LMFDB - Embedded newform 558.2.q.a.185.19

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)

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")

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);

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			185.19
Character	$\chi$	$=$	558.185
Dual form			558.2.q.a.371.19

$q$-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} +(-1.55011 - 0.772765i) q^{3} +(0.500000 - 0.866025i) q^{4} +(3.64602 + 2.10503i) q^{5} +(-1.72882 + 0.105819i) q^{6} +(-0.908070 - 1.57282i) q^{7} -1.00000i q^{8} +(1.80567 + 2.39574i) q^{9} +4.21006 q^{10} +(2.59638 + 4.49706i) q^{11} +(-1.44429 + 0.956050i) q^{12} +(-1.49949 - 0.865730i) q^{13} +(-1.57282 - 0.908070i) q^{14} +(-4.02503 - 6.08055i) q^{15} +(-0.500000 - 0.866025i) q^{16} +7.56795 q^{17} +(2.76162 + 1.17194i) q^{18} -5.86439 q^{19} +(3.64602 - 2.10503i) q^{20} +(0.192183 + 3.13977i) q^{21} +(4.49706 + 2.59638i) q^{22} +(0.111545 - 0.193202i) q^{23} +(-0.772765 + 1.55011i) q^{24} +(6.36232 + 11.0199i) q^{25} -1.73146 q^{26} +(-0.947635 - 5.10901i) q^{27} -1.81614 q^{28} +(-1.67742 - 2.90538i) q^{29} +(-6.52605 - 3.25339i) q^{30} +(3.72314 - 4.13983i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.549495 - 8.97732i) q^{33} +(6.55404 - 3.78397i) q^{34} -7.64607i q^{35} +(2.97760 - 0.365884i) q^{36} -3.81316i q^{37} +(-5.07871 + 2.93220i) q^{38} +(1.65536 + 2.50073i) q^{39} +(2.10503 - 3.64602i) q^{40} +(-2.34382 - 1.35321i) q^{41} +(1.73632 + 2.62303i) q^{42} +(5.50784 - 3.17995i) q^{43} +5.19276 q^{44} +(1.54040 + 12.5359i) q^{45} -0.223091i q^{46} +(-4.34584 + 2.50907i) q^{47} +(0.105819 + 1.72882i) q^{48} +(1.85082 - 3.20571i) q^{49} +(11.0199 + 6.36232i) q^{50} +(-11.7311 - 5.84825i) q^{51} +(-1.49949 + 0.865730i) q^{52} -7.86605 q^{53} +(-3.37518 - 3.95072i) q^{54} +21.8619i q^{55} +(-1.57282 + 0.908070i) q^{56} +(9.09044 + 4.53180i) q^{57} +(-2.90538 - 1.67742i) q^{58} +(1.78499 + 1.03057i) q^{59} +(-7.27842 + 0.445506i) q^{60} +(-4.83783 + 2.79312i) q^{61} +(1.15442 - 5.44677i) q^{62} +(2.12840 - 5.01550i) q^{63} -1.00000 q^{64} +(-3.64478 - 6.31294i) q^{65} +(-4.96454 - 7.49984i) q^{66} +(3.75336 - 6.50102i) q^{67} +(3.78397 - 6.55404i) q^{68} +(-0.322207 + 0.213286i) q^{69} +(-3.82303 - 6.62169i) q^{70} +8.91854i q^{71} +(2.39574 - 1.80567i) q^{72} +6.05621i q^{73} +(-1.90658 - 3.30230i) q^{74} +(-1.34651 - 21.9985i) q^{75} +(-2.93220 + 5.07871i) q^{76} +(4.71539 - 8.16730i) q^{77} +(2.68395 + 1.33801i) q^{78} +(-14.7131 + 8.49458i) q^{79} -4.21006i q^{80} +(-2.47913 + 8.65182i) q^{81} -2.70641 q^{82} +(-4.38316 - 7.59186i) q^{83} +(2.81521 + 1.40345i) q^{84} +(27.5929 + 15.9308i) q^{85} +(3.17995 - 5.50784i) q^{86} +(0.355007 + 5.79990i) q^{87} +(4.49706 - 2.59638i) q^{88} -0.469197 q^{89} +(7.60197 + 10.0862i) q^{90} +3.14458i q^{91} +(-0.111545 - 0.193202i) q^{92} +(-8.97039 + 3.54007i) q^{93} +(-2.50907 + 4.34584i) q^{94} +(-21.3817 - 12.3447i) q^{95} +(0.956050 + 1.44429i) q^{96} +(-1.10468 - 1.91336i) q^{97} -3.70163i q^{98} +(-6.08559 + 14.3405i) 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
$3$	−1.55011	−	0.772765i	−0.894955	−	0.446156i
$3$	−1.55011	−	0.772765i	−0.894955	−	0.446156i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	3.64602	+	2.10503i	1.63055	+	0.941399i	0.983923	+	0.178593i	$0.0571545\pi$
$5$	3.64602	+	2.10503i	1.63055	+	0.941399i	0.646628	+	0.762806i	$0.276179\pi$
$6$	−1.72882	+	0.105819i	−0.705786	+	0.0432006i
$7$	−0.908070	−	1.57282i	−0.343218	−	0.594472i	0.641810	−	0.766864i	$-0.278184\pi$
$7$	−0.908070	−	1.57282i	−0.343218	−	0.594472i	−0.985028	+	0.172392i	$0.944850\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.80567	+	2.39574i	0.601889	+	0.798580i
$10$	4.21006			1.33134
$11$	2.59638	+	4.49706i	0.782838	+	1.35592i	0.930282	+	0.366845i	$0.119562\pi$
$11$	2.59638	+	4.49706i	0.782838	+	1.35592i	−0.147444	+	0.989070i	$0.547105\pi$
$12$	−1.44429	+	0.956050i	−0.416930	+	0.275988i
$13$	−1.49949	−	0.865730i	−0.415883	−	0.240110i	0.277431	−	0.960746i	$-0.410517\pi$
$13$	−1.49949	−	0.865730i	−0.415883	−	0.240110i	−0.693315	+	0.720635i	$0.743850\pi$
$14$	−1.57282	−	0.908070i	−0.420355	−	0.242692i
$15$	−4.02503	−	6.08055i	−1.03926	−	1.56999i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	7.56795			1.83550			0.917748	−	0.397162i	$-0.130005\pi$
$17$	7.56795			1.83550			0.917748	+	0.397162i	$0.130005\pi$
$18$	2.76162	+	1.17194i	0.650921	+	0.276228i
$19$	−5.86439			−1.34538			−0.672692	−	0.739923i	$-0.734862\pi$
$19$	−5.86439			−1.34538			−0.672692	+	0.739923i	$0.734862\pi$
$20$	3.64602	−	2.10503i	0.815275	−	0.470699i
$21$	0.192183	+	3.13977i	0.0419378	+	0.685154i
$22$	4.49706	+	2.59638i	0.958777	+	0.553550i
$23$	0.111545	−	0.193202i	0.0232588	−	0.0402854i	−0.854162	−	0.520007i	$-0.825929\pi$
$23$	0.111545	−	0.193202i	0.0232588	−	0.0402854i	0.877421	+	0.479722i	$0.159262\pi$
$24$	−0.772765	+	1.55011i	−0.157740	+	0.316414i
$25$	6.36232	+	11.0199i	1.27246	+	2.20397i
$26$	−1.73146			−0.339567
$27$	−0.947635	−	5.10901i	−0.182372	−	0.983230i
$28$	−1.81614			−0.343218
$29$	−1.67742	−	2.90538i	−0.311489	−	0.539515i	0.667196	−	0.744882i	$-0.267494\pi$
$29$	−1.67742	−	2.90538i	−0.311489	−	0.539515i	−0.978685	+	0.205368i	$0.934161\pi$
$30$	−6.52605	−	3.25339i	−1.19149	−	0.593985i
$31$	3.72314	−	4.13983i	0.668696	−	0.743536i
$31$	3.72314	−	4.13983i	0.668696	−	0.743536i
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−0.549495	−	8.97732i	−0.0956548	−	1.56275i
$34$	6.55404	−	3.78397i	1.12401	−	0.648946i
$35$		−	7.64607i		−	1.29242i
$36$	2.97760	−	0.365884i	0.496267	−	0.0609807i
$37$		−	3.81316i		−	0.626880i	−0.949608	−	0.313440i	$-0.898519\pi$
$37$		−	3.81316i		−	0.626880i	0.949608	−	0.313440i	$-0.101481\pi$
$38$	−5.07871	+	2.93220i	−0.823876	+	0.475665i
$39$	1.65536	+	2.50073i	0.265070	+	0.400437i
$40$	2.10503	−	3.64602i	0.332835	−	0.576487i
$41$	−2.34382	−	1.35321i	−0.366044	−	0.211335i	0.305685	−	0.952133i	$-0.401115\pi$
$41$	−2.34382	−	1.35321i	−0.366044	−	0.211335i	−0.671729	+	0.740797i	$0.734448\pi$
$42$	1.73632	+	2.62303i	0.267920	+	0.404742i
$43$	5.50784	−	3.17995i	0.839938	−	0.484938i	−0.0173054	−	0.999850i	$-0.505509\pi$
$43$	5.50784	−	3.17995i	0.839938	−	0.484938i	0.857243	+	0.514912i	$0.172175\pi$
$44$	5.19276			0.782838
$45$	1.54040	+	12.5359i	0.229629	+	1.86874i
$46$		−	0.223091i		−	0.0328929i
$47$	−4.34584	+	2.50907i	−0.633906	+	0.365986i	−0.782263	−	0.622948i	$-0.785935\pi$
$47$	−4.34584	+	2.50907i	−0.633906	+	0.365986i	0.148357	+	0.988934i	$0.452601\pi$
$48$	0.105819	+	1.72882i	0.0152737	+	0.249533i
$49$	1.85082	−	3.20571i	0.264402	−	0.457958i
$50$	11.0199	+	6.36232i	1.55844	+	0.899768i
$51$	−11.7311	−	5.84825i	−1.64269	−	0.818919i
$52$	−1.49949	+	0.865730i	−0.207942	+	0.120055i
$53$	−7.86605			−1.08048			−0.540242	−	0.841510i	$-0.681667\pi$
$53$	−7.86605			−1.08048			−0.540242	+	0.841510i	$0.681667\pi$
$54$	−3.37518	−	3.95072i	−0.459304	−	0.537624i
$55$			21.8619i			2.94785i
$56$	−1.57282	+	0.908070i	−0.210177	+	0.121346i
$57$	9.09044	+	4.53180i	1.20406	+	0.600251i
$58$	−2.90538	−	1.67742i	−0.381494	−	0.220256i
$59$	1.78499	+	1.03057i	0.232386	+	0.134168i	0.611672	−	0.791111i	$-0.290497\pi$
$59$	1.78499	+	1.03057i	0.232386	+	0.134168i	−0.379286	+	0.925279i	$0.623830\pi$
$60$	−7.27842	+	0.445506i	−0.939640	+	0.0575146i
$61$	−4.83783	+	2.79312i	−0.619421	+	0.357623i	−0.776643	−	0.629941i	$-0.783079\pi$
$61$	−4.83783	+	2.79312i	−0.619421	+	0.357623i	0.157223	+	0.987563i	$0.449746\pi$
$62$	1.15442	−	5.44677i	0.146611	−	0.691741i
$63$	2.12840	−	5.01550i	0.268154	−	0.631893i
$64$	−1.00000			−0.125000
$65$	−3.64478	−	6.31294i	−0.452079	−	0.783024i
$66$	−4.96454	−	7.49984i	−0.611093	−	0.923167i
$67$	3.75336	−	6.50102i	0.458546	−	0.794226i	−0.540338	−	0.841448i	$-0.681704\pi$
$67$	3.75336	−	6.50102i	0.458546	−	0.794226i	0.998884	+	0.0472224i	$0.0150369\pi$
$68$	3.78397	−	6.55404i	0.458874	−	0.794794i
$69$	−0.322207	+	0.213286i	−0.0387892	+	0.0256766i
$70$	−3.82303	−	6.62169i	−0.456940	−	0.791443i
$71$			8.91854i			1.05844i	0.848486	+	0.529218i	$0.177515\pi$
$71$			8.91854i			1.05844i	−0.848486	+	0.529218i	$0.822485\pi$
$72$	2.39574	−	1.80567i	0.282341	−	0.212800i
$73$			6.05621i			0.708826i	0.935089	+	0.354413i	$0.115319\pi$
$73$			6.05621i			0.708826i	−0.935089	+	0.354413i	$0.884681\pi$
$74$	−1.90658	−	3.30230i	−0.221636	−	0.383884i
$75$	−1.34651	−	21.9985i	−0.155482	−	2.54017i
$76$	−2.93220	+	5.07871i	−0.336346	+	0.582568i
$77$	4.71539	−	8.16730i	0.537369	−	0.930750i
$78$	2.68395	+	1.33801i	0.303898	+	0.151500i
$79$	−14.7131	+	8.49458i	−1.65535	+	0.955715i	−0.680527	+	0.732723i	$0.738249\pi$
