LMFDB - Embedded newform 546.2.bu.a.71.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(71,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bu (of order $12$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			71.6
Character	$\chi$	$=$	546.71
Dual form			546.2.bu.a.323.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(1.41231 - 1.00269i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.61115 + 2.61115i) q^{5} +(-1.10467 + 1.33405i) q^{6} +(0.258819 - 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.989233 - 2.83221i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(1.41231 - 1.00269i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.61115 + 2.61115i) q^{5} +(-1.10467 + 1.33405i) q^{6} +(0.258819 - 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.989233 - 2.83221i) q^{9} +(-3.19799 - 1.84636i) q^{10} +(-1.56188 - 5.82901i) q^{11} +(0.721751 - 1.57451i) q^{12} +(1.58952 - 3.23627i) q^{13} +1.00000i q^{14} +(6.30592 + 1.06958i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.62806 + 2.81989i) q^{17} +(-0.222496 + 2.99174i) q^{18} +(-2.15510 - 0.577458i) q^{19} +(3.56689 + 0.955747i) q^{20} +(-0.602990 - 1.62370i) q^{21} +(3.01732 + 5.22615i) q^{22} +(-1.52364 + 2.63902i) q^{23} +(-0.289646 + 1.70766i) q^{24} +8.63619i q^{25} +(-0.697753 + 3.53739i) q^{26} +(-1.44272 - 4.99185i) q^{27} +(-0.258819 - 0.965926i) q^{28} +(6.11415 + 3.53000i) q^{29} +(-6.36787 + 0.598955i) q^{30} +(-4.91451 + 4.91451i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-8.05053 - 6.66628i) q^{33} +(-2.30243 - 2.30243i) q^{34} +(3.19799 - 1.84636i) q^{35} +(-0.559404 - 2.94738i) q^{36} +(7.89610 - 2.11575i) q^{37} +2.23113 q^{38} +(-1.00007 - 6.16440i) q^{39} -3.69272 q^{40} +(-4.19703 + 1.12459i) q^{41} +(1.00269 + 1.41231i) q^{42} +(6.69807 - 3.86713i) q^{43} +(-4.26713 - 4.26713i) q^{44} +(9.97836 - 4.81229i) q^{45} +(0.788694 - 2.94345i) q^{46} +(-6.62677 + 6.62677i) q^{47} +(-0.162199 - 1.72444i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(-2.23521 - 8.34192i) q^{50} +(5.12680 + 2.35011i) q^{51} +(-0.241567 - 3.59745i) q^{52} +4.59708i q^{53} +(2.68555 + 4.44835i) q^{54} +(11.1421 - 19.2987i) q^{55} +(0.500000 + 0.866025i) q^{56} +(-3.62268 + 1.34535i) q^{57} +(-6.81944 - 1.82726i) q^{58} +(-8.67455 - 2.32434i) q^{59} +(5.99587 - 2.22667i) q^{60} +(3.42268 + 5.92825i) q^{61} +(3.47509 - 6.01903i) q^{62} +(-2.47967 - 1.68856i) q^{63} -1.00000i q^{64} +(12.6008 - 4.29989i) q^{65} +(9.50158 + 4.35551i) q^{66} +(0.149573 + 0.558215i) q^{67} +(2.81989 + 1.62806i) q^{68} +(0.494265 + 5.25485i) q^{69} +(-2.61115 + 2.61115i) q^{70} +(-2.31748 + 8.64897i) q^{71} +(1.30318 + 2.70217i) q^{72} +(-0.971299 - 0.971299i) q^{73} +(-7.07945 + 4.08732i) q^{74} +(8.65940 + 12.1970i) q^{75} +(-2.15510 + 0.577458i) q^{76} -6.03463 q^{77} +(2.56146 + 5.69552i) q^{78} -4.53007 q^{79} +(3.56689 - 0.955747i) q^{80} +(-7.04284 - 5.60343i) q^{81} +(3.76296 - 2.17254i) q^{82} +(-1.86388 - 1.86388i) q^{83} +(-1.33405 - 1.10467i) q^{84} +(-3.11203 + 11.6143i) q^{85} +(-5.46895 + 5.46895i) q^{86} +(12.1746 - 1.14513i) q^{87} +(5.22615 + 3.01732i) q^{88} +(1.68996 + 6.30702i) q^{89} +(-8.39284 + 7.23090i) q^{90} +(-2.71459 - 2.37297i) q^{91} +3.04728i q^{92} +(-2.01309 + 11.8685i) q^{93} +(4.68583 - 8.11610i) q^{94} +(-4.11946 - 7.13512i) q^{95} +(0.602990 + 1.62370i) q^{96} +(-3.38977 - 0.908285i) q^{97} +(0.965926 + 0.258819i) q^{98} +(-18.0540 - 1.34268i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) $ 56 * q - 8 * q^6 + 24 * q^9	$ 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) $ 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	1.41231	−	1.00269i	0.815397	−	0.578902i
$3$	1.41231	−	1.00269i	0.815397	−	0.578902i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	2.61115	+	2.61115i	1.16774	+	1.16774i	0.982738	+	0.185003i	$0.0592295\pi$
$5$	2.61115	+	2.61115i	1.16774	+	1.16774i	0.185003	+	0.982738i	$0.440771\pi$
$6$	−1.10467	+	1.33405i	−0.450980	+	0.544626i
$7$	0.258819	−	0.965926i	0.0978244	−	0.365086i
$7$	0.258819	−	0.965926i	0.0978244	−	0.365086i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.989233	−	2.83221i	0.329744	−	0.944070i
$10$	−3.19799	−	1.84636i	−1.01129	−	0.583870i
$11$	−1.56188	−	5.82901i	−0.470924	−	1.75751i	−0.636461	−	0.771309i	$-0.719602\pi$
$11$	−1.56188	−	5.82901i	−0.470924	−	1.75751i	0.165537	−	0.986204i	$-0.447064\pi$
$12$	0.721751	−	1.57451i	0.208352	−	0.454521i
$13$	1.58952	−	3.23627i	0.440854	−	0.897579i
$13$	1.58952	−	3.23627i	0.440854	−	0.897579i
$14$			1.00000i			0.267261i
$15$	6.30592	+	1.06958i	1.62818	+	0.276165i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.62806	+	2.81989i	0.394863	+	0.683923i	0.993084	−	0.117408i	$-0.0374586\pi$
$17$	1.62806	+	2.81989i	0.394863	+	0.683923i	−0.598220	+	0.801332i	$0.704125\pi$
$18$	−0.222496	+	2.99174i	−0.0524428	+	0.705159i
$19$	−2.15510	−	0.577458i	−0.494415	−	0.132478i	0.00299203	−	0.999996i	$-0.499048\pi$
$19$	−2.15510	−	0.577458i	−0.494415	−	0.132478i	−0.497407	+	0.867518i	$0.665714\pi$
$20$	3.56689	+	0.955747i	0.797582	+	0.213711i
$21$	−0.602990	−	1.62370i	−0.131583	−	0.354320i
$22$	3.01732	+	5.22615i	0.643294	+	1.11422i
$23$	−1.52364	+	2.63902i	−0.317701	+	0.550274i	−0.980008	−	0.198958i	$-0.936244\pi$
$23$	−1.52364	+	2.63902i	−0.317701	+	0.550274i	0.662307	+	0.749233i	$0.269577\pi$
$24$	−0.289646	+	1.70766i	−0.0591237	+	0.348575i
$25$			8.63619i			1.72724i
$26$	−0.697753	+	3.53739i	−0.136841	+	0.693740i
$27$	−1.44272	−	4.99185i	−0.277652	−	0.960682i
$28$	−0.258819	−	0.965926i	−0.0489122	−	0.182543i
$29$	6.11415	+	3.53000i	1.13537	+	0.655505i	0.945279	−	0.326262i	$-0.105789\pi$
$29$	6.11415	+	3.53000i	1.13537	+	0.655505i	0.190089	+	0.981767i	$0.439122\pi$
$30$	−6.36787	+	0.598955i	−1.16261	+	0.109354i
$31$	−4.91451	+	4.91451i	−0.882673	+	0.882673i	−0.993806	−	0.111133i	$-0.964552\pi$
$31$	−4.91451	+	4.91451i	−0.882673	+	0.882673i	0.111133	+	0.993806i	$0.464552\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−8.05053	−	6.66628i	−1.40142	−	1.16045i
$34$	−2.30243	−	2.30243i	−0.394863	−	0.394863i
$35$	3.19799	−	1.84636i	0.540559	−	0.312092i
$36$	−0.559404	−	2.94738i	−0.0932340	−	0.491231i
$37$	7.89610	−	2.11575i	1.29811	−	0.347828i	0.457375	−	0.889274i	$-0.348790\pi$
$37$	7.89610	−	2.11575i	1.29811	−	0.347828i	0.840735	+	0.541446i	$0.182123\pi$
$38$	2.23113			0.361937
$39$	−1.00007	−	6.16440i	−0.160139	−	0.987094i
$40$	−3.69272			−0.583870
$41$	−4.19703	+	1.12459i	−0.655466	+	0.175632i	−0.571199	−	0.820811i	$-0.693522\pi$
$41$	−4.19703	+	1.12459i	−0.655466	+	0.175632i	−0.0842672	+	0.996443i	$0.526855\pi$
$42$	1.00269	+	1.41231i	0.154718	+	0.217924i
$43$	6.69807	−	3.86713i	1.02145	−	0.589732i	0.106923	−	0.994267i	$-0.465900\pi$
$43$	6.69807	−	3.86713i	1.02145	−	0.589732i	0.914522	+	0.404536i	$0.132567\pi$
$44$	−4.26713	−	4.26713i	−0.643294	−	0.643294i
$45$	9.97836	−	4.81229i	1.48749	−	0.717373i
$46$	0.788694	−	2.94345i	0.116287	−	0.433988i
$47$	−6.62677	+	6.62677i	−0.966614	+	0.966614i	−0.999460	−	0.0328467i	$-0.989543\pi$
$47$	−6.62677	+	6.62677i	−0.966614	+	0.966614i	0.0328467	+	0.999460i	$0.489543\pi$
$48$	−0.162199	−	1.72444i	−0.0234114	−	0.248901i
$49$	−0.866025	−	0.500000i	−0.123718	−	0.0714286i
$50$	−2.23521	−	8.34192i	−0.316106	−	1.17973i
$51$	5.12680	+	2.35011i	0.717895	+	0.329082i
$52$	−0.241567	−	3.59745i	−0.0334993	−	0.498877i
$53$			4.59708i			0.631458i	0.948849	+	0.315729i	$0.102249\pi$
$53$			4.59708i			0.631458i	−0.948849	+	0.315729i	$0.897751\pi$
$54$	2.68555	+	4.44835i	0.365457	+	0.605344i
$55$	11.1421	−	19.2987i	1.50240	−	2.60224i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	−3.62268	+	1.34535i	−0.479836	+	0.178196i
$58$	−6.81944	−	1.82726i	−0.895437	−	0.239932i
$59$	−8.67455	−	2.32434i	−1.12933	−	0.302603i	−0.354677	−	0.934989i	$-0.615409\pi$
$59$	−8.67455	−	2.32434i	−1.12933	−	0.302603i	−0.774653	+	0.632386i	$0.782076\pi$
$60$	5.99587	−	2.22667i	0.774064	−	0.287462i
$61$	3.42268	+	5.92825i	0.438229	+	0.759034i	0.997553	−	0.0699146i	$-0.0222727\pi$
$61$	3.42268	+	5.92825i	0.438229	+	0.759034i	−0.559324	+	0.828949i	$0.688939\pi$
$62$	3.47509	−	6.01903i	0.441336	−	0.764417i
$63$	−2.47967	−	1.68856i	−0.312409	−	0.212738i
$64$		−	1.00000i		−	0.125000i
$65$	12.6008	−	4.29989i	1.56294	−	0.533336i
$66$	9.50158	+	4.35551i	1.16956	+	0.536126i
$67$	0.149573	+	0.558215i	0.0182733	+	0.0681968i	0.974460	−	0.224559i	$-0.0720943\pi$
$67$	0.149573	+	0.558215i	0.0182733	+	0.0681968i	−0.956187	+	0.292756i	$0.905428\pi$
$68$	2.81989	+	1.62806i	0.341962	+	0.197432i
$69$	0.494265	+	5.25485i	0.0595026	+	0.632610i
$70$	−2.61115	+	2.61115i	−0.312092	+	0.312092i
$71$	−2.31748	+	8.64897i	−0.275035	+	1.02644i	0.680783	+	0.732485i	$0.261639\pi$
$71$	−2.31748	+	8.64897i	−0.275035	+	1.02644i	−0.955818	+	0.293959i	$0.905027\pi$
$72$	1.30318	+	2.70217i	0.153581	+	0.318454i
$73$	−0.971299	−	0.971299i	−0.113682	−	0.113682i	0.647978	−	0.761659i	$-0.275615\pi$
$73$	−0.971299	−	0.971299i	−0.113682	−	0.113682i	−0.761659	+	0.647978i	$0.775615\pi$
$74$	−7.07945	+	4.08732i	−0.822969	+	0.475141i
