LMFDB - Embedded newform 99.2.e.e.67.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(34,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("99.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$99 = 3^{2} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	99.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:	$0.790518980011$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.4
Root			$1.86526 - 0.199842i$ of defining polynomial
Character	$\chi$	$=$	99.67
Dual form			99.2.e.e.34.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36526 + 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} +(-0.500000 - 0.866025i) q^{11} +(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} +(1.36526 - 2.36469i) q^{22} +(-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} +(-1.60570 + 0.649414i) q^{33} +(-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} +5.45571 q^{44} +(-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} -0.936586 q^{55} +(-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} +(-3.72785 - 2.91037i) q^{66} +(-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} +(0.259560 - 0.449571i) q^{77} +(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} +(4.71793 + 8.17169i) q^{88} +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} +(0.727853 + 2.91037i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q - q^{2} + 5 q^{3} - 11 q^{4} - 4 q^{5} + 17 q^{6} - q^{7} - 5 q^{9} + 2 q^{10} - 4 q^{11} - 2 q^{12} - 7 q^{13} - q^{14} - q^{15} - 17 q^{16} - 10 q^{17} - 2 q^{18} + 18 q^{19} + 10 q^{20} - 13 q^{21}+ \cdots - 5 q^{99}+O(q^{100})$ 8 * q - q^2 + 5 * q^3 - 11 * q^4 - 4 * q^5 + 17 * q^6 - q^7 - 5 * q^9 + 2 * q^10 - 4 * q^11 - 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 - q^22 - 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 - 4 * q^33 - 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 + 22 * q^44 + 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 + 8 * q^55 - 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 - 19 * q^66 - 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 - q^77 + 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 - 5 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$ .

$n$	$46$	$56$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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	$0.249334\pi$
$2$	1.36526	+	2.36469i	0.965382	+	1.67209i	0.256799	+	0.966465i	$0.417332\pi$
$3$	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	0.910900	−	0.412627i	$-0.135389\pi$
$7$	0.259560	+	0.449571i	0.0981045	+	0.169922i	−0.812796	+	0.582549i	$0.802055\pi$
$8$	−9.43585			−3.33608
$9$	−2.88438	−	0.824844i	−0.961459	−	0.274948i
$10$	2.55736			0.808709
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	7.44844	+	5.81506i	2.15018	+	1.67866i
$13$	2.35267	−	4.07494i	0.652513	−	1.13019i	−0.329998	−	0.943982i	$-0.607048\pi$
$13$	2.35267	−	4.07494i	0.652513	−	1.13019i	0.982511	−	0.186205i	$-0.0596187\pi$
$14$	−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	$-0.605865\pi$
$17$	−2.69227			−0.652972			−0.326486	+	0.945202i	$0.605865\pi$
$18$	−1.98741	−	7.94679i	−0.468438	−	1.87308i
$19$	3.41747			0.784020			0.392010	−	0.919961i	$-0.371780\pi$
$19$	3.41747			0.784020			0.392010	+	0.919961i	$0.371780\pi$
$20$	2.55487	+	4.42516i	0.571286	+	0.989497i
