LMFDB - Embedded newform 55.3.i.a.51.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [55,3,Mod(6,55)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(55, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 9])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("55.6"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	55.i (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.49864145398$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			51.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	55.51
Dual form			55.3.i.a.41.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.80902 + 2.48990i) q^{2} +(-1.23607 + 3.80423i) q^{3} +(-1.69098 - 5.20431i) q^{4} +(-1.80902 + 1.31433i) q^{5} +(-7.23607 - 9.95959i) q^{6} +(7.66312 - 2.48990i) q^{7} +(4.30902 + 1.40008i) q^{8} +(-5.66312 - 4.11450i) q^{9} -6.88191i q^{10} +(-10.8713 + 1.67760i) q^{11} +21.8885 q^{12} +(-8.25329 + 11.3597i) q^{13} +(-7.66312 + 23.5847i) q^{14} +(-2.76393 - 8.50651i) q^{15} +(6.42705 - 4.66953i) q^{16} +(14.2705 + 19.6417i) q^{17} +(20.4894 - 6.65740i) q^{18} +(8.02786 + 2.60841i) q^{19} +(9.89919 + 7.19218i) q^{20} +32.2299i q^{21} +(15.4894 - 30.1033i) q^{22} -25.3820 q^{23} +(-10.6525 + 14.6619i) q^{24} +(1.54508 - 4.75528i) q^{25} +(-13.3541 - 41.0997i) q^{26} +(-6.47214 + 4.70228i) q^{27} +(-25.9164 - 35.6709i) q^{28} +(34.7984 - 11.3067i) q^{29} +(26.1803 + 8.50651i) q^{30} +(8.38197 + 6.08985i) q^{31} +42.5730i q^{32} +(7.05573 - 43.4306i) q^{33} -74.7214 q^{34} +(-10.5902 + 14.5761i) q^{35} +(-11.8369 + 36.4302i) q^{36} +(-6.26393 - 19.2784i) q^{37} +(-21.0172 + 15.2699i) q^{38} +(-33.0132 - 45.4387i) q^{39} +(-9.63525 + 3.13068i) q^{40} +(53.1140 + 17.2578i) q^{41} +(-80.2492 - 58.3045i) q^{42} +37.2752i q^{43} +(27.1140 + 53.7409i) q^{44} +15.6525 q^{45} +(45.9164 - 63.1985i) q^{46} +(26.4230 - 81.3216i) q^{47} +(9.81966 + 30.2218i) q^{48} +(12.8820 - 9.35930i) q^{49} +(9.04508 + 12.4495i) q^{50} +(-92.3607 + 30.0098i) q^{51} +(73.0755 + 23.7437i) q^{52} +(44.1525 + 32.0787i) q^{53} -24.6215i q^{54} +(17.4615 - 17.3233i) q^{55} +36.5066 q^{56} +(-19.8460 + 27.3156i) q^{57} +(-34.7984 + 107.098i) q^{58} +(18.3115 + 56.3571i) q^{59} +(-39.5967 + 28.7687i) q^{60} +(21.5836 + 29.7073i) q^{61} +(-30.3262 + 9.85359i) q^{62} +(-53.6418 - 17.4293i) q^{63} +(-80.2943 - 58.3372i) q^{64} -31.3974i q^{65} +(95.3738 + 96.1347i) q^{66} +17.8197 q^{67} +(78.0902 - 107.482i) q^{68} +(31.3738 - 96.5587i) q^{69} +(-17.1353 - 52.7369i) q^{70} +(-4.70820 + 3.42071i) q^{71} +(-18.6418 - 25.6583i) q^{72} +(48.6656 - 15.8124i) q^{73} +(59.3328 + 19.2784i) q^{74} +(16.1803 + 11.7557i) q^{75} -46.1903i q^{76} +(-79.1312 + 39.9241i) q^{77} +172.859 q^{78} +(20.1722 - 27.7647i) q^{79} +(-5.48936 + 16.8945i) q^{80} +(-29.3566 - 90.3504i) q^{81} +(-139.054 + 101.029i) q^{82} +(-85.7295 - 117.997i) q^{83} +(167.735 - 54.5002i) q^{84} +(-51.6312 - 16.7760i) q^{85} +(-92.8115 - 67.4315i) q^{86} +146.357i q^{87} +(-49.1935 - 7.99197i) q^{88} -127.949 q^{89} +(-28.3156 + 38.9731i) q^{90} +(-34.9615 + 107.600i) q^{91} +(42.9205 + 132.096i) q^{92} +(-33.5279 + 24.3594i) q^{93} +(154.683 + 212.903i) q^{94} +(-17.9508 + 5.83258i) q^{95} +(-161.957 - 52.6232i) q^{96} +(73.0689 + 53.0877i) q^{97} +49.0059i q^{98} +(68.4681 + 35.2296i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{2} + 4 q^{3} - 9 q^{4} - 5 q^{5} - 20 q^{6} + 15 q^{7} + 15 q^{8} - 7 q^{9} - q^{11} + 16 q^{12} + 5 q^{13} - 15 q^{14} - 20 q^{15} + 19 q^{16} - 10 q^{17} + 35 q^{18} + 50 q^{19} + 15 q^{20}+ \cdots + 133 q^{99}+O(q^{100}) $ 4 * q - 5 * q^2 + 4 * q^3 - 9 * q^4 - 5 * q^5 - 20 * q^6 + 15 * q^7 + 15 * q^8 - 7 * q^9 - q^11 + 16 * q^12 + 5 * q^13 - 15 * q^14 - 20 * q^15 + 19 * q^16 - 10 * q^17 + 35 * q^18 + 50 * q^19 + 15 * q^20 + 15 * q^22 - 106 * q^23 + 20 * q^24 - 5 * q^25 - 40 * q^26 - 8 * q^27 - 50 * q^28 + 90 * q^29 + 60 * q^30 + 38 * q^31 + 64 * q^33 - 120 * q^34 - 20 * q^35 - 63 * q^36 - 34 * q^37 - 55 * q^38 + 20 * q^39 - 5 * q^40 + 85 * q^41 - 160 * q^42 - 19 * q^44 + 130 * q^46 - 24 * q^47 + 84 * q^48 + 56 * q^49 + 25 * q^50 - 280 * q^51 + 100 * q^52 + 114 * q^53 + 5 * q^55 + 70 * q^56 + 180 * q^57 - 90 * q^58 - 128 * q^59 - 60 * q^60 + 140 * q^61 - 90 * q^62 - 105 * q^63 - 149 * q^64 + 140 * q^66 + 116 * q^67 + 290 * q^68 - 116 * q^69 - 35 * q^70 + 8 * q^71 + 35 * q^72 - 20 * q^73 + 130 * q^74 + 20 * q^75 - 160 * q^77 + 280 * q^78 - 210 * q^79 + 25 * q^80 + 95 * q^81 - 270 * q^82 - 410 * q^83 + 340 * q^84 - 50 * q^85 - 170 * q^86 - 78 * q^89 - 35 * q^90 - 75 * q^91 + 241 * q^92 - 152 * q^93 + 375 * q^94 + 40 * q^95 - 460 * q^96 + 176 * q^97 + 133 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−1.80902	+	2.48990i	−0.904508	+	1.24495i	0.0644990	+	0.997918i	$0.479455\pi$
$2$	−1.80902	+	2.48990i	−0.904508	+	1.24495i	−0.969007	+	0.247031i	$0.920545\pi$
$3$	−1.23607	+	3.80423i	−0.412023	+	1.26808i	0.502864	+	0.864365i	$0.332280\pi$
$3$	−1.23607	+	3.80423i	−0.412023	+	1.26808i	−0.914887	+	0.403710i	$0.867720\pi$
$4$	−1.69098	−	5.20431i	−0.422746	−	1.30108i
$5$	−1.80902	+	1.31433i	−0.361803	+	0.262866i
$5$	−1.80902	+	1.31433i	−0.361803	+	0.262866i
$6$	−7.23607	−	9.95959i	−1.20601	−	1.65993i
$7$	7.66312	−	2.48990i	1.09473	−	0.355700i	0.294658	−	0.955603i	$-0.404794\pi$
$7$	7.66312	−	2.48990i	1.09473	−	0.355700i	0.800073	+	0.599903i	$0.204794\pi$
$8$	4.30902	+	1.40008i	0.538627	+	0.175011i
$9$	−5.66312	−	4.11450i	−0.629235	−	0.457166i
$10$		−	6.88191i		−	0.688191i
$11$	−10.8713	+	1.67760i	−0.988302	+	0.152509i
$11$	−10.8713	+	1.67760i	−0.988302	+	0.152509i
$12$	21.8885			1.82405
$13$	−8.25329	+	11.3597i	−0.634868	+	0.873821i	−0.998329	−	0.0577883i	$-0.981595\pi$
$13$	−8.25329	+	11.3597i	−0.634868	+	0.873821i	0.363460	+	0.931610i	$0.381595\pi$
$14$	−7.66312	+	23.5847i	−0.547366	+	1.68462i
$15$	−2.76393	−	8.50651i	−0.184262	−	0.567101i
$16$	6.42705	−	4.66953i	0.401691	−	0.291845i
$17$	14.2705	+	19.6417i	0.839442	+	1.15539i	0.986091	+	0.166204i	$0.0531510\pi$
$17$	14.2705	+	19.6417i	0.839442	+	1.15539i	−0.146650	+	0.989188i	$0.546849\pi$
$18$	20.4894	−	6.65740i	1.13830	−	0.369855i
$19$	8.02786	+	2.60841i	0.422519	+	0.137285i	0.512556	−	0.858654i	$-0.328699\pi$
$19$	8.02786	+	2.60841i	0.422519	+	0.137285i	−0.0900372	+	0.995938i	$0.528699\pi$
$20$	9.89919	+	7.19218i	0.494959	+	0.359609i
$21$			32.2299i			1.53476i
$22$	15.4894	−	30.1033i	0.704062	−	1.36833i
$23$	−25.3820			−1.10356			−0.551782	−	0.833988i	$-0.686052\pi$
$23$	−25.3820			−1.10356			−0.551782	+	0.833988i	$0.686052\pi$
$24$	−10.6525	+	14.6619i	−0.443853	+	0.610911i
$25$	1.54508	−	4.75528i	0.0618034	−	0.190211i
$26$	−13.3541	−	41.0997i	−0.513619	−	1.58076i
$27$	−6.47214	+	4.70228i	−0.239709	+	0.174159i
$28$	−25.9164	−	35.6709i	−0.925586	−	1.27396i
$29$	34.7984	−	11.3067i	1.19994	−	0.389885i	0.360204	−	0.932874i	$-0.382707\pi$
$29$	34.7984	−	11.3067i	1.19994	−	0.389885i	0.839740	+	0.542988i	$0.182707\pi$
$30$	26.1803	+	8.50651i	0.872678	+	0.283550i
$31$	8.38197	+	6.08985i	0.270386	+	0.196447i	0.714713	−	0.699418i	$-0.246557\pi$
$31$	8.38197	+	6.08985i	0.270386	+	0.196447i	−0.444327	+	0.895865i	$0.646557\pi$
$32$			42.5730i			1.33041i
$33$	7.05573	−	43.4306i	0.213810	−	1.31608i
$34$	−74.7214			−2.19769
$35$	−10.5902	+	14.5761i	−0.302576	+	0.416461i
$36$	−11.8369	+	36.4302i	−0.328802	+	1.01195i
$37$	−6.26393	−	19.2784i	−0.169295	−	0.521038i	0.830032	−	0.557716i	$-0.188322\pi$
$37$	−6.26393	−	19.2784i	−0.169295	−	0.521038i	−0.999327	+	0.0366784i	$0.988322\pi$
$38$	−21.0172	+	15.2699i	−0.553085	+	0.401840i
$39$	−33.0132	−	45.4387i	−0.846491	−	1.16510i
$40$	−9.63525	+	3.13068i	−0.240881	+	0.0782671i
$41$	53.1140	+	17.2578i	1.29546	+	0.420921i	0.874001	−	0.485925i	$-0.161517\pi$
$41$	53.1140	+	17.2578i	1.29546	+	0.420921i	0.421462	+	0.906846i	$0.361517\pi$
$42$	−80.2492	−	58.3045i	−1.91070	−	1.38820i
$43$			37.2752i			0.866866i	0.901186	+	0.433433i	$0.142698\pi$
$43$			37.2752i			0.866866i	−0.901186	+	0.433433i	$0.857302\pi$
$44$	27.1140	+	53.7409i	0.616227	+	1.22139i
$45$	15.6525			0.347833
$46$	45.9164	−	63.1985i	0.998183	−	1.37388i
$47$	26.4230	−	81.3216i	0.562191	−	1.73025i	−0.113962	−	0.993485i	$-0.536354\pi$
$47$	26.4230	−	81.3216i	0.562191	−	1.73025i	0.676153	−	0.736761i	$-0.263646\pi$
$48$	9.81966	+	30.2218i	0.204576	+	0.629621i
$49$	12.8820	−	9.35930i	0.262897	−	0.191006i
$50$	9.04508	+	12.4495i	0.180902	+	0.248990i
$51$	−92.3607	+	30.0098i	−1.81099	+	0.588428i
$52$	73.0755	+	23.7437i	1.40530	+	0.456609i
$53$	44.1525	+	32.0787i	0.833066	+	0.605258i	0.920425	−	0.390919i	$-0.127843\pi$
$53$	44.1525	+	32.0787i	0.833066	+	0.605258i	−0.0873594	+	0.996177i	$0.527843\pi$
$54$		−	24.6215i		−	0.455953i
$55$	17.4615	−	17.3233i	0.317482	−	0.314969i
$56$	36.5066			0.651903
$57$	−19.8460	+	27.3156i	−0.348175	+	0.479222i
$58$	−34.7984	+	107.098i	−0.599972	+	1.84652i
$59$	18.3115	+	56.3571i	0.310365	+	0.955205i	0.977621	+	0.210376i	$0.0674689\pi$
$59$	18.3115	+	56.3571i	0.310365	+	0.955205i	−0.667256	+	0.744829i	$0.732531\pi$
$60$	−39.5967	+	28.7687i	−0.659946	+	0.479479i
$61$	21.5836	+	29.7073i	0.353829	+	0.487004i	0.948417	−	0.317027i	$-0.102685\pi$
