LMFDB - Embedded newform 546.2.bi.f.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bi (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			17.5
Character	$\chi$	$=$	546.17
Dual form			546.2.bi.f.257.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(-0.942473 - 1.45318i) q^{3} +1.00000 q^{4} +(3.27919 - 1.89324i) q^{5} +(-0.942473 - 1.45318i) q^{6} +(0.475130 - 2.60274i) q^{7} +1.00000 q^{8} +(-1.22349 + 2.73917i) q^{9} +(3.27919 - 1.89324i) q^{10} +(2.90419 + 5.03020i) q^{11} +(-0.942473 - 1.45318i) q^{12} +(-0.879475 - 3.49664i) q^{13} +(0.475130 - 2.60274i) q^{14} +(-5.84178 - 2.98094i) q^{15} +1.00000 q^{16} -4.53944 q^{17} +(-1.22349 + 2.73917i) q^{18} +(-1.42838 + 2.47403i) q^{19} +(3.27919 - 1.89324i) q^{20} +(-4.23006 + 1.76256i) q^{21} +(2.90419 + 5.03020i) q^{22} +4.84897i q^{23} +(-0.942473 - 1.45318i) q^{24} +(4.66874 - 8.08650i) q^{25} +(-0.879475 - 3.49664i) q^{26} +(5.13363 - 0.803642i) q^{27} +(0.475130 - 2.60274i) q^{28} +(-2.20269 - 1.27172i) q^{29} +(-5.84178 - 2.98094i) q^{30} +(-0.824954 + 1.42886i) q^{31} +1.00000 q^{32} +(4.57269 - 8.96114i) q^{33} -4.53944 q^{34} +(-3.36958 - 9.43442i) q^{35} +(-1.22349 + 2.73917i) q^{36} -0.999410i q^{37} +(-1.42838 + 2.47403i) q^{38} +(-4.25239 + 4.57353i) q^{39} +(3.27919 - 1.89324i) q^{40} +(-3.48711 - 2.01328i) q^{41} +(-4.23006 + 1.76256i) q^{42} +(-0.445979 - 0.772459i) q^{43} +(2.90419 + 5.03020i) q^{44} +(1.17386 + 11.2986i) q^{45} +4.84897i q^{46} +(6.23486 - 3.59970i) q^{47} +(-0.942473 - 1.45318i) q^{48} +(-6.54850 - 2.47328i) q^{49} +(4.66874 - 8.08650i) q^{50} +(4.27830 + 6.59665i) q^{51} +(-0.879475 - 3.49664i) q^{52} +(5.41458 + 3.12611i) q^{53} +(5.13363 - 0.803642i) q^{54} +(19.0468 + 10.9967i) q^{55} +(0.475130 - 2.60274i) q^{56} +(4.94143 - 0.256004i) q^{57} +(-2.20269 - 1.27172i) q^{58} +10.0175i q^{59} +(-5.84178 - 2.98094i) q^{60} +(-3.15624 - 1.82226i) q^{61} +(-0.824954 + 1.42886i) q^{62} +(6.54804 + 4.48589i) q^{63} +1.00000 q^{64} +(-9.50397 - 9.80111i) q^{65} +(4.57269 - 8.96114i) q^{66} +(-9.24567 + 5.33799i) q^{67} -4.53944 q^{68} +(7.04644 - 4.57002i) q^{69} +(-3.36958 - 9.43442i) q^{70} +(6.77969 + 11.7428i) q^{71} +(-1.22349 + 2.73917i) q^{72} +(2.19097 - 3.79486i) q^{73} -0.999410i q^{74} +(-16.1513 + 0.836763i) 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} +(3.27919 - 1.89324i) q^{80} +(-6.00615 - 6.70270i) q^{81} +(-3.48711 - 2.01328i) q^{82} +11.9716i q^{83} +(-4.23006 + 1.76256i) q^{84} +(-14.8857 + 8.59427i) q^{85} +(-0.445979 - 0.772459i) q^{86} +(0.227927 + 4.39948i) q^{87} +(2.90419 + 5.03020i) q^{88} -2.18827i q^{89} +(1.17386 + 11.2986i) q^{90} +(-9.51872 + 0.627686i) q^{91} +4.84897i q^{92} +(2.85390 - 0.147854i) q^{93} +(6.23486 - 3.59970i) q^{94} +10.8171i q^{95} +(-0.942473 - 1.45318i) q^{96} +(6.30970 + 10.9287i) q^{97} +(-6.54850 - 2.47328i) q^{98} +(-17.3318 + 1.80068i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20}+ \cdots - 27 q^{99}+O(q^{100}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.942473	−	1.45318i	−0.544137	−	0.838996i
$3$	−0.942473	−	1.45318i	−0.544137	−	0.838996i
$4$	1.00000			0.500000
$5$	3.27919	−	1.89324i	1.46650	−	0.846684i	0.467202	−	0.884151i	$-0.345262\pi$
$5$	3.27919	−	1.89324i	1.46650	−	0.846684i	0.999298	+	0.0374664i	$0.0119287\pi$
$6$	−0.942473	−	1.45318i	−0.384763	−	0.593260i
$7$	0.475130	−	2.60274i	0.179582	−	0.983743i
$7$	0.475130	−	2.60274i	0.179582	−	0.983743i
$8$	1.00000			0.353553
$9$	−1.22349	+	2.73917i	−0.407830	+	0.913058i
$10$	3.27919	−	1.89324i	1.03697	−	0.598696i
$11$	2.90419	+	5.03020i	0.875645	+	1.51666i	0.856074	+	0.516853i	$0.172897\pi$
$11$	2.90419	+	5.03020i	0.875645	+	1.51666i	0.0195712	+	0.999808i	$0.493770\pi$
$12$	−0.942473	−	1.45318i	−0.272069	−	0.419498i
$13$	−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
$16$	1.00000			0.250000
$17$	−4.53944			−1.10098			−0.550488	−	0.834843i	$-0.685558\pi$
$17$	−4.53944			−1.10098			−0.550488	+	0.834843i	$0.685558\pi$
$18$	−1.22349	+	2.73917i	−0.288379	+	0.645629i
$19$	−1.42838	+	2.47403i	−0.327693	+	0.567582i	−0.982054	−	0.188601i	$-0.939605\pi$
$19$	−1.42838	+	2.47403i	−0.327693	+	0.567582i	0.654360	+	0.756183i	$0.272938\pi$
$20$	3.27919	−	1.89324i	0.733250	−	0.423342i
$21$	−4.23006	+	1.76256i	−0.923074	+	0.384622i
$22$	2.90419	+	5.03020i	0.619175	+	1.07244i
$23$			4.84897i			1.01108i	0.862803	+	0.505540i	$0.168707\pi$
$23$			4.84897i			1.01108i	−0.862803	+	0.505540i	$0.831293\pi$
$24$	−0.942473	−	1.45318i	−0.192381	−	0.296630i
$25$	4.66874	−	8.08650i	0.933748	−	1.61730i
$26$	−0.879475	−	3.49664i	−0.172479	−	0.685748i
$27$	5.13363	−	0.803642i	0.987968	−	0.154661i
$28$	0.475130	−	2.60274i	0.0897911	−	0.491871i
$29$	−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	$0.742553\pi$
$30$	−5.84178	−	2.98094i	−1.06656	−	0.544243i
$31$	−0.824954	+	1.42886i	−0.148166	+	0.256631i	−0.930550	−	0.366166i	$-0.880670\pi$
$31$	−0.824954	+	1.42886i	−0.148166	+	0.256631i	0.782384	+	0.622797i	$0.214004\pi$
$32$	1.00000			0.176777
$33$	4.57269	−	8.96114i	0.796003	−	1.55993i
$34$	−4.53944			−0.778508
$35$	−3.36958	−	9.43442i	−0.569562	−	1.59471i
$36$	−1.22349	+	2.73917i	−0.203915	+	0.456529i
$37$		−	0.999410i		−	0.164302i	−0.996620	−	0.0821510i	$-0.973821\pi$
$37$		−	0.999410i		−	0.164302i	0.996620	−	0.0821510i	$-0.0261790\pi$
$38$	−1.42838	+	2.47403i	−0.231714	+	0.401341i
$39$	−4.25239	+	4.57353i	−0.680927	+	0.732351i
$40$	3.27919	−	1.89324i	0.518486	−	0.299348i
$41$	−3.48711	−	2.01328i	−0.544595	−	0.314422i	0.202344	−	0.979314i	$-0.435144\pi$
$41$	−3.48711	−	2.01328i	−0.544595	−	0.314422i	−0.746939	+	0.664893i	$0.768477\pi$
$42$	−4.23006	+	1.76256i	−0.652712	+	0.271969i
$43$	−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
$45$	1.17386	+	11.2986i	0.174989	+	1.68430i
$46$			4.84897i			0.714941i
$47$	6.23486	−	3.59970i	0.909448	−	0.525070i	0.0291943	−	0.999574i	$-0.490706\pi$
$47$	6.23486	−	3.59970i	0.909448	−	0.525070i	0.880253	+	0.474504i	$0.157373\pi$
$48$	−0.942473	−	1.45318i	−0.136034	−	0.209749i
$49$	−6.54850	−	2.47328i	−0.935501	−	0.353325i
$50$	4.66874	−	8.08650i	0.660260	−	1.14360i
$51$	4.27830	+	6.59665i	0.599082	+	0.923715i
$52$	−0.879475	−	3.49664i	−0.121961	−	0.484897i
$53$	5.41458	+	3.12611i	0.743749	+	0.429404i	0.823431	−	0.567417i	$-0.192057\pi$
$53$	5.41458	+	3.12611i	0.743749	+	0.429404i	−0.0796817	+	0.996820i	$0.525390\pi$
$54$	5.13363	−	0.803642i	0.698599	−	0.109362i
$55$	19.0468	+	10.9967i	2.56827	+	1.48279i
$56$	0.475130	−	2.60274i	0.0634919	−	0.347806i
$57$	4.94143	−	0.256004i	0.654509	−	0.0339086i
$58$	−2.20269	−	1.27172i	−0.289227	−	0.166985i
$59$			10.0175i			1.30417i	0.758144	+	0.652087i	$0.226106\pi$
$59$			10.0175i			1.30417i	−0.758144	+	0.652087i	$0.773894\pi$
$60$	−5.84178	−	2.98094i	−0.754171	−	0.384838i
$61$	−3.15624	−	1.82226i	−0.404115	−	0.233316i	0.284143	−	0.958782i	$-0.408291\pi$
$61$	−3.15624	−	1.82226i	−0.404115	−	0.233316i	−0.688258	+	0.725466i	$0.741624\pi$
$62$	−0.824954	+	1.42886i	−0.104769	+	0.181466i
$63$	6.54804	+	4.48589i	0.824975	+	0.565169i
$64$	1.00000			0.125000
$65$	−9.50397	−	9.80111i	−1.17882	−	1.21568i
$66$	4.57269	−	8.96114i	0.562859	−	1.10304i
$67$	−9.24567	+	5.33799i	−1.12954	+	0.652139i	−0.943819	−	0.330464i	$-0.892795\pi$
$67$	−9.24567	+	5.33799i	−1.12954	+	0.652139i	−0.185720	+	0.982603i	$0.559462\pi$
$68$	−4.53944			−0.550488
$69$	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	$0.535712\pi$
$72$	−1.22349	+	2.73917i	−0.144190	+	0.322815i
$73$	2.19097	−	3.79486i	0.256433	−	0.444155i	−0.708851	−	0.705359i	$-0.750786\pi$
$73$	2.19097	−	3.79486i	0.256433	−	0.444155i	0.965284	+	0.261203i	$0.0841193\pi$
$74$		−	0.999410i		−	0.116179i
$75$	−16.1513	+	0.836763i	−1.86500	+	0.0966211i
$76$	−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	−0.755203	−	0.655491i	$-0.772462\pi$
$79$	−8.40177	−	14.5523i	−0.945273	−	1.63726i	−0.190071	−	0.981770i	$-0.560872\pi$
$80$	3.27919	−	1.89324i	0.366625	−	0.211671i
$81$	−6.00615	−	6.70270i	−0.667350	−	0.744744i
$82$	−3.48711	−	2.01328i	−0.385087	−	0.222330i
$83$			11.9716i			1.31405i	0.753867	+	0.657027i	$0.228186\pi$
$83$			11.9716i			1.31405i	−0.753867	+	0.657027i	$0.771814\pi$
