LMFDB - Embedded newform 546.2.bu.b.323.11

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			323.11
Character	$\chi$	$=$	546.323
Dual form			546.2.bu.b.71.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(0.162199 + 1.72444i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.61115 + 2.61115i) q^{5} +(-0.289646 + 1.70766i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.94738 + 0.559404i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(0.162199 + 1.72444i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.61115 + 2.61115i) q^{5} +(-0.289646 + 1.70766i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.94738 + 0.559404i) 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} +(-4.92629 - 4.07924i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.62806 + 2.81989i) q^{17} +(-2.99174 - 0.222496i) q^{18} +(-2.15510 + 0.577458i) q^{19} +(-3.56689 + 0.955747i) q^{20} +(-1.62370 + 0.602990i) q^{21} +(3.01732 - 5.22615i) q^{22} +(1.52364 + 2.63902i) q^{23} +(-1.10467 + 1.33405i) 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} +(-3.70265 - 5.21526i) q^{30} +(-4.91451 - 4.91451i) q^{31} +(0.258819 + 0.965926i) q^{32} +(10.3051 + 1.74791i) q^{33} +(-2.30243 + 2.30243i) q^{34} +(-3.19799 - 1.84636i) q^{35} +(-2.83221 - 0.989233i) q^{36} +(7.89610 + 2.11575i) q^{37} -2.23113 q^{38} +(-5.32293 + 3.26595i) q^{39} -3.69272 q^{40} +(4.19703 + 1.12459i) q^{41} +(-1.72444 + 0.162199i) q^{42} +(6.69807 + 3.86713i) q^{43} +(4.26713 - 4.26713i) q^{44} +(6.23537 - 9.15674i) q^{45} +(0.788694 + 2.94345i) q^{46} +(6.62677 + 6.62677i) q^{47} +(-1.41231 + 1.00269i) 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} +(-0.101576 - 5.19516i) q^{54} +(11.1421 + 19.2987i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-1.34535 - 3.62268i) q^{57} +(-6.81944 + 1.82726i) q^{58} +(8.67455 - 2.32434i) q^{59} +(-2.22667 - 5.99587i) q^{60} +(3.42268 - 5.92825i) q^{61} +(-3.47509 - 6.01903i) q^{62} +(-1.30318 - 2.70217i) 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} +(-4.30370 + 3.05547i) q^{69} +(-2.61115 - 2.61115i) q^{70} +(2.31748 + 8.64897i) q^{71} +(-2.47967 - 1.68856i) q^{72} +(-0.971299 + 0.971299i) q^{73} +(7.07945 + 4.08732i) q^{74} +(14.8926 - 1.40078i) q^{75} +(-2.15510 - 0.577458i) q^{76} +6.03463 q^{77} +(-5.98684 + 1.77699i) q^{78} -4.53007 q^{79} +(-3.56689 - 0.955747i) q^{80} +(8.37413 - 3.29756i) q^{81} +(3.76296 + 2.17254i) q^{82} +(1.86388 - 1.86388i) q^{83} +(-1.70766 - 0.289646i) q^{84} +(-3.11203 - 11.6143i) q^{85} +(5.46895 + 5.46895i) q^{86} +(-7.07898 - 9.97091i) 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} +(7.67765 - 9.27191i) q^{93} +(4.68583 + 8.11610i) q^{94} +(4.11946 - 7.13512i) q^{95} +(-1.62370 + 0.602990i) q^{96} +(-3.38977 + 0.908285i) q^{97} +(-0.965926 + 0.258819i) q^{98} +(-1.34268 + 18.0540i) 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^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 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} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 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^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 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 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{12}\right)$

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
$3$	0.162199	+	1.72444i	0.0936456	+	0.995606i
$3$	0.162199	+	1.72444i	0.0936456	+	0.995606i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−2.61115	+	2.61115i	−1.16774	+	1.16774i	−0.185003	+	0.982738i	$0.559229\pi$
$5$	−2.61115	+	2.61115i	−1.16774	+	1.16774i	−0.982738	+	0.185003i	$0.940771\pi$
$6$	−0.289646	+	1.70766i	−0.118247	+	0.697150i
$7$	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
$9$	−2.94738	+	0.559404i	−0.982461	+	0.186468i
$10$	−3.19799	+	1.84636i	−1.01129	+	0.583870i
$11$	1.56188	−	5.82901i	0.470924	−	1.75751i	−0.165537	−	0.986204i	$-0.552936\pi$
$11$	1.56188	−	5.82901i	0.470924	−	1.75751i	0.636461	−	0.771309i	$-0.280398\pi$
$12$	−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
$15$	−4.92629	−	4.07924i	−1.27196	−	1.05326i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.62806	+	2.81989i	−0.394863	+	0.683923i	−0.993084	−	0.117408i	$-0.962541\pi$
$17$	−1.62806	+	2.81989i	−0.394863	+	0.683923i	0.598220	+	0.801332i	$0.295875\pi$
$18$	−2.99174	−	0.222496i	−0.705159	−	0.0524428i
$19$	−2.15510	+	0.577458i	−0.494415	+	0.132478i	−0.497407	−	0.867518i	$-0.665714\pi$
$19$	−2.15510	+	0.577458i	−0.494415	+	0.132478i	0.00299203	+	0.999996i	$0.499048\pi$
$20$	−3.56689	+	0.955747i	−0.797582	+	0.213711i
$21$	−1.62370	+	0.602990i	−0.354320	+	0.131583i
$22$	3.01732	−	5.22615i	0.643294	−	1.11422i
$23$	1.52364	+	2.63902i	0.317701	+	0.550274i	0.980008	−	0.198958i	$-0.0637559\pi$
$23$	1.52364	+	2.63902i	0.317701	+	0.550274i	−0.662307	+	0.749233i	$0.730423\pi$
$24$	−1.10467	+	1.33405i	−0.225490	+	0.272313i
$25$		−	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	$-0.894211\pi$
$29$	−6.11415	+	3.53000i	−1.13537	+	0.655505i	−0.190089	+	0.981767i	$0.560878\pi$
$30$	−3.70265	−	5.21526i	−0.676008	−	0.952172i
$31$	−4.91451	−	4.91451i	−0.882673	−	0.882673i	0.111133	−	0.993806i	$-0.464552\pi$
$31$	−4.91451	−	4.91451i	−0.882673	−	0.882673i	−0.993806	+	0.111133i	$0.964552\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	10.3051	+	1.74791i	1.79389	+	0.304271i
$34$	−2.30243	+	2.30243i	−0.394863	+	0.394863i
$35$	−3.19799	−	1.84636i	−0.540559	−	0.312092i
$36$	−2.83221	−	0.989233i	−0.472035	−	0.164872i
$37$	7.89610	+	2.11575i	1.29811	+	0.347828i	0.840735	−	0.541446i	$-0.182123\pi$
$37$	7.89610	+	2.11575i	1.29811	+	0.347828i	0.457375	+	0.889274i	$0.348790\pi$
$38$	−2.23113			−0.361937
$39$	−5.32293	+	3.26595i	−0.852350	+	0.522971i
$40$	−3.69272			−0.583870
$41$	4.19703	+	1.12459i	0.655466	+	0.175632i	0.571199	−	0.820811i	$-0.306478\pi$
$41$	4.19703	+	1.12459i	0.655466	+	0.175632i	0.0842672	+	0.996443i	$0.473145\pi$
$42$	−1.72444	+	0.162199i	−0.266087	+	0.0250278i
$43$	6.69807	+	3.86713i	1.02145	+	0.589732i	0.914522	−	0.404536i	$-0.132567\pi$
$43$	6.69807	+	3.86713i	1.02145	+	0.589732i	0.106923	+	0.994267i	$0.465900\pi$
$44$	4.26713	−	4.26713i	0.643294	−	0.643294i
$45$	6.23537	−	9.15674i	0.929514	−	1.36501i
$46$	0.788694	+	2.94345i	0.116287	+	0.433988i
$47$	6.62677	+	6.62677i	0.966614	+	0.966614i	0.999460	−	0.0328467i	$-0.0104573\pi$
$47$	6.62677	+	6.62677i	0.966614	+	0.966614i	−0.0328467	+	0.999460i	$0.510457\pi$
$48$	−1.41231	+	1.00269i	−0.203849	+	0.144726i
$49$	−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	$0.897751\pi$
$54$	−0.101576	−	5.19516i	−0.0138227	−	0.706972i
$55$	11.1421	+	19.2987i	1.50240	+	2.60224i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$	−1.34535	−	3.62268i	−0.178196	−	0.479836i
$58$	−6.81944	+	1.82726i	−0.895437	+	0.239932i
$59$	8.67455	−	2.32434i	1.12933	−	0.302603i	0.354677	−	0.934989i	$-0.384591\pi$
$59$	8.67455	−	2.32434i	1.12933	−	0.302603i	0.774653	+	0.632386i	$0.217924\pi$
$60$	−2.22667	−	5.99587i	−0.287462	−	0.774064i
$61$	3.42268	−	5.92825i	0.438229	−	0.759034i	−0.559324	−	0.828949i	$-0.688939\pi$
$61$	3.42268	−	5.92825i	0.438229	−	0.759034i	0.997553	+	0.0699146i	$0.0222727\pi$
$62$	−3.47509	−	6.01903i	−0.441336	−	0.764417i
$63$	−1.30318	−	2.70217i	−0.164185	−	0.340441i
$64$			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	−0.956187	−	0.292756i	$-0.905428\pi$
$67$	0.149573	−	0.558215i	0.0182733	−	0.0681968i	0.974460	+	0.224559i	$0.0720943\pi$
$68$	−2.81989	+	1.62806i	−0.341962	+	0.197432i
$69$	−4.30370	+	3.05547i	−0.518105	+	0.367836i
$70$	−2.61115	−	2.61115i	−0.312092	−	0.312092i
$71$	2.31748	+	8.64897i	0.275035	+	1.02644i	0.955818	+	0.293959i	$0.0949728\pi$
$71$	2.31748	+	8.64897i	0.275035	+	1.02644i	−0.680783	+	0.732485i	$0.738361\pi$
$72$	−2.47967	−	1.68856i	−0.292232	−	0.198998i
$73$	−0.971299	+	0.971299i	−0.113682	+	0.113682i	−0.761659	−	0.647978i	$-0.775615\pi$
$73$	−0.971299	+	0.971299i	−0.113682	+	0.113682i	0.647978	+	0.761659i	$0.275615\pi$
$74$	7.07945	+	4.08732i	0.822969	+	0.475141i
