LMFDB - Embedded newform 11.3.d.a.8.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,3,Mod(2,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("11.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	11.d (of order $10$, degree $4$, 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:	$0.299728290796$
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			8.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	11.8
Dual form			11.3.d.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80902 - 2.48990i) q^{2} +(1.11803 + 3.44095i) q^{3} +(-1.69098 + 5.20431i) q^{4} +(-3.23607 - 2.35114i) q^{5} +(6.54508 - 9.00854i) q^{6} +(-0.854102 - 0.277515i) q^{7} +(4.30902 - 1.40008i) q^{8} +(-3.30902 + 2.40414i) q^{9} +O(q^{10})$	\(q+(-1.80902 - 2.48990i) q^{2} +(1.11803 + 3.44095i) q^{3} +(-1.69098 + 5.20431i) q^{4} +(-3.23607 - 2.35114i) q^{5} +(6.54508 - 9.00854i) q^{6} +(-0.854102 - 0.277515i) q^{7} +(4.30902 - 1.40008i) q^{8} +(-3.30902 + 2.40414i) q^{9} +12.3107i q^{10} +(10.8713 - 1.67760i) q^{11} -19.7984 q^{12} +(-5.00000 - 6.88191i) q^{13} +(0.854102 + 2.62866i) q^{14} +(4.47214 - 13.7638i) q^{15} +(6.42705 + 4.66953i) q^{16} +(-14.5344 + 20.0049i) q^{17} +(11.9721 + 3.88998i) q^{18} +(11.2812 - 3.66547i) q^{19} +(17.7082 - 12.8658i) q^{20} -3.24920i q^{21} +(-23.8435 - 24.0337i) q^{22} -7.23607 q^{23} +(9.63525 + 13.2618i) q^{24} +(-2.78115 - 8.55951i) q^{25} +(-8.09017 + 24.8990i) q^{26} +(14.3713 + 10.4414i) q^{27} +(2.88854 - 3.97574i) q^{28} +(-3.29180 - 1.06957i) q^{29} +(-42.3607 + 13.7638i) q^{30} +(-26.7984 + 19.4702i) q^{31} -42.5730i q^{32} +(17.9271 + 35.5321i) q^{33} +76.1033 q^{34} +(2.11146 + 2.90617i) q^{35} +(-6.91641 - 21.2865i) q^{36} +(12.4377 - 38.2793i) q^{37} +(-29.5344 - 21.4580i) q^{38} +(18.0902 - 24.8990i) q^{39} +(-17.2361 - 5.60034i) q^{40} +(1.24265 - 0.403760i) q^{41} +(-8.09017 + 5.87785i) q^{42} +33.0625i q^{43} +(-9.65248 + 59.4145i) q^{44} +16.3607 q^{45} +(13.0902 + 18.0171i) q^{46} +(7.03444 + 21.6498i) q^{47} +(-8.88197 + 27.3359i) q^{48} +(-38.9894 - 28.3274i) q^{49} +(-16.2812 + 22.4091i) q^{50} +(-85.0861 - 27.6462i) q^{51} +(44.2705 - 14.3844i) q^{52} +(63.5410 - 46.1653i) q^{53} -54.6718i q^{54} +(-39.1246 - 20.1312i) q^{55} -4.06888 q^{56} +(25.2254 + 34.7198i) q^{57} +(3.29180 + 10.1311i) q^{58} +(9.66312 - 29.7400i) q^{59} +(64.0689 + 46.5488i) q^{60} +(-16.5066 + 22.7194i) q^{61} +(96.9574 + 31.5034i) q^{62} +(3.49342 - 1.13508i) q^{63} +(-80.2943 + 58.3372i) q^{64} +34.0260i q^{65} +(56.0410 - 108.915i) q^{66} -76.5066 q^{67} +(-79.5344 - 109.470i) q^{68} +(-8.09017 - 24.8990i) q^{69} +(3.41641 - 10.5146i) q^{70} +(50.4164 + 36.6297i) q^{71} +(-10.8926 + 14.9924i) q^{72} +(89.5344 + 29.0915i) q^{73} +(-117.812 + 38.2793i) q^{74} +(26.3435 - 19.1396i) q^{75} +64.9089i q^{76} +(-9.75078 - 1.58411i) q^{77} -94.7214 q^{78} +(38.7426 + 53.3247i) q^{79} +(-9.81966 - 30.2218i) q^{80} +(-31.2361 + 96.1347i) q^{81} +(-3.25329 - 2.36365i) q^{82} +(33.3303 - 45.8752i) q^{83} +(16.9098 + 5.49434i) q^{84} +(94.0689 - 30.5648i) q^{85} +(82.3222 - 59.8106i) q^{86} -12.5227i q^{87} +(44.4959 - 22.4496i) q^{88} -62.2968 q^{89} +(-29.5967 - 40.7364i) q^{90} +(2.36068 + 7.26543i) q^{91} +(12.2361 - 37.6587i) q^{92} +(-96.9574 - 70.4437i) q^{93} +(41.1803 - 56.6799i) q^{94} +(-45.1246 - 14.6619i) q^{95} +(146.492 - 47.5981i) q^{96} +(-58.5795 + 42.5605i) q^{97} +148.324i q^{98} +(-31.9402 + 31.6874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{2} - 9 q^{4} - 4 q^{5} + 15 q^{6} + 10 q^{7} + 15 q^{8} - 11 q^{9}+O(q^{10}) $ 4 * q - 5 * q^2 - 9 * q^4 - 4 * q^5 + 15 * q^6 + 10 * q^7 + 15 * q^8 - 11 * q^9	\( 4 q - 5 q^{2} - 9 q^{4} - 4 q^{5} + 15 q^{6} + 10 q^{7} + 15 q^{8} - 11 q^{9} + q^{11} - 30 q^{12} - 20 q^{13} - 10 q^{14} + 19 q^{16} + 30 q^{18} + 25 q^{19} + 44 q^{20} - 35 q^{22} - 20 q^{23} + 5 q^{24} + 9 q^{25} - 10 q^{26} + 15 q^{27} - 60 q^{28} - 40 q^{29} - 80 q^{30} - 58 q^{31} + 65 q^{33} + 130 q^{34} + 80 q^{35} + 26 q^{36} + 90 q^{37} - 60 q^{38} + 50 q^{39} - 60 q^{40} - 80 q^{41} - 10 q^{42} + 24 q^{44} - 24 q^{45} + 30 q^{46} - 30 q^{47} - 40 q^{48} - 109 q^{49} - 45 q^{50} - 195 q^{51} + 110 q^{52} + 120 q^{53} - 76 q^{55} + 100 q^{56} + 45 q^{57} + 40 q^{58} + 23 q^{59} + 140 q^{60} + 10 q^{61} + 200 q^{62} + 90 q^{63} - 149 q^{64} + 90 q^{66} - 230 q^{67} - 260 q^{68} - 10 q^{69} - 40 q^{70} + 148 q^{71} - 95 q^{72} + 300 q^{73} - 270 q^{74} + 45 q^{75} - 200 q^{77} - 200 q^{78} + 70 q^{79} - 84 q^{80} - 116 q^{81} + 25 q^{82} + 225 q^{83} + 90 q^{84} + 260 q^{85} + 175 q^{86} + 55 q^{88} + 122 q^{89} - 20 q^{90} - 80 q^{91} + 40 q^{92} - 200 q^{93} + 120 q^{94} - 100 q^{95} + 340 q^{96} - 165 q^{97} + 31 q^{99}+O(q^{100}) \) 4 * q - 5 * q^2 - 9 * q^4 - 4 * q^5 + 15 * q^6 + 10 * q^7 + 15 * q^8 - 11 * q^9 + q^11 - 30 * q^12 - 20 * q^13 - 10 * q^14 + 19 * q^16 + 30 * q^18 + 25 * q^19 + 44 * q^20 - 35 * q^22 - 20 * q^23 + 5 * q^24 + 9 * q^25 - 10 * q^26 + 15 * q^27 - 60 * q^28 - 40 * q^29 - 80 * q^30 - 58 * q^31 + 65 * q^33 + 130 * q^34 + 80 * q^35 + 26 * q^36 + 90 * q^37 - 60 * q^38 + 50 * q^39 - 60 * q^40 - 80 * q^41 - 10 * q^42 + 24 * q^44 - 24 * q^45 + 30 * q^46 - 30 * q^47 - 40 * q^48 - 109 * q^49 - 45 * q^50 - 195 * q^51 + 110 * q^52 + 120 * q^53 - 76 * q^55 + 100 * q^56 + 45 * q^57 + 40 * q^58 + 23 * q^59 + 140 * q^60 + 10 * q^61 + 200 * q^62 + 90 * q^63 - 149 * q^64 + 90 * q^66 - 230 * q^67 - 260 * q^68 - 10 * q^69 - 40 * q^70 + 148 * q^71 - 95 * q^72 + 300 * q^73 - 270 * q^74 + 45 * q^75 - 200 * q^77 - 200 * q^78 + 70 * q^79 - 84 * q^80 - 116 * q^81 + 25 * q^82 + 225 * q^83 + 90 * q^84 + 260 * q^85 + 175 * q^86 + 55 * q^88 + 122 * q^89 - 20 * q^90 - 80 * q^91 + 40 * q^92 - 200 * q^93 + 120 * q^94 - 100 * q^95 + 340 * q^96 - 165 * q^97 + 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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	−0.969007	−	0.247031i	$-0.920545\pi$
$2$	−1.80902	−	2.48990i	−0.904508	−	1.24495i	0.0644990	−	0.997918i	$-0.479455\pi$
$3$	1.11803	+	3.44095i	0.372678	+	1.14698i	0.945032	+	0.326978i	$0.106030\pi$
$3$	1.11803	+	3.44095i	0.372678	+	1.14698i	−0.572354	+	0.820007i	$0.693970\pi$
$4$	−1.69098	+	5.20431i	−0.422746	+	1.30108i
$5$	−3.23607	−	2.35114i	−0.647214	−	0.470228i	0.215107	−	0.976590i	$-0.430990\pi$
$5$	−3.23607	−	2.35114i	−0.647214	−	0.470228i	−0.862321	+	0.506362i	$0.830990\pi$
$6$	6.54508	−	9.00854i	1.09085	−	1.50142i
$7$	−0.854102	−	0.277515i	−0.122015	−	0.0396449i	0.247373	−	0.968920i	$-0.420433\pi$
$7$	−0.854102	−	0.277515i	−0.122015	−	0.0396449i	−0.369388	+	0.929275i	$0.620433\pi$
$8$	4.30902	−	1.40008i	0.538627	−	0.175011i
$9$	−3.30902	+	2.40414i	−0.367669	+	0.267127i
$10$			12.3107i			1.23107i
$11$	10.8713	−	1.67760i	0.988302	−	0.152509i
$11$	10.8713	−	1.67760i	0.988302	−	0.152509i
$12$	−19.7984			−1.64986
$13$	−5.00000	−	6.88191i	−0.384615	−	0.529378i	0.572185	−	0.820125i	$-0.306096\pi$
$13$	−5.00000	−	6.88191i	−0.384615	−	0.529378i	−0.956800	+	0.290747i	$0.906096\pi$
$14$	0.854102	+	2.62866i	0.0610073	+	0.187761i
$15$	4.47214	−	13.7638i	0.298142	−	0.917588i
$16$	6.42705	+	4.66953i	0.401691	+	0.291845i
$17$	−14.5344	+	20.0049i	−0.854967	+	1.17676i	0.127779	+	0.991803i	$0.459215\pi$
$17$	−14.5344	+	20.0049i	−0.854967	+	1.17676i	−0.982746	+	0.184959i	$0.940785\pi$
$18$	11.9721	+	3.88998i	0.665119	+	0.216110i
$19$	11.2812	−	3.66547i	0.593745	−	0.192919i	0.00329617	−	0.999995i	$-0.498951\pi$
$19$	11.2812	−	3.66547i	0.593745	−	0.192919i	0.590449	+	0.807075i	$0.298951\pi$
$20$	17.7082	−	12.8658i	0.885410	−	0.643288i
$21$		−	3.24920i		−	0.154724i
$22$	−23.8435	−	24.0337i	−1.08379	−	1.09244i
$23$	−7.23607			−0.314612			−0.157306	−	0.987550i	$-0.550281\pi$
$23$	−7.23607			−0.314612			−0.157306	+	0.987550i	$0.550281\pi$
$24$	9.63525	+	13.2618i	0.401469	+	0.552575i
$25$	−2.78115	−	8.55951i	−0.111246	−	0.342380i
$26$	−8.09017	+	24.8990i	−0.311160	+	0.957653i
$27$	14.3713	+	10.4414i	0.532271	+	0.386718i
$28$	2.88854	−	3.97574i	0.103162	−	0.141991i
$29$	−3.29180	−	1.06957i	−0.113510	−	0.0368817i	0.251711	−	0.967802i	$-0.419007\pi$
$29$	−3.29180	−	1.06957i	−0.113510	−	0.0368817i	−0.365221	+	0.930921i	$0.619007\pi$
$30$	−42.3607	+	13.7638i	−1.41202	+	0.458794i
$31$	−26.7984	+	19.4702i	−0.864464	+	0.628070i	−0.929096	−	0.369840i	$-0.879413\pi$
$31$	−26.7984	+	19.4702i	−0.864464	+	0.628070i	0.0646320	+	0.997909i	$0.479413\pi$
$32$		−	42.5730i		−	1.33041i
$33$	17.9271	+	35.5321i	0.543244	+	1.07673i
$34$	76.1033			2.23833
$35$	2.11146	+	2.90617i	0.0603273	+	0.0830334i
$36$	−6.91641	−	21.2865i	−0.192122	−	0.591292i
$37$	12.4377	−	38.2793i	0.336154	−	1.03458i	−0.629997	−	0.776598i	$-0.716944\pi$
$37$	12.4377	−	38.2793i	0.336154	−	1.03458i	0.966151	−	0.257978i	$-0.0830561\pi$
$38$	−29.5344	−	21.4580i	−0.777222	−	0.564685i
$39$	18.0902	−	24.8990i	0.463851	−	0.638435i
$40$	−17.2361	−	5.60034i	−0.430902	−	0.140008i
$41$	1.24265	−	0.403760i	0.0303084	−	0.00984781i	−0.293824	−	0.955860i	$-0.594928\pi$
$41$	1.24265	−	0.403760i	0.0303084	−	0.00984781i	0.324132	+	0.946012i	$0.394928\pi$
$42$	−8.09017	+	5.87785i	−0.192623	+	0.139949i
$43$			33.0625i			0.768895i	0.923147	+	0.384447i	$0.125608\pi$
$43$			33.0625i			0.768895i	−0.923147	+	0.384447i	$0.874392\pi$
$44$	−9.65248	+	59.4145i	−0.219374	+	1.35033i
$45$	16.3607			0.363571
$46$	13.0902	+	18.0171i	0.284569	+	0.391676i
$47$	7.03444	+	21.6498i	0.149669	+	0.460634i	0.997582	−	0.0695019i	$-0.0221410\pi$
$47$	7.03444	+	21.6498i	0.149669	+	0.460634i	−0.847913	+	0.530136i	$0.822141\pi$
$48$	−8.88197	+	27.3359i	−0.185041	+	0.569498i
