LMFDB - Embedded newform 540.2.be.a.11.63

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [540,2,Mod(11,540)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(540, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("540.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.be (of order $18$, degree $6$, 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:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$72$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.63
Character	$\chi$	$=$	540.11
Dual form			540.2.be.a.491.63

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.30417 + 0.546944i) q^{2} +(-0.843124 - 1.51299i) q^{3} +(1.40170 + 1.42661i) q^{4} +(-0.342020 + 0.939693i) q^{5} +(-0.272054 - 2.43433i) q^{6} +(2.44150 + 0.430502i) q^{7} +(1.04778 + 2.62720i) q^{8} +(-1.57828 + 2.55128i) q^{9} +(-0.960011 + 1.03845i) q^{10} +(1.54060 - 0.560732i) q^{11} +(0.976641 - 3.32358i) q^{12} +(-0.321054 + 0.269396i) q^{13} +(2.94866 + 1.89681i) q^{14} +(1.71011 - 0.274804i) q^{15} +(-0.0704476 + 3.99938i) q^{16} +(0.690717 - 0.398786i) q^{17} +(-3.45375 + 2.46406i) q^{18} +(4.65798 + 2.68928i) q^{19} +(-1.81999 + 0.829241i) q^{20} +(-1.40714 - 4.05693i) q^{21} +(2.31589 + 0.111333i) q^{22} +(-0.794437 - 4.50547i) q^{23} +(3.09151 - 3.80033i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(-0.566052 + 0.175739i) q^{26} +(5.19075 + 0.236883i) q^{27} +(2.80810 + 4.08651i) q^{28} +(-1.76583 + 2.10444i) q^{29} +(2.38057 + 0.576945i) q^{30} +(5.24888 - 0.925520i) q^{31} +(-2.27931 + 5.17733i) q^{32} +(-2.14730 - 1.85815i) q^{33} +(1.11892 - 0.142300i) q^{34} +(-1.23958 + 2.14702i) q^{35} +(-5.85197 + 1.32454i) q^{36} +(-2.03377 - 3.52260i) q^{37} +(4.60389 + 6.05493i) q^{38} +(0.678282 + 0.258617i) q^{39} +(-2.82712 + 0.0860377i) q^{40} +(-4.10939 - 4.89738i) q^{41} +(0.383767 - 6.06054i) q^{42} +(1.41386 + 3.88454i) q^{43} +(2.95941 + 1.41186i) q^{44} +(-1.85761 - 2.35569i) q^{45} +(1.42816 - 6.31040i) q^{46} +(1.25951 - 7.14303i) q^{47} +(6.11042 - 3.26539i) q^{48} +(-0.802271 - 0.292003i) q^{49} +(-0.647481 - 1.25729i) q^{50} +(-1.18572 - 0.708823i) q^{51} +(-0.834346 - 0.0804056i) q^{52} +9.97868i q^{53} +(6.64004 + 3.14798i) q^{54} +1.63947i q^{55} +(1.42714 + 6.86536i) q^{56} +(0.141609 - 9.31488i) q^{57} +(-3.45395 + 1.77873i) q^{58} +(-7.59008 - 2.76256i) q^{59} +(2.78911 + 2.05447i) q^{60} +(-1.77419 + 10.0619i) q^{61} +(7.35163 + 1.66381i) q^{62} +(-4.95170 + 5.54949i) q^{63} +(-5.80431 + 5.50545i) q^{64} +(-0.143343 - 0.393831i) q^{65} +(-1.78414 - 3.59779i) q^{66} +(-7.50600 - 8.94530i) q^{67} +(1.53709 + 0.426406i) q^{68} +(-6.14693 + 5.00065i) q^{69} +(-2.79092 + 2.12209i) q^{70} +(-2.34373 - 4.05946i) q^{71} +(-8.35640 - 1.47328i) q^{72} +(4.06709 - 7.04441i) q^{73} +(-0.725716 - 5.70641i) q^{74} +(-0.326661 + 1.70097i) q^{75} +(2.69254 + 10.4147i) q^{76} +(4.00277 - 0.705796i) q^{77} +(0.743144 + 0.708262i) q^{78} +(-6.85262 + 8.16664i) q^{79} +(-3.73409 - 1.43407i) q^{80} +(-4.01805 - 8.05328i) q^{81} +(-2.68074 - 8.63460i) q^{82} +(-10.8045 - 9.06606i) q^{83} +(3.81527 - 7.69406i) q^{84} +(0.138497 + 0.785455i) q^{85} +(-0.280719 + 5.83938i) q^{86} +(4.67281 + 0.897387i) q^{87} +(3.08736 + 3.45993i) q^{88} +(-3.32416 - 1.91920i) q^{89} +(-1.13421 - 4.08822i) q^{90} +(-0.899827 + 0.519515i) q^{91} +(5.31400 - 7.44870i) q^{92} +(-5.82576 - 7.16118i) q^{93} +(5.54944 - 8.62682i) q^{94} +(-4.12022 + 3.45728i) q^{95} +(9.75500 - 0.916554i) q^{96} +(6.98564 - 2.54257i) q^{97} +(-0.886586 - 0.819617i) q^{98} +(-1.00092 + 4.81549i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) $ 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	1.30417	+	0.546944i	0.922186	+	0.386748i
$2$	1.30417	+	0.546944i	0.922186	+	0.386748i
$3$	−0.843124	−	1.51299i	−0.486778	−	0.873526i
$3$	−0.843124	−	1.51299i	−0.486778	−	0.873526i
$4$	1.40170	+	1.42661i	0.700852	+	0.713306i
$5$	−0.342020	+	0.939693i	−0.152956	+	0.420243i
$5$	−0.342020	+	0.939693i	−0.152956	+	0.420243i
$6$	−0.272054	−	2.43433i	−0.111066	−	0.993813i
$7$	2.44150	+	0.430502i	0.922799	+	0.162714i	0.614810	−	0.788675i	$-0.289233\pi$
$7$	2.44150	+	0.430502i	0.922799	+	0.162714i	0.307989	+	0.951390i	$0.400344\pi$
$8$	1.04778	+	2.62720i	0.370446	+	0.928854i
$9$	−1.57828	+	2.55128i	−0.526094	+	0.850426i
$10$	−0.960011	+	1.03845i	−0.303582	+	0.328387i
$11$	1.54060	−	0.560732i	0.464508	−	0.169067i	−0.0991548	−	0.995072i	$-0.531614\pi$
$11$	1.54060	−	0.560732i	0.464508	−	0.169067i	0.563663	+	0.826005i	$0.309392\pi$
$12$	0.976641	−	3.32358i	0.281932	−	0.959434i
$13$	−0.321054	+	0.269396i	−0.0890443	+	0.0747170i	−0.686223	−	0.727391i	$-0.740733\pi$
$13$	−0.321054	+	0.269396i	−0.0890443	+	0.0747170i	0.597179	+	0.802108i	$0.296288\pi$
$14$	2.94866	+	1.89681i	0.788063	+	0.506943i
$15$	1.71011	−	0.274804i	0.441549	−	0.0709542i
$16$	−0.0704476	+	3.99938i	−0.0176119	+	0.999845i
$17$	0.690717	−	0.398786i	0.167524	−	0.0967197i	−0.413894	−	0.910325i	$-0.635832\pi$
$17$	0.690717	−	0.398786i	0.167524	−	0.0967197i	0.581418	+	0.813605i	$0.302498\pi$
$18$	−3.45375	+	2.46406i	−0.814057	+	0.580785i
$19$	4.65798	+	2.68928i	1.06861	+	0.616964i	0.927802	−	0.373073i	$-0.121696\pi$
$19$	4.65798	+	2.68928i	1.06861	+	0.616964i	0.140811	+	0.990037i	$0.455029\pi$
$20$	−1.81999	+	0.829241i	−0.406962	+	0.185424i
$21$	−1.40714	−	4.05693i	−0.307063	−	0.885295i
$22$	2.31589	+	0.111333i	0.493749	+	0.0237362i
$23$	−0.794437	−	4.50547i	−0.165651	−	0.939456i	−0.948390	−	0.317106i	$-0.897289\pi$
$23$	−0.794437	−	4.50547i	−0.165651	−	0.939456i	0.782739	−	0.622350i	$-0.213822\pi$
$24$	3.09151	−	3.80033i	0.631053	−	0.775740i
$25$	−0.766044	−	0.642788i	−0.153209	−	0.128558i
$26$	−0.566052	+	0.175739i	−0.111012	+	0.0344653i
$27$	5.19075	+	0.236883i	0.998960	+	0.0455882i
$28$	2.80810	+	4.08651i	0.530681	+	0.772277i
$29$	−1.76583	+	2.10444i	−0.327907	+	0.390784i	−0.904660	−	0.426134i	$-0.859875\pi$
$29$	−1.76583	+	2.10444i	−0.327907	+	0.390784i	0.576753	+	0.816919i	$0.304320\pi$
$30$	2.38057	+	0.576945i	0.434631	+	0.105335i
$31$	5.24888	−	0.925520i	0.942727	−	0.166228i	0.318898	−	0.947789i	$-0.396687\pi$
$31$	5.24888	−	0.925520i	0.942727	−	0.166228i	0.623829	+	0.781561i	$0.285576\pi$
$32$	−2.27931	+	5.17733i	−0.402929	+	0.915231i
$33$	−2.14730	−	1.85815i	−0.373797	−	0.323462i
$34$	1.11892	−	0.142300i	0.191894	−	0.0244042i
$35$	−1.23958	+	2.14702i	−0.209527	+	0.362912i
$36$	−5.85197	+	1.32454i	−0.975329	+	0.220757i
$37$	−2.03377	−	3.52260i	−0.334350	−	0.579111i	0.649010	−	0.760780i	$-0.275183\pi$
$37$	−2.03377	−	3.52260i	−0.334350	−	0.579111i	−0.983360	+	0.181669i	$0.941850\pi$
$38$	4.60389	+	6.05493i	0.746850	+	0.982239i
$39$	0.678282	+	0.258617i	0.108612	+	0.0414119i
$40$	−2.82712	+	0.0860377i	−0.447007	+	0.0136038i
$41$	−4.10939	−	4.89738i	−0.641779	−	0.764842i	0.342871	−	0.939382i	$-0.388600\pi$
$41$	−4.10939	−	4.89738i	−0.641779	−	0.764842i	−0.984650	+	0.174540i	$0.944156\pi$
$42$	0.383767	−	6.06054i	0.0592165	−	0.935162i
$43$	1.41386	+	3.88454i	0.215611	+	0.592386i	0.999597	−	0.0283925i	$-0.00903883\pi$
$43$	1.41386	+	3.88454i	0.215611	+	0.592386i	−0.783986	+	0.620779i	$0.786817\pi$
$44$	2.95941	+	1.41186i	0.446148	+	0.212846i
$45$	−1.85761	−	2.35569i	−0.276917	−	0.351165i
$46$	1.42816	−	6.31040i	0.210571	−	0.930418i
$47$	1.25951	−	7.14303i	0.183718	−	1.04192i	−0.743873	−	0.668321i	$-0.767013\pi$
$47$	1.25951	−	7.14303i	0.183718	−	1.04192i	0.927591	−	0.373597i	$-0.121876\pi$
$48$	6.11042	−	3.26539i	0.881963	−	0.471318i
$49$	−0.802271	−	0.292003i	−0.114610	−	0.0417147i
$50$	−0.647481	−	1.25729i	−0.0915677	−	0.177807i
$51$	−1.18572	−	0.708823i	−0.166034	−	0.0992550i
$52$	−0.834346	−	0.0804056i	−0.115703	−	0.0111502i
$53$			9.97868i			1.37068i	0.728225	+	0.685339i	$0.240346\pi$
$53$			9.97868i			1.37068i	−0.728225	+	0.685339i	$0.759654\pi$
$54$	6.64004	+	3.14798i	0.903596	+	0.428386i
$55$			1.63947i			0.221066i
$56$	1.42714	+	6.86536i	0.190710	+	0.917423i
$57$	0.141609	−	9.31488i	0.0187566	−	1.23379i
$58$	−3.45395	+	1.77873i	−0.453526	+	0.233558i
$59$	−7.59008	−	2.76256i	−0.988144	−	0.359655i	−0.203143	−	0.979149i	$-0.565116\pi$
$59$	−7.59008	−	2.76256i	−0.988144	−	0.359655i	−0.785001	+	0.619494i	$0.787338\pi$
$60$	2.78911	+	2.05447i	0.360073	+	0.265231i
$61$	−1.77419	+	10.0619i	−0.227161	+	1.28830i	0.631348	+	0.775499i	$0.282502\pi$
$61$	−1.77419	+	10.0619i	−0.227161	+	1.28830i	−0.858510	+	0.512797i	$0.828609\pi$
$62$	7.35163	+	1.66381i	0.933658	+	0.211304i
$63$	−4.95170	+	5.54949i	−0.623856	+	0.699170i
$64$	−5.80431	+	5.50545i	−0.725539	+	0.688181i
$65$	−0.143343	−	0.393831i	−0.0177795	−	0.0488487i
$66$	−1.78414	−	3.59779i	−0.219612	−	0.442857i
$67$	−7.50600	−	8.94530i	−0.917003	−	1.09284i	−0.995389	−	0.0959190i	$-0.969421\pi$
$67$	−7.50600	−	8.94530i	−0.917003	−	1.09284i	0.0783857	−	0.996923i	$-0.475023\pi$
$68$	1.53709	+	0.426406i	0.186400	+	0.0517093i
$69$	−6.14693	+	5.00065i	−0.740004	+	0.602007i
$70$	−2.79092	+	2.12209i	−0.333579	+	0.253638i
$71$	−2.34373	−	4.05946i	−0.278150	−	0.481770i	0.692775	−	0.721154i	$-0.256388\pi$
$71$	−2.34373	−	4.05946i	−0.278150	−	0.481770i	−0.970925	+	0.239384i	$0.923055\pi$
$72$	−8.35640	−	1.47328i	−0.984811	−	0.173628i
$73$	4.06709	−	7.04441i	0.476017	−	0.824486i	−0.523605	−	0.851961i	$-0.675413\pi$