$61$	21.5836	+	29.7073i	0.353829	+	0.487004i	−0.594587	+	0.804031i	$0.702685\pi$
$62$	−30.3262	+	9.85359i	−0.489133	+	0.158929i
$63$	−53.6418	−	17.4293i	−0.851458	−	0.276655i
$64$	−80.2943	−	58.3372i	−1.25460	−	0.911519i
$65$		−	31.3974i		−	0.483037i
$66$	95.3738	+	96.1347i	1.44506	+	1.45659i
$67$	17.8197			0.265965			0.132983	−	0.991118i	$-0.457545\pi$
$67$	17.8197			0.265965			0.132983	+	0.991118i	$0.457545\pi$
$68$	78.0902	−	107.482i	1.14838	−	1.58062i
$69$	31.3738	−	96.5587i	0.454693	−	1.39940i
$70$	−17.1353	−	52.7369i	−0.244789	−	0.753384i
$71$	−4.70820	+	3.42071i	−0.0663127	+	0.0481790i	−0.620448	−	0.784248i	$-0.713049\pi$
$71$	−4.70820	+	3.42071i	−0.0663127	+	0.0481790i	0.554135	+	0.832427i	$0.313049\pi$
$72$	−18.6418	−	25.6583i	−0.258914	−	0.356365i
$73$	48.6656	−	15.8124i	0.666652	−	0.216609i	0.0439101	−	0.999035i	$-0.486018\pi$
$73$	48.6656	−	15.8124i	0.666652	−	0.216609i	0.622742	+	0.782427i	$0.286018\pi$
$74$	59.3328	+	19.2784i	0.801795	+	0.260519i
$75$	16.1803	+	11.7557i	0.215738	+	0.156743i
$76$		−	46.1903i		−	0.607767i
$77$	−79.1312	+	39.9241i	−1.02768	+	0.518495i
$78$	172.859			2.21614
$79$	20.1722	−	27.7647i	0.255344	−	0.351451i	−0.662030	−	0.749478i	$-0.730305\pi$
$79$	20.1722	−	27.7647i	0.255344	−	0.351451i	0.917374	+	0.398026i	$0.130305\pi$
$80$	−5.48936	+	16.8945i	−0.0686170	+	0.211181i
$81$	−29.3566	−	90.3504i	−0.362427	−	1.11544i
$82$	−139.054	+	101.029i	−1.69578	+	1.23206i
$83$	−85.7295	−	117.997i	−1.03289	−	1.42164i	−0.902759	−	0.430147i	$-0.858462\pi$
$83$	−85.7295	−	117.997i	−1.03289	−	1.42164i	−0.130127	−	0.991497i	$-0.541538\pi$
$84$	167.735	−	54.5002i	1.99684	−	0.648812i
$85$	−51.6312	−	16.7760i	−0.607426	−	0.197365i
$86$	−92.8115	−	67.4315i	−1.07920	−	0.784087i
$87$			146.357i			1.68226i
$88$	−49.1935	−	7.99197i	−0.559017	−	0.0908178i
$89$	−127.949			−1.43763			−0.718816	−	0.695200i	$-0.755316\pi$
$89$	−127.949			−1.43763			−0.718816	+	0.695200i	$0.755316\pi$
$90$	−28.3156	+	38.9731i	−0.314618	+	0.433034i
$91$	−34.9615	+	107.600i	−0.384192	+	1.18242i
$92$	42.9205	+	132.096i	0.466527	+	1.43582i
$93$	−33.5279	+	24.3594i	−0.360515	+	0.261929i
$94$	154.683	+	212.903i	1.64556	+	2.26492i
$95$	−17.9508	+	5.83258i	−0.188956	+	0.0613956i
$96$	−161.957	−	52.6232i	−1.68706	−	0.548158i
$97$	73.0689	+	53.0877i	0.753287	+	0.547295i	0.896844	−	0.442347i	$-0.145854\pi$
$97$	73.0689	+	53.0877i	0.753287	+	0.547295i	−0.143557	+	0.989642i	$0.545854\pi$
$98$			49.0059i			0.500060i
$99$	68.4681	+	35.2296i	0.691597	+	0.355854i
$100$	−27.3607			−0.273607
$101$	63.4164	−	87.2852i	0.627885	−	0.864210i	−0.370012	−	0.929027i	$-0.620646\pi$
$101$	63.4164	−	87.2852i	0.627885	−	0.864210i	0.997897	+	0.0648171i	$0.0206464\pi$
$102$	92.3607	−	284.257i	0.905497	−	2.78683i
$103$	−5.92454	−	18.2339i	−0.0575198	−	0.177028i	0.918169	−	0.396190i	$-0.129668\pi$
$103$	−5.92454	−	18.2339i	−0.0575198	−	0.177028i	−0.975689	+	0.219162i	$0.929668\pi$
$104$	−51.4681	+	37.3937i	−0.494885	+	0.359555i
$105$	−42.3607	−	58.3045i	−0.403435	−	0.555281i
$106$	−159.745	+	51.9043i	−1.50703	+	0.489664i
$107$	−91.5542	−	29.7478i	−0.855646	−	0.278016i	−0.151837	−	0.988405i	$-0.548519\pi$
$107$	−91.5542	−	29.7478i	−0.855646	−	0.278016i	−0.703809	+	0.710389i	$0.748519\pi$
$108$	35.4164	+	25.7315i	0.327930	+	0.238255i
$109$			21.0793i			0.193388i	0.995314	+	0.0966940i	$0.0308268\pi$
$109$			21.0793i			0.193388i	−0.995314	+	0.0966940i	$0.969173\pi$
$110$	11.5451	+	74.8155i	0.104955	+	0.680141i
$111$	81.0820			0.730469
$112$	37.6246	−	51.7858i	0.335934	−	0.462374i
$113$	22.1327	−	68.1176i	0.195865	−	0.602810i	−0.804100	−	0.594493i	$-0.797353\pi$
$113$	22.1327	−	68.1176i	0.195865	−	0.602810i	0.999965	−	0.00831694i	$-0.00264740\pi$
$114$	−32.1115	−	98.8289i	−0.281679	−	0.866920i
$115$	45.9164	−	33.3602i	0.399273	−	0.290089i
$116$	−117.687	−	161.982i	−1.01454	−	1.39640i
$117$	93.4787	−	30.3731i	0.798963	−	0.259599i
$118$	−173.449	−	56.3571i	−1.46991	−	0.477602i
$119$	158.262	+	114.984i	1.32994	+	0.966255i
$120$		−	40.5244i		−	0.337704i
$121$	115.371	−	36.4754i	0.953482	−	0.301450i
$122$	−113.013			−0.926337
$123$	−131.305	+	180.726i	−1.06752	+	1.46932i
$124$	17.5197	−	53.9202i	0.141288	−	0.434840i
$125$	3.45492	+	10.6331i	0.0276393	+	0.0850651i
$126$	140.436	−	102.033i	1.11457	−	0.809784i
$127$	−15.8450	−	21.8088i	−0.124764	−	0.171723i	0.742066	−	0.670327i	$-0.233846\pi$
$127$	−15.8450	−	21.8088i	−0.124764	−	0.171723i	−0.866830	+	0.498604i	$0.833846\pi$
$128$	128.550	−	41.7685i	1.00430	−	0.326316i
$129$	−141.803	−	46.0747i	−1.09925	−	0.357168i
$130$	78.1763	+	56.7984i	0.601356	+	0.436911i
$131$		−	88.8193i		−	0.678010i	−0.940785	−	0.339005i	$-0.889910\pi$
$131$		−	88.8193i		−	0.678010i	0.940785	−	0.339005i	$-0.110090\pi$
$132$	−237.957	+	36.7202i	−1.80271	+	0.278183i
$133$	68.0132			0.511377
$134$	−32.2361	+	44.3691i	−0.240568	+	0.331113i
$135$	5.52786	−	17.0130i	0.0409471	−	0.126022i
$136$	33.9919	+	104.616i	0.249940	+	0.769237i
$137$	97.1378	−	70.5747i	0.709035	−	0.515144i	−0.173827	−	0.984776i	$-0.555613\pi$
$137$	97.1378	−	70.5747i	0.709035	−	0.515144i	0.882862	+	0.469632i	$0.155613\pi$
$138$	183.666	+	252.794i	1.33091	+	1.83184i
$139$	3.34501	−	1.08686i	0.0240648	−	0.00781914i	−0.296960	−	0.954890i	$-0.595973\pi$
$139$	3.34501	−	1.08686i	0.0240648	−	0.00781914i	0.321025	+	0.947071i	$0.395973\pi$
$140$	93.7664	+	30.4666i	0.669760	+	0.217618i
$141$	276.705	+	201.038i	1.96245	+	1.42580i
$142$		−	17.9111i		−	0.126134i
$143$	70.6672	−	137.340i	0.494176	−	0.960423i
$144$	−55.6099			−0.386180
$145$	−48.0902	+	66.1904i	−0.331656	+	0.456486i
$146$	−48.6656	+	149.777i	−0.333326	+	1.02587i
$147$	19.6819	+	60.5746i	0.133890	+	0.412072i
$148$	−89.7386	+	65.1989i	−0.606342	+	0.440533i
$149$	54.8460	+	75.4890i	0.368094	+	0.506638i	0.952381	−	0.304909i	$-0.0986260\pi$
$149$	54.8460	+	75.4890i	0.368094	+	0.506638i	−0.584288	+	0.811547i	$0.698626\pi$
$150$	−58.5410	+	19.0211i	−0.390273	+	0.126808i
$151$	93.2148	+	30.2873i	0.617316	+	0.200578i	0.600948	−	0.799288i	$-0.294790\pi$
$151$	93.2148	+	30.2873i	0.617316	+	0.200578i	0.0163680	+	0.999866i	$0.494790\pi$
$152$	30.9402	+	22.4794i	0.203554	+	0.147891i
$153$		−	169.949i		−	1.11078i
$154$	43.7426	−	269.252i	0.284043	−	1.74839i
$155$	−23.1672			−0.149466
$156$	−180.652	+	248.647i	−1.15803	+	1.59389i
$157$	−53.2304	+	163.826i	−0.339047	+	1.04348i	0.625646	+	0.780107i	$0.284835\pi$
$157$	−53.2304	+	163.826i	−0.339047	+	1.04348i	−0.964694	+	0.263374i	$0.915165\pi$
$158$	32.6393	+	100.453i	0.206578	+	0.635782i
$159$	−176.610	+	128.315i	−1.11075	+	0.807010i
$160$	−55.9549	−	77.0153i	−0.349718	−	0.481346i
$161$	−194.505	+	63.1985i	−1.20811	+	0.392537i
$162$	278.070	+	90.3504i	1.71648	+	0.557718i
$163$	−204.825	−	148.814i	−1.25659	−	0.912968i	−0.258008	−	0.966143i	$-0.583066\pi$
$163$	−204.825	−	148.814i	−1.25659	−	0.912968i	−0.998585	+	0.0531744i	$0.983066\pi$
$164$		−	305.604i		−	1.86344i
$165$	44.3181	+	87.8402i	0.268595	+	0.532365i
$166$	448.885			2.70413
$167$	44.3090	−	60.9861i	0.265323	−	0.365186i	−0.655481	−	0.755212i	$-0.727534\pi$
$167$	44.3090	−	60.9861i	0.265323	−	0.365186i	0.920804	+	0.390026i	$0.127534\pi$
$168$	−45.1246	+	138.879i	−0.268599	+	0.826662i
$169$	−8.70163	−	26.7809i	−0.0514889	−	0.158467i
$170$	135.172	−	98.2084i	0.795131	−	0.577696i
$171$	−34.7304	−	47.8024i	−0.203102	−	0.279546i
$172$	193.992	−	63.0318i	1.12786	−	0.366464i
$173$	106.578	+	34.6293i	0.616058	+	0.200169i	0.600389	−	0.799708i	$-0.295012\pi$
$173$	106.578	+	34.6293i	0.616058	+	0.200169i	0.0156685	+	0.999877i	$0.495012\pi$
$174$	−364.413	−	264.762i	−2.09433	−	1.52162i
$175$		−	40.2874i		−	0.230214i
$176$	−62.0370	+	61.5459i	−0.352483	+	0.349693i
$177$	−237.029			−1.33915
$178$	231.462	−	318.581i	1.30035	−	1.78978i
$179$	−64.4321	+	198.302i	−0.359956	+	1.10783i	0.593124	+	0.805111i	$0.297894\pi$
$179$	−64.4321	+	198.302i	−0.359956	+	1.10783i	−0.953080	+	0.302719i	$0.902106\pi$
$180$	−26.4681	−	81.4603i	−0.147045	−	0.452557i
$181$	−64.7082	+	47.0133i	−0.357504	+	0.259742i	−0.752010	−	0.659151i	$-0.770916\pi$
$181$	−64.7082	+	47.0133i	−0.357504	+	0.259742i	0.394506	+	0.918893i	$0.370916\pi$
$182$	−204.668	−	281.702i	−1.12455	−	1.54781i
$183$	−139.692	+	45.3887i	−0.763344	+	0.248025i
$184$	−109.371	−	35.5369i	−0.594409	−	0.193135i
$185$	36.6697	+	26.6421i	0.198215	+	0.144011i
$186$		−	127.548i		−	0.685740i
$187$	−188.090	−	189.591i	−1.00583	−	1.01385i
$188$	−467.904			−2.48885
$189$	−37.8885	+	52.1491i	−0.200468	+	0.275921i
$190$	17.9508	−	55.2470i	0.0944782	−	0.290774i
$191$	−26.9443	−	82.9259i	−0.141069	−	0.434167i	0.855415	−	0.517943i	$-0.173302\pi$
$191$	−26.9443	−	82.9259i	−0.141069	−	0.434167i	−0.996485	+	0.0837757i	$0.973302\pi$
$192$	321.177	−	233.349i	1.67280	−	1.21536i
$193$	110.528	+	152.129i	0.572683	+	0.788231i	0.992869	−	0.119207i	$-0.0380352\pi$
$193$	110.528	+	152.129i	0.572683	+	0.788231i	−0.420186	+	0.907438i	$0.638035\pi$
$194$	−264.366	+	85.8976i	−1.36271	+	0.442771i
$195$	119.443	+	38.8093i	0.612527	+	0.199022i
$196$	−70.4919	−	51.2153i	−0.359652	−	0.261303i
$197$		−	10.5087i		−	0.0533437i	−0.999644	−	0.0266719i	$-0.991509\pi$
