0.790828	−	0.612038i
$244$		−	1.78998i		−	0.114592i
$245$	11.1028	−	6.41020i	0.709331	−	0.409533i
$246$	−19.7446	+	2.61605i	−1.25887	+	0.166793i
$247$	6.89041	+	3.97818i	0.438426	+	0.253126i
$248$	−3.68060	−	4.17770i	−0.233719	−	0.265284i
$249$	−2.14235	−	2.78719i	−0.135766	−	0.176631i
$250$	5.61698	+	9.72889i	0.355249	+	0.615309i
$251$	−26.7812			−1.69042			−0.845208	−	0.534437i	$-0.820524\pi$
$251$	−26.7812			−1.69042			−0.845208	+	0.534437i	$0.820524\pi$
$252$	3.22345	−	0.869440i	0.203058	−	0.0547695i
$253$	3.94072			0.247751
$254$	−1.15114	−	1.99384i	−0.0722291	−	0.125104i
$255$	−16.4538	−	6.79945i	−1.03038	−	0.425798i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.66716	+	3.84929i	0.415886	+	0.240112i	0.693316	−	0.720634i	$-0.256149\pi$
$257$	6.66716	+	3.84929i	0.415886	+	0.240112i	−0.277430	+	0.960746i	$0.589483\pi$
$258$	−4.49972	+	10.8888i	−0.280140	+	0.677905i
$259$	9.48125	−	5.47400i	0.589136	−	0.340138i
$260$	7.11873			0.441485
$261$	−8.76192	−	8.73297i	−0.542349	−	0.540557i
$262$	5.36015			0.331151
$263$	8.91249	+	15.4369i	0.549567	+	0.951879i	0.998304	+	0.0582147i	$0.0185408\pi$
$263$	8.91249	+	15.4369i	0.549567	+	0.951879i	−0.448737	+	0.893664i	$0.648126\pi$
$264$	1.40136	−	1.07715i	0.0862479	−	0.0662938i
$265$	−18.9870	−	10.9621i	−1.16636	−	0.673398i
$266$	−2.39694	−	1.38388i	−0.146966	−	0.0848509i
$267$	−9.15551	+	1.21305i	−0.560308	+	0.0742376i
$268$	1.63010	+	2.82341i	0.0995741	+	0.172467i
$269$	31.1931			1.90188			0.950938	−	0.309383i	$-0.100122\pi$
$269$	31.1931			1.90188			0.950938	+	0.309383i	$0.100122\pi$
$270$	−10.6713	+	4.45124i	−0.649432	+	0.270894i
$271$			29.8901i			1.81569i	0.419301	+	0.907847i	$0.362275\pi$
$271$			29.8901i			1.81569i	−0.419301	+	0.907847i	$0.637725\pi$
$272$	2.30965	+	4.00043i	0.140043	+	0.242561i
$273$	0.809961	+	6.11318i	0.0490211	+	0.369986i
$274$	12.0926	+	6.98169i	0.730543	+	0.421779i
$275$	−0.0247693	+	0.0429018i	−0.00149365	+	0.00258707i
$276$	4.07617	+	5.30308i	0.245357	+	0.319208i
$277$	−2.47722	+	1.43022i	−0.148842	+	0.0859337i	−0.572571	−	0.819855i	$-0.694054\pi$
$277$	−2.47722	+	1.43022i	−0.148842	+	0.0859337i	0.423730	+	0.905789i	$0.360721\pi$
$278$	7.57570			0.454360
$279$	−9.22518	+	13.9247i	−0.552297	+	0.833647i
$280$	−2.47637			−0.147991
$281$	18.7340	−	10.8161i	1.11758	−	0.645235i	0.176797	−	0.984247i	$-0.443426\pi$
$281$	18.7340	−	10.8161i	1.11758	−	0.645235i	0.940782	+	0.339013i	$0.110093\pi$
$282$	6.78892	−	16.4283i	0.404275	−	0.978294i
$283$	−3.83801	+	6.64763i	−0.228146	+	0.395161i	−0.957259	−	0.289233i	$-0.906600\pi$
$283$	−3.83801	+	6.64763i	−0.228146	+	0.395161i	0.729113	+	0.684394i	$0.239933\pi$
$284$	1.03608	+	0.598183i	0.0614803	+	0.0354956i
$285$	8.85868	+	3.66080i	0.524743	+	0.216847i
$286$	1.63232	+	2.82726i	0.0965211	+	0.167180i
$287$			12.7972i			0.755398i
$288$	2.89906	+	0.771661i	0.170829	+	0.0454706i
$289$	4.33788			0.255169
$290$	4.58788	+	7.94644i	0.269410	+	0.466631i
$291$	2.23785	+	2.91143i	0.131185	+	0.170671i
$292$	5.32461	+	3.07417i	0.311599	+	0.179902i
$293$	12.5129	+	7.22431i	0.731010	+	0.422049i	0.818792	−	0.574091i	$-0.194644\pi$
$293$	12.5129	+	7.22431i	0.731010	+	0.422049i	−0.0877814	+	0.996140i	$0.527978\pi$
$294$	1.31073	+	9.89275i	0.0764434	+	0.576957i
$295$	6.56371	+	11.3687i	0.382154	+	0.661910i
$296$	9.83752			0.571795
$297$	−4.21476	−	3.21751i	−0.244565	−	0.186699i
$298$	−5.23653			−0.303344
$299$	−10.6990	+	6.17708i	−0.618740	+	0.357230i
$300$	−0.0833542	+	0.0110439i	−0.00481245	+	0.000637622i
$301$	6.55592	+	3.78506i	0.377877	+	0.218167i
$302$	4.92539	−	8.53103i	0.283424	−	0.490905i
$303$	3.14364	−	2.41633i	0.180597	−	0.138815i
$304$	−1.24351	−	2.15382i	−0.0713200	−	0.123530i
$305$	3.98303			0.228068
$306$	9.78278	−	9.81520i	0.559244	−	0.561098i
$307$	33.7966			1.92887			0.964436	−	0.264317i	$-0.0851465\pi$
$307$	33.7966			1.92887			0.964436	+	0.264317i	$0.0851465\pi$
$308$	−0.567830	−	0.983510i	−0.0323551	−	0.0560407i
$309$	−0.805181	+	1.94844i	−0.0458052	+	0.110843i
$310$	9.29616	−	8.19003i	0.527986	−	0.465162i
$311$	12.3453	+	7.12756i	0.700038	+	0.404167i	0.807361	−	0.590057i	$-0.200895\pi$
$311$	12.3453	+	7.12756i	0.700038	+	0.404167i	−0.107324	+	0.994224i	$0.534228\pi$
$312$	−2.11626	+	5.12107i	−0.119809	+	0.289924i
$313$	−7.96020	+	4.59583i	−0.449937	+	0.259771i	−0.707804	−	0.706409i	$-0.750314\pi$
$313$	−7.96020	+	4.59583i	−0.449937	+	0.259771i	0.257866	+	0.966181i	$0.416981\pi$
$314$			13.3524i			0.753520i
$315$	1.93467	+	7.17278i	0.109006	+	0.404140i
$316$		−	2.52748i		−	0.142182i
$317$	6.43584	−	3.71574i	0.361473	−	0.208696i	−0.308254	−	0.951304i	$-0.599745\pi$
$317$	6.43584	−	3.71574i	0.361473	−	0.208696i	0.669727	+	0.742608i	$0.266411\pi$
$318$	13.5304	−	10.4000i	0.758746	−	0.583204i
$319$	−2.10399	+	3.64423i	−0.117801	+	0.204037i
$320$	−1.92707	−	1.11259i	−0.107726	−	0.0621959i
$321$	−2.36490	−	17.8491i	−0.131996	−	0.996237i
$322$	3.72183	−	2.14880i	0.207409	−	0.119748i
$323$	−11.4882			−0.639223
$324$	−0.0297829	−	8.99995i	−0.00165461	−	0.499997i
$325$		−	0.155304i		−	0.00861470i
$326$	11.8259	−	6.82771i	0.654978	−	0.378152i
$327$	−19.9476	+	2.64294i	−1.10311	+	0.146155i
$328$	−5.74960	+	9.95860i	−0.317469	+	0.549872i
$329$	−9.89119	−	5.71068i	−0.545319	−	0.314840i
$330$	2.39685	+	3.11829i	0.131942	+	0.171656i
$331$	23.7405	−	13.7066i	1.30489	−	0.753381i	0.323655	−	0.946175i	$-0.395088\pi$
$331$	23.7405	−	13.7066i	1.30489	−	0.753381i	0.981239	+	0.192794i	$0.0617549\pi$
$332$	−2.02962			−0.111390
$333$	−7.68557	−	28.4943i	−0.421167	−	1.56148i
$334$			6.05959i			0.331566i
$335$	−6.28262	+	3.62727i	−0.343256	+	0.198179i
$336$	0.736175	−	1.78145i	0.0401616	−	0.0971861i
$337$	−2.96074	−	1.70938i	−0.161282	−	0.0931160i	0.417187	−	0.908821i	$-0.363016\pi$
$337$	−2.96074	−	1.70938i	−0.161282	−	0.0931160i	−0.578468	+	0.815705i	$0.696349\pi$
$338$	2.39487	+	1.38268i	0.130264	+	0.0752077i
$339$	−26.9062	−	11.1188i	−1.46134	−	0.603892i
$340$	−8.90169	+	5.13940i	−0.482762	+	0.278723i
$341$	5.38434	+	1.81407i	0.291578	+	0.0982377i
$342$	−5.26701	+	5.28447i	−0.284808	+	0.285752i
$343$	14.2020			0.766838
$344$	3.40113	+	5.89094i	0.183377	+	0.317618i
$345$	−11.8003	+	9.07024i	−0.635309	+	0.488325i
$346$	7.35730	−	12.7432i	0.395531	−	0.685080i
$347$	−7.11555	+	12.3245i	−0.381983	+	0.661613i	−0.991346	−	0.131278i	$-0.958092\pi$
