LMFDB - Embedded newform 546.2.bu.b.71.11

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			71.11
Character	$\chi$	$=$	546.71
Dual form			546.2.bu.b.323.11

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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
$3$	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	−0.982738	−	0.185003i	$-0.940771\pi$
$5$	−2.61115	−	2.61115i	−1.16774	−	1.16774i	−0.185003	−	0.982738i	$-0.559229\pi$
$6$	−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	0.636461	+	0.771309i	$0.280398\pi$
$11$	1.56188	+	5.82901i	0.470924	+	1.75751i	−0.165537	+	0.986204i	$0.552936\pi$
$12$	−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	0.598220	−	0.801332i	$-0.295875\pi$
$17$	−1.62806	−	2.81989i	−0.394863	−	0.683923i	−0.993084	+	0.117408i	$0.962541\pi$
$18$	−2.99174	+	0.222496i	−0.705159	+	0.0524428i
$19$	−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
$21$	−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	−0.662307	−	0.749233i	$-0.730423\pi$
$23$	1.52364	−	2.63902i	0.317701	−	0.550274i	0.980008	+	0.198958i	$0.0637559\pi$
$24$	−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	−0.190089	−	0.981767i	$-0.560878\pi$
$29$	−6.11415	−	3.53000i	−1.13537	−	0.655505i	−0.945279	+	0.326262i	$0.894211\pi$
$30$	−3.70265	+	5.21526i	−0.676008	+	0.952172i
$31$	−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
$33$	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	0.457375	−	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
$39$	−5.32293	−	3.26595i	−0.852350	−	0.522971i
$40$	−3.69272			−0.583870
$41$	4.19703	−	1.12459i	0.655466	−	0.175632i	0.0842672	−	0.996443i	$-0.473145\pi$
$41$	4.19703	−	1.12459i	0.655466	−	0.175632i	0.571199	+	0.820811i	$0.306478\pi$
$42$	−1.72444	−	0.162199i	−0.266087	−	0.0250278i
$43$	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
$45$	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	−0.0328467	−	0.999460i	$-0.510457\pi$
$47$	6.62677	−	6.62677i	0.966614	−	0.966614i	0.999460	+	0.0328467i	$0.0104573\pi$
$48$	−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	$-0.897751\pi$
$53$		−	4.59708i		−	0.631458i	0.948849	−	0.315729i	$-0.102249\pi$
$54$	−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	0.774653	−	0.632386i	$-0.217924\pi$
$59$	8.67455	+	2.32434i	1.12933	+	0.302603i	0.354677	+	0.934989i	$0.384591\pi$
$60$	−2.22667	+	5.99587i	−0.287462	+	0.774064i
$61$	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
$63$	−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	0.974460	−	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
$69$	−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	−0.680783	−	0.732485i	$-0.738361\pi$
$71$	2.31748	−	8.64897i	0.275035	−	1.02644i	0.955818	−	0.293959i	$-0.0949728\pi$
$72$	−2.47967	+	1.68856i	−0.292232	+	0.198998i
$73$	−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
$75$	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	0.801962	−	0.597375i	$-0.203789\pi$
$83$	1.86388	+	1.86388i	0.204588	+	0.204588i	−0.597375	+	0.801962i	$0.703789\pi$
$84$	−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	−0.995810	−	0.0914447i	$-0.970852\pi$
$89$	−1.68996	−	6.30702i	−0.179136	−	0.668543i	0.816675	−	0.577098i	$-0.195815\pi$
$90$	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	0.0825890	−	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
$99$	−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	−0.992979	−	0.118293i	$-0.962258\pi$
$101$	−3.96010	+	6.85910i	−0.394045	+	0.682506i	0.598934	+	0.800799i	$0.295591\pi$
$102$	−4.34385	+	3.59695i	−0.430105	+	0.356151i
$103$			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	0.684347	−	0.729157i	$-0.260088\pi$
$107$	4.08645	+	2.35931i	0.395052	+	0.228083i	−0.289295	+	0.957240i	$0.593421\pi$
$108$	1.24649	+	5.04443i	0.119944	+	0.485400i
$109$	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
$111$	−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	−0.678638	−	0.734473i	$-0.737429\pi$
$113$	−4.05949	+	2.34374i	−0.381884	+	0.220481i	0.296754	+	0.954954i	$0.404096\pi$
$114$	−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	0.302963	−	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	$-0.813084\pi$
$131$		−	12.6826i		−	1.10809i	0.832488	−	0.554043i	$-0.186916\pi$
$132$	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	0.881334	−	0.472493i	$-0.156646\pi$
$137$	16.4843	+	4.41694i	1.40835	+	0.377365i	0.527011	+	0.849858i	$0.323313\pi$
$138$	−4.94787	−	1.83748i	−0.421191	−	0.156417i
$139$	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
$141$	−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	0.756994	+	0.653422i	$0.226667\pi$
