LMFDB - Embedded newform 392.3.j.e.117.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(117,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, 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("392.117");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.j (of order $6$, degree $2$, not 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:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			117.8
Character	$\chi$	$=$	392.117
Dual form			392.3.j.e.325.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0483365 + 1.99942i) q^{2} +(2.78005 + 4.81519i) q^{3} +(-3.99533 - 0.193289i) q^{4} +(-1.52921 + 2.64866i) q^{5} +(-9.76195 + 5.32573i) q^{6} +(0.579586 - 7.97898i) q^{8} +(-10.9574 + 18.9787i) q^{9} +O(q^{10})$	\(q+(-0.0483365 + 1.99942i) q^{2} +(2.78005 + 4.81519i) q^{3} +(-3.99533 - 0.193289i) q^{4} +(-1.52921 + 2.64866i) q^{5} +(-9.76195 + 5.32573i) q^{6} +(0.579586 - 7.97898i) q^{8} +(-10.9574 + 18.9787i) q^{9} +(-5.22186 - 3.18554i) q^{10} +(-0.106038 + 0.0612210i) q^{11} +(-10.1765 - 19.7756i) q^{12} +4.11412 q^{13} -17.0051 q^{15} +(15.9253 + 1.54451i) q^{16} +(-17.8551 + 10.3087i) q^{17} +(-37.4167 - 22.8257i) q^{18} +(4.46893 - 7.74042i) q^{19} +(6.62164 - 10.2867i) q^{20} +(-0.117281 - 0.214973i) q^{22} +(7.51940 - 13.0240i) q^{23} +(40.0316 - 19.3912i) q^{24} +(7.82306 + 13.5499i) q^{25} +(-0.198862 + 8.22583i) q^{26} -71.8074 q^{27} -31.6239i q^{29} +(0.821966 - 34.0002i) q^{30} +(-23.0318 + 13.2974i) q^{31} +(-3.85789 + 31.7666i) q^{32} +(-0.589582 - 0.340395i) q^{33} +(-19.7483 - 36.1981i) q^{34} +(47.4467 - 73.7083i) q^{36} +(25.1405 + 14.5149i) q^{37} +(15.2603 + 9.30940i) q^{38} +(11.4375 + 19.8103i) q^{39} +(20.2473 + 13.7366i) q^{40} +9.26915i q^{41} +45.3391i q^{43} +(0.435489 - 0.224102i) q^{44} +(-33.5122 - 58.0448i) q^{45} +(25.6769 + 15.6639i) q^{46} +(68.6931 + 39.6600i) q^{47} +(36.8360 + 80.9771i) q^{48} +(-27.4701 + 14.9866i) q^{50} +(-99.2764 - 57.3172i) q^{51} +(-16.4372 - 0.795215i) q^{52} +(55.0507 - 31.7835i) q^{53} +(3.47092 - 143.573i) q^{54} -0.374478i q^{55} +49.6955 q^{57} +(63.2293 + 1.52859i) q^{58} +(-14.2561 - 24.6923i) q^{59} +(67.9409 + 3.28690i) q^{60} +(-12.6191 + 21.8569i) q^{61} +(-25.4738 - 46.6929i) q^{62} +(-63.3282 - 9.24901i) q^{64} +(-6.29133 + 10.8969i) q^{65} +(0.709090 - 1.16237i) q^{66} +(-65.4798 + 37.8048i) q^{67} +(73.3296 - 37.7353i) q^{68} +83.6173 q^{69} -2.81874 q^{71} +(145.080 + 98.4285i) q^{72} +(-11.0878 + 6.40155i) q^{73} +(-30.2365 + 49.5648i) q^{74} +(-43.4970 + 