LMFDB - Embedded newform 66.3.f.a.13.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [66,3,Mod(7,66)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("66.7"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(66, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 66 = 2 \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	66.f (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.79836974478$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.6879707136000000000000.7
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 15x^{12} - 56x^{10} + 209x^{8} - 56x^{6} + 15x^{4} - 4x^{2} + 1 $ x^16 - 4x^14 + 15x^12 - 56x^10 + 209x^8 - 56x^6 + 15x^4 - 4*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.2
Root			$1.13551 - 1.56290i$ of defining polynomial
Character	$\chi$	$=$	66.13
Dual form			66.3.f.a.61.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34500 - 0.437016i) q^{2} +(1.40126 - 1.01807i) q^{3} +(1.61803 + 1.17557i) q^{4} +(1.96126 + 6.03615i) q^{5} +(-2.32960 + 0.756934i) q^{6} +(5.91718 - 8.14430i) q^{7} +(-1.66251 - 2.28825i) q^{8} +(0.927051 - 2.85317i) q^{9} -8.97571i q^{10} +(10.7270 + 2.43542i) q^{11} +3.46410 q^{12} +(-1.07106 - 0.348007i) q^{13} +(-11.5178 + 8.36815i) q^{14} +(8.89348 + 6.46149i) q^{15} +(1.23607 + 3.80423i) q^{16} +(-18.8514 + 6.12519i) q^{17} +(-2.49376 + 3.43237i) q^{18} +(0.867726 + 1.19432i) q^{19} +(-3.92253 + 12.0723i) q^{20} -17.4364i q^{21} +(-13.3635 - 7.96351i) q^{22} -38.3012 q^{23} +(-4.65921 - 1.51387i) q^{24} +(-12.3631 + 8.98233i) q^{25} +(1.28848 + 0.936136i) q^{26} +(-1.60570 - 4.94183i) q^{27} +(19.1484 - 6.22169i) q^{28} +(10.1256 - 13.9367i) q^{29} +(-9.13793 - 12.5773i) q^{30} +(-18.5793 + 57.1814i) q^{31} -5.65685i q^{32} +(17.5108 - 7.50823i) q^{33} +28.0319 q^{34} +(60.7653 + 19.7439i) q^{35} +(4.85410 - 3.52671i) q^{36} +(-19.5450 - 14.2003i) q^{37} +(-0.645151 - 1.98557i) q^{38} +(-1.85512 + 0.602766i) q^{39} +(10.5516 - 14.5230i) q^{40} +(-19.6761 - 27.0818i) q^{41} +(-7.61998 + 23.4519i) q^{42} -42.3015i q^{43} +(14.4937 + 16.5509i) q^{44} +19.0404 q^{45} +(51.5150 + 16.7382i) q^{46} +(48.3094 - 35.0988i) q^{47} +(5.60503 + 4.07230i) q^{48} +(-16.1747 - 49.7808i) q^{49} +(20.5538 - 6.67833i) q^{50} +(-20.1798 + 27.7751i) q^{51} +(-1.32390 - 1.82219i) q^{52} +(-7.40816 + 22.8000i) q^{53} +7.34847i q^{54} +(6.33793 + 69.5263i) q^{55} -28.4735 q^{56} +(2.43182 + 0.790145i) q^{57} +(-19.7095 + 14.3198i) q^{58} +(-35.0787 - 25.4862i) q^{59} +(6.79402 + 20.9098i) q^{60} +(-97.0652 + 31.5384i) q^{61} +(49.9783 - 68.7893i) q^{62} +(-17.7515 - 24.4329i) q^{63} +(-2.47214 + 7.60845i) q^{64} -7.14758i q^{65} +(-26.8331 + 2.44607i) q^{66} +110.204 q^{67} +(-37.7028 - 12.2504i) q^{68} +(-53.6699 + 38.9934i) q^{69} +(-73.1008 - 53.1109i) q^{70} +(10.2735 + 31.6186i) q^{71} +(-8.06998 + 2.62210i) q^{72} +(-26.8929 + 37.0149i) q^{73} +(20.0822 + 27.6408i) q^{74} +(-8.17925 + 25.1731i) q^{75} +2.95253i q^{76} +(83.3084 - 72.9531i) q^{77} +2.75855 q^{78} +(73.0619 + 23.7393i) q^{79} +(-20.5386 + 14.9222i) q^{80} +(-7.28115 - 5.29007i) q^{81} +(14.6291 + 45.0237i) q^{82} +(-67.1877 + 21.8306i) q^{83} +(20.4977 - 28.2127i) q^{84} +(-73.9451 - 101.777i) q^{85} +(-18.4864 + 56.8953i) q^{86} -29.8376i q^{87} +(-12.2609 - 28.5949i) q^{88} +53.1788 q^{89} +(-25.6092 - 8.32094i) q^{90} +(-9.17190 + 6.66377i) q^{91} +(-61.9726 - 45.0258i) q^{92} +(32.1804 + 99.0410i) q^{93} +(-80.3147 + 26.0958i) q^{94} +(-5.50727 + 7.58010i) q^{95} +(-5.75910 - 7.92672i) q^{96} +(33.4207 - 102.858i) q^{97} +74.0236i q^{98} +(16.8932 - 28.3482i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 8 q^{5} + 60 q^{7} - 12 q^{9} - 4 q^{11} - 60 q^{13} - 32 q^{14} + 12 q^{15} - 16 q^{16} - 60 q^{17} - 16 q^{20} - 48 q^{22} - 8 q^{23} - 48 q^{25} + 48 q^{26} + 40 q^{28} - 160 q^{29}+ \cdots + 48 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 8 * q^5 + 60 * q^7 - 12 * q^9 - 4 * q^11 - 60 * q^13 - 32 * q^14 + 12 * q^15 - 16 * q^16 - 60 * q^17 - 16 * q^20 - 48 * q^22 - 8 * q^23 - 48 * q^25 + 48 * q^26 + 40 * q^28 - 160 * q^29 + 32 * q^31 + 36 * q^33 - 64 * q^34 + 160 * q^35 + 24 * q^36 - 84 * q^37 - 48 * q^38 - 80 * q^40 + 40 * q^41 + 96 * q^42 + 168 * q^44 + 24 * q^45 + 160 * q^46 + 372 * q^47 + 96 * q^49 + 160 * q^50 + 120 * q^51 + 40 * q^52 - 124 * q^53 + 32 * q^55 - 96 * q^56 - 120 * q^57 - 16 * q^58 - 172 * q^59 - 24 * q^60 + 100 * q^61 - 40 * q^62 - 180 * q^63 + 32 * q^64 - 216 * q^66 + 248 * q^67 - 120 * q^68 - 372 * q^69 + 8 * q^70 + 48 * q^71 + 160 * q^73 + 80 * q^74 + 192 * q^75 - 172 * q^77 - 460 * q^79 - 48 * q^80 - 36 * q^81 - 24 * q^82 - 420 * q^83 - 420 * q^85 - 456 * q^86 - 144 * q^88 - 360 * q^89 - 252 * q^91 - 64 * q^92 - 24 * q^93 - 280 * q^94 + 180 * q^95 + 324 * q^97 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/66\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$

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 $

$2$	−1.34500	−	0.437016i	−0.672499	−	0.218508i
$2$	−1.34500	−	0.437016i	−0.672499	−	0.218508i
$3$	1.40126	−	1.01807i	0.467086	−	0.339358i
$3$	1.40126	−	1.01807i	0.467086	−	0.339358i
$4$	1.61803	+	1.17557i	0.404508	+	0.293893i
$5$	1.96126	+	6.03615i	0.392253	+	1.20723i	0.931080	+	0.364814i	$0.118867\pi$
$5$	1.96126	+	6.03615i	0.392253	+	1.20723i	−0.538828	+	0.842416i	$0.681133\pi$
$6$	−2.32960	+	0.756934i	−0.388267	+	0.126156i
$7$	5.91718	−	8.14430i	0.845311	−	1.16347i	−0.139565	−	0.990213i	$-0.544570\pi$
$7$	5.91718	−	8.14430i	0.845311	−	1.16347i	0.984876	−	0.173258i	$-0.0554295\pi$
$8$	−1.66251	−	2.28825i	−0.207813	−	0.286031i
$9$	0.927051	−	2.85317i	0.103006	−	0.317019i
$10$		−	8.97571i		−	0.897571i
$11$	10.7270	+	2.43542i	0.975183	+	0.221402i
$11$	10.7270	+	2.43542i	0.975183	+	0.221402i
$12$	3.46410			0.288675
$13$	−1.07106	−	0.348007i	−0.0823889	−	0.0267698i	0.267533	−	0.963549i	$-0.413792\pi$
$13$	−1.07106	−	0.348007i	−0.0823889	−	0.0267698i	−0.349921	+	0.936779i	$0.613792\pi$
$14$	−11.5178	+	8.36815i	−0.822698	+	0.597725i
$15$	8.89348	+	6.46149i	0.592899	+	0.430766i
$16$	1.23607	+	3.80423i	0.0772542	+	0.237764i
$17$	−18.8514	+	6.12519i	−1.10891	+	0.360305i	−0.805524	−	0.592564i	$-0.798116\pi$
$17$	−18.8514	+	6.12519i	−1.10891	+	0.360305i	−0.303382	+	0.952869i	$0.598116\pi$
$18$	−2.49376	+	3.43237i	−0.138542	+	0.190687i
$19$	0.867726	+	1.19432i	0.0456698	+	0.0628591i	0.831241	−	0.555912i	$-0.187631\pi$
$19$	0.867726	+	1.19432i	0.0456698	+	0.0628591i	−0.785571	+	0.618771i	$0.787631\pi$
$20$	−3.92253	+	12.0723i	−0.196126	+	0.603615i
$21$		−	17.4364i		−	0.830304i
$22$	−13.3635	−	7.96351i	−0.607431	−	0.361978i
$23$	−38.3012			−1.66527			−0.832635	−	0.553823i	$-0.813169\pi$
$23$	−38.3012			−1.66527			−0.832635	+	0.553823i	$0.813169\pi$
$24$	−4.65921	−	1.51387i	−0.194134	−	0.0630778i
$25$	−12.3631	+	8.98233i	−0.494525	+	0.359293i
$26$	1.28848	+	0.936136i	0.0495570	+	0.0360052i
$27$	−1.60570	−	4.94183i	−0.0594703	−	0.183031i
$28$	19.1484	−	6.22169i	0.683871	−	0.222203i
$29$	10.1256	−	13.9367i	0.349159	−	0.480577i	−0.597929	−	0.801549i	$-0.704010\pi$
$29$	10.1256	−	13.9367i	0.349159	−	0.480577i	0.947089	+	0.320972i	$0.104010\pi$
$30$	−9.13793	−	12.5773i	−0.304598	−	0.419243i
$31$	−18.5793	+	57.1814i	−0.599334	+	1.84456i	−0.0674851	+	0.997720i	$0.521498\pi$
$31$	−18.5793	+	57.1814i	−0.599334	+	1.84456i	−0.531849	+	0.846839i	$0.678502\pi$
$32$		−	5.65685i		−	0.176777i
$33$	17.5108	−	7.50823i	0.530629	−	0.227522i
$34$	28.0319			0.824467
$35$	60.7653	+	19.7439i	1.73615	+	0.564110i
$36$	4.85410	−	3.52671i	0.134836	−	0.0979642i
$37$	−19.5450	−	14.2003i	−0.528243	−	0.383791i	0.291457	−	0.956584i	$-0.405860\pi$
$37$	−19.5450	−	14.2003i	−0.528243	−	0.383791i	−0.819700	+	0.572793i	$0.805860\pi$
$38$	−0.645151	−	1.98557i	−0.0169777	−	0.0522518i
$39$	−1.85512	+	0.602766i	−0.0475672	+	0.0154555i
$40$	10.5516	−	14.5230i	0.263789	−	0.363075i
$41$	−19.6761	−	27.0818i	−0.479905	−	0.660532i	0.498582	−	0.866843i	$-0.333854\pi$
$41$	−19.6761	−	27.0818i	−0.479905	−	0.660532i	−0.978487	+	0.206310i	$0.933854\pi$
$42$	−7.61998	+	23.4519i	−0.181428	+	0.558378i
$43$		−	42.3015i		−	0.983755i	−0.870664	−	0.491877i	$-0.836311\pi$
$43$		−	42.3015i		−	0.983755i	0.870664	−	0.491877i	$-0.163689\pi$
$44$	14.4937	+	16.5509i	0.329401	+	0.376158i
$45$	19.0404			0.423119
$46$	51.5150	+	16.7382i	1.11989	+	0.363875i
$47$	48.3094	−	35.0988i	1.02786	−	0.746783i	0.0599802	−	0.998200i	$-0.480896\pi$
$47$	48.3094	−	35.0988i	1.02786	−	0.746783i	0.967879	+	0.251416i	$0.0808962\pi$
$48$	5.60503	+	4.07230i	0.116772	+	0.0848395i
$49$	−16.1747	−	49.7808i	−0.330097	−	1.01593i
$50$	20.5538	−	6.67833i	0.411076	−	0.133567i
$51$	−20.1798	+	27.7751i	−0.395682	+	0.544610i
$52$	−1.32390	−	1.82219i	−0.0254596	−	0.0350421i
$53$	−7.40816	+	22.8000i	−0.139777	+	0.430188i	−0.996302	−	0.0859161i	$-0.972618\pi$
$53$	−7.40816	+	22.8000i	−0.139777	+	0.430188i	0.856526	+	0.516104i	$0.172618\pi$
$54$			7.34847i			0.136083i
$55$	6.33793	+	69.5263i	0.115235	+	1.26412i
$56$	−28.4735			−0.508456
$57$	2.43182	+	0.790145i	0.0426634	+	0.0138622i
$58$	−19.7095	+	14.3198i	−0.339819	+	0.246893i
$59$	−35.0787	−	25.4862i	−0.594554	−	0.431969i	0.249388	−	0.968404i	$-0.419771\pi$
