LMFDB - Embedded newform 561.2.m.e.511.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [561,2,Mod(103,561)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(561, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("561.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 561 = 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	561.m (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.47960755339$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			511.1
Character	$\chi$	$=$	561.511
Dual form			561.2.m.e.460.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.713092 - 2.19467i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-2.69005 + 1.95444i) q^{4} +(1.16648 - 3.59006i) q^{5} +(0.713092 - 2.19467i) q^{6} +(3.39160 - 2.46414i) q^{7} +(2.47381 + 1.79733i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.713092 - 2.19467i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-2.69005 + 1.95444i) q^{4} +(1.16648 - 3.59006i) q^{5} +(0.713092 - 2.19467i) q^{6} +(3.39160 - 2.46414i) q^{7} +(2.47381 + 1.79733i) q^{8} +(0.309017 + 0.951057i) q^{9} -8.71082 q^{10} +(3.23525 - 0.730182i) q^{11} -3.32509 q^{12} +(1.35446 + 4.16859i) q^{13} +(-7.82651 - 5.68629i) q^{14} +(3.05389 - 2.21878i) q^{15} +(0.125473 - 0.386167i) q^{16} +(0.309017 - 0.951057i) q^{17} +(1.86690 - 1.35638i) q^{18} +(0.306096 + 0.222392i) q^{19} +(3.87865 + 11.9373i) q^{20} +4.19225 q^{21} +(-3.90954 - 6.57963i) q^{22} +6.45853 q^{23} +(0.944911 + 2.90814i) q^{24} +(-7.48277 - 5.43655i) q^{25} +(8.18283 - 5.94518i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-4.30757 + 13.2574i) q^{28} +(-7.25196 + 5.26886i) q^{29} +(-7.04720 - 5.12009i) q^{30} +(1.13755 + 3.50102i) q^{31} +5.17861 q^{32} +(3.04656 + 1.31090i) q^{33} -2.30762 q^{34} +(-4.89018 - 15.0504i) q^{35} +(-2.69005 - 1.95444i) q^{36} +(-5.68441 + 4.12997i) q^{37} +(0.269802 - 0.830366i) q^{38} +(-1.35446 + 4.16859i) q^{39} +(9.33817 - 6.78458i) q^{40} +(-7.12826 - 5.17899i) q^{41} +(-2.98946 - 9.20062i) q^{42} -10.9795 q^{43} +(-7.27590 + 8.28732i) q^{44} +3.77481 q^{45} +(-4.60553 - 14.1744i) q^{46} +(2.14193 + 1.55620i) q^{47} +(0.328494 - 0.238665i) q^{48} +(3.26784 - 10.0574i) q^{49} +(-6.59554 + 20.2990i) q^{50} +(0.809017 - 0.587785i) q^{51} +(-11.7908 - 8.56652i) q^{52} +(0.664718 + 2.04579i) q^{53} +2.30762 q^{54} +(1.15246 - 12.4665i) q^{55} +12.8190 q^{56} +(0.116918 + 0.359837i) q^{57} +(16.7347 + 12.1585i) q^{58} +(-4.99727 + 3.63073i) q^{59} +(-3.87865 + 11.9373i) q^{60} +(-2.66117 + 8.19023i) q^{61} +(6.87241 - 4.99310i) q^{62} +(3.39160 + 2.46414i) q^{63} +(-3.94377 - 12.1377i) q^{64} +16.5454 q^{65} +(0.704522 - 7.62100i) q^{66} +5.18683 q^{67} +(1.02751 + 3.16235i) q^{68} +(5.22506 + 3.79623i) q^{69} +(-29.5436 + 21.4647i) q^{70} +(-2.22347 + 6.84315i) q^{71} +(-0.944911 + 2.90814i) q^{72} +(1.52630 - 1.10892i) q^{73} +(13.1174 + 9.53037i) q^{74} +(-2.85816 - 8.79653i) q^{75} -1.25806 q^{76} +(9.17340 - 10.4486i) q^{77} +10.1145 q^{78} +(-0.434449 - 1.33710i) q^{79} +(-1.24000 - 0.900914i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-6.28307 + 19.3373i) q^{82} +(-2.84627 + 8.75991i) q^{83} +(-11.2774 + 8.19349i) q^{84} +(-3.05389 - 2.21878i) q^{85} +(7.82937 + 24.0963i) q^{86} -8.96391 q^{87} +(9.31576 + 4.00847i) q^{88} +0.222644 q^{89} +(-2.69179 - 8.28448i) q^{90} +(14.8658 + 10.8006i) q^{91} +(-17.3738 + 12.6228i) q^{92} +(-1.13755 + 3.50102i) q^{93} +(1.88796 - 5.81055i) q^{94} +(1.15545 - 0.839487i) q^{95} +(4.18958 + 3.04391i) q^{96} +(1.08321 + 3.33378i) q^{97} -24.4029 q^{98} +(1.69419 + 2.85127i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + q^{2} + 10 q^{3} - 5 q^{4} - 6 q^{5} - q^{6} + 5 q^{7} - 16 q^{8} - 10 q^{9}+O(q^{10}) $ 40 * q + q^2 + 10 * q^3 - 5 * q^4 - 6 * q^5 - q^6 + 5 * q^7 - 16 * q^8 - 10 * q^9	\( 40 q + q^{2} + 10 q^{3} - 5 q^{4} - 6 q^{5} - q^{6} + 5 q^{7} - 16 q^{8} - 10 q^{9} + 8 q^{10} + 16 q^{11} - 50 q^{12} - 4 q^{13} - 4 q^{14} + q^{15} - 61 q^{16} - 10 q^{17} - 4 q^{18} - 8 q^{19} - 33 q^{20} + 10 q^{21} + 19 q^{22} - 32 q^{23} - 4 q^{24} - 8 q^{25} - 20 q^{26} + 10 q^{27} + 5 q^{28} + 18 q^{29} - 23 q^{30} - 31 q^{31} + 94 q^{32} + 9 q^{33} + 6 q^{34} - 9 q^{35} - 5 q^{36} - 38 q^{37} + 4 q^{39} + 78 q^{40} - 33 q^{41} - q^{42} + 92 q^{43} - 75 q^{44} + 14 q^{45} - 45 q^{46} + 17 q^{47} - 14 q^{48} - 59 q^{49} + 30 q^{50} + 10 q^{51} - 114 q^{52} - 3 q^{53} - 6 q^{54} + 41 q^{55} + 78 q^{56} - 2 q^{57} + 95 q^{58} - 62 q^{59} + 33 q^{60} + 34 q^{61} + 12 q^{62} + 5 q^{63} - 110 q^{64} + 52 q^{65} - 29 q^{66} + 42 q^{67} - 20 q^{68} + 2 q^{69} - 162 q^{70} + 42 q^{71} + 4 q^{72} + 15 q^{73} - 3 q^{74} + 23 q^{75} + 162 q^{76} - 21 q^{77} - 30 q^{78} + 6 q^{79} + 139 q^{80} - 10 q^{81} - 40 q^{82} - 23 q^{83} - 10 q^{84} - q^{85} + 13 q^{86} - 8 q^{87} + 11 q^{88} + 88 q^{89} - 27 q^{90} + 44 q^{91} - 71 q^{92} + 31 q^{93} - 12 q^{94} - 9 q^{95} + 31 q^{96} - 42 q^{97} + 162 q^{98} - 9 q^{99}+O(q^{100}) \) 40 * q + q^2 + 10 * q^3 - 5 * q^4 - 6 * q^5 - q^6 + 5 * q^7 - 16 * q^8 - 10 * q^9 + 8 * q^10 + 16 * q^11 - 50 * q^12 - 4 * q^13 - 4 * q^14 + q^15 - 61 * q^16 - 10 * q^17 - 4 * q^18 - 8 * q^19 - 33 * q^20 + 10 * q^21 + 19 * q^22 - 32 * q^23 - 4 * q^24 - 8 * q^25 - 20 * q^26 + 10 * q^27 + 5 * q^28 + 18 * q^29 - 23 * q^30 - 31 * q^31 + 94 * q^32 + 9 * q^33 + 6 * q^34 - 9 * q^35 - 5 * q^36 - 38 * q^37 + 4 * q^39 + 78 * q^40 - 33 * q^41 - q^42 + 92 * q^43 - 75 * q^44 + 14 * q^45 - 45 * q^46 + 17 * q^47 - 14 * q^48 - 59 * q^49 + 30 * q^50 + 10 * q^51 - 114 * q^52 - 3 * q^53 - 6 * q^54 + 41 * q^55 + 78 * q^56 - 2 * q^57 + 95 * q^58 - 62 * q^59 + 33 * q^60 + 34 * q^61 + 12 * q^62 + 5 * q^63 - 110 * q^64 + 52 * q^65 - 29 * q^66 + 42 * q^67 - 20 * q^68 + 2 * q^69 - 162 * q^70 + 42 * q^71 + 4 * q^72 + 15 * q^73 - 3 * q^74 + 23 * q^75 + 162 * q^76 - 21 * q^77 - 30 * q^78 + 6 * q^79 + 139 * q^80 - 10 * q^81 - 40 * q^82 - 23 * q^83 - 10 * q^84 - q^85 + 13 * q^86 - 8 * q^87 + 11 * q^88 + 88 * q^89 - 27 * q^90 + 44 * q^91 - 71 * q^92 + 31 * q^93 - 12 * q^94 - 9 * q^95 + 31 * q^96 - 42 * q^97 + 162 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/561\mathbb{Z}\right)^\times$.

$n$	$188$	$409$	$496$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	−0.713092	−	2.19467i	−0.504232	−	1.55187i	−0.802057	−	0.597247i	$-0.796261\pi$
$2$	−0.713092	−	2.19467i	−0.504232	−	1.55187i	0.297825	−	0.954621i	$-0.403739\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	−2.69005	+	1.95444i	−1.34503	+	0.977219i
$5$	1.16648	−	3.59006i	0.521666	−	1.60552i	−0.249149	−	0.968465i	$-0.580151\pi$
$5$	1.16648	−	3.59006i	0.521666	−	1.60552i	0.770815	−	0.637059i	$-0.219849\pi$
$6$	0.713092	−	2.19467i	0.291119	−	0.895971i
$7$	3.39160	−	2.46414i	1.28190	−	0.931358i	0.282296	−	0.959327i	$-0.408904\pi$
$7$	3.39160	−	2.46414i	1.28190	−	0.931358i	0.999609	+	0.0279691i	$0.00890401\pi$
$8$	2.47381	+	1.79733i	0.874624	+	0.635451i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−8.71082			−2.75460
$11$	3.23525	−	0.730182i	0.975464	−	0.220158i
$11$	3.23525	−	0.730182i	0.975464	−	0.220158i
$12$	−3.32509			−0.959871
$13$	1.35446	+	4.16859i	0.375659	+	1.15616i	0.943033	+	0.332698i	$0.107959\pi$
$13$	1.35446	+	4.16859i	0.375659	+	1.15616i	−0.567375	+	0.823460i	$0.692041\pi$
$14$	−7.82651	−	5.68629i	−2.09172	−	1.51973i
$15$	3.05389	−	2.21878i	0.788510	−	0.572886i
$16$	0.125473	−	0.386167i	0.0313683	−	0.0965418i
$17$	0.309017	−	0.951057i	0.0749476	−	0.230665i
$17$	0.309017	−	0.951057i	0.0749476	−	0.230665i
$18$	1.86690	−	1.35638i	0.440033	−	0.319702i
$19$	0.306096	+	0.222392i	0.0702232	+	0.0510201i	0.622343	−	0.782745i	$-0.286181\pi$
$19$	0.306096	+	0.222392i	0.0702232	+	0.0510201i	−0.552120	+	0.833765i	$0.686181\pi$
$20$	3.87865	+	11.9373i	0.867294	+	2.66926i
$21$	4.19225			0.914824
$22$	−3.90954	−	6.57963i	−0.833517	−	1.40278i
$23$	6.45853			1.34670			0.673348	−	0.739326i	$-0.264856\pi$
$23$	6.45853			1.34670			0.673348	+	0.739326i	$0.264856\pi$
$24$	0.944911	+	2.90814i	0.192879	+	0.593621i
$25$	−7.48277	−	5.43655i	−1.49655	−	1.08731i
$26$	8.18283	−	5.94518i	1.60479	−	1.16594i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−4.30757	+	13.2574i	−0.814055	+	2.50540i
$29$	−7.25196	+	5.26886i	−1.34665	+	0.978402i	−0.347484	+	0.937686i	$0.612964\pi$
$29$	−7.25196	+	5.26886i	−1.34665	+	0.978402i	−0.999171	+	0.0407161i	$0.987036\pi$
$30$	−7.04720	−	5.12009i	−1.28664	−	0.934796i
$31$	1.13755	+	3.50102i	0.204310	+	0.628801i	0.999741	+	0.0227573i	$0.00724449\pi$
$31$	1.13755	+	3.50102i	0.204310	+	0.628801i	−0.795431	+	0.606044i	$0.792756\pi$
$32$	5.17861			0.915457
$33$	3.04656	+	1.31090i	0.530338	+	0.228199i
$34$	−2.30762			−0.395753
$35$	−4.89018	−	15.0504i	−0.826591	−	2.54399i
$36$	−2.69005	−	1.95444i	−0.448342	−	0.325740i
$37$	−5.68441	+	4.12997i	−0.934511	+	0.678962i	−0.947093	−	0.320959i	$-0.895995\pi$
$37$	−5.68441	+	4.12997i	−0.934511	+	0.678962i	0.0125819	+	0.999921i	$0.495995\pi$
$38$	0.269802	−	0.830366i	0.0437677	−	0.134703i
$39$	−1.35446	+	4.16859i	−0.216887	+	0.667508i
$40$	9.33817	−	6.78458i	1.47649	−	1.07274i
$41$	−7.12826	−	5.17899i	−1.11325	−	0.808822i	−0.130076	−	0.991504i	$-0.541522\pi$
$41$	−7.12826	−	5.17899i	−1.11325	−	0.808822i	−0.983172	+	0.182682i	$0.941522\pi$
$42$	−2.98946	−	9.20062i	−0.461284	−	1.41969i
$43$	−10.9795			−1.67435			−0.837176	−	0.546933i	$-0.815795\pi$
$43$	−10.9795			−1.67435			−0.837176	+	0.546933i	$0.815795\pi$