$347$	−7.11555	+	12.3245i	−0.381983	+	0.661613i	0.609363	+	0.792891i	$0.291425\pi$
$348$	−7.08039	+	0.938111i	−0.379549	+	0.0502880i
$349$	12.1759	+	21.0892i	0.651759	+	1.12888i	0.982696	+	0.185227i	$0.0593020\pi$
$349$	12.1759	+	21.0892i	0.651759	+	1.12888i	−0.330937	+	0.943653i	$0.607365\pi$
$350$			0.0540250i			0.00288776i
$351$	16.4865	+	2.12887i	0.879982	+	0.113631i
$352$		−	1.02047i		−	0.0543911i
$353$	13.1781	+	22.8251i	0.701400	+	1.21486i	0.967975	+	0.251046i	$0.0807744\pi$
$353$	13.1781	+	22.8251i	0.701400	+	1.21486i	−0.266576	+	0.963814i	$0.585892\pi$
$354$	−10.1296	+	1.34212i	−0.538385	+	0.0713329i
$355$	−1.33107	+	2.30548i	−0.0706458	+	0.122362i
$356$	−2.66606	+	4.61776i	−0.141301	+	0.244741i
$357$	−5.42625	−	7.05953i	−0.287188	−	0.373630i
$358$	11.4044	−	6.58431i	0.602739	−	0.347992i
$359$		−	16.3382i		−	0.862297i	−0.902281	−	0.431149i	$-0.858108\pi$
$359$		−	16.3382i		−	0.862297i	0.902281	−	0.431149i	$-0.141892\pi$
$360$	−1.71709	+	6.45095i	−0.0904986	+	0.339995i
$361$	−12.8148			−0.674461
$362$	0.0915732	+	0.158609i	0.00481298	+	0.00833633i
$363$	6.58768	−	15.9413i	0.345763	−	0.836704i
$364$	3.08330	+	1.78014i	0.161609	+	0.0933049i
$365$	−6.84059	+	11.8483i	−0.358053	+	0.620166i
$366$	−1.18408	+	2.86531i	−0.0618926	+	0.149772i
$367$	−8.01274	+	4.62616i	−0.418262	+	0.241483i	−0.694333	−	0.719654i	$-0.744301\pi$
$367$	−8.01274	+	4.62616i	−0.418262	+	0.241483i	0.276072	+	0.961137i	$0.410967\pi$
$368$	3.86168			0.201304
$369$	33.3369	+	8.87349i	1.73545	+	0.461935i
$370$			21.8903i			1.13802i
$371$	−5.48249	−	9.49594i	−0.284636	−	0.493005i
$372$	3.12818	+	9.12220i	0.162189	+	0.472964i
$373$	4.49388	−	7.78363i	0.232684	−	0.403021i	−0.725913	−	0.687787i	$-0.758582\pi$
$373$	4.49388	−	7.78363i	0.232684	−	0.403021i	0.958597	+	0.284766i	$0.0919157\pi$
$374$	−4.08230	−	2.35692i	−0.211091	−	0.121873i
$375$	−2.55571	−	19.2892i	−0.131976	−	0.996090i
$376$	−5.13144	−	8.88791i	−0.264634	−	0.458359i
$377$		−	13.1920i		−	0.679425i
$378$	−5.73509	−	0.740562i	−0.294981	−	0.0380904i
$379$	−23.1494			−1.18910			−0.594552	−	0.804057i	$-0.702670\pi$
$379$	−23.1494			−1.18910			−0.594552	+	0.804057i	$0.702670\pi$
$380$	4.79264	−	2.76703i	0.245857	−	0.141946i
$381$	0.523767	+	3.95313i	0.0268334	+	0.202525i
$382$	−0.0321011	+	0.0556007i	−0.00164244	+	0.00284478i
$383$	−3.83913	+	6.64957i	−0.196170	+	0.339777i	−0.947284	−	0.320396i	$-0.896184\pi$
$383$	−3.83913	+	6.64957i	−0.196170	+	0.339777i	0.751113	+	0.660174i	$0.229517\pi$
$384$	1.37326	−	1.05554i	0.0700787	−	0.0538654i
$385$	2.18849	−	1.26353i	0.111536	−	0.0643953i
$386$		−	2.51820i		−	0.128173i
$387$	14.4059	−	14.4536i	0.732293	−	0.734720i
$388$	2.12009			0.107631
$389$	8.96129	+	15.5214i	0.454355	+	0.786967i	0.998651	−	0.0519269i	$-0.0165363\pi$
$389$	8.96129	+	15.5214i	0.454355	+	0.786967i	−0.544295	+	0.838894i	$0.683203\pi$
$390$	−11.3953	−	4.70906i	−0.577026	−	0.238453i
$391$	8.91912	−	15.4484i	0.451059	−	0.781258i
$392$	4.98960	+	2.88075i	0.252013	+	0.145500i
$393$	−8.58029	−	3.54576i	−0.432818	−	0.178860i
$394$	−15.9823	+	9.22741i	−0.805179	+	0.464870i
$395$	5.62410			0.282979
$396$	−2.95577	+	0.797241i	−0.148533	+	0.0400629i
$397$	−28.6115			−1.43597			−0.717984	−	0.696060i	$-0.754935\pi$
$397$	−28.6115			−1.43597			−0.717984	+	0.696060i	$0.754935\pi$
$398$	−13.0797	−	22.6547i	−0.655625	−	1.13558i
$399$	2.92148	+	3.80083i	0.146257	+	0.190279i
$400$	−0.0242726	+	0.0420413i	−0.00121363	+	0.00210207i
$401$	7.63116	−	13.2176i	0.381082	−	0.660053i	−0.610135	−	0.792297i	$-0.708885\pi$
$401$	7.63116	−	13.2176i	0.381082	−	0.660053i	0.991217	+	0.132244i	$0.0422182\pi$
$402$	−0.741690	−	5.59791i	−0.0369921	−	0.279198i
$403$	−17.4620	+	3.51475i	−0.869843	+	0.175082i
$404$		−	2.28919i		−	0.113891i
$405$	20.0266	−	0.0662725i	0.995128	−	0.00329311i
$406$			4.58907i			0.227752i
$407$	−8.69392	+	5.01944i	−0.430941	+	0.248804i
$408$	−1.05088	−	7.93154i	−0.0520265	−	0.392670i
$409$	−24.7600	−	14.2952i	−1.22430	−	0.706852i	−0.258471	−	0.966019i	$-0.583219\pi$
$409$	−24.7600	−	14.2952i	−1.22430	−	0.706852i	−0.965832	+	0.259167i	$0.916552\pi$
$410$	−22.1597	−	12.7939i	−1.09439	−	0.631847i
$411$	−14.7389	−	19.1753i	−0.727018	−	0.945847i
$412$	0.608600	+	1.05413i	0.0299836	+	0.0519330i
$413$			6.56541i			0.323063i
$414$	−3.01694	−	11.1853i	−0.148275	−	0.549728i
$415$		−	4.51629i		−	0.221696i
$416$	1.59958	+	2.77056i	0.0784259	+	0.135838i
$417$	−12.1268	−	5.01135i	−0.593854	−	0.245407i
$418$	2.19790	+	1.26896i	0.107503	+	0.0620667i
$419$	7.33646	+	4.23571i	0.358409	+	0.206928i	0.668383	−	0.743817i	$-0.266987\pi$
$419$	7.33646	+	4.23571i	0.358409	+	0.206928i	−0.309973	+	0.950745i	$0.600320\pi$
$420$	3.96406	+	1.63813i	0.193426	+	0.0799323i
$421$	−13.1893	−	22.8445i	−0.642807	−	1.11337i	−0.984803	−	0.173673i	$-0.944436\pi$
$421$	−13.1893	−	22.8445i	−0.642807	−	1.11337i	0.341996	−	0.939701i	$-0.388897\pi$
$422$			14.1172i			0.687217i
$423$	−21.7348	+	21.8068i	−1.05678	+	1.06028i
$424$		−	9.85277i		−	0.478493i
$425$	0.112122	+	0.194201i	0.00543872	+	0.00942014i
$426$	−1.26282	−	1.64292i	−0.0611836	−	0.0795996i
$427$	1.72515	+	0.996017i	0.0834859	+	0.0482006i
$428$	−9.00252	−	5.19761i	−0.435153	−	0.251236i
$429$	−0.742701	−	5.60554i	−0.0358580	−	0.270638i
$430$	−13.1084	+	7.56816i	−0.632145	+	0.364969i
$431$		−	20.6052i		−	0.992519i	−0.868174	−	0.496260i	$-0.834706\pi$
$431$		−	20.6052i		−	0.992519i	0.868174	−	0.496260i	$-0.165294\pi$
$432$	−4.13022	−	3.15298i	−0.198715	−	0.151698i
$433$			24.4623i			1.17558i	0.809012	+	0.587792i	$0.200003\pi$
$433$			24.4623i			1.17558i	−0.809012	+	0.587792i	$0.799997\pi$
$434$	6.07443	−	1.22266i	0.291582	−	0.0586898i
$435$	−2.08747	−	15.7552i	−0.100087	−	0.755404i
$436$	−5.80870	+	10.0610i	−0.278186	+	0.481833i
$437$	−4.80203	+	8.31736i	−0.229712	+	0.397873i
$438$	−6.48983	−	8.44323i	−0.310096	−	0.403433i
$439$	7.15542	+	12.3935i	0.341509	+	0.591512i	0.984713	−	0.174183i	$-0.0557285\pi$
$439$	7.15542	+	12.3935i	0.341509	+	0.591512i	−0.643204	+	0.765695i	$0.722395\pi$
$440$	2.27073			0.108253
$441$	4.44592	−	16.7029i	0.211711	−	0.795377i
$442$	14.7779			0.702912
$443$	4.39636	−	2.53824i	0.208877	−	0.120595i	−0.391912	−	0.920003i	$-0.628186\pi$
$443$	4.39636	−	2.53824i	0.208877	−	0.120595i	0.600789	+	0.799407i	$0.294853\pi$
$444$	−15.7475	−	6.50755i	−0.747341	−	0.308835i
