LMFDB - Embedded newform 546.2.bw.a.149.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(11,546)]

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, 8, 7]))

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

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

chi := DirichletCharacter("546.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bw (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:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			149.15
Character	$\chi$	$=$	546.149
Dual form			546.2.bw.a.11.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(1.00636 - 1.40969i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(3.29330 - 0.882438i) q^{5} +(1.10119 + 1.33693i) q^{6} +(2.64105 + 0.157578i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.974462 - 2.83733i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(1.00636 - 1.40969i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(3.29330 - 0.882438i) q^{5} +(1.10119 + 1.33693i) q^{6} +(2.64105 + 0.157578i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.974462 - 2.83733i) q^{9} +3.40948i q^{10} +(-1.92456 + 1.92456i) q^{11} +(-1.57638 + 0.717647i) q^{12} +(0.963919 + 3.47431i) q^{13} +(-0.835764 + 2.51028i) q^{14} +(2.07030 - 5.53060i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.69264 - 4.66378i) q^{17} +(2.99286 - 0.206904i) q^{18} +(-4.12264 + 4.12264i) q^{19} +(-3.29330 - 0.882438i) q^{20} +(2.88000 - 3.56449i) q^{21} +(-1.36087 - 2.35709i) q^{22} +(-0.872301 - 1.51087i) q^{23} +(-0.285196 - 1.70841i) q^{24} +(5.73702 - 3.31227i) q^{25} +(-3.60541 + 0.0318558i) q^{26} +(-4.98042 - 1.48169i) q^{27} +(-2.20843 - 1.45699i) q^{28} +(-7.19866 - 4.15615i) q^{29} +(4.80631 + 3.43118i) q^{30} +(-1.12797 - 0.302238i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(0.776227 + 4.64984i) q^{33} +(3.80796 + 3.80796i) q^{34} +(8.83685 - 1.81161i) q^{35} +(-0.574755 + 2.94443i) q^{36} +(-1.22692 + 4.57894i) q^{37} +(-2.91515 - 5.04918i) q^{38} +(5.86777 + 2.13760i) q^{39} +(1.70474 - 2.95270i) q^{40} +(-1.36866 + 0.366731i) q^{41} +(2.69764 + 3.70442i) q^{42} +(8.98015 - 5.18469i) q^{43} +(2.62899 - 0.704437i) q^{44} +(-5.71296 - 8.48428i) q^{45} +(1.68516 - 0.451536i) q^{46} +(3.34090 + 12.4684i) q^{47} +(1.72401 + 0.166691i) q^{48} +(6.95034 + 0.832346i) q^{49} +(1.71456 + 6.39882i) q^{50} +(-3.86472 - 8.48925i) q^{51} +(0.902379 - 3.49080i) q^{52} +(3.31796 - 1.91563i) q^{53} +(2.72023 - 4.42723i) q^{54} +(-4.63985 + 8.03645i) q^{55} +(1.97893 - 1.75608i) q^{56} +(1.66277 + 9.96053i) q^{57} +(5.87768 - 5.87768i) q^{58} +(0.128146 + 0.478248i) q^{59} +(-4.55823 + 3.75449i) q^{60} -12.2439 q^{61} +(0.583879 - 1.01131i) q^{62} +(-2.12651 - 7.64709i) q^{63} -1.00000i q^{64} +(6.24035 + 10.5914i) q^{65} +(-4.69230 - 0.453689i) q^{66} +(0.400365 - 0.400365i) q^{67} +(-4.66378 + 2.69264i) q^{68} +(-3.00771 - 0.290810i) q^{69} +(-0.537260 + 9.00462i) q^{70} +(-2.45699 + 9.16961i) q^{71} +(-2.69534 - 1.31724i) q^{72} +(3.53850 - 13.2059i) q^{73} +(-4.10537 - 2.37023i) q^{74} +(1.10425 - 11.4208i) q^{75} +(5.63163 - 1.50899i) q^{76} +(-5.38613 + 4.77959i) q^{77} +(-3.58345 + 5.11458i) q^{78} +(-0.696028 + 1.20556i) q^{79} +(2.41087 + 2.41087i) q^{80} +(-7.10085 + 5.52973i) q^{81} -1.41694i q^{82} +(-2.65022 - 2.65022i) q^{83} +(-4.27640 + 1.64694i) q^{84} +(4.75217 - 17.7353i) q^{85} +(2.68379 + 10.0161i) q^{86} +(-13.1034 + 5.96529i) q^{87} +2.72173i q^{88} +(-13.2538 - 3.55134i) q^{89} +(9.67381 - 3.32241i) q^{90} +(1.99829 + 9.32775i) q^{91} +1.74460i q^{92} +(-1.56121 + 1.28593i) q^{93} -12.9082 q^{94} +(-9.93913 + 17.2151i) q^{95} +(-0.607218 + 1.62212i) q^{96} +(12.8615 + 3.44622i) q^{97} +(-2.60286 + 6.49808i) q^{98} +(7.33601 + 3.58519i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 12 q^{7}+O(q^{10}) $ 152 * q + 12 * q^7	$ 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	1.00636	−	1.40969i	0.581025	−	0.813886i
$3$	1.00636	−	1.40969i	0.581025	−	0.813886i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	3.29330	−	0.882438i	1.47281	−	0.394638i	0.568916	−	0.822395i	$-0.307363\pi$
$5$	3.29330	−	0.882438i	1.47281	−	0.394638i	0.903894	+	0.427757i	$0.140696\pi$
$6$	1.10119	+	1.33693i	0.449560	+	0.545799i
$7$	2.64105	+	0.157578i	0.998225	+	0.0595590i
$7$	2.64105	+	0.157578i	0.998225	+	0.0595590i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.974462	−	2.83733i	−0.324821	−	0.945776i
$10$			3.40948i			1.07817i
$11$	−1.92456	+	1.92456i	−0.580276	+	0.580276i	−0.934979	−	0.354703i	$-0.884582\pi$
$11$	−1.92456	+	1.92456i	−0.580276	+	0.580276i	0.354703	+	0.934979i	$0.384582\pi$
$12$	−1.57638	+	0.717647i	−0.455063	+	0.207167i
$13$	0.963919	+	3.47431i	0.267343	+	0.963601i
$13$	0.963919	+	3.47431i	0.267343	+	0.963601i
$14$	−0.835764	+	2.51028i	−0.223367	+	0.670900i
$15$	2.07030	−	5.53060i	0.534549	−	1.42799i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.69264	−	4.66378i	0.653060	−	1.13113i	−0.329316	−	0.944220i	$-0.606818\pi$
$17$	2.69264	−	4.66378i	0.653060	−	1.13113i	0.982376	−	0.186913i	$-0.0598484\pi$
$18$	2.99286	−	0.206904i	0.705423	−	0.0487676i
$19$	−4.12264	+	4.12264i	−0.945798	+	0.945798i	−0.998605	−	0.0528065i	$-0.983183\pi$
$19$	−4.12264	+	4.12264i	−0.945798	+	0.945798i	0.0528065	+	0.998605i	$0.483183\pi$
$20$	−3.29330	−	0.882438i	−0.736405	−	0.197319i
$21$	2.88000	−	3.56449i	0.628468	−	0.777836i
$22$	−1.36087	−	2.35709i	−0.290138	−	0.502534i
$23$	−0.872301	−	1.51087i	−0.181887	−	0.315038i	0.760636	−	0.649179i	$-0.224887\pi$
$23$	−0.872301	−	1.51087i	−0.181887	−	0.315038i	−0.942523	+	0.334141i	$0.891554\pi$
$24$	−0.285196	−	1.70841i	−0.0582153	−	0.348728i
$25$	5.73702	−	3.31227i	1.14740	−	0.662455i
$26$	−3.60541	+	0.0318558i	−0.707079	+	0.00624744i
$27$	−4.98042	−	1.48169i	−0.958482	−	0.285152i
$28$	−2.20843	−	1.45699i	−0.417354	−	0.275346i
$29$	−7.19866	−	4.15615i	−1.33676	−	0.771778i	−0.350433	−	0.936588i	$-0.613965\pi$
$29$	−7.19866	−	4.15615i	−1.33676	−	0.771778i	−0.986325	+	0.164810i	$0.947299\pi$
$30$	4.80631	+	3.43118i	0.877509	+	0.626444i
$31$	−1.12797	−	0.302238i	−0.202589	−	0.0542836i	0.156097	−	0.987742i	$-0.450109\pi$
$31$	−1.12797	−	0.302238i	−0.202589	−	0.0542836i	−0.358687	+	0.933458i	$0.616775\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	0.776227	+	4.64984i	0.135124	+	0.809433i
$34$	3.80796	+	3.80796i	0.653060	+	0.653060i
$35$	8.83685	−	1.81161i	1.49370	−	0.306219i
$36$	−0.574755	+	2.94443i	−0.0957925	+	0.490738i
$37$	−1.22692	+	4.57894i	−0.201705	+	0.752773i	0.788724	+	0.614748i	$0.210742\pi$
$37$	−1.22692	+	4.57894i	−0.201705	+	0.752773i	−0.990429	+	0.138025i	$0.955924\pi$
$38$	−2.91515	−	5.04918i	−0.472899	−	0.819085i
$39$	5.86777	+	2.13760i	0.939595	+	0.342289i
$40$	1.70474	−	2.95270i	0.269543	−	0.466862i
$41$	−1.36866	+	0.366731i	−0.213749	+	0.0572738i	−0.364104	−	0.931358i	$-0.618625\pi$
$41$	−1.36866	+	0.366731i	−0.213749	+	0.0572738i	0.150356	+	0.988632i	$0.451958\pi$
$42$	2.69764	+	3.70442i	0.416254	+	0.571605i
$43$	8.98015	−	5.18469i	1.36946	−	0.790658i	0.378601	−	0.925560i	$-0.376405\pi$
$43$	8.98015	−	5.18469i	1.36946	−	0.790658i	0.990859	+	0.134902i	$0.0430719\pi$
$44$	2.62899	−	0.704437i	0.396336	−	0.106198i
$45$	−5.71296	−	8.48428i	−0.851638	−	1.26476i
$46$	1.68516	−	0.451536i	0.248463	−	0.0665754i
$47$	3.34090	+	12.4684i	0.487320	+	1.81870i	0.569377	+	0.822076i	$0.307184\pi$
$47$	3.34090	+	12.4684i	0.487320	+	1.81870i	−0.0820570	+	0.996628i	$0.526149\pi$
$48$	1.72401	+	0.166691i	0.248840	+	0.0240598i
$49$	6.95034	+	0.832346i	0.992905	+	0.118907i
$50$	1.71456	+	6.39882i	0.242475	+	0.904930i
$51$	−3.86472	−	8.48925i	−0.541169	−	1.18873i
$52$	0.902379	−	3.49080i	0.125137	−	0.484087i
$53$	3.31796	−	1.91563i	0.455757	−	0.263131i	−0.254501	−	0.967072i	$-0.581911\pi$
$53$	3.31796	−	1.91563i	0.455757	−	0.263131i	0.710259	+	0.703941i	$0.248578\pi$
$54$	2.72023	−	4.42723i	0.370177	−	0.602469i
$55$	−4.63985	+	8.03645i	−0.625637	+	1.08364i
$56$	1.97893	−	1.75608i	0.264446	−	0.234666i
$57$	1.66277	+	9.96053i	0.220240	+	1.31930i
$58$	5.87768	−	5.87768i	0.771778	−	0.771778i
$59$	0.128146	+	0.478248i	0.0166832	+	0.0622626i	0.973766	−	0.227553i	$-0.0730726\pi$
$59$	0.128146	+	0.478248i	0.0166832	+	0.0622626i	−0.957082	+	0.289816i	$0.906406\pi$
$60$	−4.55823	+	3.75449i	−0.588465	+	0.484702i
$61$	−12.2439			−1.56767			−0.783837	−	0.620966i	$-0.786740\pi$
$61$	−12.2439			−1.56767			−0.783837	+	0.620966i	$0.786740\pi$
$62$	0.583879	−	1.01131i	0.0741528	−	0.128436i
$63$	−2.12651	−	7.64709i	−0.267914	−	0.963443i
$64$		−	1.00000i		−	0.125000i
$65$	6.24035	+	10.5914i	0.774020	+	1.31370i
$66$	−4.69230	−	0.453689i	−0.577582	−	0.0558453i
$67$	0.400365	−	0.400365i	0.0489124	−	0.0489124i	−0.682228	−	0.731140i	$-0.738989\pi$
$67$	0.400365	−	0.400365i	0.0489124	−	0.0489124i	0.731140	+	0.682228i	$0.238989\pi$
$68$	−4.66378	+	2.69264i	−0.565566	+	0.326530i
$69$	−3.00771	−	0.290810i	−0.362086	−	0.0350094i
$70$	−0.537260	+	9.00462i	−0.0642149	+	1.07626i
$71$	−2.45699	+	9.16961i	−0.291591	+	1.08823i	0.652296	+	0.757964i	$0.273806\pi$
$71$	−2.45699	+	9.16961i	−0.291591	+	1.08823i	−0.943887	+	0.330268i	$0.892861\pi$
$72$	−2.69534	−	1.31724i	−0.317649	−	0.155239i