$73$	4.06709	−	7.04441i	0.476017	−	0.824486i	0.999622	+	0.0274752i	$0.00874671\pi$
$74$	−0.725716	−	5.70641i	−0.0843628	−	0.663357i
$75$	−0.326661	+	1.70097i	−0.0377196	+	0.196411i
$76$	2.69254	+	10.4147i	0.308856	+	1.19465i
$77$	4.00277	−	0.705796i	0.456157	−	0.0804329i
$78$	0.743144	+	0.708262i	0.0841445	+	0.0801949i
$79$	−6.85262	+	8.16664i	−0.770980	+	0.918818i	−0.998489	−	0.0549578i	$-0.982498\pi$
$79$	−6.85262	+	8.16664i	−0.770980	+	0.918818i	0.227509	+	0.973776i	$0.426942\pi$
$80$	−3.73409	−	1.43407i	−0.417484	−	0.160334i
$81$	−4.01805	−	8.05328i	−0.446449	−	0.894809i
$82$	−2.68074	−	8.63460i	−0.296038	−	0.953533i
$83$	−10.8045	−	9.06606i	−1.18595	−	0.995129i	−0.999921	−	0.0125847i	$-0.995994\pi$
$83$	−10.8045	−	9.06606i	−1.18595	−	0.995129i	−0.186028	−	0.982544i	$-0.559561\pi$
$84$	3.81527	−	7.69406i	0.416280	−	0.839491i
$85$	0.138497	+	0.785455i	0.0150221	+	0.0851945i
$86$	−0.280719	+	5.83938i	−0.0302707	+	0.629677i
$87$	4.67281	+	0.897387i	0.500978	+	0.0962100i
$88$	3.08736	+	3.45993i	0.329114	+	0.368830i
$89$	−3.32416	−	1.91920i	−0.352360	−	0.203435i	0.313364	−	0.949633i	$-0.398544\pi$
$89$	−3.32416	−	1.91920i	−0.352360	−	0.203435i	−0.665724	+	0.746198i	$0.731877\pi$
$90$	−1.13421	−	4.08822i	−0.119556	−	0.430937i
$91$	−0.899827	+	0.519515i	−0.0943275	+	0.0544600i
$92$	5.31400	−	7.44870i	0.554023	−	0.776580i
$93$	−5.82576	−	7.16118i	−0.604103	−	0.742580i
$94$	5.54944	−	8.62682i	0.572381	−	0.889789i
$95$	−4.12022	+	3.45728i	−0.422726	+	0.354709i
$96$	9.75500	−	0.916554i	0.995615	−	0.0935454i
$97$	6.98564	−	2.54257i	0.709285	−	0.258159i	0.0379148	−	0.999281i	$-0.487928\pi$
$97$	6.98564	−	2.54257i	0.709285	−	0.258159i	0.671370	+	0.741122i	$0.265706\pi$
$98$	−0.886586	−	0.819617i	−0.0895587	−	0.0827939i
$99$	−1.00092	+	4.81549i	−0.100596	+	0.483975i
$100$	−0.156759	−	1.99385i	−0.0156759	−	0.199385i
$101$	−3.83327	−	0.675908i	−0.381424	−	0.0672554i	−0.0203511	−	0.999793i	$-0.506478\pi$
$101$	−3.83327	−	0.675908i	−0.381424	−	0.0672554i	−0.361073	+	0.932538i	$0.617590\pi$
$102$	−1.15869	−	1.57295i	−0.114727	−	0.155745i
$103$	5.43179	−	14.9237i	0.535210	−	1.47048i	−0.317584	−	0.948230i	$-0.602872\pi$
$103$	5.43179	−	14.9237i	0.535210	−	1.47048i	0.852794	−	0.522247i	$-0.174906\pi$
$104$	−1.04415	−	0.561203i	−0.102387	−	0.0550305i
$105$	4.29354	+	0.0652725i	0.419006	+	0.00636994i
$106$	−5.45778	+	13.0139i	−0.530106	+	1.26402i
$107$	−10.3656			−1.00208			−0.501039	−	0.865424i	$-0.667049\pi$
$107$	−10.3656			−1.00208			−0.501039	+	0.865424i	$0.667049\pi$
$108$	6.93796	+	7.73723i	0.667605	+	0.744515i
$109$	−5.38932			−0.516204			−0.258102	−	0.966118i	$-0.583097\pi$
$109$	−5.38932			−0.516204			−0.258102	+	0.966118i	$0.583097\pi$
$110$	−0.896699	+	2.13815i	−0.0854969	+	0.203864i
$111$	−3.61493	+	6.04706i	−0.343114	+	0.573962i
$112$	−1.89374	+	9.73415i	−0.178941	+	0.919790i
$113$	−2.78157	+	7.64229i	−0.261668	+	0.718927i	0.737387	+	0.675470i	$0.236059\pi$
$113$	−2.78157	+	7.64229i	−0.261668	+	0.718927i	−0.999055	+	0.0434566i	$0.986163\pi$
$114$	5.27940	−	12.0707i	0.494461	−	1.13053i
$115$	4.50547	+	0.794437i	0.420138	+	0.0740816i
$116$	−5.47740	+	0.430641i	−0.508563	+	0.0399840i
$117$	−0.180591	−	1.24428i	−0.0166956	−	0.115034i
$118$	−8.38776	−	7.75419i	−0.772156	−	0.713831i
$119$	1.85806	−	0.676279i	0.170328	−	0.0619944i
$120$	2.51379	+	4.20486i	0.229476	+	0.383850i
$121$	−6.36746	+	5.34294i	−0.578860	+	0.485721i
$122$	−7.81714	+	12.1520i	−0.707731	+	1.10019i
$123$	−3.94496	+	10.3466i	−0.355705	+	0.932918i
$124$	8.67774	+	6.19082i	0.779284	+	0.555952i
$125$	0.866025	−	0.500000i	0.0774597	−	0.0447214i
$126$	−9.49311	+	4.52915i	−0.845713	+	0.403489i
$127$	8.13191	+	4.69496i	0.721590	+	0.416610i	0.815338	−	0.578986i	$-0.196551\pi$
$127$	8.13191	+	4.69496i	0.721590	+	0.416610i	−0.0937475	+	0.995596i	$0.529885\pi$
$128$	−10.5810	+	4.00539i	−0.935234	+	0.354030i
$129$	4.68521	−	5.41430i	0.412510	−	0.476702i
$130$	0.0284605	−	0.592021i	0.00249615	−	0.0519237i
$131$	2.80170	+	15.8892i	0.244786	+	1.38825i	0.820989	+	0.570944i	$0.193423\pi$
$131$	2.80170	+	15.8892i	0.244786	+	1.38825i	−0.576203	+	0.817306i	$0.695466\pi$
$132$	−0.359025	−	5.66794i	−0.0312492	−	0.493331i
$133$	10.2147	+	8.57115i	0.885726	+	0.743213i
$134$	−4.89650	−	15.7715i	−0.422993	−	1.36245i
$135$	−1.99794	+	4.79669i	−0.171955	+	0.412833i
$136$	1.77141	+	1.39681i	0.151897	+	0.119775i
$137$	12.4857	−	14.8799i	1.06673	−	1.27127i	0.105824	−	0.994385i	$-0.466252\pi$
$137$	12.4857	−	14.8799i	1.06673	−	1.27127i	0.960902	−	0.276889i	$-0.0893036\pi$
$138$	−10.7517	+	3.15966i	−0.915246	+	0.268968i
$139$	12.3686	−	2.18092i	1.04909	−	0.184983i	0.377580	−	0.925977i	$-0.376756\pi$
$139$	12.3686	−	2.18092i	1.04909	−	0.184983i	0.671512	+	0.740994i	$0.265645\pi$
$140$	−4.80049	+	1.24108i	−0.405715	+	0.104891i
$141$	−11.8693	+	4.11683i	−0.999572	+	0.346700i
$142$	−0.836320	−	6.57611i	−0.0701824	−	0.551855i
$143$	−0.343556	+	0.595056i	−0.0287296	+	0.0497611i
$144$	−10.0923	−	6.49188i	−0.841029	−	0.540990i
$145$	−1.37357	−	2.37910i	−0.114069	−	0.197574i
$146$	9.15706	−	6.96262i	0.757844	−	0.576230i
$147$	0.234617	+	1.46002i	0.0193508	+	0.120421i
$148$	2.17463	−	7.83904i	0.178754	−	0.644365i
$149$	−9.98635	−	11.9013i	−0.818113	−	0.974990i	0.181852	−	0.983326i	$-0.441791\pi$
$149$	−9.98635	−	11.9013i	−0.818113	−	0.974990i	−0.999965	+	0.00833641i	$0.997346\pi$
$150$	−1.35635	+	2.03968i	−0.110746	+	0.166539i
$151$	0.321119	+	0.882268i	0.0261323	+	0.0717980i	0.952073	−	0.305871i	$-0.0989478\pi$
$151$	0.321119	+	0.882268i	0.0261323	+	0.0717980i	−0.925940	+	0.377669i	$0.876726\pi$
$152$	−2.18474	+	15.0552i	−0.177206	+	1.22114i
$153$	−0.0727337	+	2.39161i	−0.00588017	+	0.193350i
$154$	5.60631	+	1.26881i	0.451769	+	0.102244i
$155$	−0.925520	+	5.24888i	−0.0743395	+	0.421600i
$156$	0.581805	+	1.33015i	0.0465817	+	0.106497i
$157$	18.7192	+	6.81323i	1.49395	+	0.543755i	0.954487	−	0.298252i	$-0.0964036\pi$
$157$	18.7192	+	6.81323i	1.49395	+	0.543755i	0.539467	+	0.842007i	$0.318626\pi$
$158$	−13.4037	+	6.90266i	−1.06634	+	0.549146i
$159$	15.0977	−	8.41327i	1.19732	−	0.667216i
$160$	−4.08553	−	3.91260i	−0.322989	−	0.309318i
$161$		−	11.3421i		−	0.893883i
$162$	−0.835511	−	12.7005i	−0.0656439	−	0.997843i
$163$		−	10.3525i		−	0.810872i	−0.914123	−	0.405436i	$-0.867120\pi$
$163$		−	10.3525i		−	0.810872i	0.914123	−	0.405436i	$-0.132880\pi$
$164$	1.22651	−	12.7272i	0.0957746	−	0.993826i
$165$	2.48051	−	1.38228i	0.193107	−	0.107610i
$166$	−9.13226	−	17.7331i	−0.708801	−	1.37636i
$167$	1.25661	+	0.457369i	0.0972395	+	0.0353923i	0.390182	−	0.920738i	$-0.372412\pi$
$167$	1.25661	+	0.457369i	0.0972395	+	0.0353923i	−0.292942	+	0.956130i	$0.594634\pi$
$168$	9.18397	−	7.94760i	0.708559	−	0.613171i
$169$	−2.22693	+	12.6295i	−0.171302	+	0.971502i
$170$	−0.248977	+	1.10011i	−0.0190956	+	0.0843749i
$171$	−14.2127	+	7.63934i	−1.08687	+	0.584195i
$172$	−3.55992	+	7.46200i	−0.271441	+	0.568972i
$173$	6.65173	+	18.2755i	0.505722	+	1.38946i	0.885611	+	0.464427i	$0.153740\pi$
$173$	6.65173	+	18.2755i	0.505722	+	1.38946i	−0.379890	+	0.925032i	$0.624038\pi$
$174$	5.60331	+	3.72611i	0.424786	+	0.282476i
$175$	−1.59357	−	1.89915i	−0.120463	−	0.143562i
$176$	2.13405	+	6.20094i	0.160860	+	0.467414i
$177$	2.21965	+	13.8129i	0.166839	+	1.03824i
$178$	−3.28556	−	4.32109i	−0.246263	−	0.323880i
$179$	−11.6734	−	20.2188i	−0.872507	−	1.51123i	−0.859394	−	0.511313i	$-0.829159\pi$
$179$	−11.6734	−	20.2188i	−0.872507	−	1.51123i	−0.0131129	−	0.999914i	$-0.504174\pi$
$180$	0.756832	−	5.95208i	0.0564109	−	0.443642i
$181$	11.5021	−	19.9221i	0.854941	−	1.48080i	−0.0217588	−	0.999763i	$-0.506927\pi$
$181$	11.5021	−	19.9221i	0.854941	−	1.48080i	0.876700	−	0.481038i	$-0.159740\pi$
$182$	−1.45767	+	0.185380i	−0.108050	+	0.0137413i
$183$	16.7195	−	5.79912i	1.23594	−	0.428683i
$184$	11.0044	−	6.80789i	0.811253	−	0.501884i
$185$	4.00575	−	0.706321i	0.294508	−	0.0519298i
$186$	−3.68100	−	12.5257i	−0.269904	−	0.918432i
$187$	0.840506	−	1.00168i	0.0614639	−	0.0732498i
$188$	11.9558	−	8.21558i	0.871966	−	0.599183i
$189$	12.5712	+	2.81298i	0.914422	+	0.204614i
$190$	−7.26439	+	2.25534i	−0.527015	+	0.163619i
$191$	2.73473	+	2.29471i	0.197878	+	0.166039i	0.736343	−	0.676609i	$-0.236551\pi$
$191$	2.73473	+	2.29471i	0.197878	+	0.166039i	−0.538465	+	0.842648i	$0.680996\pi$
$192$	13.2234	+	4.14010i	0.954320	+	0.298786i
$193$	−3.50661	−	19.8870i	−0.252411	−	1.43150i	−0.802631	−	0.596475i	$-0.796567\pi$
$193$	−3.50661	−	19.8870i	−0.252411	−	1.43150i	0.550220	−	0.835020i	$-0.314544\pi$
$194$	10.5011	+	0.504823i	0.753934	+	0.0362442i
$195$	−0.475007	+	0.548924i	−0.0340159	+	0.0393093i
$196$	−0.707972	−	1.55383i	−0.0505694	−	0.110988i
$197$	10.2213	+	5.90125i	0.728235	+	0.420446i	0.817776	−	0.575537i	$-0.195207\pi$
$197$	10.2213	+	5.90125i	0.728235	+	0.420446i	−0.0895413	+	0.995983i	$0.528540\pi$
$198$	−3.93917	+	5.73276i	−0.279944	+	0.407410i
$199$	3.16139	−	1.82523i	0.224105	−	0.129387i	−0.383745	−	0.923439i	$-0.625366\pi$
$199$	3.16139	−	1.82523i	0.224105	−	0.129387i	0.607849	+	0.794052i	$0.292032\pi$
$200$	0.886082	−	2.68605i	0.0626555	−	0.189932i
$201$	−7.20567	+	18.8985i	−0.508249	+	1.33300i
$202$	−4.62954	−	2.97808i	−0.325733	−	0.209537i
$203$	−5.21724	+	4.37779i	−0.366179	+	0.307260i
$204$	−0.650813	−	2.68512i	−0.0455660	−	0.187996i
$205$	6.00752	−	2.18656i	0.419584	−	0.152716i