75.3391i) q^{75} +(-19.3510 + 30.0617i) q^{76} +(-40.1618 + 21.9107i) q^{78} +(-35.6186 + 61.6932i) q^{79} +(-28.4439 + 39.8188i) q^{80} +(-101.012 - 174.958i) q^{81} +(-18.5329 - 0.448038i) q^{82} -30.0525 q^{83} -63.0563i q^{85} +(-90.6517 - 2.19153i) q^{86} +(152.275 - 87.9160i) q^{87} +(0.427023 + 0.881557i) q^{88} +(-15.3030 - 8.83521i) q^{89} +(117.676 - 64.1991i) q^{90} +(-32.5599 + 50.5816i) q^{92} +(-128.059 - 73.9351i) q^{93} +(-82.6172 + 135.429i) q^{94} +(13.6678 + 23.6734i) q^{95} +(-163.687 + 69.7363i) q^{96} +26.1737i q^{97} -2.68329i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 4 q^{4} - 20 q^{8} - 32 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 4 * q^4 - 20 * q^8 - 32 * q^9	$ 28 q - 2 q^{2} - 4 q^{4} - 20 q^{8} - 32 q^{9} - 24 q^{10} + 18 q^{12} + 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} + 22 q^{30} + 6 q^{31} + 88 q^{32} + 6 q^{33} + 256 q^{36} - 6 q^{38} - 20 q^{39} - 102 q^{40} - 42 q^{44} + 68 q^{46} + 294 q^{47} + 400 q^{50} + 168 q^{52} - 330 q^{54} + 124 q^{57} - 22 q^{58} - 62 q^{60} - 520 q^{64} - 52 q^{65} + 306 q^{66} + 456 q^{68} - 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} + 168 q^{86} - 48 q^{87} + 50 q^{88} + 150 q^{89} + 1020 q^{92} - 618 q^{94} + 290 q^{95} - 1044 q^{96}+O(q^{100}) $ 28 * q - 2 * q^2 - 4 * q^4 - 20 * q^8 - 32 * q^9 - 24 * q^10 + 18 * q^12 + 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 + 22 * q^30 + 6 * q^31 + 88 * q^32 + 6 * q^33 + 256 * q^36 - 6 * q^38 - 20 * q^39 - 102 * q^40 - 42 * q^44 + 68 * q^46 + 294 * q^47 + 400 * q^50 + 168 * q^52 - 330 * q^54 + 124 * q^57 - 22 * q^58 - 62 * q^60 - 520 * q^64 - 52 * q^65 + 306 * q^66 + 456 * q^68 - 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 + 168 * q^86 - 48 * q^87 + 50 * q^88 + 150 * q^89 + 1020 * q^92 - 618 * q^94 + 290 * q^95 - 1044 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.0483365	+	1.99942i	−0.0241682	+	0.999708i
$2$	−0.0483365	+	1.99942i	−0.0241682	+	0.999708i
$3$	2.78005	+	4.81519i	0.926684	+	1.60506i	0.788830	+	0.614611i	$0.210687\pi$
$3$	2.78005	+	4.81519i	0.926684	+	1.60506i	0.137854	+	0.990453i	$0.455980\pi$
$4$	−3.99533	−	0.193289i	−0.998832	−	0.0483223i
$5$	−1.52921	+	2.64866i	−0.305841	+	0.529732i	−0.977448	−	0.211175i	$-0.932271\pi$
$5$	−1.52921	+	2.64866i	−0.305841	+	0.529732i	0.671607	+	0.740907i	$0.265604\pi$
$6$	−9.76195	+	5.32573i	−1.62699	+	0.887622i
$7$		0			0
$7$		0			0
$8$	0.579586	−	7.97898i	0.0724482	−	0.997372i
$9$	−10.9574	+	18.9787i	−1.21749	+	2.10875i
$10$	−5.22186	−	3.18554i	−0.522186	−	0.318554i