$73$	3.53850	−	13.2059i	0.414150	−	1.54563i	−0.372381	−	0.928080i	$-0.621459\pi$
$73$	3.53850	−	13.2059i	0.414150	−	1.54563i	0.786531	−	0.617550i	$-0.211875\pi$
$74$	−4.10537	−	2.37023i	−0.477239	−	0.275534i
$75$	1.10425	−	11.4208i	0.127508	−	1.31876i
$76$	5.63163	−	1.50899i	0.645992	−	0.173093i
$77$	−5.38613	+	4.77959i	−0.613806	+	0.544685i
$78$	−3.58345	+	5.11458i	−0.405746	+	0.579112i
$79$	−0.696028	+	1.20556i	−0.0783093	+	0.135636i	−0.902521	−	0.430647i	$-0.858285\pi$
$79$	−0.696028	+	1.20556i	−0.0783093	+	0.135636i	0.824211	+	0.566282i	$0.191619\pi$
$80$	2.41087	+	2.41087i	0.269543	+	0.269543i
$81$	−7.10085	+	5.52973i	−0.788983	+	0.614415i
$82$		−	1.41694i		−	0.156475i
$83$	−2.65022	−	2.65022i	−0.290900	−	0.290900i	0.546536	−	0.837436i	$-0.315946\pi$
$83$	−2.65022	−	2.65022i	−0.290900	−	0.290900i	−0.837436	+	0.546536i	$0.815946\pi$
$84$	−4.27640	+	1.64694i	−0.466593	+	0.179696i
$85$	4.75217	−	17.7353i	0.515445	−	1.92367i
$86$	2.68379	+	10.0161i	0.289401	+	1.08006i
$87$	−13.1034	+	5.96529i	−1.40483	+	0.639547i
$88$			2.72173i			0.290138i
$89$	−13.2538	−	3.55134i	−1.40490	−	0.376441i	−0.524797	−	0.851227i	$-0.675859\pi$
$89$	−13.2538	−	3.55134i	−1.40490	−	0.376441i	−0.880101	+	0.474786i	$0.842525\pi$
$90$	9.67381	−	3.32241i	1.01971	−	0.350212i
$91$	1.99829	+	9.32775i	0.209477	+	0.977813i
$92$			1.74460i			0.181887i
$93$	−1.56121	+	1.28593i	−0.161890	+	0.133344i
$94$	−12.9082			−1.33138
$95$	−9.93913	+	17.2151i	−1.01973	+	1.76623i
$96$	−0.607218	+	1.62212i	−0.0619739	+	0.165557i
$97$	12.8615	+	3.44622i	1.30588	+	0.349910i	0.843671	−	0.536860i	$-0.180390\pi$
$97$	12.8615	+	3.44622i	1.30588	+	0.349910i	0.462211	+	0.886770i	$0.347056\pi$
$98$	−2.60286	+	6.49808i	−0.262929	+	0.656406i
$99$	7.33601	+	3.58519i	0.737296	+	0.360325i
$100$	−6.62455			−0.662455
$101$	2.01431			0.200431			0.100216	−	0.994966i	$-0.468047\pi$
$101$	2.01431			0.200431			0.100216	+	0.994966i	$0.468047\pi$
$102$	9.20025	−	1.53586i	0.910960	−	0.152072i
$103$	5.43794	+	3.13960i	0.535817	+	0.309354i	0.743382	−	0.668867i	$-0.233221\pi$
$103$	5.43794	+	3.13960i	0.535817	+	0.309354i	−0.207565	+	0.978221i	$0.566554\pi$
$104$	3.13831	+	1.77512i	0.307736	+	0.174065i
$105$	6.33927	−	14.2804i	0.618650	−	1.39362i
$106$	0.991601	+	3.70071i	0.0963128	+	0.359444i
$107$	−14.6983	+	8.48605i	−1.42094	+	0.820377i	−0.996379	−	0.0850240i	$-0.972903\pi$
$107$	−14.6983	+	8.48605i	−1.42094	+	0.820377i	−0.424556	+	0.905401i	$0.639570\pi$
$108$	3.57232	+	3.77339i	0.343747	+	0.363095i
$109$	−10.5475	−	2.82619i	−1.01026	−	0.270700i	−0.284525	−	0.958669i	$-0.591836\pi$
$109$	−10.5475	−	2.82619i	−1.01026	−	0.270700i	−0.725740	+	0.687969i	$0.758502\pi$
$110$	−6.56174	−	6.56174i	−0.625637	−	0.625637i
$111$	5.22016	+	6.33767i	0.495476	+	0.601545i
$112$	1.18406	+	2.36601i	0.111883	+	0.223567i
$113$	8.61977	−	4.97663i	0.810880	−	0.468162i	−0.0363813	−	0.999338i	$-0.511583\pi$
$113$	8.61977	−	4.97663i	0.810880	−	0.468162i	0.847261	+	0.531176i	$0.178250\pi$
$114$	−10.0515	−	0.971858i	−0.941408	−	0.0910229i
$115$	−4.20600	−	4.20600i	−0.392212	−	0.392212i
$116$	4.15615	+	7.19866i	0.385889	+	0.668379i
$117$	8.91846	−	6.12054i	0.824512	−	0.565844i
$118$	−0.495119			−0.0455794
$119$	7.84631	−	11.8930i	0.719270	−	1.09023i
$120$	−2.44680	−	5.37464i	−0.223361	−	0.490636i
$121$			3.59216i			0.326560i
$122$	3.16896	−	11.8267i	0.286904	−	1.07074i
$123$	−0.860392	+	2.29845i	−0.0775790	+	0.207245i
$124$	0.825730	+	0.825730i	0.0741528	+	0.0741528i
$125$	3.91656	−	3.91656i	0.350308	−	0.350308i
$126$	7.93690	−	0.0748341i	0.707075	−	0.00666675i
$127$	−12.6251	−	7.28911i	−1.12030	−	0.646804i	−0.178821	−	0.983882i	$-0.557228\pi$
$127$	−12.6251	−	7.28911i	−1.12030	−	0.646804i	−0.941477	+	0.337078i	$0.890561\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	1.72848	−	17.8769i	0.152185	−	1.57398i
$130$	−11.8456	+	3.28646i	−1.03893	+	0.288242i
$131$	−5.27411	−	3.04501i	−0.460801	−	0.266043i	0.251580	−	0.967836i	$-0.419050\pi$
$131$	−5.27411	−	3.04501i	−0.460801	−	0.266043i	−0.712381	+	0.701793i	$0.752383\pi$
$132$	1.65269	−	4.41499i	0.143848	−	0.384276i
$133$	−11.5378	+	10.2385i	−1.00045	+	0.887788i
$134$	0.283101	+	0.490345i	0.0244562	+	0.0423594i
$135$	−17.7095	−	0.484755i	−1.52419	−	0.0417211i
$136$	−1.39381	−	5.20177i	−0.119518	−	0.446048i
$137$	−2.64173	−	9.85908i	−0.225699	−	0.842318i	−0.982123	−	0.188238i	$-0.939722\pi$
$137$	−2.64173	−	9.85908i	−0.225699	−	0.842318i	0.756425	−	0.654080i	$-0.226944\pi$
$138$	1.05935	−	2.82996i	0.0901782	−	0.240902i
$139$	1.74467	+	3.02186i	0.147981	+	0.256311i	0.930481	−	0.366340i	$-0.119389\pi$
$139$	1.74467	+	3.02186i	0.147981	+	0.256311i	−0.782500	+	0.622651i	$0.786056\pi$
$140$	−8.55874	−	2.84952i	−0.723346	−	0.240828i
$141$	20.9388	+	7.83812i	1.76336	+	0.660089i
$142$	−8.22125	−	4.74654i	−0.689912	−	0.398321i
$143$	−8.54163	−	4.83140i	−0.714287	−	0.404022i
$144$	1.96997	−	2.26257i	0.164164	−	0.188548i
$145$	−27.3749	−	7.33509i	−2.27336	−	0.609146i
$146$	11.8401	+	6.83586i	0.979890	+	0.565740i
$147$	8.16792	−	8.96019i	0.673679	−	0.739024i
$148$	3.35202	−	3.35202i	0.275534	−	0.275534i
$149$	3.55240	+	3.55240i	0.291024	+	0.291024i	0.837485	−	0.546461i	$-0.184025\pi$
$149$	3.55240	+	3.55240i	0.291024	+	0.291024i	−0.546461	+	0.837485i	$0.684025\pi$
$150$	10.7458	+	4.02254i	0.877394	+	0.328439i
$151$	1.30747	−	4.87954i	0.106400	−	0.397092i	−0.892100	−	0.451838i	$-0.850768\pi$
$151$	1.30747	−	4.87954i	0.106400	−	0.397092i	0.998500	+	0.0547466i	$0.0174351\pi$
$152$			5.83029i			0.472899i
$153$	−15.8565	−	3.09521i	−1.28193	−	0.250233i
$154$	−3.22270	−	6.43965i	−0.259692	−	0.518922i
$155$	−3.98145			−0.319798
$156$	−4.01284	−	4.78510i	−0.321284	−	0.383114i
$157$	−2.10143	−	3.63978i	−0.167712	−	0.290486i	0.769903	−	0.638161i	$-0.220305\pi$
$157$	−2.10143	−	3.63978i	−0.167712	−	0.290486i	−0.937615	+	0.347675i	$0.886971\pi$
$158$	−0.984332	−	0.984332i	−0.0783093	−	0.0783093i
$159$	0.638636	−	6.60512i	0.0506471	−	0.523820i
$160$	−2.95270	+	1.70474i	−0.233431	+	0.134771i
$161$	−2.06571	−	4.12774i	−0.162801	−	0.325312i
$162$	−3.50348	−	8.29009i	−0.275259	−	0.651331i
$163$	10.9233	+	10.9233i	0.855581	+	0.855581i	0.990814	−	0.135233i	$-0.0431783\pi$
$163$	10.9233	+	10.9233i	0.855581	+	0.855581i	−0.135233	+	0.990814i	$0.543178\pi$
$164$	1.36866	+	0.366731i	0.106874	+	0.0286369i
$165$	6.65954	+	14.6284i	0.518445	+	1.13882i
$166$	3.24585	−	1.87399i	0.251926	−	0.145450i
$167$	2.99314	+	11.1706i	0.231617	+	0.864405i	0.979645	+	0.200738i	$0.0643340\pi$
$167$	2.99314	+	11.1706i	0.231617	+	0.864405i	−0.748028	+	0.663667i	$0.768999\pi$
$168$	−0.484009	−	4.55694i	−0.0373421	−	0.351576i
$169$	−11.1417	+	6.69792i	−0.857055	+	0.515224i
$170$	15.9011	+	9.18048i	1.21956	+	0.704111i
$171$	15.7146	+	7.67992i	1.20173	+	0.587298i
$172$	−10.3694			−0.790658
$173$	6.85345			0.521058			0.260529	−	0.965466i	$-0.416103\pi$
$173$	6.85345			0.521058			0.260529	+	0.965466i	$0.416103\pi$
$174$	−2.37063	−	14.2008i	−0.179717	−	1.07656i
$175$	15.6737	−	7.84386i	1.18482	−	0.592940i
$176$	−2.62899	−	0.704437i	−0.198168	−	0.0530989i
$177$	0.803144	+	0.300645i	0.0603680	+	0.0225979i
$178$	6.86066	−	11.8830i	0.514229	−	0.890670i
$179$	2.70761			0.202376			0.101188	−	0.994867i	$-0.467736\pi$
$179$	2.70761			0.202376			0.101188	+	0.994867i	$0.467736\pi$
$180$	0.705433	+	10.2041i	0.0525799	+	0.760567i
$181$			11.5327i			0.857219i	0.903490	+	0.428610i	$0.140996\pi$
$181$			11.5327i			0.857219i	−0.903490	+	0.428610i	$0.859004\pi$
$182$	−9.52711	−	0.484002i	−0.706196	−	0.0358766i
$183$	−12.3219	+	17.2602i	−0.910858	+	1.27591i
$184$	−1.68516	−	0.451536i	−0.124231	−	0.0332877i
$185$			16.1625i			1.18829i
$186$	−0.838038	−	1.84084i	−0.0614480	−	0.134977i
$187$	3.79358	+	14.1578i	0.277414	+	1.03532i
$188$	3.34090	−	12.4684i	0.243660	−	0.909352i
$189$	−12.9201	−	4.69804i	−0.939797	−	0.341732i
$190$	−14.0560	−	14.0560i	−1.01973	−	1.01973i
$191$			6.71906i			0.486174i	0.970004	+	0.243087i	$0.0781601\pi$
$191$			6.71906i			0.486174i	−0.970004	+	0.243087i	$0.921840\pi$
$192$	−1.40969	−	1.00636i	−0.101736	−	0.0726281i
$193$	−0.687259	−	0.687259i	−0.0494700	−	0.0494700i	0.681939	−	0.731409i	$-0.261137\pi$
$193$	−0.687259	−	0.687259i	−0.0494700	−	0.0494700i	−0.731409	+	0.681939i	$0.761137\pi$
$194$	−6.65758	+	11.5313i	−0.477986	+	0.827896i
$195$	21.2106	+	1.86181i	1.51892	+	0.133327i
$196$	−5.60300	−	4.19600i	−0.400214	−	0.299714i
$197$	−9.98319	+	2.67499i	−0.711272	+	0.190585i	−0.596274	−	0.802781i	$-0.703353\pi$
$197$	−9.98319	+	2.67499i	−0.711272	+	0.190585i	−0.114998	+	0.993366i	$0.536686\pi$
$198$	−5.36173	+	6.15812i	−0.381041	+	0.437639i
$199$	6.18891	+	3.57317i	0.438720	+	0.253295i	0.703055	−	0.711136i	$-0.251819\pi$
$199$	6.18891	+	3.57317i	0.438720	+	0.253295i	−0.264334	+	0.964431i	$0.585152\pi$
$200$	1.71456	−	6.39882i	0.121238	−	0.452465i
$201$	−0.161478	−	0.967305i	−0.0113898	−	0.0682285i
$202$	−0.521342	+	1.94567i	−0.0366815	+	0.136897i
$203$	−18.3571	−	12.1110i	−1.28842	−	0.850024i
$204$	−0.897677	+	9.28427i	−0.0628500	+	0.650029i
$205$	−4.18380	+	2.41552i	−0.292209	+	0.168707i
$206$	−4.44006	+	4.44006i	−0.309354	+	0.309354i
$207$	−3.43681	+	3.94729i	−0.238875	+	0.274355i
$208$	−2.52688	+	2.57194i	−0.175208	+	0.178332i