$84$	−4.23006	+	1.76256i	−0.461537	+	0.192311i
$85$	−14.8857	+	8.59427i	−1.61458	+	0.932180i
$86$	−0.445979	−	0.772459i	−0.0480912	−	0.0832963i
$87$	0.227927	+	4.39948i	0.0244363	+	0.471673i
$88$	2.90419	+	5.03020i	0.309587	+	0.536221i
$89$		−	2.18827i		−	0.231956i	−0.993252	−	0.115978i	$-0.963000\pi$
$89$		−	2.18827i		−	0.231956i	0.993252	−	0.115978i	$-0.0370003\pi$
$90$	1.17386	+	11.2986i	0.123736	+	1.19098i
$91$	−9.51872	+	0.627686i	−0.997833	+	0.0657994i
$92$			4.84897i			0.505540i
$93$	2.85390	−	0.147854i	0.295935	−	0.0153317i
$94$	6.23486	−	3.59970i	0.643077	−	0.371280i
$95$			10.8171i			1.10981i
$96$	−0.942473	−	1.45318i	−0.0961907	−	0.148315i
$97$	6.30970	+	10.9287i	0.640653	+	1.10964i	0.985287	+	0.170907i	$0.0546697\pi$
$97$	6.30970	+	10.9287i	0.640653	+	1.10964i	−0.344634	+	0.938737i	$0.611997\pi$
$98$	−6.54850	−	2.47328i	−0.661499	−	0.249839i
$99$	−17.3318	+	1.80068i	−1.74191	+	0.180975i
$100$	4.66874	−	8.08650i	0.466874	−	0.808650i
$101$	4.84579	+	8.39315i	0.482174	+	0.835150i	0.999791	−	0.0204629i	$-0.00651399\pi$
$101$	4.84579	+	8.39315i	0.482174	+	0.835150i	−0.517617	+	0.855613i	$0.673181\pi$
$102$	4.27830	+	6.59665i	0.423615	+	0.653165i
$103$	2.94432	−	1.69990i	0.290112	−	0.167496i	−0.347880	−	0.937539i	$-0.613098\pi$
$103$	2.94432	−	1.69990i	0.290112	−	0.167496i	0.637992	+	0.770043i	$0.279765\pi$
$104$	−0.879475	−	3.49664i	−0.0862397	−	0.342874i
$105$	−10.5342	+	13.7883i	−1.02803	+	1.34560i
$106$	5.41458	+	3.12611i	0.525910	+	0.303634i
$107$		−	8.84801i		−	0.855369i	−0.903928	−	0.427684i	$-0.859329\pi$
$107$		−	8.84801i		−	0.855369i	0.903928	−	0.427684i	$-0.140671\pi$
$108$	5.13363	−	0.803642i	0.493984	−	0.0773305i
$109$	2.56093	+	1.47855i	0.245292	+	0.141620i	0.617607	−	0.786487i	$-0.288102\pi$
$109$	2.56093	+	1.47855i	0.245292	+	0.141620i	−0.372314	+	0.928107i	$0.621436\pi$
$110$	19.0468	+	10.9967i	1.81604	+	1.04849i
$111$	−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	$0.176359\pi$
$114$	4.94143	−	0.256004i	0.462808	−	0.0239770i
$115$	9.18028	+	15.9007i	0.856065	+	1.48275i
$116$	−2.20269	−	1.27172i	−0.204514	−	0.118076i
$117$	10.6539	+	1.86907i	0.984958	+	0.172796i
$118$			10.0175i			0.922190i
$119$	−2.15682	+	11.8150i	−0.197716	+	1.08308i
$120$	−5.84178	−	2.98094i	−0.533279	−	0.272122i
$121$	−11.3686	+	19.6910i	−1.03351	+	1.79009i
$122$	−3.15624	−	1.82226i	−0.285753	−	0.164979i
$123$	0.360834	+	6.96487i	0.0325353	+	0.628002i
$124$	−0.824954	+	1.42886i	−0.0740830	+	0.128316i
$125$		−	16.4238i		−	1.46899i
$126$	6.54804	+	4.48589i	0.583346	+	0.399635i
$127$	−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	$0.181777\pi$
$128$	1.00000			0.0883883
$129$	−0.702201	+	1.37611i	−0.0618254	+	0.121160i
$130$	−9.50397	−	9.80111i	−0.833553	−	0.859615i
$131$	−6.27140	−	10.8624i	−0.547935	−	0.949051i	−0.998416	−	0.0562650i	$-0.982081\pi$
$131$	−6.27140	−	10.8624i	−0.547935	−	0.949051i	0.450481	−	0.892786i	$-0.351253\pi$
$132$	4.57269	−	8.96114i	0.398001	−	0.779967i
$133$	5.76059	+	4.89319i	0.499507	+	0.424294i
$134$	−9.24567	+	5.33799i	−0.798704	+	0.461132i
$135$	15.3127	−	12.3545i	1.31791	−	1.06331i
$136$	−4.53944			−0.389254
$137$	−15.5523			−1.32872			−0.664360	−	0.747413i	$-0.731296\pi$
$137$	−15.5523			−1.32872			−0.664360	+	0.747413i	$0.731296\pi$
$138$	7.04644	−	4.57002i	0.599833	−	0.389026i
$139$	−7.60046	+	4.38812i	−0.644662	+	0.372196i	−0.786408	−	0.617707i	$-0.788062\pi$
$139$	−7.60046	+	4.38812i	−0.644662	+	0.372196i	0.141746	+	0.989903i	$0.454728\pi$
$140$	−3.36958	−	9.43442i	−0.284781	−	0.797354i
$141$	−11.1072	−	5.66778i	−0.935396	−	0.477313i
$142$	6.77969	+	11.7428i	0.568939	+	0.985432i
$143$	15.0347	−	14.5788i	1.25726	−	1.21914i
$144$	−1.22349	+	2.73917i	−0.101957	+	0.228264i
$145$	−9.63072			−0.799788
$146$	2.19097	−	3.79486i	0.181326	−	0.314065i
$147$	2.57766	+	11.8472i	0.212602	+	0.977139i
$148$		−	0.999410i		−	0.0821510i
$149$	1.53689	−	2.66197i	0.125907	−	0.218077i	−0.796180	−	0.605060i	$-0.793149\pi$
$149$	1.53689	−	2.66197i	0.125907	−	0.218077i	0.922087	+	0.386982i	$0.126483\pi$
$150$	−16.1513	+	0.836763i	−1.31875	+	0.0683214i
$151$	10.9434	+	6.31820i	0.890564	+	0.514167i	0.874127	−	0.485697i	$-0.161434\pi$
$151$	10.9434	+	6.31820i	0.890564	+	0.514167i	0.0164372	+	0.999865i	$0.494768\pi$
$152$	−1.42838	+	2.47403i	−0.115857	+	0.200670i
$153$	5.55396	−	12.4343i	0.449011	−	1.00526i
$154$	14.4722	−	5.16884i	1.16620	−	0.416517i
$155$			6.24735i			0.501799i
$156$	−4.25239	+	4.57353i	−0.340463	+	0.366176i
$157$	8.31434	+	4.80029i	0.663556	+	0.383104i	0.793631	−	0.608400i	$-0.208188\pi$
$157$	8.31434	+	4.80029i	0.663556	+	0.383104i	−0.130074	+	0.991504i	$0.541522\pi$
$158$	−8.40177	−	14.5523i	−0.668409	−	1.15772i
$159$	−0.560282	−	10.8146i	−0.0444333	−	0.857657i
$160$	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
$163$	5.52266	+	3.18851i	0.432568	+	0.249743i	0.700440	−	0.713711i	$-0.252987\pi$
$163$	5.52266	+	3.18851i	0.432568	+	0.249743i	−0.267872	+	0.963454i	$0.586320\pi$
$164$	−3.48711	−	2.01328i	−0.272297	−	0.157211i
$165$	−1.97090	−	38.0425i	−0.153434	−	2.96161i
$166$			11.9716i			0.929177i
$167$	−6.39087	−	3.68977i	−0.494540	−	0.285523i	0.231916	−	0.972736i	$-0.425501\pi$
$167$	−6.39087	−	3.68977i	−0.494540	−	0.285523i	−0.726456	+	0.687213i	$0.758834\pi$
$168$	−4.23006	+	1.76256i	−0.326356	+	0.135984i
$169$	−11.4530	+	6.15043i	−0.881004	+	0.473110i
$170$	−14.8857	+	8.59427i	−1.14168	+	0.659151i
$171$	−5.02919	−	6.93954i	−0.384592	−	0.530680i
$172$	−0.445979	−	0.772459i	−0.0340056	−	0.0588994i
$173$	2.54914	−	4.41523i	0.193807	−	0.335684i	−0.752702	−	0.658362i	$-0.771250\pi$
$173$	2.54914	−	4.41523i	0.193807	−	0.335684i	0.946509	+	0.322678i	$0.104583\pi$
$174$	0.227927	+	4.39948i	0.0172791	+	0.333523i
$175$	−18.8288	−	15.9936i	−1.42332	−	1.20901i
$176$	2.90419	+	5.03020i	0.218911	+	0.379165i
$177$	14.5573	−	9.44127i	1.09420	−	0.709649i
$178$		−	2.18827i		−	0.164018i
$179$	7.44227	−	4.29680i	0.556261	−	0.321158i	−0.195382	−	0.980727i	$-0.562595\pi$
$179$	7.44227	−	4.29680i	0.556261	−	0.321158i	0.751643	+	0.659570i	$0.229261\pi$
$180$	1.17386	+	11.2986i	0.0874947	+	0.842151i
$181$			2.78775i			0.207211i	0.994618	+	0.103606i	$0.0330380\pi$
$181$			2.78775i			0.207211i	−0.994618	+	0.103606i	$0.966962\pi$
$182$	−9.51872	+	0.627686i	−0.705574	+	0.0465272i
$183$	0.326597	+	6.30402i	0.0241427	+	0.466007i
$184$			4.84897i			0.357471i
$185$	−1.89213	−	3.27726i	−0.139112	−	0.240949i
$186$	2.85390	−	0.147854i	0.209258	−	0.0108412i
$187$	−13.1834	−	22.8343i	−0.964065	−	1.66981i
$188$	6.23486	−	3.59970i	0.454724	−	0.262535i
$189$	0.347470	−	13.7433i	0.0252747	−	0.999681i
$190$			10.8171i			0.784755i
$191$	16.9062	+	9.76080i	1.22329	+	0.706267i	0.965618	−	0.259966i	$-0.0837112\pi$
$191$	16.9062	+	9.76080i	1.22329	+	0.706267i	0.257672	+	0.966232i	$0.417045\pi$
$192$	−0.942473	−	1.45318i	−0.0680171	−	0.104875i
$193$	5.49481	−	3.17243i	0.395525	−	0.228357i	−0.289026	−	0.957321i	$-0.593331\pi$
$193$	5.49481	−	3.17243i	0.395525	−	0.228357i	0.684551	+	0.728965i	$0.259998\pi$
$194$	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	$0.0685668\pi$
$198$	−17.3318	+	1.80068i	−1.23172	+	0.127969i
$199$		−	1.69156i		−	0.119912i	−0.998201	−	0.0599559i	$-0.980904\pi$
$199$		−	1.69156i		−	0.119912i	0.998201	−	0.0599559i	$-0.0190960\pi$
$200$	4.66874	−	8.08650i	0.330130	−	0.571802i
$201$	16.4709	+	8.40475i	1.16177	+	0.592825i
$202$	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
$205$	−15.2465			−1.06486
$206$	2.94432	−	1.69990i	0.205140	−	0.118438i
$207$	−13.2822	−	5.93266i	−0.923174	−	0.412348i
$208$	−0.879475	−	3.49664i	−0.0609807	−	0.242449i
$209$	−16.5932			−1.14777
$210$	−10.5342	+	13.7883i	−0.726930	+	0.951483i
$211$	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	$-0.125527\pi$
$212$	5.41458	+	3.12611i	0.371875	+	0.214702i
$213$	10.6747	−	20.9194i	0.731421	−	1.43337i
$214$		−	8.84801i		−	0.604837i
$215$	−2.92490	−	1.68869i	−0.199477	−	0.115168i
$216$	5.13363	−	0.803642i	0.349299	−	0.0546809i
$217$	3.32699	+	2.82603i	0.225851	+	0.191844i
$218$	2.56093	+	1.47855i	0.173448	+	0.100140i
$219$	−7.57956	+	0.392680i	−0.512179	+	0.0265348i
