LMFDB - Embedded newform 57.2.i.b.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,2,Mod(4,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("57.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$57 = 3 \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	57.i (of order $9$ , degree $6$ , 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:	$0.455147291521$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57$ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$3$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			43.1
Root			$0.500000 + 1.80139i$ of defining polynomial
Character	$\chi$	$=$	57.43
Dual form			57.2.i.b.4.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.23121 + 0.812094i) q^{2} +(0.173648 - 0.984808i) q^{3} +(2.78672 - 2.33833i) q^{4} +(2.16379 + 1.81563i) q^{5} +(0.412311 + 2.33833i) q^{6} +(1.05756 + 1.83175i) q^{7} +(-1.94440 + 3.36780i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(-6.30233 - 2.29386i) q^{10} +(2.41841 - 4.18882i) q^{11} +(-1.81890 - 3.15043i) q^{12} +(0.122850 + 0.696719i) q^{13} +(-3.84720 - 3.22819i) q^{14} +(2.16379 - 1.81563i) q^{15} +(0.340001 - 1.92824i) q^{16} +(-7.00302 + 2.54889i) q^{17} +2.37441 q^{18} +(-3.99418 - 1.74542i) q^{19} +10.2754 q^{20} +(1.98757 - 0.723416i) q^{21} +(-1.99428 + 11.3101i) q^{22} +(1.49621 - 1.25547i) q^{23} +(2.97899 + 2.49967i) q^{24} +(0.517210 + 2.93324i) q^{25} +(-0.839906 - 1.45476i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(7.23037 + 2.63164i) q^{28} +(3.33570 + 1.21410i) q^{29} +(-3.35340 + 5.80826i) q^{30} +(-1.78201 - 3.08653i) q^{31} +(-0.543266 - 3.08102i) q^{32} +(-3.70522 - 3.10905i) q^{33} +(13.5553 - 11.3742i) q^{34} +(-1.03745 + 5.88367i) q^{35} +(-3.41841 + 1.24420i) q^{36} -3.84882 q^{37} +(10.3293 + 0.650754i) q^{38} +0.707467 q^{39} +(-10.3220 + 3.75688i) q^{40} +(-0.673710 + 3.82080i) q^{41} +(-3.84720 + 3.22819i) q^{42} +(-3.53262 - 2.96422i) q^{43} +(-3.05541 - 17.3281i) q^{44} +(-1.41231 - 2.44619i) q^{45} +(-2.31881 + 4.01629i) q^{46} +(-0.569995 - 0.207461i) q^{47} +(-1.83991 - 0.669671i) q^{48} +(1.26312 - 2.18779i) q^{49} +(-3.53607 - 6.12466i) q^{50} +(1.29411 + 7.33924i) q^{51} +(1.97151 + 1.65429i) q^{52} +(-2.37071 + 1.98926i) q^{53} +(0.412311 - 2.33833i) q^{54} +(12.8383 - 4.67275i) q^{55} -8.22530 q^{56} +(-2.41249 + 3.63041i) q^{57} -8.42862 q^{58} +(-0.338784 + 0.123307i) q^{59} +(1.78431 - 10.1193i) q^{60} +(-2.86076 + 2.40046i) q^{61} +(6.48259 + 5.43954i) q^{62} +(-0.367288 - 2.08299i) q^{63} +(5.67220 + 9.82455i) q^{64} +(-0.999163 + 1.73060i) q^{65} +(10.7920 + 3.92796i) q^{66} +(11.6606 + 4.24409i) q^{67} +(-13.5553 + 23.4784i) q^{68} +(-0.976584 - 1.69149i) q^{69} +(-2.46332 - 13.9702i) q^{70} +(-4.43672 - 3.72285i) q^{71} +(2.97899 - 2.49967i) q^{72} +(1.08452 - 6.15063i) q^{73} +(8.58752 - 3.12560i) q^{74} +2.97849 q^{75} +(-15.2120 + 4.47573i) q^{76} +10.2305 q^{77} +(-1.57851 + 0.574530i) q^{78} +(-0.896754 + 5.08575i) q^{79} +(4.23667 - 3.55498i) q^{80} +(0.766044 + 0.642788i) q^{81} +(-1.59966 - 9.07213i) q^{82} +(-4.16395 - 7.21218i) q^{83} +(3.84720 - 6.66355i) q^{84} +(-19.7809 - 7.19966i) q^{85} +(10.2892 + 3.74498i) q^{86} +(1.77489 - 3.07420i) q^{87} +(9.40473 + 16.2895i) q^{88} +(0.344596 + 1.95430i) q^{89} +(5.13770 + 4.31105i) q^{90} +(-1.14629 + 0.961855i) q^{91} +(1.23381 - 6.99729i) q^{92} +(-3.34908 + 1.21897i) q^{93} +1.44026 q^{94} +(-5.47351 - 11.0287i) q^{95} -3.12854 q^{96} +(0.393893 - 0.143365i) q^{97} +(-1.04160 + 5.90720i) q^{98} +(-3.70522 + 3.10905i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 3 q^{6} - 9 q^{7} + 3 q^{8} - 18 q^{10} - 9 q^{11} - 6 q^{12} - 3 q^{13} - 3 q^{14} + 6 q^{15} + 33 q^{16} + 12 q^{17} - 9 q^{19} - 18 q^{20} - 24 q^{22} + 9 q^{23}+ \cdots - 9 q^{99}+O(q^{100})$ 12 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 3 * q^6 - 9 * q^7 + 3 * q^8 - 18 * q^10 - 9 * q^11 - 6 * q^12 - 3 * q^13 - 3 * q^14 + 6 * q^15 + 33 * q^16 + 12 * q^17 - 9 * q^19 - 18 * q^20 - 24 * q^22 + 9 * q^23 + 30 * q^24 - 12 * q^25 - 6 * q^27 + 30 * q^28 - 6 * q^30 - 3 * q^32 - 9 * q^33 + 21 * q^34 + 30 * q^35 - 3 * q^36 - 12 * q^37 + 18 * q^38 + 6 * q^39 - 3 * q^40 - 18 * q^41 - 3 * q^42 + 15 * q^43 + 15 * q^44 - 9 * q^45 + 27 * q^46 - 9 * q^47 - 12 * q^48 - 9 * q^49 + 9 * q^50 - 15 * q^51 - 27 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 78 * q^56 - 3 * q^57 - 24 * q^58 - 30 * q^59 - 15 * q^60 + 21 * q^61 + 3 * q^62 + 9 * q^63 - 21 * q^64 + 21 * q^65 + 30 * q^66 + 3 * q^67 - 21 * q^68 - 6 * q^69 + 18 * q^70 - 30 * q^71 + 30 * q^72 - 24 * q^73 + 39 * q^74 + 30 * q^75 - 60 * q^76 + 96 * q^77 + 9 * q^78 + 24 * q^79 + 42 * q^80 - 33 * q^82 + 3 * q^83 + 3 * q^84 + 3 * q^85 + 51 * q^86 + 15 * q^87 + 42 * q^88 + 3 * q^89 - 9 * q^90 + 24 * q^91 + 69 * q^92 - 6 * q^93 + 18 * q^94 - 54 * q^95 - 42 * q^96 - 27 * q^97 - 3 * q^98 - 9 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$ .

$n$	$20$	$40$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−2.23121	+	0.812094i	−1.57770	+	0.574237i	−0.974703	−	0.223503i	$-0.928251\pi$
$2$	−2.23121	+	0.812094i	−1.57770	+	0.574237i	−0.603001	+	0.797740i	$0.706029\pi$
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i
$4$	2.78672	−	2.33833i	1.39336	−	1.16917i
$5$	2.16379	+	1.81563i	0.967675	+	0.811975i	0.982184	−	0.187919i	$-0.0601744\pi$
$5$	2.16379	+	1.81563i	0.967675	+	0.811975i	−0.0145099	+	0.999895i	$0.504619\pi$
$6$	0.412311	+	2.33833i	0.168325	+	0.954620i
$7$	1.05756	+	1.83175i	0.399721	+	0.692337i	0.993691	−	0.112150i	$-0.0357736\pi$
$7$	1.05756	+	1.83175i	0.399721	+	0.692337i	−0.593970	+	0.804487i	$0.702440\pi$
$8$	−1.94440	+	3.36780i	−0.687449	+	1.19070i
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$	−6.30233	−	2.29386i	−1.99297	−	0.725382i
$11$	2.41841	−	4.18882i	0.729179	−	1.26298i	−0.228051	−	0.973649i	$-0.573235\pi$
$11$	2.41841	−	4.18882i	0.729179	−	1.26298i	0.957231	−	0.289326i	$-0.0934312\pi$
$12$	−1.81890	−	3.15043i	−0.525071	−	0.909450i
$13$	0.122850	+	0.696719i	0.0340725	+	0.193235i	0.997093	−	0.0761930i	$-0.0242765\pi$
$13$	0.122850	+	0.696719i	0.0340725	+	0.193235i	−0.963021	+	0.269428i	$0.913165\pi$
$14$	−3.84720	−	3.22819i	−1.02821	−	0.862769i
$15$	2.16379	−	1.81563i	0.558687	−	0.468794i
$16$	0.340001	−	1.92824i	0.0850002	−	0.482060i
$17$	−7.00302	+	2.54889i	−1.69848	+	0.618197i	−0.995651	−	0.0931593i	$-0.970303\pi$
$17$	−7.00302	+	2.54889i	−1.69848	+	0.618197i	−0.702831	+	0.711356i	$0.748081\pi$
$18$	2.37441			0.559653
$19$	−3.99418	−	1.74542i	−0.916328	−	0.400428i
$19$	−3.99418	−	1.74542i	−0.916328	−	0.400428i
$20$	10.2754			2.29765
$21$	1.98757	−	0.723416i	0.433723	−	0.157862i
$22$	−1.99428	+	11.3101i	−0.425181	+	2.41132i
$23$	1.49621	−	1.25547i	0.311982	−	0.261784i	−0.473329	−	0.880886i	$-0.656948\pi$
$23$	1.49621	−	1.25547i	0.311982	−	0.261784i	0.785311	+	0.619102i	$0.212503\pi$
$24$	2.97899	+	2.49967i	0.608085	+	0.510244i
$25$	0.517210	+	2.93324i	0.103442	+	0.586648i
$26$	−0.839906	−	1.45476i	−0.164719	−	0.285302i
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	7.23037	+	2.63164i	1.36641	+	0.497333i
$29$	3.33570	+	1.21410i	0.619425	+	0.225452i	0.632622	−	0.774461i	$-0.281979\pi$
$29$	3.33570	+	1.21410i	0.619425	+	0.225452i	−0.0131972	+	0.999913i	$0.504201\pi$
$30$	−3.35340	+	5.80826i	−0.612244	+	1.06044i
$31$	−1.78201	−	3.08653i	−0.320058	−	0.554357i	0.660442	−	0.750878i	$-0.270369\pi$
$31$	−1.78201	−	3.08653i	−0.320058	−	0.554357i	−0.980500	+	0.196520i	$0.937036\pi$
$32$	−0.543266	−	3.08102i	−0.0960368	−	0.544652i
$33$	−3.70522	−	3.10905i	−0.644997	−	0.541217i
$34$	13.5553	−	11.3742i	2.32471	−	1.95066i
$35$	−1.03745	+	5.88367i	−0.175361	+	0.994521i
$36$	−3.41841	+	1.24420i	−0.569736	+	0.207367i
$37$	−3.84882			−0.632742			−0.316371	−	0.948636i	$-0.602464\pi$
$37$	−3.84882			−0.632742			−0.316371	+	0.948636i	$0.602464\pi$
$38$	10.3293	+	0.650754i	1.67564	+	0.105566i
$39$	0.707467			0.113285
$40$	−10.3220	+	3.75688i	−1.63204	+	0.594015i
$41$	−0.673710	+	3.82080i	−0.105216	+	0.596709i	0.885918	+	0.463842i	$0.153529\pi$
$41$	−0.673710	+	3.82080i	−0.105216	+	0.596709i	−0.991134	+	0.132867i	$0.957582\pi$
$42$	−3.84720	+	3.22819i	−0.593636	+	0.498120i
$43$	−3.53262	−	2.96422i	−0.538719	−	0.452039i	0.332380	−	0.943145i	$-0.392148\pi$
$43$	−3.53262	−	2.96422i	−0.538719	−	0.452039i	−0.871100	+	0.491106i	$0.836593\pi$
$44$	−3.05541	−	17.3281i	−0.460620	−	2.61231i
$45$	−1.41231	−	2.44619i	−0.210535	−	0.364657i
$46$	−2.31881	+	4.01629i	−0.341889	+	0.592169i
$47$	−0.569995	−	0.207461i	−0.0831423	−	0.0302613i	0.300114	−	0.953903i	$-0.402975\pi$
$47$	−0.569995	−	0.207461i	−0.0831423	−	0.0302613i	−0.383256	+	0.923642i	$0.625197\pi$
$48$	−1.83991	−	0.669671i	−0.265568	−	0.0966587i
$49$	1.26312	−	2.18779i	0.180446	−	0.312542i
$50$	−3.53607	−	6.12466i	−0.500076	−	0.866157i
$51$	1.29411	+	7.33924i	0.181211	+	1.02770i
$52$	1.97151	+	1.65429i	0.273399	+	0.229409i
$53$	−2.37071	+	1.98926i	−0.325642	+	0.273246i	−0.790922	−	0.611918i	$-0.790398\pi$
