LMFDB - Embedded newform 546.2.bu.b.323.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			323.10
Character	$\chi$	$=$	546.323
Dual form			546.2.bu.b.71.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(-0.625096 + 1.61532i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.828570 - 0.828570i) q^{5} +(-1.02187 + 1.39849i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.21851 - 2.01946i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(-0.625096 + 1.61532i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.828570 - 0.828570i) q^{5} +(-1.02187 + 1.39849i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.21851 - 2.01946i) q^{9} +(1.01479 - 0.585888i) q^{10} +(-1.25192 + 4.67223i) q^{11} +(-1.34901 + 1.08636i) q^{12} +(0.0707604 + 3.60486i) q^{13} +1.00000i q^{14} +(0.820469 + 1.85634i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.258842 + 0.448327i) q^{17} +(-1.62024 - 2.52484i) q^{18} +(5.50267 - 1.47444i) q^{19} +(1.13185 - 0.303278i) q^{20} +(-1.72206 - 0.185721i) q^{21} +(-2.41852 + 4.18900i) q^{22} +(-2.54064 - 4.40052i) q^{23} +(-1.58421 + 0.700193i) q^{24} +3.62694i q^{25} +(-0.864656 + 3.50034i) q^{26} +(4.64885 - 2.32125i) q^{27} +(-0.258819 + 0.965926i) q^{28} +(1.83703 - 1.06061i) q^{29} +(0.312056 + 2.00544i) q^{30} +(4.11077 + 4.11077i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-6.76456 - 4.94284i) q^{33} +(-0.366058 + 0.366058i) q^{34} +(1.01479 + 0.585888i) q^{35} +(-0.911557 - 2.85816i) q^{36} +(-9.86282 - 2.64273i) q^{37} +5.69678 q^{38} +(-5.86723 - 2.13908i) q^{39} +1.17178 q^{40} +(-6.46664 - 1.73273i) q^{41} +(-1.61532 - 0.625096i) q^{42} +(-0.253885 - 0.146580i) q^{43} +(-3.42031 + 3.42031i) q^{44} +(-3.51145 + 0.164928i) q^{45} +(-1.31513 - 4.90814i) q^{46} +(8.54481 + 8.54481i) q^{47} +(-1.71146 + 0.266310i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-0.938722 + 3.50336i) q^{50} +(-0.562390 - 0.698360i) q^{51} +(-1.74115 + 3.15728i) q^{52} -9.52725i q^{53} +(5.09123 - 1.03894i) q^{54} +(2.83396 + 4.90857i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-1.05801 + 9.81023i) q^{57} +(2.04895 - 0.549013i) q^{58} +(1.53749 - 0.411970i) q^{59} +(-0.217623 + 2.01787i) q^{60} +(5.90367 - 10.2255i) q^{61} +(2.90675 + 5.03464i) q^{62} +(1.37645 - 2.66559i) q^{63} +1.00000i q^{64} +(3.04551 + 2.92825i) q^{65} +(-5.25477 - 6.52521i) q^{66} +(2.99192 - 11.1660i) q^{67} +(-0.448327 + 0.258842i) q^{68} +(8.69639 - 1.35320i) q^{69} +(0.828570 + 0.828570i) q^{70} +(0.487312 + 1.81867i) q^{71} +(-0.140751 - 2.99670i) q^{72} +(4.68386 - 4.68386i) q^{73} +(-8.84276 - 5.10537i) q^{74} +(-5.85867 - 2.26719i) q^{75} +(5.50267 + 1.47444i) q^{76} -4.83704 q^{77} +(-5.11367 - 3.58474i) q^{78} +2.53289 q^{79} +(1.13185 + 0.303278i) q^{80} +(0.843575 + 8.96038i) q^{81} +(-5.79783 - 3.34738i) q^{82} +(11.7215 - 11.7215i) q^{83} +(-1.39849 - 1.02187i) q^{84} +(0.157002 + 0.585939i) q^{85} +(-0.207296 - 0.207296i) q^{86} +(0.564904 + 3.63038i) q^{87} +(-4.18900 + 2.41852i) q^{88} +(-0.717827 + 2.67897i) q^{89} +(-3.43449 - 0.749523i) q^{90} +(-3.46371 + 1.00135i) q^{91} -5.08128i q^{92} +(-9.20983 + 4.07058i) q^{93} +(6.04209 + 10.4652i) q^{94} +(3.33767 - 5.78102i) q^{95} +(-1.72206 - 0.185721i) q^{96} +(3.95229 - 1.05901i) q^{97} +(-0.965926 + 0.258819i) q^{98} +(12.2128 - 7.83718i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{6} - 24 q^{9}+O(q^{10}) $ 56 * q + 8 * q^6 - 24 * q^9	$ 56 q + 8 q^{6} - 24 q^{9} + 24 q^{10} + 8 q^{11} + 24 q^{13} + 4 q^{15} + 28 q^{16} - 4 q^{17} - 8 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 16 q^{79} + 12 q^{81} - 4 q^{83} - 4 q^{84} + 32 q^{85} - 16 q^{86} - 144 q^{87} + 88 q^{89} - 8 q^{90} - 8 q^{91} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 q^{99}+O(q^{100}) $ 56 * q + 8 * q^6 - 24 * q^9 + 24 * q^10 + 8 * q^11 + 24 * q^13 + 4 * q^15 + 28 * q^16 - 4 * q^17 - 8 * q^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 16 * q^79 + 12 * q^81 - 4 * q^83 - 4 * q^84 + 32 * q^85 - 16 * q^86 - 144 * q^87 + 88 * q^89 - 8 * q^90 - 8 * q^91 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	−0.625096	+	1.61532i	−0.360899	+	0.932605i
$3$	−0.625096	+	1.61532i	−0.360899	+	0.932605i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	0.828570	−	0.828570i	0.370548	−	0.370548i	−0.497129	−	0.867677i	$-0.665612\pi$
$5$	0.828570	−	0.828570i	0.370548	−	0.370548i	0.867677	+	0.497129i	$0.165612\pi$
$6$	−1.02187	+	1.39849i	−0.417177	+	0.570932i
$7$	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
$9$	−2.21851	−	2.01946i	−0.739503	−	0.673153i
$10$	1.01479	−	0.585888i	0.320904	−	0.185274i
$11$	−1.25192	+	4.67223i	−0.377468	+	1.40873i	0.472238	+	0.881471i	$0.343446\pi$
$11$	−1.25192	+	4.67223i	−0.377468	+	1.40873i	−0.849705	+	0.527258i	$0.823220\pi$
$12$	−1.34901	+	1.08636i	−0.389425	+	0.313605i
$13$	0.0707604	+	3.60486i	0.0196254	+	0.999807i
$13$	0.0707604	+	3.60486i	0.0196254	+	0.999807i
$14$			1.00000i			0.267261i
$15$	0.820469	+	1.85634i	0.211844	+	0.479305i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.258842	+	0.448327i	−0.0627784	+	0.108735i	−0.895706	−	0.444646i	$-0.853329\pi$
$17$	−0.258842	+	0.448327i	−0.0627784	+	0.108735i	0.832928	+	0.553381i	$0.186663\pi$
$18$	−1.62024	−	2.52484i	−0.381895	−	0.595110i
$19$	5.50267	−	1.47444i	1.26240	−	0.338259i	0.435285	−	0.900293i	$-0.356648\pi$
$19$	5.50267	−	1.47444i	1.26240	−	0.338259i	0.827114	+	0.562034i	$0.189981\pi$
$20$	1.13185	−	0.303278i	0.253089	−	0.0678150i
$21$	−1.72206	−	0.185721i	−0.375785	−	0.0405276i
$22$	−2.41852	+	4.18900i	−0.515631	+	0.893098i
$23$	−2.54064	−	4.40052i	−0.529760	−	0.917572i	−0.999397	−	0.0347123i	$-0.988949\pi$
$23$	−2.54064	−	4.40052i	−0.529760	−	0.917572i	0.469637	−	0.882860i	$-0.344385\pi$
$24$	−1.58421	+	0.700193i	−0.323376	+	0.142926i
$25$			3.62694i			0.725389i
$26$	−0.864656	+	3.50034i	−0.169573	+	0.686473i
$27$	4.64885	−	2.32125i	0.894672	−	0.446724i
$28$	−0.258819	+	0.965926i	−0.0489122	+	0.182543i
$29$	1.83703	−	1.06061i	0.341129	−	0.196951i	−0.319642	−	0.947538i	$-0.603563\pi$
$29$	1.83703	−	1.06061i	0.341129	−	0.196951i	0.660771	+	0.750588i	$0.270229\pi$
$30$	0.312056	+	2.00544i	0.0569734	+	0.366142i
$31$	4.11077	+	4.11077i	0.738316	+	0.738316i	0.972252	−	0.233936i	$-0.0751607\pi$
$31$	4.11077	+	4.11077i	0.738316	+	0.738316i	−0.233936	+	0.972252i	$0.575161\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−6.76456	−	4.94284i	−1.17756	−	0.860438i
$34$	−0.366058	+	0.366058i	−0.0627784	+	0.0627784i
$35$	1.01479	+	0.585888i	0.171530	+	0.0990331i
$36$	−0.911557	−	2.85816i	−0.151926	−	0.476360i
$37$	−9.86282	−	2.64273i	−1.62144	−	0.434463i	−0.670014	−	0.742349i	$-0.733712\pi$
$37$	−9.86282	−	2.64273i	−1.62144	−	0.434463i	−0.951423	+	0.307886i	$0.900379\pi$
$38$	5.69678			0.924140
$39$	−5.86723	−	2.13908i	−0.939508	−	0.342527i
$40$	1.17178			0.185274
$41$	−6.46664	−	1.73273i	−1.00992	−	0.270607i	−0.284324	−	0.958728i	$-0.591769\pi$
$41$	−6.46664	−	1.73273i	−1.00992	−	0.270607i	−0.725596	+	0.688121i	$0.758436\pi$
$42$	−1.61532	−	0.625096i	−0.249249	−	0.0964544i
$43$	−0.253885	−	0.146580i	−0.0387170	−	0.0223533i	0.480517	−	0.876986i	$-0.340449\pi$
$43$	−0.253885	−	0.146580i	−0.0387170	−	0.0223533i	−0.519234	+	0.854632i	$0.673783\pi$
$44$	−3.42031	+	3.42031i	−0.515631	+	0.515631i
$45$	−3.51145	+	0.164928i	−0.523457	+	0.0245861i
$46$	−1.31513	−	4.90814i	−0.193906	−	0.723666i
$47$	8.54481	+	8.54481i	1.24639	+	1.24639i	0.957303	+	0.289086i	$0.0933513\pi$
$47$	8.54481	+	8.54481i	1.24639	+	1.24639i	0.289086	+	0.957303i	$0.406649\pi$
$48$	−1.71146	+	0.266310i	−0.247027	+	0.0384386i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	−0.938722	+	3.50336i	−0.132755	+	0.495450i
$51$	−0.562390	−	0.698360i	−0.0787504	−	0.0977899i
$52$	−1.74115	+	3.15728i	−0.241454	+	0.437836i
$53$		−	9.52725i		−	1.30867i	−0.756206	−	0.654334i	$-0.772949\pi$
$53$		−	9.52725i		−	1.30867i	0.756206	−	0.654334i	$-0.227051\pi$
$54$	5.09123	−	1.03894i	0.692828	−	0.141382i
$55$	2.83396	+	4.90857i	0.382132	+	0.661871i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$	−1.05801	+	9.81023i	−0.140137	+	1.29940i
$58$	2.04895	−	0.549013i	0.269040	−	0.0720890i
$59$	1.53749	−	0.411970i	0.200164	−	0.0536339i	−0.157344	−	0.987544i	$-0.550293\pi$
$59$	1.53749	−	0.411970i	0.200164	−	0.0536339i	0.357508	+	0.933910i	$0.383626\pi$
$60$	−0.217623	+	2.01787i	−0.0280950	+	0.260506i
$61$	5.90367	−	10.2255i	0.755888	−	1.30924i	−0.189044	−	0.981969i	$-0.560539\pi$
$61$	5.90367	−	10.2255i	0.755888	−	1.30924i	0.944932	−	0.327267i	$-0.106128\pi$
$62$	2.90675	+	5.03464i	0.369158	+	0.639400i
$63$	1.37645	−	2.66559i	0.173417	−	0.335833i
$64$			1.00000i			0.125000i
$65$	3.04551	+	2.92825i	0.377749	+	0.363204i
$66$	−5.25477	−	6.52521i	−0.646817	−	0.803198i
$67$	2.99192	−	11.1660i	0.365521	−	1.36414i	−0.501192	−	0.865336i	$-0.667105\pi$
$67$	2.99192	−	11.1660i	0.365521	−	1.36414i	0.866713	−	0.498807i	$-0.166228\pi$
$68$	−0.448327	+	0.258842i	−0.0543677	+	0.0313892i
$69$	8.69639	−	1.35320i	1.04692	−	0.162906i
$70$	0.828570	+	0.828570i	0.0990331	+	0.0990331i
$71$	0.487312	+	1.81867i	0.0578332	+	0.215837i	0.988795	−	0.149280i	$-0.0476957\pi$