$220$	19.0468	+	10.9967i	1.28413	+	0.741395i
$221$	3.99233	+	15.8728i	0.268553	+	1.06772i
$222$	−1.45233	+	0.941917i	−0.0974738	+	0.0632173i
$223$	8.68120	−	15.0363i	0.581336	−	1.00690i	−0.413985	−	0.910284i	$-0.635864\pi$
$223$	8.68120	−	15.0363i	0.581336	−	1.00690i	0.995321	−	0.0966199i	$-0.0308031\pi$
$224$	0.475130	−	2.60274i	0.0317459	−	0.173903i
$225$	16.4382	+	22.6822i	1.09588	+	1.51215i
$226$	8.71628	−	5.03235i	0.579798	−	0.334747i
$227$		−	19.1522i		−	1.27118i	−0.772027	−	0.635589i	$-0.780757\pi$
$227$		−	19.1522i		−	1.27118i	0.772027	−	0.635589i	$-0.219243\pi$
$228$	4.94143	−	0.256004i	0.327254	−	0.0169543i
$229$	−8.79153	−	15.2274i	−0.580960	−	1.00625i	−0.995366	−	0.0961607i	$-0.969344\pi$
$229$	−8.79153	−	15.2274i	−0.580960	−	1.00625i	0.414405	−	0.910092i	$-0.363990\pi$
$230$	9.18028	+	15.9007i	0.605330	+	1.04846i
$231$	−21.1509	−	16.1592i	−1.39163	−	1.06320i
$232$	−2.20269	−	1.27172i	−0.144614	−	0.0834927i
$233$	1.22176	−	0.705386i	0.0800405	−	0.0462114i	−0.459446	−	0.888206i	$-0.651952\pi$
$233$	1.22176	−	0.705386i	0.0800405	−	0.0462114i	0.539486	+	0.841995i	$0.318619\pi$
$234$	10.6539	+	1.86907i	0.696470	+	0.122185i
$235$	13.6302	−	23.6082i	0.889137	−	1.54003i
$236$			10.0175i			0.652087i
$237$	−13.2287	+	25.9245i	−0.859298	+	1.68398i
$238$	−2.15682	+	11.8150i	−0.139806	+	0.765852i
$239$	−22.2321			−1.43807			−0.719037	−	0.694972i	$-0.755417\pi$
$239$	−22.2321			−1.43807			−0.719037	+	0.694972i	$0.755417\pi$
$240$	−5.84178	−	2.98094i	−0.377085	−	0.192419i
$241$	12.1874			0.785057			0.392528	−	0.919740i	$-0.371600\pi$
$241$	12.1874			0.785057			0.392528	+	0.919740i	$0.371600\pi$
$242$	−11.3686	+	19.6910i	−0.730801	+	1.26578i
$243$	−4.07963	+	15.0452i	−0.261708	+	0.965147i
$244$	−3.15624	−	1.82226i	−0.202058	−	0.116658i
$245$	−26.1563	+	4.28756i	−1.67107	+	0.273922i
$246$	0.360834	+	6.96487i	0.0230059	+	0.444064i
$247$	9.90703	+	2.81870i	0.630369	+	0.179349i
$248$	−0.824954	+	1.42886i	−0.0523846	+	0.0907328i
$249$	17.3970	−	11.2829i	1.10249	−	0.715026i
$250$		−	16.4238i		−	1.03873i
$251$	−4.15920	−	7.20395i	−0.262527	−	0.454709i	0.704386	−	0.709817i	$-0.251222\pi$
$251$	−4.15920	−	7.20395i	−0.262527	−	0.454709i	−0.966913	+	0.255108i	$0.917889\pi$
$252$	6.54804	+	4.48589i	0.412488	+	0.282584i
$253$	−24.3913	+	14.0823i	−1.53347	+	0.885347i
$254$	−0.534780	+	0.926266i	−0.0335551	+	0.0581191i
$255$	26.5184	+	13.5318i	1.66065	+	0.847395i
$256$	1.00000			0.0625000
$257$	−22.0410			−1.37488			−0.687438	−	0.726243i	$-0.741265\pi$
$257$	−22.0410			−1.37488			−0.687438	+	0.726243i	$0.741265\pi$
$258$	−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
$261$	6.17843	−	4.47761i	0.382435	−	0.277157i
$262$	−6.27140	−	10.8624i	−0.387448	−	0.671080i
$263$	−14.9822	+	8.64996i	−0.923840	+	0.533379i	−0.884858	−	0.465861i	$-0.845745\pi$
$263$	−14.9822	+	8.64996i	−0.923840	+	0.533379i	−0.0389820	+	0.999240i	$0.512412\pi$
$264$	4.57269	−	8.96114i	0.281430	−	0.551520i
$265$	23.6739			1.45428
$266$	5.76059	+	4.89319i	0.353204	+	0.300021i
$267$	−3.17996	+	2.06239i	−0.194610	+	0.126216i
$268$	−9.24567	+	5.33799i	−0.564769	+	0.326070i
$269$	−7.57009			−0.461557			−0.230778	−	0.973006i	$-0.574127\pi$
$269$	−7.57009			−0.461557			−0.230778	+	0.973006i	$0.574127\pi$
$270$	15.3127	−	12.3545i	0.931900	−	0.751871i
$271$	−2.07387			−0.125979			−0.0629893	−	0.998014i	$-0.520063\pi$
$271$	−2.07387			−0.125979			−0.0629893	+	0.998014i	$0.520063\pi$
$272$	−4.53944			−0.275244
$273$	9.88328	+	13.2409i	0.598163	+	0.801374i
$274$	−15.5523			−0.939547
$275$	54.2356			3.27053
$276$	7.04644	−	4.57002i	0.424146	−	0.275083i
$277$	−23.6718			−1.42230			−0.711150	−	0.703040i	$-0.751825\pi$
$277$	−23.6718			−1.42230			−0.711150	+	0.703040i	$0.751825\pi$
$278$	−7.60046	+	4.38812i	−0.455845	+	0.263182i
$279$	−2.90458	−	4.00789i	−0.173893	−	0.239946i
$280$	−3.36958	−	9.43442i	−0.201371	−	0.563815i
$281$	25.8285			1.54080			0.770400	−	0.637561i	$-0.220056\pi$
$281$	25.8285			1.54080			0.770400	+	0.637561i	$0.220056\pi$
$282$	−11.1072	−	5.66778i	−0.661425	−	0.337512i
$283$	−14.5695	+	8.41173i	−0.866070	+	0.500026i	−0.866040	−	0.499974i	$-0.833343\pi$
$283$	−14.5695	+	8.41173i	−0.866070	+	0.500026i	−2.94496e−5		1.00000i	$0.500009\pi$
$284$	6.77969	+	11.7428i	0.402301	+	0.696805i
$285$	15.7192	−	10.1948i	0.931128	−	0.603889i
$286$	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
$289$	3.60655			0.212150
$290$	−9.63072			−0.565535
$291$	9.93473	−	19.4692i	0.582384	−	1.14130i
$292$	2.19097	−	3.79486i	0.128217	−	0.222078i
$293$	23.6154	−	13.6344i	1.37963	−	0.796529i	0.387514	−	0.921864i	$-0.373334\pi$
$293$	23.6154	−	13.6344i	1.37963	−	0.796529i	0.992115	+	0.125335i	$0.0400005\pi$
$294$	2.57766	+	11.8472i	0.150332	+	0.690942i
$295$	18.9657	+	32.8495i	1.10422	+	1.91257i
$296$		−	0.999410i		−	0.0580895i
$297$	18.9515	+	23.4893i	1.09968	+	1.36298i
$298$	1.53689	−	2.66197i	0.0890297	−	0.154204i
$299$	16.9551	−	4.26455i	0.980540	−	0.246625i
$300$	−16.1513	+	0.836763i	−0.932498	+	0.0483106i
$301$	−2.22241	+	0.793749i	−0.128097	+	0.0457510i
$302$	10.9434	+	6.31820i	0.629724	+	0.363571i
$303$	7.62977	−	14.9521i	0.438319	−	0.858978i
$304$	−1.42838	+	2.47403i	−0.0819233	+	0.141895i
$305$	−13.7999			−0.790180
$306$	5.55396	−	12.4343i	0.317499	−	0.710823i
$307$	−22.9818			−1.31164			−0.655821	−	0.754917i	$-0.727677\pi$
$307$	−22.9818			−1.31164			−0.655821	+	0.754917i	$0.727677\pi$
$308$	14.4722	−	5.16884i	0.824628	−	0.294522i
$309$	−5.24521	−	2.67652i	−0.298390	−	0.152262i
$310$			6.24735i			0.354826i
$311$	−15.9662	+	27.6543i	−0.905360	+	1.56813i	−0.0849258	+	0.996387i	$0.527065\pi$
$311$	−15.9662	+	27.6543i	−0.905360	+	1.56813i	−0.820434	+	0.571742i	$0.806268\pi$
$312$	−4.25239	+	4.57353i	−0.240744	+	0.258925i
$313$	−5.32050	+	3.07179i	−0.300732	+	0.173628i	−0.642772	−	0.766058i	$-0.722216\pi$
$313$	−5.32050	+	3.07179i	−0.300732	+	0.173628i	0.342039	+	0.939686i	$0.388882\pi$
$314$	8.31434	+	4.80029i	0.469205	+	0.270896i
$315$	29.9652	+	2.31306i	1.68835	+	0.130326i
$316$	−8.40177	−	14.5523i	−0.472637	−	0.818631i
$317$	−7.01958	−	12.1583i	−0.394259	−	0.682877i	0.598747	−	0.800938i	$-0.295665\pi$
$317$	−7.01958	−	12.1583i	−0.394259	−	0.682877i	−0.993006	+	0.118061i	$0.962332\pi$
$318$	−0.560282	−	10.8146i	−0.0314191	−	0.606455i
$319$		−	14.7733i		−	0.827145i
$320$	3.27919	−	1.89324i	0.183313	−	0.105836i
$321$	−12.8578	+	8.33901i	−0.717651	+	0.465438i
$322$	12.6206	+	2.30389i	0.703319	+	0.128391i
$323$	6.48406	−	11.2307i	0.360783	−	0.624894i
$324$	−6.00615	−	6.70270i	−0.333675	−	0.372372i
$325$	−32.3816	−	9.21305i	−1.79621	−	0.511048i
$326$	5.52266	+	3.18851i	0.305872	+	0.176595i
$327$	−0.264996	−	5.11499i	−0.0146543	−	0.282860i
$328$	−3.48711	−	2.01328i	−0.192543	−	0.111165i
$329$	−6.40671	−	17.9380i	−0.353213	−	0.988956i
$330$	−1.97090	−	38.0425i	−0.108494	−	2.09417i
$331$	−7.16125	−	4.13455i	−0.393618	−	0.227256i	0.290108	−	0.956994i	$-0.406309\pi$
$331$	−7.16125	−	4.13455i	−0.393618	−	0.227256i	−0.683727	+	0.729738i	$0.739642\pi$
$332$			11.9716i			0.657027i
$333$	2.73756	+	1.22277i	0.150017	+	0.0670073i
$334$	−6.39087	−	3.68977i	−0.349693	−	0.201895i
$335$	−20.2122	+	35.0086i	−1.10431	+	1.91272i
$336$	−4.23006	+	1.76256i	−0.230769	+	0.0961556i
$337$	8.78687			0.478651			0.239326	−	0.970939i	$-0.423074\pi$
$337$	8.78687			0.478651			0.239326	+	0.970939i	$0.423074\pi$
$338$	−11.4530	+	6.15043i	−0.622964	+	0.334539i
$339$	−15.5278	−	7.92351i	−0.843354	−	0.430346i
$340$	−14.8857	+	8.59427i	−0.807291	+	0.466090i
$341$	−9.58328			−0.518964
$342$	−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
$345$	14.4545	−	28.3266i	0.778204	−	1.52505i
$346$	2.54914	−	4.41523i	0.137042	−	0.237364i
$347$		−	16.4055i		−	0.880693i	−0.897828	−	0.440347i	$-0.854856\pi$
$347$		−	16.4055i		−	0.880693i	0.897828	−	0.440347i	$-0.145144\pi$
$348$	0.227927	+	4.39948i	0.0122182	+	0.235837i
$349$	4.38530	−	7.59556i	0.234740	−	0.406581i	−0.724457	−	0.689320i	$-0.757910\pi$
$349$	4.38530	−	7.59556i	0.234740	−	0.406581i	0.959197	+	0.282739i	$0.0912429\pi$
$350$	−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
