LMFDB - Embedded newform 546.2.bn.e.173.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(101,546)]

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([3, 1, 5]))

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

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

chi := DirichletCharacter("546.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bn (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:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			173.2
Character	$\chi$	$=$	546.173
Dual form			546.2.bn.e.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.72973 + 0.0896134i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(3.27919 + 1.89324i) q^{5} +(0.942473 + 1.45318i) q^{6} +(2.49160 + 0.889895i) q^{7} +1.00000 q^{8} +(2.98394 - 0.310014i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.72973 + 0.0896134i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(3.27919 + 1.89324i) q^{5} +(0.942473 + 1.45318i) q^{6} +(2.49160 + 0.889895i) q^{7} +1.00000 q^{8} +(2.98394 - 0.310014i) q^{9} -3.78649i q^{10} -5.80837 q^{11} +(0.787258 - 1.54280i) q^{12} +(0.879475 + 3.49664i) q^{13} +(-0.475130 - 2.60274i) q^{14} +(-5.84178 - 2.98094i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.26972 + 3.93127i) q^{17} +(-1.76045 - 2.42916i) q^{18} -2.85676 q^{19} +(-3.27919 + 1.89324i) q^{20} +(-4.38955 - 1.31600i) q^{21} +(2.90419 + 5.03020i) q^{22} +(4.19933 - 2.42448i) q^{23} +(-1.72973 + 0.0896134i) q^{24} +(4.66874 + 8.08650i) q^{25} +(2.58845 - 2.50997i) q^{26} +(-5.13363 + 0.803642i) q^{27} +(-2.01647 + 1.71284i) q^{28} +(-2.20269 - 1.27172i) q^{29} +(0.339320 + 6.54960i) q^{30} +(0.824954 + 1.42886i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(10.0469 - 0.520508i) q^{33} +4.53944 q^{34} +(6.48566 + 7.63535i) q^{35} +(-1.22349 + 2.73917i) q^{36} +(-0.865515 + 0.499705i) q^{37} +(1.42838 + 2.47403i) q^{38} +(-1.83460 - 5.96944i) q^{39} +(3.27919 + 1.89324i) q^{40} +(3.48711 + 2.01328i) q^{41} +(1.05509 + 4.45946i) q^{42} +(-0.445979 - 0.772459i) q^{43} +(2.90419 - 5.03020i) q^{44} +(10.3718 + 4.63273i) q^{45} +(-4.19933 - 2.42448i) q^{46} +(6.23486 + 3.59970i) q^{47} +(0.942473 + 1.45318i) q^{48} +(5.41617 + 4.43453i) q^{49} +(4.66874 - 8.08650i) q^{50} +(3.57371 - 7.00344i) q^{51} +(-3.46792 - 0.986674i) q^{52} +(-5.41458 + 3.12611i) q^{53} +(3.26279 + 4.04403i) q^{54} +(-19.0468 - 10.9967i) q^{55} +(2.49160 + 0.889895i) q^{56} +(4.94143 - 0.256004i) q^{57} +2.54344i q^{58} +(8.67545 + 5.00877i) q^{59} +(5.50246 - 3.56866i) q^{60} -3.64451i q^{61} +(0.824954 - 1.42886i) q^{62} +(7.71067 + 1.88296i) q^{63} +1.00000 q^{64} +(-3.73603 + 13.1312i) q^{65} +(-5.47423 - 8.44064i) q^{66} -10.6760i q^{67} +(-2.26972 - 3.93127i) q^{68} +(-7.04644 + 4.57002i) q^{69} +(3.36958 - 9.43442i) q^{70} +(6.77969 + 11.7428i) q^{71} +(2.98394 - 0.310014i) q^{72} +(-2.19097 - 3.79486i) q^{73} +(0.865515 + 0.499705i) q^{74} +(-8.80032 - 13.5691i) q^{75} +(1.42838 - 2.47403i) q^{76} +(-14.4722 - 5.16884i) q^{77} +(-4.25239 + 4.57353i) q^{78} +(-8.40177 + 14.5523i) q^{79} -3.78649i q^{80} +(8.80778 - 1.85013i) q^{81} -4.02657i q^{82} -11.9716i q^{83} +(3.33446 - 3.14346i) q^{84} +(-14.8857 + 8.59427i) q^{85} +(-0.445979 + 0.772459i) q^{86} +(3.92402 + 2.00235i) q^{87} -5.80837 q^{88} +(1.89510 - 1.09414i) q^{89} +(-1.17386 - 11.2986i) q^{90} +(-0.920344 + 9.49489i) q^{91} +4.84897i q^{92} +(-1.55499 - 2.39762i) q^{93} -7.19940i q^{94} +(-9.36788 - 5.40855i) q^{95} +(0.787258 - 1.54280i) q^{96} +(-6.30970 - 10.9287i) q^{97} +(1.13233 - 6.90781i) q^{98} +(-17.3318 + 1.80068i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.72973	+	0.0896134i	−0.998661	+	0.0517383i
$3$	−1.72973	+	0.0896134i	−0.998661	+	0.0517383i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	3.27919	+	1.89324i	1.46650	+	0.846684i	0.999298	−	0.0374664i	$-0.0119287\pi$
$5$	3.27919	+	1.89324i	1.46650	+	0.846684i	0.467202	+	0.884151i	$0.345262\pi$
$6$	0.942473	+	1.45318i	0.384763	+	0.593260i
$7$	2.49160	+	0.889895i	0.941737	+	0.336349i
$7$	2.49160	+	0.889895i	0.941737	+	0.336349i
$8$	1.00000			0.353553
$9$	2.98394	−	0.310014i	0.994646	−	0.103338i
$10$		−	3.78649i		−	1.19739i
$11$	−5.80837			−1.75129			−0.875645	−	0.482955i	$-0.839563\pi$
$11$	−5.80837			−1.75129			−0.875645	+	0.482955i	$0.839563\pi$
$12$	0.787258	−	1.54280i	0.227262	−	0.445367i
$13$	0.879475	+	3.49664i	0.243923	+	0.969795i
$13$	0.879475	+	3.49664i	0.243923	+	0.969795i
$14$	−0.475130	−	2.60274i	−0.126984	−	0.695611i
$15$	−5.84178	−	2.98094i	−1.50834	−	0.769676i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.26972	+	3.93127i	−0.550488	+	0.953474i	0.447751	+	0.894158i	$0.352225\pi$
$17$	−2.26972	+	3.93127i	−0.550488	+	0.953474i	−0.998239	+	0.0593155i	$0.981108\pi$
$18$	−1.76045	−	2.42916i	−0.414942	−	0.572558i
$19$	−2.85676			−0.655387			−0.327693	−	0.944784i	$-0.606271\pi$
$19$	−2.85676			−0.655387			−0.327693	+	0.944784i	$0.606271\pi$
$20$	−3.27919	+	1.89324i	−0.733250	+	0.423342i
$21$	−4.38955	−	1.31600i	−0.957878	−	0.287174i
$22$	2.90419	+	5.03020i	0.619175	+	1.07244i
$23$	4.19933	−	2.42448i	0.875621	−	0.505540i	0.00640879	−	0.999979i	$-0.497960\pi$
$23$	4.19933	−	2.42448i	0.875621	−	0.505540i	0.869212	+	0.494440i	$0.164627\pi$
$24$	−1.72973	+	0.0896134i	−0.353080	+	0.0182923i
$25$	4.66874	+	8.08650i	0.933748	+	1.61730i
$26$	2.58845	−	2.50997i	0.507636	−	0.492246i
$27$	−5.13363	+	0.803642i	−0.987968	+	0.154661i
$28$	−2.01647	+	1.71284i	−0.381078	+	0.323697i
$29$	−2.20269	−	1.27172i	−0.409029	−	0.236153i	0.281344	−	0.959607i	$-0.409220\pi$
$29$	−2.20269	−	1.27172i	−0.409029	−	0.236153i	−0.690372	+	0.723454i	$0.742553\pi$
$30$	0.339320	+	6.54960i	0.0619511	+	1.19579i
$31$	0.824954	+	1.42886i	0.148166	+	0.256631i	0.930550	−	0.366166i	$-0.119330\pi$
$31$	0.824954	+	1.42886i	0.148166	+	0.256631i	−0.782384	+	0.622797i	$0.785996\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	10.0469	−	0.520508i	1.74894	−	0.0906088i
$34$	4.53944			0.778508
$35$	6.48566	+	7.63535i	1.09628	+	1.29061i
$36$	−1.22349	+	2.73917i	−0.203915	+	0.456529i
$37$	−0.865515	+	0.499705i	−0.142290	+	0.0821510i	−0.569455	−	0.822023i	$-0.692846\pi$
$37$	−0.865515	+	0.499705i	−0.142290	+	0.0821510i	0.427165	+	0.904174i	$0.359512\pi$
$38$	1.42838	+	2.47403i	0.231714	+	0.401341i
$39$	−1.83460	−	5.96944i	−0.293771	−	0.955876i
$40$	3.27919	+	1.89324i	0.518486	+	0.299348i
$41$	3.48711	+	2.01328i	0.544595	+	0.314422i	0.746939	−	0.664893i	$-0.231523\pi$
$41$	3.48711	+	2.01328i	0.544595	+	0.314422i	−0.202344	+	0.979314i	$0.564856\pi$
$42$	1.05509	+	4.45946i	0.162803	+	0.688110i
$43$	−0.445979	−	0.772459i	−0.0680112	−	0.117799i	0.830015	−	0.557742i	$-0.188332\pi$
$43$	−0.445979	−	0.772459i	−0.0680112	−	0.117799i	−0.898026	+	0.439943i	$0.854999\pi$
$44$	2.90419	−	5.03020i	0.437823	−	0.758331i
$45$	10.3718	+	4.63273i	1.54614	+	0.690606i
$46$	−4.19933	−	2.42448i	−0.619157	−	0.357471i
$47$	6.23486	+	3.59970i	0.909448	+	0.525070i	0.880253	−	0.474504i	$-0.157373\pi$
$47$	6.23486	+	3.59970i	0.909448	+	0.525070i	0.0291943	+	0.999574i	$0.490706\pi$
$48$	0.942473	+	1.45318i	0.136034	+	0.209749i
$49$	5.41617	+	4.43453i	0.773739	+	0.633505i
$50$	4.66874	−	8.08650i	0.660260	−	1.14360i
$51$	3.57371	−	7.00344i	0.500420	−	0.980678i
$52$	−3.46792	−	0.986674i	−0.480914	−	0.136827i
$53$	−5.41458	+	3.12611i	−0.743749	+	0.429404i	−0.823431	−	0.567417i	$-0.807943\pi$
$53$	−5.41458	+	3.12611i	−0.743749	+	0.429404i	0.0796817	+	0.996820i	$0.474610\pi$
$54$	3.26279	+	4.04403i	0.444009	+	0.550323i
$55$	−19.0468	−	10.9967i	−2.56827	−	1.48279i
$56$	2.49160	+	0.889895i	0.332954	+	0.118917i
$57$	4.94143	−	0.256004i	0.654509	−	0.0339086i
$58$			2.54344i			0.333971i
$59$	8.67545	+	5.00877i	1.12945	+	0.652087i	0.943796	−	0.330529i	$-0.107227\pi$
$59$	8.67545	+	5.00877i	1.12945	+	0.652087i	0.185652	+	0.982616i	$0.440560\pi$
$60$	5.50246	−	3.56866i	0.710365	−	0.460712i
$61$		−	3.64451i		−	0.466632i	−0.972401	−	0.233316i	$-0.925042\pi$
$61$		−	3.64451i		−	0.466632i	0.972401	−	0.233316i	$-0.0749576\pi$
$62$	0.824954	−	1.42886i	0.104769	−	0.181466i
$63$	7.71067	+	1.88296i	0.971453	+	0.237231i
$64$	1.00000			0.125000
$65$	−3.73603	+	13.1312i	−0.463397	+	1.62873i
$66$	−5.47423	−	8.44064i	−0.673832	−	1.03897i
$67$		−	10.6760i		−	1.30428i	−0.758099	−	0.652139i	$-0.773872\pi$
$67$		−	10.6760i		−	1.30428i	0.758099	−	0.652139i	$-0.226128\pi$
$68$	−2.26972	−	3.93127i	−0.275244	−	0.476737i
$69$	−7.04644	+	4.57002i	−0.848292	+	0.550166i
$70$	3.36958	−	9.43442i	0.402741	−	1.12763i
$71$	6.77969	+	11.7428i	0.804602	+	1.39361i	0.916560	+	0.399898i	$0.130954\pi$
$71$	6.77969	+	11.7428i	0.804602	+	1.39361i	−0.111958	+	0.993713i	$0.535712\pi$
$72$	2.98394	−	0.310014i	0.351661	−	0.0365355i
$73$	−2.19097	−	3.79486i	−0.256433	−	0.444155i	0.708851	−	0.705359i	$-0.249214\pi$
