LMFDB - Embedded newform 56.3.j.a.45.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,3,Mod(5,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("56.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	56.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.52588948042$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			45.3
Character	$\chi$	$=$	56.45
Dual form			56.3.j.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70738 - 1.04157i) q^{2} +(2.78005 - 4.81519i) q^{3} +(1.83027 + 3.55670i) q^{4} +(-1.52921 - 2.64866i) q^{5} +(-9.76195 + 5.32573i) q^{6} +(0.608243 + 6.97352i) q^{7} +(0.579586 - 7.97898i) q^{8} +(-10.9574 - 18.9787i) q^{9} +O(q^{10})$	\(q+(-1.70738 - 1.04157i) q^{2} +(2.78005 - 4.81519i) q^{3} +(1.83027 + 3.55670i) q^{4} +(-1.52921 - 2.64866i) q^{5} +(-9.76195 + 5.32573i) q^{6} +(0.608243 + 6.97352i) q^{7} +(0.579586 - 7.97898i) q^{8} +(-10.9574 - 18.9787i) q^{9} +(-0.147833 + 6.11504i) q^{10} +(0.106038 + 0.0612210i) q^{11} +(22.2144 + 1.07471i) q^{12} +4.11412 q^{13} +(6.22490 - 12.5400i) q^{14} -17.0051 q^{15} +(-9.30022 + 13.0194i) q^{16} +(17.8551 + 10.3087i) q^{17} +(-1.05928 + 43.8167i) q^{18} +(4.46893 + 7.74042i) q^{19} +(6.62164 - 10.2867i) q^{20} +(35.2698 + 16.4580i) q^{21} +(-0.117281 - 0.214973i) q^{22} +(7.51940 + 13.0240i) q^{23} +(-36.8090 - 24.9728i) q^{24} +(7.82306 - 13.5499i) q^{25} +(-7.02435 - 4.28514i) q^{26} -71.8074 q^{27} +(-23.6895 + 14.9268i) q^{28} -31.6239i q^{29} +(29.0341 + 17.7120i) q^{30} +(23.0318 + 13.2974i) q^{31} +(29.4396 - 12.5423i) q^{32} +(0.589582 - 0.340395i) q^{33} +(-19.7483 - 36.1981i) q^{34} +(17.5404 - 12.2750i) q^{35} +(47.4467 - 73.7083i) q^{36} +(-25.1405 + 14.5149i) q^{37} +(0.432025 - 17.8705i) q^{38} +(11.4375 - 19.8103i) q^{39} +(-22.0199 + 10.6664i) q^{40} +9.26915i q^{41} +(-43.0767 - 64.8358i) q^{42} +45.3391i q^{43} +(-0.0236667 + 0.489196i) q^{44} +(-33.5122 + 58.0448i) q^{45} +(0.726922 - 30.0688i) q^{46} +(-68.6931 + 39.6600i) q^{47} +(36.8360 + 80.9771i) q^{48} +(-48.2601 + 8.48319i) q^{49} +(-27.4701 + 14.9866i) q^{50} +(99.2764 - 57.3172i) q^{51} +(7.52995 + 14.6327i) q^{52} +(-55.0507 - 31.7835i) q^{53} +(122.602 + 74.7923i) q^{54} -0.374478i q^{55} +(55.9941 - 0.811397i) q^{56} +49.6955 q^{57} +(-32.9384 + 53.9939i) q^{58} +(-14.2561 + 24.6923i) q^{59} +(-31.1239 - 60.4820i) q^{60} +(-12.6191 - 21.8569i) q^{61} +(-25.4738 - 46.6929i) q^{62} +(125.684 - 87.9552i) q^{63} +(-63.3282 - 9.24901i) q^{64} +(-6.29133 - 10.8969i) q^{65} +(-1.36118 - 0.0329070i) q^{66} +(65.4798 + 37.8048i) q^{67} +(-3.98511 + 82.3730i) q^{68} +83.6173 q^{69} +(-42.7333 + 2.68851i) q^{70} -2.81874 q^{71} +(-157.782 + 76.4289i) q^{72} +(11.0878 + 6.40155i) q^{73} +(58.0426 + 1.40320i) q^{74} +(-43.4970 - 75.3391i) q^{75} +(-19.3510 + 30.0617i) q^{76} +(-0.362429 + 0.776695i) q^{77} +(-40.1618 + 21.9107i) q^{78} +(-35.6186 - 61.6932i) q^{79} +(48.7061 + 4.72374i) q^{80} +(-101.012 + 174.958i) q^{81} +(9.65446 - 15.8259i) q^{82} -30.0525 q^{83} +(6.01725 + 155.567i) q^{84} -63.0563i q^{85} +(47.2238 - 77.4109i) q^{86} +(-152.275 - 87.9160i) q^{87} +(0.549939 - 0.810591i) q^{88} +(15.3030 - 8.83521i) q^{89} +(117.676 - 64.1991i) q^{90} +(2.50238 + 28.6899i) q^{91} +(-32.5599 + 50.5816i) q^{92} +(128.059 - 73.9351i) q^{93} +(158.594 + 3.83405i) q^{94} +(13.6678 - 23.6734i) q^{95} +(21.4503 - 176.626i) q^{96} +26.1737i q^{97} +(91.2340 + 35.7822i) q^{98} -2.68329i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 4 * q^4 - 4 * q^7 - 20 * q^8 - 32 * q^9	$ 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9} + 24 q^{10} - 18 q^{12} + 24 q^{14} + 28 q^{15} + 16 q^{16} - 6 q^{17} - 42 q^{18} - 92 q^{22} + 30 q^{23} - 30 q^{24} - 32 q^{25} - 30 q^{26} - 42 q^{28} + 22 q^{30} - 6 q^{31} + 88 q^{32} - 6 q^{33} + 256 q^{36} + 6 q^{38} - 20 q^{39} + 102 q^{40} + 18 q^{42} - 42 q^{44} + 68 q^{46} - 294 q^{47} - 20 q^{49} + 400 q^{50} - 168 q^{52} + 330 q^{54} - 96 q^{56} + 124 q^{57} - 22 q^{58} - 62 q^{60} + 432 q^{63} - 520 q^{64} - 52 q^{65} - 306 q^{66} - 456 q^{68} - 324 q^{70} - 136 q^{71} + 96 q^{72} + 234 q^{73} - 138 q^{74} - 956 q^{78} - 162 q^{79} + 276 q^{80} - 18 q^{81} - 642 q^{82} + 504 q^{84} + 168 q^{86} + 48 q^{87} + 50 q^{88} - 150 q^{89} + 1020 q^{92} + 618 q^{94} + 290 q^{95} + 1044 q^{96} + 424 q^{98}+O(q^{100}) $ 28 * q - 2 * q^2 - 4 * q^4 - 4 * q^7 - 20 * q^8 - 32 * q^9 + 24 * q^10 - 18 * q^12 + 24 * q^14 + 28 * q^15 + 16 * q^16 - 6 * q^17 - 42 * q^18 - 92 * q^22 + 30 * q^23 - 30 * q^24 - 32 * q^25 - 30 * q^26 - 42 * q^28 + 22 * q^30 - 6 * q^31 + 88 * q^32 - 6 * q^33 + 256 * q^36 + 6 * q^38 - 20 * q^39 + 102 * q^40 + 18 * q^42 - 42 * q^44 + 68 * q^46 - 294 * q^47 - 20 * q^49 + 400 * q^50 - 168 * q^52 + 330 * q^54 - 96 * q^56 + 124 * q^57 - 22 * q^58 - 62 * q^60 + 432 * q^63 - 520 * q^64 - 52 * q^65 - 306 * q^66 - 456 * q^68 - 324 * q^70 - 136 * q^71 + 96 * q^72 + 234 * q^73 - 138 * q^74 - 956 * q^78 - 162 * q^79 + 276 * q^80 - 18 * q^81 - 642 * q^82 + 504 * q^84 + 168 * q^86 + 48 * q^87 + 50 * q^88 - 150 * q^89 + 1020 * q^92 + 618 * q^94 + 290 * q^95 + 1044 * q^96 + 424 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−1.70738	−	1.04157i	−0.853688	−	0.520784i
$2$	−1.70738	−	1.04157i	−0.853688	−	0.520784i
$3$	2.78005	−	4.81519i	0.926684	−	1.60506i	0.137854	−	0.990453i	$-0.455980\pi$
$3$	2.78005	−	4.81519i	0.926684	−	1.60506i	0.788830	−	0.614611i	$-0.210687\pi$
$4$	1.83027	+	3.55670i	0.457568	+	0.889175i
$5$	−1.52921	−	2.64866i	−0.305841	−	0.529732i	0.671607	−	0.740907i	$-0.265604\pi$
$5$	−1.52921	−	2.64866i	−0.305841	−	0.529732i	−0.977448	+	0.211175i	$0.932271\pi$
$6$	−9.76195	+	5.32573i	−1.62699	+	0.887622i
$7$	0.608243	+	6.97352i	0.0868918	+	0.996218i
$7$	0.608243	+	6.97352i	0.0868918	+	0.996218i
$8$	0.579586	−	7.97898i	0.0724482	−	0.997372i
$9$	−10.9574	−	18.9787i	−1.21749	−	2.10875i
$10$	−0.147833	+	6.11504i	−0.0147833	+	0.611504i
$11$	0.106038	+	0.0612210i	0.00963981	+	0.00556554i	0.504812	−	0.863229i	$-0.331562\pi$
$11$	0.106038	+	0.0612210i	0.00963981	+	0.00556554i	−0.495172	+	0.868795i	$0.664895\pi$
$12$	22.2144	+	1.07471i	1.85120	+	0.0895591i
$13$	4.11412			0.316471			0.158235	−	0.987401i	$-0.449420\pi$
$13$	4.11412			0.316471			0.158235	+	0.987401i	$0.449420\pi$
$14$	6.22490	−	12.5400i	0.444636	−	0.895711i
$15$	−17.0051			−1.13367
$16$	−9.30022	+	13.0194i	−0.581264	+	0.813715i
$17$	17.8551	+	10.3087i	1.05030	+	0.606392i	0.922734	−	0.385438i	$-0.125950\pi$
$17$	17.8551	+	10.3087i	1.05030	+	0.606392i	0.127568	+	0.991830i	$0.459283\pi$
$18$	−1.05928	+	43.8167i	−0.0588490	+	2.43426i
$19$	4.46893	+	7.74042i	0.235207	+	0.407390i	0.959333	−	0.282277i	$-0.0910899\pi$
$19$	4.46893	+	7.74042i	0.235207	+	0.407390i	−0.724126	+	0.689668i	$0.757757\pi$
$20$	6.62164	−	10.2867i	0.331082	−	0.514335i
$21$	35.2698	+	16.4580i	1.67951	+	0.783712i
$22$	−0.117281	−	0.214973i	−0.00533094	−	0.00977150i
$23$	7.51940	+	13.0240i	0.326930	+	0.566260i	0.981901	−	0.189394i	$-0.0606524\pi$
$23$	7.51940	+	13.0240i	0.326930	+	0.566260i	−0.654971	+	0.755654i	$0.727319\pi$
$24$	−36.8090	−	24.9728i	−1.53371	−	1.04053i
$25$	7.82306	−	13.5499i	0.312922	−	0.541998i
$26$	−7.02435	−	4.28514i	−0.270167	−	0.164813i
$27$	−71.8074			−2.65953
$28$	−23.6895	+	14.9268i	−0.846053	+	0.533099i
$29$		−	31.6239i		−	1.09048i	−0.838280	−	0.545239i	$-0.816439\pi$
$29$		−	31.6239i		−	1.09048i	0.838280	−	0.545239i	$-0.183561\pi$
$30$	29.0341	+	17.7120i	0.967803	+	0.590399i
$31$	23.0318	+	13.2974i	0.742962	+	0.428949i	0.823145	−	0.567831i	$-0.192217\pi$
$31$	23.0318	+	13.2974i	0.742962	+	0.428949i	−0.0801833	+	0.996780i	$0.525551\pi$
$32$	29.4396	−	12.5423i	0.919988	−	0.391946i
$33$	0.589582	−	0.340395i	0.0178661	−	0.0103150i
$34$	−19.7483	−	36.1981i	−0.580831	−	1.06465i
$35$	17.5404	−	12.2750i	0.501154	−	0.350714i
$36$	47.4467	−	73.7083i	1.31796	−	2.04745i
$37$	−25.1405	+	14.5149i	−0.679474	+	0.392295i	−0.799657	−	0.600457i	$-0.794985\pi$
$37$	−25.1405	+	14.5149i	−0.679474	+	0.392295i	0.120183	+	0.992752i	$0.461652\pi$
$38$	0.432025	−	17.8705i	0.0113691	−	0.470276i
$39$	11.4375	−	19.8103i	0.293268	−	0.507956i
$40$	−22.0199	+	10.6664i	−0.550498	+	0.266659i
$41$			9.26915i			0.226077i	0.993591	+	0.113038i	$0.0360583\pi$
$41$			9.26915i			0.226077i	−0.993591	+	0.113038i	$0.963942\pi$
$42$	−43.0767	−	64.8358i	−1.02564	−	1.54371i
$43$			45.3391i			1.05440i	0.849742	+	0.527199i	$0.176758\pi$
$43$			45.3391i			1.05440i	−0.849742	+	0.527199i	$0.823242\pi$
$44$	−0.0236667	+	0.489196i	−0.000537880	+	0.0111181i
$45$	−33.5122	+	58.0448i	−0.744715	+	1.28988i
$46$	0.726922	−	30.0688i	0.0158027	−	0.653670i
$47$	−68.6931	+	39.6600i	−1.46156	+	0.843830i	−0.999083	−	0.0428039i	$-0.986371\pi$
$47$	−68.6931	+	39.6600i	−1.46156	+	0.843830i	−0.462472	+	0.886634i	$0.653038\pi$
$48$	36.8360	+	80.9771i	0.767417	+	1.68702i
$49$	−48.2601	+	8.48319i	−0.984900	+	0.173126i
$50$	−27.4701	+	14.9866i	−0.549402	+	0.299732i
$51$	99.2764	−	57.3172i	1.94660	−	1.12387i
$52$	7.52995	+	14.6327i	0.144807	+	0.281398i
$53$	−55.0507	−	31.7835i	−1.03869	−	0.599689i	−0.119229	−	0.992867i	$-0.538042\pi$
$53$	−55.0507	−	31.7835i	−1.03869	−	0.599689i	−0.919462	+	0.393178i	$0.871376\pi$
$54$	122.602	+	74.7923i	2.27041	+	1.38504i
$55$		−	0.374478i		−	0.00680869i
$56$	55.9941	−	0.811397i	0.999895	−	0.0144892i
$57$	49.6955			0.871850
$58$	−32.9384	+	53.9939i	−0.567904	+	0.930929i
$59$	−14.2561	+	24.6923i	−0.241629	+	0.418514i	−0.961178	−	0.275928i	$-0.911015\pi$