$53$	−2.37071	+	1.98926i	−0.325642	+	0.273246i	0.465279	+	0.885164i	$0.345954\pi$
$54$	0.412311	−	2.33833i	0.0561084	−	0.318207i
$55$	12.8383	−	4.67275i	1.73111	−	0.630074i
$56$	−8.22530			−1.09915
$57$	−2.41249	+	3.63041i	−0.319542	+	0.480860i
$58$	−8.42862			−1.10673
$59$	−0.338784	+	0.123307i	−0.0441059	+	0.0160532i	−0.363979	−	0.931407i	$-0.618582\pi$
$59$	−0.338784	+	0.123307i	−0.0441059	+	0.0160532i	0.319873	+	0.947460i	$0.396360\pi$
$60$	1.78431	−	10.1193i	0.230353	−	1.30640i
$61$	−2.86076	+	2.40046i	−0.366282	+	0.307347i	−0.807289	−	0.590157i	$-0.799066\pi$
$61$	−2.86076	+	2.40046i	−0.366282	+	0.307347i	0.441007	+	0.897504i	$0.354622\pi$
$62$	6.48259	+	5.43954i	0.823290	+	0.690822i
$63$	−0.367288	−	2.08299i	−0.0462739	−	0.262432i
$64$	5.67220	+	9.82455i	0.709025	+	1.22807i
$65$	−0.999163	+	1.73060i	−0.123931	+	0.214655i
$66$	10.7920	+	3.92796i	1.32840	+	0.483498i
$67$	11.6606	+	4.24409i	1.42456	+	0.518499i	0.935368	−	0.353676i	$-0.115068\pi$
$67$	11.6606	+	4.24409i	1.42456	+	0.518499i	0.489195	+	0.872174i	$0.337291\pi$
$68$	−13.5553	+	23.4784i	−1.64382	+	2.84718i
$69$	−0.976584	−	1.69149i	−0.117567	−	0.203632i
$70$	−2.46332	−	13.9702i	−0.294424	−	1.66976i
$71$	−4.43672	−	3.72285i	−0.526542	−	0.441821i	0.340364	−	0.940294i	$-0.389450\pi$
$71$	−4.43672	−	3.72285i	−0.526542	−	0.441821i	−0.866905	+	0.498473i	$0.833894\pi$
$72$	2.97899	−	2.49967i	0.351078	−	0.294589i
$73$	1.08452	−	6.15063i	0.126934	−	0.719877i	−0.853207	−	0.521573i	$-0.825346\pi$
$73$	1.08452	−	6.15063i	0.126934	−	0.719877i	0.980141	−	0.198304i	$-0.0635433\pi$
$74$	8.58752	−	3.12560i	0.998279	−	0.363344i
$75$	2.97849			0.343926
$76$	−15.2120	+	4.47573i	−1.74494	+	0.513401i
$77$	10.2305			1.16587
$78$	−1.57851	+	0.574530i	−0.178731	+	0.0650527i
$79$	−0.896754	+	5.08575i	−0.100893	+	0.572191i	0.891889	+	0.452255i	$0.149380\pi$
$79$	−0.896754	+	5.08575i	−0.100893	+	0.572191i	−0.992782	+	0.119937i	$0.961731\pi$
$80$	4.23667	−	3.55498i	0.473674	−	0.397459i
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$	−1.59966	−	9.07213i	−0.176653	−	1.00185i
$83$	−4.16395	−	7.21218i	−0.457053	−	0.791640i	0.541750	−	0.840539i	$-0.317762\pi$
$83$	−4.16395	−	7.21218i	−0.457053	−	0.791640i	−0.998804	+	0.0488998i	$0.984428\pi$
$84$	3.84720	−	6.66355i	0.419764	−	0.727053i
$85$	−19.7809	−	7.19966i	−2.14554	−	0.780912i
$86$	10.2892	+	3.74498i	1.10952	+	0.403831i
$87$	1.77489	−	3.07420i	0.190288	−	0.329589i
$88$	9.40473	+	16.2895i	1.00255	+	1.73646i
$89$	0.344596	+	1.95430i	0.0365271	+	0.207155i	0.997609	−	0.0691074i	$-0.0220151\pi$
$89$	0.344596	+	1.95430i	0.0365271	+	0.207155i	−0.961082	+	0.276263i	$0.910904\pi$
$90$	5.13770	+	4.31105i	0.541562	+	0.454424i
$91$	−1.14629	+	0.961855i	−0.120164	+	0.100830i
$92$	1.23381	−	6.99729i	0.128634	−	0.729518i
$93$	−3.34908	+	1.21897i	−0.347284	+	0.126401i
$94$	1.44026			0.148551
$95$	−5.47351	−	11.0287i	−0.561570	−	1.13152i
$96$	−3.12854			−0.319306
$97$	0.393893	−	0.143365i	0.0399938	−	0.0145565i	−0.321946	−	0.946758i	$-0.604337\pi$
$97$	0.393893	−	0.143365i	0.0399938	−	0.0145565i	0.361940	+	0.932202i	$0.382115\pi$
$98$	−1.04160	+	5.90720i	−0.105217	+	0.596717i
$99$	−3.70522	+	3.10905i	−0.372389	+	0.312472i
$100$	8.30021	+	6.96470i	0.830021	+	0.696470i
$101$	2.75126	+	15.6032i	0.273761	+	1.55258i	0.742870	+	0.669435i	$0.233464\pi$
$101$	2.75126	+	15.6032i	0.273761	+	1.55258i	−0.469110	+	0.883140i	$0.655425\pi$
$102$	−8.84758	−	15.3245i	−0.876041	−	1.51735i
$103$	0.362246	−	0.627428i	0.0356931	−	0.0618223i	−0.847627	−	0.530593i	$-0.821969\pi$
$103$	0.362246	−	0.627428i	0.0356931	−	0.0618223i	0.883320	+	0.468770i	$0.155303\pi$
$104$	−2.58528	−	0.940965i	−0.253507	−	0.0922692i
$105$	5.61413	+	2.04338i	0.547883	+	0.199413i
$106$	3.67409	−	6.36371i	0.356859	−	0.618098i
$107$	4.40533	+	7.63025i	0.425879	+	0.737644i	0.996502	−	0.0835678i	$-0.0266315\pi$
$107$	4.40533	+	7.63025i	0.425879	+	0.737644i	−0.570623	+	0.821212i	$0.693298\pi$
$108$	0.631697	+	3.58253i	0.0607851	+	0.344729i
$109$	13.1851	+	11.0636i	1.26290	+	1.05970i	0.995367	+	0.0961512i	$0.0306532\pi$
$109$	13.1851	+	11.0636i	1.26290	+	1.05970i	0.267534	+	0.963548i	$0.413791\pi$
$110$	−24.8502	+	20.8518i	−2.36937	+	1.98814i
$111$	−0.668340	+	3.79035i	−0.0634360	+	0.359764i
$112$	3.89163	−	1.41644i	0.367725	−	0.133841i
$113$	7.17430			0.674902			0.337451	−	0.941343i	$-0.390435\pi$
$113$	7.17430			0.674902			0.337451	+	0.941343i	$0.390435\pi$
$114$	2.43453	−	10.0594i	0.228015	−	0.942148i
$115$	5.51696			0.514459
$116$	12.1346	−	4.41664i	1.12667	−	0.410075i
$117$	0.122850	−	0.696719i	0.0113575	−	0.0644117i
$118$	0.655761	−	0.550249i	0.0603677	−	0.0506545i
$119$	−12.0751	−	10.1322i	−1.10692	−	0.928817i
$120$	1.90742	+	10.8175i	0.174123	+	0.987499i
$121$	−6.19745	−	10.7343i	−0.563404	−	0.975845i
$122$	4.43355	−	7.67914i	0.401395	−	0.695236i
$123$	3.64576	+	1.32695i	0.328727	+	0.119647i
$124$	−12.1833	−	4.43435i	−1.09409	−	0.398217i
$125$	2.85500	−	4.94500i	0.255359	−	0.442295i
$126$	2.51108	+	4.34932i	0.223705	+	0.387468i
$127$	−2.54344	−	14.4245i	−0.225693	−	1.27997i	−0.861355	−	0.508003i	$-0.830384\pi$
$127$	−2.54344	−	14.4245i	−0.225693	−	1.27997i	0.635662	−	0.771968i	$-0.280727\pi$
$128$	−15.8411	−	13.2923i	−1.40017	−	1.17488i
$129$	−3.53262	+	2.96422i	−0.311030	+	0.260985i
$130$	0.823932	−	4.67275i	0.0722636	−	0.409827i
$131$	−5.45869	+	1.98680i	−0.476928	+	0.173587i	−0.569288	−	0.822138i	$-0.692781\pi$
$131$	−5.45869	+	1.98680i	−0.476928	+	0.173587i	0.0923603	+	0.995726i	$0.470559\pi$
$132$	−17.5954			−1.53148
$133$	−1.02692	−	9.16225i	−0.0890449	−	0.794468i
$134$	−29.4638			−2.54528
$135$	−2.65428	+	0.966078i	−0.228444	+	0.0831467i
$136$	5.03252	−	28.5408i	0.431535	−	2.44736i
$137$	0.897245	−	0.752878i	0.0766568	−	0.0643227i	−0.603654	−	0.797246i	$-0.706289\pi$
$137$	0.897245	−	0.752878i	0.0766568	−	0.0643227i	0.680311	+	0.732924i	$0.261845\pi$
$138$	3.55262	+	2.98100i	0.302419	+	0.253759i
$139$	3.69249	+	20.9411i	0.313193	+	1.77620i	0.582179	+	0.813061i	$0.302200\pi$
$139$	3.69249	+	20.9411i	0.313193	+	1.77620i	−0.268986	+	0.963144i	$0.586689\pi$
$140$	10.8669	+	18.8220i	0.918420	+	1.59075i
$141$	−0.303288	+	0.525310i	−0.0255415	+	0.0442391i
$142$	12.9226	+	4.70343i	1.08444	+	0.394703i
$143$	3.21553	+	1.17036i	0.268896	+	0.0978701i
$144$	−0.978994	+	1.69567i	−0.0815828	+	0.141306i
$145$	5.01340	+	8.68346i	0.416340	+	0.721122i
$146$	2.57509	+	14.6041i	0.213116	+	1.20864i
$147$	−1.93521	−	1.62384i	−0.159614	−	0.133932i
$148$	−10.7256	+	8.99981i	−0.881636	+	0.739780i
$149$	3.55836	−	20.1805i	0.291512	−	1.65325i	−0.389537	−	0.921011i	$-0.627365\pi$
$149$	3.55836	−	20.1805i	0.291512	−	1.65325i	0.681049	−	0.732237i	$-0.261524\pi$
$150$	−6.64564	+	2.41882i	−0.542614	+	0.197495i
$151$	−2.21547			−0.180292			−0.0901462	−	0.995929i	$-0.528733\pi$
$151$	−2.21547			−0.180292			−0.0901462	+	0.995929i	$0.528733\pi$
$152$	13.6445	−	10.0578i	1.10672	−	0.815796i
$153$	7.45246			0.602496
$154$	−22.8264	+	8.30813i	−1.83940	+	0.669488i
$155$	1.74812	−	9.91406i	0.140412	−	0.796317i
$156$	1.97151	−	1.65429i	0.157847	−	0.132449i
$157$	9.75291	+	8.18366i	0.778367	+	0.653127i	0.942837	−	0.333255i	$-0.108147\pi$
$157$	9.75291	+	8.18366i	0.778367	+	0.653127i	−0.164470	+	0.986382i	$0.552591\pi$
$158$	−2.12926	−	12.0756i	−0.169395	−	0.960685i
$159$	1.54737	+	2.68013i	0.122715	+	0.212548i
$160$	4.41848	−	7.65303i	0.349311	−	0.605025i
$161$	3.88205	+	1.41295i	0.305949	+	0.111356i
$162$	−2.23121	−	0.812094i	−0.175300	−	0.0638042i
$163$	−8.20863	+	14.2178i	−0.642950	+	1.11362i	0.341821	+	0.939765i	$0.388956\pi$
$163$	−8.20863	+	14.2178i	−0.642950	+	1.11362i	−0.984771	+	0.173857i	$0.944377\pi$
$164$	7.05686	+	12.2228i	0.551048	+	0.954444i
$165$	−2.37242	−	13.4546i	−0.184692	−	1.04744i
$166$	15.1476	+	12.7104i	1.17568	+	0.986516i
$167$	7.35109	−	6.16830i	0.568845	−	0.477317i	−0.312418	−	0.949945i	$-0.601139\pi$
$167$	7.35109	−	6.16830i	0.568845	−	0.477317i	0.881262	+	0.472628i	$0.156694\pi$
$168$	−1.42831	+	8.10034i	−0.110196	+	0.624955i
$169$	11.7457	−	4.27508i	0.903514	−	0.328852i
$170$	49.9822			3.83346
$171$	3.15633	+	3.00625i	0.241371	+	0.229894i
$172$	−16.7757			−1.27914
$173$	21.1099	−	7.68339i	1.60496	−	0.584157i	0.624525	−	0.781005i	$-0.285293\pi$
$173$	21.1099	−	7.68339i	1.60496	−	0.584157i	0.980434	+	0.196848i	$0.0630706\pi$
$174$	−1.46361	+	8.30057i	−0.110956	+	0.629265i
$175$	−4.82599	+	4.04949i	−0.364811	+	0.306112i
$176$	−7.25478	−	6.08749i	−0.546850	−	0.458861i
$177$	0.0626047	+	0.355049i	0.00470566	+	0.0266871i
$178$	−2.35594	−	4.08061i	−0.176585	−	0.305855i
$179$	−7.14978	+	12.3838i	−0.534400	+	0.925608i	0.464792	+	0.885420i	$0.346129\pi$
$179$	−7.14978	+	12.3838i	−0.534400	+	0.925608i	−0.999192	+	0.0401881i	$0.987204\pi$
$180$	−9.65573	−	3.51440i	−0.719695	−	0.261948i
$181$	−24.3951	−	8.87908i	−1.81327	−	0.659977i	−0.996555	−	0.0829387i	$-0.973569\pi$
$181$	−24.3951	−	8.87908i	−1.81327	−	0.659977i	−0.816717	−	0.577038i	$-0.804208\pi$
