LMFDB - Embedded newform 1089.2.e.i.364.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1089,2,Mod(364,1089)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1089, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1089.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1089 = 3^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1089.e (of order $3$, 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:	$8.69570878012$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.508277025.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 15x^{5} + 21x^{4} + 3x^{3} - 22x^{2} + 3x + 19 $ x^8 - 3x^7 + 5x^6 - 15x^5 + 21x^4 + 3x^3 - 22x^2 + 3*x + 19
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			364.1
Root			$1.86526 - 0.199842i$ of defining polynomial
Character	$\chi$	$=$	1089.364
Dual form			1089.2.e.i.727.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36526 - 2.36469i) q^{2} +(0.240440 - 1.71528i) q^{3} +(-2.72785 + 4.72478i) q^{4} +(0.468293 - 0.811107i) q^{5} +(-4.38438 + 1.77323i) q^{6} +(-0.259560 - 0.449571i) q^{7} +9.43585 q^{8} +(-2.88438 - 0.824844i) q^{9} +O(q^{10})$	\(q+(-1.36526 - 2.36469i) q^{2} +(0.240440 - 1.71528i) q^{3} +(-2.72785 + 4.72478i) q^{4} +(0.468293 - 0.811107i) q^{5} +(-4.38438 + 1.77323i) q^{6} +(-0.259560 - 0.449571i) q^{7} +9.43585 q^{8} +(-2.88438 - 0.824844i) q^{9} -2.55736 q^{10} +(7.44844 + 5.81506i) q^{12} +(-2.35267 + 4.07494i) q^{13} +(-0.708733 + 1.22756i) q^{14} +(-1.27868 - 0.998277i) q^{15} +(-7.42666 - 12.8634i) q^{16} +2.69227 q^{17} +(1.98741 + 7.94679i) q^{18} -3.41747 q^{19} +(2.55487 + 4.42516i) q^{20} +(-0.833550 + 0.337124i) q^{21} +(-3.48741 + 6.04038i) q^{23} +(2.26875 - 16.1851i) q^{24} +(2.06140 + 3.57046i) q^{25} +12.8480 q^{26} +(-2.10836 + 4.74919i) q^{27} +2.83217 q^{28} +(2.09311 + 3.62537i) q^{29} +(-0.614891 + 4.38659i) q^{30} +(-2.59311 + 4.49140i) q^{31} +(-10.8427 + 18.7802i) q^{32} +(-3.67564 - 6.36640i) q^{34} -0.486201 q^{35} +(11.7654 - 11.3780i) q^{36} +2.06874 q^{37} +(4.66572 + 8.08126i) q^{38} +(6.42400 + 5.01527i) q^{39} +(4.41875 - 7.65349i) q^{40} +(0.0865763 - 0.149955i) q^{41} +(1.93520 + 1.51083i) q^{42} +(-1.13474 - 1.96543i) q^{43} +(-2.01977 + 1.95327i) q^{45} +19.0449 q^{46} +(0.153863 + 0.266499i) q^{47} +(-23.8499 + 9.64595i) q^{48} +(3.36526 - 5.82880i) q^{49} +(5.62869 - 9.74918i) q^{50} +(0.647330 - 4.61800i) q^{51} +(-12.8355 - 22.2317i) q^{52} -1.89835 q^{53} +(14.1088 - 1.49825i) q^{54} +(-2.44917 - 4.24209i) q^{56} +(-0.821695 + 5.86191i) q^{57} +(5.71527 - 9.89913i) q^{58} +(-1.98741 + 3.44230i) q^{59} +(8.20469 - 3.31833i) q^{60} +(2.25956 + 3.91367i) q^{61} +14.1610 q^{62} +(0.377844 + 1.51083i) q^{63} +29.5059 q^{64} +(2.20348 + 3.81654i) q^{65} +(-1.68823 + 2.92410i) q^{67} +(-7.34413 + 12.7204i) q^{68} +(9.52243 + 7.43424i) q^{69} +(0.663789 + 1.14972i) q^{70} +2.90367 q^{71} +(-27.2166 - 7.78310i) q^{72} -9.52444 q^{73} +(-2.82436 - 4.89193i) q^{74} +(6.61998 - 2.67741i) q^{75} +(9.32234 - 16.1468i) q^{76} +(3.08917 - 22.0379i) q^{78} +(-1.02178 - 1.76978i) q^{79} -13.9114 q^{80} +(7.63927 + 4.75832i) q^{81} -0.472796 q^{82} +(7.02970 + 12.1758i) q^{83} +(0.680966 - 4.85797i) q^{84} +(1.26077 - 2.18372i) q^{85} +(-3.09843 + 5.36664i) q^{86} +(6.72180 - 2.71859i) q^{87} +7.53751 q^{89} +(7.37640 + 2.10942i) q^{90} +2.44264 q^{91} +(-19.0263 - 32.9545i) q^{92} +(7.08052 + 5.52782i) q^{93} +(0.420126 - 0.727680i) q^{94} +(-1.60038 + 2.77193i) q^{95} +(29.6063 + 23.1139i) q^{96} +(-8.16710 - 14.1458i) q^{97} -18.3778 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 5 q^{3} - 11 q^{4} - 4 q^{5} - 17 q^{6} + q^{7} - 5 q^{9}+O(q^{10}) $ 8 * q + q^2 + 5 * q^3 - 11 * q^4 - 4 * q^5 - 17 * q^6 + q^7 - 5 * q^9	\( 8 q + q^{2} + 5 q^{3} - 11 q^{4} - 4 q^{5} - 17 q^{6} + q^{7} - 5 q^{9} - 2 q^{10} - 2 q^{12} + 7 q^{13} - q^{14} - q^{15} - 17 q^{16} + 10 q^{17} + 2 q^{18} - 18 q^{19} + 10 q^{20} + 13 q^{21} - 14 q^{23} - 18 q^{24} - 14 q^{25} + 44 q^{26} + 5 q^{27} + 2 q^{28} - 6 q^{29} + 37 q^{30} + 2 q^{31} - 34 q^{32} - 16 q^{34} + 16 q^{35} + 11 q^{36} + 6 q^{37} - 3 q^{38} + 22 q^{39} + 12 q^{40} - 2 q^{41} - q^{42} - 21 q^{43} + 49 q^{45} - 4 q^{46} + 7 q^{47} - 59 q^{48} + 15 q^{49} + 23 q^{50} + 31 q^{51} - 10 q^{52} - 12 q^{53} + 37 q^{54} - 18 q^{56} - 33 q^{57} + 21 q^{58} - 2 q^{59} + 73 q^{60} + 15 q^{61} + 40 q^{62} + 5 q^{63} + 32 q^{64} + 19 q^{65} - 14 q^{67} - 7 q^{68} - 2 q^{69} + 38 q^{70} - 6 q^{71} - 75 q^{72} - 44 q^{73} - 36 q^{74} + 10 q^{75} + 42 q^{76} + 29 q^{78} + 11 q^{79} - 68 q^{80} + 7 q^{81} - 34 q^{82} + 18 q^{83} - 34 q^{84} + 13 q^{85} + 24 q^{86} + 9 q^{87} - 12 q^{89} + 80 q^{90} + 38 q^{91} - 67 q^{92} + 20 q^{93} - 19 q^{94} - 30 q^{95} + 50 q^{96} - 26 q^{97} - 30 q^{98}+O(q^{100}) \) 8 * q + q^2 + 5 * q^3 - 11 * q^4 - 4 * q^5 - 17 * q^6 + q^7 - 5 * q^9 - 2 * q^10 - 2 * q^12 + 7 * q^13 - q^14 - q^15 - 17 * q^16 + 10 * q^17 + 2 * q^18 - 18 * q^19 + 10 * q^20 + 13 * q^21 - 14 * q^23 - 18 * q^24 - 14 * q^25 + 44 * q^26 + 5 * q^27 + 2 * q^28 - 6 * q^29 + 37 * q^30 + 2 * q^31 - 34 * q^32 - 16 * q^34 + 16 * q^35 + 11 * q^36 + 6 * q^37 - 3 * q^38 + 22 * q^39 + 12 * q^40 - 2 * q^41 - q^42 - 21 * q^43 + 49 * q^45 - 4 * q^46 + 7 * q^47 - 59 * q^48 + 15 * q^49 + 23 * q^50 + 31 * q^51 - 10 * q^52 - 12 * q^53 + 37 * q^54 - 18 * q^56 - 33 * q^57 + 21 * q^58 - 2 * q^59 + 73 * q^60 + 15 * q^61 + 40 * q^62 + 5 * q^63 + 32 * q^64 + 19 * q^65 - 14 * q^67 - 7 * q^68 - 2 * q^69 + 38 * q^70 - 6 * q^71 - 75 * q^72 - 44 * q^73 - 36 * q^74 + 10 * q^75 + 42 * q^76 + 29 * q^78 + 11 * q^79 - 68 * q^80 + 7 * q^81 - 34 * q^82 + 18 * q^83 - 34 * q^84 + 13 * q^85 + 24 * q^86 + 9 * q^87 - 12 * q^89 + 80 * q^90 + 38 * q^91 - 67 * q^92 + 20 * q^93 - 19 * q^94 - 30 * q^95 + 50 * q^96 - 26 * q^97 - 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times$.

$n$	$244$	$848$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.36526	−	2.36469i	−0.965382	−	1.67209i	−0.708584	−	0.705627i	$-0.750666\pi$
$2$	−1.36526	−	2.36469i	−0.965382	−	1.67209i	−0.256799	−	0.966465i	$-0.582668\pi$
$3$	0.240440	−	1.71528i	0.138818	−	0.990318i
$3$	0.240440	−	1.71528i	0.138818	−	0.990318i
$4$	−2.72785	+	4.72478i	−1.36393	+	2.36239i
$5$	0.468293	−	0.811107i	0.209427	−	0.362738i	−0.742107	−	0.670281i	$-0.766173\pi$
$5$	0.468293	−	0.811107i	0.209427	−	0.362738i	0.951534	+	0.307543i	$0.0995068\pi$
$6$	−4.38438	+	1.77323i	−1.78991	+	0.723919i
$7$	−0.259560	−	0.449571i	−0.0981045	−	0.169922i	0.812796	−	0.582549i	$-0.197945\pi$
$7$	−0.259560	−	0.449571i	−0.0981045	−	0.169922i	−0.910900	+	0.412627i	$0.864611\pi$
$8$	9.43585			3.33608
$9$	−2.88438	−	0.824844i	−0.961459	−	0.274948i
$10$	−2.55736			−0.808709
$11$		0			0
$11$		0			0
$12$	7.44844	+	5.81506i	2.15018	+	1.67866i
$13$	−2.35267	+	4.07494i	−0.652513	+	1.13019i	0.329998	+	0.943982i	$0.392952\pi$
$13$	−2.35267	+	4.07494i	−0.652513	+	1.13019i	−0.982511	+	0.186205i	$0.940381\pi$
$14$	−0.708733	+	1.22756i	−0.189417	+	0.328080i
$15$	−1.27868	−	0.998277i	−0.330154	−	0.257754i
$16$	−7.42666	−	12.8634i	−1.85667	−	3.21584i
$17$	2.69227			0.652972			0.326486	−	0.945202i	$-0.394135\pi$
$17$	2.69227			0.652972			0.326486	+	0.945202i	$0.394135\pi$
$18$	1.98741	+	7.94679i	0.468438	+	1.87308i
$19$	−3.41747			−0.784020			−0.392010	−	0.919961i	$-0.628220\pi$
$19$	−3.41747			−0.784020			−0.392010	+	0.919961i	$0.628220\pi$
$20$	2.55487	+	4.42516i	0.571286	+	0.989497i
$21$	−0.833550	+	0.337124i	−0.181896	+	0.0735665i
$22$		0			0
$23$	−3.48741	+	6.04038i	−0.727176	+	1.25951i	0.230896	+	0.972978i	$0.425834\pi$
$23$	−3.48741	+	6.04038i	−0.727176	+	1.25951i	−0.958072	+	0.286527i	$0.907499\pi$
$24$	2.26875	−	16.1851i	0.463108	−	3.30378i
$25$	2.06140	+	3.57046i	0.412281	+	0.714091i
$26$	12.8480			2.51970
$27$	−2.10836	+	4.74919i	−0.405754	+	0.913983i
$28$	2.83217			0.535230
$29$	2.09311	+	3.62537i	0.388681	+	0.673215i	0.992272	−	0.124079i	$-0.0395976\pi$
$29$	2.09311	+	3.62537i	0.388681	+	0.673215i	−0.603592	+	0.797294i	$0.706264\pi$
$30$	−0.614891	+	4.38659i	−0.112263	+	0.800879i
$31$	−2.59311	+	4.49140i	−0.465736	+	0.806679i	−0.999234	−	0.0391223i	$-0.987544\pi$
$31$	−2.59311	+	4.49140i	−0.465736	+	0.806679i	0.533498	+	0.845801i	$0.320877\pi$
$32$	−10.8427	+	18.7802i	−1.91674	+	3.31990i
$33$		0			0
$34$	−3.67564	−	6.36640i	−0.630368	−	1.09183i
$35$	−0.486201			−0.0821830
$36$	11.7654	−	11.3780i	1.96089	−	1.89633i
$37$	2.06874			0.340098			0.170049	−	0.985436i	$-0.445607\pi$
$37$	2.06874			0.340098			0.170049	+	0.985436i	$0.445607\pi$
$38$	4.66572	+	8.08126i	0.756880	+	1.31095i
$39$	6.42400	+	5.01527i	1.02866	+	0.803086i
$40$	4.41875	−	7.65349i	0.698665	−	1.21012i
$41$	0.0865763	−	0.149955i	0.0135209	−	0.0234190i	−0.859186	−	0.511664i	$-0.829029\pi$
$41$	0.0865763	−	0.149955i	0.0135209	−	0.0234190i	0.872707	+	0.488245i	$0.162363\pi$
$42$	1.93520	+	1.51083i	0.298609	+	0.233126i