$353$	−16.9161	+	9.76652i	−0.900353	+	0.519819i	−0.877315	−	0.479915i	$-0.840667\pi$
$353$	−16.9161	+	9.76652i	−0.900353	+	0.519819i	−0.0230385	+	0.999735i	$0.507334\pi$
$354$	14.5573	−	9.44127i	0.773714	−	0.501798i
$355$	44.4639	+	25.6712i	2.35990	+	1.36249i
$356$		−	2.18827i		−	0.115978i
$357$	19.2021	−	8.00104i	1.01628	−	0.423460i
$358$	7.44227	−	4.29680i	0.393336	−	0.227093i
$359$	−1.54798	−	2.68118i	−0.0816994	−	0.141507i	0.822281	−	0.569082i	$-0.192701\pi$
$359$	−1.54798	−	2.68118i	−0.0816994	−	0.141507i	−0.903980	+	0.427575i	$0.859368\pi$
$360$	1.17386	+	11.2986i	0.0618681	+	0.595491i
$361$	5.41945	+	9.38676i	0.285234	+	0.494040i
$362$			2.78775i			0.146521i
$363$	39.3292	−	2.03756i	2.06425	−	0.106944i
$364$	−9.51872	+	0.627686i	−0.498916	+	0.0328997i
$365$		−	16.5921i		−	0.868472i
$366$	0.326597	+	6.30402i	0.0170715	+	0.329517i
$367$	7.02340	−	4.05496i	0.366619	−	0.211667i	−0.305362	−	0.952236i	$-0.598777\pi$
$367$	7.02340	−	4.05496i	0.366619	−	0.211667i	0.671980	+	0.740569i	$0.265444\pi$
$368$			4.84897i			0.252770i
$369$	9.78117	−	7.08856i	0.509187	−	0.369016i
$370$	−1.89213	−	3.27726i	−0.0983670	−	0.170377i
$371$	10.7091	−	12.6074i	0.555987	−	0.654545i
$372$	2.85390	−	0.147854i	0.147968	−	0.00766586i
$373$	10.1944	−	17.6572i	0.527845	−	0.914255i	−0.471628	−	0.881798i	$-0.656333\pi$
$373$	10.1944	−	17.6572i	0.527845	−	0.914255i	0.999473	−	0.0324572i	$-0.0103333\pi$
$374$	−13.1834	−	22.8343i	−0.681697	−	1.18073i
$375$	−23.8668	+	15.4790i	−1.23248	+	0.799332i
$376$	6.23486	−	3.59970i	0.321538	−	0.185640i
$377$	−2.50955	+	8.82046i	−0.129248	+	0.454277i
$378$	0.347470	−	13.7433i	0.0178719	−	0.706881i
$379$	−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	$0.827018\pi$
$380$			10.8171i			0.554906i
$381$	1.85005	−	0.0958468i	0.0947809	−	0.00491038i
$382$	16.9062	+	9.76080i	0.864997	+	0.499406i
$383$	−21.4155	−	12.3643i	−1.09428	−	0.631785i	−0.159570	−	0.987187i	$-0.551011\pi$
$383$	−21.4155	−	12.3643i	−1.09428	−	0.631785i	−0.934714	+	0.355402i	$0.884344\pi$
$384$	−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
$387$	2.66155	−	0.276520i	0.135294	−	0.0140563i
$388$	6.30970	+	10.9287i	0.320327	+	0.554822i
$389$	7.93751	+	4.58272i	0.402448	+	0.232353i	0.687540	−	0.726147i	$-0.258691\pi$
$389$	7.93751	+	4.58272i	0.402448	+	0.232353i	−0.285092	+	0.958500i	$0.592024\pi$
$390$	−5.28559	+	23.0483i	−0.267646	+	1.16710i
$391$		−	22.0116i		−	1.11318i
$392$	−6.54850	−	2.47328i	−0.330749	−	0.124919i
$393$	−9.87442	+	19.3510i	−0.498099	+	0.976129i
$394$	4.25750	−	7.37421i	0.214490	−	0.371507i
$395$	−55.1021	−	31.8132i	−2.77249	−	1.60070i
$396$	−17.3318	+	1.80068i	−0.870957	+	0.0904874i
$397$	1.69223	−	2.93103i	0.0849306	−	0.147104i	−0.820431	−	0.571746i	$-0.806266\pi$
$397$	1.69223	−	2.93103i	0.0849306	−	0.147104i	0.905362	+	0.424641i	$0.139600\pi$
$398$		−	1.69156i		−	0.0847905i
$399$	1.68151	−	12.9829i	0.0841808	−	0.649958i
$400$	4.66874	−	8.08650i	0.233437	−	0.404325i
$401$	−7.25130			−0.362112			−0.181056	−	0.983473i	$-0.557952\pi$
$401$	−7.25130			−0.362112			−0.181056	+	0.983473i	$0.557952\pi$
$402$	16.4709	+	8.40475i	0.821493	+	0.419191i
$403$	5.72175	+	1.62792i	0.285021	+	0.0810925i
$404$	4.84579	+	8.39315i	0.241087	+	0.417575i
$405$	−32.3852	−	10.6084i	−1.60923	−	0.527133i
$406$	−4.35652	+	5.12879i	−0.216211	+	0.254538i
$407$	5.02723	−	2.90247i	0.249191	−	0.143870i
$408$	4.27830	+	6.59665i	0.211808	+	0.326583i
$409$	1.57460			0.0778592			0.0389296	−	0.999242i	$-0.487605\pi$
$409$	1.57460			0.0778592			0.0389296	+	0.999242i	$0.487605\pi$
$410$	−15.2465			−0.752973
$411$	14.6576	+	22.6003i	0.723006	+	1.11479i
$412$	2.94432	−	1.69990i	0.145056	−	0.0837482i
$413$	26.0731	+	4.75963i	1.28297	+	0.234206i
$414$	−13.2822	−	5.93266i	−0.652783	−	0.291574i
$415$	22.6652	+	39.2572i	1.11259	+	1.92706i
$416$	−0.879475	−	3.49664i	−0.0431198	−	0.171437i
$417$	13.5400	+	6.90917i	0.663056	+	0.338344i
$418$	−16.5932			−0.811598
$419$	−13.4922	+	23.3691i	−0.659136	+	1.14166i	0.321704	+	0.946840i	$0.395745\pi$
$419$	−13.4922	+	23.3691i	−0.659136	+	1.14166i	−0.980840	+	0.194817i	$0.937589\pi$
$420$	−10.5342	+	13.7883i	−0.514017	+	0.672800i
$421$		−	13.0461i		−	0.635827i	−0.948120	−	0.317913i	$-0.897018\pi$
$421$		−	13.0461i		−	0.635827i	0.948120	−	0.317913i	$-0.102982\pi$
$422$	11.5387	−	19.9857i	0.561697	−	0.972889i
$423$	2.23191	+	21.4826i	0.108519	+	1.04452i
$424$	5.41458	+	3.12611i	0.262955	+	0.151817i
$425$	−21.1935	+	36.7082i	−1.02804	+	1.78061i
$426$	10.6747	−	20.9194i	0.517193	−	1.01355i
$427$	−6.24248	+	7.34906i	−0.302095	+	0.355646i
$428$		−	8.84801i		−	0.427684i
$429$	−35.3555	−	8.10796i	−1.70698	−	0.391456i
$430$	−2.92490	−	1.68869i	−0.141051	−	0.0814361i
$431$	18.2521	+	31.6136i	0.879173	+	1.52277i	0.852250	+	0.523135i	$0.175238\pi$
$431$	18.2521	+	31.6136i	0.879173	+	1.52277i	0.0269232	+	0.999638i	$0.491429\pi$
$432$	5.13363	−	0.803642i	0.246992	−	0.0386652i
$433$	−23.6502	+	13.6545i	−1.13656	+	0.656192i	−0.945576	−	0.325402i	$-0.894501\pi$
$433$	−23.6502	+	13.6545i	−1.13656	+	0.656192i	−0.190982	+	0.981594i	$0.561167\pi$
$434$	3.32699	+	2.82603i	0.159701	+	0.135654i
$435$	9.07669	+	13.9952i	0.435194	+	0.671019i
$436$	2.56093	+	1.47855i	0.122646	+	0.0708098i
$437$	−11.9965	−	6.92618i	−0.573870	−	0.331324i
$438$	−7.57956	+	0.392680i	−0.362166	+	0.0187630i
$439$		−	0.455718i		−	0.0217502i	−0.999941	−	0.0108751i	$-0.996538\pi$
$439$		−	0.455718i		−	0.0217502i	0.999941	−	0.0108751i	$-0.00346172\pi$
$440$	19.0468	+	10.9967i	0.908020	+	0.524245i
$441$	14.7868	−	14.9115i	0.704131	−	0.710070i
$442$	3.99233	+	15.8728i	0.189896	+	0.754993i
$443$	−23.2231	+	13.4079i	−1.10337	+	0.637028i	−0.937103	−	0.349053i	$-0.886503\pi$
$443$	−23.2231	+	13.4079i	−1.10337	+	0.637028i	−0.166262	+	0.986082i	$0.553170\pi$
$444$	−1.45233	+	0.941917i	−0.0689244	+	0.0447014i
$445$	−4.14293	−	7.17576i	−0.196394	−	0.340164i
$446$	8.68120	−	15.0363i	0.411067	−	0.711988i
$447$	−5.31681	+	0.275452i	−0.251477	+	0.0130284i
$448$	0.475130	−	2.60274i	0.0224478	−	0.122968i
$449$	−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	$0.839373\pi$
$450$	16.4382	+	22.6822i	0.774903	+	1.06925i
$451$		−	23.3878i		−	1.10129i
$452$	8.71628	−	5.03235i	0.409979	−	0.236702i
$453$	−1.13239	−	21.8576i	−0.0532043	−	1.02696i
$454$		−	19.1522i		−	0.898859i
$455$	−30.0254	+	20.0796i	−1.40761	+	0.941344i
$456$	4.94143	−	0.256004i	0.231404	−	0.0119885i
$457$			15.2345i			0.712641i	0.934364	+	0.356321i	$0.115969\pi$
$457$			15.2345i			0.712641i	−0.934364	+	0.356321i	$0.884031\pi$
$458$	−8.79153	−	15.2274i	−0.410801	−	0.711528i
$459$	−23.3038	+	3.64809i	−1.08773	+	0.170278i
$460$	9.18028	+	15.9007i	0.428033	+	0.741374i
$461$	−11.4420	+	6.60603i	−0.532906	+	0.307673i	−0.742199	−	0.670180i	$-0.766217\pi$
$461$	−11.4420	+	6.60603i	−0.532906	+	0.307673i	0.209293	+	0.977853i	$0.432884\pi$
$462$	−21.1509	−	16.1592i	−0.984029	−	0.751795i
$463$		−	15.4572i		−	0.718355i	−0.933269	−	0.359177i	$-0.883057\pi$
$463$		−	15.4572i		−	0.718355i	0.933269	−	0.359177i	$-0.116943\pi$
$464$	−2.20269	−	1.27172i	−0.102257	−	0.0590382i
$465$	9.07856	−	5.88796i	0.421008	−	0.273048i
$466$	1.22176	−	0.705386i	0.0565972	−	0.0326764i
$467$	−0.665574	−	1.15281i	−0.0307991	−	0.0533456i	0.850215	−	0.526436i	$-0.176472\pi$
$467$	−0.665574	−	1.15281i	−0.0307991	−	0.0533456i	−0.881014	+	0.473090i	$0.843139\pi$
$468$	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
$471$	−0.860340	−	16.6064i	−0.0396424	−	0.765183i
$472$			10.0175i			0.461095i
$473$	2.59041	−	4.48673i	0.119107	−	0.206300i
$474$	−13.2287	+	25.9245i	−0.607616	+	1.19075i
$475$	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
$478$	−22.2321			−1.01687
$479$	−12.4718	+	7.20059i	−0.569851	+	0.329003i	−0.757090	−	0.653311i	$-0.773379\pi$
$479$	−12.4718	+	7.20059i	−0.569851	+	0.329003i	0.187239	+	0.982314i	$0.440046\pi$
$480$	−5.84178	−	2.98094i	−0.266640	−	0.136061i
$481$	−3.49458	+	0.878957i	−0.159339	+	0.0400770i
$482$	12.1874			0.555119
$483$	−8.54660	−	20.5114i	−0.388884	−	0.933302i
$484$	−11.3686	+	19.6910i	−0.516754	+	0.895045i
$485$	41.3815	+	23.8916i	1.87904	+	1.08486i
$486$	−4.07963	+	15.0452i	−0.185056	+	0.682462i