$182$	1.77651	−	3.07700i	0.131683	−	0.228082i
$183$	1.86723	+	3.23413i	0.138029	+	0.239074i
$184$	1.31894	+	7.48008i	0.0972336	+	0.551439i
$185$	−8.32802	−	6.98804i	−0.612288	−	0.513771i
$186$	6.48259	−	5.43954i	0.475327	−	0.398846i
$187$	−6.25937	+	35.4986i	−0.457730	+	2.59592i
$188$	−2.07353	+	0.754702i	−0.151228	+	0.0550423i
$189$	−2.11513			−0.153853
$190$	21.1689	+	20.1623i	1.53575	+	1.46273i
$191$	−2.05501			−0.148696			−0.0743478	−	0.997232i	$-0.523688\pi$
$191$	−2.05501			−0.148696			−0.0743478	+	0.997232i	$0.523688\pi$
$192$	10.6603	−	3.88002i	0.769338	−	0.280016i
$193$	0.0254073	−	0.144092i	0.00182885	−	0.0103720i	−0.983880	−	0.178832i	$-0.942768\pi$
$193$	0.0254073	−	0.144092i	0.00182885	−	0.0103720i	0.985709	+	0.168460i	$0.0538793\pi$
$194$	−0.762432	+	0.639756i	−0.0547394	+	0.0459318i
$195$	1.53081	+	1.28450i	0.109623	+	0.0919849i
$196$	−1.59582	−	9.05035i	−0.113987	−	0.646454i
$197$	3.26645	+	5.65766i	0.232725	+	0.403092i	0.958609	−	0.284725i	$-0.0919024\pi$
$197$	3.26645	+	5.65766i	0.232725	+	0.403092i	−0.725884	+	0.687817i	$0.758569\pi$
$198$	5.74229	−	9.94594i	0.408087	−	0.706827i
$199$	−7.25719	−	2.64140i	−0.514449	−	0.187244i	0.0717327	−	0.997424i	$-0.477147\pi$
$199$	−7.25719	−	2.64140i	−0.514449	−	0.187244i	−0.586181	+	0.810180i	$0.699369\pi$
$200$	−10.8842	−	3.96154i	−0.769631	−	0.280123i
$201$	6.20445	−	10.7464i	0.437628	−	0.757994i
$202$	−18.8099	−	32.5797i	−1.32346	−	2.29230i
$203$	1.30379	+	7.39417i	0.0915082	+	0.518969i
$204$	20.7679	+	17.4263i	1.45404	+	1.22009i
$205$	−8.39493	+	7.04418i	−0.586327	+	0.491987i
$206$	−0.298716	+	1.69410i	−0.0208125	+	0.118034i
$207$	−1.83538	+	0.668023i	−0.127568	+	0.0464308i
$208$	1.38521			0.0960471
$209$	−16.9708	+	12.5097i	−1.17390	+	0.865317i
$210$	−14.1857			−0.978908
$211$	20.4301	−	7.43595i	1.40647	−	0.511912i	0.476376	−	0.879241i	$-0.341950\pi$
$211$	20.4301	−	7.43595i	1.40647	−	0.511912i	0.930091	+	0.367329i	$0.119728\pi$
$212$	−1.95494	+	11.0870i	−0.134266	+	0.761460i
$213$	−4.43672	+	3.72285i	−0.303999	+	0.255085i
$214$	−16.0257	−	13.4472i	−1.09549	−	0.919229i
$215$	−2.26190	−	12.8279i	−0.154260	−	0.874854i
$216$	−1.94440	−	3.36780i	−0.132300	−	0.229150i
$217$	3.76917	−	6.52840i	0.255868	−	0.443177i
$218$	−38.4034	−	13.9777i	−2.60100	−	0.946688i
$219$	−5.86886	−	2.13609i	−0.396581	−	0.144344i
$220$	24.8502	−	43.0418i	1.67540	−	2.90188i
$221$	−2.63618	−	4.56600i	−0.177329	−	0.307143i
$222$	−1.58691	−	8.99981i	−0.106506	−	0.604028i
$223$	−11.2204	−	9.41504i	−0.751374	−	0.630478i	0.184492	−	0.982834i	$-0.440936\pi$
$223$	−11.2204	−	9.41504i	−0.751374	−	0.630478i	−0.935866	+	0.352356i	$0.885381\pi$
$224$	5.06912	−	4.25350i	0.338695	−	0.284199i
$225$	0.517210	−	2.93324i	0.0344806	−	0.195549i
$226$	−16.0074	+	5.82621i	−1.06480	+	0.387554i
$227$	−17.6277			−1.16999			−0.584995	−	0.811037i	$-0.698903\pi$
$227$	−17.6277			−1.16999			−0.584995	+	0.811037i	$0.698903\pi$
$228$	1.76619	+	15.7581i	0.116969	+	1.04361i
$229$	17.0069			1.12385			0.561924	−	0.827189i	$-0.310061\pi$
$229$	17.0069			1.12385			0.561924	+	0.827189i	$0.310061\pi$
$230$	−12.3095	+	4.48029i	−0.811664	+	0.295422i
$231$	1.77651	−	10.0751i	0.116886	−	0.662891i
$232$	−10.5748	+	8.87329i	−0.694268	+	0.582560i
$233$	−13.1412	−	11.0268i	−0.860911	−	0.722390i	0.101253	−	0.994861i	$-0.467715\pi$
$233$	−13.1412	−	11.0268i	−0.860911	−	0.722390i	−0.962164	+	0.272470i	$0.912159\pi$
$234$	0.291696	+	1.65429i	0.0190688	+	0.108144i
$235$	−0.856674	−	1.48380i	−0.0558832	−	0.0967926i
$236$	−0.655761	+	1.13581i	−0.0426864	+	0.0739350i
$237$	4.85276	+	1.76626i	0.315221	+	0.114731i
$238$	35.1703	+	12.8010i	2.27975	+	0.829763i
$239$	0.628173	−	1.08803i	0.0406331	−	0.0703786i	−0.844994	−	0.534776i	$-0.820396\pi$
$239$	0.628173	−	1.08803i	0.0406331	−	0.0703786i	0.885627	+	0.464398i	$0.153729\pi$
$240$	−2.76529	−	4.78962i	−0.178499	−	0.309169i
$241$	2.66425	+	15.1097i	0.171619	+	0.973301i	0.941974	+	0.335685i	$0.108968\pi$
$241$	2.66425	+	15.1097i	0.171619	+	0.973301i	−0.770355	+	0.637615i	$0.779921\pi$
$242$	22.5451	+	18.9176i	1.44925	+	1.21607i
$243$	0.766044	−	0.642788i	0.0491418	−	0.0412348i
$244$	−2.35904	+	13.3788i	−0.151022	+	0.856490i
$245$	6.70535	−	2.44055i	0.428389	−	0.155921i
$246$	−9.21208			−0.587341
$247$	0.725383	−	2.99725i	0.0461550	−	0.190710i
$248$	13.8598			0.880095
$249$	−7.82567	+	2.84831i	−0.495932	+	0.180504i
$250$	−2.35430	+	13.3519i	−0.148899	+	0.844447i
$251$	−5.78087	+	4.85073i	−0.364885	+	0.306175i	−0.806734	−	0.590914i	$-0.798767\pi$
$251$	−5.78087	+	4.85073i	−0.364885	+	0.306175i	0.441849	+	0.897089i	$0.354323\pi$
$252$	−5.89425	−	4.94587i	−0.371303	−	0.311560i
$253$	−1.64048	−	9.30361i	−0.103136	−	0.584913i
$254$	17.3890	+	30.1187i	1.09108	+	1.88981i
$255$	−10.5252	+	18.2302i	−0.659113	+	1.14162i
$256$	24.8190	+	9.03337i	1.55119	+	0.564586i
$257$	6.10125	+	2.22067i	0.380585	+	0.138522i	0.525227	−	0.850962i	$-0.323981\pi$
$257$	6.10125	+	2.22067i	0.380585	+	0.138522i	−0.144641	+	0.989484i	$0.546203\pi$
$258$	5.47479	−	9.48262i	0.340846	−	0.590362i
$259$	−4.07037	−	7.05008i	−0.252920	−	0.438071i
$260$	1.26234	+	7.15907i	0.0782868	+	0.443987i
$261$	−2.71929	−	2.28176i	−0.168320	−	0.141237i
$262$	10.5660	−	8.86594i	0.652770	−	0.547739i
$263$	−0.575776	+	3.26539i	−0.0355038	+	0.201352i	−0.997400	−	0.0720623i	$-0.977042\pi$
$263$	−0.575776	+	3.26539i	−0.0355038	+	0.201352i	0.961896	+	0.273415i	$0.0881531\pi$
$264$	17.6751	−	6.43321i	1.08783	−	0.395937i
$265$	−8.74149			−0.536985
$266$	9.73188	+	19.6090i	0.596700	+	1.20230i
$267$	1.98445			0.121446
$268$	42.4187	−	15.4392i	2.59114	−	0.943097i
$269$	−4.41559	+	25.0421i	−0.269223	+	1.52684i	0.487510	+	0.873117i	$0.337905\pi$
$269$	−4.41559	+	25.0421i	−0.269223	+	1.52684i	−0.756733	+	0.653724i	$0.773206\pi$
$270$	5.13770	−	4.31105i	0.312671	−	0.262362i
$271$	−7.08311	−	5.94343i	−0.430268	−	0.361038i	0.401785	−	0.915734i	$-0.368390\pi$
$271$	−7.08311	−	5.94343i	−0.430268	−	0.361038i	−0.832053	+	0.554696i	$0.812834\pi$
$272$	2.53384	+	14.3701i	0.153637	+	0.871318i
$273$	0.748190	+	1.29590i	0.0452825	+	0.0784317i
$274$	−1.39053	+	2.40848i	−0.0840053	+	0.145501i
$275$	13.5376	+	4.92729i	0.816350	+	0.297127i
$276$	−6.67673	−	2.43013i	−0.401892	−	0.146277i
$277$	−5.73815	+	9.93877i	−0.344772	+	0.597163i	−0.985312	−	0.170762i	$-0.945377\pi$
$277$	−5.73815	+	9.93877i	−0.344772	+	0.597163i	0.640540	+	0.767925i	$0.278710\pi$
$278$	−25.2449	−	43.7255i	−1.51409	−	2.62248i
$279$	0.618885	+	3.50987i	0.0370517	+	0.210131i
$280$	−17.7978	−	14.9341i	−1.06362	−	0.892484i
$281$	9.24217	−	7.75510i	0.551342	−	0.462631i	−0.324053	−	0.946039i	$-0.605046\pi$
$281$	9.24217	−	7.75510i	0.551342	−	0.462631i	0.875395	+	0.483408i	$0.160601\pi$
$282$	0.250098	−	1.41838i	0.0148931	−	0.0844631i
$283$	−20.3639	+	7.41187i	−1.21051	+	0.440590i	−0.866881	−	0.498515i	$-0.833879\pi$
$283$	−20.3639	+	7.41187i	−1.21051	+	0.440590i	−0.343630	+	0.939105i	$0.611657\pi$
$284$	−21.0691			−1.25022
$285$	−11.8116	+	3.47524i	−0.699659	+	0.205856i
$286$	−8.12496			−0.480439
$287$	−7.71125	+	2.80667i	−0.455181	+	0.165672i
$288$	−0.543266	+	3.08102i	−0.0320123	+	0.181551i
$289$	29.5227	−	24.7725i	1.73663	−	1.45721i
$290$	−18.2377	−	15.3033i	−1.07096	−	0.898639i
$291$	−0.0727884	−	0.412804i	−0.00426693	−	0.0241990i
$292$	−11.3600	−	19.6760i	−0.664791	−	1.15145i
$293$	0.535257	−	0.927093i	0.0312701	−	0.0541613i	−0.849967	−	0.526836i	$-0.823378\pi$
$293$	0.535257	−	0.927093i	0.0312701	−	0.0541613i	0.881237	+	0.472675i	$0.156711\pi$
$294$	5.63658	+	2.05155i	0.328732	+	0.119649i
$295$	−0.956937	−	0.348296i	−0.0557150	−	0.0202786i
$296$	7.48364	−	12.9620i	0.434978	−	0.753404i
$297$	2.41841	+	4.18882i	0.140331	+	0.243060i
$298$	8.44899	+	47.9166i	0.489437	+	2.77573i
$299$	1.05852	+	0.888204i	0.0612158	+	0.0513662i
$300$	8.30021	−	6.96470i	0.479213	−	0.402107i
$301$	1.69375	−	9.60573i	0.0976261	−	0.553665i
$302$	4.94318	−	1.79917i	0.284448	−	0.103531i
$303$	15.8439			0.910208
$304$	−4.72362	+	7.10830i	−0.270918	+	0.407689i
$305$	−10.5484			−0.604001
$306$	−16.6280	+	6.05210i	−0.950560	+	0.345976i
$307$	5.26215	−	29.8431i	0.300327	−	1.70324i	−0.344400	−	0.938823i	$-0.611918\pi$
$307$	5.26215	−	29.8431i	0.300327	−	1.70324i	0.644726	−	0.764413i	$-0.276971\pi$
$308$	28.5095	−	23.9223i	1.62448	−	1.36310i
$309$	−0.554993	−	0.465694i	−0.0315724	−	0.0264924i
$310$	4.15074	+	23.5400i	0.235746	+	1.33698i
$311$	1.47334	+	2.55190i	0.0835456	+	0.144705i	0.904771	−	0.425899i	$-0.140042\pi$
$311$	1.47334	+	2.55190i	0.0835456	+	0.144705i	−0.821225	+	0.570605i	$0.806709\pi$
$312$	−1.37560	+	2.38261i	−0.0778779	+	0.134888i
$313$	−2.72092	−	0.990333i	−0.153795	−	0.0559769i	0.263975	−	0.964529i	$-0.414966\pi$
$313$	−2.72092	−	0.990333i	−0.153795	−	0.0559769i	−0.417771	+	0.908552i	$0.637188\pi$
$314$	−28.4067	−	10.3392i	−1.60308	−	0.583475i
$315$	2.98722	−	5.17401i	0.168311	−	0.291522i
$316$	9.39317	+	16.2694i	0.528407	+	0.915228i