$73$	−2.19097	−	3.79486i	−0.256433	−	0.444155i	−0.965284	+	0.261203i	$0.915881\pi$
$74$	0.865515	+	0.499705i	0.100614	+	0.0580895i
$75$	−8.80032	−	13.5691i	−1.01617	−	1.56682i
$76$	1.42838	−	2.47403i	0.163847	−	0.283791i
$77$	−14.4722	−	5.16884i	−1.64926	−	0.589044i
$78$	−4.25239	+	4.57353i	−0.481488	+	0.517851i
$79$	−8.40177	+	14.5523i	−0.945273	+	1.63726i	−0.190071	+	0.981770i	$0.560872\pi$
$79$	−8.40177	+	14.5523i	−0.945273	+	1.63726i	−0.755203	+	0.655491i	$0.772462\pi$
$80$		−	3.78649i		−	0.423342i
$81$	8.80778	−	1.85013i	0.978643	−	0.205570i
$82$		−	4.02657i		−	0.444660i
$83$		−	11.9716i		−	1.31405i	−0.753867	−	0.657027i	$-0.771814\pi$
$83$		−	11.9716i		−	1.31405i	0.753867	−	0.657027i	$-0.228186\pi$
$84$	3.33446	−	3.14346i	0.363820	−	0.342980i
$85$	−14.8857	+	8.59427i	−1.61458	+	0.932180i
$86$	−0.445979	+	0.772459i	−0.0480912	+	0.0832963i
$87$	3.92402	+	2.00235i	0.420699	+	0.214674i
$88$	−5.80837			−0.619175
$89$	1.89510	−	1.09414i	0.200880	−	0.115978i	−0.396186	−	0.918170i	$-0.629666\pi$
$89$	1.89510	−	1.09414i	0.200880	−	0.115978i	0.597066	+	0.802192i	$0.296333\pi$
$90$	−1.17386	−	11.2986i	−0.123736	−	1.19098i
$91$	−0.920344	+	9.49489i	−0.0964782	+	0.995335i
$92$			4.84897i			0.505540i
$93$	−1.55499	−	2.39762i	−0.161245	−	0.248622i
$94$		−	7.19940i		−	0.742561i
$95$	−9.36788	−	5.40855i	−0.961125	−	0.554906i
$96$	0.787258	−	1.54280i	0.0803492	−	0.157461i
$97$	−6.30970	−	10.9287i	−0.640653	−	1.10964i	−0.985287	−	0.170907i	$-0.945330\pi$
$97$	−6.30970	−	10.9287i	−0.640653	−	1.10964i	0.344634	−	0.938737i	$-0.388003\pi$
$98$	1.13233	−	6.90781i	0.114383	−	0.697794i
$99$	−17.3318	+	1.80068i	−1.74191	+	0.180975i
$100$	−9.33748			−0.933748
$101$	9.69158			0.964348			0.482174	−	0.876076i	$-0.339847\pi$
$101$	9.69158			0.964348			0.482174	+	0.876076i	$0.339847\pi$
$102$	−7.85202	+	0.406795i	−0.777465	+	0.0402787i
$103$	2.94432	+	1.69990i	0.290112	+	0.167496i	0.637992	−	0.770043i	$-0.279765\pi$
$103$	2.94432	+	1.69990i	0.290112	+	0.167496i	−0.347880	+	0.937539i	$0.613098\pi$
$104$	0.879475	+	3.49664i	0.0862397	+	0.342874i
$105$	−11.9027	−	12.6259i	−1.16158	−	1.23216i
$106$	5.41458	+	3.12611i	0.525910	+	0.303634i
$107$	−7.66260	+	4.42400i	−0.740771	+	0.427684i	−0.822350	−	0.568982i	$-0.807337\pi$
$107$	−7.66260	+	4.42400i	−0.740771	+	0.427684i	0.0815784	+	0.996667i	$0.474004\pi$
$108$	1.87084	−	4.84768i	0.180022	−	0.466468i
$109$	−2.56093	+	1.47855i	−0.245292	+	0.141620i	−0.617607	−	0.786487i	$-0.711898\pi$
$109$	−2.56093	+	1.47855i	−0.245292	+	0.141620i	0.372314	+	0.928107i	$0.378564\pi$
$110$			21.9933i			2.09698i
$111$	1.45233	−	0.941917i	0.137849	−	0.0894028i
$112$	−0.475130	−	2.60274i	−0.0448955	−	0.245936i
$113$	8.71628	−	5.03235i	0.819959	−	0.473403i	−0.0304434	−	0.999536i	$-0.509692\pi$
$113$	8.71628	−	5.03235i	0.819959	−	0.473403i	0.850402	+	0.526133i	$0.176359\pi$
$114$	−2.69242	−	4.15141i	−0.252169	−	0.388815i
$115$	18.3606			1.71213
$116$	2.20269	−	1.27172i	0.204514	−	0.118076i
$117$	3.70831	+	10.1611i	0.342833	+	0.939396i
$118$		−	10.0175i		−	0.922190i
$119$	−9.15367	+	7.77536i	−0.839115	+	0.712766i
$120$	−5.84178	−	2.98094i	−0.533279	−	0.272122i
$121$	22.7372			2.06702
$122$	−3.15624	+	1.82226i	−0.285753	+	0.164979i
$123$	−6.21218	−	3.16995i	−0.560133	−	0.285824i
$124$	−1.64991			−0.148166
$125$			16.4238i			1.46899i
$126$	−2.22464	−	7.61912i	−0.198187	−	0.678765i
$127$	−0.534780	+	0.926266i	−0.0474540	+	0.0821928i	−0.888777	−	0.458340i	$-0.848444\pi$
$127$	−0.534780	+	0.926266i	−0.0474540	+	0.0821928i	0.841323	+	0.540533i	$0.181777\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	0.840647	+	1.29618i	0.0740148	+	0.114122i
$130$	13.2400	−	3.33012i	1.16122	−	0.292071i
$131$	6.27140	−	10.8624i	0.547935	−	0.949051i	−0.450481	−	0.892786i	$-0.648747\pi$
$131$	6.27140	−	10.8624i	0.547935	−	0.949051i	0.998416	−	0.0562650i	$-0.0179192\pi$
$132$	−4.57269	+	8.96114i	−0.398001	+	0.779967i
$133$	−7.11792	−	2.54222i	−0.617202	−	0.220439i
$134$	−9.24567	+	5.33799i	−0.798704	+	0.461132i
$135$	−18.3557	−	7.08391i	−1.57980	−	0.609686i
$136$	−2.26972	+	3.93127i	−0.194627	+	0.337104i
$137$	7.77614	−	13.4687i	0.664360	−	1.15071i	−0.315098	−	0.949059i	$-0.602037\pi$
$137$	7.77614	−	13.4687i	0.664360	−	1.15071i	0.979458	−	0.201647i	$-0.0646292\pi$
$138$	7.48098	+	3.81739i	0.636823	+	0.324958i
$139$	7.60046	−	4.38812i	0.644662	−	0.372196i	−0.141746	−	0.989903i	$-0.545272\pi$
$139$	7.60046	−	4.38812i	0.644662	−	0.372196i	0.786408	+	0.617707i	$0.211938\pi$
$140$	−9.85524	+	1.79907i	−0.832920	+	0.152049i
$141$	−11.1072	−	5.66778i	−0.935396	−	0.477313i
$142$	6.77969	−	11.7428i	0.568939	−	0.985432i
$143$	−5.10832	−	20.3098i	−0.427179	−	1.69839i
$144$	−1.76045	−	2.42916i	−0.146704	−	0.202430i
$145$	−4.81536	−	8.34045i	−0.399894	−	0.692637i
$146$	−2.19097	+	3.79486i	−0.181326	+	0.314065i
$147$	−9.76592	−	7.18519i	−0.805479	−	0.592624i
$148$		−	0.999410i		−	0.0821510i
$149$	−3.07378			−0.251814			−0.125907	−	0.992042i	$-0.540184\pi$
$149$	−3.07378			−0.251814			−0.125907	+	0.992042i	$0.540184\pi$
$150$	−7.35101	+	14.4058i	−0.600207	+	1.17623i
$151$	−10.9434	+	6.31820i	−0.890564	+	0.514167i	−0.874127	−	0.485697i	$-0.838566\pi$
$151$	−10.9434	+	6.31820i	−0.890564	+	0.514167i	−0.0164372	+	0.999865i	$0.505232\pi$
$152$	−2.85676			−0.231714
$153$	−5.55396	+	12.4343i	−0.449011	+	1.00526i
$154$	2.75973	+	15.1177i	0.222385	+	1.21822i
$155$			6.24735i			0.501799i
$156$	6.08699	+	1.39591i	0.487349	+	0.111762i
$157$	8.31434	−	4.80029i	0.663556	−	0.383104i	−0.130074	−	0.991504i	$-0.541522\pi$
$157$	8.31434	−	4.80029i	0.663556	−	0.383104i	0.793631	+	0.608400i	$0.208188\pi$
$158$	16.8035			1.33682
$159$	9.08562	−	5.89254i	0.720536	−	0.467309i
$160$	−3.27919	+	1.89324i	−0.259243	+	0.149674i
$161$	12.6206	−	2.30389i	0.994643	−	0.181572i
$162$	−6.00615	−	6.70270i	−0.471888	−	0.526614i
$163$		−	6.37701i		−	0.499486i	−0.968312	−	0.249743i	$-0.919654\pi$
$163$		−	6.37701i		−	0.499486i	0.968312	−	0.249743i	$-0.0803462\pi$
$164$	−3.48711	+	2.01328i	−0.272297	+	0.157211i
$165$	33.9313	+	17.3144i	2.64154	+	1.34793i
$166$	−10.3677	+	5.98580i	−0.804691	+	0.464589i
$167$	6.39087	+	3.68977i	0.494540	+	0.285523i	0.726456	−	0.687213i	$-0.241166\pi$
$167$	6.39087	+	3.68977i	0.494540	+	0.285523i	−0.231916	+	0.972736i	$0.574499\pi$
$168$	−4.38955	−	1.31600i	−0.338661	−	0.101531i
$169$	−11.4530	+	6.15043i	−0.881004	+	0.473110i
$170$	14.8857	+	8.59427i	1.14168	+	0.659151i
$171$	−8.52441	+	0.885637i	−0.651878	+	0.0677264i
$172$	0.891958			0.0680112
$173$	5.09827			0.387615			0.193807	−	0.981040i	$-0.437916\pi$
$173$	5.09827			0.387615			0.193807	+	0.981040i	$0.437916\pi$
$174$	−0.227927	−	4.39948i	−0.0172791	−	0.333523i
$175$	4.43651	+	24.3030i	0.335369	+	1.83714i
$176$	2.90419	+	5.03020i	0.218911	+	0.379165i
$177$	−15.4550	−	7.88639i	−1.16167	−	0.592778i
$178$	−1.89510	−	1.09414i	−0.142044	−	0.0820089i
$179$			8.59359i			0.642315i	0.947026	+	0.321158i	$0.104072\pi$
$179$			8.59359i			0.642315i	−0.947026	+	0.321158i	$0.895928\pi$
$180$	−9.19798	+	6.66592i	−0.685577	+	0.496848i
$181$		−	2.78775i		−	0.207211i	−0.994618	−	0.103606i	$-0.966962\pi$
$181$		−	2.78775i		−	0.207211i	0.994618	−	0.103606i	$-0.0330380\pi$
$182$	8.68299	−	3.95040i	0.643626	−	0.292823i
$183$	0.326597	+	6.30402i	0.0241427	+	0.466007i
$184$	4.19933	−	2.42448i	0.309579	−	0.178735i
$185$	−3.78425			−0.278224
$186$	−1.29890	+	2.54547i	−0.0952402	+	0.186643i
$187$	13.1834	−	22.8343i	0.964065	−	1.66981i
$188$	−6.23486	+	3.59970i	−0.454724	+	0.262535i
$189$	−13.5061	−	2.56604i	−0.982426	−	0.186652i
$190$			10.8171i			0.784755i
$191$		−	19.5216i		−	1.41253i	−0.707946	−	0.706267i	$-0.750378\pi$
$191$		−	19.5216i		−	1.41253i	0.707946	−	0.706267i	$-0.249622\pi$
$192$	−1.72973	+	0.0896134i	−0.124833	+	0.00646729i
$193$			6.34486i			0.456713i	0.973578	+	0.228357i	$0.0733352\pi$
$193$			6.34486i			0.456713i	−0.973578	+	0.228357i	$0.926665\pi$
$194$	−6.30970	+	10.9287i	−0.453010	+	0.784637i
$195$	5.28559	−	23.0483i	0.378509	−	1.65052i
$196$	−6.54850	+	2.47328i	−0.467750	+	0.176663i
$197$	4.25750	−	7.37421i	0.303334	−	0.525391i	−0.673555	−	0.739137i	$-0.735233\pi$
$197$	4.25750	−	7.37421i	0.303334	−	0.525391i	0.976889	+	0.213747i	$0.0685668\pi$
$198$	10.2253	+	14.1095i	0.726684	+	1.00272i
$199$	−1.46494	−	0.845782i	−0.103847	−	0.0599559i	0.447177	−	0.894445i	$-0.352429\pi$
$199$	−1.46494	−	0.845782i	−0.103847	−	0.0599559i	−0.551024	+	0.834489i	$0.685763\pi$
$200$	4.66874	+	8.08650i	0.330130	+	0.571802i
$201$	0.956711	+	18.4666i	0.0674812	+	1.30253i
$202$	−4.84579	−	8.39315i	−0.340948	−	0.590540i
$203$	−4.35652	−	5.12879i	−0.305768	−	0.359970i
$204$	4.27830	+	6.59665i	0.299541	+	0.461858i
$205$	7.62327	+	13.2039i	0.532432	+	0.922200i
$206$		−	3.39980i		−	0.236876i
$207$	11.7789	−	8.53636i	0.818691	−	0.593318i
$208$	2.58845	−	2.50997i	0.179476	−	0.174035i