$197$		−	10.5087i		−	0.0533437i	0.999644	−	0.0266719i	$-0.00849093\pi$
$198$	−211.578	+	106.748i	−1.06858	+	0.539129i
$199$	8.30806			0.0417490			0.0208745	−	0.999782i	$-0.493355\pi$
$199$	8.30806			0.0417490			0.0208745	+	0.999782i	$0.493355\pi$
$200$	13.3156	−	18.3273i	0.0665780	−	0.0916367i
$201$	−22.0263	+	67.7900i	−0.109584	+	0.337264i
$202$	102.610	+	315.801i	0.507970	+	1.56337i
$203$	238.512	−	173.289i	1.17493	−	0.853640i
$204$	312.361	+	429.928i	1.53118	+	2.10749i
$205$	−118.766	+	38.5896i	−0.579349	+	0.188242i
$206$	56.1180	+	18.2339i	0.272418	+	0.0885139i
$207$	143.741	+	104.434i	0.694401	+	0.504512i
$208$			111.548i			0.536289i
$209$	−91.6494	−	14.8893i	−0.438514	−	0.0712409i
$210$	221.803			1.05621
$211$	−45.0294	+	61.9777i	−0.213410	+	0.293733i	−0.902279	−	0.431152i	$-0.858107\pi$
$211$	−45.0294	+	61.9777i	−0.213410	+	0.293733i	0.688870	+	0.724885i	$0.258107\pi$
$212$	92.2862	−	284.028i	0.435312	−	1.33975i
$213$	−7.19350	−	22.1393i	−0.0337723	−	0.103940i
$214$	239.692	−	174.146i	1.12006	−	0.813768i
$215$	−48.9919	−	67.4315i	−0.227869	−	0.313635i
$216$	−34.4721	+	11.2007i	−0.159593	+	0.0518550i
$217$	79.3951	+	25.7970i	0.365876	+	0.118880i
$218$	−52.4853	−	38.1328i	−0.240758	−	0.174921i
$219$			204.680i			0.934613i
$220$	−119.683	−	61.5816i	−0.544013	−	0.279917i
$221$	−340.902			−1.54254
$222$	−146.679	+	201.886i	−0.660715	+	0.909397i
$223$	36.1190	−	111.163i	0.161969	−	0.498488i	−0.836832	−	0.547460i	$-0.815595\pi$
$223$	36.1190	−	111.163i	0.161969	−	0.498488i	0.998800	+	0.0489724i	$0.0155946\pi$
$224$	106.003	+	326.242i	0.473226	+	1.45644i
$225$	−28.3156	+	20.5725i	−0.125847	+	0.0914333i
$226$	129.567	+	178.334i	0.573307	+	0.789089i
$227$	368.761	−	119.818i	1.62450	−	0.527831i	0.651500	−	0.758649i	$-0.274140\pi$
$227$	368.761	−	119.818i	1.62450	−	0.527831i	0.972997	+	0.230818i	$0.0741401\pi$
$228$	175.718	+	57.0943i	0.770694	+	0.250414i
$229$	−112.172	−	81.4979i	−0.489835	−	0.355886i	0.315286	−	0.948997i	$-0.397900\pi$
$229$	−112.172	−	81.4979i	−0.489835	−	0.355886i	−0.805121	+	0.593111i	$0.797900\pi$
$230$			174.676i			0.759463i
$231$	−54.0689	−	350.382i	−0.234064	−	1.51680i
$232$	165.777			0.714556
$233$	−109.674	+	150.953i	−0.470703	+	0.647867i	−0.976685	−	0.214677i	$-0.931130\pi$
$233$	−109.674	+	150.953i	−0.470703	+	0.647867i	0.505982	+	0.862544i	$0.331130\pi$
$234$	−93.4787	+	287.698i	−0.399482	+	1.22948i
$235$	59.0836	+	181.841i	0.251420	+	0.773790i
$236$	262.335	−	190.598i	1.11159	−	0.807618i
$237$	80.6888	+	111.059i	0.340459	+	0.468602i
$238$	−572.599	+	186.049i	−2.40588	+	0.781717i
$239$	−165.902	−	53.9047i	−0.694149	−	0.225543i	−0.0593698	−	0.998236i	$-0.518909\pi$
$239$	−165.902	−	53.9047i	−0.694149	−	0.225543i	−0.634780	+	0.772693i	$0.718909\pi$
$240$	−57.4853	−	41.7655i	−0.239522	−	0.174023i
$241$		−	229.308i		−	0.951484i	−0.879585	−	0.475742i	$-0.842180\pi$
$241$		−	229.308i		−	0.951484i	0.879585	−	0.475742i	$-0.157820\pi$
$242$	−117.889	+	353.248i	−0.487143	+	1.45970i
$243$	308.000			1.26749
$244$	118.108	−	162.562i	0.484051	−	0.666239i
$245$	−11.0025	+	33.8623i	−0.0449082	+	0.138213i
$246$	−212.456	−	653.872i	−0.863642	−	2.65802i
$247$	−95.8870	+	69.6660i	−0.388206	+	0.282048i
$248$	27.5917	+	37.9767i	0.111257	+	0.153132i
$249$	554.853	−	180.283i	2.22832	−	0.724027i
$250$	−32.7254	−	10.6331i	−0.130902	−	0.0425325i
$251$	85.7279	+	62.2850i	0.341546	+	0.248147i	0.745314	−	0.666714i	$-0.232300\pi$
$251$	85.7279	+	62.2850i	0.341546	+	0.248147i	−0.403768	+	0.914861i	$0.632300\pi$
$252$			308.641i			1.22477i
$253$	275.936	−	42.5808i	1.09065	−	0.168303i
$254$	82.9656			0.326636
$255$	127.639	−	175.680i	0.500546	−	0.688943i
$256$	−5.87132	+	18.0701i	−0.0229349	+	0.0705862i
$257$	−79.6362	−	245.095i	−0.309869	−	0.953677i	−0.977815	−	0.209468i	$-0.932827\pi$
$257$	−79.6362	−	245.095i	−0.309869	−	0.953677i	0.667947	−	0.744209i	$-0.267173\pi$
$258$	371.246	−	269.726i	1.43894	−	1.04545i
$259$	−96.0025	−	132.136i	−0.370666	−	0.510178i
$260$	−163.402	+	53.0924i	−0.628468	+	0.204202i
$261$	−243.589	−	79.1467i	−0.933290	−	0.303244i
$262$	221.151	+	160.676i	0.844087	+	0.613265i
$263$			290.347i			1.10398i	0.833851	+	0.551990i	$0.186131\pi$
$263$			290.347i			1.10398i	−0.833851	+	0.551990i	$0.813869\pi$
$264$	91.2098	−	177.265i	0.345492	−	0.671457i
$265$	−122.034			−0.460507
$266$	−123.037	+	169.346i	−0.462545	+	0.636638i
$267$	158.154	−	486.748i	0.592337	−	1.82303i
$268$	−30.1327	−	92.7390i	−0.112436	−	0.346041i
$269$	267.615	−	194.434i	0.994851	−	0.722802i	0.0338730	−	0.999426i	$-0.489216\pi$
$269$	267.615	−	194.434i	0.994851	−	0.722802i	0.960978	+	0.276625i	$0.0892158\pi$
$270$	32.3607	+	44.5407i	0.119854	+	0.164965i
$271$	206.661	−	67.1481i	0.762585	−	0.247779i	0.0981974	−	0.995167i	$-0.468692\pi$
$271$	206.661	−	67.1481i	0.762585	−	0.247779i	0.664388	+	0.747388i	$0.268692\pi$
$272$	183.435	+	59.6015i	0.674392	+	0.219123i
$273$	−366.122	−	266.003i	−1.34110	−	0.974369i
$274$			369.534i			1.34866i
$275$	−8.81966	+	54.2882i	−0.0320715	+	0.197412i
$276$	−555.574			−2.01295
$277$	−263.699	+	362.950i	−0.951980	+	1.31029i	−0.00133803	+	0.999999i	$0.500426\pi$
$277$	−263.699	+	362.950i	−0.951980	+	1.31029i	−0.950642	+	0.310289i	$0.899574\pi$
$278$	−3.34501	+	10.2949i	−0.0120324	+	0.0370320i
$279$	−22.4114	−	68.9751i	−0.0803275	−	0.247223i
$280$	−66.0410	+	47.9816i	−0.235861	+	0.171363i
$281$	55.0658	+	75.7915i	0.195964	+	0.269721i	0.895679	−	0.444701i	$-0.146690\pi$
$281$	55.0658	+	75.7915i	0.195964	+	0.269721i	−0.699716	+	0.714421i	$0.746690\pi$
$282$	−1001.13	+	325.286i	−3.55010	+	1.15350i
$283$	−278.002	−	90.3283i	−0.982339	−	0.319181i	−0.226552	−	0.973999i	$-0.572745\pi$
$283$	−278.002	−	90.3283i	−0.982339	−	0.319181i	−0.755787	+	0.654818i	$0.772745\pi$
$284$	25.7639	+	18.7186i	0.0907181	+	0.0659105i
$285$		−	75.4986i		−	0.264907i
$286$	214.126	+	424.405i	0.748691	+	1.48393i
$287$	449.989			1.56791
$288$	175.167	−	241.096i	0.608217	−	0.837139i
$289$	−92.8419	+	285.738i	−0.321252	+	0.988713i
$290$	−77.8115	−	239.479i	−0.268316	−	0.825791i
$291$	−292.276	+	212.351i	−1.00438	+	0.729727i
$292$	−164.586	−	226.533i	−0.563649	−	0.775796i
$293$	329.140	−	106.944i	1.12335	−	0.364997i	0.312302	−	0.949983i	$-0.398900\pi$
$293$	329.140	−	106.944i	1.12335	−	0.364997i	0.811044	+	0.584986i	$0.198900\pi$
$294$	−186.430	−	60.5746i	−0.634114	−	0.206036i
$295$	−107.198	−	77.8836i	−0.363382	−	0.264012i
$296$		−	91.8410i		−	0.310274i
$297$	62.4721	−	61.9777i	0.210344	−	0.208679i
$298$	−287.177			−0.963682
$299$	209.485	−	288.331i	0.700618	−	0.964318i
$300$	33.8197	−	104.086i	0.112732	−	0.346954i
$301$	92.8115	+	285.645i	0.308344	+	0.948985i
$302$	−244.039	+	177.305i	−0.808078	+	0.587103i
$303$	253.666	+	349.141i	0.837180	+	1.15228i
$304$	63.7755	−	20.7219i	0.209788	−	0.0681642i
$305$	−78.0902	−	25.3730i	−0.256033	−	0.0831903i
$306$	423.156	+	307.441i	1.38286	+	1.00471i
$307$		−	180.826i		−	0.589009i	−0.955650	−	0.294505i	$-0.904845\pi$
$307$		−	180.826i		−	0.589009i	0.955650	−	0.294505i	$-0.0951546\pi$
$308$	341.587	+	344.312i	1.10905	+	1.11790i
$309$	76.6888			0.248184
$310$	41.9098	−	57.6839i	0.135193	−	0.186077i
$311$	−115.313	+	354.897i	−0.370782	+	1.14115i	0.575499	+	0.817802i	$0.304808\pi$
$311$	−115.313	+	354.897i	−0.370782	+	1.14115i	−0.946281	+	0.323346i	$0.895192\pi$
$312$	−78.6362	−	242.017i	−0.252039	−	0.775697i
$313$	−256.753	+	186.542i	−0.820296	+	0.595980i	−0.916797	−	0.399353i	$-0.869235\pi$
$313$	−256.753	+	186.542i	−0.820296	+	0.595980i	0.0965012	+	0.995333i	$0.469235\pi$
$314$	−311.616	−	428.903i	−0.992409	−	1.36593i
$315$	119.947	−	38.9731i	0.380783	−	0.123724i
$316$	−178.607	−	58.0329i	−0.565211	−	0.183648i
$317$	−222.314	−	161.521i	−0.701306	−	0.509529i	0.179051	−	0.983840i	$-0.442697\pi$
$317$	−222.314	−	161.521i	−0.701306	−	0.509529i	−0.880357	+	0.474311i	$0.842697\pi$
$318$		−	671.864i		−	2.11278i
$319$	−359.336	+	181.296i	−1.12645	+	0.568327i
$320$	221.928			0.693525
$321$	226.334	−	311.523i	0.705091	−	0.970475i
$322$	194.505	−	598.625i	0.604053	−	1.85908i
$323$	63.3282	+	194.904i	0.196062	+	0.603418i
$324$	−420.570	+	305.562i	−1.29806	+	0.943092i
$325$	41.2664	+	56.7984i	0.126974	+	0.174764i
$326$	741.063	−	240.786i	2.27320	−	0.738607i
$327$	−80.1904	−	26.0554i	−0.245231	−	0.0796802i
$328$	204.707	+	148.728i	0.624106	+	0.453439i
$329$		−	688.968i		−	2.09413i
$330$	−298.885	−	48.5569i	−0.905713	−	0.147142i
$331$	411.681			1.24375			0.621874	−	0.783117i	$-0.286372\pi$
$331$	411.681			1.24375			0.621874	+	0.783117i	$0.286372\pi$
$332$	−469.123	+	645.693i	−1.41302	+	1.94486i
$333$	−43.8475	+	134.949i	−0.131674	+	0.405252i
$334$	71.6935	+	220.650i	0.214651	+	0.660628i
$335$	−32.2361	+	23.4209i	−0.0962271	+	0.0699131i
$336$	150.498	+	207.143i	0.447912	+	0.616498i
$337$	−440.410	+	143.098i	−1.30686	+	0.424623i	−0.877961	−	0.478732i	$-0.841097\pi$
$337$	−440.410	+	143.098i	−1.30686	+	0.424623i	−0.428894	+	0.903355i	$0.641097\pi$
$338$	82.4230	+	26.7809i	0.243855	+	0.0792333i
$339$	231.777	+	168.396i	0.683708	+	0.496743i
$340$			297.073i			0.873743i
$341$	−101.339	−	52.1432i	−0.297183	−	0.152913i