$317$	4.05628	+	23.0043i	0.227823	+	1.29205i	0.857214	+	0.514961i	$0.172194\pi$
$317$	4.05628	+	23.0043i	0.227823	+	1.29205i	−0.629390	+	0.777089i	$0.716695\pi$
$318$	−5.62903	−	4.72332i	−0.315660	−	0.264871i
$319$	13.1527	−	11.0365i	0.736412	−	0.617923i
$320$	−5.56432	+	31.5569i	−0.311055	+	1.76408i
$321$	8.27931	−	3.01342i	0.462106	−	0.168193i
$322$	−9.80913			−0.546641
$323$	32.4203	+	2.04250i	1.80391	+	0.113648i
$324$	3.63780			0.202100
$325$	−1.98010	+	0.720699i	−0.109836	+	0.0399772i
$326$	6.76902	−	38.3890i	0.374901	−	2.12617i
$327$	13.1851	−	11.0636i	0.729136	−	0.611818i
$328$	−11.5577	−	9.69808i	−0.638169	−	0.535487i
$329$	−0.222788	−	1.26349i	−0.0122827	−	0.0696586i
$330$	16.2198	+	28.0935i	0.892871	+	1.54650i
$331$	1.46839	−	2.54332i	0.0807100	−	0.139794i	−0.822845	−	0.568266i	$-0.807615\pi$
$331$	1.46839	−	2.54332i	0.0807100	−	0.139794i	0.903555	+	0.428472i	$0.140948\pi$
$332$	−28.4682	−	10.3616i	−1.56240	−	0.568666i
$333$	3.61671	+	1.31637i	0.198194	+	0.0721368i
$334$	−11.3926	+	19.7326i	−0.623375	+	1.07972i
$335$	17.5252	+	30.3546i	0.957505	+	1.65845i
$336$	−0.719145	−	4.07847i	−0.0392326	−	0.222499i
$337$	−3.12011	−	2.61809i	−0.169963	−	0.142616i	0.553838	−	0.832624i	$-0.313163\pi$
$337$	−3.12011	−	2.61809i	−0.169963	−	0.142616i	−0.723802	+	0.690008i	$0.757607\pi$
$338$	−22.7353	+	19.0772i	−1.23664	+	1.03766i
$339$	1.24580	−	7.06531i	0.0676628	−	0.383735i
$340$	−71.9589	+	26.1909i	−3.90252	+	1.42040i
$341$	−17.2385			−0.933519
$342$	−9.48381	−	4.14434i	−0.512826	−	0.224100i
$343$	20.1492			1.08795
$344$	16.8517	−	6.13352i	0.908584	−	0.330697i
$345$	0.958010	−	5.43314i	0.0515775	−	0.292511i
$346$	−40.8611	+	34.2865i	−2.19671	+	1.84325i
$347$	−1.50886	−	1.26608i	−0.0809999	−	0.0679670i	0.601389	−	0.798957i	$-0.294614\pi$
$347$	−1.50886	−	1.26608i	−0.0809999	−	0.0679670i	−0.682389	+	0.730990i	$0.739059\pi$
$348$	−2.24239	−	12.7172i	−0.120205	−	0.681714i
$349$	2.88181	+	4.99145i	0.154260	+	0.267186i	0.932789	−	0.360422i	$-0.117367\pi$
$349$	2.88181	+	4.99145i	0.154260	+	0.267186i	−0.778529	+	0.627608i	$0.784034\pi$
$350$	7.47924	−	12.9544i	0.399782	−	0.692443i
$351$	−0.664801	−	0.241968i	−0.0354845	−	0.0129153i
$352$	−14.2196	−	5.17553i	−0.757910	−	0.275857i
$353$	7.01672	−	12.1533i	0.373462	−	0.646856i	−0.616633	−	0.787250i	$-0.711504\pi$
$353$	7.01672	−	12.1533i	0.373462	−	0.646856i	0.990096	+	0.140395i	$0.0448372\pi$
$354$	−0.428018	−	0.741348i	−0.0227489	−	0.0394022i
$355$	−2.84079	−	16.1109i	−0.150773	−	0.855078i
$356$	5.53009	+	4.64030i	0.293094	+	0.245935i
$357$	−12.0751	+	10.1322i	−0.639081	+	0.536252i
$358$	5.89587	−	33.4371i	0.311606	−	1.76721i
$359$	15.0185	−	5.46630i	0.792647	−	0.288500i	0.0862113	−	0.996277i	$-0.472524\pi$
$359$	15.0185	−	5.46630i	0.792647	−	0.288500i	0.706436	+	0.707777i	$0.250302\pi$
$360$	10.9844			0.578928
$361$	12.9070	+	13.9431i	0.679315	+	0.733846i
$362$	61.6412			3.23979
$363$	−11.6474	+	4.23930i	−0.611330	+	0.222506i
$364$	−0.945260	+	5.36083i	−0.0495451	+	0.280984i
$365$	13.5140	−	11.3396i	0.707353	−	0.593539i
$366$	−6.79259	−	5.69966i	−0.355055	−	0.297926i
$367$	5.06013	+	28.6974i	0.264137	+	1.49799i	0.771482	+	0.636251i	$0.219516\pi$
$367$	5.06013	+	28.6974i	0.264137	+	1.49799i	−0.507345	+	0.861743i	$0.669373\pi$
$368$	−1.91214	−	3.31192i	−0.0996771	−	0.172646i
$369$	1.93987	−	3.35995i	0.100986	−	0.174912i
$370$	24.2565	+	8.82865i	1.26104	+	0.458980i
$371$	−6.15102	−	2.23879i	−0.319345	−	0.116232i
$372$	−6.48259	+	11.2282i	−0.336107	+	0.582154i
$373$	−14.3897	−	24.9236i	−0.745068	−	1.29050i	−0.950163	−	0.311753i	$-0.899084\pi$
$373$	−14.3897	−	24.9236i	−0.745068	−	1.29050i	0.205095	−	0.978742i	$-0.434250\pi$
$374$	−14.8623	−	84.2882i	−0.768510	−	4.35844i
$375$	−4.37411	−	3.67032i	−0.225878	−	0.189534i
$376$	1.80699	−	1.51624i	0.0931882	−	0.0781942i
$377$	−0.436092	+	2.47320i	−0.0224599	+	0.127376i
$378$	4.71929	−	1.71768i	0.242734	−	0.0883480i
$379$	2.12215			0.109008			0.0545039	−	0.998514i	$-0.482642\pi$
$379$	2.12215			0.109008			0.0545039	+	0.998514i	$0.482642\pi$
$380$	−41.0419	−	17.9349i	−2.10540	−	0.920043i
$381$	−14.6471			−0.750392
$382$	4.58517	−	1.66887i	0.234598	−	0.0853866i
$383$	−0.451477	+	2.56045i	−0.0230694	+	0.130833i	−0.994167	−	0.107848i	$-0.965604\pi$
$383$	−0.451477	+	2.56045i	−0.0230694	+	0.130833i	0.971098	+	0.238681i	$0.0767151\pi$
$384$	−15.8411	+	13.2923i	−0.808389	+	0.678319i
$385$	22.1366	+	18.5748i	1.12819	+	0.946660i
$386$	0.0603271	+	0.342132i	0.00307057	+	0.0174141i
$387$	2.30575	+	3.99368i	0.117208	+	0.203010i
$388$	0.762432	−	1.32057i	0.0387066	−	0.0670418i
$389$	18.5833	+	6.76377i	0.942211	+	0.342937i	0.767039	−	0.641601i	$-0.221729\pi$
$389$	18.5833	+	6.76377i	0.942211	+	0.342937i	0.175172	+	0.984538i	$0.443952\pi$
$390$	−4.45869	−	1.62283i	−0.225774	−	0.0821752i
$391$	−7.27795	+	12.6058i	−0.368062	+	0.637502i
$392$	4.91203	+	8.50788i	0.248095	+	0.429713i
$393$	1.00872	+	5.72076i	0.0508834	+	0.288574i
$394$	−11.8827	−	9.97077i	−0.598642	−	0.502320i
$395$	−11.1742	+	9.37629i	−0.562237	+	0.471773i
$396$	−3.05541	+	17.3281i	−0.153540	+	0.870770i
$397$	0.547704	−	0.199348i	0.0274885	−	0.0100050i	−0.328239	−	0.944595i	$-0.606455\pi$
$397$	0.547704	−	0.199348i	0.0274885	−	0.0100050i	0.355728	+	0.934590i	$0.384233\pi$
$398$	18.3374			0.919170
$399$	−9.20138	−	0.579694i	−0.460645	−	0.0290210i
$400$	5.83185			0.291592
$401$	−31.2094	+	11.3593i	−1.55852	+	0.567256i	−0.970397	−	0.241515i	$-0.922356\pi$
$401$	−31.2094	+	11.3593i	−1.55852	+	0.567256i	−0.588125	+	0.808770i	$0.700134\pi$
$402$	−5.11633	+	29.0161i	−0.255179	+	1.44719i
$403$	1.93152	−	1.62074i	0.0962160	−	0.0807348i
$404$	44.1524	+	37.0483i	2.19667	+	1.84322i
$405$	0.490491	+	2.78171i	0.0243727	+	0.138224i
$406$	−8.91380	−	15.4392i	−0.442384	−	0.766232i
$407$	−9.30803	+	16.1220i	−0.461382	+	0.799137i
$408$	−27.2334	−	9.91213i	−1.34825	−	0.490724i
$409$	3.31138	+	1.20525i	0.163737	+	0.0595955i	0.422588	−	0.906322i	$-0.361122\pi$
$409$	3.31138	+	1.20525i	0.163737	+	0.0595955i	−0.258851	+	0.965917i	$0.583344\pi$
$410$	13.0103	−	22.5345i	0.642534	−	1.11290i
$411$	−0.585635	−	1.01435i	−0.0288872	−	0.0500342i
$412$	−0.457659	−	2.59552i	−0.0225473	−	0.127872i
$413$	−0.584154	−	0.490163i	−0.0287443	−	0.0241193i
$414$	3.55262	−	2.98100i	0.174602	−	0.146508i
$415$	4.08476	−	23.1658i	0.200513	−	1.13717i
$416$	2.07986	−	0.757007i	0.101974	−	0.0371153i
$417$	21.2642			1.04131
$418$	27.7064	−	41.6938i	1.35517	−	2.03931i
$419$	−19.8585			−0.970149			−0.485075	−	0.874473i	$-0.661208\pi$
$419$	−19.8585			−0.970149			−0.485075	+	0.874473i	$0.661208\pi$
$420$	20.4231	−	7.43339i	0.996544	−	0.362712i
$421$	4.99148	−	28.3081i	0.243270	−	1.37965i	−0.581207	−	0.813756i	$-0.697419\pi$
$421$	4.99148	−	28.3081i	0.243270	−	1.37965i	0.824477	−	0.565896i	$-0.191470\pi$
$422$	−39.5452	+	33.1824i	−1.92503	+	1.61529i
$423$	0.464664	+	0.389899i	0.0225927	+	0.0189576i
$424$	−2.08983	−	11.8520i	−0.101491	−	0.575585i
$425$	−11.0985	−	19.2232i	−0.538358	−	0.932464i
$426$	6.87595	−	11.9095i	0.333141	−	0.577017i
$427$	−7.42248	−	2.70156i	−0.359199	−	0.130738i
$428$	30.1185	+	10.9622i	1.45583	+	0.529879i
$429$	1.71095	−	2.96345i	0.0826053	−	0.143077i
$430$	15.4642	+	26.7848i	0.745751	+	1.29168i
$431$	−6.09671	−	34.5761i	−0.293668	−	1.66547i	−0.672567	−	0.740036i	$-0.734808\pi$
$431$	−6.09671	−	34.5761i	−0.293668	−	1.66547i	0.378899	−	0.925438i	$-0.376303\pi$
$432$	1.49991	+	1.25857i	0.0721642	+	0.0605530i
$433$	−19.9160	+	16.7115i	−0.957100	+	0.803102i	−0.980479	−	0.196624i	$-0.937002\pi$
$433$	−19.9160	+	16.7115i	−0.957100	+	0.803102i	0.0233788	+	0.999727i	$0.492558\pi$
$434$	−3.10814	+	17.6272i	−0.149196	+	0.846131i
$435$	9.42211	−	3.42937i	0.451755	−	0.164426i
$436$	62.6134			2.99864
$437$	−8.16748	+	2.40306i	−0.390703	+	0.114954i
$438$	14.8294			0.708575
$439$	−10.2885	+	3.74471i	−0.491043	+	0.178725i	−0.575661	−	0.817688i	$-0.695255\pi$
$439$	−10.2885	+	3.74471i	−0.491043	+	0.178725i	0.0846180	+	0.996413i	$0.473033\pi$
$440$	−9.22586	+	52.3224i	−0.439826	+	2.49437i
$441$	−1.93521	+	1.62384i	−0.0921531	+	0.0773256i
$442$	9.58991	+	8.04689i	0.456145	+	0.382752i
$443$	0.605848	+	3.43594i	0.0287847	+	0.163246i	0.995812	−	0.0914276i	$-0.0291430\pi$
$443$	0.605848	+	3.43594i	0.0287847	+	0.163246i	−0.967027	+	0.254674i	$0.918032\pi$
$444$	7.00061	+	12.1254i	0.332234	+	0.575447i
$445$	−2.80266	+	4.85434i	−0.132859	+	0.230118i
$446$	32.6810	+	11.8949i	1.54749	+	0.563240i
$447$	−19.2560	−	7.00860i	−0.910776	−	0.331496i
$448$	−11.9974	+	20.7801i	−0.566825	+	0.981770i
$449$	3.97227	+	6.88017i	0.187463	+	0.324695i	0.944404	−	0.328788i	$-0.106640\pi$
$449$	3.97227	+	6.88017i	0.187463	+	0.324695i	−0.756941	+	0.653484i	$0.773307\pi$
$450$	1.22806	+	6.96470i	0.0578915	+	0.328319i
$451$	14.3753	+	12.0623i	0.676907	+	0.567992i
$452$	19.9927	−	16.7759i	0.940380	−	0.789072i
$453$	−0.384712	+	2.18181i	−0.0180754	+	0.102511i
$454$	39.3310	−	14.3153i	1.84590	−	0.671852i
$455$	−4.22671			−0.198151