$71$	0.487312	+	1.81867i	0.0578332	+	0.215837i	−0.930962	+	0.365117i	$0.881029\pi$
$72$	−0.140751	−	2.99670i	−0.0165876	−	0.353164i
$73$	4.68386	−	4.68386i	0.548205	−	0.548205i	−0.377716	−	0.925921i	$-0.623291\pi$
$73$	4.68386	−	4.68386i	0.548205	−	0.548205i	0.925921	+	0.377716i	$0.123291\pi$
$74$	−8.84276	−	5.10537i	−1.02795	−	0.593487i
$75$	−5.85867	−	2.26719i	−0.676501	−	0.261792i
$76$	5.50267	+	1.47444i	0.631199	+	0.169129i
$77$	−4.83704			−0.551232
$78$	−5.11367	−	3.58474i	−0.579009	−	0.405892i
$79$	2.53289			0.284973			0.142486	−	0.989797i	$-0.454490\pi$
$79$	2.53289			0.284973			0.142486	+	0.989797i	$0.454490\pi$
$80$	1.13185	+	0.303278i	0.126544	+	0.0339075i
$81$	0.843575	+	8.96038i	0.0937305	+	0.995598i
$82$	−5.79783	−	3.34738i	−0.640263	−	0.369656i
$83$	11.7215	−	11.7215i	1.28660	−	1.28660i	0.349756	−	0.936841i	$-0.386264\pi$
$83$	11.7215	−	11.7215i	1.28660	−	1.28660i	0.936841	−	0.349756i	$-0.113736\pi$
$84$	−1.39849	−	1.02187i	−0.152588	−	0.111495i
$85$	0.157002	+	0.585939i	0.0170292	+	0.0635540i
$86$	−0.207296	−	0.207296i	−0.0223533	−	0.0223533i
$87$	0.564904	+	3.63038i	0.0605641	+	0.389218i
$88$	−4.18900	+	2.41852i	−0.446549	+	0.257815i
$89$	−0.717827	+	2.67897i	−0.0760895	+	0.283970i	−0.993478	−	0.114023i	$-0.963626\pi$
$89$	−0.717827	+	2.67897i	−0.0760895	+	0.283970i	0.917389	+	0.397993i	$0.130293\pi$
$90$	−3.43449	−	0.749523i	−0.362027	−	0.0790066i
$91$	−3.46371	+	1.00135i	−0.363095	+	0.104971i
$92$		−	5.08128i		−	0.529760i
$93$	−9.20983	+	4.07058i	−0.955015	+	0.422099i
$94$	6.04209	+	10.4652i	0.623194	+	1.07940i
$95$	3.33767	−	5.78102i	0.342438	−	0.593120i
$96$	−1.72206	−	0.185721i	−0.175758	−	0.0189551i
$97$	3.95229	−	1.05901i	0.401294	−	0.107526i	−0.0525264	−	0.998620i	$-0.516727\pi$
$97$	3.95229	−	1.05901i	0.401294	−	0.107526i	0.453821	+	0.891093i	$0.350061\pi$
$98$	−0.965926	+	0.258819i	−0.0975732	+	0.0261447i
$99$	12.2128	−	7.83718i	1.22743	−	0.787666i
$100$	−1.81347	+	3.14102i	−0.181347	+	0.314102i
$101$	1.81765	+	3.14826i	0.180863	+	0.313264i	0.942175	−	0.335122i	$-0.108778\pi$
$101$	1.81765	+	3.14826i	0.180863	+	0.313264i	−0.761312	+	0.648386i	$0.775444\pi$
$102$	−0.362479	−	0.820121i	−0.0358907	−	0.0812041i
$103$		−	13.3619i		−	1.31658i	−0.752763	−	0.658292i	$-0.771279\pi$
$103$		−	13.3619i		−	1.31658i	0.752763	−	0.658292i	$-0.228721\pi$
$104$	−2.49898	+	2.59905i	−0.245046	+	0.254858i
$105$	−1.58073	+	1.27297i	−0.154264	+	0.124229i
$106$	2.46583	−	9.20261i	0.239503	−	0.893837i
$107$	−1.29666	+	0.748627i	−0.125353	+	0.0723725i	−0.561365	−	0.827568i	$-0.689724\pi$
$107$	−1.29666	+	0.748627i	−0.125353	+	0.0723725i	0.436012	+	0.899941i	$0.356390\pi$
$108$	5.18665	+	0.314167i	0.499085	+	0.0302308i
$109$	−9.35366	−	9.35366i	−0.895918	−	0.895918i	0.0991537	−	0.995072i	$-0.468386\pi$
$109$	−9.35366	−	9.35366i	−0.895918	−	0.895918i	−0.995072	+	0.0991537i	$0.968386\pi$
$110$	1.46697	+	5.47480i	0.139870	+	0.522001i
$111$	10.4341	−	14.2796i	0.990358	−	1.35536i
$112$	−0.707107	+	0.707107i	−0.0668153	+	0.0668153i
$113$	14.8503	+	8.57383i	1.39700	+	0.806558i	0.994077	−	0.108676i	$-0.0346612\pi$
$113$	14.8503	+	8.57383i	1.39700	+	0.806558i	0.402922	+	0.915234i	$0.367995\pi$
$114$	−3.56103	+	9.20212i	−0.333521	+	0.861857i
$115$	−5.75124	−	1.54104i	−0.536306	−	0.143703i
$116$	2.12122			0.196951
$117$	7.12288	−	8.14031i	0.658510	−	0.752572i
$118$	1.59173			0.146530
$119$	−0.500044	−	0.133986i	−0.0458390	−	0.0122825i
$120$	−0.732472	+	1.89279i	−0.0668652	+	0.172787i
$121$	−10.7361	−	6.19850i	−0.976010	−	0.563500i
$122$	8.34905	−	8.34905i	0.755888	−	0.755888i
$123$	6.84118	−	9.36256i	0.616849	−	0.844194i
$124$	1.50465	+	5.61541i	0.135121	+	0.504279i
$125$	7.14803	+	7.14803i	0.639339	+	0.639339i
$126$	2.01946	−	2.21851i	0.179908	−	0.197641i
$127$	3.84030	−	2.21720i	0.340771	−	0.196744i	−0.319842	−	0.947471i	$-0.603630\pi$
$127$	3.84030	−	2.21720i	0.340771	−	0.196744i	0.660613	+	0.750727i	$0.270296\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	0.395476	−	0.318478i	0.0348197	−	0.0280404i
$130$	2.18385	+	3.61670i	0.191536	+	0.317206i
$131$			14.2928i			1.24877i	0.781118	+	0.624384i	$0.214650\pi$
$131$			14.2928i			1.24877i	−0.781118	+	0.624384i	$0.785350\pi$
$132$	−3.38687	−	7.66290i	−0.294789	−	0.666970i
$133$	2.84839	+	4.93356i	0.246987	+	0.427794i
$134$	5.77994	−	10.0112i	0.499311	−	0.864832i
$135$	1.92858	−	5.77521i	0.165986	−	0.497051i
$136$	−0.500044	+	0.133986i	−0.0428784	+	0.0114892i
$137$	9.27529	−	2.48531i	0.792441	−	0.212334i	0.160178	−	0.987088i	$-0.448793\pi$
$137$	9.27529	−	2.48531i	0.792441	−	0.212334i	0.632263	+	0.774754i	$0.282126\pi$
$138$	8.75030	+	0.943701i	0.744875	+	0.0803332i
$139$	−7.81211	+	13.5310i	−0.662615	+	1.14768i	0.317312	+	0.948321i	$0.397220\pi$
$139$	−7.81211	+	13.5310i	−0.662615	+	1.14768i	−0.979926	+	0.199361i	$0.936113\pi$
$140$	0.585888	+	1.01479i	0.0495165	+	0.0857652i
$141$	−19.1439	+	8.46127i	−1.61221	+	0.712567i
$142$			1.88283i			0.158003i
$143$	−16.9313	−	4.18238i	−1.41587	−	0.349748i
$144$	0.639647	−	2.93102i	0.0533039	−	0.244251i
$145$	0.643320	−	2.40090i	0.0534248	−	0.199384i
$146$	5.73654	−	3.31199i	0.474759	−	0.274102i
$147$	−0.266310	−	1.71146i	−0.0219649	−	0.141158i
$148$	−7.22008	−	7.22008i	−0.593487	−	0.593487i
$149$	1.69498	+	6.32574i	0.138858	+	0.518225i	0.999952	+	0.00977946i	$0.00311295\pi$
$149$	1.69498	+	6.32574i	0.138858	+	0.518225i	−0.861094	+	0.508445i	$0.830220\pi$
$150$	−5.07225	−	3.70627i	−0.414147	−	0.302616i
$151$	−15.6948	+	15.6948i	−1.27722	+	1.27722i	−0.335009	+	0.942215i	$0.608740\pi$
$151$	−15.6948	+	15.6948i	−1.27722	+	1.27722i	−0.942215	+	0.335009i	$0.891260\pi$
$152$	4.93356	+	2.84839i	0.400164	+	0.231035i
$153$	1.47962	−	0.471898i	0.119620	−	0.0381507i
$154$	−4.67223	−	1.25192i	−0.376499	−	0.100883i
$155$	6.81212			0.547163
$156$	−4.01163	−	4.78611i	−0.321187	−	0.383196i
$157$	−16.3039			−1.30119			−0.650597	−	0.759423i	$-0.725481\pi$
$157$	−16.3039			−1.30119			−0.650597	+	0.759423i	$0.725481\pi$
$158$	2.44659	+	0.655561i	0.194640	+	0.0521537i
$159$	15.3895	+	5.95544i	1.22047	+	0.472297i
$160$	1.01479	+	0.585888i	0.0802260	+	0.0463185i
$161$	3.59301	−	3.59301i	0.283169	−	0.283169i
$162$	−1.50429	+	8.87339i	−0.118188	+	0.697160i
$163$	−0.906537	−	3.38324i	−0.0710055	−	0.264996i	0.921292	−	0.388870i	$-0.127135\pi$
$163$	−0.906537	−	3.38324i	−0.0710055	−	0.264996i	−0.992298	+	0.123874i	$0.960468\pi$
$164$	−4.73391	−	4.73391i	−0.369656	−	0.369656i
$165$	−9.70040	+	1.50943i	−0.755175	+	0.117509i
$166$	14.3558	−	8.28832i	1.11423	−	0.643298i
$167$	3.88956	−	14.5160i	0.300983	−	1.12328i	−0.635365	−	0.772212i	$-0.719150\pi$
$167$	3.88956	−	14.5160i	0.300983	−	1.12328i	0.936348	−	0.351072i	$-0.114183\pi$
$168$	−1.08636	−	1.34901i	−0.0838144	−	0.104078i
$169$	−12.9900	+	0.510162i	−0.999230	+	0.0392432i
$170$			0.606609i			0.0465248i
$171$	−15.1853	−	7.84136i	−1.16125	−	0.599644i
$172$	−0.146580	−	0.253885i	−0.0111766	−	0.0193585i
$173$	−2.14061	+	3.70764i	−0.162748	+	0.281887i	−0.935853	−	0.352390i	$-0.885369\pi$
$173$	−2.14061	+	3.70764i	−0.162748	+	0.281887i	0.773106	+	0.634277i	$0.218702\pi$
$174$	−0.393956	+	3.65289i	−0.0298657	+	0.276925i
$175$	−3.50336	+	0.938722i	−0.264829	+	0.0709607i
$176$	−4.67223	+	1.25192i	−0.352182	+	0.0943669i
$177$	−0.295617	+	2.74106i	−0.0222200	+	0.206031i
$178$	−1.38673	+	2.40190i	−0.103940	+	0.180030i
$179$	5.33092	+	9.23342i	0.398452	+	0.690138i	0.993535	−	0.113526i	$-0.0362144\pi$
$179$	5.33092	+	9.23342i	0.398452	+	0.690138i	−0.595084	+	0.803664i	$0.702881\pi$
$180$	−3.12347	−	1.61290i	−0.232810	−	0.120218i
$181$		−	13.7234i		−	1.02005i	−0.860160	−	0.510025i	$-0.829636\pi$
$181$		−	13.7234i		−	1.02005i	0.860160	−	0.510025i	$-0.170364\pi$
$182$	−3.60486	+	0.0707604i	−0.267210	+	0.00524511i
$183$	12.8270	+	15.9282i	0.948200	+	1.17745i
$184$	1.31513	−	4.90814i	0.0969529	−	0.361833i
$185$	−10.3617	+	5.98235i	−0.761809	+	0.439831i
$186$	−9.94955	+	1.54820i	−0.729537	+	0.113519i
$187$	−1.77064	−	1.77064i	−0.129482	−	0.129482i
$188$	3.12762	+	11.6724i	0.228105	+	0.851299i
$189$	3.44536	+	3.88966i	0.250613	+	0.282931i
$190$	4.72018	−	4.72018i	0.342438	−	0.342438i
$191$	−15.7595	−	9.09873i	−1.14031	−	0.658361i	−0.193806	−	0.981040i	$-0.562083\pi$
$191$	−15.7595	−	9.09873i	−1.14031	−	0.658361i	−0.946509	+	0.322679i	$0.895417\pi$
$192$	−1.61532	−	0.625096i	−0.116576	−	0.0451124i
$193$	−0.834130	−	0.223505i	−0.0600420	−	0.0160882i	0.228673	−	0.973503i	$-0.426561\pi$
$193$	−0.834130	−	0.223505i	−0.0600420	−	0.0160882i	−0.288715	+	0.957415i	$0.593228\pi$
$194$	4.09171			0.293768
$195$	−6.63379	+	3.08903i	−0.475055	+	0.221210i
$196$	−1.00000			−0.0714286
$197$	−20.4357	−	5.47572i	−1.45598	−	0.390129i	−0.557882	−	0.829920i	$-0.688386\pi$
$197$	−20.4357	−	5.47572i	−1.45598	−	0.390129i	−0.898100	+	0.439791i	$0.855052\pi$
$198$	13.8250	−	4.40924i	0.982502	−	0.313351i
$199$	1.32932	+	0.767481i	0.0942327	+	0.0544053i	0.546376	−	0.837540i	$-0.316007\pi$
$199$	1.32932	+	0.767481i	0.0942327	+	0.0544053i	−0.452143	+	0.891945i	$0.649340\pi$
$200$	−2.56464	+	2.56464i	−0.181347	+	0.181347i
$201$	16.1664	+	11.8127i	1.14029	+	0.833205i
$202$	0.940885	+	3.51143i	0.0662004	+	0.247063i