$59$	−14.2561	+	24.6923i	−0.241629	+	0.418514i	0.719550	+	0.694441i	$0.244348\pi$
$60$	−31.1239	−	60.4820i	−0.518732	−	1.00803i
$61$	−12.6191	−	21.8569i	−0.206871	−	0.358311i	0.743856	−	0.668339i	$-0.232995\pi$
$61$	−12.6191	−	21.8569i	−0.206871	−	0.358311i	−0.950727	+	0.310029i	$0.899661\pi$
$62$	−25.4738	−	46.6929i	−0.410868	−	0.753112i
$63$	125.684	−	87.9552i	1.99498	−	1.39611i
$64$	−63.3282	−	9.24901i	−0.989503	−	0.144516i
$65$	−6.29133	−	10.8969i	−0.0967897	−	0.167645i
$66$	−1.36118	−	0.0329070i	−0.0206240	−	0.000498591i
$67$	65.4798	+	37.8048i	0.977311	+	0.564251i	0.901457	−	0.432868i	$-0.142498\pi$
$67$	65.4798	+	37.8048i	0.977311	+	0.564251i	0.0758537	+	0.997119i	$0.475832\pi$
$68$	−3.98511	+	82.3730i	−0.0586046	+	1.21137i
$69$	83.6173			1.21184
$70$	−42.7333	+	2.68851i	−0.610475	+	0.0384073i
$71$	−2.81874			−0.0397006			−0.0198503	−	0.999803i	$-0.506319\pi$
$71$	−2.81874			−0.0397006			−0.0198503	+	0.999803i	$0.506319\pi$
$72$	−157.782	+	76.4289i	−2.19141	+	1.06151i
$73$	11.0878	+	6.40155i	0.151888	+	0.0876925i	0.574018	−	0.818843i	$-0.305384\pi$
$73$	11.0878	+	6.40155i	0.151888	+	0.0876925i	−0.422130	+	0.906535i	$0.638717\pi$
$74$	58.0426	+	1.40320i	0.784360	+	0.0189621i
$75$	−43.4970	−	75.3391i	−0.579960	−	1.00452i
$76$	−19.3510	+	30.0617i	−0.254618	+	0.395549i
$77$	−0.362429	+	0.776695i	−0.00470687	+	0.0100869i
$78$	−40.1618	+	21.9107i	−0.514895	+	0.280906i
$79$	−35.6186	−	61.6932i	−0.450868	−	0.780926i	0.547572	−	0.836758i	$-0.315552\pi$
$79$	−35.6186	−	61.6932i	−0.450868	−	0.780926i	−0.998440	+	0.0558321i	$0.982219\pi$
$80$	48.7061	+	4.72374i	0.608826	+	0.0590468i
$81$	−101.012	+	174.958i	−1.24706	+	2.15997i
$82$	9.65446	−	15.8259i	0.117737	−	0.192999i
$83$	−30.0525			−0.362078			−0.181039	−	0.983476i	$-0.557946\pi$
$83$	−30.0525			−0.362078			−0.181039	+	0.983476i	$0.557946\pi$
$84$	6.01725	+	155.567i	0.0716340	+	1.85198i
$85$		−	63.0563i		−	0.741839i
$86$	47.2238	−	77.4109i	0.549114	−	0.900127i
$87$	−152.275	−	87.9160i	−1.75029	−	1.01053i
$88$	0.549939	−	0.810591i	0.00624931	−	0.00921126i
$89$	15.3030	−	8.83521i	0.171944	−	0.0992720i	−0.411558	−	0.911384i	$-0.635015\pi$
$89$	15.3030	−	8.83521i	0.171944	−	0.0992720i	0.583502	+	0.812112i	$0.301682\pi$
$90$	117.676	−	64.1991i	1.30751	−	0.713323i
$91$	2.50238	+	28.6899i	0.0274987	+	0.315274i
$92$	−32.5599	+	50.5816i	−0.353911	+	0.549800i
$93$	128.059	−	73.9351i	1.37698	−	0.795001i
$94$	158.594	+	3.83405i	1.68717	+	0.0407877i
$95$	13.6678	−	23.6734i	0.143872	−	0.249193i
$96$	21.4503	−	176.626i	0.223440	−	1.83985i
$97$			26.1737i			0.269832i	0.990857	+	0.134916i	$0.0430765\pi$
$97$			26.1737i			0.269832i	−0.990857	+	0.134916i	$0.956923\pi$
$98$	91.2340	+	35.7822i	0.930959	+	0.365124i
$99$		−	2.68329i		−	0.0271039i
$100$	62.5114	+	3.02423i	0.625114	+	0.0302423i
$101$	−67.8445	+	117.510i	−0.671727	+	1.16347i	0.305686	+	0.952132i	$0.401114\pi$
$101$	−67.8445	+	117.510i	−0.671727	+	1.16347i	−0.977414	+	0.211334i	$0.932219\pi$
$102$	−229.202	−	5.54103i	−2.24708	−	0.0543238i
$103$	110.258	−	63.6577i	1.07047	−	0.618036i	0.142160	−	0.989844i	$-0.454595\pi$
$103$	110.258	−	63.6577i	1.07047	−	0.618036i	0.928310	+	0.371807i	$0.121262\pi$
$104$	2.38448	−	32.8265i	0.0229277	−	0.315639i
$105$	−10.3432	−	118.585i	−0.0985068	−	1.12938i
$106$	60.8875	+	111.605i	0.574410	+	1.05288i
$107$	−69.1003	+	39.8951i	−0.645797	+	0.372851i	−0.786844	−	0.617152i	$-0.788287\pi$
$107$	−69.1003	+	39.8951i	−0.645797	+	0.372851i	0.141047	+	0.990003i	$0.454953\pi$
$108$	−131.427	−	255.397i	−1.21692	−	2.36479i
$109$	−27.3608	−	15.7968i	−0.251017	−	0.144925i	0.369213	−	0.929345i	$-0.379627\pi$
$109$	−27.3608	−	15.7968i	−0.251017	−	0.144925i	−0.620230	+	0.784420i	$0.712961\pi$
$110$	−0.390044	+	0.639375i	−0.00354586	+	0.00581250i
$111$			161.409i			1.45413i
$112$	−96.4482	−	56.9364i	−0.861144	−	0.508360i
$113$	57.7985			0.511491			0.255745	−	0.966744i	$-0.417679\pi$
$113$	57.7985			0.511491			0.255745	+	0.966744i	$0.417679\pi$
$114$	−84.8489	−	51.7612i	−0.744288	−	0.454046i
$115$	22.9974	−	39.8327i	0.199978	−	0.346371i
$116$	112.477	−	57.8802i	0.969626	−	0.498968i
$117$	−45.0799	−	78.0808i	−0.385299	−	0.667357i
$118$	50.0593	−	27.3103i	0.424231	−	0.231444i
$119$	−61.0275	+	130.783i	−0.512836	+	1.09902i
$120$	−9.85591	+	135.683i	−0.0821326	+	1.13069i
$121$	−60.4925	−	104.776i	−0.499938	−	0.865918i
$122$	−1.21993	+	50.4617i	−0.00999940	+	0.413621i
$123$	44.6327	+	25.7687i	0.362868	+	0.209502i
$124$	−5.14050	+	106.255i	−0.0414557	+	0.856896i
$125$	−124.313			−0.994500
$126$	−306.201	+	19.2643i	−2.43017	+	0.152891i
$127$	67.8062			0.533907			0.266954	−	0.963709i	$-0.413983\pi$
$127$	67.8062			0.533907			0.266954	+	0.963709i	$0.413983\pi$
$128$	98.4915	+	81.7522i	0.769465	+	0.638689i
$129$	218.316	+	126.045i	1.69238	+	0.977093i
$130$	−0.608202	+	25.1580i	−0.00467847	+	0.193523i
$131$	−56.0784	−	97.1307i	−0.428080	−	0.741456i	0.568623	−	0.822598i	$-0.307476\pi$
$131$	−56.0784	−	97.1307i	−0.428080	−	0.741456i	−0.996702	+	0.0811427i	$0.974143\pi$
$132$	2.28978	+	1.47395i	0.0173468	+	0.0111663i
$133$	−51.2598	+	35.8723i	−0.385412	+	0.269716i
$134$	−72.4224	−	132.749i	−0.540466	−	0.990662i
$135$	109.808	+	190.193i	0.813394	+	1.40884i
$136$	92.6012	−	136.491i	0.680891	−	1.00361i
$137$	29.3413	−	50.8207i	0.214170	−	0.370954i	−0.738845	−	0.673875i	$-0.764629\pi$
$137$	29.3413	−	50.8207i	0.214170	−	0.370954i	0.953016	+	0.302921i	$0.0979619\pi$
$138$	−142.766	−	87.0931i	−1.03454	−	0.631110i
$139$	175.260			1.26086			0.630430	−	0.776246i	$-0.282879\pi$
$139$	175.260			1.26086			0.630430	+	0.776246i	$0.282879\pi$
$140$	75.7621	+	39.9193i	0.541158	+	0.285138i
$141$			441.027i			3.12785i
$142$	4.81265	+	2.93591i	0.0338919	+	0.0206754i
$143$	0.436252	+	0.251870i	0.00305072	+	0.00176133i
$144$	348.999	+	33.8475i	2.42360	+	0.235052i
$145$	−83.7610	+	48.3594i	−0.577662	+	0.333513i
$146$	−12.2634	−	22.4786i	−0.0839960	−	0.153963i
$147$	−93.3174	+	255.965i	−0.634812	+	1.74126i
$148$	−97.6391	−	62.8512i	−0.659724	−	0.424670i
$149$	61.6922	−	35.6180i	0.414041	−	0.239047i	−0.278483	−	0.960441i	$-0.589832\pi$
$149$	61.6922	−	35.6180i	0.414041	−	0.239047i	0.692525	+	0.721394i	$0.256498\pi$
$150$	−4.20499	+	173.937i	−0.0280332	+	1.15958i
$151$	86.3801	−	149.615i	0.572053	−	0.990825i	−0.424302	−	0.905521i	$-0.639480\pi$
$151$	86.3801	−	149.615i	0.572053	−	0.990825i	0.996355	−	0.0853045i	$-0.0271863\pi$
$152$	64.3507	−	31.1713i	0.423360	−	0.205074i
$153$		−	451.824i		−	2.95310i
$154$	1.42778	−	0.948616i	0.00927133	−	0.00615984i
$155$		−	81.3380i		−	0.524761i
$156$	91.3928	+	4.42148i	0.585851	+	0.0283428i
$157$	134.922	−	233.692i	0.859378	−	1.48849i	−0.0131460	−	0.999914i	$-0.504185\pi$
$157$	134.922	−	233.692i	0.859378	−	1.48849i	0.872524	−	0.488572i	$-0.162482\pi$
$158$	−3.44335	+	142.433i	−0.0217934	+	0.901473i
$159$	−306.087	+	176.720i	−1.92508	+	1.11144i
$160$	−78.2395	−	58.7959i	−0.488997	−	0.367474i
$161$	−86.2494	+	60.3584i	−0.535711	+	0.374897i
$162$	354.696	−	193.508i	2.18948	−	1.19449i
$163$	−236.230	+	136.387i	−1.44926	+	0.836733i	−0.998438	−	0.0558788i	$-0.982204\pi$
$163$	−236.230	+	136.387i	−1.44926	+	0.836733i	−0.450826	+	0.892612i	$0.648871\pi$
$164$	−32.9676	+	16.9650i	−0.201022	+	0.103445i
$165$	−1.80318	−	1.04107i	−0.0109284	−	0.00630950i
$166$	51.3109	+	31.3017i	0.309102	+	0.188565i
$167$			82.5676i			0.494417i	0.968962	+	0.247208i	$0.0795132\pi$
$167$			82.5676i			0.494417i	−0.968962	+	0.247208i	$0.920487\pi$
$168$	151.760	−	271.878i	0.903331	−	1.61832i
$169$	−152.074			−0.899846
$170$	−65.6774	+	107.661i	−0.386338	+	0.633299i
$171$	97.9355	−	169.629i	0.572722	−	0.991984i
$172$	−161.258	+	82.9828i	−0.937544	+	0.482458i
$173$	115.129	+	199.410i	0.665488	+	1.15266i	0.979153	+	0.203125i	$0.0651097\pi$
$173$	115.129	+	199.410i	0.665488	+	1.15266i	−0.313665	+	0.949534i	$0.601557\pi$
$174$	168.420	+	308.711i	0.967932	+	1.77420i
$175$	99.2491	+	46.3127i	0.567138	+	0.264644i
$176$	−1.78324	+	0.811185i	−0.0101320	+	0.00460901i
$177$	79.2654	+	137.292i	0.447827	+	0.775660i
$178$	−35.3305	−	0.854126i	−0.198486	−	0.00479846i
$179$	−228.664	−	132.019i	−1.27745	−	0.737538i	−0.301074	−	0.953601i	$-0.597345\pi$
$179$	−228.664	−	132.019i	−1.27745	−	0.737538i	−0.976379	+	0.216063i	$0.930678\pi$
$180$	−267.784	−	12.9551i	−1.48769	−	0.0719727i
$181$	183.991			1.01653			0.508263	−	0.861202i	$-0.330288\pi$
$181$	183.991			1.01653			0.508263	+	0.861202i	$0.330288\pi$
$182$	25.6100	−	51.5909i	0.140714	−	0.283466i
$183$	−140.327			−0.766815
$184$	108.276	−	52.4486i	0.588458	−	0.285047i
$185$	76.8901	+	44.3925i	0.415622	+	0.239960i
$186$	−295.654	−	7.14752i	−1.58954	−	0.0384275i
$187$	1.26221	+	2.18622i	0.00674980	+	0.0116910i
$188$	−266.786	−	171.732i	−1.41907	−	0.913470i
$189$	−43.6763	−	500.751i	−0.231092	−	2.64947i
$190$	−47.9936	+	26.1834i	−0.252598	+	0.137807i
$191$	−148.189	−	256.671i	−0.775860	−	1.34383i	−0.934310	−	0.356462i	$-0.883983\pi$
$191$	−148.189	−	256.671i	−0.775860	−	1.34383i	0.158450	−	0.987367i	$-0.449350\pi$
$192$	−220.591	+	279.224i	−1.14891	+	1.45429i
$193$	−47.8173	+	82.8220i	−0.247758	+	0.429129i	−0.962903	−	0.269846i	$-0.913027\pi$
$193$	−47.8173	+	82.8220i	−0.247758	+	0.429129i	0.715145	+	0.698976i	$0.246360\pi$
$194$	27.2617	−	44.6884i	0.140524	−	0.230353i
$195$	−69.9609			−0.358774
$196$	−118.501	−	156.120i	−0.604598	−	0.796531i
$197$		−	161.104i		−	0.817786i	−0.912582	−	0.408893i	$-0.865915\pi$