$445$	−10.2754	−	5.93249i	−0.487099	−	0.281227i
$446$	14.3979	−	24.9380i	0.681762	−	1.18085i
$447$	8.38240	+	3.46398i	0.396474	+	0.163841i
$448$	−0.556441	−	0.963784i	−0.0262894	−	0.0455345i
$449$	34.1185			1.61015			0.805076	−	0.593172i	$-0.202125\pi$
$449$	34.1185			1.61015			0.805076	+	0.593172i	$0.202125\pi$
$450$	0.140735	+	0.0374604i	0.00663432	+	0.00176590i
$451$		−	11.7346i		−	0.552559i
$452$	−14.5565	+	8.40422i	−0.684682	+	0.395301i
$453$	−13.5276	+	10.3979i	−0.635584	+	0.488537i
$454$	7.34666	−	12.7248i	0.344796	−	0.597204i
$455$	−3.96115	+	6.86092i	−0.185702	+	0.321645i
$456$	0.565792	+	4.27031i	0.0264956	+	0.199976i
$457$	5.09131	−	2.93947i	0.238161	−	0.137503i	−0.376170	−	0.926551i	$-0.622759\pi$
$457$	5.09131	−	2.93947i	0.238161	−	0.137503i	0.614331	+	0.789048i	$0.289426\pi$
$458$	−7.02046			−0.328044
$459$	−22.1526	+	9.24039i	−1.03400	+	0.431304i
$460$			8.59296i			0.400649i
$461$	−19.7473	−	34.2032i	−0.919721	−	1.59300i	−0.799838	−	0.600216i	$-0.795081\pi$
$461$	−19.7473	−	34.2032i	−0.919721	−	1.59300i	−0.119883	−	0.992788i	$-0.538252\pi$
$462$	0.258361	+	1.94998i	0.0120200	+	0.0907212i
$463$	20.0463	+	11.5738i	0.931633	+	0.537878i	0.887328	−	0.461140i	$-0.152559\pi$
$463$	20.0463	+	11.5738i	0.931633	+	0.537878i	0.0443051	+	0.999018i	$0.485893\pi$
$464$	−2.06180	+	3.57113i	−0.0957164	+	0.165786i
$465$	−20.2986	+	6.96079i	−0.941325	+	0.322799i
$466$	−1.02441	−	1.77433i	−0.0474549	−	0.0821943i
$467$		−	6.12670i		−	0.283510i	−0.989902	−	0.141755i	$-0.954725\pi$
$467$		−	6.12670i		−	0.283510i	0.989902	−	0.141755i	$-0.0452745\pi$
$468$	6.77521	−	6.79767i	0.313184	−	0.314222i
$469$	−3.62821			−0.167535
$470$	19.7773	−	11.4184i	0.912257	−	0.526692i
$471$	8.83266	−	21.3739i	0.406988	−	0.984859i
$472$	−2.94973	+	5.10909i	−0.135772	+	0.235165i
$473$	−6.01151	−	3.47075i	−0.276409	−	0.159585i
$474$	−1.67193	+	4.04587i	−0.0767944	+	0.185833i
$475$	−0.0603662	−	0.104557i	−0.00276979	−	0.00479742i
$476$	−5.14073			−0.235625
$477$	−28.5385	+	7.69749i	−1.30669	+	0.352444i
$478$			14.8736i			0.680302i
$479$	−6.48652	+	3.74499i	−0.296377	+	0.171113i	−0.640814	−	0.767696i	$-0.721403\pi$
$479$	−6.48652	+	3.74499i	−0.296377	+	0.171113i	0.344437	+	0.938809i	$0.388070\pi$
$480$	2.34878	+	3.05575i	0.107207	+	0.139475i
$481$	15.7359	−	27.2554i	0.717496	−	1.24274i
$482$	−6.39675	+	11.0795i	−0.291364	+	0.504657i
$483$	−7.37917	+	0.977697i	−0.335764	+	0.0444867i
$484$	−4.97932	−	8.62444i	−0.226333	−	0.392020i
$485$			4.71760i			0.214215i
$486$	−5.90582	+	14.4264i	−0.267893	+	0.654395i
$487$			9.68519i			0.438878i	0.975626	+	0.219439i	$0.0704227\pi$
$487$			9.68519i			0.438878i	−0.975626	+	0.219439i	$0.929577\pi$
$488$	0.894989	+	1.55017i	0.0405142	+	0.0701727i
$489$	−23.4470	+	3.10659i	−1.06031	+	0.140485i
$490$	−6.41020	+	11.1028i	−0.289583	+	0.501573i
$491$	−8.25821	+	14.3036i	−0.372688	+	0.645514i	−0.989978	−	0.141221i	$-0.954897\pi$
$491$	−8.25821	+	14.3036i	−0.372688	+	0.645514i	0.617290	+	0.786736i	$0.288230\pi$
$492$	15.7913	−	12.1379i	0.711929	−	0.547218i
$493$	9.52404	+	16.4961i	0.428941	+	0.742948i
$494$	−7.95636			−0.357974
$495$	−1.77401	−	6.57714i	−0.0797358	−	0.295621i
$496$	5.27635	+	1.77769i	0.236915	+	0.0798207i
$497$	−1.15304	+	0.665707i	−0.0517208	+	0.0298610i
$498$	3.24893	+	1.34260i	0.145588	+	0.0601634i
$499$	16.5265	+	9.54159i	0.739829	+	0.427140i	0.822007	−	0.569477i	$-0.192854\pi$
$499$	16.5265	+	9.54159i	0.739829	+	0.427140i	−0.0821782	+	0.996618i	$0.526188\pi$
$500$	−9.72889	−	5.61698i	−0.435089	−	0.251199i
$501$	4.00844	−	9.69991i	0.179084	−	0.433360i
$502$	23.1932	−	13.3906i	1.03516	−	0.597652i
$503$			7.99974i			0.356691i	0.983968	+	0.178345i	$0.0570744\pi$
$503$			7.99974i			0.356691i	−0.983968	+	0.178345i	$0.942926\pi$
$504$	−2.35687	+	2.36468i	−0.104983	+	0.105331i
$505$	5.09386			0.226674
$506$	−3.41276	+	1.97036i	−0.151716	+	0.0875932i
$507$	−2.91895	−	3.79754i	−0.129635	−	0.168655i
$508$	1.99384	+	1.15114i	0.0884622	+	0.0510737i
$509$	8.01549	−	13.8832i	0.355280	−	0.615363i	−0.631886	−	0.775062i	$-0.717719\pi$
$509$	8.01549	−	13.8832i	0.355280	−	0.615363i	0.987166	+	0.159698i	$0.0510521\pi$
$510$	17.6491	−	2.33841i	0.781517	−	0.103547i
$511$	−5.92566	+	3.42118i	−0.262136	+	0.151344i
$512$		−	1.00000i		−	0.0441942i
$513$	11.9269	−	4.97500i	0.526585	−	0.219651i
$514$	−7.69857			−0.339569
$515$	−2.34563	+	1.35425i	−0.103361	+	0.0596753i
$516$	−1.54751	−	11.6798i	−0.0681252	−	0.514175i
$517$	9.06982	+	5.23646i	0.398890	+	0.230299i
$518$	−5.47400	+	9.48125i	−0.240514	+	0.416582i
$519$	−20.2069	+	15.5319i	−0.886985	+	0.681774i
$520$	−6.16501	+	3.55937i	−0.270353	+	0.156089i
$521$		−	33.5039i		−	1.46783i	−0.679241	−	0.733915i	$-0.737691\pi$
$521$		−	33.5039i		−	1.46783i	0.679241	−	0.733915i	$-0.262309\pi$
$522$	11.9545	+	3.18202i	0.523236	+	0.139273i
$523$			37.4112i			1.63588i	0.575304	+	0.817940i	$0.304884\pi$
$523$			37.4112i			1.63588i	−0.575304	+	0.817940i	$0.695116\pi$
$524$	−4.64203	+	2.68008i	−0.202788	+	0.117080i
$525$	0.0357377	−	0.0864807i	0.00155972	−	0.00377433i
$526$	−15.4369	−	8.91249i	−0.673080	−	0.388603i
$527$	19.2980	−	17.0018i	0.840635	−	0.740610i
$528$	−0.675042	+	1.63352i	−0.0293774	+	0.0710897i
$529$	4.04370	+	7.00390i	0.175813	+	0.304517i
$530$	21.9243			0.952329
$531$	17.1029	+	4.55239i	0.742202	+	0.197557i
$532$	2.76775			0.119997
$533$	18.3939	+	31.8592i	0.796729	+	1.37997i
$534$	7.32237	−	5.62829i	0.316870	−	0.243560i
$535$	11.5656	−	20.0323i	0.500026	−	0.866071i
$536$	−2.82341	−	1.63010i	−0.121953	−	0.0704095i
$537$	−22.6111	+	2.99584i	−0.975742	+	0.129280i
$538$	−27.0140	+	15.5965i	−1.16466	+	0.672414i
$539$	−5.87942			−0.253244
$540$	7.01596	−	9.19052i	0.301919	−	0.395497i
$541$	30.6235			1.31661			0.658303	−	0.752753i	$-0.271275\pi$
$541$	30.6235			1.31661			0.658303	+	0.752753i	$0.271275\pi$
$542$	−14.9451	−	25.8856i	−0.641945	−	1.11188i
$543$	−0.0416656	−	0.314471i	−0.00178804	−	0.0134952i
$544$	−4.00043	−	2.30965i	−0.171517	−	0.0990253i
$545$	−22.3875	−	12.9255i	−0.958977	−	0.553665i
$546$	−3.75804	−	4.88919i	−0.160829	−	0.209238i
$547$	1.58488	+	2.74509i	0.0677645	+	0.117372i	0.897917	−	0.440165i	$-0.145080\pi$
$547$	1.58488	+	2.74509i	0.0677645	+	0.117372i	−0.830152	+	0.557536i	$0.811747\pi$
$548$	−13.9634			−0.596486
$549$	3.79083	−	3.80339i	0.161789	−	0.162325i
$550$		−	0.0495387i		−	0.00211234i