$43$	−1.13474	−	1.96543i	−0.173047	−	0.299726i	0.766437	−	0.642320i	$-0.222028\pi$
$43$	−1.13474	−	1.96543i	−0.173047	−	0.299726i	−0.939484	+	0.342594i	$0.888694\pi$
$44$		0			0
$45$	−2.01977	+	1.95327i	−0.301090	+	0.291176i
$46$	19.0449			2.80801
$47$	0.153863	+	0.266499i	0.0224433	+	0.0388729i	0.877029	−	0.480438i	$-0.159522\pi$
$47$	0.153863	+	0.266499i	0.0224433	+	0.0388729i	−0.854586	+	0.519311i	$0.826189\pi$
$48$	−23.8499	+	9.64595i	−3.44244	+	1.39227i
$49$	3.36526	−	5.82880i	0.480751	−	0.832685i
$50$	5.62869	−	9.74918i	0.796017	−	1.37874i
$51$	0.647330	−	4.61800i	0.0906443	−	0.646650i
$52$	−12.8355	−	22.2317i	−1.77996	−	3.08298i
$53$	−1.89835			−0.260758			−0.130379	−	0.991464i	$-0.541619\pi$
$53$	−1.89835			−0.260758			−0.130379	+	0.991464i	$0.541619\pi$
$54$	14.1088	−	1.49825i	1.91997	−	0.203886i
$55$		0			0
$56$	−2.44917	−	4.24209i	−0.327284	−	0.566873i
$57$	−0.821695	+	5.86191i	−0.108836	+	0.776429i
$58$	5.71527	−	9.89913i	0.750451	−	1.29982i
$59$	−1.98741	+	3.44230i	−0.258739	+	0.448149i	−0.965904	−	0.258899i	$-0.916640\pi$
$59$	−1.98741	+	3.44230i	−0.258739	+	0.448149i	0.707165	+	0.707048i	$0.249974\pi$
$60$	8.20469	−	3.31833i	1.05922	−	0.428395i
$61$	2.25956	+	3.91367i	0.289307	+	0.501094i	0.973645	−	0.228071i	$-0.0732418\pi$
$61$	2.25956	+	3.91367i	0.289307	+	0.501094i	−0.684337	+	0.729165i	$0.739908\pi$
$62$	14.1610			1.79845
$63$	0.377844	+	1.51083i	0.0476038	+	0.190347i
$64$	29.5059			3.68824
$65$	2.20348	+	3.81654i	0.273308	+	0.473383i
$66$		0			0
$67$	−1.68823	+	2.92410i	−0.206250	+	0.357236i	−0.950530	−	0.310632i	$-0.899459\pi$
$67$	−1.68823	+	2.92410i	−0.206250	+	0.357236i	0.744280	+	0.667868i	$0.232793\pi$
$68$	−7.34413	+	12.7204i	−0.890606	+	1.54257i
$69$	9.52243	+	7.43424i	1.14637	+	0.894977i
$70$	0.663789	+	1.14972i	0.0793380	+	0.137417i
$71$	2.90367			0.344602			0.172301	−	0.985044i	$-0.444880\pi$
$71$	2.90367			0.344602			0.172301	+	0.985044i	$0.444880\pi$
$72$	−27.2166	−	7.78310i	−3.20750	−	0.917248i
$73$	−9.52444			−1.11475			−0.557376	−	0.830260i	$-0.688192\pi$
$73$	−9.52444			−1.11475			−0.557376	+	0.830260i	$0.688192\pi$
$74$	−2.82436	−	4.89193i	−0.328325	−	0.568675i
$75$	6.61998	−	2.67741i	0.764409	−	0.309160i
$76$	9.32234	−	16.1468i	1.06935	−	1.85216i
$77$		0			0
$78$	3.08917	−	22.0379i	0.349780	−	2.49530i
$79$	−1.02178	−	1.76978i	−0.114959	−	0.199115i	0.802804	−	0.596243i	$-0.203340\pi$
$79$	−1.02178	−	1.76978i	−0.114959	−	0.199115i	−0.917764	+	0.397127i	$0.870007\pi$
$80$	−13.9114			−1.55534
$81$	7.63927	+	4.75832i	0.848807	+	0.528702i
$82$	−0.472796			−0.0522115
$83$	7.02970	+	12.1758i	0.771609	+	1.33647i	0.936681	+	0.350185i	$0.113881\pi$
$83$	7.02970	+	12.1758i	0.771609	+	1.33647i	−0.165071	+	0.986282i	$0.552785\pi$
$84$	0.680966	−	4.85797i	0.0742995	−	0.530047i
$85$	1.26077	−	2.18372i	0.136750	−	0.236858i
$86$	−3.09843	+	5.36664i	−0.334112	+	0.578700i
$87$	6.72180	−	2.71859i	0.720653	−	0.291463i
$88$		0			0
$89$	7.53751			0.798974			0.399487	−	0.916739i	$-0.369188\pi$
$89$	7.53751			0.798974			0.399487	+	0.916739i	$0.369188\pi$
$90$	7.37640	+	2.10942i	0.777540	+	0.222353i
$91$	2.44264			0.256058
$92$	−19.0263	−	32.9545i	−1.98363	−	3.43575i
$93$	7.08052	+	5.52782i	0.734216	+	0.573209i
$94$	0.420126	−	0.727680i	0.0433327	−	0.0750545i
$95$	−1.60038	+	2.77193i	−0.164195	+	0.284394i
$96$	29.6063	+	23.1139i	3.02168	+	2.35905i
$97$	−8.16710	−	14.1458i	−0.829243	−	1.43629i	−0.898633	−	0.438702i	$-0.855438\pi$
$97$	−8.16710	−	14.1458i	−0.829243	−	1.43629i	0.0693892	−	0.997590i	$-0.477895\pi$
$98$	−18.3778			−1.85643
$99$		0			0
$100$	−22.4928			−2.24928
$101$	−4.99129	−	8.64516i	−0.496652	−	0.860226i	0.503341	−	0.864088i	$-0.332104\pi$
$101$	−4.99129	−	8.64516i	−0.496652	−	0.860226i	−0.999993	+	0.00386211i	$0.998771\pi$
$102$	−11.8039	+	4.77403i	−1.16876	+	0.472699i
$103$	−3.27747	+	5.67674i	−0.322939	+	0.559346i	−0.981093	−	0.193537i	$-0.938004\pi$
$103$	−3.27747	+	5.67674i	−0.322939	+	0.559346i	0.658154	+	0.752883i	$0.271337\pi$
$104$	−22.1995	+	38.4506i	−2.17684	+	3.77039i
$105$	−0.116902	+	0.833971i	−0.0114085	+	0.0813873i
$106$	2.59173	+	4.48901i	0.251731	+	0.436011i
$107$	−14.5151			−1.40323			−0.701614	−	0.712557i	$-0.747537\pi$
$107$	−14.5151			−1.40323			−0.701614	+	0.712557i	$0.747537\pi$
$108$	−16.6876	−	22.9166i	−1.60577	−	2.20515i
$109$	−11.6802			−1.11876			−0.559379	−	0.828912i	$-0.688960\pi$
$109$	−11.6802			−1.11876			−0.559379	+	0.828912i	$0.688960\pi$
$110$		0			0
$111$	0.497406	−	3.54846i	0.0472117	−	0.336805i
$112$	−3.85533	+	6.67763i	−0.364295	+	0.630977i
$113$	0.603036	−	1.04449i	0.0567289	−	0.0982573i	−0.836266	−	0.548323i	$-0.815266\pi$
$113$	0.603036	−	1.04449i	0.0567289	−	0.0982573i	0.892995	+	0.450066i	$0.148600\pi$
$114$	14.9835	−	6.05996i	1.40333	−	0.567567i
$115$	3.26626	+	5.65733i	0.304581	+	0.527549i
$116$	−22.8388			−2.12053
$117$	10.1472	−	9.81309i	0.938107	−	0.907221i
$118$	10.8533			0.999129
$119$	−0.698807	−	1.21037i	−0.0640595	−	0.110954i
$120$	−12.0654	−	9.41959i	−1.10142	−	0.859887i
$121$		0			0
$122$	6.16976	−	10.6863i	0.558584	−	0.967496i
$123$	−0.236398	−	0.184558i	−0.0213153	−	0.0166410i
$124$	−14.1472	−	24.5038i	−1.27046	−	2.20050i
$125$	8.54429			0.764225
$126$	3.05680	−	2.95616i	0.272321	−	0.263355i
$127$	10.4533			0.927579			0.463789	−	0.885945i	$-0.346489\pi$
$127$	10.4533			0.927579			0.463789	+	0.885945i	$0.346489\pi$
$128$	−18.5976	−	32.2120i	−1.64381	−	2.84717i
$129$	−3.64411	+	1.47383i	−0.320846	+	0.129764i
$130$	6.01663	−	10.4211i	0.527693	−	0.913991i
$131$	−6.73051	+	11.6576i	−0.588048	+	1.01853i	0.406440	+	0.913677i	$0.366770\pi$
$131$	−6.73051	+	11.6576i	−0.588048	+	1.01853i	−0.994488	+	0.104851i	$0.966563\pi$
$132$		0			0
$133$	0.887038	+	1.53640i	0.0769160	+	0.133222i
$134$	9.21948			0.796442
$135$	2.86478	+	3.93412i	0.246561	+	0.338595i
$136$	25.4039			2.17837
$137$	−10.4318	−	18.0684i	−0.891250	−	1.54369i	−0.838378	−	0.545089i	$-0.816496\pi$
$137$	−10.4318	−	18.0684i	−0.891250	−	1.54369i	−0.0528716	−	0.998601i	$-0.516837\pi$
$138$	4.57914	−	32.6673i	0.389802	−	2.78082i
$139$	0.433925	−	0.751581i	0.0368051	−	0.0637482i	−0.847036	−	0.531535i	$-0.821615\pi$
$139$	0.433925	−	0.751581i	0.0368051	−	0.0637482i	0.883841	+	0.467787i	$0.154949\pi$
$140$	1.32628	−	2.29719i	0.112092	−	0.194148i
$141$	0.494116	−	0.199842i	0.0416121	−	0.0168297i
$142$	−3.96425	−	6.86628i	−0.332673	−	0.576206i
$143$		0			0
$144$	10.8110	+	43.2286i	0.900920	+	3.60238i
$145$	3.92076			0.325601
$146$	13.0033	+	22.5224i	1.07616	+	1.86397i
$147$	−9.18888	−	7.17384i	−0.757886	−	0.591688i
$148$	−5.64321	+	9.77432i	−0.463869	+	0.803444i
$149$	3.28272	−	5.68584i	0.268931	−	0.465802i	−0.699655	−	0.714481i	$-0.746663\pi$
$149$	3.28272	−	5.68584i	0.268931	−	0.465802i	0.968586	+	0.248679i	$0.0799963\pi$
$150$	−15.3692	−	11.9989i	−1.25489	−	0.979704i
$151$	6.32096	+	10.9482i	0.514393	+	0.890954i	0.999861	+	0.0166998i	$0.00531595\pi$
$151$	6.32096	+	10.9482i	0.514393	+	0.890954i	−0.485468	+	0.874255i	$0.661351\pi$
$152$	−32.2467			−2.61555
$153$	−7.76553	−	2.22070i	−0.627806	−	0.179533i
$154$		0			0
$155$	2.42867	+	4.20658i	0.195076	+	0.337881i
$156$	−41.2198	+	16.6711i	−3.30022	+	1.33475i
$157$	−7.00919	+	12.1403i	−0.559395	+	0.968900i	0.438152	+	0.898901i	$0.355633\pi$
$157$	−7.00919	+	12.1403i	−0.559395	+	0.968900i	−0.997547	+	0.0699992i	$0.977700\pi$
$158$	−2.78999	+	4.83240i	−0.221960	+	0.384445i
$159$	−0.456438	+	3.25620i	−0.0361979	+	0.258233i
$160$	10.1552	+	17.5893i	0.802836	+	1.39055i
$161$	3.62078			0.285357
$162$	0.822412	−	24.5609i	0.0646148	−	1.92968i
$163$	−21.6245			−1.69376			−0.846881	−	0.531783i	$-0.821522\pi$
$163$	−21.6245			−1.69376			−0.846881	+	0.531783i	$0.821522\pi$
$164$	0.472335	+	0.818108i	0.0368832	+	0.0638835i
$165$		0			0
$166$	19.1947	−	33.2462i	1.48980	−	2.58040i
$167$	2.51058	−	4.34844i	0.194274	−	0.336493i	−0.752388	−	0.658720i	$-0.771098\pi$
$167$	2.51058	−	4.34844i	0.194274	−	0.336493i	0.946662	+	0.322227i	$0.104432\pi$
$168$	−7.86526	+	3.18105i	−0.606818	+	0.245423i
$169$	−4.57012	−	7.91567i	−0.351547	−	0.608898i
$170$	−6.88512			−0.528064
$171$	9.85726	+	2.81887i	0.753804	+	0.215565i
$172$	12.3816			0.944092
$173$	0.229066	+	0.396754i	0.0174155	+	0.0301646i	0.874602	−	0.484842i	$-0.161123\pi$
$173$	0.229066	+	0.396754i	0.0174155	+	0.0301646i	−0.857186	+	0.515006i	$0.827790\pi$
$174$	−15.6056	−	12.1834i	−1.18306	−	0.923624i
$175$	1.07012	−	1.85350i	0.0808932	−	0.140111i
$176$		0			0
$177$	5.42666	+	4.23664i	0.407893	+	0.318445i
$178$	−10.2906	−	17.8239i	−0.771316	−	1.33596i
$179$	9.19929			0.687587			0.343794	−	0.939045i	$-0.388288\pi$
$179$	9.19929			0.687587			0.343794	+	0.939045i	$0.388288\pi$
$180$	−3.71914	−	14.8712i	−0.277208	−	1.10843i
$181$	15.1557			1.12652			0.563258	−	0.826281i	$-0.309548\pi$
$181$	15.1557			1.12652			0.563258	+	0.826281i	$0.309548\pi$