$197$		−	161.104i		−	0.817786i	0.912582	−	0.408893i	$-0.134085\pi$
$198$	−2.79483	+	4.58138i	−0.0141153	+	0.0231383i
$199$	0.961074	+	0.554877i	0.00482952	+	0.00278832i	0.502413	−	0.864628i	$-0.332446\pi$
$199$	0.961074	+	0.554877i	0.00482952	+	0.00278832i	−0.497583	+	0.867416i	$0.665779\pi$
$200$	−103.581	−	70.2734i	−0.517903	−	0.351367i
$201$	364.075	−	210.199i	1.81132	−	1.04576i
$202$	238.231	−	129.969i	1.17936	−	0.643412i
$203$	220.530	−	19.2350i	1.08635	−	0.0947536i
$204$	385.563	+	248.190i	1.89001	+	1.21662i
$205$	24.5508	−	14.1744i	0.119760	−	0.0691436i
$206$	−254.557	−	6.15398i	−1.23571	−	0.0298737i
$207$	164.786	−	285.417i	0.796067	−	1.37883i
$208$	−38.2622	+	53.5635i	−0.183953	+	0.257517i
$209$			1.09437i			0.00523622i
$210$	−105.855	+	213.243i	−0.504072	+	1.01544i
$211$		−	214.045i		−	1.01443i	−0.861819	−	0.507216i	$-0.830675\pi$
$211$		−	214.045i		−	1.01443i	0.861819	−	0.507216i	$-0.169325\pi$
$212$	12.2868	−	253.971i	0.0579568	−	1.19798i
$213$	−7.83624	+	13.5728i	−0.0367899	+	0.0637219i
$214$	159.534	+	3.85678i	0.745485	+	0.0180223i
$215$	120.088	−	69.3328i	0.558549	−	0.322478i
$216$	−41.6185	+	572.949i	−0.192678	+	2.65254i
$217$	−78.7210	+	168.701i	−0.362770	+	0.777424i
$218$	30.2618	+	55.4692i	0.138816	+	0.254446i
$219$	61.6494	−	35.5933i	0.281504	−	0.162526i
$220$	1.33191	−	0.685396i	0.00605412	−	0.00311544i
$221$	73.4581	+	42.4111i	0.332390	+	0.191905i
$222$	168.118	−	275.585i	0.757289	−	1.24138i
$223$			290.270i			1.30166i	0.759224	+	0.650829i	$0.225579\pi$
$223$			290.270i			1.30166i	−0.759224	+	0.650829i	$0.774421\pi$
$224$	105.370	+	197.669i	0.470403	+	0.882452i
$225$	−342.881			−1.52392
$226$	−98.6837	−	60.2011i	−0.436654	−	0.266376i
$227$	−40.7118	+	70.5149i	−0.179347	+	0.310638i	−0.941657	−	0.336574i	$-0.890732\pi$
$227$	−40.7118	+	70.5149i	−0.179347	+	0.310638i	0.762310	+	0.647212i	$0.224065\pi$
$228$	90.9561	+	176.752i	0.398930	+	0.775227i
$229$	117.111	+	202.842i	0.511400	+	0.885771i	0.999913	+	0.0132145i	$0.00420642\pi$
$229$	117.111	+	202.842i	0.511400	+	0.885771i	−0.488512	+	0.872557i	$0.662460\pi$
$230$	−80.7537	+	44.0560i	−0.351103	+	0.191548i
$231$	2.73236	+	3.90442i	0.0118284	+	0.0169022i
$232$	−252.326	−	18.3288i	−1.08761	−	0.0790032i
$233$	30.9903	+	53.6768i	0.133006	+	0.230372i	0.924834	−	0.380371i	$-0.124204\pi$
$233$	30.9903	+	53.6768i	0.133006	+	0.230372i	−0.791828	+	0.610744i	$0.790871\pi$
$234$	−4.35801	+	180.267i	−0.0186240	+	0.770372i
$235$	210.092	+	121.297i	0.894008	+	0.516156i
$236$	−113.916	−	5.51111i	−0.482693	−	0.0233522i
$237$	−396.086			−1.67125
$238$	240.417	−	159.732i	1.01015	−	0.671144i
$239$	97.0822			0.406202			0.203101	−	0.979158i	$-0.434898\pi$
$239$	97.0822			0.406202			0.203101	+	0.979158i	$0.434898\pi$
$240$	158.151	−	221.397i	0.658963	−	0.922486i
$241$	−207.622	−	119.871i	−0.861502	−	0.497388i	0.00301303	−	0.999995i	$-0.499041\pi$
$241$	−207.622	−	119.871i	−0.861502	−	0.497388i	−0.864515	+	0.502607i	$0.832374\pi$
$242$	−5.84799	+	241.899i	−0.0241652	+	0.999584i
$243$	238.503	+	413.100i	0.981494	+	1.70000i
$244$	54.6422	−	84.8865i	0.223943	−	0.347895i
$245$	96.2687	+	114.852i	0.392933	+	0.468784i
$246$	−49.3650	−	90.4850i	−0.200671	−	0.367825i
$247$	18.3857	+	31.8450i	0.0744361	+	0.128927i
$248$	119.449	−	176.063i	0.481648	−	0.709933i
$249$	−83.5475	+	144.709i	−0.335532	+	0.581159i
$250$	212.248	+	129.480i	0.848993	+	0.517920i
$251$	136.078			0.542144			0.271072	−	0.962559i	$-0.412622\pi$
$251$	136.078			0.542144			0.271072	+	0.962559i	$0.412622\pi$
$252$	542.866	+	286.038i	2.15423	+	1.13507i
$253$			1.84138i			0.00727818i
$254$	−115.771	−	70.6248i	−0.455790	−	0.278051i
$255$	−303.628	−	175.300i	−1.19070	−	0.687450i
$256$	−83.0117	−	242.167i	−0.324264	−	0.945966i
$257$	−16.4497	+	9.49721i	−0.0640064	+	0.0369541i	−0.531662	−	0.846957i	$-0.678432\pi$
$257$	−16.4497	+	9.49721i	−0.0640064	+	0.0369541i	0.467655	+	0.883911i	$0.345099\pi$
$258$	−241.464	−	442.598i	−0.935906	−	1.71550i
$259$	−116.512	−	166.490i	−0.449852	−	0.642817i
$260$	27.2422	−	42.3207i	0.104778	−	0.162772i
$261$	−600.181	+	346.515i	−2.29954	+	1.32764i
$262$	−5.42127	+	224.248i	−0.0206919	+	0.855909i
$263$	−123.286	+	213.537i	−0.468767	+	0.811928i	−0.999363	−	0.0356971i	$-0.988635\pi$
$263$	−123.286	+	213.537i	−0.468767	+	0.811928i	0.530596	+	0.847625i	$0.321968\pi$
$264$	−2.37429	−	4.90155i	−0.00899353	−	0.0185665i
$265$			194.414i			0.733638i
$266$	124.883	−	7.85687i	0.469486	−	0.0295371i
$267$		−	98.2494i		−	0.367975i
$268$	−14.6145	+	302.085i	−0.0545318	+	1.12718i
$269$	−147.121	+	254.821i	−0.546918	+	0.947290i	0.451565	+	0.892238i	$0.350866\pi$
$269$	−147.121	+	254.821i	−0.546918	+	0.947290i	−0.998483	+	0.0550522i	$0.982467\pi$
$270$	10.6155	−	439.105i	0.0393166	−	1.62631i
$271$	392.032	−	226.340i	1.44661	−	0.835202i	0.448335	−	0.893866i	$-0.352017\pi$
$271$	392.032	−	226.340i	1.44661	−	0.835202i	0.998278	+	0.0586635i	$0.0186839\pi$
$272$	−300.270	+	136.591i	−1.10393	+	0.502173i
$273$	145.104	+	67.7100i	0.531517	+	0.248022i
$274$	−103.030	+	56.2091i	−0.376022	+	0.205143i
$275$	1.65908	−	0.957871i	0.00603302	−	0.00348317i
$276$	153.042	+	297.402i	0.554501	+	1.07754i
$277$	−252.424	−	145.737i	−0.911277	−	0.526126i	−0.0304353	−	0.999537i	$-0.509689\pi$
$277$	−252.424	−	145.737i	−0.911277	−	0.526126i	−0.880842	+	0.473411i	$0.843023\pi$
$278$	−299.234	−	182.545i	−1.07638	−	0.656636i
$279$		−	582.820i		−	2.08896i
$280$	−87.7756	−	147.069i	−0.313484	−	0.525245i
$281$	495.433			1.76311			0.881553	−	0.472086i	$-0.156499\pi$
$281$	495.433			1.76311			0.881553	+	0.472086i	$0.156499\pi$
$282$	459.360	−	753.000i	1.62894	−	2.67021i
$283$	−18.3685	+	31.8151i	−0.0649062	+	0.112421i	−0.896652	−	0.442735i	$-0.854008\pi$
$283$	−18.3685	+	31.8151i	−0.0649062	+	0.112421i	0.831746	+	0.555156i	$0.187341\pi$
$284$	−5.15906	−	10.0254i	−0.0181657	−	0.0353007i
$285$	−75.9946	−	131.626i	−0.266648	−	0.461847i
$286$	−0.482507	−	0.884424i	−0.00168709	−	0.00309239i
$287$	−64.6386	+	5.63789i	−0.225222	+	0.0196442i
$288$	−560.617	−	421.296i	−1.94659	−	1.46283i
$289$	68.0371	+	117.844i	0.235423	+	0.407764i
$290$	193.381	+	4.67505i	0.666832	+	0.0161208i
$291$	126.032	+	72.7644i	0.433098	+	0.250049i
$292$	−2.47470	+	51.1526i	−0.00847501	+	0.175180i
$293$	527.984			1.80199			0.900996	−	0.433828i	$-0.142837\pi$
$293$	527.984			1.80199			0.900996	+	0.433828i	$0.142837\pi$
$294$	425.933	−	339.833i	1.44875	−	1.15589i
$295$	87.2021			0.295600
$296$	101.243	+	209.008i	0.342037	+	0.706110i
$297$	−7.61430	−	4.39612i	−0.0256374	−	0.0148017i
$298$	−142.430	−	3.44329i	−0.477954	−	0.0115547i
$299$	30.9357	+	53.5822i	0.103464	+	0.179205i
$300$	188.347	−	292.597i	0.627824	−	0.975322i
$301$	−316.173	+	27.5772i	−1.05041	+	0.0916185i
$302$	−303.317	+	165.478i	−1.00436	+	0.547940i
$303$	377.222	+	653.368i	1.24496	+	2.15633i
$304$	−142.338	−	13.8046i	−0.468217	−	0.0454099i
$305$	−38.5944	+	66.8475i	−0.126539	+	0.219172i
$306$	−470.605	+	771.433i	−1.53793	+	2.52102i
$307$	−174.486			−0.568359			−0.284179	−	0.958771i	$-0.591721\pi$
$307$	−174.486			−0.568359			−0.284179	+	0.958771i	$0.591721\pi$
$308$	−3.42581	+	0.132509i	−0.0111228	+	0.000430224i
$309$		−	707.887i		−	2.29090i
$310$	−84.7191	+	138.875i	−0.273287	+	0.447983i
$311$	11.9119	+	6.87736i	0.0383020	+	0.0221137i	0.519029	−	0.854757i	$-0.326294\pi$
$311$	11.9119	+	6.87736i	0.0383020	+	0.0221137i	−0.480727	+	0.876870i	$0.659627\pi$
$312$	−151.437	−	102.741i	−0.485374	−	0.329298i
$313$	−365.368	+	210.945i	−1.16731	+	0.673947i	−0.953045	−	0.302829i	$-0.902069\pi$
$313$	−365.368	+	210.945i	−1.16731	+	0.673947i	−0.214265	+	0.976776i	$0.568736\pi$
$314$	−473.770	+	258.470i	−1.50882	+	0.823152i
$315$	−425.160	−	198.393i	−1.34971	−	0.629818i
$316$	154.233	−	239.600i	0.488078	−	0.758227i
$317$	408.352	−	235.762i	1.28818	−	0.743730i	0.309848	−	0.950786i	$-0.399722\pi$
$317$	408.352	−	235.762i	1.28818	−	0.743730i	0.978329	+	0.207056i	$0.0663883\pi$
$318$	706.672	+	17.0840i	2.22224	+	0.0537233i
$319$	1.93605	−	3.35333i	0.00606911	−	0.0105120i
$320$	72.3443	+	181.879i	0.226076	+	0.568370i
$321$			443.642i			1.38206i
$322$	210.128	−	13.2199i	0.652571	−	0.0410556i
$323$			184.275i			0.570510i
$324$	−807.151	−	39.0490i	−2.49121	−	0.120522i
$325$	32.1850	−	55.7460i	0.0990308	−	0.171526i
$326$	545.390	+	13.1850i	1.67298	+	0.0404447i
$327$	−152.129	+	87.8317i	−0.465226	+	0.268598i
$328$	73.9583	+	5.37227i	0.225483	+	0.0163789i
$329$	−318.352	−	454.910i	−0.967635	−	1.38271i
$330$	1.99437	+	3.65563i	0.00604354	+	0.0110777i
$331$	−383.707	+	221.533i	−1.15923	+	0.669284i	−0.951120	−	0.308820i	$-0.900066\pi$
$331$	−383.707	+	221.533i	−1.15923	+	0.669284i	−0.208114	+	0.978105i	$0.566732\pi$
$332$	−55.0042	−	106.888i	−0.165675	−	0.321951i
$333$	550.949	+	318.090i	1.65450	+	0.955227i
$334$	85.9998	−	140.974i	0.257484	−	0.422078i
$335$		−	231.245i		−	0.690284i
$336$	−542.290	+	306.130i	−1.61396	+	0.911102i
$337$	556.978			1.65276			0.826378	−	0.563117i	$-0.190398\pi$
$337$	556.978			1.65276			0.826378	+	0.563117i	$0.190398\pi$
$338$	259.648	+	158.396i	0.768188	+	0.468626i
$339$	160.683	−	278.311i	0.473990	−	0.820975i
$340$	224.272	−	115.410i	0.659624	−	0.339441i
$341$	1.62816	+	2.82006i	0.00477467	+	0.00826998i
$342$	−343.893	+	187.615i	−1.00554	+	0.548581i
$343$	−88.5116	−	331.383i	−0.258051	−	0.966131i
$344$	361.760	+	26.2779i	1.05163	+	0.0763892i
$345$	−127.868	−	221.474i	−0.370632	−	0.641953i
$346$	11.1299	−	460.383i	0.0321673	−	1.33059i
