LMFDB - Embedded newform 224.3.w.a.43.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(43,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 0]))

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

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

chi := DirichletCharacter("224.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.w (of order $8$, 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:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			43.10
Character	$\chi$	$=$	224.43
Dual form			224.3.w.a.99.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70535 - 1.04488i) q^{2} +(0.502742 + 1.21373i) q^{3} +(1.81645 + 3.56377i) q^{4} +(-0.0438594 + 0.105886i) q^{5} +(0.410845 - 2.59514i) q^{6} +(-1.87083 + 1.87083i) q^{7} +(0.626019 - 7.97547i) q^{8} +(5.14358 - 5.14358i) q^{9} +O(q^{10})$	\(q+(-1.70535 - 1.04488i) q^{2} +(0.502742 + 1.21373i) q^{3} +(1.81645 + 3.56377i) q^{4} +(-0.0438594 + 0.105886i) q^{5} +(0.410845 - 2.59514i) q^{6} +(-1.87083 + 1.87083i) q^{7} +(0.626019 - 7.97547i) q^{8} +(5.14358 - 5.14358i) q^{9} +(0.185434 - 0.134745i) q^{10} +(1.37483 - 3.31914i) q^{11} +(-3.41224 + 3.99634i) q^{12} +(5.53835 + 13.3708i) q^{13} +(5.14521 - 1.23563i) q^{14} -0.150567 q^{15} +(-9.40098 + 12.9469i) q^{16} +25.0349i q^{17} +(-14.1460 + 3.39720i) q^{18} +(4.85961 - 2.01292i) q^{19} +(-0.457022 + 0.0360320i) q^{20} +(-3.21122 - 1.33013i) q^{21} +(-5.81267 + 4.22377i) q^{22} +(-1.30671 - 1.30671i) q^{23} +(9.99477 - 3.24979i) q^{24} +(17.6684 + 17.6684i) q^{25} +(4.52599 - 28.5888i) q^{26} +(19.7523 + 8.18168i) q^{27} +(-10.0655 - 3.26894i) q^{28} +(15.1031 - 6.25590i) q^{29} +(0.256769 + 0.157324i) q^{30} +41.0028i q^{31} +(29.5599 - 12.2561i) q^{32} +4.71971 q^{33} +(26.1584 - 42.6933i) q^{34} +(-0.116041 - 0.280148i) q^{35} +(27.6736 + 8.98748i) q^{36} +(-9.38050 + 22.6465i) q^{37} +(-10.3906 - 1.64497i) q^{38} +(-13.4441 + 13.4441i) q^{39} +(0.817033 + 0.416086i) q^{40} +(33.4077 - 33.4077i) q^{41} +(4.08643 + 5.62368i) q^{42} +(4.08867 - 9.87092i) q^{43} +(14.3260 - 1.12947i) q^{44} +(0.319038 + 0.770227i) q^{45} +(0.863046 + 3.59375i) q^{46} +20.9665 q^{47} +(-20.4402 - 4.90129i) q^{48} -7.00000i q^{49} +(-11.6695 - 48.5921i) q^{50} +(-30.3855 + 12.5861i) q^{51} +(-37.5902 + 44.0248i) q^{52} +(71.4971 + 29.6151i) q^{53} +(-25.1358 - 34.5915i) q^{54} +(0.291151 + 0.291151i) q^{55} +(13.7496 + 16.0919i) q^{56} +(4.88626 + 4.88626i) q^{57} +(-32.2927 - 5.11238i) q^{58} +(-84.5124 - 35.0062i) q^{59} +(-0.273497 - 0.536585i) q^{60} +(-35.0338 + 14.5115i) q^{61} +(42.8430 - 69.9243i) q^{62} +19.2455i q^{63} +(-63.2162 - 9.98558i) q^{64} -1.65868 q^{65} +(-8.04877 - 4.93153i) q^{66} +(-34.1693 - 82.4920i) q^{67} +(-89.2186 + 45.4747i) q^{68} +(0.929050 - 2.24292i) q^{69} +(-0.0948298 + 0.599000i) q^{70} +(-26.1620 + 26.1620i) q^{71} +(-37.8025 - 44.2424i) q^{72} +(-22.9027 + 22.9027i) q^{73} +(39.6600 - 28.8188i) q^{74} +(-12.5619 + 30.3272i) q^{75} +(16.0009 + 13.6622i) q^{76} +(3.63746 + 8.78161i) q^{77} +(36.9744 - 8.87946i) q^{78} -120.602 q^{79} +(-0.958570 - 1.56327i) q^{80} -37.3799i q^{81} +(-91.8790 + 22.0649i) q^{82} +(-2.08476 + 0.863534i) q^{83} +(-1.09275 - 13.8602i) q^{84} +(-2.65084 - 1.09801i) q^{85} +(-17.2865 + 12.5612i) q^{86} +(15.1859 + 15.1859i) q^{87} +(-25.6110 - 13.0428i) q^{88} +(49.1699 + 49.1699i) q^{89} +(0.260721 - 1.64686i) q^{90} +(-35.3757 - 14.6531i) q^{91} +(2.28324 - 7.03039i) q^{92} +(-49.7663 + 20.6139i) q^{93} +(-35.7553 - 21.9075i) q^{94} +0.602850i q^{95} +(29.7366 + 29.7160i) q^{96} +123.684 q^{97} +(-7.31415 + 11.9375i) q^{98} +(-10.0007 - 24.1438i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 80 q^{10} + 96 q^{12} - 20 q^{16} - 60 q^{18} - 260 q^{22} + 64 q^{23} - 144 q^{24} - 200 q^{26} + 192 q^{27} - 40 q^{30} + 40 q^{32} + 120 q^{34} + 464 q^{36} + 504 q^{38} - 384 q^{39} + 360 q^{40} - 96 q^{43} + 52 q^{44} + 64 q^{46} - 104 q^{48} - 312 q^{50} - 384 q^{51} - 320 q^{52} + 160 q^{53} - 576 q^{54} - 512 q^{55} - 196 q^{56} - 360 q^{58} - 872 q^{60} + 128 q^{61} - 408 q^{62} + 832 q^{66} + 160 q^{67} + 856 q^{68} - 384 q^{69} + 336 q^{70} + 1488 q^{72} + 308 q^{74} + 768 q^{75} + 1024 q^{76} - 224 q^{77} - 408 q^{78} + 1024 q^{79} - 1040 q^{80} - 240 q^{82} - 1384 q^{86} + 896 q^{87} - 560 q^{88} - 1320 q^{90} - 380 q^{92} - 936 q^{94} - 1088 q^{96} - 512 q^{99}+O(q^{100}) $ 192 * q + 80 * q^10 + 96 * q^12 - 20 * q^16 - 60 * q^18 - 260 * q^22 + 64 * q^23 - 144 * q^24 - 200 * q^26 + 192 * q^27 - 40 * q^30 + 40 * q^32 + 120 * q^34 + 464 * q^36 + 504 * q^38 - 384 * q^39 + 360 * q^40 - 96 * q^43 + 52 * q^44 + 64 * q^46 - 104 * q^48 - 312 * q^50 - 384 * q^51 - 320 * q^52 + 160 * q^53 - 576 * q^54 - 512 * q^55 - 196 * q^56 - 360 * q^58 - 872 * q^60 + 128 * q^61 - 408 * q^62 + 832 * q^66 + 160 * q^67 + 856 * q^68 - 384 * q^69 + 336 * q^70 + 1488 * q^72 + 308 * q^74 + 768 * q^75 + 1024 * q^76 - 224 * q^77 - 408 * q^78 + 1024 * q^79 - 1040 * q^80 - 240 * q^82 - 1384 * q^86 + 896 * q^87 - 560 * q^88 - 1320 * q^90 - 380 * q^92 - 936 * q^94 - 1088 * q^96 - 512 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{8}\right)$

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 $

$2$	−1.70535	−	1.04488i	−0.852676	−	0.522440i
$2$	−1.70535	−	1.04488i	−0.852676	−	0.522440i
$3$	0.502742	+	1.21373i	0.167581	+	0.404576i	0.985252	−	0.171110i	$-0.0547353\pi$
$3$	0.502742	+	1.21373i	0.167581	+	0.404576i	−0.817671	+	0.575685i	$0.804735\pi$
$4$	1.81645	+	3.56377i	0.454114	+	0.890944i
$5$	−0.0438594	+	0.105886i	−0.00877188	+	0.0211772i	−0.928205	−	0.372070i	$-0.878648\pi$
$5$	−0.0438594	+	0.105886i	−0.00877188	+	0.0211772i	0.919433	+	0.393247i	$0.128648\pi$
$6$	0.410845	−	2.59514i	0.0684742	−	0.432523i
$7$	−1.87083	+	1.87083i	−0.267261	+	0.267261i
$7$	−1.87083	+	1.87083i	−0.267261	+	0.267261i
$8$	0.626019	−	7.97547i	0.0782523	−	0.996934i
$9$	5.14358	−	5.14358i	0.571509	−	0.571509i
$10$	0.185434	−	0.134745i	0.0185434	−	0.0134745i
$11$	1.37483	−	3.31914i	0.124985	−	0.301740i	−0.848985	−	0.528416i	$-0.822786\pi$
$11$	1.37483	−	3.31914i	0.124985	−	0.301740i	0.973970	+	0.226677i	$0.0727860\pi$
$12$	−3.41224	+	3.99634i	−0.284353	+	0.333028i
$13$	5.53835	+	13.3708i	0.426027	+	1.02852i	0.980535	+	0.196342i	$0.0629064\pi$
$13$	5.53835	+	13.3708i	0.426027	+	1.02852i	−0.554508	+	0.832178i	$0.687094\pi$
$14$	5.14521	−	1.23563i	0.367515	−	0.0882595i
$15$	−0.150567			−0.0100378
$16$	−9.40098	+	12.9469i	−0.587561	+	0.809180i
$17$			25.0349i			1.47264i	0.676634	+	0.736319i	$0.263438\pi$
$17$			25.0349i			1.47264i	−0.676634	+	0.736319i	$0.736562\pi$
$18$	−14.1460	+	3.39720i	−0.785891	+	0.188733i
$19$	4.85961	−	2.01292i	0.255769	−	0.105943i	−0.251115	−	0.967957i	$-0.580797\pi$
$19$	4.85961	−	2.01292i	0.255769	−	0.105943i	0.506884	+	0.862014i	$0.330797\pi$
$20$	−0.457022	+	0.0360320i	−0.0228511	+	0.00180160i
$21$	−3.21122	−	1.33013i	−0.152915	−	0.0633395i
$22$	−5.81267	+	4.22377i	−0.264212	+	0.191989i
$23$	−1.30671	−	1.30671i	−0.0568134	−	0.0568134i	0.678129	−	0.734943i	$-0.262791\pi$
$23$	−1.30671	−	1.30671i	−0.0568134	−	0.0568134i	−0.734943	+	0.678129i	$0.762791\pi$
$24$	9.99477	−	3.24979i	0.416449	−	0.135408i
$25$	17.6684	+	17.6684i	0.706735	+	0.706735i
$26$	4.52599	−	28.5888i	0.174077	−	1.09957i
$27$	19.7523	+	8.18168i	0.731568	+	0.303025i
$28$	−10.0655	−	3.26894i	−0.359482	−	0.116748i
$29$	15.1031	−	6.25590i	0.520796	−	0.215721i	−0.106771	−	0.994284i	$-0.534051\pi$
$29$	15.1031	−	6.25590i	0.520796	−	0.215721i	0.627566	+	0.778563i	$0.284051\pi$
$30$	0.256769	+	0.157324i	0.00855897	+	0.00524413i
$31$			41.0028i			1.32267i	0.750090	+	0.661336i	$0.230010\pi$
$31$			41.0028i			1.32267i	−0.750090	+	0.661336i	$0.769990\pi$
$32$	29.5599	−	12.2561i	0.923747	−	0.383003i
$33$	4.71971			0.143022
$34$	26.1584	−	42.6933i	0.769365	−	1.25568i
$35$	−0.116041	−	0.280148i	−0.00331546	−	0.00800423i
$36$	27.6736	+	8.98748i	0.768712	+	0.249652i
$37$	−9.38050	+	22.6465i	−0.253527	+	0.612069i	−0.998484	−	0.0550441i	$-0.982470\pi$
$37$	−9.38050	+	22.6465i	−0.253527	+	0.612069i	0.744957	+	0.667113i	$0.232470\pi$
$38$	−10.3906	−	1.64497i	−0.273437	−	0.0432888i
$39$	−13.4441	+	13.4441i	−0.344720	+	0.344720i
$40$	0.817033	+	0.416086i	0.0204258	+	0.0104021i
$41$	33.4077	−	33.4077i	0.814823	−	0.814823i	−0.170530	−	0.985353i	$-0.554548\pi$
$41$	33.4077	−	33.4077i	0.814823	−	0.814823i	0.985353	+	0.170530i	$0.0545479\pi$
$42$	4.08643	+	5.62368i	0.0972961	+	0.133897i
$43$	4.08867	−	9.87092i	0.0950853	−	0.229556i	−0.869179	−	0.494497i	$-0.835352\pi$
$43$	4.08867	−	9.87092i	0.0950853	−	0.229556i	0.964265	+	0.264941i	$0.0853523\pi$
$44$	14.3260	−	1.12947i	0.325590	−	0.0256698i
$45$	0.319038	+	0.770227i	0.00708974	+	0.0171162i
$46$	0.863046	+	3.59375i	0.0187619	+	0.0781250i
$47$	20.9665			0.446097			0.223048	−	0.974807i	$-0.428399\pi$
$47$	20.9665			0.446097			0.223048	+	0.974807i	$0.428399\pi$
$48$	−20.4402	−	4.90129i	−0.425838	−	0.102110i
$49$		−	7.00000i		−	0.142857i
$50$	−11.6695	−	48.5921i	−0.233390	−	0.971843i
$51$	−30.3855	+	12.5861i	−0.595794	+	0.246786i
$52$	−37.5902	+	44.0248i	−0.722889	+	0.846631i
$53$	71.4971	+	29.6151i	1.34900	+	0.558775i	0.936014	−	0.351962i	$-0.114485\pi$
$53$	71.4971	+	29.6151i	1.34900	+	0.558775i	0.412987	+	0.910737i	$0.364485\pi$
$54$	−25.1358	−	34.5915i	−0.465478	−	0.640583i
$55$	0.291151	+	0.291151i	0.00529365	+	0.00529365i
$56$	13.7496	+	16.0919i	0.245528	+	0.287356i