$182$	−3.33483	−	5.77609i	−0.247194	−	0.428153i
$183$	7.25634	−	2.93478i	0.536404	−	0.216945i
$184$	−32.9067	+	56.9961i	−2.42592	+	4.20181i
$185$	0.968774	−	1.67797i	0.0712257	−	0.123367i
$186$	3.40488	−	24.2902i	0.249658	−	1.78104i
$187$		0			0
$188$	−1.67887			−0.122444
$189$	2.68235	−	0.284844i	0.195112	−	0.0207194i
$190$	8.73969			0.634044
$191$	10.4716	+	18.1373i	0.757699	+	1.31237i	0.944021	+	0.329884i	$0.107010\pi$
$191$	10.4716	+	18.1373i	0.757699	+	1.31237i	−0.186323	+	0.982489i	$0.559657\pi$
$192$	7.09439	−	50.6109i	0.511993	−	3.65253i
$193$	−5.22446	+	9.04903i	−0.376065	+	0.651364i	−0.990486	−	0.137615i	$-0.956056\pi$
$193$	−5.22446	+	9.04903i	−0.376065	+	0.651364i	0.614421	+	0.788978i	$0.289390\pi$
$194$	−22.3004	+	38.6254i	−1.60107	+	2.77314i
$195$	7.07624	−	2.86194i	0.506740	−	0.204948i
$196$	18.3599	+	31.8002i	1.31142	+	2.27144i
$197$	20.9855			1.49515			0.747576	−	0.664176i	$-0.231217\pi$
$197$	20.9855			1.49515			0.747576	+	0.664176i	$0.231217\pi$
$198$		0			0
$199$	−19.0502			−1.35043			−0.675216	−	0.737620i	$-0.735950\pi$
$199$	−19.0502			−1.35043			−0.675216	+	0.737620i	$0.735950\pi$
$200$	19.4511	+	33.6903i	1.37540	+	2.38226i
$201$	4.60974	+	3.59886i	0.325146	+	0.253844i
$202$	−13.6288	+	23.6057i	−0.958917	+	1.66089i
$203$	1.08658	−	1.88201i	0.0762627	−	0.132091i
$204$	20.0532	+	15.6557i	1.40401	+	1.09612i
$205$	−0.0810862	−	0.140445i	−0.00566330	−	0.00980913i
$206$	17.8983			1.24704
$207$	15.0414	−	14.5462i	1.04545	−	1.01103i
$208$	69.8899			4.84600
$209$		0			0
$210$	2.13169	−	0.862147i	0.147100	−	0.0594938i
$211$	8.14459	−	14.1068i	0.560697	−	0.971155i	−0.436739	−	0.899588i	$-0.643867\pi$
$211$	8.14459	−	14.1068i	0.560697	−	0.971155i	0.997436	−	0.0715668i	$-0.0227999\pi$
$212$	5.17841	−	8.96926i	0.355654	−	0.616012i
$213$	0.698157	−	4.98060i	0.0478369	−	0.341265i
$214$	19.8168	+	34.3238i	1.35465	+	2.34632i
$215$	−2.12557			−0.144963
$216$	−19.8942	+	44.8127i	−1.35363	+	3.04912i
$217$	2.69227			0.182763
$218$	15.9464	+	27.6200i	1.08003	+	1.87066i
$219$	−2.29005	+	16.3371i	−0.154748	+	1.10396i
$220$		0			0
$221$	−6.33403	+	10.9709i	−0.426073	+	0.737980i
$222$	−9.07012	+	3.66835i	−0.608746	+	0.246203i
$223$	4.52251	+	7.83322i	0.302850	+	0.524551i	0.976780	−	0.214244i	$-0.0687286\pi$
$223$	4.52251	+	7.83322i	0.302850	+	0.524551i	−0.673930	+	0.738795i	$0.735395\pi$
$224$	11.2574			0.752165
$225$	−3.00080	−	11.9989i	−0.200053	−	0.799925i
$226$	−3.29320			−0.219060
$227$	−2.58585	−	4.47882i	−0.171629	−	0.297269i	0.767361	−	0.641216i	$-0.221570\pi$
$227$	−2.58585	−	4.47882i	−0.171629	−	0.297269i	−0.938989	+	0.343946i	$0.888236\pi$
$228$	−25.4548	−	19.8728i	−1.68578	−	1.31611i
$229$	−8.01186	+	13.8769i	−0.529438	+	0.917014i	0.469972	+	0.882681i	$0.344264\pi$
$229$	−8.01186	+	13.8769i	−0.529438	+	0.917014i	−0.999410	+	0.0343328i	$0.989069\pi$
$230$	8.91858	−	15.4474i	0.588074	−	1.01857i
$231$		0			0
$232$	19.7503	+	34.2085i	1.29667	+	2.24590i
$233$	16.9177			1.10832			0.554158	−	0.832412i	$-0.313040\pi$
$233$	16.9177			1.10832			0.554158	+	0.832412i	$0.313040\pi$
$234$	−37.0585	−	10.5976i	−2.42259	−	0.692786i
$235$	0.288213			0.0188009
$236$	−10.8427	−	18.7802i	−0.705803	−	1.22249i
$237$	−3.28134	+	1.32712i	−0.213146	+	0.0862055i
$238$	−1.90810	+	3.30493i	−0.123684	+	0.214227i
$239$	0.361215	−	0.625643i	0.0233651	−	0.0404695i	−0.854106	−	0.520098i	$-0.825895\pi$
$239$	0.361215	−	0.625643i	0.0233651	−	0.0404695i	0.877472	+	0.479629i	$0.159229\pi$
$240$	−3.34486	+	23.8620i	−0.215910	+	1.54028i
$241$	6.82346	+	11.8186i	0.439537	+	0.761301i	0.997654	−	0.0684616i	$-0.0218091\pi$
$241$	6.82346	+	11.8186i	0.439537	+	0.761301i	−0.558116	+	0.829763i	$0.688476\pi$
$242$		0			0
$243$	9.99864	−	11.9594i	0.641413	−	0.767196i
$244$	−24.6550			−1.57837
$245$	−3.15185	−	5.45917i	−0.201364	−	0.348774i
$246$	−0.113679	+	0.810977i	−0.00724790	+	0.0517060i
$247$	8.04017	−	13.9260i	0.511584	−	0.886089i
$248$	−24.4682	+	42.3802i	−1.55373	+	2.69114i
$249$	22.5751	−	9.13036i	1.43064	−	0.578613i
$250$	−11.6652	−	20.2046i	−0.737769	−	1.27785i
$251$	20.5733			1.29858			0.649288	−	0.760542i	$-0.275067\pi$
$251$	20.5733			1.29858			0.649288	+	0.760542i	$0.275067\pi$
$252$	−8.16904	−	2.33610i	−0.514601	−	0.147160i
$253$		0			0
$254$	−14.2714	−	24.7188i	−0.895468	−	1.55100i
$255$	−3.44256	−	2.68763i	−0.215581	−	0.168306i
$256$	−21.2752	+	36.8497i	−1.32970	+	2.30311i
$257$	−2.63208	+	4.55890i	−0.164185	+	0.284376i	−0.936365	−	0.351027i	$-0.885833\pi$
$257$	−2.63208	+	4.55890i	−0.164185	+	0.284376i	0.772181	+	0.635403i	$0.219166\pi$
$258$	8.46031	+	6.60503i	0.526716	+	0.411212i
$259$	−0.536961	−	0.930044i	−0.0333652	−	0.0577901i
$260$	−24.0431			−1.49109
$261$	−3.04695	−	12.1834i	−0.188602	−	0.754136i
$262$	36.7555			2.27076
$263$	1.29918	+	2.25025i	0.0801110	+	0.138756i	0.903297	−	0.429015i	$-0.141139\pi$
$263$	1.29918	+	2.25025i	0.0801110	+	0.138756i	−0.823186	+	0.567771i	$0.807806\pi$
$264$		0			0
$265$	−0.888982	+	1.53976i	−0.0546097	+	0.0945868i
$266$	2.42207	−	4.19515i	0.148507	−	0.257221i
$267$	1.81232	−	12.9289i	0.110912	−	0.791239i
$268$	−9.21049	−	15.9530i	−0.562620	−	0.974487i
$269$	−10.0952			−0.615516			−0.307758	−	0.951465i	$-0.599579\pi$
$269$	−10.0952			−0.615516			−0.307758	+	0.951465i	$0.599579\pi$
$270$	5.39183	−	12.1454i	0.328136	−	0.739146i
$271$	−32.3022			−1.96222			−0.981111	−	0.193447i	$-0.938033\pi$
$271$	−32.3022			−1.96222			−0.981111	+	0.193447i	$0.938033\pi$
$272$	−19.9946	−	34.6317i	−1.21235	−	2.09985i
$273$	0.587307	−	4.18981i	0.0355455	−	0.253579i
$274$	−28.4842	+	49.3361i	−1.72079	+	2.98050i
$275$		0			0
$276$	−61.1010	+	24.7119i	−3.67785	+	1.48748i
$277$	16.1690	+	28.0055i	0.971499	+	1.68269i	0.691036	+	0.722820i	$0.257155\pi$
$277$	16.1690	+	28.0055i	0.971499	+	1.68269i	0.280463	+	0.959865i	$0.409512\pi$
$278$	−2.36968			−0.142124
$279$	11.1842	−	10.8160i	0.669581	−	0.647536i
$280$	−4.58772			−0.274169
$281$	−4.77135	−	8.26422i	−0.284635	−	0.493002i	0.687886	−	0.725819i	$-0.258539\pi$
$281$	−4.77135	−	8.26422i	−0.284635	−	0.493002i	−0.972521	+	0.232817i	$0.925206\pi$
$282$	−1.14716	−	0.895598i	−0.0683124	−	0.0533321i
$283$	−2.96038	+	5.12752i	−0.175976	+	0.304800i	−0.940499	−	0.339797i	$-0.889642\pi$
$283$	−2.96038	+	5.12752i	−0.175976	+	0.304800i	0.764522	+	0.644597i	$0.222975\pi$
$284$	−7.92078	+	13.7192i	−0.470012	+	0.814084i
$285$	4.36985	+	3.41158i	0.258847	+	0.202084i
$286$		0			0
$287$	−0.0898871			−0.00530587
$288$	46.7653	−	45.2256i	2.75567	−	2.66494i
$289$	−9.75167			−0.573627
$290$	−5.35284	−	9.27139i	−0.314330	−	0.544435i
$291$	−26.2278	+	10.6077i	−1.53750	+	0.621831i
$292$	25.9813	−	45.0009i	1.52044	−	2.63348i
$293$	7.21454	−	12.4959i	0.421478	−	0.730021i	−0.574607	−	0.818430i	$-0.694845\pi$
$293$	7.21454	−	12.4959i	0.421478	−	0.730021i	0.996084	+	0.0884090i	$0.0281783\pi$
$294$	−4.41875	+	31.5230i	−0.257706	+	1.83846i
$295$	1.86138	+	3.22401i	0.108374	+	0.187709i
$296$	19.5203			1.13459
$297$		0			0
$298$	−17.9270			−1.03849
$299$	−16.4095	−	28.4220i	−0.948984	−	1.64369i
$300$	−5.40817	+	38.5815i	−0.312241	+	2.22750i
$301$	−0.589068	+	1.02030i	−0.0339533	+	0.0588089i
$302$	17.2595	−	29.8943i	0.993171	−	1.72022i
$303$	−16.0290	+	6.48282i	−0.920841	+	0.372428i
$304$	25.3804	+	43.9601i	1.45566	+	2.52128i
$305$	4.23255			0.242355
$306$	5.35066	+	21.3949i	0.305877	+	1.22307i
$307$	−9.60611			−0.548250			−0.274125	−	0.961694i	$-0.588388\pi$
$307$	−9.60611			−0.548250			−0.274125	+	0.961694i	$0.588388\pi$
$308$		0			0
$309$	8.94917	+	6.98669i	0.509101	+	0.397459i
$310$	6.63152	−	11.4861i	0.376645	−	0.652368i
$311$	−0.171704	+	0.297401i	−0.00973646	+	0.0168641i	−0.870853	−	0.491544i	$-0.836433\pi$
$311$	−0.171704	+	0.297401i	−0.00973646	+	0.0168641i	0.861116	+	0.508408i	$0.169766\pi$
$312$	60.6159	+	47.3234i	3.43170	+	2.67916i
$313$	4.17952	+	7.23914i	0.236240	+	0.409180i	0.959632	−	0.281257i	$-0.0907514\pi$
$313$	4.17952	+	7.23914i	0.236240	+	0.409180i	−0.723392	+	0.690437i	$0.757418\pi$
$314$	38.2774			2.16012
$315$	1.40239	+	0.401040i	0.0790156	+	0.0225960i
$316$	11.1491			0.627185
$317$	6.70413	+	11.6119i	0.376541	+	0.652189i	0.990556	−	0.137106i	$-0.0437799\pi$
$317$	6.70413	+	11.6119i	0.376541	+	0.652189i	−0.614015	+	0.789294i	$0.710447\pi$
$318$	8.32306	−	3.36621i	0.466734	−	0.188768i
$319$		0			0
$320$	13.8174	−	23.9324i	0.772416	−	1.33786i
$321$	−3.49001	+	24.8975i	−0.194793	+	1.38964i
$322$	−4.94329	−	8.56203i	−0.275479	−	0.477143i
$323$	−9.20075			−0.511943
$324$	−43.3208	+	23.1139i	−2.40671	+	1.28410i
$325$	−19.3992			−1.07607
$326$	29.5230	+	51.1353i	1.63513	+	2.83212i
$327$	−2.80838	+	20.0348i	−0.155304	+	1.10793i
$328$	0.816922	−	1.41495i	0.0451069	−	0.0781275i
$329$	0.0798737	−	0.138345i	0.00440358	−	0.00762722i
$330$		0			0
$331$	14.9247	+	25.8504i	0.820337	+	1.42086i	0.905432	+	0.424492i	$0.139547\pi$