$209$	16.5932			1.14777
$210$	−4.98301	+	16.6210i	−0.343860	+	1.14696i
$211$	11.5387	−	19.9857i	0.794360	−	1.37587i	−0.128885	−	0.991660i	$-0.541140\pi$
$211$	11.5387	−	19.9857i	0.794360	−	1.37587i	0.923245	−	0.384213i	$-0.125527\pi$
$212$		−	6.25221i		−	0.429404i
$213$	−12.7794	−	19.7043i	−0.875627	−	1.35012i
$214$	7.66260	+	4.42400i	0.523804	+	0.302419i
$215$		−	3.37739i		−	0.230336i
$216$	−5.13363	+	0.803642i	−0.349299	+	0.0546809i
$217$	0.783920	+	4.29428i	0.0532160	+	0.291515i
$218$	2.56093	+	1.47855i	0.173448	+	0.100140i
$219$	4.12985	+	6.36775i	0.279070	+	0.430293i
$220$	19.0468	−	10.9967i	1.28413	−	0.741395i
$221$	−15.7424	−	4.47895i	−1.05895	−	0.301287i
$222$	−1.54189	−	0.786794i	−0.103485	−	0.0528061i
$223$	−8.68120	+	15.0363i	−0.581336	+	1.00690i	0.413985	+	0.910284i	$0.364136\pi$
$223$	−8.68120	+	15.0363i	−0.581336	+	1.00690i	−0.995321	+	0.0966199i	$0.969197\pi$
$224$	−2.01647	+	1.71284i	−0.134731	+	0.114444i
$225$	16.4382	+	22.6822i	1.09588	+	1.51215i
$226$	−8.71628	−	5.03235i	−0.579798	−	0.334747i
$227$	−16.5863	−	9.57612i	−1.10087	−	0.635589i	−0.164423	−	0.986390i	$-0.552576\pi$
$227$	−16.5863	−	9.57612i	−1.10087	−	0.635589i	−0.936450	+	0.350801i	$0.885909\pi$
$228$	−2.24901	+	4.40741i	−0.148944	+	0.291888i
$229$	8.79153	−	15.2274i	0.580960	−	1.00625i	−0.414405	−	0.910092i	$-0.636010\pi$
$229$	8.79153	−	15.2274i	0.580960	−	1.00625i	0.995366	−	0.0961607i	$-0.0306563\pi$
$230$	−9.18028	−	15.9007i	−0.605330	−	1.04846i
$231$	25.4961	+	7.64381i	1.67752	+	0.502926i
$232$	−2.20269	−	1.27172i	−0.144614	−	0.0834927i
$233$	−1.22176	−	0.705386i	−0.0800405	−	0.0462114i	0.459446	−	0.888206i	$-0.348048\pi$
$233$	−1.22176	−	0.705386i	−0.0800405	−	0.0462114i	−0.539486	+	0.841995i	$0.681381\pi$
$234$	6.94564	−	8.29205i	0.454050	−	0.542068i
$235$	13.6302	+	23.6082i	0.889137	+	1.54003i
$236$	−8.67545	+	5.00877i	−0.564724	+	0.326043i
$237$	13.2287	−	25.9245i	0.859298	−	1.68398i
$238$	11.3105	+	4.03963i	0.733150	+	0.261850i
$239$	−22.2321			−1.43807			−0.719037	−	0.694972i	$-0.755417\pi$
$239$	−22.2321			−1.43807			−0.719037	+	0.694972i	$0.755417\pi$
$240$	0.339320	+	6.54960i	0.0219030	+	0.422775i
$241$	6.09368	−	10.5546i	0.392528	−	0.679879i	−0.600254	−	0.799810i	$-0.704934\pi$
$241$	6.09368	−	10.5546i	0.392528	−	0.679879i	0.992782	+	0.119930i	$0.0382671\pi$
$242$	−11.3686	−	19.6910i	−0.730801	−	1.26578i
$243$	−15.0693	+	3.98952i	−0.966696	+	0.255928i
$244$	3.15624	+	1.82226i	0.202058	+	0.116658i
$245$	9.36503	+	24.7958i	0.598310	+	1.58415i
$246$	0.360834	+	6.96487i	0.0230059	+	0.444064i
$247$	−2.51245	−	9.98909i	−0.159864	−	0.635591i
$248$	0.824954	+	1.42886i	0.0523846	+	0.0907328i
$249$	1.07282	+	20.7077i	0.0679870	+	1.31229i
$250$	14.2234	−	8.21191i	0.899570	−	0.519367i
$251$	4.15920	+	7.20395i	0.262527	+	0.454709i	0.966913	−	0.255108i	$-0.0821109\pi$
$251$	4.15920	+	7.20395i	0.262527	+	0.454709i	−0.704386	+	0.709817i	$0.748778\pi$
$252$	−5.48603	+	5.73616i	−0.345587	+	0.361344i
$253$	−24.3913	+	14.0823i	−1.53347	+	0.885347i
$254$	1.06956			0.0671101
$255$	24.9781	−	16.1997i	1.56419	−	1.01447i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.0205	−	19.0880i	−0.687438	−	1.19068i	−0.972664	−	0.232218i	$-0.925402\pi$
$257$	−11.0205	−	19.0880i	−0.687438	−	1.19068i	0.285225	−	0.958460i	$-0.407932\pi$
$258$	0.702201	−	1.37611i	0.0437171	−	0.0856729i
$259$	−2.60120	+	0.474849i	−0.161631	+	0.0295057i
$260$	−9.50397	−	9.80111i	−0.589411	−	0.607839i
$261$	−6.96694	−	3.11188i	−0.431243	−	0.192620i
$262$	−12.5428			−0.774897
$263$		−	17.2999i		−	1.06676i	−0.845876	−	0.533379i	$-0.820922\pi$
$263$		−	17.2999i		−	1.06676i	0.845876	−	0.533379i	$-0.179078\pi$
$264$	10.0469	−	0.520508i	0.618345	−	0.0320350i
$265$	−23.6739			−1.45428
$266$	1.35733	+	7.43541i	0.0832235	+	0.455894i
$267$	−3.17996	+	2.06239i	−0.194610	+	0.126216i
$268$	9.24567	+	5.33799i	0.564769	+	0.326070i
$269$	−3.78505	+	6.55589i	−0.230778	+	0.399720i	−0.958037	−	0.286643i	$-0.907461\pi$
$269$	−3.78505	+	6.55589i	−0.230778	+	0.399720i	0.727259	+	0.686363i	$0.240794\pi$
$270$	3.04298	+	19.4384i	0.185190	+	1.18298i
$271$	−1.03693	−	1.79602i	−0.0629893	−	0.109101i	0.832811	−	0.553557i	$-0.186730\pi$
$271$	−1.03693	−	1.79602i	−0.0629893	−	0.109101i	−0.895800	+	0.444457i	$0.853397\pi$
$272$	4.53944			0.275244
$273$	0.741078	−	16.5061i	0.0448521	−	0.998994i
$274$	−15.5523			−0.939547
$275$	−27.1178	−	46.9694i	−1.63526	−	2.83236i
$276$	−0.434532	−	8.38741i	−0.0261558	−	0.504863i
$277$	11.8359	−	20.5004i	0.711150	−	1.23175i	−0.253276	−	0.967394i	$-0.581508\pi$
$277$	11.8359	−	20.5004i	0.711150	−	1.23175i	0.964426	−	0.264354i	$-0.0851586\pi$
$278$	−7.60046	−	4.38812i	−0.455845	−	0.263182i
$279$	2.90458	+	4.00789i	0.173893	+	0.239946i
$280$	6.48566	+	7.63535i	0.387592	+	0.456299i
$281$	25.8285			1.54080			0.770400	−	0.637561i	$-0.220056\pi$
$281$	25.8285			1.54080			0.770400	+	0.637561i	$0.220056\pi$
$282$	0.645162	+	12.4530i	0.0384189	+	0.741566i
$283$			16.8235i			1.00005i	0.866011	+	0.500026i	$0.166676\pi$
$283$			16.8235i			1.00005i	−0.866011	+	0.500026i	$0.833324\pi$
$284$	−13.5594			−0.804602
$285$	16.6886	+	8.51585i	0.988547	+	0.504435i
$286$	−15.0347	+	14.5788i	−0.889018	+	0.862065i
$287$	6.89688	+	8.11946i	0.407110	+	0.479277i
$288$	−1.22349	+	2.73917i	−0.0720948	+	0.161407i
$289$	−1.80327	−	3.12336i	−0.106075	−	0.183727i
$290$	−4.81536	+	8.34045i	−0.282768	+	0.489768i
$291$	11.8934	+	18.3383i	0.697206	+	1.07501i
$292$	4.38193			0.256433
$293$	−23.6154	+	13.6344i	−1.37963	+	0.796529i	−0.992115	−	0.125335i	$-0.960000\pi$
$293$	−23.6154	+	13.6344i	−1.37963	+	0.796529i	−0.387514	+	0.921864i	$0.626666\pi$
$294$	−1.33960	+	12.0501i	−0.0781268	+	0.702777i
$295$	18.9657	+	32.8495i	1.10422	+	1.91257i
$296$	−0.865515	+	0.499705i	−0.0503070	+	0.0290448i
$297$	29.8180	−	4.66785i	1.73022	−	0.270856i
$298$	1.53689	+	2.66197i	0.0890297	+	0.154204i
$299$	12.1708	+	12.5513i	0.703854	+	0.725860i
$300$	16.1513	−	0.836763i	0.932498	−	0.0483106i
$301$	−0.423796	−	2.32153i	−0.0244272	−	0.133811i
$302$	10.9434	+	6.31820i	0.629724	+	0.363571i
$303$	−16.7638	+	0.868495i	−0.963056	+	0.0498937i
$304$	1.42838	+	2.47403i	0.0819233	+	0.141895i
$305$	6.89995	−	11.9511i	0.395090	−	0.684316i
$306$	13.5454	−	1.40729i	0.774340	−	0.0804495i
$307$	22.9818			1.31164			0.655821	−	0.754917i	$-0.272323\pi$
$307$	22.9818			1.31164			0.655821	+	0.754917i	$0.272323\pi$
$308$	11.7124	−	9.94884i	0.667378	−	0.566888i
$309$	−5.24521	−	2.67652i	−0.298390	−	0.152262i
$310$	5.41037	−	3.12368i	0.307288	−	0.177413i
$311$	15.9662	+	27.6543i	0.905360	+	1.56813i	0.820434	+	0.571742i	$0.193732\pi$
$311$	15.9662	+	27.6543i	0.905360	+	1.56813i	0.0849258	+	0.996387i	$0.472935\pi$
$312$	−1.83460	−	5.96944i	−0.103864	−	0.337953i
$313$	−5.32050	−	3.07179i	−0.300732	−	0.173628i	0.342039	−	0.939686i	$-0.388882\pi$
$313$	−5.32050	−	3.07179i	−0.300732	−	0.173628i	−0.642772	+	0.766058i	$0.722216\pi$
$314$	−8.31434	−	4.80029i	−0.469205	−	0.270896i
$315$	21.7199	+	20.7728i	1.22378	+	1.17041i
$316$	−8.40177	−	14.5523i	−0.472637	−	0.818631i
$317$	−7.01958	+	12.1583i	−0.394259	+	0.682877i	−0.993006	−	0.118061i	$-0.962332\pi$
$317$	−7.01958	+	12.1583i	−0.394259	+	0.682877i	0.598747	+	0.800938i	$0.295665\pi$
$318$	−9.64590	−	4.92211i	−0.540915	−	0.276018i
$319$	12.7940	+	7.38664i	0.716328	+	0.413572i
$320$	3.27919	+	1.89324i	0.183313	+	0.105836i
$321$	12.8578	−	8.33901i	0.717651	−	0.465438i
$322$	−8.30553	−	9.77782i	−0.462849	−	0.544896i
$323$	6.48406	−	11.2307i	0.360783	−	0.624894i
$324$	−2.80163	+	8.55283i	−0.155646	+	0.475157i
$325$	−24.1696	+	23.4368i	−1.34069	+	1.30004i
$326$	−5.52266	+	3.18851i	−0.305872	+	0.176595i
$327$	4.29722	−	2.78699i	0.237637	−	0.154121i
$328$	3.48711	+	2.01328i	0.192543	+	0.111165i
$329$	12.3314	+	14.5174i	0.679854	+	0.800370i
$330$	−1.97090	−	38.0425i	−0.108494	−	2.09417i
$331$			8.26910i			0.454511i	0.973835	+	0.227256i	$0.0729753\pi$
$331$			8.26910i			0.454511i	−0.973835	+	0.227256i	$0.927025\pi$
$332$	10.3677	+	5.98580i	0.569002	+	0.328514i
$333$	−2.42773	+	1.75941i	−0.133039	+	0.0964151i
$334$		−	7.37954i		−	0.403790i
$335$	20.2122	−	35.0086i	1.10431	−	1.91272i
$336$	1.05509	+	4.45946i	0.0575597	+	0.243284i
$337$	8.78687			0.478651			0.239326	−	0.970939i	$-0.423074\pi$
$337$	8.78687			0.478651			0.239326	+	0.970939i	$0.423074\pi$
$338$	11.0529	+	6.84342i	0.601201	+	0.372233i
$339$	−14.6259	+	9.48570i	−0.794368	+	0.515193i
$340$		−	17.1885i		−	0.932180i
$341$	−4.79164	−	8.29936i	−0.259482	−	0.449436i
$342$	5.02919	+	6.93954i	0.271947	+	0.375247i
$343$	9.54868	+	15.8689i	0.515580	+	0.856841i
$344$	−0.445979	−	0.772459i	−0.0240456	−	0.0416482i
$345$	−31.7588	+	1.64535i	−1.70984	+	0.0885827i
$346$	−2.54914	−	4.41523i	−0.137042	−	0.237364i
$347$	14.2076	+	8.20275i	0.762703	+	0.440347i	0.830265	−	0.557369i	$-0.188189\pi$