$79$	−14.7131	+	8.49458i	−1.65535	+	0.955715i	−0.974820	+	0.222993i	$0.928417\pi$
$80$		−	4.21006i		−	0.470699i
$81$	−2.47913	+	8.65182i	−0.275459	+	0.961313i
$82$	−2.70641			−0.298873
$83$	−4.38316	−	7.59186i	−0.481115	−	0.833315i	0.518651	−	0.854986i	$-0.326435\pi$
$83$	−4.38316	−	7.59186i	−0.481115	−	0.833315i	−0.999765	+	0.0216714i	$0.993101\pi$
$84$	2.81521	+	1.40345i	0.307165	+	0.153129i
$85$	27.5929	+	15.9308i	2.99287	+	1.72793i
$86$	3.17995	−	5.50784i	0.342903	−	0.593926i
$87$	0.355007	+	5.79990i	0.0380608	+	0.621814i
$88$	4.49706	−	2.59638i	0.479389	−	0.276775i
$89$	−0.469197			−0.0497348			−0.0248674	−	0.999691i	$-0.507916\pi$
$89$	−0.469197			−0.0497348			−0.0248674	+	0.999691i	$0.507916\pi$
$90$	7.60197	+	10.0862i	0.801318	+	1.06318i
$91$			3.14458i			0.329641i
$92$	−0.111545	−	0.193202i	−0.0116294	−	0.0201427i
$93$	−8.97039	+	3.54007i	−0.930186	+	0.367088i
$94$	−2.50907	+	4.34584i	−0.258791	+	0.448239i
$95$	−21.3817	−	12.3447i	−2.19372	−	1.26654i
$96$	0.956050	+	1.44429i	0.0975764	+	0.147407i
$97$	−1.10468	−	1.91336i	−0.112163	−	0.194273i	0.804479	−	0.593981i	$-0.202445\pi$
$97$	−1.10468	−	1.91336i	−0.112163	−	0.194273i	−0.916642	+	0.399709i	$0.869111\pi$
$98$		−	3.70163i		−	0.373921i
$99$	−6.08559	+	14.3405i	−0.611625	+	1.44127i
$100$	12.7246			1.27246
$101$	1.00415	−	0.579743i	0.0999162	−	0.0576866i	−0.449209	−	0.893427i	$-0.648294\pi$
$101$	1.00415	−	0.579743i	0.0999162	−	0.0576866i	0.549125	+	0.835740i	$0.314961\pi$
$102$	−13.0836	+	0.800836i	−1.29547	+	0.0792946i
$103$	−3.24174	+	5.61485i	−0.319418	+	0.553248i	−0.980367	−	0.197183i	$-0.936821\pi$
$103$	−3.24174	+	5.61485i	−0.319418	+	0.553248i	0.660949	+	0.750431i	$0.270154\pi$
$104$	−0.865730	+	1.49949i	−0.0848919	+	0.147037i
$105$	−5.90862	+	11.8522i	−0.576622	+	1.15666i
$106$	−6.81219	+	3.93302i	−0.661659	+	0.382009i
$107$			7.88166i			0.761949i	0.924586	+	0.380975i	$0.124411\pi$
$107$			7.88166i			0.761949i	−0.924586	+	0.380975i	$0.875589\pi$
$108$	−4.89835	−	1.73383i	−0.471344	−	0.166838i
$109$	−13.3906			−1.28258			−0.641291	−	0.767298i	$-0.721601\pi$
$109$	−13.3906			−1.28258			−0.641291	+	0.767298i	$0.721601\pi$
$110$	10.9309	+	18.9329i	1.04222	+	1.80518i
$111$	−2.94668	+	5.91081i	−0.279687	+	0.561030i
$112$	−0.908070	+	1.57282i	−0.0858046	+	0.148618i
$113$	−2.68402	−	1.54962i	−0.252492	−	0.145776i	0.368413	−	0.929662i	$-0.379901\pi$
$113$	−2.68402	−	1.54962i	−0.252492	−	0.145776i	−0.620905	+	0.783886i	$0.713235\pi$
$114$	10.1384	−	0.620566i	0.949553	−	0.0581214i
$115$	0.813393	−	0.469613i	0.0758493	−	0.0437916i
$116$	−3.35484			−0.311489
$117$	−0.633515	−	5.15561i	−0.0585684	−	0.476636i
$118$	2.06113			0.189742
$119$	−6.87223	−	11.9031i	−0.629976	−	1.09115i
$120$	−6.08055	+	4.02503i	−0.555075	+	0.367433i
$121$	−7.98238	+	13.8259i	−0.725671	+	1.25690i
$122$	−2.79312	+	4.83783i	−0.252877	+	0.437996i
$123$	2.58747	+	3.90884i	0.233304	+	0.352448i
$124$	−1.72363	−	5.29425i	−0.154786	−	0.475438i
$125$			32.5212i			2.90878i
$126$	−0.664498	−	5.40775i	−0.0591982	−	0.481761i
$127$			10.1986i			0.904979i	0.891770	+	0.452490i	$0.149464\pi$
$127$			10.1986i			0.904979i	−0.891770	+	0.452490i	$0.850536\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−10.9951	+	0.673001i	−0.968065	+	0.0592545i
$130$	−6.31294	−	3.64478i	−0.553682	−	0.319668i
$131$	2.86953	+	1.65672i	0.250712	+	0.144749i	0.620090	−	0.784530i	$-0.287096\pi$
$131$	2.86953	+	1.65672i	0.250712	+	0.144749i	−0.369378	+	0.929279i	$0.620429\pi$
$132$	−8.04934	−	4.01279i	−0.700605	−	0.349268i
$133$	5.32528	+	9.22366i	0.461760	+	0.799792i
$134$		−	7.50673i		−	0.648483i
$135$	7.29953	−	20.6224i	0.628244	−	1.77489i
$136$		−	7.56795i		−	0.648946i
$137$	4.57197	+	7.91889i	0.390610	+	0.676556i	0.992530	−	0.122000i	$-0.0389308\pi$
$137$	4.57197	+	7.91889i	0.390610	+	0.676556i	−0.601920	+	0.798556i	$0.705597\pi$
$138$	−0.172397	+	0.345814i	−0.0146754	+	0.0294377i
$139$	−14.3774	−	8.30079i	−1.21947	−	0.704064i	−0.254669	−	0.967028i	$-0.581967\pi$
$139$	−14.3774	−	8.30079i	−1.21947	−	0.704064i	−0.964806	+	0.262964i	$0.915300\pi$
$140$	−6.62169	−	3.82303i	−0.559635	−	0.323105i
$141$	8.67545	−	0.531017i	0.730604	−	0.0447197i
$142$	4.45927	+	7.72369i	0.374214	+	0.648157i
$143$		−	8.99106i		−	0.751870i
$144$	1.17194	−	2.76162i	0.0976614	−	0.230135i
$145$		−	14.1241i		−	1.17294i
$146$	3.02811	+	5.24483i	0.250608	+	0.434065i
$147$	−5.34622	+	3.53895i	−0.440949	+	0.291887i
$148$	−3.30230	−	1.90658i	−0.271447	−	0.156720i
$149$	−12.2468	−	7.07068i	−1.00329	−	0.579252i	−0.0940730	−	0.995565i	$-0.529989\pi$
$149$	−12.2468	−	7.07068i	−1.00329	−	0.579252i	−0.909221	+	0.416313i	$0.863322\pi$
$150$	−12.1654	−	18.3780i	−0.993300	−	1.50056i
$151$	7.71830	−	4.45616i	0.628107	−	0.362637i	−0.151912	−	0.988394i	$-0.548543\pi$
$151$	7.71830	−	4.45616i	0.628107	−	0.362637i	0.780018	+	0.625757i	$0.215210\pi$
$152$			5.86439i			0.475665i
$153$	13.6652	+	18.1308i	1.10477	+	1.46579i
$154$		−	9.43079i		−	0.759954i
$155$	22.2891	−	7.25659i	1.79031	−	0.582863i
$156$	2.99338	−	0.183222i	0.239662	−	0.0146695i
$157$	10.0993	−	17.4924i	0.806008	−	1.39605i	−0.109600	−	0.993976i	$-0.534957\pi$
$157$	10.0993	−	17.4924i	0.806008	−	1.39605i	0.915608	−	0.402071i	$-0.131710\pi$
$158$	−8.49458	+	14.7131i	−0.675793	+	1.17051i
$159$	12.1932	+	6.07861i	0.966985	+	0.482065i
$160$	−2.10503	−	3.64602i	−0.166417	−	0.288243i
$161$	−0.405164			−0.0319314
$162$	2.17892	+	8.73226i	0.171192	+	0.686071i
$163$	−0.374934			−0.0293671			−0.0146836	−	0.999892i	$-0.504674\pi$
$163$	−0.374934			−0.0293671			−0.0146836	+	0.999892i	$0.504674\pi$
$164$	−2.34382	+	1.35321i	−0.183022	+	0.105668i
$165$	16.8941	−	33.8882i	1.31520	−	2.63819i
$166$	−7.59186	−	4.38316i	−0.589243	−	0.340199i
$167$	10.7037	−	18.5393i	0.828273	−	1.43461i	−0.0711184	−	0.997468i	$-0.522657\pi$
$167$	10.7037	−	18.5393i	0.828273	−	1.43461i	0.899392	−	0.437144i	$-0.144010\pi$
$168$	3.13977	−	0.192183i	0.242239	−	0.0148272i
$169$	−5.00102	−	8.66202i	−0.384694	−	0.666310i
$170$	31.8615			2.44367
$171$	−10.5891	−	14.0496i	−0.809772	−	1.07440i
$172$		−	6.35991i		−	0.484938i
$173$	5.52702	−	3.19103i	0.420211	−	0.242609i	−0.274956	−	0.961457i	$-0.588663\pi$
$173$	5.52702	−	3.19103i	0.420211	−	0.242609i	0.695168	+	0.718848i	$0.255330\pi$
$174$	3.20739	+	4.84535i	0.243152	+	0.367325i
$175$	11.5549	−	20.0136i	0.873466	−	1.51289i
$176$	2.59638	−	4.49706i	0.195710	−	0.338979i
$177$	−1.97054	−	2.97687i	−0.148115	−	0.223755i
$178$	−0.406337	+	0.234598i	−0.0304562	+	0.0175839i
$179$	2.90778			0.217338			0.108669	−	0.994078i	$-0.465341\pi$
$179$	2.90778			0.217338			0.108669	+	0.994078i	$0.465341\pi$
$180$	11.6266	+	4.93393i	0.866596	+	0.367753i
$181$		−	1.20953i		−	0.0899035i	−0.998989	−	0.0449517i	$-0.985687\pi$
$181$		−	1.20953i		−	0.0899035i	0.998989	−	0.0449517i	$-0.0143134\pi$
$182$	1.57229	+	2.72328i	0.116546	+	0.201863i
$183$	9.65758	−	0.591133i	0.713909	−	0.0436978i
$184$	−0.193202	−	0.111545i	−0.0142430	−	0.00822323i
$185$	8.02683	−	13.9029i	0.590144	−	1.02216i
$186$	−5.99855	+	7.55099i	−0.439835	+	0.553665i
$187$	19.6493	+	34.0335i	1.43690	+	2.48878i
$188$			5.01815i			0.365986i
$189$	−7.17506	+	6.12980i	−0.521909	+	0.445878i
$190$	−24.6895			−1.79116
$191$	2.04359	−	1.17987i	0.147869	−	0.0853722i	−0.424240	−	0.905550i	$-0.639459\pi$
$191$	2.04359	−	1.17987i	0.147869	−	0.0853722i	0.572109	+	0.820178i	$0.306125\pi$
$192$	1.55011	+	0.772765i	0.111869	+	0.0557695i
$193$	−6.72172	+	11.6424i	−0.483840	+	0.838035i	−0.999828	−	0.0185607i	$-0.994092\pi$
$193$	−6.72172	+	11.6424i	−0.483840	+	0.838035i	0.515988	+	0.856596i	$0.327425\pi$
$194$	−1.91336	−	1.10468i	−0.137371	−	0.0793114i
$195$	0.771377	+	12.6023i	0.0552395	+	0.902470i
$196$	−1.85082	−	3.20571i	−0.132201	−	0.228979i
$197$	−18.5204			−1.31953			−0.659763	−	0.751473i	$-0.729344\pi$
$197$	−18.5204			−1.31953			−0.659763	+	0.751473i	$0.729344\pi$
$198$	1.89995	+	15.4620i	0.135024	+	1.09884i
$199$			22.2766i			1.57915i	0.613657	+	0.789573i	$0.289698\pi$
$199$			22.2766i			1.57915i	−0.613657	+	0.789573i	$0.710302\pi$
$200$	11.0199	−	6.36232i	0.779222	−	0.449884i
$201$	−10.8419	+	7.17681i	−0.764727	+	0.506213i
$202$	0.579743	−	1.00415i	0.0407906	−	0.0706514i
$203$	−3.04643	+	5.27657i	−0.213817	+	0.370343i
$204$	−10.9303	+	7.23534i	−0.765274	+	0.506575i
$205$	−5.69708	−	9.86764i	−0.397902	−	0.689186i
$206$			6.48347i			0.451725i
$207$	0.664275	−	0.0816254i	0.0461703	−	0.00567335i
$208$			1.73146i			0.120055i
$209$	−15.2262	−	26.3725i	−1.05322	−	1.82423i
$210$	0.809103	+	13.2186i	0.0558334	+	0.912173i
$211$	9.69264	−	16.7881i	0.667269	−	1.15574i	−0.311396	−	0.950280i	$-0.600797\pi$
$211$	9.69264	−	16.7881i	0.667269	−	1.15574i	0.978665	−	0.205463i	$-0.0658700\pi$