$44$	−7.27590	+	8.28732i	−1.09688	+	1.24936i
$45$	3.77481			0.562716
$46$	−4.60553	−	14.1744i	−0.679048	−	2.08989i
$47$	2.14193	+	1.55620i	0.312433	+	0.226996i	0.732940	−	0.680294i	$-0.238148\pi$
$47$	2.14193	+	1.55620i	0.312433	+	0.226996i	−0.420507	+	0.907289i	$0.638148\pi$
$48$	0.328494	−	0.238665i	0.0474140	−	0.0344483i
$49$	3.26784	−	10.0574i	0.466834	−	1.43677i
$50$	−6.59554	+	20.2990i	−0.932751	+	2.87071i
$51$	0.809017	−	0.587785i	0.113285	−	0.0823064i
$52$	−11.7908	−	8.56652i	−1.63509	−	1.18796i
$53$	0.664718	+	2.04579i	0.0913061	+	0.281011i	0.986273	−	0.165120i	$-0.0528013\pi$
$53$	0.664718	+	2.04579i	0.0913061	+	0.281011i	−0.894967	+	0.446132i	$0.852801\pi$
$54$	2.30762			0.314027
$55$	1.15246	−	12.4665i	0.155398	−	1.68098i
$56$	12.8190			1.71302
$57$	0.116918	+	0.359837i	0.0154862	+	0.0476616i
$58$	16.7347	+	12.1585i	2.19738	+	1.59649i
$59$	−4.99727	+	3.63073i	−0.650590	+	0.472681i	−0.863472	−	0.504397i	$-0.831715\pi$
$59$	−4.99727	+	3.63073i	−0.650590	+	0.472681i	0.212882	+	0.977078i	$0.431715\pi$
$60$	−3.87865	+	11.9373i	−0.500732	+	1.54110i
$61$	−2.66117	+	8.19023i	−0.340727	+	1.04865i	0.623104	+	0.782139i	$0.285871\pi$
$61$	−2.66117	+	8.19023i	−0.340727	+	1.04865i	−0.963832	+	0.266512i	$0.914129\pi$
$62$	6.87241	−	4.99310i	0.872797	−	0.634124i
$63$	3.39160	+	2.46414i	0.427302	+	0.310453i
$64$	−3.94377	−	12.1377i	−0.492972	−	1.51721i
$65$	16.5454			2.05221
$66$	0.704522	−	7.62100i	0.0867206	−	0.938080i
$67$	5.18683			0.633672			0.316836	−	0.948480i	$-0.397379\pi$
$67$	5.18683			0.633672			0.316836	+	0.948480i	$0.397379\pi$
$68$	1.02751	+	3.16235i	0.124604	+	0.383491i
$69$	5.22506	+	3.79623i	0.629023	+	0.457012i
$70$	−29.5436	+	21.4647i	−3.53114	+	2.56552i
$71$	−2.22347	+	6.84315i	−0.263878	+	0.812133i	0.728072	+	0.685501i	$0.240417\pi$
$71$	−2.22347	+	6.84315i	−0.263878	+	0.812133i	−0.991950	+	0.126632i	$0.959583\pi$
$72$	−0.944911	+	2.90814i	−0.111359	+	0.342727i
$73$	1.52630	−	1.10892i	0.178640	−	0.129790i	−0.494872	−	0.868966i	$-0.664785\pi$
$73$	1.52630	−	1.10892i	0.178640	−	0.129790i	0.673512	+	0.739176i	$0.264785\pi$
$74$	13.1174	+	9.53037i	1.52487	+	1.10788i
$75$	−2.85816	−	8.79653i	−0.330032	−	1.01574i
$76$	−1.25806			−0.144310
$77$	9.17340	−	10.4486i	1.04541	−	1.19073i
$78$	10.1145			1.14525
$79$	−0.434449	−	1.33710i	−0.0488793	−	0.150435i	0.923638	−	0.383267i	$-0.125201\pi$
$79$	−0.434449	−	1.33710i	−0.0488793	−	0.150435i	−0.972517	+	0.232832i	$0.925201\pi$
$80$	−1.24000	−	0.900914i	−0.138636	−	0.100725i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−6.28307	+	19.3373i	−0.693849	+	2.13545i
$83$	−2.84627	+	8.75991i	−0.312418	+	0.961525i	0.664386	+	0.747390i	$0.268693\pi$
$83$	−2.84627	+	8.75991i	−0.312418	+	0.961525i	−0.976804	+	0.214135i	$0.931307\pi$
$84$	−11.2774	+	8.19349i	−1.23046	+	0.893983i
$85$	−3.05389	−	2.21878i	−0.331241	−	0.240660i
$86$	7.82937	+	24.0963i	0.844263	+	2.59837i
$87$	−8.96391			−0.961032
$88$	9.31576	+	4.00847i	0.993064	+	0.427305i
$89$	0.222644			0.0236002			0.0118001	−	0.999930i	$-0.496244\pi$
$89$	0.222644			0.0236002			0.0118001	+	0.999930i	$0.496244\pi$
$90$	−2.69179	−	8.28448i	−0.283740	−	0.873261i
$91$	14.8658	+	10.8006i	1.55836	+	1.13221i
$92$	−17.3738	+	12.6228i	−1.81134	+	1.31602i
$93$	−1.13755	+	3.50102i	−0.117958	+	0.363039i
$94$	1.88796	−	5.81055i	0.194729	−	0.599313i
$95$	1.15545	−	0.839487i	0.118547	−	0.0861295i
$96$	4.18958	+	3.04391i	0.427597	+	0.310668i
$97$	1.08321	+	3.33378i	0.109983	+	0.338494i	0.990868	−	0.134837i	$-0.0430512\pi$
$97$	1.08321	+	3.33378i	0.109983	+	0.338494i	−0.880884	+	0.473332i	$0.843051\pi$
$98$	−24.4029			−2.46507
$99$	1.69419	+	2.85127i	0.170273	+	0.286563i
$100$	30.7545			3.07545
$101$	−4.45590	−	13.7138i	−0.443378	−	1.36458i	−0.884252	−	0.467009i	$-0.845331\pi$
$101$	−4.45590	−	13.7138i	−0.443378	−	1.36458i	0.440874	−	0.897569i	$-0.354669\pi$
$102$	−1.86690	−	1.35638i	−0.184851	−	0.134302i
$103$	1.53037	−	1.11188i	0.150791	−	0.109556i	−0.509831	−	0.860274i	$-0.670292\pi$
$103$	1.53037	−	1.11188i	0.150791	−	0.109556i	0.660623	+	0.750718i	$0.270292\pi$
$104$	−4.14165	+	12.7467i	−0.406122	+	1.24992i
$105$	4.89018	−	15.0504i	0.477233	−	1.46877i
$106$	4.01584	−	2.91768i	0.390053	−	0.283390i
$107$	−8.76977	−	6.37161i	−0.847805	−	0.615967i	0.0767348	−	0.997052i	$-0.475551\pi$
$107$	−8.76977	−	6.37161i	−0.847805	−	0.615967i	−0.924540	+	0.381085i	$0.875551\pi$
$108$	−1.02751	−	3.16235i	−0.0988721	−	0.304297i
$109$	17.6444			1.69003			0.845013	−	0.534746i	$-0.179593\pi$
$109$	17.6444			1.69003			0.845013	+	0.534746i	$0.179593\pi$
$110$	−28.1817	+	6.36048i	−2.68702	+	0.606448i
$111$	−7.02632			−0.666909
$112$	−0.526016	−	1.61891i	−0.0497038	−	0.152973i
$113$	6.87848	+	4.99750i	0.647073	+	0.470126i	0.862273	−	0.506444i	$-0.169040\pi$
$113$	6.87848	+	4.99750i	0.647073	+	0.470126i	−0.215200	+	0.976570i	$0.569040\pi$
$114$	0.706351	−	0.513194i	0.0661559	−	0.0480650i
$115$	7.53375	−	23.1865i	0.702526	−	2.16215i
$116$	9.21050	−	28.3470i	0.855174	−	2.63195i
$117$	−3.54601	+	2.57633i	−0.327829	+	0.238182i
$118$	11.5318	+	8.37833i	1.06159	+	0.771288i
$119$	−1.29548	−	3.98707i	−0.118756	−	0.365494i
$120$	11.5426			1.05369
$121$	9.93367	−	4.72464i	0.903061	−	0.429513i
$122$	19.8725			1.79917
$123$	−2.72275	−	8.37978i	−0.245503	−	0.755579i
$124$	−9.90259	−	7.19466i	−0.889279	−	0.646099i
$125$	−12.9766	+	9.42807i	−1.16066	+	0.843272i
$126$	2.98946	−	9.20062i	0.266322	−	0.819656i
$127$	−0.478887	+	1.47386i	−0.0424944	+	0.130784i	−0.970053	−	0.242894i	$-0.921903\pi$
$127$	−0.478887	+	1.47386i	−0.0424944	+	0.130784i	0.927559	+	0.373678i	$0.121903\pi$
$128$	−15.4468	+	11.2228i	−1.36532	+	0.991961i
$129$	−8.88257	−	6.45357i	−0.782067	−	0.568205i
$130$	−11.7984	−	36.3118i	−1.03479	−	3.18476i
$131$	2.44615			0.213721			0.106861	−	0.994274i	$-0.465920\pi$
$131$	2.44615			0.213721			0.106861	+	0.994274i	$0.465920\pi$
$132$	−10.7575	+	2.42792i	−0.936319	+	0.211323i
$133$	1.58616			0.137537
$134$	−3.69869	−	11.3834i	−0.319518	−	0.983376i
$135$	3.05389	+	2.21878i	0.262837	+	0.190962i
$136$	2.47381	−	1.79733i	0.212127	−	0.154120i
$137$	−1.89207	+	5.82318i	−0.161650	+	0.497508i	−0.998774	−	0.0495058i	$-0.984235\pi$
$137$	−1.89207	+	5.82318i	−0.161650	+	0.497508i	0.837124	+	0.547013i	$0.184235\pi$
$138$	4.60553	−	14.1744i	0.392048	−	1.20660i
$139$	−10.3639	+	7.52980i	−0.879053	+	0.638670i	−0.933001	−	0.359874i	$-0.882820\pi$
$139$	−10.3639	+	7.52980i	−0.879053	+	0.638670i	0.0539476	+	0.998544i	$0.482820\pi$
$140$	42.5700	+	30.9289i	3.59782	+	2.61397i
$141$	0.818145	+	2.51799i	0.0689002	+	0.212053i
$142$	16.6040			1.39338
$143$	7.42583	+	12.4974i	0.620979	+	1.04509i
$144$	0.406040			0.0338367
$145$	10.4562	+	32.1810i	0.868343	+	2.67249i
$146$	−3.52212	−	2.55897i	−0.291492	−	0.211782i
$147$	8.55532	−	6.21580i	0.705631	−	0.512671i
$148$	7.21961	−	22.2197i	0.593448	−	1.82644i
$149$	4.91362	−	15.1226i	0.402540	−	1.23889i	−0.520393	−	0.853927i	$-0.674214\pi$
$149$	4.91362	−	15.1226i	0.402540	−	1.23889i	0.922932	−	0.384962i	$-0.125786\pi$
$150$	−17.2674	+	12.5455i	−1.40987	+	1.02433i
$151$	−15.0489	−	10.9337i	−1.22466	−	0.889771i	−0.228186	−	0.973618i	$-0.573279\pi$
$151$	−15.0489	−	10.9337i	−1.22466	−	0.889771i	−0.996479	+	0.0838469i	$0.973279\pi$
$152$	0.357512	+	1.10031i	0.0289980	+	0.0892468i
$153$	1.00000			0.0808452
$154$	−29.4727	−	12.6818i	−2.37498	−	1.02193i
$155$	13.8958			1.11614
$156$	−4.50369	−	13.8609i	−0.360584	−	1.10976i
$157$	16.1059	+	11.7016i	1.28539	+	0.933893i	0.999702	−	0.0244285i	$-0.00777661\pi$
$157$	16.1059	+	11.7016i	1.28539	+	0.933893i	0.285692	+	0.958322i	$0.407777\pi$
$158$	−2.62468	+	1.90695i	−0.208809	+	0.151708i
$159$	−0.664718	+	2.04579i	−0.0527156	+	0.162242i
$160$	6.04075	−	18.5915i	0.477563	−	1.46979i
$161$	21.9047	−	15.9147i	1.72634	−	1.25426i
$162$	1.86690	+	1.35638i	0.146678	+	0.106567i
$163$	−0.425963	−	1.31098i	−0.0333640	−	0.102684i	0.932988	−	0.359908i	$-0.117192\pi$
$163$	−0.425963	−	1.31098i	−0.0333640	−	0.102684i	−0.966352	+	0.257224i	$0.917192\pi$
$164$	29.2974			2.28774
$165$	8.25998	−	9.40820i	0.643038	−	0.732427i
$166$	21.2548			1.64969
$167$	−2.17336	−	6.68890i	−0.168179	−	0.517603i	0.831077	−	0.556157i	$-0.187725\pi$
$167$	−2.17336	−	6.68890i	−0.168179	−	0.517603i	−0.999257	+	0.0385544i	$0.987725\pi$
$168$	10.3708	+	7.53485i	0.800127	+	0.581326i
$169$	−5.02535	+	3.65113i	−0.386565	+	0.280856i
$170$	−2.69179	+	8.28448i	−0.206451	+	0.635391i
$171$	−0.116918	+	0.359837i	−0.00894096	+	0.0275174i
$172$	29.5353	−	21.4587i	2.25205	−	1.63621i
$173$	−8.53787	−	6.20313i	−0.649123	−	0.471615i	0.213850	−	0.976867i	$-0.431400\pi$
$173$	−8.53787	−	6.20313i	−0.649123	−	0.471615i	−0.862972	+	0.505251i	$0.831400\pi$
$174$	6.39210	+	19.6729i	0.484584	+	1.49140i
$175$	−38.7750			−2.93112
$176$	0.123965	−	1.34097i	0.00934424	−	0.101079i
$177$	−6.17697			−0.464290
$178$	−0.158766	−	0.488631i	−0.0119000	−	0.0366244i
$179$	7.48333	+	5.43696i	0.559330	+	0.406377i	0.831214	−	0.555953i	$-0.187647\pi$
$179$	7.48333	+	5.43696i	0.559330	+	0.406377i	−0.271883	+	0.962330i	$0.587647\pi$
$180$	−10.1545	+	7.37764i	−0.756868	+	0.549897i
$181$	0.648979	−	1.99735i	0.0482382	−	0.148462i	−0.924036	−	0.382305i	$-0.875130\pi$
$181$	0.648979	−	1.99735i	0.0482382	−	0.148462i	0.972274	+	0.233843i	$0.0751303\pi$
$182$	13.1031	−	40.3273i	0.971270	−	2.98926i
$183$	−6.96702	+	5.06184i	−0.515017	+	0.374182i
$184$	15.9772	+	11.6081i	1.17785	+	0.855760i