$57$	4.88626	+	4.88626i	0.0857239	+	0.0857239i
$58$	−32.2927	−	5.11238i	−0.556771	−	0.0881445i
$59$	−84.5124	−	35.0062i	−1.43241	−	0.593325i	−0.474467	−	0.880273i	$-0.657359\pi$
$59$	−84.5124	−	35.0062i	−1.43241	−	0.593325i	−0.957946	+	0.286948i	$0.907359\pi$
$60$	−0.273497	−	0.536585i	−0.00455829	−	0.00894309i
$61$	−35.0338	+	14.5115i	−0.574324	+	0.237893i	−0.650891	−	0.759172i	$-0.725604\pi$
$61$	−35.0338	+	14.5115i	−0.574324	+	0.237893i	0.0765663	+	0.997064i	$0.475604\pi$
$62$	42.8430	−	69.9243i	0.691017	−	1.12781i
$63$			19.2455i			0.305484i
$64$	−63.2162	−	9.98558i	−0.987753	−	0.156025i
$65$	−1.65868			−0.0255182
$66$	−8.04877	−	4.93153i	−0.121951	−	0.0747201i
$67$	−34.1693	−	82.4920i	−0.509989	−	1.23122i	−0.943889	−	0.330262i	$-0.892863\pi$
$67$	−34.1693	−	82.4920i	−0.509989	−	1.23122i	0.433900	−	0.900961i	$-0.357137\pi$
$68$	−89.2186	+	45.4747i	−1.31204	+	0.668746i
$69$	0.929050	−	2.24292i	0.0134645	−	0.0325062i
$70$	−0.0948298	+	0.599000i	−0.00135471	+	0.00855714i
$71$	−26.1620	+	26.1620i	−0.368478	+	0.368478i	−0.866922	−	0.498444i	$-0.833905\pi$
$71$	−26.1620	+	26.1620i	−0.368478	+	0.368478i	0.498444	+	0.866922i	$0.333905\pi$
$72$	−37.8025	−	44.2424i	−0.525034	−	0.614478i
$73$	−22.9027	+	22.9027i	−0.313735	+	0.313735i	−0.846355	−	0.532620i	$-0.821208\pi$
$73$	−22.9027	+	22.9027i	−0.313735	+	0.313735i	0.532620	+	0.846355i	$0.321208\pi$
$74$	39.6600	−	28.8188i	0.535945	−	0.389444i
$75$	−12.5619	+	30.3272i	−0.167493	+	0.404363i
$76$	16.0009	+	13.6622i	0.210538	+	0.179766i
$77$	3.63746	+	8.78161i	0.0472398	+	0.114047i
$78$	36.9744	−	8.87946i	0.474030	−	0.113839i
$79$	−120.602			−1.52661			−0.763305	−	0.646038i	$-0.776425\pi$
$79$	−120.602			−1.52661			−0.763305	+	0.646038i	$0.776425\pi$
$80$	−0.958570	−	1.56327i	−0.0119821	−	0.0195409i
$81$		−	37.3799i		−	0.461480i
$82$	−91.8790	+	22.0649i	−1.12048	+	0.269084i
$83$	−2.08476	+	0.863534i	−0.0251175	+	0.0104040i	−0.395207	−	0.918592i	$-0.629327\pi$
$83$	−2.08476	+	0.863534i	−0.0251175	+	0.0104040i	0.370089	+	0.928996i	$0.379327\pi$
$84$	−1.09275	−	13.8602i	−0.0130089	−	0.165002i
$85$	−2.65084	−	1.09801i	−0.0311864	−	0.0129178i
$86$	−17.2865	+	12.5612i	−0.201006	+	0.146061i
$87$	15.1859	+	15.1859i	0.174551	+	0.174551i
$88$	−25.6110	−	13.0428i	−0.291034	−	0.148213i
$89$	49.1699	+	49.1699i	0.552470	+	0.552470i	0.927153	−	0.374683i	$-0.122248\pi$
$89$	49.1699	+	49.1699i	0.552470	+	0.552470i	−0.374683	+	0.927153i	$0.622248\pi$
$90$	0.260721	−	1.64686i	0.00289690	−	0.0182985i
$91$	−35.3757	−	14.6531i	−0.388744	−	0.161023i
$92$	2.28324	−	7.03039i	0.0248178	−	0.0764173i
$93$	−49.7663	+	20.6139i	−0.535121	+	0.221654i
$94$	−35.7553	−	21.9075i	−0.380376	−	0.233059i
$95$			0.602850i			0.00634579i
$96$	29.7366	+	29.7160i	0.309756	+	0.309542i
$97$	123.684			1.27510			0.637548	−	0.770411i	$-0.279949\pi$
$97$	123.684			1.27510			0.637548	+	0.770411i	$0.279949\pi$
$98$	−7.31415	+	11.9375i	−0.0746342	+	0.121811i
$99$	−10.0007	−	24.1438i	−0.101017	−	0.243877i
$100$	−30.8723	+	95.0600i	−0.308723	+	0.950600i
$101$	30.7964	−	74.3490i	0.304915	−	0.736129i	−0.694940	−	0.719068i	$-0.744569\pi$
$101$	30.7964	−	74.3490i	0.304915	−	0.736129i	0.999854	−	0.0170611i	$-0.00543098\pi$
$102$	64.9689	+	10.2855i	0.636950	+	0.100838i
$103$	19.7466	−	19.7466i	0.191715	−	0.191715i	−0.604722	−	0.796437i	$-0.706716\pi$
$103$	19.7466	−	19.7466i	0.191715	−	0.191715i	0.796437	+	0.604722i	$0.206716\pi$
$104$	110.105	−	35.8006i	1.05870	−	0.344237i
$105$	0.281684	−	0.281684i	0.00268271	−	0.00268271i
$106$	−90.9836	−	125.210i	−0.858336	−	1.18123i
$107$	25.0630	−	60.5074i	0.234234	−	0.565490i	−0.762434	−	0.647067i	$-0.775996\pi$
$107$	25.0630	−	60.5074i	0.234234	−	0.565490i	0.996667	+	0.0815768i	$0.0259956\pi$
$108$	6.72154	+	85.2545i	0.0622365	+	0.789394i
$109$	−63.4258	−	153.123i	−0.581888	−	1.40480i	−0.891099	−	0.453809i	$-0.850065\pi$
$109$	−63.4258	−	153.123i	−0.581888	−	1.40480i	0.309211	−	0.950994i	$-0.399935\pi$
$110$	−0.192297	−	0.800732i	−0.00174816	−	0.00727938i
$111$	−32.2027			−0.290114
$112$	−6.63375	−	41.8090i	−0.0592299	−	0.373295i
$113$		−	115.255i		−	1.01996i	−0.860188	−	0.509978i	$-0.829654\pi$
$113$		−	115.255i		−	1.01996i	0.860188	−	0.509978i	$-0.170346\pi$
$114$	−3.22725	−	13.4384i	−0.0283092	−	0.117880i
$115$	0.195674	−	0.0810506i	0.00170151	−	0.000704788i
$116$	49.7287	+	42.4604i	0.428696	+	0.366038i
$117$	97.2605	+	40.2866i	0.831287	+	0.344330i
$118$	107.546	+	148.003i	0.911408	+	1.25426i
$119$	−46.8359	−	46.8359i	−0.393579	−	0.393579i
$120$	−0.0942575	+	1.20084i	−0.000785479	+	0.0100070i
$121$	76.4334	+	76.4334i	0.631681	+	0.631681i
$122$	74.9077	+	11.8589i	0.613997	+	0.0972041i
$123$	57.3433	+	23.7524i	0.466206	+	0.193109i
$124$	−146.125	+	74.4798i	−1.17843	+	0.600644i
$125$	−5.29291	+	2.19239i	−0.0423433	+	0.0175391i
$126$	20.1092	−	32.8204i	0.159597	−	0.260479i
$127$			233.128i			1.83565i	0.396979	+	0.917827i	$0.370058\pi$
$127$			233.128i			1.83565i	−0.396979	+	0.917827i	$0.629942\pi$
$128$	97.3722	+	83.0822i	0.760720	+	0.649080i
$129$	14.0361			0.108807
$130$	2.82864	+	1.73313i	0.0217588	+	0.0133317i
$131$	−36.9624	−	89.2351i	−0.282156	−	0.681184i	0.717730	−	0.696322i	$-0.245181\pi$
$131$	−36.9624	−	89.2351i	−0.282156	−	0.681184i	−0.999885	+	0.0151377i	$0.995181\pi$
$132$	8.57314	+	16.8200i	0.0649481	+	0.127424i
$133$	−5.32568	+	12.8573i	−0.0400427	+	0.0966716i
$134$	−27.9235	+	176.381i	−0.208384	+	1.31627i
$135$	−1.73265	+	1.73265i	−0.0128344	+	0.0128344i
$136$	199.665	+	15.6723i	1.46812	+	0.115237i
$137$	154.978	−	154.978i	1.13123	−	1.13123i	0.141253	−	0.989973i	$-0.454887\pi$
$137$	154.978	−	154.978i	1.13123	−	1.13123i	0.989973	−	0.141253i	$-0.0451132\pi$
$138$	−3.92794	+	2.85423i	−0.0284634	+	0.0206828i
$139$	39.9820	−	96.5251i	0.287640	−	0.694425i	−0.712332	−	0.701843i	$-0.752361\pi$
$139$	39.9820	−	96.5251i	0.287640	−	0.694425i	0.999972	+	0.00741717i	$0.00236098\pi$
$140$	0.787601	−	0.922420i	0.00562572	−	0.00658872i
$141$	10.5408	+	25.4477i	0.0747572	+	0.180480i
$142$	71.9515	−	17.2793i	0.506700	−	0.121685i
$143$	51.9937			0.363592
$144$	18.2386	+	114.948i	0.126657	+	0.798250i
$145$			1.87358i			0.0129213i
$146$	62.9877	−	15.1266i	0.431422	−	0.103607i
$147$	8.49609	−	3.51919i	0.0577965	−	0.0239401i
$148$	−97.7464	+	7.70641i	−0.660449	+	0.0520703i
$149$	−212.248	−	87.9158i	−1.42448	−	0.590039i	−0.468498	−	0.883465i	$-0.655205\pi$
$149$	−212.248	−	87.9158i	−1.42448	−	0.590039i	−0.955982	+	0.293426i	$0.905205\pi$
$150$	53.1108	−	38.5929i	0.354072	−	0.257286i
$151$	11.1880	+	11.1880i	0.0740926	+	0.0740926i	0.743182	−	0.669089i	$-0.233316\pi$
$151$	11.1880	+	11.1880i	0.0740926	+	0.0740926i	−0.669089	+	0.743182i	$0.733316\pi$
$152$	−13.0118	−	40.0178i	−0.0856036	−	0.263275i
$153$	128.769	+	128.769i	0.841626	+	0.841626i
$154$	2.97257	−	18.7765i	0.0193024	−	0.121925i
$155$	−4.34163	−	1.79836i	−0.0280105	−	0.0116023i
$156$	−72.3323	−	23.4911i	−0.463669	−	0.150584i
$157$	−259.059	+	107.306i	−1.65006	+	0.683477i	−0.997255	−	0.0740493i	$-0.976408\pi$
$157$	−259.059	+	107.306i	−1.65006	+	0.683477i	−0.652805	+	0.757526i	$0.726408\pi$
$158$	205.669	+	126.015i	1.30170	+	0.797562i
$159$			101.667i			0.639413i
$160$	0.00126782	+	3.66752i	7.92390e−6	+	0.0229220i
$161$	4.88926			0.0303680
$162$	−39.0574	+	63.7458i	−0.241095	+	0.393493i
$163$	−66.0630	−	159.490i	−0.405295	−	0.978468i	−0.986359	−	0.164610i	$-0.947363\pi$
$163$	−66.0630	−	159.490i	−0.405295	−	0.978468i	0.581064	−	0.813858i	$-0.302637\pi$
$164$	179.741	+	58.3740i	1.09598	+	0.355939i
$165$	−0.207004	+	0.499751i	−0.00125457	+	0.00302879i
$166$	4.45753	+	0.705688i	0.0268526	+	0.00425113i
$167$	97.9708	−	97.9708i	0.586652	−	0.586652i	−0.350071	−	0.936723i	$-0.613843\pi$
$167$	97.9708	−	97.9708i	0.586652	−	0.586652i	0.936723	+	0.350071i	$0.113843\pi$
$168$	−12.6187	+	24.7783i	−0.0751113	+	0.147490i
$169$	−28.6030	+	28.6030i	−0.169248	+	0.169248i
$170$	3.37333	+	4.64231i	0.0198431	+	0.0273077i
$171$	14.6422	−	35.3494i	0.0856269	−	0.206722i
$172$	42.6046	−	3.35898i	0.247701	−	0.0195290i
$173$	28.5637	+	68.9588i	0.165108	+	0.398606i	0.984680	−	0.174370i	$-0.0557889\pi$
$173$	28.5637	+	68.9588i	0.165108	+	0.398606i	−0.819572	+	0.572976i	$0.805789\pi$
$174$	−10.0299	−	41.7648i	−0.0576430	−	0.240027i
$175$	−66.1090			−0.377766
$176$	30.0477	+	49.0029i	0.170725	+	0.278426i
$177$		−	120.174i		−	0.678949i
$178$	−32.4754	−	135.229i	−0.182446	−	0.759711i
$179$	−147.104	+	60.9323i	−0.821808	+	0.340404i	−0.753654	−	0.657271i	$-0.771711\pi$
$179$	−147.104	+	60.9323i	−0.821808	+	0.340404i	−0.0681533	+	0.997675i	$0.521711\pi$
$180$	−2.16540	+	2.53606i	−0.0120300	+	0.0140892i
$181$	51.6031	+	21.3747i	0.285100	+	0.118092i	0.520651	−	0.853770i	$-0.325689\pi$
$181$	51.6031	+	21.3747i	0.285100	+	0.118092i	−0.235551	+	0.971862i	$0.575689\pi$
$182$	45.0174	+	61.9521i	0.247348	+	0.340396i
$183$	−35.2259	−	35.2259i	−0.192491	−	0.192491i
$184$	−11.2396	+	9.60359i	−0.0610850	+	0.0521934i
$185$	−1.98653	−	1.98653i	−0.0107380	−	0.0107380i
$186$	106.408	+	16.8458i	0.572086	+	0.0905690i
$187$	83.0942	+	34.4187i	0.444354	+	0.184057i
$188$	38.0848	+	74.7200i	0.202579	+	0.397447i
$189$	−52.2598	+	21.6467i	−0.276507	+	0.114533i
$190$	0.629905	−	1.02807i	0.00331529	−	0.00541090i
$191$			92.5743i			0.484682i	0.970191	+	0.242341i	$0.0779153\pi$
$191$			92.5743i			0.484682i	−0.970191	+	0.242341i	$0.922085\pi$
$192$	−19.6617	−	81.7474i	−0.102405	−	0.425768i
$193$	−82.3723			−0.426800			−0.213400	−	0.976965i	$-0.568454\pi$