$21$	0.833550	−	0.337124i	0.181896	−	0.0735665i
$22$	1.36526	−	2.36469i	0.291074	−	0.504155i
$23$	−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	0.603592	−	0.797294i	$-0.293736\pi$
$29$	−2.09311	−	3.62537i	−0.388681	−	0.673215i	−0.992272	+	0.124079i	$0.960402\pi$
$30$	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
$33$	−1.60570	+	0.649414i	−0.279516	+	0.113048i
$34$	−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	−0.872707	−	0.488245i	$-0.837637\pi$
$41$	−0.0865763	+	0.149955i	−0.0135209	+	0.0234190i	0.859186	+	0.511664i	$0.170971\pi$
$42$	1.93520	+	1.51083i	0.298609	+	0.233126i
$43$	1.13474	+	1.96543i	0.173047	+	0.299726i	0.939484	−	0.342594i	$-0.111306\pi$
$43$	1.13474	+	1.96543i	0.173047	+	0.299726i	−0.766437	+	0.642320i	$0.777972\pi$
$44$	5.45571			0.822479
$45$	−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
$55$	−0.936586			−0.126289
$56$	−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	0.684337	−	0.729165i	$-0.260092\pi$
$61$	−2.25956	−	3.91367i	−0.289307	−	0.501094i	−0.973645	+	0.228071i	$0.926758\pi$
$62$	−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
$66$	−3.72785	−	2.91037i	−0.458867	−	0.358241i
$67$	−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	$-0.311808\pi$
$73$	9.52444			1.11475			0.557376	+	0.830260i	$0.311808\pi$
$74$	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
$77$	0.259560	−	0.449571i	0.0295796	−	0.0512334i
$78$	3.08917	−	22.0379i	0.349780	−	2.49530i
$79$	1.02178	+	1.76978i	0.114959	+	0.199115i	0.917764	−	0.397127i	$-0.129993\pi$
$79$	1.02178	+	1.76978i	0.114959	+	0.199115i	−0.802804	+	0.596243i	$0.796660\pi$
$80$	−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	$-0.886119\pi$
$83$	−7.02970	−	12.1758i	−0.771609	−	1.33647i	0.165071	−	0.986282i	$-0.447215\pi$
$84$	−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
$88$	4.71793	+	8.17169i	0.502933	+	0.871105i
$89$	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
$99$	0.727853	+	2.91037i	0.0731520	+	0.292503i
$100$	−22.4928			−2.24928
$101$	4.99129	+	8.64516i	0.496652	+	0.860226i	0.999993	−	0.00386211i	$-0.00122935\pi$
$101$	4.99129	+	8.64516i	0.496652	+	0.860226i	−0.503341	+	0.864088i	$0.667896\pi$
$102$	−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	$-0.252463\pi$
$107$	14.5151			1.40323			0.701614	+	0.712557i	$0.252463\pi$
$108$	−16.6876	−	22.9166i	−1.60577	−	2.20515i
$109$	11.6802			1.11876			0.559379	−	0.828912i	$-0.311040\pi$
$109$	11.6802			1.11876			0.559379	+	0.828912i	$0.311040\pi$
$110$	−1.27868	−	2.21474i	−0.121917	−	0.211167i
$111$	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
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	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	$-0.653511\pi$
$127$	−10.4533			−0.927579			−0.463789	+	0.885945i	$0.653511\pi$
$128$	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	$-0.633230\pi$
$131$	6.73051	−	11.6576i	0.588048	−	1.01853i	0.994488	−	0.104851i	$-0.0334366\pi$
$132$	1.31177	−	9.35807i	0.114175	−	0.814515i
$133$	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	−0.883841	−	0.467787i	$-0.845051\pi$
$139$	−0.433925	+	0.751581i	−0.0368051	+	0.0637482i	0.847036	+	0.531535i	$0.178385\pi$
$140$	−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
$143$	−4.70534			−0.393480
$144$	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	−0.968586	−	0.248679i	$-0.920004\pi$