$209$		−	15.8685i		−	1.09765i
$210$	12.1531	+	9.81930i	0.838641	+	0.677596i
$211$	−4.55240	+	7.88500i	−0.313400	+	0.542826i	−0.979096	−	0.203398i	$-0.934802\pi$
$211$	−4.55240	+	7.88500i	−0.313400	+	0.542826i	0.665696	+	0.746223i	$0.268135\pi$
$212$	−3.83125			−0.263131
$213$	10.4537	+	12.6916i	0.716275	+	0.869612i
$214$	−4.39270	−	16.3938i	−0.300279	−	1.12066i
$215$	24.9992	−	24.9992i	1.70493	−	1.70493i
$216$	−4.56940	+	2.47397i	−0.310909	+	0.168333i
$217$	−2.93140	−	0.975971i	−0.198996	−	0.0662532i
$218$	5.45977	−	9.45660i	0.369782	−	0.640482i
$219$	−15.0552	−	18.2781i	−1.01734	−	1.23512i
$220$	8.03645	−	4.63985i	0.541818	−	0.312819i
$221$	18.7989	+	4.85955i	1.26455	+	0.326889i
$222$	−7.47279	+	3.40198i	−0.501541	+	0.228326i
$223$	0.0908711	+	0.339136i	0.00608518	+	0.0227102i	0.968902	−	0.247446i	$-0.0795913\pi$
$223$	0.0908711	+	0.339136i	0.00608518	+	0.0227102i	−0.962816	+	0.270156i	$0.912925\pi$
$224$	−2.59185	+	0.531346i	−0.173175	+	0.0355021i
$225$	−14.9885	−	13.0501i	−0.999234	−	0.870009i
$226$	2.57609	+	9.61411i	0.171359	+	0.639521i
$227$	−11.4203	+	3.06006i	−0.757991	+	0.203103i	−0.617060	−	0.786916i	$-0.711676\pi$
$227$	−11.4203	+	3.06006i	−0.757991	+	0.203103i	−0.140931	+	0.990019i	$0.545010\pi$
$228$	3.54026	−	9.45746i	0.234459	−	0.626335i
$229$	20.4461	−	5.47851i	1.35112	−	0.362030i	0.490569	−	0.871402i	$-0.336789\pi$
$229$	20.4461	−	5.47851i	1.35112	−	0.362030i	0.860547	+	0.509372i	$0.170122\pi$
$230$	5.15128	−	2.97409i	0.339665	−	0.196106i
$231$	1.31734	+	12.4028i	0.0866748	+	0.816044i
$232$	−8.02906	+	2.15138i	−0.527134	+	0.141245i
$233$	8.24057	−	14.2731i	0.539857	−	0.935060i	−0.459054	−	0.888408i	$-0.651811\pi$
$233$	8.24057	−	14.2731i	0.539857	−	0.935060i	0.998911	−	0.0466520i	$-0.0148552\pi$
$234$	3.60372	+	10.1987i	0.235583	+	0.666709i
$235$	22.0052	+	38.1141i	1.43546	+	2.48629i
$236$	0.128146	−	0.478248i	0.00834160	−	0.0311313i
$237$	0.999004	+	2.19441i	0.0648923	+	0.142542i
$238$	9.45698	+	10.6571i	0.613005	+	0.690796i
$239$	2.67571	+	2.67571i	0.173077	+	0.173077i	0.788330	−	0.615253i	$-0.210946\pi$
$239$	2.67571	+	2.67571i	0.173077	+	0.173077i	−0.615253	+	0.788330i	$0.710946\pi$
$240$	5.82479	−	0.972368i	0.375988	−	0.0627661i
$241$	10.7977	−	2.89323i	0.695539	−	0.186369i	0.106307	−	0.994333i	$-0.466097\pi$
$241$	10.7977	−	2.89323i	0.695539	−	0.186369i	0.589232	+	0.807964i	$0.299431\pi$
$242$	−3.46976	−	0.929719i	−0.223045	−	0.0597646i
$243$	0.649179	+	15.5749i	0.0416449	+	0.999132i
$244$	10.6036	+	6.12196i	0.678823	+	0.391919i
$245$	23.6241	−	3.39207i	1.50929	−	0.216712i
$246$	−1.99745	−	1.42596i	−0.127353	−	0.0909158i
$247$	−18.2972	−	10.3495i	−1.16423	−	0.658520i
$248$	−1.01131	+	0.583879i	−0.0642182	+	0.0370764i
$249$	−6.40308	+	1.06891i	−0.405779	+	0.0677392i
$250$	2.76943	+	4.79679i	0.175154	+	0.303375i
$251$	−14.3537	−	24.8613i	−0.905996	−	1.56923i	−0.819574	−	0.572973i	$-0.805790\pi$
$251$	−14.3537	−	24.8613i	−0.905996	−	1.56923i	−0.0864221	−	0.996259i	$-0.527543\pi$
$252$	−1.98194	+	7.68583i	−0.124850	+	0.484162i
$253$	4.58655	+	1.22896i	0.288354	+	0.0772642i
$254$	10.3084	−	10.3084i	0.646804	−	0.646804i
$255$	−20.2189	−	24.5473i	−1.26616	−	1.53721i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.6714	+	20.2155i	0.728044	+	1.26101i	0.957709	+	0.287739i	$0.0929036\pi$
$257$	11.6714	+	20.2155i	0.728044	+	1.26101i	−0.229665	+	0.973270i	$0.573763\pi$
$258$	16.8204	+	6.29648i	1.04719	+	0.392002i
$259$	−3.96191	+	11.8999i	−0.246181	+	0.739423i
$260$	−0.108612	−	12.2926i	−0.00673582	−	0.762353i
$261$	−4.77753	+	24.4750i	−0.295722	+	1.51496i
$262$	4.30629	−	4.30629i	0.266043	−	0.266043i
$263$			0.844931i			0.0521007i	0.999661	+	0.0260503i	$0.00829302\pi$
$263$			0.844931i			0.0521007i	−0.999661	+	0.0260503i	$0.991707\pi$
$264$	3.83681	+	2.73906i	0.236139	+	0.168577i
$265$	9.23663	−	9.23663i	0.567402	−	0.567402i
$266$	−6.90342	−	13.7945i	−0.423276	−	0.845797i
$267$	−18.3444	+	15.1098i	−1.12266	+	0.924705i
$268$	−0.546909	+	0.146544i	−0.0334078	+	0.00895159i
$269$	−4.06872	−	2.34908i	−0.248074	−	0.143226i	0.370808	−	0.928710i	$-0.379081\pi$
$269$	−4.06872	−	2.34908i	−0.248074	−	0.143226i	−0.618882	+	0.785484i	$0.712414\pi$
$270$	5.05180	−	16.9806i	0.307443	−	1.03341i
$271$	3.18762	−	11.8964i	0.193634	−	0.722653i	−0.798982	−	0.601355i	$-0.794628\pi$
$271$	3.18762	−	11.8964i	0.193634	−	0.722653i	0.992616	−	0.121298i	$-0.0387057\pi$
$272$	5.38527			0.326530
$273$	15.1603	+	6.57014i	0.917540	+	0.397643i
$274$	10.2069			0.616620
$275$	−4.66657	+	17.4159i	−0.281405	+	1.05022i
$276$	2.45935	+	1.75570i	0.148036	+	0.105681i
$277$	17.7849	+	10.2681i	1.06859	+	0.616952i	0.927796	−	0.373087i	$-0.121701\pi$
$277$	17.7849	+	10.2681i	1.06859	+	0.616952i	0.140796	+	0.990039i	$0.455034\pi$
$278$	−3.37045	+	0.903109i	−0.202146	+	0.0541649i
$279$	0.241613	+	3.49494i	0.0144650	+	0.209236i
$280$	4.96759	−	7.52960i	0.296870	−	0.449980i
$281$	−4.81731	+	4.81731i	−0.287377	+	0.287377i	−0.836042	−	0.548665i	$-0.815136\pi$
$281$	−4.81731	+	4.81731i	−0.287377	+	0.287377i	0.548665	+	0.836042i	$0.315136\pi$
$282$	−12.9904	+	18.1966i	−0.773567	+	1.08359i
$283$			11.7992i			0.701390i	0.936490	+	0.350695i	$0.114055\pi$
$283$			11.7992i			0.701390i	−0.936490	+	0.350695i	$0.885945\pi$
$284$	6.71262	−	6.71262i	0.398321	−	0.398321i
$285$	14.2656	+	31.3357i	0.845019	+	1.85617i
$286$	6.87751	−	7.00013i	0.406676	−	0.413926i
$287$	−3.67249	+	0.752886i	−0.216781	+	0.0444415i
$288$	1.67561	+	2.48844i	0.0987364	+	0.146633i
$289$	−6.00057	−	10.3933i	−0.352975	−	0.611370i
$290$	14.1703	−	24.5437i	0.832109	−	1.44125i
$291$	17.8014	−	14.6625i	1.04354	−	0.859533i
$292$	−9.66737	+	9.66737i	−0.565740	+	0.565740i
$293$	−11.5266	−	3.08854i	−0.673390	−	0.180434i	−0.0941084	−	0.995562i	$-0.530000\pi$
$293$	−11.5266	−	3.08854i	−0.673390	−	0.180434i	−0.579281	+	0.815128i	$0.696667\pi$
$294$	6.54087	+	10.2087i	0.381471	+	0.595382i
$295$	0.844048	+	1.46193i	0.0491424	+	0.0851171i
$296$	2.37023	+	4.10537i	0.137767	+	0.238619i
$297$	12.4367	−	6.73350i	0.721651	−	0.390717i
$298$	−4.35078	+	2.51193i	−0.252034	+	0.145512i
$299$	4.40841	−	4.48700i	0.254945	−	0.259490i
$300$	−6.66671	+	9.33857i	−0.384902	+	0.539162i
$301$	24.5341	−	12.2780i	1.41412	−	0.707691i
$302$	4.37488	+	2.52584i	0.251746	+	0.145346i
$303$	2.02713	−	2.83956i	0.116456	−	0.163128i
$304$	−5.63163	−	1.50899i	−0.322996	−	0.0865465i
$305$	−40.3230	+	10.8045i	−2.30889	+	0.618664i
$306$	7.09372	−	14.5151i	0.405521	−	0.829776i
$307$	−10.9388	−	10.9388i	−0.624311	−	0.624311i	0.322320	−	0.946631i	$-0.395537\pi$
$307$	−10.9388	−	10.9388i	−0.624311	−	0.624311i	−0.946631	+	0.322320i	$0.895537\pi$
$308$	7.05432	−	1.44618i	0.401957	−	0.0824040i
$309$	9.89842	−	4.50624i	0.563101	−	0.256351i
$310$	1.03047	−	3.84578i	0.0585270	−	0.218426i
$311$	−4.19822	−	7.27152i	−0.238059	−	0.412330i	0.722098	−	0.691790i	$-0.243178\pi$
$311$	−4.19822	−	7.27152i	−0.238059	−	0.412330i	−0.960157	+	0.279460i	$0.909844\pi$
$312$	5.66065	−	2.63763i	0.320471	−	0.149326i
$313$	16.4060	−	28.4160i	0.927321	−	1.60617i	0.139536	−	0.990217i	$-0.455439\pi$
$313$	16.4060	−	28.4160i	0.927321	−	1.60617i	0.787785	−	0.615950i	$-0.211228\pi$
$314$	4.05965	−	1.08778i	0.229099	−	0.0613870i
$315$	−13.7513	−	23.3077i	−0.774799	−	1.31324i
$316$	1.20556	−	0.696028i	0.0678178	−	0.0391546i
$317$	29.1781	−	7.81826i	1.63881	−	0.439117i	0.682359	−	0.731017i	$-0.260954\pi$
$317$	29.1781	−	7.81826i	1.63881	−	0.439117i	0.956449	+	0.291900i	$0.0942875\pi$
$318$	6.21477	+	2.32641i	0.348507	+	0.130458i
$319$	21.8530	−	5.85549i	1.22353	−	0.327844i
$320$	−0.882438	−	3.29330i	−0.0493298	−	0.184101i
$321$	−2.82910	+	29.2601i	−0.157905	+	1.63314i
$322$	4.52174	−	0.926987i	0.251987	−	0.0516590i
$323$	8.12632	+	30.3278i	0.452161	+	1.68749i
$324$	8.91438	−	1.23847i	0.495243	−	0.0688036i
$325$	17.0379	+	16.7395i	0.945093	+	0.928538i
$326$	−13.3783	+	7.72396i	−0.740955	+	0.427790i
$327$	−14.5987	+	12.0245i	−0.807307	+	0.664957i
$328$	−0.708471	+	1.22711i	−0.0391187	+	0.0677557i
$329$	6.85875	+	33.4562i	0.378135	+	1.84450i
$330$	−15.8535	+	2.64653i	−0.872708	+	0.145687i
$331$	−1.47464	+	1.47464i	−0.0810536	+	0.0810536i	−0.746471	−	0.665418i	$-0.768253\pi$
$331$	−1.47464	+	1.47464i	−0.0810536	+	0.0810536i	0.665418	+	0.746471i	$0.268253\pi$
$332$	0.970048	+	3.62027i	0.0532383	+	0.198688i
$333$	14.1875	−	0.980820i	0.777472	−	0.0537486i
$334$	−11.5646			−0.632788
$335$	0.965227	−	1.67182i	0.0527360	−	0.0913414i
$336$	4.52694	+	0.711907i	0.246965	+	0.0388377i
$337$			5.06430i			0.275870i	0.990441	+	0.137935i	$0.0440465\pi$
$337$			5.06430i			0.275870i	−0.990441	+	0.137935i	$0.955953\pi$
$338$	−3.58600	−	12.4956i	−0.195053	−	0.679672i
$339$	1.65912	−	17.1595i	0.0901110	−	0.931978i
$340$	−12.9832	+	12.9832i	−0.704111	+	0.704111i
$341$	2.75251	−	1.58917i	0.149057	−	0.0860581i
$342$	−11.4855	+	13.1915i	−0.621064	+	0.713312i
$343$	18.2251	+	3.29349i	0.984061	+	0.177832i
$344$	2.68379	−	10.0161i	0.144700	−	0.540030i
$345$	−10.1619	+	1.69640i	−0.547100	+	0.0913309i
$346$	−1.77380	+	6.61992i	−0.0953602	+	0.355889i
$347$	−2.39696	−	1.38389i	−0.128676	−	0.0742909i	0.434280	−	0.900778i	$-0.357003\pi$