$347$	277.806	+	160.392i	0.800595	+	0.462223i	0.843679	−	0.536848i	$-0.180385\pi$
$347$	277.806	+	160.392i	0.800595	+	0.462223i	−0.0430845	+	0.999071i	$0.513718\pi$
$348$	33.9865	−	702.507i	0.0976623	−	2.01870i
$349$	−222.198			−0.636670			−0.318335	−	0.947978i	$-0.603124\pi$
$349$	−222.198			−0.636670			−0.318335	+	0.947978i	$0.603124\pi$
$350$	−121.218	−	182.448i	−0.346337	−	0.521280i
$351$	−295.424			−0.841664
$352$	3.88957	+	0.472367i	0.0110499	+	0.00134195i
$353$	−118.142	−	68.2096i	−0.334681	−	0.193228i	0.323236	−	0.946318i	$-0.395229\pi$
$353$	−118.142	−	68.2096i	−0.334681	−	0.193228i	−0.657918	+	0.753090i	$0.728562\pi$
$354$	7.66282	−	316.969i	0.0216464	−	0.895393i
$355$	4.31043	+	7.46589i	0.0121421	+	0.0210307i
$356$	59.4329	+	38.2575i	0.166946	+	0.107465i
$357$	460.087	+	657.443i	1.28876	+	1.84158i
$358$	252.909	+	463.576i	0.706449	+	1.29491i
$359$	−124.441	−	215.538i	−0.346632	−	0.600384i	0.639017	−	0.769193i	$-0.279341\pi$
$359$	−124.441	−	215.538i	−0.346632	−	0.600384i	−0.985649	+	0.168809i	$0.946008\pi$
$360$	443.715	+	301.035i	1.23254	+	0.836208i
$361$	140.557	−	243.452i	0.389355	−	0.674383i
$362$	−314.142	−	191.639i	−0.867796	−	0.529390i
$363$	−672.689			−1.85314
$364$	−97.4613	+	61.4105i	−0.267751	+	0.168710i
$365$		−	39.1572i		−	0.107280i
$366$	239.591	+	146.160i	0.654621	+	0.399345i
$367$	−225.916	−	130.432i	−0.615574	−	0.355402i	0.159570	−	0.987187i	$-0.448989\pi$
$367$	−225.916	−	130.432i	−0.615574	−	0.355402i	−0.775144	+	0.631785i	$0.782323\pi$
$368$	−239.497	−	23.2276i	−0.650807	−	0.0631184i
$369$	175.917	−	101.566i	0.476739	−	0.275245i
$370$	−85.0425	−	155.881i	−0.229845	−	0.421300i
$371$	188.159	−	403.229i	0.507167	−	1.08687i
$372$	497.348	+	320.147i	1.33696	+	0.860611i
$373$	−381.464	+	220.239i	−1.02269	+	0.590452i	−0.914883	−	0.403720i	$-0.867717\pi$
$373$	−381.464	+	220.239i	−1.02269	+	0.590452i	−0.107810	+	0.994172i	$0.534384\pi$
$374$	0.122022	−	5.04738i	0.000326262	−	0.0134957i
$375$	−345.595	+	598.589i	−0.921588	+	1.59624i
$376$	276.633	+	571.087i	0.735725	+	1.51885i
$377$		−	130.104i		−	0.345104i
$378$	−446.994	+	900.462i	−1.18252	+	2.38217i
$379$			283.715i			0.748587i	0.927310	+	0.374294i	$0.122115\pi$
$379$			283.715i			0.748587i	−0.927310	+	0.374294i	$0.877885\pi$
$380$	109.215	+	5.28369i	0.287408	+	0.0139045i
$381$	188.505	−	326.500i	0.494763	−	0.856955i
$382$	−14.3259	+	592.584i	−0.0375023	+	1.55127i
$383$	138.511	−	79.9691i	0.361646	−	0.208797i	−0.308156	−	0.951336i	$-0.599712\pi$
$383$	138.511	−	79.9691i	0.361646	−	0.208797i	0.669803	+	0.742539i	$0.266379\pi$
$384$	667.464	−	246.980i	1.73819	−	0.643178i
$385$	2.61143	−	0.227773i	0.00678294	−	0.000591619i
$386$	167.907	−	91.6033i	0.434992	−	0.237314i
$387$	860.479	−	496.798i	2.22346	−	1.28371i
$388$	−93.0921	+	47.9050i	−0.239928	+	0.123467i
$389$	−430.295	−	248.431i	−1.10616	−	0.638640i	−0.168326	−	0.985731i	$-0.553836\pi$
$389$	−430.295	−	248.431i	−1.10616	−	0.638640i	−0.937831	+	0.347091i	$0.887170\pi$
$390$	119.450	+	72.8691i	0.306281	+	0.186844i
$391$			310.060i			0.792992i
$392$	39.7163	+	389.983i	0.101317	+	0.994854i
$393$	−623.604			−1.58678
$394$	−167.801	+	275.065i	−0.425890	+	0.698134i
$395$	−108.936	+	188.683i	−0.275788	+	0.477679i
$396$	9.54364	−	4.91114i	0.0241001	−	0.0124019i
$397$	142.186	+	246.273i	0.358150	+	0.620334i	0.987652	−	0.156665i	$-0.0500743\pi$
$397$	142.186	+	246.273i	0.358150	+	0.620334i	−0.629502	+	0.776999i	$0.716741\pi$
$398$	−1.06297	−	1.94841i	−0.00267079	−	0.00489550i
$399$	30.2269	+	346.552i	0.0757566	+	0.868552i
$400$	103.656	+	227.869i	0.259141	+	0.569673i
$401$	−70.8759	−	122.761i	−0.176748	−	0.306136i	0.764017	−	0.645196i	$-0.223224\pi$
$401$	−70.8759	−	122.761i	−0.176748	−	0.306136i	−0.940765	+	0.339060i	$0.889891\pi$
$402$	−840.549	−	20.3205i	−2.09092	−	0.0505485i
$403$	94.7556	+	54.7072i	0.235126	+	0.135750i
$404$	−542.122	−	26.2272i	−1.34189	−	0.0649189i
$405$	617.872			1.52561
$406$	−396.562	−	196.856i	−0.976754	−	0.484866i
$407$	−3.55447			−0.00873333
$408$	−399.794	−	825.344i	−0.979887	−	2.02290i
$409$	−323.318	−	186.668i	−0.790508	−	0.456400i	0.0496336	−	0.998767i	$-0.484195\pi$
$409$	−323.318	−	186.668i	−0.790508	−	0.456400i	−0.840141	+	0.542368i	$0.817528\pi$
$410$	−56.6812	−	1.37028i	−0.138247	−	0.00334216i
$411$	−163.141	−	282.568i	−0.396937	−	0.687514i
$412$	428.214	+	275.645i	1.03935	+	0.669042i
$413$	−180.864	−	84.3964i	−0.437926	−	0.204350i
$414$	−578.633	+	315.679i	−1.39766	+	0.762510i
$415$	45.9565	+	79.5989i	0.110738	+	0.191805i
$416$	121.118	−	51.6004i	0.291149	−	0.124039i
$417$	487.231	−	843.908i	1.16842	−	2.02376i
$418$	1.13986	−	1.86850i	0.00272694	−	0.00447010i
$419$	418.864			0.999676			0.499838	−	0.866119i	$-0.333393\pi$
$419$	418.864			0.999676			0.499838	+	0.866119i	$0.333393\pi$
$420$	402.842	−	253.831i	0.959147	−	0.604359i
$421$		−	315.112i		−	0.748485i	−0.927331	−	0.374243i	$-0.877903\pi$
$421$		−	315.112i		−	0.748485i	0.927331	−	0.374243i	$-0.122097\pi$
$422$	−222.943	+	365.456i	−0.528300	+	0.866008i
$423$	1505.39	+	869.139i	3.55885	+	2.05470i
$424$	−285.507	+	420.827i	−0.673364	+	0.992516i
$425$	279.364	−	161.291i	0.657326	−	0.379507i
$426$	27.5164	−	15.0118i	0.0645925	−	0.0352391i
$427$	144.744	−	101.294i	0.338980	−	0.237222i
$428$	−268.367	−	172.750i	−0.627026	−	0.403622i
$429$	2.42561	−	1.40043i	0.00565410	−	0.00326440i
$430$	−277.250	−	6.70261i	−0.644768	−	0.0155875i
$431$	−111.663	+	193.405i	−0.259078	+	0.448736i	−0.965995	−	0.258560i	$-0.916752\pi$
$431$	−111.663	+	193.405i	−0.259078	+	0.448736i	0.706917	+	0.707296i	$0.250085\pi$
$432$	667.825	−	934.892i	1.54589	−	2.16410i
$433$		−	591.725i		−	1.36657i	−0.730151	−	0.683286i	$-0.760550\pi$
$433$		−	591.725i		−	1.36657i	0.730151	−	0.683286i	$-0.239450\pi$
$434$	310.120	−	206.043i	0.714562	−	0.474753i
$435$			537.767i			1.23625i
$436$	6.10670	−	126.227i	0.0140062	−	0.289510i
$437$	−67.2074	+	116.407i	−0.153793	+	0.266377i
$438$	−142.332	−	3.44091i	−0.324958	−	0.00785595i
$439$	−443.687	+	256.163i	−1.01068	+	0.583515i	−0.911390	−	0.411544i	$-0.864990\pi$
$439$	−443.687	+	256.163i	−1.01068	+	0.583515i	−0.0992873	+	0.995059i	$0.531656\pi$
$440$	−2.98795	−	0.217042i	−0.00679080	−	0.000493278i
$441$	689.804	+	822.962i	1.56418	+	1.86613i
$442$	−81.2466	−	148.923i	−0.183816	−	0.336931i
$443$	134.591	−	77.7063i	0.303818	−	0.175409i	−0.340339	−	0.940303i	$-0.610542\pi$
$443$	134.591	−	77.7063i	0.303818	−	0.175409i	0.644157	+	0.764894i	$0.277208\pi$
$444$	−574.082	+	295.422i	−1.29298	+	0.665364i
$445$	−46.8030	−	27.0217i	−0.105175	−	0.0607229i
$446$	302.336	−	495.600i	0.677883	−	1.11121i
$447$		−	396.079i		−	0.886084i
$448$	25.9793	−	447.246i	0.0579895	−	0.998317i
$449$	−369.139			−0.822136			−0.411068	−	0.911605i	$-0.634844\pi$
$449$	−369.139			−0.822136			−0.411068	+	0.911605i	$0.634844\pi$
$450$	585.427	+	357.134i	1.30095	+	0.793631i
$451$	−0.567467	+	0.982881i	−0.00125824	+	0.00217934i
$452$	105.787	+	205.572i	0.234042	+	0.454805i
$453$	−480.282	−	831.873i	−1.06023	−	1.83636i
$454$	142.957	−	77.9914i	0.314882	−	0.171787i
$455$	72.1632	−	50.5007i	0.158600	−	0.110991i
$456$	28.8028	−	396.519i	0.0631640	−	0.869559i
$457$	214.079	+	370.795i	0.468444	+	0.811369i	0.999350	−	0.0360623i	$-0.0114815\pi$
$457$	214.079	+	370.795i	0.468444	+	0.811369i	−0.530906	+	0.847431i	$0.678148\pi$
$458$	11.3214	−	468.306i	0.0247193	−	1.02250i
$459$	−1282.13	−	740.238i	−2.79331	−	1.61272i
$460$	183.764	+	8.89031i	0.399488	+	0.0193268i
$461$	−165.578			−0.359171			−0.179586	−	0.983742i	$-0.557476\pi$
$461$	−165.578			−0.359171			−0.179586	+	0.983742i	$0.557476\pi$
$462$	−0.598451	−	9.51225i	−0.00129535	−	0.0205893i
$463$	−605.376			−1.30751			−0.653754	−	0.756708i	$-0.726807\pi$
$463$	−605.376			−1.30751			−0.653754	+	0.756708i	$0.726807\pi$
$464$	411.725	+	294.109i	0.887339	+	0.633856i
$465$	−391.658	−	226.124i	−0.842275	−	0.486288i
$466$	2.99592	−	123.925i	0.00642902	−	0.265933i
$467$	−286.063	−	495.476i	−0.612555	−	1.06098i	−0.990808	−	0.135275i	$-0.956808\pi$
$467$	−286.063	−	495.476i	−0.612555	−	1.06098i	0.378253	−	0.925702i	$-0.376525\pi$
$468$	195.201	−	303.245i	0.417097	−	0.647959i
$469$	−223.805	+	479.620i	−0.477196	+	1.02264i
$470$	−232.367	−	425.924i	−0.494398	−	0.906221i
$471$	−750.182	−	1299.35i	−1.59274	−	2.75871i
$472$	188.757	+	128.060i	0.399908	+	0.271315i
$473$	−2.77570	+	4.80766i	−0.00586830	+	0.0101642i
$474$	676.268	+	412.551i	1.42673	+	0.870360i
$475$	139.843			0.294406
$476$	−576.854	+	22.3125i	−1.21188	+	0.0468750i
$477$			1393.06i			2.92045i
$478$	−165.756	−	101.118i	−0.346770	−	0.211544i
$479$	32.2540	+	18.6218i	0.0673361	+	0.0388765i	0.533290	−	0.845932i	$-0.320955\pi$
$479$	32.2540	+	18.6218i	0.0673361	+	0.0388765i	−0.465954	+	0.884809i	$0.654289\pi$
$480$	−500.623	+	213.282i	−1.04297	+	0.444338i
$481$	−103.431	+	59.7160i	−0.215034	+	0.124150i
$482$	229.635	+	420.917i	0.476422	+	0.873271i
$483$	50.8596	+	583.107i	0.105299	+	1.20726i
$484$	261.939	−	406.922i	0.541197	−	0.840748i
$485$	69.3254	−	40.0250i	0.142939	−	0.0825259i
$486$	23.0568	−	953.734i	0.0474420	−	1.96242i
$487$	−137.172	+	237.589i	−0.281668	+	0.487863i	−0.971796	−	0.235824i	$-0.924221\pi$
$487$	−137.172	+	237.589i	−0.281668	+	0.487863i	0.690128	+	0.723688i	$0.257554\pi$
$488$	−181.710	+	88.0196i	−0.372356	+	0.180368i
$489$			1516.66i			3.10155i
$490$	−44.7406	−	296.366i	−0.0913073	−	0.604829i
$491$			881.994i			1.79632i	0.439667	+	0.898161i	$0.355097\pi$
$491$			881.994i			1.79632i	−0.439667	+	0.898161i	$0.644903\pi$