$551$	−5.12771	−	8.88146i	−0.218448	−	0.378363i
$552$	−6.18160	−	2.55451i	−0.263107	−	0.108727i
$553$	2.43594	+	1.40639i	0.103587	+	0.0598058i
$554$	1.43022	−	2.47722i	0.0607643	−	0.105247i
$555$	14.4805	−	35.0410i	0.614664	−	1.48741i
$556$	−6.56075	+	3.78785i	−0.278238	+	0.160641i
$557$	2.07470			0.0879079			0.0439539	−	0.999034i	$-0.486005\pi$
$557$	2.07470			0.0879079			0.0439539	+	0.999034i	$0.486005\pi$
$558$	1.02691	−	16.6717i	0.0434726	−	0.705769i
$559$	21.7616			0.920416
$560$	2.14460	−	1.23818i	0.0906258	−	0.0523228i
$561$	4.97566	+	6.47330i	0.210072	+	0.273303i
$562$	−10.8161	+	18.7340i	−0.456250	+	0.790248i
$563$	37.5837	+	21.6990i	1.58397	+	0.914503i	0.994272	+	0.106876i	$0.0340846\pi$
$563$	37.5837	+	21.6990i	1.58397	+	0.914503i	0.589693	+	0.807627i	$0.299249\pi$
$564$	2.33479	+	17.6218i	0.0983124	+	0.742013i
$565$	−18.7009	−	32.3910i	−0.786755	−	1.36270i
$566$		−	7.67602i		−	0.322647i
$567$	8.69058	+	4.97924i	0.364970	+	0.209108i
$568$	−1.19637			−0.0501984
$569$	17.6206	+	30.5197i	0.738693	+	1.27945i	0.953084	+	0.302706i	$0.0978900\pi$
$569$	17.6206	+	30.5197i	0.738693	+	1.27945i	−0.214391	+	0.976748i	$0.568777\pi$
$570$	−9.50224	+	1.25899i	−0.398005	+	0.0527334i
$571$	31.1820	+	18.0029i	1.30492	+	0.753399i	0.981244	−	0.192768i	$-0.0617465\pi$
$571$	31.1820	+	18.0029i	1.30492	+	0.753399i	0.323680	+	0.946167i	$0.395080\pi$
$572$	−2.82726	−	1.63232i	−0.118214	−	0.0682508i
$573$	0.0881660	−	0.0677681i	0.00368319	−	0.00283105i
$574$	−6.39862	−	11.0827i	−0.267073	−	0.462585i
$575$	0.187466			0.00781786
$576$	−2.89649	+	0.781251i	−0.120687	+	0.0325521i
$577$	−32.1410			−1.33805			−0.669023	−	0.743242i	$-0.733287\pi$
$577$	−32.1410			−1.33805			−0.669023	+	0.743242i	$0.733287\pi$
$578$	−3.75671	+	2.16894i	−0.156259	+	0.0902160i
$579$	−1.66580	+	4.03102i	−0.0692282	+	0.167523i
$580$	−7.94644	−	4.58788i	−0.329958	−	0.190501i
$581$	1.12937	−	1.95612i	0.0468540	−	0.0811534i
$582$	−3.39375	−	1.40245i	−0.140675	−	0.0581333i
$583$	5.02722	+	8.70740i	0.208206	+	0.360623i
$584$	−6.14833			−0.254420
$585$	15.1261	+	15.0761i	0.625387	+	0.623320i
$586$	−14.4486			−0.596867
$587$	−6.41401	−	11.1094i	−0.264734	−	0.458533i	0.702760	−	0.711427i	$-0.251951\pi$
$587$	−6.41401	−	11.1094i	−0.264734	−	0.458533i	−0.967494	+	0.252894i	$0.918618\pi$
$588$	−6.08150	−	7.91200i	−0.250797	−	0.326286i
$589$	−10.3900	+	9.15371i	−0.428112	+	0.377172i
$590$	−11.3687	−	6.56371i	−0.468041	−	0.270223i
$591$	31.6878	−	4.19845i	1.30346	−	0.172701i
$592$	−8.51955	+	4.91876i	−0.350151	+	0.202160i
$593$		−	23.3171i		−	0.957519i	−0.877946	−	0.478760i	$-0.841087\pi$
$593$		−	23.3171i		−	0.957519i	0.877946	−	0.478760i	$-0.158913\pi$
$594$	5.25884	+	0.679066i	0.215773	+	0.0278624i
$595$		−	11.4391i		−	0.468956i
$596$	4.53497	−	2.61827i	0.185760	−	0.107248i
$597$	5.95122	+	44.9168i	0.243567	+	1.83832i
$598$	6.17708	−	10.6990i	0.252599	−	0.437515i
$599$	−22.1736	−	12.8019i	−0.905988	−	0.523073i	−0.0268500	−	0.999639i	$-0.508548\pi$
$599$	−22.1736	−	12.8019i	−0.905988	−	0.523073i	−0.879138	+	0.476567i	$0.841881\pi$
$600$	0.0666648	−	0.0512414i	0.00272158	−	0.00209192i
$601$	5.37109	−	3.10100i	0.219091	−	0.126492i	−0.386438	−	0.922315i	$-0.626295\pi$
$601$	5.37109	−	3.10100i	0.219091	−	0.126492i	0.605529	+	0.795823i	$0.292961\pi$
$602$	−7.57012			−0.308535
$603$	−2.51577	+	9.45150i	−0.102450	+	0.384895i
$604$			9.85078i			0.400823i
$605$	19.1910	−	11.0799i	0.780225	−	0.450463i
$606$	−1.51430	+	3.66442i	−0.0615144	+	0.148857i
$607$	−15.6728	+	27.1461i	−0.636141	+	1.10183i	0.350132	+	0.936700i	$0.386137\pi$
$607$	−15.6728	+	27.1461i	−0.636141	+	1.10183i	−0.986272	+	0.165127i	$0.947197\pi$
$608$	2.15382	+	1.24351i	0.0873488	+	0.0504308i
$609$	3.03568	−	7.34597i	0.123012	−	0.297674i
$610$	−3.44941	+	1.99152i	−0.139663	+	0.0806342i
$611$	−32.8326			−1.32827
$612$	−3.56453	+	13.3916i	−0.144088	+	0.541323i
$613$		−	40.9491i		−	1.65392i	−0.562261	−	0.826960i	$-0.690068\pi$
$613$		−	40.9491i		−	1.65392i	0.562261	−	0.826960i	$-0.309932\pi$
$614$	−29.2687	+	16.8983i	−1.18119	+	0.681959i
$615$	27.0091	+	35.1387i	1.08911	+	1.41693i
$616$	0.983510	+	0.567830i	0.0396267	+	0.0228785i
$617$	34.9638	+	20.1863i	1.40759	+	0.812671i	0.995155	−	0.0983164i	$-0.0313457\pi$
$617$	34.9638	+	20.1863i	1.40759	+	0.812671i	0.412433	+	0.910988i	$0.364679\pi$
$618$	−0.276911	−	2.08999i	−0.0111390	−	0.0840716i
$619$	17.5241	−	10.1175i	0.704353	−	0.406659i	−0.104614	−	0.994513i	$-0.533361\pi$
$619$	17.5241	−	10.1175i	0.704353	−	0.406659i	0.808967	+	0.587854i	$0.200027\pi$
$620$	−3.95569	+	11.7409i	−0.158864	+	0.471524i
$621$	−2.56974	+	19.9007i	−0.103120	+	0.798586i
$622$	−14.2551			−0.571578
$623$	−2.96701	−	5.13902i	−0.118871	−	0.205890i
$624$	−0.727805	−	5.49311i	−0.0291355	−	0.219900i
$625$	12.3775	−	21.4384i	0.495098	−	0.857536i
$626$	4.59583	−	7.96020i	0.183686	−	0.318154i
$627$	−2.67888	−	3.48521i	−0.106984	−	0.139186i
$628$	−6.67621	−	11.5635i	−0.266410	−	0.461435i
$629$			45.4424i			1.81191i
$630$	−5.26186	−	5.24447i	−0.209637	−	0.208945i
$631$		−	32.7799i		−	1.30495i	−0.757811	−	0.652475i	$-0.773731\pi$
$631$		−	32.7799i		−	1.30495i	0.757811	−	0.652475i	$-0.226269\pi$
$632$	1.26374	+	2.18886i	0.0502688	+	0.0870681i
$633$	9.33860	−	22.5982i	0.371176	−	0.898199i
$634$	−3.71574	+	6.43584i	−0.147571	+	0.255600i
$635$	−2.56151	+	4.43666i	−0.101650	+	0.176063i
$636$	−6.51764	+	15.7719i	−0.258441	+	0.625395i
$637$	15.9625	−	9.21598i	0.632459	−	0.365150i
$638$		−	4.20799i		−	0.166596i
$639$	0.934662	+	3.46526i	0.0369747	+	0.137084i
$640$	2.22519			0.0879582
$641$	10.6439	+	18.4357i	0.420408	+	0.728167i	0.995979	−	0.0895841i	$-0.0285538\pi$
$641$	10.6439	+	18.4357i	0.420408	+	0.728167i	−0.575572	+	0.817751i	$0.695220\pi$
$642$	10.9726	+	14.2753i	0.433054	+	0.563401i
$643$	40.7748	+	23.5413i	1.60800	+	0.928379i	0.989817	+	0.142344i	$0.0454639\pi$
$643$	40.7748	+	23.5413i	1.60800	+	0.928379i	0.618182	+	0.786035i	$0.287869\pi$
$644$	−2.14880	+	3.72183i	−0.0846745	+	0.146661i
$645$	25.9897	−	3.44349i	1.02335	−	0.135587i
$646$	9.94911	−	5.74412i	0.391443	−	0.225999i
$647$	−29.5056			−1.15998			−0.579992	−	0.814622i	$-0.696945\pi$
$647$	−29.5056			−1.15998			−0.579992	+	0.814622i	$0.696945\pi$
$648$	4.52577	+	7.77929i	0.177789	+	0.305600i
$649$		−	6.02021i		−	0.236314i
$650$	0.0776519	+	0.134497i	0.00304576	+	0.00527541i
