LMFDB - Embedded newform 55.3.i.a.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,3,Mod(6,55)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			46.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	55.46
Dual form			55.3.i.a.6.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.690983 - 0.224514i) q^{2} +(3.23607 - 2.35114i) q^{3} +(-2.80902 - 2.04087i) q^{4} +(-0.690983 - 2.12663i) q^{5} +(-2.76393 + 0.898056i) q^{6} +(-0.163119 + 0.224514i) q^{7} +(3.19098 + 4.39201i) q^{8} +(2.16312 - 6.65740i) q^{9} +1.62460i q^{10} +(10.3713 - 3.66547i) q^{11} -13.8885 q^{12} +(10.7533 + 3.49396i) q^{13} +(0.163119 - 0.118513i) q^{14} +(-7.23607 - 5.25731i) q^{15} +(3.07295 + 9.45756i) q^{16} +(-19.2705 + 6.26137i) q^{17} +(-2.98936 + 4.11450i) q^{18} +(16.9721 + 23.3601i) q^{19} +(-2.39919 + 7.38394i) q^{20} +1.11006i q^{21} +(-7.98936 + 0.204270i) q^{22} -27.6180 q^{23} +(20.6525 + 6.71040i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(-6.64590 - 4.82853i) q^{26} +(2.47214 + 7.60845i) q^{27} +(0.916408 - 0.297759i) q^{28} +(10.2016 - 14.0413i) q^{29} +(3.81966 + 5.25731i) q^{30} +(10.6180 - 32.6789i) q^{31} -28.9402i q^{32} +(24.9443 - 36.2461i) q^{33} +14.7214 q^{34} +(0.590170 + 0.191758i) q^{35} +(-19.6631 + 14.2861i) q^{36} +(-10.7361 - 7.80021i) q^{37} +(-6.48278 - 19.9519i) q^{38} +(43.0132 - 13.9758i) q^{39} +(7.13525 - 9.82084i) q^{40} +(-10.6140 - 14.6089i) q^{41} +(0.249224 - 0.767031i) q^{42} +34.7931i q^{43} +(-36.6140 - 10.8702i) q^{44} -15.6525 q^{45} +(19.0836 + 6.20063i) q^{46} +(-38.4230 + 27.9159i) q^{47} +(32.1803 + 23.3804i) q^{48} +(15.1180 + 46.5285i) q^{49} +(3.45492 - 1.12257i) q^{50} +(-47.6393 + 65.5699i) q^{51} +(-23.0755 - 31.7606i) q^{52} +(12.8475 - 39.5406i) q^{53} -5.81234i q^{54} +(-14.9615 - 19.5232i) q^{55} -1.50658 q^{56} +(109.846 + 35.6911i) q^{57} +(-10.2016 + 7.41192i) q^{58} +(-82.3115 - 59.8028i) q^{59} +(9.59675 + 29.5358i) q^{60} +(48.4164 - 15.7314i) q^{61} +(-14.6738 + 20.1967i) q^{62} +(1.14183 + 1.57160i) q^{63} +(5.79431 - 17.8330i) q^{64} -25.2825i q^{65} +(-25.3738 + 19.4451i) q^{66} +40.1803 q^{67} +(66.9098 + 21.7403i) q^{68} +(-89.3738 + 64.9339i) q^{69} +(-0.364745 - 0.265003i) q^{70} +(8.70820 + 26.8011i) q^{71} +(36.1418 - 11.7432i) q^{72} +(-58.6656 + 80.7463i) q^{73} +(5.66718 + 7.80021i) q^{74} +(-6.18034 + 19.0211i) q^{75} -100.257i q^{76} +(-0.868810 + 2.92641i) q^{77} -32.8591 q^{78} +(-125.172 - 40.6709i) q^{79} +(17.9894 - 13.0700i) q^{80} +(76.8566 + 55.8396i) q^{81} +(4.05418 + 12.4775i) q^{82} +(-119.271 + 38.7533i) q^{83} +(2.26548 - 3.11817i) q^{84} +(26.6312 + 36.6547i) q^{85} +(7.81153 - 24.0414i) q^{86} -69.4242i q^{87} +(49.1935 + 33.8545i) q^{88} +88.9493 q^{89} +(10.8156 + 3.51420i) q^{90} +(-2.53851 + 1.84433i) q^{91} +(77.5795 + 56.3648i) q^{92} +(-42.4721 - 130.716i) q^{93} +(32.8171 - 10.6629i) q^{94} +(37.9508 - 52.2349i) q^{95} +(-68.0426 - 93.6526i) q^{96} +(14.9311 - 45.9533i) q^{97} -35.5446i q^{98} +(-1.96807 - 76.9748i) 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 $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$ .

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

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

)

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

$2$	−0.690983	−	0.224514i	−0.345492	−	0.112257i	0.131131	−	0.991365i	$-0.458139\pi$
$2$	−0.690983	−	0.224514i	−0.345492	−	0.112257i	−0.476623	+	0.879108i	$0.658139\pi$
$3$	3.23607	−	2.35114i	1.07869	−	0.783714i	0.101235	−	0.994862i	$-0.467720\pi$
$3$	3.23607	−	2.35114i	1.07869	−	0.783714i	0.977454	+	0.211149i	$0.0677205\pi$
$4$	−2.80902	−	2.04087i	−0.702254	−	0.510218i
$5$	−0.690983	−	2.12663i	−0.138197	−	0.425325i
$5$	−0.690983	−	2.12663i	−0.138197	−	0.425325i
$6$	−2.76393	+	0.898056i	−0.460655	+	0.149676i
$7$	−0.163119	+	0.224514i	−0.0233027	+	0.0320734i	−0.820509	−	0.571633i	$-0.806310\pi$
$7$	−0.163119	+	0.224514i	−0.0233027	+	0.0320734i	0.797207	+	0.603706i	$0.206310\pi$
$8$	3.19098	+	4.39201i	0.398873	+	0.549001i
$9$	2.16312	−	6.65740i	0.240347	−	0.739711i
$10$			1.62460i			0.162460i
$11$	10.3713	−	3.66547i	0.942848	−	0.333224i
$11$	10.3713	−	3.66547i	0.942848	−	0.333224i
$12$	−13.8885			−1.15738
$13$	10.7533	+	3.49396i	0.827176	+	0.268766i	0.691855	−	0.722036i	$-0.256794\pi$
$13$	10.7533	+	3.49396i	0.827176	+	0.268766i	0.135321	+	0.990802i	$0.456794\pi$
$14$	0.163119	−	0.118513i	0.0116514	−	0.00846520i
$15$	−7.23607	−	5.25731i	−0.482405	−	0.350487i
$16$	3.07295	+	9.45756i	0.192059	+	0.591098i
$17$	−19.2705	+	6.26137i	−1.13356	+	0.368316i	−0.814928	−	0.579563i	$-0.803223\pi$
$17$	−19.2705	+	6.26137i	−1.13356	+	0.368316i	−0.318632	+	0.947879i	$0.603223\pi$
$18$	−2.98936	+	4.11450i	−0.166075	+	0.228583i
$19$	16.9721	+	23.3601i	0.893270	+	1.22948i	0.972565	+	0.232630i	$0.0747331\pi$
$19$	16.9721	+	23.3601i	0.893270	+	1.22948i	−0.0792950	+	0.996851i	$0.525267\pi$
$20$	−2.39919	+	7.38394i	−0.119959	+	0.369197i
$21$			1.11006i			0.0528599i
$22$	−7.98936	+	0.204270i	−0.363153	+	0.00928498i
$23$	−27.6180			−1.20078			−0.600392	−	0.799706i	$-0.704989\pi$
$23$	−27.6180			−1.20078			−0.600392	+	0.799706i	$0.704989\pi$
$24$	20.6525	+	6.71040i	0.860520	+	0.279600i
$25$	−4.04508	+	2.93893i	−0.161803	+	0.117557i
$26$	−6.64590	−	4.82853i	−0.255611	−	0.185713i
$27$	2.47214	+	7.60845i	0.0915606	+	0.281795i
$28$	0.916408	−	0.297759i	0.0327289	−	0.0106342i
$29$	10.2016	−	14.0413i	0.351780	−	0.484184i	−0.596055	−	0.802943i	$-0.703266\pi$
$29$	10.2016	−	14.0413i	0.351780	−	0.484184i	0.947836	+	0.318759i	$0.103266\pi$
$30$	3.81966	+	5.25731i	0.127322	+	0.175244i
$31$	10.6180	−	32.6789i	0.342517	−	1.05416i	−0.620382	−	0.784300i	$-0.713023\pi$
$31$	10.6180	−	32.6789i	0.342517	−	1.05416i	0.962900	−	0.269860i	$-0.0869775\pi$
$32$		−	28.9402i		−	0.904382i
$33$	24.9443	−	36.2461i	0.755887	−	1.09837i
$34$	14.7214			0.432981
$35$	0.590170	+	0.191758i	0.0168620	+	0.00547880i
$36$	−19.6631	+	14.2861i	−0.546198	+	0.396836i
$37$	−10.7361	−	7.80021i	−0.290164	−	0.210816i	0.433175	−	0.901310i	$-0.357393\pi$
$37$	−10.7361	−	7.80021i	−0.290164	−	0.210816i	−0.723339	+	0.690494i	$0.757393\pi$
$38$	−6.48278	−	19.9519i	−0.170599	−	0.525051i
$39$	43.0132	−	13.9758i	1.10290	−	0.358354i
$40$	7.13525	−	9.82084i	0.178381	−	0.245521i
$41$	−10.6140	−	14.6089i	−0.258877	−	0.356314i	0.659718	−	0.751513i	$-0.270676\pi$
$41$	−10.6140	−	14.6089i	−0.258877	−	0.356314i	−0.918596	+	0.395199i	$0.870676\pi$
$42$	0.249224	−	0.767031i	0.00593390	−	0.0182627i
$43$			34.7931i			0.809141i	0.914507	+	0.404571i	$0.132579\pi$
$43$			34.7931i			0.809141i	−0.914507	+	0.404571i	$0.867421\pi$
$44$	−36.6140	−	10.8702i	−0.832136	−	0.247049i
$45$	−15.6525			−0.347833
$46$	19.0836	+	6.20063i	0.414861	+	0.134796i
$47$	−38.4230	+	27.9159i	−0.817510	+	0.593956i	−0.915998	−	0.401182i	$-0.868599\pi$
$47$	−38.4230	+	27.9159i	−0.817510	+	0.593956i	0.0984879	+	0.995138i	$0.468599\pi$
$48$	32.1803	+	23.3804i	0.670424	+	0.487091i
$49$	15.1180	+	46.5285i	0.308531	+	0.949562i
$50$	3.45492	−	1.12257i	0.0690983	−	0.0224514i
$51$	−47.6393	+	65.5699i	−0.934104	+	1.28568i
$52$	−23.0755	−	31.7606i	−0.443759	−	0.610782i
$53$	12.8475	−	39.5406i	0.242406	−	0.746049i	−0.753646	−	0.657280i	$-0.771707\pi$
$53$	12.8475	−	39.5406i	0.242406	−	0.746049i	0.996052	−	0.0887689i	$-0.0282933\pi$
$54$		−	5.81234i		−	0.107636i
$55$	−14.9615	−	19.5232i	−0.272027	−	0.354967i
$56$	−1.50658			−0.0269032
$57$	109.846	+	35.6911i	1.92712	+	0.626160i
$58$	−10.2016	+	7.41192i	−0.175890	+	0.127792i
$59$	−82.3115	−	59.8028i	−1.39511	−	1.01361i	−0.995283	−	0.0970170i	$-0.969070\pi$
$59$	−82.3115	−	59.8028i	−1.39511	−	1.01361i	−0.399828	−	0.916590i	$-0.630930\pi$
$60$	9.59675	+	29.5358i	0.159946	+	0.492263i
$61$	48.4164	−	15.7314i	0.793712	−	0.257893i	0.116028	−	0.993246i	$-0.462984\pi$
$61$	48.4164	−	15.7314i	0.793712	−	0.257893i	0.677684	+	0.735353i	$0.262984\pi$
$62$	−14.6738	+	20.1967i	−0.236674	+	0.325753i
$63$	1.14183	+	1.57160i	0.0181243	+	0.0249460i
$64$	5.79431	−	17.8330i	0.0905361	−	0.278641i
$65$		−	25.2825i		−	0.388962i
$66$	−25.3738	+	19.4451i	−0.384452	+	0.294623i
$67$	40.1803			0.599707			0.299853	−	0.953985i	$-0.403062\pi$
$67$	40.1803			0.599707			0.299853	+	0.953985i	$0.403062\pi$
$68$	66.9098	+	21.7403i	0.983968	+	0.319711i
$69$	−89.3738	+	64.9339i	−1.29527	+	0.941071i
$70$	−0.364745	−	0.265003i	−0.00521064	−	0.00378575i
$71$	8.70820	+	26.8011i	0.122651	+	0.377480i	0.993466	−	0.114131i	$-0.0364083\pi$
$71$	8.70820	+	26.8011i	0.122651	+	0.377480i	−0.870815	+	0.491611i	$0.836408\pi$