$75$	14.8926	−	1.40078i	1.71965	−	0.161748i
$76$	−2.15510	−	0.577458i	−0.247207	−	0.0662390i
$77$	6.03463			0.687710
$78$	−5.98684	+	1.77699i	−0.677877	+	0.201205i
$79$	−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
$81$	8.37413	−	3.29756i	0.930459	−	0.366395i
$82$	3.76296	+	2.17254i	0.415549	+	0.239917i
$83$	1.86388	−	1.86388i	0.204588	−	0.204588i	−0.597375	−	0.801962i	$-0.703789\pi$
$83$	1.86388	−	1.86388i	0.204588	−	0.204588i	0.801962	+	0.597375i	$0.203789\pi$
$84$	−1.70766	−	0.289646i	−0.186321	−	0.0316029i
$85$	−3.11203	−	11.6143i	−0.337547	−	1.25974i
$86$	5.46895	+	5.46895i	0.589732	+	0.589732i
$87$	−7.07898	−	9.97091i	−0.758947	−	1.06899i
$88$	5.22615	−	3.01732i	0.557109	−	0.321647i
$89$	−1.68996	+	6.30702i	−0.179136	+	0.668543i	0.816675	+	0.577098i	$0.195815\pi$
$89$	−1.68996	+	6.30702i	−0.179136	+	0.668543i	−0.995810	+	0.0914447i	$0.970852\pi$
$90$	8.39284	−	7.23090i	0.884683	−	0.762204i
$91$	−2.71459	+	2.37297i	−0.284567	+	0.248755i
$92$			3.04728i			0.317701i
$93$	7.67765	−	9.27191i	0.796136	−	0.961453i
$94$	4.68583	+	8.11610i	0.483307	+	0.837112i
$95$	4.11946	−	7.13512i	0.422648	−	0.732048i
$96$	−1.62370	+	0.602990i	−0.165718	+	0.0615424i
$97$	−3.38977	+	0.908285i	−0.344179	+	0.0922224i	−0.426768	−	0.904361i	$-0.640348\pi$
$97$	−3.38977	+	0.908285i	−0.344179	+	0.0922224i	0.0825890	+	0.996584i	$0.473681\pi$
$98$	−0.965926	+	0.258819i	−0.0975732	+	0.0261447i
$99$	−1.34268	+	18.0540i	−0.134945	+	1.81450i
$100$	4.31809	−	7.47916i	0.431809	−	0.747916i
$101$	−3.96010	−	6.85910i	−0.394045	−	0.682506i	0.598934	−	0.800799i	$-0.295591\pi$
$101$	−3.96010	−	6.85910i	−0.394045	−	0.682506i	−0.992979	+	0.118293i	$0.962258\pi$
$102$	−4.34385	−	3.59695i	−0.430105	−	0.356151i
$103$		−	0.941362i		−	0.0927551i	−0.998924	−	0.0463776i	$-0.985232\pi$
$103$		−	0.941362i		−	0.0927551i	0.998924	−	0.0463776i	$-0.0147677\pi$
$104$	−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	$-0.593421\pi$
$107$	4.08645	−	2.35931i	0.395052	−	0.228083i	0.684347	+	0.729157i	$0.260088\pi$
$108$	1.24649	−	5.04443i	0.119944	−	0.485400i
$109$	12.4573	+	12.4573i	1.19319	+	1.19319i	0.976166	+	0.217027i	$0.0696361\pi$
$109$	12.4573	+	12.4573i	1.19319	+	1.19319i	0.217027	+	0.976166i	$0.430364\pi$
$110$	5.76758	+	21.5249i	0.549917	+	2.05232i
$111$	−2.36775	+	13.9595i	−0.224737	+	1.32498i
$112$	−0.707107	+	0.707107i	−0.0668153	+	0.0668153i
$113$	−4.05949	−	2.34374i	−0.381884	−	0.220481i	0.296754	−	0.954954i	$-0.404096\pi$
$113$	−4.05949	−	2.34374i	−0.381884	−	0.220481i	−0.678638	+	0.734473i	$0.737429\pi$
$114$	−0.361886	−	3.84744i	−0.0338938	−	0.360346i
$115$	−10.8693	−	2.91243i	−1.01357	−	0.271585i
$116$	−7.06001			−0.655505
$117$	−6.49531	−	8.64933i	−0.600492	−	0.799631i
$118$	8.98055			0.826727
$119$	−3.14518	−	0.842748i	−0.288318	−	0.0772545i
$120$	−0.598955	−	6.36787i	−0.0546769	−	0.581305i
$121$	−22.0116	−	12.7084i	−2.00105	−	1.15531i
$122$	4.84039	−	4.84039i	0.438229	−	0.438229i
$123$	−1.25854	+	7.41994i	−0.113478	+	0.669033i
$124$	−1.79884	−	6.71335i	−0.161540	−	0.602877i
$125$	9.49463	+	9.49463i	0.849226	+	0.849226i
$126$	−0.559404	−	2.94738i	−0.0498357	−	0.262574i
$127$	−4.17960	+	2.41310i	−0.370880	+	0.214128i	−0.673843	−	0.738875i	$-0.735358\pi$
$127$	−4.17960	+	2.41310i	−0.370880	+	0.214128i	0.302963	+	0.953002i	$0.402024\pi$
$128$	−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	$0.813084\pi$
$132$	8.05053	+	6.66628i	0.700709	+	0.580226i
$133$	−1.11556	−	1.93221i	−0.0967316	−	0.167544i
$134$	0.288953	−	0.500482i	0.0249618	−	0.0432350i
$135$	16.8016	+	9.26730i	1.44605	+	0.797602i
$136$	−3.14518	+	0.842748i	−0.269697	+	0.0722650i
$137$	16.4843	−	4.41694i	1.40835	−	0.377365i	0.527011	−	0.849858i	$-0.323313\pi$
$137$	16.4843	−	4.41694i	1.40835	−	0.377365i	0.881334	+	0.472493i	$0.156646\pi$
$138$	−4.94787	+	1.83748i	−0.421191	+	0.156417i
$139$	6.28943	−	10.8936i	0.533462	−	0.923984i	−0.465774	−	0.884904i	$-0.654224\pi$
$139$	6.28943	−	10.8936i	0.533462	−	0.923984i	0.999236	−	0.0390801i	$-0.0124427\pi$
$140$	−1.84636	−	3.19799i	−0.156046	−	0.270280i
$141$	−10.3526	+	12.5023i	−0.871847	+	1.05289i
$142$			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
$147$	−1.00269	−	1.41231i	−0.0827003	−	0.116485i
$148$	5.78034	+	5.78034i	0.475141	+	0.475141i
$149$	−2.75005	−	10.2633i	−0.225293	−	0.840805i	−0.982287	−	0.187383i	$-0.939999\pi$
$149$	−2.75005	−	10.2633i	−0.225293	−	0.840805i	0.756994	−	0.653422i	$-0.226667\pi$
$150$	14.7477	+	2.50144i	1.20414	+	0.204241i
$151$	14.0155	−	14.0155i	1.14056	−	1.14056i	0.152215	−	0.988347i	$-0.451359\pi$
$151$	14.0155	−	14.0155i	1.14056	−	1.14056i	0.988347	−	0.152215i	$-0.0486408\pi$
$152$	−1.93221	−	1.11556i	−0.156723	−	0.0904841i
$153$	3.22107	−	9.22204i	0.260408	−	0.745557i
$154$	5.82901	+	1.56188i	0.469715	+	0.125860i
$155$	25.6651			2.06147
$156$	−6.24277	+	0.166935i	−0.499821	+	0.0133655i
$157$	−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
$159$	−7.92739	+	0.745642i	−0.628683	+	0.0591333i
$160$	−3.19799	−	1.84636i	−0.252823	−	0.145968i
$161$	−2.15475	+	2.15475i	−0.169818	+	0.169818i
$162$	8.94226	−	1.01781i	0.702571	−	0.0799668i
$163$	−3.63359	−	13.5607i	−0.284605	−	1.06216i	−0.949128	−	0.314892i	$-0.898032\pi$
$163$	−3.63359	−	13.5607i	−0.284605	−	1.06216i	0.664523	−	0.747268i	$-0.268635\pi$
$164$	3.07244	+	3.07244i	0.239917	+	0.239917i
$165$	−31.4722	+	22.3441i	−2.45011	+	1.73949i
$166$	2.28278	−	1.31797i	0.177178	−	0.102294i
$167$	−2.36296	+	8.81869i	−0.182851	+	0.682411i	0.812229	+	0.583339i	$0.198254\pi$
$167$	−2.36296	+	8.81869i	−0.182851	+	0.682411i	−0.995080	+	0.0990718i	$0.968413\pi$
$168$	−1.57451	−	0.721751i	−0.121476	−	0.0556843i
$169$	−7.94684	+	10.2882i	−0.611295	+	0.791403i
$170$		−	12.0240i		−	0.922196i
$171$	6.02888	−	2.90756i	0.461040	−	0.222347i
$172$	3.86713	+	6.69807i	0.294866	+	0.510723i
$173$	9.16123	−	15.8677i	0.696515	−	1.20640i	−0.273152	−	0.961971i	$-0.588066\pi$
$173$	9.16123	−	15.8677i	0.696515	−	1.20640i	0.969667	−	0.244429i	$-0.0786004\pi$
$174$	−4.25711	−	11.4633i	−0.322731	−	0.869033i
$175$	8.34192	−	2.23521i	0.630590	−	0.168966i
$176$	5.82901	−	1.56188i	0.439378	−	0.117731i
$177$	5.41518	+	14.5817i	0.407030	+	1.09603i
$178$	−3.26476	+	5.65472i	−0.244704	+	0.423839i
$179$	−8.00281	−	13.8613i	−0.598158	−	1.03604i	−0.993093	−	0.117331i	$-0.962566\pi$
$179$	−8.00281	−	13.8613i	−0.598158	−	1.03604i	0.394935	−	0.918709i	$-0.370767\pi$
$180$	9.97836	−	4.81229i	0.743743	−	0.358687i
$181$		−	18.1748i		−	1.35092i	−0.737395	−	0.675462i	$-0.763944\pi$
$181$		−	18.1748i		−	1.35092i	0.737395	−	0.675462i	$-0.236056\pi$
$182$	−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
$186$	9.81579	−	6.96886i	0.719729	−	0.510981i
$187$	13.8943	+	13.8943i	1.01605	+	1.01605i
$188$	2.42557	+	9.05234i	0.176903	+	0.660209i
$189$	4.44835	−	2.68555i	0.323570	−	0.195345i
$190$	5.82580	−	5.82580i	0.422648	−	0.422648i
$191$	1.65834	+	0.957440i	0.119993	+	0.0692780i	0.558795	−	0.829306i	$-0.311264\pi$
$191$	1.65834	+	0.957440i	0.119993	+	0.0692780i	−0.438802	+	0.898584i	$0.644597\pi$
$192$	−1.72444	+	0.162199i	−0.124451	+	0.0117057i
$193$	−10.9448	−	2.93266i	−0.787826	−	0.211097i	−0.157594	−	0.987504i	$-0.550374\pi$
$193$	−10.9448	−	2.93266i	−0.787826	−	0.211097i	−0.630232	+	0.776407i	$0.717040\pi$
$194$	−3.50934			−0.251956
$195$	5.37106	−	22.4268i	0.384630	−	1.60602i
$196$	−1.00000			−0.0714286
$197$	6.81911	+	1.82717i	0.485841	+	0.130181i	0.493421	−	0.869790i	$-0.335746\pi$
$197$	6.81911	+	1.82717i	0.485841	+	0.130181i	−0.00757989	+	0.999971i	$0.502413\pi$
$198$	−5.96966	+	17.0914i	−0.424245	+	1.21463i
$199$	6.80879	+	3.93106i	0.482662	+	0.278665i	0.721525	−	0.692388i	$-0.243441\pi$
$199$	6.80879	+	3.93106i	0.482662	+	0.278665i	−0.238863	+	0.971053i	$0.576775\pi$
$200$	6.10671	−	6.10671i	0.431809	−	0.431809i
$201$	0.986868	+	0.167388i	0.0696083	+	0.0118066i
$202$	−2.04990	−	7.65033i	−0.144231	−	0.538276i
$203$	−4.99218	−	4.99218i	−0.350382	−	0.350382i
$204$	−3.26488	−	4.59866i	−0.228587	−	0.321970i
