LMFDB - Embedded newform 546.2.bm.a.205.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(205,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("546.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bm (of order $6$, degree $2$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 26x^{14} + 249x^{12} + 1144x^{10} + 2766x^{8} + 3554x^{6} + 2260x^{4} + 564x^{2} + 9 $ x^16 + 26x^14 + 249x^12 + 1144x^10 + 2766x^8 + 3554x^6 + 2260x^4 + 564*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.8
Root			$-0.130758i$ of defining polynomial
Character	$\chi$	$=$	546.205
Dual form			546.2.bm.a.277.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(0.813575 + 0.469718i) q^{5} +(0.866025 + 0.500000i) q^{6} +(2.42162 + 1.06571i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(0.813575 + 0.469718i) q^{5} +(0.866025 + 0.500000i) q^{6} +(2.42162 + 1.06571i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.469718 + 0.813575i) q^{10} +(1.02622 + 0.592488i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.78693 + 2.28758i) q^{13} +(-1.06571 + 2.42162i) q^{14} +(0.813575 - 0.469718i) q^{15} +1.00000 q^{16} +4.44440 q^{17} +(0.866025 - 0.500000i) q^{18} +(2.19336 - 1.26634i) q^{19} +(-0.813575 - 0.469718i) q^{20} +(2.13374 - 1.56433i) q^{21} +(-0.592488 + 1.02622i) q^{22} +2.62678 q^{23} +(-0.866025 - 0.500000i) q^{24} +(-2.05873 - 3.56583i) q^{25} +(-2.28758 - 2.78693i) q^{26} -1.00000 q^{27} +(-2.42162 - 1.06571i) q^{28} +(4.86076 + 8.41908i) q^{29} +(0.469718 + 0.813575i) q^{30} +(1.13679 - 0.656325i) q^{31} +1.00000i q^{32} +(1.02622 - 0.592488i) q^{33} +4.44440i q^{34} +(1.46959 + 2.00451i) q^{35} +(0.500000 + 0.866025i) q^{36} -5.99292i q^{37} +(1.26634 + 2.19336i) q^{38} +(0.587639 + 3.55734i) q^{39} +(0.469718 - 0.813575i) q^{40} +(-3.93968 + 2.27458i) q^{41} +(1.56433 + 2.13374i) q^{42} +(-3.49280 + 6.04970i) q^{43} +(-1.02622 - 0.592488i) q^{44} -0.939436i q^{45} +2.62678i q^{46} +(5.13475 + 2.96455i) q^{47} +(0.500000 - 0.866025i) q^{48} +(4.72853 + 5.16149i) q^{49} +(3.56583 - 2.05873i) q^{50} +(2.22220 - 3.84897i) q^{51} +(2.78693 - 2.28758i) q^{52} +(2.41788 + 4.18789i) q^{53} -1.00000i q^{54} +(0.556605 + 0.964067i) q^{55} +(1.06571 - 2.42162i) q^{56} -2.53267i q^{57} +(-8.41908 + 4.86076i) q^{58} -6.56803i q^{59} +(-0.813575 + 0.469718i) q^{60} +(-6.79372 - 11.7671i) q^{61} +(0.656325 + 1.13679i) q^{62} +(-0.287882 - 2.63004i) q^{63} -1.00000 q^{64} +(-3.34189 + 0.552049i) q^{65} +(0.592488 + 1.02622i) q^{66} +(-11.0546 - 6.38235i) q^{67} -4.44440 q^{68} +(1.31339 - 2.27486i) q^{69} +(-2.00451 + 1.46959i) q^{70} +(-6.59325 - 3.80661i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(7.28714 - 4.20723i) q^{73} +5.99292 q^{74} -4.11746 q^{75} +(-2.19336 + 1.26634i) q^{76} +(1.85370 + 2.52843i) q^{77} +(-3.55734 + 0.587639i) q^{78} +(-5.88779 + 10.1979i) q^{79} +(0.813575 + 0.469718i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.27458 - 3.93968i) q^{82} +12.0670i q^{83} +(-2.13374 + 1.56433i) q^{84} +(3.61586 + 2.08762i) q^{85} +(-6.04970 - 3.49280i) q^{86} +9.72152 q^{87} +(0.592488 - 1.02622i) q^{88} -14.7279i q^{89} +0.939436 q^{90} +(-9.18679 + 2.56961i) q^{91} -2.62678 q^{92} -1.31265i q^{93} +(-2.96455 + 5.13475i) q^{94} +2.37928 q^{95} +(0.866025 + 0.500000i) q^{96} +(-11.3044 - 6.52663i) q^{97} +(-5.16149 + 4.72853i) q^{98} -1.18498i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} - 16 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 - 16 * q^4 - 2 * q^7 - 8 * q^9	$ 16 q + 8 q^{3} - 16 q^{4} - 2 q^{7} - 8 q^{9} + 4 q^{10} + 6 q^{11} - 8 q^{12} - 10 q^{13} + 4 q^{14} + 16 q^{16} + 18 q^{19} + 8 q^{21} + 6 q^{22} + 32 q^{23} - 4 q^{26} - 16 q^{27} + 2 q^{28} - 4 q^{29} - 4 q^{30} - 12 q^{31} + 6 q^{33} - 2 q^{35} + 8 q^{36} - 2 q^{38} - 14 q^{39} - 4 q^{40} - 18 q^{41} + 2 q^{42} - 32 q^{43} - 6 q^{44} - 66 q^{47} + 8 q^{48} + 22 q^{49} + 36 q^{50} + 10 q^{52} + 2 q^{53} + 16 q^{55} - 4 q^{56} + 24 q^{58} + 4 q^{61} + 4 q^{62} + 10 q^{63} - 16 q^{64} + 38 q^{65} - 6 q^{66} + 36 q^{67} + 16 q^{69} + 6 q^{70} - 30 q^{71} + 18 q^{73} - 12 q^{74} - 18 q^{76} - 34 q^{77} - 2 q^{78} - 24 q^{79} - 8 q^{81} + 6 q^{82} - 8 q^{84} + 72 q^{85} - 8 q^{87} - 6 q^{88} - 8 q^{90} - 2 q^{91} - 32 q^{92} - 24 q^{94} + 80 q^{95} - 6 q^{97} - 60 q^{98}+O(q^{100}) $ 16 * q + 8 * q^3 - 16 * q^4 - 2 * q^7 - 8 * q^9 + 4 * q^10 + 6 * q^11 - 8 * q^12 - 10 * q^13 + 4 * q^14 + 16 * q^16 + 18 * q^19 + 8 * q^21 + 6 * q^22 + 32 * q^23 - 4 * q^26 - 16 * q^27 + 2 * q^28 - 4 * q^29 - 4 * q^30 - 12 * q^31 + 6 * q^33 - 2 * q^35 + 8 * q^36 - 2 * q^38 - 14 * q^39 - 4 * q^40 - 18 * q^41 + 2 * q^42 - 32 * q^43 - 6 * q^44 - 66 * q^47 + 8 * q^48 + 22 * q^49 + 36 * q^50 + 10 * q^52 + 2 * q^53 + 16 * q^55 - 4 * q^56 + 24 * q^58 + 4 * q^61 + 4 * q^62 + 10 * q^63 - 16 * q^64 + 38 * q^65 - 6 * q^66 + 36 * q^67 + 16 * q^69 + 6 * q^70 - 30 * q^71 + 18 * q^73 - 12 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 6 * q^82 - 8 * q^84 + 72 * q^85 - 8 * q^87 - 6 * q^88 - 8 * q^90 - 2 * q^91 - 32 * q^92 - 24 * q^94 + 80 * q^95 - 6 * q^97 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−1.00000			−0.500000
$5$	0.813575	+	0.469718i	0.363842	+	0.210064i	0.670765	−	0.741670i	$-0.265966\pi$
$5$	0.813575	+	0.469718i	0.363842	+	0.210064i	−0.306923	+	0.951734i	$0.599299\pi$
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	2.42162	+	1.06571i	0.915288	+	0.402800i
$7$	2.42162	+	1.06571i	0.915288	+	0.402800i
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.469718	+	0.813575i	−0.148538	+	0.257275i
$11$	1.02622	+	0.592488i	0.309417	+	0.178642i	0.646666	−	0.762774i	$-0.276163\pi$
$11$	1.02622	+	0.592488i	0.309417	+	0.178642i	−0.337249	+	0.941416i	$0.609496\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−2.78693	+	2.28758i	−0.772955	+	0.634461i
$13$	−2.78693	+	2.28758i	−0.772955	+	0.634461i
$14$	−1.06571	+	2.42162i	−0.284822	+	0.647206i
$15$	0.813575	−	0.469718i	0.210064	−	0.121281i
$16$	1.00000			0.250000
$17$	4.44440			1.07793			0.538963	−	0.842329i	$-0.318816\pi$
$17$	4.44440			1.07793			0.538963	+	0.842329i	$0.318816\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	2.19336	−	1.26634i	0.503191	−	0.290517i	−0.226840	−	0.973932i	$-0.572839\pi$
$19$	2.19336	−	1.26634i	0.503191	−	0.290517i	0.730030	+	0.683415i	$0.239506\pi$
$20$	−0.813575	−	0.469718i	−0.181921	−	0.105032i
$21$	2.13374	−	1.56433i	0.465621	−	0.341366i
$22$	−0.592488	+	1.02622i	−0.126319	+	0.218791i
$23$	2.62678			0.547723			0.273861	−	0.961769i	$-0.411699\pi$
$23$	2.62678			0.547723			0.273861	+	0.961769i	$0.411699\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	−2.05873	−	3.56583i	−0.411746	−	0.713165i
$26$	−2.28758	−	2.78693i	−0.448632	−	0.546562i
$27$	−1.00000			−0.192450
$28$	−2.42162	−	1.06571i	−0.457644	−	0.201400i
$29$	4.86076	+	8.41908i	0.902620	+	1.56338i	0.824080	+	0.566473i	$0.191693\pi$
$29$	4.86076	+	8.41908i	0.902620	+	1.56338i	0.0785404	+	0.996911i	$0.474974\pi$
$30$	0.469718	+	0.813575i	0.0857584	+	0.148538i
$31$	1.13679	−	0.656325i	0.204173	−	0.117880i	−0.394427	−	0.918927i	$-0.629057\pi$
$31$	1.13679	−	0.656325i	0.204173	−	0.117880i	0.598601	+	0.801048i	$0.295724\pi$
$32$			1.00000i			0.176777i
$33$	1.02622	−	0.592488i	0.178642	−	0.103139i
$34$			4.44440i			0.762209i
$35$	1.46959	+	2.00451i	0.248406	+	0.338825i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$		−	5.99292i		−	0.985230i	−0.870247	−	0.492615i	$-0.836041\pi$
$37$		−	5.99292i		−	0.985230i	0.870247	−	0.492615i	$-0.163959\pi$
$38$	1.26634	+	2.19336i	0.205427	+	0.355810i
$39$	0.587639	+	3.55734i	0.0940976	+	0.569631i
$40$	0.469718	−	0.813575i	0.0742689	−	0.128638i
$41$	−3.93968	+	2.27458i	−0.615275	+	0.355229i	−0.775027	−	0.631928i	$-0.782264\pi$
$41$	−3.93968	+	2.27458i	−0.615275	+	0.355229i	0.159752	+	0.987157i	$0.448930\pi$
$42$	1.56433	+	2.13374i	0.241382	+	0.329244i
$43$	−3.49280	+	6.04970i	−0.532647	+	0.922571i	0.466627	+	0.884454i	$0.345469\pi$
$43$	−3.49280	+	6.04970i	−0.532647	+	0.922571i	−0.999273	+	0.0381168i	$0.987864\pi$
$44$	−1.02622	−	0.592488i	−0.154708	−	0.0893210i
$45$		−	0.939436i		−	0.140043i
$46$			2.62678i			0.387298i
$47$	5.13475	+	2.96455i	0.748981	+	0.432424i	0.825325	−	0.564657i	$-0.190992\pi$
$47$	5.13475	+	2.96455i	0.748981	+	0.432424i	−0.0763449	+	0.997081i	$0.524325\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	4.72853	+	5.16149i	0.675505	+	0.737356i
$50$	3.56583	−	2.05873i	0.504284	−	0.291148i
$51$	2.22220	−	3.84897i	0.311171	−	0.538963i
$52$	2.78693	−	2.28758i	0.386477	−	0.317230i
$53$	2.41788	+	4.18789i	0.332122	+	0.575252i	0.982928	−	0.183993i	$-0.0589022\pi$
$53$	2.41788	+	4.18789i	0.332122	+	0.575252i	−0.650806	+	0.759244i	$0.725569\pi$
$54$		−	1.00000i		−	0.136083i
$55$	0.556605	+	0.964067i	0.0750525	+	0.129995i
$56$	1.06571	−	2.42162i	0.142411	−	0.323603i
$57$		−	2.53267i		−	0.335460i
$58$	−8.41908	+	4.86076i	−1.10548	+	0.638249i
$59$		−	6.56803i		−	0.855084i	−0.903995	−	0.427542i	$-0.859380\pi$
$59$		−	6.56803i		−	0.855084i	0.903995	−	0.427542i	$-0.140620\pi$