$456$	−7.53566	−	15.1838i	−0.352890	−	0.711044i
$457$	−34.6494			−1.62083			−0.810416	−	0.585855i	$-0.800759\pi$
$457$	−34.6494			−1.62083			−0.810416	+	0.585855i	$0.800759\pi$
$458$	−37.9460	+	13.8112i	−1.77310	+	0.645356i
$459$	1.29411	−	7.33924i	0.0604037	−	0.342566i
$460$	15.3742	−	12.9005i	0.716826	−	0.601488i
$461$	8.91270	+	7.47864i	0.415106	+	0.348315i	0.826298	−	0.563234i	$-0.190443\pi$
$461$	8.91270	+	7.47864i	0.415106	+	0.348315i	−0.411192	+	0.911549i	$0.634887\pi$
$462$	4.21815	+	23.9223i	0.196246	+	1.11297i
$463$	10.7993	+	18.7049i	0.501886	+	0.869291i	0.999998	+	0.00217872i	$0.000693509\pi$
$463$	10.7993	+	18.7049i	0.501886	+	0.869291i	−0.498112	+	0.867113i	$0.665973\pi$
$464$	3.47521	−	6.01925i	0.161333	−	0.279437i
$465$	−9.45989	−	3.44312i	−0.438692	−	0.159671i
$466$	38.2757	+	13.9312i	1.77309	+	0.645351i
$467$	−3.14527	+	5.44777i	−0.145546	+	0.252093i	−0.929576	−	0.368629i	$-0.879827\pi$
$467$	−3.14527	+	5.44777i	−0.145546	+	0.252093i	0.784031	+	0.620722i	$0.213161\pi$
$468$	−1.28681	−	2.22882i	−0.0594829	−	0.103027i
$469$	4.55764	+	25.8476i	0.210452	+	1.19353i
$470$	3.11641	+	2.61498i	0.143749	+	0.120620i
$471$	9.75291	−	8.18366i	0.449390	−	0.377083i
$472$	0.243457	−	1.38071i	0.0112060	−	0.0635526i
$473$	−20.9599	+	7.62878i	−0.963737	+	0.350772i
$474$	−12.2619			−0.563208
$475$	3.05392	−	12.6187i	0.140123	−	0.578983i
$476$	−57.3422			−2.62828
$477$	2.90811	−	1.05847i	0.133153	−	0.0484638i
$478$	−0.518005	+	2.93775i	−0.0236930	+	0.134370i
$479$	19.4038	−	16.2818i	0.886584	−	0.743932i	−0.0809381	−	0.996719i	$-0.525792\pi$
$479$	19.4038	−	16.2818i	0.886584	−	0.743932i	0.967522	+	0.252787i	$0.0813472\pi$
$480$	−6.76950	−	5.68029i	−0.308984	−	0.259268i
$481$	−0.472828	−	2.68154i	−0.0215591	−	0.122268i
$482$	−18.2150	−	31.5493i	−0.829670	−	1.43703i
$483$	2.06560	−	3.57772i	0.0939879	−	0.162792i
$484$	−42.3709	−	15.4217i	−1.92595	−	0.700988i
$485$	1.11260	+	0.404953i	0.0505205	+	0.0183880i
$486$	−1.18720	+	2.05630i	−0.0538526	+	0.0932754i
$487$	−10.7419	−	18.6056i	−0.486763	−	0.843099i	0.513121	−	0.858316i	$-0.328489\pi$
$487$	−10.7419	−	18.6056i	−0.486763	−	0.843099i	−0.999884	+	0.0152176i	$0.995156\pi$
$488$	−2.52181	−	14.3019i	−0.114157	−	0.647417i
$489$	12.5764	+	10.5528i	0.568723	+	0.477215i
$490$	−12.9791	+	10.8908i	−0.586336	+	0.491994i
$491$	4.85306	−	27.5231i	0.219015	−	1.24210i	−0.654785	−	0.755815i	$-0.727241\pi$
$491$	4.85306	−	27.5231i	0.219015	−	1.24210i	0.873801	−	0.486284i	$-0.161648\pi$
$492$	13.2626	−	4.82718i	0.597922	−	0.217626i
$493$	−26.4546			−1.19146
$494$	0.815566	+	7.27657i	0.0366941	+	0.327388i
$495$	−13.6622			−0.614071
$496$	−6.55746	+	2.38672i	−0.294439	+	0.107167i
$497$	2.12723	−	12.0641i	0.0954193	−	0.541150i
$498$	15.1476	−	12.7104i	0.678782	−	0.569565i
$499$	−16.7297	−	14.0379i	−0.748926	−	0.628424i	0.186292	−	0.982494i	$-0.440353\pi$
$499$	−16.7297	−	14.0379i	−0.748926	−	0.628424i	−0.935219	+	0.354071i	$0.884797\pi$
$500$	−3.60699	−	20.4563i	−0.161310	−	0.914832i
$501$	−4.79808	−	8.31053i	−0.214363	−	0.371287i
$502$	8.95910	−	15.5176i	0.399864	−	0.692585i
$503$	24.6753	+	8.98107i	1.10022	+	0.400446i	0.827396	−	0.561619i	$-0.189821\pi$
$503$	24.6753	+	8.98107i	1.10022	+	0.400446i	0.272820	+	0.962065i	$0.412044\pi$
$504$	7.72925	+	2.81322i	0.344288	+	0.125311i
$505$	−22.3765	+	38.7572i	−0.995741	+	1.72467i
$506$	11.2157	+	19.4261i	0.498597	+	0.863595i
$507$	−2.17051	−	12.3096i	−0.0963959	−	0.546688i
$508$	−40.8172	−	34.2497i	−1.81097	−	1.51958i
$509$	−13.6761	+	11.4756i	−0.606182	+	0.508647i	−0.893426	−	0.449211i	$-0.851705\pi$
$509$	−13.6761	+	11.4756i	−0.606182	+	0.508647i	0.287244	+	0.957857i	$0.407261\pi$
$510$	8.67931	−	49.2228i	0.384326	−	2.17962i
$511$	12.4134	−	4.51810i	0.549135	−	0.199869i
$512$	−21.3541			−0.943727
$513$	3.50867	−	2.58635i	0.154912	−	0.114190i
$514$	−15.4166			−0.679995
$515$	1.92300	−	0.699915i	0.0847375	−	0.0308419i
$516$	−2.91308	+	16.5209i	−0.128241	+	0.727291i
$517$	−2.24750	+	1.88588i	−0.0988449	+	0.0829407i
$518$	14.8072	+	12.4247i	0.650590	+	0.545910i
$519$	−3.90096	−	22.1234i	−0.171233	−	0.971111i
$520$	−3.88555	−	6.72996i	−0.170392	−	0.295128i
$521$	14.6855	−	25.4361i	0.643385	−	1.11438i	−0.341287	−	0.939959i	$-0.610863\pi$
$521$	14.6855	−	25.4361i	0.643385	−	1.11438i	0.984672	−	0.174416i	$-0.0558039\pi$
$522$	7.92031	+	2.88276i	0.346663	+	0.126175i
$523$	−25.8062	−	9.39271i	−1.12843	−	0.410714i	−0.290707	−	0.956812i	$-0.593890\pi$
$523$	−25.8062	−	9.39271i	−1.12843	−	0.410714i	−0.837721	+	0.546098i	$0.816113\pi$
$524$	−10.5660	+	18.3009i	−0.461578	+	0.799477i
$525$	3.14994	+	5.45586i	0.137475	+	0.238113i
$526$	−1.36712	−	7.75335i	−0.0596095	−	0.338062i
$527$	20.3467	+	17.0729i	0.886315	+	0.743707i
$528$	−7.25478	+	6.08749i	−0.315724	+	0.264924i
$529$	−3.33146	+	18.8937i	−0.144846	+	0.821464i
$530$	19.5041	−	7.09891i	0.847204	−	0.308357i
$531$	0.360526			0.0156455
$532$	−24.2861	−	23.1313i	−1.05294	−	1.00287i
$533$	−2.74479			−0.118890
$534$	−4.42772	+	1.61156i	−0.191606	+	0.0697390i
$535$	−4.32154	+	24.5087i	−0.186837	+	1.05960i
$536$	−36.9660	+	31.0182i	−1.59669	+	1.33978i
$537$	10.9541	+	9.19159i	0.472705	+	0.396646i
$538$	−10.4844	−	59.4600i	−0.452014	−	2.56350i
$539$	−6.10950	−	10.5820i	−0.263155	−	0.455798i
$540$	−5.13770	+	8.89877i	−0.221092	+	0.382942i
$541$	23.6467	+	8.60669i	1.01665	+	0.370030i	0.795983	−	0.605319i	$-0.206954\pi$
$541$	23.6467	+	8.60669i	1.01665	+	0.370030i	0.220667	+	0.975349i	$0.429177\pi$
$542$	20.6305	+	7.50890i	0.886157	+	0.322535i
$543$	−12.9803	+	22.4826i	−0.557040	+	0.964822i
$544$	11.6577	+	20.1917i	0.499819	+	0.865712i
$545$	8.44227	+	47.8785i	0.361627	+	2.05089i
$546$	−2.72177	−	2.28383i	−0.116481	−	0.0977391i
$547$	13.2974	−	11.1578i	0.568554	−	0.477073i	−0.312612	−	0.949881i	$-0.601204\pi$
$547$	13.2974	−	11.1578i	0.568554	−	0.477073i	0.881166	+	0.472808i	$0.156759\pi$
$548$	0.739888	−	4.19611i	0.0316064	−	0.179249i
$549$	3.50924	−	1.27726i	0.149771	−	0.0545120i
$550$	−34.2067			−1.45858
$551$	−11.2043	−	10.6715i	−0.477319	−	0.454623i
$552$	7.59548			0.323285
$553$	−10.2642	+	3.73586i	−0.436478	+	0.158865i
$554$	4.73181	−	26.8354i	0.201035	−	1.14013i
$555$	−8.32802	+	6.98804i	−0.353505	+	0.296626i
$556$	59.2573	+	49.7228i	2.51307	+	2.10871i
$557$	−5.22143	−	29.6122i	−0.221239	−	1.25471i	−0.869745	−	0.493501i	$-0.835717\pi$
$557$	−5.22143	−	29.6122i	−0.221239	−	1.25471i	0.648506	−	0.761209i	$-0.275394\pi$
$558$	−4.23121	−	7.32867i	−0.179121	−	0.310247i
$559$	1.63124	−	2.82540i	0.0689942	−	0.119502i
$560$	10.9924	+	4.00090i	0.464513	+	0.169069i
$561$	33.8724	+	12.3285i	1.43009	+	0.520512i
$562$	−14.3234	+	24.8088i	−0.604194	+	1.04650i
$563$	23.2167	+	40.2124i	0.978465	+	1.69475i	0.667991	+	0.744170i	$0.267155\pi$
$563$	23.2167	+	40.2124i	0.978465	+	1.69475i	0.310475	+	0.950582i	$0.399512\pi$
$564$	0.383172	+	2.17308i	0.0161345	+	0.0915031i
$565$	15.5237	+	13.0259i	0.653085	+	0.548004i
$566$	39.4171	−	33.0749i	1.65683	−	1.39024i
$567$	−0.367288	+	2.08299i	−0.0154246	+	0.0874774i
$568$	21.1646	−	7.70327i	0.888045	−	0.323222i
$569$	−43.8230			−1.83716			−0.918579	−	0.395238i	$-0.870662\pi$
$569$	−43.8230			−1.83716			−0.918579	+	0.395238i	$0.870662\pi$
$570$	23.5320	−	17.3461i	0.985645	−	0.726550i
$571$	30.1697			1.26256			0.631281	−	0.775555i	$-0.282530\pi$
$571$	30.1697			1.26256			0.631281	+	0.775555i	$0.282530\pi$
$572$	11.6974	−	4.25752i	0.489095	−	0.178016i
$573$	−0.356850	+	2.02379i	−0.0149076	+	0.0845452i
$574$	14.9261	−	12.5245i	0.623005	−	0.522764i
$575$	4.45646	+	3.73941i	0.185847	+	0.155944i
$576$	−1.96994	−	11.1721i	−0.0820807	−	0.465503i
$577$	1.70615	+	2.95515i	0.0710281	+	0.123024i	0.899352	−	0.437225i	$-0.144039\pi$
$577$	1.70615	+	2.95515i	0.0710281	+	0.123024i	−0.828324	+	0.560249i	$0.810705\pi$
$578$	−45.7538	+	79.2479i	−1.90311	+	3.29628i
$579$	−0.137491	−	0.0500425i	−0.00571392	−	0.00207970i
$580$	34.2757	+	12.4753i	1.42322	+	0.518011i
$581$	8.80729	−	15.2547i	0.365388	−	0.632870i
$582$	0.497642	+	0.861941i	0.0206279	+	0.0357286i
$583$	2.59930	+	14.7413i	0.107652	+	0.610524i
$584$	18.6053	+	15.6117i	0.769894	+	0.646018i
$585$	1.53081	−	1.28450i	0.0632911	−	0.0531075i
$586$	−0.441385	+	2.50322i	−0.0182335	+	0.103407i
$587$	12.1198	−	4.41125i	0.500239	−	0.182072i	−0.0795627	−	0.996830i	$-0.525352\pi$
$587$	12.1198	−	4.41125i	0.500239	−	0.182072i	0.579801	+	0.814758i	$0.303130\pi$
$588$	−9.18997			−0.378988
$589$	1.73037	+	15.4385i	0.0712986	+	0.636133i
$590$	2.41798			0.0995465
$591$	6.13892	−	2.23438i	0.252522	−	0.0919103i
$592$	−1.30860	+	7.42145i	−0.0537832	+	0.305020i
$593$	9.10425	−	7.63938i	0.373867	−	0.313712i	−0.436422	−	0.899742i	$-0.643755\pi$
$593$	9.10425	−	7.63938i	0.373867	−	0.313712i	0.810289	+	0.586030i	$0.199310\pi$
$594$	−8.79770	−	7.38215i	−0.360974	−	0.302893i
$595$	−7.73155	−	43.8478i	−0.316963	−	1.79758i
$596$	−37.2725	−	64.5579i	−1.52674	−	2.64439i
$597$	−3.86147	+	6.68826i	−0.158039	+	0.273732i
$598$	−3.08309	−	1.12215i	−0.126077	−	0.0458882i