$72$	36.1418	−	11.7432i	0.501970	−	0.163100i
$73$	−58.6656	+	80.7463i	−0.803639	+	1.10611i	0.188635	+	0.982047i	$0.439594\pi$
$73$	−58.6656	+	80.7463i	−0.803639	+	1.10611i	−0.992274	+	0.124067i	$0.960406\pi$
$74$	5.66718	+	7.80021i	0.0765836	+	0.105408i
$75$	−6.18034	+	19.0211i	−0.0824045	+	0.253615i
$76$		−	100.257i		−	1.31917i
$77$	−0.868810	+	2.92641i	−0.0112833	+	0.0380054i
$78$	−32.8591			−0.421271
$79$	−125.172	−	40.6709i	−1.58446	−	0.514822i	−0.621258	−	0.783606i	$-0.713378\pi$
$79$	−125.172	−	40.6709i	−1.58446	−	0.514822i	−0.963200	+	0.268784i	$0.913378\pi$
$80$	17.9894	−	13.0700i	0.224867	−	0.163375i
$81$	76.8566	+	55.8396i	0.948847	+	0.689378i
$82$	4.05418	+	12.4775i	0.0494412	+	0.152164i
$83$	−119.271	+	38.7533i	−1.43699	+	0.466908i	−0.920959	−	0.389660i	$-0.872593\pi$
$83$	−119.271	+	38.7533i	−1.43699	+	0.466908i	−0.516035	+	0.856567i	$0.672593\pi$
$84$	2.26548	−	3.11817i	0.0269701	−	0.0371211i
$85$	26.6312	+	36.6547i	0.313308	+	0.431232i
$86$	7.81153	−	24.0414i	0.0908317	−	0.279551i
$87$		−	69.4242i		−	0.797979i
$88$	49.1935	+	33.8545i	0.559017	+	0.384710i
$89$	88.9493			0.999430			0.499715	−	0.866190i	$-0.333438\pi$
$89$	88.9493			0.999430			0.499715	+	0.866190i	$0.333438\pi$
$90$	10.8156	+	3.51420i	0.120173	+	0.0390467i
$91$	−2.53851	+	1.84433i	−0.0278957	+	0.0202674i
$92$	77.5795	+	56.3648i	0.843256	+	0.612661i
$93$	−42.4721	−	130.716i	−0.456690	−	1.40555i
$94$	32.8171	−	10.6629i	0.349119	−	0.113436i
$95$	37.9508	−	52.2349i	0.399483	−	0.549841i
$96$	−68.0426	−	93.6526i	−0.708777	−	0.975548i
$97$	14.9311	−	45.9533i	0.153929	−	0.473745i	−0.844122	−	0.536152i	$-0.819878\pi$
$97$	14.9311	−	45.9533i	0.153929	−	0.473745i	0.998051	+	0.0624067i	$0.0198776\pi$
$98$		−	35.5446i		−	0.362700i
$99$	−1.96807	−	76.9748i	−0.0198795	−	0.777524i
$100$	17.3607			0.173607
$101$	36.5836	+	11.8867i	0.362214	+	0.117690i	0.484469	−	0.874808i	$-0.339013\pi$
$101$	36.5836	+	11.8867i	0.362214	+	0.117690i	−0.122256	+	0.992499i	$0.539013\pi$
$102$	47.6393	−	34.6120i	0.467052	−	0.339333i
$103$	−102.075	−	74.1622i	−0.991024	−	0.720021i	−0.0308788	−	0.999523i	$-0.509831\pi$
$103$	−102.075	−	74.1622i	−0.991024	−	0.720021i	−0.960145	+	0.279502i	$0.909831\pi$
$104$	18.9681	+	58.3777i	0.182385	+	0.561324i
$105$	2.36068	−	0.767031i	0.0224827	−	0.00730506i
$106$	−17.7548	+	24.4374i	−0.167499	+	0.230542i
$107$	51.5542	+	70.9582i	0.481815	+	0.663161i	0.978852	−	0.204568i	$-0.0655789\pi$
$107$	51.5542	+	70.9582i	0.481815	+	0.663161i	−0.497038	+	0.867729i	$0.665579\pi$
$108$	8.58359	−	26.4176i	0.0794777	−	0.244607i
$109$			144.692i			1.32745i	0.747978	+	0.663723i	$0.231025\pi$
$109$			144.692i			1.32745i	−0.747978	+	0.663723i	$0.768975\pi$
$110$	5.95492	+	16.8492i	0.0541356	+	0.153175i
$111$	−53.0820			−0.478217
$112$	−2.62461	−	0.852788i	−0.0234340	−	0.00761418i
$113$	104.867	−	76.1905i	0.928029	−	0.674252i	−0.0174806	−	0.999847i	$-0.505565\pi$
$113$	104.867	−	76.1905i	0.928029	−	0.674252i	0.945509	+	0.325595i	$0.105565\pi$
$114$	−67.8885	−	49.3239i	−0.595514	−	0.432666i
$115$	19.0836	+	58.7333i	0.165944	+	0.510724i
$116$	−57.3131	+	18.6221i	−0.494078	+	0.160536i
$117$	46.5213	−	64.0311i	0.397618	−	0.547274i
$118$	43.4493	+	59.8028i	0.368214	+	0.506804i
$119$	1.73762	−	5.34785i	0.0146019	−	0.0449399i
$120$		−	48.5569i		−	0.404641i
$121$	94.1287	−	76.0315i	0.777923	−	0.628360i
$122$	−36.9868			−0.303171
$123$	−68.6950	−	22.3204i	−0.558496	−	0.181466i
$124$	−96.5197	+	70.1257i	−0.778385	+	0.565530i
$125$	9.04508	+	6.57164i	0.0723607	+	0.0525731i
$126$	−0.436141	−	1.34230i	−0.00346144	−	0.0106532i
$127$	−146.655	+	47.6511i	−1.15476	+	0.375205i	−0.822936	−	0.568134i	$-0.807665\pi$
$127$	−146.655	+	47.6511i	−1.15476	+	0.375205i	−0.331828	+	0.943340i	$0.607665\pi$
$128$	−76.0501	+	104.674i	−0.594141	+	0.817766i
$129$	81.8034	+	112.593i	0.634135	+	0.872812i
$130$	−5.67627	+	17.4698i	−0.0436637	+	0.134383i
$131$			128.496i			0.980883i	0.871474	+	0.490442i	$0.163164\pi$
$131$			128.496i			0.980883i	−0.871474	+	0.490442i	$0.836836\pi$
$132$	−144.043	+	50.9080i	−1.09123	+	0.385667i
$133$	−8.01316			−0.0602493
$134$	−27.7639	−	9.02105i	−0.207194	−	0.0673213i
$135$	14.4721	−	10.5146i	0.107201	−	0.0778861i
$136$	−88.9919	−	64.6564i	−0.654352	−	0.475415i
$137$	−19.1378	−	58.9000i	−0.139692	−	0.429927i	0.856599	−	0.515984i	$-0.172573\pi$
$137$	−19.1378	−	58.9000i	−0.139692	−	0.429927i	−0.996290	+	0.0860566i	$0.972573\pi$
$138$	76.3344	−	24.8025i	0.553148	−	0.179729i
$139$	134.155	−	184.649i	0.965144	−	1.32841i	0.0206817	−	0.999786i	$-0.493416\pi$
$139$	134.155	−	184.649i	0.965144	−	1.32841i	0.944462	−	0.328620i	$-0.106584\pi$
$140$	−1.26644	−	1.74311i	−0.00904603	−	0.0124508i
$141$	−58.7051	+	180.676i	−0.416348	+	1.28139i
$142$		−	20.4742i		−	0.144185i
$143$	124.333	−	3.17891i	0.869460	−	0.0222301i
$144$	69.6099			0.483402
$145$	−36.9098	−	11.9927i	−0.254551	−	0.0827085i
$146$	58.6656	−	42.6231i	0.401819	−	0.291939i
$147$	158.318	+	115.025i	1.07699	+	0.782482i
$148$	14.2386	+	43.8218i	0.0962066	+	0.296094i
$149$	−74.8460	+	24.3189i	−0.502322	+	0.163214i	−0.549208	−	0.835686i	$-0.685070\pi$
$149$	−74.8460	+	24.3189i	−0.502322	+	0.163214i	0.0468856	+	0.998900i	$0.485070\pi$
$150$	8.54102	−	11.7557i	0.0569401	−	0.0783714i
$151$	41.7852	+	57.5124i	0.276723	+	0.380877i	0.924645	−	0.380830i	$-0.124362\pi$
$151$	41.7852	+	57.5124i	0.276723	+	0.380877i	−0.647922	+	0.761707i	$0.724362\pi$
$152$	−48.4402	+	149.084i	−0.318686	+	0.980813i
$153$			141.835i			0.927029i
$154$	1.25735	−	1.82704i	0.00816464	−	0.0118639i
$155$	−76.8328			−0.495696
$156$	−149.348	−	48.5260i	−0.957356	−	0.311064i
$157$	173.730	−	126.223i	1.10656	−	0.803965i	0.124444	−	0.992227i	$-0.460285\pi$
$157$	173.730	−	126.223i	1.10656	−	0.803965i	0.982119	+	0.188261i	$0.0602852\pi$
$158$	77.3607	+	56.2058i	0.489625	+	0.355733i
$159$	−51.3901	−	158.162i	−0.323208	−	0.994732i
$160$	−61.5451	+	19.9972i	−0.384657	+	0.124983i
$161$	4.50502	−	6.20063i	0.0279815	−	0.0385133i
$162$	−40.5698	−	55.8396i	−0.250431	−	0.344689i
$163$	−28.1753	+	86.7147i	−0.172855	+	0.531992i	−0.999529	−	0.0306887i	$-0.990230\pi$
$163$	−28.1753	+	86.7147i	−0.172855	+	0.531992i	0.826674	+	0.562681i	$0.190230\pi$
$164$			62.6983i			0.382307i
$165$	−94.3181	−	28.0017i	−0.571625	−	0.169707i
$166$	91.1146			0.548883
$167$	43.1910	+	14.0336i	0.258629	+	0.0840335i	0.435461	−	0.900207i	$-0.356585\pi$
$167$	43.1910	+	14.0336i	0.258629	+	0.0840335i	−0.176833	+	0.984241i	$0.556585\pi$
$168$	−4.87539	+	3.54218i	−0.0290202	+	0.0210844i
$169$	−33.2984	−	24.1927i	−0.197032	−	0.143152i
$170$	−10.1722	−	31.3068i	−0.0598365	−	0.184158i
$171$	192.230	−	62.4595i	1.12415	−	0.365260i
$172$	71.0081	−	97.7343i	0.412838	−	0.568223i
$173$	−89.0780	−	122.605i	−0.514902	−	0.708701i	0.469835	−	0.882754i	$-0.344314\pi$
$173$	−89.0780	−	122.605i	−0.514902	−	0.708701i	−0.984736	+	0.174053i	$0.944314\pi$
$174$	−15.5867	+	47.9709i	−0.0895787	+	0.275695i
$175$		−	1.38757i		−	0.00792899i
$176$	66.5370	+	86.8237i	0.378051	+	0.493316i
$177$	−406.971			−2.29927
$178$	−61.4625	−	19.9704i	−0.345295	−	0.112193i
$179$	137.932	−	100.214i	0.770570	−	0.559852i	−0.131564	−	0.991308i	$-0.542000\pi$
$179$	137.932	−	100.214i	0.770570	−	0.559852i	0.902134	+	0.431456i	$0.142000\pi$
$180$	43.9681	+	31.9447i	0.244267	+	0.177470i
$181$	−51.2918	−	157.860i	−0.283380	−	0.872154i	−0.986880	−	0.161458i	$-0.948380\pi$
$181$	−51.2918	−	157.860i	−0.283380	−	0.872154i	0.703499	−	0.710696i	$-0.251620\pi$
$182$	2.16814	−	0.704473i	0.0119129	−	0.00387073i
$183$	119.692	−	164.742i	0.654054	−	0.900229i
$184$	−88.1287	−	121.299i	−0.478960	−	0.659232i
$185$	−9.16970	+	28.2214i	−0.0495659	+	0.152548i
$186$			99.8580i			0.536871i
$187$	−176.910	+	135.574i	−0.946042	+	0.724995i
$188$	164.904			0.877147
$189$	−2.11146	−	0.686054i	−0.0111717	−	0.00362991i
$190$	−37.9508	+	27.5729i	−0.199741	+	0.145121i
$191$	−9.05573	−	6.57937i	−0.0474122	−	0.0344470i	0.563827	−	0.825893i	$-0.309329\pi$
$191$	−9.05573	−	6.57937i	−0.0474122	−	0.0344470i	−0.611239	+	0.791446i	$0.709329\pi$
$192$	−23.1772	−	71.3322i	−0.120715	−	0.371522i
$193$	119.472	−	38.8189i	0.619027	−	0.201134i	0.0173185	−	0.999850i	$-0.494487\pi$
$193$	119.472	−	38.8189i	0.619027	−	0.201134i	0.601708	+	0.798716i	$0.294487\pi$
$194$	−20.6343	+	28.4007i	−0.106362	+	0.146395i
$195$	−59.4427	−	81.8159i	−0.304834	−	0.419569i
$196$	52.4919	−	161.553i	0.267816	−	0.824252i
$197$		−	361.517i		−	1.83511i	−0.397607	−	0.917556i	$-0.630159\pi$
$197$		−	361.517i		−	1.83511i	0.397607	−	0.917556i	$-0.369841\pi$