$212$	−3.93302	+	6.81219i	−0.270121	+	0.467863i
$213$	6.89194	−	13.8247i	0.472228	−	0.947253i
$214$	3.94083	+	6.82572i	0.269390	+	0.466597i
$215$	26.7756			1.82608
$216$	−5.10901	+	0.947635i	−0.347624	+	0.0644784i
$217$	−9.89210	−	2.09659i	−0.671520	−	0.142326i
$218$	−11.5966	+	6.69528i	−0.785418	+	0.453461i
$219$	4.68003	−	9.38778i	0.316247	−	0.634367i
$220$	18.9329	+	10.9309i	1.27646	+	0.736963i
$221$	−11.3481	−	6.55180i	−0.763353	−	0.440722i
$222$	0.403507	+	6.59226i	0.0270816	+	0.442443i
$223$	17.9594	−	10.3689i	1.20265	−	0.694352i	0.241508	−	0.970399i	$-0.422358\pi$
$223$	17.9594	−	10.3689i	1.20265	−	0.694352i	0.961144	+	0.276047i	$0.0890246\pi$
$224$			1.81614i			0.121346i
$225$	−14.9125	+	35.1406i	−0.994165	+	2.34271i
$226$	−3.09924			−0.206159
$227$	1.87127	−	1.08038i	0.124201	−	0.0717073i	−0.436612	−	0.899650i	$-0.643822\pi$
$227$	1.87127	−	1.08038i	0.124201	−	0.0717073i	0.560813	+	0.827942i	$0.310489\pi$
$228$	8.46987	−	5.60665i	0.560931	−	0.371310i
$229$	−23.1629	−	13.3731i	−1.53065	−	0.883720i	−0.999332	−	0.0365472i	$-0.988364\pi$
$229$	−23.1629	−	13.3731i	−1.53065	−	0.883720i	−0.531317	−	0.847173i	$-0.678303\pi$
$230$	0.469613	−	0.813393i	0.0309653	−	0.0536335i
$231$	−13.6208	+	9.01630i	−0.896181	+	0.593229i
$232$	−2.90538	+	1.67742i	−0.190747	+	0.110128i
$233$		−	13.1809i		−	0.863513i	−0.901990	−	0.431756i	$-0.857894\pi$
$233$		−	13.1809i		−	0.863513i	0.901990	−	0.431756i	$-0.142106\pi$
$234$	−3.12644	−	4.14813i	−0.204382	−	0.271172i
$235$	−21.1267			−1.37815
$236$	1.78499	−	1.03057i	0.116193	−	0.0670841i
$237$	29.3711	−	1.79778i	1.90786	−	0.116779i
$238$	−11.9031	−	6.87223i	−0.771560	−	0.445461i
$239$	−1.57753	+	2.73237i	−0.102042	+	0.176742i	−0.912526	−	0.409019i	$-0.865871\pi$
$239$	−1.57753	+	2.73237i	−0.102042	+	0.176742i	0.810484	+	0.585761i	$0.199204\pi$
$240$	−3.25339	+	6.52605i	−0.210005	+	0.421255i
$241$	6.13917	−	3.54445i	0.395459	−	0.228318i	−0.289064	−	0.957310i	$-0.593344\pi$
$241$	6.13917	−	3.54445i	0.395459	−	0.228318i	0.684523	+	0.728992i	$0.260011\pi$
$242$			15.9648i			1.02625i
$243$	10.5287	−	11.4955i	0.675419	−	0.737434i
$244$			5.58624i			0.357623i
$245$	13.4962	−	7.79205i	0.862243	−	0.497816i
$246$	4.19523	+	2.09142i	0.267478	+	0.133344i
$247$	8.79359	+	5.07698i	0.559523	+	0.323041i
$248$	−4.13983	−	3.72314i	−0.262880	−	0.236420i
$249$	0.927647	+	15.1554i	0.0587873	+	0.960432i
$250$	16.2606	+	28.1642i	1.02841	+	1.78126i
$251$	−4.32927			−0.273261			−0.136631	−	0.990622i	$-0.543627\pi$
$251$	−4.32927			−0.273261			−0.136631	+	0.990622i	$0.543627\pi$
$252$	−3.27935	−	4.35100i	−0.206579	−	0.274087i
$253$	1.15846			0.0728315
$254$	5.09930	+	8.83224i	0.319958	+	0.554184i
$255$	−30.4612	−	46.0172i	−1.90756	−	2.88171i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	17.9013	+	10.3353i	1.11665	+	0.644699i	0.940544	−	0.339672i	$-0.110316\pi$
$257$	17.9013	+	10.3353i	1.11665	+	0.644699i	0.176108	+	0.984371i	$0.443649\pi$
$258$	−9.18554	+	6.08039i	−0.571866	+	0.378548i
$259$	−5.99744	+	3.46262i	−0.372663	+	0.215157i
$260$	−7.28956			−0.452079
$261$	3.93166	−	9.26480i	0.243364	−	0.573477i
$262$	3.31345			0.204706
$263$	−3.35235	−	5.80645i	−0.206715	−	0.358041i	0.743963	−	0.668221i	$-0.232944\pi$
$263$	−3.35235	−	5.80645i	−0.206715	−	0.358041i	−0.950678	+	0.310180i	$0.899611\pi$
$264$	−8.97732	+	0.549495i	−0.552516	+	0.0338191i
$265$	−28.6798	−	16.5583i	−1.76178	−	1.01717i
$266$	9.22366	+	5.32528i	0.565539	+	0.326514i
$267$	0.727306	+	0.362579i	0.0445104	+	0.0221895i
$268$	−3.75336	−	6.50102i	−0.229273	−	0.397113i
$269$	25.1806			1.53529			0.767645	−	0.640875i	$-0.221428\pi$
$269$	25.1806			1.53529			0.767645	+	0.640875i	$0.221428\pi$
$270$	−3.98960	−	21.5093i	−0.242800	−	1.30901i
$271$			4.98283i			0.302685i	0.988481	+	0.151343i	$0.0483597\pi$
$271$			4.98283i			0.302685i	−0.988481	+	0.151343i	$0.951640\pi$
$272$	−3.78397	−	6.55404i	−0.229437	−	0.397397i
$273$	2.43002	−	4.87443i	0.147072	−	0.295014i
$274$	7.91889	+	4.57197i	0.478398	+	0.276203i
$275$	−33.0380	+	57.2235i	−1.99227	+	3.45071i
$276$	0.0236073	+	0.385682i	0.00142099	+	0.0232153i
$277$	−18.7465	+	10.8233i	−1.12637	+	0.650309i	−0.943019	−	0.332739i	$-0.892027\pi$
$277$	−18.7465	+	10.8233i	−1.12637	+	0.650309i	−0.183349	+	0.983048i	$0.558694\pi$
$278$	−16.6016			−0.995697
$279$	16.6407	+	1.44452i	0.996254	+	0.0864809i
$280$	−7.64607			−0.456940
$281$	−7.60659	+	4.39166i	−0.453771	+	0.261985i	−0.709421	−	0.704785i	$-0.751044\pi$
$281$	−7.60659	+	4.39166i	−0.453771	+	0.261985i	0.255651	+	0.966769i	$0.417710\pi$
$282$	7.24765	−	4.79760i	0.431591	−	0.285693i
$283$	13.3375	−	23.1012i	0.792832	−	1.37323i	−0.131375	−	0.991333i	$-0.541939\pi$
$283$	13.3375	−	23.1012i	0.792832	−	1.37323i	0.924207	−	0.381892i	$-0.124728\pi$
$284$	7.72369	+	4.45927i	0.458316	+	0.264609i
$285$	23.6044	+	35.6587i	1.39820	+	2.11224i
$286$	−4.49553	−	7.78649i	−0.265826	−	0.460425i
$287$			4.91523i			0.290137i
$288$	−0.365884	−	2.97760i	−0.0215599	−	0.175457i
$289$	40.2738			2.36905
$290$	−7.06204	−	12.2318i	−0.414697	−	0.718277i
$291$	0.233793	+	3.81958i	0.0137052	+	0.223908i
$292$	5.24483	+	3.02811i	0.306931	+	0.177206i
$293$	−0.788407	−	0.455187i	−0.0460592	−	0.0265923i	0.476794	−	0.879015i	$-0.341799\pi$
$293$	−0.788407	−	0.455187i	−0.0460592	−	0.0265923i	−0.522853	+	0.852423i	$0.675132\pi$
$294$	−2.86049	+	5.73793i	−0.166827	+	0.334643i
$295$	4.33874	+	7.51493i	0.252611	+	0.437536i
$296$	−3.81316			−0.221636
$297$	20.5151	−	17.5265i	1.19041	−	1.01699i
$298$	−14.1414			−0.819186
$299$	−0.334522	+	0.193136i	−0.0193459	+	0.0111694i
$300$	−19.7246	−	9.83316i	−1.13880	−	0.567718i
$301$	−10.0030	−	5.77524i	−0.576564	−	0.332879i
$302$	4.45616	−	7.71830i	0.256423	−	0.444138i
$303$	−2.00454	+	0.122696i	−0.115158	+	0.00704871i
$304$	2.93220	+	5.07871i	0.168173	+	0.291284i
$305$	−23.5184			−1.34666
$306$	20.8998	+	8.86916i	1.19476	+	0.507016i
$307$	−0.346425			−0.0197715			−0.00988575	−	0.999951i	$-0.503147\pi$
$307$	−0.346425			−0.0197715			−0.00988575	+	0.999951i	$0.503147\pi$
$308$	−4.71539	−	8.16730i	−0.268684	−	0.465375i
$309$	9.36401	−	6.19853i	0.532700	−	0.352622i
$310$	15.6747	−	17.4290i	0.890261	−	0.989898i
$311$	−10.2969	−	5.94490i	−0.583882	−	0.337104i	0.178793	−	0.983887i	$-0.442781\pi$
$311$	−10.2969	−	5.94490i	−0.583882	−	0.337104i	−0.762675	+	0.646782i	$0.776114\pi$
$312$	2.50073	−	1.65536i	0.141576	−	0.0937165i
$313$	−26.1287	+	15.0854i	−1.47688	+	0.852676i	−0.999659	−	0.0261078i	$-0.991689\pi$
$313$	−26.1287	+	15.0854i	−1.47688	+	0.852676i	−0.477220	+	0.878784i	$0.658355\pi$
$314$		−	20.1985i		−	1.13987i
$315$	18.3180	−	13.8063i	1.03210	−	0.777894i
$316$			16.9892i			0.955715i
$317$	−14.6628	+	8.46560i	−0.823547	+	0.475475i	−0.851638	−	0.524130i	$-0.824391\pi$
$317$	−14.6628	+	8.46560i	−0.823547	+	0.475475i	0.0280909	+	0.999605i	$0.491057\pi$
$318$	13.5989	−	0.832380i	0.762591	−	0.0466776i
$319$	8.71044	−	15.0869i	0.487691	−	0.844705i
$320$	−3.64602	−	2.10503i	−0.203819	−	0.117675i
$321$	6.09068	−	12.2174i	0.339948	−	0.681910i
$322$	−0.350882	+	0.202582i	−0.0195539	+	0.0112895i
$323$	−44.3814			−2.46945
$324$	6.25313	+	6.47290i	0.347396	+	0.359605i
$325$		−	22.0322i		−	1.22213i
$326$	−0.324702	+	0.187467i	−0.0179836	+	0.0103828i
$327$	20.7568	+	10.3478i	1.14785	+	0.572232i
$328$	−1.35321	+	2.34382i	−0.0747183	+	0.129416i
$329$	7.89266	+	4.55683i	0.435136	+	0.251226i
$330$	−2.31341	−	37.7951i	−0.127349	−	2.08055i
$331$	−4.98563	+	2.87846i	−0.274035	+	0.158214i	−0.630720	−	0.776010i	$-0.717240\pi$
$331$	−4.98563	+	2.87846i	−0.274035	+	0.158214i	0.356685	+	0.934225i	$0.383907\pi$
$332$	−8.76632			−0.481115
$333$	9.13534	−	6.88531i	0.500614	−	0.377312i
$334$		−	21.4073i		−	1.17136i
$335$	27.3697	−	15.8019i	1.49537	−	0.863350i
$336$	2.62303	−	1.73632i	0.143098	−	0.0947241i
$337$	16.9585	+	9.79099i	0.923788	+	0.533349i	0.884842	−	0.465892i	$-0.154267\pi$
$337$	16.9585	+	9.79099i	0.923788	+	0.533349i	0.0389463	+	0.999241i	$0.487600\pi$
$338$	−8.66202	−	5.00102i	−0.471152	−	0.272020i
$339$	2.96303	+	4.47620i	0.160930	+	0.243114i
$340$	27.5929	−	15.9308i	1.49644	−	0.863967i
$341$	28.2838	+	5.99462i	1.53165	+	0.324627i
$342$	−16.1952	−	6.87270i	−0.875738	−	0.371633i
$343$	−19.4357			−1.04943
$344$	−3.17995	−	5.50784i	−0.171452	−	0.296963i
$345$	−1.62375	+	0.0993883i	−0.0874196	+	0.00535089i
$346$	3.19103	−	5.52702i	0.171551	−	0.297134i
$347$	1.53434	−	2.65755i	0.0823676	−	0.142665i	−0.821899	−	0.569633i	$-0.807085\pi$
$347$	1.53434	−	2.65755i	0.0823676	−	0.142665i	0.904266	+	0.426969i	$0.140418\pi$
$348$	5.20036	+	2.59250i	0.278769	+	0.138973i