$599$	−16.7418	−	6.09353i	−0.684053	−	0.248975i	−0.0234662	−	0.999725i	$-0.507470\pi$
$599$	−16.7418	−	6.09353i	−0.684053	−	0.248975i	−0.660587	+	0.750750i	$0.729692\pi$
$600$	−5.79138	+	10.0310i	−0.236432	+	0.409512i
$601$	−11.0420	−	19.1253i	−0.450413	−	0.780138i	0.547998	−	0.836479i	$-0.315390\pi$
$601$	−11.0420	−	19.1253i	−0.450413	−	0.780138i	−0.998412	+	0.0563409i	$0.982057\pi$
$602$	4.02165	+	22.8079i	0.163910	+	0.929581i
$603$	−9.50577	−	7.97629i	−0.387105	−	0.324819i
$604$	−6.17389	+	5.18051i	−0.251212	+	0.210792i
$605$	6.07958	−	34.4790i	0.247170	−	1.40177i
$606$	−35.3511	+	12.8667i	−1.43604	+	0.522675i
$607$	28.2599			1.14703			0.573517	−	0.819194i	$-0.305579\pi$
$607$	28.2599			1.14703			0.573517	+	0.819194i	$0.305579\pi$
$608$	−3.20777	+	13.2544i	−0.130092	+	0.537536i
$609$	7.50824			0.304249
$610$	23.5357	−	8.56631i	0.952934	−	0.346840i
$611$	0.0745180	−	0.422613i	0.00301468	−	0.0170971i
$612$	20.7679	−	17.4263i	0.839492	−	0.704418i
$613$	15.7130	+	13.1848i	0.634642	+	0.532528i	0.902368	−	0.430967i	$-0.141828\pi$
$613$	15.7130	+	13.1848i	0.634642	+	0.532528i	−0.267725	+	0.963495i	$0.586272\pi$
$614$	12.4945	+	70.8596i	0.504236	+	2.85966i
$615$	5.47940	+	9.49060i	0.220951	+	0.382698i
$616$	−19.8922	+	34.4543i	−0.801479	+	1.38820i
$617$	−43.0055	−	15.6527i	−1.73134	−	0.630155i	−0.732613	−	0.680645i	$-0.761699\pi$
$617$	−43.0055	−	15.6527i	−1.73134	−	0.630155i	−0.998725	+	0.0504900i	$0.983922\pi$
$618$	1.61649	+	0.588356i	0.0650249	+	0.0236671i
$619$	13.7331	−	23.7864i	0.551979	−	0.956055i	−0.446153	−	0.894957i	$-0.647206\pi$
$619$	13.7331	−	23.7864i	0.551979	−	0.956055i	0.998132	−	0.0610984i	$-0.0194603\pi$
$620$	−18.3109	−	31.7154i	−0.735382	−	1.27372i
$621$	0.339164	+	1.92349i	0.0136102	+	0.0771872i
$622$	−5.35973	−	4.49734i	−0.214905	−	0.180327i
$623$	−3.21536	+	2.69801i	−0.128821	+	0.108093i
$624$	0.240539	−	1.36417i	0.00962928	−	0.0546104i
$625$	29.1502	−	10.6098i	1.16601	−	0.424393i
$626$	6.87518			0.274788
$627$	9.37273	+	18.8853i	0.374311	+	0.754207i
$628$	46.3147			1.84816
$629$	26.9534	−	9.81022i	1.07470	−	0.391159i
$630$	−2.46332	+	13.9702i	−0.0981412	+	0.556586i
$631$	−35.6858	+	29.9440i	−1.42063	+	1.19205i	−0.469629	+	0.882864i	$0.655612\pi$
$631$	−35.6858	+	29.9440i	−1.42063	+	1.19205i	−0.951001	+	0.309187i	$0.899943\pi$
$632$	−15.3841	−	12.9088i	−0.611948	−	0.513485i
$633$	−3.77533	−	21.4110i	−0.150056	−	0.851010i
$634$	−27.7321	−	48.0334i	−1.10138	−	1.90765i
$635$	20.6862	−	35.8296i	0.820907	−	1.42185i
$636$	10.5791	+	3.85048i	0.419489	+	0.152682i
$637$	1.67945	+	0.611270i	0.0665422	+	0.0242194i
$638$	−20.3839	+	35.3059i	−0.807006	+	1.39778i
$639$	2.89586	+	5.01578i	0.114559	+	0.198421i
$640$	−10.1429	−	57.5233i	−0.400934	−	2.27381i
$641$	−15.4686	−	12.9797i	−0.610973	−	0.512667i	0.283979	−	0.958831i	$-0.408345\pi$
$641$	−15.4686	−	12.9797i	−0.610973	−	0.512667i	−0.894951	+	0.446164i	$0.852790\pi$
$642$	−16.0257	+	13.4472i	−0.632484	+	0.530717i
$643$	−4.85608	+	27.5402i	−0.191505	+	1.08608i	0.725803	+	0.687902i	$0.241468\pi$
$643$	−4.85608	+	27.5402i	−0.191505	+	1.08608i	−0.917308	+	0.398178i	$0.869643\pi$
$644$	14.1221	−	5.14003i	0.556490	−	0.202546i
$645$	−13.0258			−0.512889
$646$	−73.9951	+	21.7711i	−2.91130	+	0.856571i
$647$	3.34353			0.131448			0.0657239	−	0.997838i	$-0.479064\pi$
$647$	3.34353			0.131448			0.0657239	+	0.997838i	$0.479064\pi$
$648$	−3.65428	+	1.33005i	−0.143554	+	0.0522492i
$649$	−0.302808	+	1.71731i	−0.0118863	+	0.0674104i
$650$	3.83275	−	3.21606i	0.150333	−	0.126144i
$651$	−5.77471	−	4.84555i	−0.226329	−	0.189912i
$652$	10.3707	+	58.8154i	0.406150	+	2.30339i
$653$	20.4093	+	35.3499i	0.798676	+	1.38335i	0.920479	+	0.390793i	$0.127799\pi$
$653$	20.4093	+	35.3499i	0.798676	+	1.38335i	−0.121803	+	0.992554i	$0.538868\pi$
$654$	−20.4340	+	35.3927i	−0.799033	+	1.38396i
$655$	−15.4187	−	5.61196i	−0.602460	−	0.219277i
$656$	7.13836	+	2.59815i	0.278706	+	0.101441i
$657$	−3.12276	+	5.40877i	−0.121830	+	0.211016i
$658$	1.52316	+	2.63819i	0.0593790	+	0.102848i
$659$	−2.77753	−	15.7521i	−0.108197	−	0.613616i	−0.989895	−	0.141802i	$-0.954710\pi$
$659$	−2.77753	−	15.7521i	−0.108197	−	0.613616i	0.881698	−	0.471814i	$-0.156401\pi$
$660$	−38.0727	−	31.9468i	−1.48198	−	1.24353i
$661$	1.12003	−	0.939813i	0.0435639	−	0.0365545i	−0.620746	−	0.784012i	$-0.713170\pi$
$661$	1.12003	−	0.939813i	0.0435639	−	0.0365545i	0.664310	+	0.747457i	$0.268726\pi$
$662$	−1.21087	+	6.86716i	−0.0470617	+	0.266900i
$663$	−4.95441	+	1.80326i	−0.192413	+	0.0700327i
$664$	32.3856			1.25680
$665$	14.4132	−	21.6896i	0.558922	−	0.841089i
$666$	−9.13865			−0.354116
$667$	6.51519	−	2.37133i	0.252269	−	0.0918185i
$668$	6.06187	−	34.3786i	0.234541	−	1.33015i
$669$	−11.2204	+	9.41504i	−0.433806	+	0.364006i
$670$	−63.7533	−	53.4953i	−2.46300	−	2.06671i
$671$	3.13659	+	17.7885i	0.121087	+	0.686717i
$672$	−3.30863	−	5.73072i	−0.127633	−	0.221067i
$673$	−4.78112	+	8.28113i	−0.184298	+	0.319214i	−0.943340	−	0.331828i	$-0.892335\pi$
$673$	−4.78112	+	8.28113i	−0.184298	+	0.319214i	0.759041	+	0.651042i	$0.225668\pi$
$674$	9.08777	+	3.30768i	0.350048	+	0.127407i
$675$	−2.79887	−	1.01870i	−0.107728	−	0.0392099i
$676$	22.7353	−	39.3787i	0.874435	−	1.51457i
$677$	−16.4949	−	28.5701i	−0.633952	−	1.09804i	−0.986736	−	0.162332i	$-0.948098\pi$
$677$	−16.4949	−	28.5701i	−0.633952	−	1.09804i	0.352785	−	0.935705i	$-0.385235\pi$
$678$	2.95805	+	16.7759i	0.113603	+	0.644275i
$679$	0.679176	+	0.569896i	0.0260644	+	0.0218706i
$680$	62.7090	−	52.6191i	2.40478	−	2.01785i
$681$	−3.06101	+	17.3599i	−0.117298	+	0.665231i
$682$	38.4628	−	13.9993i	1.47282	−	0.536062i
$683$	35.6179			1.36288			0.681441	−	0.731873i	$-0.261354\pi$
$683$	35.6179			1.36288			0.681441	+	0.731873i	$0.261354\pi$
$684$	15.8254	+	0.997014i	0.605100	+	0.0381218i
$685$	3.30839			0.126407
$686$	−44.9571	+	16.3631i	−1.71647	+	0.624744i
$687$	2.95322	−	16.7485i	0.112672	−	0.638997i
$688$	−6.91682	+	5.80390i	−0.263701	+	0.221272i
$689$	−1.67720	−	1.40734i	−0.0638962	−	0.0536153i
$690$	2.27470	+	12.9005i	0.0865965	+	0.491113i
$691$	0.215521	+	0.373292i	0.00819879	+	0.0142007i	0.870096	−	0.492883i	$-0.164057\pi$
$691$	0.215521	+	0.373292i	0.00819879	+	0.0142007i	−0.861897	+	0.507084i	$0.830724\pi$
$692$	40.8611	−	70.7735i	1.55331	−	2.69040i
$693$	−9.61352	−	3.49904i	−0.365188	−	0.132917i
$694$	4.39477	+	1.59956i	0.166823	+	0.0607186i
$695$	−30.0317	+	52.0164i	−1.13917	+	1.97309i
$696$	6.90220	+	11.9550i	0.261627	+	0.453151i
$697$	−5.02080	−	28.4744i	−0.190176	−	1.07854i
$698$	−10.4835	−	8.79667i	−0.396805	−	0.332959i
$699$	−13.1412	+	11.0268i	−0.497047	+	0.417072i
$700$	−3.97962	+	22.5695i	−0.150415	+	0.853048i
$701$	−44.3384	+	16.1379i	−1.67464	+	0.609519i	−0.992560	−	0.121759i	$-0.961146\pi$
$701$	−44.3384	+	16.1379i	−1.67464	+	0.609519i	−0.682079	+	0.731278i	$0.738924\pi$
$702$	1.67981			0.0634004
$703$	15.3729	+	6.71782i	0.579799	+	0.253367i
$704$	54.8709			2.06803
$705$	−1.61002	+	0.585999i	−0.0606369	+	0.0220700i
$706$	−5.78614	+	32.8148i	−0.217764	+	1.23500i
$707$	−25.6715	+	21.5410i	−0.965478	+	0.810132i
$708$	1.00468	+	0.843030i	0.0377584	+	0.0316830i
$709$	−3.33153	−	18.8941i	−0.125118	−	0.709581i	−0.981238	−	0.192803i	$-0.938242\pi$
$709$	−3.33153	−	18.8941i	−0.125118	−	0.709581i	0.856119	−	0.516778i	$-0.172869\pi$
$710$	19.4220	+	33.6398i	0.728893	+	1.26248i
$711$	2.58210	−	4.47233i	0.0968364	−	0.167726i
$712$	−7.25172	−	2.63941i	−0.271770	−	0.0989161i
$713$	−6.54132	−	2.38084i	−0.244974	−	0.0891633i
$714$	18.7137	−	32.4132i	0.700344	−	1.21303i
$715$	4.83278	+	8.37062i	0.180736	+	0.313043i
$716$	9.03300	+	51.2287i	0.337579	+	1.91451i
$717$	−0.962417	−	0.807563i	−0.0359421	−	0.0301590i
$718$	−29.0703	+	24.3929i	−1.08490	+	0.910336i
$719$	−1.57227	+	8.91681i	−0.0586359	+	0.332541i	−0.999988	−	0.00488492i	$-0.998445\pi$
$719$	−1.57227	+	8.91681i	−0.0586359	+	0.332541i	0.941352	+	0.337426i	$0.109556\pi$
$720$	−5.19704	+	1.89157i	−0.193682	+	0.0704946i
$721$	1.53239			0.0570692
$722$	−40.1213	−	20.6283i	−1.49316	−	0.767704i
$723$	15.3428			0.570604
$724$	−88.7444	+	32.3003i	−3.29816	+	1.20043i
$725$	−1.83598	+	10.4124i	−0.0681866	+	0.386706i
$726$	22.5451	−	18.9176i	0.836726	−	0.702097i
$727$	−1.24559	−	1.04517i	−0.0461963	−	0.0387633i	0.619397	−	0.785078i	$-0.287377\pi$
$727$	−1.24559	−	1.04517i	−0.0461963	−	0.0387633i	−0.665593	+	0.746314i	$0.731822\pi$
$728$	−1.01048	−	5.73072i	−0.0374509	−	0.212395i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−20.9437	+	36.2755i	−0.775161	+	1.34262i
$731$	32.2945	+	11.7542i	1.19445	+	0.434746i
$732$	12.7659	+	4.64641i	0.471841	+	0.171736i
$733$	17.7006	−	30.6584i	0.653787	−	1.13239i	−0.328409	−	0.944536i	$-0.606512\pi$
$733$	17.7006	−	30.6584i	0.653787	−	1.13239i	0.982196	−	0.187857i	$-0.0601543\pi$
$734$	−34.5953	−	59.9207i	−1.27693	−	2.21172i
$735$	−1.23910	−	7.02728i	−0.0457048	−	0.259205i
$736$	−4.68097	−	3.92780i	−0.172543	−	0.144781i
$737$	45.9778	−	38.5799i	1.69361	−	1.42111i