$342$	181.851			0.531728
$343$	−156.655	+	215.617i	−0.456720	+	0.628621i
$344$	−52.1885	+	160.620i	−0.151711	+	0.466917i
$345$	70.1540	+	215.912i	0.203345	+	0.625832i
$346$	−279.025	+	202.723i	−0.806430	+	0.585906i
$347$	−100.498	−	138.324i	−0.289621	−	0.398629i	0.639270	−	0.768982i	$-0.279237\pi$
$347$	−100.498	−	138.324i	−0.289621	−	0.398629i	−0.928891	+	0.370353i	$0.879237\pi$
$348$	761.686	−	247.487i	2.18875	−	0.711169i
$349$	−164.289	−	53.3806i	−0.470741	−	0.152953i	0.0640335	−	0.997948i	$-0.479604\pi$
$349$	−164.289	−	53.3806i	−0.470741	−	0.152953i	−0.534775	+	0.844995i	$0.679604\pi$
$350$	100.312	+	72.8806i	0.286604	+	0.208230i
$351$		−	112.331i		−	0.320030i
$352$	−71.4205	−	462.825i	−0.202899	−	1.31484i
$353$	−494.535			−1.40095			−0.700474	−	0.713678i	$-0.747028\pi$
$353$	−494.535			−1.40095			−0.700474	+	0.713678i	$0.747028\pi$
$354$	428.790	−	590.179i	1.21127	−	1.66717i
$355$	4.02129	−	12.3762i	0.0113276	−	0.0348627i
$356$	216.360	+	665.888i	0.607753	+	1.87047i
$357$	−633.050	+	459.937i	−1.77325	+	1.28834i
$358$	−377.192	−	519.160i	−1.05361	−	1.45017i
$359$	146.418	−	47.5742i	0.407850	−	0.132519i	−0.0979045	−	0.995196i	$-0.531214\pi$
$359$	146.418	−	47.5742i	0.407850	−	0.132519i	0.505755	+	0.862677i	$0.331214\pi$
$360$	67.4468	+	21.9148i	0.187352	+	0.0608744i
$361$	−234.412	−	170.311i	−0.649342	−	0.471774i
$362$		−	246.165i		−	0.680013i
$363$	−3.84597	+	483.985i	−0.0105950	+	1.33329i
$364$	619.105			1.70084
$365$	−67.2542	+	92.5675i	−0.184258	+	0.253610i
$366$	139.692	−	429.928i	0.381672	−	1.17467i
$367$	−57.3820	−	176.604i	−0.156354	−	0.481209i	0.841941	−	0.539569i	$-0.181413\pi$
$367$	−57.3820	−	176.604i	−0.156354	−	0.481209i	−0.998296	+	0.0583604i	$0.981413\pi$
$368$	−163.131	+	118.522i	−0.443291	+	0.322070i
$369$	−229.784	−	316.270i	−0.622720	−	0.857100i
$370$	−132.672	+	43.1078i	−0.358574	+	0.116508i
$371$	418.218	+	135.887i	1.12727	+	0.366273i
$372$	183.469	+	133.298i	0.493196	+	0.358328i
$373$		−	268.844i		−	0.720760i	−0.932806	−	0.360380i	$-0.882647\pi$
$373$		−	268.844i		−	0.720760i	0.932806	−	0.360380i	$-0.117353\pi$
$374$	812.320	−	125.352i	2.17198	−	0.335167i
$375$	−44.7214			−0.119257
$376$	227.714	−	313.422i	0.605623	−	0.833568i
$377$	−158.761	+	488.616i	−0.421116	+	1.29606i
$378$	−61.3050	−	188.677i	−0.162182	−	0.499146i
$379$	243.935	−	177.229i	0.643627	−	0.467622i	−0.217467	−	0.976068i	$-0.569780\pi$
$379$	243.935	−	177.229i	0.643627	−	0.467622i	0.861094	+	0.508445i	$0.169780\pi$
$380$	60.7092	+	83.5590i	0.159761	+	0.219892i
$381$	102.551	−	33.3209i	0.269163	−	0.0874563i
$382$	255.220	+	82.9259i	0.668115	+	0.217084i
$383$	393.892	+	286.179i	1.02844	+	0.747204i	0.967996	−	0.250967i	$-0.0807486\pi$
$383$	393.892	+	286.179i	1.02844	+	0.747204i	0.0604431	+	0.998172i	$0.480749\pi$
$384$			540.662i			1.40797i
$385$	90.6763	−	176.228i	0.235523	−	0.457734i
$386$	−578.731			−1.49930
$387$	153.369	−	211.094i	0.396302	−	0.545463i
$388$	152.726	−	470.043i	0.393625	−	1.21145i
$389$	118.077	+	363.404i	0.303540	+	0.934200i	0.980218	+	0.197921i	$0.0634189\pi$
$389$	118.077	+	363.404i	0.303540	+	0.934200i	−0.676678	+	0.736279i	$0.736581\pi$
$390$	−312.705	+	227.194i	−0.801808	+	0.582548i
$391$	−362.214	−	498.544i	−0.926377	−	1.27505i
$392$	68.6124	−	22.2935i	0.175032	−	0.0568712i
$393$	337.889	+	109.787i	0.859767	+	0.279355i
$394$	26.1656	+	19.0104i	0.0664102	+	0.0482499i
$395$			76.7396i			0.194278i
$396$	67.5673	−	415.902i	0.170625	−	1.05026i
$397$	668.123			1.68293			0.841465	−	0.540311i	$-0.181693\pi$
$397$	668.123			1.68293			0.841465	+	0.540311i	$0.181693\pi$
$398$	−15.0294	+	20.6862i	−0.0377624	+	0.0519754i
$399$	−84.0689	+	258.737i	−0.210699	+	0.648465i
$400$	−12.2746	−	37.7773i	−0.0306864	−	0.0944431i
$401$	−291.301	+	211.642i	−0.726436	+	0.527787i	−0.888434	−	0.459004i	$-0.848206\pi$
$401$	−291.301	+	211.642i	−0.726436	+	0.527787i	0.161998	+	0.986791i	$0.448206\pi$
$402$	−128.944	−	177.477i	−0.320757	−	0.441484i
$403$	−138.358	+	44.9551i	−0.343319	+	0.111551i
$404$	−561.495	−	182.441i	−1.38984	−	0.451586i
$405$	171.857	+	124.861i	0.424337	+	0.308299i
$406$			907.352i			2.23486i
$407$	100.439	+	199.073i	0.246778	+	0.489124i
$408$	−440.000			−1.07843
$409$	−21.2846	+	29.2958i	−0.0520406	+	0.0716278i	−0.834244	−	0.551395i	$-0.814096\pi$
$409$	−21.2846	+	29.2958i	−0.0520406	+	0.0716278i	0.782204	+	0.623023i	$0.214096\pi$
$410$	118.766	−	365.526i	0.289674	−	0.891526i
$411$	148.413	+	456.769i	0.361103	+	1.11136i
$412$	−84.8763	+	61.6663i	−0.206011	+	0.149675i
$413$	280.647	+	386.277i	0.679532	+	0.935296i
$414$	−520.060	+	168.978i	−1.25618	+	0.408159i
$415$	310.172	+	100.781i	0.747403	+	0.242846i
$416$	−483.616	−	351.368i	−1.16254	−	0.844633i
$417$			14.0686i			0.0337377i
$418$	202.868	−	201.263i	0.485331	−	0.481489i
$419$	−423.543			−1.01084			−0.505421	−	0.862873i	$-0.668663\pi$
$419$	−423.543			−1.01084			−0.505421	+	0.862873i	$0.668663\pi$
$420$	−231.803	+	319.050i	−0.551913	+	0.759643i
$421$	211.289	−	650.280i	0.501873	−	1.54461i	−0.304091	−	0.952643i	$-0.598353\pi$
$421$	211.289	−	650.280i	0.501873	−	1.54461i	0.805964	−	0.591964i	$-0.201647\pi$
$422$	−72.8591	−	224.237i	−0.172652	−	0.531368i
$423$	−484.234	+	351.817i	−1.14476	+	0.831718i
$424$	145.341	+	200.045i	0.342785	+	0.471803i
$425$	115.451	−	37.5123i	0.271649	−	0.0882641i
$426$	68.1378	+	22.1393i	0.159948	+	0.0519702i
$427$	239.366	+	173.909i	0.560575	+	0.407282i
$428$			526.779i			1.23079i
$429$	435.125	+	438.596i	1.01428	+	1.02237i
$430$	256.525			0.596569
$431$	75.8653	−	104.420i	0.176022	−	0.242273i	−0.711886	−	0.702295i	$-0.752159\pi$
$431$	75.8653	−	104.420i	0.176022	−	0.242273i	0.887907	+	0.460022i	$0.152159\pi$
$432$	−19.6393	+	60.4436i	−0.0454614	+	0.139916i
$433$	−170.382	−	524.382i	−0.393492	−	1.21104i	−0.930130	−	0.367231i	$-0.880306\pi$
$433$	−170.382	−	524.382i	−0.393492	−	1.21104i	0.536638	−	0.843813i	$-0.319694\pi$
$434$	−207.859	+	151.018i	−0.478938	+	0.347969i
$435$	−192.361	−	264.762i	−0.442208	−	0.608648i
$436$	109.703	−	35.6447i	0.251613	−	0.0817540i
$437$	−203.763	−	66.2066i	−0.466277	−	0.151503i
$438$	−509.633	−	370.270i	−1.16355	−	0.845366i
$439$			470.583i			1.07194i	0.844236	+	0.535972i	$0.180055\pi$
$439$			470.583i			1.07194i	−0.844236	+	0.535972i	$0.819945\pi$
$440$	99.4959	−	50.1988i	0.226127	−	0.114088i
$441$	−111.461			−0.252746
$442$	616.697	−	848.811i	1.39524	−	1.92039i
$443$	30.6738	−	94.4041i	0.0692410	−	0.213102i	−0.910448	−	0.413622i	$-0.864263\pi$
$443$	30.6738	−	94.4041i	0.0692410	−	0.213102i	0.979689	+	0.200521i	$0.0642634\pi$
$444$	−137.108	−	421.976i	−0.308803	−	0.950397i
$445$	231.462	−	168.167i	0.520140	−	0.377904i
$446$	211.444	+	291.028i	0.474090	+	0.652529i
$447$	−354.971	+	115.337i	−0.794118	+	0.258024i
$448$	−760.559	−	247.120i	−1.69768	−	0.551608i
$449$	−110.271	−	80.1169i	−0.245593	−	0.178434i	0.458178	−	0.888860i	$-0.348502\pi$
$449$	−110.271	−	80.1169i	−0.245593	−	0.178434i	−0.703772	+	0.710426i	$0.748502\pi$
$450$		−	107.719i		−	0.239375i
$451$	−606.371	−	98.5109i	−1.34450	−	0.218428i
$452$	−391.931			−0.867104
$453$	−230.440	+	317.173i	−0.508697	+	0.700161i
$454$	−368.761	+	1134.93i	−0.812249	+	2.49984i
$455$	−78.1763	−	240.602i	−0.171816	−	0.528795i
$456$	−123.761	+	89.9175i	−0.271405	+	0.197188i
$457$	−18.1014	−	24.9144i	−0.0396092	−	0.0545174i	0.788753	−	0.614710i	$-0.210727\pi$
$457$	−18.1014	−	24.9144i	−0.0396092	−	0.0545174i	−0.828362	+	0.560193i	$0.810727\pi$
$458$	405.843	−	131.866i	0.886120	−	0.287918i
$459$	−184.721	−	60.0196i	−0.402443	−	0.130762i
$460$	−251.261	−	182.552i	−0.546219	−	0.396851i
$461$			142.653i			0.309442i	0.987958	+	0.154721i	$0.0494478\pi$
$461$			142.653i			0.309442i	−0.987958	+	0.154721i	$0.950552\pi$
$462$	970.227	+	499.221i	2.10006	+	1.08056i
$463$	490.864			1.06018			0.530091	−	0.847941i	$-0.322158\pi$
$463$	490.864			1.06018			0.530091	+	0.847941i	$0.322158\pi$
$464$	170.854	−	235.160i	0.368220	−	0.506811i
$465$	28.6362	−	88.1332i	0.0615833	−	0.189534i
$466$	−177.456	−	546.153i	−0.380807	−	1.17200i
$467$	613.182	−	445.503i	1.31302	−	0.953968i	0.313033	−	0.949742i	$-0.398655\pi$
$467$	613.182	−	445.503i	1.31302	−	0.953968i	0.999991	−	0.00422562i	$-0.00134506\pi$
$468$	−316.142	−	435.132i	−0.675517	−	0.929769i
$469$	136.554	−	44.3691i	0.291160	−	0.0946037i
$470$	−559.648	−	181.841i	−1.19074	−	0.386895i
$471$	−557.437	−	405.001i	−1.18352	−	0.859875i
$472$			268.481i			0.568816i
$473$	−62.5329	−	405.231i	−0.132205	−	0.856725i
$474$	−422.492			−0.891334
$475$	24.8075	−	34.1445i	0.0522262	−	0.0718833i
$476$	330.795	−	1018.08i	0.694948	−	2.13883i
$477$	−118.053	−	363.330i	−0.247491	−	0.761699i
$478$	434.336	−	315.564i	0.908653	−	0.660175i
$479$	−364.989	−	502.364i	−0.761981	−	1.04878i	−0.997047	−	0.0767971i	$-0.975531\pi$
$479$	−364.989	−	502.364i	−0.761981	−	1.04878i	0.235066	−	0.971979i	$-0.424469\pi$
$480$	362.148	−	117.669i	0.754475	−	0.245144i
$481$	270.694	+	87.9540i	0.562774	+	0.182856i
$482$	570.953	+	414.821i	1.18455	+	0.860625i
$483$		−	818.059i		−	1.69370i
$484$	−384.920	−	538.749i	−0.795290	−	1.11312i
$485$	−201.957			−0.416407
$486$	−557.177	+	766.889i	−1.14646	+	1.57796i