$349$	12.9798	+	22.4817i	0.694794	+	1.20342i	0.970250	+	0.242105i	$0.0778379\pi$
$349$	12.9798	+	22.4817i	0.694794	+	1.20342i	−0.275456	+	0.961314i	$0.588829\pi$
$350$		−	23.1097i		−	1.23527i
$351$	−3.00206	+	8.48130i	−0.160238	+	0.452698i
$352$		−	5.19276i		−	0.276775i
$353$	−1.86090	−	3.22317i	−0.0990456	−	0.171552i	0.812244	−	0.583317i	$-0.198246\pi$
$353$	−1.86090	−	3.22317i	−0.0990456	−	0.171552i	−0.911290	+	0.411765i	$0.864912\pi$
$354$	−3.19497	−	1.59277i	−0.169811	−	0.0846548i
$355$	−18.7738	+	32.5172i	−0.996411	+	1.72583i
$356$	−0.234598	+	0.406337i	−0.0124337	+	0.0215358i
$357$	1.45443	+	23.7616i	0.0769766	+	1.25760i
$358$	2.51821	−	1.45389i	0.133092	−	0.0768404i
$359$			13.1832i			0.695780i	0.937535	+	0.347890i	$0.113102\pi$
$359$			13.1832i			0.695780i	−0.937535	+	0.347890i	$0.886898\pi$
$360$	12.5359	−	1.54040i	0.660700	−	0.0811860i
$361$	15.3911			0.810057
$362$	−0.604764	−	1.04748i	−0.0317857	−	0.0550544i
$363$	23.0577	−	15.2631i	1.21022	−	0.801106i
$364$	2.72328	+	1.57229i	0.142739	+	0.0824103i
$365$	−12.7485	+	22.0811i	−0.667288	+	1.15578i
$366$	8.06815	−	5.34073i	0.421729	−	0.279164i
$367$	9.40858	−	5.43204i	0.491124	−	0.283550i	−0.233917	−	0.972257i	$-0.575154\pi$
$367$	9.40858	−	5.43204i	0.491124	−	0.283550i	0.725040	+	0.688706i	$0.241821\pi$
$368$	−0.223091			−0.0116294
$369$	−0.990234	−	8.05863i	−0.0515495	−	0.419515i
$370$		−	16.0537i		−	0.834590i
$371$	7.14292	+	12.3719i	0.370842	+	0.642317i
$372$	−1.41940	+	9.53862i	−0.0735926	+	0.494554i
$373$	−3.91524	+	6.78140i	−0.202724	+	0.351127i	−0.949405	−	0.314054i	$-0.898313\pi$
$373$	−3.91524	+	6.78140i	−0.202724	+	0.351127i	0.746681	+	0.665182i	$0.231646\pi$
$374$	34.0335	+	19.6493i	1.75983	+	1.01604i
$375$	25.1313	−	50.4114i	1.29777	−	2.60323i
$376$	2.50907	+	4.34584i	0.129396	+	0.224120i
$377$			5.80877i			0.299167i
$378$	−3.14888	+	8.89609i	−0.161961	+	0.457566i
$379$	−7.89272			−0.405422			−0.202711	−	0.979239i	$-0.564975\pi$
$379$	−7.89272			−0.405422			−0.202711	+	0.979239i	$0.564975\pi$
$380$	−21.3817	+	12.3447i	−1.09686	+	0.633271i
$381$	7.88112	−	15.8089i	0.403762	−	0.809916i
$382$	1.17987	−	2.04359i	0.0603672	−	0.104559i
$383$	2.99200	−	5.18230i	0.152884	−	0.264803i	−0.779402	−	0.626524i	$-0.784477\pi$
$383$	2.99200	−	5.18230i	0.152884	−	0.264803i	0.932287	+	0.361720i	$0.117810\pi$
$384$	1.72882	−	0.105819i	0.0882232	−	0.00540007i
$385$	34.3849	−	19.8521i	1.75241	−	1.01176i
$386$			13.4434i			0.684253i
$387$	17.5637	+	7.45341i	0.892811	+	0.378878i
$388$	−2.20936			−0.112163
$389$	2.86466	+	4.96173i	0.145244	+	0.251570i	0.929464	−	0.368913i	$-0.120270\pi$
$389$	2.86466	+	4.96173i	0.145244	+	0.251570i	−0.784220	+	0.620483i	$0.786937\pi$
$390$	6.96918	+	10.5282i	0.352898	+	0.533117i
$391$	0.844169	−	1.46214i	0.0426915	−	0.0739438i
$392$	−3.20571	−	1.85082i	−0.161913	−	0.0934803i
$393$	−3.16782	−	4.78558i	−0.159796	−	0.241400i
$394$	−16.0392	+	9.26022i	−0.808042	+	0.466523i
$395$	−71.5255			−3.59884
$396$	9.37640	+	12.4405i	0.471182	+	0.625159i
$397$	−18.4493			−0.925945			−0.462972	−	0.886373i	$-0.653217\pi$
$397$	−18.4493			−0.925945			−0.462972	+	0.886373i	$0.653217\pi$
$398$	11.1383	+	19.2921i	0.558312	+	0.967026i
$399$	−1.12704	−	18.4129i	−0.0564224	−	0.921796i
$400$	6.36232	−	11.0199i	0.318116	−	0.550993i
$401$	−2.93388	+	5.08163i	−0.146511	+	0.253764i	−0.929936	−	0.367722i	$-0.880138\pi$
$401$	−2.93388	+	5.08163i	−0.146511	+	0.253764i	0.783425	+	0.621487i	$0.213471\pi$
$402$	−5.80094	+	11.6362i	−0.289325	+	0.580363i
$403$	−9.16679	+	2.98440i	−0.456630	+	0.148663i
$404$		−	1.15949i		−	0.0576866i
$405$	−27.2513	+	26.3261i	−1.35413	+	1.30815i
$406$			6.09286i			0.302384i
$407$	17.1480	−	9.90042i	0.849997	−	0.490746i
$408$	−5.84825	+	11.7311i	−0.289531	+	0.580778i
$409$	−22.3628	−	12.9112i	−1.10577	−	0.638417i	−0.168040	−	0.985780i	$-0.553744\pi$
$409$	−22.3628	−	12.9112i	−1.10577	−	0.638417i	−0.937731	+	0.347363i	$0.887077\pi$
$410$	−9.86764	−	5.69708i	−0.487328	−	0.281359i
$411$	−0.967607	−	15.8082i	−0.0477285	−	0.779761i
$412$	3.24174	+	5.61485i	0.159709	+	0.276624i
$413$		−	3.74330i		−	0.184196i
$414$	0.534467	−	0.402827i	0.0262676	−	0.0197979i
$415$		−	36.9068i		−	1.81168i
$416$	0.865730	+	1.49949i	0.0424459	+	0.0735185i
$417$	15.8719	+	23.9775i	0.777252	+	1.17418i
$418$	−26.3725	−	15.2262i	−1.28992	−	0.744737i
$419$	24.0458	+	13.8829i	1.17471	+	0.678222i	0.954786	−	0.297294i	$-0.0960842\pi$
$419$	24.0458	+	13.8829i	1.17471	+	0.678222i	0.219929	+	0.975516i	$0.429418\pi$
$420$	7.31002	+	11.0431i	0.356693	+	0.538849i
$421$	−6.56081	−	11.3637i	−0.319754	−	0.553830i	0.660682	−	0.750666i	$-0.270267\pi$
$421$	−6.56081	−	11.3637i	−0.319754	−	0.553830i	−0.980437	+	0.196835i	$0.936934\pi$
$422$		−	19.3853i		−	0.943660i
$423$	−13.8582	−	5.88095i	−0.673810	−	0.285942i
$424$			7.86605i			0.382009i
$425$	48.1497	+	83.3977i	2.33560	+	4.04538i
$426$	−0.943755	−	15.4185i	−0.0457251	−	0.747030i
$427$	8.78618	+	5.07270i	0.425193	+	0.245485i
$428$	6.82572	+	3.94083i	0.329934	+	0.190487i
$429$	−6.94798	+	13.9371i	−0.335452	+	0.672890i
$430$	23.1884	−	13.3878i	1.11824	−	0.645617i
$431$		−	9.02479i		−	0.434709i	−0.976093	−	0.217355i	$-0.930257\pi$
$431$		−	9.02479i		−	0.434709i	0.976093	−	0.217355i	$-0.0697428\pi$
$432$	−3.95072	+	3.37518i	−0.190079	+	0.162388i
$433$		−	28.7422i		−	1.38126i	−0.723207	−	0.690631i	$-0.757333\pi$
$433$		−	28.7422i		−	1.38126i	0.723207	−	0.690631i	$-0.242667\pi$
$434$	−9.61511	+	3.13035i	−0.461540	+	0.150262i
$435$	−10.9146	+	21.8938i	−0.523315	+	1.04973i
$436$	−6.69528	+	11.5966i	−0.320646	+	0.555374i
$437$	−0.654145	+	1.13301i	−0.0312920	+	0.0541993i
$438$	−0.640865	−	10.4701i	−0.0306217	−	0.500279i
$439$	9.68192	+	16.7696i	0.462093	+	0.800369i	0.999065	−	0.0432314i	$-0.0137653\pi$
$439$	9.68192	+	16.7696i	0.462093	+	0.800369i	−0.536972	+	0.843600i	$0.680432\pi$
$440$	21.8619			1.04222
$441$	11.0220	−	1.35437i	0.524857	−	0.0644938i
$442$	−13.1036			−0.623275
$443$	−19.3089	+	11.1480i	−0.917395	+	0.529658i	−0.882803	−	0.469744i	$-0.844346\pi$
$443$	−19.3089	+	11.1480i	−0.917395	+	0.529658i	−0.0345916	+	0.999402i	$0.511013\pi$
$444$	3.64557	+	5.50731i	0.173011	+	0.261365i
$445$	−1.71070	−	0.987675i	−0.0810951	−	0.0468203i
$446$	10.3689	−	17.9594i	0.490981	−	0.850404i
$447$	13.5198	+	20.4242i	0.639466	+	0.966031i
$448$	0.908070	+	1.57282i	0.0429023	+	0.0743090i
$449$	30.9803			1.46205			0.731026	−	0.682350i	$-0.239042\pi$
$449$	30.9803			1.46205			0.731026	+	0.682350i	$0.239042\pi$
$450$	4.65575	+	37.8889i	0.219474	+	1.78610i
$451$		−	14.0538i		−	0.661765i
$452$	−2.68402	+	1.54962i	−0.126246	+	0.0728881i
$453$	−15.4078	+	0.943097i	−0.723920	+	0.0443106i
$454$	1.08038	−	1.87127i	0.0507047	−	0.0878232i
$455$	−6.61943	+	11.4652i	−0.310324	+	0.537497i
$456$	4.53180	−	9.09044i	0.212221	−	0.425699i
$457$	29.7318	−	17.1657i	1.39079	−	0.802976i	0.397392	−	0.917649i	$-0.369915\pi$
$457$	29.7318	−	17.1657i	1.39079	−	0.802976i	0.993403	+	0.114673i	$0.0365821\pi$
$458$	−26.7462			−1.24977
$459$	−7.17165	−	38.6647i	−0.334744	−	1.80471i
$460$		−	0.939225i		−	0.0437916i
$461$	−13.1371	−	22.7542i	−0.611857	−	1.05977i	−0.990927	−	0.134399i	$-0.957090\pi$
$461$	−13.1371	−	22.7542i	−0.611857	−	1.05977i	0.379070	−	0.925368i	$-0.376244\pi$
$462$	−7.28778	+	14.6187i	−0.339058	+	0.680125i
$463$	14.8619	+	8.58050i	0.690689	+	0.398769i	0.803870	−	0.594805i	$-0.202771\pi$
$463$	14.8619	+	8.58050i	0.690689	+	0.398769i	−0.113181	+	0.993574i	$0.536104\pi$
$464$	−1.67742	+	2.90538i	−0.0778722	+	0.134879i
$465$	−40.1582	−	5.97578i	−1.86229	−	0.277120i
$466$	−6.59047	−	11.4150i	−0.305298	−	0.528791i
$467$			18.6718i			0.864030i	0.901866	+	0.432015i	$0.142197\pi$
$467$			18.6718i			0.864030i	−0.901866	+	0.432015i	$0.857803\pi$
$468$	−4.78164	−	2.02916i	−0.221032	−	0.0937981i
$469$	−13.6333			−0.629526
$470$	−18.2963	+	10.5634i	−0.843944	+	0.487251i
$471$	−29.1725	+	19.3108i	−1.34420	+	0.889794i
$472$	1.03057	−	1.78499i	0.0474356	−	0.0821609i
$473$	28.6009	+	16.5127i	1.31507	+	0.759256i
$474$	24.5373	−	16.2425i	1.12703	−	0.746042i
$475$	−37.3111	−	64.6248i	−1.71195	−	2.96519i
$476$	−13.7445			−0.629976
$477$	−14.2035	−	18.8450i	−0.650332	−	0.862853i
$478$			3.15507i			0.144310i
$479$	−17.4889	+	10.0972i	−0.799089	+	0.461354i	−0.843152	−	0.537675i	$-0.819303\pi$
$479$	−17.4889	+	10.0972i	−0.799089	+	0.461354i	0.0440637	+	0.999029i	$0.485970\pi$
$480$	0.445506	+	7.27842i	0.0203345	+	0.332213i
$481$	−3.30117	+	5.71780i	−0.150520	+	0.260709i
$482$	3.54445	−	6.13917i	0.161445	−	0.279631i
$483$	0.628048	+	0.313097i	0.0285772	+	0.0142464i
$484$	7.98238	+	13.8259i	0.362836	+	0.628450i
$485$		−	9.30155i		−	0.422362i
$486$	3.37043	−	15.2197i	0.152886	−	0.690381i