$185$	8.19607	+	25.2249i	0.602587	+	1.85457i
$186$	8.49477			0.622866
$187$	0.305303	−	3.30254i	0.0223260	−	0.241506i
$188$	−8.80341			−0.642055
$189$	1.29548	+	3.98707i	0.0942320	+	0.290016i
$190$	−2.66634	−	1.93721i	−0.193437	−	0.140540i
$191$	16.1102	−	11.7048i	1.16570	−	0.846927i	0.175208	−	0.984531i	$-0.443940\pi$
$191$	16.1102	−	11.7048i	1.16570	−	0.846927i	0.990487	+	0.137604i	$0.0439402\pi$
$192$	3.94377	−	12.1377i	0.284617	−	0.875962i
$193$	−4.33599	+	13.3448i	−0.312111	+	0.960579i	0.664816	+	0.747007i	$0.268510\pi$
$193$	−4.33599	+	13.3448i	−0.312111	+	0.960579i	−0.976927	+	0.213572i	$0.931490\pi$
$194$	6.54413	−	4.75459i	0.469841	−	0.341360i
$195$	13.3855	+	9.72516i	0.958558	+	0.696433i
$196$	10.8659	+	33.4417i	0.776133	+	2.38869i
$197$	−5.96274			−0.424828			−0.212414	−	0.977180i	$-0.568133\pi$
$197$	−5.96274			−0.424828			−0.212414	+	0.977180i	$0.568133\pi$
$198$	5.04948	−	5.75141i	0.358851	−	0.408735i
$199$	−6.97968			−0.494776			−0.247388	−	0.968916i	$-0.579572\pi$
$199$	−6.97968			−0.494776			−0.247388	+	0.968916i	$0.579572\pi$
$200$	−8.73969	−	26.8980i	−0.617989	−	1.90197i
$201$	4.19624	+	3.04874i	0.295980	+	0.215042i
$202$	−26.9199	+	19.5585i	−1.89408	+	1.37613i
$203$	−11.6125	+	35.7397i	−0.815040	+	2.50844i
$204$	−1.02751	+	3.16235i	−0.0719400	+	0.221409i
$205$	−26.9079	+	19.5497i	−1.87933	+	1.36541i
$206$	−3.53150	−	2.56578i	−0.246051	−	0.178766i
$207$	1.99579	+	6.14242i	0.138717	+	0.426928i
$208$	1.77972			0.123401
$209$	1.15268	+	0.495987i	0.0797327	+	0.0343081i
$210$	−36.5179			−2.51998
$211$	1.52730	+	4.70053i	0.105143	+	0.323598i	0.989764	−	0.142713i	$-0.0455827\pi$
$211$	1.52730	+	4.70053i	0.105143	+	0.323598i	−0.884621	+	0.466311i	$0.845583\pi$
$212$	−5.78651	−	4.20414i	−0.397419	−	0.288742i
$213$	−5.82113	+	4.22930i	−0.398857	+	0.289787i
$214$	−7.72994	+	23.7903i	−0.528408	+	1.62627i
$215$	−12.8073	+	39.4169i	−0.873453	+	2.68821i
$216$	−2.47381	+	1.79733i	−0.168321	+	0.122293i
$217$	12.4851	+	9.07097i	0.847545	+	0.615778i
$218$	−12.5821	−	38.7237i	−0.852166	−	2.62270i
$219$	1.88661			0.127485
$220$	21.2648	+	35.7879i	1.43367	+	2.41282i
$221$	4.38311			0.294840
$222$	5.01041	+	15.4205i	0.336277	+	1.03495i
$223$	−19.5286	−	14.1884i	−1.30773	−	0.950124i	−0.307734	−	0.951472i	$-0.599571\pi$
$223$	−19.5286	−	14.1884i	−1.30773	−	0.950124i	−0.999999	+	0.00134880i	$0.999571\pi$
$224$	17.5638	−	12.7608i	1.17353	−	0.852619i
$225$	2.85816	−	8.79653i	0.190544	−	0.586435i
$226$	6.06290	−	18.6597i	0.403298	−	1.24122i
$227$	−0.218712	+	0.158903i	−0.0145164	+	0.0105468i	−0.595020	−	0.803711i	$-0.702856\pi$
$227$	−0.218712	+	0.158903i	−0.0145164	+	0.0105468i	0.580503	+	0.814258i	$0.302856\pi$
$228$	−1.01780	−	0.739472i	−0.0674052	−	0.0489727i
$229$	3.12350	+	9.61315i	0.206407	+	0.635255i	0.999653	+	0.0263532i	$0.00838946\pi$
$229$	3.12350	+	9.61315i	0.206407	+	0.635255i	−0.793246	+	0.608901i	$0.791611\pi$
$230$	−56.2590			−3.70961
$231$	13.5630	−	3.06110i	0.892378	−	0.201406i
$232$	−27.4098			−1.79954
$233$	−5.91067	−	18.1912i	−0.387221	−	1.19174i	−0.934856	−	0.355027i	$-0.884472\pi$
$233$	−5.91067	−	18.1912i	−0.387221	−	1.19174i	0.547635	−	0.836717i	$-0.315528\pi$
$234$	8.18283	+	5.94518i	0.534928	+	0.388648i
$235$	8.08539	−	5.87438i	0.527433	−	0.383202i
$236$	6.34689	−	19.5337i	0.413148	−	1.27154i
$237$	0.434449	−	1.33710i	0.0282205	−	0.0868537i
$238$	−7.82651	+	5.68629i	−0.507317	+	0.368588i
$239$	−16.7327	−	12.1570i	−1.08235	−	0.786374i	−0.104260	−	0.994550i	$-0.533247\pi$
$239$	−16.7327	−	12.1570i	−1.08235	−	0.786374i	−0.978091	+	0.208176i	$0.933247\pi$
$240$	−0.473638	−	1.45771i	−0.0305732	−	0.0940947i
$241$	26.5845			1.71246			0.856228	−	0.516598i	$-0.172802\pi$
$241$	26.5845			1.71246			0.856228	+	0.516598i	$0.172802\pi$
$242$	−17.4527	−	18.4321i	−1.12190	−	1.18486i
$243$	−1.00000			−0.0641500
$244$	−8.84862	−	27.2332i	−0.566475	−	1.74343i
$245$	−32.2947	−	23.4635i	−2.06323	−	1.49903i
$246$	−16.4493	+	11.9511i	−1.04877	+	0.761975i
$247$	−0.512465	+	1.57721i	−0.0326074	+	0.100355i
$248$	−3.47840	+	10.7054i	−0.220878	+	0.679794i
$249$	−7.45162	+	5.41392i	−0.472227	+	0.343093i
$250$	29.9451	+	21.7564i	1.89389	+	1.37599i
$251$	−2.14992	−	6.61677i	−0.135702	−	0.417647i	0.859997	−	0.510299i	$-0.170465\pi$
$251$	−2.14992	−	6.61677i	−0.135702	−	0.417647i	−0.995698	+	0.0926526i	$0.970465\pi$
$252$	−13.9396			−0.878112
$253$	20.8949	−	4.71590i	1.31365	−	0.296486i
$254$	3.57614			0.224387
$255$	−1.16648	−	3.59006i	−0.0730479	−	0.224818i
$256$	14.9954	+	10.8948i	0.937214	+	0.680926i
$257$	9.73406	−	7.07221i	0.607194	−	0.441152i	−0.241231	−	0.970468i	$-0.577551\pi$
$257$	9.73406	−	7.07221i	0.607194	−	0.441152i	0.848425	+	0.529315i	$0.177551\pi$
$258$	−7.82937	+	24.0963i	−0.487435	+	1.50017i
$259$	−9.10243	+	28.0144i	−0.565597	+	1.74073i
$260$	−44.5081	+	32.3370i	−2.76027	+	2.00546i
$261$	−7.25196	−	5.26886i	−0.448885	−	0.326134i
$262$	−1.74433	−	5.36851i	−0.107765	−	0.331668i
$263$	3.34144			0.206042			0.103021	−	0.994679i	$-0.467149\pi$
$263$	3.34144			0.206042			0.103021	+	0.994679i	$0.467149\pi$
$264$	5.18049	+	8.71859i	0.318837	+	0.536592i
$265$	8.11990			0.498802
$266$	−1.13108	−	3.48110i	−0.0693508	−	0.213440i
$267$	0.180123	+	0.130867i	0.0110233	+	0.00800892i
$268$	−13.9529	+	10.1373i	−0.852306	+	0.619237i
$269$	2.30320	−	7.08852i	0.140429	−	0.432195i	−0.855966	−	0.517032i	$-0.827037\pi$
$269$	2.30320	−	7.08852i	0.140429	−	0.432195i	0.996395	+	0.0848368i	$0.0270369\pi$
$270$	2.69179	−	8.28448i	0.163817	−	0.504177i
$271$	4.62289	−	3.35873i	0.280821	−	0.204028i	−0.438455	−	0.898753i	$-0.644474\pi$
$271$	4.62289	−	3.35873i	0.280821	−	0.204028i	0.719275	+	0.694725i	$0.244474\pi$
$272$	−0.328494	−	0.238665i	−0.0199178	−	0.0144712i
$273$	5.67822	+	17.4758i	0.343661	+	1.05768i
$274$	14.1292			0.853575
$275$	−28.1783	−	12.1248i	−1.69922	−	0.731154i
$276$	−21.4752			−1.29265
$277$	−3.13102	−	9.63629i	−0.188125	−	0.578989i	0.811863	−	0.583847i	$-0.198453\pi$
$277$	−3.13102	−	9.63629i	−0.188125	−	0.578989i	−0.999988	+	0.00485880i	$0.998453\pi$
$278$	23.9159	+	17.3759i	1.43438	+	1.04214i
$279$	−2.97814	+	2.16375i	−0.178297	+	0.129540i
$280$	14.9532	−	46.0212i	0.893623	−	2.75029i
$281$	−1.41388	+	4.35146i	−0.0843448	+	0.259587i	−0.984331	−	0.176332i	$-0.943577\pi$
$281$	−1.41388	+	4.35146i	−0.0843448	+	0.259587i	0.899986	+	0.435919i	$0.143577\pi$
$282$	4.94275	−	3.59112i	0.294337	−	0.213848i
$283$	−4.12967	−	3.00038i	−0.245483	−	0.178354i	0.458239	−	0.888829i	$-0.348480\pi$
$283$	−4.12967	−	3.00038i	−0.245483	−	0.178354i	−0.703723	+	0.710475i	$0.748480\pi$
$284$	−7.39325	−	22.7541i	−0.438709	−	1.35021i
$285$	1.42822			0.0846004
$286$	22.1324	−	25.2091i	1.30872	−	1.49064i
$287$	−36.9380			−2.18038
$288$	1.60028	+	4.92515i	0.0942973	+	0.290217i
$289$	−0.809017	−	0.587785i	−0.0475892	−	0.0345756i
$290$	63.1705	−	45.8960i	3.70950	−	2.69511i
$291$	−1.08321	+	3.33378i	−0.0634990	+	0.195430i
$292$	−1.93851	+	5.96612i	−0.113443	+	0.349141i
$293$	15.6534	−	11.3728i	0.914480	−	0.664409i	−0.0276638	−	0.999617i	$-0.508807\pi$
$293$	15.6534	−	11.3728i	0.914480	−	0.664409i	0.942144	+	0.335209i	$0.108807\pi$
$294$	−19.7424	−	14.3437i	−1.15140	−	0.836541i
$295$	7.20532	+	22.1757i	0.419510	+	1.29112i
$296$	−21.4850			−1.24879
$297$	−0.305303	+	3.30254i	−0.0177155	+	0.191633i
$298$	−36.6930			−2.12557
$299$	8.74779	+	26.9229i	0.505898	+	1.55699i
$300$	24.8809	+	18.0770i	1.43650	+	1.04368i
$301$	−37.2380	+	27.0550i	−2.14636	+	1.55942i
$302$	−13.2646	+	40.8242i	−0.763291	+	2.34917i
$303$	4.45590	−	13.7138i	0.255985	−	0.787840i
$304$	0.124287	−	0.0902999i	0.00712836	−	0.00517906i
$305$	26.2992	+	19.1075i	1.50589	+	1.09409i
$306$	−0.713092	−	2.19467i	−0.0407648	−	0.125461i
$307$	4.48483			0.255962			0.127981	−	0.991777i	$-0.459150\pi$
$307$	4.48483			0.255962			0.127981	+	0.991777i	$0.459150\pi$
$308$	−4.25580	+	46.0361i	−0.242497	+	2.62315i
$309$	1.89164			0.107611
$310$	−9.90899	−	30.4967i	−0.562793	−	1.73210i
$311$	−7.09590	−	5.15547i	−0.402372	−	0.292340i	0.368135	−	0.929772i	$-0.379997\pi$
$311$	−7.09590	−	5.15547i	−0.402372	−	0.292340i	−0.770506	+	0.637432i	$0.779997\pi$
$312$	−10.8430	+	7.87789i	−0.613863	+	0.445998i
$313$	−3.89867	+	11.9989i	−0.220366	+	0.678217i	0.778363	+	0.627814i	$0.216050\pi$
$313$	−3.89867	+	11.9989i	−0.220366	+	0.678217i	−0.998729	+	0.0504022i	$0.983950\pi$
$314$	14.1963	−	43.6916i	0.801142	−	2.46566i
$315$	12.8027	−	9.30168i	0.721348	−	0.524090i
$316$	3.78196	+	2.74776i	0.212752	+	0.154573i
$317$	−7.29534	−	22.4528i	−0.409747	−	1.26107i	−0.916866	−	0.399196i	$-0.869289\pi$
$317$	−7.29534	−	22.4528i	−0.409747	−	1.26107i	0.507118	−	0.861876i	$-0.330711\pi$
$318$	4.96385			0.278359
$319$	−19.6147	+	22.3413i	−1.09821	+	1.25087i
$320$	−48.1754			−2.69308
$321$	−3.34975	−	10.3095i	−0.186965	−	0.575419i
$322$	−50.5477	−	36.7251i	−2.81691	−	2.04661i
$323$	0.306096	−	0.222392i	0.0170316	−	0.0123742i
$324$	1.02751	−	3.16235i	0.0570838	−	0.175686i
$325$	12.5277	−	38.5562i	0.694909	−	2.13871i
$326$	−2.57342	+	1.86970i	−0.142529	+	0.103553i
$327$	14.2746	+	10.3711i	0.789388	+	0.573524i
$328$	−8.32563	−	25.6237i	−0.459706	−	1.41483i
$329$	11.0993			0.611923
$330$	−26.5380	−	11.4190i	−1.46087	−	0.628597i
$331$	27.8926			1.53311			0.766557	−	0.642176i	$-0.221968\pi$
$331$	27.8926			1.53311			0.766557	+	0.642176i	$0.221968\pi$
$332$	−9.46409	−	29.1275i	−0.519410	−	1.59858i
$333$	−5.68441	−	4.12997i	−0.311504	−	0.226321i