$206$	15.2464	−	16.4921i	1.06227	−	1.14906i
$207$	12.7486	+	5.08408i	0.886087	+	0.353368i
$208$	−1.05480	−	1.30299i	−0.0731372	−	0.0903464i
$209$	8.68404	+	1.53123i	0.600688	+	0.105917i
$210$	5.56379	+	2.43345i	0.383938	+	0.167924i
$211$	1.37473	−	3.77704i	0.0946402	−	0.260022i	−0.883335	−	0.468742i	$-0.844707\pi$
$211$	1.37473	−	3.77704i	0.0946402	−	0.260022i	0.977975	+	0.208720i	$0.0669297\pi$
$212$	−14.2357	+	13.9872i	−0.977713	+	0.960642i
$213$	−4.16587	+	6.96868i	−0.285441	+	0.477486i
$214$	−13.5185	−	5.66939i	−0.924103	−	0.387552i
$215$	−4.13384			−0.281925
$216$	4.81643	+	13.8853i	0.327716	+	0.944776i
$217$	13.2136			0.896996
$218$	−7.02858	−	2.94766i	−0.476035	−	0.199641i
$219$	−14.0872	−	0.214161i	−0.951924	−	0.0144716i
$220$	−2.33889	+	2.29806i	−0.157688	+	0.154935i
$221$	−0.114326	+	0.314108i	−0.00769040	+	0.0211292i
$222$	−8.02188	+	5.90922i	−0.538393	+	0.396601i
$223$	18.6261	+	3.28428i	1.24729	+	0.219931i	0.758039	−	0.652210i	$-0.226158\pi$
$223$	18.6261	+	3.28428i	1.24729	+	0.219931i	0.489254	+	0.872141i	$0.337269\pi$
$224$	−7.79378	+	11.6592i	−0.520744	+	0.779012i
$225$	2.84897	−	0.939892i	0.189931	−	0.0626595i
$226$	−7.80754	+	8.44547i	−0.519350	+	0.561784i
$227$	17.3568	−	6.31737i	1.15201	−	0.419298i	0.305775	−	0.952104i	$-0.401084\pi$
$227$	17.3568	−	6.31737i	1.15201	−	0.419298i	0.846238	+	0.532805i	$0.178862\pi$
$228$	13.4872	−	12.8547i	0.893213	−	0.851322i
$229$	−13.9665	+	11.7193i	−0.922931	+	0.774431i	−0.974535	−	0.224236i	$-0.928011\pi$
$229$	−13.9665	+	11.7193i	−0.922931	+	0.774431i	0.0516033	+	0.998668i	$0.483567\pi$
$230$	5.44138	+	3.50032i	0.358794	+	0.230804i
$231$	−4.44269	−	5.46107i	−0.292308	−	0.359312i
$232$	−7.37898	−	2.43420i	−0.484454	−	0.159813i
$233$	−11.8148	+	6.82129i	−0.774015	+	0.446877i	−0.834305	−	0.551303i	$-0.814131\pi$
$233$	−11.8148	+	6.82129i	−0.774015	+	0.446877i	0.0602903	+	0.998181i	$0.480797\pi$
$234$	0.445031	−	1.72152i	0.0290926	−	0.112539i
$235$	6.28147	+	3.62661i	0.409758	+	0.236574i
$236$	−6.69794	−	14.7004i	−0.435999	−	0.956914i
$237$	18.1337	+	3.48246i	1.17791	+	0.226210i
$238$	2.79311	+	0.134274i	0.181050	+	0.00870371i
$239$	−1.70326	−	9.65967i	−0.110175	−	0.624832i	−0.989027	−	0.147737i	$-0.952801\pi$
$239$	−1.70326	−	9.65967i	−0.110175	−	0.624832i	0.878852	−	0.477095i	$-0.158310\pi$
$240$	0.978573	+	6.85875i	0.0631666	+	0.442730i
$241$	19.6242	+	16.4667i	1.26411	+	1.06071i	0.995232	+	0.0975365i	$0.0310963\pi$
$241$	19.6242	+	16.4667i	1.26411	+	1.06071i	0.268875	+	0.963175i	$0.413348\pi$
$242$	−11.2265	+	3.48544i	−0.721668	+	0.224052i
$243$	−8.79683	+	12.8692i	−0.564317	+	0.825558i
$244$	−16.8413	+	11.5728i	−1.07816	+	0.740870i
$245$	0.548786	−	0.654017i	0.0350606	−	0.0417836i
$246$	−10.8039	+	11.3360i	−0.688830	+	0.722756i
$247$	−2.21994	+	0.391436i	−0.141252	+	0.0249065i
$248$	7.93120	+	12.8201i	0.503631	+	0.814077i
$249$	−4.60732	+	23.9909i	−0.291977	+	1.52036i
$250$	1.40291	−	0.178416i	0.0887281	−	0.0112840i
$251$	−13.8579	+	24.0025i	−0.874701	+	1.51503i	−0.0176198	+	0.999845i	$0.505609\pi$
$251$	−13.8579	+	24.0025i	−0.874701	+	1.51503i	−0.857081	+	0.515182i	$0.827724\pi$
$252$	−14.8578	+	0.714577i	−0.935953	+	0.0450141i
$253$	−3.75027	−	6.49566i	−0.235778	−	0.408379i
$254$	8.03749	+	10.5707i	0.504317	+	0.663265i
$255$	1.07162	−	0.871780i	0.0671072	−	0.0545930i
$256$	−15.9901	−	0.563493i	−0.999380	−	0.0352183i
$257$	−10.3367	−	12.3188i	−0.644784	−	0.768424i	0.340333	−	0.940305i	$-0.389460\pi$
$257$	−10.3367	−	12.3188i	−0.644784	−	0.768424i	−0.985118	+	0.171881i	$0.945016\pi$
$258$	9.07161	−	4.49860i	0.564774	−	0.280071i
$259$	−3.44896	−	9.47595i	−0.214308	−	0.588807i
$260$	0.360920	−	0.756529i	0.0223833	−	0.0469179i
$261$	−2.58202	−	7.82653i	−0.159823	−	0.484450i
$262$	−5.03664	+	22.2546i	−0.311165	+	1.37489i
$263$	0.632630	−	3.58782i	0.0390096	−	0.221235i	−0.959071	−	0.283167i	$-0.908615\pi$
$263$	0.632630	−	3.58782i	0.0390096	−	0.221235i	0.998080	+	0.0619320i	$0.0197262\pi$
$264$	2.63181	−	7.58830i	0.161977	−	0.467028i
$265$	−9.37689	−	3.41291i	−0.576018	−	0.209653i
$266$	8.63373	+	16.7651i	0.529368	+	1.02793i
$267$	−0.101059	+	6.64755i	−0.00618473	+	0.406823i
$268$	2.24029	−	23.2468i	0.136847	−	1.42003i
$269$		−	4.17769i		−	0.254718i	−0.991857	−	0.127359i	$-0.959350\pi$
$269$		−	4.17769i		−	0.254718i	0.991857	−	0.127359i	$-0.0406501\pi$
$270$	−5.22917	+	5.16293i	−0.318237	+	0.314206i
$271$		−	7.14709i		−	0.434155i	−0.976154	−	0.217077i	$-0.930348\pi$
$271$		−	7.14709i		−	0.434155i	0.976154	−	0.217077i	$-0.0696524\pi$
$272$	1.54624	+	2.79053i	0.0937543	+	0.169201i
$273$	1.54469	+	0.923414i	0.0934888	+	0.0558876i
$274$	24.4219	−	12.5769i	1.47538	−	0.759797i
$275$	−1.54060	−	0.560732i	−0.0929016	−	0.0338134i
$276$	−15.7502	−	1.75986i	−0.948049	−	0.105931i
$277$	−0.505277	+	2.86557i	−0.0303591	+	0.172175i	−0.996217	−	0.0868958i	$-0.972305\pi$
$277$	−0.505277	+	2.86557i	−0.0303591	+	0.172175i	0.965858	+	0.259071i	$0.0834164\pi$
$278$	17.3236	+	3.92065i	1.03900	+	0.235145i
$279$	−5.92296	+	14.8521i	−0.354599	+	0.889172i
$280$	−6.93944	−	1.00702i	−0.414711	−	0.0601809i
$281$	4.46711	+	12.2733i	0.266486	+	0.732163i	0.998694	+	0.0510831i	$0.0162673\pi$
$281$	4.46711	+	12.2733i	0.266486	+	0.732163i	−0.732209	+	0.681080i	$0.761510\pi$
$282$	−17.7312	−	1.12278i	−1.05588	−	0.0668604i
$283$	−4.32741	−	5.15720i	−0.257238	−	0.306564i	0.621934	−	0.783070i	$-0.286347\pi$
$283$	−4.32741	−	5.15720i	−0.257238	−	0.306564i	−0.879171	+	0.476506i	$0.841903\pi$
$284$	2.50606	−	9.03377i	0.148707	−	0.536055i
$285$	8.70469	+	3.31894i	0.515621	+	0.196597i
$286$	−0.773517	+	0.588147i	−0.0457390	+	0.0347779i
$287$	−7.92473	−	13.7260i	−0.467782	−	0.810222i
$288$	−9.61141	−	13.9865i	−0.566358	−	0.824159i
$289$	−8.18194	+	14.1715i	−0.481291	+	0.833620i
$290$	−0.490136	−	3.85401i	−0.0287818	−	0.226315i
$291$	−9.73665	−	8.42552i	−0.570772	−	0.493913i
$292$	15.7505	−	4.07202i	0.921729	−	0.238297i
$293$	−14.9671	+	2.63910i	−0.874386	+	0.154178i	−0.592792	−	0.805356i	$-0.701974\pi$
$293$	−14.9671	+	2.63910i	−0.874386	+	0.154178i	−0.281594	+	0.959534i	$0.590863\pi$
$294$	−0.492571	+	2.03244i	−0.0287273	+	0.118534i
$295$	5.19192	−	6.18749i	0.302285	−	0.360249i
$296$	7.12360	−	9.03402i	0.414051	−	0.525092i
$297$	8.12969	−	2.54568i	0.471733	−	0.147715i
$298$	−6.51454	−	20.9832i	−0.377377	−	1.21552i
$299$	1.46881	+	1.23248i	0.0849437	+	0.0712762i
$300$	−2.88451	+	1.91824i	−0.166537	+	0.110749i
$301$	1.77962	+	10.0927i	0.102576	+	0.581736i
$302$	−0.0637578	+	1.32626i	−0.00366885	+	0.0763177i
$303$	2.20928	+	6.36957i	0.126920	+	0.365922i
$304$	−11.0836	+	18.4396i	−0.635689	+	1.05758i
$305$	−8.84830	−	5.10857i	−0.506652	−	0.292516i
$306$	−1.40293	+	3.07928i	−0.0802003	+	0.176031i
$307$	−24.7009	+	14.2611i	−1.40976	+	0.813924i	−0.995365	−	0.0961742i	$-0.969339\pi$
$307$	−24.7009	+	14.2611i	−1.40976	+	0.813924i	−0.414393	+	0.910098i	$0.636006\pi$
$308$	6.61759	+	4.72108i	0.377072	+	0.269008i
$309$	−27.1591	+	4.36430i	−1.54503	+	0.248276i
$310$	−4.07788	+	6.33921i	−0.231608	+	0.360043i
$311$	15.6308	−	13.1158i	0.886343	−	0.743730i	−0.0811304	−	0.996703i	$-0.525853\pi$
$311$	15.6308	−	13.1158i	0.886343	−	0.743730i	0.967473	+	0.252974i	$0.0814086\pi$
$312$	0.0312531	+	2.05295i	0.00176936	+	0.116226i
$313$	−16.4372	+	5.98266i	−0.929087	+	0.338160i	−0.761848	−	0.647756i	$-0.775707\pi$
$313$	−16.4372	+	5.98266i	−0.929087	+	0.338160i	−0.167239	+	0.985916i	$0.553485\pi$
$314$	20.6865	+	19.1239i	1.16741	+	1.07923i
$315$	−3.52123	−	6.55112i	−0.198399	−	0.369114i
$316$	−21.2560	+	1.67118i	−1.19574	+	0.0940110i
$317$	27.9657	+	4.93111i	1.57071	+	0.276959i	0.890128	−	0.455711i	$-0.150615\pi$
$317$	27.9657	+	4.93111i	1.57071	+	0.276959i	0.680584	+	0.732670i	$0.261726\pi$
$318$	24.2915	−	2.71474i	1.36220	−	0.152235i
$319$	−1.54042	+	4.23226i	−0.0862467	+	0.236961i
$320$	−3.18824	−	7.33724i	−0.178228	−	0.410164i
$321$	8.73947	+	15.6830i	0.487790	+	0.875342i
$322$	6.20350	−	14.7920i	0.345707	−	0.824326i
$323$	4.28979			0.238690
$324$	5.85680	−	17.0205i	0.325378	−	0.945584i
$325$	0.419106			0.0232478
$326$	5.66225	−	13.5014i	0.313603	−	0.747775i
$327$	4.54387	+	8.15400i	0.251277	+	0.450917i
$328$	8.56063	−	15.9275i	0.472682	−	0.879451i
$329$	6.15017	−	16.8975i	0.339070	−	0.931587i
$330$	3.99102	−	0.446025i	0.219699	−	0.0245528i
$331$	20.2493	+	3.57049i	1.11300	+	0.196252i	0.699766	−	0.714373i	$-0.253288\pi$
$331$	20.2493	+	3.57049i	1.11300	+	0.196252i	0.413235	+	0.910625i	$0.364399\pi$
$332$	−2.21098	−	28.1218i	−0.121343	−	1.54338i
$333$	12.1970	+	0.370935i	0.668391	+	0.0203271i
$334$	1.38868	+	1.28378i	0.0759850	+	0.0702454i
$335$	10.9730	−	3.99386i	0.599521	−	0.218208i
$336$	16.3243	−	5.34189i	0.890565	−	0.291424i
$337$	−17.8816	+	15.0044i	−0.974071	+	0.817343i	−0.983184	−	0.182615i	$-0.941544\pi$
$337$	−17.8816	+	15.0044i	−0.974071	+	0.817343i	0.00911295	+	0.999958i	$0.497099\pi$
$338$	−9.81192	+	15.2530i	−0.533698	+	0.829654i
$339$	13.9079	−	2.23492i	0.755375	−	0.121384i
$340$	−0.926408	+	1.29856i	−0.0502415	+	0.0704241i
$341$	7.56746	−	4.36907i	0.409801	−	0.236599i
$342$	−22.7141	+	2.18942i	−1.22824	+	0.118390i
$343$	−16.8622	−	9.73537i	−0.910471	−	0.525660i
$344$	−8.72402	+	7.78461i	−0.470368	+	0.419718i
$345$	−2.59670	−	7.48655i	−0.139802	−	0.403062i