$331$	14.9247	+	25.8504i	0.820337	+	1.42086i	−0.0850951	+	0.996373i	$0.527119\pi$
$332$	−76.7039			−4.20967
$333$	−5.96701	−	1.70638i	−0.326990	−	0.0935092i
$334$	−13.7103			−0.750196
$335$	1.58117	+	2.73867i	0.0863888	+	0.149630i
$336$	10.5270	+	8.21854i	0.574297	+	0.448358i
$337$	−10.8619	+	18.8133i	−0.591683	+	1.02483i	0.402322	+	0.915498i	$0.368203\pi$
$337$	−10.8619	+	18.8133i	−0.591683	+	1.02483i	−0.994006	+	0.109328i	$0.965130\pi$
$338$	−12.4788	+	21.6139i	−0.678755	+	1.17564i
$339$	−1.64660	−	1.28551i	−0.0894309	−	0.0698195i
$340$	6.87841	+	11.9137i	0.373034	+	0.646114i
$341$		0			0
$342$	−6.79192	−	27.1579i	−0.367265	−	1.46853i
$343$	−7.12779			−0.384865
$344$	−10.7073	−	18.5455i	−0.577297	−	0.999908i
$345$	10.4893	−	4.24231i	0.564723	−	0.228398i
$346$	0.625467	−	1.08334i	0.0336253	−	0.0582408i
$347$	−14.1149	+	24.4477i	−0.757727	+	1.31242i	0.186280	+	0.982497i	$0.440357\pi$
$347$	−14.1149	+	24.4477i	−0.757727	+	1.31242i	−0.944007	+	0.329925i	$0.892977\pi$
$348$	−5.49135	+	39.1749i	−0.294367	+	2.10000i
$349$	−3.57851	−	6.19817i	−0.191553	−	0.331780i	0.754212	−	0.656631i	$-0.228019\pi$
$349$	−3.57851	−	6.19817i	−0.191553	−	0.331780i	−0.945765	+	0.324851i	$0.894686\pi$
$350$	−5.84394			−0.312372
$351$	−14.3924	−	19.7647i	−0.768211	−	1.05496i
$352$		0			0
$353$	14.8149	+	25.6602i	0.788518	+	1.36575i	0.926875	+	0.375371i	$0.122485\pi$
$353$	14.8149	+	25.6602i	0.788518	+	1.36575i	−0.138357	+	0.990382i	$0.544182\pi$
$354$	2.60957	−	18.6165i	0.138697	−	0.989455i
$355$	1.35977	−	2.35519i	0.0721689	−	0.125000i
$356$	−20.5612	+	35.6131i	−1.08974	+	1.88749i
$357$	−2.24414	+	0.907629i	−0.118773	+	0.0480368i
$358$	−12.5594	−	21.7535i	−0.663785	−	1.14971i
$359$	13.0116			0.686726			0.343363	−	0.939203i	$-0.388434\pi$
$359$	13.0116			0.686726			0.343363	+	0.939203i	$0.388434\pi$
$360$	−19.0583	+	18.4308i	−1.00446	+	0.971388i
$361$	−7.32093			−0.385312
$362$	−20.6915	−	35.8387i	−1.08752	−	1.88364i
$363$		0			0
$364$	−6.66316	+	11.5409i	−0.349244	+	0.604909i
$365$	−4.46023	+	7.72534i	−0.233459	+	0.404363i
$366$	−16.8466	−	13.1523i	−0.880587	−	0.687481i
$367$	−16.0581	−	27.8134i	−0.838225	−	1.45185i	−0.891378	−	0.453262i	$-0.850260\pi$
$367$	−16.0581	−	27.8134i	−0.838225	−	1.45185i	0.0531526	−	0.998586i	$-0.483073\pi$
$368$	103.599			5.40049
$369$	−0.373408	+	0.361114i	−0.0194388	+	0.0187988i
$370$	−5.29050			−0.275040
$371$	0.492735	+	0.853442i	0.0255815	+	0.0443085i
$372$	−45.4324	+	18.3748i	−2.35556	+	0.952690i
$373$	17.4578	−	30.2378i	0.903931	−	1.56565i	0.0815849	−	0.996666i	$-0.474002\pi$
$373$	17.4578	−	30.2378i	0.903931	−	1.56565i	0.822346	−	0.568988i	$-0.192665\pi$
$374$		0			0
$375$	2.05439	−	14.6559i	0.106088	−	0.756826i
$376$	1.45183	+	2.51465i	0.0748726	+	0.129683i
$377$	−19.6976			−1.01448
$378$	−4.33566	−	5.95405i	−0.223002	−	0.306243i
$379$	−11.4728			−0.589320			−0.294660	−	0.955602i	$-0.595206\pi$
$379$	−11.4728			−0.589320			−0.294660	+	0.955602i	$0.595206\pi$
$380$	−8.73118	−	15.1228i	−0.447900	−	0.775786i
$381$	2.51338	−	17.9303i	0.128765	−	0.918598i
$382$	28.5929	−	49.5243i	1.46294	−	2.53388i
$383$	−15.1180	+	26.1851i	−0.772492	+	1.33800i	0.163701	+	0.986510i	$0.447657\pi$
$383$	−15.1180	+	26.1851i	−0.772492	+	1.33800i	−0.936193	+	0.351485i	$0.885677\pi$
$384$	−59.7243	+	24.1551i	−3.04779	+	1.23266i
$385$		0			0
$386$	28.5309			1.45219
$387$	1.65185	+	6.60503i	0.0839684	+	0.335753i
$388$	89.1146			4.52411
$389$	13.0540	+	22.6101i	0.661863	+	1.14638i	0.980126	+	0.198377i	$0.0635671\pi$
$389$	13.0540	+	22.6101i	0.661863	+	1.14638i	−0.318263	+	0.948002i	$0.603100\pi$
$390$	−16.4285	−	12.8259i	−0.831889	−	0.649462i
$391$	−9.38907	+	16.2623i	−0.474826	+	0.822422i
$392$	31.7541	−	54.9997i	1.60382	−	2.77790i
$393$	18.3778	+	14.3477i	0.927035	+	0.723744i
$394$	−28.6506	−	49.6242i	−1.44339	−	2.50003i
$395$	−1.91397			−0.0963024
$396$		0			0
$397$	−9.94467			−0.499109			−0.249554	−	0.968361i	$-0.580284\pi$
$397$	−9.94467			−0.499109			−0.249554	+	0.968361i	$0.580284\pi$
$398$	26.0084	+	45.0479i	1.30368	+	2.25805i
$399$	2.84863	−	1.15211i	0.142610	−	0.0576776i
$400$	30.6187	−	53.0331i	1.53093	−	2.65166i
$401$	11.7984	−	20.4354i	0.589183	−	1.02050i	−0.405156	−	0.914247i	$-0.632783\pi$
$401$	11.7984	−	20.4354i	0.589183	−	1.02050i	0.994340	−	0.106248i	$-0.0338837\pi$
$402$	2.21673	−	15.8140i	0.110560	−	0.788730i
$403$	−12.2015	−	21.1336i	−0.607798	−	1.05274i
$404$	54.4620			2.70959
$405$	7.43692	−	3.96798i	0.369544	−	0.197170i
$406$	−5.93382			−0.294491
$407$		0			0
$408$	6.10811	−	43.5748i	0.302396	−	2.15728i
$409$	−1.30329	+	2.25737i	−0.0644436	+	0.111620i	−0.896447	−	0.443151i	$-0.853861\pi$
$409$	−1.30329	+	2.25737i	−0.0644436	+	0.111620i	0.832003	+	0.554770i	$0.187194\pi$
$410$	−0.221407	+	0.383488i	−0.0109345	+	0.0189391i
$411$	−33.5007	+	13.5491i	−1.65247	+	0.668329i
$412$	−17.8809	−	30.9706i	−0.880929	−	1.52581i
$413$	2.06341			0.101534
$414$	−54.9326	−	15.7090i	−2.69979	−	0.772057i
$415$	13.1678			0.646383
$416$	−51.0188	−	88.3672i	−2.50140	−	4.33256i
$417$	−1.18484	−	0.925014i	−0.0580218	−	0.0452981i
$418$		0			0
$419$	8.80232	−	15.2461i	0.430022	−	0.744819i	−0.566853	−	0.823819i	$-0.691839\pi$
$419$	8.80232	−	15.2461i	0.430022	−	0.744819i	0.996875	+	0.0789996i	$0.0251726\pi$
$420$	−3.62144	−	2.82729i	−0.176708	−	0.137958i
$421$	−3.17824	−	5.50487i	−0.154898	−	0.268291i	0.778124	−	0.628111i	$-0.216172\pi$
$421$	−3.17824	−	5.50487i	−0.154898	−	0.268291i	−0.933022	+	0.359820i	$0.882838\pi$
$422$	−44.4778			−2.16515
$423$	−0.223980	−	0.895598i	−0.0108903	−	0.0435455i
$424$	−17.9125			−0.869908
$425$	5.54986	+	9.61264i	0.269208	+	0.466282i
$426$	−12.7308	+	5.14888i	−0.616808	+	0.249464i
$427$	1.17298	−	2.03167i	0.0567647	−	0.0983193i
$428$	39.5951	−	68.5807i	1.91390	−	3.31497i
$429$		0			0
$430$	2.90195	+	5.02632i	0.139944	+	0.242391i
$431$	−29.1820			−1.40565			−0.702824	−	0.711364i	$-0.748078\pi$
$431$	−29.1820			−1.40565			−0.702824	+	0.711364i	$0.748078\pi$
$432$	76.7486	−	8.15009i	3.69257	−	0.392122i
$433$	13.7210			0.659388			0.329694	−	0.944088i	$-0.393054\pi$
$433$	13.7210			0.659388			0.329694	+	0.944088i	$0.393054\pi$
$434$	−3.67564	−	6.36640i	−0.176437	−	0.305597i
$435$	0.942706	−	6.72520i	0.0451993	−	0.322449i
$436$	31.8618	−	55.1862i	1.52590	−	2.64294i
$437$	11.9181	−	20.6428i	0.570121	−	0.987478i
$438$	41.7587	−	16.8891i	1.99531	−	0.806990i
$439$	−1.00243	−	1.73625i	−0.0478431	−	0.0828667i	0.841112	−	0.540861i	$-0.181901\pi$
$439$	−1.00243	−	1.73625i	−0.0478431	−	0.0828667i	−0.888955	+	0.457994i	$0.848568\pi$
$440$		0			0
$441$	−14.5145	+	14.0366i	−0.691167	+	0.668411i
$442$	34.5903			1.64529
$443$	−17.2972	−	29.9597i	−0.821817	−	1.42343i	−0.904328	−	0.426838i	$-0.859627\pi$
$443$	−17.2972	−	29.9597i	−0.821817	−	1.42343i	0.0825115	−	0.996590i	$-0.473706\pi$
$444$	15.4089	+	12.0298i	0.731272	+	0.570910i
$445$	3.52976	−	6.11373i	0.167327	−	0.289819i
$446$	12.3488	−	21.3887i	0.584732	−	1.01279i
$447$	−8.96352	−	6.99789i	−0.423960	−	0.330989i
$448$	−7.65856	−	13.2650i	−0.361833	−	0.626713i
$449$	−2.43875			−0.115092			−0.0575459	−	0.998343i	$-0.518328\pi$
$449$	−2.43875			−0.115092			−0.0575459	+	0.998343i	$0.518328\pi$
$450$	−24.2768	+	23.4775i	−1.14442	+	1.10674i
$451$		0			0
$452$	3.28999	+	5.69843i	0.154748	+	0.268031i
$453$	20.2991	−	8.20984i	0.953735	−	0.385732i
$454$	−7.06069	+	12.2295i	−0.331374	+	0.573957i
$455$	1.14387	−	1.98124i	0.0536255	−	0.0928821i
$456$	−7.75339	+	55.3122i	−0.363086	+	2.59023i
$457$	−20.9497	−	36.2860i	−0.979988	−	1.69739i	−0.662384	−	0.749165i	$-0.730455\pi$
$457$	−20.9497	−	36.2860i	−0.979988	−	1.69739i	−0.317604	−	0.948223i	$-0.602878\pi$
$458$	43.7530			2.04444
$459$	−5.67627	+	12.7861i	−0.264946	+	0.596805i
$460$	−35.6395			−1.66170
$461$	19.1941	+	33.2451i	0.893956	+	1.54838i	0.835091	+	0.550112i	$0.185415\pi$
$461$	19.1941	+	33.2451i	0.893956	+	1.54838i	0.0588651	+	0.998266i	$0.481252\pi$
$462$		0			0
$463$	0.121675	−	0.210748i	0.00565472	−	0.00979427i	−0.863184	−	0.504889i	$-0.831533\pi$
$463$	0.121675	−	0.210748i	0.00565472	−	0.00979427i	0.868839	+	0.495095i	$0.164867\pi$
$464$	31.0896	−	53.8488i	1.44330	−	2.49987i
$465$	7.79942	−	3.15442i	0.361689	−	0.146283i
$466$	−23.0970	−	40.0052i	−1.06995	−	1.85320i
$467$	−15.6918			−0.726129			−0.363064	−	0.931764i	$-0.618269\pi$
$467$	−15.6918			−0.726129			−0.363064	+	0.931764i	$0.618269\pi$
$468$	18.6847	+	74.7119i	0.863700	+	3.45356i
$469$	1.75279			0.0809363
$470$	−0.393484	−	0.681535i	−0.0181501	−	0.0314369i
$471$	19.1387	+	14.9417i	0.881865	+	0.688479i
$472$	−18.7529	+	32.4811i	−0.863174	+	1.49506i
$473$		0			0
$474$	7.61810	+	5.94751i	0.349911	+	0.273178i
$475$	−7.04477	−	12.2019i	−0.323236	−	0.559862i
$476$	7.62497			0.349490
$477$	5.47554	+	1.56584i	0.250708	+	0.0716948i
$478$	−1.97261			−0.0902249
$479$	−8.14023	−	14.0993i	−0.371937	−	0.644213i	0.617927	−	0.786236i	$-0.287973\pi$