$203$	1.49993	+	1.49993i	0.105275	+	0.105275i
$204$	−0.137865	−	0.885992i	−0.00965245	−	0.0620319i
$205$	−6.79375	+	3.92237i	−0.474496	+	0.273951i
$206$	3.45830	−	12.9066i	0.240951	−	0.899243i
$207$	−3.25023	+	14.8933i	−0.225907	+	1.03516i
$208$	−3.08652	+	1.86371i	−0.214011	+	0.129225i
$209$			27.5556i			1.90606i
$210$	−1.85634	+	0.820469i	−0.128100	+	0.0566178i
$211$	5.09230	+	8.82012i	0.350568	+	0.607202i	0.986349	−	0.164668i	$-0.0526551\pi$
$211$	5.09230	+	8.82012i	0.350568	+	0.607202i	−0.635781	+	0.771870i	$0.719322\pi$
$212$	4.76362	−	8.25084i	0.327167	−	0.566670i
$213$	−3.24235	−	0.349681i	−0.222162	−	0.0239597i
$214$	−1.44624	+	0.387518i	−0.0988626	+	0.0264902i
$215$	−0.331813	+	0.0889091i	−0.0226295	+	0.00606355i
$216$	4.92860	+	1.64587i	0.335349	+	0.111987i
$217$	−2.90675	+	5.03464i	−0.197323	+	0.341774i
$218$	−6.61404	−	11.4559i	−0.447959	−	0.775888i
$219$	4.63807	+	10.4938i	0.313412	+	0.709105i
$220$			5.66793i			0.382132i
$221$	−1.63447	−	0.901364i	−0.109946	−	0.0606323i
$222$	13.7744	−	11.0925i	0.924475	−	0.744482i
$223$	0.508845	−	1.89903i	0.0340748	−	0.127169i	−0.946793	−	0.321842i	$-0.895698\pi$
$223$	0.508845	−	1.89903i	0.0340748	−	0.127169i	0.980868	+	0.194673i	$0.0623647\pi$
$224$	−0.866025	+	0.500000i	−0.0578638	+	0.0334077i
$225$	7.32446	−	8.04641i	0.488297	−	0.536427i
$226$	12.1252	+	12.1252i	0.806558	+	0.806558i
$227$	−1.32281	−	4.93680i	−0.0877981	−	0.327667i	0.908031	−	0.418903i	$-0.137585\pi$
$227$	−1.32281	−	4.93680i	−0.0877981	−	0.327667i	−0.995829	+	0.0912354i	$0.970918\pi$
$228$	−5.82138	+	7.96690i	−0.385530	+	0.527621i
$229$	2.40035	−	2.40035i	0.158620	−	0.158620i	−0.623335	−	0.781955i	$-0.714223\pi$
$229$	2.40035	−	2.40035i	0.158620	−	0.158620i	0.781955	+	0.623335i	$0.214223\pi$
$230$	−5.15642	−	2.97706i	−0.340004	−	0.196302i
$231$	3.02362	−	7.81337i	0.198939	−	0.514082i
$232$	2.04895	+	0.549013i	0.134520	+	0.0360445i
$233$	−8.54899			−0.560063			−0.280032	−	0.959991i	$-0.590345\pi$
$233$	−8.54899			−0.560063			−0.280032	+	0.959991i	$0.590345\pi$
$234$	8.98704	−	6.01940i	0.587501	−	0.393500i
$235$	14.1600			0.923693
$236$	1.53749	+	0.411970i	0.100082	+	0.0268169i
$237$	−1.58330	+	4.09143i	−0.102847	+	0.265767i
$238$	−0.448327	−	0.258842i	−0.0290607	−	0.0167782i
$239$	20.0754	−	20.0754i	1.29857	−	1.29857i	0.369230	−	0.929338i	$-0.379622\pi$
$239$	20.0754	−	20.0754i	1.29857	−	1.29857i	0.929338	−	0.369230i	$-0.120378\pi$
$240$	−1.19740	+	1.63872i	−0.0772921	+	0.105779i
$241$	−5.75665	−	21.4841i	−0.370818	−	1.38391i	−0.859360	−	0.511371i	$-0.829138\pi$
$241$	−5.75665	−	21.4841i	−0.370818	−	1.38391i	0.488542	−	0.872541i	$-0.337529\pi$
$242$	−8.76600	−	8.76600i	−0.563500	−	0.563500i
$243$	−15.0012	−	4.23845i	−0.962326	−	0.271897i
$244$	10.2255	−	5.90367i	0.654618	−	0.377944i
$245$	−0.303278	+	1.13185i	−0.0193757	+	0.0723111i
$246$	9.03128	−	7.27291i	0.575814	−	0.463704i
$247$	5.70450	+	19.7320i	0.362969	+	1.25552i
$248$			5.81351i			0.369158i
$249$	11.6069	+	26.2609i	0.735555	+	1.66422i
$250$	5.05442	+	8.75451i	0.319670	+	0.553684i
$251$	−8.15438	+	14.1238i	−0.514700	+	0.891487i	0.485154	+	0.874429i	$0.338763\pi$
$251$	−8.15438	+	14.1238i	−0.514700	+	0.891487i	−0.999854	+	0.0170582i	$0.994570\pi$
$252$	2.52484	−	1.62024i	0.159050	−	0.102066i
$253$	23.7409	−	6.36136i	1.49258	−	0.399935i
$254$	4.28330	−	1.14771i	0.268758	−	0.0720135i
$255$	−1.04462	−	0.112660i	−0.0654166	−	0.00705504i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.49782	+	2.59430i	0.0934315	+	0.161828i	0.908953	−	0.416899i	$-0.136883\pi$
$257$	1.49782	+	2.59430i	0.0934315	+	0.161828i	−0.815521	+	0.578727i	$0.803550\pi$
$258$	0.464429	−	0.205269i	0.0289141	−	0.0127795i
$259$		−	10.2107i		−	0.634465i
$260$	1.17336	+	4.05869i	0.0727689	+	0.251709i
$261$	−6.21734	−	1.35684i	−0.384844	−	0.0839860i
$262$	−3.69925	+	13.8058i	−0.228540	+	0.852924i
$263$	−3.52497	+	2.03514i	−0.217359	+	0.125492i	−0.604727	−	0.796433i	$-0.706718\pi$
$263$	−3.52497	+	2.03514i	−0.217359	+	0.125492i	0.387368	+	0.921925i	$0.373384\pi$
$264$	−1.28816	−	8.27838i	−0.0792805	−	0.509499i
$265$	−7.89399	−	7.89399i	−0.484924	−	0.484924i
$266$	1.47444	+	5.50267i	0.0904034	+	0.337390i
$267$	−3.87867	−	2.83413i	−0.237371	−	0.173446i
$268$	8.17407	−	8.17407i	0.499311	−	0.499311i
$269$	2.68484	+	1.55010i	0.163698	+	0.0945110i	0.579611	−	0.814893i	$-0.303205\pi$
$269$	2.68484	+	1.55010i	0.163698	+	0.0945110i	−0.415913	+	0.909404i	$0.636538\pi$
$270$	3.35760	−	5.07927i	0.204337	−	0.309115i
$271$	14.8204	+	3.97111i	0.900275	+	0.241228i	0.679134	−	0.734014i	$-0.262355\pi$
$271$	14.8204	+	3.97111i	0.900275	+	0.241228i	0.221140	+	0.975242i	$0.429022\pi$
$272$	−0.517684			−0.0313892
$273$	0.547644	−	6.22094i	0.0331449	−	0.376508i
$274$	9.60248			0.580107
$275$	−16.9459	−	4.54064i	−1.02188	−	0.273811i
$276$	8.20789	+	3.17629i	0.494057	+	0.191190i
$277$	−1.05278	−	0.607822i	−0.0632553	−	0.0365205i	0.468039	−	0.883708i	$-0.344961\pi$
$277$	−1.05278	−	0.607822i	−0.0632553	−	0.0365205i	−0.531294	+	0.847187i	$0.678294\pi$
$278$	−11.0480	+	11.0480i	−0.662615	+	0.662615i
$279$	−0.818255	−	17.4213i	−0.0489877	−	1.04299i
$280$	0.303278	+	1.13185i	0.0181243	+	0.0676408i
$281$	−1.81570	−	1.81570i	−0.108316	−	0.108316i	0.650872	−	0.759188i	$-0.274403\pi$
$281$	−1.81570	−	1.81570i	−0.108316	−	0.108316i	−0.759188	+	0.650872i	$0.774403\pi$
$282$	−20.6815	+	3.21815i	−1.23157	+	0.191638i
$283$	−8.30363	+	4.79410i	−0.493600	+	0.284980i	−0.726067	−	0.687624i	$-0.758654\pi$
$283$	−8.30363	+	4.79410i	−0.493600	+	0.284980i	0.232467	+	0.972604i	$0.425320\pi$
$284$	−0.487312	+	1.81867i	−0.0289166	+	0.107918i
$285$	7.25182	+	9.00510i	0.429561	+	0.533416i
$286$	−15.2719	−	8.42201i	−0.903046	−	0.498004i
$287$		−	6.69476i		−	0.395179i
$288$	1.37645	−	2.66559i	0.0811084	−	0.157071i
$289$	8.36600	+	14.4903i	0.492118	+	0.852373i
$290$	1.24280	−	2.15259i	0.0729797	−	0.126405i
$291$	−0.759917	+	7.04619i	−0.0445471	+	0.413055i
$292$	6.39828	−	1.71441i	0.374431	−	0.100328i
$293$	−20.3586	+	5.45507i	−1.18936	+	0.318689i	−0.798634	−	0.601817i	$-0.794444\pi$
$293$	−20.3586	+	5.45507i	−1.18936	+	0.318689i	−0.390729	+	0.920506i	$0.627777\pi$
$294$	0.185721	−	1.72206i	0.0108315	−	0.100433i
$295$	0.932574	−	1.61527i	0.0542966	−	0.0940444i
$296$	−5.10537	−	8.84276i	−0.296744	−	0.513975i
$297$	5.02540	+	24.6265i	0.291603	+	1.42897i
$298$			6.54889i			0.379367i
$299$	15.6835	−	9.47003i	0.906998	−	0.547666i
$300$	−3.94016	−	4.89278i	−0.227485	−	0.282485i
$301$	0.0758756	−	0.283171i	0.00437339	−	0.0163217i
$302$	−19.2221	+	11.0979i	−1.10611	+	0.638612i
$303$	−6.22165	+	0.968119i	−0.357425	+	0.0556170i
$304$	4.02823	+	4.02823i	0.231035	+	0.231035i
$305$	−3.58090	−	13.3641i	−0.205042	−	0.765227i
$306$	1.55134	−	0.0728644i	0.0886842	−	0.00416538i
$307$	−1.05726	+	1.05726i	−0.0603413	+	0.0603413i	−0.736633	−	0.676292i	$-0.763586\pi$
$307$	−1.05726	+	1.05726i	−0.0603413	+	0.0603413i	0.676292	+	0.736633i	$0.263586\pi$
$308$	−4.18900	−	2.41852i	−0.238691	−	0.137808i
$309$	21.5837	+	8.35244i	1.22785	+	0.475154i
$310$	6.58000	+	1.76311i	0.373719	+	0.100138i
$311$	−6.32744			−0.358796			−0.179398	−	0.983777i	$-0.557415\pi$
$311$	−6.32744			−0.358796			−0.179398	+	0.983777i	$0.557415\pi$
$312$	−2.63620	−	5.66131i	−0.149245	−	0.320509i
$313$	−26.7529			−1.51216			−0.756081	−	0.654478i	$-0.772888\pi$
$313$	−26.7529			−1.51216			−0.756081	+	0.654478i	$0.772888\pi$
$314$	−15.7484	−	4.21977i	−0.888733	−	0.238135i
$315$	−1.06814	−	3.34912i	−0.0601829	−	0.188701i
$316$	2.19355	+	1.26645i	0.123397	+	0.0712432i
$317$	13.6159	−	13.6159i	0.764748	−	0.764748i	−0.212429	−	0.977177i	$-0.568137\pi$
$317$	13.6159	−	13.6159i	0.764748	−	0.764748i	0.977177	+	0.212429i	$0.0681374\pi$
$318$	13.3238	+	9.73562i	0.747160	+	0.545947i
$319$	2.65560	+	9.91084i	0.148685	+	0.554900i
$320$	0.828570	+	0.828570i	0.0463185	+	0.0463185i
$321$	−0.398734	−	2.56248i	−0.0222552	−	0.143024i
$322$	4.40052	−	2.54064i	0.245231	−	0.141584i
$323$	−0.763291	+	2.84864i	−0.0424707	+	0.158503i
$324$	−3.74963	+	8.18170i	−0.208313	+	0.454539i
$325$	−13.0746	+	0.256644i	−0.725249	+	0.0142360i
$326$		−	3.50259i		−	0.193991i
$327$	20.9561	−	9.26221i	1.15887	−	0.512201i
$328$	−3.34738	−	5.79783i	−0.184828	−	0.320132i
$329$	−6.04209	+	10.4652i	−0.333111	+	0.576966i
$330$	−9.76054	−	1.05265i	−0.537300	−	0.0579467i
$331$	−9.03418	+	2.42070i	−0.496564	+	0.133054i	−0.498405	−	0.866945i	$-0.666081\pi$
$331$	−9.03418	+	2.42070i	−0.496564	+	0.133054i	0.00184113	+	0.999998i	$0.499414\pi$
$332$	16.0118	−	4.29035i	0.878762	−	0.235464i
$333$	16.5439	+	25.7805i	0.906598	+	1.41276i
$334$	7.51405	−	13.0147i	0.411151	−	0.712134i
$335$	−6.77279	−	11.7308i	−0.370037	−	0.640923i
$336$	−0.700193	−	1.58421i	−0.0381987	−	0.0864259i
$337$		−	4.47748i		−	0.243904i	−0.992536	−	0.121952i	$-0.961085\pi$
$337$		−	4.47748i		−	0.243904i	0.992536	−	0.121952i	$-0.0389154\pi$
$338$	−12.6794	−	2.86928i	−0.689669	−	0.156068i
$339$	−23.1323	+	18.6285i	−1.25638	+	1.01176i
$340$	−0.157002	+	0.585939i	−0.00851462	+	0.0317770i
$341$	−24.3528	+	14.0601i	−1.31878	+	0.761396i
$342$	−12.6384	−	11.5044i	−0.683405	−	0.622087i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−0.0758756	−	0.283171i	−0.00409094	−	0.0152676i