$347$	14.2076	+	8.20275i	0.762703	+	0.440347i	−0.0675627	+	0.997715i	$0.521522\pi$
$348$	−3.69609	+	2.39713i	−0.198131	+	0.128500i
$349$	−4.38530	+	7.59556i	−0.234740	+	0.406581i	−0.959197	−	0.282739i	$-0.908757\pi$
$349$	−4.38530	+	7.59556i	−0.234740	+	0.406581i	0.724457	+	0.689320i	$0.242090\pi$
$350$	18.8288	−	15.9936i	1.00644	−	0.854897i
$351$	−7.32495	−	17.2437i	−0.390977	−	0.920400i
$352$	2.90419	−	5.03020i	0.154794	−	0.268110i
$353$			19.5330i			1.03964i	0.854276	+	0.519819i	$0.174001\pi$
$353$			19.5330i			1.03964i	−0.854276	+	0.519819i	$0.825999\pi$
$354$	0.897706	+	17.3277i	0.0477126	+	0.920955i
$355$			51.3424i			2.72497i
$356$			2.18827i			0.115978i
$357$	15.1366	−	14.2696i	0.801114	−	0.755226i
$358$	7.44227	−	4.29680i	0.393336	−	0.227093i
$359$	−1.54798	+	2.68118i	−0.0816994	+	0.141507i	−0.903980	−	0.427575i	$-0.859368\pi$
$359$	−1.54798	+	2.68118i	−0.0816994	+	0.141507i	0.822281	+	0.569082i	$0.192701\pi$
$360$	10.3718	+	4.63273i	0.546644	+	0.244166i
$361$	−10.8389			−0.570468
$362$	−2.41426	+	1.39387i	−0.126891	+	0.0732603i
$363$	−39.3292	+	2.03756i	−2.06425	+	0.106944i
$364$	−7.76265	−	5.54449i	−0.406873	−	0.290610i
$365$		−	16.5921i		−	0.868472i
$366$	5.29615	−	3.43485i	0.276834	−	0.179543i
$367$		−	8.10993i		−	0.423335i	−0.977342	−	0.211667i	$-0.932111\pi$
$367$		−	8.10993i		−	0.423335i	0.977342	−	0.211667i	$-0.0678893\pi$
$368$	−4.19933	−	2.42448i	−0.218905	−	0.126385i
$369$	11.0295	+	4.92646i	0.574171	+	0.256461i
$370$	1.89213	+	3.27726i	0.0983670	+	0.170377i
$371$	−16.2729	+	2.97061i	−0.844846	+	0.154226i
$372$	2.85390	−	0.147854i	0.147968	−	0.00766586i
$373$	−20.3888			−1.05569			−0.527845	−	0.849341i	$-0.677000\pi$
$373$	−20.3888			−1.05569			−0.527845	+	0.849341i	$0.677000\pi$
$374$	−26.3668			−1.36339
$375$	−1.47179	−	28.4088i	−0.0760031	−	1.46702i
$376$	6.23486	+	3.59970i	0.321538	+	0.185640i
$377$	2.50955	−	8.82046i	0.129248	−	0.454277i
$378$	4.53081	+	12.9797i	0.233040	+	0.667602i
$379$	−16.2771	−	9.39758i	−0.836098	−	0.482721i	0.0198382	−	0.999803i	$-0.493685\pi$
$379$	−16.2771	−	9.39758i	−0.836098	−	0.482721i	−0.855936	+	0.517082i	$0.827018\pi$
$380$	9.36788	−	5.40855i	0.480562	−	0.277453i
$381$	0.842019	−	1.65011i	0.0431379	−	0.0845379i
$382$	−16.9062	+	9.76080i	−0.864997	+	0.499406i
$383$		−	24.7285i		−	1.26357i	−0.775144	−	0.631785i	$-0.782323\pi$
$383$		−	24.7285i		−	1.26357i	0.775144	−	0.631785i	$-0.217677\pi$
$384$	0.942473	+	1.45318i	0.0480954	+	0.0741575i
$385$	−37.6711	−	44.3490i	−1.91990	−	2.26023i
$386$	5.49481	−	3.17243i	0.279679	−	0.161472i
$387$	−1.57025	−	2.16671i	−0.0798202	−	0.110140i
$388$	12.6194			0.640653
$389$	−7.93751	+	4.58272i	−0.402448	+	0.232353i	−0.687540	−	0.726147i	$-0.741309\pi$
$389$	−7.93751	+	4.58272i	−0.402448	+	0.232353i	0.285092	+	0.958500i	$0.407976\pi$
$390$	−22.6032	+	6.94670i	−1.14456	+	0.351760i
$391$			22.0116i			1.11318i
$392$	5.41617	+	4.43453i	0.273558	+	0.223978i
$393$	−9.87442	+	19.3510i	−0.498099	+	0.976129i
$394$	−8.51500			−0.428980
$395$	−55.1021	+	31.8132i	−2.77249	+	1.60070i
$396$	7.10648	−	15.9101i	0.357114	−	0.799515i
$397$	3.38446			0.169861			0.0849306	−	0.996387i	$-0.472933\pi$
$397$	3.38446			0.169861			0.0849306	+	0.996387i	$0.472933\pi$
$398$			1.69156i			0.0847905i
$399$	12.5399	+	3.75950i	0.627781	+	0.188210i
$400$	4.66874	−	8.08650i	0.233437	−	0.404325i
$401$	3.62565	+	6.27981i	0.181056	+	0.313599i	0.942240	−	0.334937i	$-0.108715\pi$
$401$	3.62565	+	6.27981i	0.181056	+	0.313599i	−0.761184	+	0.648536i	$0.775382\pi$
$402$	15.5142	−	10.0618i	0.773776	−	0.501838i
$403$	−4.27070	+	4.14122i	−0.212738	+	0.206289i
$404$	−4.84579	+	8.39315i	−0.241087	+	0.417575i
$405$	32.3852	+	10.6084i	1.60923	+	0.527133i
$406$	−2.26340	+	6.33725i	−0.112331	+	0.314513i
$407$	5.02723	−	2.90247i	0.249191	−	0.143870i
$408$	3.57371	−	7.00344i	0.176925	−	0.346722i
$409$	0.787302	−	1.36365i	0.0389296	−	0.0674280i	−0.845904	−	0.533335i	$-0.820939\pi$
$409$	0.787302	−	1.36365i	0.0389296	−	0.0674280i	0.884834	+	0.465907i	$0.154272\pi$
$410$	7.62327	−	13.2039i	0.376486	−	0.652094i
$411$	−12.2437	+	23.9940i	−0.603935	+	1.18354i
$412$	−2.94432	+	1.69990i	−0.145056	+	0.0837482i
$413$	17.1585	+	20.2001i	0.844314	+	0.993983i
$414$	−13.2822	−	5.93266i	−0.652783	−	0.291574i
$415$	22.6652	−	39.2572i	1.11259	−	1.92706i
$416$	−3.46792	−	0.986674i	−0.170029	−	0.0483757i
$417$	−12.7535	+	8.27138i	−0.624542	+	0.405051i
$418$	−8.29658	−	14.3701i	−0.405799	−	0.702864i
$419$	13.4922	−	23.3691i	0.659136	−	1.14166i	−0.321704	−	0.946840i	$-0.604255\pi$
$419$	13.4922	−	23.3691i	0.659136	−	1.14166i	0.980840	−	0.194817i	$-0.0624112\pi$
$420$	16.8857	−	3.99507i	0.823937	−	0.194940i
$421$		−	13.0461i		−	0.635827i	−0.948120	−	0.317913i	$-0.897018\pi$
$421$		−	13.0461i		−	0.635827i	0.948120	−	0.317913i	$-0.102982\pi$
$422$	−23.0775			−1.12339
$423$	19.7204	+	8.80838i	0.958839	+	0.428278i
$424$	−5.41458	+	3.12611i	−0.262955	+	0.151817i
$425$	−42.3870			−2.05607
$426$	−10.6747	+	20.9194i	−0.517193	+	1.01355i
$427$	3.24323	−	9.08068i	0.156951	−	0.439445i
$428$		−	8.84801i		−	0.427684i
$429$	10.6561	+	34.6727i	0.514479	+	1.67402i
$430$	−2.92490	+	1.68869i	−0.141051	+	0.0814361i
$431$	−36.5042			−1.75835			−0.879173	−	0.476503i	$-0.841904\pi$
$431$	−36.5042			−1.75835			−0.879173	+	0.476503i	$0.841904\pi$
$432$	3.26279	+	4.04403i	0.156981	+	0.194569i
$433$	23.6502	−	13.6545i	1.13656	−	0.656192i	0.190982	−	0.981594i	$-0.438833\pi$
$433$	23.6502	−	13.6545i	1.13656	−	0.656192i	0.945576	+	0.325402i	$0.105499\pi$
$434$	3.32699	−	2.82603i	0.159701	−	0.135654i
$435$	9.07669	+	13.9952i	0.435194	+	0.671019i
$436$		−	2.95710i		−	0.141620i
$437$	−11.9965	+	6.92618i	−0.573870	+	0.331324i
$438$	3.44971	−	6.76043i	0.164834	−	0.323026i
$439$	0.394663	−	0.227859i	0.0188362	−	0.0108751i	−0.490552	−	0.871412i	$-0.663205\pi$
$439$	0.394663	−	0.227859i	0.0188362	−	0.0108751i	0.509389	+	0.860537i	$0.329872\pi$
$440$	−19.0468	−	10.9967i	−0.908020	−	0.524245i
$441$	17.5363	+	11.5533i	0.835062	+	0.550156i
$442$	3.99233	+	15.8728i	0.189896	+	0.754993i
$443$	23.2231	+	13.4079i	1.10337	+	0.637028i	0.937103	−	0.349053i	$-0.113497\pi$
$443$	23.2231	+	13.4079i	1.10337	+	0.637028i	0.166262	+	0.986082i	$0.446830\pi$
$444$	0.0895605	+	1.72871i	0.00425035	+	0.0820410i
$445$	8.28586			0.392787
$446$	17.3624			0.822133
$447$	5.31681	−	0.275452i	0.251477	−	0.0130284i
$448$	2.49160	+	0.889895i	0.117717	+	0.0420436i
$449$	−0.402024	−	0.696326i	−0.0189727	−	0.0328616i	0.856383	−	0.516341i	$-0.172706\pi$
$449$	−0.402024	−	0.696326i	−0.0189727	−	0.0328616i	−0.875356	+	0.483479i	$0.839373\pi$
$450$	11.4243	−	25.5770i	0.538547	−	1.20571i
$451$	−20.2544	−	11.6939i	−0.953743	−	0.550644i
$452$			10.0647i			0.473403i
$453$	18.3630	−	11.9095i	0.862769	−	0.559555i
$454$			19.1522i			0.898859i
$455$	−20.9941	+	29.3932i	−0.984220	+	1.37797i
$456$	4.94143	−	0.256004i	0.231404	−	0.0119885i
$457$	13.1935	−	7.61727i	0.617166	−	0.356321i	−0.158599	−	0.987343i	$-0.550698\pi$
$457$	13.1935	−	7.61727i	0.617166	−	0.356321i	0.775765	+	0.631022i	$0.217364\pi$
$458$	−17.5831			−0.821602
$459$	8.49258	−	22.0057i	0.396400	−	1.02714i
$460$	−9.18028	+	15.9007i	−0.428033	+	0.741374i
$461$	11.4420	−	6.60603i	0.532906	−	0.307673i	−0.209293	−	0.977853i	$-0.567116\pi$
$461$	11.4420	−	6.60603i	0.532906	−	0.307673i	0.742199	+	0.670180i	$0.233783\pi$
$462$	−6.12834	−	25.9022i	−0.285116	−	1.20508i
$463$		−	15.4572i		−	0.718355i	−0.933269	−	0.359177i	$-0.883057\pi$
$463$		−	15.4572i		−	0.718355i	0.933269	−	0.359177i	$-0.116943\pi$
$464$			2.54344i			0.118076i
$465$	−0.559846	−	10.8062i	−0.0259623	−	0.501127i
$466$			1.41077i			0.0653528i
$467$	0.665574	−	1.15281i	0.0307991	−	0.0533456i	−0.850215	−	0.526436i	$-0.823528\pi$
$467$	0.665574	−	1.15281i	0.0307991	−	0.0533456i	0.881014	+	0.473090i	$0.156861\pi$
$468$	−10.6539	−	1.86907i	−0.492479	−	0.0863978i
$469$	9.50050	−	26.6003i	0.438693	−	1.22829i
$470$	13.6302	−	23.6082i	0.628715	−	1.08897i
$471$	−13.9514	+	9.04828i	−0.642847	+	0.416923i
$472$	8.67545	+	5.00877i	0.399320	+	0.230547i
$473$	2.59041	+	4.48673i	0.119107	+	0.206300i
$474$	−29.0656	+	1.50582i	−1.33503	+	0.0691647i
$475$	−13.3375	−	23.1012i	−0.611966	−	1.05996i
$476$	−2.15682	−	11.8150i	−0.0988579	−	0.541539i
$477$	−15.1876	+	11.0067i	−0.695394	+	0.503962i
$478$	11.1160	+	19.2535i	0.508436	+	0.880636i
$479$			14.4012i			0.658007i	0.944329	+	0.329003i	$0.106713\pi$
$479$			14.4012i			0.658007i	−0.944329	+	0.329003i	$0.893287\pi$
$480$	5.50246	−	3.56866i	0.251152	−	0.162886i
$481$	−2.50849	−	2.58692i	−0.114377	−	0.117953i
$482$	−12.1874			−0.555119
$483$	−21.6238	+	5.11608i	−0.983916	+	0.232790i
$484$	−11.3686	+	19.6910i	−0.516754	+	0.895045i
$485$		−	47.7832i		−	2.16972i
$486$	10.9897	+	11.0556i	0.498502	+	0.501494i
$487$	−26.4446	−	15.2678i	−1.19832	−	0.691849i	−0.238138	−	0.971231i	$-0.576537\pi$