$334$	−13.1301	+	9.53961i	−0.718449	+	0.521984i
$335$	6.05034	−	18.6210i	0.330566	−	1.01738i
$336$	0.526016	−	1.61891i	0.0286965	−	0.0883188i
$337$	−7.04929	+	5.12161i	−0.383999	+	0.278992i	−0.762992	−	0.646408i	$-0.776270\pi$
$337$	−7.04929	+	5.12161i	−0.383999	+	0.278992i	0.378993	+	0.925400i	$0.376270\pi$
$338$	11.5966	+	8.42540i	0.630770	+	0.458281i
$339$	2.62734	+	8.08613i	0.142698	+	0.439178i
$340$	12.5516			0.680706
$341$	6.23663	+	10.4960i	0.337733	+	0.568393i
$342$	0.873098			0.0472117
$343$	−4.63127	−	14.2536i	−0.250065	−	0.769621i
$344$	−27.1611	−	19.7337i	−1.46443	−	1.06397i
$345$	19.7236	−	14.3300i	1.06188	−	0.771504i
$346$	−7.52554	+	23.1612i	−0.404576	+	1.24516i
$347$	−6.74722	+	20.7658i	−0.362210	+	1.11477i	0.589500	+	0.807768i	$0.299325\pi$
$347$	−6.74722	+	20.7658i	−0.362210	+	1.11477i	−0.951710	+	0.306998i	$0.900675\pi$
$348$	24.1134	−	17.5194i	1.29261	−	0.939139i
$349$	6.56416	+	4.76914i	0.351372	+	0.255286i	0.749444	−	0.662067i	$-0.230321\pi$
$349$	6.56416	+	4.76914i	0.351372	+	0.255286i	−0.398073	+	0.917354i	$0.630321\pi$
$350$	27.6502	+	85.0985i	1.47796	+	4.54870i
$351$	−4.38311			−0.233953
$352$	16.7541	−	3.78132i	0.892996	−	0.201545i
$353$	−24.0745			−1.28136			−0.640678	−	0.767809i	$-0.721347\pi$
$353$	−24.0745			−1.28136			−0.640678	+	0.767809i	$0.721347\pi$
$354$	4.40475	+	13.5564i	0.234110	+	0.720516i
$355$	21.9737	+	15.9648i	1.16624	+	0.847324i
$356$	−0.598924	+	0.435144i	−0.0317429	+	0.0230626i
$357$	1.29548	−	3.98707i	0.0685639	−	0.211018i
$358$	6.59604	−	20.3005i	0.348611	−	1.07292i
$359$	−2.18639	+	1.58851i	−0.115393	+	0.0838381i	−0.643985	−	0.765038i	$-0.722720\pi$
$359$	−2.18639	+	1.58851i	−0.115393	+	0.0838381i	0.528592	+	0.848876i	$0.322720\pi$
$360$	9.33817	+	6.78458i	0.492165	+	0.357579i
$361$	−5.82709	−	17.9339i	−0.306689	−	0.943891i
$362$	−4.84631			−0.254717
$363$	10.8136	+	2.01655i	0.567566	+	0.105842i
$364$	−61.0988			−3.20245
$365$	−2.20070	−	6.77305i	−0.115190	−	0.354518i
$366$	16.0772	+	11.6808i	0.840369	+	0.610564i
$367$	−14.2506	+	10.3537i	−0.743876	+	0.540457i	−0.893922	−	0.448222i	$-0.852058\pi$
$367$	−14.2506	+	10.3537i	−0.743876	+	0.540457i	0.150047	+	0.988679i	$0.452058\pi$
$368$	0.810373	−	2.49407i	0.0422436	−	0.130012i
$369$	2.72275	−	8.37978i	0.141741	−	0.436234i
$370$	49.5159	−	35.9754i	2.57421	−	1.87027i
$371$	7.29559	+	5.30055i	0.378768	+	0.275191i
$372$	−3.78245	−	11.6412i	−0.196111	−	0.603568i
$373$	−7.99006			−0.413710			−0.206855	−	0.978372i	$-0.566323\pi$
$373$	−7.99006			−0.413710			−0.206855	+	0.978372i	$0.566323\pi$
$374$	−7.46571	+	1.68498i	−0.386043	+	0.0871282i
$375$	−16.0400			−0.828301
$376$	2.50172	+	7.69950i	0.129016	+	0.397072i
$377$	−31.7861	−	23.0940i	−1.63707	−	1.18940i
$378$	7.82651	−	5.68629i	0.402552	−	0.292471i
$379$	−4.54610	+	13.9915i	−0.233518	+	0.718693i	0.763797	+	0.645457i	$0.223333\pi$
$379$	−4.54610	+	13.9915i	−0.233518	+	0.718693i	−0.997315	+	0.0732367i	$0.976667\pi$
$380$	−1.46751	+	4.51653i	−0.0752816	+	0.231693i
$381$	−1.25374	+	0.910898i	−0.0642312	+	0.0466667i
$382$	−37.1762	−	27.0101i	−1.90210	−	1.38196i
$383$	1.91246	+	5.88596i	0.0977223	+	0.300758i	0.987954	−	0.154750i	$-0.0494573\pi$
$383$	1.91246	+	5.88596i	0.0977223	+	0.300758i	−0.890231	+	0.455509i	$0.849457\pi$
$384$	−19.0933			−0.974351
$385$	−26.8105	−	45.1212i	−1.36639	−	2.29959i
$386$	32.3794			1.64807
$387$	−3.39284	−	10.4421i	−0.172468	−	0.530801i
$388$	−9.42957	−	6.85098i	−0.478714	−	0.347806i
$389$	8.41777	−	6.11587i	0.426798	−	0.310087i	−0.353569	−	0.935408i	$-0.615032\pi$
$389$	8.41777	−	6.11587i	0.426798	−	0.310087i	0.780367	+	0.625321i	$0.215032\pi$
$390$	11.7984	−	36.3118i	0.597436	−	1.83872i
$391$	1.99579	−	6.14242i	0.100932	−	0.310636i
$392$	26.1604	−	19.0067i	1.32130	−	0.959981i
$393$	1.97898	+	1.43781i	0.0998264	+	0.0725281i
$394$	4.25199	+	13.0863i	0.214212	+	0.659277i
$395$	−5.30703			−0.267026
$396$	−10.1301	−	4.35887i	−0.509056	−	0.219041i
$397$	−0.899353			−0.0451372			−0.0225686	−	0.999745i	$-0.507184\pi$
$397$	−0.899353			−0.0451372			−0.0225686	+	0.999745i	$0.507184\pi$
$398$	4.97716	+	15.3181i	0.249482	+	0.767828i
$399$	1.28323	+	0.932321i	0.0642418	+	0.0466744i
$400$	−3.03831	+	2.20746i	−0.151915	+	0.110373i
$401$	7.68660	−	23.6569i	0.383850	−	1.18137i	−0.553460	−	0.832875i	$-0.686693\pi$
$401$	7.68660	−	23.6569i	0.383850	−	1.18137i	0.937311	−	0.348494i	$-0.113307\pi$
$402$	3.69869	−	11.3834i	0.184474	−	0.567752i
$403$	−13.0535	+	9.48395i	−0.650243	+	0.472429i
$404$	38.7895	+	28.1822i	1.92985	+	1.40212i
$405$	1.16648	+	3.59006i	0.0579629	+	0.178392i
$406$	86.7178			4.30373
$407$	−15.3749	+	17.5121i	−0.762103	+	0.868043i
$408$	3.05780			0.151383
$409$	−3.37341	−	10.3823i	−0.166804	−	0.513371i	0.832360	−	0.554235i	$-0.186989\pi$
$409$	−3.37341	−	10.3823i	−0.166804	−	0.513371i	−0.999165	+	0.0408636i	$0.986989\pi$
$410$	62.0930	+	45.1132i	3.06656	+	2.22798i
$411$	−4.95349	+	3.59892i	−0.244338	+	0.177522i
$412$	−1.94367	+	5.98201i	−0.0957579	+	0.294713i
$413$	−8.00212	+	24.6280i	−0.393759	+	1.21186i
$414$	12.0574	−	8.76023i	0.592590	−	0.430542i
$415$	28.1285	+	20.4365i	1.38077	+	1.00319i
$416$	7.01420	+	21.5875i	0.343899	+	1.05841i
$417$	−12.8105			−0.627331
$418$	0.266559	−	2.88344i	0.0130378	−	0.141034i
$419$	12.1272			0.592451			0.296226	−	0.955118i	$-0.404272\pi$
$419$	12.1272			0.592451			0.296226	+	0.955118i	$0.404272\pi$
$420$	16.2603	+	50.0440i	0.793421	+	2.44190i
$421$	0.246139	+	0.178830i	0.0119961	+	0.00871565i	0.593767	−	0.804637i	$-0.297640\pi$
$421$	0.246139	+	0.178830i	0.0119961	+	0.00871565i	−0.581771	+	0.813353i	$0.697640\pi$
$422$	9.22703	−	6.70383i	0.449165	−	0.326337i
$423$	−0.818145	+	2.51799i	−0.0397796	+	0.122429i
$424$	−2.03257	+	6.25562i	−0.0987105	+	0.303800i
$425$	−7.48277	+	5.43655i	−0.362968	+	0.263711i
$426$	13.4329	+	9.75960i	0.650828	+	0.472854i
$427$	11.1563	+	34.3355i	0.539890	+	1.66161i
$428$	36.0441			1.74226
$429$	−1.33818	+	14.4754i	−0.0646078	+	0.698880i
$430$	95.6401			4.61218
$431$	−5.54179	−	17.0559i	−0.266939	−	0.821553i	−0.991240	−	0.132070i	$-0.957838\pi$
$431$	−5.54179	−	17.0559i	−0.266939	−	0.821553i	0.724302	−	0.689483i	$-0.242162\pi$
$432$	0.328494	+	0.238665i	0.0158047	+	0.0114828i
$433$	25.2231	−	18.3257i	1.21214	−	0.880675i	0.216721	−	0.976234i	$-0.430464\pi$
$433$	25.2231	−	18.3257i	1.21214	−	0.880675i	0.995424	+	0.0955590i	$0.0304638\pi$
$434$	11.0048	−	33.8692i	0.528246	−	1.62577i
$435$	−10.4562	+	32.1810i	−0.501338	+	1.54296i
$436$	−47.4643	+	34.4849i	−2.27313	+	1.65153i
$437$	1.97693	+	1.43632i	0.0945693	+	0.0687086i
$438$	−1.34533	−	4.14050i	−0.0642823	−	0.197841i
$439$	20.4934			0.978095			0.489048	−	0.872257i	$-0.337344\pi$
$439$	20.4934			0.978095			0.489048	+	0.872257i	$0.337344\pi$
$440$	25.2573	−	28.7684i	1.20410	−	1.37148i
$441$	10.5750			0.503569
$442$	−3.12556	−	9.61950i	−0.148668	−	0.457553i
$443$	−3.56461	−	2.58984i	−0.169360	−	0.123047i	0.499877	−	0.866097i	$-0.333379\pi$
$443$	−3.56461	−	2.58984i	−0.169360	−	0.123047i	−0.669236	+	0.743050i	$0.733379\pi$
$444$	18.9012	−	13.7325i	0.897010	−	0.651716i
$445$	0.259710	−	0.799306i	0.0123114	−	0.0378907i
$446$	−17.2131	+	52.9765i	−0.815065	+	2.50851i
$447$	12.8640	−	9.34626i	0.608448	−	0.442063i
$448$	−43.2847	−	31.4482i	−2.04501	−	1.48579i
$449$	−2.17712	−	6.70049i	−0.102745	−	0.316216i	0.886450	−	0.462825i	$-0.153164\pi$
$449$	−2.17712	−	6.70049i	−0.102745	−	0.316216i	−0.989195	+	0.146609i	$0.953164\pi$
$450$	−21.3436			−1.00615
$451$	−26.8433	−	11.5504i	−1.26400	−	0.543886i
$452$	−28.2708			−1.32975
$453$	−5.74818	−	17.6911i	−0.270073	−	0.831199i
$454$	0.504702	+	0.366688i	0.0236868	+	0.0172095i
$455$	56.1155	−	40.7703i	2.63073	−	1.91134i
$456$	−0.357512	+	1.10031i	−0.0167420	+	0.0515267i
$457$	−2.51639	+	7.74464i	−0.117712	+	0.362279i	−0.992503	−	0.122221i	$-0.960998\pi$
$457$	−2.51639	+	7.74464i	−0.117712	+	0.362279i	0.874791	+	0.484500i	$0.160998\pi$
$458$	18.8704	−	13.7101i	0.881754	−	0.640632i
$459$	0.809017	+	0.587785i	0.0377617	+	0.0274355i
$460$	25.0504	+	77.0972i	1.16798	+	3.59468i
$461$	−13.8855			−0.646713			−0.323357	−	0.946277i	$-0.604811\pi$
$461$	−13.8855			−0.646713			−0.323357	+	0.946277i	$0.604811\pi$
$462$	−16.3898	−	27.5834i	−0.762521	−	1.28330i
$463$	14.1521			0.657703			0.328852	−	0.944382i	$-0.393338\pi$
$463$	14.1521			0.657703			0.328852	+	0.944382i	$0.393338\pi$
$464$	1.12473	+	3.46157i	0.0522144	+	0.160699i
$465$	11.2419	+	8.16774i	0.521332	+	0.378770i
$466$	−35.7088	+	25.9440i	−1.65418	+	1.20183i
$467$	9.78164	−	30.1048i	0.452640	−	1.39308i	−0.421243	−	0.906948i	$-0.638406\pi$
$467$	9.78164	−	30.1048i	0.452640	−	1.39308i	0.873883	−	0.486136i	$-0.161594\pi$
$468$	4.50369	−	13.8609i	0.208183	−	0.640721i
$469$	17.5917	−	12.7811i	0.812308	−	0.590176i
$470$	−18.6580	−	13.5558i	−0.860628	−	0.625283i
$471$	6.15192	+	18.9337i	0.283465	+	0.872417i
$472$	−18.8879			−0.869387
$473$	−35.5213	+	8.01700i	−1.63327	+	0.368622i
$474$	−3.24429			−0.149015
$475$	−1.08140	−	3.32821i	−0.0496181	−	0.152709i
$476$	11.2774	+	8.19349i	0.516898	+	0.375548i
$477$	−1.74026	+	1.26437i	−0.0796808	+	0.0578915i
$478$	−14.7488	+	45.3920i	−0.674592	+	2.07618i
$479$	3.81634	−	11.7455i	0.174373	−	0.536666i	−0.825231	−	0.564795i	$-0.808955\pi$
$479$	3.81634	−	11.7455i	0.174373	−	0.536666i	0.999604	+	0.0281297i	$0.00895515\pi$
$480$	15.8149	−	11.4902i	0.721848	−	0.524453i
$481$	−24.9154	−	18.1021i	−1.13604	−	0.825385i
$482$	−18.9572	−	58.3442i	−0.863476	−	2.65751i