$345$	6.08435	−	8.32679i	0.327570	−	0.448299i
$346$	−3.02728	+	3.02728i	−0.162748	+	0.162748i
$347$	−19.0489	−	10.9979i	−1.02260	−	0.590398i	−0.107743	−	0.994179i	$-0.534363\pi$
$347$	−19.0489	−	10.9979i	−1.02260	−	0.590398i	−0.914856	+	0.403781i	$0.867696\pi$
$348$	−1.32597	+	3.42645i	−0.0710794	+	0.183677i
$349$	34.1495	+	9.15032i	1.82798	+	0.489805i	0.997715	−	0.0675659i	$-0.0215233\pi$
$349$	34.1495	+	9.15032i	1.82798	+	0.489805i	0.830263	+	0.557371i	$0.188190\pi$
$350$	−3.62694			−0.193868
$351$	8.69671	+	16.5942i	0.464196	+	0.885732i
$352$	−4.83704			−0.257815
$353$	2.94177	+	0.788246i	0.156575	+	0.0419541i	0.336255	−	0.941771i	$-0.390840\pi$
$353$	2.94177	+	0.788246i	0.156575	+	0.0419541i	−0.179680	+	0.983725i	$0.557506\pi$
$354$	−0.994983	+	2.57115i	−0.0528827	+	0.136655i
$355$	1.91067	+	1.10313i	0.101408	+	0.0585478i
$356$	−1.96114	+	1.96114i	−0.103940	+	0.103940i
$357$	0.529006	−	0.723976i	0.0279980	−	0.0383169i
$358$	2.75949	+	10.2985i	0.145843	+	0.544295i
$359$	8.69884	+	8.69884i	0.459107	+	0.459107i	0.898362	−	0.439255i	$-0.144758\pi$
$359$	8.69884	+	8.69884i	0.459107	+	0.459107i	−0.439255	+	0.898362i	$0.644758\pi$
$360$	−2.59960	−	2.36635i	−0.137011	−	0.124718i
$361$	11.6509	−	6.72666i	0.613206	−	0.354035i
$362$	3.55187	−	13.2558i	0.186682	−	0.696707i
$363$	16.7236	−	13.4676i	0.877764	−	0.706865i
$364$	−3.50034	−	0.864656i	−0.183468	−	0.0453203i
$365$		−	7.76182i		−	0.406272i
$366$	8.26742	+	18.7053i	0.432145	+	0.977744i
$367$	7.85537	+	13.6059i	0.410047	+	0.710222i	0.994894	−	0.100921i	$-0.0321789\pi$
$367$	7.85537	+	13.6059i	0.410047	+	0.710222i	−0.584847	+	0.811143i	$0.698846\pi$
$368$	2.54064	−	4.40052i	0.132440	−	0.229393i
$369$	10.8471	+	16.9032i	0.564679	+	0.879945i
$370$	−11.5570	+	3.09669i	−0.600820	+	0.160989i
$371$	9.20261	−	2.46583i	0.477776	−	0.128020i
$372$	−10.0112	−	1.07969i	−0.519058	−	0.0559793i
$373$	−1.05627	+	1.82952i	−0.0546918	+	0.0947290i	−0.892075	−	0.451887i	$-0.850751\pi$
$373$	−1.05627	+	1.82952i	−0.0546918	+	0.0947290i	0.837383	+	0.546616i	$0.184084\pi$
$374$	−1.25203	−	2.16858i	−0.0647409	−	0.112135i
$375$	−16.0145	+	7.07814i	−0.826988	+	0.365514i
$376$			12.0842i			0.623194i
$377$	3.95334	+	6.54720i	0.203608	+	0.337198i
$378$	2.32125	+	4.64885i	0.119392	+	0.239111i
$379$	−8.89975	+	33.2143i	−0.457150	+	1.70611i	0.224540	+	0.974465i	$0.427912\pi$
$379$	−8.89975	+	33.2143i	−0.457150	+	1.70611i	−0.681690	+	0.731641i	$0.738755\pi$
$380$	5.78102	−	3.33767i	0.296560	−	0.171219i
$381$	1.18093	+	7.58927i	0.0605007	+	0.388810i
$382$	−12.8675	−	12.8675i	−0.658361	−	0.658361i
$383$	7.20127	+	26.8755i	0.367968	+	1.37327i	0.863353	+	0.504600i	$0.168360\pi$
$383$	7.20127	+	26.8755i	0.367968	+	1.37327i	−0.495385	+	0.868673i	$0.664973\pi$
$384$	−1.39849	−	1.02187i	−0.0713665	−	0.0521472i
$385$	−4.00783	+	4.00783i	−0.204258	+	0.204258i
$386$	−0.747861	−	0.431778i	−0.0380651	−	0.0219769i
$387$	0.267233	+	0.837899i	0.0135842	+	0.0425928i
$388$	3.95229	+	1.05901i	0.200647	+	0.0537632i
$389$	16.0139			0.811938			0.405969	−	0.913887i	$-0.366934\pi$
$389$	16.0139			0.811938			0.405969	+	0.913887i	$0.366934\pi$
$390$	−7.20725	+	1.26682i	−0.364953	+	0.0641481i
$391$	2.63050			0.133030
$392$	−0.965926	−	0.258819i	−0.0487866	−	0.0130723i
$393$	−23.0874	−	8.93437i	−1.16461	−	0.450679i
$394$	−18.3221	−	10.5783i	−0.923056	−	0.532926i
$395$	2.09868	−	2.09868i	0.105596	−	0.105596i
$396$	14.4952	−	0.680818i	0.728409	−	0.0342124i
$397$	−3.61458	−	13.4898i	−0.181411	−	0.677034i	−0.995370	−	0.0961128i	$-0.969359\pi$
$397$	−3.61458	−	13.4898i	−0.181411	−	0.677034i	0.813960	−	0.580921i	$-0.197308\pi$
$398$	1.08538	+	1.08538i	0.0544053	+	0.0544053i
$399$	−9.74979	+	1.51711i	−0.488100	+	0.0759506i
$400$	−3.14102	+	1.81347i	−0.157051	+	0.0906736i
$401$	−6.69859	+	24.9995i	−0.334512	+	1.24841i	0.569886	+	0.821724i	$0.306987\pi$
$401$	−6.69859	+	24.9995i	−0.334512	+	1.24841i	−0.904398	+	0.426691i	$0.859679\pi$
$402$	12.5582	+	15.5944i	0.626346	+	0.777777i
$403$	−14.5279	+	15.1096i	−0.723684	+	0.752663i
$404$			3.63530i			0.180863i
$405$	8.12326	+	6.72534i	0.403648	+	0.334185i
$406$	1.06061	+	1.83703i	0.0526373	+	0.0911705i
$407$	24.6949	−	42.7728i	1.22408	−	2.12017i
$408$	0.0961447	−	0.891485i	0.00475987	−	0.0441351i
$409$	7.28579	−	1.95222i	0.360259	−	0.0965311i	−0.0741494	−	0.997247i	$-0.523624\pi$
$409$	7.28579	−	1.95222i	0.360259	−	0.0965311i	0.434408	+	0.900716i	$0.356958\pi$
$410$	−7.57745	+	2.03037i	−0.374223	+	0.100273i
$411$	−1.78338	+	16.5361i	−0.0879678	+	0.815666i
$412$	6.68093	−	11.5717i	0.329146	−	0.570097i
$413$	0.795864	+	1.37848i	0.0391619	+	0.0678304i
$414$	−6.99415	+	13.5446i	−0.343744	+	0.665682i
$415$		−	19.4241i		−	0.953491i
$416$	−3.46371	+	1.00135i	−0.169822	+	0.0490955i
$417$	−16.9735	−	21.0772i	−0.831197	−	1.03216i
$418$	−7.13191	+	26.6166i	−0.348833	+	1.30186i
$419$	−14.3943	+	8.31054i	−0.703206	+	0.405996i	−0.808541	−	0.588440i	$-0.799742\pi$
$419$	−14.3943	+	8.31054i	−0.703206	+	0.405996i	0.105334	+	0.994437i	$0.466409\pi$
$420$	−2.00544	+	0.312056i	−0.0978555	+	0.0152268i
$421$	−8.80780	−	8.80780i	−0.429266	−	0.429266i	0.459112	−	0.888378i	$-0.348168\pi$
$421$	−8.80780	−	8.80780i	−0.429266	−	0.429266i	−0.888378	+	0.459112i	$0.848168\pi$
$422$	2.63597	+	9.83757i	0.128317	+	0.478885i
$423$	−1.70086	−	36.2126i	−0.0826986	−	1.76072i
$424$	6.73678	−	6.73678i	0.327167	−	0.327167i
$425$	−1.62606	−	0.938805i	−0.0788754	−	0.0455387i
$426$	−3.04137	−	1.17695i	−0.147355	−	0.0570233i
$427$	11.4050	+	3.05596i	0.551927	+	0.147888i
$428$	−1.49725			−0.0723725
$429$	17.3396	−	24.7350i	0.837162	−	1.19422i
$430$	−0.343518			−0.0165659
$431$	−18.4277	−	4.93767i	−0.887629	−	0.237839i	−0.213933	−	0.976848i	$-0.568627\pi$
$431$	−18.4277	−	4.93767i	−0.887629	−	0.237839i	−0.673696	+	0.739009i	$0.735294\pi$
$432$	4.33468	+	2.86540i	0.208553	+	0.137862i
$433$	−17.4264	−	10.0611i	−0.837458	−	0.483507i	0.0189413	−	0.999821i	$-0.493970\pi$
$433$	−17.4264	−	10.0611i	−0.837458	−	0.483507i	−0.856399	+	0.516314i	$0.827304\pi$
$434$	−4.11077	+	4.11077i	−0.197323	+	0.197323i
$435$	3.47609	+	2.53996i	0.166666	+	0.121782i
$436$	−3.42368	−	12.7773i	−0.163964	−	0.611924i
$437$	−20.4686	−	20.4686i	−0.979146	−	0.979146i
$438$	1.76404	+	11.3367i	0.0842889	+	0.541686i
$439$	22.2565	−	12.8498i	1.06225	−	0.613288i	0.136193	−	0.990682i	$-0.456513\pi$
$439$	22.2565	−	12.8498i	1.06225	−	0.613288i	0.926052	+	0.377395i	$0.123180\pi$
$440$	−1.46697	+	5.47480i	−0.0699349	+	0.261001i
$441$	2.93102	+	0.639647i	0.139572	+	0.0304594i
$442$	−1.34549	−	1.29368i	−0.0639983	−	0.0615342i
$443$		−	0.0356586i		−	0.00169419i	−1.00000		0.000847095i	$-0.999730\pi$
$443$		−	0.0356586i		−	0.00169419i	1.00000		0.000847095i	$-0.000269639\pi$
$444$	16.1760	−	7.14949i	0.767678	−	0.339300i
$445$	1.62494	+	2.81448i	0.0770296	+	0.133419i
$446$	0.983012	−	1.70263i	0.0465470	−	0.0806217i
$447$	−11.2776	−	1.21627i	−0.533413	−	0.0575274i
$448$	−0.965926	+	0.258819i	−0.0456357	+	0.0122281i
$449$	26.1123	−	6.99677i	1.23231	−	0.330198i	0.416834	−	0.908982i	$-0.363139\pi$
$449$	26.1123	−	6.99677i	1.23231	−	0.330198i	0.815480	+	0.578785i	$0.196473\pi$
$450$	9.15745	−	5.87653i	0.431686	−	0.277022i
$451$	16.1914	−	28.0444i	0.762424	−	1.32056i
$452$	8.57383	+	14.8503i	0.403279	+	0.698500i
$453$	−15.5413	−	35.1628i	−0.730196	−	1.65209i
$454$		−	5.11095i		−	0.239869i
$455$	−2.04023	+	3.69962i	−0.0956477	+	0.173441i
$456$	−7.68501	+	6.18875i	−0.359883	+	0.289815i
$457$	−8.04660	+	30.0303i	−0.376404	+	1.40476i	0.474878	+	0.880052i	$0.342492\pi$
$457$	−8.04660	+	30.0303i	−0.376404	+	1.40476i	−0.851282	+	0.524708i	$0.824174\pi$
$458$	2.93982	−	1.69731i	0.137369	−	0.0793099i
$459$	−0.162639	+	2.68504i	−0.00759135	+	0.125327i
$460$	−4.21020	−	4.21020i	−0.196302	−	0.196302i
$461$	4.89115	+	18.2540i	0.227804	+	0.850174i	0.981262	+	0.192679i	$0.0617175\pi$
$461$	4.89115	+	18.2540i	0.227804	+	0.850174i	−0.753458	+	0.657496i	$0.771616\pi$
$462$	4.94284	−	6.76456i	0.229962	−	0.314716i
$463$	0.959289	−	0.959289i	0.0445819	−	0.0445819i	−0.684464	−	0.729046i	$-0.739964\pi$
$463$	0.959289	−	0.959289i	0.0445819	−	0.0445819i	0.729046	+	0.684464i	$0.239964\pi$
$464$	1.83703	+	1.06061i	0.0852822	+	0.0492377i
$465$	−4.25823	+	11.0037i	−0.197471	+	0.510287i
$466$	−8.25769	−	2.21264i	−0.382530	−	0.102499i
$467$	−28.3194			−1.31046			−0.655232	−	0.755428i	$-0.727429\pi$
$467$	−28.3194			−1.31046			−0.655232	+	0.755428i	$0.727429\pi$
$468$	10.2387	−	3.48828i	0.473286	−	0.161246i
$469$	11.5599			0.533786
$470$	13.6775	+	3.66487i	0.630894	+	0.169048i
$471$	10.1915	−	26.3360i	0.469600	−	1.21350i
$472$	1.37848	+	0.795864i	0.0634496	+	0.0366326i
$473$	1.00270	−	1.00270i	0.0461042	−	0.0461042i
$474$	−2.58829	+	3.54223i	−0.118884	+	0.162700i
$475$	5.34769	+	19.9579i	0.245369	+	0.915730i
$476$	−0.366058	−	0.366058i	−0.0167782	−	0.0167782i
$477$	−19.2399	+	21.1363i	−0.880934	+	0.967765i
$478$	24.5872	−	14.1954i	1.12459	−	0.649284i
$479$	5.48863	−	20.4838i	0.250782	−	0.935930i	−0.719607	−	0.694382i	$-0.755678\pi$
$479$	5.48863	−	20.4838i	0.250782	−	0.935930i	0.970389	−	0.241549i	$-0.0776553\pi$