$49$	−38.9894	−	28.3274i	−0.795701	−	0.578111i
$50$	−16.2812	+	22.4091i	−0.325623	+	0.448182i
$51$	−85.0861	−	27.6462i	−1.66835	−	0.542081i
$52$	44.2705	−	14.3844i	0.851356	−	0.276622i
$53$	63.5410	−	46.1653i	1.19889	−	0.871043i	0.204712	−	0.978822i	$-0.434374\pi$
$53$	63.5410	−	46.1653i	1.19889	−	0.871043i	0.994175	+	0.107780i	$0.0343741\pi$
$54$		−	54.6718i		−	1.01244i
$55$	−39.1246	−	20.1312i	−0.711357	−	0.366022i
$56$	−4.06888			−0.0726586
$57$	25.2254	+	34.7198i	0.442551	+	0.609120i
$58$	3.29180	+	10.1311i	0.0567551	+	0.174674i
$59$	9.66312	−	29.7400i	0.163782	−	0.504068i	−0.835163	−	0.550003i	$-0.814627\pi$
$59$	9.66312	−	29.7400i	0.163782	−	0.504068i	0.998944	+	0.0459347i	$0.0146266\pi$
$60$	64.0689	+	46.5488i	1.06781	+	0.775813i
$61$	−16.5066	+	22.7194i	−0.270600	+	0.372448i	−0.922592	−	0.385777i	$-0.873933\pi$
$61$	−16.5066	+	22.7194i	−0.270600	+	0.372448i	0.651992	+	0.758226i	$0.273933\pi$
$62$	96.9574	+	31.5034i	1.56383	+	0.508119i
$63$	3.49342	−	1.13508i	0.0554511	−	0.0180172i
$64$	−80.2943	+	58.3372i	−1.25460	+	0.911519i
$65$			34.0260i			0.523477i
$66$	56.0410	−	108.915i	0.849106	−	1.65022i
$67$	−76.5066			−1.14189			−0.570945	−	0.820989i	$-0.693423\pi$
$67$	−76.5066			−1.14189			−0.570945	+	0.820989i	$0.693423\pi$
$68$	−79.5344	−	109.470i	−1.16962	−	1.60985i
$69$	−8.09017	−	24.8990i	−0.117249	−	0.360855i
$70$	3.41641	−	10.5146i	0.0488058	−	0.150209i
$71$	50.4164	+	36.6297i	0.710090	+	0.515911i	0.883203	−	0.468991i	$-0.155382\pi$
$71$	50.4164	+	36.6297i	0.710090	+	0.515911i	−0.173113	+	0.984902i	$0.555382\pi$
$72$	−10.8926	+	14.9924i	−0.151286	+	0.208228i
$73$	89.5344	+	29.0915i	1.22650	+	0.398514i	0.849445	−	0.527677i	$-0.176937\pi$
$73$	89.5344	+	29.0915i	1.22650	+	0.398514i	0.377054	+	0.926191i	$0.376937\pi$
$74$	−117.812	+	38.2793i	−1.59205	+	0.517288i
$75$	26.3435	−	19.1396i	0.351246	−	0.255195i
$76$			64.9089i			0.854064i
$77$	−9.75078	−	1.58411i	−0.126633	−	0.0205729i
$78$	−94.7214			−1.21438
$79$	38.7426	+	53.3247i	0.490413	+	0.674996i	0.980464	−	0.196698i	$-0.0630218\pi$
$79$	38.7426	+	53.3247i	0.490413	+	0.674996i	−0.490051	+	0.871694i	$0.663022\pi$
$80$	−9.81966	−	30.2218i	−0.122746	−	0.377773i
$81$	−31.2361	+	96.1347i	−0.385630	+	1.18685i
$82$	−3.25329	−	2.36365i	−0.0396743	−	0.0288250i
$83$	33.3303	−	45.8752i	0.401570	−	0.552714i	−0.559567	−	0.828785i	$-0.689033\pi$
$83$	33.3303	−	45.8752i	0.401570	−	0.552714i	0.961137	+	0.276071i	$0.0890326\pi$
$84$	16.9098	+	5.49434i	0.201308	+	0.0654088i
$85$	94.0689	−	30.5648i	1.10669	−	0.359586i
$86$	82.3222	−	59.8106i	0.957235	−	0.695472i
$87$		−	12.5227i		−	0.143939i
$88$	44.4959	−	22.4496i	0.505636	−	0.255109i
$89$	−62.2968			−0.699964			−0.349982	−	0.936756i	$-0.613812\pi$
$89$	−62.2968			−0.699964			−0.349982	+	0.936756i	$0.613812\pi$
$90$	−29.5967	−	40.7364i	−0.328853	−	0.452627i
$91$	2.36068	+	7.26543i	0.0259415	+	0.0798398i
$92$	12.2361	−	37.6587i	0.133001	−	0.409334i
$93$	−96.9574	−	70.4437i	−1.04255	−	0.757459i
$94$	41.1803	−	56.6799i	0.438089	−	0.602977i
$95$	−45.1246	−	14.6619i	−0.474996	−	0.154336i
$96$	146.492	−	47.5981i	1.52596	−	0.495813i
$97$	−58.5795	+	42.5605i	−0.603913	+	0.438768i	−0.847266	−	0.531170i	$-0.821753\pi$
$97$	−58.5795	+	42.5605i	−0.603913	+	0.438768i	0.243353	+	0.969938i	$0.421753\pi$
$98$			148.324i			1.51351i
$99$	−31.9402	+	31.6874i	−0.322628	+	0.320075i
$100$	49.2492			0.492492
$101$	−37.8409	−	52.0836i	−0.374663	−	0.515679i	0.579498	−	0.814974i	$-0.303249\pi$
$101$	−37.8409	−	52.0836i	−0.374663	−	0.515679i	−0.954161	+	0.299295i	$0.903249\pi$
$102$	85.0861	+	261.868i	0.834177	+	2.56733i
$103$	−10.0770	+	31.0139i	−0.0978351	+	0.301105i	−0.987982	−	0.154568i	$-0.950601\pi$
$103$	−10.0770	+	31.0139i	−0.0978351	+	0.301105i	0.890147	+	0.455673i	$0.150601\pi$
$104$	−31.1803	−	22.6538i	−0.299811	−	0.217825i
$105$	−7.63932	+	10.5146i	−0.0727554	+	0.100139i
$106$	−229.894	−	74.6969i	−2.16881	−	0.704688i
$107$	−5.13932	+	1.66987i	−0.0480310	+	0.0156062i	−0.332934	−	0.942950i	$-0.608039\pi$
$107$	−5.13932	+	1.66987i	−0.0480310	+	0.0156062i	0.284903	+	0.958556i	$0.408039\pi$
$108$	−78.6418	+	57.1366i	−0.728165	+	0.529043i
$109$		−	137.002i		−	1.25690i	−0.777850	−	0.628450i	$-0.783690\pi$
$109$		−	137.002i		−	1.25690i	0.777850	−	0.628450i	$-0.216310\pi$
$110$	20.6525	+	133.834i	0.187750	+	1.21667i
$111$	145.623			1.31192
$112$	−4.19350	−	5.77185i	−0.0374419	−	0.0515344i
$113$	−14.3713	−	44.2304i	−0.127180	−	0.391419i	0.867112	−	0.498113i	$-0.165974\pi$
$113$	−14.3713	−	44.2304i	−0.127180	−	0.391419i	−0.994292	+	0.106694i	$0.965974\pi$
$114$	40.8156	−	125.617i	0.358032	−	1.10191i
$115$	23.4164	+	17.0130i	0.203621	+	0.147939i
$116$	11.1327	−	15.3229i	0.0959719	−	0.132094i
$117$	33.0902	+	10.7516i	0.282822	+	0.0918944i
$118$	−91.5304	+	29.7400i	−0.775681	+	0.252034i
$119$	17.9656	−	13.0527i	0.150971	−	0.109687i
$120$		−	65.5699i		−	0.546416i
$121$	115.371	−	36.4754i	0.953482	−	0.301450i
$122$	86.4296			0.708439
$123$	2.77864	+	3.82447i	0.0225906	+	0.0310933i
$124$	−56.0132	−	172.391i	−0.451719	−	1.39025i
$125$	−42.0263	+	129.344i	−0.336210	+	1.03475i
$126$	−9.14590	−	6.64488i	−0.0725865	−	0.0527372i
$127$	49.0395	−	67.4970i	0.386138	−	0.531473i	−0.571060	−	0.820908i	$-0.693468\pi$
$127$	49.0395	−	67.4970i	0.386138	−	0.531473i	0.957197	+	0.289436i	$0.0934676\pi$
$128$	128.550	+	41.7685i	1.00430	+	0.326316i
$129$	−113.766	+	36.9650i	−0.881910	+	0.286550i
$130$	84.7214	−	61.5537i	0.651703	−	0.473490i
$131$			85.0901i			0.649543i	0.945793	+	0.324771i	$0.105287\pi$
$131$			85.0901i			0.649543i	−0.945793	+	0.324771i	$0.894713\pi$
$132$	−215.235	+	33.2137i	−1.63056	+	0.251619i
$133$	−10.6525			−0.0800938
$134$	138.402	+	190.494i	1.03285	+	1.42159i
$135$	−21.9574	−	67.5780i	−0.162648	−	0.500578i
$136$	−34.6205	+	106.551i	−0.254563	+	0.783464i
$137$	−47.5238	−	34.5281i	−0.346889	−	0.252030i	0.400674	−	0.916221i	$-0.368776\pi$
$137$	−47.5238	−	34.5281i	−0.346889	−	0.252030i	−0.747563	+	0.664191i	$0.768776\pi$
$138$	−47.3607	+	65.1864i	−0.343193	+	0.472365i
$139$	153.108	+	49.7479i	1.10150	+	0.357899i	0.802679	−	0.596411i	$-0.203407\pi$
$139$	153.108	+	49.7479i	1.10150	+	0.357899i	0.298820	+	0.954310i	$0.403407\pi$
$140$	−18.6950	+	6.07439i	−0.133536	+	0.0433885i
$141$	−66.6312	+	48.4104i	−0.472562	+	0.343336i
$142$		−	191.795i		−	1.35067i
$143$	−65.9017	−	66.4275i	−0.460851	−	0.464528i
$144$	−32.4934			−0.225649
$145$	8.13777	+	11.2007i	0.0561225	+	0.0772460i
$146$	−89.5344	−	275.559i	−0.613250	−	1.88739i
$147$	53.8820	−	165.832i	0.366544	−	1.12811i
$148$	178.185	+	129.459i	1.20396	+	0.874725i
$149$	−151.103	+	207.976i	−1.01412	+	1.39581i	−0.0978685	+	0.995199i	$0.531202\pi$
$149$	−151.103	+	207.976i	−1.01412	+	1.39581i	−0.916248	+	0.400612i	$0.868798\pi$
$150$	−95.3115	−	30.9686i	−0.635410	−	0.206457i
$151$	−274.087	+	89.0563i	−1.81515	+	0.589777i	−0.815202	+	0.579176i	$0.803374\pi$
$151$	−274.087	+	89.0563i	−1.81515	+	0.589777i	−0.999944	+	0.0106004i	$0.996626\pi$
$152$	43.4787	−	31.5891i	0.286044	−	0.207823i
$153$		−	101.140i		−	0.661043i
$154$	13.6950	+	27.1441i	0.0889289	+	0.176261i
$155$	132.498			0.854829
$156$	98.9919	+	136.251i	0.634563	+	0.873401i
$157$	85.4803	+	263.081i	0.544460	+	1.67568i	0.722270	+	0.691612i	$0.243099\pi$
$157$	85.4803	+	263.081i	0.544460	+	1.67568i	−0.177809	+	0.984065i	$0.556901\pi$
$158$	62.6869	−	192.930i	0.396753	−	1.22108i
$159$	229.894	+	167.027i	1.44587	+	1.05049i
$160$	−100.095	+	137.769i	−0.625595	+	0.861058i
$161$	6.18034	+	2.00811i	0.0383872	+	0.0124728i
$162$	295.872	−	96.1347i	1.82637	−	0.593424i
$163$	56.1180	−	40.7721i	0.344282	−	0.250136i	−0.402184	−	0.915559i	$-0.631749\pi$
$163$	56.1180	−	40.7721i	0.344282	−	0.250136i	0.746466	+	0.665423i	$0.231749\pi$
$164$			7.14987i			0.0435967i
$165$	25.5279	−	157.133i	0.154714	−	0.952323i
$166$	−174.520			−1.05132
$167$	−169.864	−	233.798i	−1.01715	−	1.39999i	−0.914182	−	0.405303i	$-0.867166\pi$
$167$	−169.864	−	233.798i	−1.01715	−	1.39999i	−0.102968	−	0.994685i	$-0.532834\pi$
$168$	−4.54915	−	14.0008i	−0.0270783	−	0.0833384i
$169$	29.8632	−	91.9095i	0.176705	−	0.543843i
$170$	−246.276	−	178.930i	−1.44868	−	1.05253i
$171$	−28.5172	+	39.2506i	−0.166767	+	0.229536i
$172$	−172.067	−	55.9081i	−1.00039	−	0.325047i
$173$	174.241	−	56.6144i	1.00717	−	0.327251i	0.241445	−	0.970414i	$-0.422379\pi$
$173$	174.241	−	56.6144i	1.00717	−	0.327251i	0.765729	+	0.643164i	$0.222379\pi$
$174$	−31.1803	+	22.6538i	−0.179197	+	0.130194i
$175$			8.08250i			0.0461857i
$176$	77.7041	+	39.9819i	0.441501	+	0.227170i
$177$	113.138			0.639196
$178$	112.696	+	155.113i	0.633124	+	0.871420i
$179$	0.633702	+	1.95033i	0.00354024	+	0.0108957i	0.952811	−	0.303564i	$-0.0981766\pi$
$179$	0.633702	+	1.95033i	0.00354024	+	0.0108957i	−0.949271	+	0.314460i	$0.898177\pi$
$180$	−27.6656	+	85.1461i	−0.153698	+	0.473034i
$181$	58.9787	+	42.8505i	0.325849	+	0.236743i	0.738667	−	0.674070i	$-0.235455\pi$
$181$	58.9787	+	42.8505i	0.325849	+	0.236743i	−0.412818	+	0.910814i	$0.635455\pi$
$182$	13.8197	−	19.0211i	0.0759322	−	0.104512i
$183$	−96.6312	−	31.3974i	−0.528039	−	0.171570i
$184$	−31.1803	+	10.1311i	−0.169458	+	0.0550604i
$185$	−130.249	+	94.6316i	−0.704050	+	0.511522i
$186$			368.848i			1.98305i
$187$	−124.448	+	241.863i	−0.665499	+	1.29339i
$188$	−124.567			−0.662592
$189$	−9.37694	−	12.9063i	−0.0496134	−	0.0682870i
$190$	45.1246	+	138.879i	0.237498	+	0.730944i
$191$	−32.0770	+	98.7229i	−0.167942	+	0.516874i	−0.999241	−	0.0389523i	$-0.987598\pi$
$191$	−32.0770	+	98.7229i	−0.167942	+	0.516874i	0.831299	+	0.555826i	$0.187598\pi$