$60$	−0.813575	+	0.469718i	−0.105032	+	0.0606403i
$61$	−6.79372	−	11.7671i	−0.869847	−	1.50662i	−0.862152	−	0.506649i	$-0.830884\pi$
$61$	−6.79372	−	11.7671i	−0.869847	−	1.50662i	−0.00769485	−	0.999970i	$-0.502449\pi$
$62$	0.656325	+	1.13679i	0.0833534	+	0.144372i
$63$	−0.287882	−	2.63004i	−0.0362698	−	0.331354i
$64$	−1.00000			−0.125000
$65$	−3.34189	+	0.552049i	−0.414511	+	0.0684733i
$66$	0.592488	+	1.02622i	0.0729303	+	0.126319i
$67$	−11.0546	−	6.38235i	−1.35053	−	0.779728i	−0.362205	−	0.932098i	$-0.617976\pi$
$67$	−11.0546	−	6.38235i	−1.35053	−	0.779728i	−0.988323	+	0.152370i	$0.951309\pi$
$68$	−4.44440			−0.538963
$69$	1.31339	−	2.27486i	0.158114	−	0.273861i
$70$	−2.00451	+	1.46959i	−0.239585	+	0.175650i
$71$	−6.59325	−	3.80661i	−0.782474	−	0.451762i	0.0548322	−	0.998496i	$-0.482538\pi$
$71$	−6.59325	−	3.80661i	−0.782474	−	0.451762i	−0.837306	+	0.546734i	$0.815871\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	7.28714	−	4.20723i	0.852895	−	0.492419i	−0.00873149	−	0.999962i	$-0.502779\pi$
$73$	7.28714	−	4.20723i	0.852895	−	0.492419i	0.861627	+	0.507543i	$0.169446\pi$
$74$	5.99292			0.696663
$75$	−4.11746			−0.475443
$76$	−2.19336	+	1.26634i	−0.251595	+	0.145259i
$77$	1.85370	+	2.52843i	0.211249	+	0.288142i
$78$	−3.55734	+	0.587639i	−0.402790	+	0.0665370i
$79$	−5.88779	+	10.1979i	−0.662428	+	1.14736i	0.317548	+	0.948242i	$0.397140\pi$
$79$	−5.88779	+	10.1979i	−0.662428	+	1.14736i	−0.979976	+	0.199116i	$0.936193\pi$
$80$	0.813575	+	0.469718i	0.0909605	+	0.0525161i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.27458	−	3.93968i	−0.251185	−	0.435065i
$83$			12.0670i			1.32452i	0.749274	+	0.662260i	$0.230403\pi$
$83$			12.0670i			1.32452i	−0.749274	+	0.662260i	$0.769597\pi$
$84$	−2.13374	+	1.56433i	−0.232810	+	0.170683i
$85$	3.61586	+	2.08762i	0.392195	+	0.226434i
$86$	−6.04970	−	3.49280i	−0.652356	−	0.376638i
$87$	9.72152			1.04226
$88$	0.592488	−	1.02622i	0.0631595	−	0.109395i
$89$		−	14.7279i		−	1.56115i	−0.625063	−	0.780575i	$-0.714927\pi$
$89$		−	14.7279i		−	1.56115i	0.625063	−	0.780575i	$-0.285073\pi$
$90$	0.939436			0.0990252
$91$	−9.18679	+	2.56961i	−0.963037	+	0.269369i
$92$	−2.62678			−0.273861
$93$		−	1.31265i		−	0.136116i
$94$	−2.96455	+	5.13475i	−0.305770	+	0.529609i
$95$	2.37928			0.244109
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−11.3044	−	6.52663i	−1.14779	−	0.662679i	−0.199445	−	0.979909i	$-0.563914\pi$
$97$	−11.3044	−	6.52663i	−1.14779	−	0.662679i	−0.948348	+	0.317231i	$0.897247\pi$
$98$	−5.16149	+	4.72853i	−0.521389	+	0.477654i
$99$		−	1.18498i		−	0.119095i
$100$	2.05873	+	3.56583i	0.205873	+	0.356583i
$101$	6.63776	−	11.4969i	0.660482	−	1.14399i	−0.320007	−	0.947415i	$-0.603685\pi$
$101$	6.63776	−	11.4969i	0.660482	−	1.14399i	0.980489	−	0.196574i	$-0.0629815\pi$
$102$	3.84897	+	2.22220i	0.381105	+	0.220031i
$103$	−0.475301	+	0.823246i	−0.0468328	+	0.0811169i	−0.888492	−	0.458893i	$-0.848246\pi$
$103$	−0.475301	+	0.823246i	−0.0468328	+	0.0811169i	0.841659	+	0.540010i	$0.181579\pi$
$104$	2.28758	+	2.78693i	0.224316	+	0.273281i
$105$	2.47076	−	0.270447i	0.241121	−	0.0263929i
$106$	−4.18789	+	2.41788i	−0.406764	+	0.234845i
$107$	−8.11696			−0.784696			−0.392348	−	0.919817i	$-0.628337\pi$
$107$	−8.11696			−0.784696			−0.392348	+	0.919817i	$0.628337\pi$
$108$	1.00000			0.0962250
$109$	−14.5618	+	8.40723i	−1.39476	+	0.805267i	−0.993838	−	0.110844i	$-0.964645\pi$
$109$	−14.5618	+	8.40723i	−1.39476	+	0.805267i	−0.400925	+	0.916111i	$0.631311\pi$
$110$	−0.964067	+	0.556605i	−0.0919202	+	0.0530702i
$111$	−5.19002	−	2.99646i	−0.492615	−	0.284411i
$112$	2.42162	+	1.06571i	0.228822	+	0.100700i
$113$	5.21765	−	9.03723i	0.490835	−	0.850151i	−0.509109	−	0.860702i	$-0.670025\pi$
$113$	5.21765	−	9.03723i	0.490835	−	0.850151i	0.999944	+	0.0105506i	$0.00335841\pi$
$114$	2.53267			0.237206
$115$	2.13709	+	1.23385i	0.199284	+	0.115057i
$116$	−4.86076	−	8.41908i	−0.451310	−	0.781692i
$117$	3.37457	+	1.26976i	0.311979	+	0.117389i
$118$	6.56803			0.604636
$119$	10.7627	+	4.73644i	0.986613	+	0.434188i
$120$	−0.469718	−	0.813575i	−0.0428792	−	0.0742689i
$121$	−4.79792	−	8.31023i	−0.436174	−	0.755476i
$122$	11.7671	−	6.79372i	1.06534	−	0.615075i
$123$			4.54915i			0.410183i
$124$	−1.13679	+	0.656325i	−0.102087	+	0.0589398i
$125$		−	8.56527i		−	0.766101i
$126$	2.63004	−	0.287882i	0.234303	−	0.0256466i
$127$	−6.31405	−	10.9363i	−0.560281	−	0.970435i	−0.997472	−	0.0710665i	$-0.977360\pi$
$127$	−6.31405	−	10.9363i	−0.560281	−	0.970435i	0.437190	−	0.899369i	$-0.355974\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	3.49280	+	6.04970i	0.307524	+	0.532647i
$130$	−0.552049	−	3.34189i	−0.0484179	−	0.293103i
$131$	−2.33370	+	4.04209i	−0.203896	+	0.353159i	−0.949781	−	0.312917i	$-0.898694\pi$
$131$	−2.33370	+	4.04209i	−0.203896	+	0.353159i	0.745884	+	0.666076i	$0.232027\pi$
$132$	−1.02622	+	0.592488i	−0.0893210	+	0.0515695i
$133$	6.66103	−	0.729111i	0.577585	−	0.0632220i
$134$	6.38235	−	11.0546i	0.551351	−	0.954968i
$135$	−0.813575	−	0.469718i	−0.0700214	−	0.0404269i
$136$		−	4.44440i		−	0.381105i
$137$		−	1.56879i		−	0.134030i	−0.997752	−	0.0670152i	$-0.978652\pi$
$137$		−	1.56879i		−	0.134030i	0.997752	−	0.0670152i	$-0.0213476\pi$
$138$	2.27486	+	1.31339i	0.193649	+	0.111803i
$139$	1.13892	−	1.97266i	0.0966018	−	0.167319i	−0.813674	−	0.581321i	$-0.802536\pi$
$139$	1.13892	−	1.97266i	0.0966018	−	0.167319i	0.910276	+	0.414002i	$0.135869\pi$
$140$	−1.46959	−	2.00451i	−0.124203	−	0.169412i
$141$	5.13475	−	2.96455i	0.432424	−	0.249660i
$142$	3.80661	−	6.59325i	0.319444	−	0.553293i
$143$	−4.21537	+	0.696339i	−0.352507	+	0.0582308i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$			9.13274i			0.758433i
$146$	4.20723	+	7.28714i	0.348193	+	0.603088i
$147$	6.83425	−	1.51429i	0.563679	−	0.124896i
$148$			5.99292i			0.492615i
$149$	−3.48695	+	2.01319i	−0.285662	+	0.164927i	−0.635984	−	0.771702i	$-0.719406\pi$
$149$	−3.48695	+	2.01319i	−0.285662	+	0.164927i	0.350322	+	0.936629i	$0.386072\pi$
$150$		−	4.11746i		−	0.336189i
$151$	0.673151	−	0.388644i	0.0547803	−	0.0316274i	−0.472360	−	0.881406i	$-0.656598\pi$
$151$	0.673151	−	0.388644i	0.0547803	−	0.0316274i	0.527140	+	0.849778i	$0.323264\pi$
$152$	−1.26634	−	2.19336i	−0.102713	−	0.177905i
$153$	−2.22220	−	3.84897i	−0.179654	−	0.311171i
$154$	−2.52843	+	1.85370i	−0.203747	+	0.149375i
$155$	1.23315			0.0990491
$156$	−0.587639	−	3.55734i	−0.0470488	−	0.284815i
$157$	4.24519	+	7.35289i	0.338803	+	0.586824i	0.984208	−	0.177016i	$-0.0566446\pi$
$157$	4.24519	+	7.35289i	0.338803	+	0.586824i	−0.645405	+	0.763841i	$0.723311\pi$
$158$	−10.1979	−	5.88779i	−0.811305	−	0.468407i
$159$	4.83576			0.383501
$160$	−0.469718	+	0.813575i	−0.0371345	+	0.0643188i
$161$	6.36109	+	2.79939i	0.501324	+	0.220622i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	−7.07196	+	4.08300i	−0.553918	+	0.319805i	−0.750701	−	0.660642i	$-0.770284\pi$
$163$	−7.07196	+	4.08300i	−0.553918	+	0.319805i	0.196783	+	0.980447i	$0.436951\pi$
$164$	3.93968	−	2.27458i	0.307637	−	0.177614i
$165$	1.11321			0.0866632
$166$	−12.0670			−0.936578
$167$	−9.80393	+	5.66030i	−0.758651	+	0.438007i	−0.828811	−	0.559529i	$-0.810982\pi$
$167$	−9.80393	+	5.66030i	−0.758651	+	0.438007i	0.0701604	+	0.997536i	$0.477649\pi$
$168$	−1.56433	−	2.13374i	−0.120691	−	0.164622i
$169$	2.53394	−	12.7507i	0.194919	−	0.980819i
$170$	−2.08762	+	3.61586i	−0.160113	+	0.277324i
$171$	−2.19336	−	1.26634i	−0.167730	−	0.0968391i
$172$	3.49280	−	6.04970i	0.266323	−	0.461286i
$173$	−0.930646	−	1.61193i	−0.0707557	−	0.122552i	0.828477	−	0.560023i	$-0.189208\pi$
$173$	−0.930646	−	1.61193i	−0.0707557	−	0.122552i	−0.899233	+	0.437471i	$0.855874\pi$
$174$			9.72152i			0.736986i
$175$	−1.18534	−	10.8291i	−0.0896036	−	0.818603i
$176$	1.02622	+	0.592488i	0.0773542	+	0.0446605i
$177$	−5.68808	−	3.28401i	−0.427542	−	0.246842i
$178$	14.7279			1.10390
$179$	−4.64119	+	8.03878i	−0.346899	+	0.600847i	−0.985697	−	0.168528i	$-0.946099\pi$
$179$	−4.64119	+	8.03878i	−0.346899	+	0.600847i	0.638798	+	0.769375i	$0.279432\pi$
$180$			0.939436i			0.0700214i
$181$	23.6020			1.75432			0.877160	−	0.480198i	$-0.159435\pi$
$181$	23.6020			1.75432			0.877160	+	0.480198i	$0.159435\pi$
$182$	−2.56961	−	9.18679i	−0.190472	−	0.680970i
$183$	−13.5874			−1.00441
$184$		−	2.62678i		−	0.193649i
$185$	2.81498	−	4.87569i	0.206962	−	0.358468i
$186$	1.31265			0.0962482
$187$	4.56093	+	2.63326i	0.333529	+	0.192563i
$188$	−5.13475	−	2.96455i	−0.374490	−	0.216212i
$189$	−2.42162	−	1.06571i	−0.176147	−	0.0775188i
$190$			2.37928i			0.172611i
$191$	−7.58338	−	13.1348i	−0.548714	−	0.950401i	−0.998363	−	0.0571956i	$-0.981784\pi$
$191$	−7.58338	−	13.1348i	−0.548714	−	0.950401i	0.449649	−	0.893206i	$-0.351549\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−9.38025	−	5.41569i	−0.675205	−	0.389830i	0.122841	−	0.992426i	$-0.460800\pi$
$193$	−9.38025	−	5.41569i	−0.675205	−	0.389830i	−0.798046	+	0.602597i	$0.794133\pi$
$194$	6.52663	−	11.3044i	0.468585	−	0.811612i