$149$	−3.28272	+	5.68584i	−0.268931	+	0.465802i	0.699655	+	0.714481i	$0.253337\pi$
$150$	15.3692	+	11.9989i	1.25489	+	0.979704i
$151$	−6.32096	−	10.9482i	−0.514393	−	0.890954i	−0.999861	−	0.0166998i	$-0.994684\pi$
$151$	−6.32096	−	10.9482i	−0.514393	−	0.890954i	0.485468	−	0.874255i	$-0.338649\pi$
$152$	−32.2467			−2.61555
$153$	7.76553	+	2.22070i	0.627806	+	0.179533i
$154$	1.41747			0.114223
$155$	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
$165$	−0.225193	+	1.60651i	−0.0175312	+	0.125066i
$166$	19.1947	−	33.2462i	1.48980	−	2.58040i
$167$	−2.51058	+	4.34844i	−0.194274	+	0.336493i	−0.946662	−	0.322227i	$-0.895568\pi$
$167$	−2.51058	+	4.34844i	−0.194274	+	0.336493i	0.752388	+	0.658720i	$0.228902\pi$
$168$	−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	0.857186	−	0.515006i	$-0.172210\pi$
$173$	−0.229066	−	0.396754i	−0.0174155	−	0.0301646i	−0.874602	+	0.484842i	$0.838877\pi$
$174$	−15.6056	−	12.1834i	−1.18306	−	0.923624i
$175$	−1.07012	+	1.85350i	−0.0808932	+	0.140111i
$176$	−7.42666	+	12.8634i	−0.559806	+	0.969612i
$177$	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
$187$	1.34614	+	2.33158i	0.0984393	+	0.170502i
$188$	−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	−0.614421	−	0.788978i	$-0.710610\pi$
$193$	5.22446	−	9.04903i	0.376065	−	0.651364i	0.990486	+	0.137615i	$0.0439436\pi$
$194$	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	$-0.768783\pi$
$197$	−20.9855			−1.49515			−0.747576	+	0.664176i	$0.768783\pi$
$198$	−5.88842	+	5.69455i	−0.418472	+	0.404694i
$199$	−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
$209$	−1.70873	−	2.95961i	−0.118196	−	0.204721i
$210$	2.13169	−	0.862147i	0.147100	−	0.0594938i
$211$	−8.14459	+	14.1068i	−0.560697	+	0.971155i	0.436739	+	0.899588i	$0.356133\pi$
$211$	−8.14459	+	14.1068i	−0.560697	+	0.971155i	−0.997436	+	0.0715668i	$0.977200\pi$
$212$	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
$220$	2.55487	−	4.42516i	0.172249	−	0.298344i
$221$	−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	0.938989	−	0.343946i	$-0.111764\pi$
$227$	2.58585	+	4.47882i	0.171629	+	0.297269i	−0.767361	+	0.641216i	$0.778430\pi$
$228$	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
$231$	−0.708733	−	0.553314i	−0.0466312	−	0.0364054i
$232$	19.7503	+	34.2085i	1.29667	+	2.24590i
$233$	−16.9177			−1.10832			−0.554158	−	0.832412i	$-0.686960\pi$
$233$	−16.9177			−1.10832			−0.554158	+	0.832412i	$0.686960\pi$
$234$	−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	−0.877472	−	0.479629i	$-0.840771\pi$
$239$	−0.361215	+	0.625643i	−0.0233651	+	0.0404695i	0.854106	+	0.520098i	$0.174105\pi$
$240$	−3.34486	+	23.8620i	−0.215910	+	1.54028i
$241$	−6.82346	−	11.8186i	−0.439537	−	0.761301i	0.558116	−	0.829763i	$-0.311524\pi$
$241$	−6.82346	−	11.8186i	−0.439537	−	0.761301i	−0.997654	+	0.0684616i	$0.978191\pi$
$242$	−2.73051			−0.175524
$243$	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
$253$	6.97483			0.438504
$254$	−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	0.823186	−	0.567771i	$-0.192194\pi$
$263$	−1.29918	−	2.25025i	−0.0801110	−	0.138756i	−0.903297	+	0.429015i	$0.858861\pi$
$264$	15.1511	−	6.12777i	0.932487	−	0.377138i
$265$	−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	$-0.0619667\pi$
$271$	32.3022			1.96222			0.981111	+	0.193447i	$0.0619667\pi$