$347$	−2.39696	−	1.38389i	−0.128676	−	0.0742909i	−0.562956	+	0.826487i	$0.690336\pi$
$348$	14.3305	+	1.38559i	0.768195	+	0.0742752i
$349$	−10.2283	+	2.74067i	−0.547510	+	0.146705i	−0.521962	−	0.852969i	$-0.674800\pi$
$349$	−10.2283	+	2.74067i	−0.547510	+	0.146705i	−0.0255480	+	0.999674i	$0.508133\pi$
$350$	3.51993	+	17.1698i	0.188148	+	0.917765i
$351$	0.347147	−	18.7318i	0.0185293	−	0.999828i
$352$	1.36087	−	2.35709i	0.0725345	−	0.125633i
$353$	5.73382	+	5.73382i	0.305180	+	0.305180i	0.843037	−	0.537856i	$-0.180766\pi$
$353$	5.73382	+	5.73382i	0.305180	+	0.305180i	−0.537856	+	0.843037i	$0.680766\pi$
$354$	−0.498270	+	0.697965i	−0.0264827	+	0.0370964i
$355$			32.3664i			1.71783i
$356$	9.70244	+	9.70244i	0.514229	+	0.514229i
$357$	−8.86922	−	23.0296i	−0.469409	−	1.21885i
$358$	−0.700780	+	2.61535i	−0.0370374	+	0.138225i
$359$	3.44709	+	12.8647i	0.181930	+	0.678973i	0.995267	+	0.0971798i	$0.0309822\pi$
$359$	3.44709	+	12.8647i	0.181930	+	0.678973i	−0.813336	+	0.581794i	$0.802351\pi$
$360$	−10.0390	−	1.95961i	−0.529100	−	0.103281i
$361$		−	14.9923i		−	0.789069i
$362$	−11.1397	−	2.98488i	−0.585492	−	0.156882i
$363$	5.06384	+	3.61502i	0.265782	+	0.189739i
$364$	2.93331	−	9.07721i	0.153747	−	0.475775i
$365$		−	46.6135i		−	2.43986i
$366$	−13.4829	−	16.3693i	−0.704763	−	0.855635i
$367$	3.32496			0.173561			0.0867807	−	0.996227i	$-0.472342\pi$
$367$	3.32496			0.173561			0.0867807	+	0.996227i	$0.472342\pi$
$368$	0.872301	−	1.51087i	0.0454718	−	0.0787595i
$369$	2.37424	+	3.52597i	0.123598	+	0.183555i
$370$	−15.6118	−	4.18317i	−0.811619	−	0.217473i
$371$	9.06478	−	4.53643i	0.470620	−	0.235520i
$372$	1.99501	−	0.333040i	0.103436	−	0.0172673i
$373$	2.63780			0.136580			0.0682901	−	0.997666i	$-0.478246\pi$
$373$	2.63780			0.136580			0.0682901	+	0.997666i	$0.478246\pi$
$374$	−14.6573			−0.757910
$375$	−1.57966	−	9.46263i	−0.0815731	−	0.488648i
$376$	11.1789	+	6.45412i	0.576506	+	0.332846i
$377$	7.50084	−	29.0166i	0.386313	−	1.49443i
$378$	7.88192	−	11.2639i	0.405402	−	0.579352i
$379$	3.22947	+	12.0526i	0.165887	+	0.619098i	0.997925	+	0.0643804i	$0.0205071\pi$
$379$	3.22947	+	12.0526i	0.165887	+	0.619098i	−0.832039	+	0.554718i	$0.812826\pi$
$380$	17.2151	−	9.93913i	0.883115	−	0.509866i
$381$	−22.9809	+	10.4620i	−1.17735	+	0.535985i
$382$	−6.49012	−	1.73902i	−0.332063	−	0.0889761i
$383$	−9.87370	−	9.87370i	−0.504523	−	0.504523i	0.408317	−	0.912840i	$-0.366116\pi$
$383$	−9.87370	−	9.87370i	−0.504523	−	0.504523i	−0.912840	+	0.408317i	$0.866116\pi$
$384$	1.33693	−	1.10119i	0.0682248	−	0.0561949i
$385$	−13.5205	+	20.4936i	−0.689067	+	1.04445i
$386$	0.841717	−	0.485966i	0.0428423	−	0.0247350i
$387$	−23.4615	−	20.4273i	−1.19261	−	1.03838i
$388$	−9.41524	−	9.41524i	−0.477986	−	0.477986i
$389$	1.68983	+	2.92688i	0.0856780	+	0.148399i	0.905680	−	0.423962i	$-0.139361\pi$
$389$	1.68983	+	2.92688i	0.0856780	+	0.148399i	−0.820002	+	0.572361i	$0.806028\pi$
$390$	−7.28809	+	20.0060i	−0.369047	+	1.01304i
$391$	−9.39515			−0.475133
$392$	5.50319	−	4.32607i	0.277953	−	0.218500i
$393$	−9.60019	+	4.37048i	−0.484266	+	0.220461i
$394$		−	10.3354i		−	0.520688i
$395$	−1.22840	+	4.58446i	−0.0618077	+	0.230669i
$396$	−4.56057	−	6.77287i	−0.229177	−	0.340349i
$397$	−25.8370	−	25.8370i	−1.29672	−	1.29672i	−0.930544	−	0.366179i	$-0.880666\pi$
$397$	−25.8370	−	25.8370i	−1.29672	−	1.29672i	−0.366179	−	0.930544i	$-0.619334\pi$
$398$	−5.05323	+	5.05323i	−0.253295	+	0.253295i
$399$	2.82191	+	26.5683i	0.141272	+	1.33008i
$400$	5.73702	+	3.31227i	0.286851	+	0.165614i
$401$	5.70049	+	1.52744i	0.284669	+	0.0762768i	0.398328	−	0.917243i	$-0.369591\pi$
$401$	5.70049	+	1.52744i	0.284669	+	0.0762768i	−0.113659	+	0.993520i	$0.536257\pi$
$402$	0.976139	+	0.0943809i	0.0486854	+	0.00470729i
$403$	−0.0371999	−	4.21025i	−0.00185306	−	0.209728i
$404$	−1.74444	−	1.00716i	−0.0867894	−	0.0501079i
$405$	−18.5056	+	24.4771i	−0.919551	+	1.21628i
$406$	16.4495	−	14.5971i	0.816374	−	0.724441i
$407$	−6.45115	−	11.1737i	−0.319772	−	0.553861i
$408$	−8.73558	−	3.27003i	−0.432475	−	0.161891i
$409$	−7.21568	−	26.9293i	−0.356792	−	1.33157i	−0.878214	−	0.478268i	$-0.841265\pi$
$409$	−7.21568	−	26.9293i	−0.356792	−	1.33157i	0.521422	−	0.853299i	$-0.325402\pi$
$410$	−1.25036	−	4.66642i	−0.0617510	−	0.230458i
$411$	−16.5568	−	6.19780i	−0.816687	−	0.305715i
$412$	−3.13960	−	5.43794i	−0.154677	−	0.267908i
$413$	0.263079	+	1.28327i	0.0129453	+	0.0631457i
$414$	−2.92328	−	4.34133i	−0.143671	−	0.213365i
$415$	−11.0666	−	6.38933i	−0.543240	−	0.313640i
$416$	−1.83029	−	3.10645i	−0.0897375	−	0.152306i
$417$	6.01567	+	0.581643i	0.294589	+	0.0284832i
$418$	15.3278	+	4.10707i	0.749707	+	0.200883i
$419$	−12.8370	−	7.41143i	−0.627127	−	0.362072i	0.152512	−	0.988302i	$-0.451264\pi$
$419$	−12.8370	−	7.41143i	−0.627127	−	0.362072i	−0.779639	+	0.626230i	$0.784597\pi$
$420$	−12.6302	+	9.19753i	−0.616289	+	0.448794i
$421$	18.1242	−	18.1242i	0.883318	−	0.883318i	−0.110552	−	0.993870i	$-0.535262\pi$
$421$	18.1242	−	18.1242i	0.883318	−	0.883318i	0.993870	+	0.110552i	$0.0352620\pi$
$422$	−6.43807	−	6.43807i	−0.313400	−	0.313400i
$423$	32.1214	−	21.6292i	1.56179	−	1.05165i
$424$	0.991601	−	3.70071i	0.0481564	−	0.179722i
$425$		−	35.6750i		−	1.73049i
$426$	−14.9647	+	6.81268i	−0.725043	+	0.330075i
$427$	−32.3369	−	1.92938i	−1.56489	−	0.0933692i
$428$	16.9721			0.820377
$429$	−15.4068	+	7.17892i	−0.743846	+	0.346602i
$430$	17.6771	+	30.6176i	0.852465	+	1.47651i
$431$	−1.68177	−	1.68177i	−0.0810080	−	0.0810080i	0.665442	−	0.746450i	$-0.268243\pi$
$431$	−1.68177	−	1.68177i	−0.0810080	−	0.0810080i	−0.746450	+	0.665442i	$0.768243\pi$
$432$	−1.20703	−	5.05402i	−0.0580730	−	0.243162i
$433$	−4.77905	+	2.75918i	−0.229666	+	0.132598i	−0.610418	−	0.792079i	$-0.708999\pi$
$433$	−4.77905	+	2.75918i	−0.229666	+	0.132598i	0.380752	+	0.924677i	$0.375665\pi$
$434$	1.70142	−	2.57892i	0.0816707	−	0.123792i
$435$	−37.8894	+	31.2084i	−1.81666	+	1.49633i
$436$	7.72129	+	7.72129i	0.369782	+	0.369782i
$437$	9.82495	+	2.63259i	0.469991	+	0.125934i
$438$	21.5519	−	9.81147i	1.02979	−	0.468810i
$439$	8.39974	−	4.84959i	0.400898	−	0.231458i	−0.285974	−	0.958237i	$-0.592317\pi$
$439$	8.39974	−	4.84959i	0.400898	−	0.231458i	0.686871	+	0.726779i	$0.258984\pi$
$440$	2.40176	+	8.96350i	0.114500	+	0.427318i
$441$	−4.41120	−	20.5315i	−0.210057	−	0.977689i
$442$	−9.55949	+	16.9006i	−0.454698	+	0.803881i
$443$	−16.9915	−	9.81007i	−0.807292	−	0.466090i	0.0387223	−	0.999250i	$-0.487671\pi$
$443$	−16.9915	−	9.81007i	−0.807292	−	0.466090i	−0.846015	+	0.533160i	$0.821005\pi$
$444$	−1.35196	−	8.09866i	−0.0641612	−	0.384345i
$445$	−46.7826			−2.21771
$446$	−0.351099			−0.0166250
$447$	8.58280	−	1.43278i	0.405952	−	0.0677682i
$448$	0.157578	−	2.64105i	0.00744488	−	0.124778i
$449$	13.0128	+	3.48676i	0.614111	+	0.164550i	0.552449	−	0.833547i	$-0.313693\pi$
$449$	13.0128	+	3.48676i	0.614111	+	0.164550i	0.0616615	+	0.998097i	$0.480360\pi$
$450$	16.4848	−	11.1002i	0.777100	−	0.523267i
$451$	1.92827	−	3.33986i	0.0907986	−	0.157268i
$452$	−9.95326			−0.468162
$453$	−5.56286	−	6.75373i	−0.261366	−	0.317318i
$454$		−	11.8232i		−	0.554888i
$455$	14.8121	+	28.9557i	0.694403	+	1.35747i
$456$	8.21891	+	5.86740i	0.384886	+	0.274766i
$457$	1.25028	+	0.335010i	0.0584854	+	0.0156711i	0.287943	−	0.957648i	$-0.407029\pi$
$457$	1.25028	+	0.335010i	0.0584854	+	0.0156711i	−0.229458	+	0.973319i	$0.573695\pi$
$458$			21.1674i			0.989085i
$459$	−20.3207	+	19.2379i	−0.948491	+	0.897950i
$460$	1.53950	+	5.74550i	0.0717797	+	0.267885i
$461$	7.55353	−	28.1902i	0.351803	−	1.31295i	−0.532657	−	0.846331i	$-0.678806\pi$
$461$	7.55353	−	28.1902i	0.351803	−	1.31295i	0.884460	−	0.466616i	$-0.154527\pi$
$462$	−12.3211	−	1.93762i	−0.573231	−	0.0901464i
$463$	−8.48722	−	8.48722i	−0.394434	−	0.394434i	0.481830	−	0.876265i	$-0.339972\pi$
$463$	−8.48722	−	8.48722i	−0.394434	−	0.394434i	−0.876265	+	0.481830i	$0.839972\pi$
$464$		−	8.31230i		−	0.385889i
$465$	−4.00679	+	5.61262i	−0.185810	+	0.260279i
$466$	11.6539	+	11.6539i	0.539857	+	0.539857i
$467$	−13.6695	+	23.6763i	−0.632550	+	1.09561i	0.354478	+	0.935064i	$0.384659\pi$
$467$	−13.6695	+	23.6763i	−0.632550	+	1.09561i	−0.987028	+	0.160545i	$0.948675\pi$
$468$	−10.7839	+	0.841312i	−0.498485	+	0.0388897i
$469$	1.12048	−	0.994298i	0.0517388	−	0.0459124i
$470$	−42.5108	+	11.3907i	−1.96088	+	0.525415i
$471$	−7.24578	−	0.700580i	−0.333868	−	0.0322810i
$472$	0.428785	+	0.247559i	0.0197364	+	0.0113948i
$473$	−7.30458	+	27.2611i	−0.335865	+	1.25346i
$474$	−2.37820	+	0.397008i	−0.109234	+	0.0182352i
$475$	−9.99638	+	37.3070i	−0.458665	+	1.71176i
$476$	−12.7416	+	6.37649i	−0.584010	+	0.292266i
$477$	−8.66848	−	7.54744i	−0.396903	−	0.345573i
$478$	−3.27706	+	1.89201i	−0.149889	+	0.0865385i
$479$	28.2712	−	28.2712i	1.29175	−	1.29175i	0.358040	−	0.933706i	$-0.383445\pi$
$479$	28.2712	−	28.2712i	1.29175	−	1.29175i	0.933706	−	0.358040i	$-0.116555\pi$
$480$	−0.568330	+	5.87798i	−0.0259406	+	0.268292i
$481$	−17.0913	+	0.151012i	−0.779298	+	0.00688554i
$482$			11.1786i			0.509170i
$483$	−7.89771	−	1.24199i	−0.359358	−	0.0565127i
$484$	1.79608	−	3.11090i	0.0816400	−	0.141405i
$485$	45.3977			2.06140
$486$	−15.2123	−	3.40403i	−0.690042	−	0.154410i
$487$	−2.11439	−	7.89100i	−0.0958120	−	0.357575i	0.901329	−	0.433135i	$-0.142593\pi$