$75$	8.65940	+	12.1970i	0.999902	+	1.40838i
$76$	−2.15510	+	0.577458i	−0.247207	+	0.0662390i
$77$	−6.03463			−0.687710
$78$	2.56146	+	5.69552i	0.290028	+	0.644890i
$79$	−4.53007			−0.509672			−0.254836	−	0.966984i	$-0.582022\pi$
$79$	−4.53007			−0.509672			−0.254836	+	0.966984i	$0.582022\pi$
$80$	3.56689	−	0.955747i	0.398791	−	0.106856i
$81$	−7.04284	−	5.60343i	−0.782537	−	0.622604i
$82$	3.76296	−	2.17254i	0.415549	−	0.239917i
$83$	−1.86388	−	1.86388i	−0.204588	−	0.204588i	0.597375	−	0.801962i	$-0.296211\pi$
$83$	−1.86388	−	1.86388i	−0.204588	−	0.204588i	−0.801962	+	0.597375i	$0.796211\pi$
$84$	−1.33405	−	1.10467i	−0.145557	−	0.120529i
$85$	−3.11203	+	11.6143i	−0.337547	+	1.25974i
$86$	−5.46895	+	5.46895i	−0.589732	+	0.589732i
$87$	12.1746	−	1.14513i	1.30525	−	0.122770i
$88$	5.22615	+	3.01732i	0.557109	+	0.321647i
$89$	1.68996	+	6.30702i	0.179136	+	0.668543i	0.995810	+	0.0914447i	$0.0291485\pi$
$89$	1.68996	+	6.30702i	0.179136	+	0.668543i	−0.816675	+	0.577098i	$0.804185\pi$
$90$	−8.39284	+	7.23090i	−0.884683	+	0.762204i
$91$	−2.71459	−	2.37297i	−0.284567	−	0.248755i
$92$			3.04728i			0.317701i
$93$	−2.01309	+	11.8685i	−0.208747	+	1.23071i
$94$	4.68583	−	8.11610i	0.483307	−	0.837112i
$95$	−4.11946	−	7.13512i	−0.422648	−	0.732048i
$96$	0.602990	+	1.62370i	0.0615424	+	0.165718i
$97$	−3.38977	−	0.908285i	−0.344179	−	0.0922224i	0.0825890	−	0.996584i	$-0.473681\pi$
$97$	−3.38977	−	0.908285i	−0.344179	−	0.0922224i	−0.426768	+	0.904361i	$0.640348\pi$
$98$	0.965926	+	0.258819i	0.0975732	+	0.0261447i
$99$	−18.0540	−	1.34268i	−1.81450	−	0.134945i
$100$	4.31809	+	7.47916i	0.431809	+	0.747916i
$101$	3.96010	−	6.85910i	0.394045	−	0.682506i	−0.598934	−	0.800799i	$-0.704409\pi$
$101$	3.96010	−	6.85910i	0.394045	−	0.682506i	0.992979	+	0.118293i	$0.0377421\pi$
$102$	−5.56036	−	0.943123i	−0.550558	−	0.0933831i
$103$			0.941362i			0.0927551i	0.998924	+	0.0463776i	$0.0147677\pi$
$103$			0.941362i			0.0927551i	−0.998924	+	0.0463776i	$0.985232\pi$
$104$	1.16442	+	3.41235i	0.114181	+	0.334608i
$105$	2.66523	−	5.81422i	0.260099	−	0.567410i
$106$	−1.18981	−	4.44044i	−0.115565	−	0.431294i
$107$	−4.08645	−	2.35931i	−0.395052	−	0.228083i	0.289295	−	0.957240i	$-0.406579\pi$
$107$	−4.08645	−	2.35931i	−0.395052	−	0.228083i	−0.684347	+	0.729157i	$0.739912\pi$
$108$	−3.74536	−	3.60171i	−0.360397	−	0.346574i
$109$	12.4573	−	12.4573i	1.19319	−	1.19319i	0.217027	−	0.976166i	$-0.430364\pi$
$109$	12.4573	−	12.4573i	1.19319	−	1.19319i	0.976166	−	0.217027i	$-0.0696361\pi$
$110$	−5.76758	+	21.5249i	−0.549917	+	2.05232i
$111$	9.03029	−	10.9054i	0.857117	−	1.03510i
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	4.05949	−	2.34374i	0.381884	−	0.220481i	−0.296754	−	0.954954i	$-0.595904\pi$
$113$	4.05949	−	2.34374i	0.381884	−	0.220481i	0.678638	+	0.734473i	$0.262571\pi$
$114$	3.15104	−	2.23712i	0.295122	−	0.209526i
$115$	−10.8693	+	2.91243i	−1.01357	+	0.271585i
$116$	7.06001			0.655505
$117$	−7.59338	−	7.70328i	−0.702008	−	0.712169i
$118$	8.98055			0.826727
$119$	3.14518	−	0.842748i	0.288318	−	0.0772545i
$120$	−5.21526	+	3.70265i	−0.476086	+	0.338004i
$121$	−22.0116	+	12.7084i	−2.00105	+	1.15531i
$122$	−4.84039	−	4.84039i	−0.438229	−	0.438229i
$123$	−4.79989	+	5.79659i	−0.432792	+	0.522661i
$124$	−1.79884	+	6.71335i	−0.161540	+	0.602877i
$125$	−9.49463	+	9.49463i	−0.849226	+	0.849226i
$126$	2.83221	+	0.989233i	0.252313	+	0.0881279i
$127$	−4.17960	−	2.41310i	−0.370880	−	0.214128i	0.302963	−	0.953002i	$-0.402024\pi$
$127$	−4.17960	−	2.41310i	−0.370880	−	0.214128i	−0.673843	+	0.738875i	$0.735358\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	5.58221	−	12.1777i	0.491486	−	1.07218i
$130$	−11.0586	+	7.41472i	−0.969903	+	0.650314i
$131$			12.6826i			1.10809i	0.832488	+	0.554043i	$0.186916\pi$
$131$			12.6826i			1.10809i	−0.832488	+	0.554043i	$0.813084\pi$
$132$	−10.3051	−	1.74791i	−0.896945	−	0.152136i
$133$	−1.11556	+	1.93221i	−0.0967316	+	0.167544i
$134$	−0.288953	−	0.500482i	−0.0249618	−	0.0432350i
$135$	9.26730	−	16.8016i	0.797602	−	1.44605i
$136$	−3.14518	−	0.842748i	−0.269697	−	0.0722650i
$137$	−16.4843	−	4.41694i	−1.40835	−	0.377365i	−0.527011	−	0.849858i	$-0.676687\pi$
$137$	−16.4843	−	4.41694i	−1.40835	−	0.377365i	−0.881334	+	0.472493i	$0.843354\pi$
$138$	−1.83748	−	4.94787i	−0.156417	−	0.421191i
$139$	6.28943	+	10.8936i	0.533462	+	0.923984i	0.999236	+	0.0390801i	$0.0124427\pi$
$139$	6.28943	+	10.8936i	0.533462	+	0.923984i	−0.465774	+	0.884904i	$0.654224\pi$
$140$	1.84636	−	3.19799i	0.156046	−	0.270280i
$141$	−2.71446	+	16.0036i	−0.228599	+	1.34775i
$142$		−	8.95407i		−	0.751409i
$143$	−21.3469	−	4.21068i	−1.78511	−	0.352115i
$144$	−1.95815	−	2.27281i	−0.163179	−	0.189401i
$145$	6.74758	+	25.1823i	0.560356	+	2.09128i
$146$	1.18959	+	0.686812i	0.0984515	+	0.0568410i
$147$	−1.72444	+	0.162199i	−0.142229	+	0.0133779i
$148$	5.78034	−	5.78034i	0.475141	−	0.475141i
$149$	2.75005	−	10.2633i	0.225293	−	0.840805i	−0.756994	−	0.653422i	$-0.773333\pi$
$149$	2.75005	−	10.2633i	0.225293	−	0.840805i	0.982287	−	0.187383i	$-0.0600006\pi$
$150$	−11.5212	−	9.54015i	−0.940698	−	0.778950i
$151$	14.0155	+	14.0155i	1.14056	+	1.14056i	0.988347	+	0.152215i	$0.0486408\pi$
$151$	14.0155	+	14.0155i	1.14056	+	1.14056i	0.152215	+	0.988347i	$0.451359\pi$
$152$	1.93221	−	1.11556i	0.156723	−	0.0904841i
$153$	9.59705	−	1.82149i	0.775876	−	0.147259i
$154$	5.82901	−	1.56188i	0.469715	−	0.125860i
$155$	−25.6651			−2.06147
$156$	−3.94829	−	4.83849i	−0.316116	−	0.387390i
$157$	−23.9392			−1.91055			−0.955277	−	0.295714i	$-0.904443\pi$
$157$	−23.9392			−1.91055			−0.955277	+	0.295714i	$0.904443\pi$
$158$	4.37571	−	1.17247i	0.348113	−	0.0932765i
$159$	4.60944	+	6.49250i	0.365553	+	0.514889i
$160$	−3.19799	+	1.84636i	−0.252823	+	0.145968i
$161$	2.15475	+	2.15475i	0.169818	+	0.169818i
$162$	8.25313	+	3.58968i	0.648427	+	0.282032i
$163$	−3.63359	+	13.5607i	−0.284605	+	1.06216i	0.664523	+	0.747268i	$0.268635\pi$
$163$	−3.63359	+	13.5607i	−0.284605	+	1.06216i	−0.949128	+	0.314892i	$0.898032\pi$
$164$	−3.07244	+	3.07244i	−0.239917	+	0.239917i
$165$	−3.61448	−	38.4278i	−0.281387	−	2.99160i
$166$	2.28278	+	1.31797i	0.177178	+	0.102294i
$167$	2.36296	+	8.81869i	0.182851	+	0.682411i	0.995080	+	0.0990718i	$0.0315873\pi$
$167$	2.36296	+	8.81869i	0.182851	+	0.682411i	−0.812229	+	0.583339i	$0.801746\pi$
$168$	1.57451	+	0.721751i	0.121476	+	0.0556843i
$169$	−7.94684	−	10.2882i	−0.611295	−	0.791403i
$170$		−	12.0240i		−	0.922196i
$171$	−3.76738	+	5.53247i	−0.288099	+	0.423078i
$172$	3.86713	−	6.69807i	0.294866	−	0.510723i
$173$	−9.16123	−	15.8677i	−0.696515	−	1.20640i	−0.969667	−	0.244429i	$-0.921400\pi$
$173$	−9.16123	−	15.8677i	−0.696515	−	1.20640i	0.273152	−	0.961971i	$-0.411934\pi$
$174$	−11.4633	+	4.25711i	−0.869033	+	0.322731i
$175$	8.34192	+	2.23521i	0.630590	+	0.168966i
$176$	−5.82901	−	1.56188i	−0.439378	−	0.117731i
$177$	−14.5817	+	5.41518i	−1.09603	+	0.407030i
$178$	−3.26476	−	5.65472i	−0.244704	−	0.423839i
$179$	8.00281	−	13.8613i	0.598158	−	1.03604i	−0.394935	−	0.918709i	$-0.629233\pi$
$179$	8.00281	−	13.8613i	0.598158	−	1.03604i	0.993093	−	0.117331i	$-0.0374338\pi$
$180$	6.23537	−	9.15674i	0.464757	−	0.682503i
$181$			18.1748i			1.35092i	0.737395	+	0.675462i	$0.236056\pi$
$181$			18.1748i			1.35092i	−0.737395	+	0.675462i	$0.763944\pi$
$182$	3.23627	+	1.58952i	0.239888	+	0.117823i
$183$	10.7781	+	4.94064i	0.796737	+	0.365223i
$184$	−0.788694	−	2.94345i	−0.0581433	−	0.216994i
$185$	26.1424	+	15.0933i	1.92203	+	1.10968i
$186$	−1.12731	−	11.9852i	−0.0826584	−	0.878794i
$187$	13.8943	−	13.8943i	1.01605	−	1.01605i
$188$	−2.42557	+	9.05234i	−0.176903	+	0.660209i
$189$	−5.19516	+	0.101576i	−0.377892	+	0.00738856i
$190$	5.82580	+	5.82580i	0.422648	+	0.422648i
$191$	−1.65834	+	0.957440i	−0.119993	+	0.0692780i	−0.558795	−	0.829306i	$-0.688736\pi$
$191$	−1.65834	+	0.957440i	−0.119993	+	0.0692780i	0.438802	+	0.898584i	$0.355403\pi$
$192$	−1.00269	−	1.41231i	−0.0723628	−	0.101925i
$193$	−10.9448	+	2.93266i	−0.787826	+	0.211097i	−0.630232	−	0.776407i	$-0.717040\pi$
$193$	−10.9448	+	2.93266i	−0.787826	+	0.211097i	−0.157594	+	0.987504i	$0.550374\pi$
$194$	3.50934			0.251956
$195$	13.4848	−	18.7075i	0.965669	−	1.33967i
$196$	−1.00000			−0.0714286
$197$	−6.81911	+	1.82717i	−0.485841	+	0.130181i	−0.493421	−	0.869790i	$-0.664254\pi$
$197$	−6.81911	+	1.82717i	−0.485841	+	0.130181i	0.00757989	+	0.999971i	$0.497587\pi$
$198$	17.7864	−	3.37580i	1.26402	−	0.239908i
$199$	6.80879	−	3.93106i	0.482662	−	0.278665i	−0.238863	−	0.971053i	$-0.576775\pi$
$199$	6.80879	−	3.93106i	0.482662	−	0.278665i	0.721525	+	0.692388i	$0.243441\pi$
$200$	−6.10671	−	6.10671i	−0.431809	−	0.431809i
$201$	0.770959	+	0.638397i	0.0543793	+	0.0450290i
$202$	−2.04990	+	7.65033i	−0.144231	+	0.538276i
$203$	4.99218	−	4.99218i	0.350382	−	0.350382i
$204$	5.61499	−	0.528140i	0.393128	−	0.0369772i
$205$	−13.8956	−	8.02260i	−0.970507	−	0.560323i
$206$	−0.243642	−	0.909286i	−0.0169754	−	0.0633529i
$207$	5.96703	+	6.92588i	0.414737	+	0.481382i
$208$	−2.00793	−	2.99470i	−0.139225	−	0.207645i
$209$			13.4640i			0.931327i