$205$	−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
$210$	4.07924	−	4.92629i	0.281494	−	0.339946i
$211$	−1.63268	−	2.82788i	−0.112398	−	0.194679i	0.804339	−	0.594171i	$-0.202520\pi$
$211$	−1.63268	−	2.82788i	−0.112398	−	0.194679i	−0.916737	+	0.399492i	$0.869186\pi$
$212$	−2.29854	+	3.98119i	−0.157865	+	0.273429i
$213$	−14.5387	+	5.39921i	−0.996177	+	0.369948i
$214$	4.55784	−	1.22127i	0.311567	−	0.0834842i
$215$	−27.5873	+	7.39199i	−1.88144	+	0.504130i
$216$	2.50961	−	4.54993i	0.170757	−	0.309583i
$217$	3.47509	−	6.01903i	0.235904	−	0.408598i
$218$	8.80864	+	15.2570i	0.596596	+	1.03334i
$219$	−1.83249	−	1.51740i	−0.123828	−	0.102537i
$220$			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	0.662588	+	0.748984i	$0.269458\pi$
$223$	−4.26674	+	15.9237i	−0.285722	+	1.06633i	−0.948310	+	0.317345i	$0.897209\pi$
$224$	−0.866025	+	0.500000i	−0.0578638	+	0.0334077i
$225$	4.83112	+	25.4542i	0.322075	+	1.69694i
$226$	−3.31456	−	3.31456i	−0.220481	−	0.220481i
$227$	−3.25048	−	12.1310i	−0.215742	−	0.805160i	−0.985904	−	0.167312i	$-0.946491\pi$
$227$	−3.25048	−	12.1310i	−0.215742	−	0.805160i	0.770162	−	0.637848i	$-0.220175\pi$
$228$	0.646236	−	3.81001i	0.0427980	−	0.252324i
$229$	1.81709	−	1.81709i	0.120077	−	0.120077i	−0.644515	−	0.764592i	$-0.722941\pi$
$229$	1.81709	−	1.81709i	0.120077	−	0.120077i	0.764592	+	0.644515i	$0.222941\pi$
$230$	−9.74517	−	5.62638i	−0.642578	−	0.370992i
$231$	0.978811	+	10.4064i	0.0644010	+	0.684688i
$232$	−6.81944	−	1.82726i	−0.447718	−	0.119966i
$233$	−11.6743			−0.764807			−0.382403	−	0.923995i	$-0.624904\pi$
$233$	−11.6743			−0.764807			−0.382403	+	0.923995i	$0.624904\pi$
$234$	−4.03538	−	10.0357i	−0.263801	−	0.656056i
$235$	−34.6070			−2.25751
$236$	8.67455	+	2.32434i	0.564665	+	0.151302i
$237$	−0.734771	−	7.81182i	−0.0477285	−	0.507432i
$238$	−2.81989	−	1.62806i	−0.182786	−	0.105532i
$239$	6.93024	−	6.93024i	0.448280	−	0.448280i	−0.446503	−	0.894782i	$-0.647331\pi$
$239$	6.93024	−	6.93024i	0.448280	−	0.448280i	0.894782	+	0.446503i	$0.147331\pi$
$240$	1.06958	−	6.30592i	0.0690411	−	0.407045i
$241$	−5.32635	−	19.8782i	−0.343100	−	1.28047i	−0.894816	−	0.446436i	$-0.852693\pi$
$241$	−5.32635	−	19.8782i	−0.343100	−	1.28047i	0.551715	−	0.834032i	$-0.313973\pi$
$242$	−17.9724	−	17.9724i	−1.15531	−	1.15531i
$243$	7.04471	+	13.9058i	0.451919	+	0.892059i
$244$	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
$249$	3.51648	+	2.91184i	0.222848	+	0.184530i
$250$	6.71372	+	11.6285i	0.424613	+	0.735451i
$251$	1.76209	−	3.05204i	0.111222	−	0.192643i	−0.805041	−	0.593219i	$-0.797857\pi$
$251$	1.76209	−	3.05204i	0.111222	−	0.192643i	0.916263	+	0.400576i	$0.131190\pi$
$252$	0.222496	−	2.99174i	0.0140159	−	0.188462i
$253$	17.7626	−	4.75948i	1.11673	−	0.299226i
$254$	−4.66174	+	1.24911i	−0.292504	+	0.0783761i
$255$	19.5233	−	7.25033i	1.22260	−	0.454033i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.50103	+	14.7242i	0.530279	+	0.918471i	0.999376	+	0.0353239i	$0.0112463\pi$
$257$	8.50103	+	14.7242i	0.530279	+	0.918471i	−0.469097	+	0.883147i	$0.655420\pi$
$258$	−8.54381	+	10.3179i	−0.531915	+	0.642366i
$259$			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	$-0.798023\pi$
$263$	−11.2653	+	6.50402i	−0.694647	+	0.401055i	0.110703	+	0.993854i	$0.464690\pi$
$264$	6.05086	+	8.52277i	0.372404	+	0.524540i
$265$	−12.0037	−	12.0037i	−0.737380	−	0.737380i
$266$	−0.577458	−	2.15510i	−0.0354062	−	0.132138i
$267$	−11.1502	−	1.89124i	−0.682381	−	0.115742i
$268$	0.408642	−	0.408642i	0.0249618	−	0.0249618i
$269$	−4.30147	−	2.48345i	−0.262265	−	0.151419i	0.363102	−	0.931749i	$-0.381718\pi$
$269$	−4.30147	−	2.48345i	−0.262265	−	0.151419i	−0.625367	+	0.780330i	$0.715051\pi$
$270$	13.8306	+	13.3001i	0.841701	+	0.809418i
$271$	23.3606	+	6.25946i	1.41906	+	0.380235i	0.885149	−	0.465307i	$-0.154056\pi$
$271$	23.3606	+	6.25946i	1.41906	+	0.380235i	0.533908	+	0.845543i	$0.320723\pi$
$272$	−3.25613			−0.197432
$273$	−4.53234	−	4.29626i	−0.274310	−	0.260022i
$274$	17.0658			1.03098
$275$	−50.3404	−	13.4887i	−3.03564	−	0.813398i
$276$	−5.25485	+	0.494265i	−0.316305	+	0.0297513i
$277$	11.7309	+	6.77285i	0.704843	+	0.406941i	0.809149	−	0.587604i	$-0.199929\pi$
$277$	11.7309	+	6.77285i	0.704843	+	0.406941i	−0.104306	+	0.994545i	$0.533262\pi$
$278$	8.89460	−	8.89460i	0.533462	−	0.533462i
$279$	17.2342	+	11.7358i	1.03178	+	0.702601i
$280$	−0.955747	−	3.56689i	−0.0571168	−	0.213163i
$281$	−6.47917	−	6.47917i	−0.386515	−	0.386515i	0.486927	−	0.873442i	$-0.338118\pi$
$281$	−6.47917	−	6.47917i	−0.386515	−	0.386515i	−0.873442	+	0.486927i	$0.838118\pi$
$282$	−13.2357	+	9.39686i	−0.788174	+	0.559575i
$283$	12.7025	−	7.33380i	0.755086	−	0.435949i	−0.0724426	−	0.997373i	$-0.523079\pi$
$283$	12.7025	−	7.33380i	0.755086	−	0.435949i	0.827529	+	0.561423i	$0.189746\pi$
$284$	−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
$288$	−1.30318	−	2.70217i	−0.0767907	−	0.159227i
$289$	3.19882	+	5.54052i	0.188166	+	0.325913i
$290$	13.0353	−	22.5778i	0.765460	−	1.32582i
$291$	−2.11610	−	5.69812i	−0.124048	−	0.334030i
$292$	−1.32682	+	0.355520i	−0.0776462	+	0.0208052i
$293$	23.5327	−	6.30557i	1.37479	−	0.368375i	0.505567	−	0.862787i	$-0.331283\pi$
$293$	23.5327	−	6.30557i	1.37479	−	0.368375i	0.869228	+	0.494412i	$0.164617\pi$
$294$	−0.602990	−	1.62370i	−0.0351671	−	0.0946961i
$295$	−16.5813	+	28.7197i	−0.965403	+	1.67213i
$296$	4.08732	+	7.07945i	0.237571	+	0.411485i
$297$	−31.3509	+	0.612974i	−1.81916	+	0.0355683i
$298$		−	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
$303$	11.1858	−	7.94150i	0.642606	−	0.456227i
$304$	−1.57764	−	1.57764i	−0.0904841	−	0.0904841i
$305$	6.54242	+	24.4166i	0.374618	+	1.39809i
$306$	5.49815	−	8.07413i	0.314308	−	0.461567i
$307$	−18.4360	+	18.4360i	−1.05220	+	1.05220i	−0.0536403	+	0.998560i	$0.517082\pi$
$307$	−18.4360	+	18.4360i	−1.05220	+	1.05220i	−0.998560	+	0.0536403i	$0.982918\pi$
$308$	5.22615	+	3.01732i	0.297787	+	0.171928i
$309$	1.62332	−	0.152688i	0.0923475	−	0.00868611i
$310$	24.7905	+	6.64260i	1.40801	+	0.377275i
$311$	−3.28259			−0.186139			−0.0930693	−	0.995660i	$-0.529668\pi$
$311$	−3.28259			−0.186139			−0.0930693	+	0.995660i	$0.529668\pi$
$312$	−6.07326	−	1.45450i	−0.343830	−	0.0823449i
$313$	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
$315$	10.4586	+	3.65296i	0.589273	+	0.205821i
$316$	−3.92315	−	2.26503i	−0.220695	−	0.127418i
$317$	18.9895	−	18.9895i	1.06656	−	1.06656i	0.0689377	−	0.997621i	$-0.478039\pi$
$317$	18.9895	−	18.9895i	1.06656	−	1.06656i	0.997621	−	0.0689377i	$-0.0219610\pi$
$318$	−7.85026	−	1.33153i	−0.440221	−	0.0746683i
$319$	11.0269	+	41.1528i	0.617386	+	2.30412i
$320$	−2.61115	−	2.61115i	−0.145968	−	0.145968i
$321$	4.73131	+	6.66415i	0.264076	+	0.371957i
$322$	−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
$327$	−19.4613	+	23.5024i	−1.07621	+	1.29969i
$328$	2.17254	+	3.76296i	0.119959	+	0.207775i
$329$	−4.68583	+	8.11610i	−0.258338	+	0.447455i
$330$	−36.1829	+	13.4372i	−1.99180	+	0.739691i
$331$	16.1078	−	4.31607i	0.885365	−	0.237233i	0.212645	−	0.977130i	$-0.431792\pi$
$331$	16.1078	−	4.31607i	0.885365	−	0.237233i	0.672720	+	0.739897i	$0.265126\pi$
$332$	2.54611	−	0.682229i	0.139736	−	0.0374422i
$333$	−24.4564	−	1.81882i	−1.34020	−	0.0996709i
$334$	−4.56489	+	7.90662i	−0.249780	+	0.432631i
$335$	1.06702	+	1.84814i	0.0582977	+	0.100975i
$336$	−1.33405	−	1.10467i	−0.0727787	−	0.0602647i
$337$			25.8378i			1.40748i	0.710460	+	0.703738i	$0.248487\pi$
$337$			25.8378i			1.40748i	−0.710460	+	0.703738i	$0.751513\pi$
$338$	−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
$342$	6.57599	−	1.24810i	0.355589	−	0.0674896i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	2.00177	+	7.47072i	0.107928	+	0.402794i
$345$	3.25931	−	19.2159i	0.175475	−	1.03455i
$346$	12.9559	−	12.9559i	0.696515	−	0.696515i
$347$	−25.3125	−	14.6142i	−1.35885	−	0.784531i	−0.369379	−	0.929279i	$-0.620430\pi$
$347$	−25.3125	−	14.6142i	−1.35885	−	0.784531i	−0.989469	+	0.144748i	$0.953763\pi$
$348$	−1.14513	−	12.1746i	−0.0613852	−	0.652625i
