LMFDB - Embedded newform 550.2.g.c.291.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [550,2,Mod(291,550)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(550, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([2, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("550.291"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.g (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [60] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$15$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			291.8
Character	$\chi$	$=$	550.291
Dual form			550.2.g.c.361.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.0527535 + 0.162358i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.755692 - 2.10450i) q^{5} +(0.138110 + 0.100343i) q^{6} +(3.80372 - 2.76356i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(2.40347 + 1.74623i) q^{9} +(-1.76798 - 1.36903i) q^{10} +(-0.546412 + 3.27130i) q^{11} +(0.138110 - 0.100343i) q^{12} +(-1.77505 - 1.28965i) q^{13} +(-1.45289 - 4.47154i) q^{14} +(0.301818 + 0.233713i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.177076 - 0.128653i) q^{17} +(2.40347 - 1.74623i) q^{18} +(1.93179 - 1.40352i) q^{19} +(-1.84836 + 1.25839i) q^{20} +(0.248028 + 0.763353i) q^{21} +(2.94235 + 1.53056i) q^{22} +(-2.53037 - 1.83842i) q^{23} +(-0.0527535 - 0.162358i) q^{24} +(-3.85786 - 3.18071i) q^{25} +(-1.77505 + 1.28965i) q^{26} +(-0.824637 + 0.599134i) q^{27} -4.70165 q^{28} +(3.54072 + 2.57248i) q^{29} +(0.315541 - 0.214825i) q^{30} -4.24649 q^{31} +1.00000 q^{32} +(-0.502299 - 0.261287i) q^{33} +(-0.177076 + 0.128653i) q^{34} +(-2.94149 - 10.0933i) q^{35} +(-0.918045 - 2.82545i) q^{36} +(1.73351 - 5.33520i) q^{37} +(-0.737876 - 2.27095i) q^{38} +(0.303025 - 0.220160i) q^{39} +(0.625628 + 2.14676i) q^{40} -2.30966 q^{41} +0.802637 q^{42} +3.41388 q^{43} +(2.36488 - 2.32537i) q^{44} +(5.49122 - 3.73851i) q^{45} +(-2.53037 + 1.83842i) q^{46} +(-0.361038 + 1.11116i) q^{47} -0.170714 q^{48} +(4.66787 - 14.3662i) q^{49} +(-4.21718 + 2.68615i) q^{50} +(0.0302293 - 0.0219628i) q^{51} +(0.678007 + 2.08669i) q^{52} +(-0.303938 + 0.220824i) q^{53} +(0.314983 + 0.969419i) q^{54} +(6.47155 + 3.62202i) q^{55} +(-1.45289 + 4.47154i) q^{56} +(0.125966 + 0.387682i) q^{57} +(3.54072 - 2.57248i) q^{58} +(-3.15911 + 9.72274i) q^{59} +(-0.106803 - 0.366482i) q^{60} +(-5.33948 + 3.87936i) q^{61} +(-1.31224 + 4.03865i) q^{62} +13.9679 q^{63} +(0.309017 - 0.951057i) q^{64} +(-4.05545 + 2.76101i) q^{65} +(-0.403718 + 0.396972i) q^{66} +(-2.94278 + 9.05696i) q^{67} +(0.0676369 + 0.208165i) q^{68} +(0.431969 - 0.313844i) q^{69} +(-10.5083 - 0.321492i) q^{70} +12.5235 q^{71} -2.97086 q^{72} -11.0638 q^{73} +(-4.53839 - 3.29733i) q^{74} +(0.719930 - 0.458563i) q^{75} -2.38782 q^{76} +(6.96206 + 13.9532i) q^{77} +(-0.115745 - 0.356227i) q^{78} +(-5.59246 + 4.06316i) q^{79} +(2.23502 + 0.0683784i) q^{80} +(2.70036 + 8.31087i) q^{81} +(-0.713723 + 2.19661i) q^{82} +(7.92420 + 5.75727i) q^{83} +(0.248028 - 0.763353i) q^{84} +(-0.404565 + 0.275434i) q^{85} +(1.05495 - 3.24679i) q^{86} +(-0.604449 + 0.439158i) q^{87} +(-1.48077 - 2.96771i) q^{88} +(-13.2776 - 9.64677i) q^{89} +(-1.85865 - 6.37772i) q^{90} -10.3158 q^{91} +(0.966516 + 2.97463i) q^{92} +(0.224017 - 0.689453i) q^{93} +(0.945210 + 0.686735i) q^{94} +(-1.49389 - 5.12608i) q^{95} +(-0.0527535 + 0.162358i) q^{96} +(-5.13004 + 3.72719i) q^{97} +(-12.2206 - 8.87881i) q^{98} +(-7.02572 + 6.90834i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 15 q^{2} - 4 q^{3} - 15 q^{4} + q^{6} - 3 q^{7} - 15 q^{8} - 17 q^{9} - 5 q^{10} + 7 q^{11} + q^{12} + 12 q^{13} - 3 q^{14} + 12 q^{15} - 15 q^{16} + q^{17} - 17 q^{18} + 3 q^{19} - 5 q^{20} - 4 q^{21}+ \cdots + 21 q^{99}+O(q^{100}) $ 60 * q - 15 * q^2 - 4 * q^3 - 15 * q^4 + q^6 - 3 * q^7 - 15 * q^8 - 17 * q^9 - 5 * q^10 + 7 * q^11 + q^12 + 12 * q^13 - 3 * q^14 + 12 * q^15 - 15 * q^16 + q^17 - 17 * q^18 + 3 * q^19 - 5 * q^20 - 4 * q^21 - 3 * q^22 - 3 * q^23 - 4 * q^24 + 8 * q^25 + 12 * q^26 + 2 * q^27 + 12 * q^28 + 18 * q^29 + 2 * q^30 - 20 * q^31 + 60 * q^32 + 10 * q^33 + q^34 - 19 * q^35 - 12 * q^36 - 36 * q^37 - 22 * q^38 + 13 * q^39 + 64 * q^41 + 46 * q^42 + 40 * q^43 - 8 * q^44 - 20 * q^45 - 3 * q^46 - 9 * q^47 + 6 * q^48 - 30 * q^49 + 18 * q^50 - 48 * q^51 - 8 * q^52 + 31 * q^53 - 8 * q^54 - 42 * q^55 - 3 * q^56 + 30 * q^57 + 18 * q^58 + 23 * q^59 - 8 * q^60 - 41 * q^61 - 5 * q^62 + 6 * q^63 - 15 * q^64 - 7 * q^65 - 30 * q^66 - 40 * q^67 - 4 * q^68 - 22 * q^69 - 4 * q^70 + 4 * q^71 + 58 * q^72 + 74 * q^73 - 11 * q^74 + 35 * q^75 + 38 * q^76 + 22 * q^77 - 12 * q^78 - 45 * q^79 + 10 * q^80 + 24 * q^81 - 11 * q^82 + 16 * q^83 - 4 * q^84 + 9 * q^85 - 20 * q^86 + 68 * q^87 + 7 * q^88 + q^89 + 10 * q^90 + 10 * q^91 + 2 * q^92 - 40 * q^93 - 24 * q^94 + 24 * q^95 - 4 * q^96 + 6 * q^97 - 30 * q^98 + 21 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	−0.0527535	+	0.162358i	−0.0304572	+	0.0937377i	−0.965130	−	0.261773i	$-0.915693\pi$
$3$	−0.0527535	+	0.162358i	−0.0304572	+	0.0937377i	0.934672	+	0.355510i	$0.115693\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.755692	−	2.10450i	0.337956	−	0.941162i
$5$	0.755692	−	2.10450i	0.337956	−	0.941162i
$6$	0.138110	+	0.100343i	0.0563833	+	0.0409649i
$7$	3.80372	−	2.76356i	1.43767	−	1.04453i	0.449147	−	0.893458i	$-0.351728\pi$
$7$	3.80372	−	2.76356i	1.43767	−	1.04453i	0.988523	−	0.151071i	$-0.0482721\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	2.40347	+	1.74623i	0.801158	+	0.582075i
$10$	−1.76798	−	1.36903i	−0.559084	−	0.432926i
$11$	−0.546412	+	3.27130i	−0.164749	+	0.986335i
$11$	−0.546412	+	3.27130i	−0.164749	+	0.986335i
$12$	0.138110	−	0.100343i	0.0398690	−	0.0289665i
$13$	−1.77505	−	1.28965i	−0.492309	−	0.357684i	0.313763	−	0.949501i	$-0.398410\pi$
$13$	−1.77505	−	1.28965i	−0.492309	−	0.357684i	−0.806072	+	0.591818i	$0.798410\pi$
$14$	−1.45289	−	4.47154i	−0.388301	−	1.19507i
$15$	0.301818	+	0.233713i	0.0779292	+	0.0603444i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.177076	−	0.128653i	−0.0429472	−	0.0312030i	0.566105	−	0.824333i	$-0.308450\pi$
$17$	−0.177076	−	0.128653i	−0.0429472	−	0.0312030i	−0.609052	+	0.793130i	$0.708450\pi$
$18$	2.40347	−	1.74623i	0.566504	−	0.411589i
$19$	1.93179	−	1.40352i	0.443182	−	0.321991i	−0.343716	−	0.939074i	$-0.611686\pi$
$19$	1.93179	−	1.40352i	0.443182	−	0.321991i	0.786898	+	0.617083i	$0.211686\pi$
$20$	−1.84836	+	1.25839i	−0.413306	+	0.281385i
$21$	0.248028	+	0.763353i	0.0541242	+	0.166577i
$22$	2.94235	+	1.53056i	0.627310	+	0.326316i
$23$	−2.53037	−	1.83842i	−0.527619	−	0.383338i	0.291847	−	0.956465i	$-0.405730\pi$
$23$	−2.53037	−	1.83842i	−0.527619	−	0.383338i	−0.819466	+	0.573127i	$0.805730\pi$
$24$	−0.0527535	−	0.162358i	−0.0107683	−	0.0331413i
$25$	−3.85786	−	3.18071i	−0.771572	−	0.636142i
$26$	−1.77505	+	1.28965i	−0.348115	+	0.252920i
$27$	−0.824637	+	0.599134i	−0.158701	+	0.115303i
$28$	−4.70165			−0.888529
$29$	3.54072	+	2.57248i	0.657495	+	0.477698i	0.865816	−	0.500363i	$-0.166800\pi$
$29$	3.54072	+	2.57248i	0.657495	+	0.477698i	−0.208321	+	0.978060i	$0.566800\pi$
$30$	0.315541	−	0.214825i	0.0576096	−	0.0392215i
$31$	−4.24649			−0.762691			−0.381346	−	0.924433i	$-0.624539\pi$
$31$	−4.24649			−0.762691			−0.381346	+	0.924433i	$0.624539\pi$
$32$	1.00000			0.176777
$33$	−0.502299	−	0.261287i	−0.0874390	−	0.0454843i
$34$	−0.177076	+	0.128653i	−0.0303682	+	0.0220638i
$35$	−2.94149	−	10.0933i	−0.497202	−	1.70608i
$36$	−0.918045	−	2.82545i	−0.153008	−	0.470909i
$37$	1.73351	−	5.33520i	0.284988	−	0.877101i	−0.701415	−	0.712753i	$-0.747448\pi$
$37$	1.73351	−	5.33520i	0.284988	−	0.877101i	0.986402	−	0.164348i	$-0.0525520\pi$
$38$	−0.737876	−	2.27095i	−0.119699	−	0.368397i
$39$	0.303025	−	0.220160i	0.0485228	−	0.0352539i
$40$	0.625628	+	2.14676i	0.0989205	+	0.339433i
$41$	−2.30966			−0.360708			−0.180354	−	0.983602i	$-0.557724\pi$
$41$	−2.30966			−0.360708			−0.180354	+	0.983602i	$0.557724\pi$
$42$	0.802637			0.123850
$43$	3.41388			0.520611			0.260306	−	0.965526i	$-0.416177\pi$
$43$	3.41388			0.520611			0.260306	+	0.965526i	$0.416177\pi$
$44$	2.36488	−	2.32537i	0.356519	−	0.350562i
$45$	5.49122	−	3.73851i	0.818583	−	0.557304i
$46$	−2.53037	+	1.83842i	−0.373083	+	0.271061i
$47$	−0.361038	+	1.11116i	−0.0526628	+	0.162079i	−0.973929	−	0.226853i	$-0.927156\pi$
$47$	−0.361038	+	1.11116i	−0.0526628	+	0.162079i	0.921266	+	0.388933i	$0.127156\pi$
$48$	−0.170714			−0.0246404
$49$	4.66787	−	14.3662i	0.666838	−	2.05232i
$50$	−4.21718	+	2.68615i	−0.596399	+	0.379879i
$51$	0.0302293	−	0.0219628i	0.00423294	−	0.00307541i
$52$	0.678007	+	2.08669i	0.0940227	+	0.289372i
$53$	−0.303938	+	0.220824i	−0.0417491	+	0.0303325i	−0.608464	−	0.793581i	$-0.708214\pi$
$53$	−0.303938	+	0.220824i	−0.0417491	+	0.0303325i	0.566715	+	0.823914i	$0.308214\pi$
$54$	0.314983	+	0.969419i	0.0428638	+	0.131921i
$55$	6.47155	+	3.62202i	0.872624	+	0.488393i
$56$	−1.45289	+	4.47154i	−0.194151	+	0.597534i
$57$	0.125966	+	0.387682i	0.0166846	+	0.0513498i
$58$	3.54072	−	2.57248i	0.464919	−	0.337783i
$59$	−3.15911	+	9.72274i	−0.411281	+	1.26579i	0.504254	+	0.863555i	$0.331767\pi$
$59$	−3.15911	+	9.72274i	−0.411281	+	1.26579i	−0.915535	+	0.402237i	$0.868233\pi$
$60$	−0.106803	−	0.366482i	−0.0137882	−	0.0473126i
$61$	−5.33948	+	3.87936i	−0.683650	+	0.496701i	−0.874567	−	0.484906i	$-0.838854\pi$