$480$	−1.58073	+	1.27297i	−0.0721503	+	0.0581028i
$481$	8.82878	−	35.7410i	0.402558	−	1.62965i
$482$		−	22.2420i		−	1.01309i
$483$	3.55788	+	8.04983i	0.161889	+	0.366280i
$484$	−6.19850	−	10.7361i	−0.281750	−	0.488005i
$485$	2.39728	−	4.15222i	0.108855	−	0.188542i
$486$	−13.3930	−	7.97662i	−0.607521	−	0.361827i
$487$	25.2906	−	6.77660i	1.14603	−	0.307077i	0.364655	−	0.931143i	$-0.381187\pi$
$487$	25.2906	−	6.77660i	1.14603	−	0.307077i	0.781372	+	0.624066i	$0.214520\pi$
$488$	11.4050	−	3.05596i	0.516281	−	0.138337i
$489$	6.03169	+	0.650505i	0.272762	+	0.0294168i
$490$	−0.585888	+	1.01479i	−0.0264677	+	0.0458434i
$491$	−5.30462	−	9.18788i	−0.239394	−	0.414643i	0.721146	−	0.692783i	$-0.243616\pi$
$491$	−5.30462	−	9.18788i	−0.239394	−	0.414643i	−0.960541	+	0.278140i	$0.910282\pi$
$492$	10.6059	−	4.68762i	0.478152	−	0.211334i
$493$			1.09812i			0.0494570i
$494$	0.403106	+	20.5361i	0.0181366	+	0.923962i
$495$	3.62547	−	16.6128i	0.162953	−	0.746689i
$496$	−1.50465	+	5.61541i	−0.0675606	+	0.252140i
$497$	−1.63058	+	0.941414i	−0.0731413	+	0.0422282i
$498$	4.41453	+	28.3702i	0.197820	+	1.27130i
$499$	−23.7488	−	23.7488i	−1.06314	−	1.06314i	−0.997867	−	0.0652762i	$-0.979207\pi$
$499$	−23.7488	−	23.7488i	−1.06314	−	1.06314i	−0.0652762	−	0.997867i	$-0.520793\pi$
$500$	2.61636	+	9.76439i	0.117007	+	0.436677i
$501$	21.0167	+	15.3568i	0.938956	+	0.686091i
$502$	−11.5320	+	11.5320i	−0.514700	+	0.514700i
$503$	10.3733	+	5.98900i	0.462520	+	0.267036i	0.713103	−	0.701059i	$-0.247289\pi$
$503$	10.3733	+	5.98900i	0.462520	+	0.267036i	−0.250583	+	0.968095i	$0.580622\pi$
$504$	2.85816	−	0.911557i	0.127312	−	0.0406040i
$505$	4.11461	+	1.10251i	0.183098	+	0.0490609i
$506$	24.5784			1.09264
$507$	7.29591	−	21.3019i	0.324023	−	0.946049i
$508$	4.43439			0.196744
$509$	−3.78952	−	1.01540i	−0.167967	−	0.0450067i	0.173855	−	0.984771i	$-0.444378\pi$
$509$	−3.78952	−	1.01540i	−0.167967	−	0.0450067i	−0.341823	+	0.939764i	$0.611044\pi$
$510$	−0.979867	−	0.379189i	−0.0433892	−	0.0167908i
$511$	5.73654	+	3.31199i	0.253770	+	0.146514i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	22.1586	−	19.6275i	0.978324	−	0.866574i
$514$	0.775329	+	2.89357i	0.0341983	+	0.127630i
$515$	−11.0712	−	11.0712i	−0.487857	−	0.487857i
$516$	0.501731	−	0.0780718i	0.0220875	−	0.00343692i
$517$	−50.6207	+	29.2259i	−2.22630	+	1.28535i
$518$	2.64273	−	9.86282i	0.116115	−	0.433347i
$519$	−4.65094	−	5.77540i	−0.204154	−	0.253512i
$520$	0.0829152	+	4.22408i	0.00363607	+	0.185238i
$521$			0.453994i			0.0198899i	0.999951	+	0.00994493i	$0.00316562\pi$
$521$			0.453994i			0.0198899i	−0.999951	+	0.00994493i	$0.996834\pi$
$522$	−5.65432	−	2.91977i	−0.247483	−	0.127795i
$523$	3.82939	+	6.63269i	0.167447	+	0.290027i	0.937522	−	0.347927i	$-0.113114\pi$
$523$	3.82939	+	6.63269i	0.167447	+	0.290027i	−0.770074	+	0.637954i	$0.779781\pi$
$524$	−7.14640	+	12.3779i	−0.312192	+	0.540732i
$525$	0.673600	−	6.24583i	0.0293983	−	0.272590i
$526$	−3.93159	+	1.05347i	−0.171425	+	0.0459333i
$527$	−2.90701	+	0.778931i	−0.126631	+	0.0339307i
$528$	0.898341	−	8.32970i	0.0390953	−	0.362504i
$529$	−1.40972	+	2.44171i	−0.0612922	+	0.106161i
$530$	−5.58190	−	9.66813i	−0.242462	−	0.419957i
$531$	−4.24290	−	2.19094i	−0.184126	−	0.0950788i
$532$			5.69678i			0.246987i
$533$	5.78866	−	23.4339i	0.250735	−	1.01504i
$534$	−3.01298	−	3.74143i	−0.130385	−	0.161908i
$535$	−0.454083	+	1.69466i	−0.0196317	+	0.0732667i
$536$	10.0112	−	5.77994i	0.432416	−	0.249656i
$537$	−18.2473	+	2.83936i	−0.787427	+	0.122527i
$538$	2.19217	+	2.19217i	0.0945110	+	0.0945110i
$539$	−1.25192	−	4.67223i	−0.0539240	−	0.201247i
$540$	4.55781	−	4.03719i	0.196137	−	0.173733i
$541$	13.2203	−	13.2203i	0.568384	−	0.568384i	−0.363291	−	0.931676i	$-0.618347\pi$
$541$	13.2203	−	13.2203i	0.568384	−	0.568384i	0.931676	+	0.363291i	$0.118347\pi$
$542$	13.2876	+	7.67160i	0.570751	+	0.329523i
$543$	22.1676	+	8.57842i	0.951304	+	0.368135i
$544$	−0.500044	−	0.133986i	−0.0214392	−	0.00574462i
$545$	−15.5003			−0.663961
$546$	2.13908	−	5.86723i	0.0915442	−	0.251094i
$547$	−12.2763			−0.524896			−0.262448	−	0.964946i	$-0.584530\pi$
$547$	−12.2763			−0.524896			−0.262448	+	0.964946i	$0.584530\pi$
$548$	9.27529	+	2.48531i	0.396221	+	0.106167i
$549$	−33.7472	+	10.7631i	−1.44030	+	0.459356i
$550$	−15.1933	−	8.77184i	−0.647843	−	0.374033i
$551$	8.54479	−	8.54479i	0.364020	−	0.364020i
$552$	7.10613	+	5.19242i	0.302457	+	0.221004i
$553$	0.655561	+	2.44659i	0.0278773	+	0.104040i
$554$	−0.859590	−	0.859590i	−0.0365205	−	0.0365205i
$555$	−3.18632	−	20.4770i	−0.135252	−	0.869202i
$556$	−13.5310	+	7.81211i	−0.573841	+	0.331307i
$557$	7.35055	−	27.4326i	0.311453	−	1.16236i	−0.615794	−	0.787907i	$-0.711165\pi$
$557$	7.35055	−	27.4326i	0.311453	−	1.16236i	0.927247	−	0.374450i	$-0.122169\pi$
$558$	3.71859	−	17.0395i	0.157421	−	0.721338i
$559$	0.510436	−	0.925590i	0.0215891	−	0.0391483i
$560$			1.17178i			0.0495165i
$561$	3.96696	−	1.75333i	0.167485	−	0.0740254i
$562$	−1.28389	−	2.22377i	−0.0541578	−	0.0938041i
$563$	4.58399	−	7.93971i	0.193192	−	0.334619i	−0.753114	−	0.657890i	$-0.771449\pi$
$563$	4.58399	−	7.93971i	0.193192	−	0.334619i	0.946306	+	0.323271i	$0.104783\pi$
$564$	−20.8098	−	2.24429i	−0.876249	−	0.0945016i
$565$	19.4085	−	5.20050i	0.816523	−	0.218787i
$566$	−9.26150	+	2.48161i	−0.389290	+	0.104310i
$567$	−8.43673	+	3.13395i	−0.354309	+	0.131613i
$568$	−0.941414	+	1.63058i	−0.0395008	+	0.0684175i
$569$	9.38211	+	16.2503i	0.393319	+	0.681248i	0.992885	−	0.119077i	$-0.0379936\pi$
$569$	9.38211	+	16.2503i	0.393319	+	0.681248i	−0.599566	+	0.800325i	$0.704660\pi$
$570$	4.67403	+	10.5752i	0.195774	+	0.442945i
$571$		−	40.4283i		−	1.69187i	−0.533285	−	0.845936i	$-0.679043\pi$
$571$		−	40.4283i		−	1.69187i	0.533285	−	0.845936i	$-0.320957\pi$
$572$	−12.5717	−	12.0877i	−0.525651	−	0.505412i
$573$	24.5485	−	19.7690i	1.02553	−	0.825861i
$574$	1.73273	−	6.46664i	0.0723228	−	0.269912i
$575$	15.9604	−	9.21476i	0.665596	−	0.384282i
$576$	2.01946	−	2.21851i	0.0841441	−	0.0924379i
$577$	19.6981	+	19.6981i	0.820041	+	0.820041i	0.986114	−	0.166073i	$-0.0531086\pi$
$577$	19.6981	+	19.6981i	0.820041	+	0.820041i	−0.166073	+	0.986114i	$0.553109\pi$
$578$	4.33056	+	16.1619i	0.180128	+	0.672245i
$579$	0.882442	−	1.20767i	0.0366731	−	0.0501892i
$580$	1.75758	−	1.75758i	0.0729797	−	0.0729797i
$581$	14.3558	+	8.28832i	0.595579	+	0.343857i
$582$	−2.55771	+	6.60942i	−0.106021	+	0.273969i
$583$	44.5134	+	11.9273i	1.84356	+	0.493980i
$584$	6.62398			0.274102
$585$	−0.843015	−	12.6466i	−0.0348544	−	0.522873i
$586$	−21.0768			−0.870674
$587$	−6.77509	−	1.81538i	−0.279638	−	0.0749288i	0.116274	−	0.993217i	$-0.462905\pi$
$587$	−6.77509	−	1.81538i	−0.279638	−	0.0749288i	−0.395912	+	0.918288i	$0.629572\pi$
$588$	0.625096	−	1.61532i	0.0257785	−	0.0666146i
$589$	28.6813	+	16.5591i	1.18179	+	0.682307i
$590$	1.31886	−	1.31886i	0.0542966	−	0.0542966i
$591$	21.6193	−	29.5873i	0.889299	−	1.21706i
$592$	−2.64273	−	9.86282i	−0.108616	−	0.405359i
$593$	−11.2191	−	11.2191i	−0.460714	−	0.460714i	0.438175	−	0.898890i	$-0.355625\pi$
$593$	−11.2191	−	11.2191i	−0.460714	−	0.460714i	−0.898890	+	0.438175i	$0.855625\pi$
$594$	−1.51964	+	25.0880i	−0.0623517	+	1.02937i
$595$	−0.525339	+	0.303304i	−0.0215368	+	0.0124343i
$596$	−1.69498	+	6.32574i	−0.0694290	+	0.259112i
$597$	−2.07068	+	1.66752i	−0.0847471	+	0.0682470i
$598$	17.6001	−	5.08817i	0.719721	−	0.208071i
$599$			40.3004i			1.64663i	0.567586	+	0.823314i	$0.307877\pi$
$599$			40.3004i			1.64663i	−0.567586	+	0.823314i	$0.692123\pi$
$600$	−2.53956	−	5.74585i	−0.103677	−	0.234573i
$601$	−6.18901	−	10.7197i	−0.252455	−	0.437265i	0.711746	−	0.702437i	$-0.247905\pi$
$601$	−6.18901	−	10.7197i	−0.252455	−	0.437265i	−0.964201	+	0.265172i	$0.914571\pi$
$602$	0.146580	−	0.253885i	0.00597417	−	0.0103476i
$603$	−29.1869	+	18.7298i	−1.18858	+	0.762737i
$604$	−21.4395	+	5.74469i	−0.872360	+	0.233748i
$605$	−14.0315	+	3.75973i	−0.570462	+	0.152855i
$606$	−6.26022	−	0.675152i	−0.254304	−	0.0274262i
$607$	−19.4537	+	33.6949i	−0.789603	+	1.36763i	0.136607	+	0.990625i	$0.456380\pi$
$607$	−19.4537	+	33.6949i	−0.789603	+	1.36763i	−0.926210	+	0.377007i	$0.876953\pi$
$608$	2.84839	+	4.93356i	0.115517	+	0.200082i
$609$	−3.36047	+	1.48527i	−0.136173	+	0.0601861i
$610$		−	13.8355i		−	0.560185i
$611$	−30.1982	+	31.4075i	−1.22169	+	1.27061i
$612$	1.51734	+	0.331135i	0.0613348	+	0.0133853i
$613$	11.8801	−	44.3370i	0.479831	−	1.79075i	−0.122455	−	0.992474i	$-0.539077\pi$
$613$	11.8801	−	44.3370i	0.479831	−	1.79075i	0.602286	−	0.798280i	$-0.294257\pi$
$614$	−1.29488	+	0.747599i	−0.0522571	+	0.0301706i
$615$	−2.08914	−	13.4259i	−0.0842422	−	0.541386i
$616$	−3.42031	−	3.42031i	−0.137808	−	0.137808i
$617$	−11.9499	−	44.5976i	−0.481084	−	1.79543i	−0.597081	−	0.802181i	$-0.703673\pi$
$617$	−11.9499	−	44.5976i	−0.481084	−	1.79543i	0.115996	−	0.993250i	$-0.462994\pi$
$618$	18.6864	+	13.6541i	0.751679	+	0.549249i
$619$	27.7189	−	27.7189i	1.11412	−	1.11412i	0.121530	−	0.992588i	$-0.461220\pi$
$619$	27.7189	−	27.7189i	1.11412	−	1.11412i	0.992588	−	0.121530i	$-0.0387802\pi$
$620$	5.89947	+	3.40606i	0.236928	+	0.136791i
$621$	−22.0258	−	14.5599i	−0.883863	−	0.584269i