$349$	−26.7787	−	7.17532i	−1.43343	−	0.384086i	−0.543201	−	0.839603i	$-0.682788\pi$
$349$	−26.7787	−	7.17532i	−1.43343	−	0.384086i	−0.890227	+	0.455517i	$0.849455\pi$
$350$	8.63619			0.461624
$351$	13.8617	−	12.6037i	0.739884	−	0.672735i
$352$	6.03463			0.321647
$353$	−16.7312	−	4.48311i	−0.890511	−	0.238612i	−0.215574	−	0.976487i	$-0.569162\pi$
$353$	−16.7312	−	4.48311i	−0.890511	−	0.238612i	−0.674937	+	0.737876i	$0.735829\pi$
$354$	1.45664	+	15.4864i	0.0774193	+	0.823094i
$355$	−28.6350	−	16.5324i	−1.51979	−	0.877451i
$356$	−4.61706	+	4.61706i	−0.244704	+	0.244704i
$357$	0.943123	−	5.56036i	0.0499154	−	0.294285i
$358$	−4.14256	−	15.4602i	−0.218941	−	0.817099i
$359$	9.10668	+	9.10668i	0.480632	+	0.480632i	0.905334	−	0.424701i	$-0.139621\pi$
$359$	9.10668	+	9.10668i	0.480632	+	0.480632i	−0.424701	+	0.905334i	$0.639621\pi$
$360$	10.8839	−	2.06572i	0.573630	−	0.108873i
$361$	−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
$366$	9.13207	+	7.56186i	0.477341	+	0.395265i
$367$	12.3426	+	21.3780i	0.644278	+	1.11592i	0.984468	+	0.175566i	$0.0561755\pi$
$367$	12.3426	+	21.3780i	0.644278	+	1.11592i	−0.340189	+	0.940357i	$0.610491\pi$
$368$	−1.52364	+	2.63902i	−0.0794252	+	0.137569i
$369$	−12.9994	−	0.966764i	−0.676720	−	0.0503277i
$370$	−29.1581	+	7.81289i	−1.51586	+	0.406173i
$371$	−4.44044	+	1.18981i	−0.230536	+	0.0617720i
$372$	11.2850	−	4.19088i	0.585100	−	0.217287i
$373$	−6.23279	+	10.7955i	−0.322722	+	0.558971i	−0.981049	−	0.193762i	$-0.937931\pi$
$373$	−6.23279	+	10.7955i	−0.322722	+	0.558971i	0.658327	+	0.752732i	$0.271265\pi$
$374$	9.82477	+	17.0170i	0.508027	+	0.879928i
$375$	−14.8329	+	17.9129i	−0.765968	+	0.925020i
$376$			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	−0.382491	−	0.923959i	$-0.624934\pi$
$379$	7.99617	−	29.8421i	0.410736	−	1.53289i	0.793226	−	0.608927i	$-0.208400\pi$
$380$	7.13512	−	4.11946i	0.366024	−	0.211324i
$381$	−4.83916	−	6.81607i	−0.247918	−	0.349198i
$382$	1.35403	+	1.35403i	0.0692780	+	0.0692780i
$383$	0.0112438	+	0.0419624i	0.000574530	+	0.00214418i	0.966212	−	0.257747i	$-0.0829800\pi$
$383$	0.0112438	+	0.0419624i	0.000574530	+	0.00214418i	−0.965638	+	0.259891i	$0.916313\pi$
$384$	−1.70766	−	0.289646i	−0.0871437	−	0.0147809i
$385$	−15.7573	+	15.7573i	−0.803068	+	0.803068i
$386$	−9.81287	−	5.66546i	−0.499462	−	0.288364i
$387$	−21.9051	−	7.65099i	−1.11350	−	0.388922i
$388$	−3.38977	−	0.908285i	−0.172089	−	0.0461112i
$389$	15.0907			0.765127			0.382564	−	0.923929i	$-0.375041\pi$
$389$	15.0907			0.765127			0.382564	+	0.923929i	$0.375041\pi$
$390$	10.9925	−	20.2725i	0.556629	−	1.02654i
$391$	−9.92233			−0.501794
$392$	−0.965926	−	0.258819i	−0.0487866	−	0.0130723i
$393$	−21.8704	+	2.05711i	−1.10322	+	0.103767i
$394$	6.11385	+	3.52983i	0.308011	+	0.177830i
$395$	11.8287	−	11.8287i	0.595165	−	0.595165i
$396$	−10.1898	+	14.9639i	−0.512058	+	0.751965i
$397$	−6.94286	−	25.9111i	−0.348452	−	1.30044i	−0.888527	−	0.458824i	$-0.848271\pi$
$397$	−6.94286	−	25.9111i	−0.348452	−	1.30044i	0.540075	−	0.841617i	$-0.318396\pi$
$398$	5.55935	+	5.55935i	0.278665	+	0.278665i
$399$	3.15104	−	2.23712i	0.157749	−	0.111996i
$400$	7.47916	−	4.31809i	0.373958	−	0.215905i
$401$	2.29401	−	8.56138i	0.114558	−	0.427535i	−0.884696	−	0.466169i	$-0.845634\pi$
$401$	2.29401	−	8.56138i	0.114558	−	0.427535i	0.999253	+	0.0386339i	$0.0123006\pi$
$402$	0.909918	+	0.417105i	0.0453826	+	0.0208033i
$403$	8.09295	−	23.7164i	0.403139	−	1.18140i
$404$		−	7.92021i		−	0.394045i
$405$	−13.2557	+	30.4765i	−0.658681	+	1.51439i
$406$	−3.53000	−	6.11415i	−0.175191	−	0.303440i
$407$	24.6655	−	42.7219i	1.22262	−	2.11764i
$408$	−1.96341	−	5.28697i	−0.0972033	−	0.261744i
$409$	12.2740	−	3.28881i	0.606911	−	0.162621i	0.0577405	−	0.998332i	$-0.481610\pi$
$409$	12.2740	−	3.28881i	0.606911	−	0.162621i	0.549171	+	0.835710i	$0.314944\pi$
$410$	−15.4985	+	4.15280i	−0.765415	+	0.205092i
$411$	10.2905	+	27.7097i	0.507592	+	1.36682i
$412$	0.470681	−	0.815243i	0.0231888	−	0.0401641i
$413$	4.49028	+	7.77739i	0.220952	+	0.382700i
$414$	−3.97116	−	8.23427i	−0.195172	−	0.404692i
$415$			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	$-0.662789\pi$
$419$	0.431886	−	0.249350i	0.0210990	−	0.0121815i	0.510512	+	0.859870i	$0.329456\pi$
$420$	5.21526	−	3.70265i	0.254479	−	0.180671i
$421$	−12.8276	−	12.8276i	−0.625179	−	0.625179i	0.321672	−	0.946851i	$-0.395755\pi$
$421$	−12.8276	−	12.8276i	−0.625179	−	0.625179i	−0.946851	+	0.321672i	$0.895755\pi$
$422$	−0.845135	−	3.15409i	−0.0411405	−	0.153539i
$423$	−23.2387	−	15.8246i	−1.12990	−	0.769418i
$424$	−3.25063	+	3.25063i	−0.157865	+	0.157865i
$425$	24.3531	+	14.0603i	1.18130	+	0.682023i
$426$	−15.4407	+	1.45234i	−0.748107	+	0.0703661i
$427$	6.61210	+	1.77171i	0.319982	+	0.0857389i
$428$	4.71862			0.228083
$429$	10.7235	+	36.1284i	0.517736	+	1.74430i
$430$	−28.5605			−1.37731
$431$	14.0578	+	3.76678i	0.677141	+	0.181439i	0.580969	−	0.813926i	$-0.302674\pi$
$431$	14.0578	+	3.76678i	0.677141	+	0.181439i	0.0961714	+	0.995365i	$0.469340\pi$
$432$	3.60171	−	3.74536i	0.173287	−	0.180199i
$433$	5.57566	+	3.21911i	0.267949	+	0.154700i	0.627955	−	0.778249i	$-0.283892\pi$
$433$	5.57566	+	3.21911i	0.267949	+	0.154700i	−0.360006	+	0.932950i	$0.617225\pi$
$434$	4.91451	−	4.91451i	0.235904	−	0.235904i
$435$	44.5198	+	7.55125i	2.13456	+	0.362055i
$436$	4.55969	+	17.0170i	0.218369	+	0.814966i
$437$	−4.80753	−	4.80753i	−0.229975	−	0.229975i
$438$	−1.37732	−	1.93998i	−0.0658107	−	0.0926959i
$439$	−19.4203	+	11.2123i	−0.926883	+	0.535136i	−0.885824	−	0.464021i	$-0.846406\pi$
$439$	−19.4203	+	11.2123i	−0.926883	+	0.535136i	−0.0410584	+	0.999157i	$0.513073\pi$
$440$	−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	$0.655541\pi$
$444$	−9.03029	+	10.9054i	−0.428559	+	0.517548i
$445$	−12.0558	−	20.8813i	−0.571501	−	0.989869i
$446$	−8.24271	+	14.2768i	−0.390304	+	0.676026i
$447$	17.2524	−	6.40700i	0.816013	−	0.303041i
$448$	−0.965926	+	0.258819i	−0.0456357	+	0.0122281i
$449$	−0.980852	+	0.262819i	−0.0462893	+	0.0124032i	−0.281889	−	0.959447i	$-0.590961\pi$
$449$	−0.980852	+	0.262819i	−0.0462893	+	0.0124032i	0.235600	+	0.971850i	$0.424294\pi$
$450$	−1.92152	+	25.8372i	−0.0905811	+	1.21798i
$451$	13.1105	−	22.7081i	0.617350	−	1.06928i
$452$	−2.34374	−	4.05949i	−0.110240	−	0.190942i
$453$	26.4421	+	21.8955i	1.24236	+	1.02874i
$454$		−	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	−0.999258	−	0.0385102i	$-0.987739\pi$
$457$	−2.45030	+	9.14464i	−0.114620	+	0.427768i	0.884638	+	0.466278i	$0.154405\pi$
$458$	2.22548	−	1.28488i	0.103990	−	0.0600385i
$459$	16.4253	+	4.05873i	0.766667	+	0.189445i
$460$	−7.95690	−	7.95690i	−0.370992	−	0.370992i
$461$	2.97164	+	11.0903i	0.138403	+	0.516528i	0.999961	+	0.00886793i	$0.00282279\pi$
$461$	2.97164	+	11.0903i	0.138403	+	0.516528i	−0.861557	+	0.507660i	$0.830511\pi$
$462$	−1.74791	+	10.3051i	−0.0813199	+	0.479437i
$463$	−6.07495	+	6.07495i	−0.282327	+	0.282327i	−0.834036	−	0.551709i	$-0.813976\pi$
$463$	−6.07495	+	6.07495i	−0.282327	+	0.282327i	0.551709	+	0.834036i	$0.313976\pi$
$464$	−6.11415	−	3.53000i	−0.283842	−	0.163876i
$465$	4.16284	+	44.2578i	0.193047	+	2.05241i
$466$	−11.2765	−	3.02152i	−0.522373	−	0.139969i
$467$	−11.4511			−0.529896			−0.264948	−	0.964263i	$-0.585355\pi$
$467$	−11.4511			−0.529896			−0.264948	+	0.964263i	$0.585355\pi$
$468$	−1.30044	−	10.7382i	−0.0601128	−	0.496373i
$469$	0.577907			0.0266852
$470$	−33.4278	−	8.95694i	−1.54191	−	0.413153i
$471$	−3.88291	−	41.2816i	−0.178915	−	1.90216i
$472$	7.77739	+	4.49028i	0.357983	+	0.206682i
$473$	33.0031	−	33.0031i	1.51748	−	1.51748i
$474$	1.31211	−	7.73581i	0.0602674	−	0.355318i
$475$	4.98704	+	18.6119i	0.228821	+	0.853972i
$476$	−2.30243	−	2.30243i	−0.105532	−	0.105532i
$477$	−2.57163	−	13.5494i	−0.117747	−	0.620383i
$478$	8.48777	−	4.90042i	0.388222	−	0.224140i
$479$	0.197122	−	0.735669i	0.00900673	−	0.0336136i	−0.961276	−	0.275587i	$-0.911128\pi$
$479$	0.197122	−	0.735669i	0.00900673	−	0.0336136i	0.970283	+	0.241973i	$0.0777946\pi$
$480$	2.66523	−	5.81422i	0.121650	−	0.265382i
$481$	5.70388	+	28.9169i	0.260075	+	1.31850i