$346$	−1.32069	+	27.4724i	−0.0710008	+	1.47693i
$347$	1.74622	+	9.90331i	0.0937421	+	0.531638i	0.995126	+	0.0986160i	$0.0314415\pi$
$347$	1.74622	+	9.90331i	0.0937421	+	0.531638i	−0.901383	+	0.433022i	$0.857447\pi$
$348$	5.26968	+	7.92417i	0.282485	+	0.424780i
$349$	2.41987	+	2.03051i	0.129533	+	0.108691i	0.705252	−	0.708956i	$-0.250834\pi$
$349$	2.41987	+	2.03051i	0.129533	+	0.108691i	−0.575720	+	0.817647i	$0.695278\pi$
$350$	−1.03956	−	3.34840i	−0.0555668	−	0.178980i
$351$	−1.73032	+	1.32232i	−0.0923579	+	0.0705800i
$352$	−0.608410	+	9.25427i	−0.0324284	+	0.493254i
$353$	18.0808	−	21.5478i	0.962342	−	1.14687i	−0.0267598	−	0.999642i	$-0.508519\pi$
$353$	18.0808	−	21.5478i	0.962342	−	1.14687i	0.989102	−	0.147233i	$-0.0470366\pi$
$354$	−4.66009	+	19.2284i	−0.247681	+	1.02198i
$355$	4.61625	−	0.813970i	0.245005	−	0.0432010i
$356$	−1.92153	−	7.43245i	−0.101841	−	0.393919i
$357$	−2.58978	−	2.24104i	−0.137066	−	0.118609i
$358$	−4.16543	−	32.7534i	−0.220150	−	1.73107i
$359$	−7.94117	+	13.7545i	−0.419119	+	0.725935i	−0.995851	−	0.0909979i	$-0.970994\pi$
$359$	−7.94117	+	13.7545i	−0.419119	+	0.725935i	0.576732	+	0.816933i	$0.304328\pi$
$360$	4.24249	−	7.34856i	0.223599	−	0.387303i
$361$	4.96449	+	8.59876i	0.261289	+	0.452566i
$362$	25.8969	−	19.6908i	1.36111	−	1.03493i
$363$	13.4524	+	5.12916i	0.706067	+	0.269211i
$364$	−2.00244	−	0.555498i	−0.104956	−	0.0291160i
$365$	5.22855	+	6.23115i	0.273675	+	0.326153i
$366$	24.9768	+	1.58158i	1.30556	+	0.0826707i
$367$	3.73173	+	10.2528i	0.194795	+	0.535194i	0.998183	−	0.0602622i	$-0.0191937\pi$
$367$	3.73173	+	10.2528i	0.194795	+	0.535194i	−0.803388	+	0.595456i	$0.796971\pi$
$368$	18.0751	−	2.85985i	0.942228	−	0.149080i
$369$	18.9804	−	2.75475i	0.988078	−	0.143406i
$370$	5.61048	+	1.26976i	0.291675	+	0.0660116i
$371$	−4.29584	+	24.3629i	−0.223029	+	1.26486i
$372$	2.05024	−	18.3490i	0.106300	−	0.951350i
$373$	−21.2856	−	7.74732i	−1.10213	−	0.401141i	−0.274027	−	0.961722i	$-0.588356\pi$
$373$	−21.2856	−	7.74732i	−1.10213	−	0.401141i	−0.828100	+	0.560581i	$0.810578\pi$
$374$	1.64402	−	0.846644i	0.0850103	−	0.0437789i
$375$	−1.48666	−	0.888726i	−0.0767709	−	0.0458936i
$376$	20.0858	−	4.17535i	1.03585	−	0.215327i
$377$		−	1.15135i		−	0.0592973i
$378$	14.8564	+	10.5443i	0.764133	+	0.542343i
$379$			11.8903i			0.610762i	0.952230	+	0.305381i	$0.0987839\pi$
$379$			11.8903i			0.610762i	−0.952230	+	0.305381i	$0.901216\pi$
$380$	−10.7075	−	1.03188i	−0.549285	−	0.0529343i
$381$	0.247222	−	16.2619i	0.0126656	−	0.833124i
$382$	2.31146	+	4.48842i	0.118265	+	0.229648i
$383$	20.5562	+	7.48186i	1.05037	+	0.382305i	0.808804	−	0.588078i	$-0.200115\pi$
$383$	20.5562	+	7.48186i	1.05037	+	0.382305i	0.241571	+	0.970383i	$0.422337\pi$
$384$	14.9812	+	12.6319i	0.764506	+	0.644617i
$385$	−0.705796	+	4.00277i	−0.0359707	+	0.204000i
$386$	6.30385	−	27.8538i	0.320858	−	1.41772i
$387$	−12.1420	−	2.52376i	−0.617212	−	0.128290i
$388$	13.4191	+	6.40188i	0.681250	+	0.325006i
$389$	13.1787	+	36.2081i	0.668184	+	1.83582i	0.535245	+	0.844697i	$0.320219\pi$
$389$	13.1787	+	36.2081i	0.668184	+	1.83582i	0.132939	+	0.991124i	$0.457558\pi$
$390$	−0.919719	+	0.456087i	−0.0465718	+	0.0230949i
$391$	−2.34545	−	2.79520i	−0.118614	−	0.141359i
$392$	−0.0734555	−	2.41368i	−0.00371006	−	0.121909i
$393$	21.6781	−	17.6356i	1.09352	−	0.889596i
$394$	10.1026	+	13.2867i	0.508961	+	0.669373i
$395$	−5.33039	−	9.23251i	−0.268201	−	0.464538i
$396$	−8.27283	+	5.32198i	−0.415726	+	0.267439i
$397$	12.9145	−	22.3685i	0.648160	−	1.12265i	−0.335402	−	0.942075i	$-0.608872\pi$
$397$	12.9145	−	22.3685i	0.648160	−	1.12265i	0.983562	−	0.180570i	$-0.0577944\pi$
$398$	5.12127	−	0.651301i	0.256706	−	0.0326468i
$399$	4.35581	−	22.6813i	0.218063	−	1.13548i
$400$	2.62472	−	3.01842i	0.131236	−	0.150921i
$401$	−1.22169	+	0.215418i	−0.0610085	+	0.0107574i	−0.204069	−	0.978956i	$-0.565417\pi$
$401$	−1.22169	+	0.215418i	−0.0610085	+	0.0107574i	0.143061	+	0.989714i	$0.454306\pi$
$402$	−19.7338	+	20.7057i	−0.984233	+	1.03271i
$403$	−1.43584	+	1.71117i	−0.0715244	+	0.0852394i
$404$	−4.40885	−	6.41601i	−0.219348	−	0.319208i
$405$	8.94186	−	1.02134i	0.444325	−	0.0507510i
$406$	−9.19856	+	2.85583i	−0.456517	+	0.141732i
$407$	−5.10846	−	4.28651i	−0.253217	−	0.212474i
$408$	0.619842	−	3.85781i	0.0306868	−	0.190990i
$409$	−2.31853	−	13.1490i	−0.114644	−	0.650177i	−0.986926	−	0.161174i	$-0.948472\pi$
$409$	−2.31853	−	13.1490i	−0.114644	−	0.650177i	0.872282	−	0.489003i	$-0.162639\pi$
$410$	9.03074	+	0.434139i	0.445997	+	0.0214406i
$411$	−33.0401	−	6.34517i	−1.62975	−	0.312984i
$412$	28.9041	−	13.1696i	1.42400	−	0.648819i
$413$	−17.3419	−	10.0123i	−0.853337	−	0.492675i
$414$	13.8456	+	13.6032i	0.680472	+	0.668563i
$415$	12.2147	−	7.05214i	0.599594	−	0.346176i
$416$	−0.662970	−	2.27624i	−0.0325048	−	0.111602i
$417$	−13.7280	−	16.8748i	−0.672262	−	0.826363i
$418$	10.4879	+	6.74667i	0.512982	+	0.329990i
$419$	12.5609	−	10.5398i	0.613640	−	0.514905i	−0.282157	−	0.959368i	$-0.591050\pi$
$419$	12.5609	−	10.5398i	0.613640	−	0.514905i	0.895797	+	0.444463i	$0.146606\pi$
$420$	5.92515	+	6.21671i	0.289118	+	0.303344i
$421$	−16.3285	+	5.94307i	−0.795800	+	0.289648i	−0.707745	−	0.706468i	$-0.750287\pi$
$421$	−16.3285	+	5.94307i	−0.795800	+	0.289648i	−0.0880552	+	0.996116i	$0.528065\pi$
$422$	3.85870	−	4.17399i	0.187839	−	0.203187i
$423$	16.2360	+	14.4871i	0.789421	+	0.704386i
$424$	−26.2159	+	10.4555i	−1.27316	+	0.507762i
$425$	−0.785455	−	0.138497i	−0.0381001	−	0.00671808i
$426$	−9.24447	+	6.80982i	−0.447896	+	0.329937i
$427$	−8.66335	+	23.8024i	−0.419249	+	1.15188i
$428$	−14.5295	−	14.7877i	−0.702309	−	0.714789i
$429$	1.18998	+	0.0180906i	0.0574526	+	0.000873422i
$430$	−5.39121	−	2.26098i	−0.259987	−	0.109034i
$431$	27.5337			1.32625			0.663126	−	0.748507i	$-0.269229\pi$
$431$	27.5337			1.32625			0.663126	+	0.748507i	$0.269229\pi$
$432$	−1.31306	+	20.7431i	−0.0631747	+	0.998002i
$433$	−21.5340			−1.03486			−0.517429	−	0.855726i	$-0.673111\pi$
$433$	−21.5340			−1.03486			−0.517429	+	0.855726i	$0.673111\pi$
$434$	17.2327	+	7.22708i	0.827196	+	0.346911i
$435$	−2.44146	+	4.08408i	−0.117059	+	0.195817i
$436$	−7.55424	−	7.68848i	−0.361782	−	0.368211i
$437$	8.41603	−	23.1229i	0.402593	−	1.10612i
$438$	−18.2549	−	7.98420i	−0.872254	−	0.381500i
$439$	−36.5856	−	6.45103i	−1.74614	−	0.307891i	−0.792729	−	0.609574i	$-0.791340\pi$
$439$	−36.5856	−	6.45103i	−1.74614	−	0.307891i	−0.953408	+	0.301683i	$0.902451\pi$
$440$	−4.30721	+	1.71781i	−0.205338	+	0.0818932i
$441$	2.01119	−	1.58595i	0.0957710	−	0.0755216i
$442$	−0.320900	+	0.347120i	−0.0152636	+	0.0165108i
$443$	−15.5904	+	5.67442i	−0.740720	+	0.269600i	−0.684695	−	0.728829i	$-0.740065\pi$
$443$	−15.5904	+	5.67442i	−0.740720	+	0.269600i	−0.0560246	+	0.998429i	$0.517843\pi$
$444$	−13.6939	+	3.31909i	−0.649883	+	0.157517i
$445$	2.94039	−	2.46728i	0.139388	−	0.116960i
$446$	22.4952	+	14.4707i	1.06518	+	0.685205i
$447$	−9.58677	+	25.1435i	−0.453439	+	1.18925i
$448$	−16.5413	+	10.9428i	−0.781504	+	0.516997i
$449$	−1.90305	+	1.09873i	−0.0898105	+	0.0518521i	−0.544233	−	0.838934i	$-0.683179\pi$
$449$	−1.90305	+	1.09873i	−0.0898105	+	0.0518521i	0.454422	+	0.890786i	$0.349846\pi$
$450$	4.22960	+	0.332448i	0.199385	+	0.0156717i
$451$	−9.07704	−	5.24063i	−0.427421	−	0.246772i
$452$	−14.8015	+	6.74402i	−0.696205	+	0.317212i
$453$	1.06412	−	1.22971i	0.0499967	−	0.0577769i
$454$	26.0915	+	1.25431i	1.22453	+	0.0588675i
$455$	−0.180426	−	1.02325i	−0.00845849	−	0.0479705i
$456$	24.6204	−	9.38791i	1.15295	−	0.439629i
$457$	−23.3525	−	19.5951i	−1.09239	−	0.916620i	−0.0954960	−	0.995430i	$-0.530444\pi$
$457$	−23.3525	−	19.5951i	−1.09239	−	0.916620i	−0.996890	+	0.0788094i	$0.974888\pi$
$458$	−24.6244	+	7.64501i	−1.15062	+	0.357228i
$459$	3.67981	−	1.90638i	0.171759	−	0.0889821i
$460$	5.18199	+	7.54113i	0.241612	+	0.351607i
$461$	1.80544	−	2.15164i	0.0840877	−	0.100212i	−0.722360	−	0.691517i	$-0.756943\pi$
$461$	1.80544	−	2.15164i	0.0840877	−	0.100212i	0.806448	+	0.591305i	$0.201387\pi$
$462$	−2.80711	−	9.55206i	−0.130599	−	0.444402i
$463$	6.53427	−	1.15217i	0.303673	−	0.0535458i	−0.0197352	−	0.999805i	$-0.506282\pi$
$463$	6.53427	−	1.15217i	0.303673	−	0.0535458i	0.323409	+	0.946259i	$0.395171\pi$
$464$	−8.29205	−	7.21049i	−0.384949	−	0.334739i
$465$	8.72184	−	3.02516i	0.404466	−	0.140288i
$466$	−19.1394	+	2.43406i	−0.886614	+	0.112756i
$467$	15.7546	−	27.2877i	0.729034	−	1.26272i	−0.228258	−	0.973601i	$-0.573303\pi$
$467$	15.7546	−	27.2877i	0.729034	−	1.26272i	0.957292	−	0.289123i	$-0.0933638\pi$
$468$	1.52197	−	2.00175i	0.0703532	−	0.0925308i
$469$	−14.4749	−	25.0713i	−0.668389	−	1.15768i
$470$	6.20854	+	8.16532i	0.286378	+	0.376638i
$471$	−5.47425	−	34.0664i	−0.252240	−	1.56970i
$472$	−0.694943	−	22.8352i	−0.0319874	−	1.05107i
$473$	4.35637	+	5.19172i	0.200306	+	0.238715i
$474$	21.7446	+	14.4598i	0.998763	+	0.664161i
$475$	−1.83958	−	5.05420i	−0.0844056	−	0.231903i
$476$	3.56924	+	1.70279i	0.163596	+	0.0780473i
$477$	−25.4584	−	15.7492i	−1.16566	−	0.721106i
$478$	3.06196	−	13.5294i	0.140051	−	0.618821i
$479$	−1.17300	+	6.65240i	−0.0535956	+	0.303956i	−0.999808	−	0.0195900i	$-0.993764\pi$
$479$	−1.17300	+	6.65240i	−0.0535956	+	0.303956i	0.946212	+	0.323546i	$0.104875\pi$
$480$	−2.47513	+	9.48018i	−0.112974	+	0.432709i
$481$	1.60192	+	0.583052i	0.0730414	+	0.0265849i