$210$	−1.06958	+	6.30592i	−0.0738081	+	0.435149i
$211$	−1.63268	+	2.82788i	−0.112398	+	0.194679i	−0.916737	−	0.399492i	$-0.869186\pi$
$211$	−1.63268	+	2.82788i	−0.112398	+	0.194679i	0.804339	+	0.594171i	$0.202520\pi$
$212$	2.29854	+	3.98119i	0.157865	+	0.273429i
$213$	5.39921	+	14.5387i	0.369948	+	0.996177i
$214$	4.55784	+	1.22127i	0.311567	+	0.0834842i
$215$	27.5873	+	7.39199i	1.88144	+	0.504130i
$216$	4.54993	+	2.50961i	0.309583	+	0.170757i
$217$	3.47509	+	6.01903i	0.235904	+	0.408598i
$218$	−8.80864	+	15.2570i	−0.596596	+	1.03334i
$219$	−2.34568	−	0.397864i	−0.158507	−	0.0268852i
$220$		−	22.2842i		−	1.50240i
$221$	11.7138	−	0.786572i	0.787952	−	0.0529106i
$222$	−5.90006	+	12.8710i	−0.395986	+	0.863848i
$223$	−4.26674	−	15.9237i	−0.285722	−	1.06633i	−0.948310	−	0.317345i	$-0.897209\pi$
$223$	−4.26674	−	15.9237i	−0.285722	−	1.06633i	0.662588	−	0.748984i	$-0.269458\pi$
$224$	0.866025	+	0.500000i	0.0578638	+	0.0334077i
$225$	24.4595	+	8.54321i	1.63063	+	0.569547i
$226$	−3.31456	+	3.31456i	−0.220481	+	0.220481i
$227$	3.25048	−	12.1310i	0.215742	−	0.805160i	−0.770162	−	0.637848i	$-0.779825\pi$
$227$	3.25048	−	12.1310i	0.215742	−	0.805160i	0.985904	−	0.167312i	$-0.0535087\pi$
$228$	−2.46466	+	2.97645i	−0.163226	+	0.197120i
$229$	1.81709	+	1.81709i	0.120077	+	0.120077i	0.764592	−	0.644515i	$-0.222941\pi$
$229$	1.81709	+	1.81709i	0.120077	+	0.120077i	−0.644515	+	0.764592i	$0.722941\pi$
$230$	9.74517	−	5.62638i	0.642578	−	0.370992i
$231$	−8.52277	+	6.05086i	−0.560757	+	0.398117i
$232$	−6.81944	+	1.82726i	−0.447718	+	0.119966i
$233$	11.6743			0.764807			0.382403	−	0.923995i	$-0.375096\pi$
$233$	11.6743			0.764807			0.382403	+	0.923995i	$0.375096\pi$
$234$	9.32840	+	5.47549i	0.609817	+	0.357944i
$235$	−34.6070			−2.25751
$236$	−8.67455	+	2.32434i	−0.564665	+	0.151302i
$237$	−6.39785	+	4.54224i	−0.415585	+	0.295050i
$238$	−2.81989	+	1.62806i	−0.182786	+	0.105532i
$239$	−6.93024	−	6.93024i	−0.448280	−	0.448280i	0.446503	−	0.894782i	$-0.352669\pi$
$239$	−6.93024	−	6.93024i	−0.448280	−	0.448280i	−0.894782	+	0.446503i	$0.852669\pi$
$240$	4.07924	−	4.92629i	0.263314	−	0.317991i
$241$	−5.32635	+	19.8782i	−0.343100	+	1.28047i	0.551715	+	0.834032i	$0.313973\pi$
$241$	−5.32635	+	19.8782i	−0.343100	+	1.28047i	−0.894816	+	0.446436i	$0.852693\pi$
$242$	17.9724	−	17.9724i	1.15531	−	1.15531i
$243$	−15.5652	−	0.852013i	−0.998505	−	0.0546566i
$244$	5.92825	+	3.42268i	0.379517	+	0.219114i
$245$	−0.955747	−	3.56689i	−0.0610604	−	0.227881i
$246$	3.13607	−	6.84138i	0.199949	−	0.436190i
$247$	−5.29439	+	6.05661i	−0.336874	+	0.385373i
$248$		−	6.95017i		−	0.441336i
$249$	−4.50128	−	0.763486i	−0.285257	−	0.0483840i
$250$	6.71372	−	11.6285i	0.424613	−	0.735451i
$251$	−1.76209	−	3.05204i	−0.111222	−	0.192643i	0.805041	−	0.593219i	$-0.202143\pi$
$251$	−1.76209	−	3.05204i	−0.111222	−	0.192643i	−0.916263	+	0.400576i	$0.868810\pi$
$252$	−2.99174	−	0.222496i	−0.188462	−	0.0140159i
$253$	17.7626	+	4.75948i	1.11673	+	0.299226i
$254$	4.66174	+	1.24911i	0.292504	+	0.0783761i
$255$	7.25033	+	19.5233i	0.454033	+	1.22260i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−8.50103	+	14.7242i	−0.530279	+	0.918471i	0.469097	+	0.883147i	$0.344580\pi$
$257$	−8.50103	+	14.7242i	−0.530279	+	0.918471i	−0.999376	+	0.0353239i	$0.988754\pi$
$258$	−2.24020	+	13.2075i	−0.139468	+	0.822263i
$259$		−	8.17464i		−	0.507948i
$260$	8.76271	−	10.0242i	0.543440	−	0.621677i
$261$	16.0460	−	13.8246i	0.993224	−	0.855718i
$262$	−3.28250	−	12.2505i	−0.202794	−	0.756837i
$263$	11.2653	+	6.50402i	0.694647	+	0.401055i	0.805351	−	0.592799i	$-0.201977\pi$
$263$	11.2653	+	6.50402i	0.694647	+	0.401055i	−0.110703	+	0.993854i	$0.535310\pi$
$264$	10.4064	−	0.978811i	0.640467	−	0.0602416i
$265$	−12.0037	+	12.0037i	−0.737380	+	0.737380i
$266$	0.577458	−	2.15510i	0.0354062	−	0.132138i
$267$	8.71073	+	7.21296i	0.533088	+	0.441426i
$268$	0.408642	+	0.408642i	0.0249618	+	0.0249618i
$269$	4.30147	−	2.48345i	0.262265	−	0.151419i	−0.363102	−	0.931749i	$-0.618282\pi$
$269$	4.30147	−	2.48345i	0.262265	−	0.151419i	0.625367	+	0.780330i	$0.284949\pi$
$270$	−4.60295	+	18.6277i	−0.280126	+	1.13364i
$271$	23.3606	−	6.25946i	1.41906	−	0.380235i	0.533908	−	0.845543i	$-0.320723\pi$
$271$	23.3606	−	6.25946i	1.41906	−	0.380235i	0.885149	+	0.465307i	$0.154056\pi$
$272$	3.25613			0.197432
$273$	−6.21319	−	0.629472i	−0.376040	−	0.0380974i
$274$	17.0658			1.03098
$275$	50.3404	−	13.4887i	3.03564	−	0.813398i
$276$	3.05547	+	4.30370i	0.183918	+	0.259052i
$277$	11.7309	−	6.77285i	0.704843	−	0.406941i	−0.104306	−	0.994545i	$-0.533262\pi$
$277$	11.7309	−	6.77285i	0.704843	−	0.406941i	0.809149	+	0.587604i	$0.199929\pi$
$278$	−8.89460	−	8.89460i	−0.533462	−	0.533462i
$279$	9.05734	+	18.7805i	0.542249	+	1.12436i
$280$	−0.955747	+	3.56689i	−0.0571168	+	0.213163i
$281$	6.47917	−	6.47917i	0.386515	−	0.386515i	−0.486927	−	0.873442i	$-0.661882\pi$
$281$	6.47917	−	6.47917i	0.386515	−	0.386515i	0.873442	+	0.486927i	$0.161882\pi$
$282$	−1.52007	−	16.1609i	−0.0905191	−	0.962366i
$283$	12.7025	+	7.33380i	0.755086	+	0.435949i	0.827529	−	0.561423i	$-0.189746\pi$
$283$	12.7025	+	7.33380i	0.755086	+	0.435949i	−0.0724426	+	0.997373i	$0.523079\pi$
$284$	2.31748	+	8.64897i	0.137517	+	0.513222i
$285$	−12.9723	−	5.94646i	−0.768410	−	0.352238i
$286$	21.7093	−	1.45777i	1.28370	−	0.0861996i
$287$			4.34509i			0.256482i
$288$	2.47967	+	1.68856i	0.146116	+	0.0994991i
$289$	3.19882	−	5.54052i	0.188166	−	0.325913i
$290$	−13.0353	−	22.5778i	−0.765460	−	1.32582i
$291$	−5.69812	+	2.11610i	−0.334030	+	0.124048i
$292$	−1.32682	−	0.355520i	−0.0776462	−	0.0208052i
$293$	−23.5327	−	6.30557i	−1.37479	−	0.368375i	−0.505567	−	0.862787i	$-0.668717\pi$
$293$	−23.5327	−	6.30557i	−1.37479	−	0.368375i	−0.869228	+	0.494412i	$0.835383\pi$
$294$	1.62370	−	0.602990i	0.0946961	−	0.0351671i
$295$	−16.5813	−	28.7197i	−0.965403	−	1.67213i
$296$	−4.08732	+	7.07945i	−0.237571	+	0.411485i
$297$	−26.8442	+	16.2063i	−1.55766	+	0.940385i
$298$			10.6254i			0.615512i
$299$	6.11872	+	9.12569i	0.353855	+	0.527752i
$300$	13.5977	+	6.23318i	0.785066	+	0.359873i
$301$	−2.00177	−	7.47072i	−0.115380	−	0.430605i
$302$	−17.1654	−	9.91043i	−0.987756	−	0.570281i
$303$	−1.28465	−	13.6579i	−0.0738011	−	0.784627i
$304$	−1.57764	+	1.57764i	−0.0904841	+	0.0904841i
$305$	−6.54242	+	24.4166i	−0.374618	+	1.39809i
$306$	−8.79860	+	4.24333i	−0.502983	+	0.242575i
$307$	−18.4360	−	18.4360i	−1.05220	−	1.05220i	−0.998560	−	0.0536403i	$-0.982918\pi$
$307$	−18.4360	−	18.4360i	−1.05220	−	1.05220i	−0.0536403	−	0.998560i	$-0.517082\pi$
$308$	−5.22615	+	3.01732i	−0.297787	+	0.171928i
$309$	0.943892	+	1.32949i	0.0536962	+	0.0756323i
$310$	24.7905	−	6.64260i	1.40801	−	0.377275i
$311$	3.28259			0.186139			0.0930693	−	0.995660i	$-0.470332\pi$
$311$	3.28259			0.186139			0.0930693	+	0.995660i	$0.470332\pi$
$312$	5.06605	+	3.65173i	0.286808	+	0.206739i
$313$	7.49834			0.423831			0.211915	−	0.977288i	$-0.432030\pi$
$313$	7.49834			0.423831			0.211915	+	0.977288i	$0.432030\pi$
$314$	23.1235	−	6.19591i	1.30493	−	0.349656i
$315$	−2.06572	−	10.8839i	−0.116390	−	0.613236i
$316$	−3.92315	+	2.26503i	−0.220695	+	0.127418i
$317$	−18.9895	−	18.9895i	−1.06656	−	1.06656i	−0.997621	−	0.0689377i	$-0.978039\pi$
$317$	−18.9895	−	18.9895i	−1.06656	−	1.06656i	−0.0689377	−	0.997621i	$-0.521961\pi$
$318$	−6.13276	−	5.07827i	−0.343908	−	0.284775i
$319$	11.0269	−	41.1528i	0.617386	−	2.30412i
$320$	2.61115	−	2.61115i	0.145968	−	0.145968i
$321$	−8.13698	+	0.765355i	−0.454162	+	0.0427180i
$322$	−2.63902	−	1.52364i	−0.147067	−	0.0849091i
$323$	−1.88028	−	7.01729i	−0.104621	−	0.390452i
$324$	−8.90099	−	1.33130i	−0.494500	−	0.0739610i
$325$	27.9490	+	13.7274i	1.55033	+	0.761460i
$326$		−	14.0391i		−	0.777555i
$327$	5.10277	−	30.0843i	0.282184	−	1.66367i
$328$	2.17254	−	3.76296i	0.119959	−	0.207775i
$329$	4.68583	+	8.11610i	0.258338	+	0.447455i
$330$	13.4372	+	36.1829i	0.739691	+	1.99180i
$331$	16.1078	+	4.31607i	0.885365	+	0.237233i	0.672720	−	0.739897i	$-0.265126\pi$
$331$	16.1078	+	4.31607i	0.885365	+	0.237233i	0.212645	+	0.977130i	$0.431792\pi$
$332$	−2.54611	−	0.682229i	−0.139736	−	0.0374422i
$333$	1.81882	−	24.4564i	0.0996709	−	1.34020i
$334$	−4.56489	−	7.90662i	−0.249780	−	0.432631i
$335$	−1.06702	+	1.84814i	−0.0582977	+	0.100975i
$336$	−1.70766	−	0.289646i	−0.0931605	−	0.0158015i
$337$		−	25.8378i		−	1.40748i	−0.710460	−	0.703738i	$-0.751513\pi$
$337$		−	25.8378i		−	1.40748i	0.710460	−	0.703738i	$-0.248487\pi$
$338$	10.3388	+	7.88088i	0.562359	+	0.428663i
$339$	3.38320	−	7.38049i	0.183750	−	0.400853i
$340$	3.11203	+	11.6143i	0.168774	+	0.629872i
$341$	36.3226	+	20.9709i	1.96698	+	1.13564i
$342$	2.20710	−	6.31902i	0.119347	−	0.341694i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−2.00177	+	7.47072i	−0.107928	+	0.402794i
$345$	−12.4306	+	15.0118i	−0.669241	+	0.808208i
$346$	12.9559	+	12.9559i	0.696515	+	0.696515i
$347$	25.3125	−	14.6142i	1.35885	−	0.784531i	0.369379	−	0.929279i	$-0.379570\pi$
$347$	25.3125	−	14.6142i	1.35885	−	0.784531i	0.989469	+	0.144748i	$0.0462371\pi$
$348$	9.97091	−	7.07898i	0.534497	−	0.379473i