$622$	−6.11184	−	1.63766i	−0.245062	−	0.0656643i
$623$	−2.77347			−0.111117
$624$	−1.08111	−	6.15071i	−0.0432792	−	0.246225i
$625$	−6.28943			−0.251577
$626$	−25.8413	−	6.92415i	−1.03283	−	0.276745i
$627$	−44.5110	−	17.2249i	−1.77760	−	0.687895i
$628$	−14.1196	−	8.15196i	−0.563434	−	0.325299i
$629$	3.73772	−	3.73772i	0.149033	−	0.149033i
$630$	−0.164928	−	3.51145i	−0.00657090	−	0.139900i
$631$	10.3812	+	38.7430i	0.413267	+	1.54233i	0.788281	+	0.615315i	$0.210971\pi$
$631$	10.3812	+	38.7430i	0.413267	+	1.54233i	−0.375014	+	0.927019i	$0.622362\pi$
$632$	1.79103	+	1.79103i	0.0712432	+	0.0712432i
$633$	−17.4305	+	2.71227i	−0.692800	+	0.107803i
$634$	16.6761	−	9.62793i	0.662291	−	0.382374i
$635$	1.34485	−	5.01906i	0.0533689	−	0.199175i
$636$	10.3500	+	12.8523i	0.410405	+	0.509628i
$637$	−1.86371	−	3.08652i	−0.0738428	−	0.122292i
$638$			10.2605i			0.406215i
$639$	2.59163	−	5.01885i	0.102523	−	0.198542i
$640$	0.585888	+	1.01479i	0.0231592	+	0.0401130i
$641$	24.9443	−	43.2048i	0.985241	−	1.70649i	0.344378	−	0.938831i	$-0.388090\pi$
$641$	24.9443	−	43.2048i	0.985241	−	1.70649i	0.640863	−	0.767656i	$-0.278577\pi$
$642$	0.278071	−	2.57837i	0.0109746	−	0.101760i
$643$	14.2810	−	3.82658i	0.563188	−	0.150906i	0.0340174	−	0.999421i	$-0.489170\pi$
$643$	14.2810	−	3.82658i	0.563188	−	0.150906i	0.529171	+	0.848515i	$0.322503\pi$
$644$	4.90814	−	1.31513i	0.193408	−	0.0518235i
$645$	0.0637986	−	0.591561i	0.00251207	−	0.0232927i
$646$	−1.47457	+	2.55402i	−0.0580160	+	0.100487i
$647$	9.53941	+	16.5227i	0.375033	+	0.649576i	0.990332	−	0.138718i	$-0.0442981\pi$
$647$	9.53941	+	16.5227i	0.375033	+	0.649576i	−0.615299	+	0.788294i	$0.710965\pi$
$648$	−5.73945	+	6.93244i	−0.225467	+	0.272332i
$649$			7.69926i			0.302222i
$650$	−12.6955	−	3.13606i	−0.497960	−	0.123006i
$651$	−6.31555	−	7.84247i	−0.247526	−	0.307371i
$652$	0.906537	−	3.38324i	0.0355027	−	0.132498i
$653$	3.37449	−	1.94826i	0.132054	−	0.0762415i	−0.432518	−	0.901625i	$-0.642375\pi$
$653$	3.37449	−	1.94826i	0.132054	−	0.0762415i	0.564572	+	0.825384i	$0.309041\pi$
$654$	22.6393	−	3.52278i	0.885265	−	0.137751i
$655$	11.8426	+	11.8426i	0.462728	+	0.462728i
$656$	−1.73273	−	6.46664i	−0.0676518	−	0.252480i
$657$	−19.8501	+	0.932331i	−0.774425	+	0.0363737i
$658$	−8.54481	+	8.54481i	−0.333111	+	0.333111i
$659$	3.30124	+	1.90597i	0.128598	+	0.0742462i	0.562919	−	0.826512i	$-0.309678\pi$
$659$	3.30124	+	1.90597i	0.128598	+	0.0742462i	−0.434321	+	0.900758i	$0.643012\pi$
$660$	−9.15551	−	3.54300i	−0.356378	−	0.137911i
$661$	−22.9665	−	6.15385i	−0.893292	−	0.239357i	−0.217159	−	0.976136i	$-0.569679\pi$
$661$	−22.9665	−	6.15385i	−0.893292	−	0.239357i	−0.676133	+	0.736779i	$0.736346\pi$
$662$	−9.35287			−0.363510
$663$	2.47769	−	2.07675i	0.0962256	−	0.0806544i
$664$	16.5766			0.643298
$665$	6.44789	+	1.72771i	0.250038	+	0.0669976i
$666$	9.30767	+	29.1839i	0.360665	+	1.13085i
$667$	−9.33449	−	5.38927i	−0.361433	−	0.208673i
$668$	10.6265	−	10.6265i	0.411151	−	0.411151i
$669$	2.74947	+	2.00902i	0.106301	+	0.0776734i
$670$	−3.50586	−	13.0840i	−0.135443	−	0.505480i
$671$	40.3847	+	40.3847i	1.55903	+	1.55903i
$672$	−0.266310	−	1.71146i	−0.0102732	−	0.0660208i
$673$	4.61841	−	2.66644i	0.178027	−	0.102784i	−0.408339	−	0.912831i	$-0.633892\pi$
$673$	4.61841	−	2.66644i	0.178027	−	0.102784i	0.586365	+	0.810047i	$0.300558\pi$
$674$	1.15886	−	4.32492i	0.0446375	−	0.166590i
$675$	8.41903	+	16.8611i	0.324049	+	0.648985i
$676$	−11.5047	−	6.05318i	−0.442490	−	0.232815i
$677$		−	17.4542i		−	0.670819i	−0.942072	−	0.335410i	$-0.891125\pi$
$677$		−	17.4542i		−	0.670819i	0.942072	−	0.335410i	$-0.108875\pi$
$678$	−27.1655	+	12.0067i	−1.04329	+	0.461114i
$679$	2.04586	+	3.54353i	0.0785127	+	0.135988i
$680$	−0.303304	+	0.525339i	−0.0116312	+	0.0201458i
$681$	8.80140	+	0.949212i	0.337270	+	0.0363739i
$682$	−27.1620	+	7.27804i	−1.04009	+	0.278690i
$683$	14.4342	−	3.86763i	0.552309	−	0.147991i	0.0281382	−	0.999604i	$-0.491042\pi$
$683$	14.4342	−	3.86763i	0.552309	−	0.147991i	0.524170	+	0.851613i	$0.324375\pi$
$684$	−9.23016	−	14.3835i	−0.352924	−	0.549965i
$685$	5.62597	−	9.74447i	0.214957	−	0.372317i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$	2.37688	+	5.37779i	0.0906838	+	0.205175i
$688$		−	0.293161i		−	0.0111766i
$689$	34.3444	−	0.674152i	1.30842	−	0.0256831i
$690$	8.03216	−	6.46831i	0.305779	−	0.246245i
$691$	−9.50395	+	35.4692i	−0.361547	+	1.34931i	0.510494	+	0.859881i	$0.329462\pi$
$691$	−9.50395	+	35.4692i	−0.361547	+	1.34931i	−0.872042	+	0.489432i	$0.837204\pi$
$692$	−3.70764	+	2.14061i	−0.140943	+	0.0813738i
$693$	10.7310	+	9.76821i	0.407638	+	0.371064i
$694$	−15.5534	−	15.5534i	−0.590398	−	0.590398i
$695$	4.73848	+	17.6842i	0.179741	+	0.670801i
$696$	−2.16762	+	2.96651i	−0.0821634	+	0.112445i
$697$	2.45067	−	2.45067i	0.0928256	−	0.0928256i
$698$	30.6176	+	17.6771i	1.15889	+	0.669086i
$699$	5.34394	−	13.8094i	0.202126	−	0.522318i
$700$	−3.50336	−	0.938722i	−0.132414	−	0.0354804i
$701$	−12.1730			−0.459768			−0.229884	−	0.973218i	$-0.573835\pi$
$701$	−12.1730			−0.459768			−0.229884	+	0.973218i	$0.573835\pi$
$702$	4.10549	+	18.2796i	0.154952	+	0.689920i
$703$	−58.1684			−2.19386
$704$	−4.67223	−	1.25192i	−0.176091	−	0.0471835i
$705$	−8.85133	+	22.8728i	−0.333360	+	0.861441i
$706$	2.63752	+	1.52277i	0.0992644	+	0.0573104i
$707$	−2.57055	+	2.57055i	−0.0966753	+	0.0966753i
$708$	−1.62654	+	2.22602i	−0.0611292	+	0.0836589i
$709$	−4.31325	−	16.0973i	−0.161987	−	0.604545i	−0.998405	−	0.0564528i	$-0.982021\pi$
$709$	−4.31325	−	16.0973i	−0.161987	−	0.604545i	0.836418	−	0.548092i	$-0.184646\pi$
$710$	1.56005	+	1.56005i	0.0585478	+	0.0585478i
$711$	−5.61925	−	5.11508i	−0.210738	−	0.191830i
$712$	−2.40190	+	1.38673i	−0.0900148	+	0.0519701i
$713$	7.64553	−	28.5335i	0.286327	−	1.06859i
$714$	0.698360	−	0.562390i	0.0261354	−	0.0210469i
$715$	−17.4942	+	10.5634i	−0.654244	+	0.395047i
$716$			10.6618i			0.398452i
$717$	19.8791	+	44.9772i	0.742398	+	1.67970i
$718$	6.15101	+	10.6539i	0.229554	+	0.397599i
$719$	3.40817	−	5.90313i	0.127103	−	0.220150i	−0.795450	−	0.606020i	$-0.792765\pi$
$719$	3.40817	−	5.90313i	0.127103	−	0.220150i	0.922553	+	0.385870i	$0.126099\pi$
$720$	−1.89856	−	2.95854i	−0.0707551	−	0.110258i
$721$	12.9066	−	3.45830i	0.480666	−	0.128794i
$722$	12.9949	−	3.48198i	0.483620	−	0.129586i
$723$	38.3021	+	4.13080i	1.42447	+	0.153626i
$724$	6.86168	−	11.8848i	0.255013	−	0.441695i
$725$	3.84678	+	6.66282i	0.142866	+	0.247451i
$726$	19.6395	−	8.68029i	0.728889	−	0.322156i
$727$			31.4461i			1.16627i	0.812375	+	0.583135i	$0.198174\pi$
$727$			31.4461i			1.16627i	−0.812375	+	0.583135i	$0.801826\pi$
$728$	−3.15728	−	1.74115i	−0.117017	−	0.0645312i
$729$	16.2236	−	21.5823i	0.600875	−	0.799343i
$730$	2.00891	−	7.49734i	0.0743530	−	0.277489i
$731$	0.131432	−	0.0758822i	0.00486118	−	0.00280661i
$732$	3.14442	+	20.2077i	0.116221	+	0.746899i
$733$	−3.85594	−	3.85594i	−0.142422	−	0.142422i	0.632301	−	0.774723i	$-0.282111\pi$
$733$	−3.85594	−	3.85594i	−0.142422	−	0.142422i	−0.774723	+	0.632301i	$0.782111\pi$
$734$	4.06624	+	15.1754i	0.150088	+	0.560135i
$735$	−1.63872	−	1.19740i	−0.0604450	−	0.0441669i
$736$	3.59301	−	3.59301i	0.132440	−	0.132440i
$737$	48.4244	+	27.9578i	1.78374	+	1.02984i
$738$	6.10265	+	19.1347i	0.224642	+	0.704357i
$739$	4.86945	+	1.30477i	0.179126	+	0.0479966i	0.347267	−	0.937766i	$-0.387110\pi$
$739$	4.86945	+	1.30477i	0.179126	+	0.0479966i	−0.168141	+	0.985763i	$0.553776\pi$
$740$	−11.9647			−0.439831
$741$	−35.4393	−	3.11981i	−1.30190	−	0.114609i
$742$	9.52725			0.349756
$743$	−17.4562	−	4.67738i	−0.640407	−	0.171597i	−0.0760193	−	0.997106i	$-0.524221\pi$
$743$	−17.4562	−	4.67738i	−0.640407	−	0.171597i	−0.564388	+	0.825510i	$0.690888\pi$
$744$	−9.39066	−	3.63400i	−0.344278	−	0.133229i
$745$	6.64573	+	3.83691i	0.243481	+	0.140574i
$746$	−1.49380	+	1.49380i	−0.0546918	+	0.0546918i
$747$	−49.6752	+	2.33318i	−1.81752	+	0.0853664i
$748$	−0.648098	−	2.41873i	−0.0236968	−	0.0884377i
$749$	−1.05872	−	1.05872i	−0.0386847	−	0.0386847i
$750$	−17.3008	+	2.69209i	−0.631737	+	0.0983012i
$751$	−39.0894	+	22.5683i	−1.42639	+	0.823528i	−0.996834	−	0.0795108i	$-0.974664\pi$
$751$	−39.0894	+	22.5683i	−1.42639	+	0.823528i	−0.429559	+	0.903039i	$0.641331\pi$
$752$	−3.12762	+	11.6724i	−0.114053	+	0.425650i
$753$	−17.7172	−	22.0007i	−0.645650	−	0.801749i
$754$	2.12410	+	7.34731i	0.0773551	+	0.267573i
$755$			26.0085i			0.946545i
$756$	1.03894	+	5.09123i	0.0377859	+	0.185166i
$757$	−21.5477	−	37.3217i	−0.783164	−	1.35648i	−0.930090	−	0.367333i	$-0.880271\pi$
$757$	−21.5477	−	37.3217i	−0.783164	−	1.35648i	0.146925	−	0.989148i	$-0.453062\pi$
$758$	−17.1930	+	29.7792i	−0.624478	+	1.08163i
$759$	−4.56472	+	42.3256i	−0.165689	+	1.53632i
$760$	6.44789	−	1.72771i	0.233890	−	0.0626705i
$761$	−36.4729	+	9.77289i	−1.32214	+	0.354267i	−0.849780	−	0.527137i	$-0.823265\pi$
$761$	−36.4729	+	9.77289i	−1.32214	+	0.354267i	−0.472363	+	0.881404i	$0.656599\pi$
$762$	−0.823560	+	7.63631i	−0.0298344	+	0.276634i
$763$	6.61404	−	11.4559i	0.239444	−	0.414730i
$764$	−9.09873	−	15.7595i	−0.329181	−	0.570157i
$765$	0.834969	−	1.61697i	0.0301884	−	0.0584617i
$766$			27.8236i			1.00531i