$149$	−2.75005	+	10.2633i	−0.225293	+	0.840805i	−0.982287	+	0.187383i	$0.939999\pi$
$150$	14.7477	−	2.50144i	1.20414	−	0.204241i
$151$	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
$153$	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	0.664523	+	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
$165$	−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	−0.995080	−	0.0990718i	$-0.968413\pi$
$167$	−2.36296	−	8.81869i	−0.182851	−	0.682411i	0.812229	−	0.583339i	$-0.198254\pi$
$168$	−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	0.969667	+	0.244429i	$0.0786004\pi$
$173$	9.16123	+	15.8677i	0.696515	+	1.20640i	−0.273152	+	0.961971i	$0.588066\pi$
$174$	−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	0.394935	+	0.918709i	$0.370767\pi$
$179$	−8.00281	+	13.8613i	−0.598158	+	1.03604i	−0.993093	+	0.117331i	$0.962566\pi$
$180$	9.97836	+	4.81229i	0.743743	+	0.358687i
$181$			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
$186$	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	−0.438802	−	0.898584i	$-0.644597\pi$
$191$	1.65834	−	0.957440i	0.119993	−	0.0692780i	0.558795	+	0.829306i	$0.311264\pi$
$192$	−1.72444	−	0.162199i	−0.124451	−	0.0117057i
$193$	−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
$195$	5.37106	+	22.4268i	0.384630	+	1.60602i
$196$	−1.00000			−0.0714286
$197$	6.81911	−	1.82717i	0.485841	−	0.130181i	−0.00757989	−	0.999971i	$-0.502413\pi$
$197$	6.81911	−	1.82717i	0.485841	−	0.130181i	0.493421	+	0.869790i	$0.335746\pi$
$198$	−5.96966	−	17.0914i	−0.424245	−	1.21463i
$199$	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
$201$	0.986868	−	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	−0.916737	−	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
$213$	−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	−0.948310	−	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
$225$	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	0.770162	+	0.637848i	$0.220175\pi$
$227$	−3.25048	+	12.1310i	−0.215742	+	0.805160i	−0.985904	+	0.167312i	$0.946491\pi$
$228$	0.646236	+	3.81001i	0.0427980	+	0.252324i
$229$	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
$231$	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	0.894782	−	0.446503i	$-0.147331\pi$
$239$	6.93024	+	6.93024i	0.448280	+	0.448280i	−0.446503	+	0.894782i	$0.647331\pi$
$240$	1.06958	+	6.30592i	0.0690411	+	0.407045i
$241$	−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
$243$	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	0.916263	−	0.400576i	$-0.131190\pi$
$251$	1.76209	+	3.05204i	0.111222	+	0.192643i	−0.805041	+	0.593219i	$0.797857\pi$
$252$	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	−0.469097	−	0.883147i	$-0.655420\pi$
$257$	8.50103	−	14.7242i	0.530279	−	0.918471i	0.999376	−	0.0353239i	$-0.0112463\pi$
$258$	−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	0.110703	−	0.993854i	$-0.464690\pi$
$263$	−11.2653	−	6.50402i	−0.694647	−	0.401055i	−0.805351	+	0.592799i	$0.798023\pi$
$264$	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	−0.625367	−	0.780330i	$-0.715051\pi$
$269$	−4.30147	+	2.48345i	−0.262265	+	0.151419i	0.363102	+	0.931749i	$0.381718\pi$
$270$	13.8306	−	13.3001i	0.841701	−	0.809418i
$271$	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
$273$	−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	−0.104306	−	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
$279$	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	−0.873442	−	0.486927i	$-0.838118\pi$
$281$	−6.47917	+	6.47917i	−0.386515	+	0.386515i	0.486927	+	0.873442i	$0.338118\pi$
$282$	−13.2357	−	9.39686i	−0.788174	−	0.559575i
$283$	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
$288$	−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	0.869228	−	0.494412i	$-0.164617\pi$
$293$	23.5327	+	6.30557i	1.37479	+	0.368375i	0.505567	+	0.862787i	$0.331283\pi$
$294$	−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	−0.998560	−	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
$309$	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	0.997621	+	0.0689377i	$0.0219610\pi$
$317$	18.9895	+	18.9895i	1.06656	+	1.06656i	0.0689377	+	0.997621i	$0.478039\pi$
$318$	−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	0.672720	−	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
$333$	−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	$-0.751513\pi$
$337$		−	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
$342$	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	−0.989469	−	0.144748i	$-0.953763\pi$
$347$	−25.3125	+	14.6142i	−1.35885	+	0.784531i	−0.369379	+	0.929279i	$0.620430\pi$
$348$	−1.14513	+	12.1746i	−0.0613852	+	0.652625i