$349$	−26.7787	+	7.17532i	−1.43343	+	0.384086i	−0.890227	−	0.455517i	$-0.849455\pi$
$349$	−26.7787	+	7.17532i	−1.43343	+	0.384086i	−0.543201	+	0.839603i	$0.682788\pi$
$350$	−8.63619			−0.461624
$351$	−18.4482	−	3.26562i	−0.984692	−	0.174306i
$352$	6.03463			0.321647
$353$	16.7312	−	4.48311i	0.890511	−	0.238612i	0.215574	−	0.976487i	$-0.430838\pi$
$353$	16.7312	−	4.48311i	0.890511	−	0.238612i	0.674937	+	0.737876i	$0.264171\pi$
$354$	12.6833	−	9.00469i	0.674111	−	0.478594i
$355$	−28.6350	+	16.5324i	−1.51979	+	0.877451i
$356$	4.61706	+	4.61706i	0.244704	+	0.244704i
$357$	3.59695	−	4.34385i	0.190371	−	0.229901i
$358$	−4.14256	+	15.4602i	−0.218941	+	0.817099i
$359$	−9.10668	+	9.10668i	−0.480632	+	0.480632i	−0.905334	−	0.424701i	$-0.860379\pi$
$359$	−9.10668	+	9.10668i	−0.480632	+	0.480632i	0.424701	+	0.905334i	$0.360379\pi$
$360$	−3.65296	+	10.4586i	−0.192528	+	0.551215i
$361$	−12.1435	−	7.01104i	−0.639130	−	0.369002i
$362$	−4.70399	−	17.5555i	−0.247236	−	0.922698i
$363$	−18.3446	+	40.0190i	−0.962843	+	2.10045i
$364$	−3.53739	−	0.697753i	−0.185410	−	0.0365722i
$365$		−	5.07241i		−	0.265502i
$366$	−11.6895	−	1.98273i	−0.611022	−	0.103639i
$367$	12.3426	−	21.3780i	0.644278	−	1.11592i	−0.340189	−	0.940357i	$-0.610491\pi$
$367$	12.3426	−	21.3780i	0.644278	−	1.11592i	0.984468	−	0.175566i	$-0.0561755\pi$
$368$	1.52364	+	2.63902i	0.0794252	+	0.137569i
$369$	−0.966764	+	12.9994i	−0.0503277	+	0.676720i
$370$	−29.1581	−	7.81289i	−1.51586	−	0.406173i
$371$	4.44044	+	1.18981i	0.230536	+	0.0617720i
$372$	4.19088	+	11.2850i	0.217287	+	0.585100i
$373$	−6.23279	−	10.7955i	−0.322722	−	0.558971i	0.658327	−	0.752732i	$-0.271265\pi$
$373$	−6.23279	−	10.7955i	−0.322722	−	0.558971i	−0.981049	+	0.193762i	$0.937931\pi$
$374$	−9.82477	+	17.0170i	−0.508027	+	0.879928i
$375$	−3.88920	+	22.9295i	−0.200837	+	1.18407i
$376$		−	9.37167i		−	0.483307i
$377$	21.1426	−	14.1760i	1.08890	−	0.730100i
$378$	4.99185	−	1.44272i	0.256753	−	0.0742056i
$379$	7.99617	+	29.8421i	0.410736	+	1.53289i	0.793226	+	0.608927i	$0.208400\pi$
$379$	7.99617	+	29.8421i	0.410736	+	1.53289i	−0.382491	+	0.923959i	$0.624934\pi$
$380$	−7.13512	−	4.11946i	−0.366024	−	0.211324i
$381$	−8.32247	+	0.782803i	−0.426373	+	0.0401042i
$382$	1.35403	−	1.35403i	0.0692780	−	0.0692780i
$383$	−0.0112438	+	0.0419624i	−0.000574530	+	0.00214418i	−0.966212	−	0.257747i	$-0.917020\pi$
$383$	−0.0112438	+	0.0419624i	−0.000574530	+	0.00214418i	0.965638	+	0.259891i	$0.0836866\pi$
$384$	1.33405	+	1.10467i	0.0680782	+	0.0563725i
$385$	−15.7573	−	15.7573i	−0.803068	−	0.803068i
$386$	9.81287	−	5.66546i	0.499462	−	0.288364i
$387$	−4.32658	−	22.7958i	−0.219932	−	1.15878i
$388$	−3.38977	+	0.908285i	−0.172089	+	0.0461112i
$389$	−15.0907			−0.765127			−0.382564	−	0.923929i	$-0.624959\pi$
$389$	−15.0907			−0.765127			−0.382564	+	0.923929i	$0.624959\pi$
$390$	−8.18350	+	21.5602i	−0.414387	+	1.09174i
$391$	−9.92233			−0.501794
$392$	0.965926	−	0.258819i	0.0487866	−	0.0130723i
$393$	12.7167	+	17.9118i	0.641474	+	0.903530i
$394$	6.11385	−	3.52983i	0.308011	−	0.177830i
$395$	−11.8287	−	11.8287i	−0.595165	−	0.595165i
$396$	−16.3066	+	7.86423i	−0.819438	+	0.395192i
$397$	−6.94286	+	25.9111i	−0.348452	+	1.30044i	0.540075	+	0.841617i	$0.318396\pi$
$397$	−6.94286	+	25.9111i	−0.348452	+	1.30044i	−0.888527	+	0.458824i	$0.848271\pi$
$398$	−5.55935	+	5.55935i	−0.278665	+	0.278665i
$399$	0.361886	+	3.84744i	0.0181170	+	0.192613i
$400$	7.47916	+	4.31809i	0.373958	+	0.215905i
$401$	−2.29401	−	8.56138i	−0.114558	−	0.427535i	0.884696	−	0.466169i	$-0.154366\pi$
$401$	−2.29401	−	8.56138i	−0.114558	−	0.427535i	−0.999253	+	0.0386339i	$0.987699\pi$
$402$	−0.909918	−	0.417105i	−0.0453826	−	0.0208033i
$403$	8.09295	+	23.7164i	0.403139	+	1.18140i
$404$		−	7.92021i		−	0.394045i
$405$	−3.75849	−	33.0213i	−0.186761	−	1.64084i
$406$	−3.53000	+	6.11415i	−0.175191	+	0.303440i
$407$	−24.6655	−	42.7219i	−1.22262	−	2.11764i
$408$	−5.28697	+	1.96341i	−0.261744	+	0.0972033i
$409$	12.2740	+	3.28881i	0.606911	+	0.162621i	0.549171	−	0.835710i	$-0.314944\pi$
$409$	12.2740	+	3.28881i	0.606911	+	0.162621i	0.0577405	+	0.998332i	$0.481610\pi$
$410$	15.4985	+	4.15280i	0.765415	+	0.205092i
$411$	−27.7097	+	10.2905i	−1.36682	+	0.507592i
$412$	0.470681	+	0.815243i	0.0231888	+	0.0401641i
$413$	−4.49028	+	7.77739i	−0.220952	+	0.382700i
$414$	−7.55626	−	5.14550i	−0.371370	−	0.252888i
$415$		−	9.73376i		−	0.477811i
$416$	2.71459	+	2.37297i	0.133094	+	0.116344i
$417$	19.8055	+	9.07881i	0.969880	+	0.444591i
$418$	−3.48475	−	13.0053i	−0.170445	−	0.636108i
$419$	−0.431886	−	0.249350i	−0.0210990	−	0.0121815i	0.489413	−	0.872052i	$-0.337211\pi$
$419$	−0.431886	−	0.249350i	−0.0210990	−	0.0121815i	−0.510512	+	0.859870i	$0.670544\pi$
$420$	−0.598955	−	6.36787i	−0.0292260	−	0.310720i
$421$	−12.8276	+	12.8276i	−0.625179	+	0.625179i	−0.946851	−	0.321672i	$-0.895755\pi$
$421$	−12.8276	+	12.8276i	−0.625179	+	0.625179i	0.321672	+	0.946851i	$0.395755\pi$
$422$	0.845135	−	3.15409i	0.0411405	−	0.153539i
$423$	12.2130	+	25.3238i	0.593816	+	1.23129i
$424$	−3.25063	−	3.25063i	−0.157865	−	0.157865i
$425$	−24.3531	+	14.0603i	−1.18130	+	0.682023i
$426$	−8.97814	−	12.6459i	−0.434992	−	0.612696i
$427$	6.61210	−	1.77171i	0.319982	−	0.0857389i
$428$	−4.71862			−0.228083
$429$	−34.3704	+	15.4575i	−1.65942	+	0.746293i
$430$	−28.5605			−1.37731
$431$	−14.0578	+	3.76678i	−0.677141	+	0.181439i	−0.580969	−	0.813926i	$-0.697326\pi$
$431$	−14.0578	+	3.76678i	−0.677141	+	0.181439i	−0.0961714	+	0.995365i	$0.530660\pi$
$432$	−5.04443	−	1.24649i	−0.242700	−	0.0599718i
$433$	5.57566	−	3.21911i	0.267949	−	0.154700i	−0.360006	−	0.932950i	$-0.617225\pi$
$433$	5.57566	−	3.21911i	0.267949	−	0.154700i	0.627955	+	0.778249i	$0.283892\pi$
$434$	−4.91451	−	4.91451i	−0.235904	−	0.235904i
$435$	34.7797	+	28.7995i	1.66756	+	1.38083i
$436$	4.55969	−	17.0170i	0.218369	−	0.814966i
$437$	4.80753	−	4.80753i	0.229975	−	0.229975i
$438$	2.36873	−	0.222800i	0.113182	−	0.0106458i
$439$	−19.4203	−	11.2123i	−0.926883	−	0.535136i	−0.0410584	−	0.999157i	$-0.513073\pi$
$439$	−19.4203	−	11.2123i	−0.926883	−	0.535136i	−0.885824	+	0.464021i	$0.846406\pi$
$440$	5.76758	+	21.5249i	0.274959	+	1.02616i
$441$	−2.27281	+	1.95815i	−0.108229	+	0.0932452i
$442$	−11.1110	+	3.79151i	−0.528498	+	0.180344i
$443$			37.1687i			1.76594i	0.469432	+	0.882969i	$0.344459\pi$
$443$			37.1687i			1.76594i	−0.469432	+	0.882969i	$0.655541\pi$
$444$	2.36775	−	13.9595i	0.112368	−	0.662489i
$445$	−12.0558	+	20.8813i	−0.571501	+	0.989869i
$446$	8.24271	+	14.2768i	0.390304	+	0.676026i
$447$	−6.40700	−	17.2524i	−0.303041	−	0.816013i
$448$	−0.965926	−	0.258819i	−0.0456357	−	0.0122281i
$449$	0.980852	+	0.262819i	0.0462893	+	0.0124032i	0.281889	−	0.959447i	$-0.409039\pi$
$449$	0.980852	+	0.262819i	0.0462893	+	0.0124032i	−0.235600	+	0.971850i	$0.575706\pi$
$450$	−25.8372	−	1.92152i	−1.21798	−	0.0905811i
$451$	13.1105	+	22.7081i	0.617350	+	1.06928i
$452$	2.34374	−	4.05949i	0.110240	−	0.190942i
$453$	33.8473	+	5.74103i	1.59029	+	0.269737i
$454$			12.5589i			0.589418i
$455$	−0.892039	−	13.2844i	−0.0418194	−	0.622781i
$456$	1.61032	−	3.51293i	0.0754101	−	0.164508i
$457$	−2.45030	−	9.14464i	−0.114620	−	0.427768i	0.884638	−	0.466278i	$-0.154405\pi$
$457$	−2.45030	−	9.14464i	−0.114620	−	0.427768i	−0.999258	+	0.0385102i	$0.987739\pi$
$458$	−2.22548	−	1.28488i	−0.103990	−	0.0600385i
$459$	11.7276	−	12.1954i	0.547398	−	0.569231i
$460$	−7.95690	+	7.95690i	−0.370992	+	0.370992i
$461$	−2.97164	+	11.0903i	−0.138403	+	0.516528i	0.861557	+	0.507660i	$0.169489\pi$
$461$	−2.97164	+	11.0903i	−0.138403	+	0.516528i	−0.999961	+	0.00886793i	$0.997177\pi$
$462$	6.66628	−	8.05053i	0.310144	−	0.374545i
$463$	−6.07495	−	6.07495i	−0.282327	−	0.282327i	0.551709	−	0.834036i	$-0.313976\pi$
$463$	−6.07495	−	6.07495i	−0.282327	−	0.282327i	−0.834036	+	0.551709i	$0.813976\pi$
$464$	6.11415	−	3.53000i	0.283842	−	0.163876i
$465$	−36.2470	+	25.7340i	−1.68091	+	1.19339i
$466$	−11.2765	+	3.02152i	−0.522373	+	0.139969i
$467$	11.4511			0.529896			0.264948	−	0.964263i	$-0.414645\pi$
$467$	11.4511			0.529896			0.264948	+	0.964263i	$0.414645\pi$
$468$	−10.4277	−	2.87455i	−0.482021	−	0.132876i
$469$	0.577907			0.0266852
$470$	33.4278	−	8.95694i	1.54191	−	0.413153i
$471$	−33.8095	+	24.0035i	−1.55786	+	1.10602i
$472$	7.77739	−	4.49028i	0.357983	−	0.206682i
$473$	−33.0031	−	33.0031i	−1.51748	−	1.51748i
$474$	5.00423	−	6.04336i	0.229852	−	0.277580i
$475$	4.98704	−	18.6119i	0.228821	−	0.853972i
$476$	2.30243	−	2.30243i	0.105532	−	0.105532i
$477$	13.0199	+	4.54759i	0.596141	+	0.208220i
$478$	8.48777	+	4.90042i	0.388222	+	0.224140i
$479$	−0.197122	−	0.735669i	−0.00900673	−	0.0336136i	0.961276	−	0.275587i	$-0.0888721\pi$
$479$	−0.197122	−	0.735669i	−0.00900673	−	0.0336136i	−0.970283	+	0.241973i	$0.922205\pi$
$480$	−2.66523	+	5.81422i	−0.121650	+	0.265382i
$481$	5.70388	−	28.9169i	0.260075	−	1.31850i
$482$		−	20.5794i		−	0.937368i
$483$	5.20372	+	0.882632i	0.236778	+	0.0401611i
$484$	−12.7084	+	22.0116i	−0.577655	+	1.00053i
$485$	−6.47952	−	11.2228i	−0.294220	−	0.509603i
$486$	15.2553	−	3.20558i	0.691995	−	0.145408i