$492$	−9.96164	+	205.909i	−0.0202472	+	0.418514i
$493$	326.000	−	564.648i	0.661257	−	1.14533i
$494$	1.77740	−	73.5214i	0.00359798	−	0.148829i
$495$	−7.10712	+	4.10330i	−0.0143578	+	0.00828949i
$496$	−387.326	+	176.192i	−0.780900	+	0.355227i
$497$	−1.71448	−	19.6566i	−0.00344965	−	0.0395504i
$498$	293.371	−	160.052i	0.589098	−	0.321389i
$499$	−305.733	+	176.515i	−0.612692	+	0.353738i	−0.774018	−	0.633163i	$-0.781756\pi$
$499$	−305.733	+	176.515i	−0.612692	+	0.353738i	0.161327	+	0.986901i	$0.448423\pi$
$500$	−227.526	−	442.142i	−0.455051	−	0.884285i
$501$	397.579	+	229.542i	0.793570	+	0.458168i
$502$	−232.337	−	141.735i	−0.462822	−	0.282340i
$503$		−	291.993i		−	0.580502i	−0.956951	−	0.290251i	$-0.906261\pi$
$503$		−	291.993i		−	0.580502i	0.956951	−	0.290251i	$-0.0937388\pi$
$504$	−628.948	−	1053.81i	−1.24791	−	2.09089i
$505$	414.993			0.821768
$506$	1.91792	−	3.14393i	0.00379036	−	0.00621330i
$507$	−422.774	+	732.266i	−0.833873	+	1.44431i
$508$	124.104	+	241.166i	0.244299	+	0.474737i
$509$	41.5606	+	71.9851i	0.0816515	+	0.141425i	0.903959	−	0.427618i	$-0.140647\pi$
$509$	41.5606	+	71.9851i	0.0816515	+	0.141425i	−0.822308	+	0.569043i	$0.807314\pi$
$510$	335.821	+	615.552i	0.658472	+	1.20696i
$511$	−37.8973	+	81.2148i	−0.0741630	+	0.158933i
$512$	−110.502	+	499.933i	−0.215824	+	0.976432i
$513$	−320.902	−	555.819i	−0.625541	−	1.08347i
$514$	37.9777	+	0.918123i	0.0738867	+	0.00178623i
$515$	−337.216	−	194.692i	−0.654788	−	0.378042i
$516$	−48.7263	+	1007.18i	−0.0944309	+	1.95190i
$517$	−9.71210			−0.0187855
$518$	25.5188	+	405.615i	0.0492640	+	0.783041i
$519$	1280.26			2.46679
$520$	−90.5926	+	43.8827i	−0.174216	+	0.0843898i
$521$	513.150	+	296.267i	0.984933	+	0.568651i	0.903756	−	0.428048i	$-0.140799\pi$
$521$	513.150	+	296.267i	0.984933	+	0.568651i	0.0811772	+	0.996700i	$0.474132\pi$
$522$	1385.65	+	33.4986i	2.65451	+	0.0641736i
$523$	151.233	+	261.943i	0.289164	+	0.500847i	0.973610	−	0.228217i	$-0.0732894\pi$
$523$	151.233	+	261.943i	0.289164	+	0.500847i	−0.684446	+	0.729063i	$0.739956\pi$
$524$	242.826	−	377.230i	0.463408	−	0.719904i
$525$	498.922	−	349.152i	0.950328	−	0.665051i
$526$	432.908	−	236.178i	0.823020	−	0.449007i
$527$	274.157	+	474.855i	0.520223	+	0.901052i
$528$	−1.05149	+	10.8418i	−0.00199145	+	0.0205337i
$529$	151.417	−	262.262i	0.286233	−	0.495770i
$530$	202.496	−	331.938i	0.382067	−	0.626298i
$531$	624.838			1.17672
$532$	−221.406	−	116.660i	−0.416177	−	0.219285i
$533$			38.1344i			0.0715467i
$534$	−102.333	+	167.749i	−0.191636	+	0.314136i
$535$	211.337	+	122.016i	0.395023	+	0.228067i
$536$	339.595	−	500.551i	0.633572	−	0.933864i
$537$	−1271.40	+	734.041i	−2.36759	+	1.36693i
$538$	516.605	−	281.839i	0.960232	−	0.523864i
$539$	−5.63675	−	2.05499i	−0.0104578	−	0.00381260i
$540$	−475.482	+	738.660i	−0.880523	+	1.36789i
$541$	630.140	−	363.811i	1.16477	−	0.672480i	0.212327	−	0.977199i	$-0.431896\pi$
$541$	630.140	−	363.811i	1.16477	−	0.672480i	0.952442	+	0.304719i	$0.0985626\pi$
$542$	−905.095	−	21.8809i	−1.66992	−	0.0403707i
$543$	511.505	−	885.952i	0.941997	−	1.63159i
$544$	654.942	+	79.5393i	1.20394	+	0.146212i
$545$			96.6260i			0.177296i
$546$	−177.223	−	266.742i	−0.324584	−	0.488539i
$547$		−	1033.51i		−	1.88941i	−0.327921	−	0.944705i	$-0.606348\pi$
$547$		−	1033.51i		−	1.88941i	0.327921	−	0.944705i	$-0.393652\pi$
$548$	234.457	+	11.3427i	0.427840	+	0.0206984i
$549$	−276.545	+	478.990i	−0.503724	+	0.872476i
$550$	−3.83036	−	0.0926002i	−0.00696430	−	0.000168364i
$551$	244.782	−	141.325i	0.444250	−	0.256488i
$552$	48.4634	−	667.180i	0.0877960	−	1.20866i
$553$	408.554	−	285.911i	0.738796	−	0.517019i
$554$	279.187	+	511.745i	0.503948	+	0.923727i
$555$	427.517	−	246.827i	0.770301	−	0.444734i
$556$	320.772	+	623.346i	0.576929	+	1.12113i
$557$	−625.736	−	361.269i	−1.12340	−	0.648597i	−0.181136	−	0.983458i	$-0.557977\pi$
$557$	−625.736	−	361.269i	−1.12340	−	0.648597i	−0.942268	+	0.334861i	$0.891311\pi$
$558$	−607.047	+	995.093i	−1.08790	+	1.78332i
$559$			186.530i			0.333686i
$560$	−3.31604	+	342.526i	−0.00592151	+	0.611654i
$561$	14.0361			0.0250197
$562$	−845.890	−	516.027i	−1.50514	−	0.918197i
$563$	−206.897	+	358.355i	−0.367489	+	0.636510i	−0.989172	−	0.146759i	$-0.953116\pi$
$563$	−206.897	+	358.355i	−0.367489	+	0.636510i	0.621683	+	0.783269i	$0.286449\pi$
$564$	−1568.60	+	807.199i	−2.78121	+	1.43120i
$565$	−88.3857	−	153.089i	−0.156435	−	0.270953i
$566$	64.4995	−	35.1884i	0.113957	−	0.0621702i
$567$	−1281.51	−	597.992i	−2.26016	−	1.05466i
$568$	−1.63370	+	22.4907i	−0.00287624	+	0.0395962i
$569$	258.602	+	447.911i	0.454485	+	0.787190i	0.998658	−	0.0517822i	$-0.0164901\pi$
$569$	258.602	+	447.911i	0.454485	+	0.787190i	−0.544174	+	0.838972i	$0.683157\pi$
$570$	−7.34662	+	303.889i	−0.0128888	+	0.533139i
$571$	615.938	+	355.612i	1.07870	+	0.622788i	0.930545	−	0.366177i	$-0.119333\pi$
$571$	615.938	+	355.612i	1.07870	+	0.622788i	0.148155	+	0.988964i	$0.452667\pi$
$572$	−0.0973678	+	2.01261i	−0.000170223	+	0.00351855i
$573$	−1647.89			−2.87591
$574$	116.235	+	57.6996i	0.202500	+	0.100522i
$575$	235.299			0.409215
$576$	518.376	+	1303.23i	0.899959	+	2.26256i
$577$	527.662	+	304.646i	0.914491	+	0.527982i	0.881874	−	0.471486i	$-0.156282\pi$
$577$	527.662	+	304.646i	0.914491	+	0.527982i	0.0326179	+	0.999468i	$0.489616\pi$
$578$	6.57735	−	272.069i	0.0113795	−	0.470708i
$579$	265.869	+	460.499i	0.459187	+	0.795335i
$580$	−325.305	−	209.402i	−0.560871	−	0.361038i
$581$	−18.2792	−	209.572i	−0.0314616	−	0.360709i
$582$	−139.394	−	255.507i	−0.239509	−	0.439015i
$583$	−3.89164	−	6.74051i	−0.00667519	−	0.0115618i
$584$	57.5042	−	84.7592i	0.0984661	−	0.145136i
$585$	−137.873	+	238.803i	−0.235680	+	0.408210i
$586$	−901.467	−	549.931i	−1.53834	−	0.938449i
$587$	972.801			1.65724			0.828621	−	0.559810i	$-0.189126\pi$
$587$	972.801			1.65724			0.828621	+	0.559810i	$0.189126\pi$
$588$	−1081.19	+	136.584i	−1.83875	+	0.232285i
$589$			237.701i			0.403567i
$590$	−148.887	−	90.8269i	−0.252350	−	0.153944i
$591$	−775.745	−	447.877i	−1.31260	−	0.757829i
$592$	44.8368	−	462.308i	0.0757378	−	0.780925i
$593$	−281.520	+	162.536i	−0.474739	+	0.274091i	−0.718222	−	0.695814i	$-0.755044\pi$
$593$	−281.520	+	162.536i	−0.474739	+	0.274091i	0.243482	+	0.969905i	$0.421710\pi$
$594$	8.42162	+	15.4366i	0.0141778	+	0.0259876i
$595$	439.724	−	38.3535i	0.739033	−	0.0644597i
$596$	239.596	+	154.230i	0.402006	+	0.258775i
$597$	5.34367	−	3.08517i	0.00895088	−	0.00516779i
$598$	2.99064	−	123.707i	0.00500108	−	0.206867i
$599$	−231.570	+	401.091i	−0.386595	+	0.669602i	−0.991989	−	0.126324i	$-0.959682\pi$
$599$	−231.570	+	401.091i	−0.386595	+	0.669602i	0.605394	+	0.795926i	$0.293015\pi$
$600$	−626.339	+	303.396i	−1.04390	+	0.505661i
$601$		−	325.247i		−	0.541176i	−0.962695	−	0.270588i	$-0.912782\pi$
$601$		−	325.247i		−	0.541176i	0.962695	−	0.270588i	$-0.0872182\pi$
$602$	568.550	+	282.232i	0.944436	+	0.468823i
$603$		−	1656.97i		−	2.74787i
$604$	690.233	+	33.3927i	1.14277	+	0.0552859i
$605$	−185.011	+	320.448i	−0.305803	+	0.529667i
$606$	36.4672	−	1508.45i	0.0601769	−	2.48919i
$607$	346.450	−	200.023i	0.570758	−	0.329527i	−0.186694	−	0.982418i	$-0.559777\pi$
$607$	346.450	−	200.023i	0.570758	−	0.329527i	0.757452	+	0.652891i	$0.226444\pi$
$608$	228.646	+	171.824i	0.376063	+	0.282606i
$609$	520.464	−	1115.37i	0.854621	−	1.83147i
$610$	135.522	−	73.9351i	0.222166	−	0.121205i
$611$	−282.612	+	163.166i	−0.462540	+	0.267047i
$612$	1607.00	−	826.959i	2.62582	−	1.35124i
$613$	821.365	+	474.215i	1.33991	+	0.773597i	0.986794	−	0.161982i	$-0.0517886\pi$
$613$	821.365	+	474.215i	1.33991	+	0.773597i	0.353116	+	0.935579i	$0.385122\pi$
$614$	297.913	+	181.739i	0.485201	+	0.295992i
$615$		−	157.623i		−	0.256297i
$616$	5.98717	+	3.34198i	0.00971943	+	0.00542529i
$617$	−1066.14			−1.72793			−0.863967	−	0.503548i	$-0.832028\pi$
$617$	−1066.14			−1.72793			−0.863967	+	0.503548i	$0.832028\pi$
$618$	−737.313	+	1208.63i	−1.19306	+	1.95571i
$619$	471.501	−	816.664i	0.761715	−	1.31933i	−0.180251	−	0.983621i	$-0.557691\pi$
$619$	471.501	−	816.664i	0.761715	−	1.31933i	0.941966	−	0.335708i	$-0.108976\pi$
$620$	289.295	−	148.871i	0.466605	−	0.240114i
$621$	−539.948	−	935.218i	−0.869482	−	1.50599i
$622$	−13.1749	−	24.1493i	−0.0211815	−	0.0388253i
$623$	70.9205	+	101.342i	0.113837	+	0.162668i
$624$	151.548	+	333.149i	0.242865	+	0.533893i
$625$	−5.47705	−	9.48652i	−0.00876328	−	0.0151784i
$626$	843.535	+	20.3927i	1.34750	+	0.0325762i
$627$	5.26960	+	3.04240i	0.00840446	+	0.00485232i
$628$	1078.12	+	52.1581i	1.71675	+	0.0830543i
$629$	−598.517			−0.951537
$630$	519.269	+	781.564i	0.824237	+	1.24058i
$631$	−575.646			−0.912276			−0.456138	−	0.889909i	$-0.650768\pi$
$631$	−575.646			−0.912276			−0.456138	+	0.889909i	$0.650768\pi$
$632$	−512.893	+	248.443i	−0.811539	+	0.393107i
$633$	−1030.67	−	595.056i	−1.62823	−	0.940057i
$634$	−942.774	−	22.7918i	−1.48702	−	0.0359493i
$635$	−103.690	−	179.596i	−0.163291	−	0.282828i
$636$	−1188.76	−	765.216i	−1.86912	−	1.20317i
$637$	−198.548	+	34.9008i	−0.311692	+	0.0547894i
$638$	−6.79828	+	3.70887i	−0.0106556	+	0.00581328i
$639$	30.8860	+	53.4961i	0.0483349	+	0.0837185i
$640$	65.9200	−	385.887i	0.103000	−	0.602948i
$641$	−396.899	+	687.449i	−0.619187	+	1.07246i	0.370447	+	0.928854i	$0.379204\pi$
$641$	−396.899	+	687.449i	−0.619187	+	1.07246i	−0.989634	+	0.143610i	$0.954129\pi$
$642$	462.083	−	757.464i	0.719756	−	1.17985i
$643$	−841.343			−1.30847			−0.654233	−	0.756293i	$-0.727008\pi$