$59$	−35.0787	−	25.4862i	−0.594554	−	0.431969i	−0.843942	+	0.536435i	$0.819771\pi$
$60$	6.79402	+	20.9098i	0.113234	+	0.348497i
$61$	−97.0652	+	31.5384i	−1.59123	+	0.517023i	−0.964919	−	0.262548i	$-0.915437\pi$
$61$	−97.0652	+	31.5384i	−1.59123	+	0.517023i	−0.626314	+	0.779571i	$0.715437\pi$
$62$	49.9783	−	68.7893i	0.806102	−	1.10950i
$63$	−17.7515	−	24.4329i	−0.281770	−	0.387824i
$64$	−2.47214	+	7.60845i	−0.0386271	+	0.118882i
$65$		−	7.14758i		−	0.109963i
$66$	−26.8331	+	2.44607i	−0.406563	+	0.0370617i
$67$	110.204			1.64483			0.822417	−	0.568884i	$-0.192625\pi$
$67$	110.204			1.64483			0.822417	+	0.568884i	$0.192625\pi$
$68$	−37.7028	−	12.2504i	−0.554453	−	0.180153i
$69$	−53.6699	+	38.9934i	−0.777824	+	0.565122i
$70$	−73.1008	−	53.1109i	−1.04430	−	0.758727i
$71$	10.2735	+	31.6186i	0.144697	+	0.445332i	0.996972	−	0.0777625i	$-0.0247776\pi$
$71$	10.2735	+	31.6186i	0.144697	+	0.445332i	−0.852275	+	0.523094i	$0.824778\pi$
$72$	−8.06998	+	2.62210i	−0.112083	+	0.0364180i
$73$	−26.8929	+	37.0149i	−0.368395	+	0.507053i	−0.952464	−	0.304652i	$-0.901460\pi$
$73$	−26.8929	+	37.0149i	−0.368395	+	0.507053i	0.584068	+	0.811704i	$0.301460\pi$
$74$	20.0822	+	27.6408i	0.271381	+	0.373524i
$75$	−8.17925	+	25.1731i	−0.109057	+	0.335642i
$76$			2.95253i			0.0388490i
$77$	83.3084	−	72.9531i	1.08193	−	0.947443i
$78$	2.75855			0.0353660
$79$	73.0619	+	23.7393i	0.924835	+	0.300497i	0.732449	−	0.680822i	$-0.238377\pi$
$79$	73.0619	+	23.7393i	0.924835	+	0.300497i	0.192386	+	0.981319i	$0.438377\pi$
$80$	−20.5386	+	14.9222i	−0.256733	+	0.186527i
$81$	−7.28115	−	5.29007i	−0.0898908	−	0.0653095i
$82$	14.6291	+	45.0237i	0.178404	+	0.549070i
$83$	−67.1877	+	21.8306i	−0.809490	+	0.263019i	−0.684382	−	0.729124i	$-0.739928\pi$
$83$	−67.1877	+	21.8306i	−0.809490	+	0.263019i	−0.125108	+	0.992143i	$0.539928\pi$
$84$	20.4977	−	28.2127i	0.244020	−	0.335865i
$85$	−73.9451	−	101.777i	−0.869943	−	1.19737i
$86$	−18.4864	+	56.8953i	−0.214958	+	0.661574i
$87$		−	29.8376i		−	0.342961i
$88$	−12.2609	−	28.5949i	−0.139328	−	0.324942i
$89$	53.1788			0.597514			0.298757	−	0.954329i	$-0.403428\pi$
$89$	53.1788			0.597514			0.298757	+	0.954329i	$0.403428\pi$
$90$	−25.6092	−	8.32094i	−0.284547	−	0.0924549i
$91$	−9.17190	+	6.66377i	−0.100790	+	0.0732283i
$92$	−61.9726	−	45.0258i	−0.673616	−	0.489410i
$93$	32.1804	+	99.0410i	0.346026	+	1.06496i
$94$	−80.3147	+	26.0958i	−0.854412	+	0.277615i
$95$	−5.50727	+	7.58010i	−0.0579712	+	0.0797906i
$96$	−5.75910	−	7.92672i	−0.0599906	−	0.0825700i
$97$	33.4207	−	102.858i	0.344543	−	1.06039i	−0.617285	−	0.786740i	$-0.711767\pi$
$97$	33.4207	−	102.858i	0.344543	−	1.06039i	0.961828	−	0.273655i	$-0.0882326\pi$
$98$			74.0236i			0.755343i
$99$	16.8932	−	28.3482i	0.170638	−	0.286346i
$100$	−30.5633			−0.305633
$101$	3.21182	+	1.04358i	0.0318002	+	0.0103325i	0.324874	−	0.945757i	$-0.394678\pi$
$101$	3.21182	+	1.04358i	0.0318002	+	0.0103325i	−0.293074	+	0.956090i	$0.594678\pi$
$102$	39.2799	−	28.5385i	0.385097	−	0.279789i
$103$	94.7070	+	68.8087i	0.919486	+	0.668046i	0.943396	−	0.331669i	$-0.107612\pi$
$103$	94.7070	+	68.8087i	0.919486	+	0.668046i	−0.0239101	+	0.999714i	$0.507612\pi$
$104$	0.984312	+	3.02940i	0.00946454	+	0.0291289i
$105$	105.249	−	34.1974i	1.00237	−	0.325689i
$106$	19.9279	−	27.4284i	0.187999	−	0.258759i
$107$	−35.0548	−	48.2488i	−0.327615	−	0.450923i	0.613158	−	0.789960i	$-0.289899\pi$
$107$	−35.0548	−	48.2488i	−0.327615	−	0.450923i	−0.940773	+	0.339037i	$0.889899\pi$
$108$	3.21140	−	9.88367i	0.0297352	−	0.0915155i
$109$			188.343i			1.72792i	0.503560	+	0.863961i	$0.332023\pi$
$109$			188.343i			1.72792i	−0.503560	+	0.863961i	$0.667977\pi$
$110$	21.8596	−	96.2825i	0.198724	−	0.875295i
$111$	−41.8445			−0.376978
$112$	38.2968	+	12.4434i	0.341936	+	0.111102i
$113$	−6.71498	+	4.87872i	−0.0594246	+	0.0431745i	−0.617101	−	0.786884i	$-0.711693\pi$
$113$	−6.71498	+	4.87872i	−0.0594246	+	0.0431745i	0.557676	+	0.830058i	$0.311693\pi$
$114$	−2.92548	−	2.12549i	−0.0256621	−	0.0186446i
$115$	−75.1188	−	231.192i	−0.653207	−	2.01036i
$116$	32.7672	−	10.6467i	0.282476	−	0.0917819i
$117$	−1.98585	+	2.73328i	−0.0169730	+	0.0233614i
$118$	36.0429	+	49.6088i	0.305448	+	0.420413i
$119$	−61.6617	+	189.775i	−0.518166	+	1.59475i
$120$		−	31.0928i		−	0.259106i
$121$	109.137	+	52.2496i	0.901962	+	0.431815i
$122$	144.335			1.18308
$123$	−55.1426	−	17.9169i	−0.448314	−	0.145666i
$124$	−97.2827	+	70.6800i	−0.784538	+	0.570000i
$125$	49.9003	+	36.2547i	0.399203	+	0.290038i
$126$	13.1982	+	40.6199i	0.104748	+	0.322380i
$127$	118.780	−	38.5938i	0.935272	−	0.303888i	0.198555	−	0.980090i	$-0.436375\pi$
$127$	118.780	−	38.5938i	0.935272	−	0.303888i	0.736717	+	0.676201i	$0.236375\pi$
$128$	6.65003	−	9.15298i	0.0519534	−	0.0715077i
$129$	−43.0660	−	59.2753i	−0.333845	−	0.459498i
$130$	−3.12361	+	9.61348i	−0.0240278	+	0.0739498i
$131$		−	43.0571i		−	0.328680i	−0.986404	−	0.164340i	$-0.947451\pi$
$131$		−	43.0571i		−	0.328680i	0.986404	−	0.164340i	$-0.0525494\pi$
$132$	37.1595	+	8.43654i	0.281511	+	0.0639132i
$133$	14.8614			0.111740
$134$	−148.224	−	48.1609i	−1.10615	−	0.359410i
$135$	26.6805	−	19.3845i	0.197633	−	0.143589i
$136$	45.3565	+	32.9534i	0.333504	+	0.242305i
$137$	−5.36340	−	16.5069i	−0.0391489	−	0.120488i	0.929572	−	0.368640i	$-0.120177\pi$
$137$	−5.36340	−	16.5069i	−0.0391489	−	0.120488i	−0.968721	+	0.248152i	$0.920177\pi$
$138$	89.2266	−	28.9915i	0.646569	−	0.210083i
$139$	20.9854	−	28.8839i	0.150974	−	0.207798i	−0.726831	−	0.686817i	$-0.759007\pi$
$139$	20.9854	−	28.8839i	0.150974	−	0.207798i	0.877805	+	0.479019i	$0.159007\pi$
$140$	75.1101	+	103.380i	0.536501	+	0.738430i
$141$	31.9607	−	98.3651i	0.226672	−	0.697624i
$142$		−	47.0165i		−	0.331102i
$143$	−10.6417	−	6.34154i	−0.0744173	−	0.0443465i
$144$	12.0000			0.0833333
$145$	103.983	+	33.7862i	0.717125	+	0.233008i
$146$	52.3469	−	38.0323i	0.358541	−	0.260495i
$147$	−73.3455	−	53.2886i	−0.498949	−	0.362508i
$148$	−14.9311	−	45.9531i	−0.100885	−	0.310494i
$149$	0.203427	−	0.0660976i	0.00136529	−	0.000443608i	−0.308334	−	0.951278i	$-0.599772\pi$
$149$	0.203427	−	0.0660976i	0.00136529	−	0.000443608i	0.309700	+	0.950834i	$0.399772\pi$
$150$	22.0021	−	30.2833i	0.146681	−	0.201889i
$151$	−60.5076	−	83.2816i	−0.400713	−	0.551534i	0.560210	−	0.828351i	$-0.310720\pi$
$151$	−60.5076	−	83.2816i	−0.400713	−	0.551534i	−0.960923	+	0.276817i	$0.910720\pi$
$152$	1.29030	−	3.97114i	0.00848883	−	0.0261259i
$153$			59.4646i			0.388657i
$154$	−143.931	+	61.7146i	−0.934619	+	0.400744i
$155$	−381.594			−2.46190
$156$	−3.71024	−	1.20553i	−0.0237836	−	0.00772776i
$157$	−60.8637	+	44.2201i	−0.387667	+	0.281657i	−0.764499	−	0.644625i	$-0.777013\pi$
$157$	−60.8637	+	44.2201i	−0.387667	+	0.281657i	0.376832	+	0.926282i	$0.377013\pi$
$158$	−87.8937	−	63.8585i	−0.556289	−	0.404168i
$159$	12.8313	+	39.4907i	0.0807000	+	0.248369i
$160$	34.1456	−	11.0946i	0.213410	−	0.0693412i
$161$	−226.635	+	311.936i	−1.40767	+	1.93749i
$162$	7.48128	+	10.2971i	0.0461808	+	0.0635624i
$163$	59.3669	−	182.712i	0.364214	−	1.12094i	−0.586258	−	0.810125i	$-0.699399\pi$
$163$	59.3669	−	182.712i	0.364214	−	1.12094i	0.950472	−	0.310811i	$-0.100601\pi$
$164$		−	66.9500i		−	0.408231i
$165$	79.6640	+	90.9719i	0.482812	+	0.551345i
$166$	99.9076			0.601853
$167$	−146.413	−	47.5726i	−0.876727	−	0.284866i	−0.164129	−	0.986439i	$-0.552481\pi$
$167$	−146.413	−	47.5726i	−0.876727	−	0.284866i	−0.712598	+	0.701573i	$0.752481\pi$
$168$	−39.8987	+	28.9881i	−0.237493	+	0.172548i
$169$	−135.698	−	98.5902i	−0.802946	−	0.583374i
$170$	54.9779	+	169.205i	0.323399	+	0.995321i
$171$	4.21203	−	1.36857i	0.0246318	−	0.00800334i
$172$	49.7284	−	68.4452i	0.289118	−	0.397937i
$173$	193.249	+	265.985i	1.11705	+	1.53749i	0.810602	+	0.585597i	$0.199140\pi$
$173$	193.249	+	265.985i	1.11705	+	1.53749i	0.306446	+	0.951888i	$0.400860\pi$
$174$	−13.0395	+	40.1314i	−0.0749396	+	0.230641i
$175$			153.839i			0.879080i
$176$	3.99442	+	43.8183i	0.0226956	+	0.248968i
$177$	−75.1011			−0.424300
$178$	−71.5253	−	23.2400i	−0.401828	−	0.130562i
$179$	101.266	−	73.5741i	0.565732	−	0.411029i	−0.267820	−	0.963469i	$-0.586303\pi$
$179$	101.266	−	73.5741i	0.565732	−	0.411029i	0.833552	+	0.552440i	$0.186303\pi$
$180$	30.8079	+	22.3833i	0.171155	+	0.124352i
$181$	−49.8275	−	153.353i	−0.275290	−	0.847255i	−0.989143	−	0.146959i	$-0.953051\pi$
$181$	−49.8275	−	153.353i	−0.275290	−	0.847255i	0.713853	−	0.700296i	$-0.246949\pi$
$182$	15.2483	−	4.95449i	0.0837821	−	0.0272225i
$183$	−103.905	+	143.013i	−0.567787	+	0.781492i
$184$	63.6760	+	87.6425i	0.346065	+	0.476318i
$185$	47.3821	−	145.827i	0.256119	−	0.788254i
$186$		−	147.273i		−	0.791791i
$187$	−217.137	+	19.7939i	−1.16116	+	0.105850i
$188$	119.427			0.635252
$189$	−49.7490	−	16.1644i	−0.263222	−	0.0855261i
$190$	10.7199	−	7.78845i	0.0564204	−	0.0409919i
$191$	199.335	+	144.825i	1.04364	+	0.758247i	0.970992	−	0.239110i	$-0.0768558\pi$
$191$	199.335	+	144.825i	1.04364	+	0.758247i	0.0726456	+	0.997358i	$0.476856\pi$
$192$	4.28187	+	13.1782i	0.0223014	+	0.0686366i
$193$	−258.540	+	84.0049i	−1.33959	+	0.435258i	−0.889177	−	0.457563i	$-0.848722\pi$
$193$	−258.540	+	84.0049i	−1.33959	+	0.435258i	−0.450410	+	0.892822i	$0.648722\pi$
$194$	−89.9014	+	123.739i	−0.463409	+	0.637828i