$487$	−26.4446	−	15.2678i	−1.19832	−	0.691849i	−0.960180	+	0.279382i	$0.909870\pi$
$488$		−	3.64451i		−	0.164979i
$489$	0.571466	+	11.0305i	0.0258426	+	0.498817i
$490$	16.7913	−	20.5083i	0.758553	−	0.926469i
$491$	−2.79101	−	1.61139i	−0.125957	−	0.0727211i	0.435698	−	0.900093i	$-0.356502\pi$
$491$	−2.79101	−	1.61139i	−0.125957	−	0.0727211i	−0.561655	+	0.827372i	$0.689835\pi$
$492$	5.85134	−	3.79493i	0.263799	−	0.171089i
$493$	9.99898	−	5.77291i	0.450331	−	0.259999i
$494$	−7.39458	+	7.17039i	−0.332698	+	0.322611i
$495$	−60.2435	−	26.9086i	−2.70775	−	1.20945i
$496$	0.824954	−	1.42886i	0.0370415	−	0.0641578i
$497$	6.44247	+	35.2915i	0.288984	+	1.58304i
$498$	17.3970	−	11.2829i	0.779576	−	0.505600i
$499$	−15.8562	−	9.15459i	−0.709821	−	0.409816i	0.101173	−	0.994869i	$-0.467740\pi$
$499$	−15.8562	−	9.15459i	−0.709821	−	0.409816i	−0.810995	+	0.585053i	$0.801074\pi$
$500$	−14.2234	−	8.21191i	−0.636092	−	0.367248i
$501$	−11.3851	−	5.80960i	−0.508650	−	0.259554i
$502$	4.15920	−	7.20395i	0.185634	−	0.321528i
$503$	−4.84489	−	8.39159i	−0.216023	−	0.374162i	0.737566	−	0.675275i	$-0.235975\pi$
$503$	−4.84489	−	8.39159i	−0.216023	−	0.374162i	−0.953588	+	0.301113i	$0.902642\pi$
$504$	7.71067	+	1.88296i	0.343461	+	0.0838738i
$505$	31.7806	+	18.3485i	1.41422	+	0.816498i
$506$	24.3913	+	14.0823i	1.08432	+	0.626035i
$507$	19.2595	−	11.6649i	0.855346	−	0.518058i
$508$	−0.534780	−	0.926266i	−0.0237270	−	0.0410964i
$509$	28.1382	−	16.2456i	1.24721	−	0.720074i	0.276654	−	0.960970i	$-0.410774\pi$
$509$	28.1382	−	16.2456i	1.24721	−	0.720074i	0.970551	+	0.240895i	$0.0774411\pi$
$510$	−26.5184	−	13.5318i	−1.17426	−	0.599199i
$511$	−2.08199	−	11.4050i	−0.0921016	−	0.504529i
$512$	1.00000			0.0441942
$513$	14.6656	−	2.29582i	0.647501	−	0.101363i
$514$	−11.0205	+	19.0880i	−0.486092	+	0.841937i
$515$	6.43666	+	11.1486i	0.283633	+	0.491267i
$516$	−1.54285	+	0.0799314i	−0.0679201	+	0.00351878i
$517$	−36.2144	−	20.9084i	−1.59271	−	0.919550i
$518$	1.71183	+	2.01528i	0.0752136	+	0.0885465i
$519$	−8.81864	+	0.456874i	−0.387095	+	0.0200545i
$520$	−3.73603	+	13.1312i	−0.163836	+	0.575843i
$521$	−21.3684	−	37.0111i	−0.936166	−	1.62149i	−0.772542	−	0.634964i	$-0.781015\pi$
$521$	−21.3684	−	37.0111i	−0.936166	−	1.62149i	−0.163624	−	0.986523i	$-0.552318\pi$
$522$	0.788504	+	7.58948i	0.0345119	+	0.332183i
$523$	0.432713	−	0.249827i	0.0189212	−	0.0109242i	−0.490510	−	0.871436i	$-0.663189\pi$
$523$	0.432713	−	0.249827i	0.0189212	−	0.0109242i	0.509431	+	0.860512i	$0.329856\pi$
$524$	6.27140	+	10.8624i	0.273967	+	0.474526i
$525$	−9.85185	−	41.6401i	−0.429970	−	1.81732i
$526$	−14.9822	+	8.64996i	−0.653254	+	0.377156i
$527$	−7.48966			−0.326255
$528$	−5.47423	−	8.44064i	−0.238235	−	0.367332i
$529$	0.256247	−	0.443834i	0.0111412	−	0.0192971i
$530$	11.8370	+	20.5022i	0.514165	+	0.890559i
$531$	27.4398	+	12.2564i	1.19079	+	0.531881i
$532$	5.76059	−	4.89319i	0.249753	−	0.212147i
$533$	−3.97291	+	13.9638i	−0.172086	+	0.604840i
$534$	3.37606	+	1.72273i	0.146096	+	0.0745500i
$535$	−33.5029			−1.44845
$536$		−	10.6760i		−	0.461132i
$537$	−0.770101	−	14.8646i	−0.0332323	−	0.641455i
$538$	7.57009			0.326370
$539$	−31.4591	−	25.7574i	−1.35504	−	1.10945i
$540$	15.3127	−	12.3545i	0.658953	−	0.531653i
$541$	14.9336	+	8.62192i	0.642046	+	0.370685i	0.785402	−	0.618986i	$-0.212456\pi$
$541$	14.9336	+	8.62192i	0.642046	+	0.370685i	−0.143356	+	0.989671i	$0.545790\pi$
$542$	−1.03693	+	1.79602i	−0.0445401	+	0.0771458i
$543$	0.249819	+	4.82205i	0.0107208	+	0.206934i
$544$	−2.26972	−	3.93127i	−0.0973135	−	0.168552i
$545$	−11.1970			−0.479628
$546$	−14.6652	+	7.61125i	−0.627614	+	0.325731i
$547$	22.0489			0.942741			0.471370	−	0.881935i	$-0.343759\pi$
$547$	22.0489			0.942741			0.471370	+	0.881935i	$0.343759\pi$
$548$	7.77614	+	13.4687i	0.332180	+	0.575353i
$549$	−1.12985	−	10.8750i	−0.0482208	−	0.464134i
$550$	−27.1178	+	46.9694i	−1.15631	+	2.00278i
$551$	6.29256	+	3.63301i	0.268072	+	0.154771i
$552$	−7.04644	+	4.57002i	−0.299917	+	0.194513i
$553$	−33.8839	+	28.7819i	−1.44089	+	1.22393i
$554$	−23.6718			−1.00572
$555$	6.54574	−	0.339120i	0.277851	−	0.0143948i
$556$			8.77625i			0.372196i
$557$	−15.1946			−0.643815			−0.321908	−	0.946771i	$-0.604324\pi$
$557$	−15.1946			−0.643815			−0.321908	+	0.946771i	$0.604324\pi$
$558$	2.01864	−	4.51938i	0.0854560	−	0.191321i
$559$	2.30879	−	2.23879i	0.0976512	−	0.0946907i
$560$	3.36958	−	9.43442i	0.142391	−	0.398677i
$561$	−20.7575	+	40.6786i	−0.876381	+	1.71745i
$562$	−12.9143	−	22.3682i	−0.544755	−	0.943544i
$563$	−1.31787	+	2.28262i	−0.0555416	+	0.0962008i	−0.892459	−	0.451128i	$-0.851022\pi$
$563$	−1.31787	+	2.28262i	−0.0555416	+	0.0962008i	0.836918	+	0.547329i	$0.184355\pi$
$564$	10.4620	−	6.78524i	0.440532	−	0.285710i
$565$	38.1098			1.60329
$566$	14.5695	−	8.41173i	0.612404	−	0.353571i
$567$	23.5919	+	3.22822i	0.990767	+	0.135573i
$568$	6.77969	+	11.7428i	0.284470	+	0.492716i
$569$	38.3512	−	22.1421i	1.60777	−	0.928244i	0.617896	−	0.786260i	$-0.287985\pi$
$569$	38.3512	−	22.1421i	1.60777	−	0.928244i	0.989869	−	0.141984i	$-0.0453481\pi$
$570$	−0.969357	−	18.7107i	−0.0406019	−	0.783704i
$571$	−1.88780	−	3.26977i	−0.0790021	−	0.136836i	0.823818	−	0.566855i	$-0.191840\pi$
$571$	−1.88780	−	3.26977i	−0.0790021	−	0.136836i	−0.902820	+	0.430019i	$0.858507\pi$
$572$	20.1430	+	5.73097i	0.842220	+	0.239624i
$573$	1.74940	+	33.7671i	0.0730821	+	1.41064i
$574$	3.58322	−	10.0326i	0.149561	−	0.418753i
$575$	39.2112	+	22.6386i	1.63522	+	0.944094i
$576$	2.98394	−	0.310014i	0.124331	−	0.0129173i
$577$	−11.1370	−	19.2899i	−0.463640	−	0.803048i	0.535499	−	0.844536i	$-0.320123\pi$
$577$	−11.1370	−	19.2899i	−0.463640	−	0.803048i	−0.999139	+	0.0414882i	$0.986790\pi$
$578$	−1.80327	+	3.12336i	−0.0750063	+	0.129915i
$579$	−0.568585	−	10.9749i	−0.0236296	−	0.456101i
$580$	9.63072			0.399894
$581$	10.6535	−	29.8285i	0.441981	−	1.23749i
$582$	9.93473	−	19.4692i	0.411808	−	0.807024i
$583$	31.4499	−	18.1576i	1.30252	−	0.752011i
$584$	−2.19097	−	3.79486i	−0.0906628	−	0.157033i
$585$	−7.07721	+	40.3410i	−0.292607	+	1.66790i
$586$	23.6154	+	13.6344i	0.975545	+	0.563231i
$587$	−18.7811	−	10.8433i	−0.775179	−	0.447550i	0.0595402	−	0.998226i	$-0.481037\pi$
$587$	−18.7811	−	10.8433i	−0.775179	−	0.447550i	−0.834719	+	0.550676i	$0.814370\pi$
$588$	11.1055	−	4.86494i	0.457984	−	0.200627i
$589$	−2.35670	−	4.08192i	−0.0971061	−	0.168193i
$590$	18.9657	−	32.8495i	0.780804	−	1.35239i
$591$	−6.70350	+	13.1369i	−0.275745	+	0.540381i
$592$	0.865515	+	0.499705i	0.0355724	+	0.0205378i
$593$	2.83216	+	1.63515i	0.116303	+	0.0671475i	0.557023	−	0.830497i	$-0.311944\pi$
$593$	2.83216	+	1.63515i	0.116303	+	0.0671475i	−0.440720	+	0.897645i	$0.645277\pi$
$594$	−18.9515	−	23.4893i	−0.777589	−	0.963776i
$595$	−44.7373	+	8.16679i	−1.83405	+	0.334806i
$596$	1.53689	−	2.66197i	0.0629535	−	0.109039i
$597$	2.60974	+	1.33170i	0.106810	+	0.0545028i
$598$	4.78435	−	16.8158i	0.195647	−	0.687651i
$599$	17.7669	−	10.2577i	0.725935	−	0.419119i	−0.0909981	−	0.995851i	$-0.529006\pi$
$599$	17.7669	−	10.2577i	0.725935	−	0.419119i	0.816933	+	0.576732i	$0.195672\pi$
$600$	−8.80032	−	13.5691i	−0.359272	−	0.553955i
$601$	25.4328	+	14.6836i	1.03743	+	0.598958i	0.919103	−	0.394017i	$-0.128915\pi$
$601$	25.4328	+	14.6836i	1.03743	+	0.598958i	0.118322	+	0.992975i	$0.462248\pi$
$602$	−1.79861	+	1.52779i	−0.0733059	+	0.0622679i
$603$	−3.30970	−	31.8565i	−0.134782	−	1.29730i
$604$		−	12.6364i		−	0.514167i
$605$	74.5597	+	43.0470i	3.03128	+	1.75011i
$606$	9.13405	+	14.0836i	0.371045	+	0.572109i
$607$			7.33615i			0.297765i	0.988855	+	0.148883i	$0.0475677\pi$
$607$			7.33615i			0.297765i	−0.988855	+	0.148883i	$0.952432\pi$
$608$	1.42838	−	2.47403i	0.0579286	−	0.100335i
$609$	7.99522	+	8.48102i	0.323983	+	0.343668i
$610$	−13.7999			−0.558741
$611$	−7.10346	+	24.9669i	−0.287375	+	1.01005i
$612$	−7.99146	−	11.0270i	−0.323036	−	0.445741i
$613$			9.92949i			0.401048i	0.979689	+	0.200524i	$0.0642645\pi$
$613$			9.92949i			0.401048i	−0.979689	+	0.200524i	$0.935736\pi$
$614$	−11.4909	−	19.9028i	−0.463735	−	0.803213i
$615$	−14.3694	−	22.1560i	−0.579432	−	0.893417i
$616$	−14.4722	−	5.16884i	−0.583100	−	0.208259i
$617$	−9.05420	−	15.6823i	−0.364508	−	0.631347i	0.624189	−	0.781273i	$-0.285430\pi$
$617$	−9.05420	−	15.6823i	−0.364508	−	0.631347i	−0.988697	+	0.149927i	$0.952096\pi$
$618$	0.304668	+	5.88075i	0.0122555	+	0.236558i
$619$	24.1824	+	41.8852i	0.971973	+	1.68351i	0.689582	+	0.724208i	$0.257794\pi$
$619$	24.1824	+	41.8852i	0.971973	+	1.68351i	0.282392	+	0.959299i	$0.408872\pi$
$620$	−5.41037	−	3.12368i	−0.217286	−	0.125450i
$621$	−19.6094	+	15.8212i	−0.786898	+	0.634881i
$622$	15.9662	−	27.6543i	0.640186	−	1.10883i
$623$	5.69550	−	1.03971i	0.228185	−	0.0416552i
$624$	−4.25239	+	4.57353i	−0.170232	+	0.183088i