$651$	−10.5325	−	2.06107i	−0.412800	−	0.0807798i
$652$	−6.82771	+	11.8259i	−0.267394	+	0.463139i
$653$	9.32930	+	5.38627i	0.365084	+	0.210781i	0.671308	−	0.741178i	$-0.265733\pi$
$653$	9.32930	+	5.38627i	0.365084	+	0.210781i	−0.306225	+	0.951959i	$0.599066\pi$
$654$	15.9537	−	12.2627i	0.623838	−	0.479508i
$655$	−5.96367	−	10.3294i	−0.233020	−	0.403602i
$656$		−	11.4992i		−	0.448968i
$657$	4.80339	+	17.8086i	0.187398	+	0.694779i
$658$	11.4214			0.445251
$659$	−1.37174	+	0.791977i	−0.0534356	+	0.0308510i	−0.526480	−	0.850188i	$-0.676488\pi$
$659$	−1.37174	+	0.791977i	−0.0534356	+	0.0308510i	0.473044	+	0.881039i	$0.343155\pi$
$660$	−3.63488	−	1.50209i	−0.141488	−	0.0584690i
$661$	−16.1220	+	27.9242i	−0.627075	+	1.08613i	0.361061	+	0.932542i	$0.382415\pi$
$661$	−16.1220	+	27.9242i	−0.627075	+	1.08613i	−0.988136	+	0.153583i	$0.950919\pi$
$662$	−13.7066	+	23.7405i	−0.532721	+	0.922700i
$663$	−23.6557	−	9.77561i	−0.918713	−	0.379653i
$664$	1.75771	−	1.01481i	0.0682122	−	0.0393823i
$665$			6.15876i			0.238827i
$666$	20.9030	+	20.8340i	0.809976	+	0.807300i
$667$	15.9240			0.616580
$668$	−3.02979	−	5.24776i	−0.117226	−	0.203042i
$669$	−39.5441	+	30.3953i	−1.52886	+	1.17515i
$670$	3.62727	−	6.28262i	0.140134	−	0.242719i
$671$	−1.58189	−	0.913307i	−0.0610683	−	0.0352578i
$672$	0.253179	+	1.91087i	0.00976659	+	0.0737133i
$673$	−7.10562	+	4.10243i	−0.273902	+	0.158137i	−0.630659	−	0.776060i	$-0.717215\pi$
$673$	−7.10562	+	4.10243i	−0.273902	+	0.158137i	0.356758	+	0.934197i	$0.383882\pi$
$674$	3.41877			0.131686
$675$	−0.200502	−	0.153062i	−0.00771733	−	0.00589134i
$676$	−2.76535			−0.106360
$677$	3.99517	+	6.91983i	0.153547	+	0.265951i	0.932529	−	0.361095i	$-0.117597\pi$
$677$	3.99517	+	6.91983i	0.153547	+	0.265951i	−0.778982	+	0.627046i	$0.784264\pi$
$678$	28.8608	−	3.82389i	1.10839	−	0.146856i
$679$	−1.17971	+	2.04331i	−0.0452729	+	0.0784150i
$680$	5.13940	−	8.90169i	0.197087	−	0.341364i
$681$	−20.1777	+	15.5094i	−0.773210	+	0.594322i
$682$	−5.57001	+	1.12113i	−0.213287	+	0.0429304i
$683$			19.0681i			0.729619i	0.931082	+	0.364809i	$0.118866\pi$
$683$			19.0681i			0.729619i	−0.931082	+	0.364809i	$0.881134\pi$
$684$	1.91913	−	7.21000i	0.0733798	−	0.275681i
$685$		−	31.0711i		−	1.18717i
$686$	−12.2993	+	7.10102i	−0.469590	+	0.271118i
$687$	11.2380	+	4.64405i	0.428757	+	0.177182i
$688$	−5.89094	−	3.40113i	−0.224590	−	0.129667i
$689$	−27.2977	−	15.7603i	−1.03996	−	0.600420i
$690$	5.68427	−	13.7552i	0.216397	−	0.523652i
$691$	−12.0546	−	20.8792i	−0.458580	−	0.794284i	0.540306	−	0.841469i	$-0.318308\pi$
$691$	−12.0546	−	20.8792i	−0.458580	−	0.794284i	−0.998886	+	0.0471845i	$0.984975\pi$
$692$			14.7146i			0.559365i
$693$	0.876344	−	3.29234i	0.0332896	−	0.125066i
$694$		−	14.2311i		−	0.540205i
$695$	−8.42867	−	14.5989i	−0.319718	−	0.553768i
$696$	5.66274	−	4.35262i	0.214646	−	0.164986i
$697$	−46.0017	−	26.5591i	−1.74244	−	1.00600i
$698$	−21.0892	−	12.1759i	−0.798239	−	0.460863i
$699$	0.466104	+	3.51792i	0.0176297	+	0.133060i
$700$	−0.0270125	−	0.0467870i	−0.00102098	−	0.00176838i
$701$			24.8694i			0.939303i	0.882852	+	0.469651i	$0.155620\pi$
$701$			24.8694i			0.939303i	−0.882852	+	0.469651i	$0.844380\pi$
$702$	−15.3421	+	6.39957i	−0.579051	+	0.241536i
$703$		−	24.4661i		−	0.922755i
$704$	0.510234	+	0.883751i	0.0192302	+	0.0333076i
$705$	−39.2118	+	5.19534i	−1.47680	+	0.195668i
$706$	−22.8251	−	13.1781i	−0.859036	−	0.495964i
$707$	2.20628	+	1.27380i	0.0829757	+	0.0479060i
$708$	8.10147	−	6.22713i	0.304472	−	0.234030i
$709$	11.2903	−	6.51847i	0.424017	−	0.244806i	−0.272778	−	0.962077i	$-0.587942\pi$
$709$	11.2903	−	6.51847i	0.424017	−	0.244806i	0.696794	+	0.717271i	$0.254609\pi$
$710$		−	2.66214i		−	0.0999083i
$711$	5.35271	−	5.37045i	0.200742	−	0.201408i
$712$		−	5.33213i		−	0.199830i
$713$	−4.24263	−	21.0782i	−0.158888	−	0.789385i
$714$	8.22904	+	3.40061i	0.307964	+	0.127265i
$715$	3.63222	−	6.29119i	0.135837	−	0.235277i
$716$	−6.58431	+	11.4044i	−0.246067	+	0.426201i
$717$	9.83892	−	23.8089i	0.367441	−	0.889161i
$718$	8.16910	+	14.1493i	0.304868	+	0.528047i
$719$	15.1422			0.564708			0.282354	−	0.959310i	$-0.408885\pi$
$719$	15.1422			0.564708			0.282354	+	0.959310i	$0.408885\pi$
$720$	−1.73843	−	6.44523i	−0.0647874	−	0.240199i
$721$	−1.35460			−0.0504479
$722$	11.0979	−	6.40738i	0.413022	−	0.238458i
$723$	17.5687	−	13.5041i	0.653388	−	0.502222i
$724$	−0.158609	−	0.0915732i	−0.00589467	−	0.00340329i
$725$	−0.100090	+	0.173361i	−0.00371725	+	0.00643847i
$726$	2.26558	+	17.0994i	0.0840835	+	0.634620i
$727$	−13.4296	−	23.2608i	−0.498077	−	0.862695i	0.501921	−	0.864914i	$-0.332627\pi$
$727$	−13.4296	−	23.2608i	−0.498077	−	0.862695i	−0.999998	+	0.00221912i	$0.999294\pi$
$728$	−3.56029			−0.131953
$729$	18.9969	−	19.1864i	0.703588	−	0.710608i
$730$		−	13.6812i		−	0.506364i
$731$	−27.2120	+	15.7108i	−1.00647	+	0.581086i
$732$	−0.407217	−	3.07347i	−0.0150512	−	0.113599i
$733$	−16.7337	+	28.9836i	−0.618073	+	1.07053i	0.371764	+	0.928327i	$0.378753\pi$
$733$	−16.7337	+	28.9836i	−0.618073	+	1.07053i	−0.989837	+	0.142207i	$0.954580\pi$
$734$	4.62616	−	8.01274i	0.170755	−	0.295756i
$735$	17.6057	−	13.5325i	0.649395	−	0.499153i
$736$	−3.34431	+	1.93084i	−0.123273	+	0.0711717i
$737$	3.32692			0.122549
$738$	−33.3073	+	8.98376i	−1.22606	+	0.330697i
$739$		−	18.4729i		−	0.679537i	−0.940509	−	0.339769i	$-0.889651\pi$
$739$		−	18.4729i		−	0.679537i	0.940509	−	0.339769i	$-0.110349\pi$
$740$	−10.9452	−	18.9576i	−0.402352	−	0.696894i
$741$	12.7362	+	5.26316i	0.467875	+	0.193347i
$742$	9.49594	+	5.48249i	0.348607	+	0.201268i
$743$	17.6305	−	30.5369i	0.646799	−	1.12029i	−0.337084	−	0.941475i	$-0.609441\pi$
$743$	17.6305	−	30.5369i	0.646799	−	1.12029i	0.983883	−	0.178814i	$-0.0572261\pi$
$744$	−7.27018	−	6.33596i	−0.266538	−	0.232288i
$745$	5.82613	+	10.0912i	0.213453	+	0.369711i
$746$			8.98776i			0.329065i
$747$	−4.31260	−	4.29835i	−0.157790	−	0.157268i
$748$	4.71384			0.172355
$749$	10.0187	−	5.78432i	0.366077	−	0.211355i
$750$	11.8579	+	15.4271i	0.432990	+	0.563318i
$751$	−0.496728	+	0.860358i	−0.0181259	+	0.0313949i	−0.874946	−	0.484220i	$-0.839103\pi$
$751$	−0.496728	+	0.860358i	−0.0181259	+	0.0313949i	0.856820	+	0.515615i	$0.172437\pi$
$752$	8.88791	+	5.13144i	0.324109	+	0.187124i
$753$	−45.9846	+	6.09269i	−1.67577	+	0.222030i