$193$	−82.3723			−0.426800			−0.213400	+	0.976965i	$0.568454\pi$
$194$	−210.925	−	129.235i	−1.08724	−	0.666160i
$195$	−0.833891	−	2.01319i	−0.00427636	−	0.0103241i
$196$	24.9464	−	12.7152i	0.127278	−	0.0648734i
$197$	13.2647	−	32.0238i	0.0673334	−	0.162557i	−0.886631	−	0.462478i	$-0.846960\pi$
$197$	13.2647	−	32.0238i	0.0673334	−	0.162557i	0.953964	+	0.299921i	$0.0969603\pi$
$198$	−8.17265	+	51.6232i	−0.0412760	+	0.260723i
$199$	240.256	−	240.256i	1.20732	−	1.20732i	0.235422	−	0.971893i	$-0.424353\pi$
$199$	240.256	−	240.256i	1.20732	−	1.20732i	0.971893	−	0.235422i	$-0.0756472\pi$
$200$	151.974	−	129.853i	0.759872	−	0.649264i
$201$	82.9444	−	82.9444i	0.412659	−	0.412659i
$202$	−130.204	+	94.6128i	−0.644576	+	0.468380i
$203$	−16.5516	+	39.9590i	−0.0815348	+	0.196842i
$204$	−100.048	−	85.4250i	−0.490430	−	0.418750i
$205$	2.07217	+	5.00265i	0.0101081	+	0.0244032i
$206$	−54.3078	+	13.0421i	−0.263630	+	0.0633112i
$207$	−13.4423			−0.0649387
$208$	−225.176	−	53.9940i	−1.08257	−	0.259587i
$209$		−	18.8971i		−	0.0904170i
$210$	−0.774697	+	0.186045i	−0.00368903	+	0.000885928i
$211$	−14.5042	+	6.00783i	−0.0687402	+	0.0284731i	−0.416789	−	0.909003i	$-0.636844\pi$
$211$	−14.5042	+	6.00783i	−0.0687402	+	0.0284731i	0.348048	+	0.937477i	$0.386844\pi$
$212$	24.3298	+	308.594i	0.114763	+	1.45563i
$213$	−44.9062	−	18.6008i	−0.210827	−	0.0873275i
$214$	−105.964	+	76.9987i	−0.495160	+	0.359807i
$215$	0.865865	+	0.865865i	0.00402728	+	0.00402728i
$216$	77.6181	−	152.412i	0.359343	−	0.705612i
$217$	−76.7093	−	76.7093i	−0.353499	−	0.353499i
$218$	−51.8322	+	327.402i	−0.237762	+	1.50184i
$219$	−39.3117	−	16.2834i	−0.179506	−	0.0743536i
$220$	−0.508734	+	1.56646i	−0.00231243	+	0.00712026i
$221$	−334.735	+	138.652i	−1.51464	+	0.627384i
$222$	54.9169	+	33.6479i	0.247374	+	0.151567i
$223$			105.709i			0.474030i	0.971506	+	0.237015i	$0.0761690\pi$
$223$			105.709i			0.474030i	−0.971506	+	0.237015i	$0.923831\pi$
$224$	−32.3725	+	78.2306i	−0.144520	+	0.349244i
$225$	181.757			0.807811
$226$	−120.427	+	196.550i	−0.532865	+	0.869692i
$227$	−78.8701	−	190.409i	−0.347445	−	0.838807i	−0.996920	−	0.0784239i	$-0.975011\pi$
$227$	−78.8701	−	190.409i	−0.347445	−	0.838807i	0.649475	−	0.760383i	$-0.274989\pi$
$228$	−8.53787	+	26.2892i	−0.0374468	+	0.115304i
$229$	−26.3996	+	63.7343i	−0.115282	+	0.278316i	−0.970980	−	0.239160i	$-0.923128\pi$
$229$	−26.3996	+	63.7343i	−0.115282	+	0.278316i	0.855698	+	0.517475i	$0.173128\pi$
$230$	−0.418380	−	0.0662353i	−0.00181905	−	0.000287980i
$231$	−8.82977	+	8.82977i	−0.0382241	+	0.0382241i
$232$	−40.4389	−	124.370i	−0.174306	−	0.536080i
$233$	−289.049	+	289.049i	−1.24055	+	1.24055i	−0.280780	+	0.959772i	$0.590593\pi$
$233$	−289.049	+	289.049i	−1.24055	+	1.24055i	−0.959772	+	0.280780i	$0.909407\pi$
$234$	−123.769	−	170.328i	−0.528927	−	0.727899i
$235$	−0.919580	+	2.22006i	−0.00391311	+	0.00944707i
$236$	−28.7588	−	364.770i	−0.121859	−	1.54564i
$237$	−60.6318	−	146.378i	−0.255830	−	0.617629i
$238$	30.9339	+	128.810i	0.129974	+	0.541217i
$239$	−125.138			−0.523592			−0.261796	−	0.965123i	$-0.584315\pi$
$239$	−125.138			−0.523592			−0.261796	+	0.965123i	$0.584315\pi$
$240$	1.41547	−	1.94937i	0.00589781	−	0.00812236i
$241$		−	11.1031i		−	0.0460710i	−0.999735	−	0.0230355i	$-0.992667\pi$
$241$		−	11.1031i		−	0.0460710i	0.999735	−	0.0230355i	$-0.00733308\pi$
$242$	−50.4822	−	210.210i	−0.208604	−	0.868635i
$243$	223.140	−	92.4276i	0.918271	−	0.380360i
$244$	−115.353	−	98.4931i	−0.472758	−	0.403660i
$245$	0.741202	+	0.307016i	0.00302531	+	0.00125313i
$246$	−72.9722	−	100.423i	−0.296635	−	0.408224i
$247$	53.8285	+	53.8285i	0.217929	+	0.217929i
$248$	327.017	+	25.6685i	1.31862	+	0.103502i
$249$	−2.09619	−	2.09619i	−0.00841843	−	0.00841843i
$250$	11.3171	+	1.79164i	0.0452682	+	0.00716658i
$251$	212.454	+	88.0014i	0.846431	+	0.350603i	0.763386	−	0.645943i	$-0.223535\pi$
$251$	212.454	+	88.0014i	0.846431	+	0.350603i	0.0830451	+	0.996546i	$0.473535\pi$
$252$	−68.5867	+	34.9586i	−0.272169	+	0.138725i
$253$	−6.13365	+	2.54064i	−0.0242437	+	0.0100421i
$254$	243.591	−	397.566i	0.959019	−	1.56522i
$255$		−	3.76941i		−	0.0147820i
$256$	−79.2430	−	243.427i	−0.309543	−	0.950885i
$257$	11.5021			0.0447553			0.0223777	−	0.999750i	$-0.492876\pi$
$257$	11.5021			0.0447553			0.0223777	+	0.999750i	$0.492876\pi$
$258$	−23.9366	−	14.6661i	−0.0927774	−	0.0568453i
$259$	−24.8185	−	59.9171i	−0.0958242	−	0.231340i
$260$	−3.01293	−	5.91118i	−0.0115882	−	0.0227353i
$261$	45.5062	−	109.862i	0.174353	−	0.420926i
$262$	−30.2060	+	190.799i	−0.115290	+	0.728239i
$263$	−126.388	+	126.388i	−0.480563	+	0.480563i	−0.905312	−	0.424748i	$-0.860363\pi$
$263$	−126.388	+	126.388i	−0.480563	+	0.480563i	0.424748	+	0.905312i	$0.360363\pi$
$264$	2.95463	−	37.6419i	0.0111918	−	0.142583i
$265$	−6.27164	+	6.27164i	−0.0236666	+	0.0236666i
$266$	22.5165	−	16.3616i	0.0846486	−	0.0615097i
$267$	−34.9590	+	84.3985i	−0.130933	+	0.316099i
$268$	231.916	−	271.615i	0.865358	−	1.01349i
$269$	−45.8563	−	110.707i	−0.170470	−	0.411550i	0.815437	−	0.578846i	$-0.196497\pi$
$269$	−45.8563	−	110.707i	−0.170470	−	0.411550i	−0.985907	+	0.167295i	$0.946497\pi$
$270$	4.76519	−	1.14437i	0.0176489	−	0.00423841i
$271$	318.563			1.17551			0.587755	−	0.809039i	$-0.300012\pi$
$271$	318.563			1.17551			0.587755	+	0.809039i	$0.300012\pi$
$272$	−324.123	−	235.352i	−1.19163	−	0.865266i
$273$		−	50.3032i		−	0.184261i
$274$	−426.226	+	102.359i	−1.55557	+	0.373573i
$275$	82.9348	−	34.3527i	0.301581	−	0.124919i
$276$	9.68085	−	0.763247i	0.0350756	−	0.00276539i
$277$	−66.2492	−	27.4413i	−0.239167	−	0.0990661i	0.259881	−	0.965641i	$-0.416317\pi$
$277$	−66.2492	−	27.4413i	−0.239167	−	0.0990661i	−0.499048	+	0.866575i	$0.666317\pi$
$278$	−169.041	+	122.833i	−0.608060	+	0.441845i
$279$	210.901	+	210.901i	0.755919	+	0.755919i
$280$	−2.30695	+	0.750104i	−0.00823912	+	0.00267894i
$281$	119.493	+	119.493i	0.425243	+	0.425243i	0.887004	−	0.461761i	$-0.152782\pi$
$281$	119.493	+	119.493i	0.425243	+	0.425243i	−0.461761	+	0.887004i	$0.652782\pi$
$282$	8.61401	−	54.4110i	0.0305461	−	0.192947i
$283$	479.828	+	198.751i	1.69550	+	0.702301i	0.999870	−	0.0160962i	$-0.00512379\pi$
$283$	479.828	+	198.751i	1.69550	+	0.702301i	0.695633	+	0.718397i	$0.255124\pi$
$284$	−140.757	−	45.7133i	−0.495624	−	0.160962i
$285$	−0.731695	+	0.303078i	−0.00256735	+	0.00106343i
$286$	−88.6676	−	54.3272i	−0.310027	−	0.189955i
$287$			125.000i			0.435541i
$288$	89.0036	−	215.084i	0.309040	−	0.746819i
$289$	−337.744			−1.16867
$290$	1.95767	−	3.19512i	0.00675058	−	0.0110177i
$291$	62.1813	+	150.119i	0.213681	+	0.515872i
$292$	−123.222	−	40.0183i	−0.421992	−	0.137049i
$293$	68.8973	−	166.333i	0.235144	−	0.567688i	−0.761624	−	0.648019i	$-0.775598\pi$
$293$	68.8973	−	166.333i	0.235144	−	0.567688i	0.996768	+	0.0803308i	$0.0255977\pi$
$294$	−18.1660	−	2.87592i	−0.0617890	−	0.00978203i
$295$	7.41332	−	7.41332i	0.0251299	−	0.0251299i
$296$	174.744	+	88.9911i	0.590353	+	0.300645i
$297$	54.3123	−	54.3123i	0.182870	−	0.182870i
$298$	270.095	+	371.700i	0.906361	+	1.24732i
$299$	10.2347	−	24.7087i	0.0342297	−	0.0826378i
$300$	−130.898	+	10.3201i	−0.436325	+	0.0344003i
$301$	10.8176	+	26.1160i	0.0359389	+	0.0867641i
$302$	−7.38936	−	30.7695i	−0.0244681	−	0.101886i
$303$	105.722			0.348918
$304$	−19.6242	+	81.8402i	−0.0645531	+	0.269211i
$305$		−	4.34605i		−	0.0142493i
$306$	−85.0483	−	354.144i	−0.277936	−	1.15733i
$307$	−444.545	+	184.137i	−1.44803	+	0.599793i	−0.961730	−	0.273999i	$-0.911653\pi$
$307$	−444.545	+	184.137i	−1.44803	+	0.599793i	−0.486299	+	0.873792i	$0.661653\pi$
$308$	−24.6884	+	28.9145i	−0.0801572	+	0.0938783i
$309$	33.8945	+	14.0395i	0.109691	+	0.0454354i
$310$	5.52493	+	7.60331i	0.0178224	+	0.0245268i
$311$	−54.5820	−	54.5820i	−0.175505	−	0.175505i	0.613888	−	0.789393i	$-0.289605\pi$
$311$	−54.5820	−	54.5820i	−0.175505	−	0.175505i	−0.789393	+	0.613888i	$0.789605\pi$
$312$	98.8067	+	115.639i	0.316688	+	0.370638i
$313$	285.265	+	285.265i	0.911389	+	0.911389i	0.996382	−	0.0849925i	$-0.0270866\pi$
$313$	285.265	+	285.265i	0.911389	+	0.911389i	−0.0849925	+	0.996382i	$0.527087\pi$
$314$	553.909	+	87.6913i	1.76404	+	0.279272i
$315$	−2.03783	−	0.844096i	−0.00646930	−	0.00267967i
$316$	−219.069	−	429.799i	−0.693255	−	1.36012i
$317$	−209.082	+	86.6048i	−0.659566	+	0.273201i	−0.687256	−	0.726415i	$-0.741185\pi$
$317$	−209.082	+	86.6048i	−0.659566	+	0.273201i	0.0276898	+	0.999617i	$0.491185\pi$
$318$	106.229	−	173.378i	0.334055	−	0.545212i
$319$		−	58.7300i		−	0.184107i
$320$	3.82996	−	6.25575i	0.0119686	−	0.0195492i
$321$	86.0397			0.268036
$322$	−8.33790	−	5.10868i	−0.0258941	−	0.0158655i
$323$	50.3931	+	121.660i	0.156016	+	0.376656i
$324$	133.213	−	67.8988i	0.411152	−	0.209564i
$325$	−138.386	+	334.094i	−0.425803	+	1.02798i
$326$	−53.9873	+	341.015i	−0.165605	+	1.04606i
$327$	153.963	−	153.963i	0.470836	−	0.470836i
$328$	−245.529	−	287.356i	−0.748563	−	0.876086i
$329$	−39.2248	+	39.2248i	−0.119224	+	0.119224i
$330$	0.875194	−	0.635958i	0.00265210	−	0.00192715i
$331$	165.713	−	400.066i	0.500642	−	1.20866i	−0.448492	−	0.893787i	$-0.648039\pi$
$331$	165.713	−	400.066i	0.500642	−	1.20866i	0.949134	−	0.314871i	$-0.101961\pi$
$332$	−6.86431	−	5.86103i	−0.0206756	−	0.0176537i
$333$	68.2349	+	164.734i	0.204910	+	0.494695i
$334$	−269.442	+	64.7071i	−0.806714	+	0.193734i
$335$	10.2334			0.0305474
$336$	47.4096	−	29.0707i	0.141100	−	0.0865200i