$272$	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
$275$	2.06140	−	3.57046i	0.124307	−	0.215307i
$276$	−61.1010	+	24.7119i	−3.67785	+	1.48748i
$277$	−16.1690	−	28.0055i	−0.971499	−	1.68269i	−0.691036	−	0.722820i	$-0.742845\pi$
$277$	−16.1690	−	28.0055i	−0.971499	−	1.68269i	−0.280463	−	0.959865i	$-0.590488\pi$
$278$	−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	0.972521	−	0.232817i	$-0.0747943\pi$
$281$	4.77135	+	8.26422i	0.284635	+	0.493002i	−0.687886	+	0.725819i	$0.741461\pi$
$282$	1.14716	+	0.895598i	0.0683124	+	0.0533321i
$283$	2.96038	−	5.12752i	0.175976	−	0.304800i	−0.764522	−	0.644597i	$-0.777025\pi$
$283$	2.96038	−	5.12752i	0.175976	−	0.304800i	0.940499	+	0.339797i	$0.110358\pi$
$284$	−7.92078	+	13.7192i	−0.470012	+	0.814084i
$285$	−4.36985	−	3.41158i	−0.258847	−	0.202084i
$286$	−6.42400	−	11.1267i	−0.379859	−	0.657935i
$287$	−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	−0.996084	−	0.0884090i	$-0.971822\pi$
$293$	−7.21454	+	12.4959i	−0.421478	+	0.730021i	0.574607	+	0.818430i	$0.305155\pi$
$294$	4.41875	−	31.5230i	0.257706	−	1.83846i
$295$	1.86138	+	3.22401i	0.108374	+	0.187709i
$296$	−19.5203			−1.13459
$297$	5.16710	−	0.548705i	0.299826	−	0.0318391i
$298$	−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	$-0.411612\pi$
$307$	9.60611			0.548250			0.274125	+	0.961694i	$0.411612\pi$
$308$	1.41608	+	2.45273i	0.0806889	+	0.139757i
$309$	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
$319$	−2.09311	+	3.62537i	−0.117192	+	0.202982i
$320$	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
$330$	−4.10635	+	1.66079i	−0.226047	+	0.0914232i
$331$	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	$-0.631797\pi$
$337$	10.8619	−	18.8133i	0.591683	−	1.02483i	0.994006	−	0.109328i	$-0.0348698\pi$
$338$	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
$341$	5.18622			0.280850
$342$	−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	$-0.559643\pi$
$347$	14.1149	−	24.4477i	0.757727	−	1.31242i	0.944007	−	0.329925i	$-0.107023\pi$
$348$	5.49135	−	39.1749i	0.294367	−	2.10000i
$349$	3.57851	+	6.19817i	0.191553	+	0.331780i	0.945765	−	0.324851i	$-0.105314\pi$
$349$	3.57851	+	6.19817i	0.191553	+	0.331780i	−0.754212	+	0.656631i	$0.771981\pi$
$350$	−5.84394			−0.312372
$351$	14.3924	+	19.7647i	0.768211	+	1.05496i
$352$	−21.6855			−1.15584
$353$	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	$-0.611566\pi$
$359$	−13.0116			−0.686726			−0.343363	+	0.939203i	$0.611566\pi$
$360$	19.0583	−	18.4308i	1.00446	−	0.971388i
$361$	−7.32093			−0.385312
$362$	20.6915	+	35.8387i	1.08752	+	1.88364i
$363$	1.36526	+	1.06587i	0.0716574	+	0.0559435i
$364$	−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	$0.525998\pi$
$373$	−17.4578	+	30.2378i	−0.903931	+	1.56565i	−0.822346	+	0.568988i	$0.807335\pi$
$374$	−3.67564	+	6.36640i	−0.190063	+	0.329199i
$375$	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
$385$	−0.243100	−	0.421062i	−0.0123895	−	0.0214593i
$386$	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
$396$	−15.7363	−	4.50010i	−0.790780	−	0.226139i
$397$	−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
$407$	−1.03437	−	1.79158i	−0.0512717	−	0.0888052i
$408$	6.10811	−	43.5748i	0.302396	−	2.15728i
$409$	1.30329	−	2.25737i	0.0644436	−	0.111620i	−0.832003	−	0.554770i	$-0.812806\pi$
$409$	1.30329	−	2.25737i	0.0644436	−	0.111620i	0.896447	+	0.443151i	$0.146139\pi$