$487$	−121.664	+	374.442i	−0.249823	+	0.768876i	0.744983	+	0.667084i	$0.232458\pi$
$487$	−121.664	+	374.442i	−0.249823	+	0.768876i	−0.994806	+	0.101792i	$0.967542\pi$
$488$	51.4114	+	158.228i	0.105351	+	0.324238i
$489$	819.299	−	595.255i	1.67546	−	1.21729i
$490$	−64.4098	−	88.6525i	−0.131449	−	0.180924i
$491$	−616.943	+	200.457i	−1.25650	+	0.408262i	−0.860247	−	0.509878i	$-0.829691\pi$
$491$	−616.943	+	200.457i	−1.25650	+	0.408262i	−0.396256	+	0.918140i	$0.629691\pi$
$492$	1162.59	+	377.748i	2.36298	+	0.767780i
$493$	718.673	+	522.146i	1.45775	+	1.05912i
$494$		−	364.776i		−	0.738413i
$495$	−170.163	+	26.2586i	−0.343764	+	0.0530476i
$496$	82.3081			0.165944
$497$	−27.5623	+	37.9363i	−0.0554574	+	0.0763305i
$498$	−554.853	+	1707.66i	−1.11416	+	3.42904i
$499$	−221.573	−	681.931i	−0.444034	−	1.36660i	−0.883540	−	0.468356i	$-0.844846\pi$
$499$	−221.573	−	681.931i	−0.444034	−	1.36660i	0.439506	−	0.898240i	$-0.355154\pi$
$500$	49.4959	−	35.9609i	0.0989919	−	0.0719218i
$501$	177.236	+	243.945i	0.353765	+	0.486915i
$502$	−310.167	+	100.779i	−0.617862	+	0.200755i
$503$	596.635	+	193.858i	1.18615	+	0.385404i	0.834649	−	0.550782i	$-0.185671\pi$
$503$	596.635	+	193.858i	1.18615	+	0.385404i	0.351503	+	0.936187i	$0.385671\pi$
$504$	−206.741	−	150.206i	−0.410201	−	0.298028i
$505$			241.250i			0.477723i
$506$	−393.150	+	764.081i	−0.776977	+	1.51004i
$507$	112.636			0.222162
$508$	−86.7061	+	119.341i	−0.170681	+	0.234923i
$509$	−79.8228	+	245.669i	−0.156823	+	0.482651i	−0.998341	−	0.0575779i	$-0.981662\pi$
$509$	−79.8228	+	245.669i	−0.156823	+	0.482651i	0.841518	+	0.540229i	$0.181662\pi$
$510$	206.525	+	635.618i	0.404951	+	1.24631i
$511$	333.559	−	242.345i	0.652758	−	0.474256i
$512$	283.422	+	390.097i	0.553559	+	0.761908i
$513$	−64.2229	+	20.8673i	−0.125191	+	0.0406770i
$514$	754.325	+	245.095i	1.46756	+	0.476839i
$515$	34.6829	+	25.1986i	0.0673453	+	0.0489293i
$516$			815.900i			1.58120i
$517$	−150.828	+	928.400i	−0.291737	+	1.79575i
$518$	502.676			0.970416
$519$	−263.475	+	362.643i	−0.507659	+	0.698733i
$520$	43.9590	−	135.292i	0.0845365	−	0.260177i
$521$	92.8597	+	285.793i	0.178234	+	0.548547i	0.999766	−	0.0216146i	$-0.00688069\pi$
$521$	92.8597	+	285.793i	0.178234	+	0.548547i	−0.821533	+	0.570161i	$0.806881\pi$
$522$	637.723	−	463.333i	1.22169	−	0.887611i
$523$	247.497	+	340.650i	0.473225	+	0.651338i	0.977185	−	0.212389i	$-0.0681243\pi$
$523$	247.497	+	340.650i	0.473225	+	0.651338i	−0.503961	+	0.863727i	$0.668124\pi$
$524$	−462.243	+	150.192i	−0.882143	+	0.286626i
$525$	153.262	+	49.7980i	0.291928	+	0.0948533i
$526$	−722.934	−	525.242i	−1.37440	−	0.998559i
$527$			251.541i			0.477308i
$528$	−157.453	−	312.078i	−0.298206	−	0.591056i
$529$	115.244			0.217853
$530$	220.762	−	303.853i	0.416533	−	0.573308i
$531$	128.181	−	394.500i	0.241395	−	0.742937i
$532$	−115.009	−	353.962i	−0.216183	−	0.665341i
$533$	−634.408	+	460.924i	−1.19026	+	0.864773i
$534$	925.850	+	1274.32i	1.73380	+	2.38637i
$535$	204.721	−	66.5180i	0.382657	−	0.124333i
$536$	76.7852	+	24.9490i	0.143256	+	0.0465467i
$537$	−674.741	−	490.228i	−1.25650	−	0.912902i
$538$			1018.07i			1.89232i
$539$	−124.343	+	123.359i	−0.230692	+	0.228866i
$540$	−97.8885			−0.181275
$541$	112.764	−	155.206i	0.208436	−	0.286888i	−0.691981	−	0.721916i	$-0.743262\pi$
$541$	112.764	−	155.206i	0.208436	−	0.286888i	0.900417	+	0.435028i	$0.143262\pi$
$542$	−206.661	+	636.036i	−0.381293	+	1.17350i
$543$	−98.8653	−	304.276i	−0.182072	−	0.560361i
$544$	−836.205	+	607.539i	−1.53714	+	1.11680i
$545$	−27.7051	−	38.1328i	−0.0508350	−	0.0699684i
$546$	1324.64	−	430.402i	2.42608	−	0.788281i
$547$	189.538	+	61.5846i	0.346504	+	0.112586i	0.477099	−	0.878850i	$-0.341688\pi$
$547$	189.538	+	61.5846i	0.346504	+	0.112586i	−0.130594	+	0.991436i	$0.541688\pi$
$548$	−531.551	−	386.194i	−0.969984	−	0.704734i
$549$		−	257.041i		−	0.468199i
$550$	−119.217	−	120.168i	−0.216759	−	0.218488i
$551$	308.849			0.560525
$552$	270.381	−	372.147i	0.489820	−	0.674180i
$553$	85.4508	−	262.991i	0.154522	−	0.475571i
$554$	−426.673	−	1313.16i	−0.770168	−	2.37033i
$555$	−146.679	+	106.568i	−0.264286	+	0.192015i
$556$	−11.3127	−	15.5706i	−0.0203466	−	0.0280047i
$557$	720.414	−	234.077i	1.29338	−	0.420245i	0.420108	−	0.907474i	$-0.361992\pi$
$557$	720.414	−	234.077i	1.29338	−	0.420245i	0.873274	+	0.487229i	$0.161992\pi$
$558$	212.284	+	68.9751i	0.380437	+	0.123611i
$559$	−423.435	−	307.643i	−0.757486	−	0.550346i
$560$			143.133i			0.255594i
$561$	953.738	−	481.190i	1.70007	−	0.857737i
$562$	−288.328			−0.513039
$563$	89.0871	−	122.618i	0.158236	−	0.217794i	−0.722536	−	0.691333i	$-0.757024\pi$
$563$	89.0871	−	122.618i	0.158236	−	0.217794i	0.880773	+	0.473539i	$0.157024\pi$
$564$	578.361	−	1780.01i	1.02546	−	3.15605i
$565$	49.4903	+	152.316i	0.0875935	+	0.269585i
$566$	727.818	−	528.791i	1.28590	−	0.934260i
$567$	−449.926	−	619.271i	−0.793521	−	1.09219i
$568$	−25.0770	+	8.14802i	−0.0441497	+	0.0143451i
$569$	836.163	+	271.686i	1.46953	+	0.477480i	0.930967	−	0.365104i	$-0.118967\pi$
$569$	836.163	+	271.686i	1.46953	+	0.477480i	0.538565	+	0.842584i	$0.318967\pi$
$570$	187.984	+	136.578i	0.329796	+	0.239611i
$571$			324.644i			0.568554i	0.958742	+	0.284277i	$0.0917536\pi$
$571$			324.644i			0.568554i	−0.958742	+	0.284277i	$0.908246\pi$
$572$	−834.259	−	135.534i	−1.45850	−	0.236947i
$573$	348.774			0.608681
$574$	−814.037	+	1120.43i	−1.41818	+	1.95196i
$575$	−39.2173	+	120.698i	−0.0682040	+	0.209910i
$576$	214.688	+	660.741i	0.372722	+	1.14712i
$577$	421.177	−	306.003i	0.729943	−	0.530335i	−0.159602	−	0.987181i	$-0.551021\pi$
$577$	421.177	−	306.003i	0.729943	−	0.530335i	0.889545	+	0.456847i	$0.151021\pi$
$578$	−543.506	−	748.072i	−0.940322	−	1.29424i
$579$	−715.351	+	232.432i	−1.23549	+	0.401437i
$580$	425.795	+	138.349i	0.734130	+	0.238533i
$581$	−950.755	−	690.764i	−1.63641	−	1.18892i
$582$		−	1111.88i		−	1.91045i
$583$	−533.811	−	274.667i	−0.915628	−	0.471127i
$584$	231.840			0.396986
$585$	−129.184	+	177.807i	−0.220828	+	0.303944i
$586$	−329.140	+	1012.99i	−0.561673	+	1.72865i
$587$	−305.959	−	941.646i	−0.521225	−	1.60417i	−0.771661	−	0.636034i	$-0.780574\pi$
$587$	−305.959	−	941.646i	−0.521225	−	1.60417i	0.250436	−	0.968133i	$-0.419426\pi$
$588$	281.967	−	204.861i	0.479537	−	0.348404i
$589$	51.4044	+	70.7521i	0.0872741	+	0.120122i
$590$	387.844	−	126.018i	0.657363	−	0.213590i
$591$	39.9775	+	12.9895i	0.0676439	+	0.0219788i
$592$	−130.280	−	94.6537i	−0.220067	−	0.159888i
$593$		−	289.152i		−	0.487609i	−0.969824	−	0.243804i	$-0.921604\pi$
$593$		−	289.152i		−	0.487609i	0.969824	−	0.243804i	$-0.0783955\pi$
$594$	41.3050	+	267.668i	0.0695370	+	0.450619i
$595$	−437.426			−0.735171
$596$	300.125	−	413.086i	0.503565	−	0.693097i
$597$	−10.2693	+	31.6057i	−0.0172015	+	0.0529409i
$598$	338.953	+	1043.19i	0.566812	+	1.74447i
$599$	−674.089	+	489.754i	−1.12536	+	0.817620i	−0.985013	−	0.172483i	$-0.944821\pi$
$599$	−674.089	+	489.754i	−1.12536	+	0.817620i	−0.140345	+	0.990103i	$0.544821\pi$
$600$	53.2624	+	73.3094i	0.0887706	+	0.122182i
$601$	−89.9741	+	29.2343i	−0.149707	+	0.0486428i	−0.382912	−	0.923785i	$-0.625079\pi$
$601$	−89.9741	+	29.2343i	−0.149707	+	0.0486428i	0.233205	+	0.972428i	$0.425079\pi$
$602$	−879.123	−	285.645i	−1.46034	−	0.474493i
$603$	−100.915	−	73.3189i	−0.167355	−	0.121590i
$604$		−	536.334i		−	0.887970i
$605$	−160.768	+	217.620i	−0.265732	+	0.359703i
$606$	−1328.21			−2.19177
$607$	−124.839	+	171.826i	−0.205666	+	0.283074i	−0.899373	−	0.437183i	$-0.855976\pi$
$607$	−124.839	+	171.826i	−0.205666	+	0.283074i	0.693707	+	0.720257i	$0.255976\pi$
$608$	−111.048	+	341.770i	−0.182645	+	0.562123i
$609$	364.413	+	1121.55i	0.598380	+	1.84162i
$610$	204.443	−	148.536i	0.335152	−	0.243502i
$611$	705.710	+	971.327i	1.15501	+	1.58973i
$612$	−884.468	+	287.381i	−1.44521	+	0.469577i
$613$	−750.498	−	243.852i	−1.22430	−	0.397801i	−0.375656	−	0.926759i	$-0.622583\pi$
$613$	−750.498	−	243.852i	−1.22430	−	0.397801i	−0.848648	+	0.528958i	$0.822583\pi$
$614$	450.238	+	327.117i	0.733287	+	0.532764i
$615$		−	499.514i		−	0.812217i
$616$	−396.875	+	61.2434i	−0.644277	+	0.0994211i
$617$	181.544			0.294237			0.147118	−	0.989119i	$-0.453000\pi$
$617$	181.544			0.294237			0.147118	+	0.989119i	$0.453000\pi$
$618$	−138.731	+	190.947i	−0.224484	+	0.308976i
$619$	−11.1606	+	34.3488i	−0.0180301	+	0.0554908i	−0.959667	−	0.281140i	$-0.909287\pi$
$619$	−11.1606	+	34.3488i	−0.0180301	+	0.0554908i	0.941637	+	0.336631i	$0.109287\pi$
$620$	39.1753	+	120.569i	0.0631860	+	0.194466i
$621$	164.276	−	119.353i	0.264534	−	0.192195i
$622$	−675.055	−	929.133i	−1.08530	−	1.49378i
$623$	−980.491	+	318.581i	−1.57382	+	0.511366i
$624$	−424.354	−	137.881i	−0.680055	−	0.220963i
$625$	−20.2254	−	14.6946i	−0.0323607	−	0.0235114i
$626$		−	976.745i		−	1.56030i
$627$	169.927	−	330.251i	0.271016	−	0.526716i
$628$	942.616			1.50098
$629$	289.271	−	398.147i	0.459890	−	0.632984i
$630$	−119.947	+	369.158i	−0.190392	+	0.585965i
$631$	311.846	+	959.763i	0.494209	+	1.52102i	0.818186	+	0.574954i	$0.194980\pi$
$631$	311.846	+	959.763i	0.494209	+	1.52102i	−0.323976	+	0.946065i	$0.605020\pi$