$337$		−	361.400i		−	1.07240i	−0.844090	−	0.536202i	$-0.819859\pi$
$337$		−	361.400i		−	1.07240i	0.844090	−	0.536202i	$-0.180141\pi$
$338$	78.6648	−	18.8915i	0.232736	−	0.0558920i
$339$	139.888	−	57.9435i	0.412649	−	0.170925i
$340$	−0.902057	−	11.4415i	−0.00265311	−	0.0336514i
$341$	136.094	+	56.3720i	0.399103	+	0.165314i
$342$	−61.9060	+	44.9839i	−0.181012	+	0.131532i
$343$	13.0958	+	13.0958i	0.0381802	+	0.0381802i
$344$	−76.1656	−	38.7884i	−0.221412	−	0.112757i
$345$	0.196747	+	0.196747i	0.000570280	+	0.000570280i
$346$	23.3425	−	147.445i	0.0674638	−	0.426141i
$347$	−251.891	−	104.337i	−0.725911	−	0.300682i	−0.0110405	−	0.999939i	$-0.503514\pi$
$347$	−251.891	−	104.337i	−0.725911	−	0.300682i	−0.714870	+	0.699257i	$0.753514\pi$
$348$	−26.5346	+	81.7037i	−0.0762490	+	0.234781i
$349$	−163.743	+	67.8246i	−0.469178	+	0.194340i	−0.604730	−	0.796430i	$-0.706719\pi$
$349$	−163.743	+	67.8246i	−0.469178	+	0.194340i	0.135553	+	0.990770i	$0.456719\pi$
$350$	112.739	+	69.0760i	0.322112	+	0.197360i
$351$			309.417i			0.881529i
$352$	−0.0397416	−	114.963i	−0.000112902	−	0.326601i
$353$	−516.062			−1.46193			−0.730965	−	0.682414i	$-0.760930\pi$
$353$	−516.062			−1.46193			−0.730965	+	0.682414i	$0.760930\pi$
$354$	−125.567	+	204.939i	−0.354710	+	0.578924i
$355$	−1.62274	−	3.91763i	−0.00457109	−	0.0110356i
$356$	−85.9155	+	264.545i	−0.241336	+	0.743104i
$357$	33.2996	−	80.3924i	0.0932763	−	0.225189i
$358$	314.530	+	49.7944i	0.878576	+	0.139091i
$359$	−59.5942	+	59.5942i	−0.166000	+	0.166000i	−0.785219	−	0.619218i	$-0.787450\pi$
$359$	−59.5942	+	59.5942i	−0.166000	+	0.166000i	0.619218	+	0.785219i	$0.287450\pi$
$360$	6.34264	−	2.06230i	0.0176185	−	0.00572862i
$361$	−235.702	+	235.702i	−0.652913	+	0.652913i
$362$	−65.6674	−	90.3703i	−0.181402	−	0.249642i
$363$	−54.3430	+	131.196i	−0.149705	+	0.361420i
$364$	−12.0380	−	152.688i	−0.0330715	−	0.419472i
$365$	−1.42057	−	3.42957i	−0.00389198	−	0.00939608i
$366$	23.2658	+	96.8794i	0.0635677	+	0.264698i
$367$	112.975			0.307834			0.153917	−	0.988084i	$-0.450811\pi$
$367$	112.975			0.307834			0.153917	+	0.988084i	$0.450811\pi$
$368$	29.2021	−	4.63344i	0.0793536	−	0.0125909i
$369$		−	343.671i		−	0.931357i
$370$	1.31205	+	5.46341i	0.00354608	+	0.0147660i
$371$	−189.164	+	78.3541i	−0.509875	+	0.211197i
$372$	−163.861	−	139.912i	−0.440487	−	0.376106i
$373$	297.236	+	123.119i	0.796879	+	0.330078i	0.743706	−	0.668507i	$-0.233066\pi$
$373$	297.236	+	123.119i	0.796879	+	0.330078i	0.0531735	+	0.998585i	$0.483066\pi$
$374$	−105.741	−	145.519i	−0.282731	−	0.389089i
$375$	−5.32193	−	5.32193i	−0.0141918	−	0.0141918i
$376$	13.1254	−	167.218i	0.0349081	−	0.444729i
$377$	167.292	+	167.292i	0.443746	+	0.443746i
$378$	111.739	+	17.6899i	0.295607	+	0.0467986i
$379$	547.024	+	226.585i	1.44333	+	0.597849i	0.960604	−	0.277921i	$-0.0896452\pi$
$379$	547.024	+	226.585i	1.44333	+	0.597849i	0.482730	+	0.875769i	$0.339645\pi$
$380$	−2.14842	+	1.09505i	−0.00565374	+	0.00288171i
$381$	−282.954	+	117.203i	−0.742661	+	0.307620i
$382$	96.7289	−	157.872i	0.253217	−	0.413277i
$383$			399.124i			1.04210i	0.853526	+	0.521050i	$0.174459\pi$
$383$			399.124i			1.04210i	−0.853526	+	0.521050i	$0.825541\pi$
$384$	−51.8860	+	159.952i	−0.135120	+	0.416542i
$385$	−1.08939			−0.00282957
$386$	140.474	+	86.0691i	0.363922	+	0.222977i
$387$	−29.7415	−	71.8022i	−0.0768513	−	0.185535i
$388$	224.667	+	440.783i	0.579038	+	1.13604i
$389$	235.318	−	568.107i	0.604930	−	1.46043i	−0.263520	−	0.964654i	$-0.584884\pi$
$389$	235.318	−	568.107i	0.604930	−	1.46043i	0.868450	−	0.495776i	$-0.165116\pi$
$390$	−0.681463	+	4.30451i	−0.00174734	+	0.0110372i
$391$	32.7133	−	32.7133i	0.0836656	−	0.0836656i
$392$	−55.8283	−	4.38213i	−0.142419	−	0.0111789i
$393$	89.7245	−	89.7245i	0.228307	−	0.228307i
$394$	−56.0819	+	40.7518i	−0.142340	+	0.103431i
$395$	5.28954	−	12.7701i	0.0133912	−	0.0323293i
$396$	67.8773	−	79.4963i	0.171407	−	0.200748i
$397$	192.537	+	464.826i	0.484981	+	1.17085i	0.957216	+	0.289374i	$0.0934472\pi$
$397$	192.537	+	464.826i	0.484981	+	1.17085i	−0.472236	+	0.881472i	$0.656553\pi$
$398$	−660.759	+	158.682i	−1.66020	+	0.398700i
$399$	−18.2827			−0.0458214
$400$	−394.850	+	62.6501i	−0.987126	+	0.156625i
$401$		−	178.008i		−	0.443911i	−0.975057	−	0.221956i	$-0.928756\pi$
$401$		−	178.008i		−	0.443911i	0.975057	−	0.221956i	$-0.0712440\pi$
$402$	−228.116	+	54.7825i	−0.567453	+	0.136275i
$403$	−548.239	+	227.088i	−1.36040	+	0.563494i
$404$	320.903	−	25.3003i	0.794315	−	0.0626245i
$405$	3.95800	+	1.63946i	0.00977284	+	0.00404804i
$406$	69.9786	−	50.8498i	0.172361	−	0.125246i
$407$	62.2704	+	62.2704i	0.152998	+	0.152998i
$408$	81.3580	+	250.218i	0.199407	+	0.613278i
$409$	−128.627	−	128.627i	−0.314490	−	0.314490i	0.532156	−	0.846646i	$-0.321382\pi$
$409$	−128.627	−	128.627i	−0.314490	−	0.314490i	−0.846646	+	0.532156i	$0.821382\pi$
$410$	1.69339	−	10.6965i	0.00413023	−	0.0260889i
$411$	266.015	+	110.187i	0.647239	+	0.268095i
$412$	106.241	+	34.5037i	0.257867	+	0.0837468i
$413$	223.599	−	92.6176i	0.541401	−	0.224256i
$414$	22.9239	+	14.0456i	0.0553717	+	0.0339266i
$415$		−	0.258621i		−	0.000623182i
$416$	327.586	+	327.360i	0.787468	+	0.786923i
$417$	137.256			0.329151
$418$	−19.7452	+	32.2263i	−0.0472374	+	0.0770964i
$419$	−86.1029	−	207.871i	−0.205496	−	0.496112i	0.787208	−	0.616688i	$-0.211526\pi$
$419$	−86.1029	−	207.871i	−0.205496	−	0.496112i	−0.992704	+	0.120576i	$0.961526\pi$
$420$	1.51553	+	0.492193i	0.00360840	+	0.00117189i
$421$	105.929	−	255.735i	0.251613	−	0.607447i	−0.746722	−	0.665137i	$-0.768373\pi$
$421$	105.929	−	255.735i	0.251613	−	0.607447i	0.998335	+	0.0576893i	$0.0183733\pi$
$422$	31.0122	+	4.90965i	0.0734886	+	0.0116342i
$423$	107.843	−	107.843i	0.254948	−	0.254948i
$424$	280.953	−	551.683i	0.662624	−	1.30114i
$425$	−442.326	+	442.326i	−1.04077	+	1.04077i
$426$	57.1453	+	78.6424i	0.134144	+	0.184607i
$427$	38.3937	−	92.6907i	0.0899151	−	0.217074i
$428$	261.161	−	20.5901i	0.610188	−	0.0481077i
$429$	26.1394	+	63.1062i	0.0609311	+	0.147101i
$430$	−0.571881	−	2.38133i	−0.00132996	−	0.00553798i
$431$	−601.428			−1.39543			−0.697713	−	0.716378i	$-0.745799\pi$
$431$	−601.428			−1.39543			−0.697713	+	0.716378i	$0.745799\pi$
$432$	−291.619	+	178.815i	−0.675043	+	0.413924i
$433$			307.274i			0.709639i	0.934935	+	0.354819i	$0.115458\pi$
$433$			307.274i			0.709639i	−0.934935	+	0.354819i	$0.884542\pi$
$434$	50.6644	+	210.968i	0.116738	+	0.486102i
$435$	−2.27402	+	0.941929i	−0.00522763	+	0.00216535i
$436$	430.487	−	504.177i	0.987357	−	1.15637i
$437$	−8.98039	−	3.71980i	−0.0205501	−	0.00851213i
$438$	50.0261	+	68.8450i	0.114215	+	0.157180i
$439$	93.6494	+	93.6494i	0.213324	+	0.213324i	0.805678	−	0.592354i	$-0.201801\pi$
$439$	93.6494	+	93.6494i	0.213324	+	0.213324i	−0.592354	+	0.805678i	$0.701801\pi$
$440$	2.50433	−	2.13980i	0.00569166	−	0.00486318i
$441$	−36.0050	−	36.0050i	−0.0816441	−	0.0816441i
$442$	715.716	+	113.308i	1.61927	+	0.256352i
$443$	486.277	+	201.423i	1.09769	+	0.454679i	0.856683	−	0.515844i	$-0.172522\pi$
$443$	486.277	+	201.423i	1.09769	+	0.454679i	0.241009	+	0.970523i	$0.422522\pi$
$444$	−58.4947	−	114.763i	−0.131745	−	0.258475i
$445$	−7.36296	+	3.04984i	−0.0165460	+	0.00685357i
$446$	110.453	−	180.270i	0.247652	−	0.404194i
$447$		−	301.809i		−	0.675189i
$448$	136.948	−	99.5854i	0.305687	−	0.222289i
$449$	27.5182			0.0612877			0.0306439	−	0.999530i	$-0.490244\pi$
$449$	27.5182			0.0612877			0.0306439	+	0.999530i	$0.490244\pi$
$450$	−309.960	−	189.915i	−0.688801	−	0.422032i
$451$	−64.9549	−	156.815i	−0.144024	−	0.347705i
$452$	410.743	−	209.355i	0.908723	−	0.463176i
$453$	−7.95448	+	19.2038i	−0.0175596	+	0.0423925i
$454$	−64.4533	+	407.124i	−0.141968	+	0.896750i
$455$	3.10312	−	3.10312i	0.00682003	−	0.00682003i
$456$	42.0291	−	35.9114i	0.0921692	−	0.0787530i
$457$	74.1666	−	74.1666i	0.162290	−	0.162290i	−0.621290	−	0.783580i	$-0.713391\pi$
$457$	74.1666	−	74.1666i	0.162290	−	0.162290i	0.783580	+	0.621290i	$0.213391\pi$
$458$	111.615	−	81.1051i	0.243702	−	0.177085i
$459$	−204.827	+	494.497i	−0.446247	+	1.07734i
$460$	0.644278	+	0.550112i	0.00140060	+	0.00119589i
$461$	−270.858	−	653.908i	−0.587543	−	1.41846i	−0.885844	−	0.463983i	$-0.846420\pi$
$461$	−270.858	−	653.908i	−0.587543	−	1.41846i	0.298300	−	0.954472i	$-0.403580\pi$
$462$	24.2839	−	5.83183i	0.0525626	−	0.0126230i
$463$	44.7224			0.0965927			0.0482964	−	0.998833i	$-0.484621\pi$
$463$	44.7224			0.0965927			0.0482964	+	0.998833i	$0.484621\pi$
$464$	−60.9895	+	254.349i	−0.131443	+	0.548167i
$465$		−	6.17366i		−	0.0132767i
$466$	794.951	−	190.909i	1.70590	−	0.409676i
$467$	296.025	−	122.618i	0.633887	−	0.262565i	−0.0425167	−	0.999096i	$-0.513538\pi$
$467$	296.025	−	122.618i	0.633887	−	0.262565i	0.676404	+	0.736531i	$0.263538\pi$
$468$	33.0969	+	419.793i	0.0707198	+	0.896995i
$469$	218.253	+	90.4035i	0.465359	+	0.192758i
$470$	3.88790	−	2.82514i	0.00827214	−	0.00601093i
$471$	−260.480	−	260.480i	−0.553036	−	0.553036i
$472$	−332.097	+	652.111i	−0.703595	+	1.38159i
$473$	−27.1417	−	27.1417i	−0.0573820	−	0.0573820i
$474$	−49.5489	+	312.979i	−0.104533	+	0.660294i
$475$	121.426	+	50.2965i	0.255635	+	0.105887i
$476$	81.8374	−	251.988i	0.171927	−	0.529387i
$477$	520.078	−	215.423i	1.09031	−	0.451622i
$478$	213.405	+	130.755i	0.446454	+	0.273545i
$479$		−	676.370i		−	1.41205i	−0.708189	−	0.706023i	$-0.750488\pi$
$479$		−	676.370i		−	1.41205i	0.708189	−	0.706023i	$-0.249512\pi$
$480$	−4.45073	+	1.84536i	−0.00927236	+	0.00384449i