$195$	−1.19286	+	3.17019i	−0.0854224	+	0.227022i
$196$	−4.72853	−	5.16149i	−0.337752	−	0.368678i
$197$	−1.07614	+	0.621308i	−0.0766715	+	0.0442663i	−0.537846	−	0.843043i	$-0.680762\pi$
$197$	−1.07614	+	0.621308i	−0.0766715	+	0.0442663i	0.461174	+	0.887310i	$0.347428\pi$
$198$	1.18498			0.0842126
$199$	12.5369			0.888716			0.444358	−	0.895849i	$-0.353432\pi$
$199$	12.5369			0.888716			0.444358	+	0.895849i	$0.353432\pi$
$200$	−3.56583	+	2.05873i	−0.252142	+	0.145574i
$201$	−11.0546	+	6.38235i	−0.779728	+	0.450176i
$202$	11.4969	+	6.63776i	0.808922	+	0.467031i
$203$	2.79865	+	25.5680i	0.196427	+	1.79452i
$204$	−2.22220	+	3.84897i	−0.155585	+	0.269482i
$205$	−4.27363			−0.298484
$206$	−0.823246	−	0.475301i	−0.0573583	−	0.0331158i
$207$	−1.31339	−	2.27486i	−0.0912871	−	0.158114i
$208$	−2.78693	+	2.28758i	−0.193239	+	0.158615i
$209$	3.00116			0.207594
$210$	0.270447	+	2.47076i	0.0186626	+	0.170498i
$211$	0.888244	+	1.53848i	0.0611493	+	0.105914i	0.894979	−	0.446107i	$-0.147190\pi$
$211$	0.888244	+	1.53848i	0.0611493	+	0.105914i	−0.833830	+	0.552021i	$0.813857\pi$
$212$	−2.41788	−	4.18789i	−0.166061	−	0.287626i
$213$	−6.59325	+	3.80661i	−0.451762	+	0.260825i
$214$		−	8.11696i		−	0.554864i
$215$	−5.68331	+	3.28126i	−0.387598	+	0.223780i
$216$			1.00000i			0.0680414i
$217$	3.45233	−	0.377889i	0.234359	−	0.0256528i
$218$	−8.40723	−	14.5618i	−0.569410	−	0.986246i
$219$		−	8.41446i		−	0.568597i
$220$	−0.556605	−	0.964067i	−0.0375263	−	0.0649974i
$221$	−12.3862	+	10.1669i	−0.833189	+	0.683902i
$222$	2.99646	−	5.19002i	0.201109	−	0.348332i
$223$	2.16287	−	1.24874i	0.144837	−	0.0836216i	−0.425830	−	0.904803i	$-0.640018\pi$
$223$	2.16287	−	1.24874i	0.144837	−	0.0836216i	0.570667	+	0.821181i	$0.306685\pi$
$224$	−1.06571	+	2.42162i	−0.0712056	+	0.161802i
$225$	−2.05873	+	3.56583i	−0.137249	+	0.237722i
$226$	9.03723	+	5.21765i	0.601148	+	0.347073i
$227$		−	5.53948i		−	0.367668i	−0.982957	−	0.183834i	$-0.941149\pi$
$227$		−	5.53948i		−	0.367668i	0.982957	−	0.183834i	$-0.0588509\pi$
$228$			2.53267i			0.167730i
$229$	1.41569	+	0.817352i	0.0935517	+	0.0540121i	0.546046	−	0.837755i	$-0.316132\pi$
$229$	1.41569	+	0.817352i	0.0935517	+	0.0540121i	−0.452494	+	0.891767i	$0.649466\pi$
$230$	−1.23385	+	2.13709i	−0.0813575	+	0.140915i
$231$	3.11654	−	0.341134i	0.205053	−	0.0224450i
$232$	8.41908	−	4.86076i	0.552740	−	0.319125i
$233$	4.67989	−	8.10580i	0.306590	−	0.531029i	−0.671024	−	0.741435i	$-0.734145\pi$
$233$	4.67989	−	8.10580i	0.306590	−	0.531029i	0.977614	+	0.210406i	$0.0674787\pi$
$234$	−1.26976	+	3.37457i	−0.0830068	+	0.220602i
$235$	2.78500	+	4.82377i	0.181674	+	0.314668i
$236$			6.56803i			0.427542i
$237$	5.88779	+	10.1979i	0.382453	+	0.662428i
$238$	−4.73644	+	10.7627i	−0.307018	+	0.697641i
$239$			30.2257i			1.95514i	0.210616	+	0.977569i	$0.432453\pi$
$239$			30.2257i			1.95514i	−0.210616	+	0.977569i	$0.567547\pi$
$240$	0.813575	−	0.469718i	0.0525161	−	0.0303202i
$241$			22.8980i			1.47499i	0.675353	+	0.737495i	$0.263991\pi$
$241$			22.8980i			1.47499i	−0.675353	+	0.737495i	$0.736009\pi$
$242$	8.31023	−	4.79792i	0.534202	−	0.308422i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	6.79372	+	11.7671i	0.434924	+	0.753310i
$245$	1.42257	+	6.42034i	0.0908849	+	0.410180i
$246$	−4.54915			−0.290043
$247$	−3.21589	+	8.54667i	−0.204622	+	0.543812i
$248$	−0.656325	−	1.13679i	−0.0416767	−	0.0721862i
$249$	10.4503	+	6.03348i	0.662260	+	0.382356i
$250$	8.56527			0.541715
$251$	−3.48124	+	6.02968i	−0.219734	+	0.380590i	−0.954727	−	0.297485i	$-0.903852\pi$
$251$	−3.48124	+	6.02968i	−0.219734	+	0.380590i	0.734993	+	0.678075i	$0.237186\pi$
$252$	0.287882	+	2.63004i	0.0181349	+	0.165677i
$253$	2.69566	+	1.55634i	0.169475	+	0.0978462i
$254$	10.9363	−	6.31405i	0.686201	−	0.396179i
$255$	3.61586	−	2.08762i	0.226434	−	0.130732i
$256$	1.00000			0.0625000
$257$	11.4878			0.716592			0.358296	−	0.933608i	$-0.383358\pi$
$257$	11.4878			0.716592			0.358296	+	0.933608i	$0.383358\pi$
$258$	−6.04970	+	3.49280i	−0.376638	+	0.217452i
$259$	6.38670	−	14.5126i	0.396850	−	0.901770i
$260$	3.34189	−	0.552049i	0.207255	−	0.0342366i
$261$	4.86076	−	8.41908i	0.300873	−	0.521128i
$262$	−4.04209	−	2.33370i	−0.249721	−	0.144177i
$263$	−6.77934	+	11.7422i	−0.418032	+	0.724052i	−0.995741	−	0.0921900i	$-0.970613\pi$
$263$	−6.77934	+	11.7422i	−0.418032	+	0.724052i	0.577710	+	0.816242i	$0.303947\pi$
$264$	−0.592488	−	1.02622i	−0.0364651	−	0.0631595i
$265$			4.54289i			0.279067i
$266$	0.729111	+	6.66103i	0.0447047	+	0.408414i
$267$	−12.7547	−	7.36393i	−0.780575	−	0.450665i
$268$	11.0546	+	6.38235i	0.675264	+	0.389864i
$269$	−14.4754			−0.882581			−0.441291	−	0.897364i	$-0.645479\pi$
$269$	−14.4754			−0.882581			−0.441291	+	0.897364i	$0.645479\pi$
$270$	0.469718	−	0.813575i	0.0285861	−	0.0495126i
$271$			4.89838i			0.297555i	0.988871	+	0.148778i	$0.0475339\pi$
$271$			4.89838i			0.297555i	−0.988871	+	0.148778i	$0.952466\pi$
$272$	4.44440			0.269482
$273$	−2.36805	+	9.24080i	−0.143321	+	0.559279i
$274$	1.56879			0.0947738
$275$		−	4.87909i		−	0.294220i
$276$	−1.31339	+	2.27486i	−0.0790569	+	0.136931i
$277$	12.1620			0.730742			0.365371	−	0.930862i	$-0.380942\pi$
$277$	12.1620			0.730742			0.365371	+	0.930862i	$0.380942\pi$
$278$	1.97266	+	1.13892i	0.118313	+	0.0683078i
$279$	−1.13679	−	0.656325i	−0.0680578	−	0.0392932i
$280$	2.00451	−	1.46959i	0.119793	−	0.0878249i
$281$			7.94193i			0.473776i	0.971537	+	0.236888i	$0.0761274\pi$
$281$			7.94193i			0.473776i	−0.971537	+	0.236888i	$0.923873\pi$
$282$	2.96455	+	5.13475i	0.176536	+	0.305770i
$283$	−3.40356	+	5.89513i	−0.202320	+	0.350429i	−0.949276	−	0.314445i	$-0.898182\pi$
$283$	−3.40356	+	5.89513i	−0.202320	+	0.350429i	0.746955	+	0.664874i	$0.231515\pi$
$284$	6.59325	+	3.80661i	0.391237	+	0.225881i
$285$	1.18964	−	2.06052i	0.0704682	−	0.122055i
$286$	−0.696339	−	4.21537i	−0.0411754	−	0.249260i
$287$	−11.9645	+	1.30962i	−0.706240	+	0.0773044i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	2.75273			0.161925
$290$	−9.13274			−0.536293
$291$	−11.3044	+	6.52663i	−0.662679	+	0.382598i
$292$	−7.28714	+	4.20723i	−0.426448	+	0.246210i
$293$	−1.08185	−	0.624604i	−0.0632021	−	0.0364897i	0.468066	−	0.883694i	$-0.344951\pi$
$293$	−1.08185	−	0.624604i	−0.0632021	−	0.0364897i	−0.531268	+	0.847204i	$0.678284\pi$
$294$	1.51429	+	6.83425i	0.0883149	+	0.398581i
$295$	3.08512	−	5.34358i	0.179623	−	0.311116i
$296$	−5.99292			−0.348332
$297$	−1.02622	−	0.592488i	−0.0595473	−	0.0343797i
$298$	−2.01319	−	3.48695i	−0.116621	−	0.201994i
$299$	−7.32066	+	6.00898i	−0.423365	+	0.347509i
$300$	4.11746			0.237722
$301$	−14.9055	+	10.9278i	−0.859137	+	0.629869i
$302$	0.388644	+	0.673151i	0.0223640	+	0.0387355i
$303$	−6.63776	−	11.4969i	−0.381330	−	0.660482i
$304$	2.19336	−	1.26634i	0.125798	−	0.0726293i
$305$		−	12.7645i		−	0.730895i
$306$	3.84897	−	2.22220i	0.220031	−	0.127035i
$307$		−	15.5555i		−	0.887801i	−0.896076	−	0.443901i	$-0.853594\pi$
$307$		−	15.5555i		−	0.887801i	0.896076	−	0.443901i	$-0.146406\pi$
$308$	−1.85370	−	2.52843i	−0.105624	−	0.144071i
$309$	0.475301	+	0.823246i	0.0270390	+	0.0468328i
$310$			1.23315i			0.0700383i
$311$	6.42711	+	11.1321i	0.364448	+	0.631243i	0.988687	−	0.149990i	$-0.0479243\pi$
$311$	6.42711	+	11.1321i	0.364448	+	0.631243i	−0.624239	+	0.781233i	$0.714591\pi$
$312$	3.55734	−	0.587639i	0.201395	−	0.0332685i
$313$	0.621758	−	1.07692i	0.0351438	−	0.0608709i	−0.847919	−	0.530127i	$-0.822144\pi$
$313$	0.621758	−	1.07692i	0.0351438	−	0.0608709i	0.883062	+	0.469256i	$0.155478\pi$
$314$	−7.35289	+	4.24519i	−0.414948	+	0.239570i
$315$	1.00116	−	2.27496i	0.0564092	−	0.128180i
$316$	5.88779	−	10.1979i	0.331214	−	0.573679i
$317$	24.4112	+	14.0938i	1.37107	+	0.791586i	0.991063	−	0.133398i	$-0.0425888\pi$
$317$	24.4112	+	14.0938i	1.37107	+	0.791586i	0.380005	+	0.924984i	$0.375922\pi$
$318$			4.83576i			0.271176i
$319$			11.5198i			0.644983i
$320$	−0.813575	−	0.469718i	−0.0454802	−	0.0262580i
$321$	−4.05848	+	7.02949i	−0.226522	+	0.392348i
$322$	−2.79939	+	6.36109i	−0.156004	+	0.354490i
$323$	9.74817	−	5.62811i	0.542403	−	0.313156i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	13.8946	+	5.22819i	0.770737	+	0.290008i
$326$	−4.08300	−	7.07196i	−0.226136	−	0.391679i
$327$			16.8145i			0.929842i
$328$	2.27458	+	3.93968i	0.125592	+	0.217532i
$329$	9.27510	+	12.6512i	0.511353	+	0.697482i
$330$			1.11321i			0.0612801i
$331$	−12.5419	+	7.24105i	−0.689363	+	0.398004i	−0.803374	−	0.595475i	$-0.796964\pi$
$331$	−12.5419	+	7.24105i	−0.689363	+	0.398004i	0.114010	+	0.993480i	$0.463630\pi$
$332$		−	12.0670i		−	0.662260i
$333$	−5.19002	+	2.99646i	−0.284411	+	0.164205i
$334$	−5.66030	−	9.80393i	−0.309718	−	0.536447i
$335$	−5.99581	−	10.3850i	−0.327586	−	0.567396i
$336$	2.13374	−	1.56433i	0.116405	−	0.0853415i
$337$	20.5348			1.11860			0.559300	−	0.828965i	$-0.311070\pi$
$337$	20.5348			1.11860			0.559300	+	0.828965i	$0.311070\pi$
$338$	12.7507	+	2.53394i	0.693544	+	0.137828i
$339$	−5.21765	−	9.03723i	−0.283384	−	0.490835i
$340$	−3.61586	−	2.08762i	−0.196097	−	0.113217i