$487$			30.5356i			1.38370i	0.722042	+	0.691849i	$0.243204\pi$
$487$			30.5356i			1.38370i	−0.722042	+	0.691849i	$0.756796\pi$
$488$	−3.15624	−	1.82226i	−0.142876	−	0.0824896i
$489$	−0.571466	−	11.0305i	−0.0258426	−	0.498817i
$490$	−26.1563	+	4.28756i	−1.18162	+	0.193692i
$491$	−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	$0.689835\pi$
$492$	0.360834	+	6.96487i	0.0162677	+	0.314001i
$493$	9.99898	+	5.77291i	0.450331	+	0.259999i
$494$	9.90703	+	2.81870i	0.445738	+	0.126819i
$495$	−53.4253	+	38.7181i	−2.40129	+	1.74025i
$496$	−0.824954	+	1.42886i	−0.0370415	+	0.0641578i
$497$	33.7846	−	12.0664i	1.51545	−	0.541254i
$498$	17.3970	−	11.2829i	0.779576	−	0.505600i
$499$	15.8562	−	9.15459i	0.709821	−	0.409816i	−0.101173	−	0.994869i	$-0.532260\pi$
$499$	15.8562	−	9.15459i	0.709821	−	0.409816i	0.810995	+	0.585053i	$0.198926\pi$
$500$		−	16.4238i		−	0.734495i
$501$	0.661306	+	12.7646i	0.0295450	+	0.570281i
$502$	−4.15920	−	7.20395i	−0.185634	−	0.321528i
$503$	4.84489	+	8.39159i	0.216023	+	0.374162i	0.953588	−	0.301113i	$-0.0973581\pi$
$503$	4.84489	+	8.39159i	0.216023	+	0.374162i	−0.737566	+	0.675275i	$0.764025\pi$
$504$	6.54804	+	4.48589i	0.291673	+	0.199817i
$505$	31.7806	+	18.3485i	1.41422	+	0.816498i
$506$	−24.3913	+	14.0823i	−1.08432	+	0.626035i
$507$	19.7319	+	10.8468i	0.876324	+	0.481722i
$508$	−0.534780	+	0.926266i	−0.0237270	+	0.0410964i
$509$		−	32.4912i		−	1.44015i	−0.693897	−	0.720074i	$-0.744108\pi$
$509$		−	32.4912i		−	1.44015i	0.693897	−	0.720074i	$-0.255892\pi$
$510$	26.5184	+	13.5318i	1.17426	+	0.599199i
$511$	−8.83605	−	7.50556i	−0.390884	−	0.332027i
$512$	1.00000			0.0441942
$513$	−5.34455	+	13.8487i	−0.235968	+	0.611434i
$514$	−22.0410			−0.972185
$515$	6.43666	−	11.1486i	0.283633	−	0.491267i
$516$	−0.702201	+	1.37611i	−0.0309127	+	0.0605799i
$517$	36.2144	+	20.9084i	1.59271	+	0.919550i
$518$	−2.60120	−	0.474849i	−0.114290	−	0.0208637i
$519$	−8.81864	+	0.456874i	−0.387095	+	0.0200545i
$520$	−9.50397	−	9.80111i	−0.416777	−	0.429807i
$521$	21.3684	−	37.0111i	0.936166	−	1.62149i	0.163624	−	0.986523i	$-0.447682\pi$
$521$	21.3684	−	37.0111i	0.936166	−	1.62149i	0.772542	−	0.634964i	$-0.218985\pi$
$522$	6.17843	−	4.47761i	0.270423	−	0.195979i
$523$		−	0.499654i		−	0.0218484i	−0.999940	−	0.0109242i	$-0.996523\pi$
$523$		−	0.499654i		−	0.0218484i	0.999940	−	0.0109242i	$-0.00347734\pi$
$524$	−6.27140	−	10.8624i	−0.273967	−	0.474526i
$525$	−5.49610	+	42.4353i	−0.239869	+	1.85203i
$526$	−14.9822	+	8.64996i	−0.653254	+	0.377156i
$527$	3.74483	−	6.48624i	0.163127	−	0.282545i
$528$	4.57269	−	8.96114i	0.199001	−	0.389984i
$529$	−0.512495			−0.0222824
$530$	23.6739			1.02833
$531$	−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
$534$	−3.17996	+	2.06239i	−0.137610	+	0.0892482i
$535$	−16.7514	−	29.0143i	−0.724227	−	1.25440i
$536$	−9.24567	+	5.33799i	−0.399352	+	0.230566i
$537$	−13.2582	−	6.76537i	−0.572132	−	0.291947i
$538$	−7.57009			−0.326370
$539$	−6.57700	−	40.1231i	−0.283291	−	1.72823i
$540$	15.3127	−	12.3545i	0.658953	−	0.531653i
$541$	−14.9336	+	8.62192i	−0.642046	+	0.370685i	−0.785402	−	0.618986i	$-0.787544\pi$
$541$	−14.9336	+	8.62192i	−0.642046	+	0.370685i	0.143356	+	0.989671i	$0.454210\pi$
$542$	−2.07387			−0.0890803
$543$	4.05111	−	2.62737i	0.173850	−	0.112751i
$544$	−4.53944			−0.194627
$545$	11.1970			0.479628
$546$	9.88328	+	13.2409i	0.422965	+	0.566657i
$547$	22.0489			0.942741			0.471370	−	0.881935i	$-0.343759\pi$
$547$	22.0489			0.942741			0.471370	+	0.881935i	$0.343759\pi$
$548$	−15.5523			−0.664360
$549$	8.85310	−	6.41598i	0.377841	−	0.273827i
$550$	54.2356			2.31261
$551$	6.29256	−	3.63301i	0.268072	−	0.154771i
$552$	7.04644	−	4.57002i	0.299917	−	0.194513i
$553$	−41.8678	+	14.9534i	−1.78040	+	0.635883i
$554$	−23.6718			−1.00572
$555$	−2.97918	+	5.83834i	−0.126459	+	0.247824i
$556$	−7.60046	+	4.38812i	−0.322331	+	0.186098i
$557$	7.59729	+	13.1589i	0.321908	+	0.557560i	0.980882	−	0.194605i	$-0.0623426\pi$
$557$	7.59729	+	13.1589i	0.321908	+	0.557560i	−0.658974	+	0.752166i	$0.729009\pi$
$558$	−2.90458	−	4.00789i	−0.122961	−	0.169667i
$559$	−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
$562$	25.8285			1.08951
$563$	−2.63574			−0.111083			−0.0555416	−	0.998456i	$-0.517689\pi$
$563$	−2.63574			−0.111083			−0.0555416	+	0.998456i	$0.517689\pi$
$564$	−11.1072	−	5.66778i	−0.467698	−	0.238657i
$565$	19.0549	−	33.0041i	0.801646	−	1.38849i
$566$	−14.5695	+	8.41173i	−0.612404	+	0.353571i
$567$	−20.2991	+	12.4478i	−0.852481	+	0.522758i
$568$	6.77969	+	11.7428i	0.284470	+	0.492716i
$569$			44.2841i			1.85649i	0.371973	+	0.928244i	$0.378681\pi$
$569$			44.2841i			1.85649i	−0.371973	+	0.928244i	$0.621319\pi$
$570$	15.7192	−	10.1948i	0.658407	−	0.427014i
$571$	−1.88780	+	3.26977i	−0.0790021	+	0.136836i	−0.902820	−	0.430019i	$-0.858507\pi$
$571$	−1.88780	+	3.26977i	−0.0790021	+	0.136836i	0.823818	+	0.566855i	$0.191840\pi$
$572$	15.0347	−	14.5788i	0.628630	−	0.609572i
$573$	−1.74940	−	33.7671i	−0.0730821	−	1.41064i
$574$	−6.89688	+	8.11946i	−0.287870	+	0.338900i
$575$	39.2112	+	22.6386i	1.63522	+	0.944094i
$576$	−1.22349	+	2.73917i	−0.0509787	+	0.114132i
$577$	11.1370	−	19.2899i	0.463640	−	0.803048i	−0.535499	−	0.844536i	$-0.679877\pi$
$577$	11.1370	−	19.2899i	0.463640	−	0.803048i	0.999139	+	0.0414882i	$0.0132099\pi$
$578$	3.60655			0.150013
$579$	−9.78884	−	4.99504i	−0.406810	−	0.207587i
$580$	−9.63072			−0.399894
$581$	31.1590	+	5.68807i	1.29269	+	0.235981i
$582$	9.93473	−	19.4692i	0.411808	−	0.807024i
$583$			36.3152i			1.50402i
$584$	2.19097	−	3.79486i	0.0906628	−	0.157033i
$585$	38.4750	−	14.0415i	1.59074	−	0.580543i
$586$	23.6154	−	13.6344i	0.975545	−	0.563231i
$587$	18.7811	+	10.8433i	0.775179	+	0.447550i	0.834719	−	0.550676i	$-0.185630\pi$
$587$	18.7811	+	10.8433i	0.775179	+	0.447550i	−0.0595402	+	0.998226i	$0.518963\pi$
$588$	2.57766	+	11.8472i	0.106301	+	0.488569i
$589$	−2.35670	−	4.08192i	−0.0971061	−	0.168193i
$590$	18.9657	+	32.8495i	0.780804	+	1.35239i
$591$	−14.7287	+	0.763058i	−0.605856	+	0.0313880i
$592$		−	0.999410i		−	0.0410755i
$593$	2.83216	−	1.63515i	0.116303	−	0.0671475i	−0.440720	−	0.897645i	$-0.645277\pi$
$593$	2.83216	−	1.63515i	0.116303	−	0.0671475i	0.557023	+	0.830497i	$0.311944\pi$
$594$	18.9515	+	23.4893i	0.777589	+	0.963776i
$595$	15.2960	+	42.8270i	0.627075	+	1.75574i
$596$	1.53689	−	2.66197i	0.0629535	−	0.109039i
$597$	−2.45816	+	1.59425i	−0.100606	+	0.0652485i
$598$	16.9551	−	4.26455i	0.693346	−	0.174390i
$599$	−17.7669	−	10.2577i	−0.725935	−	0.419119i	0.0909981	−	0.995851i	$-0.470994\pi$
$599$	−17.7669	−	10.2577i	−0.725935	−	0.419119i	−0.816933	+	0.576732i	$0.804328\pi$
$600$	−16.1513	+	0.836763i	−0.659375	+	0.0341607i
$601$	−25.4328	−	14.6836i	−1.03743	−	0.598958i	−0.118322	−	0.992975i	$-0.537752\pi$
$601$	−25.4328	−	14.6836i	−1.03743	−	0.598958i	−0.919103	+	0.394017i	$0.871085\pi$
$602$	−2.22241	+	0.793749i	−0.0905785	+	0.0323508i
$603$	−3.30970	−	31.8565i	−0.134782	−	1.29730i
$604$	10.9434	+	6.31820i	0.445282	+	0.257084i
$605$			86.0941i			3.50022i
$606$	7.62977	−	14.9521i	0.309938	−	0.607389i
$607$	6.35329	+	3.66808i	0.257872	+	0.148883i	0.623364	−	0.781932i	$-0.285766\pi$
$607$	6.35329	+	3.66808i	0.257872	+	0.148883i	−0.365491	+	0.930815i	$0.619099\pi$
$608$	−1.42838	+	2.47403i	−0.0579286	+	0.100335i
$609$	11.5590	+	1.49709i	0.468394	+	0.0606650i
$610$	−13.7999			−0.558741
$611$	−18.0703	−	18.6352i	−0.731045	−	0.753901i
$612$	5.55396	−	12.4343i	0.224506	−	0.502628i
$613$	8.59919	−	4.96474i	0.347318	−	0.200524i	−0.316185	−	0.948697i	$-0.602402\pi$
$613$	8.59919	−	4.96474i	0.347318	−	0.200524i	0.663503	+	0.748173i	$0.269069\pi$
$614$	−22.9818			−0.927470
$615$	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	$0.952096\pi$
$618$	−5.24521	−	2.67652i	−0.210993	−	0.107666i
$619$	−24.1824	+	41.8852i	−0.971973	+	1.68351i	−0.282392	+	0.959299i	$0.591128\pi$
$619$	−24.1824	+	41.8852i	−0.971973	+	1.68351i	−0.689582	+	0.724208i	$0.742206\pi$
$620$			6.24735i			0.250900i
$621$	3.89683	+	24.8928i	0.156375	+	0.998914i
$622$	−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
$626$	−5.32050	+	3.07179i	−0.212650	+	0.122773i
$627$	15.6386	+	24.1129i	0.624545	+	0.962977i