$192$	−290.508	−	211.066i	−1.51306	−	1.09930i
$193$	202.207	−	278.314i	1.04770	−	1.44204i	0.156919	−	0.987611i	$-0.449844\pi$
$193$	202.207	−	278.314i	1.04770	−	1.44204i	0.890784	−	0.454428i	$-0.150156\pi$
$194$	211.943	+	68.8644i	1.09249	+	0.354971i
$195$	−117.082	+	38.0423i	−0.600421	+	0.195089i
$196$	213.355	−	155.012i	1.08855	−	0.790875i
$197$		−	99.0718i		−	0.502903i	−0.967870	−	0.251451i	$-0.919092\pi$
$197$		−	99.0718i		−	0.502903i	0.967870	−	0.251451i	$-0.0809078\pi$
$198$	136.679	+	22.2048i	0.690297	+	0.112146i
$199$	−153.469			−0.771201			−0.385601	−	0.922666i	$-0.626006\pi$
$199$	−153.469			−0.771201			−0.385601	+	0.922666i	$0.626006\pi$
$200$	−23.9681	−	32.9892i	−0.119840	−	0.164946i
$201$	−85.5370	−	263.256i	−0.425557	−	1.30973i
$202$	−61.2279	+	188.440i	−0.303109	+	0.932872i
$203$	2.51471	+	1.82704i	0.0123877	+	0.00900021i
$204$	287.758	−	396.065i	1.41058	−	1.94150i
$205$	−4.97058	−	1.61504i	−0.0242467	−	0.00787825i
$206$	95.4508	−	31.0139i	0.463354	−	0.150553i
$207$	23.9443	−	17.3965i	0.115673	−	0.0840412i
$208$		−	67.5780i		−	0.324894i
$209$	116.492	−	58.7737i	0.557377	−	0.281214i
$210$	40.0000			0.190476
$211$	−196.035	−	269.820i	−0.929078	−	1.27877i	−0.960218	−	0.279251i	$-0.909914\pi$
$211$	−196.035	−	269.820i	−0.929078	−	1.27877i	0.0311405	−	0.999515i	$-0.490086\pi$
$212$	132.812	+	408.752i	0.626469	+	1.92807i
$213$	−69.6738	+	214.434i	−0.327107	+	1.00673i
$214$	13.4549	+	9.77557i	0.0628734	+	0.0456802i
$215$	77.7345	−	106.992i	0.361556	−	0.497639i
$216$	76.5451	+	24.8710i	0.354375	+	0.115144i
$217$	28.2918	−	9.19256i	0.130377	−	0.0423620i
$218$	−341.122	+	247.839i	−1.56478	+	1.13688i
$219$			340.609i			1.55529i
$220$	170.928	−	169.575i	0.776946	−	0.770796i
$221$	210.344			0.951785
$222$	−263.435	−	362.587i	−1.18664	−	1.63327i
$223$	35.2198	+	108.395i	0.157936	+	0.486078i	0.998447	−	0.0557176i	$-0.0177446\pi$
$223$	35.2198	+	108.395i	0.157936	+	0.486078i	−0.840510	+	0.541796i	$0.817745\pi$
$224$	−11.8146	+	36.3617i	−0.0527439	+	0.162329i
$225$	29.7812	+	21.6373i	0.132361	+	0.0961657i
$226$	−84.1312	+	115.797i	−0.372262	+	0.512375i
$227$	−37.1058	−	12.0564i	−0.163462	−	0.0531120i	0.226143	−	0.974094i	$-0.427388\pi$
$227$	−37.1058	−	12.0564i	−0.163462	−	0.0531120i	−0.389605	+	0.920982i	$0.627388\pi$
$228$	−223.348	+	72.5703i	−0.979599	+	0.318291i
$229$	−108.575	+	78.8847i	−0.474129	+	0.344475i	−0.799048	−	0.601267i	$-0.794663\pi$
$229$	−108.575	+	78.8847i	−0.474129	+	0.344475i	0.324919	+	0.945742i	$0.394663\pi$
$230$		−	89.0813i		−	0.387310i
$231$	−5.45085	−	35.3231i	−0.0235968	−	0.152914i
$232$	−15.6819			−0.0675944
$233$	157.139	+	216.283i	0.674415	+	0.928253i	0.999850	−	0.0173116i	$-0.00551073\pi$
$233$	157.139	+	216.283i	0.674415	+	0.928253i	−0.325435	+	0.945564i	$0.605511\pi$
$234$	−33.0902	−	101.841i	−0.141411	−	0.435218i
$235$	28.1378	−	86.5991i	0.119735	−	0.368507i
$236$	138.436	+	100.580i	0.586594	+	0.426185i
$237$	−140.172	+	192.930i	−0.591444	+	0.814053i
$238$	−65.0000	−	21.1198i	−0.273109	−	0.0887386i
$239$	104.751	−	34.0356i	0.438288	−	0.142408i	−0.0815577	−	0.996669i	$-0.525990\pi$
$239$	104.751	−	34.0356i	0.438288	−	0.142408i	0.519846	+	0.854260i	$0.325990\pi$
$240$	93.0132	−	67.5780i	0.387555	−	0.281575i
$241$		−	191.103i		−	0.792960i	−0.918043	−	0.396480i	$-0.870232\pi$
$241$		−	191.103i		−	0.792960i	0.918043	−	0.396480i	$-0.129768\pi$
$242$	−299.529	−	221.278i	−1.23772	−	0.914373i
$243$	−205.843			−0.847090
$244$	−90.3262	−	124.323i	−0.370189	−	0.509522i
$245$	59.5704	+	183.339i	0.243145	+	0.748322i
$246$	4.49593	−	13.8371i	0.0182762	−	0.0562482i
$247$	−81.6312	−	59.3085i	−0.330491	−	0.240116i
$248$	−88.2148	+	121.417i	−0.355705	+	0.489586i
$249$	195.119	+	63.3980i	0.783610	+	0.254610i
$250$	398.079	−	129.344i	1.59232	−	0.517375i
$251$	345.559	−	251.063i	1.37673	−	1.00025i	0.379553	−	0.925170i	$-0.376078\pi$
$251$	345.559	−	251.063i	1.37673	−	1.00025i	0.997177	−	0.0750826i	$-0.0239221\pi$
$252$			20.1003i			0.0797629i
$253$	−78.6656	+	12.1392i	−0.310931	+	0.0479811i
$254$	−256.774			−1.01092
$255$	210.344	+	289.514i	0.824880	+	1.13535i
$256$	−5.87132	−	18.0701i	−0.0229349	−	0.0705862i
$257$	8.73917	−	26.8964i	0.0340046	−	0.104655i	−0.932614	−	0.360877i	$-0.882478\pi$
$257$	8.73917	−	26.8964i	0.0340046	−	0.104655i	0.966618	+	0.256221i	$0.0824776\pi$
$258$	297.844	+	216.397i	1.15444	+	0.838747i
$259$	−21.2461	+	29.2428i	−0.0820313	+	0.112906i
$260$	−177.082	−	57.5374i	−0.681085	−	0.221298i
$261$	13.4640	−	4.37472i	0.0515862	−	0.0167614i
$262$	211.866	−	153.929i	0.808648	−	0.587517i
$263$			94.5506i			0.359508i	0.983712	+	0.179754i	$0.0575302\pi$
$263$			94.5506i			0.359508i	−0.983712	+	0.179754i	$0.942470\pi$
$264$	126.996	+	128.009i	0.481045	+	0.484883i
$265$	−314.164			−1.18552
$266$	19.2705	+	26.5236i	0.0724455	+	0.0997127i
$267$	−69.6500	−	214.361i	−0.260861	−	0.802848i
$268$	129.371	−	398.164i	0.482729	−	1.48569i
$269$	−189.305	−	137.538i	−0.703736	−	0.511294i	0.177411	−	0.984137i	$-0.443228\pi$
$269$	−189.305	−	137.538i	−0.703736	−	0.511294i	−0.881147	+	0.472843i	$0.843228\pi$
$270$	−128.541	+	176.922i	−0.476078	+	0.655265i
$271$	136.400	+	44.3191i	0.503322	+	0.163539i	0.549663	−	0.835387i	$-0.314756\pi$
$271$	136.400	+	44.3191i	0.503322	+	0.163539i	−0.0463413	+	0.998926i	$0.514756\pi$
$272$	−186.827	+	60.7038i	−0.686865	+	0.223176i
$273$	−22.3607	+	16.2460i	−0.0819073	+	0.0595091i
$274$			180.791i			0.659822i
$275$	−44.5942	−	88.3875i	−0.162161	−	0.321409i
$276$	143.262			0.519067
$277$	228.695	+	314.772i	0.825614	+	1.13636i	0.988724	+	0.149752i	$0.0478476\pi$
$277$	228.695	+	314.772i	0.825614	+	1.13636i	−0.163110	+	0.986608i	$0.552152\pi$
$278$	−153.108	−	471.219i	−0.550749	−	1.69503i
$279$	41.8673	−	128.854i	0.150062	−	0.461843i
$280$	13.1672	+	9.56652i	0.0470257	+	0.0341661i
$281$	−59.3860	+	81.7379i	−0.211338	+	0.290882i	−0.901505	−	0.432768i	$-0.857537\pi$
$281$	−59.3860	+	81.7379i	−0.211338	+	0.290882i	0.690167	+	0.723650i	$0.257537\pi$
$282$	241.074	+	78.3297i	0.854872	+	0.277765i
$283$	−2.01626	+	0.655123i	−0.00712460	+	0.00231492i	−0.312577	−	0.949892i	$-0.601192\pi$
$283$	−2.01626	+	0.655123i	−0.00712460	+	0.00231492i	0.305453	+	0.952207i	$0.401192\pi$
$284$	−275.885	+	200.443i	−0.971428	+	0.705783i
$285$		−	171.664i		−	0.602331i
$286$	−46.1803	+	284.257i	−0.161470	+	0.993905i
$287$	−1.17340			−0.00408849
$288$	102.352	+	140.875i	0.355387	+	0.489149i
$289$	−99.6418	−	306.666i	−0.344781	−	1.06113i
$290$	13.1672	−	40.5244i	0.0454041	−	0.139739i
$291$	−211.943	−	153.985i	−0.728325	−	0.529159i
$292$	−302.802	+	416.772i	−1.03699	+	1.42730i
$293$	−447.100	−	145.272i	−1.52594	−	0.495808i	−0.578483	−	0.815694i	$-0.696355\pi$
$293$	−447.100	−	145.272i	−1.52594	−	0.495808i	−0.947456	+	0.319886i	$0.896355\pi$
$294$	−510.377	+	165.832i	−1.73598	+	0.564053i
$295$	−101.193	+	73.5214i	−0.343029	+	0.249225i
$296$		−	182.360i		−	0.616081i
$297$	173.752	+	89.4023i	0.585023	+	0.301018i
$298$	791.187			2.65499
$299$	36.1803	+	49.7980i	0.121004	+	0.166548i
$300$	55.0623	+	169.464i	0.183541	+	0.564881i
$301$	9.17531	−	28.2387i	0.0304828	−	0.0938163i
$302$	717.569	+	521.345i	2.37606	+	1.72631i
$303$	136.910	−	188.440i	0.451848	−	0.621915i
$304$	89.6205	+	29.1195i	0.294804	+	0.0957878i
$305$	106.833	−	34.7121i	0.350272	−	0.113810i
$306$	−251.827	+	182.963i	−0.822965	+	0.597919i
$307$			99.4185i			0.323839i	0.986804	+	0.161919i	$0.0517685\pi$
$307$			99.4185i			0.323839i	−0.986804	+	0.161919i	$0.948232\pi$
$308$	24.7326	−	48.0674i	0.0803006	−	0.156063i
$309$	−117.984			−0.381824
$310$	−239.692	−	329.908i	−0.773200	−	1.06422i
$311$	104.823	+	322.611i	0.337051	+	1.03734i	0.965703	+	0.259649i	$0.0836068\pi$
$311$	104.823	+	322.611i	0.337051	+	1.03734i	−0.628652	+	0.777686i	$0.716393\pi$
$312$	43.0902	−	132.618i	0.138110	−	0.425057i
$313$	−312.595	−	227.114i	−0.998707	−	0.725603i	−0.0368962	−	0.999319i	$-0.511747\pi$
$313$	−312.595	−	227.114i	−0.998707	−	0.725603i	−0.961810	+	0.273716i	$0.911747\pi$
$314$	500.410	−	688.756i	1.59366	−	2.19349i
$315$	−13.9737	−	4.54033i	−0.0443609	−	0.0144137i
$316$	−343.031	+	111.458i	−1.08554	+	0.352714i
$317$	204.740	−	148.752i	0.645866	−	0.469249i	−0.215994	−	0.976395i	$-0.569299\pi$
$317$	204.740	−	148.752i	0.645866	−	0.469249i	0.861860	+	0.507145i	$0.169299\pi$
$318$		−	874.567i		−	2.75021i
$319$	−37.5805	−	6.10532i	−0.117807	−	0.0191389i
$320$	396.997			1.24062
$321$	−11.4919	−	15.8172i	−0.0358002	−	0.0492748i
$322$	−6.18034	−	19.0211i	−0.0191936	−	0.0590718i
$323$	−90.6378	+	278.954i	−0.280612	+	0.863636i
$324$	−447.495	−	325.124i	−1.38116	−	1.00347i
$325$	−45.0000	+	61.9372i	−0.138462	+	0.190576i
$326$	−203.037	−	65.9707i	−0.622813	−	0.202364i
$327$	471.418	−	153.173i	1.44165	−	0.468419i
$328$	4.78928	−	3.47962i	0.0146015	−	0.0106086i
$329$		−	20.4433i		−	0.0621376i
$330$	−437.426	+	220.695i	−1.32553	+	0.668773i
$331$	372.116			1.12422			0.562109	−	0.827063i	$-0.309990\pi$
$331$	372.116			1.12422			0.562109	+	0.827063i	$0.309990\pi$
$332$	182.388	+	251.035i	0.549361	+	0.756131i
$333$	50.8723	+	156.569i	0.152770	+	0.470177i
$334$	−274.846	+	845.889i	−0.822892	+	2.53260i
$335$	247.580	+	179.878i	0.739046	+	0.536949i
$336$	15.1722	−	20.8828i	0.0451554	−	0.0621511i
$337$	−78.1910	−	25.4058i	−0.232021	−	0.0753881i	0.190699	−	0.981649i	$-0.438925\pi$
$337$	−78.1910	−	25.4058i	−0.232021	−	0.0753881i	−0.422720	+	0.906260i	$0.638925\pi$
$338$	−282.868	+	91.9095i	−0.836888	+	0.271921i
$339$	136.127	−	98.9021i	0.401555	−	0.291747i
$340$			541.248i			1.59191i