$341$	1.55546			0.0842329
$342$	1.26634	−	2.19336i	0.0684756	−	0.118603i
$343$	5.95010	+	17.5384i	0.321275	+	0.946986i
$344$	6.04970	+	3.49280i	0.326178	+	0.188319i
$345$	2.13709	−	1.23385i	0.115057	−	0.0664281i
$346$	1.61193	−	0.930646i	0.0866577	−	0.0500318i
$347$	20.3826			1.09420			0.547098	−	0.837069i	$-0.315733\pi$
$347$	20.3826			1.09420			0.547098	+	0.837069i	$0.315733\pi$
$348$	−9.72152			−0.521128
$349$	8.50552	−	4.91066i	0.455290	−	0.262862i	−0.254772	−	0.967001i	$-0.582000\pi$
$349$	8.50552	−	4.91066i	0.455290	−	0.262862i	0.710062	+	0.704139i	$0.248667\pi$
$350$	10.8291	−	1.18534i	0.578840	−	0.0633593i
$351$	2.78693	−	2.28758i	0.148755	−	0.122102i
$352$	−0.592488	+	1.02622i	−0.0315797	+	0.0546977i
$353$	−7.61300	−	4.39537i	−0.405199	−	0.233942i	0.283526	−	0.958965i	$-0.408496\pi$
$353$	−7.61300	−	4.39537i	−0.405199	−	0.233942i	−0.688725	+	0.725023i	$0.741829\pi$
$354$	3.28401	−	5.68808i	0.174543	−	0.302318i
$355$	−3.57607	−	6.19393i	−0.189798	−	0.328740i
$356$			14.7279i			0.780575i
$357$	9.48321	−	6.95254i	0.501905	−	0.367967i
$358$	−8.03878	−	4.64119i	−0.424863	−	0.245295i
$359$	−28.0687	−	16.2055i	−1.48141	−	0.855293i	−0.481633	−	0.876373i	$-0.659956\pi$
$359$	−28.0687	−	16.2055i	−1.48141	−	0.855293i	−0.999778	+	0.0210807i	$0.993289\pi$
$360$	−0.939436			−0.0495126
$361$	−6.29279	+	10.8994i	−0.331199	+	0.573654i
$362$			23.6020i			1.24049i
$363$	−9.59583			−0.503651
$364$	9.18679	−	2.56961i	0.481519	−	0.134684i
$365$	7.90485			0.413759
$366$		−	13.5874i		−	0.710227i
$367$	15.1366	−	26.2174i	0.790126	−	1.36854i	−0.135763	−	0.990741i	$-0.543348\pi$
$367$	15.1366	−	26.2174i	0.790126	−	1.36854i	0.925889	−	0.377797i	$-0.123318\pi$
$368$	2.62678			0.136931
$369$	3.93968	+	2.27458i	0.205092	+	0.118410i
$370$	4.87569	+	2.81498i	0.253475	+	0.146344i
$371$	1.39213	+	12.7183i	0.0722758	+	0.660299i
$372$			1.31265i			0.0680578i
$373$	4.09941	+	7.10039i	0.212260	+	0.367644i	0.952421	−	0.304784i	$-0.0985844\pi$
$373$	4.09941	+	7.10039i	0.212260	+	0.367644i	−0.740162	+	0.672429i	$0.765251\pi$
$374$	−2.63326	+	4.56093i	−0.136162	+	0.235840i
$375$	−7.41774	−	4.28263i	−0.383050	−	0.221154i
$376$	2.96455	−	5.13475i	0.152885	−	0.264805i
$377$	−32.8059	−	12.3440i	−1.68959	−	0.635748i
$378$	1.06571	−	2.42162i	0.0548141	−	0.124555i
$379$	−24.4017	+	14.0883i	−1.25343	+	0.723669i	−0.971789	−	0.235850i	$-0.924212\pi$
$379$	−24.4017	+	14.0883i	−1.25343	+	0.723669i	−0.281642	+	0.959519i	$0.590879\pi$
$380$	−2.37928			−0.122055
$381$	−12.6281			−0.646957
$382$	13.1348	−	7.58338i	0.672035	−	0.388000i
$383$	26.0426	−	15.0357i	1.33072	−	0.768289i	0.345306	−	0.938490i	$-0.387775\pi$
$383$	26.0426	−	15.0357i	1.33072	−	0.768289i	0.985409	+	0.170201i	$0.0544418\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$	0.320473	+	2.92779i	0.0163328	+	0.149214i
$386$	5.41569	−	9.38025i	0.275651	−	0.477442i
$387$	6.98560			0.355098
$388$	11.3044	+	6.52663i	0.573896	+	0.331339i
$389$	−0.845551	−	1.46454i	−0.0428711	−	0.0742550i	0.843794	−	0.536668i	$-0.180317\pi$
$389$	−0.845551	−	1.46454i	−0.0428711	−	0.0742550i	−0.886665	+	0.462413i	$0.846984\pi$
$390$	−3.17019	−	1.19286i	−0.160529	−	0.0604027i
$391$	11.6745			0.590405
$392$	5.16149	−	4.72853i	0.260695	−	0.238827i
$393$	2.33370	+	4.04209i	0.117720	+	0.203896i
$394$	−0.621308	−	1.07614i	−0.0313010	−	0.0542150i
$395$	−9.58031	+	5.53120i	−0.482038	+	0.278305i
$396$			1.18498i			0.0595473i
$397$	17.8975	−	10.3331i	0.898248	−	0.518604i	0.0216165	−	0.999766i	$-0.493119\pi$
$397$	17.8975	−	10.3331i	0.898248	−	0.518604i	0.876631	+	0.481163i	$0.159785\pi$
$398$			12.5369i			0.628417i
$399$	2.69909	−	6.13318i	0.135123	−	0.307043i
$400$	−2.05873	−	3.56583i	−0.102937	−	0.178291i
$401$		−	28.1426i		−	1.40538i	−0.711498	−	0.702688i	$-0.751983\pi$
$401$		−	28.1426i		−	1.40538i	0.711498	−	0.702688i	$-0.248017\pi$
$402$	−6.38235	−	11.0546i	−0.318323	−	0.551351i
$403$	−1.66675	+	4.42963i	−0.0830268	+	0.220656i
$404$	−6.63776	+	11.4969i	−0.330241	+	0.571994i
$405$	−0.813575	+	0.469718i	−0.0404269	+	0.0233405i
$406$	−25.5680	+	2.79865i	−1.26892	+	0.138895i
$407$	3.55074	−	6.15005i	0.176003	−	0.304847i
$408$	−3.84897	−	2.22220i	−0.190552	−	0.110015i
$409$			1.84394i			0.0911768i	0.998960	+	0.0455884i	$0.0145163\pi$
$409$			1.84394i			0.0911768i	−0.998960	+	0.0455884i	$0.985484\pi$
$410$		−	4.27363i		−	0.211060i
$411$	−1.35861	−	0.784393i	−0.0670152	−	0.0386912i
$412$	0.475301	−	0.823246i	0.0234164	−	0.0405584i
$413$	6.99960	−	15.9053i	0.344428	−	0.782649i
$414$	2.27486	−	1.31339i	0.111803	−	0.0645497i
$415$	−5.66807	+	9.81738i	−0.278234	+	0.481916i
$416$	−2.28758	−	2.78693i	−0.112158	−	0.136640i
$417$	−1.13892	−	1.97266i	−0.0557731	−	0.0966018i
$418$			3.00116i			0.146791i
$419$	15.3525	+	26.5914i	0.750020	+	1.29907i	0.947812	+	0.318829i	$0.103290\pi$
$419$	15.3525	+	26.5914i	0.750020	+	1.29907i	−0.197792	+	0.980244i	$0.563377\pi$
$420$	−2.47076	+	0.270447i	−0.120561	+	0.0131965i
$421$		−	37.2167i		−	1.81383i	−0.421313	−	0.906915i	$-0.638431\pi$
$421$		−	37.2167i		−	1.81383i	0.421313	−	0.906915i	$-0.361569\pi$
$422$	−1.53848	+	0.888244i	−0.0748923	+	0.0432391i
$423$		−	5.92910i		−	0.288283i
$424$	4.18789	−	2.41788i	0.203382	−	0.117423i
$425$	−9.14983	−	15.8480i	−0.443832	−	0.768739i
$426$	−3.80661	−	6.59325i	−0.184431	−	0.319444i
$427$	−3.91159	−	35.7356i	−0.189295	−	1.72937i
$428$	8.11696			0.392348
$429$	−1.50464	+	3.99878i	−0.0726445	+	0.193063i
$430$	−3.28126	−	5.68331i	−0.158236	−	0.274073i
$431$	16.7190	+	9.65272i	0.805326	+	0.464955i	0.845330	−	0.534244i	$-0.179404\pi$
$431$	16.7190	+	9.65272i	0.805326	+	0.464955i	−0.0400042	+	0.999200i	$0.512737\pi$
$432$	−1.00000			−0.0481125
$433$	17.5537	−	30.4039i	0.843578	−	1.46112i	−0.0432726	−	0.999063i	$-0.513778\pi$
$433$	17.5537	−	30.4039i	0.843578	−	1.46112i	0.886850	−	0.462056i	$-0.152888\pi$
$434$	0.377889	+	3.45233i	0.0181393	+	0.165717i
$435$	7.90919	+	4.56637i	0.379217	+	0.218941i
$436$	14.5618	−	8.40723i	0.697381	−	0.402633i
$437$	5.76148	−	3.32639i	0.275609	−	0.159123i
$438$	8.41446			0.402059
$439$	−1.78072			−0.0849891			−0.0424945	−	0.999097i	$-0.513531\pi$
$439$	−1.78072			−0.0849891			−0.0424945	+	0.999097i	$0.513531\pi$
$440$	0.964067	−	0.556605i	0.0459601	−	0.0265351i
$441$	2.10571	−	6.67577i	0.100272	−	0.317894i
$442$	−10.1669	−	12.3862i	−0.483592	−	0.589153i
$443$	−13.3268	+	23.0827i	−0.633177	+	1.09669i	0.353722	+	0.935351i	$0.384916\pi$
$443$	−13.3268	+	23.0827i	−0.633177	+	1.09669i	−0.986898	+	0.161343i	$0.948417\pi$
$444$	5.19002	+	2.99646i	0.246308	+	0.142206i
$445$	6.91794	−	11.9822i	0.327942	−	0.568012i
$446$	1.24874	+	2.16287i	0.0591294	+	0.102415i
$447$			4.02638i			0.190441i
$448$	−2.42162	−	1.06571i	−0.114411	−	0.0503500i
$449$	−19.9760	−	11.5332i	−0.942726	−	0.544283i	−0.0519122	−	0.998652i	$-0.516532\pi$
$449$	−19.9760	−	11.5332i	−0.942726	−	0.544283i	−0.890814	+	0.454369i	$0.849865\pi$
$450$	−3.56583	−	2.05873i	−0.168095	−	0.0970495i
$451$	−5.39064			−0.253835
$452$	−5.21765	+	9.03723i	−0.245418	+	0.425076i
$453$		−	0.777288i		−	0.0365202i
$454$	5.53948			0.259981
$455$	−8.68114	−	2.22463i	−0.406978	−	0.104292i
$456$	−2.53267			−0.118603
$457$			21.7658i			1.01816i	0.860719	+	0.509080i	$0.170014\pi$
$457$			21.7658i			1.01816i	−0.860719	+	0.509080i	$0.829986\pi$
$458$	−0.817352	+	1.41569i	−0.0381923	+	0.0661511i
$459$	−4.44440			−0.207447
$460$	−2.13709	−	1.23385i	−0.0996422	−	0.0575285i
$461$	−26.3769	−	15.2287i	−1.22849	−	0.709271i	−0.261779	−	0.965128i	$-0.584309\pi$
$461$	−26.3769	−	15.2287i	−1.22849	−	0.709271i	−0.966715	+	0.255857i	$0.917642\pi$
$462$	0.341134	+	3.11654i	0.0158710	+	0.144994i
$463$			1.64794i			0.0765864i	0.999267	+	0.0382932i	$0.0121921\pi$
$463$			1.64794i			0.0765864i	−0.999267	+	0.0382932i	$0.987808\pi$
$464$	4.86076	+	8.41908i	0.225655	+	0.390846i
$465$	0.616576	−	1.06794i	0.0285930	−	0.0495245i
$466$	8.10580	+	4.67989i	0.375494	+	0.216792i
$467$	−11.6712	+	20.2151i	−0.540078	+	0.935443i	0.458821	+	0.888529i	$0.348272\pi$
$467$	−11.6712	+	20.2151i	−0.540078	+	0.935443i	−0.998899	+	0.0469138i	$0.985061\pi$
$468$	−3.37457	−	1.26976i	−0.155989	−	0.0586947i
$469$	−19.9683	−	27.2366i	−0.922049	−	1.25767i
$470$	−4.82377	+	2.78500i	−0.222504	+	0.128463i
$471$	8.49039			0.391216
$472$	−6.56803			−0.302318
$473$	−7.16876	+	4.13888i	−0.329620	+	0.190306i
$474$	−10.1979	+	5.88779i	−0.468407	+	0.270435i
$475$	−9.03106	−	5.21409i	−0.414374	−	0.239239i
$476$	−10.7627	−	4.73644i	−0.493307	−	0.217094i
$477$	2.41788	−	4.18789i	0.110707	−	0.191751i
$478$	−30.2257			−1.38249
$479$	−3.47135	−	2.00419i	−0.158610	−	0.0915737i	0.418594	−	0.908173i	$-0.362523\pi$
$479$	−3.47135	−	2.00419i	−0.158610	−	0.0915737i	−0.577204	+	0.816600i	$0.695856\pi$
$480$	0.469718	+	0.813575i	0.0214396	+	0.0371345i
$481$	13.7093	+	16.7018i	0.625090	+	0.761539i
$482$	−22.8980			−1.04297
$483$	5.60488	−	4.10917i	0.255031	−	0.186974i
$484$	4.79792	+	8.31023i	0.218087	+	0.377738i
$485$	−6.13135	−	10.6198i	−0.278410	−	0.482220i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$		−	34.6485i		−	1.57007i	−0.619449	−	0.785037i	$-0.712644\pi$