$479$	−8.14023	−	14.0993i	−0.371937	−	0.644213i	−0.989863	+	0.142022i	$0.954640\pi$
$480$	32.6122	−	13.1898i	1.48854	−	0.602029i
$481$	−4.86705	+	8.42998i	−0.221918	+	0.384374i
$482$	18.6315	−	32.2708i	0.848643	−	1.46989i
$483$	0.870578	−	6.21065i	0.0396127	−	0.282594i
$484$		0			0
$485$	−15.2984			−0.694664
$486$	−41.9310	−	7.31607i	−1.90203	−	0.331864i
$487$	−32.0421			−1.45197			−0.725983	−	0.687713i	$-0.758615\pi$
$487$	−32.0421			−1.45197			−0.725983	+	0.687713i	$0.758615\pi$
$488$	21.3209	+	36.9289i	0.965151	+	1.67169i
$489$	−5.19939	+	37.0921i	−0.235125	+	1.67736i
$490$	−8.60618	+	14.9063i	−0.388787	+	0.673400i
$491$	−10.4729	+	18.1396i	−0.472635	+	0.818627i	−0.999510	−	0.0313157i	$-0.990030\pi$
$491$	−10.4729	+	18.1396i	−0.472635	+	0.818627i	0.526875	+	0.849943i	$0.323364\pi$
$492$	1.51685	−	0.613481i	0.0683850	−	0.0276579i
$493$	5.63522	+	9.76049i	0.253798	+	0.439591i
$494$	−43.9076			−1.97550
$495$		0			0
$496$	77.0326			3.45887
$497$	−0.753676	−	1.30541i	−0.0338070	−	0.0585554i
$498$	−52.4114	−	40.9180i	−2.34861	−	1.83358i
$499$	−3.61552	+	6.26227i	−0.161853	+	0.280338i	−0.935533	−	0.353239i	$-0.885080\pi$
$499$	−3.61552	+	6.26227i	−0.161853	+	0.280338i	0.773680	+	0.633576i	$0.218414\pi$
$500$	−23.3076	+	40.3699i	−1.04235	+	1.80540i
$501$	−6.85516	−	5.35188i	−0.306266	−	0.239104i
$502$	−28.0879	−	48.6496i	−1.25362	−	2.17134i
$503$	5.90333			0.263216			0.131608	−	0.991302i	$-0.457986\pi$
$503$	5.90333			0.263216			0.131608	+	0.991302i	$0.457986\pi$
$504$	3.56528	+	14.2560i	0.158810	+	0.635012i
$505$	−9.34954			−0.416049
$506$		0			0
$507$	−14.6764	+	5.93579i	−0.651804	+	0.263618i
$508$	−28.5150	+	49.3895i	−1.26515	+	2.19130i
$509$	5.42002	−	9.38776i	0.240238	−	0.416105i	−0.720544	−	0.693409i	$-0.756108\pi$
$509$	5.42002	−	9.38776i	0.240238	−	0.416105i	0.960782	+	0.277304i	$0.0894411\pi$
$510$	−1.65546	+	11.8099i	−0.0733048	+	0.522951i
$511$	2.47217	+	4.28192i	0.109362	+	0.189421i
$512$	41.7940			1.84705
$513$	7.20524	−	16.2302i	0.318119	−	0.716581i
$514$	14.3739			0.634004
$515$	3.06963	+	5.31676i	0.135264	+	0.234284i
$516$	2.97704	−	21.2380i	0.131057	−	0.934951i
$517$		0			0
$518$	−1.46618	+	2.53950i	−0.0644203	+	0.111579i
$519$	0.735620	−	0.297517i	0.0322901	−	0.0130595i
$520$	20.7917	+	36.0123i	0.911776	+	1.57924i
$521$	14.7412			0.645822			0.322911	−	0.946429i	$-0.395339\pi$
$521$	14.7412			0.645822			0.322911	+	0.946429i	$0.395339\pi$
$522$	−24.6502	+	23.8386i	−1.07891	+	1.04339i
$523$	16.8230			0.735617			0.367808	−	0.929902i	$-0.380108\pi$
$523$	16.8230			0.735617			0.367808	+	0.929902i	$0.380108\pi$
$524$	−36.7197	−	63.6004i	−1.60411	−	2.77840i
$525$	−2.92197	−	2.28120i	−0.127525	−	0.0995599i
$526$	3.54744	−	6.14434i	0.154676	−	0.267906i
$527$	−6.98136	+	12.0921i	−0.304113	+	0.526739i
$528$		0			0
$529$	−12.8241	−	22.2120i	−0.557570	−	0.965739i
$530$	4.85475			0.210877
$531$	8.57181	−	8.28959i	0.371985	−	0.359738i
$532$	−9.67884			−0.419631
$533$	0.407371	+	0.705587i	0.0176452	+	0.0305624i
$534$	−33.0473	+	13.3658i	−1.43010	+	0.578393i
$535$	−6.79732	+	11.7733i	−0.293874	+	0.509004i
$536$	−15.9299	+	27.5914i	−0.688067	+	1.19177i
$537$	2.21187	−	15.7794i	0.0954494	−	0.680930i
$538$	13.7826	+	23.8721i	0.594208	+	1.02920i
$539$		0			0
$540$	−26.4025	+	2.80374i	−1.13618	+	0.120654i
$541$	22.5357			0.968886			0.484443	−	0.874823i	$-0.339022\pi$
$541$	22.5357			0.968886			0.484443	+	0.874823i	$0.339022\pi$
$542$	44.1009	+	76.3849i	1.89429	+	3.28101i
$543$	3.64404	−	25.9963i	0.156381	−	1.11561i
$544$	−29.1916	+	50.5614i	−1.25158	+	2.16780i
$545$	−5.46974	+	9.47387i	−0.234298	+	0.405816i
$546$	−10.7094	+	4.33137i	−0.458322	+	0.185365i
$547$	14.2139	+	24.6192i	0.607743	+	1.05264i	0.991612	+	0.129254i	$0.0412581\pi$
$547$	14.2139	+	24.6192i	0.607743	+	1.05264i	−0.383869	+	0.923388i	$0.625409\pi$
$548$	113.826			4.86240
$549$	−3.28926	−	13.1523i	−0.140382	−	0.561326i
$550$		0			0
$551$	−7.15313	−	12.3896i	−0.304734	−	0.527814i
$552$	89.8523	+	70.1484i	3.82437	+	2.98571i
$553$	−0.530427	+	0.918727i	−0.0225561	+	0.0390683i
$554$	44.1496	−	76.4693i	1.87574	−	3.24887i
$555$	−2.64525	−	2.06517i	−0.112285	−	0.0876616i
$556$	2.36737	+	4.10040i	0.100399	+	0.173896i
$557$	−43.1863			−1.82986			−0.914930	−	0.403612i	$-0.867755\pi$
$557$	−43.1863			−1.82986			−0.914930	+	0.403612i	$0.867755\pi$
$558$	−40.8458	−	11.6806i	−1.72914	−	0.494481i
$559$	10.6787			0.451661
$560$	3.61085	+	6.25417i	0.152586	+	0.264287i
$561$		0			0
$562$	−13.0282	+	22.5656i	−0.549563	+	0.951871i
$563$	−0.482261	+	0.835300i	−0.0203249	+	0.0352037i	−0.876009	−	0.482295i	$-0.839803\pi$
$563$	−0.482261	+	0.835300i	−0.0203249	+	0.0352037i	0.855684	+	0.517499i	$0.173137\pi$
$564$	−0.403667	+	2.87973i	−0.0169974	+	0.121259i
$565$	−0.564795	−	0.978254i	−0.0237611	−	0.0411555i
$566$	16.1667			0.679537
$567$	0.156355	−	4.66947i	0.00656631	−	0.196099i
$568$	27.3986			1.14962
$569$	4.26416	+	7.38575i	0.178763	+	0.309627i	0.941457	−	0.337133i	$-0.109457\pi$
$569$	4.26416	+	7.38575i	0.178763	+	0.309627i	−0.762694	+	0.646759i	$0.776124\pi$
$570$	2.10137	−	14.9910i	0.0880167	−	0.627905i
$571$	8.80176	−	15.2451i	0.368342	−	0.637988i	−0.620964	−	0.783839i	$-0.713259\pi$
$571$	8.80176	−	15.2451i	0.368342	−	0.637988i	0.989307	+	0.145851i	$0.0465921\pi$
$572$		0			0
$573$	33.6284	−	13.6008i	1.40485	−	0.568182i
$574$	0.122719	+	0.212555i	0.00512219	+	0.00887189i
$575$	−28.7559			−1.19920
$576$	−85.1061	−	24.3377i	−3.54609	−	1.01407i
$577$	−11.1810			−0.465472			−0.232736	−	0.972540i	$-0.574768\pi$
$577$	−11.1810			−0.465472			−0.232736	+	0.972540i	$0.574768\pi$
$578$	13.3135	+	23.0597i	0.553770	+	0.959157i
$579$	14.2655	+	11.1372i	0.592852	+	0.462845i
$580$	−10.6952	+	18.5247i	−0.444096	+	0.769197i
$581$	3.64926	−	6.32070i	0.151397	−	0.262227i
$582$	60.8915	+	47.5385i	2.52403	+	1.97053i
$583$		0			0
$584$	−89.8713			−3.71890
$585$	−3.20762	−	12.8259i	−0.132619	−	0.530284i
$586$	−39.3988			−1.62755
$587$	−10.8373	−	18.7708i	−0.447305	−	0.774755i	0.550905	−	0.834568i	$-0.314283\pi$
$587$	−10.8373	−	18.7708i	−0.447305	−	0.774755i	−0.998210	+	0.0598133i	$0.980949\pi$
$588$	58.9607	−	23.8463i	2.43150	−	0.983404i
$589$	8.86187	−	15.3492i	0.365147	−	0.632453i
$590$	5.08253	−	8.80321i	0.209245	−	0.362422i
$591$	5.04574	−	35.9960i	0.207554	−	1.48068i
$592$	−15.3638	−	26.6109i	−0.631448	−	1.09370i
$593$	7.82200			0.321211			0.160605	−	0.987019i	$-0.448655\pi$
$593$	7.82200			0.321211			0.160605	+	0.987019i	$0.448655\pi$
$594$		0			0
$595$	−1.30899			−0.0536632
$596$	17.9096	+	31.0203i	0.733605	+	1.27064i
$597$	−4.58042	+	32.6764i	−0.187464	+	1.33736i
$598$	−44.8063	+	77.6068i	−1.83227	+	3.17358i
$599$	5.25399	−	9.10018i	0.214672	−	0.371823i	−0.738499	−	0.674255i	$-0.764465\pi$
$599$	5.25399	−	9.10018i	0.214672	−	0.371823i	0.953171	+	0.302432i	$0.0977984\pi$
$600$	62.4651	−	25.2636i	2.55013	−	1.03138i
$601$	18.5488	+	32.1275i	0.756622	+	1.31051i	0.944564	+	0.328328i	$0.106485\pi$
$601$	18.5488	+	32.1275i	0.756622	+	1.31051i	−0.187942	+	0.982180i	$0.560182\pi$
$602$	3.21692			0.131112
$603$	7.28142	−	7.04169i	0.296522	−	0.286760i
$604$	−68.9706			−2.80638
$605$		0			0
$606$	37.2136	+	29.0529i	1.51170	+	1.18020i
$607$	−20.7558	+	35.9501i	−0.842451	+	1.45917i	0.0453658	+	0.998970i	$0.485555\pi$
$607$	−20.7558	+	35.9501i	−0.842451	+	1.45917i	−0.887817	+	0.460197i	$0.847779\pi$
$608$	37.0547	−	64.1806i	1.50277	−	2.60287i
$609$	−2.96691	−	2.31629i	−0.120225	−	0.0938609i
$610$	−5.77851	−	10.0087i	−0.233965	−	0.405239i
$611$	−1.44796			−0.0585782
$612$	31.6756	−	30.6327i	1.28041	−	1.23825i
$613$	−33.7344			−1.36252			−0.681259	−	0.732042i	$-0.738567\pi$
$613$	−33.7344			−1.36252			−0.681259	+	0.732042i	$0.738567\pi$
$614$	13.1148	+	22.7155i	0.529271	+	0.916724i
$615$	−0.260400	+	0.105317i	−0.0105003	+	0.00424679i
$616$		0			0
$617$	14.0298	−	24.3003i	0.564817	−	0.978292i	−0.432250	−	0.901754i	$-0.642280\pi$
$617$	14.0298	−	24.3003i	0.564817	−	0.978292i	0.997067	−	0.0765378i	$-0.0243866\pi$
$618$	4.30347	−	30.7007i	0.173111	−	1.23496i
$619$	15.9049	+	27.5480i	0.639270	+	1.10725i	0.985593	+	0.169134i	$0.0540969\pi$
$619$	15.9049	+	27.5480i	0.639270	+	1.10725i	−0.346323	+	0.938115i	$0.612570\pi$
$620$	−26.5002			−1.06427
$621$	−21.3342	−	29.2977i	−0.856112	−	1.17568i
$622$	0.937683			0.0375976
$623$	−1.95644	−	3.38865i	−0.0783830	−	0.135763i
$624$	16.8043	−	119.881i	0.672711	−	4.79908i
$625$	−6.30578	+	10.9219i	−0.252231	+	0.436877i
$626$	11.4122	−	19.7666i	0.456125	−	0.790031i
$627$		0			0
$628$	−38.2401	−	66.2338i	−1.52595	−	2.64302i
$629$	5.56960			0.222075
$630$	−0.966282	−	3.86374i	−0.0384976	−	0.153935i
$631$	−23.4280			−0.932653			−0.466326	−	0.884613i	$-0.654423\pi$
$631$	−23.4280			−0.932653			−0.466326	+	0.884613i	$0.654423\pi$
$632$	−9.64138	−	16.6994i	−0.383513	−	0.664265i
$633$	−22.2389	−	17.3621i	−0.883917	−	0.690082i
$634$	18.3057	−	31.7064i	0.727013	−	1.25922i