$487$	−2.11439	−	7.89100i	−0.0958120	−	0.357575i	−0.997141	+	0.0755591i	$0.975926\pi$
$488$	−8.65776	+	8.65776i	−0.391919	+	0.391919i
$489$	26.3914	−	4.40568i	1.19346	−	0.199232i
$490$	−2.83787	+	23.6970i	−0.128202	+	1.07052i
$491$	14.5460	−	25.1944i	0.656453	−	1.13701i	−0.325075	−	0.945688i	$-0.605389\pi$
$491$	14.5460	−	25.1944i	0.656453	−	1.13701i	0.981527	−	0.191321i	$-0.0612772\pi$
$492$	1.89435	−	1.56032i	0.0854038	−	0.0703448i
$493$	−38.7667	+	22.3820i	−1.74597	+	1.00803i
$494$	14.7325	−	14.9951i	0.662845	−	0.674663i
$495$	27.3234	+	5.33355i	1.22810	+	0.239725i
$496$	−0.302238	−	1.12797i	−0.0135709	−	0.0506473i
$497$	−7.93397	+	23.8303i	−0.355887	+	1.06893i
$498$	0.624755	−	6.46156i	0.0279959	−	0.289549i
$499$	5.20426	+	19.4226i	0.232975	+	0.869474i	0.979051	+	0.203614i	$0.0652687\pi$
$499$	5.20426	+	19.4226i	0.232975	+	0.869474i	−0.746076	+	0.665860i	$0.768065\pi$
$500$	−5.35012	+	1.43356i	−0.239265	+	0.0641108i
$501$	18.7593	+	7.02225i	0.838102	+	0.313731i
$502$	27.7292	−	7.43001i	1.23761	−	0.331618i
$503$	−1.29628	+	0.748409i	−0.0577984	+	0.0333699i	−0.528621	−	0.848858i	$-0.677291\pi$
$503$	−1.29628	+	0.748409i	−0.0577984	+	0.0333699i	0.470822	+	0.882228i	$0.343957\pi$
$504$	−6.91098	−	3.90364i	−0.307839	−	0.173882i
$505$	6.63374	−	1.77750i	0.295197	−	0.0790979i
$506$	−2.37417	+	4.11219i	−0.105545	+	0.182809i
$507$	−1.77063	+	22.4469i	−0.0786364	+	0.996903i
$508$	7.28911	+	12.6251i	0.323402	+	0.560149i
$509$	−0.562121	+	2.09786i	−0.0249156	+	0.0929862i	−0.977264	−	0.212026i	$-0.931994\pi$
$509$	−0.562121	+	2.09786i	−0.0249156	+	0.0929862i	0.952348	+	0.305012i	$0.0986605\pi$
$510$	28.9439	−	13.1767i	1.28166	−	0.583473i
$511$	11.4263	−	34.3198i	0.505471	−	1.51822i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	26.6410	−	14.4240i	1.17623	−	0.636834i
$514$	−22.5475	+	6.04158i	−0.994526	+	0.266483i
$515$	20.6793	+	5.54100i	0.911239	+	0.244166i
$516$	−10.4354	+	14.6176i	−0.459392	+	0.643506i
$517$	−30.4259	−	17.5664i	−1.33813	−	0.772570i
$518$	−10.4690	−	6.90683i	−0.459981	−	0.303469i
$519$	6.89706	−	9.66125i	0.302748	−	0.424082i
$520$	11.9018	+	3.07664i	0.521929	+	0.134920i
$521$	−30.4873	+	17.6018i	−1.33567	+	0.771151i	−0.986162	−	0.165782i	$-0.946985\pi$
$521$	−30.4873	+	17.6018i	−1.33567	+	0.771151i	−0.349510	+	0.936933i	$0.613652\pi$
$522$	−22.4045	−	10.9493i	−0.980618	−	0.479239i
$523$	−14.2777	−	24.7298i	−0.624322	−	1.08136i	−0.988672	−	0.150095i	$-0.952042\pi$
$523$	−14.2777	−	24.7298i	−0.624322	−	1.08136i	0.364350	−	0.931262i	$-0.381291\pi$
$524$	3.04501	+	5.27411i	0.133022	+	0.230400i
$525$	4.71606	−	29.9889i	0.205826	−	1.30882i
$526$	−0.816141	−	0.218684i	−0.0355854	−	0.00953509i
$527$	−4.44678	+	4.44678i	−0.193705	+	0.193705i
$528$	−3.63876	+	2.99715i	−0.158357	+	0.130434i
$529$	9.97818	−	17.2827i	0.433834	−	0.751423i
$530$	6.53129	+	11.3125i	0.283701	+	0.491384i
$531$	1.23207	−	0.829627i	0.0534674	−	0.0360027i
$532$	15.1112	−	3.09790i	0.655155	−	0.134311i
$533$	−2.59342	−	4.40166i	−0.112333	−	0.190657i
$534$	−9.84707	−	21.6301i	−0.426124	−	0.936025i
$535$	−40.9175	+	40.9175i	−1.76902	+	1.76902i
$536$		−	0.566202i		−	0.0244562i
$537$	2.72484	−	3.81689i	0.117585	−	0.164711i
$538$	3.32210	−	3.32210i	0.143226	−	0.143226i
$539$	−14.9782	+	11.7744i	−0.645158	+	0.507160i
$540$	15.0945	+	9.27458i	0.649565	+	0.399114i
$541$	15.2971	−	4.09884i	0.657672	−	0.176223i	0.0854769	−	0.996340i	$-0.472759\pi$
$541$	15.2971	−	4.09884i	0.657672	−	0.176223i	0.572195	+	0.820117i	$0.306092\pi$
$542$	10.6660	+	6.15802i	0.458144	+	0.264510i
$543$	16.2576	+	11.6061i	0.697679	+	0.498066i
$544$	−1.39381	+	5.20177i	−0.0597591	+	0.223024i
$545$	−37.2300			−1.59476
$546$	−10.2700	+	12.9432i	−0.439517	+	0.553918i
$547$	22.5516			0.964236			0.482118	−	0.876106i	$-0.339868\pi$
$547$	22.5516			0.964236			0.482118	+	0.876106i	$0.339868\pi$
$548$	−2.64173	+	9.85908i	−0.112849	+	0.421159i
$549$	11.9312	+	34.7400i	0.509213	+	1.48267i
$550$	−15.6147	−	9.01513i	−0.665811	−	0.384406i
$551$	46.8118	−	12.5432i	1.99425	−	0.534357i
$552$	−2.33241	+	1.92114i	−0.0992739	+	0.0817692i
$553$	−2.02822	+	3.07426i	−0.0862486	+	0.130731i
$554$	−14.5213	+	14.5213i	−0.616952	+	0.616952i
$555$	22.7842	+	16.2654i	0.967134	+	0.690427i
$556$		−	3.48934i		−	0.147981i
$557$	−1.52916	+	1.52916i	−0.0647926	+	0.0647926i	−0.738761	−	0.673968i	$-0.764589\pi$
$557$	−1.52916	+	1.52916i	−0.0647926	+	0.0647926i	0.673968	+	0.738761i	$0.264589\pi$
$558$	−3.43838	−	0.671175i	−0.145558	−	0.0284131i
$559$	26.6694	+	26.2022i	1.12800	+	1.10824i
$560$	5.98733	+	6.74713i	0.253011	+	0.285118i
$561$	23.7759	+	8.90017i	1.00382	+	0.375765i
$562$	−3.40635	−	5.89998i	−0.143688	−	0.248875i
$563$	8.60899	−	14.9112i	0.362826	−	0.628432i	−0.625599	−	0.780145i	$-0.715145\pi$
$563$	8.60899	−	14.9112i	0.362826	−	0.628432i	0.988425	+	0.151712i	$0.0484787\pi$
$564$	−14.2144	−	17.2574i	−0.598536	−	0.726668i
$565$	23.9960	−	23.9960i	1.00952	−	1.00952i
$566$	−11.3972	−	3.05386i	−0.479058	−	0.128363i
$567$	−19.6251	+	13.4854i	−0.824176	+	0.566333i
$568$	4.74654	+	8.22125i	0.199160	+	0.344956i
$569$	−4.81789	−	8.34483i	−0.201977	−	0.349834i	0.747189	−	0.664612i	$-0.231403\pi$
$569$	−4.81789	−	8.34483i	−0.201977	−	0.349834i	−0.949165	+	0.314778i	$0.898070\pi$
$570$	−33.9602	+	5.66919i	−1.42244	+	0.237456i
$571$	35.2570	−	20.3556i	1.47546	−	0.851856i	0.475841	−	0.879531i	$-0.342144\pi$
$571$	35.2570	−	20.3556i	1.47546	−	0.851856i	0.999617	+	0.0276752i	$0.00881041\pi$
$572$	4.98157	+	8.45493i	0.208290	+	0.353518i
$573$	9.47181	+	6.76183i	0.395690	+	0.282479i
$574$	0.223279	−	3.74222i	0.00931950	−	0.156197i
$575$	−10.0088	−	5.77860i	−0.417397	−	0.240984i
$576$	−2.83733	+	0.974462i	−0.118222	+	0.0406026i
$577$	14.0412	+	3.76233i	0.584543	+	0.156628i	0.538958	−	0.842333i	$-0.318818\pi$
$577$	14.0412	+	3.76233i	0.584543	+	0.156628i	0.0455850	+	0.998960i	$0.485485\pi$
$578$	11.5922	−	3.10612i	0.482172	−	0.129198i
$579$	−1.66046	+	0.277191i	−0.0690062	+	0.0115196i
$580$	20.0398	+	20.0398i	0.832109	+	0.832109i
$581$	−6.58176	−	7.41700i	−0.273058	−	0.307709i
$582$	9.55558	+	20.9898i	0.396091	+	0.870054i
$583$	−2.69888	+	10.0723i	−0.111776	+	0.417154i
$584$	−6.83586	−	11.8401i	−0.282870	−	0.489945i
$585$	23.9702	−	28.0268i	0.991046	−	1.15877i
$586$	5.96659	−	10.3344i	0.246478	−	0.426912i
$587$	30.9162	−	8.28397i	1.27605	−	0.341916i	0.443703	−	0.896174i	$-0.353665\pi$
$587$	30.9162	−	8.28397i	1.27605	−	0.341916i	0.832345	+	0.554258i	$0.186998\pi$
$588$	−11.5537	+	3.67579i	−0.476468	+	0.151587i
$589$	5.89623	−	3.40419i	0.242950	−	0.140267i
$590$	−1.63058	+	0.436911i	−0.0671297	+	0.0179874i
$591$	−6.27581	+	16.7652i	−0.258153	+	0.689629i
$592$	−4.57894	+	1.22692i	−0.188193	+	0.0504262i
$593$	−7.49100	−	27.9568i	−0.307619	−	1.14805i	−0.930668	−	0.365866i	$-0.880773\pi$
$593$	−7.49100	−	27.9568i	−0.307619	−	1.14805i	0.623049	−	0.782183i	$-0.285894\pi$
$594$	3.28520	+	13.7557i	0.134794	+	0.564403i
$595$	15.3454	−	46.0911i	0.629102	−	1.88955i
$596$	−1.30027	−	4.85267i	−0.0532611	−	0.198773i
$597$	11.2654	−	5.12855i	0.461061	−	0.209898i
$598$	3.19313	+	5.41952i	0.130577	+	0.221621i
$599$	−9.28946	+	5.36327i	−0.379557	+	0.219137i	−0.677626	−	0.735407i	$-0.736991\pi$
$599$	−9.28946	+	5.36327i	−0.379557	+	0.219137i	0.298068	+	0.954545i	$0.403658\pi$
$600$	−7.29489	−	8.85654i	−0.297813	−	0.361567i
$601$	9.06315	−	15.6978i	0.369694	−	0.640328i	−0.619824	−	0.784741i	$-0.712796\pi$
$601$	9.06315	−	15.6978i	0.369694	−	0.640328i	0.989518	+	0.144413i	$0.0461293\pi$
$602$	5.50973	+	26.8759i	0.224560	+	1.09538i
$603$	−1.52611	−	0.745827i	−0.0621479	−	0.0303724i
$604$	−3.57207	+	3.57207i	−0.145346	+	0.145346i
$605$	3.16986	+	11.8301i	0.128873	+	0.480961i
$606$	2.21814	+	2.69299i	0.0901059	+	0.109395i
$607$	−15.6175			−0.633893			−0.316947	−	0.948443i	$-0.602658\pi$
$607$	−15.6175			−0.633893			−0.316947	+	0.948443i	$0.602658\pi$
$608$	2.91515	−	5.04918i	0.118225	−	0.204771i
$609$	−35.5467	+	13.6899i	−1.44043	+	0.554741i
$610$		−	41.7454i		−	1.69022i
$611$	−40.0988	+	23.6259i	−1.62222	+	0.955800i
$612$	12.1846	+	10.6088i	0.492532	+	0.428835i
$613$	−17.3540	+	17.3540i	−0.700923	+	0.700923i	−0.964609	−	0.263686i	$-0.915062\pi$
$613$	−17.3540	+	17.3540i	−0.700923	+	0.700923i	0.263686	+	0.964609i	$0.415062\pi$
$614$	13.3973	−	7.73491i	0.540669	−	0.312156i
$615$	−0.805290	+	8.32875i	−0.0324724	+	0.335848i
$616$	−0.428887	+	7.18825i	−0.0172803	+	0.289623i
$617$	−8.54893	+	31.9050i	−0.344167	+	1.28445i	0.549415	+	0.835549i	$0.314851\pi$
$617$	−8.54893	+	31.9050i	−0.344167	+	1.28445i	−0.893582	+	0.448899i	$0.851816\pi$
$618$	1.79080	+	10.7274i	0.0720365	+	0.431521i
$619$	4.28754	−	16.0013i	0.172331	−	0.643147i	−0.824660	−	0.565628i	$-0.808634\pi$
$619$	4.28754	−	16.0013i	0.172331	−	0.643147i	0.996991	−	0.0775184i	$-0.0246997\pi$
$620$	3.44804	+	1.99072i	0.138476	+	0.0799494i
$621$	2.10578	+	8.81725i	0.0845020	+	0.353824i
$622$	8.11033	−	2.17316i	0.325195	−	0.0871356i
$623$	−34.4444	−	11.4678i	−1.37998	−	0.459448i
$624$	1.08267	+	6.15043i	0.0433415	+	0.246214i
$625$	−7.11906	+	12.3306i	−0.284763	+	0.493223i
$626$	23.2016	+	23.2016i	0.927321	+	0.927321i