$482$		−	20.5794i		−	0.937368i
$483$	−4.06524	−	3.36624i	−0.184975	−	0.153169i
$484$	−12.7084	−	22.0116i	−0.577655	−	1.00053i
$485$	6.47952	−	11.2228i	0.294220	−	0.509603i
$486$	3.20558	+	15.2553i	0.145408	+	0.691995i
$487$	38.0434	−	10.1937i	1.72391	−	0.461920i	0.745144	−	0.666903i	$-0.232381\pi$
$487$	38.0434	−	10.1937i	1.72391	−	0.461920i	0.978766	+	0.204983i	$0.0657138\pi$
$488$	6.61210	−	1.77171i	0.299316	−	0.0802014i
$489$	22.7953	−	8.46544i	1.03084	−	0.382821i
$490$	1.84636	−	3.19799i	0.0834101	−	0.144470i
$491$	−10.9053	−	18.8885i	−0.492149	−	0.852427i	0.507810	−	0.861469i	$-0.330455\pi$
$491$	−10.9053	−	18.8885i	−0.492149	−	0.852427i	−0.999959	+	0.00904224i	$0.997122\pi$
$492$	−4.79989	+	5.79659i	−0.216396	+	0.261330i
$493$		−	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
$498$	2.64302	+	3.72275i	0.118436	+	0.166820i
$499$	12.5058	+	12.5058i	0.559837	+	0.559837i	0.929261	−	0.369424i	$-0.120445\pi$
$499$	12.5058	+	12.5058i	0.559837	+	0.559837i	−0.369424	+	0.929261i	$0.620445\pi$
$500$	3.47528	+	12.9699i	0.155419	+	0.580032i
$501$	−15.5906	−	2.64440i	−0.696535	−	0.118143i
$502$	2.49198	−	2.49198i	0.111222	−	0.111222i
$503$	13.4468	+	7.76349i	0.599562	+	0.346157i	0.768869	−	0.639406i	$-0.220820\pi$
$503$	13.4468	+	7.76349i	0.599562	+	0.346157i	−0.169307	+	0.985563i	$0.554153\pi$
$504$	0.989233	−	2.83221i	0.0440639	−	0.126157i
$505$	28.2505	+	7.56971i	1.25713	+	0.336848i
$506$	18.3892			0.817501
$507$	−19.0304	−	12.0351i	−0.845170	−	0.534498i
$508$	−4.82619			−0.214128
$509$	11.3965	+	3.05368i	0.505141	+	0.135352i	0.502385	−	0.864644i	$-0.332456\pi$
$509$	11.3965	+	3.05368i	0.505141	+	0.135352i	0.00275582	+	0.999996i	$0.499123\pi$
$510$	20.7346	−	1.95027i	0.918144	−	0.0863596i
$511$	−1.18959	−	0.686812i	−0.0526245	−	0.0303828i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	5.99180	+	9.92484i	0.264544	+	0.438192i
$514$	4.40045	+	16.4227i	0.194096	+	0.724375i
$515$	2.45804	+	2.45804i	0.108314	+	0.108314i
$516$	−10.9232	+	7.75505i	−0.480866	+	0.341397i
$517$	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	$-0.131943\pi$
$522$	19.0773	−	9.20047i	0.834992	−	0.402694i
$523$	13.2217	+	22.9006i	0.578143	+	1.00137i	0.995692	+	0.0927183i	$0.0295556\pi$
$523$	13.2217	+	22.9006i	0.578143	+	1.00137i	−0.417550	+	0.908654i	$0.637111\pi$
$524$	−6.34131	+	10.9835i	−0.277022	+	0.479815i
$525$	5.20754	+	14.0226i	0.227275	+	0.611996i
$526$	−12.5648	+	3.36673i	−0.547851	+	0.146796i
$527$	21.8595	−	5.85724i	0.952216	−	0.255145i
$528$	3.63882	+	9.79844i	0.158359	+	0.426422i
$529$	6.85704	−	11.8767i	0.298132	−	0.516380i
$530$	−8.48788	−	14.7014i	−0.368690	−	0.638589i
$531$	−24.2670	+	11.7033i	−1.05310	+	0.507880i
$532$		−	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
$537$	22.6049	−	16.0486i	0.975472	−	0.692550i
$538$	−3.51213	−	3.51213i	−0.151419	−	0.151419i
$539$	1.56188	+	5.82901i	0.0672749	+	0.251073i
$540$	9.91698	+	16.4265i	0.426759	+	0.706885i
$541$	18.3158	−	18.3158i	0.787458	−	0.787458i	−0.193618	−	0.981077i	$-0.562022\pi$
$541$	18.3158	−	18.3158i	0.787458	−	0.787458i	0.981077	+	0.193618i	$0.0620224\pi$
$542$	20.9446	+	12.0924i	0.899646	+	0.519411i
$543$	31.3414	−	2.94793i	1.34499	−	0.126508i
$544$	−3.14518	−	0.842748i	−0.134848	−	0.0361325i
$545$	−65.0557			−2.78668
$546$	−3.26595	−	5.32293i	−0.139770	−	0.227800i
$547$	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
$549$	−6.77165	+	19.3875i	−0.289007	+	0.827437i
$550$	−45.1340	−	26.0581i	−1.92452	−	1.11112i
$551$	11.1382	−	11.1382i	0.474503	−	0.474503i
$552$	−5.20372	−	0.882632i	−0.221485	−	0.0375673i
$553$	−1.17247	−	4.37571i	−0.0498584	−	0.186074i
$554$	9.57826	+	9.57826i	0.406941	+	0.406941i
$555$	−30.2678	−	42.6329i	−1.28480	−	1.80967i
$556$	10.8936	−	6.28943i	0.461992	−	0.266731i
$557$	5.92389	−	22.1082i	0.251003	−	0.936757i	−0.719267	−	0.694733i	$-0.755522\pi$
$557$	5.92389	−	22.1082i	0.251003	−	0.936757i	0.970270	−	0.242023i	$-0.0778110\pi$
$558$	13.6095	+	15.7964i	0.576135	+	0.668715i
$559$	−1.86834	+	27.8236i	−0.0790224	+	1.17681i
$560$		−	3.69272i		−	0.156046i
$561$	−21.7063	+	26.2136i	−0.916439	+	1.10674i
$562$	−4.58147	−	7.93533i	−0.193258	−	0.334732i
$563$	−14.6097	+	25.3048i	−0.615726	+	1.06647i	0.374531	+	0.927214i	$0.377804\pi$
$563$	−14.6097	+	25.3048i	−0.615726	+	1.06647i	−0.990257	+	0.139254i	$0.955530\pi$
$564$	−15.2168	+	5.65102i	−0.640742	+	0.237951i
$565$	16.7198	−	4.48005i	0.703407	−	0.188477i
$566$	14.1678	−	3.79625i	0.595518	−	0.159568i
$567$	5.35258	+	7.23532i	0.224787	+	0.303855i
$568$	−4.47703	+	7.75445i	−0.187852	+	0.325370i
$569$	15.3604	+	26.6050i	0.643943	+	1.11534i	0.984545	+	0.175134i	$0.0560358\pi$
$569$	15.3604	+	26.6050i	0.643943	+	1.11534i	−0.340602	+	0.940208i	$0.610631\pi$
$570$	10.9912	+	9.10131i	0.460370	+	0.381212i
$571$		−	6.95592i		−	0.291096i	−0.989351	−	0.145548i	$-0.953505\pi$
$571$		−	6.95592i		−	0.291096i	0.989351	−	0.145548i	$-0.0464945\pi$
$572$	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
$576$	−0.559404	−	2.94738i	−0.0233085	−	0.122808i
$577$	−3.64763	−	3.64763i	−0.151853	−	0.151853i	0.627092	−	0.778945i	$-0.284245\pi$
$577$	−3.64763	−	3.64763i	−0.151853	−	0.151853i	−0.778945	+	0.627092i	$0.784245\pi$
$578$	1.65583	+	6.17965i	0.0688735	+	0.257039i
$579$	3.28195	−	19.3494i	0.136393	−	0.804133i
$580$	18.4347	−	18.4347i	0.765460	−	0.765460i
$581$	2.28278	+	1.31797i	0.0947058	+	0.0546784i
$582$	−0.569212	−	6.05165i	−0.0235946	−	0.250849i
$583$	26.7964	+	7.18009i	1.10980	+	0.297369i
$584$	−1.37362			−0.0568410
$585$	39.5449	+	5.62447i	1.63498	+	0.232543i
$586$	24.3628			1.00642
$587$	−4.21555	−	1.12955i	−0.173994	−	0.0466216i	0.170770	−	0.985311i	$-0.445374\pi$
$587$	−4.21555	−	1.12955i	−0.173994	−	0.0466216i	−0.344764	+	0.938689i	$0.612041\pi$
$588$	−0.162199	−	1.72444i	−0.00668897	−	0.0711147i
$589$	13.4292	+	7.75336i	0.553341	+	0.319472i
$590$	−23.4496	+	23.4496i	−0.965403	+	0.965403i
$591$	−2.04480	+	12.0555i	−0.0841118	+	0.495897i
$592$	2.11575	+	7.89610i	0.0869569	+	0.324528i
$593$	−17.3166	−	17.3166i	−0.711108	−	0.711108i	0.255659	−	0.966767i	$-0.417708\pi$
$593$	−17.3166	−	17.3166i	−0.711108	−	0.711108i	−0.966767	+	0.255659i	$0.917708\pi$
$594$	−30.4413	−	7.52212i	−1.24902	−	0.308636i
$595$	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	$0.984258\pi$
$600$	11.5212	+	9.54015i	0.470349	+	0.389475i
$601$	−9.79984	−	16.9738i	−0.399744	−	0.692377i	0.593950	−	0.804502i	$-0.297568\pi$
$601$	−9.79984	−	16.9738i	−0.399744	−	0.692377i	−0.993694	+	0.112125i	$0.964234\pi$
$602$	−3.86713	+	6.69807i	−0.157612	+	0.272993i
$603$	−0.128582	+	1.72894i	−0.00523626	+	0.0704081i
$604$	19.1455	−	5.13002i	0.779019	−	0.208737i
$605$	90.6591	−	24.2920i	3.68582	−	0.987611i
$606$	12.8600	−	4.77580i	0.522404	−	0.194004i
$607$	16.3977	−	28.4016i	0.665562	−	1.15279i	−0.313571	−	0.949565i	$-0.601525\pi$
$607$	16.3977	−	28.4016i	0.665562	−	1.15279i	0.979133	−	0.203222i	$-0.0651412\pi$
$608$	−1.11556	−	1.93221i	−0.0452421	−	0.0783616i
$609$	7.79898	−	9.41844i	0.316031	−	0.381654i
$610$			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	0.668433	+	0.743772i	$0.266965\pi$
$613$	−6.99024	+	26.0879i	−0.282333	+	1.05368i	−0.950766	+	0.309909i	$0.899701\pi$
$614$	−22.5795	+	13.0363i	−0.911232	+	0.526100i
$615$	−16.0883	−	22.6608i	−0.648744	−	0.913771i
$616$	4.26713	+	4.26713i	0.171928	+	0.171928i
$617$	−4.98729	−	18.6128i	−0.200781	−	0.749324i	−0.990694	−	0.136106i	$-0.956541\pi$
$617$	−4.98729	−	18.6128i	−0.200781	−	0.749324i	0.789914	−	0.613218i	$-0.210125\pi$
$618$	1.60753	+	0.272661i	0.0646642	+	0.0109680i
$619$	6.27677	−	6.27677i	0.252285	−	0.252285i	−0.569622	−	0.821907i	$-0.692910\pi$
$619$	6.27677	−	6.27677i	0.252285	−	0.252285i	0.821907	+	0.569622i	$0.192910\pi$
$620$	22.2266	+	12.8325i	0.892641	+	0.515367i
$621$	10.9754	−	11.4132i	0.440428	−	0.457994i
$622$	−3.17074	−	0.849597i	−0.127135	−	0.0340657i
$623$	−6.52951			−0.261599
$624$	−5.48986	−	2.97681i	−0.219770	−	0.119168i
$625$	−6.40283			−0.256113
$626$	7.24284	+	1.94071i	0.289482	+	0.0775665i