$482$	16.5869	+	32.2086i	0.755513	+	1.46706i
$483$	−17.1605	+	9.56281i	−0.780830	+	0.435123i
$484$	−16.5476	−	1.59469i	−0.752164	−	0.0724857i
$485$			7.43397i			0.337559i
$486$	−18.5113	+	11.9722i	−0.839688	+	0.543070i
$487$			24.2981i			1.10105i	0.834818	+	0.550527i	$0.185573\pi$
$487$			24.2981i			1.10105i	−0.834818	+	0.550527i	$0.814427\pi$
$488$	−28.2936	+	5.88154i	−1.28079	+	0.266245i
$489$	−15.6633	+	8.72846i	−0.708318	+	0.394715i
$490$	1.07342	−	0.552793i	0.0484921	−	0.0249726i
$491$	24.7026	+	8.99102i	1.11481	+	0.405759i	0.832757	−	0.553639i	$-0.186761\pi$
$491$	24.7026	+	8.99102i	1.11481	+	0.405759i	0.282057	+	0.959398i	$0.408983\pi$
$492$	−20.2902	+	8.87489i	−0.914754	+	0.400111i
$493$	−0.380471	+	2.15776i	−0.0171356	+	0.0971806i
$494$	−3.10927	−	0.703686i	−0.139893	−	0.0316603i
$495$	−4.18275	−	2.58755i	−0.188001	−	0.116302i
$496$	3.33173	+	21.0575i	0.149599	+	0.945508i
$497$	−3.97461	−	10.9201i	−0.178286	−	0.489836i
$498$	−19.1304	+	28.7682i	−0.857254	+	1.28914i
$499$	−15.9246	−	18.9782i	−0.712883	−	0.849581i	0.281036	−	0.959697i	$-0.409322\pi$
$499$	−15.9246	−	18.9782i	−0.712883	−	0.849581i	−0.993919	+	0.110116i	$0.964878\pi$
$500$	1.92722	+	0.534630i	0.0861878	+	0.0239094i
$501$	−0.367484	−	2.28686i	−0.0164180	−	0.102169i
$502$	−31.2010	+	23.7238i	−1.39257	+	1.05885i
$503$	−10.4191	−	18.0464i	−0.464565	−	0.804650i	0.534617	−	0.845095i	$-0.320456\pi$
$503$	−10.4191	−	18.0464i	−0.464565	−	0.804650i	−0.999182	+	0.0404446i	$0.987123\pi$
$504$	−19.7679	−	7.19445i	−0.880532	−	0.320466i
$505$	1.94620	−	3.37092i	0.0866048	−	0.150004i
$506$	−1.33822	−	10.5226i	−0.0594911	−	0.467788i
$507$	20.9859	−	7.27894i	0.932018	−	0.323269i
$508$	4.70065	+	18.1820i	0.208557	+	0.806697i
$509$	−5.38944	+	0.950303i	−0.238883	+	0.0421214i	−0.291808	−	0.956477i	$-0.594257\pi$
$509$	−5.38944	+	0.950303i	−0.238883	+	0.0421214i	0.0529250	+	0.998598i	$0.483146\pi$
$510$	1.87438	−	0.550834i	0.0829990	−	0.0243913i
$511$	12.9624	−	15.4480i	0.573424	−	0.683380i
$512$	−20.5455	−	9.48056i	−0.907993	−	0.418986i
$513$	23.5413	+	15.0628i	1.03938	+	0.665039i
$514$	−6.74308	−	21.7193i	−0.297425	−	0.957999i
$515$	12.1659	+	10.2084i	0.536095	+	0.449837i
$516$	14.2914	−	0.905263i	0.629143	−	0.0398520i
$517$	−2.06493	−	11.7108i	−0.0908154	−	0.515040i
$518$	0.684787	−	14.2446i	0.0300878	−	0.625872i
$519$	22.0424	−	25.4725i	0.967554	−	1.11812i
$520$	0.884478	−	0.789237i	0.0387869	−	0.0346103i
$521$	−16.2718	−	9.39453i	−0.712881	−	0.411582i	0.0992460	−	0.995063i	$-0.468357\pi$
$521$	−16.2718	−	9.39453i	−0.712881	−	0.411582i	−0.812127	+	0.583481i	$0.801690\pi$
$522$	0.913283	−	11.6193i	0.0399733	−	0.508564i
$523$	−7.09156	+	4.09431i	−0.310092	+	0.179032i	−0.646968	−	0.762517i	$-0.723963\pi$
$523$	−7.09156	+	4.09431i	−0.310092	+	0.179032i	0.336876	+	0.941549i	$0.390630\pi$
$524$	−18.7406	+	26.2690i	−0.818689	+	1.14757i
$525$	−1.52981	+	4.01228i	−0.0667665	+	0.175110i
$526$	2.78739	−	4.33311i	0.121536	−	0.188932i
$527$	3.25641	−	2.73245i	0.141851	−	0.119027i
$528$	7.58270	−	8.45696i	0.329995	−	0.368042i
$529$	1.94476	−	0.707837i	0.0845550	−	0.0307755i
$530$	−10.3624	−	9.57964i	−0.450112	−	0.416113i
$531$	19.0274	−	15.0043i	0.825717	−	0.651131i
$532$	2.09028	+	26.5866i	0.0906251	+	1.15268i
$533$	2.63867	+	0.465268i	0.114293	+	0.0201530i
$534$	−3.76764	+	8.61424i	−0.163042	+	0.372775i
$535$	3.54524	−	9.74046i	0.153274	−	0.421117i
$536$	15.6364	−	29.0924i	0.675390	−	1.25660i
$537$	−20.7488	+	34.7087i	−0.895378	+	1.49779i
$538$	2.28496	−	5.44841i	0.0985118	−	0.234898i
$539$	−1.39971			−0.0602899
$540$	−9.64354	+	3.87326i	−0.414992	+	0.166679i
$541$	27.7319			1.19229			0.596145	−	0.802877i	$-0.296698\pi$
$541$	27.7319			1.19229			0.596145	+	0.802877i	$0.296698\pi$
$542$	3.90906	−	9.32100i	0.167908	−	0.400371i
$543$	−39.8397	−	0.605663i	−1.70968	−	0.0259915i
$544$	0.490285	+	4.48503i	0.0210208	+	0.192294i
$545$	1.84326	−	5.06431i	0.0789565	−	0.216931i
$546$	1.50948	+	2.04914i	0.0645996	+	0.0876953i
$547$	−15.0716	−	2.65752i	−0.644414	−	0.113627i	−0.158116	−	0.987421i	$-0.550542\pi$
$547$	−15.0716	−	2.65752i	−0.644414	−	0.113627i	−0.486298	+	0.873793i	$0.661653\pi$
$548$	38.7291	−	3.04494i	1.65443	−	0.130073i
$549$	−22.8706	−	20.4070i	−0.976093	−	0.870950i
$550$	−1.70251	−	1.57391i	−0.0725953	−	0.0671118i
$551$	−13.8846	+	5.05360i	−0.591506	+	0.215290i
$552$	−19.5783	−	10.9096i	−0.833309	−	0.464344i
$553$	−20.2464	+	16.9888i	−0.860965	+	0.722435i
$554$	−2.22627	+	3.46082i	−0.0945852	+	0.147036i
$555$	−4.44600	−	5.46514i	−0.188722	−	0.231982i
$556$	20.4485	+	14.5882i	0.867208	+	0.618678i
$557$	−23.7377	+	13.7050i	−1.00580	+	0.580699i	−0.909959	−	0.414698i	$-0.863887\pi$
$557$	−23.7377	+	13.7050i	−1.00580	+	0.580699i	−0.0958409	+	0.995397i	$0.530554\pi$
$558$	−15.8478	+	16.1301i	−0.670891	+	0.682841i
$559$	−1.50040	−	0.866257i	−0.0634602	−	0.0366388i
$560$	−8.49941	−	5.10881i	−0.359166	−	0.215886i
$561$	−2.22418	−	0.427141i	−0.0939049	−	0.0180339i
$562$	−0.886940	+	18.4497i	−0.0374133	+	0.778253i
$563$	2.33926	+	13.2666i	0.0985881	+	0.559121i	0.993589	+	0.113056i	$0.0360639\pi$
$563$	2.33926	+	13.2666i	0.0985881	+	0.559121i	−0.895000	+	0.446065i	$0.852825\pi$
$564$	−22.5103	−	11.1622i	−0.947855	−	0.470015i
$565$	−6.23006	−	5.22764i	−0.262100	−	0.219928i
$566$	−2.82296	−	9.09270i	−0.118658	−	0.382195i
$567$	−6.34309	−	21.3918i	−0.266385	−	0.898373i
$568$	8.20929	−	10.4109i	0.344454	−	0.436830i
$569$	−1.83979	+	2.19258i	−0.0771281	+	0.0919177i	−0.803229	−	0.595671i	$-0.796886\pi$
$569$	−1.83979	+	2.19258i	−0.0771281	+	0.0919177i	0.726101	+	0.687589i	$0.241331\pi$
$570$	9.53709	+	9.08943i	0.399465	+	0.380714i
$571$	−0.188500	+	0.0332376i	−0.00788847	+	0.00139095i	−0.177591	−	0.984104i	$-0.556830\pi$
$571$	−0.188500	+	0.0332376i	−0.00788847	+	0.00139095i	0.169703	+	0.985495i	$0.445719\pi$
$572$	−1.33048	+	0.343972i	−0.0556301	+	0.0143822i
$573$	1.16616	−	6.07234i	0.0487169	−	0.253676i
$574$	−2.82780	−	22.2354i	−0.118030	−	0.928089i
$575$	−2.28749	+	3.96205i	−0.0953949	+	0.165229i
$576$	−4.88508	−	23.4976i	−0.203545	−	0.979066i
$577$	−11.2670	−	19.5151i	−0.469052	−	0.812422i	0.530322	−	0.847796i	$-0.322071\pi$
$577$	−11.2670	−	19.5151i	−0.469052	−	0.812422i	−0.999374	+	0.0353742i	$0.988738\pi$
$578$	−18.4217	+	14.0070i	−0.766240	+	0.582614i
$579$	−27.1323	+	22.0726i	−1.12758	+	0.917308i
$580$	1.46871	−	5.29436i	0.0609848	−	0.219836i
$581$	−22.4762	−	26.7861i	−0.932471	−	1.11128i
$582$	−8.08993	−	16.3137i	−0.335338	−	0.676224i
$583$	5.59537	+	15.3732i	0.231737	+	0.636691i
$584$	22.7685	+	3.30405i	0.942166	+	0.136723i
$585$	1.23101	+	0.255869i	0.0508959	+	0.0105789i
$586$	−20.9630	−	4.74432i	−0.865974	−	0.195986i
$587$	−2.29609	+	13.0218i	−0.0947699	+	0.537467i	0.900048	+	0.435791i	$0.143531\pi$
$587$	−2.29609	+	13.0218i	−0.0947699	+	0.537467i	−0.994818	+	0.101675i	$0.967580\pi$
$588$	−1.75402	+	2.38123i	−0.0723347	+	0.0982002i
$589$	26.9382	+	9.80469i	1.10997	+	0.403995i
$590$	10.1553	−	5.22983i	0.418089	−	0.215309i
$591$	0.310742	−	20.4402i	0.0127822	−	0.840796i
$592$	14.2315	−	7.88567i	0.584910	−	0.324099i
$593$			42.2366i			1.73445i	0.497916	+	0.867225i	$0.334099\pi$
$593$			42.2366i			1.73445i	−0.497916	+	0.867225i	$0.665901\pi$
$594$	11.9948	+	1.12649i	0.492154	+	0.0462206i
$595$			1.97731i			0.0810617i
$596$	2.98059	−	30.9287i	0.122090	−	1.26689i
$597$	−5.42699	−	3.24426i	−0.222112	−	0.132779i
$598$	1.24148	+	2.41072i	0.0507679	+	0.0985817i
$599$	1.88013	+	0.684311i	0.0768200	+	0.0279602i	0.380144	−	0.924927i	$-0.375874\pi$
$599$	1.88013	+	0.684311i	0.0768200	+	0.0279602i	−0.303324	+	0.952887i	$0.598097\pi$
$600$	−4.81104	+	0.924038i	−0.196410	+	0.0377237i
$601$	−2.88896	+	16.3841i	−0.117843	+	0.668321i	0.867460	+	0.497507i	$0.165751\pi$
$601$	−2.88896	+	16.3841i	−0.117843	+	0.668321i	−0.985303	+	0.170815i	$0.945360\pi$
$602$	−3.19924	+	14.1360i	−0.130391	+	0.576140i
$603$	34.6685	−	5.03168i	1.41181	−	0.204906i
$604$	−0.808541	+	1.69479i	−0.0328990	+	0.0689601i
$605$	−2.84292	−	7.81085i	−0.115581	−	0.317556i
$606$	−0.602532	+	9.51534i	−0.0244762	+	0.386534i
$607$	−5.19622	−	6.19261i	−0.210908	−	0.251350i	0.650211	−	0.759753i	$-0.274680\pi$
$607$	−5.19622	−	6.19261i	−0.210908	−	0.251350i	−0.861119	+	0.508403i	$0.830236\pi$
$608$	−24.5403	+	17.9862i	−0.995240	+	0.729435i
$609$	11.0223	+	4.20262i	0.446647	+	0.170299i
$610$	−8.74557	−	11.5020i	−0.354098	−	0.465701i
$611$	1.51993	+	2.63260i	0.0614899	+	0.106504i
$612$	−3.51385	+	3.24857i	−0.142039	+	0.131316i
$613$	−7.45343	+	12.9097i	−0.301041	+	0.521419i	−0.976372	−	0.216096i	$-0.930668\pi$
$613$	−7.45343	+	12.9097i	−0.301041	+	0.521419i	0.675331	+	0.737515i	$0.264001\pi$
$614$	−40.0142	+	5.08883i	−1.61484	+	0.205368i
$615$	−8.37333	−	7.24579i	−0.337645	−	0.292178i
$616$	6.04828	+	9.77653i	0.243692	+	0.393908i
$617$	8.50384	−	1.49946i	0.342352	−	0.0603659i	0.000170965	−	1.00000i	$-0.499946\pi$
$617$	8.50384	−	1.49946i	0.342352	−	0.0603659i	0.342181	+	0.939634i	$0.388834\pi$
$618$	−37.8071	−	9.16274i	−1.52082	−	0.368579i
$619$	−15.7565	+	18.7778i	−0.633306	+	0.754745i	−0.983297	−	0.182009i	$-0.941740\pi$
$619$	−15.7565	+	18.7778i	−0.633306	+	0.754745i	0.349991	+	0.936753i	$0.386185\pi$
$620$	−8.78543	+	6.03702i	−0.352831	+	0.242453i
$621$	−3.05645	−	23.5750i	−0.122651	−	0.946031i