$341$	−258.671	+	256.623i	−0.758565	+	0.752561i
$342$	149.318			0.436603
$343$	51.3050	+	70.6152i	0.149577	+	0.205875i
$344$	46.2902	+	142.467i	0.134565	+	0.414147i
$345$	−32.3607	+	99.5959i	−0.0937991	+	0.288684i
$346$	−456.169	−	331.426i	−1.31841	−	0.957879i
$347$	−134.861	+	185.620i	−0.388647	+	0.534927i	−0.957850	−	0.287270i	$-0.907252\pi$
$347$	−134.861	+	185.620i	−0.388647	+	0.534927i	0.569202	+	0.822198i	$0.307252\pi$
$348$	65.1722	+	21.1757i	0.187276	+	0.0608498i
$349$	220.997	−	71.8062i	0.633229	−	0.205749i	0.0252240	−	0.999682i	$-0.491970\pi$
$349$	220.997	−	71.8062i	0.633229	−	0.205749i	0.608005	+	0.793933i	$0.291970\pi$
$350$	20.1246	−	14.6214i	0.0574989	−	0.0417754i
$351$		−	151.109i		−	0.430510i
$352$	−71.4205	−	462.825i	−0.202899	−	1.31484i
$353$	34.6443			0.0981426			0.0490713	−	0.998795i	$-0.484374\pi$
$353$	34.6443			0.0981426			0.0490713	+	0.998795i	$0.484374\pi$
$354$	−204.668	−	281.702i	−0.578159	−	0.795767i
$355$	−77.0294	−	237.072i	−0.216984	−	0.667809i
$356$	105.343	−	324.212i	0.295907	−	0.910708i
$357$	65.0000	+	47.2253i	0.182073	+	0.132284i
$358$	3.70976	−	5.10604i	0.0103624	−	0.0142627i
$359$	−429.681	−	139.612i	−1.19688	−	0.388891i	−0.358269	−	0.933618i	$-0.616633\pi$
$359$	−429.681	−	139.612i	−1.19688	−	0.388891i	−0.838613	+	0.544728i	$0.816633\pi$
$360$	70.4984	−	22.9063i	0.195829	−	0.0636287i
$361$	−178.226	+	129.489i	−0.493702	+	0.358695i
$362$		−	224.368i		−	0.619802i
$363$	254.499	+	356.207i	0.701100	+	0.981286i
$364$	−41.8034			−0.114845
$365$	−221.341	−	304.650i	−0.606415	−	0.834658i
$366$	96.6312	+	297.400i	0.264020	+	0.812569i
$367$	113.974	−	350.775i	0.310555	−	0.955790i	−0.666991	−	0.745066i	$-0.732418\pi$
$367$	113.974	−	350.775i	0.310555	−	0.955790i	0.977546	−	0.210724i	$-0.0675821\pi$
$368$	−46.5066	−	33.7890i	−0.126377	−	0.0918180i
$369$	−3.14124	+	4.32355i	−0.00851284	+	0.0117169i
$370$	471.246	+	153.117i	1.27364	+	0.413830i
$371$	−67.0820	+	21.7963i	−0.180814	+	0.0587501i
$372$	530.564	−	385.477i	1.42625	−	1.03623i
$373$			593.166i			1.59026i	0.606440	+	0.795129i	$0.292597\pi$
$373$			593.166i			1.59026i	−0.606440	+	0.795129i	$0.707403\pi$
$374$	827.344	−	127.671i	2.21215	−	0.341366i
$375$	−492.053			−1.31214
$376$	60.6231	+	83.4405i	0.161232	+	0.221916i
$377$	9.09830	+	28.0017i	0.0241334	+	0.0742750i
$378$	−15.1722	+	46.6953i	−0.0401381	+	0.123532i
$379$	227.537	+	165.315i	0.600361	+	0.436188i	0.846007	−	0.533172i	$-0.179000\pi$
$379$	227.537	+	165.315i	0.600361	+	0.436188i	−0.245646	+	0.969360i	$0.579000\pi$
$380$	152.610	−	210.050i	0.401605	−	0.552762i
$381$	287.082	+	93.2786i	0.753496	+	0.244826i
$382$	303.838	−	98.7229i	0.795387	−	0.258437i
$383$	−515.795	+	374.747i	−1.34672	+	0.978452i	−0.347556	+	0.937659i	$0.612988\pi$
$383$	−515.795	+	374.747i	−1.34672	+	0.978452i	−0.999168	+	0.0407931i	$0.987012\pi$
$384$			489.034i			1.27353i
$385$	27.8297	+	28.0517i	0.0722850	+	0.0728617i
$386$	−1058.77			−2.74292
$387$	−79.4868	−	109.404i	−0.205392	−	0.282698i
$388$	−122.441	−	376.835i	−0.315570	−	0.971225i
$389$	206.259	−	634.801i	0.530229	−	1.63188i	−0.223507	−	0.974702i	$-0.571751\pi$
$389$	206.259	−	634.801i	0.530229	−	1.63188i	0.753737	−	0.657176i	$-0.228249\pi$
$390$	306.525	+	222.703i	0.785961	+	0.571034i
$391$	105.172	−	144.757i	0.268983	−	0.370223i
$392$	−207.667	−	67.4750i	−0.529762	−	0.172130i
$393$	−292.791	+	95.1336i	−0.745016	+	0.242070i
$394$	−246.679	+	179.223i	−0.626088	+	0.454880i
$395$		−	263.652i		−	0.667473i
$396$	−110.901	−	219.810i	−0.280052	−	0.555075i
$397$	−5.37384			−0.0135361			−0.00676805	−	0.999977i	$-0.502154\pi$
$397$	−5.37384			−0.0135361			−0.00676805	+	0.999977i	$0.502154\pi$
$398$	277.628	+	382.122i	0.697558	+	0.960106i
$399$	−11.9098	−	36.6547i	−0.0298492	−	0.0918664i
$400$	22.0942	−	67.9991i	0.0552356	−	0.169998i
$401$	228.786	+	166.223i	0.570539	+	0.414521i	0.835301	−	0.549793i	$-0.185293\pi$
$401$	228.786	+	166.223i	0.570539	+	0.414521i	−0.264762	+	0.964314i	$0.585293\pi$
$402$	−500.742	+	689.212i	−1.24563	+	1.71446i
$403$	267.984	+	87.0732i	0.664972	+	0.216063i
$404$	335.048	−	108.864i	0.829326	−	0.269464i
$405$	327.108	−	237.658i	0.807675	−	0.586810i
$406$		−	9.56652i		−	0.0235629i
$407$	70.9969	−	437.012i	0.174440	−	1.07374i
$408$	−405.344			−0.993491
$409$	−18.2554	−	25.1265i	−0.0446343	−	0.0614339i	0.786116	−	0.618078i	$-0.212089\pi$
$409$	−18.2554	−	25.1265i	−0.0446343	−	0.0614339i	−0.830751	+	0.556644i	$0.812089\pi$
$410$	4.97058	+	15.2979i	0.0121234	+	0.0373119i
$411$	65.6763	−	202.131i	0.159796	−	0.491802i
$412$	−144.366	−	104.888i	−0.350402	−	0.254582i
$413$	−16.5066	+	22.7194i	−0.0399675	+	0.0550105i
$414$	−86.6312	−	28.1482i	−0.209254	−	0.0679908i
$415$	−215.718	+	70.0911i	−0.519803	+	0.168894i
$416$	−292.984	+	212.865i	−0.704288	+	0.511695i
$417$			582.459i			1.39678i
$418$	−357.076	−	183.730i	−0.854250	−	0.439546i
$419$	−245.156			−0.585098			−0.292549	−	0.956251i	$-0.594503\pi$
$419$	−245.156			−0.585098			−0.292549	+	0.956251i	$0.594503\pi$
$420$	−41.8034	−	57.5374i	−0.0995319	−	0.136994i
$421$	−23.9211	−	73.6215i	−0.0568196	−	0.174873i	0.918619	−	0.395145i	$-0.129306\pi$
$421$	−23.9211	−	73.6215i	−0.0568196	−	0.174873i	−0.975439	+	0.220272i	$0.929306\pi$
$422$	−317.192	+	976.216i	−0.751640	+	2.31331i
$423$	−75.3262	−	54.7277i	−0.178076	−	0.129380i
$424$	209.164	−	287.890i	0.493312	−	0.678985i
$425$	211.655	+	68.7709i	0.498012	+	0.161814i
$426$	659.959	−	214.434i	1.54920	−	0.503366i
$427$	20.4033	−	14.8238i	0.0477828	−	0.0347162i
$428$		−	29.5703i		−	0.0690896i
$429$	154.894	−	301.033i	0.361057	−	0.701708i
$430$	−407.023			−0.946566
$431$	264.193	+	363.631i	0.612978	+	0.843692i	0.996818	−	0.0797077i	$-0.0253987\pi$
$431$	264.193	+	363.631i	0.612978	+	0.843692i	−0.383840	+	0.923399i	$0.625399\pi$
$432$	43.6089	+	134.215i	0.100947	+	0.310682i
$433$	44.6093	−	137.293i	0.103024	−	0.317075i	−0.886238	−	0.463231i	$-0.846690\pi$
$433$	44.6093	−	137.293i	0.103024	−	0.317075i	0.989262	+	0.146156i	$0.0466901\pi$
$434$	−74.0689	−	53.8142i	−0.170666	−	0.123996i
$435$	−29.4427	+	40.5244i	−0.0676844	+	0.0931596i
$436$	713.002	+	231.668i	1.63533	+	0.531349i
$437$	−81.6312	+	26.5236i	−0.186799	+	0.0606947i
$438$	848.082	−	616.168i	1.93626	−	1.40678i
$439$		−	155.406i		−	0.354001i	−0.984211	−	0.177000i	$-0.943361\pi$
$439$		−	155.406i		−	0.354001i	0.984211	−	0.177000i	$-0.0566394\pi$
$440$	−196.774	−	31.9679i	−0.447214	−	0.0726543i
$441$	197.120			0.446983
$442$	−380.517	−	523.736i	−0.860897	−	1.18492i
$443$	100.216	+	308.434i	0.226222	+	0.696240i	0.998165	+	0.0605483i	$0.0192849\pi$
$443$	100.216	+	308.434i	0.226222	+	0.696240i	−0.771943	+	0.635691i	$0.780715\pi$
$444$	−246.246	+	757.868i	−0.554608	+	1.70691i
$445$	201.597	+	146.469i	0.453026	+	0.329143i
$446$	206.180	−	283.783i	0.462288	−	0.636285i
$447$	−884.574	−	287.416i	−1.97891	−	0.642988i
$448$	84.7690	−	27.5431i	0.189216	−	0.0614801i
$449$	316.651	−	230.060i	0.705236	−	0.512384i	−0.176397	−	0.984319i	$-0.556444\pi$
$449$	316.651	−	230.060i	0.705236	−	0.512384i	0.881633	+	0.471935i	$0.156444\pi$
$450$		−	113.294i		−	0.251765i
$451$	12.8319	−	6.47407i	0.0284520	−	0.0143549i
$452$	254.490			0.563032
$453$	−612.877	−	843.553i	−1.35293	−	1.86215i
$454$	37.1058	+	114.200i	0.0817309	+	0.251542i
$455$	9.44272	−	29.0617i	0.0207532	−	0.0638719i
$456$	157.307	+	114.291i	0.344973	+	0.250637i
$457$	−30.7092	+	42.2675i	−0.0671973	+	0.0924891i	−0.841293	−	0.540580i	$-0.818205\pi$
$457$	−30.7092	+	42.2675i	−0.0671973	+	0.0924891i	0.774096	+	0.633069i	$0.218205\pi$
$458$	392.830	+	127.638i	0.857707	+	0.278686i
$459$	−417.758	+	135.738i	−0.910149	+	0.295725i
$460$	−128.138	+	93.0975i	−0.278560	+	0.202386i
$461$		−	339.293i		−	0.735994i	−0.929827	−	0.367997i	$-0.880044\pi$
$461$		−	339.293i		−	0.735994i	0.929827	−	0.367997i	$-0.119956\pi$
$462$	−78.0902	+	77.4721i	−0.169026	+	0.167689i
$463$	676.869			1.46192			0.730960	−	0.682420i	$-0.239072\pi$
$463$	676.869			1.46192			0.730960	+	0.682420i	$0.239072\pi$
$464$	−16.1622	−	22.2453i	−0.0348322	−	0.0479425i
$465$	148.138	+	455.921i	0.318576	+	0.980476i
$466$	254.256	−	782.519i	0.545613	−	1.67923i
$467$	−298.435	−	216.825i	−0.639046	−	0.464294i	0.220476	−	0.975392i	$-0.429239\pi$
$467$	−298.435	−	216.825i	−0.639046	−	0.464294i	−0.859522	+	0.511098i	$0.829239\pi$
$468$	−111.910	+	154.031i	−0.239124	+	0.329125i
$469$	65.3444	+	21.2317i	0.139327	+	0.0452701i
$470$	−266.525	+	86.5991i	−0.567074	+	0.184253i
$471$	−809.681	+	588.267i	−1.71907	+	1.24898i
$472$		−	141.679i		−	0.300168i
$473$	55.4656	+	359.433i	0.117263	+	0.759900i
$474$	733.951			1.54842
$475$	−62.7492	−	86.3669i	−0.132104	−	0.181825i
$476$	37.5511	+	115.570i	0.0788888	+	0.242795i
$477$	−99.2705	+	305.523i	−0.208114	+	0.640510i
$478$	−274.241	−	199.248i	−0.573726	−	0.416836i
$479$	−279.454	+	384.635i	−0.583411	+	0.802997i	−0.994064	−	0.108795i	$-0.965301\pi$
$479$	−279.454	+	384.635i	−0.583411	+	0.802997i	0.410653	+	0.911792i	$0.365301\pi$
$480$	−585.967	−	190.392i	−1.22077	−	0.396651i
$481$	−325.623	+	105.801i	−0.676971	+	0.219961i
$482$	−475.828	+	345.709i	−0.987195	+	0.717239i
$483$			23.5114i			0.0486779i
$484$	−5.26142	+	662.108i	−0.0108707	+	1.36799i
$485$	289.633			0.597182
$486$	372.373	+	512.528i	0.766200	+	1.05458i
$487$	−55.3626	−	170.389i	−0.113681	−	0.349874i	0.877989	−	0.478681i	$-0.158885\pi$
$487$	−55.3626	−	170.389i	−0.113681	−	0.349874i	−0.991670	+	0.128807i	$0.958885\pi$
$488$	−39.3181	+	121.009i	−0.0805699	+	0.247969i
$489$	203.037	+	147.515i	0.415208	+	0.301667i
$490$	348.731	−	479.988i	0.711697	−	0.979567i