$627$	−23.2179	+	2.18385i	−0.927234	+	0.0872146i
$628$	−20.7319	−	11.9696i	−0.827294	−	0.477638i
$629$	−18.8215	+	18.8215i	−0.750464	+	0.750464i
$630$	9.15674	+	6.23537i	0.364813	+	0.248423i
$631$	10.3772	+	38.7281i	0.413108	+	1.54174i	0.788595	+	0.614912i	$0.210809\pi$
$631$	10.3772	+	38.7281i	0.413108	+	1.54174i	−0.375487	+	0.926827i	$0.622525\pi$
$632$	−3.20324	−	3.20324i	−0.127418	−	0.127418i
$633$	4.61168	−	3.27413i	0.183298	−	0.130135i
$634$	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
$639$	−11.6688	−	24.1954i	−0.461610	−	0.957155i
$640$	−1.84636	−	3.19799i	−0.0729838	−	0.126412i
$641$	−13.3709	+	23.1591i	−0.528120	+	0.914731i	0.471343	+	0.881950i	$0.343770\pi$
$641$	−13.3709	+	23.1591i	−0.528120	+	0.914731i	−0.999463	+	0.0327804i	$0.989564\pi$
$642$	2.84528	+	7.66163i	0.112294	+	0.302380i
$643$	−30.2386	+	8.10240i	−1.19249	+	0.319527i	−0.799871	−	0.600173i	$-0.795099\pi$
$643$	−30.2386	+	8.10240i	−1.19249	+	0.319527i	−0.392622	+	0.919700i	$0.628432\pi$
$644$	−2.94345	+	0.788694i	−0.115988	+	0.0310789i
$645$	−17.2217	−	46.3736i	−0.678103	−	1.82596i
$646$	3.63242	−	6.29153i	0.142915	−	0.247537i
$647$	−21.4531	−	37.1579i	−0.843408	−	1.46083i	−0.886996	−	0.461776i	$-0.847212\pi$
$647$	−21.4531	−	37.1579i	−0.843408	−	1.46083i	0.0435881	−	0.999050i	$-0.486121\pi$
$648$	8.25313	+	3.58968i	0.324214	+	0.141016i
$649$		−	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	$-0.706411\pi$
$653$	−5.51209	+	3.18240i	−0.215705	+	0.124537i	0.388255	+	0.921552i	$0.373078\pi$
$654$	−24.8810	+	17.6646i	−0.972926	+	0.690742i
$655$	−33.1162	−	33.1162i	−1.29396	−	1.29396i
$656$	1.12459	+	4.19703i	0.0439079	+	0.163867i
$657$	2.31944	−	3.40614i	0.0904900	−	0.132886i
$658$	−6.62677	+	6.62677i	−0.258338	+	0.258338i
$659$	20.6511	+	11.9229i	0.804451	+	0.464450i	0.845025	−	0.534726i	$-0.179585\pi$
$659$	20.6511	+	11.9229i	0.804451	+	0.464450i	−0.0405741	+	0.999177i	$0.512919\pi$
$660$	−38.4278	+	3.61448i	−1.49580	+	0.140693i
$661$	36.3985	+	9.75295i	1.41574	+	0.379346i	0.883970	−	0.467544i	$-0.154861\pi$
$661$	36.3985	+	9.75295i	1.41574	+	0.379346i	0.531768	+	0.846890i	$0.321528\pi$
$662$	16.6760			0.648132
$663$	−0.543561	−	20.3272i	−0.0211102	−	0.789444i
$664$	2.63593			0.102294
$665$	7.95819	+	2.13239i	0.308606	+	0.0826906i
$666$	−23.1523	−	8.08663i	−0.897134	−	0.313350i
$667$	−18.6315	−	10.7569i	−0.721415	−	0.416509i
$668$	−6.45573	+	6.45573i	−0.249780	+	0.249780i
$669$	−28.1515	−	4.77493i	−1.08840	−	0.184610i
$670$	0.552332	+	2.06133i	0.0213385	+	0.0796362i
$671$	−29.2100	−	29.2100i	−1.12764	−	1.12764i
$672$	−1.00269	−	1.41231i	−0.0386795	−	0.0544810i
$673$	−30.5628	+	17.6454i	−1.17811	+	0.680182i	−0.955576	−	0.294744i	$-0.904766\pi$
$673$	−30.5628	+	17.6454i	−1.17811	+	0.680182i	−0.222533	+	0.974925i	$0.571432\pi$
$674$	−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	$-0.373505\pi$
$678$	5.17813	−	6.25337i	0.198865	−	0.240159i
$679$	−1.75467	−	3.03918i	−0.0673381	−	0.116633i
$680$	6.01198	−	10.4131i	0.230549	−	0.399323i
$681$	20.3919	−	7.57289i	0.781419	−	0.290194i
$682$	−40.5126	+	10.8553i	−1.55131	+	0.415672i
$683$	12.1169	−	3.24671i	0.463640	−	0.124232i	−0.0194346	−	0.999811i	$-0.506187\pi$
$683$	12.1169	−	3.24671i	0.463640	−	0.124232i	0.483075	+	0.875579i	$0.339520\pi$
$684$	6.67495	+	0.496416i	0.255223	+	0.0189810i
$685$	−31.5096	+	54.5762i	−1.20392	+	2.08525i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$	3.42820	+	2.83874i	0.130794	+	0.108305i
$688$			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	−0.924903	−	0.380204i	$-0.875854\pi$
$691$	1.73988	−	6.49333i	0.0661883	−	0.247018i	0.991091	+	0.133186i	$0.0425206\pi$
$692$	15.8677	−	9.16123i	0.603200	−	0.348258i
$693$	−17.7864	+	3.37580i	−0.675649	+	0.128236i
$694$	−20.6676	−	20.6676i	−0.784531	−	0.784531i
$695$	12.0222	+	44.8675i	0.456028	+	1.70192i
$696$	2.04490	−	12.0561i	0.0775118	−	0.456985i
$697$	−10.0043	+	10.0043i	−0.378938	+	0.378938i
$698$	−24.0091	−	13.8617i	−0.908757	−	0.524671i
$699$	−1.89355	−	20.1316i	−0.0716208	−	0.761446i
$700$	8.34192	+	2.23521i	0.315295	+	0.0844830i
$701$	−2.47640			−0.0935323			−0.0467661	−	0.998906i	$-0.514892\pi$
$701$	−2.47640			−0.0935323			−0.0467661	+	0.998906i	$0.514892\pi$
$702$	16.6515	−	8.58655i	0.628469	−	0.324078i
$703$	−18.2387			−0.687884
$704$	5.82901	+	1.56188i	0.219689	+	0.0588655i
$705$	−5.61321	−	59.6776i	−0.211406	−	2.24759i
$706$	−15.0008	−	8.66070i	−0.564561	−	0.325950i
$707$	5.60043	−	5.60043i	0.210626	−	0.210626i
$708$	−2.60118	+	15.3357i	−0.0977583	+	0.576352i
$709$	3.79939	+	14.1795i	0.142689	+	0.532522i	0.999847	+	0.0174695i	$0.00556101\pi$
$709$	3.79939	+	14.1795i	0.142689	+	0.532522i	−0.857158	+	0.515053i	$0.827772\pi$
$710$	−23.3804	−	23.3804i	−0.877451	−	0.877451i
$711$	13.3518	−	2.53414i	0.500733	−	0.0950376i
$712$	−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
$717$	13.0749	+	10.8267i	0.488289	+	0.404330i
$718$	6.43940	+	11.1534i	0.240316	+	0.416240i
$719$	−2.24829	+	3.89415i	−0.0838470	+	0.145227i	−0.904899	−	0.425626i	$-0.860054\pi$
$719$	−2.24829	+	3.89415i	−0.0838470	+	0.145227i	0.821052	+	0.570853i	$0.193387\pi$
$720$	11.0477	+	0.821615i	0.411722	+	0.0306198i
$721$	0.909286	−	0.243642i	0.0338636	−	0.00907372i
$722$	−13.5443	+	3.62918i	−0.504066	+	0.135064i
$723$	33.4148	−	12.4092i	1.24271	−	0.461503i
$724$	9.08741	−	15.7399i	0.337731	−	0.584967i
$725$	30.4858	+	52.8029i	1.13221	+	1.96105i
$726$	28.0772	−	33.9074i	1.04204	−	1.25842i
$727$		−	39.7600i		−	1.47462i	−0.675556	−	0.737309i	$-0.736096\pi$
$727$		−	39.7600i		−	1.47462i	0.675556	−	0.737309i	$-0.263904\pi$
$728$	−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
$732$	6.86375	+	9.66775i	0.253692	+	0.357330i
$733$	10.5520	+	10.5520i	0.389746	+	0.389746i	0.874597	−	0.484851i	$-0.161126\pi$
$733$	10.5520	+	10.5520i	0.389746	+	0.389746i	−0.484851	+	0.874597i	$0.661126\pi$
$734$	6.38900	+	23.8441i	0.235822	+	0.880101i
$735$	6.30592	+	1.06958i	0.232597	+	0.0394521i
$736$	−2.15475	+	2.15475i	−0.0794252	+	0.0794252i
$737$	−3.02022	−	1.74373i	−0.111251	−	0.0642310i
$738$	−12.3062	−	4.29831i	−0.452998	−	0.158223i
$739$	3.69172	+	0.989193i	0.135802	+	0.0363880i	0.326080	−	0.945342i	$-0.394272\pi$
$739$	3.69172	+	0.989193i	0.135802	+	0.0363880i	−0.190278	+	0.981730i	$0.560939\pi$
$740$	−30.1867			−1.10968
$741$	9.58550	−	10.1122i	0.352132	−	0.371482i
$742$	−4.59708			−0.168764
$743$	−28.5202	−	7.64195i	−1.04630	−	0.280356i	−0.305580	−	0.952166i	$-0.598850\pi$
$743$	−28.5202	−	7.64195i	−1.04630	−	0.280356i	−0.740723	+	0.671810i	$0.765517\pi$
$744$	11.9852	−	1.12731i	0.439397	−	0.0413292i
$745$	33.9799	+	19.6183i	1.24493	+	0.718759i
$746$	−8.81450	+	8.81450i	−0.322722	+	0.322722i
$747$	−4.45092	+	6.53625i	−0.162851	+	0.239149i
$748$	5.08567	+	18.9800i	0.185951	+	0.693977i
$749$	3.33657	+	3.33657i	0.121916	+	0.121916i
$750$	−18.9637	+	13.4635i	−0.692456	+	0.491619i
$751$	−30.7062	+	17.7282i	−1.12048	+	0.646912i	−0.941524	−	0.336945i	$-0.890606\pi$
$751$	−30.7062	+	17.7282i	−1.12048	+	0.646912i	−0.178959	+	0.983856i	$0.557273\pi$
$752$	−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
$756$	5.19516	−	0.101576i	0.188946	−	0.00369428i
$757$	−1.38028	−	2.39071i	−0.0501670	−	0.0868919i	0.839851	−	0.542816i	$-0.182642\pi$
$757$	−1.38028	−	2.39071i	−0.0501670	−	0.0868919i	−0.890018	+	0.455924i	$0.849309\pi$
$758$	15.4474	−	26.7557i	0.561075	−	0.971811i
$759$	11.0885	+	29.8586i	0.402488	+	1.08380i
$760$	7.95819	−	2.13239i	0.288674	−	0.0773500i
$761$	−49.8082	+	13.3461i	−1.80555	+	0.483794i	−0.994822	−	0.101634i	$-0.967593\pi$
$761$	−49.8082	+	13.3461i	−1.80555	+	0.483794i	−0.810724	+	0.585429i	$0.800926\pi$
$762$	−2.91014	−	7.83629i	−0.105423	−	0.283879i
$763$	−8.80864	+	15.2570i	−0.318894	+	0.552341i
$764$	0.957440	+	1.65834i	0.0346390	+	0.0599965i
$765$	15.6694	+	32.4908i	0.566529	+	1.17471i
$766$			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	0.470094	+	0.882616i	$0.344220\pi$
$769$	−10.4913	+	39.1542i	−0.378327	+	1.41194i	−0.848422	+	0.529321i	$0.822447\pi$