$198$	−15.9220	+	53.6302i	−0.0804143	+	0.270859i
$199$	267.692			1.34519			0.672593	−	0.740013i	$-0.265181\pi$
$199$	267.692			1.34519			0.672593	+	0.740013i	$0.265181\pi$
$200$	−25.8156	−	8.38800i	−0.129078	−	0.0419400i
$201$	130.026	−	94.4696i	0.646897	−	0.469998i
$202$	−22.6099	−	16.4271i	−0.111930	−	0.0813221i
$203$	1.48840	+	4.58082i	0.00733201	+	0.0225656i
$204$	267.639	−	86.9613i	1.31196	−	0.426281i
$205$	−23.7336	+	32.6664i	−0.115773	+	0.159348i
$206$	53.8820	+	74.1622i	0.261563	+	0.360011i
$207$	−59.7411	+	183.864i	−0.288604	+	0.888233i
$208$			112.437i			0.540561i
$209$	261.649	+	180.065i	1.25191	+	0.861554i
$210$	−1.80340			−0.00858761
$211$	−214.971	−	69.8482i	−1.01882	−	0.331034i	−0.248458	−	0.968643i	$-0.579924\pi$
$211$	−214.971	−	69.8482i	−1.01882	−	0.331034i	−0.770360	+	0.637609i	$0.779924\pi$
$212$	−116.786	+	84.8501i	−0.550878	+	0.400236i
$213$	91.1935	+	66.2560i	0.428138	+	0.311061i
$214$	−19.6919	−	60.6056i	−0.0920184	−	0.283204i
$215$	73.9919	−	24.0414i	0.344148	−	0.111821i
$216$	−25.5279	+	35.1361i	−0.118185	+	0.162667i
$217$	5.60488	+	7.71445i	0.0258289	+	0.0355505i
$218$	32.4853	−	99.9794i	0.149015	−	0.458621i
$219$			399.232i			1.82298i
$220$	2.18285	+	85.3754i	0.00992206	+	0.388070i
$221$	−229.098			−1.03664
$222$	36.6788	+	11.9177i	0.165220	+	0.0536832i
$223$	−226.619	+	164.648i	−1.01623	+	0.738333i	−0.965506	−	0.260379i	$-0.916152\pi$
$223$	−226.619	+	164.648i	−1.01623	+	0.738333i	−0.0507223	+	0.998713i	$0.516152\pi$
$224$	6.49749	+	4.72070i	0.0290066	+	0.0210746i
$225$	10.8156	+	33.2870i	0.0480693	+	0.147942i
$226$	−89.5673	+	29.1022i	−0.396316	+	0.128771i
$227$	51.2392	−	70.5247i	0.225723	−	0.310681i	−0.681102	−	0.732189i	$-0.738499\pi$
$227$	51.2392	−	70.5247i	0.225723	−	0.310681i	0.906825	+	0.421507i	$0.138499\pi$
$228$	−235.718	−	324.438i	−1.03385	−	1.42298i
$229$	33.1722	−	102.094i	0.144857	−	0.445823i	−0.852136	−	0.523321i	$-0.824693\pi$
$229$	33.1722	−	102.094i	0.144857	−	0.445823i	0.996993	+	0.0774974i	$0.0246929\pi$
$230$		−	44.8682i		−	0.195079i
$231$	4.06888	+	11.5128i	0.0176142	+	0.0498388i
$232$	94.2229			0.406133
$233$	−125.326	−	40.7210i	−0.537881	−	0.174768i	0.0274639	−	0.999623i	$-0.491257\pi$
$233$	−125.326	−	40.7210i	−0.537881	−	0.174768i	−0.565345	+	0.824855i	$0.691257\pi$
$234$	−46.5213	+	33.7997i	−0.198809	+	0.144443i
$235$	85.9164	+	62.4219i	0.365602	+	0.265625i
$236$	109.165	+	335.974i	0.462562	+	1.42362i
$237$	−500.689	+	162.684i	−2.11261	+	0.686429i
$238$	−2.40133	+	3.30515i	−0.0100896	+	0.0138872i
$239$	−54.0983	−	74.4599i	−0.226353	−	0.311548i	0.680702	−	0.732560i	$-0.261675\pi$
$239$	−54.0983	−	74.4599i	−0.226353	−	0.311548i	−0.907055	+	0.421013i	$0.861675\pi$
$240$	27.4853	−	84.5910i	0.114522	−	0.352463i
$241$		−	26.5140i		−	0.110017i	−0.998486	−	0.0550083i	$-0.982481\pi$
$241$		−	26.5140i		−	0.110017i	0.998486	−	0.0550083i	$-0.0175185\pi$
$242$	−82.1115	+	31.4033i	−0.339304	+	0.129766i
$243$	308.000			1.26749
$244$	−168.108	−	54.6217i	−0.688969	−	0.223859i
$245$	88.5025	−	64.3008i	0.361235	−	0.262452i
$246$	42.4559	+	30.8460i	0.172585	+	0.125390i
$247$	100.887	+	310.498i	0.408449	+	1.25708i
$248$	177.408	−	57.6434i	0.715356	−	0.232433i
$249$	−294.853	+	405.830i	−1.18415	+	1.62984i
$250$	−4.77458	−	6.57164i	−0.0190983	−	0.0262866i
$251$	−41.7279	+	128.425i	−0.166247	+	0.511655i	−0.999126	−	0.0417998i	$-0.986691\pi$
$251$	−41.7279	+	128.425i	−0.166247	+	0.511655i	0.832879	+	0.553455i	$0.186691\pi$
$252$		−	6.74498i		−	0.0267658i
$253$	−286.436	+	101.233i	−1.13216	+	0.400131i
$254$	112.034			0.441080
$255$	172.361	+	56.0034i	0.675924	+	0.219621i
$256$	15.3713	−	11.1679i	0.0600442	−	0.0436247i
$257$	197.636	+	143.591i	0.769013	+	0.558720i	0.901661	−	0.432443i	$-0.142348\pi$
$257$	197.636	+	143.591i	0.769013	+	0.558720i	−0.132649	+	0.991163i	$0.542348\pi$
$258$	−31.2461	−	96.1657i	−0.121109	−	0.372735i
$259$	3.50251	−	1.13804i	0.0135232	−	0.00439396i
$260$	−51.5983	+	71.0190i	−0.198455	+	0.273150i
$261$	−71.4114	−	98.2893i	−0.273607	−	0.376587i
$262$	28.8491	−	88.7883i	0.110111	−	0.338887i
$263$			1.93304i			0.00734998i	0.999993	+	0.00367499i	$0.00116979\pi$
$263$			1.93304i			0.00734998i	−0.999993	+	0.00367499i	$0.998830\pi$
$264$	238.790	−	6.10532i	0.904508	−	0.0231262i
$265$	−92.9656			−0.350813
$266$	5.53695	+	1.79907i	0.0208156	+	0.00676340i
$267$	287.846	−	209.132i	1.07807	−	0.783267i
$268$	−112.867	−	82.0029i	−0.421146	−	0.305981i
$269$	−56.6149	−	174.243i	−0.210464	−	0.647743i	−0.999445	−	0.0333242i	$-0.989391\pi$
$269$	−56.6149	−	174.243i	−0.210464	−	0.647743i	0.788980	−	0.614419i	$-0.210609\pi$
$270$	−12.3607	+	4.01623i	−0.0457803	+	0.0148749i
$271$	298.339	−	410.629i	1.10088	−	1.51524i	0.266675	−	0.963786i	$-0.414075\pi$
$271$	298.339	−	410.629i	1.10088	−	1.51524i	0.834208	−	0.551449i	$-0.185925\pi$
$272$	−118.435	−	163.011i	−0.435421	−	0.599306i
$273$	−3.87849	+	11.9368i	−0.0142069	+	0.0437245i
$274$			44.9956i			0.164217i
$275$	−31.1803	+	45.3077i	−0.113383	+	0.164755i
$276$	383.574			1.38976
$277$	33.6985	+	10.9493i	0.121655	+	0.0395282i	0.369212	−	0.929345i	$-0.379628\pi$
$277$	33.6985	+	10.9493i	0.121655	+	0.0395282i	−0.247557	+	0.968873i	$0.579628\pi$
$278$	−134.155	+	97.4693i	−0.482572	+	0.350609i
$279$	−194.589	−	141.377i	−0.697450	−	0.506727i
$280$	1.04102	+	3.20393i	0.00371793	+	0.0114426i
$281$	−325.066	+	105.620i	−1.15682	+	0.375873i	−0.823707	−	0.567015i	$-0.808098\pi$
$281$	−325.066	+	105.620i	−1.15682	+	0.375873i	−0.333110	+	0.942888i	$0.608098\pi$
$282$	81.1285	−	111.664i	0.287690	−	0.395971i
$283$	243.002	+	334.463i	0.858664	+	1.18185i	0.981886	+	0.189471i	$0.0606772\pi$
$283$	243.002	+	334.463i	0.858664	+	1.18185i	−0.123222	+	0.992379i	$0.539323\pi$
$284$	30.2361	−	93.0570i	0.106465	−	0.327666i
$285$		−	258.263i		−	0.906187i
$286$	−86.6256	−	25.7179i	−0.302887	−	0.0899227i
$287$	5.01124			0.0174608
$288$	−192.667	−	62.6012i	−0.668981	−	0.217365i
$289$	98.3419	−	71.4496i	0.340283	−	0.247230i
$290$	22.8115	+	16.5735i	0.0786604	+	0.0571502i
$291$	−59.7245	−	183.813i	−0.205239	−	0.631660i
$292$	329.586	−	107.089i	1.12872	−	0.366743i
$293$	113.360	−	156.026i	0.386893	−	0.532513i	−0.570501	−	0.821297i	$-0.693251\pi$
$293$	113.360	−	156.026i	0.386893	−	0.532513i	0.957394	+	0.288784i	$0.0932510\pi$
$294$	−83.5704	−	115.025i	−0.284253	−	0.391241i
$295$	−70.3024	+	216.369i	−0.238313	+	0.733453i
$296$		−	72.0433i		−	0.243389i
$297$	53.5279	+	69.8482i	0.180228	+	0.235179i
$298$	57.1772			0.191870
$299$	−296.985	−	96.4962i	−0.993260	−	0.322730i
$300$	56.1803	−	40.8174i	0.187268	−	0.136058i
$301$	−7.81153	−	5.67541i	−0.0259519	−	0.0188552i
$302$	−15.9605	−	49.1215i	−0.0528494	−	0.162654i
$303$	146.334	−	47.5469i	0.482952	−	0.156921i
$304$	−168.776	+	232.300i	−0.555183	+	0.764143i
$305$	−66.9098	−	92.0935i	−0.219376	−	0.301946i
$306$	31.8441	−	98.0059i	0.104066	−	0.320281i
$307$		−	335.115i		−	1.09158i	−0.837922	−	0.545790i	$-0.816230\pi$
$307$		−	335.115i		−	1.09158i	0.837922	−	0.545790i	$-0.183770\pi$
$308$	8.41294	−	6.44722i	0.0273147	−	0.0209325i
$309$	−504.689			−1.63330
$310$	53.0902	+	17.2500i	0.171259	+	0.0556453i
$311$	−175.687	+	127.644i	−0.564910	+	0.410431i	−0.833253	−	0.552893i	$-0.813524\pi$
$311$	−175.687	+	127.644i	−0.564910	+	0.410431i	0.268343	+	0.963323i	$0.413524\pi$
$312$	198.636	+	144.318i	0.636655	+	0.462557i
$313$	183.753	+	565.533i	0.587069	+	1.80681i	0.590797	+	0.806821i	$0.298814\pi$
$313$	183.753	+	565.533i	0.587069	+	1.80681i	−0.00372731	+	0.999993i	$0.501186\pi$
$314$	−148.384	+	48.2127i	−0.472559	+	0.153544i
$315$	2.55322	−	3.51420i	0.00810545	−	0.0111562i
$316$	268.607	+	369.706i	0.850022	+	1.16995i
$317$	−22.1860	+	68.2814i	−0.0699872	+	0.215399i	−0.979932	−	0.199330i	$-0.936123\pi$
$317$	−22.1860	+	68.2814i	−0.0699872	+	0.215399i	0.909945	+	0.414729i	$0.136123\pi$
$318$			120.825i			0.379954i
$319$	54.3363	−	183.021i	0.170333	−	0.573733i
$320$	−41.9280			−0.131025
$321$	333.666	+	108.415i	1.03946	+	0.337740i
$322$	−4.50502	+	3.27309i	−0.0139908	+	0.0101649i
$323$	−473.328	−	343.893i	−1.46541	−	1.06468i
$324$	−101.930	−	313.709i	−0.314599	−	0.968237i
$325$	−53.7664	+	17.4698i	−0.165435	+	0.0537532i
$326$	38.9373	−	53.5926i	0.119440	−	0.164395i
$327$	340.190	+	468.232i	1.04034	+	1.43190i
$328$	30.2933	−	93.2333i	0.0923578	−	0.284248i
$329$		−	13.1801i		−	0.0400611i
$330$	58.8854	+	40.5244i	0.178441	+	0.122801i
$331$	−292.681			−0.884232			−0.442116	−	0.896958i	$-0.645772\pi$
$331$	−292.681			−0.884232			−0.442116	+	0.896958i	$0.645772\pi$