$195$	−7.27677	−	10.0156i	−0.0373168	−	0.0513621i
$196$	32.3495	−	99.5615i	0.165048	−	0.507967i
$197$		−	371.771i		−	1.88716i	−0.331139	−	0.943582i	$-0.607433\pi$
$197$		−	371.771i		−	1.88716i	0.331139	−	0.943582i	$-0.392567\pi$
$198$	−35.1099	+	30.7457i	−0.177323	+	0.155281i
$199$	113.221			0.568951			0.284476	−	0.958683i	$-0.408180\pi$
$199$	113.221			0.568951			0.284476	+	0.958683i	$0.408180\pi$
$200$	41.1076	+	13.3567i	0.205538	+	0.0667833i
$201$	154.424	−	112.196i	0.768280	−	0.558188i
$202$	−3.86382	−	2.80723i	−0.0191278	−	0.0138972i
$203$	−53.5897	−	164.932i	−0.263989	−	0.812473i
$204$	−65.3031	+	21.2183i	−0.320113	+	0.104011i
$205$	124.880	−	171.882i	0.609170	−	0.838451i
$206$	−97.3102	−	133.936i	−0.472380	−	0.650175i
$207$	−35.5072	+	109.280i	−0.171532	+	0.527922i
$208$		−	4.50470i		−	0.0216572i
$209$	6.39943	+	14.9248i	0.0306193	+	0.0714104i
$210$	−156.504			−0.745257
$211$	125.892	+	40.9049i	0.596646	+	0.193862i	0.591744	−	0.806126i	$-0.298440\pi$
$211$	125.892	+	40.9049i	0.596646	+	0.193862i	0.00490194	+	0.999988i	$0.498440\pi$
$212$	−38.7896	+	28.1823i	−0.182970	+	0.132935i
$213$	46.5858	+	33.8466i	0.218713	+	0.158904i
$214$	26.0631	+	80.2140i	0.121790	+	0.374832i
$215$	255.338	−	82.9643i	1.18762	−	0.385881i
$216$	−8.63864	+	11.8901i	−0.0399937	+	0.0550466i
$217$	355.765	+	489.668i	1.63947	+	2.25653i
$218$	82.3091	−	253.321i	0.377565	−	1.16202i
$219$			79.2463i			0.361855i
$220$	−71.4781	+	119.947i	−0.324901	+	0.545212i
$221$	22.3225			0.101007
$222$	56.2808	+	18.2867i	0.253517	+	0.0823727i
$223$	−108.333	+	78.7084i	−0.485798	+	0.352953i	−0.803566	−	0.595216i	$-0.797067\pi$
$223$	−108.333	+	78.7084i	−0.485798	+	0.352953i	0.317768	+	0.948168i	$0.397067\pi$
$224$	−46.0711	−	33.4726i	−0.205675	−	0.149431i
$225$	14.1669	+	43.6012i	0.0629639	+	0.193783i
$226$	11.1637	−	3.62731i	0.0493969	−	0.0160500i
$227$	225.392	−	310.225i	0.992914	−	1.36663i	0.0633412	−	0.997992i	$-0.479824\pi$
$227$	225.392	−	310.225i	0.992914	−	1.36663i	0.929573	−	0.368637i	$-0.120176\pi$
$228$	3.00589	+	4.13725i	0.0131837	+	0.0181458i
$229$	31.3827	−	96.5861i	0.137042	−	0.421773i	−0.858860	−	0.512211i	$-0.828827\pi$
$229$	31.3827	−	96.5861i	0.137042	−	0.421773i	0.995902	+	0.0904376i	$0.0288266\pi$
$230$			343.780i			1.49470i
$231$	42.4649	−	187.040i	0.183831	−	0.809698i
$232$	−48.7246			−0.210020
$233$	35.8160	+	11.6373i	0.153717	+	0.0499457i	0.384865	−	0.922973i	$-0.374248\pi$
$233$	35.8160	+	11.6373i	0.153717	+	0.0499457i	−0.231148	+	0.972919i	$0.574248\pi$
$234$	3.86544	−	2.80841i	0.0165190	−	0.0120017i
$235$	306.609	+	222.765i	1.30472	+	0.947935i
$236$	−26.7977	−	82.4750i	−0.113550	−	0.349470i
$237$	126.547	−	41.1176i	0.533954	−	0.173492i
$238$	165.870	−	228.300i	0.696931	−	0.959243i
$239$	−71.1372	−	97.9120i	−0.297645	−	0.409674i	0.633833	−	0.773470i	$-0.281480\pi$
$239$	−71.1372	−	97.9120i	−0.297645	−	0.409674i	−0.931479	+	0.363796i	$0.881480\pi$
$240$	−13.5880	+	41.8197i	−0.0566168	+	0.174249i
$241$			25.2413i			0.104736i	0.998628	+	0.0523679i	$0.0166768\pi$
$241$			25.2413i			0.104736i	−0.998628	+	0.0523679i	$0.983323\pi$
$242$	−123.956	−	117.970i	−0.512213	−	0.487481i
$243$	−15.5885			−0.0641500
$244$	−194.130	−	63.0768i	−0.795616	−	0.258511i
$245$	268.761	−	195.266i	1.09698	−	0.797006i
$246$	66.3367	+	48.1964i	0.269661	+	0.195920i
$247$	−0.513750	−	1.58116i	−0.00207996	−	0.00640145i
$248$	161.733	−	52.5503i	0.652150	−	0.211896i
$249$	−71.9222	+	98.9924i	−0.288844	+	0.397560i
$250$	−51.2719	−	70.5697i	−0.205088	−	0.282279i
$251$	46.2888	−	142.462i	0.184417	−	0.567578i	−0.815520	−	0.578728i	$-0.803549\pi$
$251$	46.2888	−	142.462i	0.184417	−	0.567578i	0.999938	+	0.0111499i	$0.00354919\pi$
$252$		−	60.4014i		−	0.239688i
$253$	−410.857	−	93.2795i	−1.62394	−	0.368694i
$254$	−176.624			−0.695371
$255$	−207.232	−	67.3339i	−0.812676	−	0.264055i
$256$	−12.9443	+	9.40456i	−0.0505636	+	0.0367366i
$257$	326.640	+	237.318i	1.27097	+	0.923416i	0.999241	−	0.0389575i	$-0.0124037\pi$
$257$	326.640	+	237.318i	1.27097	+	0.923416i	0.271732	+	0.962373i	$0.412404\pi$
$258$	32.0194	+	98.5456i	0.124106	+	0.381960i
$259$	−231.303	+	75.1547i	−0.893060	+	0.290173i
$260$	8.40249	−	11.5650i	0.0323173	−	0.0444809i
$261$	−30.3769	−	41.8102i	−0.116386	−	0.160192i
$262$	−18.8166	+	57.9116i	−0.0718192	+	0.221037i
$263$			163.005i			0.619790i	0.950771	+	0.309895i	$0.100294\pi$
$263$			163.005i			0.619790i	−0.950771	+	0.309895i	$0.899706\pi$
$264$	−46.2924	−	27.5864i	−0.175350	−	0.104494i
$265$	−152.153			−0.574164
$266$	−19.9885	−	6.49467i	−0.0751449	−	0.0244161i
$267$	74.5172	−	54.1399i	0.279091	−	0.202771i
$268$	178.314	+	129.552i	0.665350	+	0.483405i
$269$	109.868	+	338.138i	0.408431	+	1.25702i	0.917996	+	0.396589i	$0.129806\pi$
$269$	109.868	+	338.138i	0.408431	+	1.25702i	−0.509566	+	0.860432i	$0.670194\pi$
$270$	−44.3565	+	14.4123i	−0.164283	+	0.0533788i
$271$	−261.630	+	360.103i	−0.965424	+	1.32879i	−0.0210996	+	0.999777i	$0.506717\pi$
$271$	−261.630	+	360.103i	−0.965424	+	1.32879i	−0.944325	+	0.329015i	$0.893283\pi$
$272$	−46.6032	−	64.1438i	−0.171335	−	0.235823i
$273$	−6.06798	+	18.6753i	−0.0222271	+	0.0684078i
$274$			24.5456i			0.0895823i
$275$	−154.495	+	66.2442i	−0.561800	+	0.240888i
$276$	−132.679			−0.480722
$277$	−97.4558	−	31.6653i	−0.351826	−	0.114315i	0.127772	−	0.991804i	$-0.459217\pi$
$277$	−97.4558	−	31.6653i	−0.351826	−	0.114315i	−0.479598	+	0.877488i	$0.659217\pi$
$278$	−40.8480	+	29.6778i	−0.146935	+	0.106755i
$279$	145.924	+	106.020i	0.523025	+	0.380000i
$280$	−55.8441	−	171.870i	−0.199443	−	0.613823i
$281$	−139.633	+	45.3696i	−0.496915	+	0.161458i	−0.546743	−	0.837300i	$-0.684133\pi$
$281$	−139.633	+	45.3696i	−0.496915	+	0.161458i	0.0498281	+	0.998758i	$0.484133\pi$
$282$	−85.9742	+	118.333i	−0.304873	+	0.419622i
$283$	−75.7942	−	104.322i	−0.267824	−	0.368628i	0.653829	−	0.756642i	$-0.273161\pi$
$283$	−75.7942	−	104.322i	−0.267824	−	0.368628i	−0.921654	+	0.388014i	$0.873161\pi$
$284$	−20.5470	+	63.2371i	−0.0723485	+	0.222666i
$285$			16.2285i			0.0569421i
$286$	11.5417	+	13.1799i	0.0403555	+	0.0460837i
$287$	−336.989			−1.17418
$288$	−16.1400	−	5.24419i	−0.0560415	−	0.0182090i
$289$	84.0512	−	61.0668i	0.290835	−	0.211304i
$290$	−125.092	−	90.8846i	−0.431351	−	0.313395i
$291$	−57.8863	−	178.156i	−0.198922	−	0.612219i
$292$	−87.0271	+	28.2768i	−0.298038	+	0.0968385i
$293$	−42.8674	+	59.0020i	−0.146305	+	0.201372i	−0.875880	−	0.482529i	$-0.839718\pi$
$293$	−42.8674	+	59.0020i	−0.146305	+	0.201372i	0.729574	+	0.683901i	$0.239718\pi$
$294$	75.3615	+	103.726i	0.256332	+	0.352810i
$295$	85.0397	−	261.725i	0.288270	−	0.887205i
$296$			68.3318i			0.230851i
$297$	−5.18891	−	56.9217i	−0.0174711	−	0.191655i
$298$	−0.302495			−0.00101508
$299$	41.0227	+	13.3291i	0.137200	+	0.0445789i
$300$	−42.8271	+	31.1157i	−0.142757	+	0.103719i
$301$	−344.516	−	250.305i	−1.14457	−	0.831579i
$302$	44.9872	+	138.456i	0.148964	+	0.458465i
$303$	5.56303	−	1.80754i	0.0183598	−	0.00596548i
$304$	−3.47090	+	4.77729i	−0.0114174	+	0.0157148i
$305$	−380.741	−	524.045i	−1.24833	−	1.71818i
$306$	25.9870	−	79.9797i	0.0849248	−	0.261372i
$307$			243.270i			0.792409i	0.918162	+	0.396204i	$0.129673\pi$
$307$			243.270i			0.792409i	−0.918162	+	0.396204i	$0.870327\pi$
$308$	220.557	−	20.1057i	0.716095	−	0.0652784i
$309$	202.761			0.656186
$310$	513.243	+	166.763i	1.65562	+	0.537944i
$311$	−127.901	+	92.9257i	−0.411258	+	0.298797i	−0.774111	−	0.633050i	$-0.781803\pi$
$311$	−127.901	+	92.9257i	−0.411258	+	0.298797i	0.362853	+	0.931846i	$0.381803\pi$
$312$	4.46343	+	3.24287i	0.0143059	+	0.0103938i
$313$	−5.38606	−	16.5766i	−0.0172079	−	0.0529604i	0.942084	−	0.335377i	$-0.108864\pi$
$313$	−5.38606	−	16.5766i	−0.0172079	−	0.0529604i	−0.959292	+	0.282417i	$0.908864\pi$
$314$	101.186	−	32.8775i	0.322250	−	0.104705i
$315$	112.665	−	155.070i	0.357667	−	0.492287i
$316$	90.3095	+	124.300i	0.285790	+	0.393356i
$317$	−22.8323	+	70.2706i	−0.0720262	+	0.221674i	−0.980589	−	0.196074i	$-0.937181\pi$
$317$	−22.8323	+	70.2706i	−0.0720262	+	0.221674i	0.908563	+	0.417748i	$0.137181\pi$
$318$		−	58.7224i		−	0.184662i
$319$	142.559	−	124.839i	0.446895	−	0.391345i
$320$	−50.7743			−0.158670
$321$	−98.2416	−	31.9206i	−0.306049	−	0.0994412i
$322$	441.145	−	320.510i	1.37001	−	0.995374i
$323$	−23.6733	−	17.1997i	−0.0732919	−	0.0532497i
$324$	−5.56231	−	17.1190i	−0.0171676	−	0.0528365i
$325$	16.3675	−	5.31812i	0.0503615	−	0.0163635i
$326$	−159.697	+	219.803i	−0.489867	+	0.674244i
$327$	191.747	+	263.918i	0.586384	+	0.807088i
$328$	−29.2582	+	90.0475i	−0.0892018	+	0.274535i
$329$		−	601.132i		−	1.82715i
$330$	−67.3917	−	157.171i	−0.204217	−	0.476277i
$331$	418.904			1.26557			0.632786	−	0.774327i	$-0.281911\pi$
$331$	418.904			1.26557			0.632786	+	0.774327i	$0.281911\pi$
$332$	−134.375	−	43.6612i	−0.404745	−	0.131510i
$333$	−58.6350	+	42.6008i	−0.176081	+	0.127930i
$334$	176.136	+	127.970i	0.527352	+	0.383144i
$335$	216.139	+	665.207i	0.645191	+	1.98569i
$336$	66.3320	−	21.5526i	0.197417	−	0.0641445i
$337$	−90.0326	+	123.919i	−0.267159	+	0.367713i	−0.921428	−	0.388549i	$-0.872976\pi$
$337$	−90.0326	+	123.919i	−0.267159	+	0.367713i	0.654269	+	0.756262i	$0.272976\pi$
$338$	139.428	+	191.906i	0.412508	+	0.567768i