$487$		−	34.6485i		−	1.57007i	0.619449	−	0.785037i	$-0.287356\pi$
$488$	−11.7671	+	6.79372i	−0.532670	+	0.307537i
$489$			8.16599i			0.369279i
$490$	−6.42034	+	1.42257i	−0.290041	+	0.0642654i
$491$	8.51783	+	14.7533i	0.384404	+	0.665808i	0.991686	−	0.128679i	$-0.0410736\pi$
$491$	8.51783	+	14.7533i	0.384404	+	0.665808i	−0.607282	+	0.794486i	$0.707740\pi$
$492$		−	4.54915i		−	0.205092i
$493$	21.6032	+	37.4178i	0.972958	+	1.68521i
$494$	−8.54667	−	3.21589i	−0.384533	−	0.144690i
$495$	0.556605	−	0.964067i	0.0250175	−	0.0433316i
$496$	1.13679	−	0.656325i	0.0510433	−	0.0294699i
$497$	−11.9096	−	16.2447i	−0.534220	−	0.728673i
$498$	−6.03348	+	10.4503i	−0.270367	+	0.468289i
$499$	1.48337	+	0.856426i	0.0664049	+	0.0383389i	0.532835	−	0.846219i	$-0.321127\pi$
$499$	1.48337	+	0.856426i	0.0664049	+	0.0383389i	−0.466430	+	0.884558i	$0.654460\pi$
$500$			8.56527i			0.383050i
$501$			11.3206i			0.505767i
$502$	−6.02968	−	3.48124i	−0.269118	−	0.155375i
$503$	21.3563	−	36.9902i	0.952229	−	1.64931i	0.211645	−	0.977347i	$-0.432118\pi$
$503$	21.3563	−	36.9902i	0.952229	−	1.64931i	0.740585	−	0.671963i	$-0.234549\pi$
$504$	−2.63004	+	0.287882i	−0.117151	+	0.0128233i
$505$	10.8006	−	6.23575i	0.480622	−	0.277487i
$506$	−1.55634	+	2.69566i	−0.0691877	+	0.119837i
$507$	−9.77542	−	8.56979i	−0.434142	−	0.380598i
$508$	6.31405	+	10.9363i	0.280141	+	0.485218i
$509$			19.4113i			0.860393i	0.902735	+	0.430196i	$0.141556\pi$
$509$			19.4113i			0.860393i	−0.902735	+	0.430196i	$0.858444\pi$
$510$	2.08762	+	3.61586i	0.0924412	+	0.160113i
$511$	22.1304	−	2.42238i	0.978991	−	0.107160i
$512$			1.00000i			0.0441942i
$513$	−2.19336	+	1.26634i	−0.0968391	+	0.0559101i
$514$			11.4878i			0.506707i
$515$	−0.773387	+	0.446515i	−0.0340795	+	0.0196758i
$516$	−3.49280	−	6.04970i	−0.153762	−	0.266323i
$517$	3.51292	+	6.08456i	0.154498	+	0.267599i
$518$	14.5126	+	6.38670i	0.637647	+	0.280616i
$519$	−1.86129			−0.0817017
$520$	0.552049	+	3.34189i	0.0242090	+	0.146552i
$521$	−5.17163	−	8.95753i	−0.226573	−	0.392436i	0.730217	−	0.683215i	$-0.239419\pi$
$521$	−5.17163	−	8.95753i	−0.226573	−	0.392436i	−0.956790	+	0.290779i	$0.906086\pi$
$522$	8.41908	+	4.86076i	0.368493	+	0.212750i
$523$	22.1148			0.967011			0.483505	−	0.875341i	$-0.339363\pi$
$523$	22.1148			0.967011			0.483505	+	0.875341i	$0.339363\pi$
$524$	2.33370	−	4.04209i	0.101948	−	0.176580i
$525$	−9.97094	−	4.38801i	−0.435168	−	0.191508i
$526$	−11.7422	−	6.77934i	−0.511982	−	0.295593i
$527$	5.05235	−	2.91698i	0.220084	−	0.127065i
$528$	1.02622	−	0.592488i	0.0446605	−	0.0257847i
$529$	−16.1000			−0.700000
$530$	−4.54289			−0.197331
$531$	−5.68808	+	3.28401i	−0.246842	+	0.142514i
$532$	−6.66103	+	0.729111i	−0.288792	+	0.0316110i
$533$	5.77633	−	15.3514i	0.250201	−	0.664944i
$534$	7.36393	−	12.7547i	0.318668	−	0.551950i
$535$	−6.60375	−	3.81268i	−0.285505	−	0.164837i
$536$	−6.38235	+	11.0546i	−0.275676	+	0.477484i
$537$	4.64119	+	8.03878i	0.200282	+	0.346899i
$538$		−	14.4754i		−	0.624079i
$539$	1.79439	+	8.09842i	0.0772900	+	0.348824i
$540$	0.813575	+	0.469718i	0.0350107	+	0.0202134i
$541$	7.56997	+	4.37052i	0.325458	+	0.187904i	0.653823	−	0.756648i	$-0.273164\pi$
$541$	7.56997	+	4.37052i	0.325458	+	0.187904i	−0.328365	+	0.944551i	$0.606497\pi$
$542$	−4.89838			−0.210403
$543$	11.8010	−	20.4399i	0.506429	−	0.877160i
$544$			4.44440i			0.190552i
$545$	−15.7961			−0.676631
$546$	−9.24080	−	2.36805i	−0.395470	−	0.101343i
$547$	−2.46344			−0.105329			−0.0526646	−	0.998612i	$-0.516771\pi$
$547$	−2.46344			−0.105329			−0.0526646	+	0.998612i	$0.516771\pi$
$548$			1.56879i			0.0670152i
$549$	−6.79372	+	11.7671i	−0.289949	+	0.502207i
$550$	4.87909			0.208045
$551$	21.3228	+	12.3107i	0.908380	+	0.524454i
$552$	−2.27486	−	1.31339i	−0.0968246	−	0.0559017i
$553$	−25.1260	+	18.4209i	−1.06847	+	0.783338i
$554$			12.1620i			0.516712i
$555$	−2.81498	−	4.87569i	−0.119489	−	0.206962i
$556$	−1.13892	+	1.97266i	−0.0483009	+	0.0836596i
$557$	37.1610	+	21.4549i	1.57456	+	0.909075i	0.995598	+	0.0937227i	$0.0298767\pi$
$557$	37.1610	+	21.4549i	1.57456	+	0.909075i	0.578965	+	0.815352i	$0.303457\pi$
$558$	0.656325	−	1.13679i	0.0277845	−	0.0481241i
$559$	−4.10501	−	24.8502i	−0.173623	−	1.05105i
$560$	1.46959	+	2.00451i	0.0621016	+	0.0847062i
$561$	4.56093	−	2.63326i	0.192563	−	0.111176i
$562$	−7.94193			−0.335010
$563$	−43.2752			−1.82383			−0.911915	−	0.410378i	$-0.865397\pi$
$563$	−43.2752			−1.82383			−0.911915	+	0.410378i	$0.865397\pi$
$564$	−5.13475	+	2.96455i	−0.216212	+	0.124830i
$565$	8.48990	−	4.90165i	0.357173	−	0.206214i
$566$	−5.89513	−	3.40356i	−0.247791	−	0.143062i
$567$	−2.13374	+	1.56433i	−0.0896088	+	0.0656959i
$568$	−3.80661	+	6.59325i	−0.159722	+	0.276646i
$569$	12.3583			0.518086			0.259043	−	0.965866i	$-0.416593\pi$
$569$	12.3583			0.518086			0.259043	+	0.965866i	$0.416593\pi$
$570$	2.06052	+	1.18964i	0.0863056	+	0.0498286i
$571$	6.32262	+	10.9511i	0.264593	+	0.458289i	0.967457	−	0.253035i	$-0.0814289\pi$
$571$	6.32262	+	10.9511i	0.264593	+	0.458289i	−0.702864	+	0.711325i	$0.748096\pi$
$572$	4.21537	−	0.696339i	0.176253	−	0.0291154i
$573$	−15.1668			−0.633601
$574$	−1.30962	−	11.9645i	−0.0546625	−	0.499387i
$575$	−5.40784	−	9.36666i	−0.225523	−	0.390617i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	1.97487	−	1.14019i	0.0822151	−	0.0474669i	−0.458329	−	0.888783i	$-0.651552\pi$
$577$	1.97487	−	1.14019i	0.0822151	−	0.0474669i	0.540544	+	0.841316i	$0.318218\pi$
$578$			2.75273i			0.114498i
$579$	−9.38025	+	5.41569i	−0.389830	+	0.225068i
$580$		−	9.13274i		−	0.379217i
$581$	−12.8599	+	29.2216i	−0.533517	+	1.21232i
$582$	−6.52663	−	11.3044i	−0.270537	−	0.468585i
$583$			5.73027i			0.237323i
$584$	−4.20723	−	7.28714i	−0.174096	−	0.301544i
$585$	2.14904	+	2.61814i	0.0888517	+	0.108247i
$586$	0.624604	−	1.08185i	0.0258021	−	0.0446906i
$587$	19.6961	−	11.3715i	0.812945	−	0.469354i	−0.0350326	−	0.999386i	$-0.511153\pi$
$587$	19.6961	−	11.3715i	0.812945	−	0.469354i	0.847978	+	0.530032i	$0.177820\pi$
$588$	−6.83425	+	1.51429i	−0.281840	+	0.0624481i
$589$	1.66226	−	2.87911i	0.0684921	−	0.118632i
$590$	5.34358	+	3.08512i	0.219992	+	0.127012i
$591$			1.24262i			0.0511144i
$592$		−	5.99292i		−	0.246308i
$593$	−33.2719	−	19.2096i	−1.36631	−	0.788842i	−0.375859	−	0.926677i	$-0.622652\pi$
$593$	−33.2719	−	19.2096i	−1.36631	−	0.788842i	−0.990455	+	0.137835i	$0.955986\pi$
$594$	0.592488	−	1.02622i	0.0243101	−	0.0421063i
$595$	6.53146	+	8.90887i	0.267764	+	0.365228i
$596$	3.48695	−	2.01319i	0.142831	−	0.0824635i
$597$	6.26844	−	10.8573i	0.256550	−	0.444358i
$598$	−6.00898	−	7.32066i	−0.245726	−	0.299364i
$599$	13.9674	+	24.1923i	0.570693	+	0.988469i	0.996495	+	0.0836526i	$0.0266586\pi$
$599$	13.9674	+	24.1923i	0.570693	+	0.988469i	−0.425802	+	0.904816i	$0.640008\pi$
$600$			4.11746i			0.168095i
$601$	17.8763	+	30.9626i	0.729189	+	1.26299i	0.957226	+	0.289340i	$0.0934359\pi$
$601$	17.8763	+	30.9626i	0.729189	+	1.26299i	−0.228037	+	0.973652i	$0.573231\pi$
$602$	−10.9278	−	14.9055i	−0.445384	−	0.607501i
$603$			12.7647i			0.519819i
$604$	−0.673151	+	0.388644i	−0.0273901	+	0.0158137i
$605$		−	9.01467i		−	0.366498i
$606$	11.4969	−	6.63776i	0.467031	−	0.269641i
$607$	−11.7708	−	20.3876i	−0.477762	−	0.827507i	0.521914	−	0.852998i	$-0.325218\pi$
$607$	−11.7708	−	20.3876i	−0.477762	−	0.827507i	−0.999675	+	0.0254912i	$0.991885\pi$
$608$	1.26634	+	2.19336i	0.0513567	+	0.0889524i
$609$	23.5419	+	10.3603i	0.953965	+	0.419821i
$610$	12.7645			0.516821
$611$	−21.0918	+	3.48417i	−0.853284	+	0.140955i
$612$	2.22220	+	3.84897i	0.0898272	+	0.155585i
$613$	−38.1837	−	22.0454i	−1.54223	−	0.890405i	−0.998698	−	0.0510146i	$-0.983754\pi$
$613$	−38.1837	−	22.0454i	−1.54223	−	0.890405i	−0.543529	−	0.839390i	$-0.682912\pi$
$614$	15.5555			0.627770
$615$	−2.13682	+	3.70108i	−0.0861648	+	0.149242i
$616$	2.52843	−	1.85370i	0.101874	−	0.0746877i
$617$	18.1877	+	10.5007i	0.732210	+	0.422742i	0.819230	−	0.573465i	$-0.194401\pi$
$617$	18.1877	+	10.5007i	0.732210	+	0.422742i	−0.0870202	+	0.996207i	$0.527734\pi$
$618$	−0.823246	+	0.475301i	−0.0331158	+	0.0191194i
$619$	−16.9417	+	9.78132i	−0.680946	+	0.393145i	−0.800212	−	0.599718i	$-0.795279\pi$
$619$	−16.9417	+	9.78132i	−0.680946	+	0.393145i	0.119265	+	0.992862i	$0.461946\pi$
$620$	−1.23315			−0.0495245
$621$	−2.62678			−0.105409
$622$	−11.1321	+	6.42711i	−0.446356	+	0.257704i
$623$	15.6956	−	35.6653i	0.628830	−	1.42890i
$624$	0.587639	+	3.55734i	0.0235244	+	0.142408i
$625$	−6.27039	+	10.8606i	−0.250816	+	0.434425i
$626$	1.07692	+	0.621758i	0.0430422	+	0.0248505i
$627$	1.50058	−	2.59908i	0.0599273	−	0.103797i
$628$	−4.24519	−	7.35289i	−0.169402	−	0.293412i
$629$		−	26.6350i		−	1.06201i
$630$	2.27496	+	1.00116i	0.0906366	+	0.0398873i
$631$	12.3813	+	7.14835i	0.492892	+	0.284571i	0.725774	−	0.687934i	$-0.241482\pi$
$631$	12.3813	+	7.14835i	0.492892	+	0.284571i	−0.232881	+	0.972505i	$0.574815\pi$
$632$	10.1979	+	5.88779i	0.405652	+	0.234204i
$633$	1.77649			0.0706091