$487$	38.0434	+	10.1937i	1.72391	+	0.461920i	0.978766	−	0.204983i	$-0.0657138\pi$
$487$	38.0434	+	10.1937i	1.72391	+	0.461920i	0.745144	+	0.666903i	$0.232381\pi$
$488$	−6.61210	−	1.77171i	−0.299316	−	0.0802014i
$489$	8.46544	+	22.7953i	0.382821	+	1.03084i
$490$	1.84636	+	3.19799i	0.0834101	+	0.144470i
$491$	10.9053	−	18.8885i	0.492149	−	0.852427i	−0.507810	−	0.861469i	$-0.669545\pi$
$491$	10.9053	−	18.8885i	0.492149	−	0.852427i	0.999959	+	0.00904224i	$0.00287827\pi$
$492$	−1.25854	+	7.41994i	−0.0567392	+	0.334517i
$493$			22.9883i			1.03534i
$494$	3.54643	−	7.22052i	0.159561	−	0.324867i
$495$	−43.6358	−	50.6477i	−1.96129	−	2.27645i
$496$	1.79884	+	6.71335i	0.0807702	+	0.301438i
$497$	7.75445	+	4.47703i	0.347835	+	0.200822i
$498$	4.54550	−	0.427545i	0.203689	−	0.0191587i
$499$	12.5058	−	12.5058i	0.559837	−	0.559837i	−0.369424	−	0.929261i	$-0.620445\pi$
$499$	12.5058	−	12.5058i	0.559837	−	0.559837i	0.929261	+	0.369424i	$0.120445\pi$
$500$	−3.47528	+	12.9699i	−0.155419	+	0.580032i
$501$	12.1796	+	10.0854i	0.544145	+	0.450582i
$502$	2.49198	+	2.49198i	0.111222	+	0.111222i
$503$	−13.4468	+	7.76349i	−0.599562	+	0.346157i	−0.768869	−	0.639406i	$-0.779180\pi$
$503$	−13.4468	+	7.76349i	−0.599562	+	0.346157i	0.169307	+	0.985563i	$0.445847\pi$
$504$	2.94738	−	0.559404i	0.131287	−	0.0249178i
$505$	28.2505	−	7.56971i	1.25713	−	0.336848i
$506$	−18.3892			−0.817501
$507$	−21.5393	−	6.56196i	−0.956593	−	0.291427i
$508$	−4.82619			−0.214128
$509$	−11.3965	+	3.05368i	−0.505141	+	0.135352i	−0.502385	−	0.864644i	$-0.667544\pi$
$509$	−11.3965	+	3.05368i	−0.505141	+	0.135352i	−0.00275582	+	0.999996i	$0.500877\pi$
$510$	−12.0563	−	16.9816i	−0.533861	−	0.751956i
$511$	−1.18959	+	0.686812i	−0.0526245	+	0.0303828i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	0.226629	+	11.5911i	0.0100059	+	0.511758i
$514$	4.40045	−	16.4227i	0.194096	−	0.724375i
$515$	−2.45804	+	2.45804i	−0.108314	+	0.108314i
$516$	−1.25449	−	13.3373i	−0.0552258	−	0.587140i
$517$	48.9777	+	28.2773i	2.15404	+	1.24363i
$518$	2.11575	+	7.89610i	0.0929609	+	0.346935i
$519$	−28.8488	−	13.2243i	−1.26632	−	0.580480i
$520$	−5.86966	+	11.9506i	−0.257402	+	0.524070i
$521$		−	18.3855i		−	0.805485i	−0.915313	−	0.402742i	$-0.868057\pi$
$521$		−	18.3855i		−	0.805485i	0.915313	−	0.402742i	$-0.131943\pi$
$522$	−11.9212	+	17.5065i	−0.521777	+	0.766239i
$523$	13.2217	−	22.9006i	0.578143	−	1.00137i	−0.417550	−	0.908654i	$-0.637111\pi$
$523$	13.2217	−	22.9006i	0.578143	−	1.00137i	0.995692	−	0.0927183i	$-0.0295556\pi$
$524$	6.34131	+	10.9835i	0.277022	+	0.479815i
$525$	14.0226	−	5.20754i	0.611996	−	0.227275i
$526$	−12.5648	−	3.36673i	−0.547851	−	0.146796i
$527$	−21.8595	−	5.85724i	−0.952216	−	0.255145i
$528$	−9.79844	+	3.63882i	−0.426422	+	0.158359i
$529$	6.85704	+	11.8767i	0.298132	+	0.516380i
$530$	8.48788	−	14.7014i	0.368690	−	0.638589i
$531$	−15.1642	+	22.2688i	−0.658069	+	0.966385i
$532$			2.23113i			0.0967316i
$533$	−3.03180	+	15.3703i	−0.131322	+	0.665761i
$534$	−10.2808	−	4.71268i	−0.444892	−	0.203938i
$535$	−4.50981	−	16.8308i	−0.194976	−	0.727660i
$536$	−0.500482	−	0.288953i	−0.0216175	−	0.0124809i
$537$	−2.59609	−	27.6007i	−0.112030	−	1.19106i
$538$	−3.51213	+	3.51213i	−0.151419	+	0.151419i
$539$	−1.56188	+	5.82901i	−0.0672749	+	0.251073i
$540$	−0.375092	−	19.1843i	−0.0161414	−	0.825560i
$541$	18.3158	+	18.3158i	0.787458	+	0.787458i	0.981077	−	0.193618i	$-0.0620224\pi$
$541$	18.3158	+	18.3158i	0.787458	+	0.787458i	−0.193618	+	0.981077i	$0.562022\pi$
$542$	−20.9446	+	12.0924i	−0.899646	+	0.519411i
$543$	18.2237	+	25.6685i	0.782053	+	1.10154i
$544$	−3.14518	+	0.842748i	−0.134848	+	0.0361325i
$545$	65.0557			2.78668
$546$	6.16440	−	1.00007i	0.263812	−	0.0427990i
$547$	1.40479			0.0600643			0.0300321	−	0.999549i	$-0.490439\pi$
$547$	1.40479			0.0600643			0.0300321	+	0.999549i	$0.490439\pi$
$548$	−16.4843	+	4.41694i	−0.704173	+	0.188683i
$549$	20.1759	−	3.82932i	0.861085	−	0.163431i
$550$	−45.1340	+	26.0581i	−1.92452	+	1.11112i
$551$	−11.1382	−	11.1382i	−0.474503	−	0.474503i
$552$	−4.06524	−	3.36624i	−0.173028	−	0.143277i
$553$	−1.17247	+	4.37571i	−0.0498584	+	0.186074i
$554$	−9.57826	+	9.57826i	−0.406941	+	0.406941i
$555$	52.0551	−	4.89624i	2.20962	−	0.207834i
$556$	10.8936	+	6.28943i	0.461992	+	0.266731i
$557$	−5.92389	−	22.1082i	−0.251003	−	0.936757i	−0.970270	−	0.242023i	$-0.922189\pi$
$557$	−5.92389	−	22.1082i	−0.251003	−	0.936757i	0.719267	−	0.694733i	$-0.244478\pi$
$558$	−13.6095	−	15.7964i	−0.576135	−	0.668715i
$559$	−1.86834	−	27.8236i	−0.0790224	−	1.17681i
$560$		−	3.69272i		−	0.156046i
$561$	5.69140	−	33.5547i	0.240291	−	1.41668i
$562$	−4.58147	+	7.93533i	−0.193258	+	0.334732i
$563$	14.6097	+	25.3048i	0.615726	+	1.06647i	0.990257	+	0.139254i	$0.0444704\pi$
$563$	14.6097	+	25.3048i	0.615726	+	1.06647i	−0.374531	+	0.927214i	$0.622196\pi$
$564$	5.65102	+	15.2168i	0.237951	+	0.640742i
$565$	16.7198	+	4.48005i	0.703407	+	0.188477i
$566$	−14.1678	−	3.79625i	−0.595518	−	0.159568i
$567$	−7.23532	+	5.35258i	−0.303855	+	0.224787i
$568$	−4.47703	−	7.75445i	−0.187852	−	0.325370i
$569$	−15.3604	+	26.6050i	−0.643943	+	1.11534i	0.340602	+	0.940208i	$0.389369\pi$
$569$	−15.3604	+	26.6050i	−0.643943	+	1.11534i	−0.984545	+	0.175134i	$0.943964\pi$
$570$	14.0693	+	2.38637i	0.589298	+	0.0999541i
$571$			6.95592i			0.291096i	0.989351	+	0.145548i	$0.0464945\pi$
$571$			6.95592i			0.291096i	−0.989351	+	0.145548i	$0.953505\pi$
$572$	−20.5923	+	7.02687i	−0.861006	+	0.293808i
$573$	−1.38207	+	3.01500i	−0.0577367	+	0.125953i
$574$	−1.12459	−	4.19703i	−0.0469395	−	0.175181i
$575$	−22.7911	−	13.1584i	−0.950454	−	0.548745i
$576$	−2.83221	−	0.989233i	−0.118009	−	0.0412180i
$577$	−3.64763	+	3.64763i	−0.151853	+	0.151853i	−0.778945	−	0.627092i	$-0.784245\pi$
$577$	−3.64763	+	3.64763i	−0.151853	+	0.151853i	0.627092	+	0.778945i	$0.284245\pi$
$578$	−1.65583	+	6.17965i	−0.0688735	+	0.257039i
$579$	−12.5169	+	15.1161i	−0.520186	+	0.628203i
$580$	18.4347	+	18.4347i	0.765460	+	0.765460i
$581$	−2.28278	+	1.31797i	−0.0947058	+	0.0546784i
$582$	4.95628	−	3.51878i	0.205444	−	0.145858i
$583$	26.7964	−	7.18009i	1.10980	−	0.297369i
$584$	1.37362			0.0568410
$585$	0.286972	−	39.9419i	0.0118648	−	1.65139i
$586$	24.3628			1.00642
$587$	4.21555	−	1.12955i	0.173994	−	0.0466216i	−0.170770	−	0.985311i	$-0.554626\pi$
$587$	4.21555	−	1.12955i	0.173994	−	0.0466216i	0.344764	+	0.938689i	$0.387959\pi$
$588$	−1.41231	+	1.00269i	−0.0582426	+	0.0413502i
$589$	13.4292	−	7.75336i	0.553341	−	0.319472i
$590$	23.4496	+	23.4496i	0.965403	+	0.965403i
$591$	−7.79860	+	9.41797i	−0.320792	+	0.387404i
$592$	2.11575	−	7.89610i	0.0869569	−	0.324528i
$593$	17.3166	−	17.3166i	0.711108	−	0.711108i	−0.255659	−	0.966767i	$-0.582292\pi$
$593$	17.3166	−	17.3166i	0.711108	−	0.711108i	0.966767	+	0.255659i	$0.0822924\pi$
$594$	21.7350	−	22.6019i	0.891797	−	0.927366i
$595$	10.4131	+	6.01198i	0.426894	+	0.246467i
$596$	−2.75005	−	10.2633i	−0.112647	−	0.420403i
$597$	5.67449	−	12.3790i	0.232241	−	0.506637i
$598$	−8.27213	−	7.23110i	−0.338273	−	0.295702i
$599$			2.41985i			0.0988725i	0.998777	+	0.0494362i	$0.0157425\pi$
$599$			2.41985i			0.0988725i	−0.998777	+	0.0494362i	$0.984258\pi$
$600$	−14.7477	−	2.50144i	−0.602072	−	0.102121i
$601$	−9.79984	+	16.9738i	−0.399744	+	0.692377i	−0.993694	−	0.112125i	$-0.964234\pi$
$601$	−9.79984	+	16.9738i	−0.399744	+	0.692377i	0.593950	+	0.804502i	$0.297568\pi$
$602$	3.86713	+	6.69807i	0.157612	+	0.272993i
$603$	1.72894	+	0.128582i	0.0704081	+	0.00523626i
$604$	19.1455	+	5.13002i	0.779019	+	0.208737i
$605$	−90.6591	−	24.2920i	−3.68582	−	0.987611i
$606$	4.77580	+	12.8600i	0.194004	+	0.522404i
$607$	16.3977	+	28.4016i	0.665562	+	1.15279i	0.979133	+	0.203222i	$0.0651412\pi$
$607$	16.3977	+	28.4016i	0.665562	+	1.15279i	−0.313571	+	0.949565i	$0.601525\pi$
$608$	1.11556	−	1.93221i	0.0452421	−	0.0783616i
$609$	2.04490	−	12.0561i	0.0828636	−	0.488538i
$610$		−	25.2780i		−	1.02348i
$611$	10.9126	+	31.9794i	0.441476	+	1.29375i
$612$	7.40055	−	6.37598i	0.299149	−	0.257734i
$613$	−6.99024	−	26.0879i	−0.282333	−	1.05368i	−0.950766	−	0.309909i	$-0.899701\pi$
$613$	−6.99024	−	26.0879i	−0.282333	−	1.05368i	0.668433	−	0.743772i	$-0.266965\pi$
$614$	22.5795	+	13.0363i	0.911232	+	0.526100i
$615$	−27.6690	+	2.60251i	−1.11572	+	0.104943i
$616$	4.26713	−	4.26713i	0.171928	−	0.171928i
$617$	4.98729	−	18.6128i	0.200781	−	0.749324i	−0.789914	−	0.613218i	$-0.789875\pi$
$617$	4.98729	−	18.6128i	0.200781	−	0.749324i	0.990694	−	0.136106i	$-0.0434587\pi$
$618$	−1.25583	−	1.03989i	−0.0505168	−	0.0418307i
$619$	6.27677	+	6.27677i	0.252285	+	0.252285i	0.821907	−	0.569622i	$-0.192910\pi$
$619$	6.27677	+	6.27677i	0.252285	+	0.252285i	−0.569622	+	0.821907i	$0.692910\pi$
$620$	−22.2266	+	12.8325i	−0.892641	+	0.515367i
$621$	15.3718	+	3.79841i	0.616849	+	0.152425i
$622$	−3.17074	+	0.849597i	−0.127135	+	0.0340657i
$623$	6.52951			0.261599
$624$	−5.83856	−	2.21612i	−0.233730	−	0.0887156i
$625$	−6.40283			−0.256113
$626$	−7.24284	+	1.94071i	−0.289482	+	0.0775665i
$627$	13.5002	+	19.0154i	0.539147	+	0.759401i
$628$	−20.7319	+	11.9696i	−0.827294	+	0.477638i