$11$	−0.106038	+	0.0612210i	−0.00963981	+	0.00556554i	−0.504812	−	0.863229i	$-0.668438\pi$
$11$	−0.106038	+	0.0612210i	−0.00963981	+	0.00556554i	0.495172	+	0.868795i	$0.335105\pi$
$12$	−10.1765	−	19.7756i	−0.848041	−	1.64797i
$13$	4.11412			0.316471			0.158235	−	0.987401i	$-0.449420\pi$
$13$	4.11412			0.316471			0.158235	+	0.987401i	$0.449420\pi$
$14$		0			0
$15$	−17.0051			−1.13367
$16$	15.9253	+	1.54451i	0.995330	+	0.0965318i
$17$	−17.8551	+	10.3087i	−1.05030	+	0.606392i	−0.922734	−	0.385438i	$-0.874050\pi$
$17$	−17.8551	+	10.3087i	−1.05030	+	0.606392i	−0.127568	+	0.991830i	$0.540717\pi$
$18$	−37.4167	−	22.8257i	−2.07871	−	1.26810i
$19$	4.46893	−	7.74042i	0.235207	−	0.407390i	−0.724126	−	0.689668i	$-0.757757\pi$
$19$	4.46893	−	7.74042i	0.235207	−	0.407390i	0.959333	+	0.282277i	$0.0910899\pi$
$20$	6.62164	−	10.2867i	0.331082	−	0.514335i
$21$		0			0
$22$	−0.117281	−	0.214973i	−0.00533094	−	0.00977150i
$23$	7.51940	−	13.0240i	0.326930	−	0.566260i	−0.654971	−	0.755654i	$-0.727319\pi$
$23$	7.51940	−	13.0240i	0.326930	−	0.566260i	0.981901	+	0.189394i	$0.0606524\pi$
$24$	40.0316	−	19.3912i	1.66798	−	0.807965i
$25$	7.82306	+	13.5499i	0.312922	+	0.541998i
$26$	−0.198862	+	8.22583i	−0.00764854	+	0.316378i
$27$	−71.8074			−2.65953
$28$		0			0
$29$		−	31.6239i		−	1.09048i	−0.838280	−	0.545239i	$-0.816439\pi$
$29$		−	31.6239i		−	1.09048i	0.838280	−	0.545239i	$-0.183561\pi$
$30$	0.821966	−	34.0002i	0.0273989	−	1.13334i
$31$	−23.0318	+	13.2974i	−0.742962	+	0.428949i	−0.823145	−	0.567831i	$-0.807783\pi$
$31$	−23.0318	+	13.2974i	−0.742962	+	0.428949i	0.0801833	+	0.996780i	$0.474449\pi$
$32$	−3.85789	+	31.7666i	−0.120559	+	0.992706i
$33$	−0.589582	−	0.340395i	−0.0178661	−	0.0103150i
$34$	−19.7483	−	36.1981i	−0.580831	−	1.06465i
$35$		0			0
$36$	47.4467	−	73.7083i	1.31796	−	2.04745i
$37$	25.1405	+	14.5149i	0.679474	+	0.392295i	0.799657	−	0.600457i	$-0.205015\pi$
$37$	25.1405	+	14.5149i	0.679474	+	0.392295i	−0.120183	+	0.992752i	$0.538348\pi$
$38$	15.2603	+	9.30940i	0.401587	+	0.244984i
$39$	11.4375	+	19.8103i	0.293268	+	0.507956i
$40$	20.2473	+	13.7366i	0.506183	+	0.343416i
$41$			9.26915i			0.226077i	0.993591	+	0.113038i	$0.0360583\pi$
$41$			9.26915i			0.226077i	−0.993591	+	0.113038i	$0.963942\pi$
$42$		0			0
$43$			45.3391i			1.05440i	0.849742	+	0.527199i	$0.176758\pi$
$43$			45.3391i			1.05440i	−0.849742	+	0.527199i	$0.823242\pi$
$44$	0.435489	−	0.224102i	0.00989748	−	0.00509322i
$45$	−33.5122	−	58.0448i	−0.744715	−	1.28988i
$46$	25.6769	+	15.6639i	0.558193	+	0.340520i