$643$	−841.343			−1.30847			−0.654233	+	0.756293i	$0.727008\pi$
$644$	−372.537	−	196.291i	−0.578473	−	0.304800i
$645$		−	770.995i		−	1.19534i
$646$	191.935	−	314.627i	0.297113	−	0.487038i
$647$	476.604	+	275.167i	0.736637	+	0.425297i	0.820845	−	0.571151i	$-0.193503\pi$
$647$	476.604	+	275.167i	0.736637	+	0.425297i	−0.0842084	+	0.996448i	$0.526836\pi$
$648$	1337.44	+	907.374i	2.06395	+	1.40027i
$649$	−3.02337	+	1.74555i	−0.00465851	+	0.00268959i
$650$	−113.015	+	61.6566i	−0.173870	+	0.0948563i
$651$	593.479	+	848.054i	0.911642	+	1.30269i
$652$	−917.454	−	590.573i	−1.40714	−	0.905787i
$653$	713.506	−	411.943i	1.09266	−	0.630847i	0.158375	−	0.987379i	$-0.449374\pi$
$653$	713.506	−	411.943i	1.09266	−	0.630847i	0.934283	+	0.356532i	$0.116041\pi$
$654$	351.224	+	8.49095i	0.537040	+	0.0129831i
$655$	−171.511	+	297.066i	−0.261849	+	0.453535i
$656$	−120.679	−	86.2052i	−0.183962	−	0.131410i
$657$		−	280.577i		−	0.427058i
$658$	69.7266	+	1108.29i	0.105967	+	1.68433i
$659$			354.257i			0.537567i	0.963201	+	0.268784i	$0.0866217\pi$
$659$			354.257i			0.537567i	−0.963201	+	0.268784i	$0.913378\pi$
$660$	0.402455	−	8.31882i	0.000609780	−	0.0126043i
$661$	84.3031	−	146.017i	0.127539	−	0.220904i	−0.795184	−	0.606369i	$-0.792626\pi$
$661$	84.3031	−	146.017i	0.127539	−	0.220904i	0.922722	+	0.385465i	$0.125959\pi$
$662$	885.873	+	21.4163i	1.33818	+	0.0323508i
$663$	408.435	−	235.810i	0.616040	−	0.355671i
$664$	−17.4180	+	239.788i	−0.0262319	+	0.361127i
$665$	173.400	+	80.9138i	0.260752	+	0.121675i
$666$	−609.364	−	1116.95i	−0.914961	−	1.67710i
$667$	411.869	−	237.793i	0.617494	−	0.356511i
$668$	−293.668	+	151.121i	−0.439623	+	0.226229i
$669$	1397.70	+	806.965i	2.08924	+	1.20623i
$670$	−240.858	+	394.823i	−0.359489	+	0.589288i
$671$		−	3.09022i		−	0.00460539i
$672$	1244.75	+	42.1527i	1.85231	+	0.0627272i
$673$	514.054			0.763824			0.381912	−	0.924199i	$-0.375266\pi$
$673$	514.054			0.763824			0.381912	+	0.924199i	$0.375266\pi$
$674$	−950.972	−	580.131i	−1.41094	−	0.860729i
$675$	−561.753	+	972.986i	−0.832227	+	1.44146i
$676$	−278.337	−	540.882i	−0.411740	−	0.800121i
$677$	260.650	+	451.460i	0.385008	+	0.666853i	0.991770	−	0.128030i	$-0.0408654\pi$
$677$	260.650	+	451.460i	0.385008	+	0.666853i	−0.606762	+	0.794883i	$0.707532\pi$
$678$	−564.226	+	307.819i	−0.832191	+	0.454010i
$679$	−182.523	+	15.9200i	−0.268812	+	0.0234462i
$680$	−503.125	−	36.5465i	−0.739889	−	0.0537449i
$681$	226.362	+	392.070i	0.332396	+	0.575727i
$682$	0.157399	−	6.51075i	0.000230791	−	0.00954656i
$683$	−441.591	−	254.953i	−0.646547	−	0.373284i	0.140585	−	0.990069i	$-0.455102\pi$
$683$	−441.591	−	254.953i	−0.646547	−	0.373284i	−0.787132	+	0.616785i	$0.788435\pi$
$684$	782.569	+	37.8598i	1.14411	+	0.0553506i
$685$	−179.476			−0.262009
$686$	−194.036	+	657.986i	−0.282851	+	0.959164i
$687$	1302.30			1.89563
$688$	−590.290	−	421.664i	−0.857979	−	0.612883i
$689$	−226.485	−	130.761i	−0.328715	−	0.189784i
$690$	−12.3614	+	511.323i	−0.0179150	+	0.741047i
$691$	−467.402	−	809.565i	−0.676415	−	1.17158i	−0.976053	−	0.217532i	$-0.930199\pi$
$691$	−467.402	−	809.565i	−0.676415	−	1.17158i	0.299639	−	0.954053i	$-0.403134\pi$
$692$	−498.523	+	774.455i	−0.720409	+	1.11915i
$693$	18.7120	−	1.63209i	0.0270014	−	0.00235511i
$694$	−307.261	−	563.203i	−0.442739	−	0.811532i
$695$	−268.008	−	464.203i	−0.385623	−	0.667919i
$696$	−789.736	+	1164.04i	−1.13468	+	1.67248i
$697$	−95.5526	+	165.502i	−0.137091	+	0.237449i
$698$	379.375	+	231.434i	0.543518	+	0.331568i
$699$	344.619			0.493017
$700$	16.9325	+	437.764i	0.0241893	+	0.625377i
$701$			364.276i			0.519651i	0.965656	+	0.259826i	$0.0836651\pi$
$701$			364.276i			0.519651i	−0.965656	+	0.259826i	$0.916335\pi$
$702$	504.400	+	307.704i	0.718519	+	0.438325i
$703$	−224.703	−	129.732i	−0.319634	−	0.184541i
$704$	−6.14895	−	4.85776i	−0.00873430	−	0.00690022i
$705$	1168.13	−	674.422i	1.65693	−	0.956626i
$706$	130.669	+	239.513i	0.185083	+	0.339253i
$707$	−860.725	−	401.640i	−1.21743	−	0.568091i
$708$	−343.228	+	533.204i	−0.484786	+	0.753113i
$709$	429.168	−	247.780i	0.605315	−	0.349479i	−0.165815	−	0.986157i	$-0.553025\pi$
$709$	429.168	−	247.780i	0.605315	−	0.349479i	0.771130	+	0.636678i	$0.219692\pi$
$710$	0.416702	−	17.2367i	0.000586905	−	0.0242770i
$711$	−780.572	+	1351.99i	−1.09785	+	1.90153i
$712$	−61.6265	−	127.223i	−0.0865541	−	0.178684i
$713$			399.955i			0.560946i
$714$	−100.770	−	1601.72i	−0.141134	−	2.24330i
$715$		−	1.54065i		−	0.00215475i
$716$	51.0359	−	1054.92i	0.0712791	−	1.47335i
$717$	269.894	−	467.470i	0.376421	−	0.651980i
$718$	−12.0301	+	497.618i	−0.0167550	+	0.693061i
$719$	−582.836	+	336.500i	−0.810620	+	0.468012i	−0.847171	−	0.531320i	$-0.821696\pi$
$719$	−582.836	+	336.500i	−0.810620	+	0.468012i	0.0365511	+	0.999332i	$0.488363\pi$
$720$	−444.040	−	976.139i	−0.616722	−	1.35575i
$721$	510.983	+	730.171i	0.708714	+	1.01272i
$722$	−493.557	+	269.265i	−0.683596	+	0.372943i
$723$	−1154.40	+	666.493i	−1.59668	+	0.921844i
$724$	336.753	+	654.401i	0.465129	+	0.903869i
$725$	−428.502	−	247.395i	−0.591037	−	0.341235i
$726$	1148.53	+	700.652i	1.58200	+	0.965085i
$727$		−	165.434i		−	0.227557i	−0.993506	−	0.113778i	$-0.963705\pi$
$727$		−	165.434i		−	0.227557i	0.993506	−	0.113778i	$-0.0362954\pi$
$728$	230.366	−	3.33818i	0.316437	−	0.00458542i
$729$	833.991			1.14402
$730$	−40.7849	+	66.8560i	−0.0558697	+	0.0915836i
$731$	−467.386	+	809.536i	−0.639378	+	1.10744i
$732$	−256.837	−	499.101i	−0.350870	−	0.681833i
$733$	474.614	+	822.055i	0.647495	+	1.12149i	0.983719	+	0.179712i	$0.0575165\pi$
$733$	474.614	+	822.055i	0.647495	+	1.12149i	−0.336225	+	0.941782i	$0.609150\pi$
$734$	249.869	+	458.004i	0.340421	+	0.623984i
$735$	820.667	−	144.257i	1.11655	−	0.196268i
$736$	384.719	+	289.111i	0.522715	+	0.392814i
$737$	4.62889	+	8.01748i	0.00628073	+	0.0108785i
$738$	−406.144	−	9.81864i	−0.550330	−	0.0133044i
$739$	62.4587	+	36.0605i	0.0845178	+	0.0487964i	0.541663	−	0.840596i	$-0.317795\pi$
$739$	62.4587	+	36.0605i	0.0845178	+	0.0487964i	−0.457145	+	0.889392i	$0.651128\pi$
$740$	−17.1612	+	354.725i	−0.0231908	+	0.479359i
$741$	204.453			0.275915
$742$	−741.249	+	492.484i	−0.998988	+	0.663725i
$743$	159.310			0.214415			0.107208	−	0.994237i	$-0.465809\pi$
$743$	159.310			0.214415			0.107208	+	0.994237i	$0.465809\pi$
$744$	−515.705	−	1064.63i	−0.693152	−	1.43096i
$745$	−188.680	−	108.934i	−0.253262	−	0.146221i
$746$	880.697	+	21.2911i	1.18056	+	0.0285404i
$747$	329.297	+	570.358i	0.440825	+	0.763532i
$748$	−5.46553	+	8.49068i	−0.00730686	+	0.0113512i
$749$	−320.239	−	457.607i	−0.427556	−	0.610957i
$750$	1213.53	−	662.055i	1.61804	−	0.882740i
$751$	−382.562	−	662.616i	−0.509403	−	0.882312i	−0.999941	−	0.0108919i	$-0.996533\pi$
$751$	−382.562	−	662.616i	−0.509403	−	0.882312i	0.490538	−	0.871420i	$-0.336800\pi$
$752$	122.510	−	1263.19i	0.162913	−	1.67978i
$753$	378.305	−	655.243i	0.502397	−	0.870176i
$754$	−135.513	+	222.137i	−0.179725	+	0.294612i
$755$	−528.371			−0.699830
$756$	1701.08	−	1071.85i	2.25011	−	1.41779i
$757$			950.822i			1.25604i	0.778197	+	0.628020i	$0.216134\pi$
$757$			950.822i			1.25604i	−0.778197	+	0.628020i	$0.783866\pi$
$758$	295.508	−	484.408i	0.389853	−	0.639060i
$759$	8.86660	+	5.11913i	0.0116819	+	0.00674457i
$760$	−180.968	−	122.776i	−0.238115	−	0.161547i
$761$	529.627	−	305.781i	0.695962	−	0.401814i	−0.109879	−	0.993945i	$-0.535046\pi$
$761$	529.627	−	305.781i	0.695962	−	0.401814i	0.805842	+	0.592131i	$0.201713\pi$
$762$	−661.921	+	361.118i	−0.868662	+	0.473908i
$763$	93.5172	−	200.410i	0.122565	−	0.262660i
$764$	641.676	−	996.842i	0.839890	−	1.30477i
$765$	−1196.73	+	690.931i	−1.56435	+	0.903178i
$766$	−319.783	−	7.73085i	−0.417471	−	0.0100925i
$767$	−58.6513	+	101.587i	−0.0764685	+	0.132447i
$768$	−1396.86	−	273.521i	−1.81883	−	0.356147i
$769$		−	979.152i		−	1.27328i	−0.771161	−	0.636640i	$-0.780324\pi$
$769$		−	979.152i		−	1.27328i	0.771161	−	0.636640i	$-0.219676\pi$
$770$	−4.69594	−	2.33109i	−0.00609862	−	0.00302739i
$771$			105.611i			0.136979i
$772$	−382.091	−	18.4851i	−0.494937	−	0.0239445i
$773$	228.660	−	396.051i	0.295809	−	0.512356i	−0.679364	−	0.733802i	$-0.737744\pi$
$773$	228.660	−	396.051i	0.295809	−	0.512356i	0.975173	+	0.221445i	$0.0710774\pi$
$774$	−1986.61	−	48.0269i	−2.56668	−	0.0620502i
$775$	360.359	−	208.053i	0.464979	−	0.268456i
$776$	208.840	+	15.1699i	0.269123	+	0.0195489i
$777$	−1125.59	+	98.1756i	−1.44863	+	0.126352i
$778$	475.918	+	872.348i	0.611720	+	1.12127i
$779$	−71.7471	+	41.4232i	−0.0921015	+	0.0531748i
$780$	−128.047	−	248.830i	−0.164163	−	0.319013i
$781$	−0.298893	−	0.172566i	−0.000382706	−	0.000220955i
$782$	322.949	−	529.389i	0.412978	−	0.676968i
$783$			2270.83i			2.90016i
$784$	338.383	−	707.215i	0.431611	−	0.902060i
$785$	−825.296			−1.05133
$786$	1064.73	+	649.526i	1.35461	+	0.826369i
$787$	−91.5206	+	158.518i	−0.116290	+	0.201421i	−0.918295	−	0.395897i	$-0.870434\pi$
$787$	−91.5206	+	158.518i	−0.116290	+	0.201421i	0.802004	+	0.597318i	$0.203767\pi$
$788$	572.998	−	294.863i	0.727154	−	0.374192i
$789$	685.481	+	1187.29i	0.868797	+	1.50480i
$790$	382.522	−	208.689i	0.484205	−	0.264163i
$791$	35.1555	+	403.059i	0.0444444	+	0.509556i
$792$	−21.4099	−	1.55519i	−0.0270327	−	0.00196363i
$793$	−51.9165	−	89.9220i	−0.0654685	−	0.113395i
$794$	13.7455	−	568.576i	0.0173117	−	0.716091i
$795$	936.141	+	540.481i	1.17754	+	0.679851i
$796$	−0.214503	+	4.43383i	−0.000269477	+	0.00557013i