$625$	−7.75058	+	13.4244i	−0.310023	+	0.536976i
$626$			6.14358i			0.245547i
$627$	−28.7017	+	1.48697i	−1.14624	+	0.0593838i
$628$			9.60057i			0.383104i
$629$		−	4.53677i		−	0.180893i
$630$	7.12981	−	29.1964i	0.284058	−	1.16321i
$631$	12.4784	−	7.20438i	0.496756	−	0.286802i	−0.230617	−	0.973045i	$-0.574075\pi$
$631$	12.4784	−	7.20438i	0.496756	−	0.286802i	0.727373	+	0.686243i	$0.240741\pi$
$632$	−8.40177	+	14.5523i	−0.334205	+	0.578859i
$633$	−18.1679	+	35.6039i	−0.722111	+	1.41513i
$634$	14.0392			0.557566
$635$	−3.50729	+	2.02494i	−0.139183	+	0.0803571i
$636$	0.560282	+	10.8146i	0.0222166	+	0.428829i
$637$	−10.7426	+	22.8385i	−0.425637	+	0.904894i
$638$		−	14.7733i		−	0.584880i
$639$	23.8706	+	32.9379i	0.944307	+	1.30300i
$640$		−	3.78649i		−	0.149674i
$641$	−6.94081	−	4.00728i	−0.274146	−	0.158278i	0.356624	−	0.934248i	$-0.383928\pi$
$641$	−6.94081	−	4.00728i	−0.274146	−	0.158278i	−0.630770	+	0.775970i	$0.717261\pi$
$642$	−13.6507	−	6.96566i	−0.538749	−	0.274913i
$643$	13.5619	+	23.4899i	0.534830	+	0.926353i	0.999172	+	0.0406964i	$0.0129576\pi$
$643$	13.5619	+	23.4899i	0.534830	+	0.926353i	−0.464342	+	0.885656i	$0.653709\pi$
$644$	−4.31507	+	12.0817i	−0.170038	+	0.476086i
$645$	0.302659	+	5.84197i	0.0119172	+	0.230027i
$646$	−12.9681			−0.510224
$647$	15.9375			0.626568			0.313284	−	0.949659i	$-0.398571\pi$
$647$	15.9375			0.626568			0.313284	+	0.949659i	$0.398571\pi$
$648$	8.80778	−	1.85013i	0.346002	−	0.0726798i
$649$	−50.3902	−	29.0928i	−1.97799	−	1.14199i
$650$	32.3816	+	9.21305i	1.27011	+	0.361366i
$651$	−1.74080	−	7.35770i	−0.0682272	−	0.288371i
$652$	5.52266	+	3.18851i	0.216284	+	0.124872i
$653$	−36.6390	+	21.1535i	−1.43379	+	0.827801i	−0.997408	−	0.0719585i	$-0.977075\pi$
$653$	−36.6390	+	21.1535i	−1.43379	+	0.827801i	−0.436386	+	0.899760i	$0.643742\pi$
$654$	−4.56221	−	2.32800i	−0.178397	−	0.0910321i
$655$	41.1303	−	23.7466i	1.60709	−	0.927856i
$656$		−	4.02657i		−	0.157211i
$657$	−7.71417	−	10.6444i	−0.300958	−	0.415278i
$658$	6.40671	−	17.9380i	0.249760	−	0.699298i
$659$	−32.3775	+	18.6932i	−1.26125	+	0.728182i	−0.973316	−	0.229469i	$-0.926301\pi$
$659$	−32.3775	+	18.6932i	−1.26125	+	0.728182i	−0.287932	+	0.957651i	$0.592968\pi$
$660$	−31.9604	+	20.7281i	−1.24406	+	0.806841i
$661$	−20.9263			−0.813940			−0.406970	−	0.913442i	$-0.633415\pi$
$661$	−20.9263			−0.813940			−0.406970	+	0.913442i	$0.633415\pi$
$662$	7.16125	−	4.13455i	0.278330	−	0.160694i
$663$	27.6315	+	6.33665i	1.07312	+	0.246095i
$664$		−	11.9716i		−	0.464589i
$665$	−18.5280	−	21.8124i	−0.718485	−	0.845849i
$666$	2.73756	+	1.22277i	0.106078	+	0.0473813i
$667$	−12.3331			−0.477539
$668$	−6.39087	+	3.68977i	−0.247270	+	0.142761i
$669$	13.6687	−	26.7867i	0.528462	−	1.03563i
$670$	−40.4245			−1.56173
$671$			21.1687i			0.817208i
$672$	3.33446	−	3.14346i	0.128630	−	0.121262i
$673$	10.6922	−	18.5194i	0.412152	−	0.713869i	−0.582973	−	0.812492i	$-0.698111\pi$
$673$	10.6922	−	18.5194i	0.412152	−	0.713869i	0.995125	+	0.0986232i	$0.0314439\pi$
$674$	−4.39343	−	7.60965i	−0.169229	−	0.293113i
$675$	−30.4662	−	37.7611i	−1.17265	−	1.45342i
$676$	0.400097	−	12.9938i	0.0153884	−	0.499763i
$677$	−12.4515	+	21.5666i	−0.478550	+	0.828873i	−0.999698	−	0.0245935i	$-0.992171\pi$
$677$	−12.4515	+	21.5666i	−0.478550	+	0.828873i	0.521147	+	0.853467i	$0.325504\pi$
$678$	15.5278	+	7.92351i	0.596341	+	0.304301i
$679$	−5.99585	−	32.8450i	−0.230100	−	1.26048i
$680$	−14.8857	+	8.59427i	−0.570841	+	0.329575i
$681$	29.5480	+	15.0778i	1.13228	+	0.577781i
$682$	−4.79164	+	8.29936i	−0.183481	+	0.317799i
$683$	8.98836	−	15.5683i	0.343930	−	0.595704i	−0.641229	−	0.767350i	$-0.721575\pi$
$683$	8.98836	−	15.5683i	0.343930	−	0.595704i	0.985159	+	0.171646i	$0.0549084\pi$
$684$	3.49522	−	7.82518i	0.133643	−	0.299203i
$685$	50.9989	−	29.4442i	1.94857	−	1.12501i
$686$	8.96855	−	16.2039i	0.342421	−	0.618666i
$687$	−13.8424	+	27.1271i	−0.528121	+	1.03496i
$688$	−0.445979	+	0.772459i	−0.0170028	+	0.0294497i
$689$	−15.6929	−	16.1835i	−0.597851	−	0.616543i
$690$	17.3043	+	26.6813i	0.658764	+	1.01574i
$691$	10.5718	+	18.3109i	0.402170	+	0.696579i	0.993988	−	0.109493i	$-0.0349227\pi$
$691$	10.5718	+	18.3109i	0.402170	+	0.696579i	−0.591817	+	0.806072i	$0.701589\pi$
$692$	−2.54914	+	4.41523i	−0.0969036	+	0.167842i
$693$	−44.7865	−	10.9369i	−1.70130	−	0.415460i
$694$		−	16.4055i		−	0.622744i
$695$	33.2312			1.26053
$696$	3.92402	+	2.00235i	0.148740	+	0.0758988i
$697$	−15.8295	+	9.13918i	−0.599586	+	0.346171i
$698$	8.77060			0.331972
$699$	2.17654	+	1.11064i	0.0823242	+	0.0420083i
$700$	−23.2653	−	8.30938i	−0.879346	−	0.314065i
$701$			22.8317i			0.862342i	0.902270	+	0.431171i	$0.141900\pi$
$701$			22.8317i			0.862342i	−0.902270	+	0.431171i	$0.858100\pi$
$702$	−11.2710	+	14.9654i	−0.425397	+	0.564834i
$703$	2.47257	−	1.42754i	0.0932548	−	0.0538407i
$704$	−5.80837			−0.218911
$705$	−25.6922	−	39.6144i	−0.967624	−	1.49197i
$706$	16.9161	−	9.76652i	0.636646	−	0.367568i
$707$	24.1476	+	8.62449i	0.908163	+	0.324357i
$708$	14.5573	−	9.44127i	0.547098	−	0.354825i
$709$			49.2396i			1.84923i	0.380902	+	0.924615i	$0.375613\pi$
$709$			49.2396i			1.84923i	−0.380902	+	0.924615i	$0.624387\pi$
$710$	44.4639	−	25.6712i	1.66870	−	0.963424i
$711$	−20.5590	+	46.0278i	−0.771021	+	1.72618i
$712$	1.89510	−	1.09414i	0.0710218	−	0.0410045i
$713$	6.92851	+	4.00017i	0.259475	+	0.149808i
$714$	−19.9261	−	5.97390i	−0.745716	−	0.223568i
$715$	21.7002	−	76.2711i	0.811543	−	2.85238i
$716$	−7.44227	−	4.29680i	−0.278131	−	0.160579i
$717$	38.4555	−	1.99229i	1.43615	−	0.0744035i
$718$	3.09596			0.115540
$719$	49.6407			1.85129			0.925643	−	0.378398i	$-0.123525\pi$
$719$	49.6407			1.85129			0.925643	+	0.378398i	$0.123525\pi$
$720$	−1.17386	−	11.2986i	−0.0437473	−	0.421076i
$721$	5.82333	+	6.85562i	0.216872	+	0.255316i
$722$	5.41945	+	9.38676i	0.201691	+	0.349339i
$723$	−9.59460	+	18.8026i	−0.356827	+	0.699277i
$724$	2.41426	+	1.39387i	0.0897252	+	0.0518029i
$725$		−	23.7494i		−	0.882029i
$726$	21.4292	+	33.0413i	0.795312	+	1.22628i
$727$			24.4519i			0.906870i	0.891289	+	0.453435i	$0.149802\pi$
$727$			24.4519i			0.906870i	−0.891289	+	0.453435i	$0.850198\pi$
$728$	−0.920344	+	9.49489i	−0.0341102	+	0.351904i
$729$	25.7083	−	8.25120i	0.952160	−	0.305600i
$730$	−14.3692	+	8.29606i	−0.531828	+	0.307051i
$731$	4.04899			0.149757
$732$	−5.62274	−	2.86917i	−0.207823	−	0.106048i
$733$	−1.21258	+	2.10024i	−0.0447875	+	0.0775743i	−0.887550	−	0.460711i	$-0.847594\pi$
$733$	−1.21258	+	2.10024i	−0.0447875	+	0.0775743i	0.842763	+	0.538285i	$0.180928\pi$
$734$	−7.02340	+	4.05496i	−0.259239	+	0.149671i
$735$	−18.4210	−	42.0509i	−0.679470	−	1.55107i
$736$			4.84897i			0.178735i
$737$			62.0101i			2.28417i
$738$	−1.24829	−	12.0150i	−0.0459503	−	0.442279i
$739$			46.8162i			1.72216i	0.508468	+	0.861081i	$0.330212\pi$
$739$			46.8162i			1.72216i	−0.508468	+	0.861081i	$0.669788\pi$
$740$	1.89213	−	3.27726i	0.0695560	−	0.120474i
$741$	5.24103	+	17.0533i	0.192534	+	0.626468i
$742$	10.7091	+	12.6074i	0.393142	+	0.462833i
$743$	3.32899	−	5.76598i	0.122129	−	0.211533i	−0.798478	−	0.602024i	$-0.794361\pi$
$743$	3.32899	−	5.76598i	0.122129	−	0.211533i	0.920607	+	0.390490i	$0.127695\pi$
$744$	−1.55499	−	2.39762i	−0.0570088	−	0.0879010i
$745$	−10.0795	−	5.81942i	−0.369285	−	0.213207i
$746$	10.1944	+	17.6572i	0.373243	+	0.646476i
$747$	−3.71137	−	35.7226i	−0.135792	−	1.30702i
$748$	13.1834	+	22.8343i	0.482032	+	0.834905i
$749$	−23.0291	+	4.20395i	−0.841463	+	0.153609i
$750$	−23.8668	+	15.4790i	−0.871494	+	0.565213i
$751$	2.99507	+	5.18762i	0.109292	+	0.189299i	0.915484	−	0.402355i	$-0.131808\pi$
$751$	2.99507	+	5.18762i	0.109292	+	0.189299i	−0.806192	+	0.591654i	$0.798475\pi$
$752$		−	7.19940i		−	0.262535i
$753$	−7.83987	−	12.0882i	−0.285701	−	0.440518i
$754$	−8.89352	+	2.23690i	−0.323883	+	0.0814630i
$755$	−47.8475			−1.74135
$756$	8.97532	−	10.4136i	0.326429	−	0.378740i
$757$	25.0828	−	43.4447i	0.911651	−	1.57903i	0.0999189	−	0.994996i	$-0.468142\pi$
$757$	25.0828	−	43.4447i	0.911651	−	1.57903i	0.811732	−	0.584030i	$-0.198525\pi$
$758$			18.7952i			0.682671i
$759$	40.9284	−	26.5444i	1.48561	−	0.963500i
$760$	−9.36788	−	5.40855i	−0.339809	−	0.196189i
$761$		−	8.35016i		−	0.302693i	−0.988481	−	0.151347i	$-0.951639\pi$
$761$		−	8.35016i		−	0.302693i	0.988481	−	0.151347i	$-0.0483610\pi$
$762$	−1.85005	+	0.0958468i	−0.0670202	+	0.00347216i
$763$	−7.69657	+	1.40501i	−0.278635	+	0.0508647i
$764$	16.9062	+	9.76080i	0.611645	+	0.353133i
$765$	−41.7537	+	30.2596i	−1.50961	+	1.09404i
$766$	−21.4155	+	12.3643i	−0.773775	+	0.446739i
$767$	−9.88405	+	34.7401i	−0.356893	+	1.25439i
$768$	0.787258	−	1.54280i	0.0284077	−	0.0556709i
$769$	−23.1255	+	40.0545i	−0.833926	+	1.44440i	0.0609760	+	0.998139i	$0.480579\pi$
$769$	−23.1255	+	40.0545i	−0.833926	+	1.44440i	−0.894902	+	0.446263i	$0.852755\pi$