$487$			20.7137i			0.938627i	0.883032	+	0.469313i	$0.155499\pi$
$487$			20.7137i			0.938627i	−0.883032	+	0.469313i	$0.844501\pi$
$488$	2.79312	+	4.83783i	0.126439	+	0.218998i
$489$	0.581188	+	0.289736i	0.0262822	+	0.0131023i
$490$	7.79205	−	13.4962i	0.352009	−	0.609698i
$491$	−5.77801	+	10.0078i	−0.260758	+	0.451646i	−0.966444	−	0.256879i	$-0.917306\pi$
$491$	−5.77801	+	10.0078i	−0.260758	+	0.451646i	0.705686	+	0.708525i	$0.250639\pi$
$492$	4.67889	−	0.286391i	0.210941	−	0.0129115i
$493$	−12.6946	−	21.9877i	−0.571737	−	0.990278i
$494$	10.1540			0.456848
$495$	−52.3753	+	39.4752i	−2.35409	+	1.77428i
$496$	−5.44677	−	1.15442i	−0.244567	−	0.0518350i
$497$	14.0273	−	8.09867i	0.629210	−	0.363275i
$498$	8.38104	+	12.6611i	0.375564	+	0.567357i
$499$	11.9110	+	6.87679i	0.533208	+	0.307848i	0.742322	−	0.670044i	$-0.233725\pi$
$499$	11.9110	+	6.87679i	0.533208	+	0.307848i	−0.209114	+	0.977891i	$0.567058\pi$
$500$	28.1642	+	16.2606i	1.25954	+	0.727196i
$501$	−30.9183	+	20.4664i	−1.38133	+	0.914373i
$502$	−3.74926	+	2.16464i	−0.167338	+	0.0966124i
$503$		−	6.72658i		−	0.299923i	−0.988692	−	0.149962i	$-0.952085\pi$
$503$		−	6.72658i		−	0.299923i	0.988692	−	0.149962i	$-0.0479150\pi$
$504$	−5.01550	−	2.12840i	−0.223408	−	0.0948066i
$505$	4.88151			0.217224
$506$	1.00325	−	0.579228i	0.0446000	−	0.0257498i
$507$	1.05841	+	17.2917i	0.0470057	+	0.767951i
$508$	8.83224	+	5.09930i	0.391867	+	0.226245i
$509$	8.65695	−	14.9943i	0.383713	−	0.664610i	−0.607877	−	0.794031i	$-0.707979\pi$
$509$	8.65695	−	14.9943i	0.383713	−	0.664610i	0.991590	+	0.129421i	$0.0413119\pi$
$510$	−49.3888	−	24.6215i	−2.18697	−	1.09026i
$511$	9.52535	−	5.49947i	0.421377	−	0.243282i
$512$			1.00000i			0.0441942i
$513$	5.55730	+	29.9612i	0.245361	+	1.32282i
$514$	20.6706			0.911742
$515$	−23.6389	+	13.6479i	−1.04165	+	0.601399i
$516$	−4.91471	+	9.85854i	−0.216358	+	0.433998i
$517$	−22.5669	−	13.0290i	−0.992492	−	0.573015i
$518$	−3.46262	+	5.99744i	−0.152139	+	0.263512i
$519$	−11.0334	+	0.675345i	−0.484312	+	0.0296443i
$520$	−6.31294	+	3.64478i	−0.276841	+	0.159834i
$521$		−	36.9113i		−	1.61711i	−0.588420	−	0.808556i	$-0.700250\pi$
$521$		−	36.9113i		−	1.61711i	0.588420	−	0.808556i	$-0.299750\pi$
$522$	−1.22748	−	9.98938i	−0.0537255	−	0.437223i
$523$		−	17.1807i		−	0.751259i	−0.926770	−	0.375629i	$-0.877427\pi$
$523$		−	17.1807i		−	0.751259i	0.926770	−	0.375629i	$-0.122573\pi$
$524$	2.86953	−	1.65672i	0.125356	−	0.0723744i
$525$	−33.3771	+	22.0941i	−1.45670	+	0.964264i
$526$	−5.80645	−	3.35235i	−0.253173	−	0.146170i
$527$	28.1765	−	31.3300i	1.22739	−	1.36476i
$528$	−7.49984	+	4.96454i	−0.326389	+	0.216054i
$529$	11.4751	+	19.8755i	0.498918	+	0.864151i
$530$	−33.1165			−1.43849
$531$	0.754135	+	6.13723i	0.0327267	+	0.266333i
$532$	10.6506			0.461760
$533$	2.34302	+	4.05824i	0.101488	+	0.175782i
$534$	0.811155	−	0.0496502i	0.0351021	−	0.00214857i
$535$	−16.5911	+	28.7367i	−0.717298	+	1.24240i
$536$	−6.50102	−	3.75336i	−0.280801	−	0.162121i
$537$	−4.50737	−	2.24703i	−0.194507	−	0.0969665i
$538$	21.8071	−	12.5903i	0.940170	−	0.542807i
$539$	19.2217			0.827937
$540$	−14.2097	−	16.6328i	−0.611489	−	0.715760i
$541$	−6.46997			−0.278166			−0.139083	−	0.990281i	$-0.544415\pi$
$541$	−6.46997			−0.278166			−0.139083	+	0.990281i	$0.544415\pi$
$542$	2.49142	+	4.31526i	0.107015	+	0.185356i
$543$	−0.934681	+	1.87490i	−0.0401110	+	0.0804596i
$544$	−6.55404	−	3.78397i	−0.281002	−	0.162237i
$545$	−48.8223	−	28.1875i	−2.09132	−	1.20742i
$546$	−0.332757	−	5.43639i	−0.0142407	−	0.232656i
$547$	16.7294	+	28.9762i	0.715298	+	1.23893i	0.962844	+	0.270057i	$0.0870426\pi$
$547$	16.7294	+	28.9762i	0.715298	+	1.23893i	−0.247546	+	0.968876i	$0.579624\pi$
$548$	9.14394			0.390610
$549$	−15.4271	−	6.54673i	−0.658413	−	0.279407i
$550$			66.0760i			2.81749i
$551$	9.83704	+	17.0383i	0.419072	+	0.725854i
$552$	0.213286	+	0.322207i	0.00907804	+	0.0137140i
$553$	26.7210	+	15.4274i	1.13629	+	0.656038i
$554$	−10.8233	+	18.7465i	−0.459838	+	0.796463i
$555$	−23.1861	+	15.3481i	−0.984196	+	0.651491i
$556$	−14.3774	+	8.30079i	−0.609737	+	0.352032i
$557$	29.5770			1.25322			0.626608	−	0.779334i	$-0.284443\pi$
$557$	29.5770			1.25322			0.626608	+	0.779334i	$0.284443\pi$
$558$	15.1335	−	7.06937i	0.640654	−	0.299270i
$559$	−11.0119			−0.465755
$560$	−6.62169	+	3.82303i	−0.279817	+	0.161553i
$561$	−4.15855	−	67.9399i	−0.175574	−	2.86843i
$562$	−4.39166	+	7.60659i	−0.185251	+	0.320864i
$563$	−25.6153	−	14.7890i	−1.07956	−	0.623281i	−0.148779	−	0.988870i	$-0.547534\pi$
$563$	−25.6153	−	14.7890i	−1.07956	−	0.623281i	−0.930776	+	0.365589i	$0.880868\pi$
$564$	3.87785	−	7.77867i	0.163287	−	0.327541i
$565$	−6.52400	−	11.2999i	−0.274467	−	0.475391i
$566$		−	26.6750i		−	1.12123i
$567$	15.8590	−	3.95722i	0.666016	−	0.166188i
$568$	8.91854			0.374214
$569$	8.48758	+	14.7009i	0.355818	+	0.616295i	0.987258	−	0.159130i	$-0.0508690\pi$
$569$	8.48758	+	14.7009i	0.355818	+	0.616295i	−0.631440	+	0.775425i	$0.717536\pi$
$570$	38.2713	+	19.0792i	1.60301	+	0.799138i
$571$	17.2038	+	9.93261i	0.719956	+	0.415667i	0.814737	−	0.579831i	$-0.196882\pi$
$571$	17.2038	+	9.93261i	0.719956	+	0.415667i	−0.0947804	+	0.995498i	$0.530215\pi$
$572$	−7.78649	−	4.49553i	−0.325569	−	0.187968i
$573$	−4.07954	+	0.249706i	−0.170425	+	0.0104316i
$574$	2.45761	+	4.25671i	0.102579	+	0.177672i
$575$	2.83875			0.118384
$576$	−1.80567	−	2.39574i	−0.0752361	−	0.0998225i
$577$	23.6618			0.985053			0.492526	−	0.870298i	$-0.336074\pi$
$577$	23.6618			0.985053			0.492526	+	0.870298i	$0.336074\pi$
$578$	34.8782	−	20.1369i	1.45074	−	0.837585i
$579$	19.4162	−	12.8526i	0.806910	−	0.534136i
$580$	−12.2318	−	7.06204i	−0.507898	−	0.293235i
$581$	−7.96044	+	13.7879i	−0.330255	+	0.572018i
$582$	2.11226	+	3.19095i	0.0875560	+	0.132269i
$583$	−20.4232	−	35.3741i	−0.845844	−	1.46505i
$584$	6.05621			0.250608
$585$	8.54291	−	20.1310i	0.353206	−	0.832315i
$586$	−0.910374			−0.0376072
$587$	−7.94170	−	13.7554i	−0.327789	−	0.567747i	0.654284	−	0.756249i	$-0.272970\pi$
$587$	−7.94170	−	13.7554i	−0.327789	−	0.567747i	−0.982073	+	0.188502i	$0.939637\pi$
$588$	0.391705	+	6.39944i	0.0161536	+	0.263908i
$589$	−21.8340	+	24.2776i	−0.899653	+	1.00034i
$590$	7.51493	+	4.33874i	0.309385	+	0.178623i
$591$	28.7087	+	14.3120i	1.18092	+	0.588715i
$592$	−3.30230	+	1.90658i	−0.135724	+	0.0783600i
$593$			15.5029i			0.636629i	0.947985	+	0.318315i	$0.103117\pi$
$593$			15.5029i			0.636629i	−0.947985	+	0.318315i	$0.896883\pi$
$594$	9.00336	−	25.4360i	0.369412	−	1.04365i
$595$		−	57.8650i		−	2.37224i
$596$	−12.2468	+	7.07068i	−0.501647	+	0.289626i
$597$	17.2146	−	34.5311i	0.704546	−	1.41326i
$598$	−0.193136	+	0.334522i	−0.00789793	+	0.0136796i
$599$	−2.10400	−	1.21475i	−0.0859672	−	0.0496332i	0.456400	−	0.889775i	$-0.349139\pi$
$599$	−2.10400	−	1.21475i	−0.0859672	−	0.0496332i	−0.542367	+	0.840141i	$0.682472\pi$
$600$	−21.9985	+	1.34651i	−0.898087	+	0.0549712i
$601$	−33.3978	+	19.2822i	−1.36232	+	0.786538i	−0.989933	−	0.141538i	$-0.954795\pi$
$601$	−33.3978	+	19.2822i	−1.36232	+	0.786538i	−0.372391	+	0.928076i	$0.621462\pi$
$602$	−11.5505			−0.470763
$603$	22.3521	−	2.74660i	0.910247	−	0.111850i
$604$		−	8.91233i		−	0.362637i
$605$	−58.2079	+	33.6063i	−2.36649	+	1.36629i
$606$	−1.67463	+	1.10853i	−0.0680273	+	0.0450308i
$607$	14.9717	−	25.9318i	0.607684	−	1.05254i	−0.383937	−	0.923359i	$-0.625432\pi$
$607$	14.9717	−	25.9318i	0.607684	−	1.05254i	0.991621	−	0.129180i	$-0.0412346\pi$
$608$	5.07871	+	2.93220i	0.205969	+	0.118916i
$609$	8.79985	−	5.82508i	0.356588	−	0.236044i
$610$	−20.3676	+	11.7592i	−0.824659	+	0.476117i
$611$	8.68872			0.351508
$612$	22.5344	−	2.76899i	0.910897	−	0.111930i
$613$			0.320149i			0.0129307i	0.999979	+	0.00646535i	$0.00205800\pi$
$613$			0.320149i			0.0129307i	−0.999979	+	0.00646535i	$0.997942\pi$
$614$	−0.300012	+	0.173212i	−0.0121075	+	0.00699028i
$615$	1.20572	+	19.6984i	0.0486195	+	0.794317i
$616$	−8.16730	−	4.71539i	−0.329070	−	0.189989i
$617$	20.7223	+	11.9640i	0.834248	+	0.481653i	0.855305	−	0.518125i	$-0.173370\pi$
$617$	20.7223	+	11.9640i	0.834248	+	0.481653i	−0.0210572	+	0.999778i	$0.506703\pi$
$618$	5.01020	−	10.0501i	0.201540	−	0.404274i
$619$	12.8013	−	7.39085i	0.514529	−	0.297063i	−0.220165	−	0.975463i	$-0.570659\pi$
$619$	12.8013	−	7.39085i	0.514529	−	0.297063i	0.734693	+	0.678399i	$0.237326\pi$
$620$	4.86018	−	22.9313i	0.195189	−	0.920941i
$621$	−1.09278	−	0.386801i	−0.0438516	−	0.0155218i
$622$	−11.8898			−0.476738
$623$	0.426064	+	0.737964i	0.0170699	+	0.0295659i
$624$	1.33801	−	2.68395i	0.0535634	−	0.107444i
$625$	−36.6466	+	63.4737i	−1.46586	+	2.53895i
$626$	−15.0854	+	26.1287i	−0.602933	+	1.04431i