$332$	414.123	+	134.557i	1.24736	+	0.405292i
$333$	−75.1525	+	54.6015i	−0.225683	+	0.163968i
$334$	−26.6935	−	19.3940i	−0.0799206	−	0.0580657i
$335$	−27.7639	−	85.4486i	−0.0828774	−	0.255070i
$336$	−10.4984	+	3.41115i	−0.0312454	+	0.0101522i
$337$	230.410	−	317.132i	0.683710	−	0.941046i	−0.316261	−	0.948672i	$-0.602428\pi$
$337$	230.410	−	317.132i	0.683710	−	0.941046i	0.999971	+	0.00762639i	$0.00242758\pi$
$338$	17.5770	+	24.1927i	0.0520030	+	0.0715760i
$339$	160.223	−	493.115i	0.472634	−	1.45462i
$340$		−	157.314i		−	0.462690i
$341$	−9.66061	−	377.844i	−0.0283302	−	1.10805i
$342$	−146.851			−0.429389
$343$	−25.8450	−	8.39755i	−0.0753499	−	0.0244827i
$344$	−152.812	+	111.024i	−0.444220	+	0.322744i
$345$	199.846	+	145.197i	0.579264	+	0.420860i
$346$	34.0248	+	104.717i	0.0983375	+	0.302652i
$347$	60.4984	−	19.6571i	0.174347	−	0.0566488i	−0.220543	−	0.975377i	$-0.570783\pi$
$347$	60.4984	−	19.6571i	0.174347	−	0.0566488i	0.394890	+	0.918729i	$0.370783\pi$
$348$	−141.686	+	195.014i	−0.407143	+	0.560384i
$349$	144.289	+	198.596i	0.413435	+	0.569044i	0.964052	−	0.265714i	$-0.0856076\pi$
$349$	144.289	+	198.596i	0.413435	+	0.569044i	−0.550617	+	0.834758i	$0.685608\pi$
$350$	−0.311529	+	0.958789i	−0.000890084	+	0.00273940i
$351$			90.4534i			0.257702i
$352$	−106.080	−	300.149i	−0.301362	−	0.852695i
$353$	216.535			0.613413			0.306707	−	0.951804i	$-0.400773\pi$
$353$	216.535			0.613413			0.306707	+	0.951804i	$0.400773\pi$
$354$	281.210	+	91.3706i	0.794378	+	0.258109i
$355$	50.9787	−	37.0382i	0.143602	−	0.104333i
$356$	−249.860	−	181.534i	−0.701854	−	0.509927i
$357$	−6.95048	−	21.3914i	−0.0194691	−	0.0599199i
$358$	−117.808	+	38.2782i	−0.329073	+	0.106922i
$359$	−401.418	+	552.505i	−1.11816	+	1.53901i	−0.309339	+	0.950952i	$0.600108\pi$
$359$	−401.418	+	552.505i	−1.11816	+	1.53901i	−0.808818	+	0.588059i	$0.799892\pi$
$360$	−49.9468	−	68.7459i	−0.138741	−	0.190961i
$361$	−146.088	+	449.612i	−0.404675	+	1.24546i
$362$			120.594i			0.333133i
$363$	125.846	−	467.353i	0.346683	−	1.28747i
$364$	10.8948			0.0299306
$365$	212.254	+	68.9656i	0.581518	+	0.188947i
$366$	−119.692	+	86.9613i	−0.327027	+	0.237599i
$367$	−59.6180	−	43.3150i	−0.162447	−	0.118025i	0.503592	−	0.863942i	$-0.332012\pi$
$367$	−59.6180	−	43.3150i	−0.162447	−	0.118025i	−0.666039	+	0.745917i	$0.732012\pi$
$368$	−84.8688	−	261.199i	−0.230622	−	0.709781i
$369$	−120.216	+	39.0607i	−0.325790	+	0.105855i
$370$	12.6722	−	17.4418i	0.0342492	−	0.0471400i
$371$	6.78175	+	9.33427i	0.0182796	+	0.0251598i
$372$	−147.469	+	453.863i	−0.396422	+	1.22006i
$373$			58.3795i			0.156514i	0.996933	+	0.0782568i	$0.0249354\pi$
$373$			58.3795i			0.156514i	−0.996933	+	0.0782568i	$0.975065\pi$
$374$	152.680	−	53.9607i	0.408235	−	0.144280i
$375$	44.7214			0.119257
$376$	−245.214	−	79.6749i	−0.652165	−	0.211901i
$377$	158.761	−	115.346i	0.421116	−	0.305959i
$378$	1.30495	+	0.948103i	0.00345225	+	0.00250821i
$379$	−57.9346	−	178.304i	−0.152862	−	0.470460i	0.845076	−	0.534646i	$-0.179555\pi$
$379$	−57.9346	−	178.304i	−0.152862	−	0.470460i	−0.997938	+	0.0641858i	$0.979555\pi$
$380$	−213.209	+	69.2759i	−0.561077	+	0.182305i
$381$	−362.551	+	499.009i	−0.951578	+	1.30973i
$382$	4.78019	+	6.57937i	0.0125136	+	0.0172235i
$383$	−1.89202	+	5.82303i	−0.00493999	+	0.0152037i	−0.953496	−	0.301405i	$-0.902544\pi$
$383$	−1.89202	+	5.82303i	−0.00493999	+	0.0152037i	0.948556	+	0.316609i	$0.102544\pi$
$384$			517.537i			1.34775i
$385$	6.82373	−	0.174467i	0.0177240	−	0.000453161i
$386$	−91.2686			−0.236447
$387$	231.631	+	75.2615i	0.598530	+	0.194474i
$388$	−135.726	+	98.6110i	−0.349810	+	0.254152i
$389$	182.923	+	132.901i	0.470239	+	0.341649i	0.797534	−	0.603273i	$-0.206137\pi$
$389$	182.923	+	132.901i	0.470239	+	0.341649i	−0.327295	+	0.944922i	$0.606137\pi$
$390$	22.7051	+	69.8791i	0.0582182	+	0.179177i
$391$	532.214	−	172.927i	1.36116	−	0.442268i
$392$	−156.112	+	214.870i	−0.398246	+	0.548139i
$393$	302.111	+	415.821i	0.768731	+	1.05807i
$394$	−81.1656	+	249.802i	−0.206004	+	0.634016i
$395$			294.298i			0.745057i
$396$	−151.567	+	220.240i	−0.382746	+	0.556162i
$397$	−215.123			−0.541873			−0.270936	−	0.962597i	$-0.587333\pi$
$397$	−215.123			−0.541873			−0.270936	+	0.962597i	$0.587333\pi$
$398$	−184.971	−	60.1006i	−0.464750	−	0.151006i
$399$	−25.9311	+	18.8401i	−0.0649903	+	0.0472182i
$400$	−40.2254	−	29.2255i	−0.100564	−	0.0730637i
$401$	−167.199	−	514.586i	−0.416955	−	1.28326i	−0.910490	−	0.413531i	$-0.864295\pi$
$401$	−167.199	−	514.586i	−0.416955	−	1.28326i	0.493535	−	0.869726i	$-0.335705\pi$
$402$	−111.056	+	36.0842i	−0.276258	+	0.0897617i
$403$	228.358	−	314.307i	0.566644	−	0.779919i
$404$	−78.5047	−	108.052i	−0.194318	−	0.267456i
$405$	65.6434	−	202.030i	0.162082	−	0.498838i
$406$		−	3.49943i		−	0.00861929i
$407$	−139.939	−	41.5458i	−0.343830	−	0.102078i
$408$	−440.000			−1.07843
$409$	348.785	+	113.327i	0.852774	+	0.277083i	0.702608	−	0.711578i	$-0.252019\pi$
$409$	348.785	+	113.327i	0.852774	+	0.277083i	0.150167	+	0.988661i	$0.452019\pi$
$410$	23.7336	−	17.2434i	0.0578867	−	0.0420572i
$411$	−200.413	−	145.609i	−0.487624	−	0.354279i
$412$	135.376	+	416.646i	0.328583	+	1.01128i
$413$	26.8531	−	8.72511i	0.0650197	−	0.0211262i
$414$	82.5602	−	113.634i	0.199421	−	0.274479i
$415$	164.828	+	226.866i	0.397175	+	0.546665i
$416$	101.116	−	311.203i	0.243067	−	0.748083i
$417$		−	912.952i		−	2.18933i
$418$	−140.368	−	183.166i	−0.335809	−	0.438195i
$419$	164.543			0.392704			0.196352	−	0.980533i	$-0.437090\pi$
$419$	164.543			0.392704			0.196352	+	0.980533i	$0.437090\pi$
$420$	−8.19660	−	2.66324i	−0.0195157	−	0.00634104i
$421$	−97.2887	+	70.6844i	−0.231090	+	0.167896i	−0.697304	−	0.716775i	$-0.745617\pi$
$421$	−97.2887	+	70.6844i	−0.231090	+	0.167896i	0.466215	+	0.884672i	$0.345617\pi$
$422$	132.859	+	96.5278i	0.314832	+	0.228739i
$423$	102.734	+	316.183i	0.242870	+	0.747476i
$424$	214.659	−	69.7470i	0.506271	−	0.164498i
$425$	59.5492	−	81.9624i	0.140116	−	0.192853i
$426$	−48.1378	−	66.2560i	−0.112999	−	0.155530i
$427$	−4.36570	+	13.4363i	−0.0102241	+	0.0314666i
$428$		−	304.538i		−	0.711538i
$429$	394.875	−	302.611i	0.920455	−	0.705387i
$430$	−56.5248			−0.131453
$431$	514.135	+	167.052i	1.19289	+	0.387593i	0.837140	−	0.546989i	$-0.184226\pi$
$431$	514.135	+	167.052i	1.19289	+	0.387593i	0.355748	+	0.934582i	$0.384226\pi$
$432$	−64.3607	+	46.7608i	−0.148983	+	0.108243i
$433$	−172.618	−	125.414i	−0.398656	−	0.289641i	0.370337	−	0.928897i	$-0.379242\pi$
$433$	−172.618	−	125.414i	−0.398656	−	0.289641i	−0.768993	+	0.639257i	$0.779242\pi$
$434$	−2.14087	−	6.58893i	−0.00493289	−	0.0151819i
$435$	−147.639	+	47.9709i	−0.339401	+	0.110278i
$436$	295.297	−	406.441i	0.677286	−	0.932205i
$437$	−468.737	−	645.161i	−1.07262	−	1.47634i
$438$	89.6331	−	275.862i	0.204642	−	0.629823i
$439$			29.8597i			0.0680175i	0.999422	+	0.0340087i	$0.0108274\pi$
$439$			29.8597i			0.0680175i	−0.999422	+	0.0340087i	$0.989173\pi$
$440$	38.0041	−	128.009i	0.0863729	−	0.290930i
$441$	342.461			0.776555
$442$	158.303	+	51.4358i	0.358152	+	0.116371i
$443$	46.3262	−	33.6580i	0.104574	−	0.0759774i	−0.534269	−	0.845314i	$-0.679413\pi$
$443$	46.3262	−	33.6580i	0.104574	−	0.0759774i	0.638843	+	0.769337i	$0.279413\pi$
$444$	149.108	+	108.334i	0.335830	+	0.243994i
$445$	−61.4625	−	189.162i	−0.138118	−	0.425083i
$446$	193.556	−	62.8901i	0.433981	−	0.141009i
$447$	−185.029	+	254.671i	−0.413936	+	0.569734i
$448$	3.05861	+	4.20981i	0.00682725	+	0.00939690i
$449$	183.771	−	565.590i	0.409291	−	1.25967i	−0.507968	−	0.861376i	$-0.669603\pi$
$449$	183.771	−	565.590i	0.409291	−	1.25967i	0.917259	−	0.398291i	$-0.130397\pi$
$450$		−	25.4290i		−	0.0565089i
$451$	−163.629	−	112.608i	−0.362814	−	0.249686i
$452$	−450.069			−0.995728
$453$	270.440	+	87.8712i	0.596997	+	0.193976i
$454$	−51.2392	+	37.2274i	−0.112862	+	0.0819988i
$455$	5.67627	+	4.12405i	0.0124753	+	0.00906386i
$456$	193.761	+	596.335i	0.424914	+	1.30775i
$457$	−451.899	+	146.831i	−0.988837	+	0.321293i	−0.758396	−	0.651794i	$-0.774017\pi$
$457$	−451.899	+	146.831i	−0.988837	+	0.321293i	−0.230441	+	0.973086i	$0.574017\pi$
$458$	−45.8429	+	63.0973i	−0.100094	+	0.137767i
$459$	−95.2786	−	131.140i	−0.207579	−	0.285708i
$460$	66.2608	−	203.930i	0.144045	−	0.443326i
$461$			290.362i			0.629853i	0.949116	+	0.314927i	$0.101980\pi$
$461$			290.362i			0.629853i	−0.949116	+	0.314927i	$0.898020\pi$
$462$	−0.226751	−	8.86865i	−0.000490803	−	0.0191962i
$463$	86.1358			0.186039			0.0930193	−	0.995664i	$-0.470348\pi$