$622$	27.5588	−	8.55604i	1.10501	−	0.343066i
$623$	−7.28971	−	6.11679i	−0.292056	−	0.245064i
$624$	−1.08209	+	2.69449i	−0.0433183	+	0.107866i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	−24.7091	−	1.18785i	−0.987573	−	0.0474760i
$627$	−5.00499	−	14.4299i	−0.199880	−	0.576275i
$628$	16.5189	+	36.2552i	0.659177	+	1.44674i
$629$	−2.80952	−	1.62208i	−0.112023	−	0.0646765i
$630$	−1.00918	−	10.4697i	−0.0402066	−	0.417121i
$631$	33.5553	−	19.3732i	1.33582	−	0.771234i	0.349632	−	0.936887i	$-0.386307\pi$
$631$	33.5553	−	19.3732i	1.33582	−	0.771234i	0.986184	+	0.165653i	$0.0529733\pi$
$632$	−28.6354	−	9.44633i	−1.13905	−	0.375755i
$633$	−6.87369	+	1.10456i	−0.273205	+	0.0439023i
$634$	33.7749	+	21.7267i	1.34137	+	0.862877i
$635$	−7.19309	+	6.03572i	−0.285449	+	0.239520i
$636$	33.1649	+	9.74559i	1.31507	+	0.386438i
$637$	0.336236	−	0.122380i	0.0133222	−	0.00484887i
$638$	−4.32377	+	4.67705i	−0.171180	+	0.185166i
$639$	14.0559	+	0.427468i	0.556043	+	0.0169104i
$640$	−0.144934	−	11.3128i	−0.00572901	−	0.447177i
$641$	3.98093	+	0.701946i	0.157237	+	0.0277252i	0.251713	−	0.967802i	$-0.419006\pi$
$641$	3.98093	+	0.701946i	0.157237	+	0.0277252i	−0.0944752	+	0.995527i	$0.530117\pi$
$642$	2.82000	+	25.2333i	0.111296	+	0.995879i
$643$	−9.30242	+	25.5582i	−0.366851	+	1.00792i	0.609700	+	0.792632i	$0.291290\pi$
$643$	−9.30242	+	25.5582i	−0.366851	+	1.00792i	−0.976552	+	0.215284i	$0.930932\pi$
$644$	16.1808	−	15.8983i	0.637613	−	0.626480i
$645$	3.48534	+	6.25446i	0.137235	+	0.246269i
$646$	5.59461	+	2.34628i	0.220117	+	0.0923130i
$647$	34.3856			1.35184			0.675919	−	0.736976i	$-0.263747\pi$
$647$	34.3856			1.35184			0.675919	+	0.736976i	$0.263747\pi$
$648$	16.9475	−	18.9943i	0.665761	−	0.746165i
$649$	−13.2423			−0.519807
$650$	0.546584	+	0.229227i	0.0214388	+	0.00899104i
$651$	−11.1407	−	19.9920i	−0.436638	−	0.783549i
$652$	14.7690	−	14.5112i	0.578400	−	0.568302i
$653$	2.59500	−	7.12971i	0.101550	−	0.279007i	−0.878505	−	0.477734i	$-0.841458\pi$
$653$	2.59500	−	7.12971i	0.101550	−	0.279007i	0.980055	+	0.198727i	$0.0636806\pi$
$654$	1.46619	+	13.1194i	0.0573324	+	0.513010i
$655$	−15.8892	−	2.80170i	−0.620844	−	0.109472i
$656$	19.8760	−	16.0900i	0.776026	−	0.628209i
$657$	11.5532	+	21.4944i	0.450734	+	0.838575i
$658$	17.2628	−	18.6733i	0.672975	−	0.727962i
$659$	6.67702	−	2.43024i	0.260100	−	0.0946686i	−0.208679	−	0.977984i	$-0.566916\pi$
$659$	6.67702	−	2.43024i	0.260100	−	0.0946686i	0.468779	+	0.883316i	$0.344694\pi$
$660$	5.44891	+	1.60117i	0.212099	+	0.0623256i
$661$	−0.733943	+	0.615851i	−0.0285471	+	0.0239538i	−0.656950	−	0.753935i	$-0.728154\pi$
$661$	−0.733943	+	0.615851i	−0.0285471	+	0.0239538i	0.628402	+	0.777888i	$0.283709\pi$
$662$	24.4556	+	15.7317i	0.950493	+	0.611431i
$663$	0.571634	−	0.0918579i	0.0222004	−	0.00356747i
$664$	12.4976	−	37.8848i	0.484999	−	1.47021i
$665$	−11.5479	+	6.66717i	−0.447807	+	0.258542i
$666$	15.7040	+	7.15483i	0.608519	+	0.277244i
$667$	10.8843	+	6.28407i	0.421443	+	0.243320i
$668$	1.10891	+	2.43379i	0.0429050	+	0.0941663i
$669$	−10.7350	−	30.9501i	−0.415039	−	1.19660i
$670$	16.4951	+	0.792975i	0.637261	+	0.0306353i
$671$	2.90873	+	16.4962i	0.112290	+	0.636830i
$672$	24.2114	+	1.96178i	0.933974	+	0.0756773i
$673$	24.4680	+	20.5311i	0.943171	+	0.791414i	0.978134	−	0.207974i	$-0.0666870\pi$
$673$	24.4680	+	20.5311i	0.943171	+	0.791414i	−0.0349635	+	0.999389i	$0.511131\pi$
$674$	−31.5271	+	9.78806i	−1.21438	+	0.377022i
$675$	−3.82408	−	3.51801i	−0.147189	−	0.135408i
$676$	−21.1389	+	14.5259i	−0.813036	+	0.558688i
$677$	−15.4287	+	18.3872i	−0.592973	+	0.706678i	−0.976175	−	0.216987i	$-0.930377\pi$
$677$	−15.4287	+	18.3872i	−0.592973	+	0.706678i	0.383201	+	0.923665i	$0.374822\pi$
$678$	19.3606	+	4.69215i	0.743541	+	0.180201i
$679$	18.1500	−	3.20034i	0.696534	−	0.122818i
$680$	−1.91843	+	1.18684i	−0.0735684	+	0.0455133i
$681$	−24.1921	−	20.9344i	−0.927043	−	0.802208i
$682$	12.2589	−	1.55903i	0.469416	−	0.0596983i
$683$	−2.44322	+	4.23178i	−0.0934872	+	0.161925i	−0.908976	−	0.416848i	$-0.863135\pi$
$683$	−2.44322	+	4.23178i	−0.0934872	+	0.161925i	0.815489	+	0.578773i	$0.196468\pi$
$684$	−30.8204	−	9.56794i	−1.17845	−	0.365839i
$685$	9.71215	+	16.8219i	0.371082	+	0.642733i
$686$	−16.6664	−	21.9192i	−0.636325	−	0.836879i
$687$	29.5066	+	11.2504i	1.12575	+	0.429228i
$688$	−15.6353	+	5.38089i	−0.596091	+	0.205144i
$689$	−2.68822	−	3.20369i	−0.102413	−	0.122051i
$690$	0.708193	−	11.1840i	0.0269604	−	0.425766i
$691$	−1.46781	−	4.03276i	−0.0558379	−	0.153413i	0.908638	−	0.417585i	$-0.137124\pi$
$691$	−1.46781	−	4.03276i	−0.0558379	−	0.153413i	−0.964476	+	0.264172i	$0.914901\pi$
$692$	−16.7483	+	35.1063i	−0.636673	+	1.33454i
$693$	−4.51682	+	11.3261i	−0.171580	+	0.430244i
$694$	−3.13919	+	13.8707i	−0.119162	+	0.526523i
$695$	−2.18092	+	12.3686i	−0.0827270	+	0.469168i
$696$	2.53847	+	13.2167i	0.0962205	+	0.500976i
$697$	−4.79143	−	1.74394i	−0.181488	−	0.0660563i
$698$	2.04534	+	3.97166i	0.0774172	+	0.150330i
$699$	20.2819	+	12.1245i	0.767132	+	0.458591i
$700$	0.475628	−	4.93546i	0.0179770	−	0.186543i
$701$			43.7914i			1.65398i	0.562218	+	0.826989i	$0.309948\pi$
$701$			43.7914i			1.65398i	−0.562218	+	0.826989i	$0.690052\pi$
$702$	−2.97987	+	0.778130i	−0.112468	+	0.0293686i
$703$		−	21.8776i		−	0.825128i
$704$	−5.85504	+	11.7364i	−0.220670	+	0.442331i
$705$	0.190966	−	12.5615i	0.00719220	−	0.473093i
$706$	35.3658	−	18.2128i	1.33101	−	0.685448i
$707$	−9.06793	−	3.30046i	−0.341035	−	0.124126i
$708$	−16.5944	+	22.5282i	−0.623655	+	0.846661i
$709$	6.95189	−	39.4261i	0.261084	−	1.48068i	−0.518876	−	0.854850i	$-0.673649\pi$
$709$	6.95189	−	39.4261i	0.261084	−	1.48068i	0.779960	−	0.625830i	$-0.215240\pi$
$710$	6.46556	+	1.46328i	0.242648	+	0.0549158i
$711$	−10.0200	−	30.3722i	−0.375779	−	1.13905i
$712$	1.55914	−	10.7441i	0.0584311	−	0.402653i
$713$	−8.33981	−	22.9134i	−0.312328	−	0.858115i
$714$	−2.15178	−	4.33916i	−0.0805285	−	0.162389i
$715$	−0.441667	−	0.526358i	−0.0165174	−	0.0196847i
$716$	12.4819	−	44.9942i	0.466469	−	1.68151i
$717$	−13.1789	+	10.7213i	−0.492176	+	0.400395i
$718$	−17.8796	+	13.5948i	−0.667259	+	0.507354i
$719$	21.3934	+	37.0544i	0.797838	+	1.38190i	0.921021	+	0.389512i	$0.127356\pi$
$719$	21.3934	+	37.0544i	0.797838	+	1.38190i	−0.123183	+	0.992384i	$0.539310\pi$
$720$	9.55216	−	7.26335i	0.355988	−	0.270689i
$721$	19.6864	−	34.0978i	0.733159	−	1.26987i
$722$	1.77149	+	13.9295i	0.0659282	+	0.518403i
$723$	8.36827	−	43.5747i	0.311219	−	1.62056i
$724$	44.5437	−	11.5160i	1.65545	−	0.427988i
$725$	2.70541	−	0.477037i	0.100477	−	0.0177167i
$726$	14.7388	+	14.0470i	0.547008	+	0.521332i
$727$	−13.8890	+	16.5523i	−0.515115	+	0.613890i	−0.959418	−	0.281986i	$-0.909007\pi$
$727$	−13.8890	+	16.5523i	−0.515115	+	0.613890i	0.444304	+	0.895876i	$0.353451\pi$
$728$	−2.30769	−	1.81968i	−0.0855287	−	0.0674420i
$729$	26.8878	+	2.45920i	0.995843	+	0.0910816i
$730$	3.41082	+	10.9862i	0.126240	+	0.406617i
$731$	2.52567	+	2.11929i	0.0934153	+	0.0783848i
$732$	31.7088	+	15.7235i	1.17199	+	0.581158i
$733$	−8.35263	−	47.3701i	−0.308511	−	1.74965i	−0.606498	−	0.795085i	$-0.707426\pi$
$733$	−8.35263	−	47.3701i	−0.308511	−	1.74965i	0.297987	−	0.954570i	$-0.403685\pi$
$734$	−0.740930	+	15.4125i	−0.0273482	+	0.568884i
$735$	−1.45222	−	0.278890i	−0.0535658	−	0.0102870i
$736$	25.1371	+	6.15632i	0.926565	+	0.226925i
$737$	−16.5797	−	9.57227i	−0.610719	−	0.352599i
$738$	26.2602	+	6.78854i	0.966653	+	0.249890i
$739$	−15.1356	+	8.73852i	−0.556771	+	0.321452i	−0.751848	−	0.659336i	$-0.770837\pi$
$739$	−15.1356	+	8.73852i	−0.556771	+	0.321452i	0.195078	+	0.980788i	$0.437504\pi$
$740$	6.62252	+	4.72460i	0.243449	+	0.173680i
$741$	2.46393	+	3.02872i	0.0905146	+	0.111263i
$742$	−18.9276	+	29.4237i	−0.694856	+	1.08018i
$743$	−18.1348	+	15.2169i	−0.665300	+	0.558253i	−0.911670	−	0.410923i	$-0.865207\pi$
$743$	−18.1348	+	15.2169i	−0.665300	+	0.558253i	0.246370	+	0.969176i	$0.420762\pi$
$744$	12.7097	−	22.8088i	0.465961	−	0.836210i
$745$	14.5991	−	5.31362i	0.534868	−	0.194676i
$746$	−23.5226	−	21.7458i	−0.861225	−	0.796171i
$747$	40.1826	−	13.2565i	1.47020	−	0.485030i
$748$	2.60715	−	0.204978i	0.0953267	−	0.00749472i
$749$	−25.3075	−	4.46240i	−0.924718	−	0.163053i
$750$	−1.45277	−	1.97217i	−0.0530478	−	0.0720134i
$751$	2.77514	−	7.62464i	0.101266	−	0.278227i	−0.878705	−	0.477365i	$-0.841592\pi$
$751$	2.77514	−	7.62464i	0.101266	−	0.278227i	0.979971	+	0.199138i	$0.0638142\pi$
$752$	28.4789	+	5.54046i	1.03852	+	0.202040i
$753$	47.9995	+	0.729713i	1.74920	+	0.0265922i
$754$	0.629722	−	1.50155i	0.0229331	−	0.0546832i
$755$	−0.938890			−0.0341697
$756$	13.6081	+	21.8772i	0.494922	+	0.795667i
$757$	48.1035			1.74835			0.874176	−	0.485610i	$-0.161402\pi$
$757$	48.1035			1.74835			0.874176	+	0.485610i	$0.161402\pi$
$758$	−6.50331	+	15.5069i	−0.236211	+	0.563236i
$759$	−6.66593	+	11.1508i	−0.241958	+	0.404748i
$760$	−13.4000	−	7.20216i	−0.486070	−	0.261250i
$761$	10.7766	−	29.6086i	0.390653	−	1.07331i	−0.576051	−	0.817414i	$-0.695407\pi$
$761$	10.7766	−	29.6086i	0.390653	−	1.07331i	0.966704	−	0.255897i	$-0.0823706\pi$
$762$	9.21679	−	21.0731i	0.333889	−	0.763397i
$763$	−13.1580	−	2.32011i	−0.476352	−	0.0839938i
$764$	0.559619	+	7.11790i	0.0202463	+	0.257516i
$765$	−2.22250	−	0.886326i	−0.0803547	−	0.0320452i
$766$	22.7166	+	21.0007i	0.820785	+	0.758786i