$629$	18.8215	+	18.8215i	0.750464	+	0.750464i
$630$	4.81229	+	9.97836i	0.191726	+	0.397547i
$631$	10.3772	−	38.7281i	0.413108	−	1.54174i	−0.375487	−	0.926827i	$-0.622525\pi$
$631$	10.3772	−	38.7281i	0.413108	−	1.54174i	0.788595	−	0.614912i	$-0.210809\pi$
$632$	3.20324	−	3.20324i	0.127418	−	0.127418i
$633$	0.529636	+	5.63090i	0.0210511	+	0.223808i
$634$	23.2573	+	13.4276i	0.923667	+	0.533279i
$635$	−4.61262	−	17.2145i	−0.183046	−	0.683137i
$636$	7.23815	+	3.31795i	0.287011	+	0.131565i
$637$	−2.99470	+	2.00793i	−0.118654	+	0.0795570i
$638$			42.6046i			1.68673i
$639$	22.2032	+	15.1194i	0.878344	+	0.598116i
$640$	−1.84636	+	3.19799i	−0.0729838	+	0.126412i
$641$	13.3709	+	23.1591i	0.528120	+	0.914731i	0.999463	+	0.0327804i	$0.0104362\pi$
$641$	13.3709	+	23.1591i	0.528120	+	0.914731i	−0.471343	+	0.881950i	$0.656230\pi$
$642$	7.66163	−	2.84528i	0.302380	−	0.112294i
$643$	−30.2386	−	8.10240i	−1.19249	−	0.319527i	−0.392622	−	0.919700i	$-0.628432\pi$
$643$	−30.2386	−	8.10240i	−1.19249	−	0.319527i	−0.799871	+	0.600173i	$0.795099\pi$
$644$	2.94345	+	0.788694i	0.115988	+	0.0310789i
$645$	46.3736	−	17.2217i	1.82596	−	0.678103i
$646$	3.63242	+	6.29153i	0.142915	+	0.247537i
$647$	21.4531	−	37.1579i	0.843408	−	1.46083i	−0.0435881	−	0.999050i	$-0.513879\pi$
$647$	21.4531	−	37.1579i	0.843408	−	1.46083i	0.886996	−	0.461776i	$-0.152788\pi$
$648$	8.94226	−	1.01781i	0.351285	−	0.0399834i
$649$			54.1944i			2.12731i
$650$	−30.5496	−	6.02593i	−1.19825	−	0.236356i
$651$	10.9431	+	5.01630i	0.428894	+	0.196604i
$652$	3.63359	+	13.5607i	0.142302	+	0.531080i
$653$	5.51209	+	3.18240i	0.215705	+	0.124537i	0.603960	−	0.797015i	$-0.293589\pi$
$653$	5.51209	+	3.18240i	0.215705	+	0.124537i	−0.388255	+	0.921552i	$0.626922\pi$
$654$	2.85750	+	30.3799i	0.111737	+	1.18795i
$655$	−33.1162	+	33.1162i	−1.29396	+	1.29396i
$656$	−1.12459	+	4.19703i	−0.0439079	+	0.163867i
$657$	−3.71177	+	1.79008i	−0.144810	+	0.0698378i
$658$	−6.62677	−	6.62677i	−0.258338	−	0.258338i
$659$	−20.6511	+	11.9229i	−0.804451	+	0.464450i	−0.845025	−	0.534726i	$-0.820415\pi$
$659$	−20.6511	+	11.9229i	−0.804451	+	0.464450i	0.0405741	+	0.999177i	$0.487081\pi$
$660$	−22.3441	−	31.4722i	−0.869744	−	1.22505i
$661$	36.3985	−	9.75295i	1.41574	−	0.379346i	0.531768	−	0.846890i	$-0.321528\pi$
$661$	36.3985	−	9.75295i	1.41574	−	0.379346i	0.883970	+	0.467544i	$0.154861\pi$
$662$	−16.6760			−0.648132
$663$	15.7548	−	12.8561i	0.611864	−	0.499290i
$664$	2.63593			0.102294
$665$	−7.95819	+	2.13239i	−0.308606	+	0.0826906i
$666$	4.57293	+	24.0938i	0.177197	+	0.933616i
$667$	−18.6315	+	10.7569i	−0.721415	+	0.416509i
$668$	6.45573	+	6.45573i	0.249780	+	0.249780i
$669$	−21.9925	−	18.2110i	−0.850278	−	0.704077i
$670$	0.552332	−	2.06133i	0.0213385	−	0.0796362i
$671$	29.2100	−	29.2100i	1.12764	−	1.12764i
$672$	1.72444	−	0.162199i	0.0665217	−	0.00625696i
$673$	−30.5628	−	17.6454i	−1.17811	−	0.680182i	−0.222533	−	0.974925i	$-0.571432\pi$
$673$	−30.5628	−	17.6454i	−1.17811	−	0.680182i	−0.955576	+	0.294744i	$0.904766\pi$
$674$	6.68732	+	24.9574i	0.257586	+	0.961324i
$675$	43.1106	−	12.4596i	1.65933	−	0.479571i
$676$	−12.0263	−	4.93645i	−0.462549	−	0.189863i
$677$		−	47.9832i		−	1.84414i	−0.387020	−	0.922071i	$-0.626495\pi$
$677$		−	47.9832i		−	1.84414i	0.387020	−	0.922071i	$-0.373505\pi$
$678$	−1.35771	+	8.00464i	−0.0521426	+	0.307416i
$679$	−1.75467	+	3.03918i	−0.0673381	+	0.116633i
$680$	−6.01198	−	10.4131i	−0.230549	−	0.399323i
$681$	−7.57289	−	20.3919i	−0.290194	−	0.781419i
$682$	−40.5126	−	10.8553i	−1.55131	−	0.415672i
$683$	−12.1169	−	3.24671i	−0.463640	−	0.124232i	0.0194346	−	0.999811i	$-0.493813\pi$
$683$	−12.1169	−	3.24671i	−0.463640	−	0.124232i	−0.483075	+	0.875579i	$0.660480\pi$
$684$	−0.496416	+	6.67495i	−0.0189810	+	0.255223i
$685$	−31.5096	−	54.5762i	−1.20392	−	2.08525i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$	4.38828	+	0.744320i	0.167423	+	0.0283976i
$688$		−	7.73426i		−	0.294866i
$689$	14.8774	+	7.30717i	0.566783	+	0.278381i
$690$	8.12169	−	17.7176i	0.309188	−	0.674496i
$691$	1.73988	+	6.49333i	0.0661883	+	0.247018i	0.991091	−	0.133186i	$-0.0425206\pi$
$691$	1.73988	+	6.49333i	0.0661883	+	0.247018i	−0.924903	+	0.380204i	$0.875854\pi$
$692$	−15.8677	−	9.16123i	−0.603200	−	0.348258i
$693$	−5.96966	+	17.0914i	−0.226769	+	0.649247i
$694$	−20.6676	+	20.6676i	−0.784531	+	0.784531i
$695$	−12.0222	+	44.8675i	−0.456028	+	1.70192i
$696$	−7.79898	+	9.41844i	−0.295620	+	0.357005i
$697$	−10.0043	−	10.0043i	−0.378938	−	0.378938i
$698$	24.0091	−	13.8617i	0.908757	−	0.524671i
$699$	16.4877	−	11.7057i	0.623621	−	0.442748i
$700$	8.34192	−	2.23521i	0.315295	−	0.0844830i
$701$	2.47640			0.0935323			0.0467661	−	0.998906i	$-0.485108\pi$
$701$	2.47640			0.0935323			0.0467661	+	0.998906i	$0.485108\pi$
$702$	18.6648	−	1.62039i	0.704457	−	0.0611578i
$703$	−18.2387			−0.687884
$704$	−5.82901	+	1.56188i	−0.219689	+	0.0588655i
$705$	−48.8757	+	34.7000i	−1.84077	+	1.30688i
$706$	−15.0008	+	8.66070i	−0.564561	+	0.325950i
$707$	−5.60043	−	5.60043i	−0.210626	−	0.210626i
$708$	−9.92056	+	11.9806i	−0.372837	+	0.450257i
$709$	3.79939	−	14.1795i	0.142689	−	0.532522i	−0.857158	−	0.515053i	$-0.827772\pi$
$709$	3.79939	−	14.1795i	0.142689	−	0.532522i	0.999847	−	0.0174695i	$-0.00556101\pi$
$710$	23.3804	−	23.3804i	0.877451	−	0.877451i
$711$	−4.48129	+	12.8301i	−0.168062	+	0.481166i
$712$	−5.65472	−	3.26476i	−0.211920	−	0.122352i
$713$	−5.48156	−	20.4575i	−0.205286	−	0.766138i
$714$	−2.35011	+	5.12680i	−0.0879508	+	0.191866i
$715$	−44.7451	−	66.7345i	−1.67337	−	2.49573i
$716$		−	16.0056i		−	0.598158i
$717$	−16.7365	−	2.83877i	−0.625036	−	0.106016i
$718$	6.43940	−	11.1534i	0.240316	−	0.416240i
$719$	2.24829	+	3.89415i	0.0838470	+	0.145227i	0.904899	−	0.425626i	$-0.139946\pi$
$719$	2.24829	+	3.89415i	0.0838470	+	0.145227i	−0.821052	+	0.570853i	$0.806613\pi$
$720$	0.821615	−	11.0477i	0.0306198	−	0.411722i
$721$	0.909286	+	0.243642i	0.0338636	+	0.00907372i
$722$	13.5443	+	3.62918i	0.504066	+	0.135064i
$723$	12.4092	+	33.4148i	0.461503	+	1.24271i
$724$	9.08741	+	15.7399i	0.337731	+	0.584967i
$725$	−30.4858	+	52.8029i	−1.13221	+	1.96105i
$726$	7.36187	−	43.4033i	0.273225	−	1.61085i
$727$			39.7600i			1.47462i	0.675556	+	0.737309i	$0.263904\pi$
$727$			39.7600i			1.47462i	−0.675556	+	0.737309i	$0.736096\pi$
$728$	3.59745	−	0.241567i	0.133330	−	0.00895306i
$729$	−22.8371	+	14.4037i	−0.845819	+	0.533470i
$730$	1.31284	+	4.89957i	0.0485903	+	0.181341i
$731$	21.8097	+	12.5919i	0.806663	+	0.465727i
$732$	11.8044	−	1.11031i	0.436303	−	0.0410382i
$733$	10.5520	−	10.5520i	0.389746	−	0.389746i	−0.484851	−	0.874597i	$-0.661126\pi$
$733$	10.5520	−	10.5520i	0.389746	−	0.389746i	0.874597	+	0.484851i	$0.161126\pi$
$734$	−6.38900	+	23.8441i	−0.235822	+	0.880101i
$735$	−4.92629	−	4.07924i	−0.181709	−	0.150465i
$736$	−2.15475	−	2.15475i	−0.0794252	−	0.0794252i
$737$	3.02022	−	1.74373i	0.111251	−	0.0642310i
$738$	−2.43066	−	12.8066i	−0.0894739	−	0.471419i
$739$	3.69172	−	0.989193i	0.135802	−	0.0363880i	−0.190278	−	0.981730i	$-0.560939\pi$
$739$	3.69172	−	0.989193i	0.135802	−	0.0363880i	0.326080	+	0.945342i	$0.394272\pi$
$740$	30.1867			1.10968
$741$	−1.40443	+	13.8624i	−0.0515931	+	0.509249i
$742$	−4.59708			−0.168764
$743$	28.5202	−	7.64195i	1.04630	−	0.280356i	0.305580	−	0.952166i	$-0.401150\pi$
$743$	28.5202	−	7.64195i	1.04630	−	0.280356i	0.740723	+	0.671810i	$0.234483\pi$
$744$	−6.96886	−	9.81579i	−0.255491	−	0.359864i
$745$	33.9799	−	19.6183i	1.24493	−	0.718759i
$746$	8.81450	+	8.81450i	0.322722	+	0.322722i
$747$	−7.12273	+	3.43510i	−0.260607	+	0.125684i
$748$	5.08567	−	18.9800i	0.185951	−	0.693977i
$749$	−3.33657	+	3.33657i	−0.121916	+	0.121916i
$750$	−2.17791	−	23.1548i	−0.0795262	−	0.845494i
$751$	−30.7062	−	17.7282i	−1.12048	−	0.646912i	−0.178959	−	0.983856i	$-0.557273\pi$
$751$	−30.7062	−	17.7282i	−1.12048	−	0.646912i	−0.941524	+	0.336945i	$0.890606\pi$
$752$	2.42557	+	9.05234i	0.0884513	+	0.330105i
$753$	−5.54886	−	2.54359i	−0.202212	−	0.0926935i
$754$	−16.7532	+	19.1651i	−0.610114	+	0.697950i
$755$			73.1929i			2.66376i
$756$	−4.44835	+	2.68555i	−0.161785	+	0.0976724i
$757$	−1.38028	+	2.39071i	−0.0501670	+	0.0868919i	−0.890018	−	0.455924i	$-0.849309\pi$
$757$	−1.38028	+	2.39071i	−0.0501670	+	0.0868919i	0.839851	+	0.542816i	$0.182642\pi$
$758$	−15.4474	−	26.7557i	−0.561075	−	0.971811i
$759$	29.8586	−	11.0885i	1.08380	−	0.402488i
$760$	7.95819	+	2.13239i	0.288674	+	0.0773500i
$761$	49.8082	+	13.3461i	1.80555	+	0.483794i	0.994822	−	0.101634i	$-0.0324072\pi$
$761$	49.8082	+	13.3461i	1.80555	+	0.483794i	0.810724	+	0.585429i	$0.199074\pi$
$762$	7.83629	−	2.91014i	0.283879	−	0.105423i
$763$	−8.80864	−	15.2570i	−0.318894	−	0.552341i
$764$	−0.957440	+	1.65834i	−0.0346390	+	0.0599965i
$765$	29.8155	+	20.3031i	1.07798	+	0.734062i
$766$		−	0.0434426i		−	0.00156965i
$767$	−21.3106	+	24.3786i	−0.769480	+	0.880259i
$768$	−1.57451	−	0.721751i	−0.0568152	−	0.0260440i
$769$	−10.4913	−	39.1542i	−0.378327	−	1.41194i	−0.848422	−	0.529321i	$-0.822447\pi$
$769$	−10.4913	−	39.1542i	−0.378327	−	1.41194i	0.470094	−	0.882616i	$-0.344220\pi$