$628$	8.31434	+	4.80029i	0.331778	+	0.191552i
$629$			4.53677i			0.180893i
$630$	29.9652	+	2.31306i	1.19384	+	0.0921545i
$631$	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
$633$	−39.9179	+	2.06805i	−1.58659	+	0.0821977i
$634$	−7.01958	−	12.1583i	−0.278783	−	0.482867i
$635$			4.04987i			0.160714i
$636$	−0.560282	−	10.8146i	−0.0222166	−	0.428829i
$637$	−2.88892	+	25.0730i	−0.114463	+	0.993427i
$638$		−	14.7733i		−	0.584880i
$639$	−40.4604	+	4.20360i	−1.60059	+	0.166292i
$640$	3.27919	−	1.89324i	0.129622	−	0.0748370i
$641$			8.01456i			0.316556i	0.987395	+	0.158278i	$0.0505942\pi$
$641$			8.01456i			0.316556i	−0.987395	+	0.158278i	$0.949406\pi$
$642$	−12.8578	+	8.33901i	−0.507456	+	0.329114i
$643$	−13.5619	−	23.4899i	−0.534830	−	0.926353i	−0.999172	−	0.0406964i	$-0.987042\pi$
$643$	−13.5619	−	23.4899i	−0.534830	−	0.926353i	0.464342	−	0.885656i	$-0.346291\pi$
$644$	12.6206	+	2.30389i	0.497321	+	0.0907859i
$645$	0.302659	+	5.84197i	0.0119172	+	0.230027i
$646$	6.48406	−	11.2307i	0.255112	−	0.441867i
$647$	7.96876	+	13.8023i	0.313284	+	0.542624i	0.979071	−	0.203518i	$-0.0652374\pi$
$647$	7.96876	+	13.8023i	0.313284	+	0.542624i	−0.665787	+	0.746142i	$0.731904\pi$
$648$	−6.00615	−	6.70270i	−0.235944	−	0.263307i
$649$	−50.3902	+	29.0928i	−1.97799	+	1.14199i
$650$	−32.3816	−	9.21305i	−1.27011	−	0.361366i
$651$	0.971146	−	7.49820i	0.0380622	−	0.293878i
$652$	5.52266	+	3.18851i	0.216284	+	0.124872i
$653$		−	42.3070i		−	1.65560i	−0.561022	−	0.827801i	$-0.689592\pi$
$653$		−	42.3070i		−	1.65560i	0.561022	−	0.827801i	$-0.310408\pi$
$654$	−0.264996	−	5.11499i	−0.0103622	−	0.200012i
$655$	−41.1303	−	23.7466i	−1.60709	−	0.927856i
$656$	−3.48711	−	2.01328i	−0.136149	−	0.0786055i
$657$	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	$0.592968\pi$
$660$	−1.97090	−	38.0425i	−0.0767170	−	1.48080i
$661$	−10.4632	−	18.1227i	−0.406970	−	0.704892i	0.587579	−	0.809167i	$-0.300081\pi$
$661$	−10.4632	−	18.1227i	−0.406970	−	0.704892i	−0.994549	+	0.104275i	$0.966748\pi$
$662$	−7.16125	−	4.13455i	−0.278330	−	0.160694i
$663$	19.3035	−	20.7613i	0.749685	−	0.806302i
$664$			11.9716i			0.464589i
$665$	28.1541	+	5.13953i	1.09177	+	0.199302i
$666$	2.73756	+	1.22277i	0.106078	+	0.0473813i
$667$	6.16654	−	10.6808i	0.238769	−	0.413561i
$668$	−6.39087	−	3.68977i	−0.247270	−	0.142761i
$669$	−30.0323	+	1.55590i	−1.16111	+	0.0601547i
$670$	−20.2122	+	35.0086i	−0.780867	+	1.35250i
$671$		−	21.1687i		−	0.817208i
$672$	−4.23006	+	1.76256i	−0.163178	+	0.0679922i
$673$	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	$0.0314439\pi$
$674$	8.78687			0.338458
$675$	17.4689	−	45.2651i	0.672380	−	1.74225i
$676$	−11.4530	+	6.15043i	−0.440502	+	0.236555i
$677$	12.4515	+	21.5666i	0.478550	+	0.828873i	0.999698	−	0.0245935i	$-0.00782915\pi$
$677$	12.4515	+	21.5666i	0.478550	+	0.828873i	−0.521147	+	0.853467i	$0.674496\pi$
$678$	−15.5278	−	7.92351i	−0.596341	−	0.304301i
$679$	31.4425	−	11.2299i	1.20665	−	0.430966i
$680$	−14.8857	+	8.59427i	−0.570841	+	0.329575i
$681$	−27.8317	+	18.0505i	−1.06651	+	0.691695i
$682$	−9.58328			−0.366963
$683$	−17.9767			−0.687860			−0.343930	−	0.938995i	$-0.611758\pi$
$683$	−17.9767			−0.687860			−0.343930	+	0.938995i	$0.611758\pi$
$684$	−5.02919	−	6.93954i	−0.192296	−	0.265340i
$685$	−50.9989	+	29.4442i	−1.94857	+	1.12501i
$686$	−9.54868	+	15.8689i	−0.364570	+	0.605878i
$687$	−13.8424	+	27.1271i	−0.528121	+	1.03496i
$688$	−0.445979	−	0.772459i	−0.0170028	−	0.0294497i
$689$	6.16890	−	21.6822i	0.235016	−	0.826025i
$690$	14.4545	−	28.3266i	0.550273	−	1.07838i
$691$	21.1436			0.804341			0.402170	−	0.915565i	$-0.368256\pi$
$691$	21.1436			0.804341			0.402170	+	0.915565i	$0.368256\pi$
$692$	2.54914	−	4.41523i	0.0969036	−	0.167842i
$693$	−3.54817	+	45.9658i	−0.134784	+	1.74610i
$694$		−	16.4055i		−	0.622744i
$695$	−16.6156	+	28.7790i	−0.630265	+	1.09165i
$696$	0.227927	+	4.39948i	0.00863954	+	0.166762i
$697$	15.8295	+	9.13918i	0.599586	+	0.346171i
$698$	4.38530	−	7.59556i	0.165986	−	0.287496i
$699$	−2.17654	−	1.11064i	−0.0823242	−	0.0420083i
$700$	−18.8288	−	15.9936i	−0.711661	−	0.604503i
$701$			22.8317i			0.862342i	0.902270	+	0.431171i	$0.141900\pi$
$701$			22.8317i			0.862342i	−0.902270	+	0.431171i	$0.858100\pi$
$702$	−7.32495	−	17.2437i	−0.276462	−	0.650821i
$703$	2.47257	+	1.42754i	0.0932548	+	0.0538407i
$704$	2.90419	+	5.03020i	0.109456	+	0.189583i
$705$	−47.1532	+	2.44290i	−1.77589	+	0.0920049i
$706$	−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
$709$	−42.6427	−	24.6198i	−1.60148	−	0.924615i	−0.991191	−	0.132437i	$-0.957720\pi$
$709$	−42.6427	−	24.6198i	−1.60148	−	0.924615i	−0.610289	−	0.792179i	$-0.708947\pi$
$710$	44.4639	+	25.6712i	1.66870	+	0.963424i
$711$	50.1408	−	5.20934i	1.88043	−	0.195365i
$712$		−	2.18827i		−	0.0820089i
$713$	−6.92851	−	4.00017i	−0.259475	−	0.149808i
$714$	19.2021	−	8.00104i	0.718621	−	0.299432i
$715$	21.7002	−	76.2711i	0.811543	−	2.85238i
$716$	7.44227	−	4.29680i	0.278131	−	0.160579i
$717$	20.9531	+	32.3073i	0.782509	+	1.20654i
$718$	−1.54798	−	2.68118i	−0.0577702	−	0.100061i
$719$	24.8204	−	42.9901i	0.925643	−	1.60326i	0.135119	−	0.990829i	$-0.456858\pi$
$719$	24.8204	−	42.9901i	0.925643	−	1.60326i	0.790524	−	0.612431i	$-0.209808\pi$
$720$	1.17386	+	11.2986i	0.0437473	+	0.421076i
$721$	−3.02547	−	8.47096i	−0.112674	−	0.315475i
$722$	5.41945	+	9.38676i	0.201691	+	0.349339i
$723$	−11.4863	−	17.7105i	−0.427179	−	0.658660i
$724$			2.78775i			0.103606i
$725$	−20.5676	+	11.8747i	−0.763860	+	0.441015i
$726$	39.3292	−	2.03756i	1.45964	−	0.0756208i
$727$		−	24.4519i		−	0.906870i	−0.891289	−	0.453435i	$-0.850198\pi$
$727$		−	24.4519i		−	0.906870i	0.891289	−	0.453435i	$-0.149802\pi$
$728$	−9.51872	+	0.627686i	−0.352787	+	0.0232636i
$729$	25.7083	−	8.25120i	0.952160	−	0.305600i
$730$		−	16.5921i		−	0.614102i
$731$	2.02450	+	3.50653i	0.0748787	+	0.129694i
$732$	0.326597	+	6.30402i	0.0120714	+	0.233003i
$733$	1.21258	+	2.10024i	0.0447875	+	0.0775743i	0.887550	−	0.460711i	$-0.152406\pi$
$733$	1.21258	+	2.10024i	0.0447875	+	0.0775743i	−0.842763	+	0.538285i	$0.819072\pi$
$734$	7.02340	−	4.05496i	0.259239	−	0.149671i
$735$	30.8822	+	33.9691i	1.13911	+	1.25297i
$736$			4.84897i			0.178735i
$737$	−53.7023	−	31.0050i	−1.97815	−	1.14209i
$738$	9.78117	−	7.08856i	0.360050	−	0.260934i
$739$	40.5440	−	23.4081i	1.49144	−	0.861081i	0.491484	−	0.870887i	$-0.336455\pi$
$739$	40.5440	−	23.4081i	1.49144	−	0.861081i	0.999952	+	0.00980593i	$0.00312138\pi$
$740$	−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	$0.127695\pi$
$744$	2.85390	−	0.147854i	0.104629	−	0.00542058i
$745$		−	11.6388i		−	0.426414i
$746$	10.1944	−	17.6572i	0.373243	−	0.646476i
$747$	−32.7923	−	14.6471i	−1.19981	−	0.535911i
$748$	−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
$751$	−5.99014			−0.218583			−0.109292	−	0.994010i	$-0.534858\pi$
$751$	−5.99014			−0.218583			−0.109292	+	0.994010i	$0.534858\pi$
$752$	6.23486	−	3.59970i	0.227362	−	0.131267i
$753$	−6.54873	+	12.8336i	−0.238649	+	0.467683i
$754$	−2.50955	+	8.82046i	−0.0913925	+	0.321222i
$755$	47.8475			1.74135
$756$	0.347470	−	13.7433i	0.0126373	−	0.499840i
$757$	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	$-0.198525\pi$
$758$	−16.2771	−	9.39758i	−0.591210	−	0.341335i
$759$	43.4523	+	22.1728i	1.57722	+	0.804822i
$760$			10.8171i			0.392378i
$761$	−7.23145	−	4.17508i	−0.262140	−	0.151347i	0.363170	−	0.931723i	$-0.381694\pi$
$761$	−7.23145	−	4.17508i	−0.262140	−	0.151347i	−0.625310	+	0.780376i	$0.715028\pi$
$762$	1.85005	−	0.0958468i	0.0670202	−	0.00347216i
$763$	5.06506	−	5.96292i	0.183367	−	0.215872i
$764$	16.9062	+	9.76080i	0.611645	+	0.353133i
$765$	−5.32869	−	51.2896i	−0.192659	−	1.85438i
$766$	−21.4155	−	12.3643i	−0.773775	−	0.446739i
$767$	35.0278	−	8.81019i	1.26478	−	0.318117i
$768$	−0.942473	−	1.45318i	−0.0340086	−	0.0524373i
$769$	23.1255	−	40.0545i	0.833926	−	1.44440i	−0.0609760	−	0.998139i	$-0.519421\pi$
$769$	23.1255	−	40.0545i	0.833926	−	1.44440i	0.894902	−	0.446263i	$-0.147245\pi$
$770$	37.6711	−	44.3490i	1.35757	−	1.59823i
$771$	20.7730	+	32.0296i	0.748121	+	1.15352i
$772$	5.49481	−	3.17243i	0.197763	−	0.114178i