$339$	−4.44253	+	13.6727i	−0.0131048	+	0.0403324i
$340$		−	251.606i		−	0.740017i
$341$	−338.561	+	568.136i	−0.992849	+	1.66609i
$342$	−6.26325			−0.0183136
$343$	−32.0026	−	10.3983i	−0.0933020	−	0.0303157i
$344$	−96.7961	+	70.3265i	−0.281384	+	0.204438i
$345$	−340.631	−	247.483i	−0.987337	−	0.717342i
$346$	−143.680	−	442.202i	−0.415261	−	1.27804i
$347$	288.706	−	93.8063i	0.832006	−	0.270335i	0.138116	−	0.990416i	$-0.455895\pi$
$347$	288.706	−	93.8063i	0.832006	−	0.270335i	0.693890	+	0.720081i	$0.255895\pi$
$348$	35.0762	−	48.2782i	0.100794	−	0.138730i
$349$	270.255	+	371.974i	0.774369	+	1.06583i	0.995881	+	0.0906698i	$0.0289008\pi$
$349$	270.255	+	371.974i	0.774369	+	1.06583i	−0.221512	+	0.975158i	$0.571099\pi$
$350$	67.2301	−	206.913i	0.192086	−	0.591180i
$351$			5.85177i			0.0166717i
$352$	13.7768	−	60.6811i	0.0391387	−	0.172390i
$353$	−35.2031			−0.0997256			−0.0498628	−	0.998756i	$-0.515878\pi$
$353$	−35.2031			−0.0997256			−0.0498628	+	0.998756i	$0.515878\pi$
$354$	101.011	+	32.8204i	0.285341	+	0.0927130i
$355$	−170.705	+	124.025i	−0.480860	+	0.349365i
$356$	86.0451	+	62.5154i	0.241700	+	0.175605i
$357$	106.801	+	328.700i	0.299163	+	0.920729i
$358$	−168.356	+	54.7021i	−0.470267	+	0.152799i
$359$	123.345	−	169.770i	0.343581	−	0.472898i	−0.601902	−	0.798570i	$-0.705590\pi$
$359$	123.345	−	169.770i	0.343581	−	0.472898i	0.945483	+	0.325672i	$0.105590\pi$
$360$	−31.6547	−	43.5690i	−0.0879298	−	0.121025i
$361$	110.882	−	341.259i	0.307151	−	0.945315i
$362$			228.035i			0.629931i
$363$	206.124	−	37.8949i	0.567834	−	0.104394i
$364$	−22.6742			−0.0622917
$365$	−276.171	−	89.7335i	−0.756634	−	0.245845i
$366$	202.251	−	146.944i	0.552598	−	0.401486i
$367$	−316.777	−	230.152i	−0.863154	−	0.627118i	0.0655873	−	0.997847i	$-0.479108\pi$
$367$	−316.777	−	230.152i	−0.863154	−	0.627118i	−0.928741	+	0.370729i	$0.879108\pi$
$368$	−47.3429	−	145.706i	−0.128649	−	0.395941i
$369$	−95.5098	+	31.0330i	−0.258834	+	0.0841003i
$370$	−127.458	+	175.430i	−0.344480	+	0.474136i
$371$	141.854	+	195.246i	0.382357	+	0.526269i
$372$	−64.3607	+	198.082i	−0.173013	+	0.532479i
$373$		−	352.395i		−	0.944758i	−0.881395	−	0.472379i	$-0.843395\pi$
$373$		−	352.395i		−	0.944758i	0.881395	−	0.472379i	$-0.156605\pi$
$374$	300.698	+	68.2694i	0.804006	+	0.182539i
$375$	106.833			0.284889
$376$	−160.629	−	52.1917i	−0.427206	−	0.138808i
$377$	−15.6952	+	11.4032i	−0.0416318	+	0.0302472i
$378$	59.8481	+	43.4822i	0.158328	+	0.115032i
$379$	−171.786	−	528.702i	−0.453260	−	1.39499i	−0.873166	−	0.487424i	$-0.837937\pi$
$379$	−171.786	−	528.702i	−0.453260	−	1.39499i	0.419905	−	0.907568i	$-0.362063\pi$
$380$	−17.8219	+	5.79068i	−0.0468997	+	0.0152386i
$381$	127.150	−	175.006i	0.333726	−	0.459334i
$382$	−204.814	−	281.902i	−0.536162	−	0.737963i
$383$	−62.8828	+	193.533i	−0.164185	+	0.505309i	−0.998975	−	0.0452588i	$-0.985589\pi$
$383$	−62.8828	+	193.533i	−0.164185	+	0.505309i	0.834790	+	0.550568i	$0.185589\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	603.746	+	359.782i	1.56817	+	0.934498i
$386$	384.448			0.995978
$387$	−120.693	−	39.2156i	−0.311869	−	0.101332i
$388$	174.993	−	127.140i	0.451013	−	0.327680i
$389$	−350.258	−	254.477i	−0.900407	−	0.654184i	0.0381637	−	0.999272i	$-0.487849\pi$
$389$	−350.258	−	254.477i	−0.900407	−	0.654184i	−0.938570	+	0.345088i	$0.887849\pi$
$390$	5.41025	+	16.6510i	0.0138724	+	0.0426950i
$391$	722.031	−	234.602i	1.84663	−	0.600005i
$392$	−87.0200	+	119.773i	−0.221990	+	0.305543i
$393$	−43.8353	−	60.3341i	−0.111540	−	0.153522i
$394$	−162.470	+	500.031i	−0.412360	+	1.26911i
$395$			487.572i			1.23436i
$396$	60.6590	−	26.0093i	0.153179	−	0.0656800i
$397$	−216.304			−0.544847			−0.272423	−	0.962177i	$-0.587825\pi$
$397$	−216.304			−0.544847			−0.272423	+	0.962177i	$0.587825\pi$
$398$	−152.282	−	49.4795i	−0.382619	−	0.124320i
$399$	20.8247	−	15.1300i	0.0521921	−	0.0379198i
$400$	−49.4525	−	35.9293i	−0.123631	−	0.0898233i
$401$	24.4920	+	75.3786i	0.0610773	+	0.187977i	0.976940	−	0.213516i	$-0.0684916\pi$
$401$	24.4920	+	75.3786i	0.0610773	+	0.187977i	−0.915862	+	0.401493i	$0.868492\pi$
$402$	−256.731	+	83.4171i	−0.638635	+	0.207505i
$403$	39.7990	−	54.7786i	0.0987568	−	0.135927i
$404$	3.97003	+	5.46427i	0.00982680	+	0.0135254i
$405$	17.6514	−	54.3253i	0.0435836	−	0.134137i
$406$			245.253i			0.604071i
$407$	−175.076	−	199.927i	−0.430162	−	0.491221i
$408$	97.1053			0.238003
$409$	306.832	+	99.6958i	0.750201	+	0.243755i	0.659068	−	0.752084i	$-0.270951\pi$
$409$	306.832	+	99.6958i	0.750201	+	0.243755i	0.0911333	+	0.995839i	$0.470951\pi$
$410$	−243.079	+	176.607i	−0.592874	+	0.430749i
$411$	−24.3207	−	17.6700i	−0.0591745	−	0.0429928i
$412$	72.3497	+	222.670i	0.175606	+	0.540460i
$413$	−415.134	+	134.885i	−1.00517	+	0.326598i
$414$	95.5141	−	131.464i	0.230710	−	0.317545i
$415$	−263.546	−	362.739i	−0.635050	−	0.874071i
$416$	−1.96862	+	6.05880i	−0.00473227	+	0.0145644i
$417$		−	61.8385i		−	0.148294i
$418$	−2.08484	−	22.8704i	−0.00498766	−	0.0547140i
$419$	609.683			1.45509			0.727546	−	0.686059i	$-0.240661\pi$
$419$	609.683			1.45509			0.727546	+	0.686059i	$0.240661\pi$
$420$	210.497	+	68.3947i	0.501184	+	0.162845i
$421$	−25.3634	+	18.4276i	−0.0602457	+	0.0437711i	−0.617501	−	0.786570i	$-0.711855\pi$
$421$	−25.3634	+	18.4276i	−0.0602457	+	0.0437711i	0.557255	+	0.830342i	$0.311855\pi$
$422$	−151.449	−	110.034i	−0.358883	−	0.260744i
$423$	−55.3576	−	170.373i	−0.130869	−	0.402774i
$424$	64.4880	−	20.9534i	0.152094	−	0.0494185i
$425$	178.044	−	245.056i	0.418926	−	0.576602i
$426$	−47.8663	−	65.8823i	−0.112362	−	0.154653i
$427$	−317.494	+	977.146i	−0.743546	+	2.28840i
$428$		−	119.278i		−	0.278686i
$429$	−21.3679	+	1.94787i	−0.0498086	+	0.00454049i
$430$	−379.686			−0.882990
$431$	345.006	+	112.099i	0.800478	+	0.260091i	0.680560	−	0.732693i	$-0.261737\pi$
$431$	345.006	+	112.099i	0.800478	+	0.260091i	0.119918	+	0.992784i	$0.461737\pi$
$432$	16.8151	−	12.2169i	0.0389238	−	0.0282798i
$433$	71.7297	+	52.1147i	0.165658	+	0.120357i	0.667525	−	0.744587i	$-0.267354\pi$
$433$	71.7297	+	52.1147i	0.165658	+	0.120357i	−0.501868	+	0.864944i	$0.667354\pi$
$434$	−264.510	−	814.077i	−0.609469	−	1.87575i
$435$	180.104	−	58.5194i	0.414032	−	0.134527i
$436$	−221.411	+	304.746i	−0.507823	+	0.698959i
$437$	−33.2349	−	45.7440i	−0.0760525	−	0.104677i
$438$	34.6319	−	106.586i	0.0790683	−	0.243347i
$439$			373.125i			0.849944i	0.905207	+	0.424972i	$0.139716\pi$
$439$			373.125i			0.849944i	−0.905207	+	0.424972i	$0.860284\pi$
$440$	148.556	−	130.091i	0.337628	−	0.295661i
$441$	−157.028			−0.356072
$442$	−30.0237	−	9.75529i	−0.0679269	−	0.0220708i
$443$	−440.508	+	320.048i	−0.994375	+	0.722456i	−0.960875	−	0.276983i	$-0.910665\pi$
$443$	−440.508	+	320.048i	−0.994375	+	0.722456i	−0.0335003	+	0.999439i	$0.510665\pi$
$444$	−67.7059	−	49.1912i	−0.152491	−	0.110791i
$445$	104.298	+	320.995i	0.234377	+	0.721337i
$446$	180.104	−	58.5194i	0.403821	−	0.131209i
$447$	0.217762	−	0.299724i	0.000487164	−	0.000670524i
$448$	47.3374	+	65.1544i	0.105664	+	0.145434i
$449$	26.6050	−	81.8817i	0.0592539	−	0.182365i	−0.917048	−	0.398776i	$-0.869435\pi$
$449$	26.6050	−	81.8817i	0.0592539	−	0.182365i	0.976302	+	0.216411i	$0.0694352\pi$
$450$		−	64.8346i		−	0.144077i
$451$	−145.110	−	338.427i	−0.321752	−	0.750391i
$452$	−16.6003			−0.0367264
$453$	−169.574	−	55.0978i	−0.374335	−	0.121629i
$454$	−438.724	+	318.752i	−0.966353	+	0.702096i
$455$	−58.2120	−	42.2935i	−0.127939	−	0.0929528i
$456$	−2.23487	−	6.87822i	−0.00490103	−	0.0150838i
$457$	−399.616	+	129.843i	−0.874434	+	0.284121i	−0.711644	−	0.702540i	$-0.752049\pi$
$457$	−399.616	+	129.843i	−0.874434	+	0.284121i	−0.162790	+	0.986661i	$0.552049\pi$
$458$	−84.4194	+	116.193i	−0.184322	+	0.253697i
$459$	60.5393	+	83.3253i	0.131894	+	0.181537i
$460$	150.238	−	462.384i	0.326603	−	1.00518i
$461$		−	169.900i		−	0.368546i	−0.982875	−	0.184273i	$-0.941007\pi$
$461$		−	169.900i		−	0.368546i	0.982875	−	0.184273i	$-0.0589930\pi$
$462$	−138.855	+	233.011i	−0.300552	+	0.504352i
$463$	23.1381			0.0499743			0.0249872	−	0.999688i	$-0.492046\pi$
$463$	23.1381			0.0499743			0.0249872	+	0.999688i	$0.492046\pi$
$464$	65.5344	+	21.2934i	0.141238	+	0.0458910i
$465$	−534.712	+	388.491i	−1.14992	+	0.835465i
$466$	−43.0868	−	31.3044i	−0.0924609	−	0.0671768i
$467$	−86.8147	−	267.188i	−0.185899	−	0.572137i	0.814064	−	0.580775i	$-0.197250\pi$
$467$	−86.8147	−	267.188i	−0.185899	−	0.572137i	−0.999963	+	0.00863779i	$0.997250\pi$
$468$	−6.42633	+	2.08804i	−0.0137315	+	0.00446163i
$469$	652.096	−	897.534i	1.39040	−	1.91372i
$470$	−315.037	−	433.611i	−0.670291	−	0.922576i
$471$	−40.2665	+	123.928i	−0.0854915	+	0.263116i
$472$			122.640i			0.259830i
$473$	103.022	−	453.768i	0.217805	−	0.959341i
$474$	−188.174			−0.396992
$475$	−21.4556	−	6.97135i	−0.0451697	−	0.0146765i
$476$	−322.865	+	234.575i	−0.678288	+	0.492805i
$477$	58.1844	+	42.2735i	0.121980	+	0.0886236i
$478$	52.8902	+	162.779i	0.110649	+	0.340543i
$479$	237.369	−	77.1258i	0.495551	−	0.161014i	−0.0505703	−	0.998721i	$-0.516104\pi$
$479$	237.369	−	77.1258i	0.495551	−	0.161014i	0.546121	+	0.837706i	$0.316104\pi$
$480$	36.5517	−	50.3091i	0.0761494	−	0.104811i
$481$	15.9920	+	22.0111i	0.0332474	+	0.0457611i