$627$	3.22245	+	52.6465i	0.128692	+	2.10250i
$628$	−10.0993	−	17.4924i	−0.403004	−	0.698023i
$629$		−	28.8578i		−	1.15064i
$630$	8.96071	−	21.1156i	0.357003	−	0.841264i
$631$			25.3268i			1.00824i	0.863632	+	0.504122i	$0.168184\pi$
$631$			25.3268i			1.00824i	−0.863632	+	0.504122i	$0.831816\pi$
$632$	8.49458	+	14.7131i	0.337896	+	0.585254i
$633$	−27.9979	+	18.5333i	−1.11282	+	0.736632i
$634$	−8.46560	+	14.6628i	−0.336212	+	0.582336i
$635$	−21.4684	+	37.1843i	−0.851946	+	1.47561i
$636$	11.3608	−	7.52033i	0.450486	−	0.298201i
$637$	−5.55056	+	3.20462i	−0.219921	+	0.126971i
$638$		−	17.4209i		−	0.689699i
$639$	−21.3665	+	16.1039i	−0.845246	+	0.637061i
$640$	−4.21006			−0.166417
$641$	−14.8007	−	25.6356i	−0.584594	−	1.01255i	−0.994926	−	0.100610i	$-0.967921\pi$
$641$	−14.8007	−	25.6356i	−0.584594	−	1.01255i	0.410332	−	0.911936i	$-0.365413\pi$
$642$	−0.834033	−	13.6259i	−0.0329167	−	0.537773i
$643$	37.8418	+	21.8480i	1.49234	+	0.861600i	0.999961	−	0.00878368i	$-0.00279597\pi$
$643$	37.8418	+	21.8480i	1.49234	+	0.861600i	0.492374	+	0.870384i	$0.336129\pi$
$644$	−0.202582	+	0.350882i	−0.00798285	+	0.0138267i
$645$	−41.5051	−	20.6913i	−1.63426	−	0.814718i
$646$	−38.4354	+	22.1907i	−1.51222	+	0.873082i
$647$	−22.5487			−0.886481			−0.443241	−	0.896403i	$-0.646171\pi$
$647$	−22.5487			−0.886481			−0.443241	+	0.896403i	$0.646171\pi$
$648$	8.65182	+	2.47913i	0.339875	+	0.0973894i
$649$			10.7030i			0.420128i
$650$	−11.0161	−	19.0805i	−0.432087	−	0.748397i
$651$	13.7137	+	10.8942i	0.537481	+	0.426978i
$652$	−0.187467	+	0.324702i	−0.00734178	+	0.0127163i
$653$	23.0873	+	13.3295i	0.903476	+	0.521622i	0.878326	−	0.478062i	$-0.158661\pi$
$653$	23.0873	+	13.3295i	0.903476	+	0.521622i	0.0251494	+	0.999684i	$0.491994\pi$
$654$	23.1498	−	1.41698i	0.905229	−	0.0554083i
$655$	6.97492	+	12.0809i	0.272533	+	0.472040i
$656$			2.70641i			0.105668i
$657$	−14.5091	+	10.9355i	−0.566054	+	0.426635i
$658$	9.11366			0.355287
$659$	−38.5658	+	22.2659i	−1.50231	+	0.867358i	−0.502312	+	0.864686i	$0.667517\pi$
$659$	−38.5658	+	22.2659i	−1.50231	+	0.867358i	−0.999996	+	0.00267181i	$0.999150\pi$
$660$	−20.9010	−	31.5748i	−0.813571	−	1.22905i
$661$	−1.86662	+	3.23309i	−0.0726032	+	0.125752i	−0.900041	−	0.435804i	$-0.856464\pi$
$661$	−1.86662	+	3.23309i	−0.0726032	+	0.125752i	0.827438	+	0.561557i	$0.189797\pi$
$662$	−2.87846	+	4.98563i	−0.111874	+	0.193772i
$663$	12.5277	+	18.9254i	0.486536	+	0.735001i
$664$	−7.59186	+	4.38316i	−0.294621	+	0.170100i
$665$			44.8395i			1.73880i
$666$	4.46879	−	10.5305i	0.173162	−	0.408049i
$667$	−0.748433			−0.0289794
$668$	−10.7037	−	18.5393i	−0.414137	−	0.717306i
$669$	−35.8518	+	2.19446i	−1.38611	+	0.0848426i
$670$	15.8019	−	27.3697i	0.610481	−	1.05738i
$671$	−25.1217	−	14.5040i	−0.969812	−	0.559921i
$672$	1.40345	−	2.81521i	0.0541393	−	0.108599i
$673$	8.73480	−	5.04304i	0.336702	−	0.194395i	−0.322111	−	0.946702i	$-0.604392\pi$
$673$	8.73480	−	5.04304i	0.336702	−	0.194395i	0.658813	+	0.752307i	$0.271059\pi$
$674$	19.5820			0.754270
$675$	50.2714	−	42.9479i	1.93495	−	1.65307i
$676$	−10.0020			−0.384694
$677$	−4.91631	−	8.51530i	−0.188949	−	0.327270i	0.755951	−	0.654628i	$-0.227175\pi$
$677$	−4.91631	−	8.51530i	−0.188949	−	0.327270i	−0.944900	+	0.327359i	$0.893841\pi$
$678$	4.80416	+	2.39499i	0.184503	+	0.0919789i
$679$	−2.00626	+	3.47494i	−0.0769930	+	0.133356i
$680$	15.9308	−	27.5929i	0.610917	−	1.05814i
$681$	−3.73555	+	0.228650i	−0.143147	+	0.00876190i
$682$	27.4918	−	8.95039i	1.05271	−	0.342728i
$683$			22.4782i			0.860105i	0.902804	+	0.430052i	$0.141505\pi$
$683$			22.4782i			0.860105i	−0.902804	+	0.430052i	$0.858495\pi$
$684$	−17.4618	+	2.14569i	−0.667670	+	0.0820425i
$685$			38.4966i			1.47088i
$686$	−16.8318	+	9.71784i	−0.642641	+	0.371029i
$687$	25.5707	+	38.6293i	0.975584	+	1.47380i
$688$	−5.50784	−	3.17995i	−0.209984	−	0.121235i
$689$	11.7950	+	6.80987i	0.449356	+	0.259436i
$690$	−1.35651	+	0.897946i	−0.0516415	+	0.0341842i
$691$	−7.27606	−	12.6025i	−0.276794	−	0.479422i	0.693792	−	0.720176i	$-0.255939\pi$
$691$	−7.27606	−	12.6025i	−0.276794	−	0.479422i	−0.970586	+	0.240754i	$0.922605\pi$
$692$		−	6.38205i		−	0.242609i
$693$	28.0812	−	3.45058i	1.06671	−	0.131077i
$694$		−	3.06868i		−	0.116485i
$695$	−34.9469	−	60.5297i	−1.32561	−	2.29602i
$696$	5.79990	−	0.355007i	0.219844	−	0.0134565i
$697$	−17.7379	−	10.2410i	−0.671872	−	0.387905i
$698$	22.4817	+	12.9798i	0.850946	+	0.491294i
$699$	−10.1858	+	20.4319i	−0.385262	+	0.772805i
$700$	−11.5549	−	20.0136i	−0.436733	−	0.756443i
$701$		−	36.4963i		−	1.37844i	−0.724550	−	0.689222i	$-0.757952\pi$
$701$		−	36.4963i		−	1.37844i	0.724550	−	0.689222i	$-0.242048\pi$
$702$	1.64079	+	8.84605i	0.0619277	+	0.333873i
$703$			22.3619i			0.843394i
$704$	−2.59638	−	4.49706i	−0.0978548	−	0.169489i
$705$	32.7487	+	16.3260i	1.23339	+	0.614872i
$706$	−3.22317	−	1.86090i	−0.121306	−	0.0700358i
$707$	−1.82367	−	1.05290i	−0.0685861	−	0.0395982i
$708$	−3.56331	+	0.218108i	−0.133918	+	0.00819698i
$709$	0.538620	−	0.310973i	0.0202283	−	0.0116788i	−0.489852	−	0.871806i	$-0.662949\pi$
$709$	0.538620	−	0.310973i	0.0202283	−	0.0116788i	0.510080	+	0.860127i	$0.329616\pi$
$710$			37.5476i			1.40914i
$711$	−46.9177	−	19.9102i	−1.75955	−	0.746692i
$712$			0.469197i			0.0175839i
$713$	−0.384525	−	1.18110i	−0.0144006	−	0.0442325i
$714$	13.1404	+	19.8510i	0.491767	+	0.742904i
$715$	18.9265	−	32.7816i	0.707810	−	1.22596i
$716$	1.45389	−	2.51821i	0.0543344	−	0.0941099i
$717$	4.55683	−	3.01640i	0.170178	−	0.112650i
$718$	6.59158	+	11.4169i	0.245995	+	0.426077i
$719$	21.6032			0.805664			0.402832	−	0.915274i	$-0.368026\pi$
$719$	21.6032			0.805664			0.402832	+	0.915274i	$0.368026\pi$
$720$	10.0862	−	7.60197i	0.375891	−	0.283309i
$721$	11.7749			0.438520
$722$	13.3291	−	7.69554i	0.496057	−	0.286398i
$723$	−12.2554	+	0.750143i	−0.455783	+	0.0278981i
$724$	−1.04748	−	0.604764i	−0.0389293	−	0.0224759i
$725$	21.3445	−	36.9698i	0.792717	−	1.37303i
$726$	12.3370	−	24.7471i	0.457870	−	0.918451i
$727$	21.7774	+	37.7195i	0.807678	+	1.39894i	0.914468	+	0.404658i	$0.132609\pi$
$727$	21.7774	+	37.7195i	0.807678	+	1.39894i	−0.106790	+	0.994282i	$0.534057\pi$
$728$	3.14458			0.116546
$729$	−25.2040	+	9.68295i	−0.933481	+	0.358628i
$730$			25.4970i			0.943687i
$731$	41.6830	−	24.0657i	1.54170	−	0.890103i
$732$	4.31686	−	8.65928i	0.159556	−	0.320056i
$733$	12.8345	−	22.2300i	0.474053	−	0.821084i	−0.525506	−	0.850790i	$-0.676124\pi$
$733$	12.8345	−	22.2300i	0.474053	−	0.821084i	0.999559	+	0.0297062i	$0.00945716\pi$
$734$	5.43204	−	9.40858i	0.200500	−	0.347277i
$735$	−26.9420	+	1.64910i	−0.993772	+	0.0608280i
$736$	−0.193202	+	0.111545i	−0.00712152	+	0.00411161i
$737$	38.9806			1.43587
$738$	−4.88688	−	6.48386i	−0.179889	−	0.238674i
$739$		−	22.8947i		−	0.842197i	−0.907015	−	0.421098i	$-0.861645\pi$
$739$		−	22.8947i		−	0.842197i	0.907015	−	0.421098i	$-0.138355\pi$
$740$	−8.02683	−	13.9029i	−0.295072	−	0.511080i
$741$	−9.70770	−	14.6653i	−0.356621	−	0.538741i
$742$	12.3719	+	7.14292i	0.454187	+	0.262225i
$743$	8.28985	−	14.3584i	0.304125	−	0.526760i	−0.672941	−	0.739696i	$-0.734969\pi$
$743$	8.28985	−	14.3584i	0.304125	−	0.526760i	0.977066	+	0.212936i	$0.0683025\pi$
$744$	3.54007	+	8.97039i	0.129785	+	0.328870i
$745$	−29.7680	−	51.5597i	−1.09061	−	1.88900i
$746$			7.83048i			0.286694i
$747$	10.2736	−	24.2093i	0.375891	−	0.885772i
$748$	39.2985			1.43690
$749$	12.3965	−	7.15710i	0.452957	−	0.261515i
$750$	−3.44137	−	56.2232i	−0.125661	−	2.05298i
$751$	−9.17560	+	15.8926i	−0.334822	+	0.579929i	−0.983451	−	0.181176i	$-0.942010\pi$
$751$	−9.17560	+	15.8926i	−0.334822	+	0.579929i	0.648628	+	0.761105i	$0.275343\pi$
$752$	4.34584	+	2.50907i	0.158477	+	0.0914965i
$753$	6.71083	+	3.34551i	0.244556	+	0.121917i
$754$	2.90439	+	5.03054i	0.105771	+	0.183202i
$755$	37.5215			1.36555
$756$	1.72104	+	9.27868i	0.0625936	+	0.337462i
$757$			31.8883i			1.15900i	0.814973	+	0.579499i	$0.196752\pi$
$757$			31.8883i			1.15900i	−0.814973	+	0.579499i	$0.803248\pi$
$758$	−6.83530	+	3.94636i	−0.248269	+	0.143338i
$759$	−1.79573	−	0.895215i	−0.0651809	−	0.0324942i
$760$	−12.3447	+	21.3817i	−0.447790	+	0.775596i
$761$	26.5319	−	45.9545i	0.961779	−	1.66585i	0.243750	−	0.969838i	$-0.421622\pi$
$761$	26.5319	−	45.9545i	0.961779	−	1.66585i	0.718029	−	0.696013i	$-0.245044\pi$
$762$	−1.07921	−	17.6315i	−0.0390956	−	0.638722i
$763$	12.1596	+	21.0610i	0.440206	+	0.762459i
$764$		−	2.35973i		−	0.0853722i
$765$	11.6576	+	94.8711i	0.421483	+	3.43007i
$766$		−	5.98401i		−	0.216211i
$767$	−1.78438	−	3.09064i	−0.0644303	−	0.111597i
$768$	1.44429	−	0.956050i	0.0521163	−	0.0344985i