$738$	−1.59966	+	9.07213i	−0.0588843	+	0.333950i
$739$	−25.1981	+	9.17137i	−0.926928	+	0.337374i	−0.760991	−	0.648762i	$-0.775287\pi$
$739$	−25.1981	+	9.17137i	−0.926928	+	0.337374i	−0.165937	+	0.986136i	$0.553065\pi$
$740$	−39.5482			−1.45382
$741$	−2.82575	−	1.23483i	−0.103807	−	0.0453626i
$742$	15.5423			0.570577
$743$	20.9604	−	7.62897i	0.768963	−	0.279880i	0.0724005	−	0.997376i	$-0.476934\pi$
$743$	20.9604	−	7.62897i	0.768963	−	0.279880i	0.696563	+	0.717496i	$0.254712\pi$
$744$	2.40672	−	13.6492i	0.0882347	−	0.500404i
$745$	44.3398	−	37.2055i	1.62449	−	1.36311i
$746$	52.3467	+	43.9241i	1.91655	+	1.60817i
$747$	1.44613	+	8.20139i	0.0529110	+	0.300073i
$748$	65.5646	+	113.561i	2.39728	+	4.15221i
$749$	−9.31782	+	16.1389i	−0.340466	+	0.589704i
$750$	12.7402	+	4.63706i	0.465207	+	0.169321i
$751$	−40.9886	−	14.9186i	−1.49570	−	0.544389i	−0.540754	−	0.841181i	$-0.681861\pi$
$751$	−40.9886	−	14.9186i	−1.49570	−	0.544389i	−0.954942	+	0.296792i	$0.904083\pi$
$752$	−0.593834	+	1.02855i	−0.0216549	+	0.0375074i
$753$	3.77320	+	6.53537i	0.137503	+	0.238162i
$754$	−1.03546	−	5.87238i	−0.0377092	−	0.213859i
$755$	−4.79381	−	4.02248i	−0.174464	−	0.146393i
$756$	−5.89425	+	4.94587i	−0.214372	+	0.179879i
$757$	4.88251	−	27.6901i	0.177458	−	1.00641i	−0.757810	−	0.652475i	$-0.773731\pi$
$757$	4.88251	−	27.6901i	0.177458	−	1.00641i	0.935268	−	0.353939i	$-0.115158\pi$
$758$	−4.73497	+	1.72339i	−0.171982	+	0.0625963i
$759$	−9.44713			−0.342909
$760$	47.7851	+	3.01050i	1.73335	+	0.109202i
$761$	−33.0309			−1.19737			−0.598685	−	0.800985i	$-0.704310\pi$
$761$	−33.0309			−1.19737			−0.598685	+	0.800985i	$0.704310\pi$
$762$	32.6807	−	11.8948i	1.18390	−	0.430903i
$763$	−6.32171	+	35.8522i	−0.228861	+	1.29794i
$764$	−5.72674	+	4.80531i	−0.207186	+	0.173850i
$765$	16.1255	+	13.5309i	0.583020	+	0.489212i
$766$	−1.07199	−	6.07955i	−0.0387326	−	0.219663i
$767$	−0.127530	−	0.220889i	−0.00460485	−	0.00797583i
$768$	13.2059	−	22.8733i	0.476527	−	0.825369i
$769$	−0.841766	−	0.306378i	−0.0303549	−	0.0110483i	0.326798	−	0.945094i	$-0.394030\pi$
$769$	−0.841766	−	0.306378i	−0.0303549	−	0.0110483i	−0.357153	+	0.934046i	$0.616253\pi$
$770$	−64.4759	−	23.4673i	−2.32355	−	0.845704i
$771$	3.24641	−	5.62294i	0.116916	−	0.202505i
$772$	−0.266132	−	0.460953i	−0.00957829	−	0.0165901i
$773$	−5.94588	−	33.7208i	−0.213858	−	1.21285i	−0.882876	−	0.469605i	$-0.844396\pi$
$773$	−5.94588	−	33.7208i	−0.213858	−	1.21285i	0.669018	−	0.743246i	$-0.266715\pi$
$774$	−8.38787	−	7.03826i	−0.301496	−	0.252985i
$775$	8.13186	−	6.82344i	0.292105	−	0.245105i
$776$	−0.283060	+	1.60531i	−0.0101613	+	0.0576273i
$777$	−7.64979	+	2.78429i	−0.274435	+	0.0998860i
$778$	−46.9561			−1.68346
$779$	9.35983	−	14.0851i	0.335351	−	0.504650i
$780$	7.26951			0.260290
$781$	−26.3241	+	9.58121i	−0.941952	+	0.342842i
$782$	6.00156	−	34.0365i	0.214615	−	1.21714i
$783$	−2.71929	+	2.28176i	−0.0971795	+	0.0815433i
$784$	−3.78913	−	3.17945i	−0.135326	−	0.113552i
$785$	6.24469	+	35.4154i	0.222883	+	1.26403i
$786$	−6.89648	−	11.9450i	−0.245989	−	0.426066i
$787$	−12.2366	+	21.1944i	−0.436187	+	0.755498i	−0.997392	−	0.0721791i	$-0.977005\pi$
$787$	−12.2366	+	21.1944i	−0.436187	+	0.755498i	0.561205	+	0.827677i	$0.310338\pi$
$788$	22.3322	+	8.12824i	0.795551	+	0.289557i
$789$	3.11579	+	1.13406i	0.110925	+	0.0403735i
$790$	17.3176	−	29.9950i	0.616134	−	1.06717i
$791$	7.58728	+	13.1415i	0.269772	+	0.467260i
$792$	−3.26623	−	18.5237i	−0.116060	−	0.658211i
$793$	−2.02389	−	1.69824i	−0.0718704	−	0.0603064i
$794$	−1.06015	+	0.889574i	−0.0376234	+	0.0315698i
$795$	−1.51794	+	8.60868i	−0.0538359	+	0.305319i
$796$	−26.4002	+	9.60889i	−0.935731	+	0.340578i
$797$	44.8586			1.58897			0.794486	−	0.607282i	$-0.207740\pi$
$797$	44.8586			1.58897			0.794486	+	0.607282i	$0.207740\pi$
$798$	21.0010	−	6.17897i	0.743427	−	0.218733i
$799$	4.52048			0.159923
$800$	8.75638	−	3.18706i	0.309585	−	0.112680i
$801$	0.344596	−	1.95430i	0.0121757	−	0.0690518i
$802$	60.4099	−	50.6899i	2.13315	−	1.78992i
$803$	−23.1410	−	19.4176i	−0.816629	−	0.685233i
$804$	−7.83867	−	44.4553i	−0.276448	−	1.56782i
$805$	5.83453	+	10.1057i	0.205640	+	0.356179i
$806$	−2.99344	+	5.18479i	−0.105439	+	0.182626i
$807$	23.8948	+	8.69701i	0.841138	+	0.306149i
$808$	−57.8980	−	21.0731i	−2.03684	−	0.741350i
$809$	6.52074	−	11.2943i	0.229257	−	0.397085i	−0.728331	−	0.685225i	$-0.759704\pi$
$809$	6.52074	−	11.2943i	0.229257	−	0.397085i	0.957588	+	0.288140i	$0.0930370\pi$
$810$	−3.35340	−	5.80826i	−0.117826	−	0.204081i
$811$	−4.97200	−	28.1976i	−0.174591	−	0.990153i	−0.938615	−	0.344966i	$-0.887891\pi$
$811$	−4.97200	−	28.1976i	−0.174591	−	0.990153i	0.764025	−	0.645187i	$-0.223221\pi$
$812$	20.9233	+	17.5568i	0.734265	+	0.616121i
$813$	−7.08311	+	5.94343i	−0.248415	+	0.208445i
$814$	7.67561	−	43.5305i	0.269030	−	1.52574i
$815$	−43.5760	+	15.8604i	−1.52640	+	0.555564i
$816$	14.5918			0.510816
$817$	8.93611	+	18.0055i	0.312635	+	0.629934i
$818$	−8.36717			−0.292551
$819$	1.40614	−	0.511792i	0.0491344	−	0.0178835i
$820$	−6.92265	+	39.2603i	−0.241749	+	1.37103i
$821$	9.56672	−	8.02743i	0.333881	−	0.280159i	−0.460398	−	0.887713i	$-0.652293\pi$
$821$	9.56672	−	8.02743i	0.333881	−	0.280159i	0.794279	+	0.607553i	$0.207849\pi$
$822$	2.13042	+	1.78764i	0.0743070	+	0.0623510i
$823$	−1.01151	−	5.73654i	−0.0352589	−	0.199963i	0.962090	−	0.272733i	$-0.0879274\pi$
$823$	−1.01151	−	5.73654i	−0.0352589	−	0.199963i	−0.997349	+	0.0727693i	$0.976816\pi$
$824$	1.40870	+	2.43994i	0.0490744	+	0.0849994i
$825$	7.20322	−	12.4763i	0.250784	−	0.434371i
$826$	1.70143	+	0.619269i	0.0592003	+	0.0215471i
$827$	−23.5312	−	8.56465i	−0.818259	−	0.297822i	−0.101228	−	0.994863i	$-0.532277\pi$
$827$	−23.5312	−	8.56465i	−0.818259	−	0.297822i	−0.717031	+	0.697041i	$0.754499\pi$
$828$	−3.55262	+	6.15331i	−0.123462	+	0.213842i
$829$	13.6415	+	23.6278i	0.473789	+	0.820627i	0.999550	−	0.0300055i	$-0.00955249\pi$
$829$	13.6415	+	23.6278i	0.473789	+	0.820627i	−0.525760	+	0.850633i	$0.676219\pi$
$830$	9.69887	+	55.0051i	0.336653	+	1.90925i
$831$	8.79136	+	7.37682i	0.304969	+	0.255899i
$832$	−6.14811	+	5.15888i	−0.213147	+	0.178852i
$833$	−3.26923	+	18.5407i	−0.113272	+	0.642398i
$834$	−47.4449	+	17.2685i	−1.64288	+	0.597960i
$835$	27.1056			0.938026
$836$	−18.0410	+	74.5446i	−0.623961	+	2.57818i
$837$	3.56402			0.123190
$838$	44.3084	−	16.1269i	1.53061	−	0.557096i
$839$	−3.54389	+	20.0984i	−0.122349	+	0.693874i	0.860498	+	0.509453i	$0.170152\pi$
$839$	−3.54389	+	20.0984i	−0.122349	+	0.693874i	−0.982847	+	0.184421i	$0.940959\pi$
$840$	−17.7978	+	14.9341i	−0.614082	+	0.515276i
$841$	−12.5624	−	10.5411i	−0.433186	−	0.363486i
$842$	11.8518	+	67.2149i	0.408440	+	2.31638i
$843$	−6.03240	−	10.4484i	−0.207767	−	0.359863i
$844$	39.5452	−	68.4943i	1.36120	−	2.35767i
$845$	33.1771	+	12.0755i	1.14133	+	0.415409i
$846$	−1.35340	−	0.492597i	−0.0465308	−	0.0169358i
$847$	13.1084	−	22.7044i	0.450409	−	0.780132i
$848$	3.02974	+	5.24766i	0.104042	+	0.180205i
$849$	3.76311	+	21.3416i	0.129149	+	0.732443i
$850$	40.3743	+	33.8780i	1.38483	+	1.16201i
$851$	−5.75865	+	4.83208i	−0.197404	+	0.165642i
$852$	−3.65862	+	20.7490i	−0.125342	+	0.710851i
$853$	−13.3291	+	4.85138i	−0.456378	+	0.166108i	−0.559972	−	0.828512i	$-0.689188\pi$
$853$	−13.3291	+	4.85138i	−0.456378	+	0.166108i	0.103594	+	0.994620i	$0.466966\pi$
$854$	18.7550			0.641784
$855$	1.37138	+	12.2356i	0.0469003	+	0.418450i
$856$	−34.2629			−1.17108
$857$	−29.2633	+	10.6510i	−0.999616	+	0.363831i	−0.789437	−	0.613832i	$-0.789627\pi$
$857$	−29.2633	+	10.6510i	−0.999616	+	0.363831i	−0.210180	+	0.977663i	$0.567405\pi$
$858$	−1.41088	+	8.00153i	−0.0481668	+	0.273168i
$859$	−12.6608	+	10.6237i	−0.431982	+	0.362476i	−0.832699	−	0.553726i	$-0.813205\pi$
$859$	−12.6608	+	10.6237i	−0.431982	+	0.362476i	0.400717	+	0.916202i	$0.368761\pi$
$860$	−36.2991	−	30.4586i	−1.23779	−	1.03863i
$861$	1.42498	+	8.08147i	0.0485632	+	0.275416i
$862$	41.6821	+	72.1956i	1.41970	+	2.45899i
$863$	16.2861	−	28.2083i	0.554385	−	0.960223i	−0.443566	−	0.896242i	$-0.646287\pi$
$863$	16.2861	−	28.2083i	0.554385	−	0.960223i	0.997951	−	0.0639813i	$-0.0203798\pi$
$864$	2.93987	+	1.07003i	0.100016	+	0.0364030i
$865$	59.6276	+	21.7027i	2.02740	+	0.737913i
$866$	30.8654	−	53.4605i	1.04885	−	1.81666i
$867$	−19.2696	−	33.3759i	−0.654430	−	1.13351i
$868$	−4.76195	−	27.0064i	−0.161631	−	0.916656i
$869$	19.1345	+	16.0558i	0.649095	+	0.544655i
$870$	−18.2377	+	15.3033i	−0.618317	+	0.518830i
$871$	−1.52444	+	8.64551i	−0.0516536	+	0.292942i
$872$	−62.8970	+	22.8926i	−2.12996	+	0.775242i
$873$	−0.419172			−0.0141868
$874$	16.2719	−	11.9945i	0.550404	−	0.405720i
$875$	12.0774			0.408290
$876$	−21.3497	+	7.77067i	−0.721341	+	0.262547i
$877$	0.491243	−	2.78598i	0.0165881	−	0.0940758i	−0.975390	−	0.220488i	$-0.929235\pi$
$877$	0.491243	−	2.78598i	0.0165881	−	0.0940758i	0.991978	+	0.126412i	$0.0403462\pi$
$878$	19.9147	−	16.7105i	0.672090	−	0.563951i
$879$	−0.820062	−	0.688114i	−0.0276600	−	0.0232095i