$634$	−14.0938	+	24.4112i	−0.559736	+	0.969491i
$635$		−	11.8633i		−	0.470780i
$636$	−4.83576			−0.191751
$637$	−24.9854	−	3.56780i	−0.989958	−	0.141361i
$638$	−11.5198			−0.456072
$639$			7.61322i			0.301175i
$640$	0.469718	−	0.813575i	0.0185672	−	0.0321594i
$641$	−8.70364			−0.343773			−0.171887	−	0.985117i	$-0.554986\pi$
$641$	−8.70364			−0.343773			−0.171887	+	0.985117i	$0.554986\pi$
$642$	−7.02949	−	4.05848i	−0.277432	−	0.160175i
$643$	20.3684	+	11.7597i	0.803251	+	0.463757i	0.844607	−	0.535387i	$-0.179834\pi$
$643$	20.3684	+	11.7597i	0.803251	+	0.463757i	−0.0413555	+	0.999144i	$0.513168\pi$
$644$	−6.36109	−	2.79939i	−0.250662	−	0.110311i
$645$			6.56252i			0.258399i
$646$	5.62811	+	9.74817i	0.221435	+	0.383537i
$647$	15.8242	−	27.4083i	0.622113	−	1.07753i	−0.366979	−	0.930229i	$-0.619608\pi$
$647$	15.8242	−	27.4083i	0.622113	−	1.07753i	0.989092	−	0.147301i	$-0.0470588\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	3.89148	−	6.74024i	0.152754	−	0.264578i
$650$	−5.22819	+	13.8946i	−0.205066	+	0.544993i
$651$	1.39890	−	3.17875i	0.0548273	−	0.124585i
$652$	7.07196	−	4.08300i	0.276959	−	0.159902i
$653$	10.5936			0.414558			0.207279	−	0.978282i	$-0.433539\pi$
$653$	10.5936			0.414558			0.207279	+	0.978282i	$0.433539\pi$
$654$	−16.8145			−0.657498
$655$	−3.79728	+	2.19236i	−0.148372	+	0.0856627i
$656$	−3.93968	+	2.27458i	−0.153819	+	0.0888072i
$657$	−7.28714	−	4.20723i	−0.284298	−	0.164140i
$658$	−12.6512	+	9.27510i	−0.493194	+	0.361581i
$659$	−22.6698	+	39.2652i	−0.883089	+	1.52955i	−0.0352000	+	0.999380i	$0.511207\pi$
$659$	−22.6698	+	39.2652i	−0.883089	+	1.52955i	−0.847889	+	0.530174i	$0.822127\pi$
$660$	−1.11321			−0.0433316
$661$	−31.8850	−	18.4088i	−1.24018	−	0.716019i	−0.271051	−	0.962565i	$-0.587371\pi$
$661$	−31.8850	−	18.4088i	−1.24018	−	0.716019i	−0.969131	+	0.246546i	$0.920704\pi$
$662$	−7.24105	−	12.5419i	−0.281431	−	0.487454i
$663$	2.61171	+	15.8103i	0.101430	+	0.614020i
$664$	12.0670			0.468289
$665$	5.76173	+	2.53562i	0.223430	+	0.0983271i
$666$	−2.99646	−	5.19002i	−0.116111	−	0.201109i
$667$	12.7682	+	22.1151i	0.494386	+	0.856301i
$668$	9.80393	−	5.66030i	0.379325	−	0.219004i
$669$		−	2.49747i		−	0.0965579i
$670$	10.3850	−	5.99581i	0.401209	−	0.231638i
$671$		−	16.1008i		−	0.621565i
$672$	1.56433	+	2.13374i	0.0603455	+	0.0823109i
$673$	12.8749	+	22.3000i	0.496291	+	0.859601i	0.999991	−	0.00427796i	$-0.00136172\pi$
$673$	12.8749	+	22.3000i	0.496291	+	0.859601i	−0.503700	+	0.863878i	$0.668028\pi$
$674$			20.5348i			0.790970i
$675$	2.05873	+	3.56583i	0.0792406	+	0.137249i
$676$	−2.53394	+	12.7507i	−0.0974593	+	0.490410i
$677$	21.8961	−	37.9251i	0.841534	−	1.45758i	−0.0470640	−	0.998892i	$-0.514986\pi$
$677$	21.8961	−	37.9251i	0.841534	−	1.45758i	0.888598	−	0.458687i	$-0.151680\pi$
$678$	9.03723	−	5.21765i	0.347073	−	0.200383i
$679$	−20.4197	−	27.8523i	−0.783635	−	1.06887i
$680$	2.08762	−	3.61586i	0.0800564	−	0.138662i
$681$	−4.79733	−	2.76974i	−0.183834	−	0.106137i
$682$			1.55546i			0.0595617i
$683$		−	24.9798i		−	0.955824i	−0.878408	−	0.477912i	$-0.841394\pi$
$683$		−	24.9798i		−	0.955824i	0.878408	−	0.477912i	$-0.158606\pi$
$684$	2.19336	+	1.26634i	0.0838651	+	0.0484195i
$685$	0.736886	−	1.27632i	0.0281550	−	0.0487659i
$686$	−17.5384	+	5.95010i	−0.669620	+	0.227176i
$687$	1.41569	−	0.817352i	0.0540121	−	0.0311839i
$688$	−3.49280	+	6.04970i	−0.133162	+	0.230643i
$689$	−16.3186	−	6.14026i	−0.621690	−	0.233925i
$690$	1.23385	+	2.13709i	0.0469718	+	0.0813575i
$691$			15.7024i			0.597348i	0.954355	+	0.298674i	$0.0965443\pi$
$691$			15.7024i			0.597348i	−0.954355	+	0.298674i	$0.903456\pi$
$692$	0.930646	+	1.61193i	0.0353779	+	0.0612762i
$693$	1.26284	−	2.86957i	0.0479713	−	0.109006i
$694$			20.3826i			0.773713i
$695$	1.85319	−	1.06994i	0.0702956	−	0.0405852i
$696$		−	9.72152i		−	0.368493i
$697$	−17.5095	+	10.1091i	−0.663221	+	0.382911i
$698$	4.91066	+	8.50552i	0.185871	+	0.321939i
$699$	−4.67989	−	8.10580i	−0.177010	−	0.306590i
$700$	1.18534	+	10.8291i	0.0448018	+	0.409301i
$701$	−13.0907			−0.494427			−0.247214	−	0.968961i	$-0.579515\pi$
$701$	−13.0907			−0.494427			−0.247214	+	0.968961i	$0.579515\pi$
$702$	2.28758	+	2.78693i	0.0863392	+	0.105186i
$703$	−7.58905	−	13.1446i	−0.286226	−	0.495759i
$704$	−1.02622	−	0.592488i	−0.0386771	−	0.0223302i
$705$	5.57001			0.209779
$706$	4.39537	−	7.61300i	0.165422	−	0.286519i
$707$	28.3266	−	20.7674i	1.06533	−	0.781037i
$708$	5.68808	+	3.28401i	0.213771	+	0.123421i
$709$	−7.72214	+	4.45838i	−0.290011	+	0.167438i	−0.637947	−	0.770080i	$-0.720216\pi$
$709$	−7.72214	+	4.45838i	−0.290011	+	0.167438i	0.347936	+	0.937518i	$0.386883\pi$
$710$	6.19393	−	3.57607i	0.232454	−	0.134207i
$711$	11.7756			0.441618
$712$	−14.7279			−0.551950
$713$	2.98610	−	1.72403i	0.111830	−	0.0645653i
$714$	6.95254	+	9.48321i	0.260192	+	0.354900i
$715$	−3.75660	−	1.41351i	−0.140489	−	0.0528622i
$716$	4.64119	−	8.03878i	0.173450	−	0.300423i
$717$	26.1762	+	15.1128i	0.977569	+	0.564400i
$718$	16.2055	−	28.0687i	0.604783	−	1.04752i
$719$	6.05601	+	10.4893i	0.225851	+	0.391185i	0.956574	−	0.291488i	$-0.0941504\pi$
$719$	6.05601	+	10.4893i	0.225851	+	0.391185i	−0.730723	+	0.682674i	$0.760817\pi$
$720$		−	0.939436i		−	0.0350107i
$721$	−2.02834	+	1.48706i	−0.0755394	+	0.0553810i
$722$	−10.8994	−	6.29279i	−0.405635	−	0.234193i
$723$	19.8302	+	11.4490i	0.737495	+	0.425793i
$724$	−23.6020			−0.877160
$725$	20.0140	−	34.6652i	0.743301	−	1.28743i
$726$		−	9.59583i		−	0.356135i
$727$	10.1387			0.376023			0.188011	−	0.982167i	$-0.439796\pi$
$727$	10.1387			0.376023			0.188011	+	0.982167i	$0.439796\pi$
$728$	2.56961	+	9.18679i	0.0952362	+	0.340485i
$729$	1.00000			0.0370370
$730$			7.90485i			0.292572i
$731$	−15.5234	+	26.8873i	−0.574154	+	0.994464i
$732$	13.5874			0.502207
$733$	17.9444	+	10.3602i	0.662791	+	0.382663i	0.793340	−	0.608779i	$-0.208341\pi$
$733$	17.9444	+	10.3602i	0.662791	+	0.382663i	−0.130549	+	0.991442i	$0.541674\pi$
$734$	26.2174	+	15.1366i	0.967703	+	0.558703i
$735$	6.27146	+	1.97818i	0.231326	+	0.0729664i
$736$			2.62678i			0.0968246i
$737$	−7.56293	−	13.0994i	−0.278584	−	0.482522i
$738$	−2.27458	+	3.93968i	−0.0837283	+	0.145022i
$739$	−24.7644	−	14.2977i	−0.910971	−	0.525950i	−0.0302278	−	0.999543i	$-0.509623\pi$
$739$	−24.7644	−	14.2977i	−0.910971	−	0.525950i	−0.880744	+	0.473593i	$0.842957\pi$
$740$	−2.81498	+	4.87569i	−0.103481	+	0.179234i
$741$	5.79369	+	7.05837i	0.212837	+	0.259296i
$742$	−12.7183	+	1.39213i	−0.466902	+	0.0511067i
$743$	39.8419	−	23.0027i	1.46166	−	0.843889i	0.462570	−	0.886583i	$-0.346927\pi$
$743$	39.8419	−	23.0027i	1.46166	−	0.843889i	0.999088	+	0.0426939i	$0.0135940\pi$
$744$	−1.31265			−0.0481241
$745$	−3.78253			−0.138581
$746$	−7.10039	+	4.09941i	−0.259964	+	0.150090i
$747$	10.4503	−	6.03348i	0.382356	−	0.220753i
$748$	−4.56093	−	2.63326i	−0.166764	−	0.0962814i
$749$	−19.6562	−	8.65030i	−0.718223	−	0.316075i
$750$	4.28263	−	7.41774i	0.156380	−	0.270858i
$751$	39.7860			1.45181			0.725906	−	0.687793i	$-0.241421\pi$
$751$	39.7860			1.45181			0.725906	+	0.687793i	$0.241421\pi$
$752$	5.13475	+	2.96455i	0.187245	+	0.108106i
$753$	3.48124	+	6.02968i	0.126863	+	0.219734i
$754$	12.3440	−	32.8059i	0.449542	−	1.19472i
$755$	0.730212			0.0265752
$756$	2.42162	+	1.06571i	0.0880736	+	0.0387594i
$757$	3.31837	+	5.74759i	0.120608	+	0.208900i	0.920008	−	0.391900i	$-0.128182\pi$
$757$	3.31837	+	5.74759i	0.120608	+	0.208900i	−0.799399	+	0.600800i	$0.794849\pi$
$758$	−14.0883	−	24.4017i	−0.511711	−	0.886310i
$759$	2.69566	−	1.55634i	0.0978462	−	0.0564915i
$760$		−	2.37928i		−	0.0863056i
$761$	26.7991	−	15.4725i	0.971467	−	0.560877i	0.0717837	−	0.997420i	$-0.477131\pi$
$761$	26.7991	−	15.4725i	0.971467	−	0.560877i	0.899683	+	0.436544i	$0.143798\pi$
$762$		−	12.6281i		−	0.457468i
$763$	−44.2228	+	4.84059i	−1.60097	+	0.175241i
$764$	7.58338	+	13.1348i	0.274357	+	0.475201i
$765$		−	4.17523i		−	0.150956i
$766$	15.0357	+	26.0426i	0.543262	+	0.940958i
$767$	15.0249	+	18.3046i	0.542518	+	0.660942i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−28.1231	+	16.2369i	−1.01415	+	0.585518i	−0.912403	−	0.409293i	$-0.865775\pi$
$769$	−28.1231	+	16.2369i	−1.01415	+	0.585518i	−0.101744	+	0.994811i	$0.532442\pi$
$770$	−2.92779	+	0.320473i	−0.105510	+	0.0115491i
$771$	5.74392	−	9.94876i	0.206862	−	0.358296i
$772$	9.38025	+	5.41569i	0.337603	+	0.194915i
$773$			38.7964i			1.39541i	0.716385	+	0.697705i	$0.245795\pi$
$773$			38.7964i			1.39541i	−0.716385	+	0.697705i	$0.754205\pi$
$774$			6.98560i			0.251092i
$775$	−4.68068	−	2.70239i	−0.168135	−	0.0970729i
$776$	−6.52663	+	11.3044i	−0.234292	+	0.405806i
$777$	−9.37494	−	12.7874i	−0.336324	−	0.458744i
$778$	1.46454	−	0.845551i	0.0525062	−	0.0303145i
$779$	−5.76075	+	9.97791i	−0.206400	+	0.357496i
$780$	1.19286	−	3.17019i	0.0427112	−	0.113511i
$781$	−4.51075	−	7.81284i	−0.161407	−	0.279565i
$782$			11.6745i			0.417479i
$783$	−4.86076	−	8.41908i	−0.173709	−	0.300873i
$784$	4.72853	+	5.16149i	0.168876	+	0.184339i
$785$			7.97617i			0.284682i