$797$	619.727			0.777575			0.388787	−	0.921328i	$-0.372894\pi$
$797$	619.727			0.777575			0.388787	+	0.921328i	$0.372894\pi$
$798$	309.349	−	623.179i	0.387656	−	0.780926i
$799$	−1635.37			−2.04677
$800$	60.3610	−	497.024i	0.0754512	−	0.621280i
$801$	−335.362	−	193.621i	−0.418679	−	0.241725i
$802$	−6.85178	+	283.421i	−0.00854336	+	0.353392i
$803$	0.783819	+	1.35761i	0.000976113	+	0.00169068i
$804$	1413.97	+	910.184i	1.75867	+	1.13207i
$805$	291.762	+	136.145i	0.362438	+	0.169124i
$806$	−104.802	−	192.100i	−0.130028	−	0.238338i
$807$	818.008	+	1416.83i	1.01364	+	1.75568i
$808$	898.289	+	609.437i	1.11174	+	0.754253i
$809$	335.874	−	581.750i	0.415171	−	0.719098i	−0.580275	−	0.814421i	$-0.697055\pi$
$809$	335.874	−	581.750i	0.415171	−	0.719098i	0.995446	+	0.0953227i	$0.0303883\pi$
$810$	−1054.94	−	643.556i	−1.30239	−	0.794513i
$811$	−1133.22			−1.39732			−0.698658	−	0.715456i	$-0.746219\pi$
$811$	−1133.22			−1.39732			−0.698658	+	0.715456i	$0.746219\pi$
$812$	472.042	+	749.153i	0.581333	+	0.922603i
$813$		−	2516.95i		−	3.09587i
$814$	6.06881	+	3.70222i	0.00745554	+	0.00454818i
$815$	722.489	+	417.129i	0.886489	+	0.511815i
$816$	−177.054	+	1825.59i	−0.216978	+	2.23724i
$817$	−350.944	+	202.617i	−0.429551	+	0.248002i
$818$	357.598	+	655.469i	0.437161	+	0.801307i
$819$	517.079	−	361.858i	0.631354	−	0.441829i
$820$	95.3489	+	61.3769i	0.116279	+	0.0748499i
$821$	−620.954	+	358.508i	−0.756338	+	0.436672i	−0.827979	−	0.560758i	$-0.810510\pi$
$821$	−620.954	+	358.508i	−0.756338	+	0.436672i	0.0716414	+	0.997430i	$0.477176\pi$
$822$	−15.7713	+	652.373i	−0.0191865	+	0.793641i
$823$	362.895	−	628.553i	0.440942	−	0.763734i	−0.556818	−	0.830635i	$-0.687978\pi$
$823$	362.895	−	628.553i	0.440942	−	0.763734i	0.997760	+	0.0669009i	$0.0213111\pi$
$824$	−444.019	−	916.645i	−0.538859	−	1.11243i
$825$		−	10.6517i		−	0.0129112i
$826$	220.898	+	332.478i	0.267430	+	0.402516i
$827$		−	436.858i		−	0.528244i	−0.964489	−	0.264122i	$-0.914918\pi$
$827$		−	436.858i		−	0.528244i	0.964489	−	0.264122i	$-0.0850822\pi$
$828$	1316.75	+	63.7027i	1.59027	+	0.0769356i
$829$	−588.361	+	1019.07i	−0.709724	+	1.22928i	0.255235	+	0.966879i	$0.417847\pi$
$829$	−588.361	+	1019.07i	−0.709724	+	1.22928i	−0.964959	+	0.262399i	$0.915486\pi$
$830$	4.44275	−	183.772i	0.00535271	−	0.221412i
$831$	−1403.50	+	810.313i	−1.68893	+	0.975105i
$832$	−260.540	−	38.0515i	−0.313148	−	0.0457350i
$833$	−949.140	−	346.029i	−1.13942	−	0.415400i
$834$	−1710.87	+	933.385i	−2.05141	+	1.11917i
$835$	218.694	−	126.263i	0.261909	−	0.151213i
$836$	−3.89234	+	2.00299i	−0.00465591	+	0.00239592i
$837$	−1653.85	−	954.853i	−1.97593	−	1.14080i
$838$	−715.159	−	436.276i	−0.853412	−	0.520616i
$839$		−	1551.16i		−	1.84881i	−0.381407	−	0.924407i	$-0.624560\pi$
$839$		−	1551.16i		−	1.84881i	0.381407	−	0.924407i	$-0.375440\pi$
$840$	−952.185	+	13.7979i	−1.13355	+	0.0164260i
$841$	−159.070			−0.189143
$842$	−328.211	+	538.015i	−0.389799	+	0.638973i
$843$	1377.33	−	2385.60i	1.63384	−	2.82990i
$844$	761.294	−	391.760i	0.902007	−	0.464171i
$845$	232.552	+	402.793i	0.275210	+	0.476678i
$846$	−1665.01	−	3051.92i	−1.96809	−	3.60747i
$847$	693.864	−	485.575i	0.819202	−	0.573288i
$848$	925.787	−	421.135i	1.09173	−	0.496622i
$849$	102.131	+	176.895i	0.120295	+	0.208357i
$850$	−644.974	−	15.5924i	−0.758793	−	0.0183440i
$851$	−378.084	−	218.287i	−0.444282	−	0.256506i
$852$	−62.6167	−	3.02933i	−0.0734938	−	0.00355555i
$853$	138.736			0.162645			0.0813225	−	0.996688i	$-0.474086\pi$
$853$	138.736			0.162645			0.0813225	+	0.996688i	$0.474086\pi$
$854$	−352.638	+	22.1858i	−0.412925	+	0.0259787i
$855$	−599.054			−0.700648
$856$	278.272	+	574.473i	0.325085	+	0.671113i
$857$	1475.23	+	851.725i	1.72139	+	0.993844i	0.916087	+	0.400980i	$0.131330\pi$
$857$	1475.23	+	851.725i	1.72139	+	0.993844i	0.805302	+	0.592865i	$0.202003\pi$
$858$	−5.60007	−	0.135383i	−0.00652688	−	0.000157789i
$859$	256.796	+	444.784i	0.298948	+	0.517793i	0.975896	−	0.218238i	$-0.0700310\pi$
$859$	256.796	+	444.784i	0.298948	+	0.517793i	−0.676948	+	0.736031i	$0.736698\pi$
$860$	466.389	+	300.219i	0.542313	+	0.349092i
$861$	−152.551	+	326.921i	−0.177179	+	0.379699i
$862$	392.095	−	213.911i	0.454866	−	0.248157i
$863$	−117.938	−	204.275i	−0.136661	−	0.236703i	0.789570	−	0.613660i	$-0.210304\pi$
$863$	−117.938	−	204.275i	−0.136661	−	0.236703i	−0.926231	+	0.376958i	$0.876970\pi$
$864$	−2113.98	+	900.628i	−2.44674	+	1.04239i
$865$	352.113	−	609.878i	0.407067	−	0.705061i
$866$	−616.323	+	1010.30i	−0.711689	+	1.16663i
$867$	756.587			0.872649
$868$	−744.100	+	28.7815i	−0.857258	+	0.0331584i
$869$		−	8.72242i		−	0.0100373i
$870$	560.121	−	918.170i	0.643817	−	1.05537i
$871$	269.392	+	155.533i	0.309290	+	0.178569i
$872$	−141.900	+	209.156i	−0.162729	+	0.239857i
$873$	496.745	−	286.796i	0.569009	−	0.328517i
$874$	235.994	−	128.749i	0.270016	−	0.147310i
$875$	−75.6122	−	866.897i	−0.0864139	−	0.990739i
$876$	239.430	+	154.123i	0.273322	+	0.175940i
$877$	−384.546	+	222.017i	−0.438478	+	0.253156i	−0.702952	−	0.711237i	$-0.748135\pi$
$877$	−384.546	+	222.017i	−0.438478	+	0.253156i	0.264474	+	0.964393i	$0.414802\pi$
$878$	1024.35	+	24.7640i	1.16669	+	0.0282050i
$879$	1467.82	−	2542.34i	1.66988	−	2.89231i
$880$	4.87549	+	3.48273i	0.00554033	+	0.00395765i
$881$		−	71.7252i		−	0.0814134i	−0.999171	−	0.0407067i	$-0.987039\pi$
$881$		−	71.7252i		−	0.0814134i	0.999171	−	0.0407067i	$-0.0129609\pi$
$882$	−320.584	−	2123.58i	−0.363474	−	2.40769i
$883$			973.840i			1.10288i	0.834216	+	0.551438i	$0.185921\pi$
$883$			973.840i			1.10288i	−0.834216	+	0.551438i	$0.814079\pi$
$884$	−16.3952	+	338.892i	−0.0185466	+	0.383362i
$885$	242.426	−	419.895i	0.273928	−	0.474457i
$886$	−310.735	−	7.51210i	−0.350716	−	0.00847867i
$887$	715.042	−	412.830i	0.806135	−	0.465422i	−0.0394767	−	0.999220i	$-0.512569\pi$
$887$	715.042	−	412.830i	0.806135	−	0.465422i	0.845612	+	0.533798i	$0.179236\pi$
$888$	1287.88	+	93.5502i	1.45031	+	0.105349i
$889$	41.2426	+	472.848i	0.0463922	+	0.531888i
$890$	51.7653	+	94.8847i	0.0581633	+	0.106612i
$891$	−21.4222	+	12.3681i	−0.0240428	+	0.0138811i
$892$	−1032.40	+	531.272i	−1.15740	+	0.595597i
$893$	−613.970	−	354.476i	−0.687536	−	0.396949i
$894$	−412.544	+	676.257i	−0.461458	+	0.756439i
$895$			807.539i			0.902278i
$896$	−510.194	+	736.558i	−0.569413	+	0.822052i
$897$	344.011			0.383513
$898$	630.259	+	384.484i	0.701848	+	0.428156i
$899$	420.516	−	728.355i	0.467760	−	0.810184i
$900$	−627.565	−	1219.52i	−0.697294	−	1.35503i
$901$	−655.291	−	1135.00i	−0.727293	−	1.25971i
$902$	1.99262	−	1.08709i	0.00220911	−	0.00120520i
$903$	−746.189	+	1599.10i	−0.826344	+	1.77088i
$904$	33.4992	−	461.173i	0.0370566	−	0.510147i
$905$	−281.360	−	487.330i	−0.310895	−	0.538486i
$906$	−46.4303	+	1920.57i	−0.0512475	+	2.11983i
$907$	−637.046	−	367.799i	−0.702366	−	0.405511i	0.105862	−	0.994381i	$-0.466240\pi$
$907$	−637.046	−	367.799i	−0.702366	−	0.405511i	−0.808228	+	0.588870i	$0.799573\pi$
$908$	−325.314	−	15.7383i	−0.358275	−	0.0173330i
$909$	2973.59			3.27128
$910$	−175.810	+	11.0608i	−0.193197	+	0.0121548i
$911$	235.528			0.258538			0.129269	−	0.991610i	$-0.458737\pi$
$911$	235.528			0.258538			0.129269	+	0.991610i	$0.458737\pi$
$912$	−462.179	+	647.007i	−0.506775	+	0.709438i
$913$	−3.18670	−	1.83984i	−0.00349036	−	0.00201516i
$914$	20.6956	−	856.065i	0.0226429	−	0.936614i
$915$	214.589	+	371.679i	0.234524	+	0.406207i
$916$	−507.103	+	787.783i	−0.553606	+	0.860025i
$917$	643.234	−	450.143i	0.701455	−	0.490887i
$918$	1418.07	+	2599.29i	1.54474	+	2.83147i
$919$	717.115	+	1242.08i	0.780321	+	1.35156i	0.931755	+	0.363088i	$0.118278\pi$
$919$	717.115	+	1242.08i	0.780321	+	1.35156i	−0.151434	+	0.988467i	$0.548389\pi$
$920$	−304.495	−	206.582i	−0.330973	−	0.224546i
$921$	−485.080	+	840.184i	−0.526689	+	0.912252i
$922$	282.704	+	172.461i	0.306620	+	0.187051i
$923$	−11.5966			−0.0125641
$924$	−8.88588	+	16.8643i	−0.00961676	+	0.0182514i
$925$			454.204i			0.491031i
$926$	1033.60	+	630.540i	1.11620	+	0.680929i
$927$	−2416.29	−	1395.04i	−2.60657	−	1.50490i
$928$	−396.635	−	930.995i	−0.427409	−	1.00323i
$929$	−1194.57	+	689.687i	−1.28587	+	0.742397i	−0.977915	−	0.209003i	$-0.932978\pi$
$929$	−1194.57	+	689.687i	−1.28587	+	0.742397i	−0.307955	+	0.951401i	$0.599645\pi$
$930$	433.184	+	794.017i	0.465790	+	0.853782i
$931$	−281.334	−	335.642i	−0.302185	−	0.360518i
$932$	−134.192	+	208.466i	−0.143982	+	0.223676i
$933$	66.2316	−	38.2388i	0.0709878	−	0.0409848i
$934$	−27.6546	+	1143.92i	−0.0296088	+	1.22475i
$935$	3.86037	−	6.68635i	0.00412874	−	0.00715118i
$936$	−649.132	+	314.437i	−0.693517	+	0.335937i
$937$		−	541.545i		−	0.577956i	−0.957336	−	0.288978i	$-0.906685\pi$
$937$		−	541.545i		−	0.577956i	0.957336	−	0.288978i	$-0.0933154\pi$
$938$	881.676	−	585.783i	0.939953	−	0.624502i
$939$			2345.76i			2.49814i
$940$	−46.8907	+	969.239i	−0.0498837	+	1.03111i
$941$	48.9285	−	84.7467i	0.0519963	−	0.0900603i	−0.838856	−	0.544354i	$-0.816775\pi$
$941$	48.9285	−	84.7467i	0.0519963	−	0.0900603i	0.890852	+	0.454294i	$0.150108\pi$
$942$	−72.5223	+	2999.85i	−0.0769876	+	3.18456i
$943$	−120.721	+	69.6984i	−0.128018	+	0.0739114i
$944$	−188.895	−	415.250i	−0.200101	−	0.439884i
$945$	−1259.53	+	881.434i	−1.33283	+	0.932735i
$946$	9.74668	−	5.31740i	0.0103030	−	0.00562093i
$947$	674.176	−	389.236i	0.711907	−	0.411020i	−0.0998594	−	0.995002i	$-0.531839\pi$
$947$	674.176	−	389.236i	0.711907	−	0.411020i	0.811767	+	0.583982i	$0.198506\pi$
$948$	−724.944	−	1408.76i	−0.764709	−	1.48603i