$880$	−4.64516	−	26.3440i	−0.156588	−	0.888057i
$881$	4.16139	+	7.20775i	0.140201	+	0.242835i	0.927572	−	0.373644i	$-0.121892\pi$
$881$	4.16139	+	7.20775i	0.140201	+	0.242835i	−0.787371	+	0.616479i	$0.788558\pi$
$882$	2.99916	−	5.19470i	0.100987	−	0.174915i
$883$	−22.7308	−	8.27333i	−0.764952	−	0.278420i	−0.0700684	−	0.997542i	$-0.522322\pi$
$883$	−22.7308	−	8.27333i	−0.764952	−	0.278420i	−0.694883	+	0.719123i	$0.744544\pi$
$884$	−18.0231	−	6.55988i	−0.606184	−	0.220633i
$885$	−0.509175	+	0.881918i	−0.0171157	+	0.0296453i
$886$	−4.14208	−	7.17430i	−0.139156	−	0.241025i
$887$	5.65093	+	32.0480i	0.189740	+	1.07607i	0.919713	+	0.392592i	$0.128422\pi$
$887$	5.65093	+	32.0480i	0.189740	+	1.07607i	−0.729973	+	0.683476i	$0.760467\pi$
$888$	−11.4656	−	9.62078i	−0.384760	−	0.322852i
$889$	23.7323	−	19.9138i	0.795957	−	0.667887i
$890$	2.31113	−	13.1071i	0.0774694	−	0.439351i
$891$	4.54513	−	1.65429i	0.152268	−	0.0554209i
$892$	−53.2836			−1.78407
$893$	1.91456	+	1.82352i	0.0640682	+	0.0610218i
$894$	48.6558			1.62729
$895$	−37.9550	+	13.8145i	−1.26870	+	0.461768i
$896$	7.59519	−	43.0745i	0.253737	−	1.43902i
$897$	1.05852	−	0.888204i	0.0353430	−	0.0296563i
$898$	−14.4503	−	12.1253i	−0.482213	−	0.404625i
$899$	−2.19691	−	12.4593i	−0.0732710	−	0.415540i
$900$	−5.41758	−	9.38352i	−0.180586	−	0.312784i
$901$	11.5317	−	19.9736i	0.384178	−	0.665416i
$902$	−41.8701	−	15.2395i	−1.39412	−	0.507419i
$903$	−9.16568	−	3.33604i	−0.305015	−	0.111016i
$904$	−13.9497	+	24.1616i	−0.463961	+	0.803603i
$905$	−36.6646	−	63.5049i	−1.21877	−	2.11097i
$906$	−0.913463	−	5.18051i	−0.0303478	−	0.172111i
$907$	−18.7226	−	15.7102i	−0.621675	−	0.521647i	0.276655	−	0.960969i	$-0.410774\pi$
$907$	−18.7226	−	15.7102i	−0.621675	−	0.521647i	−0.898330	+	0.439322i	$0.855219\pi$
$908$	−49.1233	+	41.2193i	−1.63021	+	1.36791i
$909$	2.75126	−	15.6032i	0.0912536	−	0.517525i
$910$	9.43068	−	3.43249i	0.312624	−	0.113786i
$911$	24.9218			0.825697			0.412848	−	0.910800i	$-0.364534\pi$
$911$	24.9218			0.825697			0.412848	+	0.910800i	$0.364534\pi$
$912$	6.18006	+	5.88620i	0.204642	+	0.194912i
$913$	−40.2807			−1.33309
$914$	77.3102	−	28.1386i	2.55719	−	0.930743i
$915$	−1.83171	+	10.3882i	−0.0605546	+	0.343422i
$916$	47.3934	−	39.7678i	1.56592	−	1.31397i
$917$	−9.41223	−	7.89780i	−0.310819	−	0.260808i
$918$	3.07273	+	17.4263i	0.101415	+	0.575155i
$919$	−15.6869	−	27.1704i	−0.517462	−	0.896270i	−0.999794	−	0.0202817i	$-0.993544\pi$
$919$	−15.6869	−	27.1704i	−0.517462	−	0.896270i	0.482333	−	0.875988i	$-0.339790\pi$
$920$	−10.7272	+	18.5800i	−0.353665	+	0.612565i
$921$	−28.4760	−	10.3644i	−0.938315	−	0.341519i
$922$	−25.9595	−	9.44847i	−0.854929	−	0.311169i
$923$	2.04873	−	3.54850i	0.0674346	−	0.116800i
$924$	−18.6082	−	32.2304i	−0.612166	−	1.06030i
$925$	−1.99064	−	11.2895i	−0.0654520	−	0.371197i
$926$	−39.2857	−	32.9646i	−1.29101	−	1.08328i
$927$	−0.554993	+	0.465694i	−0.0182284	+	0.0152954i
$928$	1.92848	−	10.9369i	0.0633054	−	0.359022i
$929$	−2.08904	+	0.760350i	−0.0685393	+	0.0249463i	−0.376062	−	0.926594i	$-0.622722\pi$
$929$	−2.08904	+	0.760350i	−0.0685393	+	0.0249463i	0.307523	+	0.951541i	$0.400500\pi$
$930$	23.9031			0.783815
$931$	−8.86376	+	6.53376i	−0.290498	+	0.214135i
$932$	−62.4053			−2.04415
$933$	2.76898	−	1.00783i	0.0906523	−	0.0329947i
$934$	2.59366	−	14.7094i	0.0848672	−	0.481306i
$935$	−77.9964	+	65.4468i	−2.55076	+	2.14034i
$936$	2.10754	+	1.76843i	0.0688871	+	0.0578031i
$937$	6.43614	+	36.5011i	0.210259	+	1.19244i	0.888946	+	0.458012i	$0.151438\pi$
$937$	6.43614	+	36.5011i	0.210259	+	1.19244i	−0.678686	+	0.734428i	$0.737450\pi$
$938$	−31.1598	−	53.9703i	−1.01740	−	1.76219i
$939$	−1.44777	+	2.50761i	−0.0472462	+	0.0818328i
$940$	−5.85693	−	2.13175i	−0.191032	−	0.0695300i
$941$	34.3766	+	12.5121i	1.12064	+	0.407881i	0.834887	−	0.550421i	$-0.185533\pi$
$941$	34.3766	+	12.5121i	1.12064	+	0.407881i	0.285757	+	0.958302i	$0.407755\pi$
$942$	−15.1149	+	26.1798i	−0.492470	+	0.852983i
$943$	3.78889	+	6.56255i	0.123383	+	0.213706i
$944$	0.122579	+	0.695182i	0.00398962	+	0.0226262i
$945$	−4.57668	−	3.84029i	−0.148879	−	0.124925i
$946$	40.5707	−	34.0428i	1.31907	−	1.10683i
$947$	0.200666	−	1.13803i	0.00652076	−	0.0369811i	−0.981374	−	0.192108i	$-0.938468\pi$
$947$	0.200666	−	1.13803i	0.00652076	−	0.0369811i	0.987895	+	0.155127i	$0.0495787\pi$
$948$	17.6534	−	6.42531i	0.573355	−	0.208684i
$949$	4.41849			0.143430
$950$	3.43360	+	30.6349i	0.111401	+	0.993929i
$951$	23.3592			0.757473
$952$	57.6020	−	20.9654i	1.86689	−	0.679493i
$953$	−7.29414	+	41.3671i	−0.236280	+	1.34001i	0.603620	+	0.797272i	$0.293724\pi$
$953$	−7.29414	+	41.3671i	−0.236280	+	1.34001i	−0.839901	+	0.542740i	$0.817387\pi$
$954$	−5.62903	+	4.72332i	−0.182247	+	0.152923i
$955$	−4.44661	−	3.73115i	−0.143889	−	0.120737i
$956$	−0.793630	−	4.50090i	−0.0256678	−	0.145570i
$957$	−8.58484	−	14.8694i	−0.277509	−	0.480659i
$958$	−30.0717	+	52.0858i	−0.971574	+	1.68281i
$959$	2.32798	+	0.847315i	0.0751743	+	0.0273612i
$960$	30.1112	+	10.9596i	0.971835	+	0.353719i
$961$	9.14889	−	15.8463i	0.295125	−	0.511172i
$962$	3.23265	+	5.59911i	0.104225	+	0.180522i
$963$	−1.52995	−	8.67680i	−0.0493021	−	0.279606i
$964$	42.7560	+	35.8765i	1.37708	+	1.15551i
$965$	0.316594	−	0.265654i	0.0101915	−	0.00855169i
$966$	−1.70334	+	9.66011i	−0.0548040	+	0.310809i
$967$	30.9787	−	11.2753i	0.996208	−	0.362590i	0.208087	−	0.978110i	$-0.433276\pi$
$967$	30.9787	−	11.2753i	0.996208	−	0.362590i	0.788121	+	0.615520i	$0.211054\pi$
$968$	48.2013			1.54925
$969$	7.64119	−	31.5730i	0.245470	−	1.01427i
$970$	−2.81130			−0.0902655
$971$	−14.4836	+	5.27159i	−0.464800	+	0.169173i	−0.563795	−	0.825915i	$-0.690659\pi$
$971$	−14.4836	+	5.27159i	−0.464800	+	0.169173i	0.0989955	+	0.995088i	$0.468437\pi$
$972$	0.631697	−	3.58253i	0.0202617	−	0.114910i
$973$	−34.4540	+	28.9103i	−1.10454	+	0.926822i
$974$	39.0770	+	32.7895i	1.25211	+	1.05064i
$975$	0.365908	+	2.07517i	0.0117184	+	0.0664586i
$976$	3.65600	+	6.33239i	0.117026	+	0.202695i
$977$	1.43863	−	2.49177i	0.0460257	−	0.0797189i	−0.842095	−	0.539330i	$-0.818678\pi$
$977$	1.43863	−	2.49177i	0.0460257	−	0.0797189i	0.888121	+	0.459611i	$0.152011\pi$
$978$	−36.6304	−	13.3324i	−1.17131	−	0.426322i
$979$	9.01957	+	3.28286i	0.288267	+	0.104921i
$980$	12.9791	−	22.4805i	0.414602	−	0.718112i
$981$	−8.60594	−	14.9059i	−0.274767	−	0.475910i
$982$	11.5231	+	65.3509i	0.367718	+	2.08543i
$983$	−13.6112	−	11.4212i	−0.434130	−	0.364279i	0.399377	−	0.916787i	$-0.369226\pi$
$983$	−13.6112	−	11.4212i	−0.434130	−	0.364279i	−0.833508	+	0.552508i	$0.813671\pi$
$984$	−11.5577	+	9.69808i	−0.368447	+	0.309164i
$985$	−3.20433	+	18.1726i	−0.102098	+	0.579029i
$986$	59.0258	−	21.4836i	1.87977	−	0.684179i
$987$	−1.28298			−0.0408378
$988$	−4.98713	−	10.0487i	−0.158662	−	0.319691i
$989$	−9.00704			−0.286407
$990$	30.4833	−	11.0950i	0.968822	−	0.352622i
$991$	−3.08536	+	17.4979i	−0.0980097	+	0.555840i	0.895774	+	0.444510i	$0.146622\pi$
$991$	−3.08536	+	17.4979i	−0.0980097	+	0.555840i	−0.993783	+	0.111330i	$0.964489\pi$
$992$	−8.54154	+	7.16720i	−0.271194	+	0.227559i
$993$	−2.24970	−	1.88772i	−0.0713922	−	0.0599051i
$994$	5.05090	+	28.6451i	0.160205	+	0.908567i
$995$	−10.9072	−	18.8918i	−0.345781	−	0.598911i
$996$	−15.1476	+	26.2365i	−0.479971	+	0.831334i
$997$	−25.2089	−	9.17531i	−0.798375	−	0.290585i	−0.0895623	−	0.995981i	$-0.528547\pi$
$997$	−25.2089	−	9.17531i	−0.798375	−	0.290585i	−0.708813	+	0.705396i	$0.750769\pi$
$998$	48.7277	+	17.7354i	1.54245	+	0.561405i
$999$	1.92441	−	3.33317i	0.0608856	−	0.105457i

Display

a_p

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p

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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	57.2.i.b.43.1	yes	12
3.2	odd	2		171.2.u.e.100.2		12
4.3	odd	2		912.2.bo.j.385.2		12
19.2	odd	18		1083.2.a.p.1.1		6
19.4	even	9	inner	57.2.i.b.4.1	✓	12
19.17	even	9		1083.2.a.q.1.6		6
57.2	even	18		3249.2.a.bg.1.6		6
57.17	odd	18		3249.2.a.bh.1.1		6
57.23	odd	18		171.2.u.e.118.2		12
76.23	odd	18		912.2.bo.j.289.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.i.b.4.1	✓	12	19.4	even	9	inner
57.2.i.b.43.1	yes	12	1.1	even	1	trivial
171.2.u.e.100.2		12	3.2	odd	2
171.2.u.e.118.2		12	57.23	odd	18
912.2.bo.j.289.2		12	76.23	odd	18
912.2.bo.j.385.2		12	4.3	odd	2
1083.2.a.p.1.1		6	19.2	odd	18
1083.2.a.q.1.6		6	19.17	even	9
3249.2.a.bg.1.6		6	57.2	even	18
3249.2.a.bh.1.1		6	57.17	odd	18

Overview	Random
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Hilbert	Bianchi

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

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Newspace parameters

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$q$ -expansion

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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	57.2.i.b.43.1

Level	$57$
Weight	$2$
Character	57.43
Analytic conductor	$0.455$
Analytic rank	$0$
Dimension	$12$
Inner twists	$2$