$786$	−4.04209	+	2.33370i	−0.144177	+	0.0832404i
$787$		−	7.91161i		−	0.282019i	−0.990008	−	0.141009i	$-0.954965\pi$
$787$		−	7.91161i		−	0.282019i	0.990008	−	0.141009i	$-0.0450347\pi$
$788$	1.07614	−	0.621308i	0.0383358	−	0.0221332i
$789$	6.77934	+	11.7422i	0.241351	+	0.418032i
$790$	−5.53120	−	9.58031i	−0.196791	−	0.340852i
$791$	22.2662	−	16.3243i	0.791696	−	0.580425i
$792$	−1.18498			−0.0421063
$793$	45.8518	+	17.2528i	1.62824	+	0.612665i
$794$	10.3331	+	17.8975i	0.366708	+	0.635157i
$795$	3.93426	+	2.27144i	0.139534	+	0.0805598i
$796$	−12.5369			−0.444358
$797$	−9.55133	+	16.5434i	−0.338325	+	0.585997i	−0.984118	−	0.177516i	$-0.943194\pi$
$797$	−9.55133	+	16.5434i	−0.338325	+	0.585997i	0.645793	+	0.763513i	$0.276527\pi$
$798$	6.13318	+	2.69909i	0.217112	+	0.0955467i
$799$	22.8209	+	13.1757i	0.807346	+	0.466121i
$800$	3.56583	−	2.05873i	0.126071	−	0.0727871i
$801$	−12.7547	+	7.36393i	−0.450665	+	0.260192i
$802$	28.1426			0.993751
$803$	9.97094			0.351867
$804$	11.0546	−	6.38235i	0.389864	−	0.225088i
$805$	3.86030	+	5.26543i	0.136058	+	0.185582i
$806$	−4.42963	−	1.66675i	−0.156027	−	0.0587088i
$807$	−7.23771	+	12.5361i	−0.254779	+	0.441291i
$808$	−11.4969	−	6.63776i	−0.404461	−	0.233516i
$809$	18.5633	−	32.1525i	0.652650	−	1.13042i	−0.329827	−	0.944041i	$-0.606990\pi$
$809$	18.5633	−	32.1525i	0.652650	−	1.13042i	0.982477	−	0.186382i	$-0.0596762\pi$
$810$	−0.469718	−	0.813575i	−0.0165042	−	0.0285861i
$811$		−	14.0686i		−	0.494016i	−0.969013	−	0.247008i	$-0.920553\pi$
$811$		−	14.0686i		−	0.494016i	0.969013	−	0.247008i	$-0.0794475\pi$
$812$	−2.79865	−	25.5680i	−0.0982135	−	0.897261i
$813$	4.24212	+	2.44919i	0.148778	+	0.0858968i
$814$	6.15005	+	3.55074i	0.215559	+	0.124453i
$815$	−7.67142			−0.268718
$816$	2.22220	−	3.84897i	0.0777926	−	0.134741i
$817$			17.6922i			0.618972i
$818$	−1.84394			−0.0644717
$819$	6.81874	+	6.67119i	0.238266	+	0.233110i
$820$	4.27363			0.149242
$821$		−	5.61651i		−	0.196017i	−0.995186	−	0.0980087i	$-0.968753\pi$
$821$		−	5.61651i		−	0.196017i	0.995186	−	0.0980087i	$-0.0312473\pi$
$822$	0.784393	−	1.35861i	0.0273588	−	0.0473869i
$823$	−1.99484			−0.0695358			−0.0347679	−	0.999395i	$-0.511069\pi$
$823$	−1.99484			−0.0695358			−0.0347679	+	0.999395i	$0.511069\pi$
$824$	0.823246	+	0.475301i	0.0286791	+	0.0165579i
$825$	−4.22542	−	2.43955i	−0.147110	−	0.0849341i
$826$	15.9053	+	6.99960i	0.553416	+	0.243547i
$827$			27.8461i			0.968304i	0.874984	+	0.484152i	$0.160872\pi$
$827$			27.8461i			0.968304i	−0.874984	+	0.484152i	$0.839128\pi$
$828$	1.31339	+	2.27486i	0.0456435	+	0.0790569i
$829$	−11.7483	+	20.3487i	−0.408036	+	0.706739i	−0.994670	−	0.103113i	$-0.967120\pi$
$829$	−11.7483	+	20.3487i	−0.408036	+	0.706739i	0.586634	+	0.809852i	$0.300453\pi$
$830$	−9.81738	−	5.66807i	−0.340766	−	0.196741i
$831$	6.08098	−	10.5326i	0.210947	−	0.365371i
$832$	2.78693	−	2.28758i	0.0966194	−	0.0793076i
$833$	21.0155	+	22.9397i	0.728144	+	0.794815i
$834$	1.97266	−	1.13892i	0.0683078	−	0.0394375i
$835$	−10.6350			−0.368039
$836$	−3.00116			−0.103797
$837$	−1.13679	+	0.656325i	−0.0392932	+	0.0226859i
$838$	−26.5914	+	15.3525i	−0.918584	+	0.530344i
$839$	33.2962	+	19.2236i	1.14951	+	0.663671i	0.948768	−	0.315972i	$-0.102331\pi$
$839$	33.2962	+	19.2236i	1.14951	+	0.663671i	0.200744	+	0.979644i	$0.435664\pi$
$840$	−0.270447	−	2.47076i	−0.00933131	−	0.0852492i
$841$	−32.7540	+	56.7315i	−1.12945	+	1.95626i
$842$	37.2167			1.28257
$843$	6.87791	+	3.97097i	0.236888	+	0.136767i
$844$	−0.888244	−	1.53848i	−0.0305746	−	0.0529568i
$845$	8.05076	−	9.18338i	0.276955	−	0.315918i
$846$	5.92910			0.203847
$847$	−2.76247	−	25.2374i	−0.0949196	−	0.867169i
$848$	2.41788	+	4.18789i	0.0830304	+	0.143813i
$849$	3.40356	+	5.89513i	0.116810	+	0.202320i
$850$	15.8480	−	9.14983i	0.543581	−	0.313837i
$851$		−	15.7421i		−	0.539633i
$852$	6.59325	−	3.80661i	0.225881	−	0.130412i
$853$		−	4.05487i		−	0.138836i	−0.997588	−	0.0694181i	$-0.977886\pi$
$853$		−	4.05487i		−	0.138836i	0.997588	−	0.0694181i	$-0.0221143\pi$
$854$	35.7356	−	3.91159i	1.22285	−	0.133852i
$855$	−1.18964	−	2.06052i	−0.0406849	−	0.0704682i
$856$			8.11696i			0.277432i
$857$	5.96185	+	10.3262i	0.203653	+	0.352737i	0.949703	−	0.313153i	$-0.101385\pi$
$857$	5.96185	+	10.3262i	0.203653	+	0.352737i	−0.746050	+	0.665890i	$0.768052\pi$
$858$	−3.99878	−	1.50464i	−0.136516	−	0.0513674i
$859$	−2.16832	+	3.75564i	−0.0739822	+	0.128141i	−0.900643	−	0.434559i	$-0.856904\pi$
$859$	−2.16832	+	3.75564i	−0.0739822	+	0.128141i	0.826661	+	0.562700i	$0.190237\pi$
$860$	5.68331	−	3.28126i	0.193799	−	0.111890i
$861$	−4.84807	+	11.0163i	−0.165222	+	0.375436i
$862$	−9.65272	+	16.7190i	−0.328773	+	0.569451i
$863$	2.46863	+	1.42526i	0.0840331	+	0.0485165i	0.541428	−	0.840747i	$-0.317884\pi$
$863$	2.46863	+	1.42526i	0.0840331	+	0.0485165i	−0.457395	+	0.889264i	$0.651217\pi$
$864$		−	1.00000i		−	0.0340207i
$865$		−	1.74856i		−	0.0594530i
$866$	30.4039	+	17.5537i	1.03317	+	0.596500i
$867$	1.37636	−	2.38393i	0.0467438	−	0.0809626i
$868$	−3.45233	+	0.377889i	−0.117180	+	0.0128264i
$869$	−12.0843	+	6.97689i	−0.409933	+	0.236675i
$870$	−4.56637	+	7.90919i	−0.154814	+	0.268147i
$871$	45.4084	−	7.50104i	1.53860	−	0.254163i
$872$	8.40723	+	14.5618i	0.284705	+	0.493123i
$873$			13.0533i			0.441786i
$874$	3.32639	+	5.76148i	0.112517	+	0.194885i
$875$	9.12807	−	20.7419i	0.308585	−	0.701203i
$876$			8.41446i			0.284298i
$877$	−36.9405	+	21.3276i	−1.24739	+	0.720182i	−0.970589	−	0.240744i	$-0.922609\pi$
$877$	−36.9405	+	21.3276i	−1.24739	+	0.720182i	−0.276804	+	0.960926i	$0.589275\pi$
$878$		−	1.78072i		−	0.0600964i
$879$	−1.08185	+	0.624604i	−0.0364897	+	0.0210674i
$880$	0.556605	+	0.964067i	0.0187631	+	0.0324987i
$881$	−21.4442	−	37.1425i	−0.722475	−	1.25136i	−0.960005	−	0.279983i	$-0.909671\pi$
$881$	−21.4442	−	37.1425i	−0.722475	−	1.25136i	0.237530	−	0.971380i	$-0.423662\pi$
$882$	6.67577	+	2.10571i	0.224785	+	0.0709031i
$883$	0.0680314			0.00228944			0.00114472	−	0.999999i	$-0.499636\pi$
$883$	0.0680314			0.00228944			0.00114472	+	0.999999i	$0.499636\pi$
$884$	12.3862	−	10.1669i	0.416594	−	0.341951i
$885$	−3.08512	−	5.34358i	−0.103705	−	0.179623i
$886$	−23.0827	−	13.3268i	−0.775480	−	0.447724i
$887$	−19.0143			−0.638439			−0.319220	−	0.947681i	$-0.603421\pi$
$887$	−19.0143			−0.638439			−0.319220	+	0.947681i	$0.603421\pi$
$888$	−2.99646	+	5.19002i	−0.100555	+	0.174166i
$889$	−3.63541	−	33.2124i	−0.121928	−	1.11391i
$890$	11.9822	+	6.91794i	0.401645	+	0.231890i
$891$	−1.02622	+	0.592488i	−0.0343797	+	0.0198491i
$892$	−2.16287	+	1.24874i	−0.0724184	+	0.0418108i
$893$	15.0165			0.502507
$894$	−4.02638			−0.134662
$895$	−7.55192	+	4.36010i	−0.252433	+	0.145742i
$896$	1.06571	−	2.42162i	0.0356028	−	0.0809008i
$897$	1.54360	+	9.34437i	0.0515394	+	0.311999i
$898$	11.5332	−	19.9760i	0.384866	−	0.666608i
$899$	11.0513	+	6.38048i	0.368582	+	0.212801i
$900$	2.05873	−	3.56583i	0.0686243	−	0.118861i
$901$	10.7460	+	18.6127i	0.358003	+	0.620079i
$902$		−	5.39064i		−	0.179489i
$903$	2.01103	+	18.3724i	0.0669229	+	0.611396i
$904$	−9.03723	−	5.21765i	−0.300574	−	0.173536i
$905$	19.2020	+	11.0863i	0.638295	+	0.368520i
$906$	0.777288			0.0258237
$907$	−16.0501	+	27.7996i	−0.532934	+	0.923070i	0.466326	+	0.884613i	$0.345577\pi$
$907$	−16.0501	+	27.7996i	−0.532934	+	0.923070i	−0.999260	+	0.0384565i	$0.987756\pi$
$908$			5.53948i			0.183834i
$909$	−13.2755			−0.440322
$910$	2.22463	−	8.68114i	0.0737456	−	0.287777i
$911$	−45.4229			−1.50493			−0.752465	−	0.658633i	$-0.771135\pi$
$911$	−45.4229			−1.50493			−0.752465	+	0.658633i	$0.771135\pi$
$912$		−	2.53267i		−	0.0838651i
$913$	−7.14953	+	12.3833i	−0.236615	+	0.409829i
$914$	−21.7658			−0.719947
$915$	−11.0544	−	6.38227i	−0.365448	−	0.210991i
$916$	−1.41569	−	0.817352i	−0.0467759	−	0.0270061i
$917$	−9.95904	+	7.30138i	−0.328876	+	0.241113i
$918$		−	4.44440i		−	0.146687i
$919$	19.1327	+	33.1388i	0.631130	+	1.09315i	0.987321	+	0.158736i	$0.0507420\pi$
$919$	19.1327	+	33.1388i	0.631130	+	1.09315i	−0.356191	+	0.934413i	$0.615925\pi$
$920$	1.23385	−	2.13709i	0.0406788	−	0.0704577i
$921$	−13.4715	−	7.77777i	−0.443901	−	0.256286i
$922$	15.2287	−	26.3769i	0.501530	−	0.868676i
$923$	27.0828	−	4.47383i	0.891443	−	0.147258i
$924$	−3.11654	+	0.341134i	−0.102527	+	0.0112225i
$925$	−21.3697	+	12.3378i	−0.702632	+	0.405665i
$926$	−1.64794			−0.0541548
$927$	0.950603			0.0312219
$928$	−8.41908	+	4.86076i	−0.276370	+	0.159562i
$929$	−43.8292	+	25.3048i	−1.43799	+	0.830223i	−0.997710	−	0.0676377i	$-0.978454\pi$
$929$	−43.8292	+	25.3048i	−1.43799	+	0.830223i	−0.440279	+	0.897861i	$0.645120\pi$
$930$	1.06794	+	0.616576i	0.0350191	+	0.0202183i
$931$	16.9075	+	5.33308i	0.554122	+	0.174785i
$932$	−4.67989	+	8.10580i	−0.153295	+	0.265514i
$933$	12.8542			0.420829
$934$	−20.2151	−	11.6712i	−0.661458	−	0.381893i
$935$	2.47378	+	4.28471i	0.0809011	+	0.140125i
$936$	1.26976	−	3.37457i	0.0415034	−	0.110301i
$937$	28.6987			0.937547			0.468773	−	0.883319i	$-0.344696\pi$
$937$	28.6987			0.937547			0.468773	+	0.883319i	$0.344696\pi$