$482$	11.0309	−	33.9495i	0.0228856	−	0.0704346i
$483$			667.835i			1.38268i
$484$	115.165	+	212.840i	0.237944	+	0.439753i
$485$	686.415			1.41529
$486$	20.9664	+	6.81241i	0.0431408	+	0.0140173i
$487$	−464.398	+	337.405i	−0.953590	+	0.692824i	−0.951653	−	0.307174i	$-0.900617\pi$
$487$	−464.398	+	337.405i	−0.953590	+	0.692824i	−0.00193685	+	0.999998i	$0.500617\pi$
$488$	233.539	+	169.676i	0.478564	+	0.347697i
$489$	−102.826	−	316.467i	−0.210279	−	0.647172i
$490$	−446.818	+	145.180i	−0.911872	+	0.296285i
$491$	35.6948	−	49.1297i	0.0726982	−	0.100060i	−0.771119	−	0.636690i	$-0.780303\pi$
$491$	35.6948	−	49.1297i	0.0726982	−	0.100060i	0.843818	+	0.536630i	$0.180303\pi$
$492$	−68.1600	−	93.8142i	−0.138537	−	0.190679i
$493$	−105.517	+	324.748i	−0.214030	+	0.658718i
$494$			2.35117i			0.00475946i
$495$	204.246	+	46.3713i	0.412618	+	0.0936793i
$496$	−240.496			−0.484871
$497$	318.301	+	103.422i	0.640445	+	0.208093i
$498$	139.996	−	101.713i	0.281117	−	0.204244i
$499$	−461.638	−	335.399i	−0.925126	−	0.672143i	0.0196689	−	0.999807i	$-0.493739\pi$
$499$	−461.638	−	335.399i	−0.925126	−	0.672143i	−0.944795	+	0.327663i	$0.893739\pi$
$500$	38.1205	+	117.323i	0.0762409	+	0.234645i
$501$	−253.595	+	82.3981i	−0.506178	+	0.164467i
$502$	−124.517	+	171.382i	−0.248041	+	0.341399i
$503$	−110.960	−	152.723i	−0.220595	−	0.303624i	0.684348	−	0.729156i	$-0.260087\pi$
$503$	−110.960	−	152.723i	−0.220595	−	0.303624i	−0.904943	+	0.425532i	$0.860087\pi$
$504$	−26.3964	+	81.2397i	−0.0523738	+	0.161190i
$505$			21.4338i			0.0424431i
$506$	511.837	+	305.012i	1.01154	+	0.602790i
$507$	−290.520			−0.573018
$508$	237.559	+	77.1877i	0.467636	+	0.151944i
$509$	92.8025	−	67.4249i	0.182323	−	0.132465i	−0.492880	−	0.870097i	$-0.664056\pi$
$509$	92.8025	−	67.4249i	0.182323	−	0.132465i	0.675203	+	0.737632i	$0.264056\pi$
$510$	249.301	+	181.128i	0.488826	+	0.355153i
$511$	142.330	+	438.047i	0.278533	+	0.857235i
$512$	21.5200	−	6.99226i	0.0420312	−	0.0136568i
$513$	4.50884	−	6.20588i	0.00878915	−	0.0120972i
$514$	−335.618	−	461.939i	−0.652953	−	0.898713i
$515$	−229.594	+	706.618i	−0.445814	+	1.37207i
$516$		−	146.537i		−	0.283986i
$517$	603.696	−	258.852i	1.16769	−	0.500680i
$518$	343.945			0.663987
$519$	541.585	+	175.972i	1.04352	+	0.339059i
$520$	−16.3554	+	11.8829i	−0.0314527	+	0.0228518i
$521$	403.744	+	293.337i	0.774940	+	0.563027i	0.903456	−	0.428681i	$-0.141021\pi$
$521$	403.744	+	293.337i	0.774940	+	0.563027i	−0.128516	+	0.991707i	$0.541021\pi$
$522$	22.5851	+	69.5097i	0.0432664	+	0.133160i
$523$	484.403	−	157.392i	0.926201	−	0.300941i	0.193193	−	0.981161i	$-0.438116\pi$
$523$	484.403	−	157.392i	0.926201	−	0.300941i	0.733008	+	0.680220i	$0.238116\pi$
$524$	50.6166	−	69.6678i	0.0965966	−	0.132954i
$525$	156.619	+	215.568i	0.298323	+	0.410606i
$526$	71.2357	−	219.241i	0.135429	−	0.416808i
$527$		−	1191.75i		−	2.26139i
$528$	50.2075	+	57.3342i	0.0950900	+	0.108587i
$529$	937.982			1.77312
$530$	204.646	+	66.4935i	0.386124	+	0.125459i
$531$	−105.236	+	76.4585i	−0.198185	+	0.143990i
$532$	24.0463	+	17.4706i	0.0451997	+	0.0328395i
$533$	11.6495	+	35.8535i	0.0218565	+	0.0672674i
$534$	−123.885	+	40.2528i	−0.231995	+	0.0753798i
$535$	222.485	−	306.224i	0.415860	−	0.572382i
$536$	−183.215	−	252.174i	−0.341819	−	0.470473i
$537$	66.9961	−	206.193i	0.124760	−	0.383972i
$538$		−	502.809i		−	0.934590i
$539$	−52.2696	−	573.391i	−0.0969751	−	1.06381i
$540$	65.9577			0.122144
$541$	−1003.39	−	326.021i	−1.85469	−	0.602627i	−0.995917	−	0.0902771i	$-0.971225\pi$
$541$	−1003.39	−	326.021i	−1.85469	−	0.602627i	−0.858777	−	0.512349i	$-0.828775\pi$
$542$	509.262	−	370.001i	0.939598	−	0.682658i
$543$	−225.946	−	164.159i	−0.416107	−	0.302319i
$544$	34.6493	+	106.640i	0.0636936	+	0.196029i
$545$	−1136.87	+	369.391i	−2.08600	+	0.677782i
$546$	16.3228	−	22.4665i	0.0298953	−	0.0411474i
$547$	90.1315	+	124.055i	0.164774	+	0.226792i	0.883418	−	0.468587i	$-0.155237\pi$
$547$	90.1315	+	124.055i	0.164774	+	0.226792i	−0.718643	+	0.695379i	$0.755237\pi$
$548$	10.7268	−	33.0137i	0.0195745	−	0.0602440i
$549$			306.181i			0.557707i
$550$	236.745	−	21.5814i	0.430446	−	0.0392389i
$551$	25.4312			0.0461546
$552$	178.453	+	57.9830i	0.323285	+	0.105042i
$553$	625.660	−	454.569i	1.13139	−	0.822005i
$554$	117.239	+	85.1795i	0.211624	+	0.153754i
$555$	−82.0682	−	252.580i	−0.147871	−	0.455099i
$556$	67.9101	−	22.0653i	0.122140	−	0.0396859i
$557$	−97.4126	+	134.077i	−0.174888	+	0.240713i	−0.887458	−	0.460888i	$-0.847531\pi$
$557$	−97.4126	+	134.077i	−0.174888	+	0.240713i	0.712570	+	0.701601i	$0.247531\pi$
$558$	−149.935	−	206.368i	−0.268701	−	0.369835i
$559$	−14.7212	+	45.3072i	−0.0263349	+	0.0810504i
$560$			255.570i			0.456375i
$561$	−284.113	+	248.797i	−0.506440	+	0.443489i
$562$	207.633			0.369455
$563$	511.675	+	166.253i	0.908837	+	0.295299i	0.725879	−	0.687822i	$-0.241433\pi$
$563$	511.675	+	166.253i	0.908837	+	0.295299i	0.182957	+	0.983121i	$0.441433\pi$
$564$	167.349	−	121.586i	0.296717	−	0.215578i
$565$	−42.6185	−	30.9642i	−0.0754310	−	0.0548039i
$566$	56.3527	+	173.436i	0.0995631	+	0.306424i
$567$	−86.1678	+	27.9976i	−0.151971	+	0.0493785i
$568$	55.2713	−	76.0744i	0.0973086	−	0.133934i
$569$	−15.9900	−	22.0083i	−0.0281019	−	0.0386789i	0.794735	−	0.606957i	$-0.207610\pi$
$569$	−15.9900	−	22.0083i	−0.0281019	−	0.0386789i	−0.822837	+	0.568278i	$0.807610\pi$
$570$	7.09211	−	21.8273i	0.0124423	−	0.0382935i
$571$		−	372.459i		−	0.652292i	−0.945319	−	0.326146i	$-0.894250\pi$
$571$		−	372.459i		−	0.652292i	0.945319	−	0.326146i	$-0.105750\pi$
$572$	−9.76366	−	22.7709i	−0.0170693	−	0.0398092i
$573$	426.762			0.744786
$574$	453.250	+	147.270i	0.789634	+	0.256568i
$575$	473.522	−	344.034i	0.823517	−	0.598320i
$576$	19.4164	+	14.1068i	0.0337090	+	0.0244911i
$577$	329.373	+	1013.71i	0.570837	+	1.75686i	0.649935	+	0.759989i	$0.274796\pi$
$577$	329.373	+	1013.71i	0.570837	+	1.75686i	−0.0790983	+	0.996867i	$0.525204\pi$
$578$	−139.736	+	45.4029i	−0.241757	+	0.0785518i
$579$	−276.759	+	380.926i	−0.477994	+	0.657903i
$580$	128.530	+	176.907i	0.221604	+	0.305011i
$581$	−219.767	+	676.372i	−0.378256	+	1.16415i
$582$			264.916i			0.455183i
$583$	−134.995	+	226.533i	−0.231552	+	0.388565i
$584$	129.409			0.221590
$585$	−20.3933	−	6.62617i	−0.0348603	−	0.0113268i
$586$	83.4414	−	60.6237i	0.142391	−	0.103453i
$587$	−474.689	−	344.882i	−0.808670	−	0.587533i	0.104775	−	0.994496i	$-0.466588\pi$
$587$	−474.689	−	344.882i	−0.808670	−	0.587533i	−0.913445	+	0.406963i	$0.866588\pi$
$588$	−56.0310	−	172.446i	−0.0952908	−	0.293275i
$589$	−84.4147	+	27.4280i	−0.143319	+	0.0465671i
$590$	−228.756	+	314.856i	−0.387723	+	0.533654i
$591$	−378.491	−	520.948i	−0.640424	−	0.881468i
$592$	29.8621	−	91.9061i	0.0504427	−	0.155247i
$593$			173.493i			0.292568i	0.989243	+	0.146284i	$0.0467314\pi$
$593$			173.493i			0.292568i	−0.989243	+	0.146284i	$0.953269\pi$
$594$	−17.8966	+	78.8271i	−0.0301290	+	0.132706i
$595$	−1266.45			−2.12848
$596$	0.406855	+	0.132195i	0.000682643	+	0.000221804i
$597$	158.652	−	115.268i	0.265749	−	0.193078i
$598$	−49.3504	−	35.8551i	−0.0825257	−	0.0599584i
$599$	−281.948	−	867.747i	−0.470698	−	1.44866i	−0.851673	−	0.524074i	$-0.824411\pi$
$599$	−281.948	−	867.747i	−0.470698	−	1.44866i	0.380974	−	0.924586i	$-0.375589\pi$
$600$	71.2004	−	23.1344i	0.118667	−	0.0385574i
$601$	−57.0756	+	78.5579i	−0.0949678	+	0.130712i	−0.853857	−	0.520508i	$-0.825743\pi$
$601$	−57.0756	+	78.5579i	−0.0949678	+	0.130712i	0.758889	+	0.651220i	$0.225743\pi$
$602$	353.985	+	487.219i	0.588015	+	0.809334i
$603$	102.165	−	314.431i	0.169427	−	0.521444i
$604$		−	205.884i		−	0.340867i
$605$	−101.339	+	761.245i	−0.167502	+	1.25826i
$606$	−8.27219			−0.0136505
$607$	−922.931	−	299.878i	−1.52048	−	0.494034i	−0.574567	−	0.818457i	$-0.694830\pi$
$607$	−922.931	−	299.878i	−1.52048	−	0.494034i	−0.945912	+	0.324424i	$0.894830\pi$
$608$	6.75611	−	4.90860i	0.0111120	−	0.00807335i
$609$	−243.006	−	176.554i	−0.399025	−	0.289908i
$610$	283.079	+	871.229i	0.464065	+	1.42824i
$611$	−63.9566	+	20.7808i	−0.104675	+	0.0340111i
$612$	−69.9048	+	96.2157i	−0.114224	+	0.157215i
$613$	−269.859	−	371.429i	−0.440227	−	0.605920i	0.530036	−	0.847975i	$-0.322178\pi$
$613$	−269.859	−	371.429i	−0.440227	−	0.605920i	−0.970262	+	0.242055i	$0.922178\pi$
$614$	106.313	−	327.197i	0.173148	−	0.532894i
$615$		−	367.989i		−	0.598356i
$616$	−305.436	−	69.3450i	−0.495837	−	0.112573i
$617$	−836.518			−1.35578			−0.677891	−	0.735162i	$-0.737106\pi$
$617$	−836.518			−1.35578			−0.677891	+	0.735162i	$0.737106\pi$
$618$	−272.713	−	88.6100i	−0.441284	−	0.143382i
$619$	154.261	−	112.077i	0.249210	−	0.181062i	−0.456166	−	0.889894i	$-0.650778\pi$
$619$	154.261	−	112.077i	0.249210	−	0.181062i	0.705377	+	0.708833i	$0.250778\pi$
$620$	−617.432	−	448.591i	−0.995859	−	0.723534i
$621$	61.5002	+	189.278i	0.0990342	+	0.304796i
$622$	212.637	−	69.0899i	0.341860	−	0.111077i
$623$	314.668	−	433.104i	0.505086	−	0.695191i
$624$	−4.58611	−	6.31224i	−0.00734954	−	0.0101158i
$625$	−239.028	+	735.654i	−0.382446	+	1.17705i
$626$			24.6493i			0.0393758i
$627$	24.1618	+	14.3984i	0.0385355	+	0.0229639i
$628$	−150.463			−0.239591
$629$	455.430	+	147.978i	0.724054	+	0.235259i
$630$	−219.302	+	159.333i	−0.348099	+	0.252909i