$767$	3.18105	−	1.15781i	0.114861	−	0.0418059i
$768$	12.6291	+	24.6679i	0.455712	+	0.890127i
$769$	19.1663	−	16.0824i	0.691153	−	0.579946i	−0.228088	−	0.973640i	$-0.573247\pi$
$769$	19.1663	−	16.0824i	0.691153	−	0.579946i	0.919242	+	0.393694i	$0.128803\pi$
$770$	−3.10976	+	4.83425i	−0.112068	+	0.174214i
$771$	−9.92309	+	26.0256i	−0.357371	+	0.937288i
$772$	23.4558	−	32.8782i	0.844192	−	1.18331i
$773$	−19.3165	+	11.1524i	−0.694765	+	0.401123i	−0.805395	−	0.592739i	$-0.798047\pi$
$773$	−19.3165	+	11.1524i	−0.694765	+	0.401123i	0.110629	+	0.993862i	$0.464713\pi$
$774$	−14.4548	−	9.93239i	−0.519568	−	0.357012i
$775$	−4.61579	−	2.66493i	−0.165804	−	0.0957270i
$776$	13.9992	+	15.6886i	0.502543	+	0.563188i
$777$	−11.4291	+	13.2077i	−0.410017	+	0.473822i
$778$	−2.61660	+	54.4293i	−0.0938098	+	1.95139i
$779$	−5.97099	−	33.8632i	−0.213933	−	1.21327i
$780$	−1.44892	+	0.0917794i	−0.0518797	+	0.00328623i
$781$	−5.88702	−	4.93980i	−0.210654	−	0.176760i
$782$	−1.53004	−	4.92824i	−0.0547142	−	0.176233i
$783$	−9.66451	+	10.5053i	−0.345381	+	0.375429i
$784$	1.22435	−	3.18801i	0.0437267	−	0.113858i
$785$	−12.8047	+	15.2600i	−0.457019	+	0.544654i
$786$	37.9175	−	11.1430i	1.35247	−	0.397458i
$787$	−40.1204	+	7.07432i	−1.43014	+	0.252172i	−0.834468	−	0.551056i	$-0.814225\pi$
$787$	−40.1204	+	7.07432i	−1.43014	+	0.252172i	−0.595671	+	0.803228i	$0.703114\pi$
$788$	5.90840	+	22.8536i	0.210478	+	0.814125i
$789$	−5.96173	+	2.06782i	−0.212243	+	0.0736162i
$790$	−1.90206	−	14.9562i	−0.0676722	−	0.532116i
$791$	−10.0812	+	17.4612i	−0.358447	+	0.620848i
$792$	−13.7000	+	2.41597i	−0.486808	+	0.0858478i
$793$	−2.14103	−	3.70838i	−0.0760303	−	0.131688i
$794$	29.0770	−	22.1088i	1.03190	−	0.784613i
$795$	2.74218	+	17.0647i	0.0972552	+	0.605221i
$796$	7.03522	+	1.95164i	0.249357	+	0.0691742i
$797$	4.48871	+	5.34944i	0.158998	+	0.189487i	0.839662	−	0.543109i	$-0.182753\pi$
$797$	4.48871	+	5.34944i	0.158998	+	0.189487i	−0.680664	+	0.732596i	$0.738309\pi$
$798$	18.0861	−	27.1978i	0.640241	−	0.962792i
$799$	−1.97857	−	5.43608i	−0.0699969	−	0.192315i
$800$	5.07398	−	2.50095i	0.179392	−	0.0884220i
$801$	10.1429	−	5.45181i	0.358381	−	0.192630i
$802$	−1.71112	−	0.387258i	−0.0604216	−	0.0136745i
$803$	2.31573	−	13.1332i	0.0817204	−	0.463459i
$804$	−37.0611	+	16.2104i	−1.30704	+	0.571698i
$805$	10.6581	+	3.87923i	0.375649	+	0.136725i
$806$	−2.80849	+	1.44633i	−0.0989249	+	0.0509447i
$807$	−6.32081	+	3.52231i	−0.222503	+	0.123991i
$808$	−2.24068	−	10.7789i	−0.0788268	−	0.379202i
$809$			3.67323i			0.129144i	0.997913	+	0.0645719i	$0.0205682\pi$
$809$			3.67323i			0.129144i	−0.997913	+	0.0645719i	$0.979432\pi$
$810$	12.2203	+	3.55869i	0.429378	+	0.125040i
$811$			31.4214i			1.10336i	0.834057	+	0.551678i	$0.186012\pi$
$811$			31.4214i			1.10336i	−0.834057	+	0.551678i	$0.813988\pi$
$812$	−13.5584	−	1.30662i	−0.475808	−	0.0458534i
$813$	−10.8135	+	6.02589i	−0.379245	+	0.211337i
$814$	−4.31781	−	8.38436i	−0.151339	−	0.293872i
$815$	9.72819	+	3.54077i	0.340764	+	0.124028i
$816$	2.91838	−	4.69221i	0.102164	−	0.164260i
$817$	−3.86091	+	21.8963i	−0.135076	+	0.766056i
$818$	4.16803	−	18.4166i	0.145732	−	0.643922i
$819$	0.0947533	−	3.11565i	0.00331095	−	0.108870i
$820$	11.5401	+	5.50550i	0.402999	+	0.192260i
$821$	10.2271	+	28.0988i	0.356929	+	0.980653i	0.980089	+	0.198559i	$0.0636262\pi$
$821$	10.2271	+	28.0988i	0.356929	+	0.980653i	−0.623160	+	0.782094i	$0.714152\pi$
$822$	−39.6194	−	26.3463i	−1.38189	−	0.918931i
$823$	22.7383	+	27.0985i	0.792608	+	0.944594i	0.999429	−	0.0337849i	$-0.0107561\pi$
$823$	22.7383	+	27.0985i	0.792608	+	0.944594i	−0.206821	+	0.978379i	$0.566312\pi$
$824$	44.8988	−	1.36641i	1.56413	−	0.0476011i
$825$	0.450534	+	2.80368i	0.0156856	+	0.0976116i
$826$	−17.1405	−	22.5428i	−0.596395	−	0.784364i
$827$	−21.2628	−	36.8282i	−0.739379	−	1.28064i	−0.952775	−	0.303676i	$-0.901786\pi$
$827$	−21.2628	−	36.8282i	−0.739379	−	1.28064i	0.213397	−	0.976966i	$-0.431547\pi$
$828$	10.6167	+	25.3136i	0.368956	+	0.879710i
$829$	3.03505	−	5.25687i	0.105412	−	0.182579i	−0.808495	−	0.588504i	$-0.799717\pi$
$829$	3.03505	−	5.25687i	0.105412	−	0.182579i	0.913906	+	0.405925i	$0.133051\pi$
$830$	19.7871	−	2.51643i	0.686820	−	0.0873467i
$831$	4.76159	−	1.65155i	0.165178	−	0.0572916i
$832$	0.380350	−	3.33120i	0.0131863	−	0.115489i
$833$	−0.670589	+	0.118243i	−0.0232345	+	0.00409687i
$834$	−8.67402	−	29.5160i	−0.300357	−	1.02206i
$835$	−0.859573	+	1.02440i	−0.0297467	+	0.0354508i
$836$	9.98799	+	14.5351i	0.345442	+	0.502707i
$837$	27.4649	−	3.56077i	0.949325	−	0.123078i
$838$	22.1462	−	6.87561i	0.765028	−	0.237514i
$839$	24.0797	+	20.2053i	0.831325	+	0.697564i	0.955595	−	0.294684i	$-0.0952145\pi$
$839$	24.0797	+	20.2053i	0.831325	+	0.697564i	−0.124270	+	0.992248i	$0.539659\pi$
$840$	4.32720	+	11.3484i	0.149303	+	0.391555i
$841$	3.72530	+	21.1273i	0.128459	+	0.728526i
$842$	−24.5456	−	1.17999i	−0.845896	−	0.0406651i
$843$	14.8031	−	17.1066i	0.509844	−	0.589183i
$844$	7.31533	−	3.33308i	0.251804	−	0.114729i
$845$	−11.1062	−	6.41218i	−0.382065	−	0.220586i
$846$	13.2508	+	27.7737i	0.455573	+	0.954881i
$847$	−17.8463	+	10.3036i	−0.613206	+	0.354034i
$848$	−39.9085	−	0.702974i	−1.37046	−	0.0241402i
$849$	−4.15426	+	10.8955i	−0.142574	+	0.373932i
$850$	−0.948614	−	0.610223i	−0.0325372	−	0.0209305i
$851$	−14.2553	+	11.9616i	−0.488664	+	0.410038i
$852$	−15.7809	+	3.82494i	−0.540646	+	0.131040i
$853$	41.3762	−	15.0597i	1.41669	−	0.515635i	0.483608	−	0.875285i	$-0.339326\pi$
$853$	41.3762	−	15.0597i	1.41669	−	0.515635i	0.933087	+	0.359650i	$0.117104\pi$
$854$	−24.3170	+	26.3039i	−0.832111	+	0.900101i
$855$	−2.31760	−	15.9684i	−0.0792602	−	0.546108i
$856$	−10.8609	−	27.2324i	−0.371216	−	0.930785i
$857$	−6.45660	−	1.13847i	−0.220553	−	0.0388895i	0.0622794	−	0.998059i	$-0.480163\pi$
$857$	−6.45660	−	1.13847i	−0.220553	−	0.0388895i	−0.282833	+	0.959169i	$0.591274\pi$
$858$	1.54203	+	0.674443i	0.0526441	+	0.0230251i
$859$	−9.67815	+	26.5905i	−0.330214	+	0.907256i	0.657841	+	0.753157i	$0.271470\pi$
$859$	−9.67815	+	26.5905i	−0.330214	+	0.907256i	−0.988055	+	0.154099i	$0.950752\pi$
$860$	−5.79442	−	5.89738i	−0.197588	−	0.201099i
$861$	−14.0858	+	23.5628i	−0.480044	+	0.803018i
$862$	35.9086	+	15.0594i	1.22305	+	0.512925i
$863$	35.5620			1.21054			0.605272	−	0.796019i	$-0.293064\pi$
$863$	35.5620			1.21054			0.605272	+	0.796019i	$0.293064\pi$
$864$	−13.0578	+	26.3343i	−0.444234	+	0.895911i
$865$	−19.4484			−0.661264
$866$	−28.0839	−	11.7779i	−0.954330	−	0.400229i
$867$	28.3398	+	0.430836i	0.962470	+	0.0146319i
$868$	18.5215	+	18.8506i	0.628661	+	0.639833i
$869$	−5.97785	+	16.4240i	−0.202785	+	0.557146i
$870$	−5.41784	+	3.99098i	−0.183682	+	0.135307i
$871$	4.81966	+	0.849835i	0.163308	+	0.0287956i
$872$	−5.64683	−	14.1588i	−0.191226	−	0.479478i
$873$	−4.53853	+	21.8352i	−0.153606	+	0.739010i
$874$	23.6228	−	25.5530i	0.799054	−	0.864342i
$875$	2.32965	−	0.847923i	0.0787565	−	0.0286650i
$876$	−19.4406	−	20.3972i	−0.656836	−	0.689156i
$877$	−27.3256	+	22.9289i	−0.922721	+	0.774255i	−0.974496	−	0.224404i	$-0.927957\pi$
$877$	−27.3256	+	22.9289i	−0.922721	+	0.774255i	0.0517751	+	0.998659i	$0.483512\pi$
$878$	−44.1854	−	28.4235i	−1.49119	−	0.959247i
$879$	16.6120	+	20.4200i	0.560310	+	0.688748i
$880$	−6.55687	−	0.115497i	−0.221032	−	0.00389340i
$881$	26.4015	−	15.2429i	0.889489	−	0.513547i	0.0157139	−	0.999877i	$-0.494998\pi$
$881$	26.4015	−	15.2429i	0.889489	−	0.513547i	0.873775	+	0.486330i	$0.161665\pi$
$882$	3.49036	−	0.968340i	0.117526	−	0.0326057i
$883$	−21.4953	−	12.4103i	−0.723373	−	0.417640i	0.0926198	−	0.995702i	$-0.470476\pi$
$883$	−21.4953	−	12.4103i	−0.723373	−	0.417640i	−0.815993	+	0.578062i	$0.803809\pi$
$884$	−0.608362	+	0.277188i	−0.0204614	+	0.00932284i
$885$	−13.7390	−	2.63850i	−0.461833	−	0.0886924i
$886$	−23.4360	−	1.12665i	−0.787348	−	0.0378505i
$887$	−1.35374	−	7.67744i	−0.0454541	−	0.257783i	0.953610	−	0.301046i	$-0.0973358\pi$
$887$	−1.35374	−	7.67744i	−0.0454541	−	0.257783i	−0.999064	+	0.0432629i	$0.986225\pi$
$888$	−19.6745	−	3.16114i	−0.660232	−	0.106081i
$889$	17.8328	+	14.9635i	0.598094	+	0.501861i
$890$	5.18423	−	1.60952i	0.173776	−	0.0539512i
$891$	−10.7059	−	10.1538i	−0.358662	−	0.340166i
$892$	21.4228	+	31.1758i	0.717290	+	1.04384i
$893$	25.0764	−	29.8849i	0.839149	−	1.00006i
$894$	−26.2548	+	27.5479i	−0.878093	+	0.921339i
$895$	22.9920	−	4.05411i	0.768538	−	0.135514i
$896$	−27.5577	+	5.22403i	−0.920639	+	0.174523i
$897$	0.626340	−	3.26144i	0.0209129	−	0.108896i
$898$	−3.08284	+	0.392062i	−0.102876	+	0.0130833i
$899$	−7.32095	+	12.6803i	−0.244167	+	0.422910i
$900$	5.33427	+	2.74692i	0.177809	+	0.0915640i
$901$	3.97936	+	6.89245i	0.132572	+	0.229621i
$902$	−8.97165	−	11.7993i	−0.298723	−	0.392873i
$903$	13.7698	−	11.2020i	0.458230	−	0.372779i
$904$	−22.9923	+	0.699724i	−0.764712	+	0.0232725i
$905$	14.7868	+	17.6222i	0.491528	+	0.585781i
$906$	2.06037	−	1.02174i	0.0684514	−	0.0339449i
$907$	−6.35984	−	17.4735i	−0.211175	−	0.580198i	0.788205	−	0.615413i	$-0.211011\pi$
$907$	−6.35984	−	17.4735i	−0.211175	−	0.580198i	−0.999380	+	0.0352146i	$0.988789\pi$
$908$	33.3416	+	15.9064i	1.10648	+	0.527872i
$909$	7.77441	−	8.71295i	0.257861	−	0.288990i
$910$	0.324353	−	1.43317i	0.0107522	−	0.0475090i
$911$	−0.551493	+	3.12767i	−0.0182718	+	0.103624i	−0.992580	−	0.121595i	$-0.961199\pi$