$463$	86.1358			0.186039			0.0930193	+	0.995664i	$0.470348\pi$
$464$	164.146	+	53.3342i	0.353763	+	0.114944i
$465$	−248.636	+	180.645i	−0.534702	+	0.388483i
$466$	77.4559	+	56.2750i	0.166214	+	0.120762i
$467$	69.8177	+	214.877i	0.149503	+	0.460122i	0.997563	−	0.0697786i	$-0.0222293\pi$
$467$	69.8177	+	214.877i	0.149503	+	0.460122i	−0.848060	+	0.529900i	$0.822229\pi$
$468$	−261.358	+	84.9204i	−0.558458	+	0.181454i
$469$	−6.55418	+	9.02105i	−0.0139748	+	0.0192346i
$470$	−45.3522	−	62.4219i	−0.0964940	−	0.132813i
$471$	265.437	−	816.930i	0.563559	−	1.73446i
$472$		−	552.343i		−	1.17022i
$473$	127.533	+	360.850i	0.269626	+	0.762897i
$474$	382.492			0.806946
$475$	−137.307	−	44.6139i	−0.289068	−	0.0939240i
$476$	−15.7953	+	11.4759i	−0.0331833	+	0.0241091i
$477$	−235.447	−	171.062i	−0.493599	−	0.358621i
$478$	20.6637	+	63.5964i	0.0432295	+	0.133047i
$479$	79.9888	−	25.9899i	0.166991	−	0.0542587i	−0.224328	−	0.974514i	$-0.572019\pi$
$479$	79.9888	−	25.9899i	0.166991	−	0.0542587i	0.391319	+	0.920255i	$0.372019\pi$
$480$	−152.148	+	209.414i	−0.316975	+	0.436278i
$481$	−88.1945	−	121.389i	−0.183356	−	0.252369i
$482$	−5.95277	+	18.3207i	−0.0123501	+	0.0380098i
$483$		−	30.6576i		−	0.0634733i
$484$	−419.580	+	21.4694i	−0.866900	+	0.0443583i
$485$	−108.043			−0.222768
$486$	−212.823	−	69.1503i	−0.437907	−	0.142285i
$487$	−535.336	+	388.945i	−1.09925	+	0.798654i	−0.980938	−	0.194322i	$-0.937749\pi$
$487$	−535.336	+	388.945i	−1.09925	+	0.798654i	−0.118315	+	0.992976i	$0.537749\pi$
$488$	223.589	+	162.447i	0.458173	+	0.332882i
$489$	112.701	+	346.859i	0.230473	+	0.709323i
$490$	−75.5902	+	24.5607i	−0.154266	+	0.0501239i
$491$	−438.057	+	602.934i	−0.892174	+	1.22797i	0.0807242	+	0.996736i	$0.474277\pi$
$491$	−438.057	+	602.934i	−0.892174	+	1.22797i	−0.972898	+	0.231235i	$0.925723\pi$
$492$	147.413	+	202.896i	0.299619	+	0.412390i
$493$	−108.673	+	334.460i	−0.220431	+	0.678417i
$494$		−	237.200i		−	0.480161i
$495$	−162.337	+	57.3737i	−0.327953	+	0.115906i
$496$	341.692			0.688895
$497$	−7.43769	−	2.41665i	−0.0149652	−	0.00486248i
$498$	294.853	−	214.223i	0.592074	−	0.430167i
$499$	−224.927	−	163.419i	−0.450756	−	0.327493i	0.339138	−	0.940736i	$-0.389864\pi$
$499$	−224.927	−	163.419i	−0.450756	−	0.327493i	−0.789894	+	0.613243i	$0.789864\pi$
$500$	−11.9959	−	36.9197i	−0.0239919	−	0.0738394i
$501$	172.764	−	56.1344i	0.344838	−	0.112045i
$502$	57.6666	−	79.3713i	0.114874	−	0.158110i
$503$	158.365	+	217.971i	0.314842	+	0.433342i	0.936884	−	0.349642i	$-0.113697\pi$
$503$	158.365	+	217.971i	0.314842	+	0.433342i	−0.622042	+	0.782984i	$0.713697\pi$
$504$	−3.25891	+	10.0299i	−0.00646609	+	0.0199006i
$505$		−	86.0132i		−	0.170323i
$506$	220.650	−	5.64152i	0.436068	−	0.0111493i
$507$	−164.636			−0.324726
$508$	509.206	+	165.451i	1.00237	+	0.325691i
$509$	−424.177	+	308.183i	−0.833354	+	0.605467i	−0.920506	−	0.390728i	$-0.872223\pi$
$509$	−424.177	+	308.183i	−0.833354	+	0.605467i	0.0871522	+	0.996195i	$0.472223\pi$
$510$	−106.525	−	77.3948i	−0.208872	−	0.151754i
$511$	−8.55920	−	26.3425i	−0.0167499	−	0.0515509i
$512$	479.078	−	155.662i	0.935699	−	0.304027i
$513$	−135.777	+	186.881i	−0.264673	+	0.364291i
$514$	−104.325	−	143.591i	−0.202967	−	0.279360i
$515$	−87.1829	+	268.321i	−0.169287	+	0.521012i
$516$		−	483.225i		−	0.936483i
$517$	−296.172	+	430.363i	−0.572867	+	0.832424i
$518$	−2.67568			−0.00516541
$519$	−576.525	−	187.324i	−1.11084	−	0.360933i
$520$	111.041	−	80.6760i	0.213540	−	0.155146i
$521$	308.640	+	224.240i	0.592400	+	0.430404i	0.843173	−	0.537642i	$-0.180685\pi$
$521$	308.640	+	224.240i	0.592400	+	0.430404i	−0.250773	+	0.968046i	$0.580685\pi$
$522$	27.2767	+	83.9491i	0.0522543	+	0.160822i
$523$	607.503	−	197.390i	1.16157	−	0.377418i	0.336083	−	0.941832i	$-0.390898\pi$
$523$	607.503	−	197.390i	1.16157	−	0.377418i	0.825492	+	0.564414i	$0.190898\pi$
$524$	262.243	−	360.947i	0.500464	−	0.688829i
$525$	−3.26238	−	4.49028i	−0.00621406	−	0.00855291i
$526$	0.433995	−	1.33570i	0.000825086	−	0.00253935i
$527$			696.223i			1.32111i
$528$	419.453	+	124.529i	0.794418	+	0.235851i
$529$	233.756			0.441882
$530$	64.2376	+	20.8721i	0.121203	+	0.0393813i
$531$	−576.181	+	418.620i	−1.08509	+	0.788361i
$532$	22.5091	+	16.3538i	0.0423103	+	0.0307402i
$533$	−63.0923	−	194.178i	−0.118372	−	0.364312i
$534$	−245.850	+	79.8814i	−0.460393	+	0.149591i
$535$	115.279	−	158.667i	0.215474	−	0.296575i
$536$	128.215	+	176.473i	0.239207	+	0.329240i
$537$	210.741	−	648.596i	0.392442	−	1.20781i
$538$			133.110i			0.247416i
$539$	327.343	+	427.148i	0.607315	+	0.792482i
$540$	−62.1115			−0.115021
$541$	117.236	+	38.0923i	0.216703	+	0.0704109i	0.415356	−	0.909659i	$-0.363657\pi$
$541$	117.236	+	38.0923i	0.216703	+	0.0704109i	−0.198654	+	0.980070i	$0.563657\pi$
$542$	−298.339	+	216.756i	−0.550442	+	0.399919i
$543$	−537.135	−	390.251i	−0.989198	−	0.718695i
$544$	181.205	+	557.693i	0.333098	+	1.02517i
$545$	307.705	−	99.9794i	0.564597	−	0.183449i
$546$	5.35995	−	7.37733i	0.00981675	−	0.0135116i
$547$	−199.538	−	274.640i	−0.364786	−	0.502085i	0.586688	−	0.809813i	$-0.300431\pi$
$547$	−199.538	−	274.640i	−0.364786	−	0.502085i	−0.951474	+	0.307728i	$0.900431\pi$
$548$	−66.4489	+	204.509i	−0.121257	+	0.373191i
$549$		−	356.356i		−	0.649100i
$550$	31.7173	−	24.3064i	0.0576678	−	0.0441935i
$551$	501.151			0.909530
$552$	−570.381	−	185.328i	−1.03330	−	0.335739i
$553$	29.5492	−	21.4687i	0.0534343	−	0.0388223i
$554$	−20.8268	−	15.1316i	−0.0375936	−	0.0273133i
$555$	36.6788	+	112.886i	0.0660879	+	0.203398i
$556$	−753.687	+	244.888i	−1.35555	+	0.440446i
$557$	−310.414	+	427.248i	−0.557296	+	0.767052i	−0.990980	−	0.134013i	$-0.957213\pi$
$557$	−310.414	+	427.248i	−0.557296	+	0.767052i	0.433684	+	0.901065i	$0.357213\pi$
$558$	102.716	+	141.377i	0.184079	+	0.253364i
$559$	−121.565	+	374.140i	−0.217469	+	0.669302i
$560$			6.17083i			0.0110193i
$561$	−253.738	+	854.667i	−0.452297	+	1.52347i
$562$	248.328			0.441865
$563$	−244.087	−	79.3087i	−0.433547	−	0.140868i	0.0841094	−	0.996457i	$-0.473195\pi$
$563$	−244.087	−	79.3087i	−0.433547	−	0.140868i	−0.517657	+	0.855589i	$0.673195\pi$
$564$	533.639	−	387.712i	0.946169	−	0.687432i
$565$	−234.490	−	170.367i	−0.415027	−	0.301535i
$566$	−92.8185	−	285.666i	−0.163990	−	0.504710i
$567$	−25.0735	+	8.14689i	−0.0442214	+	0.0143684i
$568$	−89.9230	+	123.768i	−0.158315	+	0.217902i
$569$	146.337	+	201.415i	0.257182	+	0.353981i	0.918010	−	0.396556i	$-0.129795\pi$
$569$	146.337	+	201.415i	0.257182	+	0.353981i	−0.660828	+	0.750537i	$0.729795\pi$
$570$	−57.9837	+	178.456i	−0.101726	+	0.313080i
$571$			393.435i			0.689028i	0.938781	+	0.344514i	$0.111956\pi$
$571$			393.435i			0.689028i	−0.938781	+	0.344514i	$0.888044\pi$
$572$	−355.741	−	244.818i	−0.621924	−	0.428003i
$573$	−44.7740			−0.0781396
$574$	−3.46268	−	1.12509i	−0.00603254	−	0.00196009i
$575$	111.717	−	81.1674i	0.194291	−	0.141161i
$576$	−106.188	−	77.1500i	−0.184354	−	0.133941i
$577$	76.8228	+	236.436i	0.133142	+	0.409768i	0.995296	−	0.0968772i	$-0.0308854\pi$
$577$	76.8228	+	236.436i	0.133142	+	0.409768i	−0.862155	+	0.506645i	$0.830885\pi$
$578$	−83.9940	+	27.2913i	−0.145318	+	0.0472168i
$579$	295.351	−	406.516i	0.510106	−	0.702101i
$580$	79.2047	+	109.016i	0.136560	+	0.187959i
$581$	10.7546	−	33.0993i	0.0185105	−	0.0569695i
$582$			140.421i			0.241273i
$583$	−11.6891	−	457.181i	−0.0200499	−	0.784186i
$584$	−541.840			−0.927808
$585$	−168.316	−	54.6891i	−0.287719	−	0.0934856i
$586$	−113.360	+	82.3607i	−0.193447	+	0.140547i
$587$	308.959	+	224.472i	0.526336	+	0.382406i	0.818986	−	0.573814i	$-0.194537\pi$
$587$	308.959	+	224.472i	0.526336	+	0.382406i	−0.292649	+	0.956220i	$0.594537\pi$
$588$	−209.967	−	646.213i	−0.357088	−	1.09900i
$589$	943.596	−	306.593i	1.60203	−	0.520531i
$590$	97.1556	−	133.723i	0.164670	−	0.226649i
$591$	−849.978	−	1169.89i	−1.43820	−	1.97952i
$592$	40.7796	−	125.507i	0.0688845	−	0.212005i
$593$			467.858i			0.788968i	0.918903	+	0.394484i	$0.129077\pi$
$593$			467.858i			0.788968i	−0.918903	+	0.394484i	$0.870923\pi$
$594$	−21.3050	−	60.2817i	−0.0358669	−	0.101484i
$595$	−12.5735			−0.0211320
$596$	259.875	+	84.4386i	0.436033	+	0.141676i
$597$	866.269	−	629.382i	1.45104	−	1.05424i
$598$	183.547	+	133.354i	0.306934	+	0.223001i
$599$	180.089	+	554.257i	0.300649	+	0.925304i	0.981265	+	0.192663i	$0.0617124\pi$
$599$	180.089	+	554.257i	0.300649	+	0.925304i	−0.680616	+	0.732641i	$0.738288\pi$
$600$	−103.262	+	33.5520i	−0.172104	+	0.0559200i
$601$	439.974	−	605.572i	0.732070	−	1.00761i	−0.266966	−	0.963706i	$-0.586021\pi$