$770$	19.2987	+	11.1421i	0.695477	+	0.401534i
$771$	2.75771	+	29.3190i	0.0993166	+	1.05590i
$772$	−8.01217	+	8.01217i	−0.288364	+	0.288364i
$773$	−3.76133	+	14.0375i	−0.135286	+	0.504892i	0.864711	+	0.502270i	$0.167502\pi$
$773$	−3.76133	+	14.0375i	−0.135286	+	0.504892i	−0.999997	+	0.00262276i	$0.999165\pi$
$774$	10.0791	+	20.8993i	0.362287	+	0.751209i
$775$	−42.4427	−	42.4427i	−1.52459	−	1.52459i
$776$	3.03918	−	1.75467i	0.109100	−	0.0629891i
$777$	−8.19662	−	11.5451i	−0.294052	−	0.414179i
$778$	14.5765	−	3.90575i	0.522591	−	0.140028i
$779$	9.69444			0.347339
$780$	2.32446	−	22.9436i	0.0832291	−	0.821512i
$781$	54.0345			1.93351
$782$	9.58423	−	2.56809i	0.342732	−	0.0918346i
$783$	8.80024	−	35.6137i	0.314495	−	1.27273i
$784$	−0.866025	+	0.500000i	−0.0309295	+	0.0178571i
$785$	−62.5087	−	62.5087i	−2.23103	−	2.23103i
$786$	−16.9193	−	14.0101i	−0.603492	−	0.499725i
$787$	−0.785160	+	2.93026i	−0.0279879	+	0.104452i	−0.978507	−	0.206214i	$-0.933886\pi$
$787$	−0.785160	+	2.93026i	−0.0279879	+	0.104452i	0.950519	+	0.310667i	$0.100552\pi$
$788$	−4.99193	+	4.99193i	−0.177830	+	0.177830i
$789$	22.4316	−	2.10989i	0.798585	−	0.0751140i
$790$	14.4871	+	8.36413i	0.515428	+	0.297583i
$791$	−1.21321	−	4.52777i	−0.0431368	−	0.160989i
$792$	13.7156	−	11.8167i	0.487361	−	0.419889i
$793$	24.6258	−	1.65361i	0.874488	−	0.0587214i
$794$		−	26.8252i		−	0.951989i
$795$	−4.91695	+	28.9888i	−0.174386	+	1.02813i
$796$	3.93106	−	6.80879i	0.139333	−	0.241331i
$797$	−4.53506	−	7.85495i	−0.160640	−	0.278237i	0.774458	−	0.632625i	$-0.218022\pi$
$797$	−4.53506	−	7.85495i	−0.160640	−	0.278237i	−0.935098	+	0.354388i	$0.884689\pi$
$798$	−1.34535	−	3.62268i	−0.0476248	−	0.128242i
$799$	−29.4756	−	7.89795i	−1.04277	−	0.279409i
$800$	−8.34192	−	2.23521i	−0.294931	−	0.0790266i
$801$	19.5346	+	1.45279i	0.690221	+	0.0513318i
$802$	4.43170	+	7.67592i	0.156489	+	0.271046i
$803$	−4.14466	+	7.17876i	−0.146262	+	0.253333i
$804$	0.986868	+	0.167388i	0.0348042	+	0.00590332i
$805$			11.2528i			0.396608i
$806$	−13.9554	−	20.8137i	−0.491560	−	0.733131i
$807$	3.58487	−	7.82043i	0.126193	−	0.275292i
$808$	2.04990	+	7.65033i	0.0721153	+	0.269138i
$809$	−29.7204	−	17.1591i	−1.04491	−	0.603280i	−0.123691	−	0.992321i	$-0.539473\pi$
$809$	−29.7204	−	17.1591i	−1.04491	−	0.603280i	−0.921221	+	0.389040i	$0.872807\pi$
$810$	12.1770	+	30.9233i	0.427855	+	1.08654i
$811$	−4.95616	+	4.95616i	−0.174034	+	0.174034i	−0.788749	−	0.614715i	$-0.789271\pi$
$811$	−4.95616	+	4.95616i	−0.174034	+	0.174034i	0.614715	+	0.788749i	$0.289271\pi$
$812$	1.82726	−	6.81944i	0.0641244	−	0.239316i
$813$	26.7161	−	32.2637i	0.936976	−	1.13154i
$814$	34.8823	+	34.8823i	1.22262	+	1.22262i
$815$	−44.8970	+	25.9213i	−1.57267	+	0.907982i
$816$	4.59866	−	3.26488i	0.160985	−	0.114294i
$817$	−16.6681	+	4.46621i	−0.583144	+	0.156253i
$818$	−12.7070			−0.444290
$819$	−9.40611	+	5.34089i	−0.328676	+	0.186626i
$820$	−16.0452			−0.560323
$821$	34.3531	−	9.20487i	1.19893	−	0.321252i	0.396520	−	0.918026i	$-0.370218\pi$
$821$	34.3531	−	9.20487i	1.19893	−	0.321252i	0.802410	+	0.596774i	$0.203551\pi$
$822$	24.1021	−	17.1116i	0.840658	−	0.596837i
$823$	−14.6251	+	8.44381i	−0.509799	+	0.294333i	−0.732751	−	0.680497i	$-0.761764\pi$
$823$	−14.6251	+	8.44381i	−0.509799	+	0.294333i	0.222952	+	0.974829i	$0.428431\pi$
$824$	−0.665643	−	0.665643i	−0.0231888	−	0.0231888i
$825$	57.5713	−	69.5259i	2.00438	−	2.42058i
$826$	2.32434	−	8.67455i	0.0808741	−	0.301826i
$827$	4.77974	−	4.77974i	0.166208	−	0.166208i	−0.619102	−	0.785310i	$-0.712503\pi$
$827$	4.77974	−	4.77974i	0.166208	−	0.166208i	0.785310	+	0.619102i	$0.212503\pi$
$828$	8.63054	+	3.01447i	0.299932	+	0.104760i
$829$	−13.2762	−	7.66500i	−0.461100	−	0.266216i	0.251406	−	0.967882i	$-0.419107\pi$
$829$	−13.2762	−	7.66500i	−0.461100	−	0.266216i	−0.712507	+	0.701665i	$0.752440\pi$
$830$	2.51928	+	9.40209i	0.0874455	+	0.326351i
$831$	9.77663	−	21.3278i	0.339148	−	0.739854i
$832$	−3.23627	−	1.58952i	−0.112197	−	0.0551068i
$833$		−	3.25613i		−	0.112818i
$834$	−21.4804	−	3.64341i	−0.743806	−	0.126161i
$835$	−16.8569	+	29.1969i	−0.583356	+	1.01040i
$836$	6.73202	+	11.6602i	0.232832	+	0.403276i
$837$	31.6228	+	17.4422i	1.09304	+	0.602892i
$838$	0.481706	+	0.129073i	0.0166403	+	0.00445875i
$839$	28.9502	+	7.75719i	0.999473	+	0.267808i	0.721225	−	0.692701i	$-0.243580\pi$
$839$	28.9502	+	7.75719i	0.999473	+	0.267808i	0.278248	+	0.960509i	$0.410246\pi$
$840$	2.22667	+	5.99587i	0.0768275	+	0.206877i
$841$	10.4218	+	18.0512i	0.359374	+	0.622454i
$842$	9.07049	−	15.7105i	0.312590	−	0.541421i
$843$	2.65400	−	15.6472i	0.0914088	−	0.538918i
$844$			3.26535i			0.112398i
$845$	6.11372	−	47.6145i	0.210318	−	1.63799i
$846$	−18.3511	−	21.3000i	−0.630925	−	0.732309i
$847$	6.57835	+	24.5508i	0.226035	+	0.843574i
$848$	3.98119	+	2.29854i	0.136715	+	0.0789323i
$849$	25.2934	−	2.37907i	0.868067	−	0.0816494i
$850$	19.8842	−	19.8842i	0.682023	−	0.682023i
$851$	−6.44729	+	24.0616i	−0.221010	+	0.824822i
$852$	11.9452	+	9.89130i	0.409236	+	0.338870i
$853$	13.6498	+	13.6498i	0.467359	+	0.467359i	0.901058	−	0.433699i	$-0.142792\pi$
$853$	13.6498	+	13.6498i	0.467359	+	0.467359i	−0.433699	+	0.901058i	$0.642792\pi$
$854$	−5.92825	+	3.42268i	−0.202860	+	0.117122i
$855$	−24.2833	+	4.60889i	−0.830471	+	0.157621i
$856$	4.55784	−	1.22127i	0.155784	−	0.0417421i
$857$	20.5087			0.700565			0.350283	−	0.936644i	$-0.386086\pi$
$857$	20.5087			0.700565			0.350283	+	0.936644i	$0.386086\pi$
$858$	29.1985	−	23.8265i	0.996822	−	0.813422i
$859$	11.5015			0.392426			0.196213	−	0.980561i	$-0.437136\pi$
$859$	11.5015			0.392426			0.196213	+	0.980561i	$0.437136\pi$
$860$	27.5873	−	7.39199i	0.940719	−	0.252065i
$861$	4.35677	+	6.13661i	0.148478	+	0.209135i
$862$	12.6039	−	7.27686i	0.429290	−	0.247851i
$863$	34.7688	+	34.7688i	1.18354	+	1.18354i	0.978820	+	0.204724i	$0.0656296\pi$
$863$	34.7688	+	34.7688i	1.18354	+	1.18354i	0.204724	+	0.978820i	$0.434370\pi$
$864$	5.19516	−	0.101576i	0.176743	−	0.00345568i
$865$	17.5116	−	65.3543i	0.595413	−	2.22211i
$866$	−4.55251	+	4.55251i	−0.154700	+	0.154700i
$867$	−1.03769	−	11.0323i	−0.0352418	−	0.374678i
$868$	6.01903	+	3.47509i	0.204299	+	0.117952i
$869$	7.07541	+	26.4058i	0.240017	+	0.895755i
$870$	−41.0484	−	18.8165i	−1.39167	−	0.637940i
$871$	2.04428	+	0.403236i	0.0692678	+	0.0136631i
$872$			17.6173i			0.596596i
$873$	−5.92572	+	8.70203i	−0.200555	+	0.294519i
$874$	−3.39943	+	5.88799i	−0.114988	+	0.199164i
$875$	6.71372	+	11.6285i	0.226965	+	0.393115i
$876$	−2.23035	+	0.828282i	−0.0753567	+	0.0279850i
$877$	−29.7957	−	7.98373i	−1.00613	−	0.269591i	−0.282118	−	0.959380i	$-0.591037\pi$
$877$	−29.7957	−	7.98373i	−1.00613	−	0.269591i	−0.724011	+	0.689788i	$0.757704\pi$
$878$	21.6606	+	5.80394i	0.731009	+	0.195873i
$879$	−39.5580	+	14.6905i	−1.33426	+	0.495500i
$880$	−11.1421	−	19.2987i	−0.375600	−	0.650559i
$881$	5.44155	−	9.42505i	0.183331	−	0.317538i	−0.759682	−	0.650295i	$-0.774645\pi$
$881$	5.44155	−	9.42505i	0.183331	−	0.317538i	0.943013	+	0.332757i	$0.107979\pi$
$882$	1.68856	−	2.47967i	0.0568566	−	0.0834949i
$883$			41.3070i			1.39009i	0.718966	+	0.695045i	$0.244616\pi$
$883$			41.3070i			1.39009i	−0.718966	+	0.695045i	$0.755384\pi$
$884$	9.75112	−	6.53807i	0.327966	−	0.219899i
$885$	−52.2149	−	23.9352i	−1.75518	−	0.804573i
$886$	−9.61996	−	35.9022i	−0.323189	−	1.20616i
$887$	12.9659	+	7.48586i	0.435352	+	0.251350i	0.701624	−	0.712547i	$-0.252459\pi$
$887$	12.9659	+	7.48586i	0.435352	+	0.251350i	−0.266272	+	0.963898i	$0.585792\pi$
$888$	1.32592	+	14.0967i	0.0444949	+	0.473053i
$889$	−3.41263	+	3.41263i	−0.114456	+	0.114456i
$890$	6.24056	−	23.2901i	0.209184	−	0.780685i
$891$	−21.6624	+	49.8046i	−0.725718	+	1.66852i
$892$	−11.6570	−	11.6570i	−0.390304	−	0.390304i
$893$	18.1081	−	10.4547i	0.605963	−	0.349853i
$894$	10.6539	+	15.0063i	0.356321	+	0.501887i
$895$	57.0903	−	15.2973i	1.90832	−	0.511333i
$896$	1.00000			0.0334077
$897$	17.7917	+	6.75313i	0.594049	+	0.225480i
$898$	−1.01545			−0.0338861
$899$	−47.3963	+	12.6998i	−1.58076	+	0.423562i
$900$	25.4542	−	4.83112i	0.848472	−	0.161037i
$901$	−12.9633	+	7.48434i	−0.431869	+	0.249340i
$902$	−18.5411	−	18.5411i	−0.617350	−	0.617350i
$903$	−10.3179	−	8.54381i	−0.343359	−	0.284320i
$904$	−1.21321	+	4.52777i	−0.0403508	+	0.150591i
$905$	−47.4571	+	47.4571i	−1.57753	+	1.57753i
$906$	−34.1799	+	3.21492i	−1.13555	+	0.106809i
$907$	−14.3811	−	8.30294i	−0.477517	−	0.275695i	0.241864	−	0.970310i	$-0.422241\pi$
$907$	−14.3811	−	8.30294i	−0.477517	−	0.275695i	−0.719381	+	0.694615i	$0.755575\pi$
$908$	−3.25048	−	12.1310i	−0.107871	−	0.402580i
$909$	−15.5090	−	18.0011i	−0.514400	−	0.597059i
$910$	4.29989	+	12.6008i	0.142540	+	0.417714i
$911$			20.2591i			0.671213i	0.942002	+	0.335607i	$0.108941\pi$
$911$			20.2591i			0.671213i	−0.942002	+	0.335607i	$0.891059\pi$
$912$	−0.646236	+	3.81001i	−0.0213990	+	0.126162i
$913$	−7.95344	+	13.7758i	−0.263220	+	0.455911i
$914$	4.73361	+	8.19886i	0.156574	+	0.271194i
$915$	15.2424	+	41.0439i	0.503897	+	1.35687i
$916$	2.48220	+	0.665103i	0.0820141	+	0.0219756i