$483$	27.0758			1.23199
$484$	−17.4881	+	32.1243i	−0.794913	+	1.46019i
$485$	13.2320			0.600835
$486$	0.713092	+	2.19467i	0.0323465	+	0.0995524i
$487$	−16.0248	−	11.6427i	−0.726153	−	0.527581i	0.162191	−	0.986759i	$-0.448144\pi$
$487$	−16.0248	−	11.6427i	−0.726153	−	0.527581i	−0.888344	+	0.459178i	$0.848144\pi$
$488$	−21.3037	+	15.4781i	−0.964375	+	0.700660i
$489$	0.425963	−	1.31098i	0.0192627	−	0.0592846i
$490$	−28.4656	+	87.6080i	−1.28594	+	3.95773i
$491$	−33.6908	+	24.4778i	−1.52045	+	1.10467i	−0.559181	+	0.829045i	$0.688884\pi$
$491$	−33.6908	+	24.4778i	−1.52045	+	1.10467i	−0.961266	+	0.275624i	$0.911116\pi$
$492$	23.7021	+	17.2206i	1.06857	+	0.776364i
$493$	2.77000	+	8.52519i	0.124755	+	0.383955i
$494$	3.82689			0.172180
$495$	12.2125	−	2.75630i	0.548909	−	0.123886i
$496$	1.49471			0.0671145
$497$	9.32136	+	28.6882i	0.418120	+	1.28684i
$498$	17.1955	+	12.4932i	0.770548	+	0.559836i
$499$	29.4728	−	21.4132i	1.31938	−	0.958588i	0.319443	−	0.947605i	$-0.396504\pi$
$499$	29.4728	−	21.4132i	1.31938	−	0.958588i	0.999940	−	0.0109826i	$-0.00349593\pi$
$500$	16.4812	−	50.7240i	0.737063	−	2.26845i
$501$	2.17336	−	6.68890i	0.0970984	−	0.298838i
$502$	−12.9886	+	9.43674i	−0.579707	+	0.421182i
$503$	−26.0646	−	18.9370i	−1.16216	−	0.844359i	−0.172111	−	0.985077i	$-0.555059\pi$
$503$	−26.0646	−	18.9370i	−1.16216	−	0.844359i	−0.990050	+	0.140718i	$0.955059\pi$
$504$	3.96130	+	12.1916i	0.176450	+	0.543059i
$505$	−54.4312			−2.42216
$506$	−25.2499	−	42.4947i	−1.12249	−	1.88912i
$507$	−6.21167			−0.275870
$508$	−1.59234	−	4.90073i	−0.0706488	−	0.217435i
$509$	0.572427	+	0.415892i	0.0253724	+	0.0184341i	0.600399	−	0.799700i	$-0.295008\pi$
$509$	0.572427	+	0.415892i	0.0253724	+	0.0184341i	−0.575027	+	0.818135i	$0.695008\pi$
$510$	−7.04720	+	5.12009i	−0.312055	+	0.226721i
$511$	2.44406	−	7.52205i	0.108119	−	0.332756i
$512$	1.41712	−	4.36145i	0.0626285	−	0.192751i
$513$	−0.306096	+	0.222392i	−0.0135145	+	0.00981883i
$514$	−22.4625	−	16.3199i	−0.990777	−	0.719842i
$515$	−2.20656	−	6.79109i	−0.0972326	−	0.299251i
$516$	36.5077			1.60716
$517$	8.06599	+	3.47071i	0.354742	+	0.152642i
$518$	67.9733			2.98658
$519$	−3.26118	−	10.0369i	−0.143150	−	0.440570i
$520$	40.9302	+	29.7376i	1.79491	+	1.30408i
$521$	−34.4512	+	25.0302i	−1.50933	+	1.09659i	−0.542860	+	0.839823i	$0.682659\pi$
$521$	−34.4512	+	25.0302i	−1.50933	+	1.09659i	−0.966472	+	0.256771i	$0.917341\pi$
$522$	−6.39210	+	19.6729i	−0.279775	+	0.861058i
$523$	12.1056	−	37.2573i	0.529343	−	1.62915i	−0.226223	−	0.974076i	$-0.572638\pi$
$523$	12.1056	−	37.2573i	0.529343	−	1.62915i	0.755565	−	0.655073i	$-0.227362\pi$
$524$	−6.58029	+	4.78086i	−0.287461	+	0.208853i
$525$	−31.3696	−	22.7914i	−1.36908	−	0.994697i
$526$	−2.38276	−	7.33338i	−0.103893	−	0.319750i
$527$	3.68119			0.160355
$528$	0.888490	−	1.01200i	0.0386666	−	0.0440416i
$529$	18.7126			0.813590
$530$	−5.79024	−	17.8205i	−0.251512	−	0.774074i
$531$	−4.99727	−	3.63073i	−0.216863	−	0.157560i
$532$	−4.26685	+	3.10005i	−0.184992	+	0.134404i
$533$	11.9341	−	36.7295i	0.516925	−	1.59093i
$534$	0.158766	−	0.488631i	0.00687047	−	0.0211451i
$535$	−33.1042	+	24.0516i	−1.43122	+	1.03984i
$536$	12.8312	+	9.32244i	0.554225	+	0.402668i
$537$	2.85838	+	8.79718i	0.123348	+	0.379626i
$538$	−17.1994			−0.741518
$539$	3.22856	−	34.9242i	0.139064	−	1.50429i
$540$	−12.5516			−0.540134
$541$	4.91194	+	15.1174i	0.211181	+	0.649948i	0.999403	+	0.0345566i	$0.0110019\pi$
$541$	4.91194	+	15.1174i	0.211181	+	0.649948i	−0.788222	+	0.615391i	$0.788998\pi$
$542$	−10.6679	−	7.75065i	−0.458224	−	0.332919i
$543$	1.69905	−	1.23443i	0.0729131	−	0.0529745i
$544$	1.60028	−	4.92515i	0.0686114	−	0.211164i
$545$	20.5818	−	63.3444i	0.881629	−	2.71338i
$546$	34.3045	−	24.9237i	1.46810	−	1.06663i
$547$	−0.145784	−	0.105918i	−0.00623327	−	0.00452873i	0.584664	−	0.811275i	$-0.301226\pi$
$547$	−0.145784	−	0.105918i	−0.00623327	−	0.00452873i	−0.590898	+	0.806747i	$0.701226\pi$
$548$	−6.29129	−	19.3626i	−0.268750	−	0.827129i
$549$	−8.61172			−0.367539
$550$	−6.51627	+	70.4883i	−0.277855	+	3.00563i
$551$	−3.39154			−0.144485
$552$	6.10273	+	18.7823i	0.259750	+	0.799427i
$553$	−4.76827	−	3.46435i	−0.202767	−	0.147319i
$554$	−18.9158	+	13.7431i	−0.803655	+	0.583890i
$555$	−8.19607	+	25.2249i	−0.347904	+	1.07074i
$556$	13.1629	−	40.5111i	0.558230	−	1.71806i
$557$	−12.6260	+	9.17335i	−0.534982	+	0.388687i	−0.822218	−	0.569173i	$-0.807264\pi$
$557$	−12.6260	+	9.17335i	−0.534982	+	0.388687i	0.287236	+	0.957860i	$0.407264\pi$
$558$	6.87241	+	4.99310i	0.290932	+	0.211375i
$559$	−14.8712	−	45.7689i	−0.628985	−	1.93582i
$560$	−6.42557			−0.271530
$561$	2.18818	−	2.49236i	0.0923851	−	0.105228i
$562$	10.5583			0.445373
$563$	13.8950	+	42.7644i	0.585604	+	1.80230i	0.596831	+	0.802367i	$0.296426\pi$
$563$	13.8950	+	42.7644i	0.585604	+	1.80230i	−0.0112267	+	0.999937i	$0.503574\pi$
$564$	−7.12211	−	5.17452i	−0.299895	−	0.217886i
$565$	25.9650	−	18.8646i	1.09235	−	0.793642i
$566$	−3.64002	+	11.2028i	−0.153001	+	0.470890i
$567$	−1.29548	+	3.98707i	−0.0544049	+	0.167441i
$568$	−17.7998	+	12.9323i	−0.746865	+	0.542629i
$569$	33.2976	+	24.1922i	1.39591	+	1.01419i	0.995188	+	0.0979884i	$0.0312408\pi$
$569$	33.2976	+	24.1922i	1.39591	+	1.01419i	0.400722	+	0.916200i	$0.368759\pi$
$570$	−1.01845	−	3.13448i	−0.0426583	−	0.131289i
$571$	21.9293			0.917714			0.458857	−	0.888510i	$-0.348259\pi$
$571$	21.9293			0.917714			0.458857	+	0.888510i	$0.348259\pi$
$572$	−44.4013	−	19.1054i	−1.85651	−	0.798837i
$573$	19.9133			0.831892
$574$	26.3402	+	81.0668i	1.09942	+	3.38366i
$575$	−48.3277	−	35.1121i	−2.01540	−	1.46428i
$576$	10.3249	−	7.50150i	0.430205	−	0.312563i
$577$	8.38213	−	25.7975i	0.348952	−	1.07397i	−0.610481	−	0.792031i	$-0.709024\pi$
$577$	8.38213	−	25.7975i	0.348952	−	1.07397i	0.959434	−	0.281935i	$-0.0909761\pi$
$578$	−0.713092	+	2.19467i	−0.0296607	+	0.0912864i
$579$	−11.3518	+	8.24754i	−0.471763	+	0.342756i
$580$	−91.0236	−	66.1325i	−3.77955	−	2.74600i
$581$	11.9323	+	36.7237i	0.495034	+	1.52356i
$582$	8.08899			0.335299
$583$	3.64433	+	6.13328i	0.150933	+	0.254015i
$584$	5.76888			0.238718
$585$	5.11282	+	15.7356i	0.211389	+	0.650589i
$586$	−36.1220	−	26.2442i	−1.49219	−	1.08414i
$587$	−20.5918	+	14.9608i	−0.849914	+	0.617499i	−0.925122	−	0.379669i	$-0.876038\pi$
$587$	−20.5918	+	14.9608i	−0.849914	+	0.617499i	0.0752082	+	0.997168i	$0.476038\pi$
$588$	−10.8659	+	33.4417i	−0.448101	+	1.37911i
$589$	−0.430398	+	1.32463i	−0.0177342	+	0.0545803i
$590$	43.5303	−	31.6266i	1.79212	−	1.30205i
$591$	−4.82396	−	3.50481i	−0.198431	−	0.144169i
$592$	0.881616	+	2.71333i	0.0362342	+	0.111517i
$593$	−16.2842			−0.668712			−0.334356	−	0.942447i	$-0.608519\pi$
$593$	−16.2842			−0.668712			−0.334356	+	0.942447i	$0.608519\pi$
$594$	7.46571	−	1.68498i	0.306322	−	0.0691355i
$595$	−15.8250			−0.648760
$596$	16.3382	+	50.2839i	0.669240	+	2.05971i
$597$	−5.64668	−	4.10255i	−0.231103	−	0.167906i
$598$	52.8490	−	38.3971i	2.16116	−	1.57017i
$599$	−9.01565	+	27.7473i	−0.368369	+	1.13372i	0.579475	+	0.814990i	$0.303258\pi$
$599$	−9.01565	+	27.7473i	−0.368369	+	1.13372i	−0.947844	+	0.318734i	$0.896742\pi$
$600$	8.73969	−	26.8980i	0.356796	−	1.09811i
$601$	−5.72648	+	4.16053i	−0.233588	+	0.169711i	−0.698422	−	0.715686i	$-0.746114\pi$
$601$	−5.72648	+	4.16053i	−0.233588	+	0.169711i	0.464834	+	0.885398i	$0.346114\pi$
$602$	85.9309	+	62.4325i	3.50228	+	2.54456i
$603$	1.60282	+	4.93297i	0.0652718	+	0.200886i
$604$	61.8516			2.51671
$605$	−5.37430	−	41.1737i	−0.218496	−	1.67395i
$606$	−33.2749			−1.35170
$607$	3.07627	+	9.46779i	0.124862	+	0.384286i	0.993876	−	0.110502i	$-0.0352458\pi$
$607$	3.07627	+	9.46779i	0.124862	+	0.384286i	−0.869014	+	0.494788i	$0.835246\pi$
$608$	1.58515	+	1.15168i	0.0642863	+	0.0467067i
$609$	−30.4020	+	22.0884i	−1.23195	+	0.895065i
$610$	23.1809	−	71.3436i	0.938569	−	2.88862i
$611$	−3.58602	+	11.0366i	−0.145075	+	0.446494i
$612$	−2.69005	+	1.95444i	−0.108739	+	0.0790035i
$613$	5.15896	+	3.74820i	0.208368	+	0.151388i	0.687075	−	0.726586i	$-0.258894\pi$
$613$	5.15896	+	3.74820i	0.208368	+	0.151388i	−0.478707	+	0.877975i	$0.658894\pi$
$614$	−3.19809	−	9.84272i	−0.129065	−	0.397220i
$615$	−33.2600			−1.34117
$616$	41.4728	−	9.36023i	1.67099	−	0.377134i
$617$	33.7189			1.35747			0.678735	−	0.734383i	$-0.262528\pi$
$617$	33.7189			1.35747			0.678735	+	0.734383i	$0.262528\pi$
$618$	−1.34891	−	4.15152i	−0.0542612	−	0.166999i
$619$	1.11628	+	0.811021i	0.0448669	+	0.0325977i	0.609993	−	0.792407i	$-0.291172\pi$
$619$	1.11628	+	0.811021i	0.0448669	+	0.0325977i	−0.565126	+	0.825005i	$0.691172\pi$
$620$	−37.3804	+	27.1585i	−1.50123	+	1.09071i
$621$	−1.99579	+	6.14242i	−0.0800885	+	0.246487i
$622$	−6.25455	+	19.2495i	−0.250784	+	0.771835i
$623$	0.755120	−	0.548627i	0.0302532	−	0.0219803i
$624$	1.43982	+	1.04609i	0.0576391	+	0.0418772i
$625$	4.41953	+	13.6019i	0.176781	+	0.544076i
$626$	29.1137			1.16362
$627$	0.641006	+	1.07879i	0.0255993	+	0.0430828i
$628$	−66.1960			−2.64151
$629$	2.17125	+	6.68242i	0.0865735	+	0.266446i
$630$	−29.5436	−	21.4647i	−1.17705	−	0.855174i
$631$	−21.1478	+	15.3647i	−0.841879	+	0.611661i	−0.922895	−	0.385052i	$-0.874184\pi$
$631$	−21.1478	+	15.3647i	−0.841879	+	0.611661i	0.0810158	+	0.996713i	$0.474184\pi$
$632$	1.32846	−	4.08857i	0.0528431	−	0.162634i
$633$	−1.52730	+	4.70053i	−0.0607046	+	0.186829i
$634$	−44.0742	+	32.0218i	−1.75041	+	1.27175i
$635$	4.73265	+	3.43847i	0.187809	+	0.136451i