$767$	1.59389	+	5.51329i	0.0575519	+	0.199073i
$768$	−1.08636	−	1.34901i	−0.0392006	−	0.0486781i
$769$	−7.35795	+	27.4602i	−0.265335	+	0.990242i	0.696711	+	0.717352i	$0.254646\pi$
$769$	−7.35795	+	27.4602i	−0.265335	+	0.990242i	−0.962045	+	0.272890i	$0.912021\pi$
$770$	−4.90857	+	2.83396i	−0.176893	+	0.102129i
$771$	−5.12691	+	0.797771i	−0.184641	+	0.0287310i
$772$	−0.610626	−	0.610626i	−0.0219769	−	0.0219769i
$773$	2.26818	+	8.46496i	0.0815808	+	0.304464i	0.994645	−	0.103353i	$-0.0329571\pi$
$773$	2.26818	+	8.46496i	0.0815808	+	0.304464i	−0.913064	+	0.407816i	$0.866290\pi$
$774$	0.0412626	+	0.878513i	0.00148315	+	0.0315775i
$775$	−14.9095	+	14.9095i	−0.535566	+	0.535566i
$776$	3.54353	+	2.04586i	0.127205	+	0.0734419i
$777$	16.4936	+	6.38269i	0.591705	+	0.228978i
$778$	15.4683	+	4.14471i	0.554564	+	0.148595i
$779$	−38.1386			−1.36646
$780$	−7.28954	−	0.641715i	−0.261007	−	0.0229771i
$781$	−9.10732			−0.325885
$782$	2.54087	+	0.680823i	0.0908612	+	0.0243462i
$783$	6.07816	−	9.19484i	0.217216	−	0.328597i
$784$	−0.866025	−	0.500000i	−0.0309295	−	0.0178571i
$785$	−13.5089	+	13.5089i	−0.482155	+	0.482155i
$786$	−19.9884	−	14.6054i	−0.712961	−	0.520957i
$787$	−5.18723	−	19.3590i	−0.184905	−	0.690074i	−0.994651	−	0.103294i	$-0.967062\pi$
$787$	−5.18723	−	19.3590i	−0.184905	−	0.690074i	0.809746	−	0.586781i	$-0.199605\pi$
$788$	−14.9600	−	14.9600i	−0.532926	−	0.532926i
$789$	−1.08396	−	6.96611i	−0.0385900	−	0.248000i
$790$	2.57035	−	1.48399i	0.0914489	−	0.0527980i
$791$	−4.43814	+	16.5634i	−0.157802	+	0.588925i
$792$	14.1774	+	3.09400i	0.503774	+	0.109941i
$793$	37.2791	+	20.5583i	1.32382	+	0.730048i
$794$		−	13.9657i		−	0.495623i
$795$	17.6858	−	7.81681i	0.627251	−	0.277234i
$796$	0.767481	+	1.32932i	0.0272026	+	0.0471163i
$797$	−5.16123	+	8.93952i	−0.182820	+	0.316654i	−0.942840	−	0.333246i	$-0.891856\pi$
$797$	−5.16123	+	8.93952i	−0.182820	+	0.316654i	0.760020	+	0.649900i	$0.225189\pi$
$798$	−9.81023	−	1.05801i	−0.347278	−	0.0374532i
$799$	−6.04263	+	1.61912i	−0.213773	+	0.0572802i
$800$	−3.50336	+	0.938722i	−0.123862	+	0.0331888i
$801$	7.00257	−	4.49369i	0.247424	−	0.158777i
$802$	−12.9407	+	22.4139i	−0.456951	+	0.791463i
$803$	16.0202	+	27.7479i	0.565342	+	0.979202i
$804$	8.09416	+	18.3133i	0.285459	+	0.645861i
$805$		−	5.95412i		−	0.209855i
$806$	−17.9435	+	10.8347i	−0.632032	+	0.381635i
$807$	−4.18218	+	3.36792i	−0.147220	+	0.118556i
$808$	−0.940885	+	3.51143i	−0.0331002	+	0.123532i
$809$	−42.5731	+	24.5796i	−1.49679	+	0.864172i	−0.999993	−	0.00369576i	$-0.998824\pi$
$809$	−42.5731	+	24.5796i	−1.49679	+	0.864172i	−0.496796	+	0.867867i	$0.665490\pi$
$810$	6.10582	+	8.59864i	0.214537	+	0.302125i
$811$	9.89969	+	9.89969i	0.347625	+	0.347625i	0.859224	−	0.511599i	$-0.170947\pi$
$811$	9.89969	+	9.89969i	0.347625	+	0.347625i	−0.511599	+	0.859224i	$0.670947\pi$
$812$	0.549013	+	2.04895i	0.0192666	+	0.0719039i
$813$	−15.6788	+	21.4573i	−0.549879	+	0.752541i
$814$	34.9239	−	34.9239i	1.22408	−	1.22408i
$815$	−3.55438	−	2.05212i	−0.124505	−	0.0718828i
$816$	0.323602	−	0.836224i	0.0113283	−	0.0292737i
$817$	−1.61317	−	0.432246i	−0.0564375	−	0.0151224i
$818$	7.54280			0.263728
$819$	9.70647	+	4.77330i	0.339172	+	0.166793i
$820$	−7.84475			−0.273951
$821$	16.1341	+	4.32313i	0.563085	+	0.150878i	0.529123	−	0.848545i	$-0.322521\pi$
$821$	16.1341	+	4.32313i	0.563085	+	0.150878i	0.0339617	+	0.999423i	$0.489188\pi$
$822$	−6.00247	+	15.5111i	−0.209360	+	0.541011i
$823$	4.33765	+	2.50434i	0.151201	+	0.0872959i	0.573692	−	0.819071i	$-0.305511\pi$
$823$	4.33765	+	2.50434i	0.151201	+	0.0872959i	−0.422491	+	0.906367i	$0.638844\pi$
$824$	9.44826	−	9.44826i	0.329146	−	0.329146i
$825$	17.9274	−	24.5347i	0.624152	−	0.854188i
$826$	0.411970	+	1.53749i	0.0143343	+	0.0534962i
$827$	−20.9459	−	20.9459i	−0.728359	−	0.728359i	0.241934	−	0.970293i	$-0.422218\pi$
$827$	−20.9459	−	20.9459i	−0.728359	−	0.728359i	−0.970293	+	0.241934i	$0.922218\pi$
$828$	−10.2614	+	11.2729i	−0.356610	+	0.391760i
$829$	31.5815	−	18.2336i	1.09687	−	0.633280i	0.161475	−	0.986877i	$-0.448375\pi$
$829$	31.5815	−	18.2336i	1.09687	−	0.633280i	0.935398	+	0.353597i	$0.115042\pi$
$830$	5.02733	−	18.7622i	0.174501	−	0.651247i
$831$	1.63991	−	1.32063i	0.0568880	−	0.0458120i
$832$	−3.60486	+	0.0707604i	−0.124976	+	0.00245317i
$833$		−	0.517684i		−	0.0179367i
$834$	−10.9400	−	24.7521i	−0.378820	−	0.857095i
$835$	−8.80478	−	15.2503i	−0.304702	−	0.527759i
$836$	−13.7778	+	23.8638i	−0.476515	+	0.825348i
$837$	28.6525	+	9.56825i	0.990374	+	0.330727i
$838$	−16.0547	+	4.30185i	−0.554601	+	0.148605i
$839$	49.7434	−	13.3287i	1.71733	−	0.460158i	0.740130	−	0.672464i	$-0.234764\pi$
$839$	49.7434	−	13.3287i	1.71733	−	0.460158i	0.977203	+	0.212306i	$0.0680973\pi$
$840$	−2.01787	−	0.217623i	−0.0696232	−	0.00750872i
$841$	−12.2502	+	21.2180i	−0.422421	+	0.731654i
$842$	−6.22805	−	10.7873i	−0.214633	−	0.371755i
$843$	4.06792	−	1.79795i	0.140107	−	0.0619246i
$844$			10.1846i			0.350568i
$845$	−10.3404	+	11.1858i	−0.355721	+	0.384804i
$846$	7.72962	−	35.4189i	0.265750	−	1.21773i
$847$	3.20858	−	11.9746i	0.110248	−	0.411451i
$848$	8.25084	−	4.76362i	0.283335	−	0.163584i
$849$	−2.55344	−	16.4098i	−0.0876339	−	0.563183i
$850$	−1.32767	−	1.32767i	−0.0455387	−	0.0455387i
$851$	13.4285	+	50.1158i	0.460322	+	1.71795i
$852$	−2.63312	−	1.92401i	−0.0902091	−	0.0659154i
$853$	−14.1855	+	14.1855i	−0.485702	+	0.485702i	−0.906947	−	0.421245i	$-0.861593\pi$
$853$	−14.1855	+	14.1855i	−0.485702	+	0.485702i	0.421245	+	0.906947i	$0.361593\pi$
$854$	10.2255	+	5.90367i	0.349908	+	0.202019i
$855$	−19.0792	+	6.08496i	−0.652495	+	0.208101i
$856$	−1.44624	−	0.387518i	−0.0494313	−	0.0132451i
$857$	10.4375			0.356538			0.178269	−	0.983982i	$-0.442950\pi$
$857$	10.4375			0.356538			0.178269	+	0.983982i	$0.442950\pi$
$858$	23.1506	−	19.4044i	0.790349	−	0.662456i
$859$	−34.6814			−1.18331			−0.591656	−	0.806190i	$-0.701526\pi$
$859$	−34.6814			−1.18331			−0.591656	+	0.806190i	$0.701526\pi$
$860$	−0.331813	−	0.0889091i	−0.0113147	−	0.00303177i
$861$	10.8142	+	4.18486i	0.368546	+	0.142620i
$862$	−16.5218	−	9.53886i	−0.562734	−	0.324895i
$863$	31.2962	−	31.2962i	1.06533	−	1.06533i	0.0676228	−	0.997711i	$-0.478459\pi$
$863$	31.2962	−	31.2962i	1.06533	−	1.06533i	0.997711	−	0.0676228i	$-0.0215415\pi$
$864$	3.44536	+	3.88966i	0.117214	+	0.132329i
$865$	1.29840	+	4.84569i	0.0441469	+	0.164758i
$866$	−14.2286	−	14.2286i	−0.483507	−	0.483507i
$867$	−28.6361	+	4.45591i	−0.972532	+	0.151331i
$868$	−5.03464	+	2.90675i	−0.170887	+	0.0986616i
$869$	−3.17098	+	11.8343i	−0.107568	+	0.401450i
$870$	2.70025	+	3.35309i	0.0915471	+	0.113680i
$871$	40.4635	+	9.99533i	1.37105	+	0.338679i
$872$		−	13.2281i		−	0.447959i
$873$	−10.9068	−	5.63205i	−0.369140	−	0.190616i
$874$	−14.4735	−	25.0688i	−0.489573	−	0.847965i
$875$	−5.05442	+	8.75451i	−0.170871	+	0.295956i
$876$	−1.23021	+	11.4069i	−0.0415650	+	0.385404i
$877$	−10.6929	+	2.86516i	−0.361075	+	0.0967497i	−0.434795	−	0.900529i	$-0.643179\pi$
$877$	−10.6929	+	2.86516i	−0.361075	+	0.0967497i	0.0737208	+	0.997279i	$0.476513\pi$
$878$	24.8239	−	6.65155i	0.837766	−	0.224479i
$879$	3.91440	−	36.2956i	0.132030	−	1.22422i
$880$	−2.83396	+	4.90857i	−0.0955329	+	0.165468i
$881$	−14.9885	−	25.9608i	−0.504974	−	0.874641i	−0.999983	−	0.00575302i	$-0.998169\pi$
$881$	−14.9885	−	25.9608i	−0.504974	−	0.874641i	0.495009	−	0.868888i	$-0.335165\pi$
$882$	2.66559	+	1.37645i	0.0897551	+	0.0463476i
$883$			23.3378i			0.785381i	0.919671	+	0.392690i	$0.128456\pi$
$883$			23.3378i			0.785381i	−0.919671	+	0.392690i	$0.871544\pi$
$884$	−0.964811	−	1.59784i	−0.0324501	−	0.0537412i
$885$	2.02622	+	2.51610i	0.0681107	+	0.0845778i
$886$	0.00922912	−	0.0344435i	0.000310058	−	0.00115715i
$887$	−14.8835	+	8.59297i	−0.499738	+	0.288524i	−0.728605	−	0.684934i	$-0.759831\pi$
$887$	−14.8835	+	8.59297i	−0.499738	+	0.288524i	0.228868	+	0.973458i	$0.426498\pi$
$888$	17.4752	−	2.71923i	0.586430	−	0.0912513i
$889$	3.13559	+	3.13559i	0.105164	+	0.105164i
$890$	0.841132	+	3.13915i	0.0281948	+	0.105224i
$891$	−42.9210	−	7.27630i	−1.43791	−	0.243765i
$892$	1.39019	−	1.39019i	0.0465470	−	0.0465470i
$893$	59.6180	+	34.4205i	1.99504	+	1.15184i
$894$	−10.5785	−	4.09368i	−0.353799	−	0.136913i
$895$	12.0676	+	3.23350i	0.403375	+	0.108084i
$896$	−1.00000			−0.0334077
$897$	5.49345	+	31.2535i	0.183421	+	1.04352i
$898$	27.0334			0.902117
$899$	11.9116	+	3.19169i	0.397273	+	0.106449i
$900$	10.3664	−	3.30617i	0.345546	−	0.110206i
$901$	4.27132	+	2.46605i	0.142298	+	0.0821560i
$902$	22.8981	−	22.8981i	0.762424	−	0.762424i
$903$	0.409983	+	0.299573i	0.0136434	+	0.00996915i
$904$	4.43814	+	16.5634i	0.147610	+	0.550889i
$905$	−11.3708	−	11.3708i	−0.377977	−	0.377977i
$906$	−5.91097	−	37.9871i	−0.196379	−	1.26204i
$907$	20.9403	−	12.0899i	0.695311	−	0.401438i	−0.110288	−	0.993900i	$-0.535177\pi$
$907$	20.9403	−	12.0899i	0.695311	−	0.401438i	0.805598	+	0.592462i	$0.201844\pi$
$908$	1.32281	−	4.93680i	0.0438991	−	0.163834i
$909$	2.32531	−	10.6551i	0.0771257	−	0.353408i
$910$	−2.92825	+	3.04551i	−0.0970704	+	0.100958i
$911$			20.0949i			0.665774i	0.942967	+	0.332887i	$0.108023\pi$
$911$			20.0949i			0.665774i	−0.942967	+	0.332887i	$0.891977\pi$