$938$	27.2366	−	19.9683i	0.889306	−	0.651987i
$939$	−0.621758	−	1.07692i	−0.0202903	−	0.0351438i
$940$	−2.78500	−	4.82377i	−0.0908368	−	0.157334i
$941$	−24.7100	+	14.2663i	−0.805523	+	0.465069i	−0.845399	−	0.534136i	$-0.820637\pi$
$941$	−24.7100	+	14.2663i	−0.805523	+	0.465069i	0.0398758	+	0.999205i	$0.487304\pi$
$942$			8.49039i			0.276632i
$943$	−10.3487	+	5.97482i	−0.337000	+	0.194567i
$944$		−	6.56803i		−	0.213771i
$945$	−1.46959	−	2.00451i	−0.0478058	−	0.0652068i
$946$	−4.13888	−	7.16876i	−0.134567	−	0.233076i
$947$		−	27.0752i		−	0.879824i	−0.898041	−	0.439912i	$-0.855010\pi$
$947$		−	27.0752i		−	0.879824i	0.898041	−	0.439912i	$-0.144990\pi$
$948$	−5.88779	−	10.1979i	−0.191226	−	0.331214i
$949$	−10.6844	+	28.3952i	−0.346829	+	0.921747i
$950$	5.21409	−	9.03106i	0.169167	−	0.293006i
$951$	24.4112	−	14.0938i	0.791586	−	0.457023i
$952$	4.73644	−	10.7627i	0.153509	−	0.348820i
$953$	−24.5550	+	42.5304i	−0.795413	+	1.37770i	0.127163	+	0.991882i	$0.459413\pi$
$953$	−24.5550	+	42.5304i	−0.795413	+	1.37770i	−0.922576	+	0.385814i	$0.873921\pi$
$954$	4.18789	+	2.41788i	0.135588	+	0.0782818i
$955$		−	14.2482i		−	0.461061i
$956$		−	30.2257i		−	0.977569i
$957$	9.97641	+	5.75989i	0.322492	+	0.186191i
$958$	2.00419	−	3.47135i	0.0647524	−	0.112154i
$959$	1.67187	−	3.79901i	0.0539874	−	0.122676i
$960$	−0.813575	+	0.469718i	−0.0262580	+	0.0151601i
$961$	−14.6385	+	25.3546i	−0.472209	+	0.817890i
$962$	−16.7018	+	13.7093i	−0.538489	+	0.442005i
$963$	4.05848	+	7.02949i	0.130783	+	0.226522i
$964$		−	22.8980i		−	0.737495i
$965$	−5.08769	−	8.81214i	−0.163779	−	0.283673i
$966$	4.10917	+	5.60488i	0.132210	+	0.180334i
$967$		−	37.0937i		−	1.19285i	−0.802667	−	0.596427i	$-0.796587\pi$
$967$		−	37.0937i		−	1.19285i	0.802667	−	0.596427i	$-0.203413\pi$
$968$	−8.31023	+	4.79792i	−0.267101	+	0.154211i
$969$		−	11.2562i		−	0.361602i
$970$	10.6198	−	6.13135i	0.340981	−	0.196866i
$971$	−26.3368	−	45.6167i	−0.845189	−	1.46391i	−0.885457	−	0.464722i	$-0.846154\pi$
$971$	−26.3368	−	45.6167i	−0.845189	−	1.46391i	0.0402670	−	0.999189i	$-0.487179\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	4.86032	−	3.56330i	0.155815	−	0.114234i
$974$	34.6485			1.11021
$975$	11.4751	−	9.41903i	0.367496	−	0.301650i
$976$	−6.79372	−	11.7671i	−0.217462	−	0.376655i
$977$	−2.69540	−	1.55619i	−0.0862336	−	0.0497870i	0.456263	−	0.889845i	$-0.349188\pi$
$977$	−2.69540	−	1.55619i	−0.0862336	−	0.0497870i	−0.542497	+	0.840058i	$0.682521\pi$
$978$	−8.16599			−0.261120
$979$	8.72608	−	15.1140i	0.278887	−	0.483046i
$980$	−1.42257	−	6.42034i	−0.0454425	−	0.205090i
$981$	14.5618	+	8.40723i	0.464921	+	0.268422i
$982$	−14.7533	+	8.51783i	−0.470797	+	0.271815i
$983$	−11.5929	+	6.69318i	−0.369757	+	0.213479i	−0.673352	−	0.739322i	$-0.735146\pi$
$983$	−11.5929	+	6.69318i	−0.369757	+	0.213479i	0.303595	+	0.952801i	$0.401813\pi$
$984$	4.54915			0.145022
$985$	−1.16736			−0.0371951
$986$	−37.4178	+	21.6032i	−1.19163	+	0.687985i
$987$	15.5938	−	1.70688i	0.496356	−	0.0543307i
$988$	3.21589	−	8.54667i	0.102311	−	0.271906i
$989$	−9.17483	+	15.8913i	−0.291743	+	0.505313i
$990$	0.964067	+	0.556605i	0.0306401	+	0.0176901i
$991$	−5.88182	+	10.1876i	−0.186842	+	0.323620i	−0.944196	−	0.329385i	$-0.893159\pi$
$991$	−5.88182	+	10.1876i	−0.186842	+	0.323620i	0.757353	+	0.653005i	$0.226492\pi$
$992$	0.656325	+	1.13679i	0.0208384	+	0.0360931i
$993$			14.4821i			0.459576i
$994$	16.2447	−	11.9096i	0.515249	−	0.377751i
$995$	10.1997	+	5.88880i	0.323352	+	0.186687i
$996$	−10.4503	−	6.03348i	−0.331130	−	0.191178i
$997$	−53.8369			−1.70503			−0.852516	−	0.522701i	$-0.824924\pi$
$997$	−53.8369			−1.70503			−0.852516	+	0.522701i	$0.824924\pi$
$998$	−0.856426	+	1.48337i	−0.0271097	+	0.0469554i
$999$			5.99292i			0.189608i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bm.a.205.8	yes	16
3.2	odd	2		1638.2.dt.a.1297.1		16
7.4	even	3		546.2.bd.a.361.1	yes	16
13.4	even	6		546.2.bd.a.121.1	✓	16
21.11	odd	6		1638.2.cr.a.361.8		16
39.17	odd	6		1638.2.cr.a.667.8		16
91.4	even	6	inner	546.2.bm.a.277.4	yes	16
273.95	odd	6		1638.2.dt.a.1369.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.a.121.1	✓	16	13.4	even	6
546.2.bd.a.361.1	yes	16	7.4	even	3
546.2.bm.a.205.8	yes	16	1.1	even	1	trivial
546.2.bm.a.277.4	yes	16	91.4	even	6	inner
1638.2.cr.a.361.8		16	21.11	odd	6
1638.2.cr.a.667.8		16	39.17	odd	6
1638.2.dt.a.1297.1		16	3.2	odd	2
1638.2.dt.a.1369.5		16	273.95	odd	6

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.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(0.813575 + 0.469718i) q^{5} +(0.866025 + 0.500000i) q^{6} +(2.42162 + 1.06571i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(0.813575 + 0.469718i) q^{5} +(0.866025 + 0.500000i) q^{6} +(2.42162 + 1.06571i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.469718 + 0.813575i) q^{10} +(1.02622 + 0.592488i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.78693 + 2.28758i) q^{13} +(-1.06571 + 2.42162i) q^{14} +(0.813575 - 0.469718i) q^{15} +1.00000 q^{16} +4.44440 q^{17} +(0.866025 - 0.500000i) q^{18} +(2.19336 - 1.26634i) q^{19} +(-0.813575 - 0.469718i) q^{20} +(2.13374 - 1.56433i) q^{21} +(-0.592488 + 1.02622i) q^{22} +2.62678 q^{23} +(-0.866025 - 0.500000i) q^{24} +(-2.05873 - 3.56583i) q^{25} +(-2.28758 - 2.78693i) q^{26} -1.00000 q^{27} +(-2.42162 - 1.06571i) q^{28} +(4.86076 + 8.41908i) q^{29} +(0.469718 + 0.813575i) q^{30} +(1.13679 - 0.656325i) q^{31} +1.00000i q^{32} +(1.02622 - 0.592488i) q^{33} +4.44440i q^{34} +(1.46959 + 2.00451i) q^{35} +(0.500000 + 0.866025i) q^{36} -5.99292i q^{37} +(1.26634 + 2.19336i) q^{38} +(0.587639 + 3.55734i) q^{39} +(0.469718 - 0.813575i) q^{40} +(-3.93968 + 2.27458i) q^{41} +(1.56433 + 2.13374i) q^{42} +(-3.49280 + 6.04970i) q^{43} +(-1.02622 - 0.592488i) q^{44} -0.939436i q^{45} +2.62678i q^{46} +(5.13475 + 2.96455i) q^{47} +(0.500000 - 0.866025i) q^{48} +(4.72853 + 5.16149i) q^{49} +(3.56583 - 2.05873i) q^{50} +(2.22220 - 3.84897i) q^{51} +(2.78693 - 2.28758i) q^{52} +(2.41788 + 4.18789i) q^{53} -1.00000i q^{54} +(0.556605 + 0.964067i) q^{55} +(1.06571 - 2.42162i) q^{56} -2.53267i q^{57} +(-8.41908 + 4.86076i) q^{58} -6.56803i q^{59} +(-0.813575 + 0.469718i) q^{60} +(-6.79372 - 11.7671i) q^{61} +(0.656325 + 1.13679i) q^{62} +(-0.287882 - 2.63004i) q^{63} -1.00000 q^{64} +(-3.34189 + 0.552049i) q^{65} +(0.592488 + 1.02622i) q^{66} +(-11.0546 - 6.38235i) q^{67} -4.44440 q^{68} +(1.31339 - 2.27486i) q^{69} +(-2.00451 + 1.46959i) q^{70} +(-6.59325 - 3.80661i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(7.28714 - 4.20723i) q^{73} +5.99292 q^{74} -4.11746 q^{75} +(-2.19336 + 1.26634i) q^{76} +(1.85370 + 2.52843i) q^{77} +(-3.55734 + 0.587639i) q^{78} +(-5.88779 + 10.1979i) q^{79} +(0.813575 + 0.469718i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.27458 - 3.93968i) q^{82} +12.0670i q^{83} +(-2.13374 + 1.56433i) q^{84} +(3.61586 + 2.08762i) q^{85} +(-6.04970 - 3.49280i) q^{86} +9.72152 q^{87} +(0.592488 - 1.02622i) q^{88} -14.7279i q^{89} +0.939436 q^{90} +(-9.18679 + 2.56961i) q^{91} -2.62678 q^{92} -1.31265i q^{93} +(-2.96455 + 5.13475i) q^{94} +2.37928 q^{95} +(0.866025 + 0.500000i) q^{96} +(-11.3044 - 6.52663i) q^{97} +(-5.16149 + 4.72853i) q^{98} -1.18498i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} - 16 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 - 16 * q^4 - 2 * q^7 - 8 * q^9	\( 16 q + 8 q^{3} - 16 q^{4} - 2 q^{7} - 8 q^{9} + 4 q^{10} + 6 q^{11} - 8 q^{12} - 10 q^{13} + 4 q^{14} + 16 q^{16} + 18 q^{19} + 8 q^{21} + 6 q^{22} + 32 q^{23} - 4 q^{26} - 16 q^{27} + 2 q^{28} - 4 q^{29} - 4 q^{30} - 12 q^{31} + 6 q^{33} - 2 q^{35} + 8 q^{36} - 2 q^{38} - 14 q^{39} - 4 q^{40} - 18 q^{41} + 2 q^{42} - 32 q^{43} - 6 q^{44} - 66 q^{47} + 8 q^{48} + 22 q^{49} + 36 q^{50} + 10 q^{52} + 2 q^{53} + 16 q^{55} - 4 q^{56} + 24 q^{58} + 4 q^{61} + 4 q^{62} + 10 q^{63} - 16 q^{64} + 38 q^{65} - 6 q^{66} + 36 q^{67} + 16 q^{69} + 6 q^{70} - 30 q^{71} + 18 q^{73} - 12 q^{74} - 18 q^{76} - 34 q^{77} - 2 q^{78} - 24 q^{79} - 8 q^{81} + 6 q^{82} - 8 q^{84} + 72 q^{85} - 8 q^{87} - 6 q^{88} - 8 q^{90} - 2 q^{91} - 32 q^{92} - 24 q^{94} + 80 q^{95} - 6 q^{97} - 60 q^{98}+O(q^{100}) \) 16 * q + 8 * q^3 - 16 * q^4 - 2 * q^7 - 8 * q^9 + 4 * q^10 + 6 * q^11 - 8 * q^12 - 10 * q^13 + 4 * q^14 + 16 * q^16 + 18 * q^19 + 8 * q^21 + 6 * q^22 + 32 * q^23 - 4 * q^26 - 16 * q^27 + 2 * q^28 - 4 * q^29 - 4 * q^30 - 12 * q^31 + 6 * q^33 - 2 * q^35 + 8 * q^36 - 2 * q^38 - 14 * q^39 - 4 * q^40 - 18 * q^41 + 2 * q^42 - 32 * q^43 - 6 * q^44 - 66 * q^47 + 8 * q^48 + 22 * q^49 + 36 * q^50 + 10 * q^52 + 2 * q^53 + 16 * q^55 - 4 * q^56 + 24 * q^58 + 4 * q^61 + 4 * q^62 + 10 * q^63 - 16 * q^64 + 38 * q^65 - 6 * q^66 + 36 * q^67 + 16 * q^69 + 6 * q^70 - 30 * q^71 + 18 * q^73 - 12 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 6 * q^82 - 8 * q^84 + 72 * q^85 - 8 * q^87 - 6 * q^88 - 8 * q^90 - 2 * q^91 - 32 * q^92 - 24 * q^94 + 80 * q^95 - 6 * q^97 - 60 * q^98

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