$635$	4.89520	−	8.47873i	0.194260	−	0.336468i
$636$	−14.1397	−	11.0390i	−0.560676	−	0.437724i
$637$	15.8347	+	27.4265i	0.627393	+	1.08668i
$638$		0			0
$639$	−8.37527	−	2.39507i	−0.331321	−	0.0947475i
$640$	−34.8366			−1.37704
$641$	−7.75779	−	13.4369i	−0.306414	−	0.530725i	0.671161	−	0.741312i	$-0.265796\pi$
$641$	−7.75779	−	13.4369i	−0.306414	−	0.530725i	−0.977575	+	0.210587i	$0.932463\pi$
$642$	63.6397	−	25.7386i	2.51166	−	1.01582i
$643$	5.47372	−	9.48075i	0.215862	−	0.373884i	−0.737677	−	0.675154i	$-0.764077\pi$
$643$	5.47372	−	9.48075i	0.215862	−	0.373884i	0.953539	+	0.301270i	$0.0974104\pi$
$644$	−9.87694	+	17.1074i	−0.389206	+	0.674125i
$645$	−0.511071	+	3.64595i	−0.0201234	+	0.143559i
$646$	12.5614	+	21.7570i	0.494221	+	0.856016i
$647$	16.9732			0.667287			0.333643	−	0.942699i	$-0.391722\pi$
$647$	16.9732			0.667287			0.333643	+	0.942699i	$0.391722\pi$
$648$	72.0830	+	44.8988i	2.83169	+	1.76379i
$649$		0			0
$650$	26.4849	+	45.8732i	1.03882	+	1.79930i
$651$	0.647330	−	4.61800i	0.0253708	−	0.180994i
$652$	58.9885	−	102.171i	2.31017	−	4.00133i
$653$	−0.227291	+	0.393679i	−0.00889458	+	0.0154059i	−0.870438	−	0.492277i	$-0.836165\pi$
$653$	−0.227291	+	0.393679i	−0.00889458	+	0.0154059i	0.861544	+	0.507683i	$0.169498\pi$
$654$	51.2103	−	20.7117i	2.00248	−	0.809890i
$655$	6.30371	+	10.9183i	0.246306	+	0.426615i
$656$	−2.57189			−0.100415
$657$	27.4721	+	7.85617i	1.07179	+	0.306499i
$658$	−0.436192			−0.0170045
$659$	−1.57851	−	2.73406i	−0.0614901	−	0.106504i	0.833642	−	0.552306i	$-0.186252\pi$
$659$	−1.57851	−	2.73406i	−0.0614901	−	0.106504i	−0.895132	+	0.445802i	$0.852919\pi$
$660$		0			0
$661$	13.2786	−	22.9992i	0.516478	−	0.894566i	−0.483339	−	0.875433i	$-0.660576\pi$
$661$	13.2786	−	22.9992i	0.516478	−	0.894566i	0.999817	−	0.0191324i	$-0.00609042\pi$
$662$	40.7521	−	70.5848i	1.58388	−	2.74336i
$663$	17.2952	+	13.5025i	0.671688	+	0.524393i
$664$	66.3312	+	114.889i	2.57415	+	4.45856i
$665$	1.66158			0.0644331
$666$	4.11143	+	16.4398i	0.159315	+	0.637030i
$667$	−29.1982			−1.13056
$668$	13.6970	+	23.7238i	0.529951	+	0.917903i
$669$	14.5236	−	5.87396i	0.561514	−	0.227100i
$670$	4.31742	−	7.47799i	0.166796	−	0.288900i
$671$		0			0
$672$	2.70672	−	19.3096i	0.104414	−	0.744883i
$673$	−13.6485	−	23.6398i	−0.526110	−	0.911248i	−0.999537	−	0.0304158i	$-0.990317\pi$
$673$	−13.6485	−	23.6398i	−0.526110	−	0.911248i	0.473428	−	0.880833i	$-0.343016\pi$
$674$	59.3169			2.28480
$675$	−21.3030	+	2.26220i	−0.819951	+	0.0870723i
$676$	49.8664			1.91794
$677$	−0.200168	−	0.346700i	−0.00769307	−	0.0133248i	0.862153	−	0.506648i	$-0.169115\pi$
$677$	−0.200168	−	0.346700i	−0.00769307	−	0.0133248i	−0.869846	+	0.493323i	$0.835782\pi$
$678$	−0.791815	+	5.64876i	−0.0304095	+	0.216939i
$679$	−4.23971	+	7.34339i	−0.162705	+	0.281813i
$680$	11.8965	−	20.6053i	0.456209	−	0.790177i
$681$	−8.30417	+	3.35857i	−0.318216	+	0.128701i
$682$		0			0
$683$	−26.2154			−1.00310			−0.501552	−	0.865127i	$-0.667238\pi$
$683$	−26.2154			−1.00310			−0.501552	+	0.865127i	$0.667238\pi$
$684$	−40.2077	+	38.8839i	−1.53738	+	1.48676i
$685$	−19.5406			−0.746607
$686$	9.73127	+	16.8550i	0.371541	+	0.643529i
$687$	21.8765	+	17.0792i	0.834640	+	0.651610i
$688$	−16.8547	+	29.1932i	−0.642579	+	1.11298i
$689$	4.46618	−	7.73565i	0.170148	−	0.294705i
$690$	−24.3523	−	19.0120i	−0.927076	−	0.723776i
$691$	7.79814	+	13.5068i	0.296655	+	0.513822i	0.975369	−	0.220581i	$-0.0707955\pi$
$691$	7.79814	+	13.5068i	0.296655	+	0.513822i	−0.678713	+	0.734403i	$0.737462\pi$
$692$	−2.49943			−0.0950141
$693$		0			0
$694$	77.0818			2.92599
$695$	−0.406408	−	0.703920i	−0.0154160	−	0.0267012i
$696$	63.4259	−	25.6522i	2.40415	−	0.972344i
$697$	0.233087	−	0.403719i	0.00882880	−	0.0152919i
$698$	−9.77118	+	16.9242i	−0.369845	+	0.640590i
$699$	4.06769	−	29.0186i	0.153854	−	1.09758i
$700$	5.83824	+	10.1121i	0.220665	+	0.382203i
$701$	−27.4965			−1.03853			−0.519265	−	0.854613i	$-0.673794\pi$
$701$	−27.4965			−1.03853			−0.519265	+	0.854613i	$0.673794\pi$
$702$	−27.0882	+	61.0176i	−1.02238	+	2.30296i
$703$	−7.06983			−0.266644
$704$		0			0
$705$	0.0692978	−	0.494366i	0.00260991	−	0.0186189i
$706$	40.4523	−	70.0655i	1.52244	−	2.63695i
$707$	−2.59108	+	4.48788i	−0.0974476	+	0.168784i
$708$	−34.8203	+	14.0828i	−1.30863	+	0.529266i
$709$	15.3257	+	26.5449i	0.575570	+	0.996916i	0.995979	+	0.0895815i	$0.0285529\pi$
$709$	15.3257	+	26.5449i	0.575570	+	0.996916i	−0.420410	+	0.907334i	$0.638114\pi$
$710$	−7.42572			−0.278682
$711$	1.48741	+	5.94751i	0.0557824	+	0.223049i
$712$	71.1228			2.66544
$713$	−18.0865	−	31.3267i	−0.677345	−	1.17320i
$714$	5.21010	+	4.06757i	0.194983	+	0.152225i
$715$		0			0
$716$	−25.0943	+	43.4646i	−0.937818	+	1.62435i
$717$	−0.986303	−	0.770015i	−0.0368342	−	0.0287567i
$718$	−17.7642	−	30.7685i	−0.662954	−	1.14827i
$719$	−19.7250			−0.735620			−0.367810	−	0.929901i	$-0.619892\pi$
$719$	−19.7250			−0.735620			−0.367810	+	0.929901i	$0.619892\pi$
$720$	40.1258	+	11.4747i	1.49540	+	0.427638i
$721$	3.40280			0.126727
$722$	9.99495	+	17.3118i	0.371973	+	0.644277i
$723$	21.9128	−	8.86249i	0.814946	−	0.329599i
$724$	−41.3426	+	71.6075i	−1.53649	+	2.66127i
$725$	−8.62949	+	14.9467i	−0.320491	+	0.555107i
$726$		0			0
$727$	2.70607	+	4.68705i	0.100363	+	0.173833i	0.911834	−	0.410559i	$-0.134666\pi$
$727$	2.70607	+	4.68705i	0.100363	+	0.173833i	−0.811471	+	0.584392i	$0.801333\pi$
$728$	23.0484			0.854230
$729$	−18.1097	−	20.0260i	−0.670728	−	0.741703i
$730$	24.3574			0.901509
$731$	−3.05504	−	5.29148i	−0.112995	−	0.195713i
$732$	−5.92804	+	42.2902i	−0.219107	+	1.56309i
$733$	−0.819020	+	1.41858i	−0.0302512	+	0.0523966i	−0.880755	−	0.473573i	$-0.842964\pi$
$733$	−0.819020	+	1.41858i	−0.0302512	+	0.0523966i	0.850503	+	0.525969i	$0.176297\pi$
$734$	−43.8468	+	75.9449i	−1.61842	+	2.80318i
$735$	−10.1218	+	4.09371i	−0.373350	+	0.150999i
$736$	−75.6263	−	130.989i	−2.78762	−	4.82830i
$737$		0			0
$738$	1.36372	+	0.389982i	0.0501993	+	0.0143555i
$739$	12.8306			0.471980			0.235990	−	0.971755i	$-0.424167\pi$
$739$	12.8306			0.471980			0.235990	+	0.971755i	$0.424167\pi$
$740$	5.28535	+	9.15449i	0.194293	+	0.336526i
$741$	−21.9538	−	17.1395i	−0.806493	−	0.629636i
$742$	1.34542	−	2.33033i	0.0493919	−	0.0855493i
$743$	18.1559	−	31.4469i	0.666074	−	1.15367i	−0.312919	−	0.949780i	$-0.601307\pi$
$743$	18.1559	−	31.4469i	0.666074	−	1.15367i	0.978993	−	0.203894i	$-0.0653598\pi$
$744$	66.8108	+	52.1597i	2.44940	+	1.91227i
$745$	−3.07455	−	5.32528i	−0.112643	−	0.195103i
$746$	−95.3376			−3.49056
$747$	−10.2332	−	40.9180i	−0.374412	−	1.49711i
$748$		0			0
$749$	3.76754	+	6.52557i	0.137663	+	0.238439i
$750$	−37.4614	+	15.1510i	−1.36790	+	0.553237i
$751$	−10.3163	+	17.8683i	−0.376447	+	0.652025i	−0.990542	−	0.137207i	$-0.956188\pi$
$751$	−10.3163	+	17.8683i	−0.376447	+	0.652025i	0.614096	+	0.789232i	$0.289521\pi$
$752$	2.28538	−	3.95840i	0.0833394	−	0.144348i
$753$	4.94665	−	35.2890i	0.180266	−	1.28600i
$754$	26.8923	+	46.5788i	0.979359	+	1.69630i
$755$	11.8403			0.430911
$756$	−5.97122	+	13.4505i	−0.217171	+	0.489190i
$757$	13.5638			0.492986			0.246493	−	0.969145i	$-0.420722\pi$
$757$	13.5638			0.492986			0.246493	+	0.969145i	$0.420722\pi$
$758$	15.6634	+	27.1298i	0.568919	+	0.985397i
$759$		0			0
$760$	−15.1009	+	26.1555i	−0.547768	+	0.948761i
$761$	7.99799	−	13.8529i	0.289927	−	0.502168i	−0.683865	−	0.729608i	$-0.739702\pi$
$761$	7.99799	−	13.8529i	0.289927	−	0.502168i	0.973792	+	0.227440i	$0.0730357\pi$
$762$	−45.8311	+	18.5361i	−1.66029	+	0.671492i
$763$	3.03171	+	5.25107i	0.109755	+	0.190102i
$764$	−114.260			−4.13378
$765$	−5.43777	+	5.25874i	−0.196603	+	0.190130i
$766$	82.5596			2.98300
$767$	−9.35146	−	16.1972i	−0.337662	−	0.584847i
$768$	58.0923	+	45.3531i	2.09622	+	1.63654i
$769$	13.2839	−	23.0083i	0.479028	−	0.829701i	−0.520683	−	0.853750i	$-0.674323\pi$
$769$	13.2839	−	23.0083i	0.479028	−	0.829701i	0.999711	+	0.0240494i	$0.00765589\pi$
$770$		0			0
$771$	7.18694	+	5.61090i	0.258831	+	0.202072i
$772$	−28.5031	−	49.3689i	−1.02585	−	1.77682i
$773$	24.2035			0.870539			0.435269	−	0.900300i	$-0.356653\pi$
$773$	24.2035			0.870539			0.435269	+	0.900300i	$0.356653\pi$
$774$	13.3637	−	12.9237i	0.480348	−	0.464533i
$775$	−21.3818			−0.768056
$776$	−77.0636	−	133.478i	−2.76642	−	4.79158i
$777$	−1.72439	+	0.697420i	−0.0618623	+	0.0250198i
$778$	35.6440	−	61.7373i	1.27790	−	2.21339i
$779$	−0.295872	+	0.512465i	−0.0106007	+	0.0183610i
$780$	−5.78091	+	41.2406i	−0.206990	+	1.47665i
$781$		0			0
$782$	51.2740			1.83355
$783$	−21.6306	+	2.29700i	−0.773015	+	0.0820881i
$784$	−99.9705			−3.57037
$785$	6.56471	+	11.3704i	0.234305	+	0.405828i
$786$	8.83749	−	63.0461i	0.315223	−	2.24878i
$787$	−13.6162	+	23.5839i	−0.485364	+	0.840675i	−0.999859	−	0.0168185i	$-0.994646\pi$
$787$	−13.6162	+	23.5839i	−0.485364	+	0.840675i	0.514494	+	0.857494i	$0.327980\pi$