$491$	611.297	+	198.622i	1.24500	+	0.404526i	0.856128	−	0.516764i	$-0.172863\pi$
$491$	611.297	+	198.622i	1.24500	+	0.404526i	0.388876	+	0.921290i	$0.372863\pi$
$492$	−24.6024	+	7.99379i	−0.0500048	+	0.0162475i
$493$	69.2411	−	50.3066i	0.140448	−	0.102042i
$494$			310.543i			0.628631i
$495$	177.862	−	27.4467i	0.359318	−	0.0554478i
$496$	−263.151			−0.530546
$497$	−32.8955	−	45.2768i	−0.0661881	−	0.0911001i
$498$	−195.119	−	600.515i	−0.391805	−	1.20585i
$499$	−162.446	+	499.958i	−0.325543	+	1.00192i	0.645651	+	0.763632i	$0.276586\pi$
$499$	−162.446	+	499.958i	−0.325543	+	1.00192i	−0.971195	+	0.238287i	$0.923414\pi$
$500$	−602.079	−	437.436i	−1.20416	−	0.874872i
$501$	614.574	−	845.889i	1.22670	−	1.68840i
$502$	−1250.24	−	406.229i	−2.49053	−	0.809222i
$503$	609.941	−	198.182i	1.21261	−	0.394000i	0.368222	−	0.929738i	$-0.379967\pi$
$503$	609.941	−	198.182i	1.21261	−	0.394000i	0.844384	+	0.535738i	$0.179967\pi$
$504$	13.4640	−	9.78217i	0.0267143	−	0.0194091i
$505$			257.515i			0.509932i
$506$	172.533	+	173.909i	0.340974	+	0.343694i
$507$	349.644			0.689634
$508$	268.351	+	369.353i	0.528249	+	0.727073i
$509$	−140.705	−	433.046i	−0.276434	−	0.850778i	−0.988836	−	0.149006i	$-0.952393\pi$
$509$	−140.705	−	433.046i	−0.276434	−	0.850778i	0.712402	−	0.701772i	$-0.247607\pi$
$510$	340.344	−	1047.47i	0.667342	−	2.05387i
$511$	−68.3982	−	49.6942i	−0.133852	−	0.0972490i
$512$	283.422	−	390.097i	0.553559	−	0.761908i
$513$	200.398	+	65.1131i	0.390639	+	0.126926i
$514$	−82.7786	+	26.8964i	−0.161048	+	0.0523276i
$515$	105.528	−	76.6705i	0.204908	−	0.148875i
$516$		−	654.583i		−	1.26857i
$517$	112.793	+	223.561i	0.218169	+	0.432419i
$518$	111.246			0.214761
$519$	389.615	+	536.259i	0.750703	+	1.03325i
$520$	47.6393	+	146.619i	0.0916141	+	0.281959i
$521$	−56.0044	+	172.364i	−0.107494	+	0.330833i	−0.990308	−	0.138891i	$-0.955646\pi$
$521$	−56.0044	+	172.364i	−0.107494	+	0.330833i	0.882814	+	0.469723i	$0.155646\pi$
$522$	−35.2492	−	25.6101i	−0.0675272	−	0.0490614i
$523$	−201.474	+	277.305i	−0.385227	+	0.530219i	−0.956960	−	0.290220i	$-0.906271\pi$
$523$	−201.474	+	277.305i	−0.385227	+	0.530219i	0.571733	+	0.820440i	$0.306271\pi$
$524$	−442.835	−	143.886i	−0.845106	−	0.274591i
$525$	−27.8115	+	9.03651i	−0.0529743	+	0.0172124i
$526$	235.421	−	171.044i	0.447569	−	0.325178i
$527$		−	819.088i		−	1.55425i
$528$	−50.7001	+	312.078i	−0.0960229	+	0.591056i
$529$	−476.639			−0.901020
$530$	568.328	+	782.237i	1.07232	+	1.47592i
$531$	39.5238	+	121.642i	0.0744328	+	0.229080i
$532$	18.0132	−	55.4388i	0.0338593	−	0.104208i
$533$	−8.99187	−	6.53298i	−0.0168703	−	0.0122570i
$534$	−407.738	+	561.203i	−0.763554	+	1.05094i
$535$	20.5573	+	6.67947i	0.0384248	+	0.0124850i
$536$	−329.668	+	107.116i	−0.615053	+	0.199843i
$537$	−6.00251	+	4.36108i	−0.0111779	+	0.00812119i
$538$			720.159i			1.33859i
$539$	−471.388	−	242.548i	−0.874560	−	0.449996i
$540$	388.827			0.720049
$541$	179.366	+	246.876i	0.331545	+	0.456332i	0.941948	−	0.335759i	$-0.108993\pi$
$541$	179.366	+	246.876i	0.331545	+	0.456332i	−0.610403	+	0.792091i	$0.708993\pi$
$542$	−136.400	−	419.796i	−0.251661	−	0.774532i
$543$	−81.5066	+	250.851i	−0.150104	+	0.461973i
$544$	851.671	+	618.775i	1.56557	+	1.13745i
$545$	−322.111	+	443.348i	−0.591030	+	0.813483i
$546$	80.9017	+	26.2866i	0.148172	+	0.0481439i
$547$	143.880	−	46.7494i	0.263034	−	0.0854651i	−0.174531	−	0.984652i	$-0.555841\pi$
$547$	143.880	−	46.7494i	0.263034	−	0.0854651i	0.437565	+	0.899187i	$0.355841\pi$
$548$	260.057	−	188.942i	0.474556	−	0.344785i
$549$		−	114.863i		−	0.209222i
$550$	−139.404	+	270.930i	−0.253462	+	0.492599i
$551$	−41.0557			−0.0745113
$552$	−69.7214	−	95.9632i	−0.126307	−	0.173846i
$553$	−18.2918	−	56.2964i	−0.0330774	−	0.101802i
$554$	370.036	−	1138.85i	0.667936	−	2.05569i
$555$	−471.246	−	342.380i	−0.849092	−	0.616902i
$556$	−517.807	+	712.701i	−0.931308	+	1.28184i
$557$	−103.677	−	33.6867i	−0.186134	−	0.0604787i	0.214467	−	0.976731i	$-0.431199\pi$
$557$	−103.677	−	33.6867i	−0.186134	−	0.0604787i	−0.400601	+	0.916253i	$0.631199\pi$
$558$	−396.572	+	128.854i	−0.710703	+	0.230921i
$559$	227.533	−	165.312i	0.407036	−	0.295729i
$560$			28.5376i			0.0509600i
$561$	−971.378	−	157.810i	−1.73151	−	0.281301i
$562$	310.949			0.553291
$563$	−585.827	−	806.321i	−1.04054	−	1.43219i	−0.896728	−	0.442583i	$-0.854062\pi$
$563$	−585.827	−	806.321i	−1.04054	−	1.43219i	−0.143817	−	0.989604i	$-0.545938\pi$
$564$	−139.271	−	428.631i	−0.246934	−	0.759983i
$565$	−57.4853	+	176.922i	−0.101744	+	0.313135i
$566$	5.27864	+	3.83516i	0.00932622	+	0.00677590i
$567$	53.3576	−	73.4404i	0.0941051	−	0.129525i
$568$	268.530	+	87.2506i	0.472764	+	0.153610i
$569$	94.4665	−	30.6940i	0.166022	−	0.0539438i	−0.224827	−	0.974399i	$-0.572182\pi$
$569$	94.4665	−	30.6940i	0.166022	−	0.0539438i	0.390849	+	0.920455i	$0.372182\pi$
$570$	−427.426	+	310.543i	−0.749871	+	0.544813i
$571$		−	930.127i		−	1.62894i	−0.580202	−	0.814472i	$-0.697027\pi$
$571$		−	930.127i		−	1.62894i	0.580202	−	0.814472i	$-0.302973\pi$
$572$	457.148	−	230.645i	0.799209	−	0.403226i
$573$	−375.564			−0.655435
$574$	2.12269	+	2.92164i	0.00369807	+	0.00508996i
$575$	20.1246	+	61.9372i	0.0349993	+	0.107717i
$576$	125.444	−	386.078i	0.217785	−	0.670274i
$577$	281.012	+	204.167i	0.487022	+	0.353842i	0.804038	−	0.594578i	$-0.202681\pi$
$577$	281.012	+	204.167i	0.487022	+	0.353842i	−0.317016	+	0.948420i	$0.602681\pi$
$578$	−583.313	+	802.862i	−1.00919	+	1.38903i
$579$	1183.74	+	384.620i	2.04445	+	0.664283i
$580$	−72.0526	+	23.4113i	−0.124229	+	0.0403643i
$581$	−41.1985	+	29.9325i	−0.0709097	+	0.0515189i
$582$			806.278i			1.38536i
$583$	613.328	−	608.474i	1.05202	−	1.04369i
$584$	426.536			0.730370
$585$	−81.8034	−	112.593i	−0.139835	−	0.192466i
$586$	447.100	+	1376.03i	0.762970	+	2.34818i
$587$	−196.347	+	604.294i	−0.334492	+	1.02946i	0.632479	+	0.774577i	$0.282037\pi$
$587$	−196.347	+	604.294i	−0.334492	+	1.02946i	−0.966972	+	0.254884i	$0.917963\pi$
$588$	771.926	+	560.837i	1.31280	+	0.953804i
$589$	−230.949	+	317.874i	−0.392104	+	0.539685i
$590$	366.122	+	118.960i	0.620545	+	0.201627i
$591$	340.902	−	110.766i	0.576822	−	0.187421i
$592$	258.684	−	187.945i	0.436966	−	0.317474i
$593$			341.152i			0.575299i	0.957736	+	0.287650i	$0.0928739\pi$
$593$			341.152i			0.575299i	−0.957736	+	0.287650i	$0.907126\pi$
$594$	−91.7173	−	594.354i	−0.154406	−	1.00060i
$595$	−88.8266			−0.149288
$596$	−826.858	−	1138.07i	−1.38735	−	1.90952i
$597$	−171.584	−	528.080i	−0.287410	−	0.884556i
$598$	58.5410	−	180.171i	0.0978947	−	0.301289i
$599$	362.164	+	263.128i	0.604614	+	0.439278i	0.847514	−	0.530773i	$-0.178098\pi$
$599$	362.164	+	263.128i	0.604614	+	0.439278i	−0.242899	+	0.970052i	$0.578098\pi$
$600$	86.7173	−	119.356i	0.144529	−	0.198927i
$601$	−762.584	−	247.779i	−1.26886	−	0.412277i	−0.404215	−	0.914664i	$-0.632455\pi$
$601$	−762.584	−	247.779i	−1.26886	−	0.412277i	−0.864643	+	0.502387i	$0.832455\pi$
$602$	−86.9098	+	28.2387i	−0.144368	+	0.0469082i
$603$	253.162	−	183.933i	0.419837	−	0.305029i
$604$		−	1577.03i		−	2.61097i
$605$	−459.108	−	153.217i	−0.758857	−	0.253252i
$606$	−716.869			−1.18295
$607$	599.237	+	824.779i	0.987211	+	1.35878i	0.932853	+	0.360257i	$0.117311\pi$
$607$	599.237	+	824.779i	0.987211	+	1.35878i	0.0543575	+	0.998522i	$0.482689\pi$
$608$	−156.050	−	480.273i	−0.256661	−	0.789922i
$609$	−3.47524	+	10.6957i	−0.00570647	+	0.0175627i
$610$	−279.692	−	203.208i	−0.458511	−	0.333128i
$611$	113.820	−	156.659i	0.186284	−	0.256398i
$612$	526.362	+	171.025i	0.860068	+	0.279453i
$613$	−711.597	+	231.212i	−1.16084	+	0.377181i	−0.825218	−	0.564814i	$-0.808948\pi$
$613$	−711.597	+	231.212i	−1.16084	+	0.377181i	−0.335626	+	0.941995i	$0.608948\pi$
$614$	247.542	−	179.850i	0.403163	−	0.292915i
$615$		−	18.9092i		−	0.0307467i
$616$	−44.2341	+	6.82596i	−0.0718087	+	0.0110811i
$617$	517.100			0.838088			0.419044	−	0.907966i	$-0.362365\pi$
$617$	517.100			0.838088			0.419044	+	0.907966i	$0.362365\pi$
$618$	213.435	+	293.768i	0.345363	+	0.475352i
$619$	−214.219	−	659.299i	−0.346073	−	1.06510i	−0.961007	−	0.276525i	$-0.910817\pi$
$619$	−214.219	−	659.299i	−0.346073	−	1.06510i	0.614934	−	0.788579i	$-0.289183\pi$
$620$	−224.053	+	689.563i	−0.361375	+	1.11220i
$621$	−103.992	−	75.5545i	−0.167459	−	0.121666i
$622$	613.643	−	844.607i	0.986565	−	1.35789i
$623$	53.2078	+	17.2883i	0.0854058	+	0.0277500i
$624$	232.533	−	75.5545i	0.372649	−	0.121081i
$625$	258.076	−	187.503i	0.412922	−	0.300006i
$626$			1189.18i			1.89965i
$627$	332.480	+	335.132i	0.530271	+	0.534501i
$628$	−1513.70			−2.41035
$629$	585.000	+	805.183i	0.930048	+	1.28010i
$630$	13.9737	+	43.0066i	0.0221805	+	0.0682644i
$631$	−277.128	+	852.911i	−0.439188	+	1.35168i	0.449545	+	0.893258i	$0.351586\pi$
$631$	−277.128	+	852.911i	−0.439188	+	1.35168i	−0.888733	+	0.458425i	$0.848414\pi$
$632$	241.602	+	175.534i	0.382281	+	0.277744i
$633$	709.263	−	976.216i	1.12048	−	1.54221i
$634$	−740.755	−	240.686i	−1.16838	−	0.379631i
$635$	−317.390	+	103.126i	−0.499827	+	0.162404i
$636$	−1258.01	+	913.997i	−1.97800	+	1.43710i
$637$			409.958i			0.643577i
$638$	52.7821	+	104.616i	0.0827306	+	0.163975i
$639$	−254.892			−0.398891
$640$	−317.793	−	437.405i	−0.496552	−	0.683445i
$641$	175.756	+	540.922i	0.274191	+	0.843872i	0.989432	+	0.144995i	$0.0463165\pi$
$641$	175.756	+	540.922i	0.274191	+	0.843872i	−0.715242	+	0.698877i	$0.753683\pi$
$642$	−18.5942	+	57.2272i	−0.0289630	+	0.0891389i
$643$	−534.364	−	388.238i	−0.831048	−	0.603791i	0.0888080	−	0.996049i	$-0.471694\pi$
$643$	−534.364	−	388.238i	−0.831048	−	0.603791i	−0.919855	+	0.392257i	$0.871694\pi$