$754$	6.59602	+	11.4246i	0.240213	+	0.416061i
$755$	−21.9198			−0.797744
$756$	5.33701	−	2.22620i	0.194105	−	0.0809660i
$757$			11.9119i			0.432946i	0.976289	+	0.216473i	$0.0694553\pi$
$757$			11.9119i			0.432946i	−0.976289	+	0.216473i	$0.930545\pi$
$758$	20.0479	−	11.5747i	0.728174	−	0.420412i
$759$	6.76639	−	0.896508i	0.245605	−	0.0325412i
$760$	−2.76703	+	4.79264i	−0.100371	+	0.173847i
$761$	−26.4497	+	45.8122i	−0.958800	+	1.66069i	−0.233378	+	0.972386i	$0.574978\pi$
$761$	−26.4497	+	45.8122i	−0.958800	+	1.66069i	−0.725422	+	0.688305i	$0.758355\pi$
$762$	−2.43016	−	3.16163i	−0.0880354	−	0.114534i
$763$	−6.46440	−	11.1967i	−0.234027	−	0.405347i
$764$		−	0.0642022i		−	0.00232275i
$765$	−29.7988	−	7.93175i	−1.07738	−	0.286773i
$766$		−	7.67826i		−	0.277427i
$767$	9.43668	+	16.3448i	0.340739	+	0.590177i
$768$	−0.661503	+	1.60075i	−0.0238699	+	0.0577622i
$769$	−13.1731	+	22.8165i	−0.475036	+	0.822786i	−0.999591	−	0.0285904i	$-0.990898\pi$
$769$	−13.1731	+	22.8165i	−0.475036	+	0.822786i	0.524556	+	0.851376i	$0.324231\pi$
$770$	−1.26353	+	2.18849i	−0.0455343	+	0.0788678i
$771$	12.3235	+	5.09263i	0.443821	+	0.183407i
$772$	1.25910	+	2.18083i	0.0453160	+	0.0784896i
$773$	41.3321			1.48661			0.743305	−	0.668952i	$-0.233257\pi$
$773$	41.3321			1.48661			0.743305	+	0.668952i	$0.233257\pi$
$774$	−5.24905	+	19.7202i	−0.188673	+	0.708827i
$775$	0.256141	+	0.0862982i	0.00920085	+	0.00309992i
$776$	−1.83605	+	1.06005i	−0.0659105	+	0.0380534i
$777$	15.0344	−	11.5561i	0.539356	−	0.414572i
$778$	−15.5214	−	8.96129i	−0.556469	−	0.321278i
$779$	24.7672	+	14.2993i	0.887376	+	0.512327i
$780$	12.2232	−	1.61950i	0.437660	−	0.0579875i
$781$	1.05729	−	0.610426i	0.0378328	−	0.0218428i
$782$			17.8382i			0.637894i
$783$	−17.0313	−	13.0016i	−0.608651	−	0.464639i
$784$	−5.76149			−0.205768
$785$	25.7310	−	14.8558i	0.918379	−	0.530226i
$786$	9.20363	−	1.21943i	0.328282	−	0.0434955i
$787$	1.17396	+	0.677787i	0.0418472	+	0.0241605i	0.520778	−	0.853692i	$-0.325642\pi$
$787$	1.17396	+	0.677787i	0.0418472	+	0.0241605i	−0.478930	+	0.877853i	$0.658975\pi$
$788$	9.22741	−	15.9823i	0.328713	−	0.569347i
$789$	18.8150	+	24.4782i	0.669832	+	0.871449i
$790$	−4.87062	+	2.81205i	−0.173289	+	0.100048i
$791$		−	18.7058i		−	0.665102i
$792$	2.16115	−	2.16832i	0.0767932	−	0.0770478i
$793$	5.72643			0.203352
$794$	24.7782	−	14.3057i	0.879347	−	0.507691i
$795$	−35.0954	−	14.5030i	−1.24470	−	0.514367i
$796$	22.6547	+	13.0797i	0.802973	+	0.463597i
$797$	−4.91284	+	8.50928i	−0.174022	+	0.301414i	−0.939822	−	0.341664i	$-0.889010\pi$
$797$	−4.91284	+	8.50928i	−0.174022	+	0.301414i	0.765801	+	0.643078i	$0.222343\pi$
$798$	−4.43049	−	1.83088i	−0.156838	−	0.0648123i
$799$	41.0559	−	23.7036i	1.45245	−	0.838574i
$800$		−	0.0485451i		−	0.00171633i
$801$	−15.4444	+	4.16573i	−0.545703	+	0.147189i
$802$			15.2623i			0.538931i
$803$	5.43359	−	3.13709i	0.191747	−	0.110705i
$804$	3.44128	+	4.47708i	0.121364	+	0.157895i
$805$	−8.28176	−	4.78148i	−0.291894	−	0.168525i
$806$	13.3651	−	11.7749i	0.470767	−	0.414751i
$807$	53.5599	−	7.09638i	1.88540	−	0.249804i
$808$	1.14459	+	1.98249i	0.0402666	+	0.0697438i
$809$	−32.6168			−1.14674			−0.573372	−	0.819295i	$-0.694365\pi$
$809$	−32.6168			−1.14674			−0.573372	+	0.819295i	$0.694365\pi$
$810$	−17.3104	+	10.0707i	−0.608225	+	0.353848i
$811$	50.1843			1.76221			0.881105	−	0.472921i	$-0.156800\pi$
$811$	50.1843			1.76221			0.881105	+	0.472921i	$0.156800\pi$
$812$	−2.29453	−	3.97425i	−0.0805224	−	0.139469i
$813$	6.79996	+	51.3227i	0.238485	+	1.79996i
$814$	5.01944	−	8.69392i	0.175931	−	0.304722i
$815$	−26.3149	−	15.1929i	−0.921771	−	0.532185i
$816$	4.87586	+	6.34347i	0.170689	+	0.222066i
$817$	14.6508	−	8.45867i	0.512568	−	0.295931i
$818$	28.5904			0.999640
$819$	2.78148	+	10.3123i	0.0971927	+	0.360342i
$820$	25.5879			0.893567
$821$	11.0576	+	19.1523i	0.385912	+	0.668420i	0.991895	−	0.127058i	$-0.0405534\pi$
$821$	11.0576	+	19.1523i	0.385912	+	0.668420i	−0.605983	+	0.795478i	$0.707220\pi$
$822$	22.3519	+	9.23682i	0.779614	+	0.322171i
$823$	−28.0176	−	16.1759i	−0.976631	−	0.563858i	−0.0753796	−	0.997155i	$-0.524017\pi$
$823$	−28.0176	−	16.1759i	−0.976631	−	0.563858i	−0.901251	+	0.433297i	$0.857350\pi$
$824$	−1.05413	−	0.608600i	−0.0367222	−	0.0212016i
$825$	−0.0327700	+	0.0792993i	−0.00114090	+	0.00276085i
$826$	−3.28270	−	5.68581i	−0.114220	−	0.197835i
$827$	−15.7673			−0.548282			−0.274141	−	0.961690i	$-0.588393\pi$
$827$	−15.7673			−0.548282			−0.274141	+	0.961690i	$0.588393\pi$
$828$	8.20541	+	8.17830i	0.285158	+	0.284216i
$829$		−	8.39199i		−	0.291466i	−0.989324	−	0.145733i	$-0.953446\pi$
$829$		−	8.39199i		−	0.291466i	0.989324	−	0.145733i	$-0.0465540\pi$
$830$	2.25814	+	3.91122i	0.0783814	+	0.135760i
$831$	−3.92812	+	3.01932i	−0.136265	+	0.104739i
$832$	−2.77056	−	1.59958i	−0.0960518	−	0.0554555i
$833$	−13.3070	+	23.0484i	−0.461061	+	0.798581i
$834$	13.0078	−	1.72346i	0.450424	−	0.0596786i
$835$	11.6772	−	6.74186i	0.404107	−	0.233312i
$836$	−2.53792			−0.0877756
$837$	−12.6722	+	26.0080i	−0.438016	+	0.898967i
$838$	−8.47141			−0.292640
$839$	27.8508	−	16.0797i	0.961516	−	0.555131i	0.0648765	−	0.997893i	$-0.479335\pi$
$839$	27.8508	−	16.0797i	0.961516	−	0.555131i	0.896639	+	0.442762i	$0.146001\pi$
$840$	−4.25204	+	0.563370i	−0.146709	+	0.0194381i
$841$	5.99800	−	10.3888i	0.206828	−	0.358236i
$842$	22.8445	+	13.1893i	0.787275	+	0.454533i
$843$	29.7065	−	22.8337i	1.02315	−	0.786435i
$844$	−7.05862	−	12.2259i	−0.242968	−	0.420833i
$845$		−	6.15343i		−	0.211684i
$846$	7.91947	−	29.7527i	0.272277	−	1.02292i
$847$	11.0828			0.380809
$848$	4.92639	+	8.53275i	0.169173	+	0.293016i
$849$	−5.07771	+	12.2874i	−0.174267	+	0.421703i
$850$	−0.194201	−	0.112122i	−0.00666104	−	0.00384576i
$851$	32.8998	+	18.9947i	1.12779	+	0.651130i
$852$	1.91509	+	0.791400i	0.0656099	+	0.0271129i
$853$	3.42036	+	5.92425i	0.117111	+	0.202842i	0.918622	−	0.395138i	$-0.129303\pi$
$853$	3.42036	+	5.92425i	0.117111	+	0.202842i	−0.801511	+	0.597981i	$0.795970\pi$
$854$	−1.99203			−0.0681660
$855$	16.0436	+	4.27043i	0.548679	+	0.146046i
$856$	10.3952			0.355301
$857$	−33.3784	+	19.2710i	−1.14018	+	0.658285i	−0.946476	−	0.322774i	$-0.895385\pi$
$857$	−33.3784	+	19.2710i	−1.14018	+	0.658285i	−0.193707	+	0.981059i	$0.562051\pi$
$858$	3.44597	+	4.48319i	0.117643	+	0.153053i
$859$	−16.4040	−	9.47085i	−0.559697	−	0.323141i	0.193327	−	0.981134i	$-0.438072\pi$