$349$	−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
$351$	13.8617	+	12.6037i	0.739884	+	0.672735i
$352$	6.03463			0.321647
$353$	−16.7312	+	4.48311i	−0.890511	+	0.238612i	−0.674937	−	0.737876i	$-0.735829\pi$
$353$	−16.7312	+	4.48311i	−0.890511	+	0.238612i	−0.215574	+	0.976487i	$0.569162\pi$
$354$	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	−0.424701	−	0.905334i	$-0.639621\pi$
$359$	9.10668	−	9.10668i	0.480632	−	0.480632i	0.905334	+	0.424701i	$0.139621\pi$
$360$	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	−0.340189	−	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
$369$	−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	0.658327	−	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
$375$	−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	0.793226	+	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
$381$	−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	−0.965638	−	0.259891i	$-0.916313\pi$
$383$	0.0112438	−	0.0419624i	0.000574530	−	0.00214418i	0.966212	+	0.257747i	$0.0829800\pi$
$384$	−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	0.540075	+	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
$399$	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	0.999253	−	0.0386339i	$-0.0123006\pi$
$401$	2.29401	+	8.56138i	0.114558	+	0.427535i	−0.884696	+	0.466169i	$0.845634\pi$
$402$	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	0.549171	−	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
$411$	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	0.510512	−	0.859870i	$-0.329456\pi$
$419$	0.431886	+	0.249350i	0.0210990	+	0.0121815i	−0.489413	+	0.872052i	$0.662789\pi$
$420$	5.21526	+	3.70265i	0.254479	+	0.180671i
$421$	−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
$423$	−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	0.0961714	−	0.995365i	$-0.469340\pi$
$431$	14.0578	−	3.76678i	0.677141	−	0.181439i	0.580969	+	0.813926i	$0.302674\pi$
$432$	3.60171	+	3.74536i	0.173287	+	0.180199i
$433$	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
$435$	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	−0.0410584	−	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	$-0.655541\pi$
$443$		−	37.1687i		−	1.76594i	0.469432	−	0.882969i	$-0.344459\pi$
$444$	−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	0.235600	−	0.971850i	$-0.424294\pi$
$449$	−0.980852	−	0.262819i	−0.0462893	−	0.0124032i	−0.281889	+	0.959447i	$0.590961\pi$
$450$	−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	0.884638	−	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
$459$	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	−0.861557	−	0.507660i	$-0.830511\pi$
$461$	2.97164	−	11.0903i	0.138403	−	0.516528i	0.999961	−	0.00886793i	$-0.00282279\pi$
$462$	−1.74791	−	10.3051i	−0.0813199	−	0.479437i
$463$	−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
$465$	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	0.970283	−	0.241973i	$-0.0777946\pi$
$479$	0.197122	+	0.735669i	0.00900673	+	0.0336136i	−0.961276	+	0.275587i	$0.911128\pi$
$480$	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	0.978766	−	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
$489$	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	−0.999959	−	0.00904224i	$-0.997122\pi$
$491$	−10.9053	+	18.8885i	−0.492149	+	0.852427i	0.507810	+	0.861469i	$0.330455\pi$
$492$	−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	−0.369424	−	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
$501$	−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	−0.169307	−	0.985563i	$-0.554153\pi$
$503$	13.4468	−	7.76349i	0.599562	−	0.346157i	0.768869	+	0.639406i	$0.220820\pi$
$504$	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	0.00275582	−	0.999996i	$-0.499123\pi$
$509$	11.3965	−	3.05368i	0.505141	−	0.135352i	0.502385	+	0.864644i	$0.332456\pi$
$510$	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	$0.131943\pi$
$521$			18.3855i			0.805485i	−0.915313	+	0.402742i	$0.868057\pi$
$522$	19.0773	+	9.20047i	0.834992	+	0.402694i
$523$	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
$525$	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	0.981077	−	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
$543$	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	0.970270	+	0.242023i	$0.0778110\pi$
$557$	5.92389	+	22.1082i	0.251003	+	0.936757i	−0.719267	+	0.694733i	$0.755522\pi$
$558$	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	−0.990257	−	0.139254i	$-0.955530\pi$
$563$	−14.6097	−	25.3048i	−0.615726	−	1.06647i	0.374531	−	0.927214i	$-0.377804\pi$