$61$	−5.33948	+	3.87936i	−0.683650	+	0.496701i	0.190917	+	0.981606i	$0.438854\pi$
$62$	−1.31224	+	4.03865i	−0.166654	+	0.512909i
$63$	13.9679			1.75979
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−4.05545	+	2.76101i	−0.503017	+	0.342462i
$66$	−0.403718	+	0.396972i	−0.0496942	+	0.0488639i
$67$	−2.94278	+	9.05696i	−0.359518	+	1.10648i	0.593825	+	0.804594i	$0.297617\pi$
$67$	−2.94278	+	9.05696i	−0.359518	+	1.10648i	−0.953343	+	0.301889i	$0.902383\pi$
$68$	0.0676369	+	0.208165i	0.00820218	+	0.0252437i
$69$	0.431969	−	0.313844i	0.0520030	−	0.0377824i
$70$	−10.5083	−	0.321492i	−1.25598	−	0.0384256i
$71$	12.5235			1.48627			0.743134	−	0.669142i	$-0.233338\pi$
$71$	12.5235			1.48627			0.743134	+	0.669142i	$0.233338\pi$
$72$	−2.97086			−0.350119
$73$	−11.0638			−1.29492			−0.647459	−	0.762100i	$-0.724168\pi$
$73$	−11.0638			−1.29492			−0.647459	+	0.762100i	$0.724168\pi$
$74$	−4.53839	−	3.29733i	−0.527577	−	0.383307i
$75$	0.719930	−	0.458563i	0.0831304	−	0.0529503i
$76$	−2.38782			−0.273901
$77$	6.96206	+	13.9532i	0.793400	+	1.59011i
$78$	−0.115745	−	0.356227i	−0.0131056	−	0.0403348i
$79$	−5.59246	+	4.06316i	−0.629201	+	0.457141i	−0.856123	−	0.516772i	$-0.827134\pi$
$79$	−5.59246	+	4.06316i	−0.629201	+	0.457141i	0.226922	+	0.973913i	$0.427134\pi$
$80$	2.23502	+	0.0683784i	0.249883	+	0.00764494i
$81$	2.70036	+	8.31087i	0.300040	+	0.923429i
$82$	−0.713723	+	2.19661i	−0.0788175	+	0.242575i
$83$	7.92420	+	5.75727i	0.869794	+	0.631943i	0.930532	−	0.366211i	$-0.119345\pi$
$83$	7.92420	+	5.75727i	0.869794	+	0.631943i	−0.0607375	+	0.998154i	$0.519345\pi$
$84$	0.248028	−	0.763353i	0.0270621	−	0.0832886i
$85$	−0.404565	+	0.275434i	−0.0438813	+	0.0298750i
$86$	1.05495	−	3.24679i	0.113758	−	0.350110i
$87$	−0.604449	+	0.439158i	−0.0648038	+	0.0470827i
$88$	−1.48077	−	2.96771i	−0.157850	−	0.316359i
$89$	−13.2776	−	9.64677i	−1.40743	−	1.02256i	−0.993690	−	0.112159i	$-0.964223\pi$
$89$	−13.2776	−	9.64677i	−1.40743	−	1.02256i	−0.413737	−	0.910397i	$-0.635777\pi$
$90$	−1.85865	−	6.37772i	−0.195919	−	0.672271i
$91$	−10.3158			−1.08139
$92$	0.966516	+	2.97463i	0.100766	+	0.310127i
$93$	0.224017	−	0.689453i	0.0232295	−	0.0714929i
$94$	0.945210	+	0.686735i	0.0974910	+	0.0708313i
$95$	−1.49389	−	5.12608i	−0.153269	−	0.525925i
$96$	−0.0527535	+	0.162358i	−0.00538413	+	0.0165706i
$97$	−5.13004	+	3.72719i	−0.520877	+	0.378439i	−0.816934	−	0.576731i	$-0.804328\pi$
$97$	−5.13004	+	3.72719i	−0.520877	+	0.378439i	0.296057	+	0.955170i	$0.404328\pi$
$98$	−12.2206	−	8.87881i	−1.23447	−	0.896896i
$99$	−7.02572	+	6.90834i	−0.706112	+	0.694314i
$100$	1.25150	+	4.84084i	0.125150	+	0.484084i
$101$	4.75397	+	14.6312i	0.473038	+	1.45586i	0.848585	+	0.529058i	$0.177455\pi$
$101$	4.75397	+	14.6312i	0.473038	+	1.45586i	−0.375547	+	0.926803i	$0.622545\pi$
$102$	−0.0115466	−	0.0355366i	−0.00114328	−	0.00351865i
$103$	4.19744	+	3.04962i	0.413586	+	0.300488i	0.775052	−	0.631897i	$-0.217724\pi$
$103$	4.19744	+	3.04962i	0.413586	+	0.300488i	−0.361466	+	0.932385i	$0.617724\pi$
$104$	2.19408			0.215147
$105$	1.79391	+	0.0548831i	0.175068	+	0.00535604i
$106$	0.116094	+	0.357301i	0.0112760	+	0.0347041i
$107$	11.0343	+	8.01689i	1.06673	+	0.775022i	0.975321	−	0.220792i	$-0.0708642\pi$
$107$	11.0343	+	8.01689i	1.06673	+	0.775022i	0.0914051	+	0.995814i	$0.470864\pi$
$108$	1.01931			0.0980829
$109$	12.3688	−	8.98649i	1.18472	−	0.860749i	0.192024	−	0.981390i	$-0.438495\pi$
$109$	12.3688	−	8.98649i	1.18472	−	0.860749i	0.992696	+	0.120641i	$0.0384949\pi$
$110$	5.44457	−	5.03554i	0.519119	−	0.480120i
$111$	0.774766	+	0.562900i	0.0735375	+	0.0534281i
$112$	3.80372	+	2.76356i	0.359417	+	0.261132i
$113$	16.1036			1.51490			0.757452	−	0.652891i	$-0.226444\pi$
$113$	16.1036			1.51490			0.757452	+	0.652891i	$0.226444\pi$
$114$	0.407633			0.0381784
$115$	−5.78115	+	3.93589i	−0.539095	+	0.367024i
$116$	−1.35243	−	4.16236i	−0.125570	−	0.386466i
$117$	−2.01426	−	6.19926i	−0.186219	−	0.573122i
$118$	8.27065	+	6.00898i	0.761375	+	0.553172i
$119$	−1.02909			−0.0943362
$120$	−0.381549	−	0.0116731i	−0.0348305	−	0.00106561i
$121$	−10.4029	−	3.57496i	−0.945715	−	0.324996i
$122$	2.03950	+	6.27693i	0.184647	+	0.568287i
$123$	0.121842	−	0.374992i	0.0109861	−	0.0338119i
$124$	3.43548	+	2.49602i	0.308515	+	0.224149i
$125$	−9.60916	+	5.71524i	−0.859470	+	0.511187i
$126$	4.31633	−	13.2843i	0.384529	−	1.18346i
$127$	10.3236	−	7.50052i	0.916069	−	0.665563i	−0.0264731	−	0.999650i	$-0.508428\pi$
$127$	10.3236	−	7.50052i	0.916069	−	0.665563i	0.942543	+	0.334086i	$0.108428\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−0.180094	+	0.554272i	−0.0158564	+	0.0488009i
$130$	1.37268	+	4.71016i	0.120392	+	0.413109i
$131$	−5.13377	+	15.8001i	−0.448540	+	1.38046i	0.430015	+	0.902822i	$0.358508\pi$
$131$	−5.13377	+	15.8001i	−0.448540	+	1.38046i	−0.878555	+	0.477642i	$0.841492\pi$
$132$	0.252787	+	0.506630i	0.0220023	+	0.0440964i
$133$	3.46924	−	10.6772i	0.300821	−	0.925832i
$134$	7.70431	+	5.59751i	0.665551	+	0.483551i
$135$	0.637707	+	2.18821i	0.0548851	+	0.188331i
$136$	0.218878			0.0187686
$137$	−3.52820	−	10.8587i	−0.301434	−	0.927719i	−0.980984	−	0.194089i	$-0.937825\pi$
$137$	−3.52820	−	10.8587i	−0.301434	−	0.927719i	0.679550	−	0.733629i	$-0.262175\pi$
$138$	−0.164998	−	0.507810i	−0.0140455	−	0.0432277i
$139$	−18.8647			−1.60008			−0.800041	−	0.599945i	$-0.795189\pi$
$139$	−18.8647			−1.60008			−0.800041	+	0.599945i	$0.795189\pi$
$140$	−3.55300	+	9.89464i	−0.300283	+	0.836250i
$141$	−0.161360	−	0.117235i	−0.0135890	−	0.00987298i
$142$	3.86998	−	11.9106i	0.324762	−	0.999513i
$143$	5.18873	−	5.10204i	0.433904	−	0.426654i
$144$	−0.918045	+	2.82545i	−0.0765038	+	0.235454i
$145$	8.08949	−	5.50745i	0.671795	−	0.457368i
$146$	−3.41890	+	10.5223i	−0.282950	+	0.870830i
$147$	2.08623	+	1.51574i	0.172069	+	0.125016i
$148$	−4.53839	+	3.29733i	−0.373053	+	0.271039i
$149$	−1.00551	+	3.09465i	−0.0823749	+	0.253524i	−0.983758	−	0.179498i	$-0.942553\pi$
$149$	−1.00551	+	3.09465i	−0.0823749	+	0.253524i	0.901383	+	0.433022i	$0.142553\pi$
$150$	−0.213648	−	0.826398i	−0.0174443	−	0.0674751i
$151$	−1.17505	−	0.853724i	−0.0956242	−	0.0694750i	0.538946	−	0.842340i	$-0.318823\pi$
$151$	−1.17505	−	0.853724i	−0.0956242	−	0.0694750i	−0.634570	+	0.772865i	$0.718823\pi$
$152$	−0.737876	+	2.27095i	−0.0598497	+	0.184198i
$153$	−0.200940	−	0.618428i	−0.0162450	−	0.0499970i
$154$	15.4216	−	2.30955i	1.24271	−	0.186109i
$155$	−3.20903	+	8.93674i	−0.257756	+	0.717816i
$156$	−0.374559			−0.0299887
$157$	−3.65227	−	2.65353i	−0.291483	−	0.211775i	0.432428	−	0.901669i	$-0.357657\pi$
$157$	−3.65227	−	2.65353i	−0.291483	−	0.211775i	−0.723910	+	0.689894i	$0.757657\pi$
$158$	2.13613	+	6.57433i	0.169941	+	0.523026i
$159$	−0.0198188	−	0.0609961i	−0.00157174	−	0.00483731i
$160$	0.755692	−	2.10450i	0.0597427	−	0.166376i
$161$	−14.7054			−1.15895
$162$	8.73856			0.686566
$163$	13.9096	+	10.1059i	1.08948	+	0.791555i	0.979312	−	0.202358i	$-0.0648604\pi$
$163$	13.9096	+	10.1059i	1.08948	+	0.791555i	0.110170	+	0.993913i	$0.464860\pi$
$164$	1.86855	+	1.35758i	0.145909	+	0.106009i
$165$	−0.929462	+	0.859636i	−0.0723586	+	0.0669226i
$166$	7.92420	−	5.75727i	0.615037	−	0.446851i
$167$	21.8503			1.69083			0.845415	−	0.534109i	$-0.179353\pi$
$167$	21.8503			1.69083			0.845415	+	0.534109i	$0.179353\pi$
$168$	−0.649347	−	0.471778i	−0.0500982	−	0.0363985i
$169$	−2.52962	−	7.78537i	−0.194586	−	0.598875i
$170$	0.136936	+	0.469878i	0.0105025	+	0.0360380i
$171$	7.09386			0.542481
$172$	−2.76189	−	2.00663i	−0.210592	−	0.153004i
$173$	3.59012	+	11.0493i	0.272952	+	0.840060i	0.989754	+	0.142783i	$0.0456051\pi$
$173$	3.59012	+	11.0493i	0.272952	+	0.840060i	−0.716802	+	0.697277i	$0.754395\pi$
$174$	0.230879	+	0.710573i	0.0175029	+	0.0538684i
$175$	−23.4643	−	1.43708i	−1.77373	−	0.108633i
$176$	−3.28005	+	0.491220i	−0.247243	+	0.0370271i
$177$	−1.41191	−	1.02582i	−0.106126	−	0.0771050i
$178$	−13.2776	+	9.64677i	−0.995201	+	0.723056i
$179$	4.34442	−	13.3707i	0.324717	−	0.999377i	−0.646851	−	0.762616i	$-0.723914\pi$
$179$	4.34442	−	13.3707i	0.324717	−	0.999377i	0.971568	−	0.236760i	$-0.0760856\pi$
$180$	−6.63993	−	0.203143i	−0.494911	−	0.0151414i
$181$	7.70255	+	5.59623i	0.572526	+	0.415965i	0.836022	−	0.548696i	$-0.184875\pi$
$181$	7.70255	+	5.59623i	0.572526	+	0.415965i	−0.263496	+	0.964661i	$0.584875\pi$
$182$	−3.18775	+	9.81090i	−0.236292	+	0.727232i
$183$	−0.348170	−	1.07156i	−0.0257375	−	0.0792119i
$184$	3.12771			0.230578
$185$	−9.91794	−	7.67994i	−0.729181	−	0.564641i
$186$	−0.586484	−	0.426105i	−0.0430031	−	0.0312436i
$187$	0.517620	−	0.508971i	0.0378521	−	0.0372197i
$188$	0.945210	−	0.686735i	0.0689365	−	0.0500853i
$189$	−1.48094	+	4.55787i	−0.107723	+	0.331536i
$190$	−5.33683	−	0.163275i	−0.387174	−	0.0118452i
$191$	2.03239	−	6.25506i	0.147059	−	0.452600i	−0.850211	−	0.526442i	$-0.823526\pi$
$191$	2.03239	−	6.25506i	0.147059	−	0.452600i	0.997270	+	0.0738414i	$0.0235259\pi$
$192$	0.138110	+	0.100343i	0.00996725	+	0.00724163i
$193$	6.02166	−	18.5328i	0.433449	−	1.33402i	−0.461219	−	0.887286i	$-0.652588\pi$
$193$	6.02166	−	18.5328i	0.433449	−	1.33402i	0.894668	−	0.446732i	$-0.147412\pi$
$194$	1.95950	+	6.03073i	0.140684	+	0.432981i
$195$	−0.234335	−	0.804090i	−0.0167811	−	0.0575821i
$196$	−12.2206	+	8.87881i	−0.872903	+	0.634201i
$197$	−2.62106	−	8.06680i	−0.186743	−	0.574735i	0.813231	−	0.581941i	$-0.197706\pi$