$773$		−	0.668313i		−	0.0240375i	−0.999928	−	0.0120188i	$-0.996174\pi$
$773$		−	0.668313i		−	0.0240375i	0.999928	−	0.0120188i	$-0.00382578\pi$
$774$	2.66155	−	0.276520i	0.0956674	−	0.00993929i
$775$	7.70299	+	13.3420i	0.276700	+	0.479258i
$776$	6.30970	+	10.9287i	0.226505	+	0.392318i
$777$	1.76152	+	4.22756i	0.0631942	+	0.151663i
$778$	7.93751	+	4.58272i	0.284574	+	0.164299i
$779$	9.96185	−	5.75147i	0.356920	−	0.206068i
$780$	−5.28559	+	23.0483i	−0.189254	+	0.825262i
$781$	−39.3790	+	68.2064i	−1.40909	+	2.44062i
$782$		−	22.0116i		−	0.787134i
$783$	−12.3298	−	4.75838i	−0.440631	−	0.170051i
$784$	−6.54850	−	2.47328i	−0.233875	−	0.0883313i
$785$	36.3524			1.29747
$786$	−9.87442	+	19.3510i	−0.352209	+	0.690228i
$787$	3.24383			0.115630			0.0578150	−	0.998327i	$-0.481587\pi$
$787$	3.24383			0.115630			0.0578150	+	0.998327i	$0.481587\pi$
$788$	4.25750	−	7.37421i	0.151667	−	0.262695i
$789$	26.6903	+	13.6195i	0.950199	+	0.484867i
$790$	−55.1021	−	31.8132i	−1.96044	−	1.13186i
$791$	−8.95653	−	25.0772i	−0.318457	−	0.891644i
$792$	−17.3318	+	1.80068i	−0.615860	+	0.0639843i
$793$	−3.59595	+	12.6389i	−0.127696	+	0.448820i
$794$	1.69223	−	2.93103i	0.0600550	−	0.104018i
$795$	−22.3120	−	34.4026i	−0.791326	−	1.22013i
$796$		−	1.69156i		−	0.0599559i
$797$	−22.9206	−	39.6996i	−0.811889	−	1.40623i	−0.911541	−	0.411210i	$-0.865106\pi$
$797$	−22.9206	−	39.6996i	−0.811889	−	1.40623i	0.0996520	−	0.995022i	$-0.468227\pi$
$798$	1.68151	−	12.9829i	0.0595248	−	0.459590i
$799$	−28.3028	+	16.3406i	−1.00128	+	0.578090i
$800$	4.66874	−	8.08650i	0.165065	−	0.285901i
$801$	5.99406	+	2.67733i	0.211790	+	0.0945987i
$802$	−7.25130			−0.256052
$803$	25.4519			0.898178
$804$	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
$807$	7.13461	+	11.0007i	0.251150	+	0.387244i
$808$	4.84579	+	8.39315i	0.170474	+	0.295270i
$809$	7.44117	−	4.29616i	0.261618	−	0.151045i	−0.363455	−	0.931612i	$-0.618403\pi$
$809$	7.44117	−	4.29616i	0.261618	−	0.151045i	0.625072	+	0.780567i	$0.285069\pi$
$810$	−32.3852	−	10.6084i	−1.13790	−	0.372740i
$811$	37.1687			1.30517			0.652585	−	0.757716i	$-0.273685\pi$
$811$	37.1687			1.30517			0.652585	+	0.757716i	$0.273685\pi$
$812$	−4.35652	+	5.12879i	−0.152884	+	0.179985i
$813$	1.95456	+	3.01371i	0.0685496	+	0.105696i
$814$	5.02723	−	2.90247i	0.176204	−	0.101732i
$815$	24.1465			0.845814
$816$	4.27830	+	6.59665i	0.149771	+	0.230929i
$817$	2.54811			0.0891473
$818$	1.57460			0.0550547
$819$	9.92671	−	26.8414i	0.346867	−	0.937914i
$820$	−15.2465			−0.532432
$821$	−4.63795			−0.161866			−0.0809328	−	0.996720i	$-0.525790\pi$
$821$	−4.63795			−0.161866			−0.0809328	+	0.996720i	$0.525790\pi$
$822$	14.6576	+	22.6003i	0.511242	+	0.788277i
$823$	−35.0288			−1.22103			−0.610514	−	0.792006i	$-0.709037\pi$
$823$	−35.0288			−1.22103			−0.610514	+	0.792006i	$0.709037\pi$
$824$	2.94432	−	1.69990i	0.102570	−	0.0592189i
$825$	−51.1156	−	78.8143i	−1.77962	−	2.74396i
$826$	26.0731	+	4.75963i	0.907198	+	0.165609i
$827$	−21.1109			−0.734098			−0.367049	−	0.930202i	$-0.619632\pi$
$827$	−21.1109			−0.734098			−0.367049	+	0.930202i	$0.619632\pi$
$828$	−13.2822	−	5.93266i	−0.461587	−	0.206174i
$829$	−44.9376	+	25.9448i	−1.56075	+	0.901099i	−0.563567	+	0.826070i	$0.690572\pi$
$829$	−44.9376	+	25.9448i	−1.56075	+	0.901099i	−0.997181	+	0.0750287i	$0.976095\pi$
$830$	22.6652	+	39.2572i	0.786720	+	1.36264i
$831$	22.3100	+	34.3995i	0.773926	+	1.19330i
$832$	−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
$835$	−27.9425			−0.966991
$836$	−16.5932			−0.573886
$837$	−3.08671	+	7.99822i	−0.106692	+	0.276459i
$838$	−13.4922	+	23.3691i	−0.466080	+	0.807274i
$839$	38.8948	−	22.4560i	1.34280	−	0.775266i	0.355582	−	0.934645i	$-0.384283\pi$
$839$	38.8948	−	22.4560i	1.34280	−	0.775266i	0.987217	+	0.159380i	$0.0509494\pi$
$840$	−10.5342	+	13.7883i	−0.363465	+	0.475742i
$841$	−11.2654	−	19.5123i	−0.388464	−	0.672839i
$842$		−	13.0461i		−	0.449597i
$843$	−24.3427	−	37.5336i	−0.838407	−	1.29273i
$844$	11.5387	−	19.9857i	0.397180	−	0.687936i
$845$	−25.9125	+	41.8518i	−0.891417	+	1.43975i
$846$	2.23191	+	21.4826i	0.0767348	+	0.738586i
$847$	45.8489	+	38.9453i	1.57539	+	1.33818i
$848$	5.41458	+	3.12611i	0.185937	+	0.107351i
$849$	25.9552	+	13.2444i	0.890780	+	0.454547i
$850$	−21.1935	+	36.7082i	−0.726931	+	1.25908i
$851$	4.84611			0.166122
$852$	10.6747	−	20.9194i	0.365710	−	0.716686i
$853$	26.1545			0.895513			0.447756	−	0.894156i	$-0.352223\pi$
$853$	26.1545			0.895513			0.447756	+	0.894156i	$0.352223\pi$
$854$	−6.24248	+	7.34906i	−0.213613	+	0.251480i
$855$	−29.6299	−	13.2346i	−1.01332	−	0.452614i
$856$		−	8.84801i		−	0.302419i
$857$	10.1488	−	17.5783i	0.346678	−	0.600464i	−0.638979	−	0.769224i	$-0.720643\pi$
$857$	10.1488	−	17.5783i	0.346678	−	0.600464i	0.985657	+	0.168760i	$0.0539764\pi$
$858$	−35.3555	−	8.10796i	−1.20702	−	0.276801i
$859$	38.0174	−	21.9494i	1.29714	−	0.748903i	0.317229	−	0.948349i	$-0.397248\pi$
$859$	38.0174	−	21.9494i	1.29714	−	0.748903i	0.979909	+	0.199446i	$0.0639143\pi$
$860$	−2.92490	−	1.68869i	−0.0997384	−	0.0575840i
$861$	18.2992	+	2.37006i	0.623635	+	0.0807715i
$862$	18.2521	+	31.6136i	0.621669	+	1.07676i
$863$	9.06101	+	15.6941i	0.308440	+	0.534234i	0.978021	−	0.208505i	$-0.0668597\pi$
$863$	9.06101	+	15.6941i	0.308440	+	0.534234i	−0.669581	+	0.742739i	$0.733526\pi$
$864$	5.13363	−	0.803642i	0.174650	−	0.0273405i
$865$		−	19.3045i		−	0.656374i
$866$	−23.6502	+	13.6545i	−0.803668	+	0.463998i
$867$	−3.39907	−	5.24098i	−0.115439	−	0.177993i
$868$	3.32699	+	2.82603i	0.112926	+	0.0959219i
$869$	48.8006	−	84.5252i	1.65545	−	2.86732i
$870$	9.07669	+	13.9952i	0.307729	+	0.474482i
$871$	26.7964	+	27.6342i	0.907961	+	0.936349i
$872$	2.56093	+	1.47855i	0.0867239	+	0.0500701i
$873$	−37.6555	+	3.91219i	−1.27445	+	0.132408i
$874$	−11.9965	−	6.92618i	−0.405788	−	0.234282i
$875$	−42.7469	−	7.80344i	−1.44511	−	0.263805i
$876$	−7.57956	+	0.392680i	−0.256090	+	0.0132674i
$877$	31.6001	+	18.2443i	1.06706	+	0.616068i	0.927377	−	0.374128i	$-0.122058\pi$
$877$	31.6001	+	18.2443i	1.06706	+	0.616068i	0.139684	+	0.990196i	$0.455391\pi$
$878$		−	0.455718i		−	0.0153797i
$879$	−42.0702	−	21.4676i	−1.41899	−	0.724083i
$880$	19.0468	+	10.9967i	0.642067	+	0.370697i
$881$	−26.9414	+	46.6639i	−0.907679	+	1.57215i	−0.0903999	+	0.995906i	$0.528815\pi$
$881$	−26.9414	+	46.6639i	−0.907679	+	1.57215i	−0.817280	+	0.576241i	$0.804519\pi$
$882$	14.7868	−	14.9115i	0.497896	−	0.502095i
$883$	14.2182			0.478482			0.239241	−	0.970960i	$-0.423101\pi$
$883$	14.2182			0.478482			0.239241	+	0.970960i	$0.423101\pi$
$884$	3.99233	+	15.8728i	0.134277	+	0.533861i
$885$	29.8617	−	58.5203i	1.00379	−	1.96714i
$886$	−23.2231	+	13.4079i	−0.780197	+	0.450447i
$887$	6.50075			0.218274			0.109137	−	0.994027i	$-0.465191\pi$
$887$	6.50075			0.218274			0.109137	+	0.994027i	$0.465191\pi$
$888$	−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
$891$	16.2729	−	49.6780i	0.545164	−	1.66428i
$892$	8.68120	−	15.0363i	0.290668	−	0.503452i
$893$			20.5670i			0.688248i
$894$	−5.31681	+	0.275452i	−0.177821	+	0.00921249i
$895$	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
$899$	3.63423	−	2.09822i	0.121208	−	0.0699797i
$900$	16.4382	+	22.6822i	0.547939	+	0.756075i
$901$	−24.5792	−	14.1908i	−0.818851	−	0.472764i
$902$		−	23.3878i		−	0.778728i
$903$	3.24802	+	2.48148i	0.108087	+	0.0825784i
$904$	8.71628	−	5.03235i	0.289899	−	0.167373i
$905$	5.27788	+	9.14156i	0.175443	+	0.303876i
$906$	−1.13239	−	21.8576i	−0.0376211	−	0.726169i
$907$	−11.8262	−	20.4836i	−0.392683	−	0.680147i	0.600119	−	0.799911i	$-0.295120\pi$
$907$	−11.8262	−	20.4836i	−0.392683	−	0.680147i	−0.992802	+	0.119763i	$0.961786\pi$
$908$		−	19.1522i		−	0.635589i
$909$	−28.9191	+	3.00453i	−0.959185	+	0.0996538i
$910$	−30.0254	+	20.0796i	−0.995331	+	0.665631i
$911$			55.8572i			1.85063i	0.379197	+	0.925316i	$0.376200\pi$
$911$			55.8572i			1.85063i	−0.379197	+	0.925316i	$0.623800\pi$
$912$	4.94143	−	0.256004i	0.163627	−	0.00847715i
$913$	−60.2196	+	34.7678i	−1.99298	+	1.15065i
$914$			15.2345i			0.503914i
$915$	13.0060	+	20.0538i	0.429966	+	0.662958i
$916$	−8.79153	−	15.2274i	−0.290480	−	0.503127i