$564$	−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	−0.340602	−	0.940208i	$-0.610631\pi$
$569$	15.3604	−	26.6050i	0.643943	−	1.11534i	0.984545	−	0.175134i	$-0.0560358\pi$
$570$	10.9912	−	9.10131i	0.460370	−	0.381212i
$571$			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
$576$	−0.559404	+	2.94738i	−0.0233085	+	0.122808i
$577$	−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
$579$	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	−0.344764	−	0.938689i	$-0.612041\pi$
$587$	−4.21555	+	1.12955i	−0.173994	+	0.0466216i	0.170770	+	0.985311i	$0.445374\pi$
$588$	−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	−0.966767	−	0.255659i	$-0.917708\pi$
$593$	−17.3166	+	17.3166i	−0.711108	+	0.711108i	0.255659	+	0.966767i	$0.417708\pi$
$594$	−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	$-0.984258\pi$
$599$		−	2.41985i		−	0.0988725i	0.998777	−	0.0494362i	$-0.0157425\pi$
$600$	11.5212	−	9.54015i	0.470349	−	0.389475i
$601$	−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
$603$	−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	0.979133	+	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
$609$	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	−0.950766	−	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
$615$	−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	0.789914	+	0.613218i	$0.210125\pi$
$617$	−4.98729	+	18.6128i	−0.200781	+	0.749324i	−0.990694	+	0.136106i	$0.956541\pi$
$618$	1.60753	−	0.272661i	0.0646642	−	0.0109680i
$619$	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
$621$	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	−0.375487	−	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
$633$	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	−0.999463	−	0.0327804i	$-0.989564\pi$
$641$	−13.3709	−	23.1591i	−0.528120	−	0.914731i	0.471343	−	0.881950i	$-0.343770\pi$
$642$	2.84528	−	7.66163i	0.112294	−	0.302380i
$643$	−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
$645$	−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	0.0435881	+	0.999050i	$0.486121\pi$
$647$	−21.4531	+	37.1579i	−0.843408	+	1.46083i	−0.886996	+	0.461776i	$0.847212\pi$
$648$	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	0.388255	−	0.921552i	$-0.373078\pi$
$653$	−5.51209	−	3.18240i	−0.215705	−	0.124537i	−0.603960	+	0.797015i	$0.706411\pi$
$654$	−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	−0.0405741	−	0.999177i	$-0.512919\pi$
$659$	20.6511	−	11.9229i	0.804451	−	0.464450i	0.845025	+	0.534726i	$0.179585\pi$
$660$	−38.4278	−	3.61448i	−1.49580	−	0.140693i
$661$	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
$663$	−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	−0.222533	−	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	$0.373505\pi$
$677$			47.9832i			1.84414i	−0.387020	+	0.922071i	$0.626495\pi$
$678$	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	0.483075	−	0.875579i	$-0.339520\pi$
$683$	12.1169	+	3.24671i	0.463640	+	0.124232i	−0.0194346	+	0.999811i	$0.506187\pi$
$684$	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	0.991091	−	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
$693$	−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	−0.857158	−	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
$711$	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	0.821052	−	0.570853i	$-0.193387\pi$
$719$	−2.24829	−	3.89415i	−0.0838470	−	0.145227i	−0.904899	+	0.425626i	$0.860054\pi$
$720$	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	$0.263904\pi$
$727$			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
$732$	6.86375	−	9.66775i	0.253692	−	0.357330i
$733$	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
$735$	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	−0.190278	−	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
$741$	9.58550	+	10.1122i	0.352132	+	0.371482i
$742$	−4.59708			−0.168764
$743$	−28.5202	+	7.64195i	−1.04630	+	0.280356i	−0.740723	−	0.671810i	$-0.765517\pi$
$743$	−28.5202	+	7.64195i	−1.04630	+	0.280356i	−0.305580	+	0.952166i	$0.598850\pi$
$744$	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	−0.178959	−	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
$756$	5.19516	+	0.101576i	0.188946	+	0.00369428i
$757$	−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
$759$	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	−0.810724	−	0.585429i	$-0.800926\pi$
$761$	−49.8082	−	13.3461i	−1.80555	−	0.483794i	−0.994822	+	0.101634i	$0.967593\pi$
$762$	−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	−0.848422	−	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
$771$	−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	−0.864711	−	0.502270i	$-0.832498\pi$