$481$	−354.754			−0.737534
$482$	−11.6014	+	18.9347i	−0.0240693	+	0.0392836i
$483$	2.45803	+	5.93422i	0.00508910	+	0.0122862i
$484$	−133.554	+	411.229i	−0.275937	+	0.849647i
$485$	−5.42472	+	13.0964i	−0.0111850	+	0.0270029i
$486$	−477.108	−	75.5327i	−0.981703	−	0.155417i
$487$	630.190	−	630.190i	1.29402	−	1.29402i	0.361750	−	0.932275i	$-0.382180\pi$
$487$	630.190	−	630.190i	1.29402	−	1.29402i	0.932275	−	0.361750i	$-0.117820\pi$
$488$	93.8039	+	288.495i	0.192221	+	0.591179i
$489$	160.365	−	160.365i	0.327945	−	0.327945i
$490$	−0.943216	−	1.29804i	−0.00192493	−	0.00264905i
$491$	−41.5293	+	100.261i	−0.0845810	+	0.204197i	−0.960511	−	0.278241i	$-0.910249\pi$
$491$	−41.5293	+	100.261i	−0.0845810	+	0.204197i	0.875930	+	0.482438i	$0.160249\pi$
$492$	19.5134	+	247.504i	0.0396614	+	0.503057i
$493$	156.616	+	378.104i	0.317679	+	0.766944i
$494$	−35.5523	−	148.041i	−0.0719682	−	0.299678i
$495$	2.99511			0.00605073
$496$	−530.859	−	385.467i	−1.07028	−	0.777151i
$497$		−	97.8891i		−	0.196960i
$498$	1.38448	+	5.76501i	0.00278008	+	0.0115763i
$499$	627.249	−	259.815i	1.25701	−	0.520671i	0.348021	−	0.937487i	$-0.386854\pi$
$499$	627.249	−	259.815i	1.25701	−	0.520671i	0.908991	+	0.416815i	$0.136854\pi$
$500$	−17.4275	−	14.8803i	−0.0348550	−	0.0297607i
$501$	168.164	+	69.6558i	0.335656	+	0.139033i
$502$	−270.358	−	372.062i	−0.538563	−	0.741160i
$503$	−668.772	−	668.772i	−1.32957	−	1.32957i	−0.905747	−	0.423819i	$-0.860689\pi$
$503$	−668.772	−	668.772i	−1.32957	−	1.32957i	−0.423819	−	0.905747i	$-0.639311\pi$
$504$	153.492	+	12.0480i	0.304547	+	0.0239049i
$505$	6.52181	+	6.52181i	0.0129145	+	0.0129145i
$506$	13.1147	+	2.07623i	0.0259184	+	0.00410323i
$507$	−49.0961	−	20.3363i	−0.0968365	−	0.0401110i
$508$	−830.816	+	423.467i	−1.63547	+	0.833596i
$509$	454.172	−	188.124i	0.892283	−	0.369596i	0.111035	−	0.993816i	$-0.464583\pi$
$509$	454.172	−	188.124i	0.892283	−	0.369596i	0.781248	+	0.624221i	$0.214583\pi$
$510$	−3.93858	+	6.42818i	−0.00772271	+	0.0126043i
$511$		−	85.6940i		−	0.167699i
$512$	−119.214	+	497.928i	−0.232840	+	0.972515i
$513$	112.458			0.219216
$514$	−19.6152	−	12.0183i	−0.0381618	−	0.0233819i
$515$	1.22481	+	2.95696i	0.00237828	+	0.00574168i
$516$	25.4960	+	50.0217i	0.0494109	+	0.0969412i
$517$	28.8255	−	69.5908i	0.0557553	−	0.134605i
$518$	−20.2819	+	128.112i	−0.0391542	+	0.247321i
$519$	−69.3370	+	69.3370i	−0.133597	+	0.133597i
$520$	−1.03837	+	13.2288i	−0.00199686	+	0.0254400i
$521$	−665.541	+	665.541i	−1.27743	+	1.27743i	−0.335329	+	0.942101i	$0.608847\pi$
$521$	−665.541	+	665.541i	−1.27743	+	1.27743i	−0.942101	+	0.335329i	$0.891153\pi$
$522$	−192.396	+	139.804i	−0.368575	+	0.267824i
$523$	−76.5057	+	184.701i	−0.146282	+	0.353157i	−0.979989	−	0.199050i	$-0.936214\pi$
$523$	−76.5057	+	184.701i	−0.146282	+	0.353157i	0.833707	+	0.552207i	$0.186214\pi$
$524$	250.873	−	293.817i	0.478766	−	0.560720i
$525$	−33.2358	−	80.2383i	−0.0633063	−	0.152835i
$526$	347.597	−	83.4760i	0.660830	−	0.158700i
$527$	−1026.50			−1.94782
$528$	−44.3699	+	61.1055i	−0.0840340	+	0.115730i
$529$		−	525.585i		−	0.993544i
$530$	17.2485	−	4.14225i	0.0325443	−	0.00781557i
$531$	−614.753	+	254.639i	−1.15773	+	0.479546i
$532$	−55.4945	+	4.37523i	−0.104313	+	0.00822412i
$533$	631.711	+	261.663i	1.18520	+	0.490925i
$534$	147.804	−	107.401i	0.276786	−	0.201126i
$535$	5.30764	+	5.30764i	0.00992081	+	0.00992081i
$536$	−679.303	+	220.875i	−1.26736	+	0.412080i
$537$	−147.910	−	147.910i	−0.275438	−	0.275438i
$538$	−37.4742	+	236.709i	−0.0696547	+	0.439979i
$539$	−23.2340	−	9.62382i	−0.0431057	−	0.0178550i
$540$	−9.32206	−	3.02750i	−0.0172631	−	0.00560647i
$541$	−319.044	+	132.153i	−0.589731	+	0.244275i	−0.657535	−	0.753424i	$-0.728401\pi$
$541$	−319.044	+	132.153i	−0.589731	+	0.244275i	0.0678039	+	0.997699i	$0.478401\pi$
$542$	−543.262	−	332.860i	−1.00233	−	0.614133i
$543$			73.3780i			0.135134i
$544$	306.830	+	740.028i	0.564025	+	1.36035i
$545$	18.9954			0.0348540
$546$	−52.5608	+	85.7847i	−0.0962651	+	0.157115i
$547$	−299.065	−	722.007i	−0.546737	−	1.31994i	−0.919892	−	0.392171i	$-0.871724\pi$
$547$	−299.065	−	722.007i	−0.546737	−	1.31994i	0.373155	−	0.927769i	$-0.378276\pi$
$548$	833.818	+	270.796i	1.52157	+	0.494154i
$549$	−105.558	+	254.840i	−0.192273	+	0.464189i
$550$	−177.328	−	28.0734i	−0.322414	−	0.0510425i
$551$	60.8025	−	60.8025i	0.110349	−	0.110349i
$552$	−17.3068	−	8.81372i	−0.0313528	−	0.0159669i
$553$	225.626	−	225.626i	0.408004	−	0.408004i
$554$	84.3054	+	116.019i	0.152176	+	0.209421i
$555$	1.41239	−	3.40981i	0.00254485	−	0.00614380i
$556$	416.619	−	32.8466i	0.749315	−	0.0590767i
$557$	−101.235	−	244.402i	−0.181750	−	0.438783i	0.806578	−	0.591128i	$-0.201317\pi$
$557$	−101.235	−	244.402i	−0.181750	−	0.438783i	−0.988327	+	0.152346i	$0.951317\pi$
$558$	−139.295	−	580.028i	−0.249632	−	1.03948i
$559$	154.626			0.276612
$560$	4.71794	+	1.13130i	0.00842489	+	0.00202017i
$561$			118.157i			0.210619i
$562$	−78.9222	−	328.634i	−0.140431	−	0.584759i
$563$	−888.243	+	367.922i	−1.57770	+	0.653503i	−0.988047	−	0.154155i	$-0.950734\pi$
$563$	−888.243	+	367.922i	−1.57770	+	0.653503i	−0.589650	+	0.807659i	$0.700734\pi$
$564$	−71.5429	+	83.7894i	−0.126849	+	0.148563i
$565$	12.2039	+	5.05501i	0.0215998	+	0.00894692i
$566$	−610.604	−	840.303i	−1.07881	−	1.48463i
$567$	69.9313	+	69.9313i	0.123336	+	0.123336i
$568$	192.276	+	225.032i	0.338514	+	0.396183i
$569$	−467.459	−	467.459i	−0.821546	−	0.821546i	0.164784	−	0.986330i	$-0.447307\pi$
$569$	−467.459	−	467.459i	−0.821546	−	0.821546i	−0.986330	+	0.164784i	$0.947307\pi$
$570$	1.56448	+	0.247678i	0.00274470	+	0.000434523i
$571$	−549.011	−	227.408i	−0.961491	−	0.398263i	−0.153953	−	0.988078i	$-0.549200\pi$
$571$	−549.011	−	227.408i	−0.961491	−	0.398263i	−0.807538	+	0.589816i	$0.799200\pi$
$572$	94.4442	+	185.294i	0.165112	+	0.323940i
$573$	−112.360	+	46.5410i	−0.196091	+	0.0812234i
$574$	130.610	−	213.170i	0.227544	−	0.371376i
$575$		−	46.1748i		−	0.0803041i
$576$	−376.519	+	273.796i	−0.653679	+	0.475340i
$577$	−141.741			−0.245652			−0.122826	−	0.992428i	$-0.539196\pi$
$577$	−141.741			−0.245652			−0.122826	+	0.992428i	$0.539196\pi$
$578$	575.973	+	352.902i	0.996493	+	0.610557i
$579$	−41.4120	−	99.9775i	−0.0715234	−	0.172673i
$580$	−6.67703	+	3.40328i	−0.0115121	+	0.00586772i
$581$	2.28470	−	5.51575i	0.00393235	−	0.00949354i
$582$	50.8151	−	320.978i	0.0873112	−	0.551508i
$583$	196.593	−	196.593i	0.337209	−	0.337209i
$584$	168.322	+	196.997i	0.288223	+	0.337324i
$585$	−8.53158	+	8.53158i	−0.0145839	+	0.0145839i
$586$	−291.292	+	211.667i	−0.497085	+	0.361206i
$587$	−446.045	+	1076.85i	−0.759873	+	1.83450i	−0.269439	+	0.963018i	$0.586838\pi$
$587$	−446.045	+	1076.85i	−0.759873	+	1.83450i	−0.490434	+	0.871478i	$0.663162\pi$
$588$	27.9744	+	23.8857i	0.0475755	+	0.0406219i
$589$	82.5354	+	199.258i	0.140128	+	0.338299i
$590$	−20.3884	+	4.89630i	−0.0345565	+	0.00829882i
$591$	45.5368			0.0770504
$592$	−205.016	−	334.348i	−0.346311	−	0.564777i
$593$		−	881.498i		−	1.48651i	−0.669011	−	0.743253i	$-0.733282\pi$
$593$		−	881.498i		−	1.48651i	0.669011	−	0.743253i	$-0.266718\pi$
$594$	−149.371	+	35.8718i	−0.251467	+	0.0603902i
$595$	7.01346	−	2.90507i	0.0117873	−	0.00488247i
$596$	−72.2259	−	916.097i	−0.121184	−	1.53708i
$597$	412.391	+	170.818i	0.690773	+	0.286128i
$598$	−43.2714	+	31.4430i	−0.0723601	+	0.0525803i
$599$	−22.3963	−	22.3963i	−0.0373895	−	0.0373895i	0.688165	−	0.725554i	$-0.258417\pi$
$599$	−22.3963	−	22.3963i	−0.0373895	−	0.0373895i	−0.725554	+	0.688165i	$0.758417\pi$
$600$	234.010	+	119.173i	0.390016	+	0.198621i
$601$	214.917	+	214.917i	0.357599	+	0.357599i	0.862927	−	0.505328i	$-0.168629\pi$
$601$	214.917	+	214.917i	0.357599	+	0.357599i	−0.505328	+	0.862927i	$0.668629\pi$
$602$	8.84024	−	55.8401i	0.0146848	−	0.0927576i
$603$	−600.056	−	248.551i	−0.995118	−	0.412191i
$604$	−19.5490	+	60.1939i	−0.0323659	+	0.0996588i
$605$	−11.4455	+	4.74090i	−0.0189183	+	0.00783620i
$606$	−180.293	−	110.467i	−0.297514	−	0.182288i
$607$		−	544.542i		−	0.897103i	−0.893757	−	0.448552i	$-0.851940\pi$
$607$		−	544.542i		−	0.897103i	0.893757	−	0.448552i	$-0.148060\pi$
$608$	118.979	−	119.062i	0.195690	−	0.195825i
$609$	−56.8205			−0.0933012
$610$	−4.54110	+	7.41155i	−0.00744442	+	0.0121501i
$611$	116.120	+	280.339i	0.190049	+	0.458820i
$612$	−225.000	+	692.806i	−0.367648	+	1.13204i
$613$	350.821	−	846.957i	0.572302	−	1.38166i	−0.327289	−	0.944924i	$-0.606135\pi$
$613$	350.821	−	846.957i	0.572302	−	1.38166i	0.899591	−	0.436734i	$-0.143865\pi$
$614$	950.506	+	150.478i	1.54806	+	0.245078i
$615$	−5.03009	+	5.03009i	−0.00817901	+	0.00817901i
$616$	72.3146	−	23.5130i	0.117394	−	0.0381705i
$617$	281.218	−	281.218i	0.455783	−	0.455783i	−0.441485	−	0.897269i	$-0.645548\pi$
$617$	281.218	−	281.218i	0.455783	−	0.455783i	0.897269	+	0.441485i	$0.145548\pi$
$618$	−43.1324	−	59.3580i	−0.0697935	−	0.0960485i
$619$	381.822	−	921.800i	0.616837	−	1.48918i	−0.238520	−	0.971138i	$-0.576662\pi$
$619$	381.822	−	921.800i	0.616837	−	1.48918i	0.855357	−	0.518039i	$-0.173338\pi$
$620$	−1.47742	−	18.7392i	−0.00238293	−	0.0302245i
$621$	−15.1195	−	36.5016i	−0.0243470	−	0.0587788i
$622$	36.0500	+	150.113i	0.0579581	+	0.241340i
$623$	−183.977			−0.295308
$624$	−47.6713	−	300.447i	−0.0763962	−	0.481485i
$625$			624.015i			0.998424i
$626$	−188.410	−	784.544i	−0.300974	−	1.25327i
$627$	22.9360	−	9.50039i	0.0365805	−	0.0151521i
$628$	−852.984	−	728.313i	−1.35825	−	1.15973i