$197$	−2.62106	−	8.06680i	−0.186743	−	0.574735i	−0.999974	+	0.00720531i	$0.997706\pi$
$198$	4.39915	+	8.81665i	0.312634	+	0.626572i
$199$	0.277121			0.0196446			0.00982230	−	0.999952i	$-0.496873\pi$
$199$	0.277121			0.0196446			0.00982230	+	0.999952i	$0.496873\pi$
$200$	4.99065	+	0.305655i	0.352892	+	0.0216131i
$201$	−1.31523	−	0.955572i	−0.0927693	−	0.0674008i
$202$	15.3842			1.08243
$203$	20.5771			1.44423
$204$	−0.0373654			−0.00261610
$205$	−1.74539	+	4.86067i	−0.121903	+	0.339484i
$206$	4.19744	−	3.04962i	0.292450	−	0.212477i
$207$	−2.87138	−	8.83720i	−0.199575	−	0.614228i
$208$	0.678007	−	2.08669i	0.0470113	−	0.144686i
$209$	3.53580	+	7.08636i	0.244577	+	0.490174i
$210$	0.606546	−	1.68915i	0.0418556	−	0.116563i
$211$	−8.61668	+	26.5194i	−0.593197	+	1.82567i	−0.0296913	+	0.999559i	$0.509452\pi$
$211$	−8.61668	+	26.5194i	−0.593197	+	1.82567i	−0.563505	+	0.826112i	$0.690548\pi$
$212$	0.375688			0.0258024
$213$	−0.660659	+	2.03330i	−0.0452676	+	0.139319i
$214$	11.0343	−	8.01689i	0.754289	−	0.548023i
$215$	2.57984	−	7.18451i	0.175944	−	0.489980i
$216$	0.314983	−	0.969419i	0.0214319	−	0.0659606i
$217$	−16.1524	+	11.7354i	−1.09650	+	0.796653i
$218$	−4.72448	−	14.5404i	−0.319982	−	0.984803i
$219$	0.583653	−	1.79630i	0.0394396	−	0.121383i
$220$	−3.10662	−	6.73416i	−0.209448	−	0.454017i
$221$	0.148401	+	0.456730i	0.00998251	+	0.0307230i
$222$	0.774766	−	0.562900i	0.0519989	−	0.0377794i
$223$	−1.07672	−	3.31381i	−0.0721027	−	0.221909i	0.908511	−	0.417861i	$-0.137220\pi$
$223$	−1.07672	−	3.31381i	−0.0721027	−	0.221909i	−0.980613	+	0.195952i	$0.937220\pi$
$224$	3.80372	−	2.76356i	0.254147	−	0.184648i
$225$	−3.71803	−	14.3814i	−0.247869	−	0.958763i
$226$	4.97630	−	15.3155i	0.331019	−	1.01877i
$227$	−6.95735			−0.461776			−0.230888	−	0.972980i	$-0.574163\pi$
$227$	−6.95735			−0.461776			−0.230888	+	0.972980i	$0.574163\pi$
$228$	0.125966	−	0.387682i	0.00834228	−	0.0256749i
$229$	9.86604	−	7.16810i	0.651966	−	0.473681i	−0.211974	−	0.977275i	$-0.567989\pi$
$229$	9.86604	−	7.16810i	0.651966	−	0.473681i	0.863940	+	0.503594i	$0.167989\pi$
$230$	1.95678	+	6.71445i	0.129027	+	0.442738i
$231$	−2.63269	+	0.394271i	−0.173218	+	0.0259412i
$232$	−4.37657			−0.287336
$233$	−23.7571			−1.55638			−0.778190	−	0.628029i	$-0.783862\pi$
$233$	−23.7571			−1.55638			−0.778190	+	0.628029i	$0.783862\pi$
$234$	−6.51829			−0.426114
$235$	2.06561	+	1.59950i	0.134745	+	0.104340i
$236$	8.27065	−	6.00898i	0.538374	−	0.391151i
$237$	−0.364667	−	1.12233i	−0.0236876	−	0.0729031i
$238$	−0.318005	+	0.978720i	−0.0206132	+	0.0634410i
$239$	9.16146	+	28.1961i	0.592606	+	1.82385i	0.566301	+	0.824199i	$0.308374\pi$
$239$	9.16146	+	28.1961i	0.592606	+	1.82385i	0.0263049	+	0.999654i	$0.491626\pi$
$240$	−0.129007	+	0.359268i	−0.00832736	+	0.0231906i
$241$	−1.01434	+	0.736960i	−0.0653393	+	0.0474718i	−0.619975	−	0.784621i	$-0.712857\pi$
$241$	−1.01434	+	0.736960i	−0.0653393	+	0.0474718i	0.554636	+	0.832093i	$0.312857\pi$
$242$	−6.61465	+	8.78899i	−0.425206	+	0.564978i
$243$	−4.54971			−0.291864
$244$	6.59995			0.422519
$245$	−26.7063	−	20.6800i	−1.70620	−	1.32120i
$246$	−0.318987	−	0.231758i	−0.0203379	−	0.0147763i
$247$	−5.23906			−0.333353
$248$	3.43548	−	2.49602i	0.218153	−	0.158498i
$249$	−1.35277	+	0.982845i	−0.0857283	+	0.0622853i
$250$	2.46612	+	10.9050i	0.155971	+	0.689690i
$251$	−4.29325	−	13.2133i	−0.270987	−	0.834014i	−0.990253	−	0.139279i	$-0.955522\pi$
$251$	−4.29325	−	13.2133i	−0.270987	−	0.834014i	0.719266	−	0.694735i	$-0.244478\pi$
$252$	−11.3003	−	8.21015i	−0.711852	−	0.517191i
$253$	7.39667	−	7.27308i	0.465024	−	0.457255i
$254$	−3.94326	−	12.1361i	−0.247422	−	0.761486i
$255$	−0.0233769	−	0.0802147i	−0.00146392	−	0.00502324i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−4.57497	+	3.32391i	−0.285379	+	0.207340i	−0.721260	−	0.692664i	$-0.756437\pi$
$257$	−4.57497	+	3.32391i	−0.285379	+	0.207340i	0.435881	+	0.900004i	$0.356437\pi$
$258$	0.471492	+	0.342559i	0.0293538	+	0.0213268i
$259$	−8.15037	−	25.0843i	−0.506439	−	1.55866i
$260$	4.90381	+	0.150028i	0.304121	+	0.00930432i
$261$	4.01789	+	12.3658i	0.248701	+	0.765423i
$262$	13.4404	+	9.76502i	0.830350	+	0.603285i
$263$	−20.6911	+	15.0330i	−1.27587	+	0.926972i	−0.999420	−	0.0340568i	$-0.989157\pi$
$263$	−20.6911	+	15.0330i	−1.27587	+	0.926972i	−0.276448	+	0.961029i	$0.589157\pi$
$264$	0.559949	−	0.0838580i	0.0344625	−	0.00516111i
$265$	0.235041	+	0.806513i	0.0144385	+	0.0495437i
$266$	−9.08258	−	6.59888i	−0.556889	−	0.404604i
$267$	2.26668	−	1.64684i	0.138718	−	0.100785i
$268$	7.70431	−	5.59751i	0.470616	−	0.341922i
$269$	−25.1973	−	18.3069i	−1.53631	−	1.11619i	−0.952598	−	0.304233i	$-0.901600\pi$
$269$	−25.1973	−	18.3069i	−1.53631	−	1.11619i	−0.583712	−	0.811961i	$-0.698400\pi$
$270$	2.27817	+	0.0696987i	0.138645	+	0.00424173i
$271$	−0.535662	−	0.389181i	−0.0325391	−	0.0236411i	0.571397	−	0.820674i	$-0.306402\pi$
$271$	−0.535662	−	0.389181i	−0.0325391	−	0.0236411i	−0.603936	+	0.797033i	$0.706402\pi$
$272$	0.0676369	−	0.208165i	0.00410109	−	0.0126219i
$273$	0.544194	−	1.67486i	0.0329361	−	0.101367i
$274$	−11.4175			−0.689755
$275$	12.5131	−	10.8823i	0.754565	−	0.656225i
$276$	−0.533943			−0.0321396
$277$	−0.422768	+	1.30115i	−0.0254017	+	0.0781784i	−0.962954	−	0.269667i	$-0.913086\pi$
$277$	−0.422768	+	1.30115i	−0.0254017	+	0.0781784i	0.937552	+	0.347845i	$0.113086\pi$
$278$	−5.82951	+	17.9414i	−0.349631	+	1.07605i
$279$	−10.2063	−	7.41532i	−0.611036	−	0.443944i
$280$	8.31242	+	6.43672i	0.496762	+	0.384667i
$281$	15.6850	+	11.3958i	0.935687	+	0.679816i	0.947379	−	0.320115i	$-0.103722\pi$
$281$	15.6850	+	11.3958i	0.935687	+	0.679816i	−0.0116918	+	0.999932i	$0.503722\pi$
$282$	−0.161360	+	0.117235i	−0.00960887	+	0.00698125i
$283$	16.9798	−	12.3365i	1.00934	−	0.733330i	0.0452714	−	0.998975i	$-0.485585\pi$
$283$	16.9798	−	12.3365i	1.00934	−	0.733330i	0.964071	+	0.265644i	$0.0855847\pi$
$284$	−10.1317	−	7.36114i	−0.601208	−	0.436803i
$285$	0.911070	+	0.0278733i	0.0539671	+	0.00165107i
$286$	−3.24892	−	6.51139i	−0.192113	−	0.385027i
$287$	−8.78528	+	6.38288i	−0.518578	+	0.376769i
$288$	2.40347	+	1.74623i	0.141626	+	0.102897i
$289$	−5.23848	−	16.1224i	−0.308146	−	0.948376i
$290$	−2.73810	−	9.39545i	−0.160787	−	0.551720i
$291$	−0.334514	−	1.02953i	−0.0196096	−	0.0603520i
$292$	8.95079	+	6.50313i	0.523805	+	0.380567i
$293$	−14.2221	+	10.3329i	−0.830862	+	0.603657i	−0.919803	−	0.392380i	$-0.871652\pi$
$293$	−14.2221	+	10.3329i	−0.830862	+	0.603657i	0.0889410	+	0.996037i	$0.471652\pi$
$294$	2.08623	−	1.51574i	0.121671	−	0.0883995i
$295$	18.0742	+	13.9957i	1.05232	+	0.814864i
$296$	1.73351	+	5.33520i	0.100758	+	0.310102i
$297$	−1.50936	−	3.02501i	−0.0875818	−	0.175529i
$298$	2.63247	+	1.91260i	0.152495	+	0.110794i
$299$	2.12061	+	6.52657i	0.122638	+	0.377441i
$300$	−0.851972	−	0.0521795i	−0.0491886	−	0.00301258i
$301$	12.9854	−	9.43446i	0.748468	−	0.543793i
$302$	−1.17505	+	0.853724i	−0.0676165	+	0.0491263i
$303$	−2.62629			−0.150877
$304$	1.93179	+	1.40352i	0.110795	+	0.0804976i
$305$	4.12912	+	14.1685i	0.236433	+	0.811288i
$306$	−0.650254			−0.0371726
$307$	−2.41170			−0.137643			−0.0688215	−	0.997629i	$-0.521924\pi$
$307$	−2.41170			−0.137643			−0.0688215	+	0.997629i	$0.521924\pi$
$308$	2.56904	−	15.3805i	0.146385	−	0.876388i
$309$	−0.716561	+	0.520612i	−0.0407637	+	0.0296166i
$310$	7.50770	+	5.81358i	0.426409	+	0.330189i
$311$	−7.05784	−	21.7218i	−0.400213	−	1.23173i	−0.924827	−	0.380389i	$-0.875790\pi$
$311$	−7.05784	−	21.7218i	−0.400213	−	1.23173i	0.524613	−	0.851341i	$-0.324210\pi$
$312$	−0.115745	+	0.356227i	−0.00655278	+	0.0201674i
$313$	0.660900	+	2.03404i	0.0373563	+	0.114971i	0.967996	−	0.250967i	$-0.0807484\pi$
$313$	0.660900	+	2.03404i	0.0373563	+	0.114971i	−0.930639	+	0.365937i	$0.880748\pi$
$314$	−3.65227	+	2.65353i	−0.206109	+	0.149747i
$315$	10.5555	−	29.3956i	0.594732	−	1.65625i
$316$	6.91266			0.388868
$317$	−32.8862			−1.84707			−0.923536	−	0.383512i	$-0.874715\pi$
$317$	−32.8862			−1.84707			−0.923536	+	0.383512i	$0.874715\pi$
$318$	−0.0641351			−0.00359652
$319$	−10.3501	+	10.1771i	−0.579492	+	0.569810i
$320$	−1.76798	−	1.36903i	−0.0988330	−	0.0765312i
$321$	−1.88371	+	1.36859i	−0.105138	+	0.0763874i
$322$	−4.54422	+	13.9857i	−0.253240	+	0.779392i
$323$	−0.522640			−0.0290805
$324$	2.70036	−	8.31087i	0.150020	−	0.461715i
$325$	2.74589	+	10.6212i	0.152314	+	0.589157i
$326$	13.9096	−	10.1059i	0.770380	−	0.559714i
$327$	0.806533	+	2.48225i	0.0446014	+	0.137269i
$328$	1.86855	−	1.35758i	0.103173	−	0.0749599i
$329$	1.69748	+	5.22429i	0.0935849	+	0.288025i
$330$	0.530343	+	1.14961i	0.0291944	+	0.0632841i
$331$	1.24588	−	3.83442i	0.0684796	−	0.210759i	−0.910961	−	0.412494i	$-0.864658\pi$
$331$	1.24588	−	3.83442i	0.0684796	−	0.210759i	0.979440	+	0.201735i	$0.0646579\pi$
$332$	−3.02678	−	9.31546i	−0.166116	−	0.511252i
$333$	13.4829	−	9.79591i	0.738859	−	0.536812i
$334$	6.75213	−	20.7809i	0.369460	−	1.13708i
$335$	16.8366	+	13.0374i	0.919879	+	0.712307i
$336$	−0.649347	+	0.471778i	−0.0354248	+	0.0257376i
$337$	−0.580069	+	1.78527i	−0.0315984	+	0.0972499i	−0.965612	−	0.259988i	$-0.916281\pi$
$337$	−0.580069	+	1.78527i	−0.0315984	+	0.0972499i	0.934013	+	0.357238i	$0.116281\pi$
$338$	−8.18602			−0.445261
$339$	−0.849523	+	2.61456i	−0.0461397	+	0.142004i
$340$	0.489196	+	0.0149665i	0.0265304	+	0.000811673i