$632$	125.795	−	91.3956i	0.199043	−	0.144613i
$633$	−180.118	−	247.911i	−0.284546	−	0.391644i
$634$	804.340	−	261.346i	1.26867	−	0.412217i
$635$	57.3278	+	18.6269i	0.0902800	+	0.0293337i
$636$	966.433	+	702.155i	1.51955	+	1.10402i
$637$			223.580i			0.350989i
$638$	198.636	−	1222.68i	0.311342	−	1.91642i
$639$	40.7376			0.0637521
$640$	−177.652	+	244.517i	−0.277581	+	0.382058i
$641$	−33.2415	+	102.307i	−0.0518588	+	0.159605i	−0.973632	−	0.228125i	$-0.926741\pi$
$641$	−33.2415	+	102.307i	−0.0518588	+	0.159605i	0.921773	+	0.387730i	$0.126741\pi$
$642$	366.217	+	1127.10i	0.570431	+	1.75561i
$643$	21.8723	−	15.8911i	0.0340160	−	0.0247141i	−0.570647	−	0.821195i	$-0.693308\pi$
$643$	21.8723	−	15.8911i	0.0340160	−	0.0247141i	0.604663	+	0.796481i	$0.293308\pi$
$644$	657.809	+	905.397i	1.02144	+	1.40590i
$645$	317.082	−	103.026i	0.491600	−	0.159731i
$646$	−599.853	−	194.904i	−0.928565	−	0.301709i
$647$	903.123	+	656.158i	1.39586	+	1.01415i	0.995193	+	0.0979314i	$0.0312226\pi$
$647$	903.123	+	656.158i	1.39586	+	1.01415i	0.400670	+	0.916222i	$0.368777\pi$
$648$		−	430.423i		−	0.664233i
$649$	−293.615	−	581.957i	−0.452412	−	0.896698i
$650$	−216.074			−0.332421
$651$	−196.276	+	270.150i	−0.301499	+	0.414977i
$652$	−428.118	+	1317.61i	−0.656623	+	2.02088i
$653$	−338.002	−	1040.26i	−0.517615	−	1.59305i	−0.778474	−	0.627677i	$-0.784006\pi$
$653$	−338.002	−	1040.26i	−0.517615	−	1.59305i	0.260859	−	0.965377i	$-0.415994\pi$
$654$	209.941	−	152.531i	0.321011	−	0.233228i
$655$	116.738	+	160.676i	0.178225	+	0.245306i
$656$	421.952	−	137.100i	0.643219	−	0.208995i
$657$	−340.659	−	110.687i	−0.518507	−	0.168473i
$658$	1715.46	+	1246.35i	2.60708	+	1.89416i
$659$			587.822i			0.891991i	0.895035	+	0.445996i	$0.147150\pi$
$659$			587.822i			0.891991i	−0.895035	+	0.445996i	$0.852850\pi$
$660$	382.207	−	379.182i	0.579101	−	0.574517i
$661$	389.155			0.588736			0.294368	−	0.955692i	$-0.404891\pi$
$661$	389.155			0.588736			0.294368	+	0.955692i	$0.404891\pi$
$662$	−744.737	+	1025.04i	−1.12498	+	1.54840i
$663$	421.378	−	1296.87i	0.635562	−	1.95606i
$664$	−204.205	−	628.478i	−0.307537	−	0.946502i
$665$	−123.037	+	89.3916i	−0.185018	+	0.134423i
$666$	−256.688	−	353.301i	−0.385417	−	0.530481i
$667$	−883.251	+	286.986i	−1.32421	+	0.430263i
$668$	−392.317	−	127.471i	−0.587300	−	0.190825i
$669$	378.243	+	274.810i	0.565386	+	0.410777i
$670$		−	122.633i		−	0.183035i
$671$	−284.479	−	286.749i	−0.423963	−	0.427345i
$672$	−1372.13			−2.04185
$673$	602.060	−	828.664i	0.894591	−	1.23130i	−0.0775708	−	0.996987i	$-0.524716\pi$
$673$	602.060	−	828.664i	0.894591	−	1.23130i	0.972162	−	0.234312i	$-0.0752836\pi$
$674$	440.410	−	1355.44i	0.653428	−	2.01104i
$675$	12.3607	+	38.0423i	0.0183121	+	0.0563589i
$676$	−124.662	+	90.5719i	−0.184411	+	0.133982i
$677$	145.396	+	200.121i	0.214766	+	0.295599i	0.902784	−	0.430093i	$-0.141519\pi$
$677$	145.396	+	200.121i	0.214766	+	0.295599i	−0.688019	+	0.725693i	$0.741519\pi$
$678$	−838.577	+	272.470i	−1.23684	+	0.401874i
$679$	692.118	+	224.883i	1.01932	+	0.331197i
$680$	−198.992	−	144.576i	−0.292635	−	0.212612i
$681$			1550.95i			2.27746i
$682$	313.156	−	157.997i	0.459173	−	0.231667i
$683$	−979.967			−1.43480			−0.717399	−	0.696662i	$-0.754668\pi$
$683$	−979.967			−1.43480			−0.717399	+	0.696662i	$0.754668\pi$
$684$	−190.050	+	261.581i	−0.277851	+	0.382428i
$685$	−82.9656	+	255.342i	−0.121118	+	0.372762i
$686$	−253.473	−	780.110i	−0.369494	−	1.13719i
$687$	448.689	−	325.992i	0.653113	−	0.474515i
$688$	174.058	+	239.570i	0.252991	+	0.348212i
$689$	−728.806	+	236.804i	−1.05777	+	0.343692i
$690$	−664.508	−	215.912i	−0.963056	−	0.312916i
$691$	537.473	+	390.497i	0.777818	+	0.565118i	0.904323	−	0.426848i	$-0.140376\pi$
$691$	537.473	+	390.497i	0.777818	+	0.565118i	−0.126505	+	0.991966i	$0.540376\pi$
$692$		−	613.222i		−	0.886160i
$693$	612.397	+	99.4899i	0.883690	+	0.143564i
$694$	526.217			0.758237
$695$	−4.62269	+	6.36259i	−0.00665136	+	0.00915481i
$696$	−204.912	+	630.654i	−0.294413	+	0.906111i
$697$	418.992	+	1289.52i	0.601136	+	1.85011i
$698$	430.113	−	312.496i	0.616208	−	0.447702i
$699$	−438.695	−	603.812i	−0.627604	−	0.863823i
$700$	−209.668	+	68.1253i	−0.299526	+	0.0973219i
$701$	−984.515	−	319.888i	−1.40444	−	0.456332i	−0.493819	−	0.869565i	$-0.664399\pi$
$701$	−984.515	−	319.888i	−1.40444	−	0.456332i	−0.910625	+	0.413233i	$0.864399\pi$
$702$	279.692	+	203.208i	0.398422	+	0.289470i
$703$		−	171.103i		−	0.243390i
$704$	970.772	+	499.501i	1.37894	+	0.709519i
$705$	−764.794			−1.08481
$706$	894.622	−	1231.34i	1.26717	−	1.74411i
$707$	268.636	−	826.777i	0.379966	−	1.16942i
$708$	400.813	+	1233.57i	0.566120	+	1.74234i
$709$	996.643	−	724.104i	1.40570	−	1.02130i	0.411773	−	0.911287i	$-0.364910\pi$
$709$	996.643	−	724.104i	1.40570	−	1.02130i	0.993930	−	0.110016i	$-0.0350903\pi$
$710$	23.5410	+	32.4014i	0.0331564	+	0.0456358i
$711$	−228.475	+	74.2361i	−0.321344	+	0.104411i
$712$	−551.336	−	179.140i	−0.774348	−	0.251601i
$713$	−212.751	−	154.572i	−0.298388	−	0.216792i
$714$		−	2408.26i		−	3.37292i
$715$	52.6722	+	341.331i	0.0736674	+	0.477386i
$716$	1140.98			1.59354
$717$	410.132	−	564.498i	0.572011	−	0.787305i
$718$	−146.418	+	450.629i	−0.203925	+	0.627617i
$719$	229.638	+	706.754i	0.319385	+	0.982967i	0.973912	+	0.226928i	$0.0728682\pi$
$719$	229.638	+	706.754i	0.319385	+	0.982967i	−0.654526	+	0.756039i	$0.727132\pi$
$720$	100.599	−	73.0896i	0.139721	−	0.101513i
$721$	−90.8009	−	124.977i	−0.125937	−	0.173338i
$722$	848.112	−	275.568i	1.17467	−	0.381673i
$723$	872.338	+	283.440i	1.20655	+	0.392033i
$724$	354.092	+	257.263i	0.489077	+	0.355336i
$725$		−	182.946i		−	0.252339i
$726$	−1198.12	−	885.113i	−1.65030	−	1.21916i
$727$	−10.4678			−0.0143987			−0.00719934	−	0.999974i	$-0.502292\pi$
$727$	−10.4678			−0.0143987			−0.00719934	+	0.999974i	$0.502292\pi$
$728$	−301.299	+	414.703i	−0.413873	+	0.569647i
$729$	−116.499	+	358.548i	−0.159807	+	0.491836i
$730$	−108.820	−	334.912i	−0.149068	−	0.458784i
$731$	−732.148	+	531.937i	−1.00157	+	0.727683i
$732$	472.433	+	650.249i	0.645401	+	0.888318i
$733$	961.151	−	312.297i	1.31126	−	0.426053i	0.431773	−	0.901982i	$-0.357888\pi$
$733$	961.151	−	312.297i	1.31126	−	0.426053i	0.879484	+	0.475929i	$0.157888\pi$
$734$	543.530	+	176.604i	0.740504	+	0.240604i
$735$	−115.220	−	83.7121i	−0.156762	−	0.113894i
$736$		−	1080.59i		−	1.46819i
$737$	−193.723	+	29.8942i	−0.262854	+	0.0405621i
$738$	1203.16			1.63030
$739$	−339.077	+	466.699i	−0.458832	+	0.631528i	−0.974266	−	0.225401i	$-0.927631\pi$
$739$	−339.077	+	466.699i	−0.458832	+	0.631528i	0.515434	+	0.856929i	$0.327631\pi$
$740$	76.6459	−	235.892i	0.103576	−	0.318773i
$741$	−146.502	−	450.888i	−0.197709	−	0.608485i
$742$	−1094.91	+	795.498i	−1.47562	+	1.07210i
$743$	677.947	+	933.113i	0.912445	+	1.25587i	0.966325	+	0.257325i	$0.0828412\pi$
$743$	677.947	+	933.113i	0.912445	+	1.25587i	−0.0538800	+	0.998547i	$0.517159\pi$
$744$	−178.577	+	58.0233i	−0.240023	+	0.0779883i
$745$	−198.435	−	64.4753i	−0.266355	−	0.0865440i
$746$	669.393	+	486.342i	0.897310	+	0.651934i
$747$			1020.96i			1.36675i
$748$	−668.632	+	1299.47i	−0.893893	+	1.73727i
$749$	−775.659			−1.03559
$750$	80.9017	−	111.352i	0.107869	−	0.148469i
$751$	447.403	−	1376.97i	0.595743	−	1.83351i	0.0447527	−	0.998998i	$-0.485750\pi$
$751$	447.403	−	1376.97i	0.595743	−	1.83351i	0.550991	−	0.834511i	$-0.314250\pi$
$752$	−209.911	−	646.041i	−0.279137	−	0.859097i
$753$	−342.912	+	249.140i	−0.455394	+	0.330863i
$754$	−929.402	−	1279.21i	−1.23263	−	1.69657i
$755$	−208.435	+	67.7245i	−0.276072	+	0.0897013i
$756$	335.469	+	109.000i	0.443742	+	0.144181i
$757$	−427.516	−	310.608i	−0.564750	−	0.410315i	0.268444	−	0.963295i	$-0.413490\pi$
$757$	−427.516	−	310.608i	−0.564750	−	0.410315i	−0.833194	+	0.552980i	$0.813490\pi$
$758$			927.982i			1.22425i
$759$	−179.088	+	1102.35i	−0.235953	+	1.45238i
$760$	−85.5166			−0.112522
$761$	128.577	−	176.972i	0.168958	−	0.232551i	−0.716138	−	0.697958i	$-0.754092\pi$
$761$	128.577	−	176.972i	0.168958	−	0.232551i	0.885097	+	0.465407i	$0.154092\pi$
$762$	−102.551	+	315.620i	−0.134581	+	0.414199i
$763$	52.4853	+	161.533i	0.0687881	+	0.211708i
$764$	−386.010	+	280.453i	−0.505249	+	0.367085i
$765$	223.369	+	307.441i	0.291985	+	0.401883i
$766$	−1425.11	+	463.048i	−1.86046	+	0.604501i
$767$	−791.329	−	257.118i	−1.03172	−	0.335226i
$768$	−61.4853	−	44.6717i	−0.0800590	−	0.0581662i
$769$		−	162.687i		−	0.211557i	−0.994390	−	0.105778i	$-0.966267\pi$
$769$		−	162.687i		−	0.211557i	0.994390	−	0.105778i	$-0.0337334\pi$
$770$	274.754	+	544.574i	0.356824	+	0.707239i
$771$	1030.83			1.33701
$772$	604.823	−	832.468i	0.783450	−	1.07833i
$773$	100.881	−	310.480i	0.130506	−	0.401656i	−0.864358	−	0.502877i	$-0.832275\pi$
$773$	100.881	−	310.480i	0.130506	−	0.401656i	0.994864	+	0.101221i	$0.0322750\pi$
$774$	248.156	+	763.745i	0.320615	+	0.986751i
$775$	41.9098	−	30.4493i	0.0540772	−	0.0392894i
$776$	240.528	+	331.058i	0.309959	+	0.426621i
$777$	621.341	−	201.886i	0.799667	−	0.259828i
$778$	−1118.44	−	363.404i	−1.43759	−	0.467100i
$779$	381.376	+	277.086i	0.489572	+	0.355695i
$780$		−	687.243i		−	0.881081i