$644$	−20.9017	+	28.7687i	−0.0324561	+	0.0446719i
$645$	455.066	+	147.860i	0.705528	+	0.229240i
$646$	858.533	−	278.954i	1.32900	−	0.431818i
$647$	−28.5999	+	20.7790i	−0.0442038	+	0.0321159i	−0.609668	−	0.792657i	$-0.708697\pi$
$647$	−28.5999	+	20.7790i	−0.0442038	+	0.0321159i	0.565464	+	0.824773i	$0.308697\pi$
$648$			457.979i			0.706758i
$649$	55.1591	−	339.524i	0.0849908	−	0.523150i
$650$	235.623			0.362497
$651$	63.2624	+	87.0732i	0.0971772	+	0.133753i
$652$	117.296	+	361.001i	0.179902	+	0.553682i
$653$	129.615	−	398.914i	0.198491	−	0.610894i	−0.801427	−	0.598093i	$-0.795925\pi$
$653$	129.615	−	398.914i	0.198491	−	0.610894i	0.999918	−	0.0128008i	$-0.00407473\pi$
$654$	−1234.19	−	896.691i	−1.88714	−	1.37109i
$655$	200.059	−	275.357i	0.305433	−	0.420393i
$656$	9.87192	+	3.20758i	0.0150487	+	0.00488960i
$657$	−366.211	+	118.989i	−0.557399	+	0.181110i
$658$	−50.9017	+	36.9822i	−0.0773582	+	0.0562040i
$659$			1281.39i			1.94445i	0.234058	+	0.972223i	$0.424800\pi$
$659$			1281.39i			1.94445i	−0.234058	+	0.972223i	$0.575200\pi$
$660$	774.604	+	398.565i	1.17364	+	0.603886i
$661$	70.6950			0.106952			0.0534758	−	0.998569i	$-0.482970\pi$
$661$	70.6950			0.106952			0.0534758	+	0.998569i	$0.482970\pi$
$662$	−673.165	−	926.532i	−1.01687	−	1.39960i
$663$	235.172	+	723.786i	0.354709	+	1.09168i
$664$	79.3916	−	244.342i	0.119566	−	0.367986i
$665$	34.4721	+	25.0455i	0.0518378	+	0.0376624i
$666$	297.812	−	409.902i	0.447164	−	0.615469i
$667$	23.8197	+	7.73948i	0.0357116	+	0.0116034i
$668$	1503.99	−	488.677i	2.25149	−	0.731553i
$669$	−333.607	+	242.380i	−0.498665	+	0.362301i
$670$		−	941.852i		−	1.40575i
$671$	−141.334	+	274.681i	−0.210632	+	0.409360i
$672$	−138.328			−0.205845
$673$	−470.230	−	647.216i	−0.698708	−	0.961689i	−0.999967	−	0.00814624i	$-0.997407\pi$
$673$	−470.230	−	647.216i	−0.698708	−	0.961689i	0.301259	−	0.953542i	$-0.402593\pi$
$674$	78.1910	+	240.647i	0.116010	+	0.357043i
$675$	49.4042	−	152.051i	0.0731914	−	0.225260i
$676$	427.827	+	310.835i	0.632880	+	0.459815i
$677$	550.202	−	757.288i	0.812706	−	1.11859i	−0.178195	−	0.983995i	$-0.557026\pi$
$677$	550.202	−	757.288i	0.812706	−	1.11859i	0.990900	−	0.134598i	$-0.0429743\pi$
$678$	−492.513	−	160.027i	−0.726420	−	0.236028i
$679$	61.8441	−	20.0944i	0.0910811	−	0.0295940i
$680$	362.551	−	263.409i	0.533163	−	0.387366i
$681$		−	141.159i		−	0.207282i
$682$	1106.91	+	179.828i	1.62303	+	0.263677i
$683$	−241.319			−0.353322			−0.176661	−	0.984272i	$-0.556530\pi$
$683$	−241.319			−0.353322			−0.176661	+	0.984272i	$0.556530\pi$
$684$	−156.050	−	214.785i	−0.228143	−	0.314013i
$685$	72.6099	+	223.470i	0.106000	+	0.326234i
$686$	83.0132	−	255.488i	0.121010	−	0.372432i
$687$	−392.830	−	285.407i	−0.571805	−	0.415440i
$688$	−154.386	+	212.494i	−0.224398	+	0.308858i
$689$	−635.410	−	206.457i	−0.922221	−	0.299648i
$690$	306.525	−	99.5959i	0.444239	−	0.144342i
$691$	736.915	−	535.400i	1.06645	−	0.774819i	0.0911771	−	0.995835i	$-0.470937\pi$
$691$	736.915	−	535.400i	1.06645	−	0.774819i	0.975270	+	0.221015i	$0.0709371\pi$
$692$			1002.54i			1.44876i
$693$	36.0739	−	18.2004i	0.0520547	−	0.0262632i
$694$	706.140			1.01749
$695$	−378.505	−	520.967i	−0.544611	−	0.749593i
$696$	−17.5329	−	53.9607i	−0.0251909	−	0.0775297i
$697$	−9.98397	+	30.7275i	−0.0143242	+	0.0440853i
$698$	−578.577	−	420.361i	−0.828907	−	0.602236i
$699$	−568.533	+	782.519i	−0.813352	+	1.11948i
$700$	−42.0639	−	13.6674i	−0.0600912	−	0.0195248i
$701$	−410.902	+	133.510i	−0.586165	+	0.190457i	−0.587061	−	0.809543i	$-0.699715\pi$
$701$	−410.902	+	133.510i	−0.586165	+	0.190457i	0.000895496		1.00000i	$0.499715\pi$
$702$	−376.246	+	273.359i	−0.535963	+	0.389400i
$703$		−	477.424i		−	0.679124i
$704$	−775.039	+	768.905i	−1.10091	+	1.09219i
$705$	329.443			0.467295
$706$	−62.6722	−	86.2609i	−0.0887708	−	0.122183i
$707$	17.8661	+	54.9861i	0.0252703	+	0.0777739i
$708$	−191.314	+	588.804i	−0.270218	+	0.831644i
$709$	708.956	+	515.087i	0.999938	+	0.726498i	0.962075	−	0.272785i	$-0.0879448\pi$
$709$	708.956	+	515.087i	0.999938	+	0.726498i	0.0378633	+	0.999283i	$0.487945\pi$
$710$	−450.938	+	620.663i	−0.635124	+	0.874173i
$711$	−256.400	−	83.3095i	−0.360619	−	0.117172i
$712$	−268.438	+	87.2208i	−0.377020	+	0.122501i
$713$	193.915	−	140.887i	0.271970	−	0.197598i
$714$		−	247.275i		−	0.346323i
$715$	57.0820	+	369.908i	0.0798350	+	0.517354i
$716$	−11.2217			−0.0156728
$717$	234.230	+	322.390i	0.326680	+	0.449637i
$718$	429.681	+	1322.42i	0.598441	+	1.84181i
$719$	155.218	−	477.712i	0.215880	−	0.664411i	−0.783210	−	0.621758i	$-0.786419\pi$
$719$	155.218	−	477.712i	0.215880	−	0.664411i	0.999090	−	0.0426534i	$-0.0135811\pi$
$720$	105.151	+	76.3966i	0.146043	+	0.106106i
$721$	17.2136	−	23.6925i	0.0238746	−	0.0328606i
$722$	644.829	+	209.518i	0.893115	+	0.290191i
$723$	657.578	−	213.660i	0.909514	−	0.295519i
$724$	−322.740	+	234.484i	−0.445773	+	0.323873i
$725$			31.1508i			0.0429666i
$726$	426.525	−	1278.06i	0.587500	−	1.76042i
$727$	−393.878			−0.541786			−0.270893	−	0.962609i	$-0.587319\pi$
$727$	−393.878			−0.541786			−0.270893	+	0.962609i	$0.587319\pi$
$728$	20.3444	+	28.0017i	0.0279456	+	0.0384639i
$729$	50.9853	+	156.917i	0.0699387	+	0.215249i
$730$	−358.138	+	1102.23i	−0.490600	+	1.50991i
$731$	−661.413	−	480.544i	−0.904805	−	0.657380i
$732$	326.803	−	449.806i	0.446453	−	0.614489i
$733$	−590.381	−	191.826i	−0.805431	−	0.261700i	−0.122769	−	0.992435i	$-0.539178\pi$
$733$	−590.381	−	191.826i	−0.805431	−	0.261700i	−0.682661	+	0.730735i	$0.739178\pi$
$734$	−1079.57	+	350.775i	−1.47081	+	0.477895i
$735$	−564.259	+	409.958i	−0.767700	+	0.557766i
$736$			308.061i			0.418562i
$737$	−831.728	+	128.347i	−1.12853	+	0.174148i
$738$	16.4477			0.0222869
$739$	−499.618	−	687.666i	−0.676074	−	0.930535i	0.323805	−	0.946124i	$-0.395038\pi$
$739$	−499.618	−	687.666i	−0.676074	−	0.930535i	−0.999878	+	0.0155884i	$0.995038\pi$
$740$	−272.243	−	837.878i	−0.367896	−	1.13227i
$741$	112.812	−	347.198i	0.152242	−	0.468554i
$742$	175.623	+	127.598i	0.236689	+	0.171964i
$743$	238.416	−	328.152i	0.320883	−	0.441658i	−0.617853	−	0.786293i	$-0.711997\pi$
$743$	238.416	−	328.152i	0.320883	−	0.441658i	0.938737	+	0.344635i	$0.111997\pi$
$744$	−516.418	−	167.794i	−0.694111	−	0.225530i
$745$	977.961	−	317.759i	1.31270	−	0.426522i
$746$	1476.92	−	1073.05i	1.97979	−	1.43840i
$747$			231.933i			0.310486i
$748$	−1048.29	−	1056.65i	−1.40146	−	1.41264i
$749$	4.85292			0.00647919
$750$	890.132	+	1225.16i	1.18684	+	1.63355i
$751$	−262.486	−	807.849i	−0.349515	−	1.07570i	−0.959122	−	0.282993i	$-0.908673\pi$
$751$	−262.486	−	807.849i	−0.349515	−	1.07570i	0.609606	−	0.792704i	$-0.291327\pi$
$752$	−55.8835	+	171.992i	−0.0743132	+	0.228712i
$753$	1250.24	+	908.356i	1.66035	+	1.20632i
$754$	53.2624	−	73.3094i	0.0706398	−	0.0972273i
$755$	1096.35	+	356.225i	1.45212	+	0.471821i
$756$	83.0244	−	26.9763i	0.109821	−	0.0356829i
$757$	−485.832	+	352.977i	−0.641786	+	0.466284i	−0.860463	−	0.509513i	$-0.829826\pi$
$757$	−485.832	+	352.977i	−0.641786	+	0.466284i	0.218678	+	0.975797i	$0.429826\pi$
$758$		−	865.602i		−	1.14196i
$759$	−129.721	−	257.113i	−0.170911	−	0.338752i
$760$	−214.971			−0.282856
$761$	205.275	+	282.537i	0.269744	+	0.371271i	0.922303	−	0.386467i	$-0.126305\pi$
$761$	205.275	+	282.537i	0.269744	+	0.371271i	−0.652559	+	0.757738i	$0.726305\pi$
$762$	−287.082	−	883.548i	−0.376748	−	1.15951i
$763$	−38.0201	+	117.014i	−0.0498298	+	0.153360i
$764$	−459.543	−	333.877i	−0.601496	−	0.437012i
$765$	−237.793	+	327.294i	−0.310841	+	0.427836i
$766$	1866.16	+	606.354i	2.43625	+	0.791584i
$767$	−252.984	+	82.1994i	−0.329835	+	0.107170i
$768$	55.6140	−	40.4059i	0.0724140	−	0.0526119i
$769$		−	768.616i		−	0.999500i	−0.866170	−	0.499750i	$-0.833425\pi$
$769$		−	768.616i		−	0.999500i	0.866170	−	0.499750i	$-0.166575\pi$
$770$	19.5016	−	120.039i	0.0253267	−	0.155895i
$771$	102.320			0.132711
$772$	1106.50	+	1522.97i	1.43329	+	1.97276i
$773$	2.15905	+	6.64488i	0.00279308	+	0.00859623i	0.952443	−	0.304716i	$-0.0985615\pi$
$773$	2.15905	+	6.64488i	0.00279308	+	0.00859623i	−0.949650	+	0.313312i	$0.898561\pi$
$774$	−128.612	+	395.828i	−0.166166	+	0.511406i
$775$	241.185	+	175.231i	0.311207	+	0.226105i
$776$	−192.832	+	265.410i	−0.248495	+	0.342024i
$777$	−124.377	−	40.4125i	−0.160073	−	0.0520110i
$778$	−1953.72	+	634.801i	−2.51120	+	0.815939i
$779$	12.5385	−	9.10976i	0.0160956	−	0.0116942i
$780$		−	673.660i		−	0.863667i
$781$	609.543	+	313.634i	0.780465	+	0.401581i
$782$	−550.689			−0.704206
$783$	−36.1397	−	49.7420i	−0.0461554	−	0.0635275i
$784$	−118.311	−	364.124i	−0.150907	−	0.464443i
$785$	341.921	−	1052.32i	0.435568	−	1.34054i
$786$	766.537	+	556.922i	0.975238	+	0.708552i
$787$	−648.159	+	892.115i	−0.823582	+	1.13356i	0.165501	+	0.986210i	$0.447076\pi$
$787$	−648.159	+	892.115i	−0.823582	+	1.13356i	−0.989084	+	0.147354i	$0.952924\pi$
$788$	515.601	+	167.529i	0.654315	+	0.212600i
$789$	−325.344	+	105.711i	−0.412350	+	0.133981i
$790$	−656.466	+	476.950i	−0.830970	+	0.603735i
$791$			41.7655i			0.0528009i
$792$	−93.2659	+	181.261i	−0.117760	+	0.228864i
$793$	238.885			0.301243
$794$	9.72136	+	13.3803i	0.0122435	+	0.0168518i
$795$	−351.246	−	1081.02i	−0.441819	−	1.35978i
$796$	259.514	−	798.700i	0.326022	−	1.00339i
$797$	583.596	+	424.007i	0.732240	+	0.532004i	0.890271	−	0.455430i	$-0.150515\pi$
$797$	583.596	+	424.007i	0.732240	+	0.532004i	−0.158031	+	0.987434i	$0.550515\pi$
$798$	−69.7214	+	95.9632i	−0.0873701	+	0.120255i
$799$	−535.344	−	173.944i	−0.670018	−	0.217702i
$800$	−364.404	+	118.402i	−0.455505	+	0.148003i