$629$	−566.953	−	234.840i	−0.901356	−	0.373354i
$630$	2.59324	+	3.56877i	0.00411625	+	0.00566471i
$631$	−521.466	−	521.466i	−0.826413	−	0.826413i	0.160606	−	0.987019i	$-0.448655\pi$
$631$	−521.466	−	521.466i	−0.826413	−	0.826413i	−0.987019	+	0.160606i	$0.948655\pi$
$632$	−75.4992	+	961.859i	−0.119461	+	1.52193i
$633$	−14.5837	−	14.5837i	−0.0230390	−	0.0230390i
$634$	447.051	+	70.7742i	0.705128	+	0.111631i
$635$	−24.6850	−	10.2249i	−0.0388740	−	0.0161021i
$636$	−362.317	+	184.673i	−0.569681	+	0.290366i
$637$	93.5954	−	38.7685i	0.146931	−	0.0608610i
$638$	−61.3658	+	100.155i	−0.0961846	+	0.156983i
$639$			269.132i			0.421177i
$640$	−13.0679	+	6.66641i	−0.0204186	+	0.0104163i
$641$	337.238			0.526112			0.263056	−	0.964781i	$-0.415270\pi$
$641$	337.238			0.526112			0.263056	+	0.964781i	$0.415270\pi$
$642$	−146.728	−	89.9011i	−0.228548	−	0.140033i
$643$	316.087	+	763.103i	0.491582	+	1.18678i	0.953915	+	0.300078i	$0.0970127\pi$
$643$	316.087	+	763.103i	0.491582	+	1.18678i	−0.462332	+	0.886707i	$0.652987\pi$
$644$	8.88111	+	17.4242i	0.0137905	+	0.0270562i
$645$	−0.615617	+	1.48623i	−0.000954445	+	0.00230423i
$646$	41.1817	−	260.127i	0.0637488	−	0.402674i
$647$	428.698	−	428.698i	0.662594	−	0.662594i	−0.293397	−	0.955991i	$-0.594786\pi$
$647$	428.698	−	428.698i	0.662594	−	0.662594i	0.955991	+	0.293397i	$0.0947858\pi$
$648$	−298.122	−	23.4005i	−0.460065	−	0.0361119i
$649$	−232.381	+	232.381i	−0.358060	+	0.358060i
$650$	585.084	−	425.150i	0.900130	−	0.654078i
$651$	54.5391	−	131.669i	0.0837775	−	0.202257i
$652$	448.387	−	525.141i	0.687710	−	0.805430i
$653$	201.780	+	487.139i	0.309004	+	0.746002i	0.999738	+	0.0228926i	$0.00728757\pi$
$653$	201.780	+	487.139i	0.309004	+	0.746002i	−0.690734	+	0.723109i	$0.742712\pi$
$654$	−423.435	+	101.689i	−0.647453	+	0.155487i
$655$	11.0699			0.0169006
$656$	118.460	+	746.591i	0.180579	+	1.13810i
$657$			235.603i			0.358605i
$658$	107.877	−	25.9069i	0.163947	−	0.0393723i
$659$	7.55233	−	3.12828i	0.0114603	−	0.00474701i	−0.376946	−	0.926235i	$-0.623026\pi$
$659$	7.55233	−	3.12828i	0.0114603	−	0.00474701i	0.388406	+	0.921488i	$0.373026\pi$
$660$	−2.15701	+	0.170061i	−0.00326820	+	0.000257668i
$661$	−134.823	−	55.8457i	−0.203969	−	0.0844867i	0.278360	−	0.960477i	$-0.410209\pi$
$661$	−134.823	−	55.8457i	−0.203969	−	0.0844867i	−0.482329	+	0.875990i	$0.660209\pi$
$662$	−700.619	+	509.103i	−1.05834	+	0.769038i
$663$	−336.571	−	336.571i	−0.507649	−	0.507649i
$664$	5.58200	+	17.1675i	0.00840662	+	0.0258547i
$665$	−1.12783	−	1.12783i	−0.00169598	−	0.00169598i
$666$	55.7622	−	352.226i	0.0837270	−	0.528868i
$667$	−27.9100	−	11.5607i	−0.0418440	−	0.0173324i
$668$	527.106	+	171.186i	0.789080	+	0.256267i
$669$	−128.301	+	53.1442i	−0.191781	+	0.0794382i
$670$	−17.4515	−	10.6927i	−0.0260471	−	0.0159592i
$671$			136.233i			0.203029i
$672$	−111.226	+	0.0384495i	−0.165514	+	5.72165e-5i
$673$	−652.697			−0.969832			−0.484916	−	0.874561i	$-0.661150\pi$
$673$	−652.697			−0.969832			−0.484916	+	0.874561i	$0.661150\pi$
$674$	−377.619	+	616.314i	−0.560266	+	0.914413i
$675$	204.435	+	493.549i	0.302866	+	0.731183i
$676$	−153.891	−	49.9786i	−0.227649	−	0.0739328i
$677$	100.307	−	242.162i	0.148163	−	0.357698i	−0.832321	−	0.554293i	$-0.812989\pi$
$677$	100.307	−	242.162i	0.148163	−	0.357698i	0.980485	+	0.196595i	$0.0629885\pi$
$678$	−299.102	−	47.3520i	−0.441154	−	0.0698406i
$679$	−231.392	+	231.392i	−0.340784	+	0.340784i
$680$	−10.4167	+	20.4543i	−0.0153186	+	0.0300799i
$681$	191.453	−	191.453i	0.281136	−	0.281136i
$682$	−173.186	−	238.336i	−0.253939	−	0.349466i
$683$	−91.1509	+	220.058i	−0.133457	+	0.322193i	−0.976454	−	0.215724i	$-0.930789\pi$
$683$	−91.1509	+	220.058i	−0.133457	+	0.322193i	0.842998	+	0.537917i	$0.180789\pi$
$684$	152.574	−	12.0291i	0.223062	−	0.0175864i
$685$	9.61276	+	23.2072i	0.0140332	+	0.0338792i
$686$	−8.64943	−	36.0165i	−0.0126085	−	0.0525022i
$687$	−90.6283			−0.131919
$688$	89.3600	+	145.732i	0.129884	+	0.211820i
$689$			1119.99i			1.62553i
$690$	−0.129946	−	0.541099i	−0.000188327	−	0.000784201i
$691$	149.012	−	61.7227i	0.215646	−	0.0893237i	−0.272245	−	0.962228i	$-0.587766\pi$
$691$	149.012	−	61.7227i	0.215646	−	0.0893237i	0.487892	+	0.872904i	$0.337766\pi$
$692$	−193.869	+	227.055i	−0.280158	+	0.328114i
$693$	63.8785	+	26.4593i	0.0921767	+	0.0381809i
$694$	320.544	+	441.127i	0.461879	+	0.635629i
$695$	8.46707	+	8.46707i	0.0121828	+	0.0121828i
$696$	130.621	−	111.608i	0.187674	−	0.160356i
$697$	836.358	+	836.358i	1.19994	+	1.19994i
$698$	350.108	+	55.4269i	0.501587	+	0.0794081i
$699$	−496.143	−	205.509i	−0.709790	−	0.294005i
$700$	−120.084	−	235.598i	−0.171549	−	0.336568i
$701$	1082.83	−	448.521i	1.54469	−	0.639830i	0.562341	−	0.826906i	$-0.309901\pi$
$701$	1082.83	−	448.521i	1.54469	−	0.639830i	0.982346	+	0.187076i	$0.0599009\pi$
$702$	323.303	−	527.665i	0.460546	−	0.751659i
$703$			128.936i			0.183408i
$704$	−120.055	+	196.095i	−0.170533	+	0.278544i
$705$	−3.15686			−0.00447782
$706$	880.067	+	539.222i	1.24655	+	0.763771i
$707$	81.4795	+	196.709i	0.115247	+	0.278231i
$708$	428.273	−	218.291i	0.604906	−	0.308320i
$709$	77.1824	−	186.335i	0.108861	−	0.262813i	−0.860056	−	0.510199i	$-0.829572\pi$
$709$	77.1824	−	186.335i	0.108861	−	0.262813i	0.968917	+	0.247386i	$0.0795716\pi$
$710$	−1.32611	+	8.37651i	−0.00186777	+	0.0117979i
$711$	−620.327	+	620.327i	−0.872471	+	0.872471i
$712$	422.934	−	361.371i	0.594008	−	0.507544i
$713$	53.5788	−	53.5788i	0.0751455	−	0.0751455i
$714$	−140.788	+	102.303i	−0.197182	+	0.143282i
$715$	−2.28041	+	5.50540i	−0.00318939	+	0.00769987i
$716$	−484.356	−	413.563i	−0.676475	−	0.577602i
$717$	−62.9123	−	151.884i	−0.0877439	−	0.211832i
$718$	163.898	−	39.3604i	0.228270	−	0.0548194i
$719$	151.151			0.210224			0.105112	−	0.994460i	$-0.466480\pi$
$719$	151.151			0.210224			0.105112	+	0.994460i	$0.466480\pi$
$720$	−12.9713	−	3.11034i	−0.0180157	−	0.00431992i
$721$			73.8851i			0.102476i
$722$	648.234	−	155.675i	0.897831	−	0.215616i
$723$	13.4761	−	5.58200i	0.0186392	−	0.00772061i
$724$	17.5601	+	222.728i	0.0242542	+	0.307635i
$725$	377.379	+	156.315i	0.520522	+	0.215607i
$726$	229.757	−	166.953i	0.316470	−	0.229963i
$727$	−164.336	−	164.336i	−0.226047	−	0.226047i	0.584992	−	0.811039i	$-0.301098\pi$
$727$	−164.336	−	164.336i	−0.226047	−	0.226047i	−0.811039	+	0.584992i	$0.801098\pi$
$728$	−139.011	+	272.965i	−0.190949	+	0.374952i
$729$	−13.5203	−	13.5203i	−0.0185463	−	0.0185463i
$730$	−1.16091	+	7.33295i	−0.00159028	+	0.0100451i
$731$	247.117	+	102.359i	0.338053	+	0.140026i
$732$	61.5509	−	189.523i	0.0840860	−	0.258912i
$733$	125.388	−	51.9372i	0.171061	−	0.0708557i	−0.295510	−	0.955340i	$-0.595489\pi$
$733$	125.388	−	51.9372i	0.171061	−	0.0708557i	0.466570	+	0.884484i	$0.345489\pi$
$734$	−192.662	−	118.045i	−0.262483	−	0.160825i
$735$			1.05397i			0.00143397i
$736$	−54.6413	−	22.6111i	−0.0742409	−	0.0307215i
$737$	−320.779			−0.435250
$738$	−359.094	+	586.080i	−0.486578	+	0.794146i
$739$	498.598	+	1203.72i	0.674693	+	1.62885i	0.773539	+	0.633749i	$0.218485\pi$
$739$	498.598	+	1203.72i	0.674693	+	1.62885i	−0.0988460	+	0.995103i	$0.531515\pi$
$740$	3.47110	−	10.6880i	0.00469067	−	0.0144432i
$741$	−38.2712	+	92.3949i	−0.0516481	+	0.124690i
$742$	404.461	+	64.0317i	0.545096	+	0.0862961i
$743$	−738.261	+	738.261i	−0.993622	+	0.993622i	−0.999980	−	0.00635773i	$-0.997976\pi$
$743$	−738.261	+	738.261i	−0.993622	+	0.993622i	0.00635773	+	0.999980i	$0.497976\pi$
$744$	133.251	+	409.814i	0.179100	+	0.550825i
$745$	18.6181	−	18.6181i	0.0249907	−	0.0249907i
$746$	−378.247	−	520.537i	−0.507034	−	0.697771i
$747$	−6.28145	+	15.1648i	−0.00840890	+	0.0203009i
$748$	28.2762	+	358.649i	0.0378024	+	0.479477i
$749$	66.3104	+	160.088i	0.0885319	+	0.213735i
$750$	3.51500	+	14.6366i	0.00468666	+	0.0195154i
$751$	1212.63			1.61469			0.807344	−	0.590081i	$-0.200904\pi$
$751$	1212.63			1.61469			0.807344	+	0.590081i	$0.200904\pi$
$752$	−197.106	+	271.451i	−0.262109	+	0.360972i
$753$			302.103i			0.401200i
$754$	−110.492	−	460.093i	−0.146541	−	0.610203i
$755$	−1.67535	+	0.693952i	−0.00221900	+	0.000919142i
$756$	−172.071	−	146.922i	−0.227608	−	0.194341i
$757$	507.696	+	210.295i	0.670669	+	0.277800i	0.691920	−	0.721974i	$-0.256765\pi$
$757$	507.696	+	210.295i	0.670669	+	0.277800i	−0.0212514	+	0.999774i	$0.506765\pi$
$758$	−696.115	−	957.980i	−0.918357	−	1.26383i
$759$	−6.16729	−	6.16729i	−0.00812554	−	0.00812554i
$760$	4.80801	+	0.377395i	0.00632633	+	0.000496573i
$761$	150.165	+	150.165i	0.197326	+	0.197326i	0.798853	−	0.601527i	$-0.205441\pi$
$761$	150.165	+	150.165i	0.197326	+	0.197326i	−0.601527	+	0.798853i	$0.705441\pi$
$762$	604.999	+	95.7796i	0.793963	+	0.125695i
$763$	405.127	+	167.809i	0.530965	+	0.219933i
$764$	−329.914	+	168.157i	−0.431824	+	0.220101i
$765$	−19.2825	+	7.98708i	−0.0252059	+	0.0104406i
$766$	417.037	−	680.647i	0.544434	−	0.888574i
$767$		−	1323.87i		−	1.72604i
$768$	255.615	−	218.560i	0.332832	−	0.284584i
$769$	830.546			1.08003			0.540017	−	0.841654i	$-0.318418\pi$
$769$	830.546			1.08003			0.540017	+	0.841654i	$0.318418\pi$
$770$	1.85779	+	1.13828i	0.00241271	+	0.00147828i
$771$	5.78260	+	13.9604i	0.00750012	+	0.0181069i
$772$	−149.626	−	293.556i	−0.193816	−	0.380254i
$773$	−125.118	+	302.062i	−0.161861	+	0.390766i	−0.983914	−	0.178645i	$-0.942829\pi$
$773$	−125.118	+	302.062i	−0.161861	+	0.390766i	0.822053	+	0.569411i	$0.192829\pi$
$774$	−24.3050	+	153.524i	−0.0314018	+	0.198352i