$410$	−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
$418$	4.66572	−	8.08126i	0.228208	−	0.395267i
$419$	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
$429$	−1.13135	+	8.07098i	−0.0546221	+	0.389671i
$430$	2.90195	+	5.02632i	0.139944	+	0.242391i
$431$	29.1820			1.40565			0.702824	−	0.711364i	$-0.251922\pi$
$431$	29.1820			1.40565			0.702824	+	0.711364i	$0.251922\pi$
$432$	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	0.888955	−	0.457994i	$-0.151432\pi$
$439$	1.00243	+	1.73625i	0.0478431	+	0.0828667i	−0.841112	+	0.540861i	$0.818099\pi$
$440$	8.83749			0.421311
$441$	−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
$451$	0.173153			0.00815344
$452$	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	$0.269545\pi$
$457$	20.9497	+	36.2860i	0.979988	+	1.69739i	0.317604	+	0.948223i	$0.397122\pi$
$458$	−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	$-0.814585\pi$
$461$	−19.1941	−	33.2451i	−0.893956	−	1.54838i	−0.0588651	−	0.998266i	$-0.518748\pi$
$462$	0.340815	−	2.43135i	0.0158562	−	0.113117i
$463$	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
$473$	1.13474	−	1.96543i	0.0521755	−	0.0903707i
$474$	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	0.989863	−	0.142022i	$-0.0453605\pi$
$479$	8.14023	+	14.0993i	0.371937	+	0.644213i	−0.617927	+	0.786236i	$0.712027\pi$
$480$	−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
$484$	−2.72785	−	4.72478i	−0.123993	−	0.214763i
$485$	−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	−0.526875	−	0.849943i	$-0.676636\pi$
$491$	10.4729	−	18.1396i	0.472635	−	0.818627i	0.999510	+	0.0313157i	$0.00996972\pi$
$492$	−1.51685	+	0.613481i	−0.0683850	+	0.0276579i
$493$	5.63522	+	9.76049i	0.253798	+	0.439591i
$494$	43.9076			1.97550
$495$	2.70147	+	0.772537i	0.121422	+	0.0347230i
$496$	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	$-0.542014\pi$
$503$	−5.90333			−0.263216			−0.131608	+	0.991302i	$0.542014\pi$
$504$	3.56528	+	14.2560i	0.158810	+	0.635012i
$505$	9.34954			0.416049
$506$	9.52243	+	16.4933i	0.423324	+	0.733218i
$507$	−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
$517$	0.153863	−	0.266499i	0.00676691	−	0.0117206i
$518$	−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	$-0.619892\pi$
$523$	−16.8230			−0.735617			−0.367808	+	0.929902i	$0.619892\pi$
$524$	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
$528$	20.2786	+	15.8317i	0.882513	+	0.688985i
$529$	−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
$539$	−6.73051			−0.289904
$540$	−26.4025	+	2.80374i	−1.13618	+	0.120654i
$541$	−22.5357			−0.968886			−0.484443	−	0.874823i	$-0.660978\pi$
$541$	−22.5357			−0.968886			−0.484443	+	0.874823i	$0.660978\pi$
$542$	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	$-0.958742\pi$
$547$	−14.2139	−	24.6192i	−0.607743	−	1.05264i	0.383869	−	0.923388i	$-0.374591\pi$
$548$	113.826			4.86240
$549$	3.28926	+	13.1523i	0.140382	+	0.561326i
$550$	11.2574			0.480016
$551$	−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	$-0.132245\pi$
$557$	43.1863			1.82986			0.914930	+	0.403612i	$0.132245\pi$
$558$	40.8458	+	11.6806i	1.72914	+	0.494481i
$559$	10.6787			0.451661
$560$	−3.61085	−	6.25417i	−0.152586	−	0.264287i
$561$	4.32297	−	1.74840i	0.182516	−	0.0738174i
$562$	−13.0282	+	22.5656i	−0.549563	+	0.951871i