$636$	−2.21025	−	6.80244i	−0.0876420	−	0.269734i
$637$	46.3512			1.83650
$638$	63.0189	+	27.1164i	2.49494	+	1.07355i
$639$	−7.19531			−0.284642
$640$	22.2720	+	68.5461i	0.880378	+	2.70952i
$641$	13.7894	+	10.0186i	0.544647	+	0.395709i	0.825808	−	0.563952i	$-0.190720\pi$
$641$	13.7894	+	10.0186i	0.544647	+	0.395709i	−0.281161	+	0.959661i	$0.590720\pi$
$642$	−20.2372	+	14.7032i	−0.798700	+	0.580290i
$643$	1.63538	−	5.03319i	0.0644933	−	0.198490i	−0.913617	−	0.406575i	$-0.866723\pi$
$643$	1.63538	−	5.03319i	0.0644933	−	0.198490i	0.978111	+	0.208085i	$0.0667231\pi$
$644$	−27.8206	+	85.6230i	−1.09628	+	3.37402i
$645$	−33.5301	+	24.3610i	−1.32024	+	0.959214i
$646$	−0.706351	−	0.513194i	−0.0277910	−	0.0201914i
$647$	−10.0929	−	31.0627i	−0.396792	−	1.22120i	−0.927557	−	0.373681i	$-0.878096\pi$
$647$	−10.0929	−	31.0627i	−0.396792	−	1.22120i	0.530766	−	0.847519i	$-0.321904\pi$
$648$	−3.05780			−0.120122
$649$	−13.5163	+	15.3952i	−0.530562	+	0.604316i
$650$	−93.5515			−3.66939
$651$	4.76889	+	14.6771i	0.186908	+	0.575242i
$652$	3.70809	+	2.69409i	0.145220	+	0.105509i
$653$	−6.80369	+	4.94317i	−0.266249	+	0.193441i	−0.712897	−	0.701268i	$-0.752617\pi$
$653$	−6.80369	+	4.94317i	−0.266249	+	0.193441i	0.446648	+	0.894710i	$0.352617\pi$
$654$	12.5821	−	38.7237i	0.491998	−	1.51421i
$655$	2.85339	−	8.78184i	0.111491	−	0.343135i
$656$	−2.89436	+	2.10288i	−0.113006	+	0.0821036i
$657$	1.52630	+	1.10892i	0.0595467	+	0.0432632i
$658$	−7.91481	−	24.3593i	−0.308552	−	0.949624i
$659$	27.2003			1.05957			0.529786	−	0.848131i	$-0.322272\pi$
$659$	27.2003			1.05957			0.529786	+	0.848131i	$0.322272\pi$
$660$	−3.83204	+	41.4522i	−0.149162	+	1.61352i
$661$	−16.1211			−0.627040			−0.313520	−	0.949582i	$-0.601508\pi$
$661$	−16.1211			−0.627040			−0.313520	+	0.949582i	$0.601508\pi$
$662$	−19.8900	−	61.2151i	−0.773046	−	2.37919i
$663$	3.54601	+	2.57633i	0.137716	+	0.100056i
$664$	−22.7856	+	16.5547i	−0.884251	+	0.642446i
$665$	1.85022	−	5.69441i	0.0717486	−	0.220820i
$666$	−5.01041	+	15.4205i	−0.194150	+	0.597531i
$667$	−46.8370	+	34.0290i	−1.81353	+	1.31761i
$668$	18.9195	+	13.7458i	0.732017	+	0.531841i
$669$	−7.45927	−	22.9573i	−0.288392	−	0.887579i
$670$	−45.1815			−1.74552
$671$	−2.62918	+	28.4406i	−0.101498	+	1.09794i
$672$	21.7100			0.837482
$673$	−4.89616	−	15.0688i	−0.188733	−	0.580861i	0.811259	−	0.584686i	$-0.198782\pi$
$673$	−4.89616	−	15.0688i	−0.188733	−	0.580861i	−0.999993	+	0.00382515i	$0.998782\pi$
$674$	16.2670	+	11.8187i	0.626583	+	0.455239i
$675$	7.48277	−	5.43655i	0.288012	−	0.209253i
$676$	6.38255	−	19.6435i	0.245483	−	0.755518i
$677$	−12.3415	+	37.9832i	−0.474322	+	1.45981i	0.372549	+	0.928013i	$0.378484\pi$
$677$	−12.3415	+	37.9832i	−0.474322	+	1.45981i	−0.846870	+	0.531799i	$0.821516\pi$
$678$	15.8729	−	11.5323i	0.609594	−	0.442896i
$679$	11.8887	+	8.63767i	0.456248	+	0.331483i
$680$	−3.56686	−	10.9777i	−0.136783	−	0.420975i
$681$	−0.270342			−0.0103595
$682$	18.5881	−	21.1720i	0.711775	−	0.810719i
$683$	2.64273			0.101121			0.0505606	−	0.998721i	$-0.483899\pi$
$683$	2.64273			0.101121			0.0505606	+	0.998721i	$0.483899\pi$
$684$	−0.388763	−	1.19649i	−0.0148647	−	0.0457490i
$685$	18.6985	+	13.5853i	0.714433	+	0.519066i
$686$	−27.9794	+	20.3282i	−1.06826	+	0.776136i
$687$	−3.12350	+	9.61315i	−0.119169	+	0.366764i
$688$	−1.37763	+	4.23991i	−0.0525217	+	0.161645i
$689$	−7.62773	+	5.54187i	−0.290594	+	0.211129i
$690$	−45.5145	−	33.0682i	−1.73271	−	1.25889i
$691$	−0.674298	−	2.07528i	−0.0256515	−	0.0789472i	0.937411	−	0.348224i	$-0.113215\pi$
$691$	−0.674298	−	2.07528i	−0.0256515	−	0.0789472i	−0.963063	+	0.269277i	$0.913215\pi$
$692$	35.0910			1.33396
$693$	12.7719	+	5.49563i	0.485166	+	0.208762i
$694$	50.3855			1.91261
$695$	14.9432	+	45.9903i	0.566827	+	1.74451i
$696$	−22.1750	−	16.1111i	−0.840542	−	0.610689i
$697$	−7.12826	+	5.17899i	−0.270002	+	0.196168i
$698$	5.78586	−	17.8070i	0.218998	−	0.674006i
$699$	5.91067	−	18.1912i	0.223562	−	0.688054i
$700$	104.307	−	75.7834i	3.94243	−	2.86434i
$701$	−31.8203	−	23.1188i	−1.20184	−	0.873186i	−0.207373	−	0.978262i	$-0.566491\pi$
$701$	−31.8203	−	23.1188i	−1.20184	−	0.873186i	−0.994464	+	0.105076i	$0.966491\pi$
$702$	3.12556	+	9.61950i	0.117967	+	0.363064i
$703$	−2.65844			−0.100265
$704$	−21.6218	−	36.3888i	−0.814902	−	1.37145i
$705$	9.99409			0.376399
$706$	17.1674	+	52.8357i	0.646102	+	1.98850i
$707$	−48.9055	−	35.5319i	−1.83928	−	1.33632i
$708$	16.6164	−	12.0725i	0.624482	−	0.453713i
$709$	9.71869	−	29.9111i	0.364993	−	1.12333i	−0.584992	−	0.811039i	$-0.698902\pi$
$709$	9.71869	−	29.9111i	0.364993	−	1.12333i	0.949985	−	0.312295i	$-0.101098\pi$
$710$	19.3683	−	59.6094i	0.726879	−	2.23710i
$711$	1.13740	−	0.826370i	0.0426559	−	0.0309913i
$712$	0.550779	+	0.400164i	0.0206413	+	0.0149968i
$713$	7.34689	+	22.6114i	0.275143	+	0.846804i
$714$	−9.67410			−0.362044
$715$	53.5286	−	12.0812i	2.00186	−	0.451810i
$716$	−30.7568			−1.14943
$717$	−6.39134	−	19.6705i	−0.238689	−	0.734609i
$718$	5.04535	+	3.66566i	0.188291	+	0.136801i
$719$	32.7319	−	23.7811i	1.22069	−	0.886887i	0.224537	−	0.974466i	$-0.427913\pi$
$719$	32.7319	−	23.7811i	1.22069	−	0.886887i	0.996158	+	0.0875789i	$0.0279130\pi$
$720$	0.473638	−	1.45771i	0.0176515	−	0.0543256i
$721$	2.45057	−	7.54208i	0.0912640	−	0.280882i
$722$	−35.2039	+	25.5771i	−1.31015	+	0.951881i
$723$	21.5073	+	15.6260i	0.799865	+	0.581136i
$724$	2.15791	+	6.64137i	0.0801981	+	0.246825i
$725$	82.9092			3.07917
$726$	−3.28541	−	25.1703i	−0.121933	−	0.934156i
$727$	−16.3981			−0.608171			−0.304085	−	0.952645i	$-0.598351\pi$
$727$	−16.3981			−0.608171			−0.304085	+	0.952645i	$0.598351\pi$
$728$	17.3628	+	53.4373i	0.643509	+	1.98052i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−13.2953	+	9.65962i	−0.492082	+	0.357519i
$731$	−3.39284	+	10.4421i	−0.125489	+	0.386215i
$732$	8.84862	−	27.2332i	0.327054	−	1.00657i
$733$	41.4954	−	30.1482i	1.53267	−	1.11355i	0.577937	−	0.816081i	$-0.303858\pi$
$733$	41.4954	−	30.1482i	1.53267	−	1.11355i	0.954732	−	0.297468i	$-0.0961421\pi$
$734$	32.8849	+	23.8923i	1.21380	+	0.881881i
$735$	−12.3355	−	37.9647i	−0.455001	−	1.40035i
$736$	33.4462			1.23284
$737$	16.7807	−	3.78733i	0.618125	−	0.139508i
$738$	−20.3324			−0.748448
$739$	9.29094	+	28.5946i	0.341773	+	1.05187i	0.963289	+	0.268467i	$0.0865170\pi$
$739$	9.29094	+	28.5946i	0.341773	+	1.05187i	−0.621516	+	0.783401i	$0.713483\pi$
$740$	−71.3484	−	51.8376i	−2.62282	−	1.90559i
$741$	−1.34165	+	0.974767i	−0.0492868	+	0.0358090i
$742$	6.43055	−	19.7912i	0.236073	−	0.726558i
$743$	−11.9604	+	36.8102i	−0.438783	+	1.35044i	0.450376	+	0.892839i	$0.351290\pi$
$743$	−11.9604	+	36.8102i	−0.438783	+	1.35044i	−0.889159	+	0.457598i	$0.848710\pi$
$744$	−9.10656	+	6.61630i	−0.333863	+	0.242565i
$745$	−48.5593	−	35.2804i	−1.77908	−	1.29257i
$746$	5.69765	+	17.5356i	0.208606	+	0.642023i
$747$	−9.21071			−0.337002
$748$	5.63334	+	9.48071i	0.205975	+	0.346649i
$749$	−45.4441			−1.66049
$750$	11.4380	+	35.2025i	0.417656	+	1.28541i
$751$	25.6514	+	18.6369i	0.936035	+	0.680069i	0.947463	−	0.319866i	$-0.103638\pi$
$751$	25.6514	+	18.6369i	0.936035	+	0.680069i	−0.0114282	+	0.999935i	$0.503638\pi$
$752$	0.869710	−	0.631881i	0.0317151	−	0.0230423i
$753$	2.14992	−	6.61677i	0.0783474	−	0.241128i
$754$	−28.0173	+	86.2283i	−1.02033	+	3.14025i
$755$	−56.8069	+	41.2726i	−2.06741	+	1.50206i
$756$	−11.2774	−	8.19349i	−0.410154	−	0.297994i
$757$	9.26403	+	28.5118i	0.336707	+	1.03628i	0.965875	+	0.259008i	$0.0833957\pi$
$757$	9.26403	+	28.5118i	0.336707	+	1.03628i	−0.629168	+	0.777269i	$0.716604\pi$
$758$	33.9485			1.23306
$759$	19.6763	+	8.46650i	0.714204	+	0.307314i
$760$	4.36721			0.158415
$761$	13.8946	+	42.7630i	0.503677	+	1.55016i	0.802983	+	0.596002i	$0.203245\pi$
$761$	13.8946	+	42.7630i	0.503677	+	1.55016i	−0.299306	+	0.954157i	$0.596755\pi$
$762$	2.89316	+	2.10200i	0.104808	+	0.0761475i
$763$	59.8427	−	43.4783i	2.16645	−	1.57402i
$764$	−20.4611	+	62.9729i	−0.740258	+	2.27828i
$765$	1.16648	−	3.59006i	0.0421742	−	0.129799i
$766$	11.5540	−	8.39446i	0.417463	−	0.303304i
$767$	−21.9036	−	15.9139i	−0.790894	−	0.574618i
$768$	5.72774	+	17.6282i	0.206682	+	0.636102i
$769$	19.1560			0.690782			0.345391	−	0.938459i	$-0.387746\pi$
$769$	19.1560			0.690782			0.345391	+	0.938459i	$0.387746\pi$
$770$	−79.9078	+	91.0158i	−2.87968	+	3.27998i
$771$	12.0320			0.433321
$772$	−14.4175	−	44.3726i	−0.518899	−	1.59701i
$773$	7.71996	+	5.60888i	0.277668	+	0.201737i	0.717899	−	0.696147i	$-0.245104\pi$
$773$	7.71996	+	5.60888i	0.277668	+	0.201737i	−0.440232	+	0.897884i	$0.645104\pi$
$774$	−20.4976	+	14.8924i	−0.736770	+	0.535295i
$775$	10.5214	−	32.3817i	0.377941	−	1.16318i
$776$	−3.31224	+	10.1940i	−0.118902	+	0.365944i
$777$	−23.8305	+	17.3138i	−0.854913	+	0.621131i
$778$	−19.4250	−	14.1131i	−0.696419	−	0.505978i
$779$	−1.03017	−	3.17053i	−0.0369096	−	0.113596i
$780$	−55.0150			−1.96985
$781$	−2.19675	+	23.7628i	−0.0786059	+	0.850301i
$782$	−14.9038			−0.532959
$783$	−2.77000	−	8.52519i	−0.0989918	−	0.304665i
$784$	−3.47380	−	2.52387i	−0.124064	−	0.0901381i
$785$	60.7969	−	44.1715i	2.16993	−	1.57655i
$786$	1.74433	−	5.36851i	0.0622183	−	0.191488i
$787$	−7.27738	+	22.3975i	−0.259411	+	0.798383i	0.733518	+	0.679670i	$0.237877\pi$
$787$	−7.27738	+	22.3975i	−0.259411	+	0.798383i	−0.992929	+	0.118713i	$0.962123\pi$
$788$	16.0401	−	11.6538i	0.571405	−	0.415150i
$789$	2.70328	+	1.96405i	0.0962395	+	0.0699221i