$801$	206.141	−	149.770i	0.257355	−	0.186979i
$802$		−	870.354i		−	1.08523i
$803$	1022.16	+	166.060i	1.27293	+	0.206800i
$804$	1514.71			1.88396
$805$	−15.2786	−	21.0292i	−0.0189797	−	0.0261233i
$806$	−267.984	−	824.769i	−0.332486	−	1.02329i
$807$	261.613	−	805.162i	0.324180	−	0.997722i
$808$	−235.979	−	171.449i	−0.292053	−	0.212189i
$809$	−471.682	+	649.215i	−0.583044	+	0.802491i	−0.994025	−	0.109153i	$-0.965186\pi$
$809$	−471.682	+	649.215i	−0.583044	+	0.802491i	0.410981	+	0.911644i	$0.365186\pi$
$810$	−1183.49	−	384.539i	−1.46110	−	0.474739i
$811$	−471.598	+	153.232i	−0.581502	+	0.188942i	−0.584973	−	0.811052i	$-0.698895\pi$
$811$	−471.598	+	153.232i	−0.581502	+	0.188942i	0.00347122	+	0.999994i	$0.498895\pi$
$812$	−13.7608	+	9.99783i	−0.0169468	+	0.0123126i
$813$			518.897i			0.638250i
$814$	−1216.55	+	613.787i	−1.49453	+	0.754038i
$815$	−277.463			−0.340445
$816$	−417.758	−	574.995i	−0.511959	−	0.704651i
$817$	121.189	+	372.983i	0.148335	+	0.456527i
$818$	−29.5379	+	90.9084i	−0.0361099	+	0.111135i
$819$	−25.2786	−	18.3660i	−0.0308653	−	0.0224249i
$820$	16.8103	−	23.1375i	0.0205004	−	0.0282164i
$821$	−276.921	−	89.9771i	−0.337297	−	0.109595i	0.135471	−	0.990781i	$-0.456745\pi$
$821$	−276.921	−	89.9771i	−0.337297	−	0.109595i	−0.472768	+	0.881187i	$0.656745\pi$
$822$	−622.095	+	202.131i	−0.756806	+	0.245901i
$823$	−869.681	+	631.860i	−1.05672	+	0.767752i	−0.973479	−	0.228777i	$-0.926527\pi$
$823$	−869.681	+	631.860i	−1.05672	+	0.767752i	−0.0832414	+	0.996529i	$0.526527\pi$
$824$			147.748i			0.179306i
$825$	254.280	−	252.267i	0.308218	−	0.305778i
$826$	86.4296			0.104636
$827$	−268.497	−	369.554i	−0.324664	−	0.446861i	0.615220	−	0.788355i	$-0.289067\pi$
$827$	−268.497	−	369.554i	−0.324664	−	0.446861i	−0.939884	+	0.341494i	$0.889067\pi$
$828$	50.0476	+	154.031i	0.0604440	+	0.186027i
$829$	0.679973	−	2.09274i	0.000820233	−	0.00252442i	−0.950646	−	0.310279i	$-0.899578\pi$
$829$	0.679973	−	2.09274i	0.000820233	−	0.00252442i	0.951466	+	0.307755i	$0.0995776\pi$
$830$	564.758	+	410.321i	0.680431	+	0.494362i
$831$	−827.426	+	1138.85i	−0.995700	+	1.37046i
$832$	802.943	+	260.892i	0.965076	+	0.313572i
$833$	1133.38	−	368.257i	1.36060	−	0.442085i
$834$	1450.26	−	1053.68i	1.73892	−	1.26340i
$835$			1155.96i			1.38438i
$836$	108.891	+	705.645i	0.130252	+	0.844073i
$837$	−588.423			−0.703015
$838$	443.491	+	610.413i	0.529226	+	0.728417i
$839$	448.822	+	1381.33i	0.534948	+	1.64640i	0.743761	+	0.668446i	$0.233040\pi$
$839$	448.822	+	1381.33i	0.534948	+	1.64640i	−0.208813	+	0.977956i	$0.566960\pi$
$840$	−18.1966	+	56.0034i	−0.0216626	+	0.0666707i
$841$	−670.691	−	487.286i	−0.797493	−	0.579412i
$842$	−140.036	+	192.744i	−0.166314	+	0.228912i
$843$	−347.652	−	112.959i	−0.412398	−	0.133996i
$844$	1735.72	−	563.969i	2.05654	−	0.668209i
$845$	−312.731	+	227.213i	−0.370096	+	0.268891i
$846$			286.558i			0.338721i
$847$	−108.661	−	0.863474i	−0.128290	−	0.00101945i
$848$	623.951			0.735792
$849$	−4.50850	−	6.20541i	−0.00531036	−	0.00730909i
$850$	−211.655	−	651.407i	−0.249006	−	0.766361i
$851$	−90.0000	+	276.992i	−0.105758	+	0.325489i
$852$	−998.163	−	725.208i	−1.17155	−	0.851183i
$853$	622.757	−	857.151i	0.730079	−	1.00487i	−0.269050	−	0.963126i	$-0.586710\pi$
$853$	622.757	−	857.151i	0.730079	−	1.00487i	0.999128	−	0.0417407i	$-0.0132903\pi$
$854$	−73.8197	−	23.9855i	−0.0864399	−	0.0280860i
$855$	184.567	−	59.9696i	0.215868	−	0.0701398i
$856$	−19.8075	+	14.3910i	−0.0231396	+	0.0168119i
$857$		−	951.067i		−	1.10976i	−0.831929	−	0.554882i	$-0.812763\pi$
$857$		−	951.067i		−	1.10976i	0.831929	−	0.554882i	$-0.187237\pi$
$858$	−1029.75	+	158.904i	−1.20017	+	0.185203i
$859$	1146.23			1.33438			0.667188	−	0.744890i	$-0.267498\pi$
$859$	1146.23			1.33438			0.667188	+	0.744890i	$0.267498\pi$
$860$	425.374	+	585.477i	0.494621	+	0.680787i
$861$	−1.31190	−	4.03760i	−0.00152369	−	0.00468943i
$862$	427.474	−	1315.63i	0.495910	−	1.52625i
$863$	−764.758	−	555.629i	−0.886162	−	0.643834i	0.0487126	−	0.998813i	$-0.484488\pi$
$863$	−764.758	−	555.629i	−0.886162	−	0.643834i	−0.934874	+	0.354979i	$0.884488\pi$
$864$	444.521	−	611.831i	0.514492	−	0.708137i
$865$	−696.964	−	226.457i	−0.805739	−	0.261801i
$866$	−422.545	+	137.293i	−0.487928	+	0.158537i
$867$	943.821	−	685.726i	1.08861	−	0.790918i
$868$			162.784i			0.187539i
$869$	510.641	+	514.715i	0.587619	+	0.592307i
$870$	154.164			0.177200
$871$	382.533	+	526.511i	0.439188	+	0.604491i
$872$	−191.815	−	590.345i	−0.219971	−	0.677001i
$873$	91.5191	−	281.667i	0.104833	−	0.322643i
$874$	213.713	+	155.272i	0.244523	+	0.177656i
$875$	71.7895	−	98.8098i	0.0820452	−	0.112925i
$876$	−1772.64	−	575.964i	−2.02356	−	0.657494i
$877$	150.931	−	49.0405i	0.172099	−	0.0559185i	−0.221700	−	0.975115i	$-0.571161\pi$
$877$	150.931	−	49.0405i	0.172099	−	0.0559185i	0.393799	+	0.919196i	$0.371161\pi$
$878$	−386.946	+	281.133i	−0.440713	+	0.320197i
$879$		−	1700.87i		−	1.93501i
$880$	−157.453	−	312.078i	−0.178924	−	0.354634i
$881$	402.370			0.456719			0.228360	−	0.973577i	$-0.426664\pi$
$881$	402.370			0.456719			0.228360	+	0.973577i	$0.426664\pi$
$882$	−356.593	−	490.808i	−0.404300	−	0.556471i
$883$	244.512	+	752.530i	0.276910	+	0.852243i	0.988708	+	0.149858i	$0.0478816\pi$
$883$	244.512	+	752.530i	0.276910	+	0.852243i	−0.711797	+	0.702385i	$0.752118\pi$
$884$	−355.689	+	1094.70i	−0.402363	+	1.23835i
$885$	−366.122	−	266.003i	−0.413697	−	0.300568i
$886$	586.677	−	807.491i	0.662163	−	0.911390i
$887$	805.659	+	261.775i	0.908297	+	0.295124i	0.725657	−	0.688056i	$-0.241536\pi$
$887$	805.659	+	261.775i	0.908297	+	0.295124i	0.182640	+	0.983180i	$0.441536\pi$
$888$	627.492	−	203.885i	0.706635	−	0.229600i
$889$	−60.6161	+	44.0402i	−0.0681846	+	0.0495390i
$890$		−	766.920i		−	0.861707i
$891$	−178.302	+	1097.51i	−0.200114	+	1.23178i
$892$	−623.680			−0.699192
$893$	158.713	+	218.450i	0.177730	+	0.244625i
$894$	884.574	+	2722.44i	0.989457	+	3.04523i
$895$	2.53481	−	7.80134i	0.00283219	−	0.00871658i
$896$	−98.2035	−	71.3491i	−0.109602	−	0.0796306i
$897$	−130.902	+	180.171i	−0.145933	+	0.200859i
$898$	−1145.65	−	372.245i	−1.27578	−	0.414527i
$899$	109.039	−	35.4291i	0.121290	−	0.0394094i
$900$	−162.967	+	118.402i	−0.181074	+	0.131558i
$901$			1942.12i			2.15552i
$902$	−39.3328	−	20.2383i	−0.0436062	−	0.0224372i
$903$	107.426			0.118966
$904$	−123.853	−	170.468i	−0.137005	−	0.188571i
$905$	−90.1115	−	277.335i	−0.0995707	−	0.306447i
$906$	−991.656	+	3052.00i	−1.09454	+	3.36866i
$907$	−345.216	−	250.814i	−0.380613	−	0.276532i	0.380985	−	0.924581i	$-0.375585\pi$
$907$	−345.216	−	250.814i	−0.380613	−	0.276532i	−0.761598	+	0.648049i	$0.775585\pi$
$908$	125.491	−	172.723i	0.138206	−	0.190224i
$909$	250.433	+	81.3705i	0.275503	+	0.0895165i
$910$	−89.4427	+	29.0617i	−0.0982887	+	0.0319359i
$911$	−113.353	+	82.3554i	−0.124427	+	0.0904011i	−0.648258	−	0.761421i	$-0.724502\pi$
$911$	−113.353	+	82.3554i	−0.124427	+	0.0904011i	0.523831	+	0.851822i	$0.324502\pi$
$912$			340.937i			0.373834i
$913$	285.384	−	554.639i	0.312579	−	0.607491i
$914$	160.795			0.175925
$915$	238.885	+	328.798i	0.261077	+	0.359342i
$916$	−226.941	−	698.453i	−0.247752	−	0.762503i
$917$	23.6137	−	72.6756i	0.0257511	−	0.0792537i
$918$	1093.71	+	794.624i	1.19140	+	0.865603i
$919$	611.124	−	841.140i	0.664988	−	0.915278i	−0.334645	−	0.942344i	$-0.608617\pi$
$919$	611.124	−	841.140i	0.664988	−	0.915278i	0.999634	+	0.0270664i	$0.00861655\pi$
$920$	124.721	+	40.5244i	0.135567	+	0.0440483i
$921$	−342.095	+	111.153i	−0.371438	+	0.120688i
$922$	−844.805	+	613.787i	−0.916275	+	0.665713i
$923$		−	530.109i		−	0.574333i
$924$	193.050	+	31.3628i	0.208928	+	0.0339424i
$925$	−362.243			−0.391614
$926$	−1224.47	−	1685.34i	−1.32232	−	1.82002i
$927$	−41.2167	−	126.852i	−0.0444625	−	0.136841i
$928$	−45.5348	+	140.142i	−0.0490677	+	0.151015i
$929$	−1329.96	−	966.270i	−1.43160	−	1.04012i	−0.989716	−	0.143046i	$-0.954310\pi$
$929$	−1329.96	−	966.270i	−1.43160	−	1.04012i	−0.441884	−	0.897072i	$-0.645690\pi$
$930$	867.214	−	1193.62i	0.932488	−	1.28346i
$931$	−543.678	−	176.652i	−0.583972	−	0.189744i
$932$	−1391.32	+	452.068i	−1.49284	+	0.485052i
$933$	−992.895	+	721.381i	−1.06420	+	0.773184i
$934$			1135.31i			1.21554i
$935$	971.378	−	490.090i	1.03891	−	0.524160i
$936$	157.639			0.168418
$937$	−426.456	−	586.966i	−0.455129	−	0.626431i	0.518361	−	0.855162i	$-0.326542\pi$
$937$	−426.456	−	586.966i	−0.455129	−	0.626431i	−0.973490	+	0.228731i	$0.926542\pi$
$938$	−65.3444	−	201.109i	−0.0696636	−	0.214402i
$939$	431.996	−	1329.55i	0.460060	−	1.41592i
$940$	403.108	+	292.875i	0.428839	+	0.311570i
$941$	−107.800	+	148.374i	−0.114559	+	0.157677i	−0.862446	−	0.506149i	$-0.831069\pi$
$941$	−107.800	+	148.374i	−0.114559	+	0.157677i	0.747887	+	0.663826i	$0.231069\pi$
$942$	2929.45	+	951.837i	3.10982	+	1.01044i
$943$	−8.99187	+	2.92164i	−0.00953539	+	0.00309823i
$944$	200.977	−	146.018i	0.212900	−	0.154681i
$945$			63.8120i			0.0675259i
$946$	794.613	−	788.324i	0.839971	−	0.833323i
$947$	−926.439			−0.978288			−0.489144	−	0.872203i	$-0.662691\pi$
$947$	−926.439			−0.978288			−0.489144	+	0.872203i	$0.662691\pi$
$948$	−767.041	−	1055.74i	−0.809115	−	1.11365i
$949$	−247.467	−	761.625i	−0.260766	−	0.802556i
$950$	−101.530	+	312.478i	−0.106874	+	0.328925i
$951$	740.755	+	538.190i	0.778922	+	0.565920i
$952$	59.1390	−	81.3978i	0.0621207	−	0.0855019i
$953$	237.606	+	77.2030i	0.249325	+	0.0810105i	0.431013	−	0.902346i	$-0.358156\pi$
$953$	237.606	+	77.2030i	0.249325	+	0.0810105i	−0.181688	+	0.983356i	$0.558156\pi$
$954$	940.304	−	305.523i	0.985643	−	0.320255i