$341$	2.32033	−	13.8915i	0.125653	−	0.752270i
$342$	2.19212	−	6.74667i	0.118537	−	0.364818i
$343$	−11.7765	−	36.2442i	−0.635869	−	1.95700i
$344$	−2.76189	+	2.00663i	−0.148911	+	0.108190i
$345$	−0.334050	−	1.14625i	−0.0179846	−	0.0617120i
$346$	11.6179			0.624581
$347$	−12.8437			−0.689486			−0.344743	−	0.938697i	$-0.612034\pi$
$347$	−12.8437			−0.689486			−0.344743	+	0.938697i	$0.612034\pi$
$348$	0.747140			0.0400509
$349$	−13.2426	−	9.62131i	−0.708860	−	0.515017i	0.173946	−	0.984755i	$-0.444348\pi$
$349$	−13.2426	−	9.62131i	−0.708860	−	0.515017i	−0.882806	+	0.469738i	$0.844348\pi$
$350$	−8.61761	+	21.8718i	−0.460631	+	1.16910i
$351$	2.23644			0.119372
$352$	−0.546412	+	3.27130i	−0.0291239	+	0.174361i
$353$	4.32476	+	13.3102i	0.230184	+	0.708433i	0.997724	+	0.0674318i	$0.0214805\pi$
$353$	4.32476	+	13.3102i	0.230184	+	0.708433i	−0.767540	+	0.641001i	$0.778519\pi$
$354$	−1.41191	+	1.02582i	−0.0750424	+	0.0545215i
$355$	9.46392	−	26.3558i	0.502293	−	1.39882i
$356$	5.07161	+	15.6088i	0.268795	+	0.827265i
$357$	0.0542879	−	0.167081i	0.00287322	−	0.00884286i
$358$	−11.3738	−	8.26358i	−0.601126	−	0.436744i
$359$	−2.11731	+	6.51640i	−0.111747	+	0.343923i	−0.991255	−	0.131962i	$-0.957872\pi$
$359$	−2.11731	+	6.51640i	−0.111747	+	0.343923i	0.879507	+	0.475885i	$0.157872\pi$
$360$	−2.24505	+	6.25218i	−0.118325	+	0.329519i
$361$	−4.10941	+	12.6475i	−0.216285	+	0.665656i
$362$	7.70255	−	5.59623i	0.404837	−	0.294131i
$363$	1.12921	−	1.50040i	0.0592683	−	0.0787507i
$364$	8.34565	+	6.06347i	0.437431	+	0.317812i
$365$	−8.36081	+	23.2838i	−0.437625	+	1.21873i
$366$	−1.12670			−0.0588937
$367$	−5.98410	−	18.4172i	−0.312368	−	0.961368i	−0.976824	−	0.214042i	$-0.931337\pi$
$367$	−5.98410	−	18.4172i	−0.312368	−	0.961368i	0.664457	−	0.747327i	$-0.268663\pi$
$368$	0.966516	−	2.97463i	0.0503831	−	0.155063i
$369$	−5.55120	−	4.03318i	−0.288984	−	0.209959i
$370$	−10.3689	+	7.05929i	−0.539052	+	0.366995i
$371$	−0.545834	+	1.67990i	−0.0283383	+	0.0872163i
$372$	−0.586484	+	0.426105i	−0.0304078	+	0.0220925i
$373$	21.2629	+	15.4484i	1.10095	+	0.799889i	0.981215	−	0.192917i	$-0.0617948\pi$
$373$	21.2629	+	15.4484i	1.10095	+	0.799889i	0.119737	+	0.992806i	$0.461795\pi$
$374$	−0.324107	−	0.649566i	−0.0167592	−	0.0335883i
$375$	−0.421001	−	1.86163i	−0.0217404	−	0.0961340i
$376$	−0.361038	−	1.11116i	−0.0186191	−	0.0573038i
$377$	−2.96734	−	9.13255i	−0.152826	−	0.470350i
$378$	3.87716	+	2.81692i	0.199419	+	0.144887i
$379$	13.4922			0.693050			0.346525	−	0.938041i	$-0.387362\pi$
$379$	13.4922			0.693050			0.346525	+	0.938041i	$0.387362\pi$
$380$	−1.80445	+	5.02517i	−0.0925665	+	0.257786i
$381$	0.673168	+	2.07180i	0.0344874	+	0.106141i
$382$	−5.32087	−	3.86584i	−0.272240	−	0.197794i
$383$	4.59910			0.235003			0.117502	−	0.993073i	$-0.462511\pi$
$383$	4.59910			0.235003			0.117502	+	0.993073i	$0.462511\pi$
$384$	0.138110	−	0.100343i	0.00704791	−	0.00512061i
$385$	34.6256	−	4.10738i	1.76469	−	0.209331i
$386$	−15.7649	−	11.4539i	−0.802413	−	0.582987i
$387$	8.20517	+	5.96140i	0.417092	+	0.303035i
$388$	6.34108			0.321920
$389$	−6.38232			−0.323596			−0.161798	−	0.986824i	$-0.551729\pi$
$389$	−6.38232			−0.323596			−0.161798	+	0.986824i	$0.551729\pi$
$390$	−0.837148	−	0.0256118i	−0.0423906	−	0.00129690i
$391$	0.211549	+	0.651080i	0.0106985	+	0.0329265i
$392$	4.66787	+	14.3662i	0.235763	+	0.725604i
$393$	−2.29446	−	1.66702i	−0.115740	−	0.0840902i
$394$	−8.48193			−0.427314
$395$	4.32475	+	14.8398i	0.217602	+	0.746673i
$396$	9.74455	−	1.45934i	0.489682	−	0.0733348i
$397$	−6.84229	−	21.0584i	−0.343405	−	1.05689i	−0.962432	−	0.271522i	$-0.912473\pi$
$397$	−6.84229	−	21.0584i	−0.343405	−	1.05689i	0.619027	−	0.785369i	$-0.287527\pi$
$398$	0.0856352	−	0.263558i	0.00429250	−	0.0132110i
$399$	1.55052	+	1.12652i	0.0776232	+	0.0563965i
$400$	1.83289	−	4.65194i	0.0916445	−	0.232597i
$401$	2.99832	−	9.22787i	0.149729	−	0.460818i	−0.847860	−	0.530220i	$-0.822109\pi$
$401$	2.99832	−	9.22787i	0.149729	−	0.460818i	0.997589	+	0.0694023i	$0.0221092\pi$
$402$	−1.31523	+	0.955572i	−0.0655978	+	0.0476596i
$403$	7.53771	+	5.47646i	0.375480	+	0.272802i
$404$	4.75397	−	14.6312i	0.236519	−	0.727931i
$405$	19.5309	+	0.597529i	0.970497	+	0.0296915i
$406$	6.35867	−	19.5700i	0.315576	−	0.971242i
$407$	16.5059	+	8.58606i	0.818165	+	0.425595i
$408$	−0.0115466	+	0.0355366i	−0.000571640	+	0.00175933i
$409$	−2.66259	−	1.93449i	−0.131657	−	0.0956543i	0.520008	−	0.854162i	$-0.325929\pi$
$409$	−2.66259	−	1.93449i	−0.131657	−	0.0956543i	−0.651665	+	0.758507i	$0.725929\pi$
$410$	4.08342	+	3.16199i	0.201666	+	0.156160i
$411$	1.94912			0.0961431
$412$	−1.60328	−	4.93439i	−0.0789880	−	0.243100i
$413$	14.8530	+	45.7129i	0.730870	+	2.24939i
$414$	−9.29198			−0.456676
$415$	18.1044	−	12.3258i	0.888712	−	0.605049i
$416$	−1.77505	−	1.28965i	−0.0870288	−	0.0632301i
$417$	0.995178	−	3.06284i	0.0487341	−	0.149988i
$418$	7.83215	−	1.17294i	0.383083	−	0.0573706i
$419$	−7.42409	+	22.8490i	−0.362691	+	1.11625i	0.588724	+	0.808334i	$0.299631\pi$
$419$	−7.42409	+	22.8490i	−0.362691	+	1.11625i	−0.951415	+	0.307913i	$0.900369\pi$
$420$	−1.41905	−	1.09884i	−0.0692423	−	0.0536177i
$421$	7.27806	−	22.3996i	0.354711	−	1.09169i	−0.601466	−	0.798899i	$-0.705416\pi$
$421$	7.27806	−	22.3996i	0.354711	−	1.09169i	0.956177	−	0.292790i	$-0.0945836\pi$
$422$	22.5588	+	16.3899i	1.09814	+	0.797848i
$423$	−2.80808	+	2.04019i	−0.136534	+	0.0991975i
$424$	0.116094	−	0.357301i	0.00563802	−	0.0173521i
$425$	0.273925	+	1.05955i	0.0132873	+	0.0513958i
$426$	1.72963	+	1.25665i	0.0838007	+	0.0608848i
$427$	−9.58901	+	29.5119i	−0.464045	+	1.42818i
$428$	−4.21473	−	12.9716i	−0.203727	−	0.627006i
$429$	0.554635	+	1.11158i	0.0267780	+	0.0536678i
$430$	−6.03566	−	4.67371i	−0.291066	−	0.225386i
$431$	21.1041			1.01655			0.508275	−	0.861195i	$-0.330283\pi$
$431$	21.1041			1.01655			0.508275	+	0.861195i	$0.330283\pi$
$432$	−0.824637	−	0.599134i	−0.0396754	−	0.0288258i
$433$	−6.21354	−	19.1233i	−0.298603	−	0.919007i	−0.981987	−	0.188948i	$-0.939492\pi$
$433$	−6.21354	−	19.1233i	−0.298603	−	0.919007i	0.683384	−	0.730059i	$-0.260508\pi$
$434$	6.16968	+	18.9883i	0.296154	+	0.911469i
$435$	0.467432	+	1.60393i	0.0224116	+	0.0769027i
$436$	−15.2887			−0.732197
$437$	−7.46841			−0.357262
$438$	−1.52802	−	1.11017i	−0.0730117	−	0.0530461i
$439$	25.5250	+	18.5450i	1.21824	+	0.885104i	0.995953	−	0.0898775i	$-0.0286475\pi$
$439$	25.5250	+	18.5450i	1.21824	+	0.885104i	0.222288	+	0.974981i	$0.428648\pi$
$440$	−7.36456	+	0.873603i	−0.351092	+	0.0416474i
$441$	36.3058	−	26.3777i	1.72885	−	1.25608i
$442$	0.480235			0.0228424
$443$	−13.0227	−	9.46153i	−0.618726	−	0.449531i	0.233750	−	0.972297i	$-0.424900\pi$
$443$	−13.0227	−	9.46153i	−0.618726	−	0.449531i	−0.852476	+	0.522766i	$0.824900\pi$
$444$	−0.295934	−	0.910792i	−0.0140444	−	0.0432243i
$445$	−30.3354	+	20.6528i	−1.43804	+	0.979038i
$446$	−3.48435			−0.164989
$447$	−0.449399	−	0.326507i	−0.0212558	−	0.0154433i
$448$	−1.45289	−	4.47154i	−0.0686426	−	0.211260i
$449$	4.40590	+	13.5600i	0.207927	+	0.639934i	0.999580	+	0.0289636i	$0.00922068\pi$
$449$	4.40590	+	13.5600i	0.207927	+	0.639934i	−0.791653	+	0.610971i	$0.790779\pi$
$450$	−14.8265	−	0.908056i	−0.698928	−	0.0428062i
$451$	1.26202	−	7.55559i	0.0594263	−	0.355779i
$452$	−13.0281	−	9.46549i	−0.612791	−	0.445219i
$453$	0.200597	−	0.145742i	0.00942488	−	0.00684757i
$454$	−2.14994	+	6.61683i	−0.100902	+	0.310543i
$455$	−7.79556	+	21.7096i	−0.365461	+	1.01776i
$456$	−0.329782	−	0.239601i	−0.0154435	−	0.0112203i
$457$	2.16777	−	6.67171i	0.101404	−	0.312089i	−0.887466	−	0.460874i	$-0.847536\pi$
$457$	2.16777	−	6.67171i	0.101404	−	0.312089i	0.988870	+	0.148784i	$0.0475360\pi$
$458$	−3.76849	−	11.5982i	−0.176090	−	0.541950i
$459$	0.223104			0.0104136
$460$	6.99051	+	0.213868i	0.325934	+	0.00997165i
$461$	−24.3916	−	17.7216i	−1.13603	−	0.825375i	−0.149470	−	0.988766i	$-0.547757\pi$
$461$	−24.3916	−	17.7216i	−1.13603	−	0.825375i	−0.986561	+	0.163391i	$0.947757\pi$
$462$	−0.438570	+	2.62567i	−0.0204041	+	0.122157i
$463$	−32.5332	+	23.6368i	−1.51195	+	1.09849i	−0.546644	+	0.837365i	$0.684095\pi$
$463$	−32.5332	+	23.6368i	−1.51195	+	1.09849i	−0.965304	+	0.261130i	$0.915905\pi$
$464$	−1.35243	+	4.16236i	−0.0627852	+	0.193233i
$465$	−1.28167	−	0.992458i	−0.0594359	−	0.0460241i
$466$	−7.34135	+	22.5943i	−0.340081	+	1.04666i
$467$	−14.6892	−	10.6723i	−0.679735	−	0.493857i	0.193535	−	0.981093i	$-0.438005\pi$
$467$	−14.6892	−	10.6723i	−0.679735	−	0.493857i	−0.873270	+	0.487237i	$0.838005\pi$
$468$	−2.01426	+	6.19926i	−0.0931093	+	0.286561i
$469$	13.8359	+	42.5827i	0.638885	+	1.96629i
$470$	2.15952	−	1.47024i	0.0996114	−	0.0678170i
$471$	0.623493	−	0.452994i	0.0287290	−	0.0208729i
$472$	−3.15911	−	9.72274i	−0.145410	−	0.447525i
$473$	−1.86538	+	11.1678i	−0.0857704	+	0.513498i
$474$	−1.18009			−0.0542032
$475$	−11.9168	−	0.729848i	−0.546778	−	0.0334877i
$476$	0.832549	+	0.604882i	0.0381598	+	0.0277247i
$477$	−1.11612			−0.0511034
$478$	29.6471			1.35603
$479$	−31.7529			−1.45083			−0.725414	−	0.688313i	$-0.758352\pi$
$479$	−31.7529			−1.45083			−0.725414	+	0.688313i	$0.758352\pi$
$480$	0.301818	+	0.233713i	0.0137761	+	0.0106675i
$481$	−9.95758	+	7.23461i	−0.454027	+	0.329870i
$482$	0.387443	+	1.19243i	0.0176475	+	0.0543136i
$483$	0.775761	−	2.38755i	0.0352984	−	0.108637i