$770$	−19.2987	+	11.1421i	−0.695477	+	0.401534i
$771$	−24.0121	+	17.0478i	−0.864776	+	0.613960i
$772$	−8.01217	−	8.01217i	−0.288364	−	0.288364i
$773$	3.76133	+	14.0375i	0.135286	+	0.504892i	0.999997	+	0.00262276i	$0.000834851\pi$
$773$	3.76133	+	14.0375i	0.135286	+	0.504892i	−0.864711	+	0.502270i	$0.832498\pi$
$774$	−19.1784	−	13.0597i	−0.689355	−	0.469422i
$775$	−42.4427	+	42.4427i	−1.52459	+	1.52459i
$776$	−3.03918	−	1.75467i	−0.109100	−	0.0629891i
$777$	−14.0967	+	1.32592i	−0.505715	+	0.0475670i
$778$	14.5765	+	3.90575i	0.522591	+	0.140028i
$779$	−9.69444			−0.347339
$780$	15.8649	−	16.7367i	0.568054	−	0.599269i
$781$	54.0345			1.93351
$782$	−9.58423	−	2.56809i	−0.342732	−	0.0918346i
$783$	26.4423	+	25.4281i	0.944969	+	0.908725i
$784$	−0.866025	−	0.500000i	−0.0309295	−	0.0178571i
$785$	62.5087	−	62.5087i	2.23103	−	2.23103i
$786$	−21.6576	−	3.67347i	−0.772502	−	0.131028i
$787$	−0.785160	−	2.93026i	−0.0279879	−	0.104452i	0.950519	−	0.310667i	$-0.100552\pi$
$787$	−0.785160	−	2.93026i	−0.0279879	−	0.104452i	−0.978507	+	0.206214i	$0.933886\pi$
$788$	4.99193	+	4.99193i	0.177830	+	0.177830i
$789$	−13.0430	−	18.3714i	−0.464343	−	0.654038i
$790$	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
$795$	18.7526	−	22.6466i	0.665087	−	0.803192i
$796$	3.93106	+	6.80879i	0.139333	+	0.241331i
$797$	4.53506	−	7.85495i	0.160640	−	0.278237i	−0.774458	−	0.632625i	$-0.781978\pi$
$797$	4.53506	−	7.85495i	0.160640	−	0.278237i	0.935098	+	0.354388i	$0.115311\pi$
$798$	3.62268	−	1.34535i	0.128242	−	0.0476248i
$799$	−29.4756	+	7.89795i	−1.04277	+	0.279409i
$800$	8.34192	−	2.23521i	0.294931	−	0.0790266i
$801$	1.45279	−	19.5346i	0.0513318	−	0.690221i
$802$	4.43170	−	7.67592i	0.156489	−	0.271046i
$803$	4.14466	+	7.17876i	0.146262	+	0.253333i
$804$	0.770959	+	0.638397i	0.0271896	+	0.0225145i
$805$		−	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	$-0.460527\pi$
$809$	29.7204	−	17.1591i	1.04491	−	0.603280i	0.921221	+	0.389040i	$0.127193\pi$
$810$	−20.6919	+	26.0072i	−0.727040	+	0.913801i
$811$	−4.95616	−	4.95616i	−0.174034	−	0.174034i	0.614715	−	0.788749i	$-0.289271\pi$
$811$	−4.95616	−	4.95616i	−0.174034	−	0.174034i	−0.788749	+	0.614715i	$0.789271\pi$
$812$	−1.82726	−	6.81944i	−0.0641244	−	0.239316i
$813$	−7.00499	+	41.2993i	−0.245676	+	1.44843i
$814$	34.8823	−	34.8823i	1.22262	−	1.22262i
$815$	44.8970	+	25.9213i	1.57267	+	0.907982i
$816$	−0.528140	−	5.61499i	−0.0184886	−	0.196564i
$817$	−16.6681	−	4.46621i	−0.583144	−	0.156253i
$818$	12.7070			0.444290
$819$	6.67350	−	8.51260i	0.233191	−	0.297454i
$820$	−16.0452			−0.560323
$821$	−34.3531	−	9.20487i	−1.19893	−	0.321252i	−0.396520	−	0.918026i	$-0.629782\pi$
$821$	−34.3531	−	9.20487i	−1.19893	−	0.321252i	−0.802410	+	0.596774i	$0.796449\pi$
$822$	2.76805	+	29.4289i	0.0965468	+	1.02645i
$823$	−14.6251	−	8.44381i	−0.509799	−	0.294333i	0.222952	−	0.974829i	$-0.428431\pi$
$823$	−14.6251	−	8.44381i	−0.509799	−	0.294333i	−0.732751	+	0.680497i	$0.761764\pi$
$824$	0.665643	−	0.665643i	0.0231888	−	0.0231888i
$825$	15.0952	−	88.9969i	0.525549	−	3.09847i
$826$	2.32434	+	8.67455i	0.0808741	+	0.301826i
$827$	−4.77974	−	4.77974i	−0.166208	−	0.166208i	0.619102	−	0.785310i	$-0.287497\pi$
$827$	−4.77974	−	4.77974i	−0.166208	−	0.166208i	−0.785310	+	0.619102i	$0.787497\pi$
$828$	−1.70466	−	8.98150i	−0.0592411	−	0.312129i
$829$	−13.2762	+	7.66500i	−0.461100	+	0.266216i	−0.712507	−	0.701665i	$-0.752440\pi$
$829$	−13.2762	+	7.66500i	−0.461100	+	0.266216i	0.251406	+	0.967882i	$0.419107\pi$
$830$	−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
$834$	16.7809	+	13.8955i	0.581074	+	0.481162i
$835$	−16.8569	−	29.1969i	−0.583356	−	1.01040i
$836$	−6.73202	+	11.6602i	−0.232832	+	0.403276i
$837$	−17.4422	+	31.6228i	−0.602892	+	1.09304i
$838$	0.481706	−	0.129073i	0.0166403	−	0.00445875i
$839$	−28.9502	+	7.75719i	−0.999473	+	0.267808i	−0.721225	−	0.692701i	$-0.756420\pi$
$839$	−28.9502	+	7.75719i	−0.999473	+	0.267808i	−0.278248	+	0.960509i	$0.589754\pi$
$840$	5.99587	−	2.22667i	0.206877	−	0.0768275i
$841$	10.4218	−	18.0512i	0.359374	−	0.622454i
$842$	−9.07049	−	15.7105i	−0.312590	−	0.541421i
$843$	10.1220	−	12.2239i	0.348621	−	0.421012i
$844$		−	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
$849$	14.7070	+	20.7152i	0.504744	+	0.710943i
$850$	19.8842	+	19.8842i	0.682023	+	0.682023i
$851$	6.44729	+	24.0616i	0.221010	+	0.824822i
$852$	−15.2905	−	2.59351i	−0.523844	−	0.0888521i
$853$	13.6498	−	13.6498i	0.467359	−	0.467359i	−0.433699	−	0.901058i	$-0.642792\pi$
$853$	13.6498	−	13.6498i	0.467359	−	0.467359i	0.901058	+	0.433699i	$0.142792\pi$
$854$	5.92825	+	3.42268i	0.202860	+	0.117122i
$855$	−8.15022	+	23.3344i	−0.278732	+	0.798019i
$856$	4.55784	+	1.22127i	0.155784	+	0.0417421i
$857$	−20.5087			−0.700565			−0.350283	−	0.936644i	$-0.613914\pi$
$857$	−20.5087			−0.700565			−0.350283	+	0.936644i	$0.613914\pi$
$858$	1.00739	+	37.6728i	0.0343918	+	1.28613i
$859$	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
$861$	−7.49284	+	0.704768i	−0.255355	+	0.0240184i
$862$	12.6039	+	7.27686i	0.429290	+	0.247851i
$863$	−34.7688	+	34.7688i	−1.18354	+	1.18354i	−0.204724	+	0.978820i	$0.565630\pi$
$863$	−34.7688	+	34.7688i	−1.18354	+	1.18354i	−0.978820	+	0.204724i	$0.934370\pi$
$864$	4.44835	−	2.68555i	0.151336	−	0.0913642i
$865$	17.5116	+	65.3543i	0.595413	+	2.22211i
$866$	4.55251	+	4.55251i	0.154700	+	0.154700i
$867$	−9.03544	+	6.41484i	−0.306860	+	0.217859i
$868$	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
$873$	9.48284	−	4.57331i	0.320946	−	0.154783i
$874$	−3.39943	−	5.88799i	−0.114988	−	0.199164i
$875$	−6.71372	+	11.6285i	−0.226965	+	0.393115i
$876$	−0.828282	−	2.23035i	−0.0279850	−	0.0753567i
$877$	−29.7957	+	7.98373i	−1.00613	+	0.269591i	−0.724011	−	0.689788i	$-0.757704\pi$
$877$	−29.7957	+	7.98373i	−1.00613	+	0.269591i	−0.282118	+	0.959380i	$0.591037\pi$
$878$	−21.6606	+	5.80394i	−0.731009	+	0.195873i
$879$	14.6905	+	39.5580i	0.495500	+	1.33426i
$880$	−11.1421	+	19.2987i	−0.375600	+	0.650559i
$881$	−5.44155	−	9.42505i	−0.183331	−	0.317538i	0.759682	−	0.650295i	$-0.225355\pi$
$881$	−5.44155	−	9.42505i	−0.183331	−	0.317538i	−0.943013	+	0.332757i	$0.892021\pi$
$882$	2.70217	−	1.30318i	0.0909868	−	0.0438804i
$883$		−	41.3070i		−	1.39009i	−0.718966	−	0.695045i	$-0.755384\pi$
$883$		−	41.3070i		−	1.39009i	0.718966	−	0.695045i	$-0.244616\pi$
$884$	−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	$-0.747541\pi$
$887$	−12.9659	+	7.48586i	−0.435352	+	0.251350i	0.266272	+	0.963898i	$0.414208\pi$
$888$	−11.5451	+	8.19662i	−0.387429	+	0.275060i
$889$	−3.41263	−	3.41263i	−0.114456	−	0.114456i
$890$	−6.24056	−	23.2901i	−0.209184	−	0.780685i
$891$	−6.14211	−	53.9633i	−0.205769	−	1.80784i
$892$	−11.6570	+	11.6570i	−0.390304	+	0.390304i
$893$	−18.1081	−	10.4547i	−0.605963	−	0.349853i
$894$	18.3228	−	1.72343i	0.612807	−	0.0576400i
$895$	57.0903	+	15.2973i	1.90832	+	0.511333i
$896$	−1.00000			−0.0334077
$897$	−16.7291	−	9.07118i	−0.558570	−	0.302878i
$898$	−1.01545			−0.0338861
$899$	47.3963	+	12.6998i	1.58076	+	0.423562i
$900$	−8.54321	+	24.4595i	−0.284774	+	0.815317i
$901$	−12.9633	−	7.48434i	−0.431869	−	0.249340i
$902$	18.5411	−	18.5411i	0.617350	−	0.617350i
$903$	−13.2075	−	2.24020i	−0.439518	−	0.0745490i
$904$	−1.21321	−	4.52777i	−0.0403508	−	0.150591i
$905$	47.4571	+	47.4571i	1.57753	+	1.57753i
$906$	19.8741	+	27.9932i	0.660274	+	0.930011i
$907$	−14.3811	+	8.30294i	−0.477517	+	0.275695i	−0.719381	−	0.694615i	$-0.755575\pi$
$907$	−14.3811	+	8.30294i	−0.477517	+	0.275695i	0.241864	+	0.970310i	$0.422241\pi$
$908$	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	$0.891059\pi$
$912$	2.46466	−	2.97645i	0.0816131	−	0.0985600i
$913$	−7.95344	−	13.7758i	−0.263220	−	0.455911i
$914$	−4.73361	+	8.19886i	−0.156574	+	0.271194i
$915$	−41.0439	+	15.2424i	−1.35687	+	0.503897i
$916$	2.48220	−	0.665103i	0.0820141	−	0.0219756i
$917$	−12.2505	+	3.28250i	−0.404546	+	0.108398i
$918$	14.8151	+	8.17162i	0.488973	+	0.269704i
$919$	14.3842	−	24.9141i	0.474490	−	0.821841i	−0.525083	−	0.851051i	$-0.675966\pi$