$769$	16.0678	−	27.8303i	0.579420	−	1.00359i	−0.416126	−	0.909307i	$-0.636612\pi$
$769$	16.0678	−	27.8303i	0.579420	−	1.00359i	0.995546	−	0.0942782i	$-0.0300543\pi$
$770$	19.8521	−	34.3849i	0.715420	−	1.23914i
$771$	−19.7622	−	29.8543i	−0.711717	−	1.07518i
$772$	6.72172	+	11.6424i	0.241920	+	0.419018i
$773$	−0.289016			−0.0103952			−0.00519760	−	0.999986i	$-0.501654\pi$
$773$	−0.289016			−0.0103952			−0.00519760	+	0.999986i	$0.501654\pi$
$774$	18.9373	−	2.32699i	0.680687	−	0.0836419i
$775$	69.3082	+	14.6896i	2.48962	+	0.527665i
$776$	−1.91336	+	1.10468i	−0.0686857	+	0.0396557i
$777$	11.9725	−	0.732825i	0.429510	−	0.0262900i
$778$	4.96173	+	2.86466i	0.177887	+	0.102703i
$779$	13.7451	+	7.93573i	0.492469	+	0.284327i
$780$	11.2996	+	5.63312i	0.404591	+	0.201698i
$781$	−40.1073	+	23.1559i	−1.43515	+	0.828585i
$782$		−	1.68834i		−	0.0603748i
$783$	−13.2540	+	11.3232i	−0.473660	+	0.404658i
$784$	−3.70163			−0.132201
$785$	73.6442	−	42.5185i	2.62847	−	1.51755i
$786$	−5.13620	−	2.56052i	−0.183202	−	0.0913307i
$787$	−20.5233	−	11.8491i	−0.731575	−	0.422375i	0.0874231	−	0.996171i	$-0.472137\pi$
$787$	−20.5233	−	11.8491i	−0.731575	−	0.422375i	−0.818998	+	0.573796i	$0.805470\pi$
$788$	−9.26022	+	16.0392i	−0.329882	+	0.571372i
$789$	0.709488	+	11.5912i	0.0252584	+	0.412658i
$790$	−61.9429	+	35.7627i	−2.20383	+	1.27238i
$791$			5.62866i			0.200132i
$792$	14.3405	+	6.08559i	0.509566	+	0.216242i
$793$	9.67236			0.343476
$794$	−15.9776	+	9.22466i	−0.567023	+	0.327371i
$795$	31.6611	+	47.8298i	1.12290	+	1.69635i
$796$	19.2921	+	11.1383i	0.683790	+	0.394787i
$797$	8.39559	−	14.5416i	0.297387	−	0.515090i	−0.678150	−	0.734923i	$-0.737218\pi$
$797$	8.39559	−	14.5416i	0.297387	−	0.515090i	0.975537	+	0.219834i	$0.0705515\pi$
$798$	−10.1825	−	15.3825i	−0.360455	−	0.544534i
$799$	−32.8891	+	18.9885i	−1.16353	+	0.671766i
$800$		−	12.7246i		−	0.449884i
$801$	−0.847214	−	1.12407i	−0.0299348	−	0.0397172i
$802$			5.86776i			0.207198i
$803$	−27.2352	+	15.7242i	−0.961108	+	0.554896i
$804$	0.794358	+	12.9777i	0.0280148	+	0.457690i
$805$	−1.47724	−	0.852883i	−0.0520657	−	0.0300602i
$806$	−6.44647	+	7.16796i	−0.227067	+	0.252481i
$807$	−39.0327	−	19.4587i	−1.37402	−	0.684980i
$808$	−0.579743	−	1.00415i	−0.0203953	−	0.0353257i
$809$	24.8323			0.873059			0.436529	−	0.899690i	$-0.356208\pi$
$809$	24.8323			0.873059			0.436529	+	0.899690i	$0.356208\pi$
$810$	−10.4373	+	36.4247i	−0.366729	+	1.27983i
$811$	3.41524			0.119925			0.0599626	−	0.998201i	$-0.480902\pi$
$811$	3.41524			0.119925			0.0599626	+	0.998201i	$0.480902\pi$
$812$	3.04643	+	5.27657i	0.106909	+	0.185171i
$813$	3.85056	−	7.72393i	0.135045	−	0.270890i
$814$	9.90042	−	17.1480i	0.347010	−	0.601038i
$815$	−1.36702	−	0.789248i	−0.0478845	−	0.0276462i
$816$	0.800836	+	13.0836i	0.0280349	+	0.458017i
$817$	−32.3001	+	18.6485i	−1.13004	+	0.652428i
$818$	−25.8224			−0.902858
$819$	−7.53359	+	5.67806i	−0.263245	+	0.198407i
$820$	−11.3942			−0.397902
$821$	19.8940	+	34.4575i	0.694306	+	1.20257i	0.970414	+	0.241447i	$0.0776220\pi$
$821$	19.8940	+	34.4575i	0.694306	+	1.20257i	−0.276108	+	0.961127i	$0.589045\pi$
$822$	−8.74207	−	13.2065i	−0.304915	−	0.460629i
$823$	−7.92086	−	4.57311i	−0.276104	−	0.159409i	0.355554	−	0.934656i	$-0.384292\pi$
$823$	−7.92086	−	4.57311i	−0.276104	−	0.159409i	−0.631658	+	0.775247i	$0.717625\pi$
$824$	5.61485	+	3.24174i	0.195603	+	0.112931i
$825$	95.4328	−	63.1719i	3.32254	−	2.19936i
$826$	−1.87165	−	3.24180i	−0.0651231	−	0.112796i
$827$	−32.9890			−1.14714			−0.573571	−	0.819156i	$-0.694442\pi$
$827$	−32.9890			−1.14714			−0.573571	+	0.819156i	$0.694442\pi$
$828$	0.261448	−	0.616092i	0.00908595	−	0.0214107i
$829$			14.6266i			0.508004i	0.967204	+	0.254002i	$0.0817470\pi$
$829$			14.6266i			0.508004i	−0.967204	+	0.254002i	$0.918253\pi$
$830$	−18.4534	−	31.9622i	−0.640527	−	1.10942i
$831$	37.4230	−	2.29063i	1.29819	−	0.0794611i
$832$	1.49949	+	0.865730i	0.0519854	+	0.0300138i
$833$	14.0069	−	24.2606i	0.485310	−	0.840581i
$834$	25.7342	+	12.8291i	0.891104	+	0.444236i
$835$	78.0515	−	45.0630i	2.70108	−	1.55947i
$836$	−30.4524			−1.05322
$837$	−24.6786	−	15.0985i	−0.853018	−	0.521881i
$838$	27.7657			0.959150
$839$	26.9782	−	15.5759i	0.931392	−	0.537740i	0.0441408	−	0.999025i	$-0.485945\pi$
$839$	26.9782	−	15.5759i	0.931392	−	0.537740i	0.887252	+	0.461286i	$0.152612\pi$
$840$	11.8522	+	5.90862i	0.408941	+	0.203867i
$841$	8.87253	−	15.3677i	0.305949	−	0.529920i
$842$	−11.3637	−	6.56081i	−0.391617	−	0.226100i
$843$	15.1848	−	0.929447i	0.522991	−	0.0320118i
$844$	−9.69264	−	16.7881i	−0.333634	−	0.577872i
$845$		−	42.1092i		−	1.44860i
$846$	−14.9421	+	1.83606i	−0.513718	+	0.0631251i
$847$	28.9943			0.996255
$848$	3.93302	+	6.81219i	0.135061	+	0.233932i
$849$	−38.5264	+	25.5026i	−1.32222	+	0.875248i
$850$	83.3977	+	48.1497i	2.86052	+	1.65152i
$851$	−0.736711	−	0.425340i	−0.0252541	−	0.0145805i
$852$	−8.52657	−	12.8809i	−0.292116	−	0.441294i
$853$	7.96891	+	13.8026i	0.272850	+	0.472591i	0.969591	−	0.244733i	$-0.0787003\pi$
$853$	7.96891	+	13.8026i	0.272850	+	0.472591i	−0.696740	+	0.717324i	$0.745367\pi$
$854$	10.1454			0.347169
$855$	−9.03349	−	73.5154i	−0.308939	−	2.51418i
$856$	7.88166			0.269390
$857$	20.2176	−	11.6727i	0.690622	−	0.398731i	−0.113223	−	0.993570i	$-0.536118\pi$
$857$	20.2176	−	11.6727i	0.690622	−	0.398731i	0.803845	+	0.594839i	$0.202784\pi$
$858$	0.951429	+	15.5439i	0.0324813	+	0.530660i
$859$	−2.82549	−	1.63130i	−0.0964044	−	0.0556591i	0.451023	−	0.892512i	$-0.351059\pi$
$859$	−2.82549	−	1.63130i	−0.0964044	−	0.0556591i	−0.547427	+	0.836853i	$0.684393\pi$
$860$	13.3878	−	23.1884i	0.456520	−	0.790716i
$861$	3.79832	−	7.61913i	0.129446	−	0.259659i
$862$	−4.51240	−	7.81570i	−0.153693	−	0.266204i
$863$	−43.2865			−1.47349			−0.736744	−	0.676172i	$-0.763638\pi$
$863$	−43.2865			−1.47349			−0.736744	+	0.676172i	$0.763638\pi$
$864$	−1.73383	+	4.89835i	−0.0589861	+	0.166645i
$865$	26.8688			0.913568
$866$	−14.3711	−	24.8915i	−0.488350	−	0.845847i
$867$	−62.4288	−	31.1222i	−2.12019	−	1.05697i
$868$	−6.76175	+	7.51852i	−0.229509	+	0.255195i
$869$	−76.4014	−	44.1103i	−2.59174	−	1.49634i
$870$	1.49460	+	24.4179i	0.0506718	+	0.827845i
$871$	−11.2563	+	6.49880i	−0.381404	+	0.220204i
$872$			13.3906i			0.453461i
$873$	2.58923	−	6.10142i	0.0876322	−	0.206502i
$874$			1.30829i			0.0442536i
$875$	51.1501	−	29.5315i	1.72919	−	0.998348i
$876$	−5.79004	−	8.74691i	−0.195627	−	0.295531i
$877$	−23.2797	+	40.3217i	−0.786101	+	1.36157i	0.142239	+	0.989832i	$0.454570\pi$
$877$	−23.2797	+	40.3217i	−0.786101	+	1.36157i	−0.928339	+	0.371734i	$0.878763\pi$
$878$	16.7696	+	9.68192i	0.565946	+	0.326749i
$879$	0.870363	+	1.31484i	0.0293566	+	0.0443485i
$880$	18.9329	−	10.9309i	0.638229	−	0.368481i
$881$	37.2379			1.25458			0.627289	−	0.778787i	$-0.284165\pi$
$881$	37.2379			1.25458			0.627289	+	0.778787i	$0.284165\pi$
$882$	8.86814	−	6.68392i	0.298606	−	0.225059i
$883$		−	11.7875i		−	0.396682i	−0.980133	−	0.198341i	$-0.936445\pi$
$883$		−	11.7875i		−	0.396682i	0.980133	−	0.198341i	$-0.0635553\pi$
$884$	−11.3481	+	6.55180i	−0.381676	+	0.220361i
$885$	−0.918247	−	15.0018i	−0.0308665	−	0.504279i
$886$	−11.1480	+	19.3089i	−0.374525	+	0.648696i
$887$	−7.54414	−	4.35561i	−0.253307	−	0.146247i	0.367970	−	0.929838i	$-0.380053\pi$
$887$	−7.54414	−	4.35561i	−0.253307	−	0.146247i	−0.621278	+	0.783590i	$0.713386\pi$
$888$	5.91081	+	2.94668i	0.198354	+	0.0988841i
$889$	16.0406	−	9.26105i	0.537984	−	0.310605i
$890$	−1.97535			−0.0662139
$891$	−45.3445	+	11.3146i	−1.51910	+	0.379053i
$892$		−	20.7378i		−	0.694352i
$893$	25.4857	−	14.7142i	0.852847	−	0.492391i
$894$	21.9206	+	10.9279i	0.733135	+	0.365485i
$895$	10.6018	+	6.12096i	0.354380	+	0.204601i
$896$	1.57282	+	0.908070i	0.0525444	+	0.0303365i
$897$	0.667794	−	0.0408751i	0.0222970	−	0.00136478i
$898$	26.8297	−	15.4902i	0.895320	−	0.516913i
$899$	−18.2730	−	3.87289i	−0.609440	−	0.129168i
$900$	22.9765	+	30.4849i	0.765882	+	1.01616i
$901$	−59.5298			−1.98323
$902$	−7.02688	−	12.1709i	−0.233969	−	0.405247i
$903$	11.0428	+	16.6822i	0.367483	+	0.555150i
$904$	−1.54962	+	2.68402i	−0.0515396	+	0.0892693i
$905$	2.54609	−	4.40996i	0.0846350	−	0.146592i
$906$	−12.8720	+	8.52063i	−0.427643	+	0.283079i
$907$	−3.09416	−	5.35925i	−0.102740	−	0.177951i	0.810073	−	0.586330i	$-0.199428\pi$
$907$	−3.09416	−	5.35925i	−0.102740	−	0.177951i	−0.912813	+	0.408379i	$0.866094\pi$
$908$		−	2.16076i		−	0.0717073i
$909$	3.20207	+	1.35885i	0.106206	+	0.0450701i
$910$			13.2389i			0.438864i
$911$	18.3112	+	31.7160i	0.606678	+	1.05080i	0.991784	+	0.127924i	$0.0408314\pi$
$911$	18.3112	+	31.7160i	0.606678	+	1.05080i	−0.385106	+	0.922872i	$0.625835\pi$
$912$	−0.620566	−	10.1384i	−0.0205490	−	0.335718i