$781$	45.4458	−	45.0861i	0.0581893	−	0.0577287i
$782$	1896.58			2.42529
$783$	−172.053	+	236.810i	−0.219735	+	0.302439i
$784$	39.0896	−	120.305i	0.0498592	−	0.153451i
$785$	−119.027	−	366.327i	−0.151627	−	0.466659i
$786$	−884.604	+	642.702i	−1.12545	+	0.817687i
$787$	227.621	+	313.294i	0.289226	+	0.398086i	0.928763	−	0.370675i	$-0.120874\pi$
$787$	227.621	+	313.294i	0.289226	+	0.398086i	−0.639536	+	0.768761i	$0.720874\pi$
$788$	−54.6906	+	17.7701i	−0.0694043	+	0.0225508i
$789$	−1104.54	−	358.888i	−1.39993	−	0.454865i
$790$	−191.074	−	138.823i	−0.241866	−	0.175726i
$791$		−	577.101i		−	0.729585i
$792$	245.706	+	247.666i	0.310234	+	0.312710i
$793$	−515.601			−0.650190
$794$	−1208.65	+	1663.56i	−1.52222	+	2.09516i
$795$	150.843	−	464.247i	0.189739	−	0.583958i
$796$	−14.0488	−	43.2377i	−0.0176492	−	0.0543187i
$797$	17.7812	−	12.9188i	0.0223101	−	0.0162092i	−0.576574	−	0.817045i	$-0.695611\pi$
$797$	17.7812	−	12.9188i	0.0223101	−	0.0162092i	0.598884	+	0.800835i	$0.295611\pi$
$798$	−492.148	−	677.383i	−0.616727	−	0.848851i
$799$	1974.36	−	641.509i	2.47104	−	0.802890i
$800$	202.447	+	65.7789i	0.253058	+	0.0822237i
$801$	724.592	+	526.447i	0.904609	+	0.657237i
$802$		−	1108.17i		−	1.38176i
$803$	−502.533	+	253.543i	−0.625819	+	0.315745i
$804$	390.046			0.485132
$805$	268.799	−	369.971i	0.333912	−	0.459591i
$806$	138.358	−	425.821i	0.171660	−	0.528314i
$807$	408.879	+	1258.40i	0.506666	+	1.55936i
$808$	395.469	−	287.325i	0.489442	−	0.355600i
$809$	599.477	+	825.109i	0.741010	+	1.01991i	0.998560	+	0.0536476i	$0.0170848\pi$
$809$	599.477	+	825.109i	0.741010	+	1.01991i	−0.257550	+	0.966265i	$0.582915\pi$
$810$	−621.783	+	202.030i	−0.767633	+	0.249419i
$811$	−940.701	−	305.652i	−1.15993	−	0.376883i	−0.335053	−	0.942199i	$-0.608754\pi$
$811$	−940.701	−	305.652i	−1.15993	−	0.376883i	−0.824875	+	0.565316i	$0.808754\pi$
$812$	−1305.17	−	948.260i	−1.60735	−	1.16781i
$813$			869.183i			1.06911i
$814$	−677.368	−	110.045i	−0.832147	−	0.135190i
$815$	566.122			0.694628
$816$	−453.475	+	624.155i	−0.555729	+	0.764896i
$817$	−97.2291	+	299.240i	−0.119007	+	0.366267i
$818$	−34.4392	−	105.993i	−0.0421018	−	0.129576i
$819$	640.713	−	465.505i	0.782311	−	0.568382i
$820$	401.664	+	552.843i	0.489834	+	0.674199i
$821$	−729.758	+	237.113i	−0.888864	+	0.288810i	−0.717633	−	0.696421i	$-0.754775\pi$
$821$	−729.758	+	237.113i	−0.888864	+	0.288810i	−0.171231	+	0.985231i	$0.554775\pi$
$822$	−1405.79	−	456.769i	−1.71021	−	0.555680i
$823$	−674.965	−	490.391i	−0.820128	−	0.595858i	0.0966212	−	0.995321i	$-0.469196\pi$
$823$	−674.965	−	490.391i	−0.820128	−	0.595858i	−0.916749	+	0.399463i	$0.869196\pi$
$824$		−	86.8648i		−	0.105418i
$825$	−195.623	−	100.656i	−0.237119	−	0.122007i
$826$	−1469.49			−1.77904
$827$	−329.248	+	453.171i	−0.398123	+	0.547970i	−0.960272	−	0.279067i	$-0.909975\pi$
$827$	−329.248	+	453.171i	−0.398123	+	0.547970i	0.562148	+	0.827036i	$0.309975\pi$
$828$	300.443	−	924.669i	0.362854	−	1.11675i
$829$	−371.006	−	1141.84i	−0.447534	−	1.37737i	−0.879681	−	0.475565i	$-0.842244\pi$
$829$	−371.006	−	1141.84i	−0.447534	−	1.37737i	0.432147	−	0.901803i	$-0.357756\pi$
$830$	−812.041	+	589.983i	−0.978363	+	0.710822i
$831$	−1054.79	−	1451.80i	−1.26931	−	1.74705i
$832$	1325.38	−	430.643i	1.59301	−	0.517600i
$833$	367.664	+	119.461i	0.441374	+	0.143411i
$834$	−35.0294	−	25.4504i	−0.0420017	−	0.0305160i
$835$			168.562i			0.201870i
$836$	77.4888	+	502.149i	0.0926899	+	0.600657i
$837$	−82.8854			−0.0990268
$838$	766.196	−	1054.58i	0.914315	−	1.25845i
$839$	162.370	−	499.723i	0.193528	−	0.595618i	−0.806463	−	0.591285i	$-0.798621\pi$
$839$	162.370	−	499.723i	0.193528	−	0.595618i	0.999991	−	0.00433286i	$-0.00137920\pi$
$840$	−100.902	−	310.543i	−0.120121	−	0.369695i
$841$	402.703	−	292.581i	0.478838	−	0.347896i
$842$	1236.91	+	1702.45i	1.46901	+	2.02192i
$843$	−356.393	+	115.799i	−0.422768	+	0.137366i
$844$	398.695	+	129.544i	0.472387	+	0.153488i
$845$	50.9402	+	37.0102i	0.0602843	+	0.0437991i
$846$		−	1842.14i		−	2.17746i
$847$	793.284	−	566.779i	0.936581	−	0.669160i
$848$	433.562			0.511276
$849$	687.259	−	945.930i	0.809492	−	1.11417i
$850$	−115.451	+	355.321i	−0.135825	+	0.418025i
$851$	158.991	+	489.324i	0.186828	+	0.574998i
$852$	−103.056	+	74.8744i	−0.120957	+	0.0878807i
$853$	563.318	+	775.340i	0.660396	+	0.908957i	0.999494	−	0.0317938i	$-0.0101220\pi$
$853$	563.318	+	775.340i	0.660396	+	0.908957i	−0.339099	+	0.940751i	$0.610122\pi$
$854$	−866.033	+	281.391i	−1.01409	+	0.329498i
$855$	125.656	+	40.8281i	0.146966	+	0.0477522i
$856$	−352.859	−	256.367i	−0.412219	−	0.299494i
$857$		−	56.2536i		−	0.0656402i	−0.999461	−	0.0328201i	$-0.989551\pi$
$857$		−	56.2536i		−	0.0656402i	0.999461	−	0.0328201i	$-0.0104488\pi$
$858$	−1879.21	+	289.988i	−2.19022	+	0.337982i
$859$	−1517.29			−1.76634			−0.883171	−	0.469051i	$-0.844596\pi$
$859$	−1517.29			−1.76634			−0.883171	+	0.469051i	$0.844596\pi$
$860$	−268.090	+	368.994i	−0.311733	+	0.429063i
$861$	−556.217	+	1711.86i	−0.646012	+	1.98822i
$862$	122.753	+	377.794i	0.142405	+	0.438276i
$863$	887.101	−	644.517i	1.02793	−	0.746833i	0.0600344	−	0.998196i	$-0.480879\pi$
$863$	887.101	−	644.517i	1.02793	−	0.746833i	0.967893	+	0.251363i	$0.0808789\pi$
$864$	−200.190	−	275.538i	−0.231702	−	0.318910i
$865$	−238.316	+	77.4334i	−0.275509	+	0.0895184i
$866$	1613.88	+	524.382i	1.86360	+	0.605522i
$867$	−972.253	−	706.383i	−1.12140	−	0.814744i
$868$		−	456.819i		−	0.526289i
$869$	−172.721	+	335.680i	−0.198758	+	0.386283i
$870$	1007.21			1.15772
$871$	−147.071	+	202.426i	−0.168853	+	0.232406i
$872$	−29.5128	+	90.8310i	−0.0338449	+	0.104164i
$873$	−195.369	−	601.283i	−0.223790	−	0.688755i
$874$	533.458	−	387.580i	0.610364	−	0.443456i
$875$	52.9508	+	72.8806i	0.0605153	+	0.0832921i
$876$	1065.22	−	346.111i	1.21600	−	0.395104i
$877$	−1081.62	−	351.441i	−1.23332	−	0.400731i	−0.381405	−	0.924408i	$-0.624560\pi$
$877$	−1081.62	−	351.441i	−1.23332	−	0.400731i	−0.851917	+	0.523677i	$0.824560\pi$
$878$	−1171.70	−	851.293i	−1.33451	−	0.969582i
$879$			1384.31i			1.57487i
$880$	31.3344	−	192.875i	0.0356072	−	0.219176i
$881$	850.822			0.965746			0.482873	−	0.875690i	$-0.339593\pi$
$881$	850.822			0.965746			0.482873	+	0.875690i	$0.339593\pi$
$882$	201.635	−	277.526i	0.228611	−	0.314656i
$883$	157.572	−	484.958i	0.178451	−	0.549216i	−0.821323	−	0.570463i	$-0.806764\pi$
$883$	157.572	−	484.958i	0.178451	−	0.549216i	0.999774	+	0.0212471i	$0.00676368\pi$
$884$	576.459	+	1774.16i	0.652103	+	2.00697i
$885$	428.790	−	311.534i	0.484509	−	0.352016i
$886$	179.567	+	247.153i	0.202672	+	0.278954i
$887$	−554.947	+	180.313i	−0.625645	+	0.203284i	−0.604645	−	0.796495i	$-0.706685\pi$
$887$	−554.947	+	180.313i	−0.625645	+	0.203284i	−0.0209998	+	0.999779i	$0.506685\pi$
$888$	349.384	+	113.522i	0.393450	+	0.127840i
$889$	−175.724	−	127.671i	−0.197665	−	0.143612i
$890$			880.535i			0.989366i
$891$	470.717	+	932.979i	0.528302	+	1.04711i
$892$	−639.603			−0.717043
$893$	424.240	−	583.917i	0.475073	−	0.653882i
$894$	354.971	−	1092.49i	0.397059	−	1.22202i
$895$	−144.075	−	443.416i	−0.160977	−	0.495437i
$896$	881.096	−	640.153i	0.983366	−	0.714457i
$897$	837.939	+	1153.32i	0.934157	+	1.28576i
$898$	398.966	−	129.632i	0.444283	−	0.144356i
$899$	360.535	+	117.145i	0.401040	+	0.130306i
$900$	154.947	+	112.575i	0.172163	+	0.125084i
$901$			1325.01i			1.47060i
$902$	1342.22	−	1331.59i	1.48805	−	1.47627i
$903$	−1201.38			−1.33043
$904$	190.741	−	262.532i	0.210996	−	0.290412i
$905$	55.2674	−	170.096i	0.0610690	−	0.187951i
$906$	−372.859	−	1147.54i	−0.411544	−	1.26660i
$907$	−518.177	+	376.478i	−0.571309	+	0.415080i	−0.835580	−	0.549368i	$-0.814868\pi$
$907$	−518.177	+	376.478i	−0.571309	+	0.415080i	0.264272	+	0.964448i	$0.414868\pi$
$908$	−1247.14	−	1716.54i	−1.37350	−	1.89046i
$909$	−718.269	+	233.380i	−0.790175	+	0.256744i
$910$	740.496	+	240.602i	0.813732	+	0.264398i
$911$	885.922	+	643.660i	0.972472	+	0.706542i	0.956014	−	0.293322i	$-0.0947609\pi$
$911$	885.922	+	643.660i	0.972472	+	0.706542i	0.0164582	+	0.999865i	$0.494761\pi$
$912$			268.230i			0.294112i
$913$	1129.94	+	1138.96i	1.23762	+	1.24749i
$914$	94.7802			0.103698
$915$	193.050	−	265.710i	0.210983	−	0.290393i
$916$	−234.459	+	721.591i	−0.255960	+	0.787763i
$917$	−221.151	−	680.633i	−0.241168	−	0.742238i
$918$	483.607	−	351.361i	0.526805	−	0.382746i
$919$	−729.402	−	1003.94i	−0.793691	−	1.09242i	−0.993639	−	0.112615i	$-0.964077\pi$
$919$	−729.402	−	1003.94i	−0.793691	−	1.09242i	0.199948	−	0.979807i	$-0.435923\pi$
$920$	244.562	−	79.4629i	0.265828	−	0.0863727i
$921$	687.902	+	223.513i	0.746908	+	0.242685i
$922$	−355.190	−	258.061i	−0.385239	−	0.279893i
$923$		−	81.7158i		−	0.0885328i
$924$	−1732.07	+	873.881i	−1.87453	+	0.945759i
$925$	−101.353			−0.109570
$926$	−887.982	+	1222.20i	−0.958943	+	1.31987i
$927$	−41.4718	+	127.637i	−0.0447376	+	0.137688i
$928$	481.359	+	1481.47i	0.518706	+	1.59641i
$929$	−834.947	+	606.624i	−0.898758	+	0.652986i	−0.938147	−	0.346238i	$-0.887459\pi$
$929$	−834.947	+	606.624i	−0.898758	+	0.652986i	0.0393884	+	0.999224i	$0.487459\pi$
$930$	167.639	+	230.736i	0.180257	+	0.248103i
$931$	127.828	−	41.5337i	0.137301	−	0.0446119i