$919$	14.3842	−	24.9141i	0.474490	−	0.821841i	0.999573	+	0.0292098i	$0.00929909\pi$
$920$	−5.62638	−	9.74517i	−0.185496	−	0.321289i
$921$	−34.7821	−	28.8015i	−1.14611	−	0.949043i
$922$			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
$927$	0.526602	+	2.77455i	0.0172959	+	0.0911283i
$928$	−4.99218	−	4.99218i	−0.163876	−	0.163876i
$929$	−3.07752	−	11.4855i	−0.100970	−	0.376825i	0.896887	−	0.442260i	$-0.145823\pi$
$929$	−3.07752	−	11.4855i	−0.100970	−	0.376825i	−0.997857	+	0.0654348i	$0.979157\pi$
$930$	−7.43377	+	43.8272i	−0.243763	+	1.43715i
$931$	1.57764	−	1.57764i	0.0517052	−	0.0517052i
$932$	−10.1102	−	5.83714i	−0.331171	−	0.191202i
$933$	−0.532433	−	5.66063i	−0.0174311	−	0.185321i
$934$	−11.0610	−	2.96377i	−0.361925	−	0.0969776i
$935$	−72.5602			−2.37297
$936$	1.52312	−	10.7089i	0.0497848	−	0.350031i
$937$	−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
$939$	1.21622	+	12.9304i	0.0396899	+	0.421968i
$940$	−29.9705	−	17.3035i	−0.977530	−	0.564377i
$941$	−19.5744	+	19.5744i	−0.638107	+	0.638107i	−0.950088	−	0.311981i	$-0.899007\pi$
$941$	−19.5744	+	19.5744i	−0.638107	+	0.638107i	0.311981	+	0.950088i	$0.399007\pi$
$942$	6.93388	−	40.8800i	0.225918	−	1.33194i
$943$	3.42695	+	12.7895i	0.111597	+	0.416485i
$944$	6.35021	+	6.35021i	0.206682	+	0.206682i
$945$	−4.60295	+	18.6277i	−0.149734	+	0.605958i
$946$	40.4204	−	23.3367i	1.31418	−	0.758742i
$947$	−0.624843	+	2.33194i	−0.0203047	+	0.0757780i	−0.975335	−	0.220731i	$-0.929156\pi$
$947$	−0.624843	+	2.33194i	−0.0203047	+	0.0757780i	0.955030	+	0.296509i	$0.0958224\pi$
$948$	3.26958	−	7.13262i	0.106191	−	0.231657i
$949$	−4.68728	−	1.59948i	−0.152156	−	0.0519214i
$950$			19.2684i			0.625151i
$951$	35.8264	+	29.6662i	1.16175	+	0.961993i
$952$	−1.62806	−	2.81989i	−0.0527658	−	0.0913931i
$953$	5.46528	−	9.46615i	0.177038	−	0.306639i	−0.763827	−	0.645421i	$-0.776682\pi$
$953$	5.46528	−	9.46615i	0.177038	−	0.306639i	0.940865	+	0.338783i	$0.110015\pi$
$954$	1.02283	−	13.7533i	0.0331154	−	0.445279i
$955$	−6.83018	+	1.83014i	−0.221019	+	0.0592220i
$956$	9.46688	−	2.53664i	0.306181	−	0.0820409i
$957$	−69.1770	+	25.6901i	−2.23618	+	0.830444i
$958$	0.380810	−	0.659583i	0.0123034	−	0.0213101i
$959$	8.53288	+	14.7794i	0.275541	+	0.477251i
$960$	4.07924	−	4.92629i	0.131657	−	0.158995i
$961$			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
$966$	−3.05547	−	4.30370i	−0.0983082	−	0.138469i
$967$	−22.2162	−	22.2162i	−0.714424	−	0.714424i	0.253034	−	0.967457i	$-0.418572\pi$
$967$	−22.2162	−	22.2162i	−0.714424	−	0.714424i	−0.967457	+	0.253034i	$0.918572\pi$
$968$	−6.57835	−	24.5508i	−0.211436	−	0.789091i
$969$	12.4059	+	2.10423i	0.398534	+	0.0675975i
$970$	9.16342	−	9.16342i	0.294220	−	0.294220i
$971$	29.9084	+	17.2676i	0.959807	+	0.554145i	0.896114	−	0.443824i	$-0.146379\pi$
$971$	29.9084	+	17.2676i	0.959807	+	0.554145i	0.0636936	+	0.997969i	$0.479712\pi$
$972$	−0.852013	+	15.5652i	−0.0273283	+	0.499253i
$973$	12.1502	+	3.25565i	0.389519	+	0.104371i
$974$	39.3854			1.26199
$975$	28.2054	+	45.9698i	0.903295	+	1.47221i
$976$	6.84535			0.219114
$977$	30.9849	+	8.30239i	0.991296	+	0.265617i	0.717795	−	0.696255i	$-0.245152\pi$
$977$	30.9849	+	8.30239i	0.991296	+	0.265617i	0.273501	+	0.961872i	$0.411818\pi$
$978$	24.2096	−	2.27713i	0.774138	−	0.0728145i
$979$	34.1242	+	19.7016i	1.09061	+	0.629666i
$980$	2.61115	−	2.61115i	0.0834101	−	0.0834101i
$981$	−43.6851	−	29.7478i	−1.39476	−	0.949773i
$982$	−5.64499	−	21.0674i	−0.180139	−	0.672288i
$983$	−5.07300	−	5.07300i	−0.161803	−	0.161803i	0.621562	−	0.783365i	$-0.286499\pi$
$983$	−5.07300	−	5.07300i	−0.161803	−	0.161803i	−0.783365	+	0.621562i	$0.786499\pi$
$984$	−6.13661	+	4.35677i	−0.195628	+	0.138889i
$985$	−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
$990$	−29.0404	−	60.2157i	−0.922964	−	1.91378i
$991$	2.46413	+	4.26799i	0.0782755	+	0.135577i	0.902506	−	0.430677i	$-0.141725\pi$
$991$	2.46413	+	4.26799i	0.0782755	+	0.135577i	−0.824230	+	0.566254i	$0.808392\pi$
$992$	3.47509	−	6.01903i	0.110334	−	0.191104i
$993$	10.0555	+	27.0769i	0.319101	+	0.859259i
$994$	−8.64897	+	2.31748i	−0.274329	+	0.0735061i
$995$	−28.0433	+	7.51418i	−0.889033	+	0.238216i
$996$	1.58944	+	4.27996i	0.0503633	+	0.135616i
$997$	−15.6483	+	27.1036i	−0.495586	+	0.858379i	−0.999987	−	0.00508984i	$-0.998380\pi$
$997$	−15.6483	+	27.1036i	−0.495586	+	0.858379i	0.504401	+	0.863469i	$0.331713\pi$
$998$	8.84294	+	15.3164i	0.279918	+	0.484833i
$999$	−0.830347	−	42.4686i	−0.0262710	−	1.34365i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.71.6	✓	56	13.6	odd	12
546.2.bu.a.323.6	yes	56	3.2	odd	2
546.2.bu.b.71.11	yes	56	39.32	even	12	inner
546.2.bu.b.323.11	yes	56	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.162199 + 1.72444i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.61115 + 2.61115i) q^{5} +(-0.289646 + 1.70766i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.94738 + 0.559404i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.162199 + 1.72444i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.61115 + 2.61115i) q^{5} +(-0.289646 + 1.70766i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.94738 + 0.559404i) 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} +(-4.92629 - 4.07924i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.62806 + 2.81989i) q^{17} +(-2.99174 - 0.222496i) q^{18} +(-2.15510 + 0.577458i) q^{19} +(-3.56689 + 0.955747i) q^{20} +(-1.62370 + 0.602990i) q^{21} +(3.01732 - 5.22615i) q^{22} +(1.52364 + 2.63902i) q^{23} +(-1.10467 + 1.33405i) 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} +(-3.70265 - 5.21526i) q^{30} +(-4.91451 - 4.91451i) q^{31} +(0.258819 + 0.965926i) q^{32} +(10.3051 + 1.74791i) q^{33} +(-2.30243 + 2.30243i) q^{34} +(-3.19799 - 1.84636i) q^{35} +(-2.83221 - 0.989233i) q^{36} +(7.89610 + 2.11575i) q^{37} -2.23113 q^{38} +(-5.32293 + 3.26595i) q^{39} -3.69272 q^{40} +(4.19703 + 1.12459i) q^{41} +(-1.72444 + 0.162199i) q^{42} +(6.69807 + 3.86713i) q^{43} +(4.26713 - 4.26713i) q^{44} +(6.23537 - 9.15674i) q^{45} +(0.788694 + 2.94345i) q^{46} +(6.62677 + 6.62677i) q^{47} +(-1.41231 + 1.00269i) 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} +(-0.101576 - 5.19516i) q^{54} +(11.1421 + 19.2987i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-1.34535 - 3.62268i) q^{57} +(-6.81944 + 1.82726i) q^{58} +(8.67455 - 2.32434i) q^{59} +(-2.22667 - 5.99587i) q^{60} +(3.42268 - 5.92825i) q^{61} +(-3.47509 - 6.01903i) q^{62} +(-1.30318 - 2.70217i) 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} +(-4.30370 + 3.05547i) q^{69} +(-2.61115 - 2.61115i) q^{70} +(2.31748 + 8.64897i) q^{71} +(-2.47967 - 1.68856i) q^{72} +(-0.971299 + 0.971299i) q^{73} +(7.07945 + 4.08732i) q^{74} +(14.8926 - 1.40078i) q^{75} +(-2.15510 - 0.577458i) q^{76} +6.03463 q^{77} +(-5.98684 + 1.77699i) q^{78} -4.53007 q^{79} +(-3.56689 - 0.955747i) q^{80} +(8.37413 - 3.29756i) q^{81} +(3.76296 + 2.17254i) q^{82} +(1.86388 - 1.86388i) q^{83} +(-1.70766 - 0.289646i) q^{84} +(-3.11203 - 11.6143i) q^{85} +(5.46895 + 5.46895i) q^{86} +(-7.07898 - 9.97091i) 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} +(7.67765 - 9.27191i) q^{93} +(4.68583 + 8.11610i) q^{94} +(4.11946 - 7.13512i) q^{95} +(-1.62370 + 0.602990i) q^{96} +(-3.38977 + 0.908285i) q^{97} +(-0.965926 + 0.258819i) q^{98} +(-1.34268 + 18.0540i) 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	\( 56 q + 8 q^{6} - 24 q^{9} + 24 q^{10} + 8 q^{11} + 24 q^{13} + 4 q^{15} + 28 q^{16} - 4 q^{17} - 8 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 16 q^{79} + 12 q^{81} - 4 q^{83} - 4 q^{84} + 32 q^{85} - 16 q^{86} - 144 q^{87} + 88 q^{89} - 8 q^{90} - 8 q^{91} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 q^{99}+O(q^{100}) \) 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^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 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 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * q^99

Introduction

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