$859$	−16.4040	−	9.47085i	−0.559697	−	0.323141i	−0.753024	+	0.657993i	$0.771406\pi$
$860$	7.56816	−	13.1084i	0.258072	−	0.446994i
$861$	2.91136	+	21.9735i	0.0992187	+	0.748853i
$862$	10.3026	+	17.8447i	0.350909	+	0.607792i
$863$	−1.15240			−0.0392282			−0.0196141	−	0.999808i	$-0.506244\pi$
$863$	−1.15240			−0.0392282			−0.0196141	+	0.999808i	$0.506244\pi$
$864$	5.15337	+	0.665446i	0.175321	+	0.0226389i
$865$	−32.7427			−1.11329
$866$	−12.2312	−	21.1850i	−0.415631	−	0.719895i
$867$	7.44834	−	0.986862i	0.252959	−	0.0335156i
$868$	−4.64928	+	4.09608i	−0.157807	+	0.139030i
$869$	−2.23366	−	1.28960i	−0.0757716	−	0.0437468i
$870$	9.68540	+	12.6007i	0.328366	+	0.427202i
$871$	−9.03256	+	5.21495i	−0.306057	+	0.176702i
$872$		−	11.6174i		−	0.393415i
$873$	4.50483	+	4.48995i	0.152465	+	0.151962i
$874$		−	9.60405i		−	0.324862i
$875$	10.8271	−	6.25103i	0.366023	−	0.211323i
$876$	9.84197	+	4.06714i	0.332529	+	0.137416i
$877$	−28.7645	+	49.8216i	−0.971309	+	1.68236i	−0.279696	+	0.960089i	$0.590234\pi$
$877$	−28.7645	+	49.8216i	−0.971309	+	1.68236i	−0.691613	+	0.722268i	$0.743100\pi$
$878$	−12.3935	−	7.15542i	−0.418262	−	0.241484i
$879$	23.1287	+	9.55781i	0.780112	+	0.322377i
$880$	−1.96651	+	1.13536i	−0.0662910	+	0.0382731i
$881$	−1.62120			−0.0546197			−0.0273098	−	0.999627i	$-0.508694\pi$
$881$	−1.62120			−0.0546197			−0.0273098	+	0.999627i	$0.508694\pi$
$882$	4.50117	+	16.6881i	0.151562	+	0.561918i
$883$		−	23.7417i		−	0.798971i	−0.916739	−	0.399486i	$-0.869189\pi$
$883$		−	23.7417i		−	0.798971i	0.916739	−	0.399486i	$-0.130811\pi$
$884$	−12.7980	+	7.38894i	−0.430444	+	0.248517i
$885$	13.8565	+	18.0273i	0.465782	+	0.605981i
$886$	−2.53824	+	4.39636i	−0.0852738	+	0.147698i
$887$	3.06497	+	1.76956i	0.102912	+	0.0594160i	0.550572	−	0.834787i	$-0.314409\pi$
$887$	3.06497	+	1.76956i	0.102912	+	0.0594160i	−0.447661	+	0.894203i	$0.647743\pi$
$888$	16.8915	−	2.23802i	0.566841	−	0.0751031i
$889$	−2.21890	+	1.28109i	−0.0744197	+	0.0429662i
$890$	11.8650			0.397715
$891$	−7.96891	−	4.56576i	−0.266968	−	0.152959i
$892$			28.7959i			0.964158i
$893$	−22.1044	+	12.7620i	−0.739694	+	0.427063i
$894$	−8.99137	+	1.19130i	−0.300716	+	0.0398432i
$895$	−25.3768	−	14.6513i	−0.848254	−	0.489740i
$896$	0.963784	+	0.556441i	0.0321978	+	0.0185894i
$897$	−16.9654	+	13.0403i	−0.566458	+	0.435404i
$898$	−29.5475	+	17.0592i	−0.986012	+	0.569274i
$899$	21.7575	+	7.33047i	0.725653	+	0.244485i
$900$	−0.140610	+	0.0379259i	−0.00468701	+	0.00126420i
$901$	45.5129			1.51625
$902$	5.86728	+	10.1624i	0.195359	+	0.338372i
$903$	12.1179	+	5.00766i	0.403258	+	0.166644i
$904$	8.40422	−	14.5565i	0.279520	−	0.484143i
$905$	0.203767	−	0.352936i	0.00677346	−	0.0117320i
$906$	6.51632	−	15.7687i	0.216490	−	0.523879i
$907$	−18.0502	−	31.2639i	−0.599347	−	1.03810i	−0.992918	−	0.118805i	$-0.962094\pi$
$907$	−18.0502	−	31.2639i	−0.599347	−	1.03810i	0.393570	−	0.919295i	$-0.371240\pi$
$908$			14.6933i			0.487615i
$909$	4.84805	−	4.86412i	0.160800	−	0.161333i
$910$		−	7.92231i		−	0.262622i
$911$	−23.2080	−	40.1975i	−0.768916	−	1.33180i	−0.938151	−	0.346226i	$-0.887463\pi$
$911$	−23.2080	−	40.1975i	−0.768916	−	1.33180i	0.169235	−	0.985576i	$-0.445870\pi$
$912$	−2.62515	−	3.41530i	−0.0869273	−	0.113092i
$913$	−1.03558	+	1.79368i	−0.0342728	+	0.0593622i
$914$	−2.93947	+	5.09131i	−0.0972290	+	0.168406i
$915$	6.83905	−	0.906135i	0.226092	−	0.0299559i
$916$	6.07989	−	3.51023i	0.200885	−	0.115981i
$917$		−	5.96522i		−	0.196989i
$918$	14.5645	−	19.0787i	0.480701	−	0.629691i
$919$	−56.6374			−1.86829			−0.934147	−	0.356888i	$-0.883838\pi$
$919$	−56.6374			−1.86829			−0.934147	+	0.356888i	$0.883838\pi$
$920$	−4.29648	−	7.44172i	−0.141651	−	0.245346i
$921$	58.0302	−	7.68867i	1.91216	−	0.253350i
$922$	34.2032	+	19.7473i	1.12642	+	0.650341i
$923$	−1.91369	+	3.31460i	−0.0629897	+	0.109101i
$924$	−1.19874	−	1.55955i	−0.0394355	−	0.0513054i
$925$	−0.413582	+	0.238782i	−0.0135985	+	0.00785110i
$926$	−23.1475			−0.760675
$927$	−0.939266	+	3.52873i	−0.0308495	+	0.115899i
$928$		−	4.12359i		−	0.135364i
$929$	−24.5733	−	42.5622i	−0.806224	−	1.39642i	−0.915461	−	0.402406i	$-0.868174\pi$
$929$	−24.5733	−	42.5622i	−0.806224	−	1.39642i	0.109237	−	0.994016i	$-0.465159\pi$
$930$	14.0987	−	16.1775i	0.462315	−	0.530482i
$931$	7.16446	−	12.4092i	0.234806	−	0.406695i
$932$	1.77433	+	1.02441i	0.0581201	+	0.0335557i
$933$	22.8189	+	9.42981i	0.747059	+	0.308718i
$934$	3.06335	+	5.30588i	0.100236	+	0.173614i
$935$			10.4892i			0.343033i
$936$	−2.46867	+	9.27456i	−0.0806910	+	0.303148i
$937$	3.03674			0.0992059			0.0496029	−	0.998769i	$-0.484204\pi$
$937$	3.03674			0.0992059			0.0496029	+	0.998769i	$0.484204\pi$
$938$	3.14212	−	1.81411i	0.102594	−	0.0592327i
$939$	−12.6225	+	9.70218i	−0.411919	+	0.316619i
$940$	−11.4184	+	19.7773i	−0.372427	+	0.645063i
$941$	−11.1294	+	19.2767i	−0.362809	+	0.628404i	−0.988422	−	0.151730i	$-0.951516\pi$
$941$	−11.1294	+	19.2767i	−0.362809	+	0.628404i	0.625613	+	0.780134i	$0.284849\pi$
$942$	3.03766	+	22.9267i	0.0989722	+	0.746992i
$943$	−38.4569	+	22.2031i	−1.25233	+	0.723033i
$944$		−	5.89947i		−	0.192011i
$945$	4.95370	+	11.8758i	0.161144	+	0.386321i
$946$	6.94149			0.225687
$947$	25.6560	+	44.4375i	0.833708	+	1.44403i	0.895078	+	0.445910i	$0.147120\pi$
$947$	25.6560	+	44.4375i	0.833708	+	1.44403i	−0.0613692	+	0.998115i	$0.519547\pi$
$948$	−0.574997	−	4.33979i	−0.0186750	−	0.140950i
$949$	−9.83476	+	17.0343i	−0.319250	+	0.552957i
$950$	0.104557	+	0.0603662i	0.00339229	+	0.00195854i
$951$	10.2053	−	7.84423i	0.330930	−	0.254367i
$952$	4.45200	−	2.57036i	0.144290	−	0.0833060i
$953$	28.3831			0.919417			0.459709	−	0.888070i	$-0.347954\pi$
$953$	28.3831			0.919417			0.459709	+	0.888070i	$0.347954\pi$
$954$	20.8663	−	20.9354i	0.675571	−	0.677810i
$955$	0.142862			0.00462290
$956$	−7.43679	−	12.8809i	−0.240523	−	0.416598i
$957$	−2.78360	+	6.73596i	−0.0899809	+	0.217743i
$958$	3.74499	−	6.48652i	0.120995	−	0.209570i
$959$	7.76980	−	13.4577i	0.250900	−	0.434571i
$960$	−3.56198	−	1.47197i	−0.114962	−	0.0475076i
$961$	3.90631	−	30.7529i	0.126010	−	0.992029i
$962$			31.4718i			1.01469i
$963$	−8.12127	−	30.1096i	−0.261704	−	0.970269i
$964$		−	12.7935i		−	0.412051i
$965$	−4.85274	+	2.80173i	−0.156215	+	0.0901910i
$966$	5.90170	−	4.53629i	0.189884	−	0.145953i