$788$	−57.2453	+	99.1517i	−2.03928	+	3.53213i
$789$	4.17219	−	1.68741i	0.148534	−	0.0600735i
$790$	2.61306	+	4.52596i	0.0929686	+	0.161026i
$791$	−0.626097			−0.0222614
$792$		0			0
$793$	−21.2640			−0.755107
$794$	13.5770	+	23.5161i	0.481831	+	0.834555i
$795$	2.42738	+	1.89507i	0.0860902	+	0.0672113i
$796$	51.9661	−	90.0079i	1.84189	−	3.19025i
$797$	−19.2846	+	33.4019i	−0.683095	+	1.18316i	0.290936	+	0.956742i	$0.406033\pi$
$797$	−19.2846	+	33.4019i	−0.683095	+	1.18316i	−0.974031	+	0.226413i	$0.927300\pi$
$798$	−6.61350	−	5.16321i	−0.234115	−	0.182776i
$799$	0.414242	+	0.717489i	0.0146548	+	0.0253829i
$800$	−89.4051			−3.16095
$801$	−21.7410	−	6.21727i	−0.768181	−	0.219676i
$802$	−64.4313			−2.27515
$803$		0			0
$804$	−29.5785	+	11.9628i	−1.04315	+	0.421897i
$805$	1.69558	−	2.93684i	0.0597615	−	0.103510i
$806$	−33.3163	+	57.7055i	−1.17352	+	2.03259i
$807$	−2.42729	+	17.3161i	−0.0854446	+	0.609556i
$808$	−47.0971	−	81.5745i	−1.65687	−	2.86978i
$809$	12.0951			0.425240			0.212620	−	0.977135i	$-0.431800\pi$
$809$	12.0951			0.425240			0.212620	+	0.977135i	$0.431800\pi$
$810$	−19.5364	−	12.1687i	−0.686438	−	0.427566i
$811$	−35.0487			−1.23073			−0.615364	−	0.788243i	$-0.710991\pi$
$811$	−35.0487			−1.23073			−0.615364	+	0.788243i	$0.710991\pi$
$812$	5.92804	+	10.2677i	0.208033	+	0.360325i
$813$	−7.76674	+	55.4074i	−0.272392	+	1.94322i
$814$		0			0
$815$	−10.1266	+	17.5398i	−0.354719	+	0.614392i
$816$	−64.2105	+	25.9695i	−2.24782	+	0.909115i
$817$	3.87795	+	6.71680i	0.135672	+	0.234991i
$818$	7.11731			0.248851
$819$	−7.04549	−	2.01479i	−0.246189	−	0.0704026i
$820$	0.884765			0.0308973
$821$	10.0398	+	17.3894i	0.350391	+	0.606895i	0.986318	−	0.164854i	$-0.0527153\pi$
$821$	10.0398	+	17.3894i	0.350391	+	0.606895i	−0.635927	+	0.771749i	$0.719382\pi$
$822$	77.7765	+	60.7208i	2.71277	+	2.11788i
$823$	12.8058	−	22.1803i	0.446382	−	0.773156i	−0.551766	−	0.833999i	$-0.686046\pi$
$823$	12.8058	−	22.1803i	0.446382	−	0.773156i	0.998147	+	0.0608436i	$0.0193791\pi$
$824$	−30.9257	+	53.5649i	−1.07735	+	1.86602i
$825$		0			0
$826$	−2.81709	−	4.87934i	−0.0980191	−	0.169774i
$827$	0.864167			0.0300500			0.0150250	−	0.999887i	$-0.495217\pi$
$827$	0.864167			0.0300500			0.0150250	+	0.999887i	$0.495217\pi$
$828$	27.6967	+	110.747i	0.962527	+	3.84872i
$829$	38.1823			1.32613			0.663064	−	0.748563i	$-0.269256\pi$
$829$	38.1823			1.32613			0.663064	+	0.748563i	$0.269256\pi$
$830$	−17.9775	−	31.1379i	−0.624007	−	1.08081i
$831$	51.9249	−	21.0007i	1.80125	−	0.728506i
$832$	−69.4176	+	120.235i	−2.40662	+	4.16839i
$833$	9.06019	−	15.6927i	0.313917	−	0.543720i
$834$	−0.569765	+	4.06466i	−0.0197293	+	0.140748i
$835$	−2.35137	−	4.07269i	−0.0813725	−	0.140941i
$836$		0			0
$837$	−15.8633	−	21.7847i	−0.548316	−	0.752988i
$838$	−48.0697			−1.66054
$839$	−5.85122	−	10.1346i	−0.202007	−	0.349886i	0.747168	−	0.664635i	$-0.231413\pi$
$839$	−5.85122	−	10.1346i	−0.202007	−	0.349886i	−0.949175	+	0.314749i	$0.898080\pi$
$840$	−1.10307	+	7.86923i	−0.0380596	+	0.271514i
$841$	5.73778	−	9.93812i	0.197854	−	0.342694i
$842$	−8.67822	+	15.0311i	−0.299071	+	0.518007i
$843$	−15.3227	+	6.19716i	−0.527741	+	0.213441i
$844$	44.4345	+	76.9628i	1.52950	+	2.64917i
$845$	−8.56062			−0.294494
$846$	−1.81203	+	1.75237i	−0.0622987	+	0.0602476i
$847$		0			0
$848$	14.0984	+	24.4191i	0.484140	+	0.838555i
$849$	8.08335	+	6.31074i	0.277420	+	0.216584i
$850$	15.1540	−	26.2474i	0.519777	−	0.900280i
$851$	−7.21454	+	12.4959i	−0.247311	+	0.428355i
$852$	21.6278	+	16.8850i	0.740956	+	0.578470i
$853$	−8.73776	−	15.1343i	−0.299175	−	0.518187i	0.676772	−	0.736193i	$-0.263378\pi$
$853$	−8.73776	−	15.1343i	−0.299175	−	0.518187i	−0.975948	+	0.218006i	$0.930045\pi$
$854$	−6.40570			−0.219198
$855$	6.90250	−	6.67524i	0.236060	−	0.228288i
$856$	−136.962			−4.68128
$857$	−17.8130	−	30.8530i	−0.608480	−	1.05392i	−0.991491	−	0.130174i	$-0.958446\pi$
$857$	−17.8130	−	30.8530i	−0.608480	−	1.05392i	0.383011	−	0.923744i	$-0.374887\pi$
$858$		0			0
$859$	5.95893	−	10.3212i	0.203316	−	0.352154i	−0.746279	−	0.665633i	$-0.768161\pi$
$859$	5.95893	−	10.3212i	0.203316	−	0.352154i	0.949595	+	0.313480i	$0.101495\pi$
$860$	5.79824	−	10.0428i	0.197718	−	0.342458i
$861$	−0.0216124	+	0.154182i	−0.000736550	+	0.00525449i
$862$	39.8409	+	69.0065i	1.35699	+	2.35037i
$863$	−1.22689			−0.0417637			−0.0208818	−	0.999782i	$-0.506647\pi$
$863$	−1.22689			−0.0417637			−0.0208818	+	0.999782i	$0.506647\pi$
$864$	−66.3303	−	91.0896i	−2.25660	−	3.09893i
$865$	0.429080			0.0145891
$866$	−18.7326	−	32.4459i	−0.636561	−	1.10256i
$867$	−2.34469	+	16.7268i	−0.0796298	+	0.568073i
$868$	−7.34413	+	12.7204i	−0.249276	+	0.431758i
$869$		0			0
$870$	−17.1901	+	6.95241i	−0.582798	+	0.235709i
$871$	−7.94370	−	13.7589i	−0.269162	−	0.466202i
$872$	−110.212			−3.73226
$873$	11.8889	+	47.5385i	0.402378	+	1.60893i
$874$	−65.0852			−2.20154
$875$	−2.21776	−	3.84127i	−0.0749739	−	0.129859i
$876$	−70.9422	−	55.3852i	−2.39692	−	1.87129i
$877$	12.9867	−	22.4936i	0.438529	−	0.759555i	−0.559047	−	0.829136i	$-0.688833\pi$
$877$	12.9867	−	22.4936i	0.438529	−	0.759555i	0.997576	+	0.0695812i	$0.0221663\pi$
$878$	−2.73714	+	4.74086i	−0.0923738	+	0.159996i
$879$	−19.6994	−	15.3795i	−0.664444	−	0.518737i
$880$		0			0
$881$	53.5351			1.80364			0.901822	−	0.432107i	$-0.142230\pi$
$881$	53.5351			1.80364			0.901822	+	0.432107i	$0.142230\pi$
$882$	53.0084	+	15.1588i	1.78489	+	0.510423i
$883$	17.3818			0.584945			0.292472	−	0.956274i	$-0.405522\pi$
$883$	17.3818			0.584945			0.292472	+	0.956274i	$0.405522\pi$
$884$	−34.5566	−	59.8538i	−1.16226	−	2.01310i
$885$	5.97764	−	2.41762i	0.200936	−	0.0812673i
$886$	−47.2304	+	81.8054i	−1.58673	+	2.74831i
$887$	20.0080	−	34.6549i	0.671803	−	1.16360i	−0.305589	−	0.952163i	$-0.598853\pi$
$887$	20.0080	−	34.6549i	0.671803	−	1.16360i	0.977392	−	0.211434i	$-0.0678132\pi$
$888$	4.69345	−	33.4828i	0.157502	−	1.12361i
$889$	−2.71326	−	4.69950i	−0.0909997	−	0.157616i
$890$	−19.2761			−0.646138
$891$		0			0
$892$	−49.3470			−1.65226
$893$	−0.525823	−	0.910752i	−0.0175960	−	0.0304772i
$894$	−4.31037	+	30.7499i	−0.144160	+	1.02843i
$895$	4.30796	−	7.46161i	0.143999	−	0.249414i
$896$	−9.65441	+	16.7219i	−0.322531	+	0.558641i
$897$	−52.6973	+	21.3131i	−1.75951	+	0.711622i
$898$	3.32952	+	5.76690i	0.111108	+	0.192444i
$899$	−21.7107			−0.724091
$900$	64.8778	+	18.5531i	2.16259	+	0.618435i
$901$	−5.11086			−0.170268
$902$		0			0
$903$	1.60846	+	1.25574i	0.0535262	+	0.0417883i
$904$	5.69016	−	9.85565i	0.189252	−	0.327794i
$905$	7.09732	−	12.2929i	0.235923	−	0.408631i
$906$	−47.1272	−	36.7926i	−1.56570	−	1.22235i
$907$	14.9046	+	25.8156i	0.494900	+	0.857192i	0.999983	−	0.00587889i	$-0.00187132\pi$
$907$	14.9046	+	25.8156i	0.494900	+	0.857192i	−0.505083	+	0.863071i	$0.668538\pi$
$908$	28.2152			0.936355
$909$	7.26585	+	29.0529i	0.240993	+	0.963625i
$910$	−6.24671			−0.207076
$911$	−3.75956	−	6.51175i	−0.124560	−	0.215744i	0.797001	−	0.603978i	$-0.206419\pi$
$911$	−3.75956	−	6.51175i	−0.124560	−	0.215744i	−0.921561	+	0.388234i	$0.873085\pi$
$912$	81.5063	−	32.9647i	2.69894	−	1.09157i
$913$		0			0
$914$	−57.2036	+	99.0795i	−1.89213	+	3.27726i
$915$	1.01767	−	7.26000i	0.0336432	−	0.240008i
$916$	−43.7103	−	75.7085i	−1.44423	−	2.50148i
$917$	6.98789			0.230761
$918$	37.9848	−	4.03369i	1.25369	−	0.133132i
$919$	48.1441			1.58813			0.794064	−	0.607835i	$-0.207962\pi$
$919$	48.1441			1.58813			0.794064	+	0.607835i	$0.207962\pi$
$920$	30.8200	+	53.3818i	1.01610	+	1.75995i
$921$	−2.30969	+	16.4772i	−0.0761069	+	0.542942i
$922$	52.4096	−	90.7761i	1.72602	−	2.98955i
$923$	−6.83137	+	11.8323i	−0.224857	+	0.389464i
$924$		0			0
$925$	4.26450	+	7.38633i	0.140216	+	0.242861i
$926$	−0.664472			−0.0218359
$927$	14.1359	−	13.6705i	0.464283	−	0.448997i
$928$	−90.7802			−2.98001
$929$	19.5885	+	33.9283i	0.642678	+	1.11315i	0.984833	+	0.173507i	$0.0555100\pi$
$929$	19.5885	+	33.9283i	0.642678	+	1.11315i	−0.342155	+	0.939644i	$0.611157\pi$
$930$	−18.1075	−	14.1366i	−0.593767	−	0.463559i
$931$	−11.5007	+	19.9197i	−0.376919	+	0.652842i
$932$	−46.1490	+	79.9324i	−1.51166	+	2.61827i
$933$	0.468841	+	0.366028i	0.0153492	+	0.0119832i
$934$	21.4233	+	37.1062i	0.700992	+	1.21415i
$935$		0			0
$936$	95.7473	−	92.5949i	3.12960	−	3.02656i
$937$	−36.6480			−1.19724			−0.598620	−	0.801033i	$-0.704284\pi$
$937$	−36.6480			−1.19724			−0.598620	+	0.801033i	$0.704284\pi$
$938$	−2.39301	−	4.14481i	−0.0781345	−	0.135333i
$939$	13.4221	−	5.42847i	0.438013	−	0.177151i
$940$	−0.786202	+	1.36174i	−0.0256431	+	0.0444151i
$941$	1.94861	−	3.37509i	0.0635229	−	0.110025i	−0.832515	−	0.554003i	$-0.813100\pi$
$941$	1.94861	−	3.37509i	0.0635229	−	0.110025i	0.896038	+	0.443978i	$0.146433\pi$
$942$	9.20341	−	65.6565i	0.299863	−	2.13920i
$943$	0.603855	+	1.04591i	0.0196642	+	0.0340594i
$944$	59.0394			1.92157
$945$	1.02509	−	2.30906i	0.0333460	−	0.0751138i
$946$		0			0