$563$	0.482261	−	0.835300i	0.0203249	−	0.0352037i	−0.855684	−	0.517499i	$-0.826863\pi$
$563$	0.482261	−	0.835300i	0.0203249	−	0.0352037i	0.876009	+	0.482295i	$0.160197\pi$
$564$	−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	0.762694	−	0.646759i	$-0.223876\pi$
$569$	−4.26416	−	7.38575i	−0.178763	−	0.309627i	−0.941457	+	0.337133i	$0.890543\pi$
$570$	2.10137	−	14.9910i	0.0880167	−	0.627905i
$571$	−8.80176	+	15.2451i	−0.368342	+	0.637988i	−0.989307	−	0.145851i	$-0.953408\pi$
$571$	−8.80176	+	15.2451i	−0.368342	+	0.637988i	0.620964	+	0.783839i	$0.286741\pi$
$572$	12.8355	−	22.2317i	0.536678	−	0.929554i
$573$	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
$583$	0.949173	+	1.64402i	0.0393107	+	0.0680882i
$584$	−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	$-0.551345\pi$
$593$	−7.82200			−0.321211			−0.160605	+	0.987019i	$0.551345\pi$
$594$	8.35194	+	11.4695i	0.342684	+	0.470599i
$595$	−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	$-0.893515\pi$
$601$	−18.5488	−	32.1275i	−0.756622	−	1.31051i	0.187942	−	0.982180i	$-0.439818\pi$
$602$	−3.21692			−0.131112
$603$	7.28142	−	7.04169i	0.296522	−	0.286760i
$604$	68.9706			2.80638
$605$	0.468293	+	0.811107i	0.0190388	+	0.0329762i
$606$	37.2136	+	29.0529i	1.51170	+	1.18020i
$607$	20.7558	−	35.9501i	0.842451	−	1.45917i	−0.0453658	−	0.998970i	$-0.514445\pi$
$607$	20.7558	−	35.9501i	0.842451	−	1.45917i	0.887817	−	0.460197i	$-0.152221\pi$
$608$	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	$-0.261433\pi$
$613$	33.7344			1.36252			0.681259	+	0.732042i	$0.261433\pi$
$614$	13.1148	+	22.7155i	0.529271	+	0.916724i
$615$	0.260400	−	0.105317i	0.0105003	−	0.00424679i
$616$	−2.44917	+	4.24209i	−0.0986800	+	0.170919i
$617$	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
$627$	−5.48741	+	2.21935i	−0.219146	+	0.0886322i
$628$	−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
$638$	−11.4305			−0.452539
$639$	−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
$649$	3.97483			0.156026
$650$	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	0.895132	−	0.445802i	$-0.147081\pi$
$659$	1.57851	+	2.73406i	0.0614901	+	0.106504i	−0.833642	+	0.552306i	$0.813748\pi$
$660$	−6.97611	−	5.44630i	−0.271545	−	0.211997i
$661$	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
$671$	−2.25956	+	3.91367i	−0.0872294	+	0.151086i
$672$	2.70672	−	19.3096i	0.104414	−	0.744883i
$673$	13.6485	+	23.6398i	0.526110	+	0.911248i	0.999537	+	0.0304158i	$0.00968314\pi$
$673$	13.6485	+	23.6398i	0.526110	+	0.911248i	−0.473428	+	0.880833i	$0.656984\pi$
$674$	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	0.869846	−	0.493323i	$-0.164218\pi$
$677$	0.200168	+	0.346700i	0.00769307	+	0.0133248i	−0.862153	+	0.506648i	$0.830885\pi$
$678$	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
$682$	7.08052	+	12.2638i	0.271127	+	0.469606i
$683$	−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
$693$	−1.11950	+	1.08264i	−0.0425261	+	0.0411260i
$694$	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	$-0.326206\pi$
$701$	27.4965			1.03853			0.519265	+	0.854613i	$0.326206\pi$
$702$	−27.0882	+	61.0176i	−1.02238	+	2.30296i
$703$	7.06983			0.266644
$704$	−14.7529	−	25.5529i	−0.556023	−	0.963059i
$705$	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
$715$	−2.20348	+	3.81654i	−0.0824054	+	0.142730i
$716$	−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