$601$	439.974	−	605.572i	0.732070	−	1.00761i	0.999036	−	0.0439019i	$-0.0139789\pi$
$602$	4.12343	+	5.67541i	0.00684954	+	0.00942759i
$603$	86.9149	−	267.496i	0.144137	−	0.443609i
$604$		−	246.832i		−	0.408662i
$605$	−226.732	−	147.640i	−0.374764	−	0.244033i
$606$	−111.790			−0.184471
$607$	−715.161	−	232.370i	−1.17819	−	0.382817i	−0.346496	−	0.938052i	$-0.612628\pi$
$607$	−715.161	−	232.370i	−1.17819	−	0.382817i	−0.831694	+	0.555235i	$0.812628\pi$
$608$	676.048	−	491.178i	1.11192	−	0.807858i
$609$	15.5867	+	11.3244i	0.0255939	+	0.0185951i
$610$	25.5573	+	78.6572i	0.0418972	+	0.128946i
$611$	−510.710	+	165.940i	−0.835860	+	0.271587i
$612$	289.468	−	398.418i	0.472987	−	0.651010i
$613$	−589.502	−	811.379i	−0.961666	−	1.32362i	−0.946146	−	0.323741i	$-0.895059\pi$
$613$	−589.502	−	811.379i	−0.961666	−	1.32362i	−0.0155207	−	0.999880i	$-0.504941\pi$
$614$	−75.2380	+	231.559i	−0.122537	+	0.377131i
$615$			161.512i			0.262621i
$616$	−15.6252	+	5.52231i	−0.0253656	+	0.00896480i
$617$	436.456			0.707384			0.353692	−	0.935362i	$-0.384926\pi$
$617$	436.456			0.707384			0.353692	+	0.935362i	$0.384926\pi$
$618$	348.731	+	113.310i	0.564290	+	0.183349i
$619$	−102.839	+	74.7172i	−0.166138	+	0.120706i	−0.667748	−	0.744388i	$-0.732741\pi$
$619$	−102.839	+	74.7172i	−0.166138	+	0.120706i	0.501610	+	0.865094i	$0.332741\pi$
$620$	215.825	+	156.806i	0.348104	+	0.252913i
$621$	−68.2755	−	210.130i	−0.109945	−	0.338374i
$622$	150.055	−	48.7557i	0.241245	−	0.0783853i
$623$	−14.5093	+	19.9704i	−0.0232894	+	0.0320552i
$624$	264.354	+	363.853i	0.423645	+	0.583097i
$625$	7.72542	−	23.7764i	0.0123607	−	0.0380423i
$626$		−	432.028i		−	0.690141i
$627$	1270.07	−	32.4729i	2.02563	−	0.0517908i
$628$	−745.616			−1.18729
$629$	255.729	+	83.0915i	0.406565	+	0.132101i
$630$	−2.55322	+	1.85502i	−0.00405272	+	0.00294448i
$631$	182.154	+	132.343i	0.288675	+	0.209735i	0.722692	−	0.691170i	$-0.242904\pi$
$631$	182.154	+	132.343i	0.288675	+	0.209735i	−0.434017	+	0.900905i	$0.642904\pi$
$632$	−220.795	−	679.538i	−0.349360	−	1.07522i
$633$	−859.882	+	279.393i	−1.35842	+	0.441379i
$634$	30.6602	−	42.2002i	0.0483600	−	0.0665618i
$635$	202.672	+	278.954i	0.319169	+	0.439298i
$636$	−178.433	+	549.162i	−0.280556	+	0.863462i
$637$			553.156i			0.868377i
$638$	−78.6362	+	114.265i	−0.123254	+	0.179099i
$639$	197.262			0.308705
$640$	275.152	+	89.4023i	0.429925	+	0.139691i
$641$	852.241	−	619.190i	1.32955	−	0.965975i	0.329790	−	0.944054i	$-0.393022\pi$
$641$	852.241	−	619.190i	1.32955	−	0.965975i	0.999760	−	0.0219202i	$-0.00697799\pi$
$642$	−206.217	−	149.825i	−0.321210	−	0.233373i
$643$	−259.872	−	799.805i	−0.404156	−	1.24386i	−0.921598	−	0.388146i	$-0.873116\pi$
$643$	−259.872	−	799.805i	−0.404156	−	1.24386i	0.517442	−	0.855718i	$-0.326884\pi$
$644$	−25.3094	+	8.22352i	−0.0393003	+	0.0127694i
$645$	182.918	−	251.765i	0.283594	−	0.390333i
$646$	249.853	+	343.893i	0.386769	+	0.532342i
$647$	19.8766	−	61.1738i	0.0307211	−	0.0945499i	−0.934520	−	0.355910i	$-0.884171\pi$
$647$	19.8766	−	61.1738i	0.0307211	−	0.0945499i	0.965241	+	0.261360i	$0.0841710\pi$
$648$			515.738i			0.795892i
$649$	−1072.88	−	318.524i	−1.65314	−	0.490792i
$650$	41.0739			0.0631906
$651$	36.2755	+	11.7866i	0.0557228	+	0.0181054i
$652$	256.118	−	186.081i	0.392820	−	0.285400i
$653$	865.002	+	628.461i	1.32466	+	0.962421i	0.999862	+	0.0166374i	$0.00529610\pi$
$653$	865.002	+	628.461i	1.32466	+	0.962421i	0.324797	+	0.945784i	$0.394704\pi$
$654$	−129.941	−	399.918i	−0.198687	−	0.611495i
$655$	273.262	−	88.7883i	0.417194	−	0.135555i
$656$	105.548	−	145.275i	0.160897	−	0.221455i
$657$	410.659	+	565.224i	0.625052	+	0.860311i
$658$	−2.95912	+	9.10724i	−0.00449714	+	0.0138408i
$659$			283.355i			0.429978i	0.976617	+	0.214989i	$0.0689715\pi$
$659$			283.355i			0.429978i	−0.976617	+	0.214989i	$0.931028\pi$
$660$	207.793	+	271.148i	0.314838	+	0.410831i
$661$	−845.155			−1.27860			−0.639300	−	0.768957i	$-0.720776\pi$
$661$	−845.155			−1.27860			−0.639300	+	0.768957i	$0.720776\pi$
$662$	202.237	+	65.7109i	0.305495	+	0.0992612i
$663$	−741.378	+	538.642i	−1.11822	+	0.812432i
$664$	−550.795	−	400.176i	−0.829511	−	0.602675i
$665$	5.53695	+	17.0410i	0.00832625	+	0.0256256i
$666$	64.1879	−	20.8559i	0.0963782	−	0.0313152i
$667$	−281.749	+	387.794i	−0.422412	+	0.581400i
$668$	−92.6834	−	127.568i	−0.138748	−	0.190970i
$669$	−346.243	+	1065.63i	−0.517553	+	1.59286i
$670$			65.2769i			0.0974282i
$671$	444.479	−	340.625i	0.662413	−	0.507637i
$672$	32.1253			0.0478056
$673$	−422.060	−	137.135i	−0.627132	−	0.203767i	−0.0218275	−	0.999762i	$-0.506948\pi$
$673$	−422.060	−	137.135i	−0.627132	−	0.203767i	−0.605304	+	0.795994i	$0.706948\pi$
$674$	−230.410	+	167.403i	−0.341855	+	0.248372i
$675$	−32.3607	−	23.5114i	−0.0479417	−	0.0348317i
$676$	44.1616	+	135.915i	0.0653278	+	0.201058i
$677$	914.604	−	297.173i	1.35097	−	0.438955i	0.457949	−	0.888979i	$-0.348584\pi$
$677$	914.604	−	297.173i	1.35097	−	0.438955i	0.893017	+	0.450023i	$0.148584\pi$
$678$	−221.423	+	304.762i	−0.326582	+	0.449502i
$679$	7.88160	+	10.8481i	0.0116077	+	0.0159766i
$680$	−76.0081	+	233.929i	−0.111777	+	0.344013i
$681$		−	348.693i		−	0.512031i
$682$	−78.1559	+	263.253i	−0.114598	+	0.386001i
$683$	−488.033			−0.714542			−0.357271	−	0.934001i	$-0.616293\pi$
$683$	−488.033			−0.714542			−0.357271	+	0.934001i	$0.616293\pi$
$684$	−667.450	−	216.868i	−0.975804	−	0.317058i
$685$	−112.034	+	81.3978i	−0.163554	+	0.118829i
$686$	15.9731	+	11.6051i	0.0232844	+	0.0169171i
$687$	−132.689	−	408.374i	−0.193142	−	0.594431i
$688$	−329.058	+	106.917i	−0.478281	+	0.155403i
$689$	276.306	−	380.303i	0.401025	−	0.551964i
$690$	−105.492	−	145.197i	−0.152886	−	0.210430i
$691$	−153.473	+	472.340i	−0.222102	+	0.683560i	0.776471	+	0.630153i	$0.217008\pi$
$691$	−153.473	+	472.340i	−0.222102	+	0.683560i	−0.998573	+	0.0534066i	$0.982992\pi$
$692$			526.197i			0.760400i
$693$	17.6030	+	12.1142i	0.0254011	+	0.0174808i
$694$	−46.2167			−0.0665947
$695$	−485.377	−	157.709i	−0.698385	−	0.226919i
$696$	304.912	−	221.531i	0.438092	−	0.318292i
$697$	296.008	+	215.062i	0.424689	+	0.308555i
$698$	−55.1134	−	169.622i	−0.0789590	−	0.243011i
$699$	−501.305	+	162.884i	−0.717174	+	0.233024i
$700$	−2.83186	+	3.89772i	−0.00404551	+	0.00556816i
$701$	294.515	+	405.366i	0.420136	+	0.578268i	0.965654	−	0.259831i	$-0.0836670\pi$
$701$	294.515	+	405.366i	0.420136	+	0.578268i	−0.545518	+	0.838099i	$0.683667\pi$
$702$	20.3081	−	62.5018i	0.0289289	−	0.0890339i
$703$		−	383.182i		−	0.545067i
$704$	−5.27184	−	206.191i	−0.00748840	−	0.292885i
$705$	424.794			0.602545
$706$	−149.622	−	48.6151i	−0.211929	−	0.0688599i
$707$	−8.63621	+	6.27458i	−0.0122153	+	0.00887493i
$708$	1143.19	+	830.574i	1.61467	+	1.17313i
$709$	−0.643159	−	1.97944i	−0.000907135	−	0.00279188i	0.950602	−	0.310413i	$-0.100467\pi$
$709$	−0.643159	−	1.97944i	−0.000907135	−	0.00279188i	−0.951509	+	0.307621i	$0.900467\pi$
$710$	−43.5410	+	14.1473i	−0.0613254	+	0.0199258i
$711$	−541.525	+	745.345i	−0.761638	+	1.04831i
$712$	283.836	+	390.666i	0.398646	+	0.548689i
$713$	−293.249	+	902.528i	−0.411289	+	1.26582i
$714$			16.3416i			0.0228873i
$715$	−92.6722	−	262.213i	−0.129611	−	0.366731i
$716$	−591.976			−0.826783
$717$	−350.132	−	113.765i	−0.488329	−	0.158668i
$718$	401.418	−	291.647i	0.559078	−	0.406194i
$719$	−568.638	−	413.140i	−0.790874	−	0.574603i	0.117349	−	0.993091i	$-0.462560\pi$
$719$	−568.638	−	413.140i	−0.790874	−	0.574603i	−0.908223	+	0.418487i	$0.862560\pi$
$720$	−48.0993	−	148.034i	−0.0668045	−	0.205603i
$721$	33.3009	−	10.8201i	0.0461871	−	0.0150071i
$722$	201.888	−	277.875i	0.279624	−	0.384869i
$723$	−62.3382	−	85.8012i	−0.0862216	−	0.118674i
$724$	−178.092	+	548.111i	−0.245984	+	0.757060i
$725$			86.7802i			0.119697i
$726$	−191.885	+	294.679i	−0.264304	+	0.405894i
$727$	1163.47			1.60037			0.800184	−	0.599754i	$-0.204735\pi$
$727$	1163.47			1.60037			0.800184	+	0.599754i	$0.204735\pi$
$728$	−16.2007	−	5.26392i	−0.0222537	−	0.00723065i
$729$	304.999	−	221.595i	0.418381	−	0.303971i
$730$	−131.180	−	95.3081i	−0.179699	−	0.130559i
$731$	−217.852	−	670.480i	−0.298019	−	0.917209i
$732$	−672.433	+	218.487i	−0.918625	+	0.298479i
$733$	768.849	−	1058.23i	1.04891	−	1.44370i	0.159155	−	0.987254i	$-0.449123\pi$
$733$	768.849	−	1058.23i	1.04891	−	1.44370i	0.889752	−	0.456443i	$-0.150877\pi$
$734$	31.4702	+	43.3150i	0.0428750	+	0.0590123i
$735$	135.220	−	416.164i	0.183973	−	0.566209i
$736$			799.272i			1.08597i
$737$	416.723	−	147.280i	0.565432	−	0.199837i
$738$	91.8371			0.124441
$739$	−1085.92	−	352.838i	−1.46945	−	0.477453i	−0.538508	−	0.842621i	$-0.681012\pi$