$912$	−9.02491	+	3.98885i	−0.298845	+	0.132084i
$913$	40.0910	+	69.4396i	1.32682	+	2.29812i
$914$	−15.5448	+	26.9245i	−0.514178	+	0.890582i
$915$	23.8257	+	2.56955i	0.787654	+	0.0849468i
$916$	3.27894	−	0.878590i	0.108339	−	0.0290294i
$917$	−13.8058	+	3.69925i	−0.455907	+	0.122160i
$918$	−0.852038	+	2.55146i	−0.0281214	+	0.0842106i
$919$	−13.4305	+	23.2624i	−0.443032	+	0.767354i	−0.997913	−	0.0645756i	$-0.979431\pi$
$919$	−13.4305	+	23.2624i	−0.443032	+	0.767354i	0.554881	+	0.831930i	$0.312764\pi$
$920$	−2.97706	−	5.15642i	−0.0981508	−	0.170002i
$921$	−1.04693	−	2.36871i	−0.0344974	−	0.0780517i
$922$			18.8979i			0.622371i
$923$	−6.52157	+	1.88538i	−0.214660	+	0.0620580i
$924$	6.52521	−	5.25477i	0.214664	−	0.172869i
$925$	9.58505	−	35.7719i	0.315154	−	1.17617i
$926$	1.17488	−	0.678320i	0.0386091	−	0.0222910i
$927$	−26.9837	+	29.6434i	−0.886262	+	0.973618i
$928$	1.49993	+	1.49993i	0.0492377	+	0.0492377i
$929$	−4.56360	−	17.0316i	−0.149727	−	0.558789i	−0.999499	−	0.0316389i	$-0.989927\pi$
$929$	−4.56360	−	17.0316i	−0.149727	−	0.558789i	0.849772	−	0.527150i	$-0.176739\pi$
$930$	−6.96111	+	9.52669i	−0.228264	+	0.312393i
$931$	−4.02823	+	4.02823i	−0.132020	+	0.132020i
$932$	−7.40365	−	4.27450i	−0.242515	−	0.140016i
$933$	3.95526	−	10.2208i	0.129489	−	0.334615i
$934$	−27.3544	−	7.32959i	−0.895064	−	0.239832i
$935$	−2.93419			−0.0959584
$936$	10.7927	−	0.719434i	0.352770	−	0.0235154i
$937$	53.8449			1.75904			0.879519	−	0.475864i	$-0.157865\pi$
$937$	53.8449			1.75904			0.879519	+	0.475864i	$0.157865\pi$
$938$	11.1660	+	2.99192i	0.364583	+	0.0976896i
$939$	16.7231	−	43.2144i	0.545738	−	1.41025i
$940$	12.2629	+	7.07998i	0.399971	+	0.230923i
$941$	−5.19843	+	5.19843i	−0.169464	+	0.169464i	−0.786744	−	0.617280i	$-0.788235\pi$
$941$	−5.19843	+	5.19843i	−0.169464	+	0.169464i	0.617280	+	0.786744i	$0.288235\pi$
$942$	16.6605	−	22.8009i	0.542829	−	0.742894i
$943$	8.80449	+	32.8588i	0.286714	+	1.07003i
$944$	1.12552	+	1.12552i	0.0366326	+	0.0366326i
$945$	6.07758	+	0.368134i	0.197704	+	0.0119754i
$946$	1.22805	−	0.709015i	0.0399274	−	0.0230521i
$947$	−9.58848	+	35.7847i	−0.311584	+	1.16285i	0.615544	+	0.788102i	$0.288936\pi$
$947$	−9.58848	+	35.7847i	−0.311584	+	1.16285i	−0.927128	+	0.374744i	$0.877731\pi$
$948$	−3.41690	+	2.75163i	−0.110976	+	0.0893689i
$949$	17.2161	+	16.5532i	0.558858	+	0.537340i
$950$			20.6619i			0.670361i
$951$	13.4828	+	30.5054i	0.437210	+	0.989204i
$952$	−0.258842	−	0.448327i	−0.00838911	−	0.0145304i
$953$	−5.85318	+	10.1380i	−0.189603	+	0.328402i	−0.945118	−	0.326729i	$-0.894053\pi$
$953$	−5.85318	+	10.1380i	−0.189603	+	0.328402i	0.755515	+	0.655131i	$0.227387\pi$
$954$	−24.0548	+	15.4364i	−0.778802	+	0.499773i
$955$	−20.5968	+	5.51889i	−0.666496	+	0.178587i
$956$	27.4235	−	7.34810i	0.886938	−	0.237654i
$957$	−17.6692	−	1.90558i	−0.571163	−	0.0615987i
$958$	10.6032	−	18.3653i	0.342574	−	0.593356i
$959$	4.80124	+	8.31599i	0.155040	+	0.268537i
$960$	−1.85634	+	0.820469i	−0.0599131	+	0.0264805i
$961$			2.79684i			0.0902207i
$962$	17.7784	−	32.2381i	0.573199	−	1.03940i
$963$	4.38847	+	0.957714i	0.141417	+	0.0308619i
$964$	5.75665	−	21.4841i	0.185409	−	0.691956i
$965$	−0.876325	+	0.505946i	−0.0282099	+	0.0162870i
$966$	1.35320	+	8.69639i	0.0435385	+	0.279802i
$967$	−25.0831	−	25.0831i	−0.806617	−	0.806617i	0.177503	−	0.984120i	$-0.443198\pi$
$967$	−25.0831	−	25.0831i	−0.806617	−	0.806617i	−0.984120	+	0.177503i	$0.943198\pi$
$968$	−3.20858	−	11.9746i	−0.103128	−	0.384877i
$969$	−4.12433	−	3.01363i	−0.132493	−	0.0968118i
$970$	3.39027	−	3.39027i	0.108855	−	0.108855i
$971$	16.3331	+	9.42992i	0.524154	+	0.302621i	0.738633	−	0.674108i	$-0.235472\pi$
$971$	16.3331	+	9.42992i	0.524154	+	0.302621i	−0.214478	+	0.976729i	$0.568805\pi$
$972$	−10.8722	−	11.1712i	−0.348725	−	0.358316i
$973$	−15.0918	−	4.04385i	−0.483822	−	0.129640i
$974$	26.1828			0.838950
$975$	7.75832	−	21.2801i	0.248465	−	0.681508i
$976$	11.8073			0.377944
$977$	41.4004	+	11.0932i	1.32452	+	0.354903i	0.850668	−	0.525703i	$-0.176198\pi$
$977$	41.4004	+	11.0932i	1.32452	+	0.354903i	0.473849	+	0.880606i	$0.342864\pi$
$978$	5.65780	+	2.18946i	0.180917	+	0.0700111i
$979$	−11.6181	−	6.70770i	−0.371315	−	0.214379i
$980$	−0.828570	+	0.828570i	−0.0264677	+	0.0264677i
$981$	1.86186	+	39.6405i	0.0594447	+	1.26562i
$982$	−2.74587	−	10.2477i	−0.0876244	−	0.327019i
$983$	−20.7752	−	20.7752i	−0.662625	−	0.662625i	0.293373	−	0.955998i	$-0.405222\pi$
$983$	−20.7752	−	20.7752i	−0.662625	−	0.662625i	−0.955998	+	0.293373i	$0.905222\pi$
$984$	11.4578	−	1.78288i	0.365261	−	0.0568363i
$985$	−21.4694	+	12.3954i	−0.684073	+	0.394949i
$986$	−0.284215	+	1.06071i	−0.00905126	+	0.0337797i
$987$	−13.1278	−	16.3017i	−0.417862	−	0.518888i
$988$	−4.92576	+	19.9407i	−0.156709	+	0.634397i
$989$			1.48963i			0.0473675i
$990$	7.80164	−	15.1084i	0.247953	−	0.480176i
$991$	−3.23933	−	5.61068i	−0.102901	−	0.178229i	0.809978	−	0.586460i	$-0.199479\pi$
$991$	−3.23933	−	5.61068i	−0.102901	−	0.178229i	−0.912879	+	0.408231i	$0.866146\pi$
$992$	−2.90675	+	5.03464i	−0.0922895	+	0.159850i
$993$	1.73703	−	16.1063i	0.0551228	−	0.511117i
$994$	−1.81867	+	0.487312i	−0.0576848	+	0.0154566i
$995$	1.73734	−	0.465519i	0.0550775	−	0.0147580i
$996$	−3.07863	+	28.5461i	−0.0975501	+	0.904516i
$997$	21.9402	−	38.0016i	0.694854	−	1.20352i	−0.275376	−	0.961337i	$-0.588802\pi$
$997$	21.9402	−	38.0016i	0.694854	−	1.20352i	0.970230	−	0.242185i	$-0.0778642\pi$
$998$	−16.7930	−	29.0863i	−0.531572	−	0.920709i
$999$	−51.9852	+	10.6084i	−1.64474	+	0.335633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.b.323.10	yes	56
3.2	odd	2		546.2.bu.a.323.7	yes	56
13.6	odd	12		546.2.bu.a.71.7	✓	56
39.32	even	12	inner	546.2.bu.b.71.10	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.71.7	✓	56	13.6	odd	12
546.2.bu.a.323.7	yes	56	3.2	odd	2
546.2.bu.b.71.10	yes	56	39.32	even	12	inner
546.2.bu.b.323.10	yes	56	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.625096 + 1.61532i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.828570 - 0.828570i) q^{5} +(-1.02187 + 1.39849i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.21851 - 2.01946i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.625096 + 1.61532i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.828570 - 0.828570i) q^{5} +(-1.02187 + 1.39849i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.21851 - 2.01946i) q^{9} +(1.01479 - 0.585888i) q^{10} +(-1.25192 + 4.67223i) q^{11} +(-1.34901 + 1.08636i) q^{12} +(0.0707604 + 3.60486i) q^{13} +1.00000i q^{14} +(0.820469 + 1.85634i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.258842 + 0.448327i) q^{17} +(-1.62024 - 2.52484i) q^{18} +(5.50267 - 1.47444i) q^{19} +(1.13185 - 0.303278i) q^{20} +(-1.72206 - 0.185721i) q^{21} +(-2.41852 + 4.18900i) q^{22} +(-2.54064 - 4.40052i) q^{23} +(-1.58421 + 0.700193i) q^{24} +3.62694i q^{25} +(-0.864656 + 3.50034i) q^{26} +(4.64885 - 2.32125i) q^{27} +(-0.258819 + 0.965926i) q^{28} +(1.83703 - 1.06061i) q^{29} +(0.312056 + 2.00544i) q^{30} +(4.11077 + 4.11077i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-6.76456 - 4.94284i) q^{33} +(-0.366058 + 0.366058i) q^{34} +(1.01479 + 0.585888i) q^{35} +(-0.911557 - 2.85816i) q^{36} +(-9.86282 - 2.64273i) q^{37} +5.69678 q^{38} +(-5.86723 - 2.13908i) q^{39} +1.17178 q^{40} +(-6.46664 - 1.73273i) q^{41} +(-1.61532 - 0.625096i) q^{42} +(-0.253885 - 0.146580i) q^{43} +(-3.42031 + 3.42031i) q^{44} +(-3.51145 + 0.164928i) q^{45} +(-1.31513 - 4.90814i) q^{46} +(8.54481 + 8.54481i) q^{47} +(-1.71146 + 0.266310i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-0.938722 + 3.50336i) q^{50} +(-0.562390 - 0.698360i) q^{51} +(-1.74115 + 3.15728i) q^{52} -9.52725i q^{53} +(5.09123 - 1.03894i) q^{54} +(2.83396 + 4.90857i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-1.05801 + 9.81023i) q^{57} +(2.04895 - 0.549013i) q^{58} +(1.53749 - 0.411970i) q^{59} +(-0.217623 + 2.01787i) q^{60} +(5.90367 - 10.2255i) q^{61} +(2.90675 + 5.03464i) q^{62} +(1.37645 - 2.66559i) q^{63} +1.00000i q^{64} +(3.04551 + 2.92825i) q^{65} +(-5.25477 - 6.52521i) q^{66} +(2.99192 - 11.1660i) q^{67} +(-0.448327 + 0.258842i) q^{68} +(8.69639 - 1.35320i) q^{69} +(0.828570 + 0.828570i) q^{70} +(0.487312 + 1.81867i) q^{71} +(-0.140751 - 2.99670i) q^{72} +(4.68386 - 4.68386i) q^{73} +(-8.84276 - 5.10537i) q^{74} +(-5.85867 - 2.26719i) q^{75} +(5.50267 + 1.47444i) q^{76} -4.83704 q^{77} +(-5.11367 - 3.58474i) q^{78} +2.53289 q^{79} +(1.13185 + 0.303278i) q^{80} +(0.843575 + 8.96038i) q^{81} +(-5.79783 - 3.34738i) q^{82} +(11.7215 - 11.7215i) q^{83} +(-1.39849 - 1.02187i) q^{84} +(0.157002 + 0.585939i) q^{85} +(-0.207296 - 0.207296i) q^{86} +(0.564904 + 3.63038i) q^{87} +(-4.18900 + 2.41852i) q^{88} +(-0.717827 + 2.67897i) q^{89} +(-3.43449 - 0.749523i) q^{90} +(-3.46371 + 1.00135i) q^{91} -5.08128i q^{92} +(-9.20983 + 4.07058i) q^{93} +(6.04209 + 10.4652i) q^{94} +(3.33767 - 5.78102i) q^{95} +(-1.72206 - 0.185721i) q^{96} +(3.95229 - 1.05901i) q^{97} +(-0.965926 + 0.258819i) q^{98} +(12.2128 - 7.83718i) 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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