$913$	22.7607	−	39.4227i	0.753270	−	1.30470i
$914$	17.1657	−	29.7318i	0.567790	−	0.983440i
$915$	36.4561	+	18.1742i	1.20520	+	0.600822i
$916$	−23.1629	+	13.3731i	−0.765324	+	0.441860i
$917$		−	6.01769i		−	0.198722i
$918$	−25.5432	−	29.8988i	−0.843051	−	0.986808i
$919$	−47.6460			−1.57170			−0.785848	−	0.618420i	$-0.787773\pi$
$919$	−47.6460			−1.57170			−0.785848	+	0.618420i	$0.787773\pi$
$920$	−0.469613	−	0.813393i	−0.0154827	−	0.0268168i
$921$	0.536995	+	0.267705i	0.0176946	+	0.00882117i
$922$	−22.7542	−	13.1371i	−0.749369	−	0.432648i
$923$	7.72106	−	13.3733i	0.254142	−	0.440186i
$924$	0.997960	+	16.3041i	0.0328305	+	0.536365i
$925$	42.0205	−	24.2606i	1.38163	−	0.797682i
$926$	17.1610			0.563945
$927$	−19.3052	+	2.37220i	−0.634067	+	0.0779133i
$928$			3.35484i			0.110128i
$929$	10.0597	+	17.4239i	0.330049	+	0.571661i	0.982521	−	0.186152i	$-0.0596016\pi$
$929$	10.0597	+	17.4239i	0.330049	+	0.571661i	−0.652473	+	0.757812i	$0.726268\pi$
$930$	−37.7659	+	14.9039i	−1.23839	+	0.488719i
$931$	−10.8539	+	18.7995i	−0.355723	+	0.616130i
$932$	−11.4150	−	6.59047i	−0.373912	−	0.215878i
$933$	11.3672	+	17.1723i	0.372147	+	0.562196i
$934$	9.33592	+	16.1703i	0.305481	+	0.529108i
$935$			165.449i			5.41077i
$936$	−5.15561	+	0.633515i	−0.168516	+	0.0207071i
$937$	12.7682			0.417118			0.208559	−	0.978010i	$-0.433123\pi$
$937$	12.7682			0.417118			0.208559	+	0.978010i	$0.433123\pi$
$938$	−11.8068	+	6.81664i	−0.385505	+	0.222571i
$939$	52.1597	−	3.19265i	1.70217	−	0.104188i
$940$	−10.5634	+	18.2963i	−0.344539	+	0.596759i
$941$	0.787814	−	1.36453i	0.0256820	−	0.0444825i	−0.852899	−	0.522076i	$-0.825158\pi$
$941$	0.787814	−	1.36453i	0.0256820	−	0.0444825i	0.878581	+	0.477594i	$0.158491\pi$
$942$	−15.6087	+	31.3099i	−0.508559	+	1.02013i
$943$	−0.522885	+	0.301888i	−0.0170275	+	0.00983081i
$944$		−	2.06113i		−	0.0670841i
$945$	−39.0638	+	7.24568i	−1.27075	+	0.235702i
$946$	33.0255			1.07375
$947$	1.51437	+	2.62296i	0.0492104	+	0.0852348i	0.889581	−	0.456777i	$-0.150996\pi$
$947$	1.51437	+	2.62296i	0.0492104	+	0.0852348i	−0.840371	+	0.542012i	$0.817663\pi$
$948$	13.1286	−	26.3350i	0.426398	−	0.855322i
$949$	5.24305	−	9.08122i	0.170196	−	0.294789i
$950$	−64.6248	−	37.3111i	−2.09670	−	1.21053i
$951$	29.2709	−	1.79165i	0.949174	−	0.0580982i
$952$	−11.9031	+	6.87223i	−0.385780	+	0.222730i
$953$	−1.01622			−0.0329185			−0.0164593	−	0.999865i	$-0.505239\pi$
$953$	−1.01622			−0.0329185			−0.0164593	+	0.999865i	$0.505239\pi$
$954$	−21.7231	−	9.21851i	−0.703310	−	0.298460i
$955$	9.93463			0.321477
$956$	1.57753	+	2.73237i	0.0510211	+	0.0883712i
$957$	−25.1608	+	16.6552i	−0.813332	+	0.538387i
$958$	−10.0972	+	17.4889i	−0.326227	+	0.565041i
$959$	8.30335	−	14.3818i	0.268129	−	0.464413i
$960$	4.02503	+	6.08055i	0.129907	+	0.196249i
$961$	−3.27643	−	30.8264i	−0.105691	−	0.994399i
$962$			6.60234i			0.212868i
$963$	−18.8824	+	14.2317i	−0.608477	+	0.458609i
$964$		−	7.08890i		−	0.228318i
$965$	−49.0151	+	28.2989i	−1.57785	+	0.910973i
$966$	0.700454	−	0.0428742i	0.0225367	−	0.00137945i
$967$	−11.7796	−	6.80093i	−0.378805	−	0.218703i	0.298493	−	0.954412i	$-0.403516\pi$
$967$	−11.7796	−	6.80093i	−0.378805	−	0.218703i	−0.677298	+	0.735709i	$0.736849\pi$
$968$	13.8259	+	7.98238i	0.444381	+	0.256564i
$969$	68.7960	+	34.2964i	2.21004	+	1.10176i
$970$	−4.65077	−	8.05538i	−0.149327	−	0.258643i
$971$		−	31.3322i		−	1.00550i	−0.864432	−	0.502750i	$-0.832322\pi$
$971$		−	31.3322i		−	1.00550i	0.864432	−	0.502750i	$-0.167678\pi$
$972$	−4.69099	−	14.8659i	−0.150464	−	0.476824i
$973$			30.1508i			0.966591i
$974$	10.3568	+	17.9386i	0.331855	+	0.574789i
$975$	−17.0257	+	34.1523i	−0.545260	+	1.09375i
$976$	4.83783	+	2.79312i	0.154855	+	0.0894057i
$977$	29.6453	+	17.1157i	0.948438	+	0.547581i	0.892595	−	0.450859i	$-0.148882\pi$
$977$	29.6453	+	17.1157i	0.948438	+	0.547581i	0.0558424	+	0.998440i	$0.482216\pi$
$978$	0.648192	−	0.0396753i	0.0207269	−	0.00126868i
$979$	−1.21821	−	2.11001i	−0.0389343	−	0.0674362i
$980$		−	15.5841i		−	0.497816i
$981$	−24.1789	−	32.0803i	−0.771972	−	1.02424i
$982$			11.5560i			0.368767i
$983$	−20.5030	−	35.5122i	−0.653944	−	1.13266i	−0.982157	−	0.188061i	$-0.939780\pi$
$983$	−20.5030	−	35.5122i	−0.653944	−	1.13266i	0.328213	−	0.944604i	$-0.393554\pi$
$984$	3.90884	−	2.58747i	0.124609	−	0.0824854i
$985$	−67.5259	−	38.9861i	−2.15156	−	1.24220i
$986$	−21.9877	−	12.6946i	−0.700232	−	0.404279i
$987$	−8.71311	−	13.1628i	−0.277341	−	0.418975i
$988$	8.79359	−	5.07698i	0.279761	−	0.161520i
$989$		−	1.41883i		−	0.0451163i
$990$	−25.6207	+	60.3742i	−0.814280	+	1.91882i
$991$			27.1850i			0.863561i	0.901979	+	0.431780i	$0.142114\pi$
$991$			27.1850i			0.863561i	−0.901979	+	0.431780i	$0.857886\pi$
$992$	−5.29425	+	1.72363i	−0.168093	+	0.0547253i
$993$	9.95264	−	0.609193i	0.315838	−	0.0193322i
$994$	8.09867	−	14.0273i	0.256874	−	0.444919i
$995$	−46.8929	+	81.2210i	−1.48661	+	2.57488i
$996$	13.5887	+	6.77431i	0.430576	+	0.214652i
$997$	10.9222	+	18.9178i	0.345910	+	0.599134i	0.985519	−	0.169567i	$-0.0542369\pi$
$997$	10.9222	+	18.9178i	0.345910	+	0.599134i	−0.639609	+	0.768701i	$0.720904\pi$
$998$	13.7536			0.435362
$999$	−19.4815	+	3.61349i	−0.616367	+	0.114326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.q.a.185.19	✓	64
3.2	odd	2		1674.2.q.a.557.1		64
9.2	odd	6	inner	558.2.q.a.371.30	yes	64
9.7	even	3		1674.2.q.a.1115.12		64
31.30	odd	2	inner	558.2.q.a.185.30	yes	64
93.92	even	2		1674.2.q.a.557.12		64
279.61	odd	6		1674.2.q.a.1115.1		64
279.92	even	6	inner	558.2.q.a.371.19	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.q.a.185.19	✓	64	1.1	even	1	trivial
558.2.q.a.185.30	yes	64	31.30	odd	2	inner
558.2.q.a.371.19	yes	64	279.92	even	6	inner
558.2.q.a.371.30	yes	64	9.2	odd	6	inner
1674.2.q.a.557.1		64	3.2	odd	2
1674.2.q.a.557.12		64	93.92	even	2
1674.2.q.a.1115.1		64	279.61	odd	6
1674.2.q.a.1115.12		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} +(-1.55011 - 0.772765i) q^{3} +(0.500000 - 0.866025i) q^{4} +(3.64602 + 2.10503i) q^{5} +(-1.72882 + 0.105819i) q^{6} +(-0.908070 - 1.57282i) q^{7} -1.00000i q^{8} +(1.80567 + 2.39574i) q^{9} +4.21006 q^{10} +(2.59638 + 4.49706i) q^{11} +(-1.44429 + 0.956050i) q^{12} +(-1.49949 - 0.865730i) q^{13} +(-1.57282 - 0.908070i) q^{14} +(-4.02503 - 6.08055i) q^{15} +(-0.500000 - 0.866025i) q^{16} +7.56795 q^{17} +(2.76162 + 1.17194i) q^{18} -5.86439 q^{19} +(3.64602 - 2.10503i) q^{20} +(0.192183 + 3.13977i) q^{21} +(4.49706 + 2.59638i) q^{22} +(0.111545 - 0.193202i) q^{23} +(-0.772765 + 1.55011i) q^{24} +(6.36232 + 11.0199i) q^{25} -1.73146 q^{26} +(-0.947635 - 5.10901i) q^{27} -1.81614 q^{28} +(-1.67742 - 2.90538i) q^{29} +(-6.52605 - 3.25339i) q^{30} +(3.72314 - 4.13983i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.549495 - 8.97732i) q^{33} +(6.55404 - 3.78397i) q^{34} -7.64607i q^{35} +(2.97760 - 0.365884i) q^{36} -3.81316i q^{37} +(-5.07871 + 2.93220i) q^{38} +(1.65536 + 2.50073i) q^{39} +(2.10503 - 3.64602i) q^{40} +(-2.34382 - 1.35321i) q^{41} +(1.73632 + 2.62303i) q^{42} +(5.50784 - 3.17995i) q^{43} +5.19276 q^{44} +(1.54040 + 12.5359i) q^{45} -0.223091i q^{46} +(-4.34584 + 2.50907i) q^{47} +(0.105819 + 1.72882i) q^{48} +(1.85082 - 3.20571i) q^{49} +(11.0199 + 6.36232i) q^{50} +(-11.7311 - 5.84825i) q^{51} +(-1.49949 + 0.865730i) q^{52} -7.86605 q^{53} +(-3.37518 - 3.95072i) q^{54} +21.8619i q^{55} +(-1.57282 + 0.908070i) q^{56} +(9.09044 + 4.53180i) q^{57} +(-2.90538 - 1.67742i) q^{58} +(1.78499 + 1.03057i) q^{59} +(-7.27842 + 0.445506i) q^{60} +(-4.83783 + 2.79312i) q^{61} +(1.15442 - 5.44677i) q^{62} +(2.12840 - 5.01550i) q^{63} -1.00000 q^{64} +(-3.64478 - 6.31294i) q^{65} +(-4.96454 - 7.49984i) q^{66} +(3.75336 - 6.50102i) q^{67} +(3.78397 - 6.55404i) q^{68} +(-0.322207 + 0.213286i) q^{69} +(-3.82303 - 6.62169i) q^{70} +8.91854i q^{71} +(2.39574 - 1.80567i) q^{72} +6.05621i q^{73} +(-1.90658 - 3.30230i) q^{74} +(-1.34651 - 21.9985i) q^{75} +(-2.93220 + 5.07871i) q^{76} +(4.71539 - 8.16730i) q^{77} +(2.68395 + 1.33801i) q^{78} +(-14.7131 + 8.49458i) q^{79} -4.21006i q^{80} +(-2.47913 + 8.65182i) q^{81} -2.70641 q^{82} +(-4.38316 - 7.59186i) q^{83} +(2.81521 + 1.40345i) q^{84} +(27.5929 + 15.9308i) q^{85} +(3.17995 - 5.50784i) q^{86} +(0.355007 + 5.79990i) q^{87} +(4.49706 - 2.59638i) q^{88} -0.469197 q^{89} +(7.60197 + 10.0862i) q^{90} +3.14458i q^{91} +(-0.111545 - 0.193202i) q^{92} +(-8.97039 + 3.54007i) q^{93} +(-2.50907 + 4.34584i) q^{94} +(-21.3817 - 12.3447i) q^{95} +(0.956050 + 1.44429i) q^{96} +(-1.10468 - 1.91336i) q^{97} -3.70163i q^{98} +(-6.08559 + 14.3405i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more