$484$	6.31479	+	9.00686i	0.287036	+	0.409403i
$485$	3.96716	+	13.6128i	0.180139	+	0.618125i
$486$	−1.40594	+	4.32704i	−0.0637747	+	0.196278i
$487$	−27.3332			−1.23859			−0.619293	−	0.785160i	$-0.712581\pi$
$487$	−27.3332			−1.23859			−0.619293	+	0.785160i	$0.712581\pi$
$488$	2.03950	−	6.27693i	0.0923237	−	0.284143i
$489$	−2.37456	+	1.72522i	−0.107381	+	0.0780169i
$490$	−27.9205	+	19.0087i	−1.26132	+	0.858726i
$491$	6.47429	−	19.9258i	0.292181	−	0.899240i	−0.691973	−	0.721923i	$-0.743258\pi$
$491$	6.47429	−	19.9258i	0.292181	−	0.899240i	0.984154	−	0.177317i	$-0.0567416\pi$
$492$	−0.318987	+	0.231758i	−0.0143811	+	0.0104484i
$493$	−0.296018	−	0.911048i	−0.0133320	−	0.0410316i
$494$	−1.61896	+	4.98264i	−0.0728403	+	0.224180i
$495$	9.22933	+	20.0062i	0.414827	+	0.899213i
$496$	−1.31224	−	4.03865i	−0.0589211	−	0.181341i
$497$	47.6359	−	34.6095i	2.13676	−	1.55245i
$498$	0.516712	+	1.59028i	0.0231544	+	0.0712620i
$499$	−0.723360	+	0.525552i	−0.0323820	+	0.0235269i	−0.603859	−	0.797091i	$-0.706371\pi$
$499$	−0.723360	+	0.525552i	−0.0323820	+	0.0235269i	0.571477	+	0.820618i	$0.306371\pi$
$500$	11.1333	+	1.02440i	0.497897	+	0.0458125i
$501$	−1.15268	+	3.54759i	−0.0514980	+	0.158495i
$502$	−13.8932			−0.620086
$503$	−6.60282	+	20.3214i	−0.294405	+	0.906086i	0.689015	+	0.724747i	$0.258043\pi$
$503$	−6.60282	+	20.3214i	−0.294405	+	0.906086i	−0.983421	+	0.181340i	$0.941957\pi$
$504$	−11.3003	+	8.21015i	−0.503355	+	0.365709i
$505$	34.3840	+	1.05195i	1.53007	+	0.0468110i
$506$	−4.63142	−	9.28215i	−0.205892	−	0.412642i
$507$	1.39747			0.0620637
$508$	−12.7606			−0.566162
$509$	39.2527			1.73985			0.869923	−	0.493188i	$-0.164169\pi$
$509$	39.2527			1.73985			0.869923	+	0.493188i	$0.164169\pi$
$510$	−0.0835126	−	0.00255499i	−0.00369800	−	0.000113137i
$511$	−42.0835	+	30.5754i	−1.86166	+	1.35258i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−0.752123	+	2.31480i	−0.0332070	+	0.102201i
$514$	1.74748	+	5.37820i	0.0770782	+	0.237222i
$515$	9.58991	−	6.52896i	0.422582	−	0.287700i
$516$	0.471492	−	0.342559i	0.0207563	−	0.0150803i
$517$	−3.43767	−	1.78822i	−0.151189	−	0.0786457i
$518$	−26.3751			−1.15886
$519$	−1.98333			−0.0870586
$520$	1.65805	−	4.61744i	0.0727101	−	0.202488i
$521$	−5.09207	−	3.69960i	−0.223087	−	0.162083i	0.470628	−	0.882332i	$-0.344027\pi$
$521$	−5.09207	−	3.69960i	−0.223087	−	0.162083i	−0.693715	+	0.720249i	$0.744027\pi$
$522$	13.0022			0.569089
$523$	8.96273	−	6.51180i	0.391913	−	0.284741i	−0.374326	−	0.927297i	$-0.622126\pi$
$523$	8.96273	−	6.51180i	0.391913	−	0.284741i	0.766239	+	0.642556i	$0.222126\pi$
$524$	13.4404	−	9.76502i	0.587146	−	0.426587i
$525$	1.47115	−	3.73382i	0.0642060	−	0.162957i
$526$	7.90330	+	24.3238i	0.344600	+	1.06057i
$527$	0.751950	+	0.546323i	0.0327554	+	0.0237982i
$528$	0.0932800	−	0.558457i	0.00405949	−	0.0243037i
$529$	−4.08441	−	12.5705i	−0.177583	−	0.546544i
$530$	0.839671	+	0.0256890i	0.0364730	+	0.00111586i
$531$	−24.5709	+	17.8518i	−1.06629	+	0.774703i
$532$	−9.08258	+	6.59888i	−0.393780	+	0.286098i
$533$	4.09974	+	2.97864i	0.177580	+	0.129019i
$534$	−0.865793	−	2.66464i	−0.0374665	−	0.115310i
$535$	25.2101	−	17.1634i	1.08993	−	0.742039i
$536$	−2.94278	−	9.05696i	−0.127109	−	0.391201i
$537$	1.94167	+	1.41071i	0.0837893	+	0.0608765i
$538$	−25.1973	+	18.3069i	−1.08633	+	0.789268i
$539$	44.4457	+	23.1199i	1.91441	+	0.995845i
$540$	0.770282	−	2.14513i	0.0331477	−	0.0923119i
$541$	21.7894	+	15.8309i	0.936800	+	0.680625i	0.947648	−	0.319316i	$-0.103453\pi$
$541$	21.7894	+	15.8309i	0.936800	+	0.680625i	−0.0108484	+	0.999941i	$0.503453\pi$
$542$	−0.535662	+	0.389181i	−0.0230086	+	0.0167168i
$543$	−1.31493	+	0.955354i	−0.0564291	+	0.0409982i
$544$	−0.177076	−	0.128653i	−0.00759206	−	0.00551595i
$545$	−9.56506	−	32.8213i	−0.409722	−	1.40591i
$546$	−1.42472	−	1.03512i	−0.0609723	−	0.0442989i
$547$	2.86486	−	8.81713i	0.122492	−	0.376993i	−0.870943	−	0.491383i	$-0.836491\pi$
$547$	2.86486	−	8.81713i	0.122492	−	0.376993i	0.993436	+	0.114390i	$0.0364914\pi$
$548$	−3.52820	+	10.8587i	−0.150717	+	0.463859i
$549$	−19.6075			−0.836829
$550$	−6.48290	−	15.2634i	−0.276432	−	0.650834i
$551$	10.4504			0.445204
$552$	−0.164998	+	0.507810i	−0.00702276	+	0.0216138i
$553$	−10.0433	+	30.9102i	−0.427086	+	1.31444i
$554$	1.10682	+	0.804153i	0.0470244	+	0.0341652i
$555$	1.77011	−	1.20512i	0.0751370	−	0.0511544i
$556$	15.2619	+	11.0884i	0.647247	+	0.470253i
$557$	−19.3753	+	14.0770i	−0.820958	+	0.596461i	−0.916987	−	0.398917i	$-0.869386\pi$
$557$	−19.3753	+	14.0770i	−0.820958	+	0.596461i	0.0960285	+	0.995379i	$0.469386\pi$
$558$	−10.2063	+	7.41532i	−0.432068	+	0.313916i
$559$	−6.05979	−	4.40269i	−0.256302	−	0.186214i
$560$	8.69036	−	5.91653i	0.367235	−	0.250019i
$561$	0.0553295	+	0.110890i	0.00233601	+	0.00468178i
$562$	15.6850	−	11.3958i	0.661630	−	0.480703i
$563$	−4.66068	−	3.38618i	−0.196424	−	0.142711i	0.485226	−	0.874389i	$-0.338737\pi$
$563$	−4.66068	−	3.38618i	−0.196424	−	0.142711i	−0.681650	+	0.731678i	$0.738737\pi$
$564$	0.0616342	+	0.189690i	0.00259527	+	0.00798741i
$565$	12.1694	−	33.8902i	0.511970	−	1.42577i
$566$	−6.48569	−	19.9609i	−0.272614	−	0.839020i
$567$	33.2390	+	24.1496i	1.39591	+	1.01419i
$568$	−10.1317	+	7.36114i	−0.425118	+	0.308867i
$569$	7.74004	−	5.62347i	0.324479	−	0.235748i	−0.413605	−	0.910456i	$-0.635731\pi$
$569$	7.74004	−	5.62347i	0.324479	−	0.235748i	0.738085	+	0.674708i	$0.235731\pi$
$570$	0.308045	−	0.857865i	0.0129026	−	0.0359320i
$571$	−3.00435	−	9.24645i	−0.125728	−	0.386952i	0.868305	−	0.496031i	$-0.165210\pi$
$571$	−3.00435	−	9.24645i	−0.125728	−	0.386952i	−0.994033	+	0.109079i	$0.965210\pi$
$572$	−7.19667	+	1.07777i	−0.300908	+	0.0450640i
$573$	0.908346	+	0.659952i	0.0379467	+	0.0275699i
$574$	3.35568	+	10.3277i	0.140063	+	0.431070i
$575$	3.91433	+	15.1408i	0.163239	+	0.631413i
$576$	2.40347	−	1.74623i	0.100145	−	0.0727594i
$577$	23.9688	−	17.4143i	0.997833	−	0.724968i	0.0362106	−	0.999344i	$-0.488471\pi$
$577$	23.9688	−	17.4143i	0.997833	−	0.724968i	0.961622	+	0.274376i	$0.0884713\pi$
$578$	−16.9521			−0.705114
$579$	2.69129	+	1.95534i	0.111846	+	0.0812610i
$580$	−9.78173	−	0.299263i	−0.406164	−	0.0124262i
$581$	46.0520			1.91056
$582$	−1.08251			−0.0448715
$583$	−0.556307	−	1.11493i	−0.0230399	−	0.0461759i
$584$	8.95079	−	6.50313i	0.370386	−	0.269101i
$585$	−14.5685	−	0.445711i	−0.602334	−	0.0184279i
$586$	5.43235	+	16.7190i	0.224408	+	0.690657i
$587$	−4.67148	+	14.3773i	−0.192812	+	0.593416i	0.807183	+	0.590302i	$0.200991\pi$
$587$	−4.67148	+	14.3773i	−0.192812	+	0.593416i	−0.999995	+	0.00311397i	$0.999009\pi$
$588$	−0.796869	−	2.45251i	−0.0328623	−	0.101140i
$589$	−8.20330	+	5.96005i	−0.338011	+	0.245579i
$590$	18.8960	−	12.8647i	0.777935	−	0.529630i
$591$	1.44798			0.0595620
$592$	5.60976			0.230560
$593$	35.5872			1.46139			0.730695	−	0.682704i	$-0.239196\pi$
$593$	35.5872			1.46139			0.730695	+	0.682704i	$0.239196\pi$
$594$	−3.34338	+	0.500704i	−0.137180	+	0.0205441i
$595$	−0.777672	+	2.16572i	−0.0318815	+	0.0887857i
$596$	2.63247	−	1.91260i	0.107830	−	0.0783432i
$597$	−0.0146191	+	0.0449930i	−0.000598320	+	0.00184144i
$598$	6.86244			0.280626
$599$	0.479674	−	1.47628i	0.0195989	−	0.0603194i	−0.940779	−	0.339021i	$-0.889904\pi$
$599$	0.479674	−	1.47628i	0.0195989	−	0.0603194i	0.960378	+	0.278702i	$0.0899041\pi$
$600$	−0.312900	+	0.794150i	−0.0127741	+	0.0324210i
$601$	−15.6247	+	11.3520i	−0.637345	+	0.463059i	−0.858937	−	0.512081i	$-0.828875\pi$
$601$	−15.6247	+	11.3520i	−0.637345	+	0.463059i	0.221592	+	0.975140i	$0.428875\pi$
$602$	−4.95999	−	15.2653i	−0.202154	−	0.622167i
$603$	−22.8884	+	16.6294i	−0.932088	+	0.677201i
$604$	0.448829	+	1.38135i	0.0182626	+	0.0562065i
$605$	−15.3849	+	19.1913i	−0.625484	+	0.780237i
$606$	−0.811569	+	2.49775i	−0.0329677	+	0.101464i
$607$	−10.2166	−	31.4436i	−0.414680	−	1.27626i	−0.912536	−	0.408995i	$-0.865879\pi$
$607$	−10.2166	−	31.4436i	−0.414680	−	1.27626i	0.497856	−	0.867260i	$-0.334121\pi$
$608$	1.93179	−	1.40352i	0.0783442	−	0.0569204i
$609$	−1.08551	+	3.34087i	−0.0439872	+	0.135379i
$610$	14.7510	+	0.451295i	0.597252	+	0.0182724i
$611$	2.07386	−	1.50675i	0.0838995	−	0.0609566i
$612$	−0.200940	+	0.618428i	−0.00812250	+	0.0249985i
$613$	−35.4602			−1.43222			−0.716111	−	0.697986i	$-0.754080\pi$
$613$	−35.4602			−1.43222			−0.716111	+	0.697986i	$0.754080\pi$
$614$	−0.745257	+	2.29366i	−0.0300761	+	0.0925648i
$615$	−0.697096	−	0.539796i	−0.0281096	−	0.0217667i
$616$	−13.8339	−	7.19615i	−0.557383	−	0.289941i
$617$	6.44417	−	19.8331i	0.259433	−	0.798451i	−0.733491	−	0.679699i	$-0.762110\pi$
$617$	6.44417	−	19.8331i	0.259433	−	0.798451i	0.992924	−	0.118753i	$-0.0378895\pi$
$618$	0.273702	+	0.842368i	0.0110099	+	0.0338850i
$619$	29.0492	−	21.1055i	1.16758	−	0.848300i	0.176867	−	0.984235i	$-0.443404\pi$
$619$	29.0492	−	21.1055i	1.16758	−	0.848300i	0.990718	+	0.135935i	$0.0434039\pi$
$620$	7.84905	−	5.34375i	0.315225	−	0.214610i
$621$	3.18810			0.127934
$622$	−22.8396			−0.915786
$623$	−77.1638			−3.09150
$624$	0.303025	+	0.220160i	0.0121307	+	0.00881347i
$625$	4.76617	+	24.5415i	0.190647	+	0.981659i
$626$	2.13872			0.0854804
$627$	−1.33706	+	0.200238i	−0.0533969	+	0.00799672i
$628$	1.39504	+	4.29350i	0.0556683	+	0.171329i
$629$	−0.993353	+	0.721713i	−0.0396076	+	0.0287766i
$630$	−24.6950	−	19.1226i	−0.983873	−	0.761861i
$631$	10.5579	+	32.4940i	0.420305	+	1.29356i	0.907419	+	0.420227i	$0.138049\pi$