$949$	45.6166	+	26.3367i	0.0480680	+	0.0277521i
$950$	−238.764	−	145.656i	−0.251331	−	0.153322i
$951$		−	2621.73i		−	2.75681i
$952$	1008.15	+	562.737i	1.05898	+	0.591110i
$953$	348.435			0.365620			0.182810	−	0.983148i	$-0.441481\pi$
$953$	348.435			0.365620			0.182810	+	0.983148i	$0.441481\pi$
$954$	1450.96	−	2378.47i	1.52093	−	2.49316i
$955$	−453.224	+	785.006i	−0.474580	+	0.821996i
$956$	177.687	+	345.292i	0.185865	+	0.361184i
$957$	−10.7646	−	18.6449i	−0.0112483	−	0.0194826i
$958$	−35.6738	−	65.3892i	−0.0372377	−	0.0682560i
$959$	372.246	+	173.701i	0.388161	+	0.181128i
$960$	1076.90	+	157.280i	1.12177	+	0.163833i
$961$	−126.857	−	219.722i	−0.132005	−	0.228639i
$962$	238.794	+	5.77292i	0.248227	+	0.00600096i
$963$	1514.32	+	874.291i	1.57250	+	0.907883i
$964$	46.3394	−	957.845i	0.0480699	−	0.993615i
$965$	292.490			0.303098
$966$	520.510	−	1048.56i	0.538830	−	1.08546i
$967$	−1055.75			−1.09177			−0.545887	−	0.837859i	$-0.683807\pi$
$967$	−1055.75			−1.09177			−0.545887	+	0.837859i	$0.683807\pi$
$968$	−871.067	+	421.942i	−0.899862	+	0.435890i
$969$	887.319	+	512.294i	0.915706	+	0.528683i
$970$	−160.053	−	3.86934i	−0.165003	−	0.00398901i
$971$	426.302	+	738.377i	0.439034	+	0.760429i	0.997615	−	0.0690206i	$-0.0219874\pi$
$971$	426.302	+	738.377i	0.439034	+	0.760429i	−0.558581	+	0.829450i	$0.688654\pi$
$972$	−1032.75	+	1604.37i	−1.06250	+	1.65058i
$973$	106.600	+	1222.18i	0.109558	+	1.25609i
$974$	481.670	−	262.780i	0.494528	−	0.269795i
$975$	−178.952	−	309.954i	−0.183540	−	0.317901i
$976$	401.926	+	38.9807i	0.411809	+	0.0399392i
$977$	−169.835	+	294.163i	−0.173834	+	0.301089i	−0.939757	−	0.341843i	$-0.888949\pi$
$977$	−169.835	+	294.163i	−0.173834	+	0.301089i	0.765923	+	0.642932i	$0.222282\pi$
$978$	1579.70	−	2589.50i	1.61524	−	2.64776i
$979$	2.16360			0.00221001
$980$	−232.297	+	552.609i	−0.237037	+	0.563887i
$981$			692.365i			0.705774i
$982$	918.657	−	1505.90i	0.935496	−	1.53350i
$983$	−905.444	−	522.759i	−0.921103	−	0.531799i	−0.0371164	−	0.999311i	$-0.511817\pi$
$983$	−905.444	−	522.759i	−0.921103	−	0.531799i	−0.883987	+	0.467512i	$0.845151\pi$
$984$	231.477	−	341.188i	0.235240	−	0.346736i
$985$	−426.709	+	246.361i	−0.433208	+	0.250112i
$986$	−1144.72	+	624.516i	−1.16098	+	0.633384i
$987$	−3075.52	+	268.252i	−3.11602	+	0.271785i
$988$	−79.6122	+	123.677i	−0.0805792	+	0.125180i
$989$	−590.496	+	340.923i	−0.597063	+	0.344715i
$990$	16.4084	+	0.396678i	0.0165741	+	0.000400685i
$991$	409.911	−	709.987i	0.413634	−	0.716435i	−0.581650	−	0.813439i	$-0.697593\pi$
$991$	409.911	−	709.987i	0.413634	−	0.716435i	0.995284	+	0.0970040i	$0.0309260\pi$
$992$	844.828	+	102.600i	0.851641	+	0.103427i
$993$			2463.49i			2.48086i
$994$	−17.5464	+	35.3469i	−0.0176523	+	0.0355602i
$995$		−	3.39408i		−	0.00341114i
$996$	−667.599	−	32.2977i	−0.670280	−	0.0324274i
$997$	380.211	−	658.545i	0.381355	−	0.660526i	−0.609901	−	0.792478i	$-0.708791\pi$
$997$	380.211	−	658.545i	0.381355	−	0.660526i	0.991256	+	0.131951i	$0.0421242\pi$
$998$	705.854	+	17.0642i	0.707269	+	0.0170984i
$999$	1805.28	−	1042.28i	1.80708	−	1.04332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.3.j.a.45.3	yes	28
4.3	odd	2		224.3.n.a.17.1		28
7.2	even	3		392.3.j.e.117.8		28
7.3	odd	6		392.3.h.a.293.22		28
7.4	even	3		392.3.h.a.293.21		28
7.5	odd	6	inner	56.3.j.a.5.8	yes	28
7.6	odd	2		392.3.j.e.325.3		28
8.3	odd	2		224.3.n.a.17.14		28
8.5	even	2	inner	56.3.j.a.45.8	yes	28
28.3	even	6		1568.3.h.a.881.1		28
28.11	odd	6		1568.3.h.a.881.27		28
28.19	even	6		224.3.n.a.145.14		28
56.3	even	6		1568.3.h.a.881.28		28
56.5	odd	6	inner	56.3.j.a.5.3	✓	28
56.11	odd	6		1568.3.h.a.881.2		28
56.13	odd	2		392.3.j.e.325.8		28
56.19	even	6		224.3.n.a.145.1		28
56.37	even	6		392.3.j.e.117.3		28
56.45	odd	6		392.3.h.a.293.23		28
56.53	even	6		392.3.h.a.293.24		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.3	✓	28	56.5	odd	6	inner
56.3.j.a.5.8	yes	28	7.5	odd	6	inner
56.3.j.a.45.3	yes	28	1.1	even	1	trivial
56.3.j.a.45.8	yes	28	8.5	even	2	inner
224.3.n.a.17.1		28	4.3	odd	2
224.3.n.a.17.14		28	8.3	odd	2
224.3.n.a.145.1		28	56.19	even	6
224.3.n.a.145.14		28	28.19	even	6
392.3.h.a.293.21		28	7.4	even	3
392.3.h.a.293.22		28	7.3	odd	6
392.3.h.a.293.23		28	56.45	odd	6
392.3.h.a.293.24		28	56.53	even	6
392.3.j.e.117.3		28	56.37	even	6
392.3.j.e.117.8		28	7.2	even	3
392.3.j.e.325.3		28	7.6	odd	2
392.3.j.e.325.8		28	56.13	odd	2
1568.3.h.a.881.1		28	28.3	even	6
1568.3.h.a.881.2		28	56.11	odd	6
1568.3.h.a.881.27		28	28.11	odd	6
1568.3.h.a.881.28		28	56.3	even	6

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:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	56.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70738 - 1.04157i) q^{2} +(2.78005 - 4.81519i) q^{3} +(1.83027 + 3.55670i) q^{4} +(-1.52921 - 2.64866i) q^{5} +(-9.76195 + 5.32573i) q^{6} +(0.608243 + 6.97352i) q^{7} +(0.579586 - 7.97898i) q^{8} +(-10.9574 - 18.9787i) q^{9} +O(q^{10})\)	\(q+(-1.70738 - 1.04157i) q^{2} +(2.78005 - 4.81519i) q^{3} +(1.83027 + 3.55670i) q^{4} +(-1.52921 - 2.64866i) q^{5} +(-9.76195 + 5.32573i) q^{6} +(0.608243 + 6.97352i) q^{7} +(0.579586 - 7.97898i) q^{8} +(-10.9574 - 18.9787i) q^{9} +(-0.147833 + 6.11504i) q^{10} +(0.106038 + 0.0612210i) q^{11} +(22.2144 + 1.07471i) q^{12} +4.11412 q^{13} +(6.22490 - 12.5400i) q^{14} -17.0051 q^{15} +(-9.30022 + 13.0194i) q^{16} +(17.8551 + 10.3087i) q^{17} +(-1.05928 + 43.8167i) q^{18} +(4.46893 + 7.74042i) q^{19} +(6.62164 - 10.2867i) q^{20} +(35.2698 + 16.4580i) q^{21} +(-0.117281 - 0.214973i) q^{22} +(7.51940 + 13.0240i) q^{23} +(-36.8090 - 24.9728i) q^{24} +(7.82306 - 13.5499i) q^{25} +(-7.02435 - 4.28514i) q^{26} -71.8074 q^{27} +(-23.6895 + 14.9268i) q^{28} -31.6239i q^{29} +(29.0341 + 17.7120i) q^{30} +(23.0318 + 13.2974i) q^{31} +(29.4396 - 12.5423i) q^{32} +(0.589582 - 0.340395i) q^{33} +(-19.7483 - 36.1981i) q^{34} +(17.5404 - 12.2750i) q^{35} +(47.4467 - 73.7083i) q^{36} +(-25.1405 + 14.5149i) q^{37} +(0.432025 - 17.8705i) q^{38} +(11.4375 - 19.8103i) q^{39} +(-22.0199 + 10.6664i) q^{40} +9.26915i q^{41} +(-43.0767 - 64.8358i) q^{42} +45.3391i q^{43} +(-0.0236667 + 0.489196i) q^{44} +(-33.5122 + 58.0448i) q^{45} +(0.726922 - 30.0688i) q^{46} +(-68.6931 + 39.6600i) q^{47} +(36.8360 + 80.9771i) q^{48} +(-48.2601 + 8.48319i) q^{49} +(-27.4701 + 14.9866i) q^{50} +(99.2764 - 57.3172i) q^{51} +(7.52995 + 14.6327i) q^{52} +(-55.0507 - 31.7835i) q^{53} +(122.602 + 74.7923i) q^{54} -0.374478i q^{55} +(55.9941 - 0.811397i) q^{56} +49.6955 q^{57} +(-32.9384 + 53.9939i) q^{58} +(-14.2561 + 24.6923i) q^{59} +(-31.1239 - 60.4820i) q^{60} +(-12.6191 - 21.8569i) q^{61} +(-25.4738 - 46.6929i) q^{62} +(125.684 - 87.9552i) q^{63} +(-63.3282 - 9.24901i) q^{64} +(-6.29133 - 10.8969i) q^{65} +(-1.36118 - 0.0329070i) q^{66} +(65.4798 + 37.8048i) q^{67} +(-3.98511 + 82.3730i) q^{68} +83.6173 q^{69} +(-42.7333 + 2.68851i) q^{70} -2.81874 q^{71} +(-157.782 + 76.4289i) q^{72} +(11.0878 + 6.40155i) q^{73} +(58.0426 + 1.40320i) q^{74} +(-43.4970 - 75.3391i) q^{75} +(-19.3510 + 30.0617i) q^{76} +(-0.362429 + 0.776695i) q^{77} +(-40.1618 + 21.9107i) q^{78} +(-35.6186 - 61.6932i) q^{79} +(48.7061 + 4.72374i) q^{80} +(-101.012 + 174.958i) q^{81} +(9.65446 - 15.8259i) q^{82} -30.0525 q^{83} +(6.01725 + 155.567i) q^{84} -63.0563i q^{85} +(47.2238 - 77.4109i) q^{86} +(-152.275 - 87.9160i) q^{87} +(0.549939 - 0.810591i) q^{88} +(15.3030 - 8.83521i) q^{89} +(117.676 - 64.1991i) q^{90} +(2.50238 + 28.6899i) q^{91} +(-32.5599 + 50.5816i) q^{92} +(128.059 - 73.9351i) q^{93} +(158.594 + 3.83405i) q^{94} +(13.6678 - 23.6734i) q^{95} +(21.4503 - 176.626i) q^{96} +26.1737i q^{97} +(91.2340 + 35.7822i) q^{98} -2.68329i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 4 * q^4 - 4 * q^7 - 20 * q^8 - 32 * q^9	\( 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9} + 24 q^{10} - 18 q^{12} + 24 q^{14} + 28 q^{15} + 16 q^{16} - 6 q^{17} - 42 q^{18} - 92 q^{22} + 30 q^{23} - 30 q^{24} - 32 q^{25} - 30 q^{26} - 42 q^{28} + 22 q^{30} - 6 q^{31} + 88 q^{32} - 6 q^{33} + 256 q^{36} + 6 q^{38} - 20 q^{39} + 102 q^{40} + 18 q^{42} - 42 q^{44} + 68 q^{46} - 294 q^{47} - 20 q^{49} + 400 q^{50} - 168 q^{52} + 330 q^{54} - 96 q^{56} + 124 q^{57} - 22 q^{58} - 62 q^{60} + 432 q^{63} - 520 q^{64} - 52 q^{65} - 306 q^{66} - 456 q^{68} - 324 q^{70} - 136 q^{71} + 96 q^{72} + 234 q^{73} - 138 q^{74} - 956 q^{78} - 162 q^{79} + 276 q^{80} - 18 q^{81} - 642 q^{82} + 504 q^{84} + 168 q^{86} + 48 q^{87} + 50 q^{88} - 150 q^{89} + 1020 q^{92} + 618 q^{94} + 290 q^{95} + 1044 q^{96} + 424 q^{98}+O(q^{100}) \) 28 * q - 2 * q^2 - 4 * q^4 - 4 * q^7 - 20 * q^8 - 32 * q^9 + 24 * q^10 - 18 * q^12 + 24 * q^14 + 28 * q^15 + 16 * q^16 - 6 * q^17 - 42 * q^18 - 92 * q^22 + 30 * q^23 - 30 * q^24 - 32 * q^25 - 30 * q^26 - 42 * q^28 + 22 * q^30 - 6 * q^31 + 88 * q^32 - 6 * q^33 + 256 * q^36 + 6 * q^38 - 20 * q^39 + 102 * q^40 + 18 * q^42 - 42 * q^44 + 68 * q^46 - 294 * q^47 - 20 * q^49 + 400 * q^50 - 168 * q^52 + 330 * q^54 - 96 * q^56 + 124 * q^57 - 22 * q^58 - 62 * q^60 + 432 * q^63 - 520 * q^64 - 52 * q^65 - 306 * q^66 - 456 * q^68 - 324 * q^70 - 136 * q^71 + 96 * q^72 + 234 * q^73 - 138 * q^74 - 956 * q^78 - 162 * q^79 + 276 * q^80 - 18 * q^81 - 642 * q^82 + 504 * q^84 + 168 * q^86 + 48 * q^87 + 50 * q^88 - 150 * q^89 + 1020 * q^92 + 618 * q^94 + 290 * q^95 + 1044 * q^96 + 424 * q^98

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