$770$	−19.5718	+	54.7986i	−0.705317	+	1.97481i
$771$	20.7730	+	32.0296i	0.748121	+	1.15352i
$772$	−5.49481	−	3.17243i	−0.197763	−	0.114178i
$773$	−0.578776	−	0.334156i	−0.0208171	−	0.0120188i	0.489555	−	0.871972i	$-0.337159\pi$
$773$	−0.578776	−	0.334156i	−0.0208171	−	0.0120188i	−0.510372	+	0.859953i	$0.670492\pi$
$774$	−1.09130	+	2.44323i	−0.0392260	+	0.0878200i
$775$	−7.70299	+	13.3420i	−0.276700	+	0.479258i
$776$	−6.30970	−	10.9287i	−0.226505	−	0.392318i
$777$	4.45683	−	1.05446i	0.159888	−	0.0378287i
$778$	7.93751	+	4.58272i	0.284574	+	0.164299i
$779$	−9.96185	−	5.75147i	−0.356920	−	0.206068i
$780$	17.3176	+	16.1016i	0.620070	+	0.576530i
$781$	−39.3790	−	68.2064i	−1.40909	−	2.44062i
$782$	19.0626	−	11.0058i	0.681678	−	0.393567i
$783$	12.3298	+	4.75838i	0.440631	+	0.170051i
$784$	1.13233	−	6.90781i	0.0404404	−	0.246707i
$785$	36.3524			1.29747
$786$	21.6957	−	1.12400i	0.773859	−	0.0400919i
$787$	1.62192	−	2.80924i	0.0578150	−	0.100139i	−0.835669	−	0.549233i	$-0.814920\pi$
$787$	1.62192	−	2.80924i	0.0578150	−	0.100139i	0.893484	+	0.449094i	$0.148253\pi$
$788$	4.25750	+	7.37421i	0.151667	+	0.262695i
$789$	1.55030	+	29.9242i	0.0551923	+	1.06533i
$790$	55.1021	+	31.8132i	1.96044	+	1.13186i
$791$	26.1958	−	4.78204i	0.931415	−	0.170030i
$792$	−17.3318	+	1.80068i	−0.615860	+	0.0639843i
$793$	12.7436	−	3.20526i	0.452537	−	0.113822i
$794$	−1.69223	−	2.93103i	−0.0600550	−	0.104018i
$795$	40.9495	−	2.12150i	1.45233	−	0.0752419i
$796$	1.46494	−	0.845782i	0.0519234	−	0.0299780i
$797$	22.9206	+	39.6996i	0.811889	+	1.40623i	0.911541	+	0.411210i	$0.134894\pi$
$797$	22.9206	+	39.6996i	0.811889	+	1.40623i	−0.0996520	+	0.995022i	$0.531773\pi$
$798$	−3.01413	−	12.7396i	−0.106699	−	0.450978i
$799$	−28.3028	+	16.3406i	−1.00128	+	0.578090i
$800$	−9.33748			−0.330130
$801$	5.31566	−	3.85234i	0.187820	−	0.136116i
$802$	3.62565	−	6.27981i	0.128026	−	0.221748i
$803$	12.7259	+	22.0420i	0.449089	+	0.777845i
$804$	−16.4709	−	8.40475i	−0.580883	−	0.296413i
$805$	45.7472	+	16.3390i	1.61238	+	0.575873i
$806$	5.72175	+	1.62792i	0.201540	+	0.0573411i
$807$	5.95962	−	11.6791i	0.209788	−	0.411124i
$808$	9.69158			0.340948
$809$			8.59232i			0.302090i	0.988527	+	0.151045i	$0.0482638\pi$
$809$			8.59232i			0.302090i	−0.988527	+	0.151045i	$0.951736\pi$
$810$	−7.00548	−	33.3506i	−0.246147	−	1.17182i
$811$	−37.1687			−1.30517			−0.652585	−	0.757716i	$-0.726315\pi$
$811$	−37.1687			−1.30517			−0.652585	+	0.757716i	$0.726315\pi$
$812$	6.61992	−	1.20847i	0.232314	−	0.0424088i
$813$	1.95456	+	3.01371i	0.0685496	+	0.105696i
$814$	−5.02723	−	2.90247i	−0.176204	−	0.101732i
$815$	12.0732	−	20.9115i	0.422907	−	0.732497i
$816$	−7.85202	+	0.406795i	−0.274876	+	0.0142407i
$817$	1.27406	+	2.20673i	0.0445736	+	0.0772038i
$818$	−1.57460			−0.0550547
$819$	0.197301	+	28.6175i	0.00689426	+	0.999976i
$820$	−15.2465			−0.532432
$821$	2.31898	+	4.01658i	0.0809328	+	0.140180i	0.903651	−	0.428270i	$-0.140877\pi$
$821$	2.31898	+	4.01658i	0.0809328	+	0.140180i	−0.822718	+	0.568450i	$0.807543\pi$
$822$	26.9013	−	1.39369i	0.938289	−	0.0486106i
$823$	17.5144	−	30.3358i	0.610514	−	1.05744i	−0.380640	−	0.924723i	$-0.624296\pi$
$823$	17.5144	−	30.3358i	0.610514	−	1.05744i	0.991154	−	0.132717i	$-0.0423703\pi$
$824$	2.94432	+	1.69990i	0.102570	+	0.0592189i
$825$	51.1156	+	78.8143i	1.77962	+	2.74396i
$826$	8.91457	−	24.9598i	0.310178	−	0.868461i
$827$	−21.1109			−0.734098			−0.367049	−	0.930202i	$-0.619632\pi$
$827$	−21.1109			−0.734098			−0.367049	+	0.930202i	$0.619632\pi$
$828$	1.50325	+	14.4690i	0.0522415	+	0.502833i
$829$			51.8895i			1.80220i	0.433614	+	0.901099i	$0.357238\pi$
$829$			51.8895i			1.80220i	−0.433614	+	0.901099i	$0.642762\pi$
$830$	−45.3303			−1.57344
$831$	−18.6358	+	36.5208i	−0.646469	+	1.26689i
$832$	0.879475	+	3.49664i	0.0304903	+	0.121224i
$833$	−29.7266	+	11.2273i	−1.02996	+	0.389003i
$834$	13.5400	+	6.90917i	0.468851	+	0.239245i
$835$	13.9713	+	24.1989i	0.483496	+	0.837439i
$836$	−8.29658	+	14.3701i	−0.286943	+	0.497000i
$837$	−5.38330	−	6.67228i	−0.186074	−	0.230628i
$838$	−26.9844			−0.932159
$839$	−38.8948	+	22.4560i	−1.34280	+	0.775266i	−0.987217	−	0.159380i	$-0.949051\pi$
$839$	−38.8948	+	22.4560i	−1.34280	+	0.775266i	−0.355582	+	0.934645i	$0.615717\pi$
$840$	−11.9027	−	12.6259i	−0.410681	−	0.435635i
$841$	−11.2654	−	19.5123i	−0.388464	−	0.672839i
$842$	−11.2982	+	6.52304i	−0.389363	+	0.224799i
$843$	−44.6764	+	2.31458i	−1.53874	+	0.0797184i
$844$	11.5387	+	19.9857i	0.397180	+	0.687936i
$845$	−49.2010	−	1.51496i	−1.69257	−	0.0521163i
$846$	−2.23191	−	21.4826i	−0.0767348	−	0.738586i
$847$	56.6521	+	20.2337i	1.94659	+	0.695239i
$848$	5.41458	+	3.12611i	0.185937	+	0.107351i
$849$	−1.50761	−	29.1001i	−0.0517410	−	0.998712i
$850$	21.1935	+	36.7082i	0.726931	+	1.25908i
$851$	−2.42305	+	4.19685i	−0.0830612	+	0.143866i
$852$	23.4541	−	1.21510i	0.803524	−	0.0416287i
$853$	−26.1545			−0.895513			−0.447756	−	0.894156i	$-0.647777\pi$
$853$	−26.1545			−0.895513			−0.447756	+	0.894156i	$0.647777\pi$
$854$	−9.48571	+	1.73162i	−0.324594	+	0.0592547i
$855$	−29.6299	−	13.2346i	−1.01332	−	0.452614i
$856$	−7.66260	+	4.42400i	−0.261902	+	0.151209i
$857$	−10.1488	−	17.5783i	−0.346678	−	0.600464i	0.638979	−	0.769224i	$-0.279357\pi$
$857$	−10.1488	−	17.5783i	−0.346678	−	0.600464i	−0.985657	+	0.168760i	$0.946024\pi$
$858$	24.6994	−	26.5648i	0.843225	−	0.906907i
$859$	38.0174	+	21.9494i	1.29714	+	0.748903i	0.979909	−	0.199446i	$-0.0639143\pi$
$859$	38.0174	+	21.9494i	1.29714	+	0.748903i	0.317229	+	0.948349i	$0.397248\pi$
$860$	2.92490	+	1.68869i	0.0997384	+	0.0575840i
$861$	−12.6574	−	13.4264i	−0.431362	−	0.457572i
$862$	18.2521	+	31.6136i	0.621669	+	1.07676i
$863$	9.06101	−	15.6941i	0.308440	−	0.534234i	−0.669581	−	0.742739i	$-0.733526\pi$
$863$	9.06101	−	15.6941i	0.308440	−	0.534234i	0.978021	+	0.208505i	$0.0668597\pi$
$864$	1.87084	−	4.84768i	0.0636473	−	0.164921i
$865$	16.7182	+	9.65227i	0.568437	+	0.328187i
$866$	−23.6502	−	13.6545i	−0.803668	−	0.463998i
$867$	3.39907	+	5.24098i	0.115439	+	0.177993i
$868$	−4.11091	−	1.46824i	−0.139534	−	0.0498355i
$869$	48.8006	−	84.5252i	1.65545	−	2.86732i
$870$	7.58186	−	14.8583i	0.257049	−	0.503742i
$871$	37.3301	−	9.38926i	1.26488	−	0.318143i
$872$	−2.56093	+	1.47855i	−0.0867239	+	0.0500701i
$873$	−22.2158	−	30.6545i	−0.751892	−	1.03750i
$874$	11.9965	+	6.92618i	0.405788	+	0.234282i
$875$	−14.6155	+	40.9216i	−0.494093	+	1.38340i
$876$	−7.57956	+	0.392680i	−0.256090	+	0.0132674i
$877$		−	36.4887i		−	1.23214i	−0.787693	−	0.616068i	$-0.788725\pi$
$877$		−	36.4887i		−	1.23214i	0.787693	−	0.616068i	$-0.211275\pi$
$878$	−0.394663	−	0.227859i	−0.0133192	−	0.00768986i
$879$	39.6265	−	25.7001i	1.33657	−	0.866842i
$880$			21.9933i			0.741395i
$881$	26.9414	−	46.6639i	0.907679	−	1.57215i	0.0903999	−	0.995906i	$-0.471185\pi$
$881$	26.9414	−	46.6639i	0.907679	−	1.57215i	0.817280	−	0.576241i	$-0.195481\pi$
$882$	1.23729	−	20.9635i	0.0416617	−	0.705878i
$883$	14.2182			0.478482			0.239241	−	0.970960i	$-0.423101\pi$
$883$	14.2182			0.478482			0.239241	+	0.970960i	$0.423101\pi$
$884$	11.7501	−	11.3939i	0.395199	−	0.383217i
$885$	−35.7492	−	55.1212i	−1.20170	−	1.85288i
$886$		−	26.8158i		−	0.900894i
$887$	3.25038	+	5.62982i	0.109137	+	0.189031i	0.915421	−	0.402498i	$-0.131858\pi$
$887$	3.25038	+	5.62982i	0.109137	+	0.189031i	−0.806284	+	0.591529i	$0.798525\pi$
$888$	1.45233	−	0.941917i	0.0487369	−	0.0316087i
$889$	−2.15674	+	1.83199i	−0.0723347	+	0.0614429i
$890$	−4.14293	−	7.17576i	−0.138871	−	0.240532i
$891$	−51.1589	+	10.7462i	−1.71389	+	0.360012i
$892$	−8.68120	−	15.0363i	−0.290668	−	0.503452i
$893$	−17.8115	−	10.2835i	−0.596040	−	0.344124i
$894$	−2.89696	−	4.46677i	−0.0968887	−	0.149391i
$895$	−16.2698	+	28.1800i	−0.543838	+	0.941955i
$896$	−0.475130	−	2.60274i	−0.0158730	−	0.0869514i
$897$	−22.1769	−	20.6197i	−0.740466	−	0.688471i
$898$	−0.402024	+	0.696326i	−0.0134157	+	0.0232367i
$899$		−	4.19645i		−	0.139959i
$900$	−27.8625	+	2.89475i	−0.928749	+	0.0964917i
$901$		−	28.3816i		−	0.945527i
$902$			23.3878i			0.778728i
$903$	0.941093	+	3.97765i	0.0313176	+	0.132368i
$904$	8.71628	−	5.03235i	0.289899	−	0.167373i
$905$	5.27788	−	9.14156i	0.175443	−	0.303876i
$906$	−19.4954	−	9.94810i	−0.647691	−	0.330504i
$907$	23.6524			0.785366			0.392683	−	0.919674i	$-0.371547\pi$
$907$	23.6524			0.785366			0.392683	+	0.919674i	$0.371547\pi$
$908$	16.5863	−	9.57612i	0.550436	−	0.317795i
$909$	28.9191	−	3.00453i	0.959185	−	0.0996538i
$910$	35.9523	+	3.48487i	1.19181	+	0.115522i
$911$			55.8572i			1.85063i	0.379197	+	0.925316i	$0.376200\pi$
$911$			55.8572i			1.85063i	−0.379197	+	0.925316i	$0.623800\pi$
$912$	−2.69242	−	4.15141i	−0.0891550	−	0.137467i
$913$			69.5356i			2.30129i
$914$	−13.1935	−	7.61727i	−0.436402	−	0.251957i
$915$	−10.8641	+	21.2904i	−0.359155	+	0.703840i
$916$	8.79153	+	15.2274i	0.290480	+	0.503127i