$47$	68.6931	+	39.6600i	1.46156	+	0.843830i	0.999083	−	0.0428039i	$-0.0136291\pi$
$47$	68.6931	+	39.6600i	1.46156	+	0.843830i	0.462472	+	0.886634i	$0.346962\pi$
$48$	36.8360	+	80.9771i	0.767417	+	1.68702i
$49$		0			0
$50$	−27.4701	+	14.9866i	−0.549402	+	0.299732i
$51$	−99.2764	−	57.3172i	−1.94660	−	1.12387i
$52$	−16.4372	−	0.795215i	−0.316101	−	0.0152926i
$53$	55.0507	−	31.7835i	1.03869	−	0.599689i	0.119229	−	0.992867i	$-0.461958\pi$
$53$	55.0507	−	31.7835i	1.03869	−	0.599689i	0.919462	+	0.393178i	$0.128624\pi$
$54$	3.47092	−	143.573i	0.0642762	−	2.65876i
$55$		−	0.374478i		−	0.00680869i
$56$		0			0
$57$	49.6955			0.871850
$58$	63.2293	+	1.52859i	1.09016	+	0.0263549i
$59$	−14.2561	−	24.6923i	−0.241629	−	0.418514i	0.719550	−	0.694441i	$-0.244348\pi$
$59$	−14.2561	−	24.6923i	−0.241629	−	0.418514i	−0.961178	+	0.275928i	$0.911015\pi$
$60$	67.9409	+	3.28690i	1.13235	+	0.0547817i
$61$	−12.6191	+	21.8569i	−0.206871	+	0.358311i	−0.950727	−	0.310029i	$-0.899661\pi$
$61$	−12.6191	+	21.8569i	−0.206871	+	0.358311i	0.743856	+	0.668339i	$0.232995\pi$
$62$	−25.4738	−	46.6929i	−0.410868	−	0.753112i
$63$		0			0
$64$	−63.3282	−	9.24901i	−0.989503	−	0.144516i
$65$	−6.29133	+	10.8969i	−0.0967897	+	0.167645i
$66$	0.709090	−	1.16237i	0.0107438	−	0.0176116i
$67$	−65.4798	+	37.8048i	−0.977311	+	0.564251i	−0.901457	−	0.432868i	$-0.857502\pi$
$67$	−65.4798	+	37.8048i	−0.977311	+	0.564251i	−0.0758537	+	0.997119i	$0.524168\pi$
$68$	73.3296	−	37.7353i	1.07838	−	0.554931i
$69$	83.6173			1.21184
$70$		0			0
$71$	−2.81874			−0.0397006			−0.0198503	−	0.999803i	$-0.506319\pi$
$71$	−2.81874			−0.0397006			−0.0198503	+	0.999803i	$0.506319\pi$
$72$	145.080	+	98.4285i	2.01500	+	1.36706i
$73$	−11.0878	+	6.40155i	−0.151888	+	0.0876925i	−0.574018	−	0.818843i	$-0.694616\pi$
$73$	−11.0878	+	6.40155i	−0.151888	+	0.0876925i	0.422130	+	0.906535i	$0.361283\pi$
$74$	−30.2365	+	49.5648i	−0.408602	+	0.669795i
$75$	−43.4970	+	75.3391i	−0.579960	+	1.00452i
$76$	−19.3510	+	30.0617i	−0.254618	+	0.395549i
$77$		0			0
$78$	−40.1618	+	21.9107i	−0.514895	+	0.280906i
$79$	−35.6186	+	61.6932i	−0.450868	+	0.780926i	−0.998440	−	0.0558321i	$-0.982219\pi$
$79$	−35.6186	+	61.6932i	−0.450868	+	0.780926i	0.547572	+	0.836758i	$0.315552\pi$
$80$	−28.4439	+	39.8188i	−0.355549	+	0.497735i
$81$	−101.012	−	174.958i	−1.24706	−	2.15997i
$82$	−18.5329	−	0.448038i	−0.226011	−	0.00546388i
$83$	−30.0525			−0.362078			−0.181039	−	0.983476i	$-0.557946\pi$
$83$	−30.0525			−0.362078			−0.181039	+	0.983476i	$0.557946\pi$
$84$		0			0