$773$	3.76133	−	14.0375i	0.135286	−	0.504892i	0.999997	−	0.00262276i	$-0.000834851\pi$
$774$	−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	−0.978507	−	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
$789$	−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	0.935098	−	0.354388i	$-0.115311\pi$
$797$	4.53506	+	7.85495i	0.160640	+	0.278237i	−0.774458	+	0.632625i	$0.781978\pi$
$798$	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	0.921221	−	0.389040i	$-0.127193\pi$
$809$	29.7204	+	17.1591i	1.04491	+	0.603280i	0.123691	+	0.992321i	$0.460527\pi$
$810$	−20.6919	−	26.0072i	−0.727040	−	0.913801i
$811$	−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
$813$	−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	−0.802410	−	0.596774i	$-0.796449\pi$
$821$	−34.3531	+	9.20487i	−1.19893	+	0.321252i	−0.396520	+	0.918026i	$0.629782\pi$
$822$	2.76805	−	29.4289i	0.0965468	−	1.02645i
$823$	−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
$825$	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	−0.785310	−	0.619102i	$-0.787497\pi$
$827$	−4.77974	+	4.77974i	−0.166208	+	0.166208i	0.619102	+	0.785310i	$0.287497\pi$
$828$	−1.70466	+	8.98150i	−0.0592411	+	0.312129i
$829$	−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
$834$	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	−0.278248	−	0.960509i	$-0.589754\pi$
$839$	−28.9502	−	7.75719i	−0.999473	−	0.267808i	−0.721225	+	0.692701i	$0.756420\pi$
$840$	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	0.901058	−	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
$855$	−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	−0.978820	−	0.204724i	$-0.934370\pi$
$863$	−34.7688	−	34.7688i	−1.18354	−	1.18354i	−0.204724	−	0.978820i	$-0.565630\pi$
$864$	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	−0.282118	−	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
$879$	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	−0.943013	−	0.332757i	$-0.892021\pi$
$881$	−5.44155	+	9.42505i	−0.183331	+	0.317538i	0.759682	+	0.650295i	$0.225355\pi$
$882$	2.70217	+	1.30318i	0.0909868	+	0.0438804i
$883$			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	0.266272	−	0.963898i	$-0.414208\pi$
$887$	−12.9659	−	7.48586i	−0.435352	−	0.251350i	−0.701624	+	0.712547i	$0.747541\pi$
$888$	−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	0.241864	−	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	$-0.891059\pi$
$911$		−	20.2591i		−	0.671213i	0.942002	−	0.335607i	$-0.108941\pi$
$912$	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	0.999573	−	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
$921$	−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	−0.997857	−	0.0654348i	$-0.979157\pi$
$929$	−3.07752	+	11.4855i	−0.100970	+	0.376825i	0.896887	+	0.442260i	$0.145823\pi$
$930$	−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	0.311981	−	0.950088i	$-0.399007\pi$
$941$	−19.5744	−	19.5744i	−0.638107	−	0.638107i	−0.950088	+	0.311981i	$0.899007\pi$
$942$	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	0.955030	−	0.296509i	$-0.0958224\pi$
$947$	−0.624843	−	2.33194i	−0.0203047	−	0.0757780i	−0.975335	+	0.220731i	$0.929156\pi$
$948$	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	0.940865	−	0.338783i	$-0.110015\pi$
$953$	5.46528	+	9.46615i	0.177038	+	0.306639i	−0.763827	+	0.645421i	$0.776682\pi$
$954$	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	−0.967457	−	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
$969$	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	0.0636936	−	0.997969i	$-0.479712\pi$
$971$	29.9084	−	17.2676i	0.959807	−	0.554145i	0.896114	+	0.443824i	$0.146379\pi$
$972$	−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	0.273501	−	0.961872i	$-0.411818\pi$
$977$	30.9849	−	8.30239i	0.991296	−	0.265617i	0.717795	+	0.696255i	$0.245152\pi$
$978$	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	−0.783365	−	0.621562i	$-0.786499\pi$
$983$	−5.07300	+	5.07300i	−0.161803	+	0.161803i	0.621562	+	0.783365i	$0.286499\pi$
$984$	−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	−0.824230	−	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
$993$	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	0.504401	−	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
$999$	−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.71.11	yes	56
3.2	odd	2		546.2.bu.a.71.6	✓	56
13.11	odd	12		546.2.bu.a.323.6	yes	56
39.11	even	12	inner	546.2.bu.b.323.11	yes	56

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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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