$627$	−22.3697	−	15.9695i	−0.893360	−	0.637760i
$628$			4.20286i			0.167712i
$629$	18.0515	+	18.0515i	0.719761	+	0.719761i
$630$	26.0726	−	7.25027i	1.03876	−	0.288858i
$631$	−11.8770	+	44.3257i	−0.472817	+	1.76458i	0.156758	+	0.987637i	$0.449896\pi$
$631$	−11.8770	+	44.3257i	−0.472817	+	1.76458i	−0.629575	+	0.776940i	$0.716771\pi$
$632$	0.360291	+	1.34462i	0.0143316	+	0.0534862i
$633$	6.53404	+	14.3527i	0.259705	+	0.570467i
$634$			30.2074i			1.19969i
$635$	−48.0105	−	12.8644i	−1.90524	−	0.510507i
$636$	−3.85564	+	5.40088i	−0.152886	+	0.214159i
$637$	3.80773	+	24.9500i	0.150868	+	0.988554i
$638$			22.6239i			0.895688i
$639$	28.4114	−	1.96415i	1.12394	−	0.0777006i
$640$	3.40948			0.134771
$641$	18.0247	−	31.2198i	0.711934	−	1.23311i	−0.252196	−	0.967676i	$-0.581153\pi$
$641$	18.0247	−	31.2198i	0.711934	−	1.23311i	0.964130	−	0.265430i	$-0.0855140\pi$
$642$	−27.5308	−	10.3058i	−1.08656	−	0.406736i
$643$	−42.4343	−	11.3702i	−1.67345	−	0.448399i	−0.707409	−	0.706804i	$-0.750136\pi$
$643$	−42.4343	−	11.3702i	−1.67345	−	0.448399i	−0.966037	+	0.258405i	$0.916803\pi$
$644$	−0.274911	+	4.60759i	−0.0108330	+	0.181564i
$645$	−10.0829	−	60.3995i	−0.397012	−	2.37823i
$646$	−31.3977			−1.23533
$647$	25.9919			1.02185			0.510923	−	0.859626i	$-0.329304\pi$
$647$	25.9919			1.02185			0.510923	+	0.859626i	$0.329304\pi$
$648$	−1.11095	+	8.93117i	−0.0436421	+	0.350849i
$649$	−1.16704	−	0.673791i	−0.0458103	−	0.0264486i
$650$	−20.5788	+	12.1249i	−0.807167	+	0.475576i
$651$	−4.32588	+	3.15019i	−0.169544	+	0.123466i
$652$	−3.99821	−	14.9215i	−0.156582	−	0.584373i
$653$	4.14316	−	2.39205i	0.162134	−	0.0936083i	−0.416737	−	0.909027i	$-0.636827\pi$
$653$	4.14316	−	2.39205i	0.162134	−	0.0936083i	0.578872	+	0.815419i	$0.303493\pi$
$654$	−7.83638	−	17.2134i	−0.306427	−	0.673097i
$655$	−20.0563	−	5.37406i	−0.783663	−	0.209982i
$656$	−1.00193	−	1.00193i	−0.0391187	−	0.0391187i
$657$	−40.9175	+	2.82873i	−1.59634	+	0.110359i
$658$	−34.0914	−	2.03406i	−1.32902	−	0.0792959i
$659$	8.85320	−	5.11140i	0.344872	−	0.199112i	−0.317552	−	0.948241i	$-0.602861\pi$
$659$	8.85320	−	5.11140i	0.344872	−	0.199112i	0.662424	+	0.749129i	$0.269528\pi$
$660$	1.54684	−	15.9983i	0.0602108	−	0.622733i
$661$	−0.924413	−	0.924413i	−0.0359555	−	0.0359555i	0.688900	−	0.724856i	$-0.258094\pi$
$661$	−0.924413	−	0.924413i	−0.0359555	−	0.0359555i	−0.724856	+	0.688900i	$0.758094\pi$
$662$	−1.04273	−	1.80606i	−0.0405268	−	0.0701945i
$663$	25.7690	−	21.6102i	1.00079	−	0.839271i
$664$	−3.74798			−0.145450
$665$	−28.9625	+	43.8998i	−1.12312	+	1.70236i
$666$	−2.72461	+	13.9580i	−0.105576	+	0.540860i
$667$			14.5017i			0.561506i
$668$	2.99314	−	11.1706i	0.115808	−	0.432202i
$669$	0.569526	+	0.213194i	0.0220191	+	0.00824254i
$670$	1.36504	+	1.36504i	0.0527360	+	0.0527360i
$671$	23.5641	−	23.5641i	0.909684	−	0.909684i
$672$	−1.85931	+	4.18843i	−0.0717244	+	0.161572i
$673$	−22.6777	−	13.0930i	−0.874163	−	0.504698i	−0.00543356	−	0.999985i	$-0.501730\pi$
$673$	−22.6777	−	13.0930i	−0.874163	−	0.504698i	−0.868729	+	0.495287i	$0.835063\pi$
$674$	−4.89174	−	1.31074i	−0.188423	−	0.0504878i
$675$	−33.4806	+	7.99600i	−1.28867	+	0.307766i
$676$	12.9980	−	0.229707i	0.499922	−	0.00883488i
$677$	−3.98352	−	2.29989i	−0.153099	−	0.0883918i	0.421493	−	0.906831i	$-0.361506\pi$
$677$	−3.98352	−	2.29989i	−0.153099	−	0.0883918i	−0.574592	+	0.818440i	$0.694839\pi$
$678$	16.1454	+	6.04380i	0.620061	+	0.232111i
$679$	33.4247	+	11.1283i	1.28272	+	0.427066i
$680$	−9.18048	−	15.9011i	−0.352055	−	0.609778i
$681$	−7.17924	+	19.1786i	−0.275109	+	0.734927i
$682$	0.822612	+	3.07003i	0.0314995	+	0.117558i
$683$	−0.419644	−	1.56613i	−0.0160572	−	0.0599263i	0.957432	−	0.288658i	$-0.0932089\pi$
$683$	−0.419644	−	1.56613i	−0.0160572	−	0.0599263i	−0.973490	+	0.228731i	$0.926542\pi$
$684$	−9.76931	−	14.5083i	−0.373539	−	0.554739i
$685$	−17.4001	−	30.1378i	−0.664822	−	1.15151i
$686$	−7.89826	+	16.7516i	−0.301557	+	0.639581i
$687$	12.8532	−	34.3361i	0.490380	−	1.31000i
$688$	8.98015	+	5.18469i	0.342365	+	0.197665i
$689$	9.85373	+	9.68113i	0.375397	+	0.368822i
$690$	0.991509	−	10.2547i	0.0377461	−	0.390391i
$691$	6.94583	+	1.86113i	0.264232	+	0.0708007i	0.388503	−	0.921448i	$-0.372992\pi$
$691$	6.94583	+	1.86113i	0.264232	+	0.0708007i	−0.124271	+	0.992248i	$0.539659\pi$
$692$	−5.93526	−	3.42672i	−0.225625	−	0.130264i
$693$	18.8098	+	10.6247i	0.714527	+	0.403598i
$694$	1.95711	−	1.95711i	0.0742909	−	0.0742909i
$695$	8.41234	+	8.41234i	0.319098	+	0.319098i
$696$	−5.04738	+	13.4836i	−0.191320	+	0.511094i
$697$	−1.97495	+	7.37060i	−0.0748065	+	0.279182i
$698$		−	10.5891i		−	0.400805i
$699$	−11.8276	−	25.9806i	−0.447362	−	0.982676i
$700$	−17.4958	−	1.04388i	−0.661279	−	0.0394551i
$701$	23.2544			0.878306			0.439153	−	0.898412i	$-0.355279\pi$
$701$	23.2544			0.878306			0.439153	+	0.898412i	$0.355279\pi$
$702$	18.0037	+	5.18346i	0.679504	+	0.195637i
$703$	−13.8192	−	23.9355i	−0.521199	−	0.902744i
$704$	1.92456	+	1.92456i	0.0725345	+	0.0725345i
$705$	75.8744	+	7.33614i	2.85759	+	0.276295i
$706$	−7.02246	+	4.05442i	−0.264294	+	0.152590i
$707$	5.31991	+	0.317412i	0.200076	+	0.0119375i
$708$	−0.545220	−	0.661938i	−0.0204906	−	0.0248772i
$709$	19.0385	+	19.0385i	0.715006	+	0.715006i	0.967578	−	0.252572i	$-0.0812766\pi$
$709$	19.0385	+	19.0385i	0.715006	+	0.715006i	−0.252572	+	0.967578i	$0.581277\pi$
$710$	−31.2636	−	8.37705i	−1.17330	−	0.314385i
$711$	4.09881	+	0.800091i	0.153717	+	0.0300057i
$712$	−11.8830	+	6.86066i	−0.445335	+	0.257114i
$713$	0.527285	+	1.96786i	0.0197470	+	0.0736968i
$714$	24.5404	−	2.60652i	0.918400	−	0.0975465i
$715$	−32.3936	−	8.37380i	−1.21145	−	0.313162i
$716$	−2.34486	−	1.35380i	−0.0876314	−	0.0505940i
$717$	6.46465	−	1.07919i	0.241427	−	0.0403029i
$718$	−13.3185			−0.497043
$719$	−9.04678			−0.337388			−0.168694	−	0.985668i	$-0.553955\pi$
$719$	−9.04678			−0.337388			−0.168694	+	0.985668i	$0.553955\pi$
$720$	4.49112	−	9.18971i	0.167374	−	0.342480i
$721$	13.8672	+	9.14875i	0.516441	+	0.340717i
$722$	14.4815	+	3.88029i	0.538944	+	0.144410i
$723$	6.78783	−	18.1330i	0.252442	−	0.674375i
$724$	5.76635	−	9.98762i	0.214305	−	0.371187i
$725$	−55.0652			−2.04507
$726$	−4.80246	+	3.95565i	−0.178236	+	0.146808i
$727$		−	46.9466i		−	1.74115i	−0.492034	−	0.870576i	$-0.663747\pi$
$727$		−	46.9466i		−	1.74115i	0.492034	−	0.870576i	$-0.336253\pi$
$728$	8.00871	+	5.18271i	0.296823	+	0.192084i
$729$	22.6092	+	14.7589i	0.837377	+	0.546626i
$730$	45.0251	+	12.0644i	1.66646	+	0.446525i
$731$		−	55.8419i		−	2.06539i
$732$	19.3011	−	8.78682i	0.713390	−	0.324770i
$733$	−1.02536	−	3.82669i	−0.0378725	−	0.141342i	0.944401	−	0.328796i	$-0.106643\pi$
$733$	−1.02536	−	3.82669i	−0.0378725	−	0.141342i	−0.982273	+	0.187454i	$0.939976\pi$
$734$	−0.860562	+	3.21166i	−0.0317639	+	0.118545i
$735$	18.9926	−	36.7163i	0.700554	−	1.35430i
$736$	1.23362	+	1.23362i	0.0454718	+	0.0454718i
$737$			1.54105i			0.0567654i
$738$	−4.02033	+	1.38076i	−0.147990	+	0.0508263i
$739$	2.62110	+	2.62110i	0.0964189	+	0.0964189i	0.753671	−	0.657252i	$-0.228281\pi$
$739$	2.62110	+	2.62110i	0.0964189	+	0.0964189i	−0.657252	+	0.753671i	$0.728281\pi$
$740$	8.08126	−	13.9972i	0.297073	−	0.514546i
$741$	−33.0032	+	15.3781i	−1.21240	+	0.564930i
$742$	2.03572	+	9.93002i	0.0747337	+	0.364542i
$743$	17.3795	−	4.65682i	0.637592	−	0.170842i	0.0744795	−	0.997223i	$-0.476270\pi$
$743$	17.3795	−	4.65682i	0.637592	−	0.170842i	0.563112	+	0.826380i	$0.309604\pi$
$744$	−0.194655	+	2.01323i	−0.00713640	+	0.0738086i
$745$	14.8339	+	8.56436i	0.543472	+	0.313774i
$746$	−0.682713	+	2.54792i	−0.0249959	+	0.0932860i
$747$	−4.93701	+	10.1021i	−0.180636	+	0.369616i
$748$	3.79358	−	14.1578i	0.138707	−	0.517662i
$749$	−40.1561	+	20.0960i	−1.46727	+	0.734292i
$750$	9.54904	+	0.923278i	0.348682	+	0.0337133i
$751$	35.7030	−	20.6131i	1.30282	−	0.752183i	0.321933	−	0.946763i	$-0.395668\pi$
$751$	35.7030	−	20.6131i	1.30282	−	0.752183i	0.980887	+	0.194580i	$0.0623342\pi$
$752$	−9.12751	+	9.12751i	−0.332846	+	0.332846i
$753$	−49.4918	−	4.78526i	−1.80358	−	0.174385i
$754$	26.0865	+	14.7553i	0.950015	+	0.537357i
$755$		−	17.2236i		−	0.626830i
$756$	8.84010	+	10.5287i	0.321511	+	0.382924i
$757$	16.3398	−	28.3014i	0.593880	−	1.02863i	−0.399824	−	0.916592i	$-0.630929\pi$
$757$	16.3398	−	28.3014i	0.593880	−	1.02863i	0.993704	−	0.112038i	$-0.0357379\pi$
$758$	−12.4777			−0.453211
$759$	6.34820	−	5.22884i	0.230425	−	0.189795i
$760$	5.14487	+	19.2009i	0.186624	+	0.696491i
$761$	−29.3774	+	29.3774i	−1.06493	+	1.06493i	−0.0671913	+	0.997740i	$0.521404\pi$
$761$	−29.3774	+	29.3774i	−1.06493	+	1.06493i	−0.997740	+	0.0671913i	$0.978596\pi$
$762$	−4.15764	−	24.9056i	−0.150616	−	0.902234i
$763$	−27.4111	−	9.12617i	−0.992349	−	0.330389i
$764$	3.35953	−	5.81888i	0.121544	−	0.210520i
$765$	−54.9517	+	3.79895i	−1.98678	+	0.137351i
$766$	12.0928	−	6.98176i	0.436929	−	0.252261i
$767$	−1.53806	+	0.906212i	−0.0555362	+	0.0327214i
$768$	0.717647	+	1.57638i	0.0258958	+	0.0568828i
$769$	−11.7559	−	43.8736i	−0.423929	−	1.58212i	−0.766251	−	0.642541i	$-0.777880\pi$
$769$	−11.7559	−	43.8736i	−0.423929	−	1.58212i	0.342323	−	0.939582i	$-0.388786\pi$
$770$	−16.2959	−	18.3639i	−0.587264	−	0.661789i
$771$	40.2433	+	3.89105i	1.44933	+	0.140133i