$85$		−	63.0563i		−	0.741839i
$86$	−90.6517	−	2.19153i	−1.05409	−	0.0254829i
$87$	152.275	−	87.9160i	1.75029	−	1.01053i
$88$	0.427023	+	0.881557i	0.00485253	+	0.0100177i
$89$	−15.3030	−	8.83521i	−0.171944	−	0.0992720i	0.411558	−	0.911384i	$-0.364985\pi$
$89$	−15.3030	−	8.83521i	−0.171944	−	0.0992720i	−0.583502	+	0.812112i	$0.698318\pi$
$90$	117.676	−	64.1991i	1.30751	−	0.713323i
$91$		0			0
$92$	−32.5599	+	50.5816i	−0.353911	+	0.549800i
$93$	−128.059	−	73.9351i	−1.37698	−	0.795001i
$94$	−82.6172	+	135.429i	−0.878906	+	1.44074i
$95$	13.6678	+	23.6734i	0.143872	+	0.249193i
$96$	−163.687	+	69.7363i	−1.70508	+	0.726420i
$97$			26.1737i			0.269832i	0.990857	+	0.134916i	$0.0430765\pi$
$97$			26.1737i			0.269832i	−0.990857	+	0.134916i	$0.956923\pi$
$98$		0			0
$99$		−	2.68329i		−	0.0271039i
$100$	−28.6366	−	55.6485i	−0.286366	−	0.556485i
$101$	−67.8445	−	117.510i	−0.671727	−	1.16347i	−0.977414	−	0.211334i	$-0.932219\pi$
$101$	−67.8445	−	117.510i	−0.671727	−	1.16347i	0.305686	−	0.952132i	$-0.401114\pi$
$102$	119.400	−	195.724i	1.17059	−	1.91887i
$103$	−110.258	−	63.6577i	−1.07047	−	0.618036i	−0.142160	−	0.989844i	$-0.545405\pi$
$103$	−110.258	−	63.6577i	−1.07047	−	0.618036i	−0.928310	+	0.371807i	$0.878738\pi$
$104$	2.38448	−	32.8265i	0.0229277	−	0.315639i
$105$		0			0
$106$	60.8875	+	111.605i	0.574410	+	1.05288i
$107$	69.1003	+	39.8951i	0.645797	+	0.372851i	0.786844	−	0.617152i	$-0.211713\pi$
$107$	69.1003	+	39.8951i	0.645797	+	0.372851i	−0.141047	+	0.990003i	$0.545047\pi$
$108$	286.894	+	13.8796i	2.65643	+	0.128515i
$109$	27.3608	−	15.7968i	0.251017	−	0.144925i	−0.369213	−	0.929345i	$-0.620373\pi$
$109$	27.3608	−	15.7968i	0.251017	−	0.144925i	0.620230	+	0.784420i	$0.287039\pi$
$110$	0.748737	+	0.0181009i	0.00680670	+	0.000164554i
$111$			161.409i			1.45413i
$112$		0			0
$113$	57.7985			0.511491			0.255745	−	0.966744i	$-0.417679\pi$
$113$	57.7985			0.511491			0.255745	+	0.966744i	$0.417679\pi$
$114$	−2.40210	+	99.3619i	−0.0210711	+	0.871595i
$115$	22.9974	+	39.8327i	0.199978	+	0.346371i
$116$	−6.11256	+	126.348i	−0.0526945	+	1.08920i
$117$	−45.0799	+	78.0808i	−0.385299	+	0.667357i
$118$	50.0593	−	27.3103i	0.424231	−	0.231444i
$119$		0			0
$120$	−9.85591	+	135.683i	−0.0821326	+	1.13069i
$121$	−60.4925	+	104.776i	−0.499938	+	0.865918i
$122$	−43.0912	−	26.2873i	−0.353206	−	0.215470i
$123$	−44.6327	+	25.7687i	−0.362868	+	0.209502i
$124$	94.5899	−	48.6758i	0.762822	−	0.392547i
$125$	−124.313			−0.994500
$126$		0			0
$127$	67.8062			0.533907			0.266954	−	0.963709i	$-0.413983\pi$