$911$	−0.551493	+	3.12767i	−0.0182718	+	0.103624i	0.974308	+	0.225220i	$0.0723100\pi$
$912$	37.2437	+	1.22256i	1.23326	+	0.0404830i
$913$	−21.7290	−	7.90873i	−0.719127	−	0.261741i
$914$	−19.7382	−	38.3278i	−0.652881	−	1.26777i
$915$	−0.269002	+	17.6946i	−0.00889292	+	0.584964i
$916$	−36.2958	−	3.49781i	−1.19925	−	0.115571i
$917$			39.9997i			1.32091i
$918$	5.84176	−	0.473588i	0.192807	−	0.0156307i
$919$			10.6947i			0.352785i	0.984320	+	0.176393i	$0.0564429\pi$
$919$			10.6947i			0.352785i	−0.984320	+	0.176393i	$0.943557\pi$
$920$	2.63361	+	12.6692i	0.0868274	+	0.417690i
$921$	42.4029	+	25.3484i	1.39722	+	0.835259i
$922$	3.53142	−	1.81862i	0.116301	−	0.0598932i
$923$	1.84607	+	0.671913i	0.0607640	+	0.0221163i
$924$	1.56350	−	13.9928i	0.0514353	−	0.460330i
$925$	−0.706321	+	4.00575i	−0.0232237	+	0.131708i
$926$	9.15195	+	2.07126i	0.300752	+	0.0680658i
$927$	29.5017	+	37.4119i	0.968962	+	1.22877i
$928$	−6.87049	−	13.9390i	−0.225535	−	0.457569i
$929$	3.28170	+	9.01639i	0.107669	+	0.295818i	0.981814	−	0.189848i	$-0.0607994\pi$
$929$	3.28170	+	9.01639i	0.107669	+	0.295818i	−0.874145	+	0.485666i	$0.838577\pi$
$930$	13.0293	+	0.825046i	0.427249	+	0.0270543i
$931$	−2.95168	−	3.51768i	−0.0967374	−	0.115287i
$932$	−26.2922	−	7.29374i	−0.861230	−	0.238914i
$933$	−33.0228	−	12.5910i	−1.08112	−	0.412212i
$934$	35.4714	−	26.9709i	1.16066	−	0.882514i
$935$	0.653798	+	1.13241i	0.0213815	+	0.0370338i
$936$	3.07975	−	1.77818i	0.100665	−	0.0581216i
$937$	−17.6356	+	30.5457i	−0.576129	+	0.997884i	0.419789	+	0.907622i	$0.362104\pi$
$937$	−17.6356	+	30.5457i	−0.576129	+	0.997884i	−0.995918	+	0.0902625i	$0.971229\pi$
$938$	−5.16512	−	40.6141i	−0.168647	−	1.32610i
$939$	22.9103	+	19.8252i	0.747650	+	0.646972i
$940$	3.63100	+	14.0447i	0.118430	+	0.458086i
$941$	−33.3980	+	5.88897i	−1.08874	+	0.191975i	−0.689079	−	0.724686i	$-0.741985\pi$
$941$	−33.3980	+	5.88897i	−1.08874	+	0.191975i	−0.399665	+	0.916661i	$0.630874\pi$
$942$	11.4930	−	47.4223i	0.374464	−	1.54510i
$943$	−18.8004	+	22.4054i	−0.612224	+	0.729620i
$944$	11.5832	−	30.1610i	0.377002	−	0.981656i
$945$	−6.94295	+	10.8510i	−0.225854	+	0.352983i
$946$	2.84186	+	9.15356i	0.0923967	+	0.297608i
$947$	−27.2107	−	22.8325i	−0.884228	−	0.741955i	0.0828159	−	0.996565i	$-0.473609\pi$
$947$	−27.2107	−	22.8325i	−0.884228	−	0.741955i	−0.967044	+	0.254609i	$0.918053\pi$
$948$	20.4499	+	30.7511i	0.664182	+	0.998749i
$949$	0.591981	+	3.35729i	0.0192165	+	0.108982i
$950$	0.365246	−	7.59767i	0.0118501	−	0.246501i
$951$	−16.1179	−	46.4694i	−0.522657	−	1.50687i
$952$	3.72356	+	4.17290i	0.120681	+	0.135244i
$953$	4.19300	+	2.42083i	0.135825	+	0.0784184i	0.566373	−	0.824149i	$-0.308346\pi$
$953$	4.19300	+	2.42083i	0.135825	+	0.0784184i	−0.430548	+	0.902568i	$0.641680\pi$
$954$	−24.5881	−	34.4639i	−0.796069	−	1.11581i
$955$	−3.09165	+	1.78497i	−0.100043	+	0.0577601i
$956$	11.3931	−	15.9699i	0.368480	−	0.516503i
$957$	7.70213	−	1.23768i	0.248974	−	0.0400086i
$958$	−5.16827	+	8.03428i	−0.166979	+	0.259576i
$959$	36.8896	−	30.9541i	1.19123	−	0.999559i
$960$	−8.41310	+	11.0100i	−0.271532	+	0.355346i
$961$	−2.43630	+	0.886739i	−0.0785902	+	0.0286045i
$962$	1.77028	+	1.63656i	0.0570761	+	0.0527648i
$963$	16.3598	−	26.4455i	0.527188	−	0.852194i
$964$	4.01579	+	51.0776i	0.129340	+	1.64510i
$965$	19.8870	+	3.50661i	0.640184	+	0.112882i
$966$	−27.6105	+	3.08567i	−0.888353	+	0.0992796i
$967$	−6.34608	+	17.4357i	−0.204076	+	0.560694i	−0.998937	−	0.0460973i	$-0.985322\pi$
$967$	−6.34608	+	17.4357i	−0.204076	+	0.560694i	0.794861	+	0.606792i	$0.207544\pi$
$968$	−20.7086	−	11.1303i	−0.665601	−	0.357743i
$969$	−3.61683	−	6.49042i	−0.116189	−	0.208502i
$970$	−4.06596	+	9.69514i	−0.130550	+	0.311292i
$971$	61.7936			1.98305			0.991525	−	0.129915i	$-0.0414705\pi$
$971$	61.7936			1.98305			0.991525	+	0.129915i	$0.0414705\pi$
$972$	−30.6899	+	5.48913i	−0.984379	+	0.176064i
$973$	31.1368			0.998200
$974$	−13.2897	+	31.6888i	−0.425830	+	1.01538i
$975$	−0.353358	−	0.634103i	−0.0113165	−	0.0203076i
$976$	−40.1164	−	7.80449i	−1.28410	−	0.249816i
$977$	−4.94839	+	13.5956i	−0.158313	+	0.434961i	−0.993336	−	0.115253i	$-0.963232\pi$
$977$	−4.94839	+	13.5956i	−0.158313	+	0.434961i	0.835023	+	0.550215i	$0.185454\pi$
$978$	−25.2015	+	2.81644i	−0.805855	+	0.0900600i
$979$	−6.19736	−	1.09276i	−0.198068	−	0.0349248i
$980$	1.70226	−	0.133835i	0.0543768	−	0.00427519i
$981$	8.50588	−	13.7497i	0.271572	−	0.438993i
$982$	27.2988	+	25.2367i	0.871139	+	0.805337i
$983$	−32.7700	+	11.9273i	−1.04520	+	0.380422i	−0.806850	−	0.590757i	$-0.798829\pi$
$983$	−32.7700	+	11.9273i	−1.04520	+	0.380422i	−0.238352	+	0.971179i	$0.576607\pi$
$984$	−31.3159	+	0.476737i	−0.998315	+	0.0151978i
$985$	−9.04124	+	7.58650i	−0.288078	+	0.241726i
$986$	−1.67637	+	2.60598i	−0.0533866	+	0.0829914i
$987$	−30.7511	+	4.94150i	−0.978817	+	0.157290i
$988$	−3.67013	−	2.61832i	−0.116762	−	0.0832999i
$989$	16.3785	−	9.45610i	0.520805	−	0.300687i
$990$	−4.03976	−	5.66233i	−0.128392	−	0.179961i
$991$	−4.20842	−	2.42973i	−0.133685	−	0.0771829i	0.431666	−	0.902033i	$-0.357926\pi$
$991$	−4.20842	−	2.42973i	−0.133685	−	0.0771829i	−0.565351	+	0.824851i	$0.691259\pi$
$992$	−7.17212	+	29.2847i	−0.227715	+	0.929791i
$993$	−11.6705	−	33.6473i	−0.370353	−	1.06777i
$994$	0.789153	−	16.4156i	0.0250304	−	0.520671i
$995$	0.633895	+	3.59500i	0.0200958	+	0.113969i
$996$	−40.6839	+	27.0553i	−1.28912	+	0.857281i
$997$	−7.06434	−	5.92769i	−0.223730	−	0.187732i	0.524032	−	0.851699i	$-0.324427\pi$
$997$	−7.06434	−	5.92769i	−0.223730	−	0.187732i	−0.747762	+	0.663967i	$0.768872\pi$
$998$	−10.3883	−	33.4606i	−0.328837	−	1.05918i
$999$	−9.72236	−	18.7667i	−0.307602	−	0.593751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.be.a.11.63	yes	432
4.3	odd	2	inner	540.2.be.a.11.22	✓	432
27.5	odd	18	inner	540.2.be.a.491.22	yes	432
108.59	even	18	inner	540.2.be.a.491.63	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.2.be.a.11.22	✓	432	4.3	odd	2	inner
540.2.be.a.11.63	yes	432	1.1	even	1	trivial
540.2.be.a.491.22	yes	432	27.5	odd	18	inner
540.2.be.a.491.63	yes	432	108.59	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30417 + 0.546944i) q^{2} +(-0.843124 - 1.51299i) q^{3} +(1.40170 + 1.42661i) q^{4} +(-0.342020 + 0.939693i) q^{5} +(-0.272054 - 2.43433i) q^{6} +(2.44150 + 0.430502i) q^{7} +(1.04778 + 2.62720i) q^{8} +(-1.57828 + 2.55128i) q^{9} +(-0.960011 + 1.03845i) q^{10} +(1.54060 - 0.560732i) q^{11} +(0.976641 - 3.32358i) q^{12} +(-0.321054 + 0.269396i) q^{13} +(2.94866 + 1.89681i) q^{14} +(1.71011 - 0.274804i) q^{15} +(-0.0704476 + 3.99938i) q^{16} +(0.690717 - 0.398786i) q^{17} +(-3.45375 + 2.46406i) q^{18} +(4.65798 + 2.68928i) q^{19} +(-1.81999 + 0.829241i) q^{20} +(-1.40714 - 4.05693i) q^{21} +(2.31589 + 0.111333i) q^{22} +(-0.794437 - 4.50547i) q^{23} +(3.09151 - 3.80033i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(-0.566052 + 0.175739i) q^{26} +(5.19075 + 0.236883i) q^{27} +(2.80810 + 4.08651i) q^{28} +(-1.76583 + 2.10444i) q^{29} +(2.38057 + 0.576945i) q^{30} +(5.24888 - 0.925520i) q^{31} +(-2.27931 + 5.17733i) q^{32} +(-2.14730 - 1.85815i) q^{33} +(1.11892 - 0.142300i) q^{34} +(-1.23958 + 2.14702i) q^{35} +(-5.85197 + 1.32454i) q^{36} +(-2.03377 - 3.52260i) q^{37} +(4.60389 + 6.05493i) q^{38} +(0.678282 + 0.258617i) q^{39} +(-2.82712 + 0.0860377i) q^{40} +(-4.10939 - 4.89738i) q^{41} +(0.383767 - 6.06054i) q^{42} +(1.41386 + 3.88454i) q^{43} +(2.95941 + 1.41186i) q^{44} +(-1.85761 - 2.35569i) q^{45} +(1.42816 - 6.31040i) q^{46} +(1.25951 - 7.14303i) q^{47} +(6.11042 - 3.26539i) q^{48} +(-0.802271 - 0.292003i) q^{49} +(-0.647481 - 1.25729i) q^{50} +(-1.18572 - 0.708823i) q^{51} +(-0.834346 - 0.0804056i) q^{52} +9.97868i q^{53} +(6.64004 + 3.14798i) q^{54} +1.63947i q^{55} +(1.42714 + 6.86536i) q^{56} +(0.141609 - 9.31488i) q^{57} +(-3.45395 + 1.77873i) q^{58} +(-7.59008 - 2.76256i) q^{59} +(2.78911 + 2.05447i) q^{60} +(-1.77419 + 10.0619i) q^{61} +(7.35163 + 1.66381i) q^{62} +(-4.95170 + 5.54949i) q^{63} +(-5.80431 + 5.50545i) q^{64} +(-0.143343 - 0.393831i) q^{65} +(-1.78414 - 3.59779i) q^{66} +(-7.50600 - 8.94530i) q^{67} +(1.53709 + 0.426406i) q^{68} +(-6.14693 + 5.00065i) q^{69} +(-2.79092 + 2.12209i) q^{70} +(-2.34373 - 4.05946i) q^{71} +(-8.35640 - 1.47328i) q^{72} +(4.06709 - 7.04441i) q^{73} +(-0.725716 - 5.70641i) q^{74} +(-0.326661 + 1.70097i) q^{75} +(2.69254 + 10.4147i) q^{76} +(4.00277 - 0.705796i) q^{77} +(0.743144 + 0.708262i) q^{78} +(-6.85262 + 8.16664i) q^{79} +(-3.73409 - 1.43407i) q^{80} +(-4.01805 - 8.05328i) q^{81} +(-2.68074 - 8.63460i) q^{82} +(-10.8045 - 9.06606i) q^{83} +(3.81527 - 7.69406i) q^{84} +(0.138497 + 0.785455i) q^{85} +(-0.280719 + 5.83938i) q^{86} +(4.67281 + 0.897387i) q^{87} +(3.08736 + 3.45993i) q^{88} +(-3.32416 - 1.91920i) q^{89} +(-1.13421 - 4.08822i) q^{90} +(-0.899827 + 0.519515i) q^{91} +(5.31400 - 7.44870i) q^{92} +(-5.82576 - 7.16118i) q^{93} +(5.54944 - 8.62682i) q^{94} +(-4.12022 + 3.45728i) q^{95} +(9.75500 - 0.916554i) q^{96} +(6.98564 - 2.54257i) q^{97} +(-0.886586 - 0.819617i) q^{98} +(-1.00092 + 4.81549i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) \) 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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