$631$	10.5579	+	32.4940i	0.420305	+	1.29356i	−0.487114	+	0.873338i	$0.661951\pi$
$632$	2.13613	−	6.57433i	0.0849707	−	0.261513i
$633$	−3.85109	−	2.79798i	−0.153067	−	0.111210i
$634$	−10.1624	+	31.2766i	−0.403600	+	1.24215i
$635$	−7.98342	−	27.3941i	−0.316812	−	1.08710i
$636$	−0.0198188	+	0.0609961i	−0.000785868	+	0.00241865i
$637$	−26.8130	+	19.4808i	−1.06237	+	0.771858i
$638$	6.48068	+	12.9884i	0.256573	+	0.514216i
$639$	30.1000	+	21.8689i	1.19074	+	0.865120i
$640$	−1.84836	+	1.25839i	−0.0730630	+	0.0497424i
$641$	−11.5874			−0.457674			−0.228837	−	0.973465i	$-0.573492\pi$
$641$	−11.5874			−0.457674			−0.228837	+	0.973465i	$0.573492\pi$
$642$	0.719512	+	2.21443i	0.0283969	+	0.0873966i
$643$	8.09260	−	24.9065i	0.319141	−	0.982215i	−0.654875	−	0.755737i	$-0.727279\pi$
$643$	8.09260	−	24.9065i	0.319141	−	0.982215i	0.974016	−	0.226478i	$-0.0727211\pi$
$644$	11.8969	+	8.64363i	0.468805	+	0.340607i
$645$	1.03037	+	0.797866i	0.0405708	+	0.0314160i
$646$	−0.161505	+	0.497060i	−0.00635431	+	0.0195566i
$647$	7.38077	−	5.36244i	0.290168	−	0.210819i	−0.433172	−	0.901311i	$-0.642606\pi$
$647$	7.38077	−	5.36244i	0.290168	−	0.210819i	0.723340	+	0.690492i	$0.242606\pi$
$648$	−7.06964	−	5.13640i	−0.277722	−	0.201777i
$649$	−30.0799	−	15.6470i	−1.18074	−	0.614200i
$650$	10.9499	+	0.670630i	0.429489	+	0.0263043i
$651$	−1.05325	−	3.24157i	−0.0412801	−	0.127047i
$652$	−5.31298	−	16.3517i	−0.208073	−	0.640381i
$653$	3.94753	+	2.86805i	0.154479	+	0.112235i	0.662340	−	0.749204i	$-0.269564\pi$
$653$	3.94753	+	2.86805i	0.154479	+	0.112235i	−0.507861	+	0.861439i	$0.669564\pi$
$654$	2.61000			0.102059
$655$	29.3719	+	22.7441i	1.14765	+	0.888684i
$656$	−0.713723	−	2.19661i	−0.0278662	−	0.0857633i
$657$	−26.5915	−	19.3199i	−1.03743	−	0.753740i
$658$	5.49315			0.214145
$659$	−10.3340	+	7.50807i	−0.402554	+	0.292473i	−0.770581	−	0.637343i	$-0.780034\pi$
$659$	−10.3340	+	7.50807i	−0.402554	+	0.292473i	0.368026	+	0.929815i	$0.380034\pi$
$660$	1.25723	−	0.149136i	0.0489377	−	0.00580512i
$661$	24.2834	+	17.6429i	0.944513	+	0.686229i	0.949503	−	0.313758i	$-0.101588\pi$
$661$	24.2834	+	17.6429i	0.944513	+	0.686229i	−0.00498943	+	0.999988i	$0.501588\pi$
$662$	−3.26175	−	2.36980i	−0.126771	−	0.0921049i
$663$	−0.0819826			−0.00318394
$664$	−9.79485			−0.380114
$665$	−19.8486	−	15.3697i	−0.769694	−	0.596012i
$666$	−5.15001	−	15.8501i	−0.199559	−	0.614179i
$667$	−4.23002	−	13.0187i	−0.163787	−	0.504085i
$668$	−17.6773	−	12.8433i	−0.683955	−	0.496923i
$669$	0.594826			0.0229973
$670$	17.6020	−	11.9837i	0.680026	−	0.462972i
$671$	−9.77300	−	19.5868i	−0.377283	−	0.756139i
$672$	0.248028	+	0.763353i	0.00956790	+	0.0294470i
$673$	8.64920	−	26.6195i	0.333402	−	1.02611i	−0.634102	−	0.773250i	$-0.718630\pi$
$673$	8.64920	−	26.6195i	0.333402	−	1.02611i	0.967504	−	0.252856i	$-0.0813700\pi$
$674$	1.51864	+	1.10336i	0.0584959	+	0.0424997i
$675$	5.08701	+	0.311556i	0.195799	+	0.0119918i
$676$	−2.52962	+	7.78537i	−0.0972931	+	0.299437i
$677$	22.5501	−	16.3836i	0.866672	−	0.629674i	−0.0630195	−	0.998012i	$-0.520073\pi$
$677$	22.5501	−	16.3836i	0.866672	−	0.629674i	0.929692	+	0.368338i	$0.120073\pi$
$678$	2.22408	+	1.61589i	0.0854153	+	0.0620578i
$679$	−9.21290	+	28.3544i	−0.353559	+	1.08814i
$680$	0.165404	−	0.460629i	0.00634295	−	0.0176643i
$681$	0.367024	−	1.12958i	0.0140644	−	0.0432858i
$682$	−12.4946	−	6.49949i	−0.478444	−	0.248878i
$683$	−6.16497	+	18.9738i	−0.235896	+	0.726013i	0.761105	+	0.648628i	$0.224657\pi$
$683$	−6.16497	+	18.9738i	−0.235896	+	0.726013i	−0.997001	+	0.0773848i	$0.975343\pi$
$684$	−5.73906	−	4.16967i	−0.219438	−	0.159431i
$685$	−25.5183	−	0.780710i	−0.975005	−	0.0298294i
$686$	−38.1094			−1.45503
$687$	0.643333	+	1.97998i	0.0245447	+	0.0755408i
$688$	1.05495	+	3.24679i	0.0402194	+	0.123783i
$689$	0.824289			0.0314029
$690$	−1.19338	−	0.0365102i	−0.0454310	−	0.00138992i
$691$	5.62486	+	4.08670i	0.213980	+	0.155465i	0.689612	−	0.724179i	$-0.257781\pi$
$691$	5.62486	+	4.08670i	0.213980	+	0.155465i	−0.475633	+	0.879644i	$0.657781\pi$
$692$	3.59012	−	11.0493i	0.136476	−	0.420030i
$693$	−7.63225	+	45.6934i	−0.289925	+	1.73575i
$694$	−3.96892	+	12.2151i	−0.150658	+	0.463678i
$695$	−14.2559	+	39.7008i	−0.540757	+	1.50594i
$696$	0.230879	−	0.710573i	0.00875145	−	0.0269342i
$697$	0.408984	+	0.297144i	0.0154914	+	0.0112551i
$698$	−13.2426	+	9.62131i	−0.501240	+	0.364172i
$699$	1.25327	−	3.85717i	0.0474030	−	0.145891i
$700$	18.1383	+	14.9546i	0.685564	+	0.565230i
$701$	10.8193	+	7.86071i	0.408641	+	0.296895i	0.773051	−	0.634344i	$-0.218730\pi$
$701$	10.8193	+	7.86071i	0.408641	+	0.296895i	−0.364411	+	0.931238i	$0.618730\pi$
$702$	0.691098	−	2.12698i	0.0260838	−	0.0802777i
$703$	−4.13931	−	12.7395i	−0.156117	−	0.480479i
$704$	2.94235	+	1.53056i	0.110894	+	0.0576851i
$705$	−0.368660	+	0.250990i	−0.0138846	+	0.00945282i
$706$	13.9952			0.526717
$707$	58.5171	+	42.5152i	2.20076	+	1.59895i
$708$	0.539303	+	1.65980i	0.0202683	+	0.0623793i
$709$	9.46083	+	29.1174i	0.355309	+	1.09353i	0.955830	+	0.293919i	$0.0949597\pi$
$709$	9.46083	+	29.1174i	0.355309	+	1.09353i	−0.600521	+	0.799609i	$0.705040\pi$
$710$	−22.1413	−	17.1451i	−0.830949	−	0.643444i
$711$	−20.5365			−0.770180
$712$	16.4121			0.615068
$713$	10.7452	+	7.80684i	0.402410	+	0.292368i
$714$	−0.142128	−	0.103262i	−0.00531899	−	0.00386447i
$715$	−6.81617	−	14.7753i	−0.254910	−	0.552564i
$716$	−11.3738	+	8.26358i	−0.425060	+	0.308824i
$717$	−5.06117			−0.189013
$718$	5.54318	+	4.02736i	0.206870	+	0.150300i
$719$	−7.20244	−	22.1668i	−0.268606	−	0.826684i	−0.990841	−	0.135036i	$-0.956885\pi$
$719$	−7.20244	−	22.1668i	−0.268606	−	0.826684i	0.722235	−	0.691648i	$-0.243115\pi$
$720$	5.25241	+	4.06720i	0.195746	+	0.151576i
$721$	24.3937			0.908469
$722$	10.7586	+	7.81656i	0.400393	+	0.290902i
$723$	−0.0661418	−	0.203564i	−0.00245984	−	0.00757061i
$724$	−2.94211	−	9.05490i	−0.109343	−	0.336523i
$725$	−5.47728	−	21.1863i	−0.203421	−	0.786838i
$726$	−1.07802	−	1.53759i	−0.0400091	−	0.0570655i
$727$	−21.4290	−	15.5690i	−0.794756	−	0.577424i	0.114615	−	0.993410i	$-0.463437\pi$
$727$	−21.4290	−	15.5690i	−0.794756	−	0.577424i	−0.909371	+	0.415986i	$0.863437\pi$
$728$	8.34565	−	6.06347i	0.309310	−	0.224727i
$729$	−7.86108	+	24.1939i	−0.291151	+	0.896071i
$730$	19.5605	+	15.1467i	0.723968	+	0.560604i
$731$	−0.604515	−	0.439206i	−0.0223588	−	0.0162446i
$732$	−0.348170	+	1.07156i	−0.0128687	+	0.0396059i
$733$	−5.01490	−	15.4343i	−0.185230	−	0.570078i	0.814723	−	0.579851i	$-0.196889\pi$
$733$	−5.01490	−	15.4343i	−0.185230	−	0.570078i	−0.999952	+	0.00977264i	$0.996889\pi$
$734$	−19.3650			−0.714774
$735$	4.76642	−	3.24505i	0.175812	−	0.119695i
$736$	−2.53037	−	1.83842i	−0.0932707	−	0.0677652i
$737$	−28.0201	−	14.5756i	−1.03213	−	0.536898i
$738$	−5.55120	+	4.03318i	−0.204342	+	0.148463i
$739$	−3.49898	+	10.7687i	−0.128712	+	0.396135i	−0.994559	−	0.104174i	$-0.966780\pi$
$739$	−3.49898	+	10.7687i	−0.128712	+	0.396135i	0.865847	+	0.500309i	$0.166780\pi$
$740$	3.50962	+	12.0428i	0.129016	+	0.442703i
$741$	0.276378	−	0.850605i	0.0101530	−	0.0312478i
$742$	1.42901	+	1.03824i	0.0524607	+	0.0381149i
$743$	12.6515	−	38.9374i	0.464140	−	1.42848i	−0.395921	−	0.918285i	$-0.629575\pi$
$743$	12.6515	−	38.9374i	0.464140	−	1.42848i	0.860061	−	0.510191i	$-0.170425\pi$
$744$	0.224017	+	0.689453i	0.00821285	+	0.0252766i
$745$	5.75285	+	4.45471i	0.210768	+	0.163208i
$746$	21.2629	−	15.4484i	0.778491	−	0.565607i
$747$	8.99212	+	27.6749i	0.329004	+	1.01257i
$748$	−0.717929	+	0.107517i	−0.0262501	+	0.00393121i
$749$	64.1265			2.34313
$750$	−1.90061	−	0.174879i	−0.0694004	−	0.00638567i
$751$	−15.5890	−	11.3261i	−0.568851	−	0.413294i	0.265837	−	0.964018i	$-0.414352\pi$
$751$	−15.5890	−	11.3261i	−0.568851	−	0.413294i	−0.834688	+	0.550724i	$0.814352\pi$
$752$	−1.16834			−0.0426051
$753$	2.37177			0.0864320
$754$	−9.60253			−0.349703
$755$	−2.68464	+	1.82774i	−0.0977040	+	0.0665184i
$756$	3.87716	−	2.81692i	0.141011	−	0.102450i
$757$	−4.27973	−	13.1716i	−0.155549	−	0.478732i	0.842667	−	0.538435i	$-0.180984\pi$
$757$	−4.27973	−	13.1716i	−0.155549	−	0.478732i	−0.998216	+	0.0597038i	$0.980984\pi$
$758$	4.16933	−	12.8319i	0.151437	−	0.466075i
$759$	0.790646	+	1.58459i	0.0286986	+	0.0575170i
$760$	4.22161	+	3.26900i	0.153134	+	0.118579i
$761$	7.49081	−	23.0543i	0.271542	−	0.835719i	−0.718572	−	0.695452i	$-0.755204\pi$
$761$	7.49081	−	23.0543i	0.271542	−	0.835719i	0.990114	−	0.140267i	$-0.0447959\pi$
$762$	2.17842			0.0789157
$763$	22.2128	−	68.3641i	0.804159	−	2.47495i
$764$	−5.32087	+	3.86584i	−0.192502	+	0.139861i
$765$	−1.45333	−	0.0444634i	−0.0525453	−	0.00160758i
$766$	1.42120	−	4.37401i	0.0513501	−	0.158039i
$767$	18.1465	−	13.1842i	0.655231	−	0.476053i
$768$	−0.0527535	−	0.162358i	−0.00190358	−	0.00585861i
$769$	−15.3145	+	47.1332i	−0.552255	+	1.69967i	0.150830	+	0.988560i	$0.451805\pi$
$769$	−15.3145	+	47.1332i	−0.552255	+	1.69967i	−0.703085	+	0.711106i	$0.748195\pi$
$770$	6.79356	−	34.2002i	0.244823	−	1.23249i
$771$	−0.298320	−	0.918134i	−0.0107437	−	0.0330658i
$772$	−15.7649	+	11.4539i	−0.567392	+	0.412234i
$773$	5.18142	+	15.9468i	0.186363	+	0.573566i	0.999969	−	0.00785043i	$-0.00249889\pi$
$773$	5.18142	+	15.9468i	0.186363	+	0.573566i	−0.813606	+	0.581416i	$0.802499\pi$
$774$	8.20517	−	5.96140i	0.294929	−	0.214278i
$775$	16.3823	+	13.5068i	0.588471	+	0.485180i