$127$	67.8062			0.533907			0.266954	+	0.963709i	$0.413983\pi$
$128$	21.5537	−	126.172i	0.168388	−	0.985721i
$129$	−218.316	+	126.045i	−1.69238	+	0.977093i
$130$	−21.4833	−	13.1057i	−0.165257	−	0.100813i
$131$	−56.0784	+	97.1307i	−0.428080	+	0.741456i	−0.996702	−	0.0811427i	$-0.974143\pi$
$131$	−56.0784	+	97.1307i	−0.428080	+	0.741456i	0.568623	+	0.822598i	$0.307476\pi$
$132$	2.28978	+	1.47395i	0.0173468	+	0.0111663i
$133$		0			0
$134$	−72.4224	−	132.749i	−0.540466	−	0.990662i
$135$	109.808	−	190.193i	0.813394	−	1.40884i
$136$	71.9040	+	148.440i	0.528706	+	1.09147i
$137$	29.3413	+	50.8207i	0.214170	+	0.370954i	0.953016	−	0.302921i	$-0.0979619\pi$
$137$	29.3413	+	50.8207i	0.214170	+	0.370954i	−0.738845	+	0.673875i	$0.764629\pi$
$138$	−4.04176	+	167.186i	−0.0292881	+	1.21149i
$139$	175.260			1.26086			0.630430	−	0.776246i	$-0.282879\pi$
$139$	175.260			1.26086			0.630430	+	0.776246i	$0.282879\pi$
$140$		0			0
$141$			441.027i			3.12785i
$142$	0.136248	−	5.63583i	0.000959492	−	0.0396890i
$143$	−0.436252	+	0.251870i	−0.00305072	+	0.00176133i
$144$	−203.812	+	285.318i	−1.41536	+	1.98137i
$145$	83.7610	+	48.3594i	0.577662	+	0.333513i
$146$	−12.2634	−	22.4786i	−0.0839960	−	0.153963i
$147$		0			0
$148$	−97.6391	−	62.8512i	−0.659724	−	0.424670i
$149$	−61.6922	−	35.6180i	−0.414041	−	0.239047i	0.278483	−	0.960441i	$-0.410168\pi$
$149$	−61.6922	−	35.6180i	−0.414041	−	0.239047i	−0.692525	+	0.721394i	$0.743502\pi$
$150$	−148.532	−	90.6103i	−0.990211	−	0.604068i
$151$	86.3801	+	149.615i	0.572053	+	0.990825i	0.996355	+	0.0853045i	$0.0271863\pi$
$151$	86.3801	+	149.615i	0.572053	+	0.990825i	−0.424302	+	0.905521i	$0.639480\pi$
$152$	−59.1705	−	40.1437i	−0.389279	−	0.264104i
$153$		−	451.824i		−	2.95310i
$154$		0			0
$155$		−	81.3380i		−	0.524761i
$156$	−41.8673	−	81.3592i	−0.268380	−	0.521534i
$157$	134.922	+	233.692i	0.859378	+	1.48849i	0.872524	+	0.488572i	$0.162482\pi$
$157$	134.922	+	233.692i	0.859378	+	1.48849i	−0.0131460	+	0.999914i	$0.504185\pi$
$158$	−121.629	−	74.1984i	−0.769802	−	0.469610i
$159$	306.087	+	176.720i	1.92508	+	1.11144i
$160$	−78.2395	−	58.7959i	−0.488997	−	0.367474i
$161$		0			0
$162$	354.696	−	193.508i	2.18948	−	1.19449i
$163$	236.230	+	136.387i	1.44926	+	0.836733i	0.998438	−	0.0558788i	$-0.0177960\pi$
$163$	236.230	+	136.387i	1.44926	+	0.836733i	0.450826	+	0.892612i	$0.351129\pi$
$164$	1.79163	−	37.0333i	0.0109246	−	0.225813i
$165$	1.80318	−	1.04107i	0.0109284	−	0.00630950i
$166$	1.45263	−	60.0874i	0.00875079	−	0.361973i
$167$			82.5676i			0.494417i	0.968962	+	0.247208i	$0.0795132\pi$