$631$	−228.528	−	166.035i	−0.362168	−	0.263130i	0.391788	−	0.920056i	$-0.371857\pi$
$631$	−228.528	−	166.035i	−0.362168	−	0.263130i	−0.753956	+	0.656925i	$0.771857\pi$
$632$	−67.1448	−	206.650i	−0.106242	−	0.326978i
$633$	218.052	−	70.8493i	0.344474	−	0.111926i
$634$	61.4188	−	84.5357i	0.0968750	−	0.133337i
$635$	465.916	+	641.279i	0.733726	+	1.00989i
$636$	−25.6626	+	78.9814i	−0.0403500	+	0.124185i
$637$			58.9469i			0.0925382i
$638$	−246.299	+	105.608i	−0.386048	+	0.165529i
$639$	99.7372			0.156083
$640$	68.2912	+	22.1892i	0.106705	+	0.0346706i
$641$	−531.987	+	386.511i	−0.829933	+	0.602982i	−0.919540	−	0.392996i	$-0.871439\pi$
$641$	−531.987	+	386.511i	−0.829933	+	0.602982i	0.0896074	+	0.995977i	$0.471439\pi$
$642$	118.185	+	85.8663i	0.184089	+	0.133748i
$643$	171.361	+	527.393i	0.266502	+	0.820207i	0.991344	+	0.131292i	$0.0419127\pi$
$643$	171.361	+	527.393i	0.266502	+	0.820207i	−0.724842	+	0.688915i	$0.758087\pi$
$644$	−733.406	+	238.298i	−1.13883	+	0.370028i
$645$	273.331	−	376.207i	0.423768	−	0.583267i
$646$	24.3240	+	33.4791i	0.0376532	+	0.0518252i
$647$	−217.679	+	669.949i	−0.336444	+	1.03547i	0.629562	+	0.776950i	$0.283234\pi$
$647$	−217.679	+	669.949i	−0.336444	+	1.03547i	−0.966006	+	0.258519i	$0.916766\pi$
$648$			25.4558i			0.0392837i
$649$	−314.220	−	358.822i	−0.484160	−	0.552884i
$650$	−24.3383			−0.0374436
$651$	997.036	+	323.957i	1.53155	+	0.497629i
$652$	310.849	−	225.845i	0.476762	−	0.346388i
$653$	114.090	+	82.8910i	0.174716	+	0.126939i	0.671707	−	0.740817i	$-0.265562\pi$
$653$	114.090	+	82.8910i	0.174716	+	0.126939i	−0.496990	+	0.867756i	$0.665562\pi$
$654$	−142.564	−	438.765i	−0.217987	−	0.670895i
$655$	259.899	−	84.4463i	0.396792	−	0.128926i
$656$	78.7044	−	108.327i	0.119976	−	0.165133i
$657$	80.6786	+	111.045i	0.122798	+	0.169018i
$658$	−262.704	+	808.521i	−0.399247	+	1.22875i
$659$			346.909i			0.526418i	0.964739	+	0.263209i	$0.0847808\pi$
$659$			346.909i			0.526418i	−0.964739	+	0.263209i	$0.915219\pi$
$660$	21.9552	+	240.846i	0.0332655	+	0.364919i
$661$	527.348			0.797803			0.398902	−	0.916994i	$-0.369392\pi$
$661$	527.348			0.797803			0.398902	+	0.916994i	$0.369392\pi$
$662$	−563.425	−	183.068i	−0.851095	−	0.276538i
$663$	31.2796	−	22.7259i	0.0471789	−	0.0342774i
$664$	161.654	+	117.448i	0.243455	+	0.176880i
$665$	29.1471	+	89.7057i	0.0438303	+	0.134896i
$666$	97.4811	−	31.6735i	0.146368	−	0.0475579i
$667$	−387.823	+	533.793i	−0.581444	+	0.800289i
$668$	−180.977	−	249.093i	−0.270923	−	0.372894i
$669$	−71.6713	+	220.582i	−0.107132	+	0.329719i
$670$		−	989.158i		−	1.47636i
$671$	−1118.03	+	101.918i	−1.66621	+	0.151890i
$672$	−98.6351			−0.146778
$673$	157.775	+	51.2641i	0.234435	+	0.0761726i	0.423878	−	0.905719i	$-0.360668\pi$
$673$	157.775	+	51.2641i	0.234435	+	0.0761726i	−0.189443	+	0.981892i	$0.560668\pi$
$674$	175.248	−	127.325i	0.260012	−	0.188910i
$675$	64.2407	+	46.6736i	0.0951714	+	0.0691460i
$676$	−103.664	−	319.045i	−0.153349	−	0.471960i
$677$	781.310	−	253.863i	1.15408	−	0.374982i	0.331399	−	0.943491i	$-0.392479\pi$
$677$	781.310	−	253.863i	1.15408	−	0.374982i	0.822678	+	0.568508i	$0.192479\pi$
$678$	11.9504	−	16.4483i	0.0176259	−	0.0242600i
$679$	−639.952	−	880.819i	−0.942492	−	1.29723i
$680$	−109.956	+	338.409i	−0.161700	+	0.497661i
$681$		−	664.171i		−	0.975287i
$682$	703.649	−	616.185i	1.03174	−	0.903497i
$683$	−674.547			−0.987623			−0.493812	−	0.869569i	$-0.664397\pi$
$683$	−674.547			−0.987623			−0.493812	+	0.869569i	$0.664397\pi$
$684$	8.42406	+	2.73714i	0.0123159	+	0.00400167i
$685$	89.1188	−	64.7486i	0.130100	−	0.0945235i
$686$	38.4992	+	27.9713i	0.0561212	+	0.0407745i
$687$	−54.3565	−	167.292i	−0.0791215	−	0.243511i
$688$	160.924	−	52.2875i	0.233902	−	0.0759993i
$689$	15.8691	−	21.8419i	0.0230321	−	0.0317009i
$690$	349.994	+	481.725i	0.507237	+	0.698152i
$691$	74.7079	−	229.927i	0.108116	−	0.332746i	−0.882333	−	0.470625i	$-0.844029\pi$
$691$	74.7079	−	229.927i	0.108116	−	0.332746i	0.990449	+	0.137879i	$0.0440285\pi$
$692$			657.551i			0.950218i
$693$	−130.917	−	305.324i	−0.188913	−	0.440583i
$694$	−429.304			−0.618593
$695$	215.505	+	70.0219i	0.310080	+	0.100751i
$696$	−68.2757	+	49.6052i	−0.0980973	+	0.0712718i
$697$	536.803	+	390.010i	0.770162	+	0.559556i
$698$	−200.933	−	618.409i	−0.287870	−	0.885973i
$699$	62.0352	−	20.1565i	0.0887485	−	0.0288361i
$700$	−180.849	+	248.917i	−0.258355	+	0.355595i
$701$	266.793	+	367.210i	0.380590	+	0.523837i	0.955741	−	0.294211i	$-0.0950567\pi$
$701$	266.793	+	367.210i	0.380590	+	0.523837i	−0.575151	+	0.818047i	$0.695057\pi$
$702$	2.55732	−	7.87062i	0.00364290	−	0.0112117i
$703$		−	35.6650i		−	0.0507325i
$704$	−45.0484	+	75.5952i	−0.0639892	+	0.107380i
$705$	656.430			0.931106
$706$	47.3481	+	15.3843i	0.0670653	+	0.0217908i
$707$	27.5042	−	19.9829i	0.0389026	−	0.0282644i
$708$	−121.516	−	88.2867i	−0.171633	−	0.124699i
$709$	133.611	+	411.212i	0.188450	+	0.579989i	0.999991	−	0.00430687i	$-0.00137093\pi$
$709$	133.611	+	411.212i	0.188450	+	0.579989i	−0.811541	+	0.584295i	$0.801371\pi$
$710$	283.799	−	92.2119i	0.399717	−	0.129876i
$711$	135.464	−	186.451i	0.190526	−	0.262237i
$712$	−88.4101	−	121.686i	−0.124172	−	0.170907i
$713$	711.611	−	2190.11i	0.998052	−	3.07169i
$714$		−	488.775i		−	0.684559i
$715$	17.4074	−	76.6722i	0.0243460	−	0.107234i
$716$	250.344			0.349642
$717$	−199.363	−	64.7770i	−0.278052	−	0.0903446i
$718$	−240.092	+	174.437i	−0.334389	+	0.242948i
$719$	328.819	+	238.901i	0.457328	+	0.332268i	0.792482	−	0.609895i	$-0.208788\pi$
$719$	328.819	+	238.901i	0.457328	+	0.332268i	−0.335154	+	0.942163i	$0.608788\pi$
$720$	23.5352	+	72.4338i	0.0326877	+	0.100602i
$721$	1120.80	−	364.169i	1.55450	−	0.505089i
$722$	−298.271	+	410.535i	−0.413118	+	0.568608i
$723$	25.6975	+	35.3696i	0.0355429	+	0.0489206i
$724$	99.6550	−	306.706i	0.137645	−	0.423628i
$725$			263.253i			0.363108i
$726$	−293.796	−	39.1109i	−0.404678	−	0.0538717i
$727$	−710.158			−0.976834			−0.488417	−	0.872610i	$-0.662425\pi$
$727$	−710.158			−0.976834			−0.488417	+	0.872610i	$0.662425\pi$
$728$	30.4967	+	9.90898i	0.0418911	+	0.0136112i
$729$	−21.8435	+	15.8702i	−0.0299636	+	0.0217698i
$730$	332.235	+	241.383i	0.455116	+	0.330661i
$731$	259.104	+	797.442i	0.354452	+	1.09089i
$732$	−336.244	+	109.252i	−0.459349	+	0.149252i
$733$	−237.868	+	327.397i	−0.324513	+	0.446654i	−0.939838	−	0.341619i	$-0.889025\pi$
$733$	−237.868	+	327.397i	−0.324513	+	0.446654i	0.615325	+	0.788273i	$0.289025\pi$
$734$	325.484	+	447.991i	0.443439	+	0.610342i
$735$	177.808	−	547.237i	0.241916	−	0.744541i
$736$			216.664i			0.294381i
$737$	1182.16	+	268.393i	1.60401	+	0.364169i
$738$	142.022			0.192442
$739$	953.767	+	309.898i	1.29062	+	0.419347i	0.872308	−	0.488957i	$-0.162623\pi$
$739$	953.767	+	309.898i	1.29062	+	0.419347i	0.418310	+	0.908304i	$0.362623\pi$
$740$	248.096	−	180.252i	0.335265	−	0.243584i
$741$	−2.32963	−	1.69258i	−0.00314390	−	0.00228418i
$742$	−105.468	−	324.598i	−0.142140	−	0.437463i
$743$	132.883	−	43.1762i	0.178846	−	0.0581106i	−0.218225	−	0.975898i	$-0.570027\pi$
$743$	132.883	−	43.1762i	0.178846	−	0.0581106i	0.397071	+	0.917788i	$0.370027\pi$
$744$	173.130	−	238.293i	0.232702	−	0.320286i
$745$	0.797950	+	1.09828i	0.00107107	+	0.00147421i
$746$	−154.002	+	473.970i	−0.206437	+	0.635349i
$747$			211.936i			0.283716i
$748$	−374.603	−	223.232i	−0.500807	−	0.298439i
$749$	−600.378			−0.801572
$750$	−143.690	−	46.6878i	−0.191587	−	0.0622505i
$751$	24.0224	−	17.4533i	0.0319872	−	0.0232401i	−0.571677	−	0.820479i	$-0.693707\pi$
$751$	24.0224	−	17.4533i	0.0319872	−	0.0232401i	0.603664	+	0.797239i	$0.293707\pi$
$752$	193.238	+	140.395i	0.256965	+	0.186696i
$753$	−80.1745	−	246.752i	−0.106473	−	0.327692i
$754$	26.0933	−	8.47824i	0.0346066	−	0.0112444i
$755$	384.029	−	528.570i	0.508648	−	0.700093i
$756$	−61.4931	−	84.6380i	−0.0813401	−	0.111955i
$757$	119.458	−	367.655i	0.157805	−	0.485674i	−0.840629	−	0.541611i	$-0.817815\pi$
$757$	119.458	−	367.655i	0.157805	−	0.485674i	0.998434	+	0.0559369i	$0.0178146\pi$
$758$			786.175i			1.03717i
$759$	−670.683	+	287.574i	−0.883640	+	0.378886i
$760$	26.5010			0.0348698
$761$	−312.620	−	101.576i	−0.410801	−	0.133477i	0.0963236	−	0.995350i	$-0.469292\pi$
$761$	−312.620	−	101.576i	−0.410801	−	0.133477i	−0.507125	+	0.861873i	$0.669292\pi$
$762$	−247.496	+	179.817i	−0.324798	+	0.235980i
$763$	1533.92	+	1114.46i	2.01039	+	1.46063i
$764$	152.278	+	468.664i	0.199317	+	0.613435i
$765$	−358.937	+	116.626i	−0.469199	+	0.152452i
$766$	169.154	−	232.821i	0.220828	−	0.303944i
$767$	28.7019	+	39.5047i	0.0374209	+	0.0515055i
$768$	−8.56373	+	26.3565i	−0.0111507	+	0.0343183i
$769$			240.314i			0.312502i	0.987717	+	0.156251i	$0.0499409\pi$
$769$			240.314i			0.312502i	−0.987717	+	0.156251i	$0.950059\pi$
$770$	−654.806	−	747.752i	−0.850397	−	0.971106i
$771$	699.314			0.907022
$772$	−517.081	−	168.010i	−0.669794	−	0.217629i
$773$	513.626	−	373.171i	0.664458	−	0.482757i	−0.203708	−	0.979032i	$-0.565299\pi$
$773$	513.626	−	373.171i	0.664458	−	0.482757i	0.868165	+	0.496275i	$0.165299\pi$
$774$	145.194	+	105.490i	0.187589	+	0.136292i
$775$	−283.923	−	873.826i	−0.366353	−	1.12752i
$776$	−290.927	+	94.5280i	−0.374906	+	0.121814i
$777$	−247.602	+	340.794i	−0.318664	+	0.438603i