$917$	12.2505	+	3.28250i	0.404546	+	0.108398i
$918$	−8.17162	+	14.8151i	−0.269704	+	0.488973i
$919$	14.3842	+	24.9141i	0.474490	+	0.821841i	0.999573	−	0.0292098i	$-0.00929909\pi$
$919$	14.3842	+	24.9141i	0.474490	+	0.821841i	−0.525083	+	0.851051i	$0.675966\pi$
$920$	5.62638	−	9.74517i	0.185496	−	0.321289i
$921$	−44.5230	−	7.55179i	−1.46708	−	0.248840i
$922$		−	11.4816i		−	0.378125i
$923$	24.3067	+	21.2477i	0.800064	+	0.699377i
$924$	−4.35551	+	9.50158i	−0.143286	+	0.312579i
$925$	18.2720	+	68.1922i	0.600781	+	2.24215i
$926$	7.44027	+	4.29564i	0.244502	+	0.141164i
$927$	2.66613	+	0.931226i	0.0875674	+	0.0305855i
$928$	−4.99218	+	4.99218i	−0.163876	+	0.163876i
$929$	3.07752	−	11.4855i	0.100970	−	0.376825i	−0.896887	−	0.442260i	$-0.854177\pi$
$929$	3.07752	−	11.4855i	0.100970	−	0.376825i	0.997857	+	0.0654348i	$0.0208434\pi$
$930$	28.3514	−	34.2386i	0.929680	−	1.12273i
$931$	1.57764	+	1.57764i	0.0517052	+	0.0517052i
$932$	10.1102	−	5.83714i	0.331171	−	0.191202i
$933$	4.63603	−	3.29141i	0.151777	−	0.107756i
$934$	−11.0610	+	2.96377i	−0.361925	+	0.0969776i
$935$	72.5602			2.37297
$936$	10.8164	+	0.0777129i	0.353544	+	0.00254013i
$937$	−5.97424			−0.195170			−0.0975850	−	0.995227i	$-0.531112\pi$
$937$	−5.97424			−0.195170			−0.0975850	+	0.995227i	$0.531112\pi$
$938$	−0.558215	+	0.149573i	−0.0182264	+	0.00488374i
$939$	10.5900	−	7.51849i	0.345590	−	0.245357i
$940$	−29.9705	+	17.3035i	−0.977530	+	0.564377i
$941$	19.5744	+	19.5744i	0.638107	+	0.638107i	0.950088	−	0.311981i	$-0.100993\pi$
$941$	19.5744	+	19.5744i	0.638107	+	0.638107i	−0.311981	+	0.950088i	$0.600993\pi$
$942$	26.4449	−	31.9362i	0.861621	−	1.04054i
$943$	3.42695	−	12.7895i	0.111597	−	0.416485i
$944$	−6.35021	+	6.35021i	−0.206682	+	0.206682i
$945$	−13.8306	−	13.3001i	−0.449908	−	0.432652i
$946$	40.4204	+	23.3367i	1.31418	+	0.758742i
$947$	0.624843	+	2.33194i	0.0203047	+	0.0757780i	0.975335	−	0.220731i	$-0.0708442\pi$
$947$	0.624843	+	2.33194i	0.0203047	+	0.0757780i	−0.955030	+	0.296509i	$0.904178\pi$
$948$	−3.26958	+	7.13262i	−0.106191	+	0.231657i
$949$	−4.68728	+	1.59948i	−0.152156	+	0.0519214i
$950$			19.2684i			0.625151i
$951$	−45.8597	−	7.77851i	−1.48710	−	0.252235i
$952$	−1.62806	+	2.81989i	−0.0527658	+	0.0913931i
$953$	−5.46528	−	9.46615i	−0.177038	−	0.306639i	0.763827	−	0.645421i	$-0.223318\pi$
$953$	−5.46528	−	9.46615i	−0.177038	−	0.306639i	−0.940865	+	0.338783i	$0.889985\pi$
$954$	−13.7533	−	1.02283i	−0.445279	−	0.0331154i
$955$	−6.83018	−	1.83014i	−0.221019	−	0.0592220i
$956$	−9.46688	−	2.53664i	−0.306181	−	0.0820409i
$957$	−25.6901	−	69.1770i	−0.830444	−	2.23618i
$958$	0.380810	+	0.659583i	0.0123034	+	0.0213101i
$959$	−8.53288	+	14.7794i	−0.275541	+	0.477251i
$960$	1.06958	−	6.30592i	0.0345206	−	0.203523i
$961$		−	17.3049i		−	0.558223i
$962$	1.97472	+	29.4079i	0.0636676	+	0.948148i
$963$	−10.7245	+	9.23977i	−0.345593	+	0.297747i
$964$	5.32635	+	19.8782i	0.171550	+	0.640234i
$965$	−36.2362	−	20.9210i	−1.16648	−	0.673470i
$966$	−5.25485	+	0.494265i	−0.169072	+	0.0159027i
$967$	−22.2162	+	22.2162i	−0.714424	+	0.714424i	−0.967457	−	0.253034i	$-0.918572\pi$
$967$	−22.2162	+	22.2162i	−0.714424	+	0.714424i	0.253034	+	0.967457i	$0.418572\pi$
$968$	6.57835	−	24.5508i	0.211436	−	0.789091i
$969$	−9.69168	−	8.02525i	−0.311342	−	0.257808i
$970$	9.16342	+	9.16342i	0.294220	+	0.294220i
$971$	−29.9084	+	17.2676i	−0.959807	+	0.554145i	−0.896114	−	0.443824i	$-0.853621\pi$
$971$	−29.9084	+	17.2676i	−0.959807	+	0.554145i	−0.0636936	+	0.997969i	$0.520288\pi$
$972$	−13.9058	+	7.04471i	−0.446030	+	0.225959i
$973$	12.1502	−	3.25565i	0.389519	−	0.104371i
$974$	−39.3854			−1.26199
$975$	53.2370	−	8.63679i	1.70495	−	0.276599i
$976$	6.84535			0.219114
$977$	−30.9849	+	8.30239i	−0.991296	+	0.265617i	−0.717795	−	0.696255i	$-0.754848\pi$
$977$	−30.9849	+	8.30239i	−0.991296	+	0.265617i	−0.273501	+	0.961872i	$0.588182\pi$
$978$	−14.0769	−	19.8276i	−0.450128	−	0.634016i
$979$	34.1242	−	19.7016i	1.09061	−	0.629666i
$980$	−2.61115	−	2.61115i	−0.0834101	−	0.0834101i
$981$	−22.9585	−	47.6049i	−0.733009	−	1.51991i
$982$	−5.64499	+	21.0674i	−0.180139	+	0.672288i
$983$	5.07300	−	5.07300i	0.161803	−	0.161803i	−0.621562	−	0.783365i	$-0.713501\pi$
$983$	5.07300	−	5.07300i	0.161803	−	0.161803i	0.783365	+	0.621562i	$0.213501\pi$
$984$	−0.704768	−	7.49284i	−0.0224672	−	0.238863i
$985$	−22.5767	−	13.0347i	−0.719354	−	0.415319i
$986$	−5.94980	−	22.2050i	−0.189480	−	0.707150i
$987$	14.7558	+	6.76401i	0.469681	+	0.215301i
$988$	−1.55678	+	7.89237i	−0.0495276	+	0.251090i
$989$			23.5685i			0.749433i
$990$	55.2576	+	37.6282i	1.75620	+	1.19590i
$991$	2.46413	−	4.26799i	0.0782755	−	0.135577i	−0.824230	−	0.566254i	$-0.808392\pi$
$991$	2.46413	−	4.26799i	0.0782755	−	0.135577i	0.902506	+	0.430677i	$0.141725\pi$
$992$	−3.47509	−	6.01903i	−0.110334	−	0.191104i
$993$	27.0769	−	10.0555i	0.859259	−	0.319101i
$994$	−8.64897	−	2.31748i	−0.274329	−	0.0735061i
$995$	28.0433	+	7.51418i	0.889033	+	0.238216i
$996$	−4.27996	+	1.58944i	−0.135616	+	0.0503633i
$997$	−15.6483	−	27.1036i	−0.495586	−	0.858379i	0.504401	−	0.863469i	$-0.331713\pi$
$997$	−15.6483	−	27.1036i	−0.495586	−	0.858379i	−0.999987	+	0.00508984i	$0.998380\pi$
$998$	−8.84294	+	15.3164i	−0.279918	+	0.484833i
$999$	−21.9534	−	36.3637i	−0.694574	−	1.15050i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.a.71.6	✓	56
3.2	odd	2		546.2.bu.b.71.11	yes	56
13.11	odd	12		546.2.bu.b.323.11	yes	56
39.11	even	12	inner	546.2.bu.a.323.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.71.6	✓	56	1.1	even	1	trivial
546.2.bu.a.323.6	yes	56	39.11	even	12	inner
546.2.bu.b.71.11	yes	56	3.2	odd	2
546.2.bu.b.323.11	yes	56	13.11	odd	12

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(1.41231 - 1.00269i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.61115 + 2.61115i) q^{5} +(-1.10467 + 1.33405i) q^{6} +(0.258819 - 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.989233 - 2.83221i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(1.41231 - 1.00269i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.61115 + 2.61115i) q^{5} +(-1.10467 + 1.33405i) q^{6} +(0.258819 - 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.989233 - 2.83221i) q^{9} +(-3.19799 - 1.84636i) q^{10} +(-1.56188 - 5.82901i) q^{11} +(0.721751 - 1.57451i) q^{12} +(1.58952 - 3.23627i) q^{13} +1.00000i q^{14} +(6.30592 + 1.06958i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.62806 + 2.81989i) q^{17} +(-0.222496 + 2.99174i) q^{18} +(-2.15510 - 0.577458i) q^{19} +(3.56689 + 0.955747i) q^{20} +(-0.602990 - 1.62370i) q^{21} +(3.01732 + 5.22615i) q^{22} +(-1.52364 + 2.63902i) q^{23} +(-0.289646 + 1.70766i) q^{24} +8.63619i q^{25} +(-0.697753 + 3.53739i) q^{26} +(-1.44272 - 4.99185i) q^{27} +(-0.258819 - 0.965926i) q^{28} +(6.11415 + 3.53000i) q^{29} +(-6.36787 + 0.598955i) q^{30} +(-4.91451 + 4.91451i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-8.05053 - 6.66628i) q^{33} +(-2.30243 - 2.30243i) q^{34} +(3.19799 - 1.84636i) q^{35} +(-0.559404 - 2.94738i) q^{36} +(7.89610 - 2.11575i) q^{37} +2.23113 q^{38} +(-1.00007 - 6.16440i) q^{39} -3.69272 q^{40} +(-4.19703 + 1.12459i) q^{41} +(1.00269 + 1.41231i) q^{42} +(6.69807 - 3.86713i) q^{43} +(-4.26713 - 4.26713i) q^{44} +(9.97836 - 4.81229i) q^{45} +(0.788694 - 2.94345i) q^{46} +(-6.62677 + 6.62677i) q^{47} +(-0.162199 - 1.72444i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(-2.23521 - 8.34192i) q^{50} +(5.12680 + 2.35011i) q^{51} +(-0.241567 - 3.59745i) q^{52} +4.59708i q^{53} +(2.68555 + 4.44835i) q^{54} +(11.1421 - 19.2987i) q^{55} +(0.500000 + 0.866025i) q^{56} +(-3.62268 + 1.34535i) q^{57} +(-6.81944 - 1.82726i) q^{58} +(-8.67455 - 2.32434i) q^{59} +(5.99587 - 2.22667i) q^{60} +(3.42268 + 5.92825i) q^{61} +(3.47509 - 6.01903i) q^{62} +(-2.47967 - 1.68856i) q^{63} -1.00000i q^{64} +(12.6008 - 4.29989i) q^{65} +(9.50158 + 4.35551i) q^{66} +(0.149573 + 0.558215i) q^{67} +(2.81989 + 1.62806i) q^{68} +(0.494265 + 5.25485i) q^{69} +(-2.61115 + 2.61115i) q^{70} +(-2.31748 + 8.64897i) q^{71} +(1.30318 + 2.70217i) q^{72} +(-0.971299 - 0.971299i) q^{73} +(-7.07945 + 4.08732i) q^{74} +(8.65940 + 12.1970i) q^{75} +(-2.15510 + 0.577458i) q^{76} -6.03463 q^{77} +(2.56146 + 5.69552i) q^{78} -4.53007 q^{79} +(3.56689 - 0.955747i) q^{80} +(-7.04284 - 5.60343i) q^{81} +(3.76296 - 2.17254i) q^{82} +(-1.86388 - 1.86388i) q^{83} +(-1.33405 - 1.10467i) q^{84} +(-3.11203 + 11.6143i) q^{85} +(-5.46895 + 5.46895i) q^{86} +(12.1746 - 1.14513i) q^{87} +(5.22615 + 3.01732i) q^{88} +(1.68996 + 6.30702i) q^{89} +(-8.39284 + 7.23090i) q^{90} +(-2.71459 - 2.37297i) q^{91} +3.04728i q^{92} +(-2.01309 + 11.8685i) q^{93} +(4.68583 - 8.11610i) q^{94} +(-4.11946 - 7.13512i) q^{95} +(0.602990 + 1.62370i) q^{96} +(-3.38977 - 0.908285i) q^{97} +(0.965926 + 0.258819i) q^{98} +(-18.0540 - 1.34268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) \) 56 * q - 8 * q^6 + 24 * q^9	\( 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) \) 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Introduction

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