$917$	−31.2517	+	11.1618i	−1.03202	+	0.368594i
$918$	−23.3038	+	3.64809i	−0.769141	+	0.120405i
$919$	11.7813	−	20.4058i	0.388630	−	0.673126i	−0.603636	−	0.797260i	$-0.706282\pi$
$919$	11.7813	−	20.4058i	0.388630	−	0.673126i	0.992265	+	0.124134i	$0.0396152\pi$
$920$	9.18028	+	15.9007i	0.302665	+	0.524231i
$921$	21.6597	+	33.3968i	0.713712	+	1.10046i
$922$	−11.4420	+	6.60603i	−0.376821	+	0.217558i
$923$	35.0977	−	34.0337i	1.15526	−	1.12023i
$924$	−21.1509	−	16.1592i	−0.695814	−	0.531599i
$925$	−8.08173	−	4.66599i	−0.265726	−	0.153417i
$926$		−	15.4572i		−	0.507954i
$927$	1.05399	+	10.1448i	0.0346175	+	0.333199i
$928$	−2.20269	−	1.27172i	−0.0723068	−	0.0417463i
$929$	20.6071	+	11.8975i	0.676098	+	0.390345i	0.798383	−	0.602150i	$-0.205689\pi$
$929$	20.6071	+	11.8975i	0.676098	+	0.390345i	−0.122285	+	0.992495i	$0.539022\pi$
$930$	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
$933$	55.2344	−	2.86157i	1.80829	−	0.0936836i
$934$	−0.665574	−	1.15281i	−0.0217782	−	0.0377210i
$935$	−86.4618	−	49.9187i	−2.82760	−	1.63252i
$936$	10.6539	+	1.86907i	0.348235	+	0.0610925i
$937$			8.86156i			0.289495i	0.989469	+	0.144747i	$0.0462369\pi$
$937$			8.86156i			0.289495i	−0.989469	+	0.144747i	$0.953763\pi$
$938$	9.50050	+	26.6003i	0.310202	+	0.868531i
$939$	9.47831	+	4.83659i	0.309313	+	0.157836i
$940$	13.6302	−	23.6082i	0.444568	−	0.770015i
$941$	−11.5201	−	6.65114i	−0.375545	−	0.216821i	0.300333	−	0.953834i	$-0.402902\pi$
$941$	−11.5201	−	6.65114i	−0.375545	−	0.216821i	−0.675878	+	0.737013i	$0.736235\pi$
$942$	−0.860340	−	16.6064i	−0.0280314	−	0.541066i
$943$	9.76234	−	16.9089i	0.317906	−	0.550629i
$944$			10.0175i			0.326043i
$945$	−24.8801	−	45.7249i	−0.809348	−	1.48743i
$946$	2.59041	−	4.48673i	0.0842216	−	0.145876i
$947$	28.1586			0.915033			0.457516	−	0.889201i	$-0.348739\pi$
$947$	28.1586			0.915033			0.457516	+	0.889201i	$0.348739\pi$
$948$	−13.2287	+	25.9245i	−0.429649	+	0.841988i
$949$	−15.1962	−	4.32354i	−0.493289	−	0.140348i
$950$	13.3375	+	23.1012i	0.432725	+	0.749502i
$951$	−11.0524	+	21.6596i	−0.358400	+	0.702360i
$952$	−2.15682	+	11.8150i	−0.0699031	+	0.382926i
$953$	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	$0.297470\pi$
$954$	−15.1876	+	11.0067i	−0.491718	+	0.356355i
$955$	73.9183			2.39194
$956$	−22.2321			−0.719037
$957$	−21.4683	+	13.9234i	−0.693971	+	0.450080i
$958$	−12.4718	+	7.20059i	−0.402945	+	0.232641i
$959$	−7.38935	+	40.4785i	−0.238614	+	1.30712i
$960$	−5.84178	−	2.98094i	−0.188543	−	0.0962095i
$961$	14.1389	+	24.4893i	0.456094	+	0.789977i
$962$	−3.49458	+	0.878957i	−0.112670	+	0.0283387i
$963$	24.2362	+	10.8254i	0.781001	+	0.348845i
$964$	12.1874			0.392528
$965$	12.0124	−	20.8060i	0.386692	−	0.669770i
$966$	−8.54660	−	20.5114i	−0.274982	−	0.659944i
$967$			54.9103i			1.76580i	0.469563	+	0.882899i	$0.344411\pi$
$967$			54.9103i			1.76580i	−0.469563	+	0.882899i	$0.655589\pi$
$968$	−11.3686	+	19.6910i	−0.365401	+	0.632892i
$969$	−22.4314	+	1.16212i	−0.720599	+	0.0373326i
$970$	41.3815	+	23.8916i	1.32868	+	0.767113i
$971$	15.1332	−	26.2115i	0.485649	−	0.841169i	−0.514215	−	0.857661i	$-0.671917\pi$
$971$	15.1332	−	26.2115i	0.485649	−	0.841169i	0.999864	+	0.0164927i	$0.00525003\pi$
$972$	−4.07963	+	15.0452i	−0.130854	+	0.482574i
$973$	7.80994	+	21.8669i	0.250375	+	0.701022i
$974$			30.5356i			0.978423i
$975$	17.1306	+	55.7396i	0.548617	+	1.78509i
$976$	−3.15624	−	1.82226i	−0.101029	−	0.0583290i
$977$	25.8818	+	44.8286i	0.828031	+	1.43419i	0.899580	+	0.436755i	$0.143872\pi$
$977$	25.8818	+	44.8286i	0.828031	+	1.43419i	−0.0715488	+	0.997437i	$0.522794\pi$
$978$	−0.571466	−	11.0305i	−0.0182735	−	0.352717i
$979$	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
$982$	−2.79101	−	1.61139i	−0.0890648	−	0.0514216i
$983$	−20.1979	−	11.6613i	−0.644213	−	0.371936i	0.142023	−	0.989863i	$-0.454639\pi$
$983$	−20.1979	−	11.6613i	−0.644213	−	0.371936i	−0.786235	+	0.617927i	$0.787973\pi$
$984$	0.360834	+	6.96487i	0.0115030	+	0.222032i
$985$		−	32.2419i		−	1.02731i
$986$	9.99898	+	5.77291i	0.318432	+	0.183847i
$987$	−20.0291	+	26.2162i	−0.637534	+	0.834472i
$988$	9.90703	+	2.81870i	0.315185	+	0.0896747i
$989$	3.74563	−	2.16254i	0.119104	−	0.0687647i
$990$	−53.4253	+	38.7181i	−1.69797	+	1.23054i
$991$	−12.1157	−	20.9851i	−0.384869	−	0.666612i	0.606882	−	0.794792i	$-0.292420\pi$
$991$	−12.1157	−	20.9851i	−0.384869	−	0.666612i	−0.991751	+	0.128179i	$0.959087\pi$
$992$	−0.824954	+	1.42886i	−0.0261923	+	0.0453664i
$993$	0.741022	+	14.3033i	0.0235156	+	0.453902i
$994$	33.7846	−	12.0664i	1.07158	−	0.382724i
$995$	−3.20254	−	5.54697i	−0.101527	−	0.175851i
$996$	17.3970	−	11.2829i	0.551244	−	0.357513i
$997$		−	13.5078i		−	0.427797i	−0.976856	−	0.213898i	$-0.931384\pi$
$997$		−	13.5078i		−	0.427797i	0.976856	−	0.213898i	$-0.0686161\pi$
$998$	15.8562	−	9.15459i	0.501920	−	0.289783i
$999$	−0.803168	−	5.13060i	−0.0254111	−	0.162325i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.10	✓	34	3.2	odd	2
546.2.bi.e.257.10	yes	34	91.75	odd	6
546.2.bi.f.17.5	yes	34	1.1	even	1	trivial
546.2.bi.f.257.5	yes	34	273.257	even	6	inner
546.2.bn.e.101.2	yes	34	39.23	odd	6
546.2.bn.e.173.2	yes	34	7.5	odd	6
546.2.bn.f.101.16	yes	34	13.10	even	6
546.2.bn.f.173.16	yes	34	21.5	even	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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.942473 - 1.45318i) q^{3} +1.00000 q^{4} +(3.27919 - 1.89324i) q^{5} +(-0.942473 - 1.45318i) q^{6} +(0.475130 - 2.60274i) q^{7} +1.00000 q^{8} +(-1.22349 + 2.73917i) q^{9} +(3.27919 - 1.89324i) q^{10} +(2.90419 + 5.03020i) q^{11} +(-0.942473 - 1.45318i) q^{12} +(-0.879475 - 3.49664i) q^{13} +(0.475130 - 2.60274i) q^{14} +(-5.84178 - 2.98094i) q^{15} +1.00000 q^{16} -4.53944 q^{17} +(-1.22349 + 2.73917i) q^{18} +(-1.42838 + 2.47403i) q^{19} +(3.27919 - 1.89324i) q^{20} +(-4.23006 + 1.76256i) q^{21} +(2.90419 + 5.03020i) q^{22} +4.84897i q^{23} +(-0.942473 - 1.45318i) q^{24} +(4.66874 - 8.08650i) q^{25} +(-0.879475 - 3.49664i) q^{26} +(5.13363 - 0.803642i) q^{27} +(0.475130 - 2.60274i) q^{28} +(-2.20269 - 1.27172i) q^{29} +(-5.84178 - 2.98094i) q^{30} +(-0.824954 + 1.42886i) q^{31} +1.00000 q^{32} +(4.57269 - 8.96114i) q^{33} -4.53944 q^{34} +(-3.36958 - 9.43442i) q^{35} +(-1.22349 + 2.73917i) q^{36} -0.999410i q^{37} +(-1.42838 + 2.47403i) q^{38} +(-4.25239 + 4.57353i) q^{39} +(3.27919 - 1.89324i) q^{40} +(-3.48711 - 2.01328i) q^{41} +(-4.23006 + 1.76256i) q^{42} +(-0.445979 - 0.772459i) q^{43} +(2.90419 + 5.03020i) q^{44} +(1.17386 + 11.2986i) q^{45} +4.84897i q^{46} +(6.23486 - 3.59970i) q^{47} +(-0.942473 - 1.45318i) q^{48} +(-6.54850 - 2.47328i) q^{49} +(4.66874 - 8.08650i) q^{50} +(4.27830 + 6.59665i) q^{51} +(-0.879475 - 3.49664i) q^{52} +(5.41458 + 3.12611i) q^{53} +(5.13363 - 0.803642i) q^{54} +(19.0468 + 10.9967i) q^{55} +(0.475130 - 2.60274i) q^{56} +(4.94143 - 0.256004i) q^{57} +(-2.20269 - 1.27172i) q^{58} +10.0175i q^{59} +(-5.84178 - 2.98094i) q^{60} +(-3.15624 - 1.82226i) q^{61} +(-0.824954 + 1.42886i) q^{62} +(6.54804 + 4.48589i) q^{63} +1.00000 q^{64} +(-9.50397 - 9.80111i) q^{65} +(4.57269 - 8.96114i) q^{66} +(-9.24567 + 5.33799i) q^{67} -4.53944 q^{68} +(7.04644 - 4.57002i) q^{69} +(-3.36958 - 9.43442i) q^{70} +(6.77969 + 11.7428i) q^{71} +(-1.22349 + 2.73917i) q^{72} +(2.19097 - 3.79486i) q^{73} -0.999410i q^{74} +(-16.1513 + 0.836763i) 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} +(3.27919 - 1.89324i) q^{80} +(-6.00615 - 6.70270i) q^{81} +(-3.48711 - 2.01328i) q^{82} +11.9716i q^{83} +(-4.23006 + 1.76256i) q^{84} +(-14.8857 + 8.59427i) q^{85} +(-0.445979 - 0.772459i) q^{86} +(0.227927 + 4.39948i) q^{87} +(2.90419 + 5.03020i) q^{88} -2.18827i q^{89} +(1.17386 + 11.2986i) q^{90} +(-9.51872 + 0.627686i) q^{91} +4.84897i q^{92} +(2.85390 - 0.147854i) q^{93} +(6.23486 - 3.59970i) q^{94} +10.8171i q^{95} +(-0.942473 - 1.45318i) q^{96} +(6.30970 + 10.9287i) q^{97} +(-6.54850 - 2.47328i) q^{98} +(-17.3318 + 1.80068i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20}+ \cdots - 27 q^{99}+O(q^{100}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

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