$726$	−0.656524	+	4.68360i	−0.0243659	+	0.173825i
$727$	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	−0.850503	−	0.525969i	$-0.823703\pi$
$733$	0.819020	−	1.41858i	0.0302512	−	0.0523966i	0.880755	+	0.473573i	$0.157036\pi$
$734$	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
$737$	3.37646			0.124374
$738$	1.36372	+	0.389982i	0.0501993	+	0.0143555i
$739$	−12.8306			−0.471980			−0.235990	−	0.971755i	$-0.575833\pi$
$739$	−12.8306			−0.471980			−0.235990	+	0.971755i	$0.575833\pi$
$740$	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	$0.398693\pi$
$743$	−18.1559	+	31.4469i	−0.666074	+	1.15367i	−0.978993	+	0.203894i	$0.934640\pi$
$744$	−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
$748$	−14.6883			−0.537056
$749$	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
$759$	1.67703	−	11.9638i	0.0608722	−	0.434258i
$760$	−15.1009	+	26.1555i	−0.547768	+	0.948761i
$761$	−7.99799	+	13.8529i	−0.289927	+	0.502168i	−0.973792	−	0.227440i	$-0.926964\pi$
$761$	−7.99799	+	13.8529i	−0.289927	+	0.502168i	0.683865	+	0.729608i	$0.260298\pi$
$762$	−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	−0.999711	−	0.0240494i	$-0.992344\pi$
$769$	−13.2839	+	23.0083i	−0.479028	+	0.829701i	0.520683	+	0.853750i	$0.325677\pi$
$770$	0.663789	−	1.14972i	0.0239213	−	0.0414329i
$771$	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
$781$	−1.45183	−	2.51465i	−0.0519507	−	0.0899812i
$782$	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	−0.514494	−	0.857494i	$-0.672020\pi$
$787$	13.6162	−	23.5839i	0.485364	−	0.840675i	0.999859	+	0.0168185i	$0.00535373\pi$
$788$	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
$792$	−6.86792	−	27.4618i	−0.244041	−	0.975812i
$793$	−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
$803$	−4.76222	−	8.24841i	−0.168055	−	0.291080i
$804$	−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	$-0.568200\pi$
$809$	−12.0951			−0.425240			−0.212620	+	0.977135i	$0.568200\pi$
$810$	19.5364	+	12.1687i	0.686438	+	0.427566i
$811$	35.0487			1.23073			0.615364	−	0.788243i	$-0.289009\pi$
$811$	35.0487			1.23073			0.615364	+	0.788243i	$0.289009\pi$
$812$	5.92804	+	10.2677i	0.208033	+	0.360325i
$813$	7.76674	−	55.4074i	0.272392	−	1.94322i
$814$	2.82436	−	4.89193i	0.0989936	−	0.171462i
$815$	−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	0.635927	−	0.771749i	$-0.280618\pi$
$821$	−10.0398	−	17.3894i	−0.350391	−	0.606895i	−0.986318	+	0.164854i	$0.947285\pi$
$822$	−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
$825$	−5.62869	−	4.39437i	−0.195966	−	0.152992i
$826$	−2.81709	−	4.87934i	−0.0980191	−	0.169774i
$827$	−0.864167			−0.0300500			−0.0150250	−	0.999887i	$-0.504783\pi$
$827$	−0.864167			−0.0300500			−0.0150250	+	0.999887i	$0.504783\pi$
$828$	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
$836$	18.6447			0.644840
$837$	−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
$847$	−0.519120			−0.0178372
$848$	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	0.975948	−	0.218006i	$-0.0699551\pi$
$853$	8.73776	+	15.1343i	0.299175	+	0.518187i	−0.676772	+	0.736193i	$0.736622\pi$
$854$	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	$0.0415537\pi$
$857$	17.8130	+	30.8530i	0.608480	+	1.05392i	−0.383011	+	0.923744i	$0.625113\pi$
$858$	−20.6300	+	8.34366i	−0.704296	+	0.284848i