$776$	1.95950	−	6.03073i	0.0703420	−	0.216490i
$777$	4.50260			0.161530
$778$	−1.97225	+	6.06995i	−0.0707084	+	0.217618i
$779$	−4.46176	+	3.24166i	−0.159859	+	0.116144i
$780$	−0.283051	+	0.788261i	−0.0101349	+	0.0282243i
$781$	−6.84300	+	40.9683i	−0.244862	+	1.46596i
$782$	0.684586			0.0244808
$783$	−4.46107			−0.159426
$784$	15.1055			0.539484
$785$	−8.34435	+	5.68096i	−0.297823	+	0.202762i
$786$	−2.29446	+	1.66702i	−0.0818407	+	0.0594607i
$787$	−3.67872	−	11.3219i	−0.131132	−	0.403583i	0.863836	−	0.503773i	$-0.168055\pi$
$787$	−3.67872	−	11.3219i	−0.131132	−	0.403583i	−0.994968	+	0.100190i	$0.968055\pi$
$788$	−2.62106	+	8.06680i	−0.0933714	+	0.287368i
$789$	−1.34920	−	4.15241i	−0.0480328	−	0.147830i
$790$	15.4500	+	0.472677i	0.549685	+	0.0168171i
$791$	61.2537	−	44.5034i	2.17793	−	1.58236i
$792$	1.62331	−	9.71858i	0.0576819	−	0.345335i
$793$	14.4808			0.514229
$794$	−22.1421			−0.785795
$795$	−0.143343	−	0.00438546i	−0.00508387	−	0.000155536i
$796$	−0.224196	−	0.162888i	−0.00794641	−	0.00577341i
$797$	29.8452			1.05717			0.528585	−	0.848880i	$-0.322723\pi$
$797$	29.8452			1.05717			0.528585	+	0.848880i	$0.322723\pi$
$798$	1.55052	−	1.12652i	0.0548879	−	0.0398784i
$799$	0.206885	−	0.150311i	0.00731908	−	0.00531762i
$800$	−3.85786	−	3.18071i	−0.136396	−	0.112455i
$801$	−15.0670	−	46.3715i	−0.532367	−	1.63846i
$802$	−7.84970	−	5.70314i	−0.277182	−	0.201385i
$803$	6.04538	−	36.1930i	0.213337	−	1.27722i
$804$	0.502374	+	1.54615i	0.0177174	+	0.0545284i
$805$	−11.1128	+	30.9476i	−0.391673	+	1.09076i
$806$	7.53771	−	5.47646i	0.265504	−	0.192900i
$807$	4.30153	−	3.12525i	0.151421	−	0.110014i
$808$	−12.4461	−	9.04260i	−0.437851	−	0.318117i
$809$	−9.94195	−	30.5982i	−0.349540	−	1.07577i	−0.959108	−	0.283040i	$-0.908657\pi$
$809$	−9.94195	−	30.5982i	−0.349540	−	1.07577i	0.609568	−	0.792734i	$-0.291343\pi$
$810$	6.60366	−	18.3903i	0.232029	−	0.646170i
$811$	−4.85092	−	14.9296i	−0.170339	−	0.524249i	0.829051	−	0.559173i	$-0.188881\pi$
$811$	−4.85092	−	14.9296i	−0.170339	−	0.524249i	−0.999390	+	0.0349240i	$0.988881\pi$
$812$	−16.6472	−	12.0949i	−0.584203	−	0.424448i
$813$	0.0914449	−	0.0664386i	0.00320711	−	0.00233010i
$814$	13.2664	−	13.0448i	0.464988	−	0.457219i
$815$	31.7792	−	21.6358i	1.11318	−	0.757869i
$816$	0.0302293	+	0.0219628i	0.00105824	+	0.000768853i
$817$	6.59488	−	4.79146i	0.230726	−	0.167632i
$818$	−2.66259	+	1.93449i	−0.0930954	+	0.0676378i
$819$	−24.7937	−	18.0137i	−0.866363	−	0.629450i
$820$	4.26908	−	2.90646i	0.149083	−	0.101498i
$821$	−27.6328	−	20.0764i	−0.964393	−	0.700672i	−0.0102259	−	0.999948i	$-0.503255\pi$
$821$	−27.6328	−	20.0764i	−0.964393	−	0.700672i	−0.954167	+	0.299275i	$0.903255\pi$
$822$	0.602312	−	1.85372i	0.0210080	−	0.0646561i
$823$	14.1355	−	43.5047i	0.492734	−	1.51648i	−0.327725	−	0.944773i	$-0.606282\pi$
$823$	14.1355	−	43.5047i	0.492734	−	1.51648i	0.820459	−	0.571706i	$-0.193718\pi$
$824$	−5.18832			−0.180744
$825$	1.10672	+	2.60568i	0.0385310	+	0.0907180i
$826$	48.0654			1.67241
$827$	3.65191	−	11.2394i	0.126989	−	0.390833i	−0.867269	−	0.497840i	$-0.834127\pi$
$827$	3.65191	−	11.2394i	0.126989	−	0.390833i	0.994258	+	0.107007i	$0.0341267\pi$
$828$	−2.87138	+	8.83720i	−0.0997874	+	0.307114i
$829$	27.8159	+	20.2095i	0.966087	+	0.701903i	0.954556	−	0.298030i	$-0.0963296\pi$
$829$	27.8159	+	20.2095i	0.966087	+	0.701903i	0.0115305	+	0.999934i	$0.496330\pi$
$830$	−6.12794	−	21.0272i	−0.212704	−	0.729866i
$831$	−0.188950	−	0.137280i	−0.00655459	−	0.00476219i
$832$	−1.77505	+	1.28965i	−0.0615386	+	0.0447104i
$833$	−2.67483	+	1.94337i	−0.0926772	+	0.0673339i
$834$	−2.60541	−	1.89294i	−0.0902180	−	0.0655472i
$835$	16.5121	−	45.9841i	0.571426	−	1.59135i
$836$	1.30473	−	7.81128i	0.0451251	−	0.270159i
$837$	3.50181	−	2.54421i	0.121040	−	0.0879409i
$838$	19.4365	+	14.1215i	0.671424	+	0.487818i
$839$	−12.5403	−	38.5952i	−0.432940	−	1.33245i	−0.895182	−	0.445700i	$-0.852955\pi$
$839$	−12.5403	−	38.5952i	−0.432940	−	1.33245i	0.462242	−	0.886754i	$-0.347045\pi$
$840$	−1.48356	+	1.01003i	−0.0511878	+	0.0348495i
$841$	−3.04247	−	9.36377i	−0.104913	−	0.322889i
$842$	−19.0542	−	13.8437i	−0.656652	−	0.477085i
$843$	−2.67764	+	1.94542i	−0.0922228	+	0.0670038i
$844$	22.5588	−	16.3899i	0.776504	−	0.564164i
$845$	−18.2959	−	0.559748i	−0.629400	−	0.0192559i
$846$	1.07259	+	3.30110i	0.0368765	+	0.113494i
$847$	−49.4492	+	15.1508i	−1.69909	+	0.520589i
$848$	−0.303938	−	0.220824i	−0.0104373	−	0.00758313i
$849$	1.10720	+	3.40760i	0.0379989	+	0.116949i
$850$	1.09234	+	0.0669010i	0.0374670	+	0.00229468i
$851$	−14.1948	+	10.3131i	−0.486591	+	0.353529i
$852$	1.72963	−	1.25665i	0.0592561	−	0.0430521i
$853$	15.6954			0.537402			0.268701	−	0.963224i	$-0.413406\pi$
$853$	15.6954			0.537402			0.268701	+	0.963224i	$0.413406\pi$
$854$	25.1044	+	18.2394i	0.859054	+	0.624139i
$855$	5.36077	−	14.9291i	0.183335	−	0.510563i
$856$	−13.6391			−0.466176
$857$	39.0023			1.33229			0.666146	−	0.745821i	$-0.267943\pi$
$857$	39.0023			1.33229			0.666146	+	0.745821i	$0.267943\pi$
$858$	1.22857	−	0.183991i	0.0419427	−	0.00628135i
$859$	−14.1946	+	10.3130i	−0.484313	+	0.351874i	−0.802993	−	0.595988i	$-0.796760\pi$
$859$	−14.1946	+	10.3130i	−0.484313	+	0.351874i	0.318680	+	0.947862i	$0.396760\pi$
$860$	−6.31008	+	4.29600i	−0.215172	+	0.146492i
$861$	−0.572860	−	1.76308i	−0.0195230	−	0.0600857i
$862$	6.52154	−	20.0712i	0.222124	−	0.683629i
$863$	−15.3033	−	47.0986i	−0.520929	−	1.60325i	−0.772228	−	0.635345i	$-0.780858\pi$
$863$	−15.3033	−	47.0986i	−0.520929	−	1.60325i	0.251299	−	0.967909i	$-0.419142\pi$
$864$	−0.824637	+	0.599134i	−0.0280547	+	0.0203829i
$865$	25.9662	+	0.794412i	0.882878	+	0.0270108i
$866$	−20.1074			−0.683278
$867$	2.89396			0.0982839
$868$	19.9655			0.677673
$869$	−10.2360	−	20.5148i	−0.347234	−	0.695917i
$870$	1.66988	+	0.0510883i	0.0566141	+	0.00173206i
$871$	16.9038	−	12.2814i	0.572765	−	0.416138i
$872$	−4.72448	+	14.5404i	−0.159991	+	0.492402i
$873$	−18.8384			−0.637585
$874$	−2.30786	+	7.10288i	−0.0780647	+	0.240258i
$875$	−20.7561	+	48.2947i	−0.701685	+	1.63266i
$876$	−1.52802	+	1.11017i	−0.0516271	+	0.0375093i
$877$	2.00806	+	6.18016i	0.0678072	+	0.208689i	0.979219	−	0.202807i	$-0.0650064\pi$
$877$	2.00806	+	6.18016i	0.0678072	+	0.208689i	−0.911412	+	0.411496i	$0.865006\pi$
$878$	25.5250	−	18.5450i	0.861426	−	0.625863i
$879$	−0.927376	−	2.85417i	−0.0312796	−	0.0962688i
$880$	−1.44493	+	7.27408i	−0.0487086	+	0.245209i
$881$	−2.72488	+	8.38632i	−0.0918036	+	0.282542i	−0.986407	−	0.164318i	$-0.947458\pi$
$881$	−2.72488	+	8.38632i	−0.0918036	+	0.282542i	0.894604	+	0.446860i	$0.147458\pi$
$882$	−13.8676	−	42.6800i	−0.466945	−	1.43711i
$883$	−21.7419	+	15.7964i	−0.731672	+	0.531591i	−0.890092	−	0.455781i	$-0.849360\pi$
$883$	−21.7419	+	15.7964i	−0.731672	+	0.531591i	0.158420	+	0.987372i	$0.449360\pi$
$884$	0.148401	−	0.456730i	0.00499125	−	0.0153615i
$885$	−3.22580	+	2.19618i	−0.108434	+	0.0738237i
$886$	−13.0227	+	9.46153i	−0.437505	+	0.317866i
$887$	−1.29966	+	3.99994i	−0.0436383	+	0.134305i	−0.970502	−	0.241093i	$-0.922494\pi$
$887$	−1.29966	+	3.99994i	−0.0436383	+	0.134305i	0.926864	+	0.375398i	$0.122494\pi$
$888$	−0.957663			−0.0321371
$889$	18.5398	−	57.0597i	0.621806	−	1.91372i
$890$	10.2678	+	35.2328i	0.344179	+	1.18101i
$891$	−28.6629	+	4.29256i	−0.960243	+	0.143806i
$892$	−1.07672	+	3.31381i	−0.0360514	+	0.110955i
$893$	0.862093	+	2.65325i	0.0288488	+	0.0887876i
$894$	−0.449399	+	0.326507i	−0.0150301	+	0.0109200i
$895$	−24.8557	−	19.2470i	−0.830835	−	0.643356i
$896$	−4.70165			−0.157071
$897$	−1.17151			−0.0391157
$898$	14.2578			0.475789
$899$	−15.0356	−	10.9240i	−0.501466	−	0.364336i
$900$	−5.44525	+	13.8202i	−0.181508	+	0.460675i
$901$	0.0822297			0.00273947
$902$	−6.79580	−	3.53506i	−0.226275	−	0.117705i
$903$	0.846739	+	2.60599i	0.0281777	+	0.0867220i
$904$	−13.0281	+	9.46549i	−0.433309	+	0.314817i
$905$	17.5980	−	11.9810i	0.584979	−	0.398262i
$906$	−0.0766213	−	0.235816i	−0.00254557	−	0.00783446i
$907$	−10.3731	+	31.9250i	−0.344432	+	1.06005i	0.617455	+	0.786606i	$0.288164\pi$
$907$	−10.3731	+	31.9250i	−0.344432	+	1.06005i	−0.961887	+	0.273447i	$0.911836\pi$
$908$	5.62861	+	4.08943i	0.186792	+	0.135712i
$909$	−14.1234	+	43.4673i	−0.468443	+	1.44172i
$910$	18.2381	+	14.1227i	0.604587	+	0.468161i
$911$	7.89221	−	24.2897i	0.261481	−	0.804755i	−0.731003	−	0.682375i	$-0.760947\pi$
$911$	7.89221	−	24.2897i	0.261481	−	0.804755i	0.992483	−	0.122380i	$-0.0390527\pi$
$912$	−0.329782	+	0.239601i	−0.0109202	+	0.00793398i
$913$	−23.1637	+	22.7766i	−0.766605	+	0.753797i
$914$	−5.67530	−	4.12334i	−0.187722	−	0.136388i
$915$	−2.51821	−	0.0770422i	−0.0832493	−	0.00254694i
$916$	−12.1951			−0.402937
$917$	24.1372	+	74.2867i	0.797081	+	2.45316i
$918$	0.0689428	−	0.212184i	0.00227545	−	0.00700312i
$919$	18.5779	+	13.4976i	0.612829	+	0.445246i	0.850409	−	0.526122i	$-0.176354\pi$
$919$	18.5779	+	13.4976i	0.612829	+	0.445246i	−0.237580	+	0.971368i	$0.576354\pi$
$920$	2.36359	−	6.58228i	0.0779251	−	0.217011i
$921$	0.127226	−	0.391560i	0.00419223	−	0.0129023i
$922$	−24.3916	+	17.7216i	−0.803296	+	0.583629i
$923$	−22.2298	−	16.1509i	−0.731704	−	0.531614i
$924$	2.36163	+	1.22848i	0.0776921	+	0.0404141i
$925$	−23.6574	+	15.0687i	−0.777849	+	0.495454i
$926$	12.4266	+	38.2451i	0.408363	+	1.25681i
$927$	4.76312	+	14.6594i	0.156441	+	0.481477i