$772$	0.251554	+	0.938814i	0.00905364	+	0.0337886i
$773$	29.8578	−	8.00036i	1.07391	−	0.287753i	0.321811	−	0.946804i	$-0.395709\pi$
$773$	29.8578	−	8.00036i	1.07391	−	0.287753i	0.752098	+	0.659051i	$0.229042\pi$
$774$	25.8036	−	17.3751i	0.927490	−	0.624534i
$775$	−7.47228	+	2.00219i	−0.268412	+	0.0719208i
$776$	11.5313	−	6.65758i	0.413948	−	0.238993i
$777$	12.7881	+	17.5607i	0.458769	+	0.629987i
$778$	−3.26451	+	0.874722i	−0.117038	+	0.0313603i
$779$	4.13059	−	7.15439i	0.147994	−	0.256333i
$780$	−17.4380	−	12.2177i	−0.624382	−	0.437464i
$781$	−12.9188	−	22.3761i	−0.462272	−	0.800678i
$782$	2.43164	−	9.07502i	0.0869554	−	0.324522i
$783$	29.6942	+	31.3656i	1.06118	+	1.12091i
$784$	2.75434	+	6.43534i	0.0983691	+	0.229834i
$785$	−10.1325	−	10.1325i	−0.361646	−	0.361646i
$786$	−1.73684	−	10.4042i	−0.0619512	−	0.371107i
$787$	−32.8448	+	8.80075i	−1.17079	+	0.313713i	−0.791268	−	0.611469i	$-0.790579\pi$
$787$	−32.8448	+	8.80075i	−1.17079	+	0.313713i	−0.379524	+	0.925182i	$0.623912\pi$
$788$	9.98319	+	2.67499i	0.355636	+	0.0952924i
$789$	1.19109	+	0.850308i	0.0424040	+	0.0302718i
$790$	−4.11032	−	2.37309i	−0.146238	−	0.0844308i
$791$	23.5495	−	11.7853i	0.837324	−	0.419036i
$792$	7.72245	−	2.65223i	0.274405	−	0.0942428i
$793$	−11.8022	−	42.5393i	−0.419107	−	1.51061i
$794$	31.6438	−	18.2695i	1.12300	−	0.648362i
$795$	−3.72539	−	22.3162i	−0.132126	−	0.791475i
$796$	−3.57317	−	6.18891i	−0.126648	−	0.219360i
$797$	20.2706	+	35.1098i	0.718022	+	1.24365i	0.961782	+	0.273816i	$0.0882858\pi$
$797$	20.2706	+	35.1098i	0.718022	+	1.24365i	−0.243760	+	0.969836i	$0.578381\pi$
$798$	−26.3934	−	4.15063i	−0.934316	−	0.146931i
$799$	67.1457	+	17.9916i	2.37545	+	0.636499i
$800$	−4.68426	+	4.68426i	−0.165614	+	0.165614i
$801$	2.83899	+	41.0660i	0.100311	+	1.45099i
$802$	−2.95079	+	5.11092i	−0.104196	+	0.180473i
$803$	18.6054	+	32.2255i	0.656570	+	1.13721i
$804$	−0.343808	+	0.918450i	−0.0121252	+	0.0323912i
$805$	−10.4455	−	11.7711i	−0.368156	−	0.414875i
$806$	4.07642	+	1.05376i	0.143586	+	0.0371171i
$807$	−7.40610	+	3.37162i	−0.260707	+	0.118687i
$808$	1.42433	−	1.42433i	0.0501079	−	0.0501079i
$809$			34.3519i			1.20775i	0.797080	+	0.603874i	$0.206377\pi$
$809$			34.3519i			1.20775i	−0.797080	+	0.603874i	$0.793623\pi$
$810$	−18.8535	−	24.2102i	−0.662445	−	0.850659i
$811$	15.0214	−	15.0214i	0.527472	−	0.527472i	−0.392346	−	0.919818i	$-0.628336\pi$
$811$	15.0214	−	15.0214i	0.527472	−	0.527472i	0.919818	+	0.392346i	$0.128336\pi$
$812$	9.84226	+	19.6670i	0.345396	+	0.690176i
$813$	−13.5623	−	16.4657i	−0.475651	−	0.577476i
$814$	12.4627	−	3.33936i	0.436816	−	0.117045i
$815$	45.6130	+	26.3347i	1.59775	+	0.922463i
$816$	5.41954	−	7.59157i	0.189722	−	0.265758i
$817$	−15.6473	+	58.3965i	−0.547430	+	2.04304i
$818$	27.8792			0.974774
$819$	24.5186	−	14.7593i	0.856750	−	0.515733i
$820$	4.83103			0.168707
$821$	1.36480	−	5.09351i	0.0476319	−	0.177765i	−0.938012	−	0.346603i	$-0.887335\pi$
$821$	1.36480	−	5.09351i	0.0476319	−	0.177765i	0.985644	+	0.168839i	$0.0540017\pi$
$822$	10.2718	−	14.3885i	0.358271	−	0.501858i
$823$	−5.70754	−	3.29525i	−0.198952	−	0.114865i	0.397214	−	0.917726i	$-0.369977\pi$
$823$	−5.70754	−	3.29525i	−0.198952	−	0.114865i	−0.596167	+	0.802861i	$0.703310\pi$
$824$	6.06524	−	1.62518i	0.211293	−	0.0566157i
$825$	19.8548	+	24.1052i	0.691254	+	0.839234i
$826$	−1.30764	−	0.0780200i	−0.0454984	−	0.00271466i
$827$	−2.56220	+	2.56220i	−0.0890965	+	0.0890965i	−0.750250	−	0.661154i	$-0.770067\pi$
$827$	−2.56220	+	2.56220i	−0.0890965	+	0.0890965i	0.661154	+	0.750250i	$0.270067\pi$
$828$	4.95001	−	1.70005i	0.172025	−	0.0590807i
$829$			30.0700i			1.04437i	0.852831	+	0.522187i	$0.174884\pi$
$829$			30.0700i			1.04437i	−0.852831	+	0.522187i	$0.825116\pi$
$830$	9.03587	−	9.03587i	0.313640	−	0.313640i
$831$	32.3730	−	14.7378i	1.12301	−	0.511248i
$832$	3.47431	−	0.963919i	0.120450	−	0.0334179i
$833$	22.5966	−	30.1736i	0.782926	−	1.04545i
$834$	−2.11879	+	5.66015i	−0.0733678	+	0.195995i
$835$	19.7147	+	34.1468i	0.682254	+	1.18170i
$836$	−7.93425	+	13.7425i	−0.274412	+	0.475295i
$837$	5.16993	+	3.17658i	0.178699	+	0.109799i
$838$	10.4813	−	10.4813i	0.362072	−	0.362072i
$839$	−49.2913	−	13.2076i	−1.70172	−	0.455976i	−0.728352	−	0.685203i	$-0.759713\pi$
$839$	−49.2913	−	13.2076i	−1.70172	−	0.455976i	−0.973373	+	0.229227i	$0.926380\pi$
$840$	−5.61521	−	14.5803i	−0.193743	−	0.503068i
$841$	20.0472	+	34.7227i	0.691281	+	1.19733i
$842$	12.8157	+	22.1975i	0.441659	+	0.764976i
$843$	1.94295	+	11.6389i	0.0669189	+	0.400865i
$844$	7.88500	−	4.55240i	0.271413	−	0.156700i
$845$	−30.7826	+	31.8902i	−1.05895	+	1.09705i
$846$	12.5786	+	36.6249i	0.432461	+	1.25919i
$847$	−0.566046	+	9.48709i	−0.0194496	+	0.325980i
$848$	3.31796	+	1.91563i	0.113939	+	0.0657829i
$849$	16.6332	+	11.8743i	0.570851	+	0.407525i
$850$	34.4594	+	9.23336i	1.18195	+	0.316702i
$851$	7.98843	−	2.14049i	0.273840	−	0.0733751i
$852$	−2.70738	−	16.2181i	−0.0927534	−	0.555622i
$853$	19.5111	+	19.5111i	0.668047	+	0.668047i	0.957264	−	0.289217i	$-0.0933948\pi$
$853$	19.5111	+	19.5111i	0.668047	+	0.668047i	−0.289217	+	0.957264i	$0.593395\pi$
$854$	10.2330	−	30.7357i	0.350167	−	1.05175i
$855$	58.5301	+	11.4251i	2.00169	+	0.390731i
$856$	−4.39270	+	16.3938i	−0.150139	+	0.560328i
$857$	−5.38338	−	9.32429i	−0.183893	−	0.318512i	0.759310	−	0.650729i	$-0.225537\pi$
$857$	−5.38338	−	9.32429i	−0.183893	−	0.318512i	−0.943203	+	0.332217i	$0.892203\pi$
$858$	−2.94674	−	16.7398i	−0.100600	−	0.571489i
$859$	−1.58901	+	2.75225i	−0.0542163	+	0.0939054i	−0.891860	−	0.452312i	$-0.850599\pi$
$859$	−1.58901	+	2.75225i	−0.0542163	+	0.0939054i	0.837644	+	0.546217i	$0.183933\pi$
$860$	−34.1495	+	9.15034i	−1.16449	+	0.312024i
$861$	−2.63453	+	5.93476i	−0.0897845	+	0.202256i
$862$	2.05974	−	1.18919i	0.0701550	−	0.0405040i
$863$	23.6823	−	6.34567i	0.806156	−	0.216009i	0.167871	−	0.985809i	$-0.446311\pi$
$863$	23.6823	−	6.34567i	0.806156	−	0.216009i	0.638285	+	0.769800i	$0.279644\pi$
$864$	5.19421	+	0.142179i	0.176711	+	0.00483702i
$865$	22.5705	−	6.04774i	0.767419	−	0.205629i
$866$	−1.42826	−	5.33033i	−0.0485342	−	0.181132i
$867$	−20.6901	−	2.00048i	−0.702672	−	0.0679400i
$868$	2.05068	+	2.31092i	0.0696047	+	0.0784376i
$869$	−0.980615	−	3.65971i	−0.0332651	−	0.124147i
$870$	−20.3385	−	44.6756i	−0.689541	−	1.51465i
$871$	1.77692	+	1.00508i	0.0602085	+	0.0340557i
$872$	−9.45660	+	5.45977i	−0.320241	+	0.184891i
$873$	−2.75495	−	39.8503i	−0.0932410	−	1.34873i
$874$	−5.08577	+	8.80881i	−0.172029	+	0.297962i
$875$	10.9610	−	9.72668i	0.370550	−	0.328822i
$876$	3.89912	+	23.3569i	0.131739	+	0.789157i
$877$	−24.3830	+	24.3830i	−0.823354	+	0.823354i	−0.986588	−	0.163233i	$-0.947808\pi$
$877$	−24.3830	+	24.3830i	−0.823354	+	0.823354i	0.163233	+	0.986588i	$0.447808\pi$
$878$	2.51033	+	9.36869i	0.0847196	+	0.316178i
$879$	−15.9538	+	13.1407i	−0.538109	+	0.443226i
$880$	−9.27970			−0.312819
$881$	−10.2732	+	17.7938i	−0.346114	+	0.599487i	−0.985556	−	0.169353i	$-0.945832\pi$
$881$	−10.2732	+	17.7938i	−0.346114	+	0.599487i	0.639441	+	0.768840i	$0.279166\pi$
$882$	20.9736	+	1.05304i	0.706217	+	0.0354578i
$883$			53.0600i			1.78561i	0.450443	+	0.892805i	$0.351266\pi$
$883$			53.0600i			1.78561i	−0.450443	+	0.892805i	$0.648734\pi$
$884$	−13.8506	−	13.6080i	−0.465845	−	0.457685i
$885$	2.91030	+	0.281391i	0.0978286	+	0.00945885i
$886$	13.8735	−	13.8735i	0.466090	−	0.466090i
$887$	7.97474	−	4.60422i	0.267766	−	0.154594i	−0.360106	−	0.932911i	$-0.617260\pi$
$887$	7.97474	−	4.60422i	0.267766	−	0.154594i	0.627872	+	0.778317i	$0.283926\pi$
$888$	8.17262	+	0.790194i	0.274255	+	0.0265172i
$889$	−32.1950	−	21.2404i	−1.07979	−	0.712380i
$890$	12.1082	−	45.1885i	0.405869	−	1.51472i
$891$	3.02370	−	24.3083i	0.101298	−	0.814358i
$892$	0.0908711	−	0.339136i	0.00304259	−	0.0113551i
$893$	−65.1761	−	37.6294i	−2.18103	−	1.25922i
$894$	−0.837432	+	8.66117i	−0.0280079	+	0.289673i
$895$	8.91697	−	2.38930i	0.298062	−	0.0798653i
$896$	2.51028	+	0.835764i	0.0838625	+	0.0279209i
$897$	−1.88883	−	10.7301i	−0.0630661	−	0.358266i
$898$	−6.73590	+	11.6669i	−0.224780	+	0.389330i
$899$	6.86372	+	6.86372i	0.228918	+	0.228918i
$900$	6.45537	+	18.7960i	0.215179	+	0.626533i
$901$		−	20.6323i		−	0.687363i
$902$	2.72698	+	2.72698i	0.0907986	+	0.0907986i
$903$	7.38204	−	46.9416i	0.245659	−	1.56212i
$904$	2.57609	−	9.61411i	0.0856796	−	0.319760i
$905$	10.1769	+	37.9807i	0.338292	+	1.26252i
$906$	7.96338	−	3.62532i	0.264565	−	0.120443i
$907$		−	52.9775i		−	1.75909i	−0.475817	−	0.879544i	$-0.657848\pi$
$907$		−	52.9775i		−	1.75909i	0.475817	−	0.879544i	$-0.342152\pi$
$908$	11.4203	+	3.06006i	0.378996	+	0.101552i
$909$	−1.96287	−	5.71526i	−0.0651043	−	0.189563i
$910$	−31.8028	+	6.81312i	−1.05425	+	0.225853i
$911$			41.9787i			1.39082i	0.718614	+	0.695409i	$0.244777\pi$
$911$			41.9787i			1.39082i	−0.718614	+	0.695409i	$0.755223\pi$
$912$	−7.79468	+	6.42027i	−0.258108	+	0.212596i
$913$	10.2010			0.337604
$914$	−0.647190	+	1.12097i	−0.0214072	+	0.0370783i
$915$	−25.3486	+	67.7162i	−0.837998	+	2.23863i
$916$	−20.4461	−	5.47851i	−0.675558	−	0.181015i
$917$	−13.4494	−	8.87311i	−0.444137	−	0.293016i
$918$	−13.3230	−	24.6075i	−0.439725	−	0.812168i