$778$	359.886	+	495.340i	0.462578	+	0.636684i
$779$	15.2710	−	46.9992i	0.0196033	−	0.0603327i
$780$		−	24.7600i		−	0.0317435i
$781$	33.1994	+	364.193i	0.0425088	+	0.466316i
$782$	−1073.65			−1.37296
$783$	−85.1317	−	27.6610i	−0.108725	−	0.0353269i
$784$	169.384	−	123.065i	0.216051	−	0.156970i
$785$	−386.289	−	280.655i	−0.492088	−	0.357523i
$786$	32.5914	+	100.306i	0.0414648	+	0.127616i
$787$	21.2998	−	6.92071i	0.0270645	−	0.00879379i	−0.295453	−	0.955357i	$-0.595471\pi$
$787$	21.2998	−	6.92071i	0.0270645	−	0.00879379i	0.322518	+	0.946563i	$0.395471\pi$
$788$	437.043	−	601.539i	0.554624	−	0.763374i
$789$	165.951	+	228.412i	0.210331	+	0.289496i
$790$	213.077	−	655.783i	0.269717	−	0.830105i
$791$			83.5571i			0.105635i
$792$	−92.9527	+	8.47345i	−0.117364	+	0.0106988i
$793$	114.938			0.144940
$794$	290.928	+	94.5284i	0.366409	+	0.119053i
$795$	−213.206	+	154.903i	−0.268184	+	0.194847i
$796$	183.196	+	133.100i	0.230146	+	0.167211i
$797$	−317.613	−	977.511i	−0.398510	−	1.22649i	−0.926194	−	0.377047i	$-0.876939\pi$
$797$	−317.613	−	977.511i	−0.398510	−	1.22649i	0.527684	−	0.849441i	$-0.323061\pi$
$798$	−34.6212	+	11.2491i	−0.0433849	+	0.0140966i
$799$	−695.712	+	957.566i	−0.870729	+	1.19846i
$800$	50.8118	+	69.9364i	0.0635147	+	0.0874205i
$801$	49.2994	−	151.728i	0.0615474	−	0.189423i
$802$		−	112.087i		−	0.139760i
$803$	−378.627	+	331.563i	−0.471515	+	0.412906i
$804$	381.758			0.474823
$805$	−2327.39	−	756.213i	−2.89116	−	0.939396i
$806$	−77.4687	+	56.2843i	−0.0961150	+	0.0698316i
$807$	498.203	+	361.966i	0.617352	+	0.448533i
$808$	−2.95170	−	9.08440i	−0.00365309	−	0.0112431i
$809$	−1403.99	+	456.183i	−1.73546	+	0.563886i	−0.994221	−	0.107354i	$-0.965762\pi$
$809$	−1403.99	+	456.183i	−1.73546	+	0.563886i	−0.741240	+	0.671240i	$0.765762\pi$
$810$	−47.4821	+	65.3535i	−0.0586199	+	0.0806833i
$811$	−163.293	−	224.753i	−0.201347	−	0.277131i	0.696389	−	0.717665i	$-0.254789\pi$
$811$	−163.293	−	224.753i	−0.201347	−	0.277131i	−0.897736	+	0.440534i	$0.854789\pi$
$812$	107.179	−	329.864i	0.131994	−	0.406237i
$813$			770.956i			0.948285i
$814$	148.105	+	345.412i	0.181947	+	0.424339i
$815$	1219.31			1.49609
$816$	−130.606	−	42.4366i	−0.160057	−	0.0520056i
$817$	50.5216	−	36.7061i	0.0618379	−	0.0449279i
$818$	−369.120	−	268.181i	−0.451247	−	0.327850i
$819$	10.5101	+	32.3466i	0.0128328	+	0.0394953i
$820$	404.120	−	131.307i	0.492829	−	0.160130i
$821$	594.868	−	818.766i	0.724565	−	0.997279i	−0.274794	−	0.961503i	$-0.588610\pi$
$821$	594.868	−	818.766i	0.724565	−	0.997279i	0.999360	−	0.0357757i	$-0.0113902\pi$
$822$	24.9892	+	34.3947i	0.0304005	+	0.0418427i
$823$	173.629	−	534.375i	0.210971	−	0.649301i	−0.788444	−	0.615106i	$-0.789113\pi$
$823$	173.629	−	534.375i	0.210971	−	0.649301i	0.999415	−	0.0341951i	$-0.0108868\pi$
$824$		−	331.108i		−	0.401830i
$825$	−149.046	+	250.113i	−0.180662	+	0.303167i
$826$	617.301			0.747337
$827$	−707.503	−	229.882i	−0.855506	−	0.277971i	−0.151755	−	0.988418i	$-0.548493\pi$
$827$	−707.503	−	229.882i	−0.855506	−	0.277971i	−0.703750	+	0.710447i	$0.748493\pi$
$828$	−185.918	+	135.077i	−0.224539	+	0.163137i
$829$	−258.334	−	187.690i	−0.311621	−	0.226406i	0.420971	−	0.907074i	$-0.361689\pi$
$829$	−258.334	−	187.690i	−0.311621	−	0.226406i	−0.732592	+	0.680668i	$0.761689\pi$
$830$	195.945	+	603.057i	0.236078	+	0.726575i
$831$	−168.798	+	54.8459i	−0.203127	+	0.0659999i
$832$	5.29559	−	7.28875i	0.00636489	−	0.00876052i
$833$	609.833	+	839.363i	0.732093	+	1.00764i
$834$	−27.0244	+	83.1726i	−0.0324034	+	0.0997273i
$835$		−	977.075i		−	1.17015i
$836$	−7.19064	+	31.6718i	−0.00860125	+	0.0378849i
$837$	312.414			0.373254
$838$	−820.022	−	266.441i	−0.978547	−	0.317949i
$839$	−1135.17	+	824.751i	−1.35301	+	0.983016i	−0.354150	+	0.935189i	$0.615230\pi$
$839$	−1135.17	+	824.751i	−1.35301	+	0.983016i	−0.998856	+	0.0478277i	$0.984770\pi$
$840$	−253.229	−	183.981i	−0.301463	−	0.219026i
$841$	168.179	+	517.603i	0.199975	+	0.615461i
$842$	42.1669	−	13.7009i	0.0500795	−	0.0162718i
$843$	−149.473	+	205.731i	−0.177310	+	0.244047i
$844$	155.611	+	214.181i	0.184374	+	0.253769i
$845$	328.966	−	1012.45i	0.389309	−	1.19817i
$846$			253.344i			0.299461i
$847$	1071.32	−	579.678i	1.26484	−	0.684390i
$848$	−95.8932			−0.113082
$849$	−212.415	−	69.0177i	−0.250194	−	0.0812929i
$850$	−346.562	+	251.792i	−0.407719	+	0.296226i
$851$	748.597	+	543.888i	0.879667	+	0.639116i
$852$	35.5884	+	109.530i	0.0417704	+	0.128556i
$853$	−1380.33	+	448.496i	−1.61821	+	0.525787i	−0.971518	−	0.236967i	$-0.923847\pi$
$853$	−1380.33	+	448.496i	−1.61821	+	0.525787i	−0.646689	+	0.762754i	$0.723847\pi$
$854$	854.057	−	1175.51i	1.00007	−	1.37647i
$855$	16.5218	+	22.7403i	0.0193237	+	0.0265969i
$856$	−52.1262	+	160.428i	−0.0608951	+	0.187416i
$857$			598.032i			0.697820i	0.937156	+	0.348910i	$0.113448\pi$
$857$			598.032i			0.697820i	−0.937156	+	0.348910i	$0.886552\pi$
$858$	29.5910	+	6.71823i	0.0344884	+	0.00783011i
$859$	−1338.18			−1.55784			−0.778919	−	0.627125i	$-0.784232\pi$
$859$	−1338.18			−1.55784			−0.778919	+	0.627125i	$0.784232\pi$
$860$	510.676	+	165.929i	0.593809	+	0.192940i
$861$	−472.209	+	343.080i	−0.548443	+	0.398467i
$862$	−415.043	−	301.546i	−0.481488	−	0.349822i
$863$	−328.226	−	1010.17i	−0.380331	−	1.17054i	−0.939811	−	0.341695i	$-0.888999\pi$
$863$	−328.226	−	1010.17i	−0.380331	−	1.17054i	0.559480	−	0.828844i	$-0.311001\pi$
$864$	−27.9552	+	9.08321i	−0.0323556	+	0.0105130i
$865$	−1226.51	+	1688.15i	−1.41793	+	1.95162i
$866$	−73.7013	−	101.441i	−0.0851054	−	0.117138i
$867$	55.6070	−	171.141i	0.0641373	−	0.197394i
$868$			1210.53i			1.39462i
$869$	725.921	+	432.588i	0.835352	+	0.497800i
$870$	−267.813			−0.307831
$871$	−118.034	−	38.3517i	−0.135516	−	0.0440318i
$872$	430.976	−	313.122i	0.494238	−	0.359085i
$873$	−262.489	−	190.710i	−0.300675	−	0.218453i
$874$	24.7100	+	76.0497i	0.0282724	+	0.0870134i
$875$	590.538	−	191.878i	0.674901	−	0.219289i
$876$	−93.1596	+	128.223i	−0.106347	+	0.146374i
$877$	98.0905	+	135.010i	0.111848	+	0.153945i	0.861271	−	0.508146i	$-0.169669\pi$
$877$	98.0905	+	135.010i	0.111848	+	0.153945i	−0.749423	+	0.662091i	$0.769669\pi$
$878$	163.062	−	501.852i	0.185720	−	0.571586i
$879$			126.319i			0.143708i
$880$	−256.660	+	110.050i	−0.291659	+	0.125057i
$881$	−1345.57			−1.52732			−0.763662	−	0.645616i	$-0.776601\pi$
$881$	−1345.57			−1.52732			−0.763662	+	0.645616i	$0.776601\pi$
$882$	211.202	+	68.6236i	0.239458	+	0.0778046i
$883$	826.040	−	600.153i	0.935493	−	0.679675i	−0.0118386	−	0.999930i	$-0.503768\pi$
$883$	826.040	−	600.153i	0.935493	−	0.679675i	0.947332	+	0.320255i	$0.103768\pi$
$884$	36.1185	+	26.2417i	0.0408581	+	0.0296851i
$885$	−147.293	−	453.322i	−0.166433	−	0.512228i
$886$	732.348	−	237.954i	0.826578	−	0.268572i
$887$	−399.837	+	550.329i	−0.450775	+	0.620438i	−0.972564	−	0.232636i	$-0.925265\pi$
$887$	−399.837	+	550.329i	−0.450775	+	0.620438i	0.521789	+	0.853075i	$0.325265\pi$
$888$	69.5669	+	95.7506i	0.0783411	+	0.107827i
$889$	388.520	−	1195.74i	0.437031	−	1.34504i
$890$		−	477.317i		−	0.536311i
$891$	−65.2215	−	74.4793i	−0.0732003	−	0.0835907i
$892$	−267.814			−0.300239
$893$	83.8386	+	27.2408i	0.0938842	+	0.0305048i
$894$	−0.423874	+	0.307962i	−0.000474132	+	0.000344477i
$895$	642.714	+	466.959i	0.718116	+	0.521742i
$896$	−35.1952	−	108.320i	−0.0392803	−	0.120892i
$897$	71.0534	−	23.0866i	0.0792122	−	0.0257376i
$898$	−71.5673	+	98.5039i	−0.0796963	+	0.109693i
$899$	608.793	+	837.932i	0.677189	+	0.932071i
$900$	−28.3338	+	87.2023i	−0.0314820	+	0.0968915i
$901$		−	475.188i		−	0.527400i
$902$	47.2748	+	518.598i	0.0524110	+	0.574942i
$903$	−737.585			−0.816816
$904$	22.3274	+	7.25462i	0.0246985	+	0.00802502i
$905$	827.938	−	601.532i	0.914849	−	0.664677i
$906$	203.997	+	148.213i	0.225163	+	0.163590i
$907$	256.982	+	790.909i	0.283332	+	0.872005i	0.986894	+	0.161372i	$0.0515918\pi$
$907$	256.982	+	790.909i	0.283332	+	0.872005i	−0.703562	+	0.710634i	$0.748408\pi$
$908$	729.382	−	236.991i	0.803285	−	0.261003i
$909$	5.95504	−	8.19641i	0.00655120	−	0.00901695i
$910$	59.8121	+	82.3243i	0.0657276	+	0.0904662i
$911$	264.873	−	815.195i	0.290750	−	0.894835i	−0.693866	−	0.720104i	$-0.744094\pi$
$911$	264.873	−	815.195i	0.290750	−	0.894835i	0.984616	−	0.174732i	$-0.0559058\pi$
$912$			10.2279i			0.0112147i
$913$	−773.890	+	70.5468i	−0.847634	+	0.0772692i
$914$	594.226			0.650138
$915$	−1067.03	−	346.700i	−1.16616	−	0.378907i
$916$	164.322	−	119.387i	0.179391	−	0.130335i
$917$	−350.670	−	254.776i	−0.382410	−	0.277837i
$918$	−45.0108	−	138.529i	−0.0490313	−	0.150903i
$919$	193.329	−	62.8163i	0.210369	−	0.0683529i	−0.201937	−	0.979399i	$-0.564724\pi$
$919$	193.329	−	62.8163i	0.210369	−	0.0683529i	0.412306	+	0.911046i	$0.364724\pi$
$920$	−404.138	+	556.248i	−0.439280	+	0.604618i
$921$	247.666	+	340.884i	0.268910	+	0.370123i
$922$	−74.2489	+	228.515i	−0.0805302	+	0.247847i
$923$		−	37.4405i		−	0.0405639i
$924$	288.589	−	252.717i	0.312326	−	0.273503i
$925$	369.189			0.399123
$926$	−31.1207	−	10.1117i	−0.0336077	−	0.0109198i
$927$	284.121	−	206.426i	0.306495	−	0.222682i
$928$	−78.8380	−	57.2791i	−0.0849547	−	0.0617232i
$929$	−324.572	−	998.929i	−0.349378	−	1.07527i	−0.959198	−	0.282734i	$-0.908758\pi$