$955$	335.915	−	244.056i	0.351743	−	0.255556i
$956$			602.709i			0.630449i
$957$	−21.0081	−	136.139i	−0.0219521	−	0.142256i
$958$	1463.24			1.52739
$959$	31.0081	+	42.6790i	0.0323338	+	0.0445037i
$960$	443.856	+	1366.05i	0.462350	+	1.42297i
$961$	42.1004	−	129.572i	0.0438090	−	0.134830i
$962$	852.492	+	619.372i	0.886167	+	0.643838i
$963$	12.9915	−	17.8813i	0.0134907	−	0.0185683i
$964$	994.562	+	323.153i	1.03170	+	0.335221i
$965$	−1308.71	+	425.225i	−1.35618	+	0.440648i
$966$	58.5410	−	42.5325i	0.0606015	−	0.0440295i
$967$			554.026i			0.572933i	0.958090	+	0.286466i	$0.0924806\pi$
$967$			554.026i			0.572933i	−0.958090	+	0.286466i	$0.907519\pi$
$968$	446.068	−	318.703i	0.460814	−	0.329239i
$969$	−1061.21			−1.09516
$970$	−523.951	−	721.157i	−0.540156	−	0.743461i
$971$	−352.634	−	1085.30i	−0.363166	−	1.11771i	−0.951121	−	0.308817i	$-0.900067\pi$
$971$	−352.634	−	1085.30i	−0.363166	−	1.11771i	0.587955	−	0.808893i	$-0.299933\pi$
$972$	348.077	−	1071.27i	0.358104	−	1.10213i
$973$	−116.964	−	84.9796i	−0.120210	−	0.0873377i
$974$	−324.098	+	446.083i	−0.332750	+	0.457991i
$975$	−263.435	−	85.5951i	−0.270189	−	0.0877898i
$976$	−212.177	+	68.9406i	−0.217395	+	0.0706358i
$977$	−104.116	+	75.6451i	−0.106568	+	0.0774258i	−0.639793	−	0.768547i	$-0.720980\pi$
$977$	−104.116	+	75.6451i	−0.106568	+	0.0774258i	0.533225	+	0.845973i	$0.320980\pi$
$978$		−	772.398i		−	0.789773i
$979$	−677.249	+	104.509i	−0.691776	+	0.106751i
$980$	−1054.89			−1.07641
$981$	329.373	+	453.343i	0.335752	+	0.462123i
$982$	−611.297	−	1881.38i	−0.622502	−	1.91586i
$983$	−412.497	+	1269.53i	−0.419630	+	1.29149i	0.488413	+	0.872613i	$0.337576\pi$
$983$	−412.497	+	1269.53i	−0.419630	+	1.29149i	−0.908043	+	0.418876i	$0.862424\pi$
$984$	17.3278	+	12.5894i	0.0176095	+	0.0127941i
$985$	−232.932	+	320.603i	−0.236479	+	0.325485i
$986$	−250.517	−	81.3978i	−0.254074	−	0.0825535i
$987$	70.3444	−	22.8563i	0.0712709	−	0.0231573i
$988$	446.697	−	324.544i	0.452122	−	0.328486i
$989$		−	239.242i		−	0.241903i
$990$	−390.095	−	393.207i	−0.394036	−	0.397179i
$991$	762.024			0.768944			0.384472	−	0.923137i	$-0.374383\pi$
$991$	762.024			0.768944			0.384472	+	0.923137i	$0.374383\pi$
$992$	828.904	+	1140.89i	0.835588	+	1.15009i
$993$	416.039	+	1280.44i	0.418972	+	1.28946i
$994$	−53.2260	+	163.813i	−0.0535473	+	0.164802i
$995$	496.636	+	360.827i	0.499132	+	0.362641i
$996$	−659.886	+	908.255i	−0.662536	+	0.911903i
$997$	1146.56	+	372.540i	1.15001	+	0.373661i	0.821147	−	0.570716i	$-0.193334\pi$
$997$	1146.56	+	372.540i	1.15001	+	0.373661i	0.328864	+	0.944377i	$0.393334\pi$
$998$	1538.71	−	499.958i	1.54180	−	0.500960i
$999$	578.435	−	420.257i	0.579014	−	0.420678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.3.d.a.8.1	yes	4
3.2	odd	2		99.3.k.a.19.1		4
4.3	odd	2		176.3.n.a.129.1		4
5.2	odd	4		275.3.q.d.74.2		8
5.3	odd	4		275.3.q.d.74.1		8
5.4	even	2		275.3.x.e.151.1		4
11.2	odd	10		121.3.b.b.120.1		4
11.3	even	5		121.3.d.a.94.1		4
11.4	even	5		121.3.d.d.40.1		4
11.5	even	5		121.3.d.c.112.1		4
11.6	odd	10		121.3.d.a.112.1		4
11.7	odd	10	inner	11.3.d.a.7.1	✓	4
11.8	odd	10		121.3.d.c.94.1		4
11.9	even	5		121.3.b.b.120.4		4
11.10	odd	2		121.3.d.d.118.1		4
33.2	even	10		1089.3.c.e.604.4		4
33.20	odd	10		1089.3.c.e.604.1		4
33.29	even	10		99.3.k.a.73.1		4
44.7	even	10		176.3.n.a.161.1		4
55.7	even	20		275.3.q.d.249.1		8
55.18	even	20		275.3.q.d.249.2		8
55.29	odd	10		275.3.x.e.51.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.3.d.a.7.1	✓	4	11.7	odd	10	inner
11.3.d.a.8.1	yes	4	1.1	even	1	trivial
99.3.k.a.19.1		4	3.2	odd	2
99.3.k.a.73.1		4	33.29	even	10
121.3.b.b.120.1		4	11.2	odd	10
121.3.b.b.120.4		4	11.9	even	5
121.3.d.a.94.1		4	11.3	even	5
121.3.d.a.112.1		4	11.6	odd	10
121.3.d.c.94.1		4	11.8	odd	10
121.3.d.c.112.1		4	11.5	even	5
121.3.d.d.40.1		4	11.4	even	5
121.3.d.d.118.1		4	11.10	odd	2
176.3.n.a.129.1		4	4.3	odd	2
176.3.n.a.161.1		4	44.7	even	10
275.3.q.d.74.1		8	5.3	odd	4
275.3.q.d.74.2		8	5.2	odd	4
275.3.q.d.249.1		8	55.7	even	20
275.3.q.d.249.2		8	55.18	even	20
275.3.x.e.51.1		4	55.29	odd	10
275.3.x.e.151.1		4	5.4	even	2
1089.3.c.e.604.1		4	33.20	odd	10
1089.3.c.e.604.4		4	33.2	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.80902 - 2.48990i) q^{2} +(1.11803 + 3.44095i) q^{3} +(-1.69098 + 5.20431i) q^{4} +(-3.23607 - 2.35114i) q^{5} +(6.54508 - 9.00854i) q^{6} +(-0.854102 - 0.277515i) q^{7} +(4.30902 - 1.40008i) q^{8} +(-3.30902 + 2.40414i) q^{9} +O(q^{10})\)	\(q+(-1.80902 - 2.48990i) q^{2} +(1.11803 + 3.44095i) q^{3} +(-1.69098 + 5.20431i) q^{4} +(-3.23607 - 2.35114i) q^{5} +(6.54508 - 9.00854i) q^{6} +(-0.854102 - 0.277515i) q^{7} +(4.30902 - 1.40008i) q^{8} +(-3.30902 + 2.40414i) q^{9} +12.3107i q^{10} +(10.8713 - 1.67760i) q^{11} -19.7984 q^{12} +(-5.00000 - 6.88191i) q^{13} +(0.854102 + 2.62866i) q^{14} +(4.47214 - 13.7638i) q^{15} +(6.42705 + 4.66953i) q^{16} +(-14.5344 + 20.0049i) q^{17} +(11.9721 + 3.88998i) q^{18} +(11.2812 - 3.66547i) q^{19} +(17.7082 - 12.8658i) q^{20} -3.24920i q^{21} +(-23.8435 - 24.0337i) q^{22} -7.23607 q^{23} +(9.63525 + 13.2618i) q^{24} +(-2.78115 - 8.55951i) q^{25} +(-8.09017 + 24.8990i) q^{26} +(14.3713 + 10.4414i) q^{27} +(2.88854 - 3.97574i) q^{28} +(-3.29180 - 1.06957i) q^{29} +(-42.3607 + 13.7638i) q^{30} +(-26.7984 + 19.4702i) q^{31} -42.5730i q^{32} +(17.9271 + 35.5321i) q^{33} +76.1033 q^{34} +(2.11146 + 2.90617i) q^{35} +(-6.91641 - 21.2865i) q^{36} +(12.4377 - 38.2793i) q^{37} +(-29.5344 - 21.4580i) q^{38} +(18.0902 - 24.8990i) q^{39} +(-17.2361 - 5.60034i) q^{40} +(1.24265 - 0.403760i) q^{41} +(-8.09017 + 5.87785i) q^{42} +33.0625i q^{43} +(-9.65248 + 59.4145i) q^{44} +16.3607 q^{45} +(13.0902 + 18.0171i) q^{46} +(7.03444 + 21.6498i) q^{47} +(-8.88197 + 27.3359i) q^{48} +(-38.9894 - 28.3274i) q^{49} +(-16.2812 + 22.4091i) q^{50} +(-85.0861 - 27.6462i) q^{51} +(44.2705 - 14.3844i) q^{52} +(63.5410 - 46.1653i) q^{53} -54.6718i q^{54} +(-39.1246 - 20.1312i) q^{55} -4.06888 q^{56} +(25.2254 + 34.7198i) q^{57} +(3.29180 + 10.1311i) q^{58} +(9.66312 - 29.7400i) q^{59} +(64.0689 + 46.5488i) q^{60} +(-16.5066 + 22.7194i) q^{61} +(96.9574 + 31.5034i) q^{62} +(3.49342 - 1.13508i) q^{63} +(-80.2943 + 58.3372i) q^{64} +34.0260i q^{65} +(56.0410 - 108.915i) q^{66} -76.5066 q^{67} +(-79.5344 - 109.470i) q^{68} +(-8.09017 - 24.8990i) q^{69} +(3.41641 - 10.5146i) q^{70} +(50.4164 + 36.6297i) q^{71} +(-10.8926 + 14.9924i) q^{72} +(89.5344 + 29.0915i) q^{73} +(-117.812 + 38.2793i) q^{74} +(26.3435 - 19.1396i) q^{75} +64.9089i q^{76} +(-9.75078 - 1.58411i) q^{77} -94.7214 q^{78} +(38.7426 + 53.3247i) q^{79} +(-9.81966 - 30.2218i) q^{80} +(-31.2361 + 96.1347i) q^{81} +(-3.25329 - 2.36365i) q^{82} +(33.3303 - 45.8752i) q^{83} +(16.9098 + 5.49434i) q^{84} +(94.0689 - 30.5648i) q^{85} +(82.3222 - 59.8106i) q^{86} -12.5227i q^{87} +(44.4959 - 22.4496i) q^{88} -62.2968 q^{89} +(-29.5967 - 40.7364i) q^{90} +(2.36068 + 7.26543i) q^{91} +(12.2361 - 37.6587i) q^{92} +(-96.9574 - 70.4437i) q^{93} +(41.1803 - 56.6799i) q^{94} +(-45.1246 - 14.6619i) q^{95} +(146.492 - 47.5981i) q^{96} +(-58.5795 + 42.5605i) q^{97} +148.324i q^{98} +(-31.9402 + 31.6874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{2} - 9 q^{4} - 4 q^{5} + 15 q^{6} + 10 q^{7} + 15 q^{8} - 11 q^{9}+O(q^{10}) \) 4 * q - 5 * q^2 - 9 * q^4 - 4 * q^5 + 15 * q^6 + 10 * q^7 + 15 * q^8 - 11 * q^9	\( 4 q - 5 q^{2} - 9 q^{4} - 4 q^{5} + 15 q^{6} + 10 q^{7} + 15 q^{8} - 11 q^{9} + q^{11} - 30 q^{12} - 20 q^{13} - 10 q^{14} + 19 q^{16} + 30 q^{18} + 25 q^{19} + 44 q^{20} - 35 q^{22} - 20 q^{23} + 5 q^{24} + 9 q^{25} - 10 q^{26} + 15 q^{27} - 60 q^{28} - 40 q^{29} - 80 q^{30} - 58 q^{31} + 65 q^{33} + 130 q^{34} + 80 q^{35} + 26 q^{36} + 90 q^{37} - 60 q^{38} + 50 q^{39} - 60 q^{40} - 80 q^{41} - 10 q^{42} + 24 q^{44} - 24 q^{45} + 30 q^{46} - 30 q^{47} - 40 q^{48} - 109 q^{49} - 45 q^{50} - 195 q^{51} + 110 q^{52} + 120 q^{53} - 76 q^{55} + 100 q^{56} + 45 q^{57} + 40 q^{58} + 23 q^{59} + 140 q^{60} + 10 q^{61} + 200 q^{62} + 90 q^{63} - 149 q^{64} + 90 q^{66} - 230 q^{67} - 260 q^{68} - 10 q^{69} - 40 q^{70} + 148 q^{71} - 95 q^{72} + 300 q^{73} - 270 q^{74} + 45 q^{75} - 200 q^{77} - 200 q^{78} + 70 q^{79} - 84 q^{80} - 116 q^{81} + 25 q^{82} + 225 q^{83} + 90 q^{84} + 260 q^{85} + 175 q^{86} + 55 q^{88} + 122 q^{89} - 20 q^{90} - 80 q^{91} + 40 q^{92} - 200 q^{93} + 120 q^{94} - 100 q^{95} + 340 q^{96} - 165 q^{97} + 31 q^{99}+O(q^{100}) \) 4 * q - 5 * q^2 - 9 * q^4 - 4 * q^5 + 15 * q^6 + 10 * q^7 + 15 * q^8 - 11 * q^9 + q^11 - 30 * q^12 - 20 * q^13 - 10 * q^14 + 19 * q^16 + 30 * q^18 + 25 * q^19 + 44 * q^20 - 35 * q^22 - 20 * q^23 + 5 * q^24 + 9 * q^25 - 10 * q^26 + 15 * q^27 - 60 * q^28 - 40 * q^29 - 80 * q^30 - 58 * q^31 + 65 * q^33 + 130 * q^34 + 80 * q^35 + 26 * q^36 + 90 * q^37 - 60 * q^38 + 50 * q^39 - 60 * q^40 - 80 * q^41 - 10 * q^42 + 24 * q^44 - 24 * q^45 + 30 * q^46 - 30 * q^47 - 40 * q^48 - 109 * q^49 - 45 * q^50 - 195 * q^51 + 110 * q^52 + 120 * q^53 - 76 * q^55 + 100 * q^56 + 45 * q^57 + 40 * q^58 + 23 * q^59 + 140 * q^60 + 10 * q^61 + 200 * q^62 + 90 * q^63 - 149 * q^64 + 90 * q^66 - 230 * q^67 - 260 * q^68 - 10 * q^69 - 40 * q^70 + 148 * q^71 - 95 * q^72 + 300 * q^73 - 270 * q^74 + 45 * q^75 - 200 * q^77 - 200 * q^78 + 70 * q^79 - 84 * q^80 - 116 * q^81 + 25 * q^82 + 225 * q^83 + 90 * q^84 + 260 * q^85 + 175 * q^86 + 55 * q^88 + 122 * q^89 - 20 * q^90 - 80 * q^91 + 40 * q^92 - 200 * q^93 + 120 * q^94 - 100 * q^95 + 340 * q^96 - 165 * q^97 + 31 * q^99

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