$928$	3.54072	+	2.57248i	0.116230	+	0.0844459i
$929$	−8.25844			−0.270951			−0.135475	−	0.990781i	$-0.543256\pi$
$929$	−8.25844			−0.270951			−0.135475	+	0.990781i	$0.543256\pi$
$930$	−1.33994	+	0.912252i	−0.0439384	+	0.0299139i
$931$	−11.1460	−	34.3039i	−0.365296	−	1.12427i
$932$	19.2199	+	13.9641i	0.629569	+	0.457408i
$933$	3.89904			0.127649
$934$	−14.6892	+	10.6723i	−0.480645	+	0.349209i
$935$	−0.679970	−	1.47396i	−0.0222374	−	0.0482035i
$936$	5.27341	+	3.83135i	0.172367	+	0.125232i
$937$	−20.5789	−	14.9514i	−0.672283	−	0.488442i	0.198506	−	0.980100i	$-0.436391\pi$
$937$	−20.5789	−	14.9514i	−0.672283	−	0.488442i	−0.870789	+	0.491657i	$0.836391\pi$
$938$	44.7741			1.46193
$939$	−0.365109			−0.0119149
$940$	−0.730949	−	2.50816i	−0.0238409	−	0.0818071i
$941$	1.81971	+	5.60049i	0.0593209	+	0.182571i	0.976326	−	0.216305i	$-0.0694005\pi$
$941$	1.81971	+	5.60049i	0.0593209	+	0.182571i	−0.917005	+	0.398876i	$0.869400\pi$
$942$	−0.238153	−	0.732960i	−0.00775944	−	0.0238811i
$943$	5.84429	+	4.24612i	0.190316	+	0.138273i
$944$	−10.2231			−0.332733
$945$	8.47292	+	6.56099i	0.275624	+	0.213429i
$946$	10.0448	+	5.22514i	0.326585	+	0.169884i
$947$	−17.9096	−	55.1202i	−0.581985	−	1.79116i	−0.611056	−	0.791587i	$-0.709255\pi$
$947$	−17.9096	−	55.1202i	−0.581985	−	1.79116i	0.0290711	−	0.999577i	$-0.490745\pi$
$948$	−0.364667	+	1.12233i	−0.0118438	+	0.0364515i
$949$	19.6387	+	14.2684i	0.637500	+	0.463171i
$950$	−4.37661	+	11.1080i	−0.141996	+	0.360390i
$951$	1.73486	−	5.33935i	0.0562567	−	0.173140i
$952$	0.832549	−	0.604882i	0.0269831	−	0.0196043i
$953$	20.5395	+	14.9228i	0.665339	+	0.483397i	0.868462	−	0.495756i	$-0.165109\pi$
$953$	20.5395	+	14.9228i	0.665339	+	0.483397i	−0.203122	+	0.979153i	$0.565109\pi$
$954$	−0.344899	+	1.06149i	−0.0111665	+	0.0343670i
$955$	−11.6279	−	9.00407i	−0.376271	−	0.291365i
$956$	9.16146	−	28.1961i	0.296303	−	0.911926i
$957$	−1.10634	−	2.21730i	−0.0357629	−	0.0716751i
$958$	−9.81219	+	30.1988i	−0.317018	+	0.975680i
$959$	−43.4289	−	31.5529i	−1.40239	−	1.01890i
$960$	0.315541	−	0.214825i	0.0101840	−	0.00693345i
$961$	−12.9674			−0.418302
$962$	3.80346	+	11.7058i	0.122628	+	0.377411i
$963$	12.5214	+	38.5368i	0.403495	+	1.24183i
$964$	1.25379			0.0403819
$965$	−34.4517	−	26.6777i	−1.10904	−	0.858784i
$966$	−2.03097	−	1.47559i	−0.0653454	−	0.0474762i
$967$	1.61021	−	4.95572i	0.0517809	−	0.159365i	−0.921822	−	0.387613i	$-0.873300\pi$
$967$	1.61021	−	4.95572i	0.0517809	−	0.159365i	0.973603	+	0.228248i	$0.0732996\pi$
$968$	10.5174	−	3.22245i	0.338042	−	0.103573i
$969$	0.0275711	−	0.0848550i	0.000885710	−	0.00272594i
$970$	14.1725	+	0.433593i	0.455050	+	0.0139218i
$971$	−17.1534	+	52.7927i	−0.550479	+	1.69420i	0.157116	+	0.987580i	$0.449780\pi$
$971$	−17.1534	+	52.7927i	−0.550479	+	1.69420i	−0.707594	+	0.706619i	$0.750220\pi$
$972$	3.68080	+	2.67426i	0.118062	+	0.0857768i
$973$	−71.7560	+	52.1338i	−2.30039	+	1.67133i
$974$	−8.44642	+	25.9954i	−0.270641	+	0.832947i
$975$	−1.86929	−	0.114486i	−0.0598653	−	0.00366648i
$976$	−5.33948	−	3.87936i	−0.170912	−	0.124175i
$977$	−7.24737	+	22.3051i	−0.231864	+	0.713603i	0.765658	+	0.643248i	$0.222413\pi$
$977$	−7.24737	+	22.3051i	−0.231864	+	0.713603i	−0.997522	+	0.0703558i	$0.977587\pi$
$978$	0.906999	+	2.79146i	0.0290026	+	0.0892610i
$979$	38.8126	−	38.1641i	1.24046	−	1.21973i
$980$	9.45045	+	32.4280i	0.301884	+	1.03587i
$981$	45.4206			1.45017
$982$	−16.9499	−	12.3148i	−0.540894	−	0.392982i
$983$	−0.910248	−	2.80146i	−0.0290324	−	0.0893526i	0.935490	−	0.353352i	$-0.114958\pi$
$983$	−0.910248	−	2.80146i	−0.0290324	−	0.0893526i	−0.964523	+	0.264000i	$0.914958\pi$
$984$	0.121842	+	0.374992i	0.00388419	+	0.0119543i
$985$	−18.9573	−	0.579981i	−0.604030	−	0.0184797i
$986$	−0.957933			−0.0305068
$987$	−0.937756			−0.0298491
$988$	4.23849	+	3.07944i	0.134844	+	0.0979701i
$989$	−8.63838	−	6.27615i	−0.274685	−	0.199570i
$990$	21.8791	−	2.59535i	0.695362	−	0.0824857i
$991$	−9.89533	+	7.18938i	−0.314336	+	0.228378i	−0.733755	−	0.679415i	$-0.762234\pi$
$991$	−9.89533	+	7.18938i	−0.314336	+	0.228378i	0.419419	+	0.907793i	$0.362234\pi$
$992$	−4.24649			−0.134826
$993$	0.556826	+	0.404557i	0.0176703	+	0.0128382i
$994$	−18.1953	−	55.9994i	−0.577120	−	1.77619i
$995$	0.209418	−	0.583202i	0.00663900	−	0.0184888i
$996$	1.67212			0.0529830
$997$	−19.2800	−	14.0078i	−0.610604	−	0.443630i	0.239023	−	0.971014i	$-0.423173\pi$
$997$	−19.2800	−	14.0078i	−0.610604	−	0.443630i	−0.849627	+	0.527384i	$0.823173\pi$
$998$	0.276299	+	0.850361i	0.00874609	+	0.0269177i
$999$	1.76698	+	5.43821i	0.0559048	+	0.172057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.g.c.291.8	✓	60
11.9	even	5		550.2.j.c.141.8	yes	60
25.11	even	5		550.2.j.c.511.8	yes	60
275.86	even	5	inner	550.2.g.c.361.8	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.g.c.291.8	✓	60	1.1	even	1	trivial
550.2.g.c.361.8	yes	60	275.86	even	5	inner
550.2.j.c.141.8	yes	60	11.9	even	5
550.2.j.c.511.8	yes	60	25.11	even	5

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:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.0527535 + 0.162358i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.755692 - 2.10450i) q^{5} +(0.138110 + 0.100343i) q^{6} +(3.80372 - 2.76356i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(2.40347 + 1.74623i) q^{9} +(-1.76798 - 1.36903i) q^{10} +(-0.546412 + 3.27130i) q^{11} +(0.138110 - 0.100343i) q^{12} +(-1.77505 - 1.28965i) q^{13} +(-1.45289 - 4.47154i) q^{14} +(0.301818 + 0.233713i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.177076 - 0.128653i) q^{17} +(2.40347 - 1.74623i) q^{18} +(1.93179 - 1.40352i) q^{19} +(-1.84836 + 1.25839i) q^{20} +(0.248028 + 0.763353i) q^{21} +(2.94235 + 1.53056i) q^{22} +(-2.53037 - 1.83842i) q^{23} +(-0.0527535 - 0.162358i) q^{24} +(-3.85786 - 3.18071i) q^{25} +(-1.77505 + 1.28965i) q^{26} +(-0.824637 + 0.599134i) q^{27} -4.70165 q^{28} +(3.54072 + 2.57248i) q^{29} +(0.315541 - 0.214825i) q^{30} -4.24649 q^{31} +1.00000 q^{32} +(-0.502299 - 0.261287i) q^{33} +(-0.177076 + 0.128653i) q^{34} +(-2.94149 - 10.0933i) q^{35} +(-0.918045 - 2.82545i) q^{36} +(1.73351 - 5.33520i) q^{37} +(-0.737876 - 2.27095i) q^{38} +(0.303025 - 0.220160i) q^{39} +(0.625628 + 2.14676i) q^{40} -2.30966 q^{41} +0.802637 q^{42} +3.41388 q^{43} +(2.36488 - 2.32537i) q^{44} +(5.49122 - 3.73851i) q^{45} +(-2.53037 + 1.83842i) q^{46} +(-0.361038 + 1.11116i) q^{47} -0.170714 q^{48} +(4.66787 - 14.3662i) q^{49} +(-4.21718 + 2.68615i) q^{50} +(0.0302293 - 0.0219628i) q^{51} +(0.678007 + 2.08669i) q^{52} +(-0.303938 + 0.220824i) q^{53} +(0.314983 + 0.969419i) q^{54} +(6.47155 + 3.62202i) q^{55} +(-1.45289 + 4.47154i) q^{56} +(0.125966 + 0.387682i) q^{57} +(3.54072 - 2.57248i) q^{58} +(-3.15911 + 9.72274i) q^{59} +(-0.106803 - 0.366482i) q^{60} +(-5.33948 + 3.87936i) q^{61} +(-1.31224 + 4.03865i) q^{62} +13.9679 q^{63} +(0.309017 - 0.951057i) q^{64} +(-4.05545 + 2.76101i) q^{65} +(-0.403718 + 0.396972i) q^{66} +(-2.94278 + 9.05696i) q^{67} +(0.0676369 + 0.208165i) q^{68} +(0.431969 - 0.313844i) q^{69} +(-10.5083 - 0.321492i) q^{70} +12.5235 q^{71} -2.97086 q^{72} -11.0638 q^{73} +(-4.53839 - 3.29733i) q^{74} +(0.719930 - 0.458563i) q^{75} -2.38782 q^{76} +(6.96206 + 13.9532i) q^{77} +(-0.115745 - 0.356227i) q^{78} +(-5.59246 + 4.06316i) q^{79} +(2.23502 + 0.0683784i) q^{80} +(2.70036 + 8.31087i) q^{81} +(-0.713723 + 2.19661i) q^{82} +(7.92420 + 5.75727i) q^{83} +(0.248028 - 0.763353i) q^{84} +(-0.404565 + 0.275434i) q^{85} +(1.05495 - 3.24679i) q^{86} +(-0.604449 + 0.439158i) q^{87} +(-1.48077 - 2.96771i) q^{88} +(-13.2776 - 9.64677i) q^{89} +(-1.85865 - 6.37772i) q^{90} -10.3158 q^{91} +(0.966516 + 2.97463i) q^{92} +(0.224017 - 0.689453i) q^{93} +(0.945210 + 0.686735i) q^{94} +(-1.49389 - 5.12608i) q^{95} +(-0.0527535 + 0.162358i) q^{96} +(-5.13004 + 3.72719i) q^{97} +(-12.2206 - 8.87881i) q^{98} +(-7.02572 + 6.90834i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 15 q^{2} - 4 q^{3} - 15 q^{4} + q^{6} - 3 q^{7} - 15 q^{8} - 17 q^{9} - 5 q^{10} + 7 q^{11} + q^{12} + 12 q^{13} - 3 q^{14} + 12 q^{15} - 15 q^{16} + q^{17} - 17 q^{18} + 3 q^{19} - 5 q^{20} - 4 q^{21}+ \cdots + 21 q^{99}+O(q^{100}) \) 60 * q - 15 * q^2 - 4 * q^3 - 15 * q^4 + q^6 - 3 * q^7 - 15 * q^8 - 17 * q^9 - 5 * q^10 + 7 * q^11 + q^12 + 12 * q^13 - 3 * q^14 + 12 * q^15 - 15 * q^16 + q^17 - 17 * q^18 + 3 * q^19 - 5 * q^20 - 4 * q^21 - 3 * q^22 - 3 * q^23 - 4 * q^24 + 8 * q^25 + 12 * q^26 + 2 * q^27 + 12 * q^28 + 18 * q^29 + 2 * q^30 - 20 * q^31 + 60 * q^32 + 10 * q^33 + q^34 - 19 * q^35 - 12 * q^36 - 36 * q^37 - 22 * q^38 + 13 * q^39 + 64 * q^41 + 46 * q^42 + 40 * q^43 - 8 * q^44 - 20 * q^45 - 3 * q^46 - 9 * q^47 + 6 * q^48 - 30 * q^49 + 18 * q^50 - 48 * q^51 - 8 * q^52 + 31 * q^53 - 8 * q^54 - 42 * q^55 - 3 * q^56 + 30 * q^57 + 18 * q^58 + 23 * q^59 - 8 * q^60 - 41 * q^61 - 5 * q^62 + 6 * q^63 - 15 * q^64 - 7 * q^65 - 30 * q^66 - 40 * q^67 - 4 * q^68 - 22 * q^69 - 4 * q^70 + 4 * q^71 + 58 * q^72 + 74 * q^73 - 11 * q^74 + 35 * q^75 + 38 * q^76 + 22 * q^77 - 12 * q^78 - 45 * q^79 + 10 * q^80 + 24 * q^81 - 11 * q^82 + 16 * q^83 - 4 * q^84 + 9 * q^85 - 20 * q^86 + 68 * q^87 + 7 * q^88 + q^89 + 10 * q^90 + 10 * q^91 + 2 * q^92 - 40 * q^93 - 24 * q^94 + 24 * q^95 - 4 * q^96 + 6 * q^97 - 30 * q^98 + 21 * q^99

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