$929$	−324.572	−	998.929i	−0.349378	−	1.07527i	0.609821	−	0.792540i	$-0.291242\pi$
$930$	888.963	−	288.842i	0.955874	−	0.310582i
$931$	45.4190	−	62.5139i	0.0487852	−	0.0671471i
$932$	44.2711	+	60.9339i	0.0475011	+	0.0653797i
$933$	−84.6175	+	260.426i	−0.0906940	+	0.279127i
$934$			397.307i			0.425382i
$935$	−545.341	−	1271.85i	−0.583252	−	1.36026i
$936$	9.55590			0.0102093
$937$	576.198	+	187.218i	0.614940	+	0.199806i	0.599892	−	0.800081i	$-0.295210\pi$
$937$	576.198	+	187.218i	0.614940	+	0.199806i	0.0150473	+	0.999887i	$0.495210\pi$
$938$	−1269.30	+	922.204i	−1.35320	+	0.983159i
$939$	−24.4235	−	17.7447i	−0.0260101	−	0.0188974i
$940$	234.229	+	720.881i	0.249179	+	0.766895i
$941$	564.679	−	183.475i	0.600084	−	0.194979i	0.00680637	−	0.999977i	$-0.497833\pi$
$941$	564.679	−	183.475i	0.600084	−	0.194979i	0.593278	+	0.804998i	$0.297833\pi$
$942$	108.317	−	149.085i	0.114986	−	0.158264i
$943$	753.618	+	1037.27i	0.799171	+	1.09996i
$944$	53.5955	−	164.950i	0.0567749	−	0.174735i
$945$		−	331.995i		−	0.351317i
$946$	−336.868	+	565.295i	−0.356097	+	0.597563i
$947$	141.939			0.149883			0.0749413	−	0.997188i	$-0.476123\pi$
$947$	141.939			0.149883			0.0749413	+	0.997188i	$0.476123\pi$
$948$	253.094	+	82.2352i	0.266977	+	0.0867460i
$949$	41.6852	−	30.2860i	0.0439254	−	0.0319136i
$950$	25.8111	+	18.7529i	0.0271696	+	0.0197399i
$951$	39.5467	+	121.712i	0.0415843	+	0.127983i
$952$	536.765	−	174.406i	0.563829	−	0.183199i
$953$	−996.086	+	1371.00i	−1.04521	+	1.43861i	−0.152323	+	0.988331i	$0.548675\pi$
$953$	−996.086	+	1371.00i	−1.04521	+	1.43861i	−0.892888	+	0.450279i	$0.851325\pi$
$954$	−59.7837	−	82.2852i	−0.0626664	−	0.0862528i
$955$	−483.239	+	1487.26i	−0.506009	+	1.55734i
$956$		−	242.052i		−	0.253192i
$957$	72.6670	−	320.068i	0.0759321	−	0.334449i
$958$	−352.966			−0.368440
$959$	−166.173	−	53.9929i	−0.173277	−	0.0563012i
$960$	−71.1479	+	51.6920i	−0.0741124	+	0.0538458i
$961$	−2147.05	−	1559.92i	−2.23418	−	1.62323i
$962$	−11.8900	−	36.5936i	−0.0123596	−	0.0380391i
$963$	−170.159	+	55.2882i	−0.176697	+	0.0574124i
$964$	−29.6729	+	40.8413i	−0.0307811	+	0.0423665i
$965$	−1014.13	−	1395.83i	−1.05091	−	1.44646i
$966$	291.854	−	898.236i	0.302127	−	0.929851i
$967$			1285.89i			1.32978i	0.746943	+	0.664888i	$0.231521\pi$
$967$			1285.89i			1.32978i	−0.746943	+	0.664888i	$0.768479\pi$
$968$	−61.8820	−	336.599i	−0.0639277	−	0.347726i
$969$	−50.6829			−0.0523044
$970$	−923.226	−	299.974i	−0.951779	−	0.309252i
$971$	329.891	−	239.680i	0.339744	−	0.246838i	−0.404810	−	0.914401i	$-0.632662\pi$
$971$	329.891	−	239.680i	0.339744	−	0.246838i	0.744554	+	0.667562i	$0.232662\pi$
$972$	−25.2227	−	18.3253i	−0.0259492	−	0.0188532i
$973$	−111.065	−	341.822i	−0.114147	−	0.351308i
$974$	772.066	−	250.859i	0.792675	−	0.257556i
$975$	17.5209	−	24.1154i	0.0179701	−	0.0247337i
$976$	−239.958	−	330.274i	−0.245859	−	0.338396i
$977$	−323.762	+	996.436i	−0.331383	+	1.01989i	0.637093	+	0.770787i	$0.280137\pi$
$977$	−323.762	+	996.436i	−0.331383	+	1.01989i	−0.968476	+	0.249106i	$0.919863\pi$
$978$			470.584i			0.481170i
$979$	570.449	+	129.513i	0.582686	+	0.132291i
$980$	664.414			0.677974
$981$	537.376	+	174.604i	0.547784	+	0.177986i
$982$	−69.4799	+	50.4801i	−0.0707534	+	0.0514054i
$983$	−58.5745	−	42.5568i	−0.0595875	−	0.0432928i	0.557593	−	0.830115i	$-0.311725\pi$
$983$	−58.5745	−	42.5568i	−0.0595875	−	0.0432928i	−0.617180	+	0.786822i	$0.711725\pi$
$984$	50.6767	+	155.967i	0.0515007	+	0.158503i
$985$	2244.07	−	729.142i	2.27824	−	0.740245i
$986$	283.840	−	390.672i	0.287870	−	0.396219i
$987$	−611.997	−	842.341i	−0.620058	−	0.853436i
$988$	1.02750	−	3.16232i	0.00103998	−	0.00320073i
$989$			1620.20i			1.63822i
$990$	−254.445	−	151.628i	−0.257015	−	0.153160i
$991$	1335.55			1.34768			0.673838	−	0.738879i	$-0.264644\pi$
$991$	1335.55			1.34768			0.673838	+	0.738879i	$0.264644\pi$
$992$	323.467	+	105.101i	0.326075	+	0.105948i
$993$	586.993	−	426.475i	0.591131	−	0.429482i
$994$	−382.917	−	278.205i	−0.385228	−	0.279885i
$995$	222.057	+	683.421i	0.223173	+	0.686855i
$996$	−232.745	+	75.6234i	−0.233680	+	0.0759271i
$997$	300.433	−	413.510i	0.301337	−	0.414754i	−0.631318	−	0.775524i	$-0.717486\pi$
$997$	300.433	−	413.510i	0.301337	−	0.414754i	0.932655	+	0.360769i	$0.117486\pi$
$998$	474.326	+	652.854i	0.475277	+	0.654163i
$999$	−38.7920	+	119.390i	−0.0388308	+	0.119509i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	66.3.f.a.13.2	✓	16
3.2	odd	2		198.3.j.b.145.3		16
4.3	odd	2		528.3.bf.c.145.2		16
11.4	even	5		726.3.d.e.241.3		16
11.6	odd	10	inner	66.3.f.a.61.2	yes	16
11.7	odd	10		726.3.d.e.241.11		16
33.17	even	10		198.3.j.b.127.3		16
33.26	odd	10		2178.3.d.m.1693.10		16
33.29	even	10		2178.3.d.m.1693.2		16
44.39	even	10		528.3.bf.c.193.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.3.f.a.13.2	✓	16	1.1	even	1	trivial
66.3.f.a.61.2	yes	16	11.6	odd	10	inner
198.3.j.b.127.3		16	33.17	even	10
198.3.j.b.145.3		16	3.2	odd	2
528.3.bf.c.145.2		16	4.3	odd	2
528.3.bf.c.193.2		16	44.39	even	10
726.3.d.e.241.3		16	11.4	even	5
726.3.d.e.241.11		16	11.7	odd	10
2178.3.d.m.1693.2		16	33.29	even	10
2178.3.d.m.1693.10		16	33.26	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	66.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34500 - 0.437016i) q^{2} +(1.40126 - 1.01807i) q^{3} +(1.61803 + 1.17557i) q^{4} +(1.96126 + 6.03615i) q^{5} +(-2.32960 + 0.756934i) q^{6} +(5.91718 - 8.14430i) q^{7} +(-1.66251 - 2.28825i) q^{8} +(0.927051 - 2.85317i) q^{9} -8.97571i q^{10} +(10.7270 + 2.43542i) q^{11} +3.46410 q^{12} +(-1.07106 - 0.348007i) q^{13} +(-11.5178 + 8.36815i) q^{14} +(8.89348 + 6.46149i) q^{15} +(1.23607 + 3.80423i) q^{16} +(-18.8514 + 6.12519i) q^{17} +(-2.49376 + 3.43237i) q^{18} +(0.867726 + 1.19432i) q^{19} +(-3.92253 + 12.0723i) q^{20} -17.4364i q^{21} +(-13.3635 - 7.96351i) q^{22} -38.3012 q^{23} +(-4.65921 - 1.51387i) q^{24} +(-12.3631 + 8.98233i) q^{25} +(1.28848 + 0.936136i) q^{26} +(-1.60570 - 4.94183i) q^{27} +(19.1484 - 6.22169i) q^{28} +(10.1256 - 13.9367i) q^{29} +(-9.13793 - 12.5773i) q^{30} +(-18.5793 + 57.1814i) q^{31} -5.65685i q^{32} +(17.5108 - 7.50823i) q^{33} +28.0319 q^{34} +(60.7653 + 19.7439i) q^{35} +(4.85410 - 3.52671i) q^{36} +(-19.5450 - 14.2003i) q^{37} +(-0.645151 - 1.98557i) q^{38} +(-1.85512 + 0.602766i) q^{39} +(10.5516 - 14.5230i) q^{40} +(-19.6761 - 27.0818i) q^{41} +(-7.61998 + 23.4519i) q^{42} -42.3015i q^{43} +(14.4937 + 16.5509i) q^{44} +19.0404 q^{45} +(51.5150 + 16.7382i) q^{46} +(48.3094 - 35.0988i) q^{47} +(5.60503 + 4.07230i) q^{48} +(-16.1747 - 49.7808i) q^{49} +(20.5538 - 6.67833i) q^{50} +(-20.1798 + 27.7751i) q^{51} +(-1.32390 - 1.82219i) q^{52} +(-7.40816 + 22.8000i) q^{53} +7.34847i q^{54} +(6.33793 + 69.5263i) q^{55} -28.4735 q^{56} +(2.43182 + 0.790145i) q^{57} +(-19.7095 + 14.3198i) q^{58} +(-35.0787 - 25.4862i) q^{59} +(6.79402 + 20.9098i) q^{60} +(-97.0652 + 31.5384i) q^{61} +(49.9783 - 68.7893i) q^{62} +(-17.7515 - 24.4329i) q^{63} +(-2.47214 + 7.60845i) q^{64} -7.14758i q^{65} +(-26.8331 + 2.44607i) q^{66} +110.204 q^{67} +(-37.7028 - 12.2504i) q^{68} +(-53.6699 + 38.9934i) q^{69} +(-73.1008 - 53.1109i) q^{70} +(10.2735 + 31.6186i) q^{71} +(-8.06998 + 2.62210i) q^{72} +(-26.8929 + 37.0149i) q^{73} +(20.0822 + 27.6408i) q^{74} +(-8.17925 + 25.1731i) q^{75} +2.95253i q^{76} +(83.3084 - 72.9531i) q^{77} +2.75855 q^{78} +(73.0619 + 23.7393i) q^{79} +(-20.5386 + 14.9222i) q^{80} +(-7.28115 - 5.29007i) q^{81} +(14.6291 + 45.0237i) q^{82} +(-67.1877 + 21.8306i) q^{83} +(20.4977 - 28.2127i) q^{84} +(-73.9451 - 101.777i) q^{85} +(-18.4864 + 56.8953i) q^{86} -29.8376i q^{87} +(-12.2609 - 28.5949i) q^{88} +53.1788 q^{89} +(-25.6092 - 8.32094i) q^{90} +(-9.17190 + 6.66377i) q^{91} +(-61.9726 - 45.0258i) q^{92} +(32.1804 + 99.0410i) q^{93} +(-80.3147 + 26.0958i) q^{94} +(-5.50727 + 7.58010i) q^{95} +(-5.75910 - 7.92672i) q^{96} +(33.4207 - 102.858i) q^{97} +74.0236i q^{98} +(16.8932 - 28.3482i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 8 q^{5} + 60 q^{7} - 12 q^{9} - 4 q^{11} - 60 q^{13} - 32 q^{14} + 12 q^{15} - 16 q^{16} - 60 q^{17} - 16 q^{20} - 48 q^{22} - 8 q^{23} - 48 q^{25} + 48 q^{26} + 40 q^{28} - 160 q^{29}+ \cdots + 48 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 8 * q^5 + 60 * q^7 - 12 * q^9 - 4 * q^11 - 60 * q^13 - 32 * q^14 + 12 * q^15 - 16 * q^16 - 60 * q^17 - 16 * q^20 - 48 * q^22 - 8 * q^23 - 48 * q^25 + 48 * q^26 + 40 * q^28 - 160 * q^29 + 32 * q^31 + 36 * q^33 - 64 * q^34 + 160 * q^35 + 24 * q^36 - 84 * q^37 - 48 * q^38 - 80 * q^40 + 40 * q^41 + 96 * q^42 + 168 * q^44 + 24 * q^45 + 160 * q^46 + 372 * q^47 + 96 * q^49 + 160 * q^50 + 120 * q^51 + 40 * q^52 - 124 * q^53 + 32 * q^55 - 96 * q^56 - 120 * q^57 - 16 * q^58 - 172 * q^59 - 24 * q^60 + 100 * q^61 - 40 * q^62 - 180 * q^63 + 32 * q^64 - 216 * q^66 + 248 * q^67 - 120 * q^68 - 372 * q^69 + 8 * q^70 + 48 * q^71 + 160 * q^73 + 80 * q^74 + 192 * q^75 - 172 * q^77 - 460 * q^79 - 48 * q^80 - 36 * q^81 - 24 * q^82 - 420 * q^83 - 420 * q^85 - 456 * q^86 - 144 * q^88 - 360 * q^89 - 252 * q^91 - 64 * q^92 - 24 * q^93 - 280 * q^94 + 180 * q^95 + 324 * q^97 + 48 * q^99

Introduction

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