$739$	−1085.92	−	352.838i	−1.46945	−	0.477453i	−0.930942	+	0.365167i	$0.881012\pi$
$740$	83.3541	−	60.5603i	0.112641	−	0.0818382i
$741$	1056.50	+	767.594i	1.42578	+	1.03589i
$742$	−2.59040	−	7.97242i	−0.00349110	−	0.0107445i
$743$	−542.947	+	176.414i	−0.730749	+	0.237435i	−0.650677	−	0.759354i	$-0.725515\pi$
$743$	−542.947	+	176.414i	−0.730749	+	0.237435i	−0.0800717	+	0.996789i	$0.525515\pi$
$744$	438.577	−	603.650i	0.589486	−	0.811357i
$745$	103.435	+	142.365i	0.138838	+	0.191095i
$746$	13.1070	−	40.3393i	0.0175697	−	0.0540741i
$747$			877.859i			1.17518i
$748$	773.632	−	19.7800i	1.03427	−	0.0264438i
$749$	−24.3406			−0.0324974
$750$	−30.9017	−	10.0406i	−0.0412023	−	0.0133874i
$751$	496.597	−	360.799i	0.661247	−	0.480424i	−0.205837	−	0.978586i	$-0.565992\pi$
$751$	496.597	−	360.799i	0.661247	−	0.480424i	0.867084	+	0.498162i	$0.165992\pi$
$752$	−382.089	−	277.604i	−0.508097	−	0.369154i
$753$	166.912	+	513.702i	0.221662	+	0.682207i
$754$	−135.598	+	44.0584i	−0.179838	+	0.0584329i
$755$	93.4346	−	128.602i	0.123754	−	0.170333i
$756$	4.53097	+	6.23634i	0.00599335	+	0.00824913i
$757$	−251.984	+	775.528i	−0.332872	+	1.02448i	0.634888	+	0.772604i	$0.281046\pi$
$757$	−251.984	+	775.528i	−0.332872	+	1.02448i	−0.967761	+	0.251872i	$0.918954\pi$
$758$			136.212i			0.179700i
$759$	−688.912	+	1001.05i	−0.907657	+	1.31890i
$760$	350.517			0.461206
$761$	−488.577	−	158.748i	−0.642020	−	0.208605i	−0.0301278	−	0.999546i	$-0.509591\pi$
$761$	−488.577	−	158.748i	−0.642020	−	0.208605i	−0.611892	+	0.790941i	$0.709591\pi$
$762$	362.551	−	263.409i	0.475789	−	0.345681i
$763$	−32.4853	−	23.6019i	−0.0425757	−	0.0309331i
$764$	12.0100	+	36.9631i	0.0157200	+	0.0483811i
$765$	301.631	−	98.0059i	0.394289	−	0.128112i
$766$	2.61470	−	3.59883i	0.00341345	−	0.00469821i
$767$	−676.171	−	930.670i	−0.881579	−	1.21339i
$768$	23.4853	−	72.2803i	0.0305798	−	0.0941150i
$769$		−	501.416i		−	0.652036i	−0.945364	−	0.326018i	$-0.894293\pi$
$769$		−	501.416i		−	0.652036i	0.945364	−	0.326018i	$-0.105707\pi$
$770$	−4.75425	−	1.41147i	−0.00617435	−	0.00183308i
$771$	977.167			1.26740
$772$	−414.823	−	134.784i	−0.537336	−	0.174591i
$773$	363.619	−	264.185i	0.470400	−	0.341765i	−0.327197	−	0.944956i	$-0.606104\pi$
$773$	363.619	−	264.185i	0.470400	−	0.341765i	0.797597	+	0.603191i	$0.206104\pi$
$774$	−143.156	−	104.009i	−0.184956	−	0.134378i
$775$	53.0902	+	163.395i	0.0685034	+	0.210832i
$776$	249.472	−	81.0584i	0.321485	−	0.104457i
$777$	8.65869	−	11.9177i	0.0111437	−	0.0153380i
$778$	−96.5585	−	132.901i	−0.124111	−	0.170824i
$779$	161.124	−	495.888i	0.206834	−	0.636569i
$780$			351.137i			0.450176i
$781$	188.554	+	246.043i	0.241427	+	0.315036i
$782$	−406.575			−0.519917
$783$	132.053	+	42.9065i	0.168650	+	0.0547976i
$784$	−393.590	+	285.960i	−0.502028	+	0.364744i
$785$	−388.473	−	282.242i	−0.494870	−	0.359544i
$786$	−115.396	−	355.153i	−0.146815	−	0.451849i
$787$	547.379	−	177.854i	0.695526	−	0.225990i	0.0601458	−	0.998190i	$-0.480843\pi$
$787$	547.379	−	177.854i	0.695526	−	0.225990i	0.635380	+	0.772200i	$0.280843\pi$
$788$	−737.809	+	1015.51i	−0.936306	+	1.28872i
$789$	4.54486	+	6.25546i	0.00576028	+	0.00792834i
$790$	66.0739	−	203.355i	0.0836379	−	0.257411i
$791$			35.9723i			0.0454770i
$792$	331.794	−	254.269i	0.418932	−	0.321047i
$793$	575.601			0.725852
$794$	148.647	+	48.2982i	0.187212	+	0.0608290i
$795$	−300.843	+	218.575i	−0.378419	+	0.274937i
$796$	−751.951	−	546.325i	−0.944662	−	0.686337i
$797$	7.71885	+	23.7562i	0.00968488	+	0.0298070i	0.955782	−	0.294076i	$-0.0950117\pi$
$797$	7.71885	+	23.7562i	0.00968488	+	0.0298070i	−0.946097	+	0.323883i	$0.895012\pi$
$798$	22.1478	−	7.19626i	0.0277542	−	0.00901787i
$799$	565.639	−	778.535i	0.707933	−	0.974386i
$800$	85.0532	+	117.066i	0.106317	+	0.146332i
$801$	192.408	−	592.171i	0.240210	−	0.739289i
$802$			393.109i			0.490160i
$803$	−312.467	+	1052.48i	−0.389125	+	1.31069i
$804$	−558.046			−0.694088
$805$	−16.2993	−	5.29597i	−0.0202476	−	0.00657885i
$806$	−228.358	+	165.911i	−0.283322	+	0.205846i
$807$	−592.879	−	430.752i	−0.734671	−	0.533769i
$808$	64.5310	+	198.606i	0.0798651	+	0.245799i
$809$	−711.977	+	231.335i	−0.880070	+	0.285952i	−0.713987	−	0.700159i	$-0.753112\pi$
$809$	−711.977	+	231.335i	−0.880070	+	0.285952i	−0.166084	+	0.986112i	$0.553112\pi$
$810$	−90.7169	+	124.861i	−0.111996	+	0.154150i
$811$	138.201	+	190.218i	0.170409	+	0.234547i	0.885676	−	0.464303i	$-0.153695\pi$
$811$	138.201	+	190.218i	0.170409	+	0.234547i	−0.715268	+	0.698851i	$0.753695\pi$
$812$	5.16792	−	15.9052i	0.00636443	−	0.0195877i
$813$		−	2030.26i		−	2.49725i
$814$	87.3676	+	60.1256i	0.107331	+	0.0738644i
$815$	203.878			0.250158
$816$	−766.525	−	249.059i	−0.939369	−	0.305219i
$817$	−812.771	+	590.513i	−0.994824	+	0.722782i
$818$	−215.561	−	156.614i	−0.263522	−	0.191460i
$819$	6.78736	+	20.8894i	0.00828738	+	0.0255059i
$820$	133.336	−	43.3235i	0.162605	−	0.0528335i
$821$	−90.2423	+	124.208i	−0.109918	+	0.151288i	−0.860432	−	0.509566i	$-0.829806\pi$
$821$	−90.2423	+	124.208i	−0.109918	+	0.151288i	0.750514	+	0.660854i	$0.229806\pi$
$822$	105.791	+	145.609i	0.128699	+	0.177140i
$823$	399.465	−	1229.43i	0.485377	−	1.49384i	−0.346057	−	0.938214i	$-0.612480\pi$
$823$	399.465	−	1229.43i	0.485377	−	1.49384i	0.831434	−	0.555624i	$-0.187520\pi$
$824$		−	684.967i		−	0.831270i
$825$	5.62306	+	219.928i	0.00681583	+	0.266580i
$826$	−20.5140			−0.0248353
$827$	594.248	+	193.083i	0.718559	+	0.233474i	0.645398	−	0.763846i	$-0.276691\pi$
$827$	594.248	+	193.083i	0.718559	+	0.233474i	0.0731605	+	0.997320i	$0.476691\pi$
$828$	543.057	−	394.554i	0.655866	−	0.476514i
$829$	1192.01	+	866.043i	1.43788	+	1.04468i	0.988479	+	0.151355i	$0.0483638\pi$
$829$	1192.01	+	866.043i	1.43788	+	1.04468i	0.449405	+	0.893328i	$0.351636\pi$
$830$	−62.9586	−	193.767i	−0.0758538	−	0.233454i
$831$	134.794	−	43.7973i	0.162207	−	0.0527043i
$832$	124.616	−	171.519i	0.149779	−	0.206152i
$833$	−582.664	−	801.969i	−0.699477	−	0.962748i
$834$	−204.971	+	630.835i	−0.245768	+	0.756396i
$835$		−	101.548i		−	0.121614i
$836$	−367.489	−	1039.80i	−0.439580	−	1.24378i
$837$	274.885			0.328417
$838$	−113.696	−	36.9422i	−0.135676	−	0.0440838i
$839$	1083.63	−	787.303i	1.29157	−	0.938383i	0.291737	−	0.956498i	$-0.405767\pi$
$839$	1083.63	−	787.303i	1.29157	−	0.938383i	0.999836	+	0.0181155i	$0.00576666\pi$
$840$	10.9017	+	7.92055i	0.0129782	+	0.00942922i
$841$	166.797	+	513.350i	0.198332	+	0.610404i
$842$	83.0945	−	26.9990i	0.0986870	−	0.0320654i
$843$	−803.607	+	1106.07i	−0.953270	+	1.31206i
$844$	461.305	+	634.932i	0.546570	+	0.752289i
$845$	−28.4402	+	87.5300i	−0.0336570	+	0.103586i
$846$		−	241.542i		−	0.285511i
$847$	1.71597	+	33.5354i	0.00202594	+	0.0395931i
$848$	413.438			0.487544
$849$	1572.74	+	511.015i	1.85246	+	0.601902i
$850$	−59.5492	+	43.2650i	−0.0700578	+	0.0509000i
$851$	296.509	+	215.426i	0.348424	+	0.253145i
$852$	−120.944	−	372.228i	−0.141953	−	0.436888i
$853$	1106.68	−	359.583i	1.29740	−	0.421551i	0.422724	−	0.906259i	$-0.361074\pi$
$853$	1106.68	−	359.583i	1.29740	−	0.421551i	0.874676	+	0.484708i	$0.161074\pi$
$854$	6.03326	−	8.30406i	0.00706470	−	0.00972373i
$855$	−265.656	−	365.644i	−0.310709	−	0.427654i
$856$	−147.141	+	452.853i	−0.171894	+	0.529034i
$857$		−	1069.27i		−	1.24769i	−0.781549	−	0.623844i	$-0.785570\pi$
$857$		−	1069.27i		−	1.24769i	0.781549	−	0.623844i	$-0.214430\pi$
$858$	−340.793	+	120.444i	−0.397194	+	0.140378i
$859$	998.288			1.16215			0.581076	−	0.813849i	$-0.302632\pi$
$859$	998.288			1.16215			0.581076	+	0.813849i	$0.302632\pi$
$860$	−256.910	−	83.4751i	−0.298732	−	0.0970640i
$861$	16.2167	−	11.7821i	0.0188347	−	0.0136842i
$862$	−317.753	−	230.861i	−0.368623	−	0.267820i
$863$	217.399	+	669.085i	0.251911	+	0.775301i	0.994423	+	0.105468i	$0.0336342\pi$
$863$	217.399	+	669.085i	0.251911	+	0.775301i	−0.742512	+	0.669833i	$0.766366\pi$
$864$	220.190	−	71.5442i	0.254850	−	0.0828058i
$865$	−199.184	+	274.154i	−0.230271	+	0.316941i
$866$	91.1189	+	125.414i	0.105218	+	0.144820i
$867$	150.253	−	462.431i	0.173302	−	0.533370i
$868$		−	33.1089i		−	0.0381438i
$869$	−1447.28	+	37.0036i	−1.66545	+	0.0425818i
$870$	112.786			0.129640
$871$	432.071	+	140.388i	0.496063	+	0.161181i
$872$	−635.487	+	461.708i	−0.728770	+	0.529482i
$873$	−273.631	−	198.805i	−0.313438	−	0.227726i
$874$	179.042	+	551.033i	0.204853	+	0.630473i
$875$	−2.95085	+	0.958789i	−0.00337240	+	0.00109576i
$876$	814.780	−	1121.45i	0.930114	−	1.28019i
$877$	−198.377	−	273.042i	−0.226199	−	0.311336i	0.680800	−	0.732470i	$-0.261632\pi$