$967$	5.33559	+	3.08050i	0.171581	+	0.0990624i	0.583331	−	0.812234i	$-0.301749\pi$
$967$	5.33559	+	3.08050i	0.171581	+	0.0990624i	−0.411750	+	0.911297i	$0.635082\pi$
$968$	8.62444	+	4.97932i	0.277200	+	0.160042i
$969$	−19.7258	+	2.61356i	−0.633685	+	0.0839596i
$970$	−2.35880	−	4.08556i	−0.0757365	−	0.131179i
$971$		−	25.5833i		−	0.821007i	−0.911859	−	0.410504i	$-0.865353\pi$
$971$		−	25.5833i		−	0.821007i	0.911859	−	0.410504i	$-0.134647\pi$
$972$	−2.09861	−	15.4465i	−0.0673131	−	0.495448i
$973$		−	8.43086i		−	0.270281i
$974$	−4.84260	−	8.38762i	−0.155167	−	0.268757i
$975$	−0.0353314	−	0.266664i	−0.00113151	−	0.00854007i
$976$	−1.55017	−	0.894989i	−0.0496196	−	0.0286479i
$977$	−27.8940	−	16.1046i	−0.892408	−	0.515232i	−0.0176784	−	0.999844i	$-0.505627\pi$
$977$	−27.8940	−	16.1046i	−0.892408	−	0.515232i	−0.874729	+	0.484612i	$0.838961\pi$
$978$	18.7524	−	14.4139i	0.599635	−	0.460905i
$979$	2.72063	+	4.71227i	0.0869517	+	0.150605i
$980$		−	12.8204i		−	0.409533i
$981$	−33.6497	+	9.07611i	−1.07435	+	0.289778i
$982$		−	16.5164i		−	0.527060i
$983$	7.45474	+	12.9120i	0.237769	+	0.411829i	0.960074	−	0.279747i	$-0.0902504\pi$
$983$	7.45474	+	12.9120i	0.237769	+	0.411829i	−0.722305	+	0.691575i	$0.756917\pi$
$984$	−7.60676	+	18.4074i	−0.242495	+	0.586806i
$985$	35.5637	+	20.5327i	1.13315	+	0.654227i
$986$	−16.4961	−	9.52404i	−0.525344	−	0.303307i
$987$	−18.2828	−	7.55527i	−0.581948	−	0.240487i
$988$	6.89041	−	3.97818i	0.219213	−	0.126563i
$989$			26.2682i			0.835280i
$990$	4.82491	+	4.80897i	0.153346	+	0.152839i
$991$			45.0132i			1.42989i	0.699181	+	0.714945i	$0.253548\pi$
$991$			45.0132i			1.42989i	−0.699181	+	0.714945i	$0.746452\pi$
$992$	−5.45829	+	1.09865i	−0.173301	+	0.0348821i
$993$	37.6452	−	28.9357i	1.19464	−	0.918247i
$994$	0.665707	−	1.15304i	0.0211149	−	0.0365722i
$995$	−29.1047	+	50.4108i	−0.922681	+	1.59813i
$996$	−3.48495	+	0.461736i	−0.110425	+	0.0146307i
$997$	7.75035	+	13.4240i	0.245456	+	0.425142i	0.962260	−	0.272133i	$-0.0877290\pi$
$997$	7.75035	+	13.4240i	0.245456	+	0.425142i	−0.716804	+	0.697275i	$0.754396\pi$
$998$	−19.0832			−0.604068
$999$	−19.6789	−	47.1775i	−0.622612	−	1.49263i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.q.a.185.15	yes	64
3.2	odd	2		1674.2.q.a.557.23		64
9.2	odd	6	inner	558.2.q.a.371.2	yes	64
9.7	even	3		1674.2.q.a.1115.26		64
31.30	odd	2	inner	558.2.q.a.185.2	✓	64
93.92	even	2		1674.2.q.a.557.26		64
279.61	odd	6		1674.2.q.a.1115.23		64
279.92	even	6	inner	558.2.q.a.371.15	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.q.a.185.2	✓	64	31.30	odd	2	inner
558.2.q.a.185.15	yes	64	1.1	even	1	trivial
558.2.q.a.371.2	yes	64	9.2	odd	6	inner
558.2.q.a.371.15	yes	64	279.92	even	6	inner
1674.2.q.a.557.23		64	3.2	odd	2
1674.2.q.a.557.26		64	93.92	even	2
1674.2.q.a.1115.23		64	279.61	odd	6
1674.2.q.a.1115.26		64	9.7	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.71705 - 0.227499i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.92707 + 1.11259i) q^{5} +(-1.37326 + 1.05554i) q^{6} +(0.556441 + 0.963784i) q^{7} +1.00000i q^{8} +(2.89649 - 0.781251i) q^{9} -2.22519 q^{10} +(-0.510234 - 0.883751i) q^{11} +(0.661503 - 1.60075i) q^{12} +(2.77056 + 1.59958i) q^{13} +(-0.963784 - 0.556441i) q^{14} +(3.56198 + 1.47197i) q^{15} +(-0.500000 - 0.866025i) q^{16} -4.61929 q^{17} +(-2.11781 + 2.12483i) q^{18} +2.48701 q^{19} +(1.92707 - 1.11259i) q^{20} +(1.17469 + 1.52827i) q^{21} +(0.883751 + 0.510234i) q^{22} +(-1.93084 + 3.34431i) q^{23} +(0.227499 + 1.71705i) q^{24} +(-0.0242726 - 0.0420413i) q^{25} -3.19916 q^{26} +(4.79567 - 2.00039i) q^{27} +1.11288 q^{28} +(-2.06180 - 3.57113i) q^{29} +(-3.82075 + 0.506227i) q^{30} +(-4.17770 + 3.68060i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.07715 - 1.40136i) q^{33} +(4.00043 - 2.30965i) q^{34} +2.47637i q^{35} +(0.771661 - 2.89906i) q^{36} -9.83752i q^{37} +(-2.15382 + 1.24351i) q^{38} +(5.12107 + 2.11626i) q^{39} +(-1.11259 + 1.92707i) q^{40} +(9.95860 + 5.74960i) q^{41} +(-1.78145 - 0.736175i) q^{42} +(5.89094 - 3.40113i) q^{43} -1.02047 q^{44} +(6.45095 + 1.71709i) q^{45} -3.86168i q^{46} +(-8.88791 + 5.13144i) q^{47} +(-1.05554 - 1.37326i) q^{48} +(2.88075 - 4.98960i) q^{49} +(0.0420413 + 0.0242726i) q^{50} +(-7.93154 + 1.05088i) q^{51} +(2.77056 - 1.59958i) q^{52} -9.85277 q^{53} +(-3.15298 + 4.13022i) q^{54} -2.27073i q^{55} +(-0.963784 + 0.556441i) q^{56} +(4.27031 - 0.565792i) q^{57} +(3.57113 + 2.06180i) q^{58} +(5.10909 + 2.94973i) q^{59} +(3.05575 - 2.34878i) q^{60} +(1.55017 - 0.894989i) q^{61} +(1.77769 - 5.27635i) q^{62} +(2.36468 + 2.35687i) q^{63} -1.00000 q^{64} +(3.55937 + 6.16501i) q^{65} +(1.63352 + 0.675042i) q^{66} +(-1.63010 + 2.82341i) q^{67} +(-2.30965 + 4.00043i) q^{68} +(-2.55451 + 6.18160i) q^{69} +(-1.23818 - 2.14460i) q^{70} +1.19637i q^{71} +(0.781251 + 2.89649i) q^{72} +6.14833i q^{73} +(4.91876 + 8.51955i) q^{74} +(-0.0512414 - 0.0666648i) q^{75} +(1.24351 - 2.15382i) q^{76} +(0.567830 - 0.983510i) q^{77} +(-5.49311 + 0.727805i) q^{78} +(2.18886 - 1.26374i) q^{79} -2.22519i q^{80} +(7.77929 - 4.52577i) q^{81} -11.4992 q^{82} +(-1.01481 - 1.75771i) q^{83} +(1.91087 - 0.253179i) q^{84} +(-8.90169 - 5.13940i) q^{85} +(-3.40113 + 5.89094i) q^{86} +(-4.35262 - 5.66274i) q^{87} +(0.883751 - 0.510234i) q^{88} -5.33213 q^{89} +(-6.44523 + 1.73843i) q^{90} +3.56029i q^{91} +(1.93084 + 3.34431i) q^{92} +(-6.33596 + 7.27018i) q^{93} +(5.13144 - 8.88791i) q^{94} +(4.79264 + 2.76703i) q^{95} +(1.60075 + 0.661503i) q^{96} +(1.06005 + 1.83605i) q^{97} +5.76149i q^{98} +(-2.16832 - 2.16115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} + 12 q^{5} - 4 q^{7} - 4 q^{9} - 32 q^{16} + 8 q^{18} - 8 q^{19} + 12 q^{20} + 44 q^{25} - 8 q^{28} + 8 q^{31} - 36 q^{33} - 8 q^{36} + 36 q^{38} - 8 q^{39} + 24 q^{41} - 8 q^{45} - 48 q^{47}+ \cdots - 16 q^{97}+O(q^{100}) \) 64 * q + 32 * q^4 + 12 * q^5 - 4 * q^7 - 4 * q^9 - 32 * q^16 + 8 * q^18 - 8 * q^19 + 12 * q^20 + 44 * q^25 - 8 * q^28 + 8 * q^31 - 36 * q^33 - 8 * q^36 + 36 * q^38 - 8 * q^39 + 24 * q^41 - 8 * q^45 - 48 * q^47 - 36 * q^49 - 32 * q^51 - 12 * q^59 - 52 * q^63 - 64 * q^64 - 16 * q^66 + 16 * q^67 + 112 * q^69 - 12 * q^70 - 8 * q^72 - 4 * q^76 - 28 * q^78 + 60 * q^81 + 44 * q^87 + 56 * q^90 - 64 * q^93 - 180 * q^95 - 16 * q^97

Introduction

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