$790$	3.78440	+	11.6472i	0.134643	+	0.414389i
$791$	35.6436			1.26734
$792$	−0.933554	+	10.0985i	−0.0331724	+	0.358835i
$793$	−37.7461			−1.34040
$794$	0.641322	+	1.97378i	0.0227597	+	0.0700470i
$795$	6.56914	+	4.77276i	0.232983	+	0.169272i
$796$	18.7757	−	13.6414i	0.665488	−	0.483505i
$797$	0.313493	−	0.964834i	0.0111045	−	0.0341762i	−0.945351	−	0.326055i	$-0.894280\pi$
$797$	0.313493	−	0.964834i	0.0111045	−	0.0341762i	0.956455	+	0.291879i	$0.0942805\pi$
$798$	1.13108	−	3.48110i	0.0400397	−	0.123230i
$799$	2.14193	−	1.55620i	0.0757761	−	0.0550545i
$800$	−38.7503	−	28.1538i	−1.37003	−	0.995386i
$801$	0.0688008	+	0.211747i	0.00243096	+	0.00748171i
$802$	−57.4004			−2.02688
$803$	4.12825	−	4.70212i	0.145683	−	0.165934i
$804$	−17.2467			−0.608243
$805$	−31.5834	−	97.2036i	−1.11317	−	3.42598i
$806$	30.1225	+	21.8853i	1.06102	+	0.770877i
$807$	6.02986	−	4.38095i	0.212261	−	0.154217i
$808$	13.6252	−	41.9341i	0.479334	−	1.47524i
$809$	13.6306	−	41.9506i	0.479226	−	1.47490i	−0.360947	−	0.932586i	$-0.617547\pi$
$809$	13.6306	−	41.9506i	0.479226	−	1.47490i	0.840173	−	0.542318i	$-0.182453\pi$
$810$	7.04720	−	5.12009i	0.247613	−	0.179902i
$811$	3.27475	+	2.37924i	0.114992	+	0.0835465i	0.643795	−	0.765198i	$-0.277359\pi$
$811$	3.27475	+	2.37924i	0.114992	+	0.0835465i	−0.528803	+	0.848745i	$0.677359\pi$
$812$	−38.6127	−	118.838i	−1.35504	−	4.17039i
$813$	5.71421			0.200406
$814$	49.3971	+	21.2550i	1.73137	+	0.744988i
$815$	−5.20338			−0.182266
$816$	−0.125473	−	0.386167i	−0.00439245	−	0.0135186i
$817$	−3.36077	−	2.44174i	−0.117578	−	0.0854257i
$818$	−20.3802	+	14.8071i	−0.712576	+	0.517717i
$819$	−5.67822	+	17.4758i	−0.198413	+	0.610652i
$820$	34.1749	−	105.180i	1.19344	−	3.67303i
$821$	13.7587	−	9.99628i	0.480182	−	0.348872i	−0.321214	−	0.947007i	$-0.604091\pi$
$821$	13.7587	−	9.99628i	0.480182	−	0.348872i	0.801396	+	0.598134i	$0.204091\pi$
$822$	11.4308	+	8.30493i	0.398693	+	0.289668i
$823$	1.99822	+	6.14990i	0.0696537	+	0.214372i	0.979824	−	0.199862i	$-0.0640495\pi$
$823$	1.99822	+	6.14990i	0.0696537	+	0.214372i	−0.910170	+	0.414234i	$0.864049\pi$
$824$	5.78424			0.201503
$825$	−15.6699	−	26.3720i	−0.545557	−	0.918154i
$826$	59.7566			2.07920
$827$	−3.02585	−	9.31260i	−0.105219	−	0.323831i	0.884563	−	0.466421i	$-0.154457\pi$
$827$	−3.02585	−	9.31260i	−0.105219	−	0.323831i	−0.989782	+	0.142590i	$0.954457\pi$
$828$	−17.3738	−	12.6228i	−0.603781	−	0.438672i
$829$	−30.2294	+	21.9629i	−1.04991	+	0.762804i	−0.972195	−	0.234172i	$-0.924762\pi$
$829$	−30.2294	+	21.9629i	−1.04991	+	0.762804i	−0.0777141	+	0.996976i	$0.524762\pi$
$830$	24.7933	−	76.3060i	0.860588	−	2.64862i
$831$	3.13102	−	9.63629i	0.108614	−	0.334279i
$832$	45.2553	−	32.8799i	1.56895	−	1.13991i
$833$	−8.55532	−	6.21580i	−0.296424	−	0.215365i
$834$	9.13505	+	28.1148i	0.316321	+	0.973535i
$835$	−26.5487			−0.918757
$836$	−4.07015	+	0.918616i	−0.140769	+	0.0317710i
$837$	−3.68119			−0.127240
$838$	−8.64780	−	26.6152i	−0.298733	−	0.919406i
$839$	−16.7595	−	12.1765i	−0.578602	−	0.420379i	0.259618	−	0.965711i	$-0.416403\pi$
$839$	−16.7595	−	12.1765i	−0.578602	−	0.420379i	−0.838220	+	0.545333i	$0.816403\pi$
$840$	39.1479	−	28.4426i	1.35073	−	0.981364i
$841$	15.8686	−	48.8384i	0.547192	−	1.68408i
$842$	0.216954	−	0.667716i	0.00747674	−	0.0230110i
$843$	−3.70158	+	2.68935i	−0.127489	+	0.0926262i
$844$	−13.2954	−	9.65968i	−0.457647	−	0.332500i
$845$	7.24580	+	22.3003i	0.249263	+	0.767153i
$846$	6.10958			0.210052
$847$	22.0489	−	40.5021i	0.757608	−	1.39167i
$848$	0.873423			0.0299935
$849$	−1.57739	−	4.85472i	−0.0541360	−	0.166613i
$850$	17.2674	+	12.5455i	0.592266	+	0.430306i
$851$	−36.7129	+	26.6735i	−1.25850	+	0.914356i
$852$	7.39325	−	22.7541i	0.253289	−	0.779542i
$853$	−2.89304	+	8.90386i	−0.0990557	+	0.304862i	−0.988289	−	0.152591i	$-0.951238\pi$
$853$	−2.89304	+	8.90386i	−0.0990557	+	0.304862i	0.889234	+	0.457453i	$0.151238\pi$
$854$	67.3997	−	48.9687i	2.30637	−	1.67568i
$855$	1.15545	+	0.839487i	0.0395157	+	0.0287098i
$856$	−10.2429	−	31.5243i	−0.350094	−	1.07748i
$857$	57.1849			1.95340			0.976700	−	0.214611i	$-0.0688482\pi$
$857$	57.1849			1.95340			0.976700	+	0.214611i	$0.0688482\pi$
$858$	32.7230	−	7.38545i	1.11715	−	0.252135i
$859$	10.1796			0.347323			0.173662	−	0.984805i	$-0.444440\pi$
$859$	10.1796			0.347323			0.173662	+	0.984805i	$0.444440\pi$
$860$	−42.5856	−	131.065i	−1.45216	−	4.46927i
$861$	−29.8835	−	21.7116i	−1.01843	−	0.739930i
$862$	−33.4803	+	24.3249i	−1.14034	+	0.828508i
$863$	−11.0628	+	34.0478i	−0.376582	+	1.15900i	0.565823	+	0.824527i	$0.308559\pi$
$863$	−11.0628	+	34.0478i	−0.376582	+	1.15900i	−0.942405	+	0.334474i	$0.891441\pi$
$864$	−1.60028	+	4.92515i	−0.0544426	+	0.167557i
$865$	−32.2289	+	23.4157i	−1.09581	+	0.796156i
$866$	−58.2052	−	42.2886i	−1.97789	−	1.43702i
$867$	−0.309017	−	0.951057i	−0.0104948	−	0.0322996i
$868$	−51.3143			−1.74172
$869$	−2.38187	−	4.00861i	−0.0807995	−	0.135983i
$870$	78.0830			2.64726
$871$	7.02534	+	21.6218i	0.238044	+	0.732625i
$872$	43.6488	+	31.7127i	1.47814	+	1.07393i
$873$	−2.83588	+	2.06039i	−0.0959801	+	0.0697336i
$874$	1.74252	−	5.36294i	0.0589418	−	0.181404i
$875$	−20.7794	+	63.9525i	−0.702473	+	2.16199i
$876$	−5.07509	+	3.68727i	−0.171471	+	0.124581i
$877$	−7.08018	−	5.14405i	−0.239081	−	0.173702i	0.461793	−	0.886988i	$-0.347206\pi$
$877$	−7.08018	−	5.14405i	−0.239081	−	0.173702i	−0.700874	+	0.713285i	$0.747206\pi$
$878$	−14.6137	−	44.9762i	−0.493187	−	1.51787i
$879$	19.3486			0.652613
$880$	−4.66954	−	2.00925i	−0.157410	−	0.0677320i
$881$	29.8492			1.00564			0.502822	−	0.864390i	$-0.332295\pi$
$881$	29.8492			1.00564			0.502822	+	0.864390i	$0.332295\pi$
$882$	−7.54092	−	23.2086i	−0.253916	−	0.781473i
$883$	−36.5435	−	26.5504i	−1.22979	−	0.893494i	−0.232914	−	0.972497i	$-0.574826\pi$
$883$	−36.5435	−	26.5504i	−1.22979	−	0.893494i	−0.996874	+	0.0790038i	$0.974826\pi$
$884$	−11.7908	+	8.56652i	−0.396568	+	0.288123i
$885$	−7.20532	+	22.1757i	−0.242204	+	0.745428i
$886$	−3.14196	+	9.66995i	−0.105556	+	0.324868i
$887$	−3.10828	+	2.25830i	−0.104366	+	0.0758262i	−0.638744	−	0.769419i	$-0.720546\pi$
$887$	−3.10828	+	2.25830i	−0.104366	+	0.0758262i	0.534378	+	0.845245i	$0.320546\pi$
$888$	−17.3818	−	12.6286i	−0.583294	−	0.423788i
$889$	2.00761	+	6.17880i	0.0673332	+	0.207230i
$890$	−1.93941			−0.0650092
$891$	−2.18818	+	2.49236i	−0.0733068	+	0.0834972i
$892$	80.2633			2.68742
$893$	0.309549	+	0.952695i	0.0103587	+	0.0318807i
$894$	−29.6852	−	21.5676i	−0.992823	−	0.721328i
$895$	28.2482	−	20.5235i	0.944232	−	0.686025i
$896$	−24.7349	+	76.1263i	−0.826336	+	2.54320i
$897$	−8.74779	+	26.9229i	−0.292080	+	0.898931i
$898$	−13.1529	+	9.55613i	−0.438918	+	0.318892i
$899$	−26.6958	−	19.3956i	−0.890355	−	0.646881i
$900$	9.50365	+	29.2492i	0.316788	+	0.974974i
$901$	2.15107			0.0716627
$902$	−6.20755	+	67.1488i	−0.206689	+	2.23581i
$903$	−46.0287			−1.53174
$904$	8.03388	+	24.7258i	0.267203	+	0.822366i
$905$	−6.41359	−	4.65974i	−0.213195	−	0.154895i
$906$	−34.7271	+	25.2307i	−1.15373	+	0.838235i
$907$	4.47168	−	13.7624i	0.148480	−	0.456974i	−0.848962	−	0.528454i	$-0.822772\pi$
$907$	4.47168	−	13.7624i	0.148480	−	0.456974i	0.997442	+	0.0714796i	$0.0227721\pi$
$908$	0.277779	−	0.854916i	0.00921843	−	0.0283714i
$909$	11.6657	−	8.47562i	0.386927	−	0.281119i
$910$	−129.493	−	94.0822i	−4.29265	−	3.11879i
$911$	−1.25347	−	3.85777i	−0.0415292	−	0.127814i	0.928142	−	0.372225i	$-0.121405\pi$
$911$	−1.25347	−	3.85777i	−0.0415292	−	0.127814i	−0.969672	+	0.244412i	$0.921405\pi$
$912$	0.153627			0.00508711
$913$	−2.81206	+	30.4188i	−0.0930655	+	1.00671i
$914$	18.7914			0.621563
$915$	10.0454	+	30.9166i	0.332091	+	1.02207i
$916$	−27.1907	−	19.7552i	−0.898406	−	0.652730i
$917$	8.29638	−	6.02767i	0.273971	−	0.199051i
$918$	0.713092	−	2.19467i	0.0235356	−	0.0724350i
$919$	6.00142	−	18.4705i	0.197969	−	0.609285i	−0.801960	−	0.597377i	$-0.796210\pi$
$919$	6.00142	−	18.4705i	0.197969	−	0.609285i	0.999929	−	0.0119077i	$-0.00379044\pi$
$920$	60.3108	−	43.8184i	1.98839	−	1.44465i
$921$	3.62830	+	2.63611i	0.119557	+	0.0868629i
$922$	9.90166	+	30.4742i	0.326094	+	1.00361i
$923$	−31.5379			−1.03808
$924$	−30.5024	+	34.7425i	−1.00345	+	1.14295i
$925$	64.9879			2.13679
$926$	−10.0917	−	31.0592i	−0.331635	−	1.02067i
$927$	1.53037	+	1.11188i	0.0502638	+	0.0365188i
$928$	−37.5551	+	27.2853i	−1.23280	+	0.895685i
$929$	−9.07941	+	27.9436i	−0.297886	+	0.916799i	0.684351	+	0.729153i	$0.260086\pi$
$929$	−9.07941	+	27.9436i	−0.297886	+	0.916799i	−0.982237	+	0.187646i	$0.939914\pi$
$930$	9.90899	−	30.4967i	0.324928	−	1.00003i
$931$	3.23695	−	2.35178i	0.106087	−	0.0770765i
$932$	51.4536	+	37.3832i	1.68542	+	1.22453i
$933$	−2.71039	−	8.34173i	−0.0887343	−	0.273096i
$934$	−73.0454			−2.39012
$935$	−11.5002	−	4.94841i	−0.376097	−	0.161830i
$936$	−13.4027			−0.438080
$937$	−4.58281	−	14.1045i	−0.149714	−	0.460772i	0.847873	−	0.530199i	$-0.177883\pi$
$937$	−4.58281	−	14.1045i	−0.149714	−	0.460772i	−0.997587	+	0.0694270i	$0.977883\pi$
$938$	−40.5948	−	29.4938i	−1.32547	−	0.963008i
$939$	−10.2069	+	7.41571i	−0.333088	+	0.242003i
$940$	−10.2690	+	31.6048i	−0.334938	+	1.03083i
$941$	−15.2028	+	46.7894i	−0.495597	+	1.52529i	0.320429	+	0.947273i	$0.396173\pi$
$941$	−15.2028	+	46.7894i	−0.495597	+	1.52529i	−0.816025	+	0.578017i	$0.803827\pi$
$942$	37.1663	−	27.0029i	1.21094	−	0.879802i
$943$	−46.0381	−	33.4486i	−1.49921	−	1.08924i
$944$	0.775045	+	2.38534i	0.0252256	+	0.0776363i