$877$	−198.377	−	273.042i	−0.226199	−	0.311336i	−0.906999	+	0.421133i	$0.861632\pi$
$878$	6.70391	−	20.6325i	0.00763544	−	0.0234995i
$879$		−	771.436i		−	0.877629i
$880$	138.666	−	201.493i	0.157575	−	0.228969i
$881$	−1011.82			−1.14849			−0.574246	−	0.818682i	$-0.694705\pi$
$881$	−1011.82			−1.14849			−0.574246	+	0.818682i	$0.694705\pi$
$882$	−236.635	−	76.8873i	−0.268293	−	0.0871738i
$883$	−260.572	+	189.317i	−0.295099	+	0.214402i	−0.725476	−	0.688247i	$-0.758380\pi$
$883$	−260.572	+	189.317i	−0.295099	+	0.214402i	0.430377	+	0.902649i	$0.358380\pi$
$884$	643.541	+	467.560i	0.727988	+	0.528914i
$885$	281.210	+	865.475i	0.317751	+	0.977937i
$886$	−39.5673	+	12.8562i	−0.0446584	+	0.0145104i
$887$	−437.553	+	602.240i	−0.493296	+	0.678963i	−0.980992	−	0.194050i	$-0.937837\pi$
$887$	−437.553	+	602.240i	−0.493296	+	0.678963i	0.487696	+	0.873014i	$0.337837\pi$
$888$	−169.384	−	233.137i	−0.190748	−	0.262542i
$889$	13.2239	−	40.6989i	0.0148750	−	0.0457805i
$890$			144.507i			0.162367i
$891$	1001.78	+	297.415i	1.12434	+	0.333799i
$892$	972.603			1.09036
$893$	−1304.24	−	423.773i	−1.46052	−	0.474550i
$894$	185.029	−	134.432i	0.206968	−	0.150371i
$895$	−308.425	−	224.084i	−0.344609	−	0.250373i
$896$	−11.0956	−	34.1486i	−0.0123834	−	0.0381123i
$897$	−1187.94	+	385.985i	−1.32435	+	0.430306i
$898$	−253.966	+	349.554i	−0.282813	+	0.389258i
$899$	−350.535	−	482.470i	−0.389916	−	0.536674i
$900$	37.5532	−	115.577i	0.0417258	−	0.128419i
$901$			842.411i			0.934973i
$902$	87.7829	+	114.547i	0.0973203	+	0.126993i
$903$	−38.6223			−0.0427711
$904$	669.259	+	217.456i	0.740331	+	0.240548i
$905$	−300.267	+	218.157i	−0.331787	+	0.241058i
$906$	−167.141	−	121.435i	−0.184482	−	0.134034i
$907$	−173.823	−	534.971i	−0.191646	−	0.589825i	−0.999999	−	0.00112787i	$-0.999641\pi$
$907$	−173.823	−	534.971i	−0.191646	−	0.589825i	0.808354	−	0.588697i	$-0.200359\pi$
$908$	−287.863	+	93.5325i	−0.317030	+	0.103009i
$909$	158.269	−	217.839i	0.174114	−	0.239647i
$910$	−2.99630	−	4.12405i	−0.00329264	−	0.00453193i
$911$	−21.9218	+	67.4684i	−0.0240634	+	0.0740597i	−0.962367	−	0.271753i	$-0.912397\pi$
$911$	−21.9218	+	67.4684i	−0.0240634	+	0.0740597i	0.938304	+	0.345813i	$0.112397\pi$
$912$			1148.55i			1.25938i
$913$	−1094.94	+	839.106i	−1.19928	+	0.919064i
$914$	345.220			0.377702
$915$	−433.050	−	140.706i	−0.473278	−	0.153777i
$916$	−301.541	+	219.082i	−0.329193	+	0.239173i
$917$	−28.8491	−	20.9601i	−0.0314603	−	0.0228572i
$918$	36.3932	+	112.007i	0.0396440	+	0.122012i
$919$	64.4021	−	20.9255i	0.0700784	−	0.0227699i	−0.273768	−	0.961796i	$-0.588270\pi$
$919$	64.4021	−	20.9255i	0.0700784	−	0.0227699i	0.343846	+	0.939026i	$0.388270\pi$
$920$	−197.062	+	271.232i	−0.214198	+	0.294818i
$921$	−787.902	−	1084.45i	−0.855486	−	1.17748i
$922$	65.1904	−	200.635i	0.0707054	−	0.217609i
$923$			318.626i			0.345207i
$924$	12.0665	−	40.6436i	0.0130590	−	0.0439866i
$925$	66.3525			0.0717325
$926$	−59.5184	−	19.3387i	−0.0642747	−	0.0208841i
$927$	−714.528	+	519.135i	−0.770796	+	0.560016i
$928$	−406.359	−	295.237i	−0.437887	−	0.318144i
$929$	385.947	+	1187.82i	0.415443	+	1.27860i	0.911854	+	0.410515i	$0.134651\pi$
$929$	385.947	+	1187.82i	0.415443	+	1.27860i	−0.496411	+	0.868088i	$0.665349\pi$
$930$	212.361	−	69.0002i	0.228345	−	0.0741937i
$931$	−830.328	+	1142.85i	−0.891866	+	1.22755i
$932$	268.937	+	370.160i	0.288559	+	0.397168i
$933$	−268.426	+	826.129i	−0.287702	+	0.885455i
$934$		−	164.151i		−	0.175751i
$935$	410.557	+	282.542i	0.439099	+	0.302184i
$936$	429.674			0.459053
$937$	−515.209	−	167.401i	−0.549849	−	0.178657i	0.0208996	−	0.999782i	$-0.493347\pi$
$937$	−515.209	−	167.401i	−0.549849	−	0.178657i	−0.570749	+	0.821125i	$0.693347\pi$
$938$	6.55418	−	4.76189i	0.00698739	−	0.00507664i
$939$	1924.28	+	1398.07i	2.04929	+	1.48890i
$940$	−113.946	−	350.688i	−0.121219	−	0.373073i
$941$	−561.217	+	182.350i	−0.596405	+	0.193784i	−0.591636	−	0.806205i	$-0.701518\pi$
$941$	−561.217	+	182.350i	−0.596405	+	0.193784i	−0.00476834	+	0.999989i	$0.501518\pi$
$942$	−366.824	+	504.890i	−0.389410	+	0.535977i
$943$	293.137	+	403.468i	0.310856	+	0.427856i
$944$	312.650	−	962.238i	0.331197	−	1.01932i
$945$			4.96433i			0.00525326i
$946$	−7.10716	−	277.974i	−0.00751286	−	0.293842i
$947$	−527.364			−0.556878			−0.278439	−	0.960454i	$-0.589817\pi$
$947$	−527.364			−0.556878			−0.278439	+	0.960454i	$0.589817\pi$
$948$	1738.46	+	564.860i	1.83382	+	0.595844i
$949$	−912.973	+	663.313i	−0.962036	+	0.698960i
$950$	84.8607	+	61.6549i	0.0893270	+	0.0648999i
$951$	88.7438	+	273.125i	0.0933163	+	0.287198i
$952$	29.0325	−	9.43324i	0.0304963	−	0.00990886i
$953$	1038.40	−	1429.23i	1.08961	−	1.49972i	0.241125	−	0.970494i	$-0.422483\pi$
$953$	1038.40	−	1429.23i	1.08961	−	1.49972i	0.848483	−	0.529223i	$-0.177517\pi$
$954$	124.284	+	171.062i	0.130277	+	0.179310i
$955$	−7.73452	+	23.8044i	−0.00809897	+	0.0249261i
$956$			319.567i			0.334275i
$957$	−254.472	−	720.021i	−0.265906	−	0.752373i
$958$	−61.1060			−0.0637849
$959$	16.3456	+	5.31101i	0.0170444	+	0.00553807i
$960$	−135.682	+	98.5787i	−0.141335	+	0.102686i
$961$	−177.706	−	129.111i	−0.184917	−	0.134350i
$962$	33.6873	+	103.679i	0.0350180	+	0.107774i
$963$	583.915	−	189.725i	0.606350	−	0.197015i
$964$	−54.1117	+	74.4783i	−0.0561325	+	0.0772597i
$965$	−165.106	−	227.250i	−0.171095	−	0.235492i
$966$	−6.88307	+	21.1839i	−0.00712533	+	0.0219295i
$967$			1457.23i			1.50696i	0.657470	+	0.753481i	$0.271627\pi$
$967$			1457.23i			1.50696i	−0.657470	+	0.753481i	$0.728373\pi$
$968$	634.294	+	170.799i	0.655263	+	0.176445i
$969$	−2340.26			−2.41513
$970$	74.6556	+	24.2571i	0.0769645	+	0.0250073i
$971$	−151.983	+	110.422i	−0.156522	+	0.113720i	−0.663290	−	0.748363i	$-0.730840\pi$
$971$	−151.983	+	110.422i	−0.156522	+	0.113720i	0.506768	+	0.862083i	$0.330840\pi$
$972$	−865.177	−	628.588i	−0.890100	−	0.646696i
$973$	19.5729	+	60.2393i	0.0201161	+	0.0619109i
$974$	457.232	−	148.564i	0.469437	−	0.152529i
$975$	−132.918	+	182.946i	−0.136326	+	0.187637i
$976$	297.562	+	409.559i	0.304879	+	0.419631i
$977$	389.172	−	1197.75i	0.398334	−	1.22595i	−0.528001	−	0.849244i	$-0.677058\pi$
$977$	389.172	−	1197.75i	0.398334	−	1.22595i	0.926335	−	0.376702i	$-0.122942\pi$
$978$		−	264.977i		−	0.270937i
$979$	922.522	−	326.041i	0.942310	−	0.333035i
$980$	−379.835			−0.387586
$981$	963.269	+	312.985i	0.981926	+	0.319047i
$982$	438.057	−	318.267i	0.446087	−	0.324101i
$983$	842.819	+	612.344i	0.857395	+	0.622934i	0.927175	−	0.374628i	$-0.122230\pi$
$983$	842.819	+	612.344i	0.857395	+	0.622934i	−0.0697799	+	0.997562i	$0.522230\pi$
$984$	−121.173	−	372.933i	−0.123144	−	0.378997i
$985$	−768.812	+	249.802i	−0.780520	+	0.253606i
$986$	150.182	−	206.708i	0.152314	−	0.209643i
$987$	−30.9883	−	42.6518i	−0.0313965	−	0.0432135i
$988$	350.293	−	1078.09i	0.354548	−	1.09119i
$989$		−	960.916i		−	0.971604i
$990$	125.053	−	3.19732i	0.126316	−	0.00322962i
$991$	−664.312			−0.670345			−0.335173	−	0.942157i	$-0.608795\pi$
$991$	−664.312			−0.670345			−0.335173	+	0.942157i	$0.608795\pi$
$992$	−945.736	−	307.288i	−0.953363	−	0.309767i
$993$	−947.135	+	688.134i	−0.953811	+	0.692985i
$994$	4.59675	+	3.33973i	0.00462449	+	0.00335989i
$995$	−184.971	−	569.281i	−0.185900	−	0.572142i
$996$	1656.49	−	538.227i	1.66315	−	0.540389i
$997$	−116.026	+	159.697i	−0.116375	+	0.160177i	−0.863231	−	0.504809i	$-0.831563\pi$
$997$	−116.026	+	159.697i	−0.116375	+	0.160177i	0.746855	+	0.664987i	$0.231563\pi$
$998$	118.731	+	163.419i	0.118969	+	0.163747i
$999$	32.8065	−	100.968i	0.0328393	−	0.101069i

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.3.i.a.46.1	yes	4
5.2	odd	4		275.3.q.c.24.2		8
5.3	odd	4		275.3.q.c.24.1		8
5.4	even	2		275.3.x.d.101.1		4
11.4	even	5		605.3.c.a.241.2		4
11.6	odd	10	inner	55.3.i.a.6.1	✓	4
11.7	odd	10		605.3.c.a.241.3		4
55.17	even	20		275.3.q.c.149.1		8
55.28	even	20		275.3.q.c.149.2		8
55.39	odd	10		275.3.x.d.226.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.i.a.6.1	✓	4	11.6	odd	10	inner
55.3.i.a.46.1	yes	4	1.1	even	1	trivial
275.3.q.c.24.1		8	5.3	odd	4
275.3.q.c.24.2		8	5.2	odd	4
275.3.q.c.149.1		8	55.17	even	20
275.3.q.c.149.2		8	55.28	even	20
275.3.x.d.101.1		4	5.4	even	2
275.3.x.d.226.1		4	55.39	odd	10
605.3.c.a.241.2		4	11.4	even	5
605.3.c.a.241.3		4	11.7	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

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

Label	55.3.i.a.46.1

Level	$55$
Weight	$3$
Character	55.46
Analytic conductor	$1.499$
Analytic rank	$0$
Dimension	$4$
Inner twists	$2$