$932$	971.063	+	315.517i	1.04191	+	0.338538i
$933$	−1207.57	−	877.354i	−1.29429	−	0.940358i
$934$			2332.68i			2.49752i
$935$	589.443	+	95.7608i	0.630420	+	0.102418i
$936$	445.326			0.475776
$937$	180.209	−	248.036i	0.192325	−	0.264713i	−0.701954	−	0.712222i	$-0.747689\pi$
$937$	180.209	−	248.036i	0.192325	−	0.264713i	0.894279	+	0.447509i	$0.147689\pi$
$938$	−136.554	+	420.271i	−0.145580	+	0.448050i
$939$	−392.283	−	1207.32i	−0.417767	−	1.28575i
$940$	846.446	−	614.979i	0.900474	−	0.654233i
$941$	11.2167	+	15.4385i	0.0119200	+	0.0164064i	0.814935	−	0.579552i	$-0.196772\pi$
$941$	11.2167	+	15.4385i	0.0119200	+	0.0164064i	−0.803015	+	0.595958i	$0.796772\pi$
$942$	2016.82	−	655.306i	2.14100	−	0.695654i
$943$	−1348.14	−	438.036i	−1.42963	−	0.464514i
$944$	380.850	+	276.704i	0.403443	+	0.293118i
$945$		−	144.137i		−	0.152525i
$946$	1122.11	+	577.369i	1.18616	+	0.610327i
$947$	−804.636			−0.849669			−0.424834	−	0.905271i	$-0.639668\pi$
$947$	−804.636			−0.849669			−0.424834	+	0.905271i	$0.639668\pi$
$948$	441.540	−	607.728i	0.465760	−	0.641063i
$949$	−222.027	+	683.330i	−0.233959	+	0.720053i
$950$	40.1393	+	123.536i	0.0422519	+	0.130038i
$951$	889.256	−	646.082i	0.935075	−	0.679372i
$952$	520.967	+	717.050i	0.547235	+	0.753204i
$953$	−1763.40	+	572.962i	−1.85036	+	0.601220i	−0.853591	+	0.520944i	$0.825580\pi$
$953$	−1763.40	+	572.962i	−1.85036	+	0.601220i	−0.996773	+	0.0802758i	$0.974420\pi$
$954$	1118.22	+	363.330i	1.17213	+	0.380850i
$955$	157.735	+	114.601i	0.165167	+	0.120001i
$956$			954.556i			0.998489i
$957$	−245.528	−	1591.09i	−0.256560	−	1.66258i
$958$	1911.11			1.99489
$959$	568.654	−	782.686i	0.592966	−	0.816148i
$960$	−274.318	+	844.264i	−0.285748	+	0.879442i
$961$	−263.794	−	811.875i	−0.274500	−	0.844824i
$962$	−708.687	+	514.891i	−0.736681	+	0.535230i
$963$	396.085	+	545.164i	0.411303	+	0.566111i
$964$	−1193.39	+	387.755i	−1.23795	+	0.402236i
$965$	−399.894	−	129.933i	−0.414397	−	0.134646i
$966$	2036.88	+	1479.88i	2.10857	+	1.53197i
$967$		−	660.803i		−	0.683353i	−0.939818	−	0.341677i	$-0.889005\pi$
$967$		−	660.803i		−	0.683353i	0.939818	−	0.341677i	$-0.110995\pi$
$968$	548.206	+	4.35630i	0.566328	+	0.00450031i
$969$	−819.737			−0.845962
$970$	365.344	−	502.853i	0.376644	−	0.518406i
$971$	−166.517	+	512.487i	−0.171490	+	0.527793i	−0.999456	−	0.0329859i	$-0.989498\pi$
$971$	−166.517	+	512.487i	−0.171490	+	0.527793i	0.827965	+	0.560779i	$0.189498\pi$
$972$	−520.823	−	1602.93i	−0.535826	−	1.64910i
$973$	22.9271	−	16.6575i	0.0235633	−	0.0171197i
$974$	−712.232	−	980.303i	−0.731244	−	1.00647i
$975$	−267.082	+	86.7802i	−0.273930	+	0.0890053i
$976$	277.438	+	90.1450i	0.284260	+	0.0923617i
$977$	243.828	+	177.151i	0.249568	+	0.181322i	0.705535	−	0.708675i	$-0.250707\pi$
$977$	243.828	+	177.151i	0.249568	+	0.181322i	−0.455967	+	0.889996i	$0.650707\pi$
$978$			3116.80i			3.18691i
$979$	1390.98	−	214.648i	1.42082	−	0.219252i
$980$	194.835			0.198811
$981$	86.7307	−	119.375i	0.0884105	−	0.121687i
$982$	616.943	−	1898.75i	0.628251	−	1.93356i
$983$	−238.319	−	733.472i	−0.242441	−	0.746156i	−0.996047	−	0.0888299i	$-0.971687\pi$
$983$	−238.319	−	733.472i	−0.242441	−	0.746156i	0.753606	−	0.657327i	$-0.228313\pi$
$984$	−818.827	+	594.912i	−0.832141	+	0.604586i
$985$	13.8119	+	19.0104i	0.0140222	+	0.0192999i
$986$	−2600.18	+	844.850i	−2.63710	+	0.856846i
$987$	2620.99	+	851.611i	2.65551	+	0.862827i
$988$	524.707	+	381.222i	0.531080	+	0.385852i
$989$		−	946.119i		−	0.956642i
$990$	242.447	−	471.191i	0.244896	−	0.475951i
$991$	118.312			0.119386			0.0596932	−	0.998217i	$-0.480988\pi$
$991$	118.312			0.119386			0.0596932	+	0.998217i	$0.480988\pi$
$992$	−259.264	+	356.846i	−0.261354	+	0.359723i
$993$	−508.865	+	1566.13i	−0.512453	+	1.57717i
$994$	−44.5967	−	137.255i	−0.0448659	−	0.138083i
$995$	−15.0294	+	10.9195i	−0.0151049	+	0.0109744i
$996$	−1876.49	−	2582.77i	−1.88403	−	2.59314i
$997$	36.0263	−	11.7057i	0.0361347	−	0.0117409i	−0.290894	−	0.956755i	$-0.593953\pi$
$997$	36.0263	−	11.7057i	0.0361347	−	0.0117409i	0.327029	+	0.945014i	$0.393953\pi$
$998$	2098.77	+	681.931i	2.10298	+	0.683298i
$999$	131.193	+	95.3177i	0.131325	+	0.0954131i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.3.i.a.51.1	yes	4
5.2	odd	4		275.3.q.c.249.1		8
5.3	odd	4		275.3.q.c.249.2		8
5.4	even	2		275.3.x.d.51.1		4
11.5	even	5		605.3.c.a.241.1		4
11.6	odd	10		605.3.c.a.241.4		4
11.8	odd	10	inner	55.3.i.a.41.1	✓	4
55.8	even	20		275.3.q.c.74.1		8
55.19	odd	10		275.3.x.d.151.1		4
55.52	even	20		275.3.q.c.74.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.i.a.41.1	✓	4	11.8	odd	10	inner
55.3.i.a.51.1	yes	4	1.1	even	1	trivial
275.3.q.c.74.1		8	55.8	even	20
275.3.q.c.74.2		8	55.52	even	20
275.3.q.c.249.1		8	5.2	odd	4
275.3.q.c.249.2		8	5.3	odd	4
275.3.x.d.51.1		4	5.4	even	2
275.3.x.d.151.1		4	55.19	odd	10
605.3.c.a.241.1		4	11.5	even	5
605.3.c.a.241.4		4	11.6	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	55.i (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80902 + 2.48990i) q^{2} +(-1.23607 + 3.80423i) q^{3} +(-1.69098 - 5.20431i) q^{4} +(-1.80902 + 1.31433i) q^{5} +(-7.23607 - 9.95959i) q^{6} +(7.66312 - 2.48990i) q^{7} +(4.30902 + 1.40008i) q^{8} +(-5.66312 - 4.11450i) q^{9} -6.88191i q^{10} +(-10.8713 + 1.67760i) q^{11} +21.8885 q^{12} +(-8.25329 + 11.3597i) q^{13} +(-7.66312 + 23.5847i) q^{14} +(-2.76393 - 8.50651i) q^{15} +(6.42705 - 4.66953i) q^{16} +(14.2705 + 19.6417i) q^{17} +(20.4894 - 6.65740i) q^{18} +(8.02786 + 2.60841i) q^{19} +(9.89919 + 7.19218i) q^{20} +32.2299i q^{21} +(15.4894 - 30.1033i) q^{22} -25.3820 q^{23} +(-10.6525 + 14.6619i) q^{24} +(1.54508 - 4.75528i) q^{25} +(-13.3541 - 41.0997i) q^{26} +(-6.47214 + 4.70228i) q^{27} +(-25.9164 - 35.6709i) q^{28} +(34.7984 - 11.3067i) q^{29} +(26.1803 + 8.50651i) q^{30} +(8.38197 + 6.08985i) q^{31} +42.5730i q^{32} +(7.05573 - 43.4306i) q^{33} -74.7214 q^{34} +(-10.5902 + 14.5761i) q^{35} +(-11.8369 + 36.4302i) q^{36} +(-6.26393 - 19.2784i) q^{37} +(-21.0172 + 15.2699i) q^{38} +(-33.0132 - 45.4387i) q^{39} +(-9.63525 + 3.13068i) q^{40} +(53.1140 + 17.2578i) q^{41} +(-80.2492 - 58.3045i) q^{42} +37.2752i q^{43} +(27.1140 + 53.7409i) q^{44} +15.6525 q^{45} +(45.9164 - 63.1985i) q^{46} +(26.4230 - 81.3216i) q^{47} +(9.81966 + 30.2218i) q^{48} +(12.8820 - 9.35930i) q^{49} +(9.04508 + 12.4495i) q^{50} +(-92.3607 + 30.0098i) q^{51} +(73.0755 + 23.7437i) q^{52} +(44.1525 + 32.0787i) q^{53} -24.6215i q^{54} +(17.4615 - 17.3233i) q^{55} +36.5066 q^{56} +(-19.8460 + 27.3156i) q^{57} +(-34.7984 + 107.098i) q^{58} +(18.3115 + 56.3571i) q^{59} +(-39.5967 + 28.7687i) q^{60} +(21.5836 + 29.7073i) q^{61} +(-30.3262 + 9.85359i) q^{62} +(-53.6418 - 17.4293i) q^{63} +(-80.2943 - 58.3372i) q^{64} -31.3974i q^{65} +(95.3738 + 96.1347i) q^{66} +17.8197 q^{67} +(78.0902 - 107.482i) q^{68} +(31.3738 - 96.5587i) q^{69} +(-17.1353 - 52.7369i) q^{70} +(-4.70820 + 3.42071i) q^{71} +(-18.6418 - 25.6583i) q^{72} +(48.6656 - 15.8124i) q^{73} +(59.3328 + 19.2784i) q^{74} +(16.1803 + 11.7557i) q^{75} -46.1903i q^{76} +(-79.1312 + 39.9241i) q^{77} +172.859 q^{78} +(20.1722 - 27.7647i) q^{79} +(-5.48936 + 16.8945i) q^{80} +(-29.3566 - 90.3504i) q^{81} +(-139.054 + 101.029i) q^{82} +(-85.7295 - 117.997i) q^{83} +(167.735 - 54.5002i) q^{84} +(-51.6312 - 16.7760i) q^{85} +(-92.8115 - 67.4315i) q^{86} +146.357i q^{87} +(-49.1935 - 7.99197i) q^{88} -127.949 q^{89} +(-28.3156 + 38.9731i) q^{90} +(-34.9615 + 107.600i) q^{91} +(42.9205 + 132.096i) q^{92} +(-33.5279 + 24.3594i) q^{93} +(154.683 + 212.903i) q^{94} +(-17.9508 + 5.83258i) q^{95} +(-161.957 - 52.6232i) q^{96} +(73.0689 + 53.0877i) q^{97} +49.0059i q^{98} +(68.4681 + 35.2296i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{2} + 4 q^{3} - 9 q^{4} - 5 q^{5} - 20 q^{6} + 15 q^{7} + 15 q^{8} - 7 q^{9} - q^{11} + 16 q^{12} + 5 q^{13} - 15 q^{14} - 20 q^{15} + 19 q^{16} - 10 q^{17} + 35 q^{18} + 50 q^{19} + 15 q^{20}+ \cdots + 133 q^{99}+O(q^{100}) \) 4 * q - 5 * q^2 + 4 * q^3 - 9 * q^4 - 5 * q^5 - 20 * q^6 + 15 * q^7 + 15 * q^8 - 7 * q^9 - q^11 + 16 * q^12 + 5 * q^13 - 15 * q^14 - 20 * q^15 + 19 * q^16 - 10 * q^17 + 35 * q^18 + 50 * q^19 + 15 * q^20 + 15 * q^22 - 106 * q^23 + 20 * q^24 - 5 * q^25 - 40 * q^26 - 8 * q^27 - 50 * q^28 + 90 * q^29 + 60 * q^30 + 38 * q^31 + 64 * q^33 - 120 * q^34 - 20 * q^35 - 63 * q^36 - 34 * q^37 - 55 * q^38 + 20 * q^39 - 5 * q^40 + 85 * q^41 - 160 * q^42 - 19 * q^44 + 130 * q^46 - 24 * q^47 + 84 * q^48 + 56 * q^49 + 25 * q^50 - 280 * q^51 + 100 * q^52 + 114 * q^53 + 5 * q^55 + 70 * q^56 + 180 * q^57 - 90 * q^58 - 128 * q^59 - 60 * q^60 + 140 * q^61 - 90 * q^62 - 105 * q^63 - 149 * q^64 + 140 * q^66 + 116 * q^67 + 290 * q^68 - 116 * q^69 - 35 * q^70 + 8 * q^71 + 35 * q^72 - 20 * q^73 + 130 * q^74 + 20 * q^75 - 160 * q^77 + 280 * q^78 - 210 * q^79 + 25 * q^80 + 95 * q^81 - 270 * q^82 - 410 * q^83 + 340 * q^84 - 50 * q^85 - 170 * q^86 - 78 * q^89 - 35 * q^90 - 75 * q^91 + 241 * q^92 - 152 * q^93 + 375 * q^94 + 40 * q^95 - 460 * q^96 + 176 * q^97 + 133 * q^99

Introduction

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