$945$	15.8250			0.514786
$946$	42.9247	+	72.2408i	1.39560	+	2.34875i
$947$	−34.9524			−1.13580			−0.567900	−	0.823098i	$-0.692244\pi$
$947$	−34.9524			−1.13580			−0.567900	+	0.823098i	$0.692244\pi$
$948$	1.44458	+	4.44596i	0.0469178	+	0.144398i
$949$	6.68995	+	4.86053i	0.217165	+	0.157780i
$950$	−6.53319	+	4.74664i	−0.211965	+	0.154001i
$951$	7.29534	−	22.4528i	0.236568	−	0.728080i
$952$	3.96130	−	12.1916i	0.128387	−	0.395133i
$953$	−26.9503	+	19.5805i	−0.873006	+	0.634276i	−0.931392	−	0.364018i	$-0.881405\pi$
$953$	−26.9503	+	19.5805i	−0.873006	+	0.634276i	0.0583862	+	0.998294i	$0.481405\pi$
$954$	4.01584	+	2.91768i	0.130018	+	0.0944633i
$955$	−23.2285	−	71.4901i	−0.751658	−	2.31337i
$956$	68.7722			2.22425
$957$	−29.0005	+	6.54528i	−0.937453	+	0.211579i
$958$	−28.4989			−0.920759
$959$	7.93201	+	24.4122i	0.256138	+	0.788311i
$960$	−38.9747	−	28.3168i	−1.25790	−	0.913920i
$961$	14.1164	−	10.2562i	0.455368	−	0.330845i
$962$	−21.9612	+	67.5896i	−0.708058	+	2.17918i
$963$	3.34975	−	10.3095i	0.107944	−	0.332218i
$964$	−71.5136	+	51.9577i	−2.30330	+	1.67344i
$965$	42.8508	+	31.1329i	1.37941	+	1.00220i
$966$	−19.3075	−	59.4224i	−0.621209	−	1.91189i
$967$	−33.5204			−1.07794			−0.538971	−	0.842324i	$-0.681187\pi$
$967$	−33.5204			−1.07794			−0.538971	+	0.842324i	$0.681187\pi$
$968$	33.0657	+	6.16621i	1.06277	+	0.198189i
$969$	0.378355			0.0121545
$970$	−9.43565	−	29.0400i	−0.302961	−	0.932417i
$971$	−9.68353	−	7.03550i	−0.310759	−	0.225780i	0.421463	−	0.906846i	$-0.361517\pi$
$971$	−9.68353	−	7.03550i	−0.310759	−	0.225780i	−0.732222	+	0.681066i	$0.761517\pi$
$972$	2.69005	−	1.95444i	0.0862835	−	0.0626886i
$973$	−16.5957	+	51.0762i	−0.532032	+	1.63743i
$974$	−14.1248	+	43.4715i	−0.452586	+	1.39292i
$975$	32.7978	−	23.8290i	1.05037	−	0.763139i
$976$	2.82889	+	2.05531i	0.0905507	+	0.0657889i
$977$	−1.72348	−	5.30431i	−0.0551389	−	0.169700i	0.919695	−	0.392635i	$-0.128436\pi$
$977$	−1.72348	−	5.30431i	−0.0551389	−	0.169700i	−0.974833	+	0.222935i	$0.928436\pi$
$978$	−3.18092			−0.101715
$979$	0.720309	−	0.162571i	0.0230212	−	0.00519578i
$980$	132.733			4.23998
$981$	5.45241	+	16.7808i	0.174082	+	0.535770i
$982$	77.7455	+	56.4854i	2.48096	+	1.80252i
$983$	4.92634	−	3.57919i	0.157126	−	0.114159i	−0.506444	−	0.862273i	$-0.669040\pi$
$983$	4.92634	−	3.57919i	0.157126	−	0.114159i	0.663570	+	0.748114i	$0.269040\pi$
$984$	8.32563	−	25.6237i	0.265411	−	0.816852i
$985$	−6.95543	+	21.4066i	−0.221618	+	0.682071i
$986$	16.7347	−	12.1585i	0.532942	−	0.387205i
$987$	8.97951	+	6.52399i	0.285821	+	0.207661i
$988$	−1.70399	−	5.24435i	−0.0542112	−	0.166845i
$989$	−70.9112			−2.25484
$990$	−14.7578	−	24.8369i	−0.469033	−	0.789367i
$991$	30.0580			0.954822			0.477411	−	0.878680i	$-0.341575\pi$
$991$	30.0580			0.954822			0.477411	+	0.878680i	$0.341575\pi$
$992$	5.89092	+	18.1304i	0.187037	+	0.575641i
$993$	22.5656	+	16.3948i	0.716097	+	0.520275i
$994$	56.3142	−	40.9147i	1.78618	−	1.29773i
$995$	−8.14167	+	25.0575i	−0.258108	+	0.794375i
$996$	9.46409	−	29.1275i	0.299881	−	0.922940i
$997$	15.8008	−	11.4800i	0.500417	−	0.363574i	−0.308759	−	0.951140i	$-0.599914\pi$
$997$	15.8008	−	11.4800i	0.500417	−	0.363574i	0.809176	+	0.587566i	$0.199914\pi$
$998$	−68.0119	−	49.4135i	−2.15288	−	1.56416i
$999$	−2.17125	−	6.68242i	−0.0686954	−	0.211423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	561.2.m.e.511.1	yes	40
11.3	even	5		6171.2.a.bs.1.3		20
11.8	odd	10		6171.2.a.bp.1.18		20
11.9	even	5	inner	561.2.m.e.460.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
561.2.m.e.460.1	✓	40	11.9	even	5	inner
561.2.m.e.511.1	yes	40	1.1	even	1	trivial
6171.2.a.bp.1.18		20	11.8	odd	10
6171.2.a.bs.1.3		20	11.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 561 = 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	561.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.713092 - 2.19467i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-2.69005 + 1.95444i) q^{4} +(1.16648 - 3.59006i) q^{5} +(0.713092 - 2.19467i) q^{6} +(3.39160 - 2.46414i) q^{7} +(2.47381 + 1.79733i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.713092 - 2.19467i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-2.69005 + 1.95444i) q^{4} +(1.16648 - 3.59006i) q^{5} +(0.713092 - 2.19467i) q^{6} +(3.39160 - 2.46414i) q^{7} +(2.47381 + 1.79733i) q^{8} +(0.309017 + 0.951057i) q^{9} -8.71082 q^{10} +(3.23525 - 0.730182i) q^{11} -3.32509 q^{12} +(1.35446 + 4.16859i) q^{13} +(-7.82651 - 5.68629i) q^{14} +(3.05389 - 2.21878i) q^{15} +(0.125473 - 0.386167i) q^{16} +(0.309017 - 0.951057i) q^{17} +(1.86690 - 1.35638i) q^{18} +(0.306096 + 0.222392i) q^{19} +(3.87865 + 11.9373i) q^{20} +4.19225 q^{21} +(-3.90954 - 6.57963i) q^{22} +6.45853 q^{23} +(0.944911 + 2.90814i) q^{24} +(-7.48277 - 5.43655i) q^{25} +(8.18283 - 5.94518i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-4.30757 + 13.2574i) q^{28} +(-7.25196 + 5.26886i) q^{29} +(-7.04720 - 5.12009i) q^{30} +(1.13755 + 3.50102i) q^{31} +5.17861 q^{32} +(3.04656 + 1.31090i) q^{33} -2.30762 q^{34} +(-4.89018 - 15.0504i) q^{35} +(-2.69005 - 1.95444i) q^{36} +(-5.68441 + 4.12997i) q^{37} +(0.269802 - 0.830366i) q^{38} +(-1.35446 + 4.16859i) q^{39} +(9.33817 - 6.78458i) q^{40} +(-7.12826 - 5.17899i) q^{41} +(-2.98946 - 9.20062i) q^{42} -10.9795 q^{43} +(-7.27590 + 8.28732i) q^{44} +3.77481 q^{45} +(-4.60553 - 14.1744i) q^{46} +(2.14193 + 1.55620i) q^{47} +(0.328494 - 0.238665i) q^{48} +(3.26784 - 10.0574i) q^{49} +(-6.59554 + 20.2990i) q^{50} +(0.809017 - 0.587785i) q^{51} +(-11.7908 - 8.56652i) q^{52} +(0.664718 + 2.04579i) q^{53} +2.30762 q^{54} +(1.15246 - 12.4665i) q^{55} +12.8190 q^{56} +(0.116918 + 0.359837i) q^{57} +(16.7347 + 12.1585i) q^{58} +(-4.99727 + 3.63073i) q^{59} +(-3.87865 + 11.9373i) q^{60} +(-2.66117 + 8.19023i) q^{61} +(6.87241 - 4.99310i) q^{62} +(3.39160 + 2.46414i) q^{63} +(-3.94377 - 12.1377i) q^{64} +16.5454 q^{65} +(0.704522 - 7.62100i) q^{66} +5.18683 q^{67} +(1.02751 + 3.16235i) q^{68} +(5.22506 + 3.79623i) q^{69} +(-29.5436 + 21.4647i) q^{70} +(-2.22347 + 6.84315i) q^{71} +(-0.944911 + 2.90814i) q^{72} +(1.52630 - 1.10892i) q^{73} +(13.1174 + 9.53037i) q^{74} +(-2.85816 - 8.79653i) q^{75} -1.25806 q^{76} +(9.17340 - 10.4486i) q^{77} +10.1145 q^{78} +(-0.434449 - 1.33710i) q^{79} +(-1.24000 - 0.900914i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-6.28307 + 19.3373i) q^{82} +(-2.84627 + 8.75991i) q^{83} +(-11.2774 + 8.19349i) q^{84} +(-3.05389 - 2.21878i) q^{85} +(7.82937 + 24.0963i) q^{86} -8.96391 q^{87} +(9.31576 + 4.00847i) q^{88} +0.222644 q^{89} +(-2.69179 - 8.28448i) q^{90} +(14.8658 + 10.8006i) q^{91} +(-17.3738 + 12.6228i) q^{92} +(-1.13755 + 3.50102i) q^{93} +(1.88796 - 5.81055i) q^{94} +(1.15545 - 0.839487i) q^{95} +(4.18958 + 3.04391i) q^{96} +(1.08321 + 3.33378i) q^{97} -24.4029 q^{98} +(1.69419 + 2.85127i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + q^{2} + 10 q^{3} - 5 q^{4} - 6 q^{5} - q^{6} + 5 q^{7} - 16 q^{8} - 10 q^{9}+O(q^{10}) \) 40 * q + q^2 + 10 * q^3 - 5 * q^4 - 6 * q^5 - q^6 + 5 * q^7 - 16 * q^8 - 10 * q^9	\( 40 q + q^{2} + 10 q^{3} - 5 q^{4} - 6 q^{5} - q^{6} + 5 q^{7} - 16 q^{8} - 10 q^{9} + 8 q^{10} + 16 q^{11} - 50 q^{12} - 4 q^{13} - 4 q^{14} + q^{15} - 61 q^{16} - 10 q^{17} - 4 q^{18} - 8 q^{19} - 33 q^{20} + 10 q^{21} + 19 q^{22} - 32 q^{23} - 4 q^{24} - 8 q^{25} - 20 q^{26} + 10 q^{27} + 5 q^{28} + 18 q^{29} - 23 q^{30} - 31 q^{31} + 94 q^{32} + 9 q^{33} + 6 q^{34} - 9 q^{35} - 5 q^{36} - 38 q^{37} + 4 q^{39} + 78 q^{40} - 33 q^{41} - q^{42} + 92 q^{43} - 75 q^{44} + 14 q^{45} - 45 q^{46} + 17 q^{47} - 14 q^{48} - 59 q^{49} + 30 q^{50} + 10 q^{51} - 114 q^{52} - 3 q^{53} - 6 q^{54} + 41 q^{55} + 78 q^{56} - 2 q^{57} + 95 q^{58} - 62 q^{59} + 33 q^{60} + 34 q^{61} + 12 q^{62} + 5 q^{63} - 110 q^{64} + 52 q^{65} - 29 q^{66} + 42 q^{67} - 20 q^{68} + 2 q^{69} - 162 q^{70} + 42 q^{71} + 4 q^{72} + 15 q^{73} - 3 q^{74} + 23 q^{75} + 162 q^{76} - 21 q^{77} - 30 q^{78} + 6 q^{79} + 139 q^{80} - 10 q^{81} - 40 q^{82} - 23 q^{83} - 10 q^{84} - q^{85} + 13 q^{86} - 8 q^{87} + 11 q^{88} + 88 q^{89} - 27 q^{90} + 44 q^{91} - 71 q^{92} + 31 q^{93} - 12 q^{94} - 9 q^{95} + 31 q^{96} - 42 q^{97} + 162 q^{98} - 9 q^{99}+O(q^{100}) \) 40 * q + q^2 + 10 * q^3 - 5 * q^4 - 6 * q^5 - q^6 + 5 * q^7 - 16 * q^8 - 10 * q^9 + 8 * q^10 + 16 * q^11 - 50 * q^12 - 4 * q^13 - 4 * q^14 + q^15 - 61 * q^16 - 10 * q^17 - 4 * q^18 - 8 * q^19 - 33 * q^20 + 10 * q^21 + 19 * q^22 - 32 * q^23 - 4 * q^24 - 8 * q^25 - 20 * q^26 + 10 * q^27 + 5 * q^28 + 18 * q^29 - 23 * q^30 - 31 * q^31 + 94 * q^32 + 9 * q^33 + 6 * q^34 - 9 * q^35 - 5 * q^36 - 38 * q^37 + 4 * q^39 + 78 * q^40 - 33 * q^41 - q^42 + 92 * q^43 - 75 * q^44 + 14 * q^45 - 45 * q^46 + 17 * q^47 - 14 * q^48 - 59 * q^49 + 30 * q^50 + 10 * q^51 - 114 * q^52 - 3 * q^53 - 6 * q^54 + 41 * q^55 + 78 * q^56 - 2 * q^57 + 95 * q^58 - 62 * q^59 + 33 * q^60 + 34 * q^61 + 12 * q^62 + 5 * q^63 - 110 * q^64 + 52 * q^65 - 29 * q^66 + 42 * q^67 - 20 * q^68 + 2 * q^69 - 162 * q^70 + 42 * q^71 + 4 * q^72 + 15 * q^73 - 3 * q^74 + 23 * q^75 + 162 * q^76 - 21 * q^77 - 30 * q^78 + 6 * q^79 + 139 * q^80 - 10 * q^81 - 40 * q^82 - 23 * q^83 - 10 * q^84 - q^85 + 13 * q^86 - 8 * q^87 + 11 * q^88 + 88 * q^89 - 27 * q^90 + 44 * q^91 - 71 * q^92 + 31 * q^93 - 12 * q^94 - 9 * q^95 + 31 * q^96 - 42 * q^97 + 162 * q^98 - 9 * q^99

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