$775$	−724.454	+	724.454i	−0.934779	+	0.934779i
$776$	77.4286	−	986.440i	0.0997792	−	1.27119i
$777$	60.2457	−	60.2457i	0.0775363	−	0.0775363i
$778$	−994.903	+	722.945i	−1.27880	+	0.929235i
$779$	95.1017	−	229.596i	0.122082	−	0.294731i
$780$	5.65983	−	6.62867i	0.00725619	−	0.00849829i
$781$	50.8669	+	122.803i	0.0651304	+	0.157239i
$782$	−89.9691	+	21.6062i	−0.115050	+	0.0276295i
$783$	349.505			0.446366
$784$	90.6281	+	65.8069i	0.115597	+	0.0839374i
$785$		−	32.1371i		−	0.0409390i
$786$	−246.763	+	59.2606i	−0.313948	+	0.0753952i
$787$	786.823	−	325.913i	0.999775	−	0.414121i	0.178061	−	0.984020i	$-0.443018\pi$
$787$	786.823	−	325.913i	0.999775	−	0.414121i	0.821715	+	0.569899i	$0.193018\pi$
$788$	138.220	−	10.8974i	0.175406	−	0.0138292i
$789$	−216.941	−	89.8600i	−0.274957	−	0.113891i
$790$	−22.3637	+	16.2506i	−0.0283085	+	0.0205703i
$791$	215.622	+	215.622i	0.272594	+	0.272594i
$792$	−198.819	+	64.6457i	−0.251034	+	0.0816234i
$793$	−388.059	−	388.059i	−0.489355	−	0.489355i
$794$	157.343	−	993.871i	0.198165	−	1.25173i
$795$	−10.7651	−	4.45904i	−0.0135410	−	0.00560885i
$796$	1292.63	+	419.804i	1.62391	+	0.527392i
$797$	1076.18	−	445.767i	1.35028	−	0.559306i	0.413913	−	0.910316i	$-0.364162\pi$
$797$	1076.18	−	445.767i	1.35028	−	0.559306i	0.936372	+	0.351010i	$0.114162\pi$
$798$	31.1785	+	19.1032i	0.0390708	+	0.0239389i
$799$			524.895i			0.656939i
$800$	738.821	+	305.731i	0.923526	+	0.382163i
$801$	505.818			0.631483
$802$	−185.997	+	303.567i	−0.231917	+	0.378513i
$803$	44.5298	+	107.504i	0.0554543	+	0.133879i
$804$	446.260	+	144.930i	0.555049	+	0.180262i
$805$	−0.214440	+	0.517703i	−0.000266385	+	0.000643110i
$806$	1172.22	+	185.579i	1.45437	+	0.230246i
$807$	111.314	−	111.314i	0.137936	−	0.137936i
$808$	−573.689	−	292.159i	−0.710011	−	0.361583i
$809$	547.972	−	547.972i	0.677345	−	0.677345i	−0.282054	−	0.959399i	$-0.591016\pi$
$809$	547.972	−	547.972i	0.677345	−	0.677345i	0.959399	+	0.282054i	$0.0910156\pi$
$810$	−5.03675	−	6.93149i	−0.00621821	−	0.00855739i
$811$	−497.746	+	1201.67i	−0.613744	+	1.48171i	0.245114	+	0.969494i	$0.421174\pi$
$811$	−497.746	+	1201.67i	−0.613744	+	1.48171i	−0.858858	+	0.512214i	$0.828826\pi$
$812$	−172.470	+	13.5977i	−0.212401	+	0.0167459i
$813$	160.155	+	386.648i	0.196993	+	0.475582i
$814$	−41.1279	−	171.258i	−0.0505257	−	0.210391i
$815$	19.7853			0.0242764
$816$	122.703	−	511.718i	0.150371	−	0.627106i
$817$		−	56.1990i		−	0.0687870i
$818$	84.9544	+	353.753i	0.103856	+	0.432461i
$819$	−257.327	+	106.588i	−0.314197	+	0.130145i
$820$	−14.0643	+	16.4718i	−0.0171516	+	0.0200876i
$821$	1109.04	+	459.379i	1.35084	+	0.559536i	0.936526	−	0.350598i	$-0.114022\pi$
$821$	1109.04	+	459.379i	1.35084	+	0.559536i	0.414314	+	0.910134i	$0.364022\pi$
$822$	−338.517	−	465.861i	−0.411822	−	0.566741i
$823$	865.297	+	865.297i	1.05139	+	1.05139i	0.998606	+	0.0527884i	$0.0168109\pi$
$823$	865.297	+	865.297i	1.05139	+	1.05139i	0.0527884	+	0.998606i	$0.483189\pi$
$824$	−145.127	−	169.850i	−0.176125	−	0.206129i
$825$	83.3897	+	83.3897i	0.101078	+	0.101078i
$826$	−478.089	−	75.6880i	−0.578800	−	0.0916319i
$827$	260.547	+	107.922i	0.315051	+	0.130498i	0.534605	−	0.845102i	$-0.320460\pi$
$827$	260.547	+	107.922i	0.315051	+	0.130498i	−0.219554	+	0.975600i	$0.570460\pi$
$828$	−24.4174	−	47.9054i	−0.0294896	−	0.0578567i
$829$	−436.242	+	180.698i	−0.526227	+	0.217970i	−0.629950	−	0.776636i	$-0.716925\pi$
$829$	−436.242	+	180.698i	−0.526227	+	0.217970i	0.103723	+	0.994606i	$0.466925\pi$
$830$	−0.270227	+	0.441039i	−0.000325575	+	0.000531373i
$831$		−	94.2043i		−	0.113363i
$832$	−216.599	−	900.553i	−0.260335	−	1.08240i
$833$	175.244			0.210377
$834$	−234.069	−	143.416i	−0.280659	−	0.171961i
$835$	6.07679	+	14.6707i	0.00727760	+	0.0175697i
$836$	67.3452	−	34.3258i	0.0805564	−	0.0410596i
$837$	−335.472	+	809.902i	−0.400803	+	0.967625i
$838$	−70.3641	+	444.460i	−0.0839667	+	0.530382i
$839$	973.336	−	973.336i	1.16011	−	1.16011i	0.175664	−	0.984450i	$-0.443793\pi$
$839$	973.336	−	973.336i	1.16011	−	1.16011i	0.984450	−	0.175664i	$-0.0562072\pi$
$840$	−2.07022	−	2.42290i	−0.00246455	−	0.00288441i
$841$	−405.710	+	405.710i	−0.482414	+	0.482414i
$842$	−447.859	+	325.436i	−0.531899	+	0.386503i
$843$	−84.9580	+	205.107i	−0.100780	+	0.243306i
$844$	−47.7567	−	40.7767i	−0.0565838	−	0.0483136i
$845$	−1.77414	−	4.28316i	−0.00209958	−	0.00506883i
$846$	−296.593	+	71.2275i	−0.350583	+	0.0841932i
$847$	−285.988			−0.337648
$848$	−1055.57	+	647.253i	−1.24477	+	0.763270i
$849$			682.300i			0.803651i
$850$	1216.50	−	292.144i	1.43117	−	0.343699i
$851$	41.8500	−	17.3348i	0.0491774	−	0.0203700i
$852$	−15.2812	−	193.823i	−0.0179356	−	0.227492i
$853$	−1447.51	−	599.580i	−1.69697	−	0.702907i	−0.697068	−	0.717005i	$-0.745512\pi$
$853$	−1447.51	−	599.580i	−1.69697	−	0.702907i	−0.999901	+	0.0140978i	$0.995512\pi$
$854$	−162.325	+	117.953i	−0.190077	+	0.138119i
$855$	3.10081	+	3.10081i	0.00362667	+	0.00362667i
$856$	−466.885	−	237.768i	−0.545426	−	0.277766i
$857$	−156.450	−	156.450i	−0.182555	−	0.182555i	0.609913	−	0.792468i	$-0.291204\pi$
$857$	−156.450	−	156.450i	−0.182555	−	0.182555i	−0.792468	+	0.609913i	$0.791204\pi$
$858$	21.3614	−	134.931i	0.0248967	−	0.157262i
$859$	−495.482	−	205.235i	−0.576812	−	0.238923i	0.0751535	−	0.997172i	$-0.476055\pi$
$859$	−495.482	−	205.235i	−0.576812	−	0.238923i	−0.651966	+	0.758249i	$0.726055\pi$
$860$	−1.51294	+	4.65855i	−0.00175924	+	0.00541692i
$861$	−151.716	+	62.8429i	−0.176209	+	0.0729883i
$862$	1025.65	+	628.420i	1.18985	+	0.729026i
$863$			190.961i			0.221276i	0.993861	+	0.110638i	$0.0352894\pi$
$863$			190.961i			0.221276i	−0.993861	+	0.110638i	$0.964711\pi$
$864$	684.153	−	0.236504i	0.791843	−	0.000273732i
$865$	−8.55455			−0.00988966
$866$	321.064	−	524.010i	0.370743	−	0.605092i
$867$	−169.798	−	409.929i	−0.195846	−	0.472814i
$868$	134.036	−	412.714i	0.154419	−	0.475477i
$869$	−165.808	+	400.295i	−0.190803	+	0.460639i
$870$	4.86221	+	0.769753i	0.00558874	+	0.000884774i
$871$	913.739	−	913.739i	1.04907	−	1.04907i
$872$	−1260.94	+	409.992i	−1.44603	+	0.470175i
$873$	636.180	−	636.180i	0.728728	−	0.728728i
$874$	11.4280	+	15.7270i	0.0130755	+	0.0179943i
$875$	5.80053	−	14.0037i	0.00662918	−	0.0160042i
$876$	−13.3774	−	169.676i	−0.0152710	−	0.193694i
$877$	−150.409	−	363.119i	−0.171504	−	0.414047i	0.814634	−	0.579975i	$-0.196938\pi$
$877$	−150.409	−	363.119i	−0.171504	−	0.414047i	−0.986138	+	0.165929i	$0.946938\pi$
$878$	−61.8529	−	257.557i	−0.0704475	−	0.293346i
$879$	236.520			0.269078
$880$	−6.50659	+	1.03239i	−0.00739386	+	0.00117317i
$881$		−	193.624i		−	0.219777i	−0.993944	−	0.109889i	$-0.964951\pi$
$881$		−	193.624i		−	0.219777i	0.993944	−	0.109889i	$-0.0350494\pi$
$882$	23.7804	+	99.0222i	0.0269619	+	0.112270i
$883$	40.2949	−	16.6907i	0.0456341	−	0.0189023i	−0.359750	−	0.933049i	$-0.617138\pi$
$883$	40.2949	−	16.6907i	0.0456341	−	0.0189023i	0.405384	+	0.914147i	$0.367138\pi$
$884$	−1102.16	−	941.066i	−1.24678	−	1.06455i
$885$	12.7247	+	5.27076i	0.0143782	+	0.00595566i
$886$	−618.812	−	851.598i	−0.698434	−	0.961172i
$887$	−613.864	−	613.864i	−0.692067	−	0.692067i	0.270619	−	0.962686i	$-0.412772\pi$
$887$	−613.864	−	613.864i	−0.692067	−	0.692067i	−0.962686	+	0.270619i	$0.912772\pi$
$888$	−20.1595	+	256.831i	−0.0227021	+	0.289225i
$889$	−436.143	−	436.143i	−0.490599	−	0.490599i
$890$	15.7432	+	2.49235i	0.0176889	+	0.00280040i
$891$	−124.069	−	51.3910i	−0.139247	−	0.0576779i
$892$	−376.722	+	192.015i	−0.422334	+	0.215263i
$893$	101.889	−	42.2039i	0.114098	−	0.0472608i
$894$	−315.354	+	514.692i	−0.352745	+	0.575718i
$895$		−	18.2487i		−	0.0203896i
$896$	−337.599	+	26.7340i	−0.376785	+	0.0298371i
$897$	35.1350			0.0391695
$898$	−46.9282	−	28.7532i	−0.0522586	−	0.0320191i
$899$	256.510	+	619.269i	0.285328	+	0.688842i
$900$	330.154	+	647.742i	0.366838	+	0.719714i
$901$	−741.409	+	1789.92i	−0.822874	+	1.98659i
$902$	−53.0817	+	335.295i	−0.0588489	+	0.371724i
$903$	−26.2592	+	26.2592i	−0.0290800	+	0.0290800i
$904$	−919.212	−	72.1517i	−1.01683	−	0.0798139i
$905$	−4.52656	+	4.52656i	−0.00500172	+	0.00500172i
$906$	33.6309	−	24.4378i	0.0371202	−	0.0269733i
$907$	237.293	−	572.877i	0.261624	−	0.631617i	−0.737415	−	0.675440i	$-0.763954\pi$
$907$	237.293	−	572.877i	0.261624	−	0.631617i	0.999039	+	0.0438228i	$0.0139537\pi$
$908$	535.312	−	626.945i	0.589550	−	0.690468i
$909$	−224.016	−	540.824i	−0.246443	−	0.594965i
$910$	−8.53429	+	2.04952i	−0.00937834	+	0.00225223i
$911$	−799.807			−0.877944			−0.438972	−	0.898501i	$-0.644657\pi$
$911$	−799.807			−0.877944			−0.438972	+	0.898501i	$0.644657\pi$
$912$	−109.198	+	17.3261i	−0.119734	+	0.0189980i
$913$			8.10681i			0.00887931i
$914$	−203.975	+	48.9851i	−0.223168	+	0.0535942i
$915$	5.27492	−	2.18494i	0.00576493	−	0.00238791i
$916$	−275.089	+	21.6882i	−0.300315	+	0.0236771i
$917$	236.094	+	97.7933i	0.257463	+	0.106645i
$918$	865.992	−	629.272i	0.943347	−	0.685481i
$919$	1101.16	+	1101.16i	1.19821	+	1.19821i	0.974702	+	0.223510i	$0.0717517\pi$
$919$	1101.16	+	1101.16i	1.19821	+	1.19821i	0.223510	+	0.974702i	$0.428248\pi$
$920$	−0.523921	−	1.61133i	−0.000569480	−	0.00175144i
$921$	−446.983	−	446.983i	−0.485323	−	0.485323i
$922$	−221.347	+	1398.16i	−0.240073	+	1.51644i
$923$	−494.700	−	204.911i	−0.535969	−	0.222006i
$924$	−47.5062	−	15.4284i	−0.0514136	−	0.0166974i
$925$	−565.866	+	234.389i	−0.611747	+	0.253394i
$926$	−76.2675	−	46.7295i	−0.0823623	−	0.0504639i
$927$		−	203.137i		−	0.219133i
$928$	369.773	−	370.029i	0.398462	−	0.398738i