$947$	−22.2020	−	38.4551i	−0.721469	−	1.24962i	−0.960411	−	0.278587i	$-0.910134\pi$
$947$	−22.2020	−	38.4551i	−0.721469	−	1.24962i	0.238942	−	0.971034i	$-0.423200\pi$
$948$	2.68068	−	19.1238i	0.0870645	−	0.621112i
$949$	22.4079	−	38.8116i	0.727390	−	1.25988i
$950$	−19.2359	+	33.3175i	−0.624094	+	1.08096i
$951$	21.5296	−	8.70750i	0.698145	−	0.282360i
$952$	−6.59384	−	11.4209i	−0.213708	−	0.370152i
$953$	−20.1218			−0.651810			−0.325905	−	0.945403i	$-0.605669\pi$
$953$	−20.1218			−0.651810			−0.325905	+	0.945403i	$0.605669\pi$
$954$	−3.77280	−	15.0858i	−0.122149	−	0.488419i
$955$	19.6151			0.634730
$956$	1.97068	+	3.41332i	0.0637365	+	0.110395i
$957$		0			0
$958$	−22.2270	+	38.4983i	−0.718122	+	1.24382i
$959$	−5.41537	+	9.37969i	−0.174871	+	0.302886i
$960$	−37.7286	−	29.4550i	−1.21769	−	0.950657i
$961$	2.05156	+	3.55340i	0.0661793	+	0.114626i
$962$	26.5791			0.856945
$963$	41.8670	+	11.9727i	1.34915	+	0.385814i
$964$	−74.4535			−2.39799
$965$	4.89316	+	8.47520i	0.157516	+	0.272826i
$966$	−15.8748	+	6.42048i	−0.510765	+	0.206575i
$967$	11.5692	−	20.0385i	0.372041	−	0.644394i	−0.617838	−	0.786305i	$-0.711991\pi$
$967$	11.5692	−	20.0385i	0.372041	−	0.644394i	0.989879	+	0.141911i	$0.0453248\pi$
$968$		0			0
$969$	−2.21223	+	15.7819i	−0.0710670	+	0.506987i
$970$	20.8862	+	36.1760i	0.670616	+	1.16154i
$971$	28.3629			0.910209			0.455104	−	0.890438i	$-0.349602\pi$
$971$	28.3629			0.910209			0.455104	+	0.890438i	$0.349602\pi$
$972$	29.2307	+	79.8649i	0.937575	+	2.56167i
$973$	−0.450519			−0.0144430
$974$	43.7457	+	75.7698i	1.40170	+	2.42782i
$975$	−4.66434	+	33.2751i	−0.149378	+	1.06566i
$976$	33.5620	−	58.1310i	1.07429	−	1.86073i
$977$	−7.84482	+	13.5876i	−0.250978	+	0.434707i	−0.963795	−	0.266643i	$-0.914086\pi$
$977$	−7.84482	+	13.5876i	−0.250978	+	0.434707i	0.712817	+	0.701350i	$0.247419\pi$
$978$	94.8100	−	38.3453i	3.03169	−	1.22615i
$979$		0			0
$980$	34.3912			1.09859
$981$	33.6900	+	9.63431i	1.07564	+	0.307600i
$982$	57.1927			1.82509
$983$	−18.0658	−	31.2909i	−0.576210	−	0.998026i	−0.995909	−	0.0903621i	$-0.971198\pi$
$983$	−18.0658	−	31.2909i	−0.576210	−	0.998026i	0.419699	−	0.907664i	$-0.362136\pi$
$984$	−2.23062	−	1.74146i	−0.0711094	−	0.0555157i
$985$	9.82735	−	17.0215i	0.313125	−	0.542349i
$986$	15.3871	−	26.6512i	0.490024	−	0.848746i
$987$	−0.218096	−	0.170269i	−0.00694208	−	0.00541974i
$988$	43.8648	+	75.9761i	1.39553	+	2.41712i
$989$	15.8293			0.503342
$990$		0			0
$991$	−8.69420			−0.276180			−0.138090	−	0.990420i	$-0.544096\pi$
$991$	−8.69420			−0.276180			−0.138090	+	0.990420i	$0.544096\pi$
$992$	−56.2329	−	97.3982i	−1.78540	−	3.09240i
$993$	47.9291	−	19.3846i	1.52099	−	0.615152i
$994$	−2.05792	+	3.56443i	−0.0652734	+	0.113057i
$995$	−8.92107	+	15.4517i	−0.282817	+	0.489853i
$996$	−18.4427	+	131.569i	−0.584378	+	4.16892i
$997$	17.7648	+	30.7695i	0.562616	+	0.974480i	0.997267	+	0.0738808i	$0.0235384\pi$
$997$	17.7648	+	30.7695i	0.562616	+	0.974480i	−0.434651	+	0.900599i	$0.643128\pi$
$998$	19.7445			0.625000
$999$	−4.36163	+	9.82482i	−0.137996	+	0.310844i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1089.2.e.i.364.1		8
9.4	even	3		9801.2.a.bi.1.4		4
9.5	odd	6		9801.2.a.bl.1.1		4
9.7	even	3	inner	1089.2.e.i.727.1		8
11.10	odd	2		99.2.e.e.67.4	yes	8
33.32	even	2		297.2.e.e.199.1		8
99.32	even	6		891.2.a.p.1.4		4
99.43	odd	6		99.2.e.e.34.4	✓	8
99.65	even	6		297.2.e.e.100.1		8
99.76	odd	6		891.2.a.q.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.e.e.34.4	✓	8	99.43	odd	6
99.2.e.e.67.4	yes	8	11.10	odd	2
297.2.e.e.100.1		8	99.65	even	6
297.2.e.e.199.1		8	33.32	even	2
891.2.a.p.1.4		4	99.32	even	6
891.2.a.q.1.1		4	99.76	odd	6
1089.2.e.i.364.1		8	1.1	even	1	trivial
1089.2.e.i.727.1		8	9.7	even	3	inner
9801.2.a.bi.1.4		4	9.4	even	3
9801.2.a.bl.1.1		4	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1089.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36526 - 2.36469i) q^{2} +(0.240440 - 1.71528i) q^{3} +(-2.72785 + 4.72478i) q^{4} +(0.468293 - 0.811107i) q^{5} +(-4.38438 + 1.77323i) q^{6} +(-0.259560 - 0.449571i) q^{7} +9.43585 q^{8} +(-2.88438 - 0.824844i) q^{9} +O(q^{10})\)	\(q+(-1.36526 - 2.36469i) q^{2} +(0.240440 - 1.71528i) q^{3} +(-2.72785 + 4.72478i) q^{4} +(0.468293 - 0.811107i) q^{5} +(-4.38438 + 1.77323i) q^{6} +(-0.259560 - 0.449571i) q^{7} +9.43585 q^{8} +(-2.88438 - 0.824844i) q^{9} -2.55736 q^{10} +(7.44844 + 5.81506i) q^{12} +(-2.35267 + 4.07494i) q^{13} +(-0.708733 + 1.22756i) q^{14} +(-1.27868 - 0.998277i) q^{15} +(-7.42666 - 12.8634i) q^{16} +2.69227 q^{17} +(1.98741 + 7.94679i) q^{18} -3.41747 q^{19} +(2.55487 + 4.42516i) q^{20} +(-0.833550 + 0.337124i) q^{21} +(-3.48741 + 6.04038i) q^{23} +(2.26875 - 16.1851i) q^{24} +(2.06140 + 3.57046i) q^{25} +12.8480 q^{26} +(-2.10836 + 4.74919i) q^{27} +2.83217 q^{28} +(2.09311 + 3.62537i) q^{29} +(-0.614891 + 4.38659i) q^{30} +(-2.59311 + 4.49140i) q^{31} +(-10.8427 + 18.7802i) q^{32} +(-3.67564 - 6.36640i) q^{34} -0.486201 q^{35} +(11.7654 - 11.3780i) q^{36} +2.06874 q^{37} +(4.66572 + 8.08126i) q^{38} +(6.42400 + 5.01527i) q^{39} +(4.41875 - 7.65349i) q^{40} +(0.0865763 - 0.149955i) q^{41} +(1.93520 + 1.51083i) q^{42} +(-1.13474 - 1.96543i) q^{43} +(-2.01977 + 1.95327i) q^{45} +19.0449 q^{46} +(0.153863 + 0.266499i) q^{47} +(-23.8499 + 9.64595i) q^{48} +(3.36526 - 5.82880i) q^{49} +(5.62869 - 9.74918i) q^{50} +(0.647330 - 4.61800i) q^{51} +(-12.8355 - 22.2317i) q^{52} -1.89835 q^{53} +(14.1088 - 1.49825i) q^{54} +(-2.44917 - 4.24209i) q^{56} +(-0.821695 + 5.86191i) q^{57} +(5.71527 - 9.89913i) q^{58} +(-1.98741 + 3.44230i) q^{59} +(8.20469 - 3.31833i) q^{60} +(2.25956 + 3.91367i) q^{61} +14.1610 q^{62} +(0.377844 + 1.51083i) q^{63} +29.5059 q^{64} +(2.20348 + 3.81654i) q^{65} +(-1.68823 + 2.92410i) q^{67} +(-7.34413 + 12.7204i) q^{68} +(9.52243 + 7.43424i) q^{69} +(0.663789 + 1.14972i) q^{70} +2.90367 q^{71} +(-27.2166 - 7.78310i) q^{72} -9.52444 q^{73} +(-2.82436 - 4.89193i) q^{74} +(6.61998 - 2.67741i) q^{75} +(9.32234 - 16.1468i) q^{76} +(3.08917 - 22.0379i) q^{78} +(-1.02178 - 1.76978i) q^{79} -13.9114 q^{80} +(7.63927 + 4.75832i) q^{81} -0.472796 q^{82} +(7.02970 + 12.1758i) q^{83} +(0.680966 - 4.85797i) q^{84} +(1.26077 - 2.18372i) q^{85} +(-3.09843 + 5.36664i) q^{86} +(6.72180 - 2.71859i) q^{87} +7.53751 q^{89} +(7.37640 + 2.10942i) q^{90} +2.44264 q^{91} +(-19.0263 - 32.9545i) q^{92} +(7.08052 + 5.52782i) q^{93} +(0.420126 - 0.727680i) q^{94} +(-1.60038 + 2.77193i) q^{95} +(29.6063 + 23.1139i) q^{96} +(-8.16710 - 14.1458i) q^{97} -18.3778 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 5 q^{3} - 11 q^{4} - 4 q^{5} - 17 q^{6} + q^{7} - 5 q^{9}+O(q^{10}) \) 8 * q + q^2 + 5 * q^3 - 11 * q^4 - 4 * q^5 - 17 * q^6 + q^7 - 5 * q^9	\( 8 q + q^{2} + 5 q^{3} - 11 q^{4} - 4 q^{5} - 17 q^{6} + q^{7} - 5 q^{9} - 2 q^{10} - 2 q^{12} + 7 q^{13} - q^{14} - q^{15} - 17 q^{16} + 10 q^{17} + 2 q^{18} - 18 q^{19} + 10 q^{20} + 13 q^{21} - 14 q^{23} - 18 q^{24} - 14 q^{25} + 44 q^{26} + 5 q^{27} + 2 q^{28} - 6 q^{29} + 37 q^{30} + 2 q^{31} - 34 q^{32} - 16 q^{34} + 16 q^{35} + 11 q^{36} + 6 q^{37} - 3 q^{38} + 22 q^{39} + 12 q^{40} - 2 q^{41} - q^{42} - 21 q^{43} + 49 q^{45} - 4 q^{46} + 7 q^{47} - 59 q^{48} + 15 q^{49} + 23 q^{50} + 31 q^{51} - 10 q^{52} - 12 q^{53} + 37 q^{54} - 18 q^{56} - 33 q^{57} + 21 q^{58} - 2 q^{59} + 73 q^{60} + 15 q^{61} + 40 q^{62} + 5 q^{63} + 32 q^{64} + 19 q^{65} - 14 q^{67} - 7 q^{68} - 2 q^{69} + 38 q^{70} - 6 q^{71} - 75 q^{72} - 44 q^{73} - 36 q^{74} + 10 q^{75} + 42 q^{76} + 29 q^{78} + 11 q^{79} - 68 q^{80} + 7 q^{81} - 34 q^{82} + 18 q^{83} - 34 q^{84} + 13 q^{85} + 24 q^{86} + 9 q^{87} - 12 q^{89} + 80 q^{90} + 38 q^{91} - 67 q^{92} + 20 q^{93} - 19 q^{94} - 30 q^{95} + 50 q^{96} - 26 q^{97} - 30 q^{98}+O(q^{100}) \) 8 * q + q^2 + 5 * q^3 - 11 * q^4 - 4 * q^5 - 17 * q^6 + q^7 - 5 * q^9 - 2 * q^10 - 2 * q^12 + 7 * q^13 - q^14 - q^15 - 17 * q^16 + 10 * q^17 + 2 * q^18 - 18 * q^19 + 10 * q^20 + 13 * q^21 - 14 * q^23 - 18 * q^24 - 14 * q^25 + 44 * q^26 + 5 * q^27 + 2 * q^28 - 6 * q^29 + 37 * q^30 + 2 * q^31 - 34 * q^32 - 16 * q^34 + 16 * q^35 + 11 * q^36 + 6 * q^37 - 3 * q^38 + 22 * q^39 + 12 * q^40 - 2 * q^41 - q^42 - 21 * q^43 + 49 * q^45 - 4 * q^46 + 7 * q^47 - 59 * q^48 + 15 * q^49 + 23 * q^50 + 31 * q^51 - 10 * q^52 - 12 * q^53 + 37 * q^54 - 18 * q^56 - 33 * q^57 + 21 * q^58 - 2 * q^59 + 73 * q^60 + 15 * q^61 + 40 * q^62 + 5 * q^63 + 32 * q^64 + 19 * q^65 - 14 * q^67 - 7 * q^68 - 2 * q^69 + 38 * q^70 - 6 * q^71 - 75 * q^72 - 44 * q^73 - 36 * q^74 + 10 * q^75 + 42 * q^76 + 29 * q^78 + 11 * q^79 - 68 * q^80 + 7 * q^81 - 34 * q^82 + 18 * q^83 - 34 * q^84 + 13 * q^85 + 24 * q^86 + 9 * q^87 - 12 * q^89 + 80 * q^90 + 38 * q^91 - 67 * q^92 + 20 * q^93 - 19 * q^94 - 30 * q^95 + 50 * q^96 - 26 * q^97 - 30 * q^98

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