$859$	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
$869$	1.02178	−	1.76978i	0.0346616	−	0.0600356i
$870$	−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	−0.997576	−	0.0695812i	$-0.977834\pi$
$877$	−12.9867	+	22.4936i	−0.438529	+	0.759555i	0.559047	+	0.829136i	$0.311167\pi$
$878$	−2.73714	+	4.74086i	−0.0923738	+	0.159996i
$879$	19.6994	+	15.3795i	0.664444	+	0.518737i
$880$	6.95571	+	12.0476i	0.234477	+	0.406126i
$881$	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	$0.401147\pi$
$887$	−20.0080	+	34.6549i	−0.671803	+	1.16360i	−0.977392	+	0.211434i	$0.932187\pi$
$888$	−4.69345	+	33.4828i	−0.157502	+	1.12361i
$889$	−2.71326	−	4.69950i	−0.0909997	−	0.157616i
$890$	19.2761			0.646138
$891$	0.301193	−	8.99496i	0.0100903	−	0.301342i
$892$	−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
$902$	0.236398	+	0.409453i	0.00787119	+	0.0136333i
$903$	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
$913$	−7.02970	+	12.1758i	−0.232649	+	0.402960i
$914$	−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	$-0.792038\pi$
$919$	−48.1441			−1.58813			−0.794064	+	0.607835i	$0.792038\pi$
$920$	−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
$924$	4.54760	−	1.83925i	0.149605	−	0.0605068i
$925$	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
$935$	2.52155			0.0824634
$936$	95.7473	−	92.5949i	3.12960	−	3.02656i
$937$	36.6480			1.19724			0.598620	−	0.801033i	$-0.295716\pi$
$937$	36.6480			1.19724			0.598620	+	0.801033i	$0.295716\pi$
$938$	−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	−0.896038	−	0.443978i	$-0.853567\pi$
$941$	−1.94861	+	3.37509i	−0.0635229	+	0.110025i	0.832515	+	0.554003i	$0.186900\pi$
$942$	−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
$946$	6.19686			0.201477
$947$	−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	$-0.394331\pi$
$953$	20.1218			0.651810			0.325905	+	0.945403i	$0.394331\pi$
$954$	3.77280	+	15.0858i	0.122149	+	0.488419i
$955$	19.6151			0.634730
$956$	−1.97068	−	3.41332i	−0.0637365	−	0.110395i
$957$	5.71527	+	4.46196i	0.184748	+	0.144235i
$958$	−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	−0.989879	−	0.141911i	$-0.954675\pi$
$967$	−11.5692	+	20.0385i	−0.372041	+	0.644394i	0.617838	+	0.786305i	$0.288009\pi$
$968$	4.71793	−	8.17169i	0.151640	−	0.262648i
$969$	−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
$979$	−3.76875	−	6.52767i	−0.120450	−	0.208625i
$980$	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
$990$	1.86138	+	7.44286i	0.0591587	+	0.236550i
$991$	−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	$-0.976462\pi$
$997$	−17.7648	−	30.7695i	−0.562616	−	0.974480i	0.434651	−	0.900599i	$-0.356872\pi$
$998$	−19.7445			−0.625000
$999$	−4.36163	+	9.82482i	−0.137996	+	0.310844i

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

)

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.e.e.34.4	✓	8	9.7	even	3	inner
99.2.e.e.67.4	yes	8	1.1	even	1	trivial
297.2.e.e.100.1		8	9.2	odd	6
297.2.e.e.199.1		8	3.2	odd	2
891.2.a.p.1.4		4	9.5	odd	6
891.2.a.q.1.1		4	9.4	even	3
1089.2.e.i.364.1		8	11.10	odd	2
1089.2.e.i.727.1		8	99.43	odd	6
9801.2.a.bi.1.4		4	99.76	odd	6
9801.2.a.bl.1.1		4	99.32	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	99.2.e.e.67.4

Level	$99$
Weight	$2$
Character	99.67
Analytic conductor	$0.791$
Analytic rank	$0$
Dimension	$8$
Inner twists	$2$