$919$	50.1941			1.65575			0.827874	−	0.560913i	$-0.189550\pi$
$919$	50.1941			1.65575			0.827874	+	0.560913i	$0.189550\pi$
$920$	−5.94818			−0.196106
$921$	−26.4288	+	4.41192i	−0.870858	+	0.145378i
$922$	25.2746	+	14.5923i	0.832375	+	0.480572i
$923$	−34.2264	+	0.302410i	−1.12658	+	0.00995394i
$924$	5.06054	−	11.3998i	0.166480	−	0.375026i
$925$	8.12781	+	30.3334i	0.267241	+	0.997356i
$926$	10.3947	−	6.00137i	0.341590	−	0.197217i
$927$	3.60900	−	18.4886i	0.118535	−	0.607247i
$928$	8.02906	+	2.15138i	0.263567	+	0.0706225i
$929$	−3.35028	−	3.35028i	−0.109919	−	0.109919i	0.650008	−	0.759927i	$-0.274765\pi$
$929$	−3.35028	−	3.35028i	−0.109919	−	0.109919i	−0.759927	+	0.650008i	$0.774765\pi$
$930$	−4.38434	−	5.32291i	−0.143768	−	0.174545i
$931$	−32.0852	+	25.2223i	−1.05155	+	0.826627i
$932$	−14.2731	+	8.24057i	−0.467530	+	0.269929i
$933$	−14.4755	−	1.39961i	−0.473908	−	0.0458212i
$934$	−19.3316	−	19.3316i	−0.632550	−	0.632550i
$935$	24.9868	+	43.2785i	0.817157	+	1.41536i
$936$	1.97843	−	10.6342i	0.0646670	−	0.347589i
$937$	−57.5838			−1.88118			−0.940590	−	0.339545i	$-0.889727\pi$
$937$	−57.5838			−1.88118			−0.940590	+	0.339545i	$0.889727\pi$
$938$	0.670418	+	1.33964i	0.0218899	+	0.0437408i
$939$	−23.5474	−	51.7242i	−0.768440	−	1.68796i
$940$		−	44.0104i		−	1.43546i
$941$	−1.10610	+	4.12801i	−0.0360577	+	0.134569i	−0.981608	−	0.190906i	$-0.938858\pi$
$941$	−1.10610	+	4.12801i	−0.0360577	+	0.134569i	0.945551	+	0.325475i	$0.105524\pi$
$942$	2.55205	−	6.81756i	0.0831504	−	0.222128i
$943$	1.74797	+	1.74797i	0.0569216	+	0.0569216i
$944$	−0.350102	+	0.350102i	−0.0113948	+	0.0113948i
$945$	−46.6955	−	4.07091i	−1.51900	−	0.132427i
$946$	−24.4416	−	14.1114i	−0.794665	−	0.458800i
$947$	46.9515	+	12.5806i	1.52572	+	0.408815i	0.921619	−	0.388095i	$-0.126867\pi$
$947$	46.9515	+	12.5806i	1.52572	+	0.408815i	0.604098	+	0.796910i	$0.293533\pi$
$948$	0.232043	−	2.39992i	0.00753642	−	0.0779458i
$949$	49.2922	−	0.435524i	1.60009	−	0.0141377i
$950$	−33.4485	−	19.3115i	−1.08521	−	0.626548i
$951$	18.3425	−	49.0002i	0.594796	−	1.58894i
$952$	−2.86144	−	13.9578i	−0.0927399	−	0.452375i
$953$	6.03192	+	10.4476i	0.195393	+	0.338431i	0.947029	−	0.321147i	$-0.104068\pi$
$953$	6.03192	+	10.4476i	0.195393	+	0.338431i	−0.751636	+	0.659578i	$0.770735\pi$
$954$	9.53383	−	6.41969i	0.308669	−	0.207845i
$955$	5.92916	+	22.1279i	0.191863	+	0.716043i
$956$	−0.979376	−	3.65508i	−0.0316753	−	0.118214i
$957$	13.7376	−	36.6987i	0.444074	−	1.18630i
$958$	19.9908	+	34.6251i	0.645873	+	1.11868i
$959$	−5.42338	−	26.4547i	−0.175130	−	0.854265i
$960$	−5.53060	−	2.07030i	−0.178499	−	0.0668186i
$961$	−25.6658	−	14.8182i	−0.827930	−	0.478005i
$962$	4.27770	−	16.5480i	0.137918	−	0.533530i
$963$	38.4006	+	33.4345i	1.23744	+	1.07741i
$964$	−10.7977	−	2.89323i	−0.347770	−	0.0931846i
$965$	−2.86982	−	1.65689i	−0.0923827	−	0.0533372i
$966$	3.24375	−	7.30715i	0.104366	−	0.235104i
$967$	14.9192	−	14.9192i	0.479768	−	0.479768i	−0.425290	−	0.905057i	$-0.639828\pi$
$967$	14.9192	−	14.9192i	0.479768	−	0.479768i	0.905057	+	0.425290i	$0.139828\pi$
$968$	2.54004	+	2.54004i	0.0816400	+	0.0816400i
$969$	50.9310	+	19.0653i	1.63614	+	0.612464i
$970$	−11.7498	+	43.8508i	−0.377263	+	1.40797i
$971$		−	20.0117i		−	0.642207i	−0.947044	−	0.321103i	$-0.895946\pi$
$971$		−	20.0117i		−	0.642207i	0.947044	−	0.321103i	$-0.104054\pi$
$972$	7.22526	−	13.8129i	0.231750	−	0.443048i
$973$	4.13159	+	8.25582i	0.132453	+	0.264670i
$974$	8.16937			0.261763
$975$	40.7438	−	7.17220i	1.30485	−	0.229694i
$976$	−6.12196	−	10.6036i	−0.195959	−	0.339411i
$977$	−17.9127	−	17.9127i	−0.573078	−	0.573078i	0.359909	−	0.932987i	$-0.382808\pi$
$977$	−17.9127	−	17.9127i	−0.573078	−	0.573078i	−0.932987	+	0.359909i	$0.882808\pi$
$978$	−2.57503	+	26.6324i	−0.0823404	+	0.851610i
$979$	32.3424	−	18.6729i	1.03367	−	0.596789i
$980$	−22.1551	−	8.87441i	−0.707718	−	0.283483i
$981$	2.25929	+	32.6806i	0.0721337	+	1.04341i
$982$	20.5712	+	20.5712i	0.656453	+	0.656453i
$983$	19.0093	+	5.09353i	0.606302	+	0.162458i	0.548893	−	0.835893i	$-0.315049\pi$
$983$	19.0093	+	5.09353i	0.606302	+	0.162458i	0.0574092	+	0.998351i	$0.481716\pi$
$984$	1.01686	+	2.23364i	0.0324164	+	0.0712059i
$985$	−30.5171	+	17.6191i	−0.972357	+	0.561391i
$986$	−11.5858	−	43.2387i	−0.368966	−	1.37700i
$987$	54.0653	+	24.0004i	1.72092	+	0.763941i
$988$	10.6711	+	18.1115i	0.339494	+	0.576204i
$989$	−15.6668	−	9.04522i	−0.498175	−	0.287621i
$990$	−12.2236	+	25.0120i	−0.388493	+	0.794932i
$991$	−47.8857			−1.52114			−0.760570	−	0.649256i	$-0.775080\pi$
$991$	−47.8857			−1.52114			−0.760570	+	0.649256i	$0.775080\pi$
$992$	1.16776			0.0370764
$993$	0.594763	+	3.56282i	0.0188742	+	0.113063i
$994$	−20.9648	−	13.8314i	−0.664963	−	0.438704i
$995$	23.5351	+	6.30620i	0.746112	+	0.199920i
$996$	6.07969	+	2.27584i	0.192642	+	0.0721128i
$997$	−18.5047	+	32.0510i	−0.586048	+	1.01507i	0.408696	+	0.912671i	$0.365984\pi$
$997$	−18.5047	+	32.0510i	−0.586048	+	1.01507i	−0.994744	+	0.102395i	$0.967350\pi$
$998$	−20.1077			−0.636499
$999$	12.8952	−	20.9871i	0.407985	−	0.664003i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bw.a.149.15	yes	152
3.2	odd	2	inner	546.2.bw.a.149.34	yes	152
7.4	even	3		546.2.ch.a.305.2	yes	152
13.11	odd	12		546.2.ch.a.401.31	yes	152
21.11	odd	6		546.2.ch.a.305.31	yes	152
39.11	even	12		546.2.ch.a.401.2	yes	152
91.11	odd	12	inner	546.2.bw.a.11.34	yes	152
273.11	even	12	inner	546.2.bw.a.11.15	✓	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.11.15	✓	152	273.11	even	12	inner
546.2.bw.a.11.34	yes	152	91.11	odd	12	inner
546.2.bw.a.149.15	yes	152	1.1	even	1	trivial
546.2.bw.a.149.34	yes	152	3.2	odd	2	inner
546.2.ch.a.305.2	yes	152	7.4	even	3
546.2.ch.a.305.31	yes	152	21.11	odd	6
546.2.ch.a.401.2	yes	152	39.11	even	12
546.2.ch.a.401.31	yes	152	13.11	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(1.00636 - 1.40969i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(3.29330 - 0.882438i) q^{5} +(1.10119 + 1.33693i) q^{6} +(2.64105 + 0.157578i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.974462 - 2.83733i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(1.00636 - 1.40969i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(3.29330 - 0.882438i) q^{5} +(1.10119 + 1.33693i) q^{6} +(2.64105 + 0.157578i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.974462 - 2.83733i) q^{9} +3.40948i q^{10} +(-1.92456 + 1.92456i) q^{11} +(-1.57638 + 0.717647i) q^{12} +(0.963919 + 3.47431i) q^{13} +(-0.835764 + 2.51028i) q^{14} +(2.07030 - 5.53060i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.69264 - 4.66378i) q^{17} +(2.99286 - 0.206904i) q^{18} +(-4.12264 + 4.12264i) q^{19} +(-3.29330 - 0.882438i) q^{20} +(2.88000 - 3.56449i) q^{21} +(-1.36087 - 2.35709i) q^{22} +(-0.872301 - 1.51087i) q^{23} +(-0.285196 - 1.70841i) q^{24} +(5.73702 - 3.31227i) q^{25} +(-3.60541 + 0.0318558i) q^{26} +(-4.98042 - 1.48169i) q^{27} +(-2.20843 - 1.45699i) q^{28} +(-7.19866 - 4.15615i) q^{29} +(4.80631 + 3.43118i) q^{30} +(-1.12797 - 0.302238i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(0.776227 + 4.64984i) q^{33} +(3.80796 + 3.80796i) q^{34} +(8.83685 - 1.81161i) q^{35} +(-0.574755 + 2.94443i) q^{36} +(-1.22692 + 4.57894i) q^{37} +(-2.91515 - 5.04918i) q^{38} +(5.86777 + 2.13760i) q^{39} +(1.70474 - 2.95270i) q^{40} +(-1.36866 + 0.366731i) q^{41} +(2.69764 + 3.70442i) q^{42} +(8.98015 - 5.18469i) q^{43} +(2.62899 - 0.704437i) q^{44} +(-5.71296 - 8.48428i) q^{45} +(1.68516 - 0.451536i) q^{46} +(3.34090 + 12.4684i) q^{47} +(1.72401 + 0.166691i) q^{48} +(6.95034 + 0.832346i) q^{49} +(1.71456 + 6.39882i) q^{50} +(-3.86472 - 8.48925i) q^{51} +(0.902379 - 3.49080i) q^{52} +(3.31796 - 1.91563i) q^{53} +(2.72023 - 4.42723i) q^{54} +(-4.63985 + 8.03645i) q^{55} +(1.97893 - 1.75608i) q^{56} +(1.66277 + 9.96053i) q^{57} +(5.87768 - 5.87768i) q^{58} +(0.128146 + 0.478248i) q^{59} +(-4.55823 + 3.75449i) q^{60} -12.2439 q^{61} +(0.583879 - 1.01131i) q^{62} +(-2.12651 - 7.64709i) q^{63} -1.00000i q^{64} +(6.24035 + 10.5914i) q^{65} +(-4.69230 - 0.453689i) q^{66} +(0.400365 - 0.400365i) q^{67} +(-4.66378 + 2.69264i) q^{68} +(-3.00771 - 0.290810i) q^{69} +(-0.537260 + 9.00462i) q^{70} +(-2.45699 + 9.16961i) q^{71} +(-2.69534 - 1.31724i) q^{72} +(3.53850 - 13.2059i) q^{73} +(-4.10537 - 2.37023i) q^{74} +(1.10425 - 11.4208i) q^{75} +(5.63163 - 1.50899i) q^{76} +(-5.38613 + 4.77959i) q^{77} +(-3.58345 + 5.11458i) q^{78} +(-0.696028 + 1.20556i) q^{79} +(2.41087 + 2.41087i) q^{80} +(-7.10085 + 5.52973i) q^{81} -1.41694i q^{82} +(-2.65022 - 2.65022i) q^{83} +(-4.27640 + 1.64694i) q^{84} +(4.75217 - 17.7353i) q^{85} +(2.68379 + 10.0161i) q^{86} +(-13.1034 + 5.96529i) q^{87} +2.72173i q^{88} +(-13.2538 - 3.55134i) q^{89} +(9.67381 - 3.32241i) q^{90} +(1.99829 + 9.32775i) q^{91} +1.74460i q^{92} +(-1.56121 + 1.28593i) q^{93} -12.9082 q^{94} +(-9.93913 + 17.2151i) q^{95} +(-0.607218 + 1.62212i) q^{96} +(12.8615 + 3.44622i) q^{97} +(-2.60286 + 6.49808i) q^{98} +(7.33601 + 3.58519i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 12 q^{7}+O(q^{10}) \) 152 * q + 12 * q^7	\( 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Introduction

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