$917$	25.2922	−	21.4839i	0.835223	−	0.709460i
$918$	−23.3038	+	3.64809i	−0.769141	+	0.120405i
$919$	−23.5626			−0.777259			−0.388630	−	0.921394i	$-0.627051\pi$
$919$	−23.5626			−0.777259			−0.388630	+	0.921394i	$0.627051\pi$
$920$	18.3606			0.605330
$921$	−39.7523	+	2.05948i	−1.30988	+	0.0678621i
$922$	−11.4420	−	6.60603i	−0.376821	−	0.217558i
$923$	−35.0977	+	34.0337i	−1.15526	+	1.12023i
$924$	−19.3678	+	18.2584i	−0.637154	+	0.600657i
$925$	−8.08173	−	4.66599i	−0.265726	−	0.153417i
$926$	−13.3863	+	7.72858i	−0.439901	+	0.253977i
$927$	9.31266	+	4.15962i	0.305868	+	0.136620i
$928$	2.20269	−	1.27172i	0.0723068	−	0.0417463i
$929$			23.7951i			0.780691i	0.920669	+	0.390345i	$0.127644\pi$
$929$			23.7951i			0.780691i	−0.920669	+	0.390345i	$0.872356\pi$
$930$	−9.07856	+	5.88796i	−0.297698	+	0.193074i
$931$	−15.4727	−	12.6684i	−0.507098	−	0.415190i
$932$	1.22176	−	0.705386i	0.0400202	−	0.0231057i
$933$	−30.0954	−	46.4036i	−0.985279	−	1.51919i
$934$	−1.33115			−0.0435565
$935$	86.4618	−	49.9187i	2.82760	−	1.63252i
$936$	3.70831	+	10.1611i	0.121210	+	0.332127i
$937$		−	8.86156i		−	0.289495i	−0.989469	−	0.144747i	$-0.953763\pi$
$937$		−	8.86156i		−	0.289495i	0.989469	−	0.144747i	$-0.0462369\pi$
$938$	−27.7868	+	5.07247i	−0.907271	+	0.165622i
$939$	9.47831	+	4.83659i	0.309313	+	0.157836i
$940$	−27.2604			−0.889137
$941$	−11.5201	+	6.65114i	−0.375545	+	0.216821i	−0.675878	−	0.737013i	$-0.736235\pi$
$941$	−11.5201	+	6.65114i	−0.375545	+	0.216821i	0.300333	+	0.953834i	$0.402902\pi$
$942$	14.8117	+	7.55813i	0.482593	+	0.246257i
$943$	19.5247			0.635811
$944$		−	10.0175i		−	0.326043i
$945$	−39.4311	−	33.9849i	−1.28269	−	1.10553i
$946$	2.59041	−	4.48673i	0.0842216	−	0.145876i
$947$	−14.0793	−	24.3861i	−0.457516	−	0.792441i	0.541313	−	0.840821i	$-0.317928\pi$
$947$	−14.0793	−	24.3861i	−0.457516	−	0.792441i	−0.998829	+	0.0483799i	$0.984594\pi$
$948$	15.8369	+	24.4187i	0.514358	+	0.793081i
$949$	11.3424	−	10.9985i	0.368190	−	0.357027i
$950$	−13.3375	+	23.1012i	−0.432725	+	0.749502i
$951$	11.0524	−	21.6596i	0.358400	−	0.702360i
$952$	−9.15367	+	7.77536i	−0.296672	+	0.252001i
$953$	6.01165	−	3.47083i	0.194736	−	0.112431i	−0.399462	−	0.916750i	$-0.630803\pi$
$953$	6.01165	−	3.47083i	0.194736	−	0.112431i	0.594198	+	0.804319i	$0.297470\pi$
$954$	17.1259	+	7.64952i	0.554471	+	0.247662i
$955$	36.9591	−	64.0151i	1.19597	−	2.07148i
$956$	11.1160	−	19.2535i	0.359518	−	0.622704i
$957$	−22.7922	−	11.6304i	−0.736766	−	0.375957i
$958$	12.4718	−	7.20059i	0.402945	−	0.232641i
$959$	31.3607	−	26.6386i	1.01269	−	0.860206i
$960$	−5.84178	−	2.98094i	−0.188543	−	0.0962095i
$961$	14.1389	−	24.4893i	0.456094	−	0.789977i
$962$	−0.986092	+	3.46588i	−0.0317929	+	0.111744i
$963$	−21.4932	+	15.5765i	−0.692609	+	0.501945i
$964$	6.09368	+	10.5546i	0.196264	+	0.339940i
$965$	−12.0124	+	20.8060i	−0.386692	+	0.669770i
$966$	15.2426	+	16.1687i	0.490421	+	0.520220i
$967$			54.9103i			1.76580i	0.469563	+	0.882899i	$0.344411\pi$
$967$			54.9103i			1.76580i	−0.469563	+	0.882899i	$0.655589\pi$
$968$	22.7372			0.730801
$969$	−10.2093	+	20.0072i	−0.327969	+	0.642723i
$970$	−41.3815	+	23.8916i	−1.32868	+	0.767113i
$971$	30.2665			0.971298			0.485649	−	0.874154i	$-0.338583\pi$
$971$	30.2665			0.971298			0.485649	+	0.874154i	$0.338583\pi$
$972$	4.07963	−	15.0452i	0.130854	−	0.482574i
$973$	22.8423	−	4.16986i	0.732290	−	0.133679i
$974$			30.5356i			0.978423i
$975$	39.7066	−	42.7053i	1.27163	−	1.36766i
$976$	−3.15624	+	1.82226i	−0.101029	+	0.0583290i
$977$	−51.7636			−1.65606			−0.828031	−	0.560682i	$-0.810539\pi$
$977$	−51.7636			−1.65606			−0.828031	+	0.560682i	$0.810539\pi$
$978$	9.26698	−	6.01016i	0.296325	−	0.192184i
$979$	−11.0074	+	6.35515i	−0.351799	+	0.203111i
$980$	−26.1563	−	4.28756i	−0.835533	−	0.136961i
$981$	−7.18328	+	5.20583i	−0.229344	+	0.166209i
$982$			3.22279i			0.102843i
$983$	−20.1979	+	11.6613i	−0.644213	+	0.371936i	−0.786235	−	0.617927i	$-0.787973\pi$
$983$	−20.1979	+	11.6613i	−0.644213	+	0.371936i	0.142023	+	0.989863i	$0.454639\pi$
$984$	−6.21218	−	3.16995i	−0.198037	−	0.101054i
$985$	27.9223	−	16.1210i	0.889680	−	0.513657i
$986$	−9.99898	−	5.77291i	−0.318432	−	0.183847i
$987$	−22.6310	−	24.0061i	−0.720354	−	0.764123i
$988$	9.90703	+	2.81870i	0.315185	+	0.0896747i
$989$	−3.74563	−	2.16254i	−0.119104	−	0.0687647i
$990$	6.81824	+	65.6267i	0.216698	+	2.08575i
$991$	24.2315			0.769738			0.384869	−	0.922971i	$-0.374247\pi$
$991$	24.2315			0.769738			0.384869	+	0.922971i	$0.374247\pi$
$992$	−1.64991			−0.0523846
$993$	−0.741022	−	14.3033i	−0.0235156	−	0.453902i
$994$	27.3421	−	23.2251i	0.867240	−	0.736656i
$995$	−3.20254	−	5.54697i	−0.101527	−	0.175851i
$996$	−18.4698	−	9.42475i	−0.585237	−	0.298635i
$997$	−11.6981	−	6.75390i	−0.370483	−	0.213898i	0.303187	−	0.952931i	$-0.401949\pi$
$997$	−11.6981	−	6.75390i	−0.370483	−	0.213898i	−0.673669	+	0.739033i	$0.735283\pi$
$998$			18.3092i			0.579567i
$999$	4.04165	−	3.26086i	0.127872	−	0.103169i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bn.e.173.2	yes	34
3.2	odd	2		546.2.bn.f.173.16	yes	34
7.3	odd	6		546.2.bi.f.17.5	yes	34
13.10	even	6		546.2.bi.e.257.10	yes	34
21.17	even	6		546.2.bi.e.17.10	✓	34
39.23	odd	6		546.2.bi.f.257.5	yes	34
91.10	odd	6		546.2.bn.f.101.16	yes	34
273.101	even	6	inner	546.2.bn.e.101.2	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.10	✓	34	21.17	even	6
546.2.bi.e.257.10	yes	34	13.10	even	6
546.2.bi.f.17.5	yes	34	7.3	odd	6
546.2.bi.f.257.5	yes	34	39.23	odd	6
546.2.bn.e.101.2	yes	34	273.101	even	6	inner
546.2.bn.e.173.2	yes	34	1.1	even	1	trivial
546.2.bn.f.101.16	yes	34	91.10	odd	6
546.2.bn.f.173.16	yes	34	3.2	odd	2

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.72973 + 0.0896134i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(3.27919 + 1.89324i) q^{5} +(0.942473 + 1.45318i) q^{6} +(2.49160 + 0.889895i) q^{7} +1.00000 q^{8} +(2.98394 - 0.310014i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.72973 + 0.0896134i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(3.27919 + 1.89324i) q^{5} +(0.942473 + 1.45318i) q^{6} +(2.49160 + 0.889895i) q^{7} +1.00000 q^{8} +(2.98394 - 0.310014i) q^{9} -3.78649i q^{10} -5.80837 q^{11} +(0.787258 - 1.54280i) q^{12} +(0.879475 + 3.49664i) q^{13} +(-0.475130 - 2.60274i) q^{14} +(-5.84178 - 2.98094i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.26972 + 3.93127i) q^{17} +(-1.76045 - 2.42916i) q^{18} -2.85676 q^{19} +(-3.27919 + 1.89324i) q^{20} +(-4.38955 - 1.31600i) q^{21} +(2.90419 + 5.03020i) q^{22} +(4.19933 - 2.42448i) q^{23} +(-1.72973 + 0.0896134i) q^{24} +(4.66874 + 8.08650i) q^{25} +(2.58845 - 2.50997i) q^{26} +(-5.13363 + 0.803642i) q^{27} +(-2.01647 + 1.71284i) q^{28} +(-2.20269 - 1.27172i) q^{29} +(0.339320 + 6.54960i) q^{30} +(0.824954 + 1.42886i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(10.0469 - 0.520508i) q^{33} +4.53944 q^{34} +(6.48566 + 7.63535i) q^{35} +(-1.22349 + 2.73917i) q^{36} +(-0.865515 + 0.499705i) q^{37} +(1.42838 + 2.47403i) q^{38} +(-1.83460 - 5.96944i) q^{39} +(3.27919 + 1.89324i) q^{40} +(3.48711 + 2.01328i) q^{41} +(1.05509 + 4.45946i) q^{42} +(-0.445979 - 0.772459i) q^{43} +(2.90419 - 5.03020i) q^{44} +(10.3718 + 4.63273i) q^{45} +(-4.19933 - 2.42448i) q^{46} +(6.23486 + 3.59970i) q^{47} +(0.942473 + 1.45318i) q^{48} +(5.41617 + 4.43453i) q^{49} +(4.66874 - 8.08650i) q^{50} +(3.57371 - 7.00344i) q^{51} +(-3.46792 - 0.986674i) q^{52} +(-5.41458 + 3.12611i) q^{53} +(3.26279 + 4.04403i) q^{54} +(-19.0468 - 10.9967i) q^{55} +(2.49160 + 0.889895i) q^{56} +(4.94143 - 0.256004i) q^{57} +2.54344i q^{58} +(8.67545 + 5.00877i) q^{59} +(5.50246 - 3.56866i) q^{60} -3.64451i q^{61} +(0.824954 - 1.42886i) q^{62} +(7.71067 + 1.88296i) q^{63} +1.00000 q^{64} +(-3.73603 + 13.1312i) q^{65} +(-5.47423 - 8.44064i) q^{66} -10.6760i q^{67} +(-2.26972 - 3.93127i) q^{68} +(-7.04644 + 4.57002i) q^{69} +(3.36958 - 9.43442i) q^{70} +(6.77969 + 11.7428i) q^{71} +(2.98394 - 0.310014i) q^{72} +(-2.19097 - 3.79486i) q^{73} +(0.865515 + 0.499705i) q^{74} +(-8.80032 - 13.5691i) q^{75} +(1.42838 - 2.47403i) q^{76} +(-14.4722 - 5.16884i) q^{77} +(-4.25239 + 4.57353i) q^{78} +(-8.40177 + 14.5523i) q^{79} -3.78649i q^{80} +(8.80778 - 1.85013i) q^{81} -4.02657i q^{82} -11.9716i q^{83} +(3.33446 - 3.14346i) q^{84} +(-14.8857 + 8.59427i) q^{85} +(-0.445979 + 0.772459i) q^{86} +(3.92402 + 2.00235i) q^{87} -5.80837 q^{88} +(1.89510 - 1.09414i) q^{89} +(-1.17386 - 11.2986i) q^{90} +(-0.920344 + 9.49489i) q^{91} +4.84897i q^{92} +(-1.55499 - 2.39762i) q^{93} -7.19940i q^{94} +(-9.36788 - 5.40855i) q^{95} +(0.787258 - 1.54280i) q^{96} +(-6.30970 - 10.9287i) q^{97} +(1.13233 - 6.90781i) q^{98} +(-17.3318 + 1.80068i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

Introduction

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