$929$	−1584.16			−1.70524			−0.852618	−	0.522535i	$-0.824987\pi$
$929$	−1584.16			−1.70524			−0.852618	+	0.522535i	$0.824987\pi$
$930$	−6.45073	+	10.5283i	−0.00693627	+	0.0113207i
$931$	−14.0904	−	34.0173i	−0.0151347	−	0.0365384i
$932$	−1555.15	−	505.061i	−1.66861	−	0.541911i
$933$	38.8070	−	93.6883i	0.0415938	−	0.100416i
$934$	−632.948	−	100.204i	−0.677674	−	0.107285i
$935$	−7.28892	+	7.28892i	−0.00779564	+	0.00779564i
$936$	382.192	−	750.478i	0.408324	−	0.801793i
$937$	−362.033	+	362.033i	−0.386375	+	0.386375i	−0.873392	−	0.487018i	$-0.838085\pi$
$937$	−362.033	+	362.033i	−0.386375	+	0.386375i	0.487018	+	0.873392i	$0.338085\pi$
$938$	−277.738	−	382.218i	−0.296096	−	0.407482i
$939$	−202.819	+	489.648i	−0.215995	+	0.521457i
$940$	−9.58218	+	0.755467i	−0.0101938	+	0.000803688i
$941$	−198.037	−	478.103i	−0.210454	−	0.508080i	0.783040	−	0.621972i	$-0.213668\pi$
$941$	−198.037	−	478.103i	−0.210454	−	0.508080i	−0.993493	+	0.113892i	$0.963668\pi$
$942$	172.040	+	716.380i	0.182633	+	0.760489i
$943$	−87.3084			−0.0925857
$944$	1247.72	−	765.079i	1.32174	−	0.810465i
$945$		−	6.48298i		−	0.00686030i
$946$	17.9264	+	74.6460i	0.0189497	+	0.0789070i
$947$	741.185	−	307.009i	0.782667	−	0.324191i	0.0446755	−	0.999002i	$-0.485775\pi$
$947$	741.185	−	307.009i	0.782667	−	0.324191i	0.737991	+	0.674810i	$0.235775\pi$
$948$	411.524	−	481.968i	0.434097	−	0.508405i
$949$	−433.069	−	179.383i	−0.456343	−	0.189023i
$950$	−154.521	−	212.649i	−0.162654	−	0.223841i
$951$	−210.229	−	210.229i	−0.221061	−	0.221061i
$952$	−402.859	+	344.218i	−0.423171	+	0.361574i
$953$	−1098.50	−	1098.50i	−1.15268	−	1.15268i	−0.986014	−	0.166661i	$-0.946701\pi$
$953$	−1098.50	−	1098.50i	−1.15268	−	1.15268i	−0.166661	−	0.986014i	$-0.553299\pi$
$954$	−1112.01	−	176.046i	−1.16563	−	0.184535i
$955$	−9.80231	−	4.06025i	−0.0102642	−	0.00425157i
$956$	−227.308	−	445.965i	−0.237770	−	0.466491i
$957$	71.2822	−	29.5260i	0.0744850	−	0.0308527i
$958$	−706.725	+	1153.45i	−0.737708	+	1.20402i
$959$			579.875i			0.604666i
$960$	9.51825	+	1.50349i	0.00991484	+	0.00156614i
$961$	−720.233			−0.749463
$962$	604.981	+	370.675i	0.628878	+	0.385317i
$963$	−182.311	−	440.138i	−0.189316	−	0.457049i
$964$	39.5690	−	20.1683i	0.0410467	−	0.0209215i
$965$	3.61280	−	8.72207i	0.00374383	−	0.00903841i
$966$	2.00873	−	12.6883i	0.00207943	−	0.0131349i
$967$	−448.949	+	448.949i	−0.464270	+	0.464270i	−0.900052	−	0.435782i	$-0.856472\pi$
$967$	−448.949	+	448.949i	−0.464270	+	0.464270i	0.435782	+	0.900052i	$0.356472\pi$
$968$	657.441	−	561.744i	0.679175	−	0.580314i
$969$	−122.327	+	122.327i	−0.126240	+	0.126240i
$970$	22.9352	−	16.6658i	0.0236446	−	0.0171813i
$971$	−286.432	+	691.509i	−0.294987	+	0.712161i	0.705009	+	0.709199i	$0.250943\pi$
$971$	−286.432	+	691.509i	−0.294987	+	0.712161i	−0.999996	+	0.00296270i	$0.999057\pi$
$972$	734.715	+	627.330i	0.755879	+	0.645401i
$973$	105.782	+	255.381i	0.108718	+	0.262468i
$974$	−1733.17	+	416.224i	−1.77943	+	0.427334i
$975$	−475.071			−0.487252
$976$	141.474	−	590.000i	0.144953	−	0.604508i
$977$			1284.44i			1.31467i	0.753597	+	0.657337i	$0.228317\pi$
$977$			1284.44i			1.31467i	−0.753597	+	0.657337i	$0.771683\pi$
$978$	−441.041	+	105.917i	−0.450962	+	0.108299i
$979$	230.802	−	95.6013i	0.235753	−	0.0976520i
$980$	0.252224	+	3.19916i	0.000257372	+	0.00326444i
$981$	−1113.84	−	461.367i	−1.13541	−	0.470303i
$982$	175.582	−	127.587i	0.178801	−	0.129925i
$983$	690.418	+	690.418i	0.702358	+	0.702358i	0.964916	−	0.262558i	$-0.0845662\pi$
$983$	690.418	+	690.418i	0.702358	+	0.702358i	−0.262558	+	0.964916i	$0.584566\pi$
$984$	225.334	−	442.471i	0.228998	−	0.449665i
$985$	2.80909	+	2.80909i	0.00285186	+	0.00285186i
$986$	127.988	−	808.444i	0.129805	−	0.819923i
$987$	−67.3282	−	27.8882i	−0.0682150	−	0.0282556i
$988$	−94.0556	+	289.610i	−0.0951980	+	0.293127i
$989$	−18.2411	+	7.55572i	−0.0184440	+	0.00763975i
$990$	−5.10772	−	3.12953i	−0.00515932	−	0.00316114i
$991$		−	260.959i		−	0.263329i	−0.991294	−	0.131664i	$-0.957968\pi$
$991$		−	260.959i		−	0.263329i	0.991294	−	0.131664i	$-0.0420321\pi$
$992$	502.535	+	1212.04i	0.506587	+	1.22181i
$993$	568.881			0.572891
$994$	−102.282	+	166.935i	−0.102900	+	0.167943i
$995$	14.9022	+	35.9772i	0.0149771	+	0.0361580i
$996$	3.66271	−	11.2780i	0.00367742	−	0.0113233i
$997$	198.541	−	479.321i	0.199138	−	0.480763i	−0.792490	−	0.609885i	$-0.791216\pi$
$997$	198.541	−	479.321i	0.199138	−	0.480763i	0.991629	+	0.129122i	$0.0412158\pi$
$998$	−1341.16	−	212.323i	−1.34384	−	0.212749i
$999$	−370.574	+	370.574i	−0.370945	+	0.370945i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.w.a.43.10	✓	192
32.3	odd	8	inner	224.3.w.a.99.10	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.w.a.43.10	✓	192	1.1	even	1	trivial
224.3.w.a.99.10	yes	192	32.3	odd	8	inner

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70535 - 1.04488i) q^{2} +(0.502742 + 1.21373i) q^{3} +(1.81645 + 3.56377i) q^{4} +(-0.0438594 + 0.105886i) q^{5} +(0.410845 - 2.59514i) q^{6} +(-1.87083 + 1.87083i) q^{7} +(0.626019 - 7.97547i) q^{8} +(5.14358 - 5.14358i) q^{9} +O(q^{10})\)	\(q+(-1.70535 - 1.04488i) q^{2} +(0.502742 + 1.21373i) q^{3} +(1.81645 + 3.56377i) q^{4} +(-0.0438594 + 0.105886i) q^{5} +(0.410845 - 2.59514i) q^{6} +(-1.87083 + 1.87083i) q^{7} +(0.626019 - 7.97547i) q^{8} +(5.14358 - 5.14358i) q^{9} +(0.185434 - 0.134745i) q^{10} +(1.37483 - 3.31914i) q^{11} +(-3.41224 + 3.99634i) q^{12} +(5.53835 + 13.3708i) q^{13} +(5.14521 - 1.23563i) q^{14} -0.150567 q^{15} +(-9.40098 + 12.9469i) q^{16} +25.0349i q^{17} +(-14.1460 + 3.39720i) q^{18} +(4.85961 - 2.01292i) q^{19} +(-0.457022 + 0.0360320i) q^{20} +(-3.21122 - 1.33013i) q^{21} +(-5.81267 + 4.22377i) q^{22} +(-1.30671 - 1.30671i) q^{23} +(9.99477 - 3.24979i) q^{24} +(17.6684 + 17.6684i) q^{25} +(4.52599 - 28.5888i) q^{26} +(19.7523 + 8.18168i) q^{27} +(-10.0655 - 3.26894i) q^{28} +(15.1031 - 6.25590i) q^{29} +(0.256769 + 0.157324i) q^{30} +41.0028i q^{31} +(29.5599 - 12.2561i) q^{32} +4.71971 q^{33} +(26.1584 - 42.6933i) q^{34} +(-0.116041 - 0.280148i) q^{35} +(27.6736 + 8.98748i) q^{36} +(-9.38050 + 22.6465i) q^{37} +(-10.3906 - 1.64497i) q^{38} +(-13.4441 + 13.4441i) q^{39} +(0.817033 + 0.416086i) q^{40} +(33.4077 - 33.4077i) q^{41} +(4.08643 + 5.62368i) q^{42} +(4.08867 - 9.87092i) q^{43} +(14.3260 - 1.12947i) q^{44} +(0.319038 + 0.770227i) q^{45} +(0.863046 + 3.59375i) q^{46} +20.9665 q^{47} +(-20.4402 - 4.90129i) q^{48} -7.00000i q^{49} +(-11.6695 - 48.5921i) q^{50} +(-30.3855 + 12.5861i) q^{51} +(-37.5902 + 44.0248i) q^{52} +(71.4971 + 29.6151i) q^{53} +(-25.1358 - 34.5915i) q^{54} +(0.291151 + 0.291151i) q^{55} +(13.7496 + 16.0919i) q^{56} +(4.88626 + 4.88626i) q^{57} +(-32.2927 - 5.11238i) q^{58} +(-84.5124 - 35.0062i) q^{59} +(-0.273497 - 0.536585i) q^{60} +(-35.0338 + 14.5115i) q^{61} +(42.8430 - 69.9243i) q^{62} +19.2455i q^{63} +(-63.2162 - 9.98558i) q^{64} -1.65868 q^{65} +(-8.04877 - 4.93153i) q^{66} +(-34.1693 - 82.4920i) q^{67} +(-89.2186 + 45.4747i) q^{68} +(0.929050 - 2.24292i) q^{69} +(-0.0948298 + 0.599000i) q^{70} +(-26.1620 + 26.1620i) q^{71} +(-37.8025 - 44.2424i) q^{72} +(-22.9027 + 22.9027i) q^{73} +(39.6600 - 28.8188i) q^{74} +(-12.5619 + 30.3272i) q^{75} +(16.0009 + 13.6622i) q^{76} +(3.63746 + 8.78161i) q^{77} +(36.9744 - 8.87946i) q^{78} -120.602 q^{79} +(-0.958570 - 1.56327i) q^{80} -37.3799i q^{81} +(-91.8790 + 22.0649i) q^{82} +(-2.08476 + 0.863534i) q^{83} +(-1.09275 - 13.8602i) q^{84} +(-2.65084 - 1.09801i) q^{85} +(-17.2865 + 12.5612i) q^{86} +(15.1859 + 15.1859i) q^{87} +(-25.6110 - 13.0428i) q^{88} +(49.1699 + 49.1699i) q^{89} +(0.260721 - 1.64686i) q^{90} +(-35.3757 - 14.6531i) q^{91} +(2.28324 - 7.03039i) q^{92} +(-49.7663 + 20.6139i) q^{93} +(-35.7553 - 21.9075i) q^{94} +0.602850i q^{95} +(29.7366 + 29.7160i) q^{96} +123.684 q^{97} +(-7.31415 + 11.9375i) q^{98} +(-10.0007 - 24.1438i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 80 q^{10} + 96 q^{12} - 20 q^{16} - 60 q^{18} - 260 q^{22} + 64 q^{23} - 144 q^{24} - 200 q^{26} + 192 q^{27} - 40 q^{30} + 40 q^{32} + 120 q^{34} + 464 q^{36} + 504 q^{38} - 384 q^{39} + 360 q^{40} - 96 q^{43} + 52 q^{44} + 64 q^{46} - 104 q^{48} - 312 q^{50} - 384 q^{51} - 320 q^{52} + 160 q^{53} - 576 q^{54} - 512 q^{55} - 196 q^{56} - 360 q^{58} - 872 q^{60} + 128 q^{61} - 408 q^{62} + 832 q^{66} + 160 q^{67} + 856 q^{68} - 384 q^{69} + 336 q^{70} + 1488 q^{72} + 308 q^{74} + 768 q^{75} + 1024 q^{76} - 224 q^{77} - 408 q^{78} + 1024 q^{79} - 1040 q^{80} - 240 q^{82} - 1384 q^{86} + 896 q^{87} - 560 q^{88} - 1320 q^{90} - 380 q^{92} - 936 q^{94} - 1088 q^{96} - 512 q^{99}+O(q^{100}) \) 192 * q + 80 * q^10 + 96 * q^12 - 20 * q^16 - 60 * q^18 - 260 * q^22 + 64 * q^23 - 144 * q^24 - 200 * q^26 + 192 * q^27 - 40 * q^30 + 40 * q^32 + 120 * q^34 + 464 * q^36 + 504 * q^38 - 384 * q^39 + 360 * q^40 - 96 * q^43 + 52 * q^44 + 64 * q^46 - 104 * q^48 - 312 * q^50 - 384 * q^51 - 320 * q^52 + 160 * q^53 - 576 * q^54 - 512 * q^55 - 196 * q^56 - 360 * q^58 - 872 * q^60 + 128 * q^61 - 408 * q^62 + 832 * q^66 + 160 * q^67 + 856 * q^68 - 384 * q^69 + 336 * q^70 + 1488 * q^72 + 308 * q^74 + 768 * q^75 + 1024 * q^76 - 224 * q^77 - 408 * q^78 + 1024 * q^79 - 1040 * q^80 - 240 * q^82 - 1384 * q^86 + 896 * q^87 - 560 * q^88 - 1320 * q^90 - 380 * q^92 - 936 * q^94 - 1088 * q^96 - 512 * q^99

Introduction

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