$167$			82.5676i			0.494417i	−0.968962	+	0.247208i	$0.920487\pi$
$168$		0			0
$169$	−152.074			−0.899846
$170$	126.076	+	3.04792i	0.741622	+	0.0179289i
$171$	97.9355	+	169.629i	0.572722	+	0.991984i
$172$	8.76357	−	181.145i	0.0509510	−	1.05317i
$173$	115.129	−	199.410i	0.665488	−	1.15266i	−0.313665	−	0.949534i	$-0.601557\pi$
$173$	115.129	−	199.410i	0.665488	−	1.15266i	0.979153	−	0.203125i	$-0.0651097\pi$
$174$	168.420	+	308.711i	0.967932	+	1.77420i
$175$		0			0
$176$	−1.78324	+	0.811185i	−0.0101320	+	0.00460901i
$177$	79.2654	−	137.292i	0.447827	−	0.775660i
$178$	18.4050	−	30.1701i	0.103399	−	0.169495i
$179$	228.664	−	132.019i	1.27745	−	0.737538i	0.301074	−	0.953601i	$-0.402655\pi$
$179$	228.664	−	132.019i	1.27745	−	0.737538i	0.976379	+	0.216063i	$0.0693216\pi$
$180$	122.673	+	238.385i	0.681515	+	1.32436i
$181$	183.991			1.01653			0.508263	−	0.861202i	$-0.330288\pi$
$181$	183.991			1.01653			0.508263	+	0.861202i	$0.330288\pi$
$182$		0			0
$183$	−140.327			−0.766815
$184$	−99.5599	−	67.5456i	−0.541086	−	0.367096i
$185$	−76.8901	+	44.3925i	−0.415622	+	0.239960i
$186$	154.017	−	252.470i	0.828048	−	1.35737i
$187$	1.26221	−	2.18622i	0.00674980	−	0.0116910i
$188$	−266.786	−	171.732i	−1.41907	−	0.913470i
$189$		0			0
$190$	−47.9936	+	26.1834i	−0.252598	+	0.137807i
$191$	−148.189	+	256.671i	−0.775860	+	1.34383i	0.158450	+	0.987367i	$0.449350\pi$
$191$	−148.189	+	256.671i	−0.775860	+	1.34383i	−0.934310	+	0.356462i	$0.883983\pi$
$192$	−131.520	−	330.650i	−0.684999	−	1.72213i
$193$	−47.8173	−	82.8220i	−0.247758	−	0.429129i	0.715145	−	0.698976i	$-0.246360\pi$
$193$	−47.8173	−	82.8220i	−0.247758	−	0.429129i	−0.962903	+	0.269846i	$0.913027\pi$
$194$	−52.3322	−	1.26515i	−0.269754	−	0.00652137i
$195$	−69.9609			−0.358774
$196$		0			0
$197$		−	161.104i		−	0.817786i	−0.912582	−	0.408893i	$-0.865915\pi$
$197$		−	161.104i		−	0.817786i	0.912582	−	0.408893i	$-0.134085\pi$
$198$	5.36500	+	0.129701i	0.0270960	+	0.000655053i
$199$	−0.961074	+	0.554877i	−0.00482952	+	0.00278832i	−0.502413	−	0.864628i	$-0.667554\pi$
$199$	−0.961074	+	0.554877i	−0.00482952	+	0.00278832i	0.497583	+	0.867416i	$0.334221\pi$
$200$	112.649	−	54.5667i	0.563244	−	0.272833i
$201$	−364.075	−	210.199i	−1.81132	−	1.04576i
$202$	238.231	−	129.969i	1.17936	−	0.643412i
$203$		0			0
$204$	385.563	+	248.190i	1.89001	+	1.21662i
$205$	−24.5508	−	14.1744i	−0.119760	−	0.0691436i
$206$	132.608	−	217.375i	0.643727	−	1.05522i
$207$	164.786	+	285.417i	0.796067	+	1.37883i
$208$	65.5185	+	6.35429i	0.314993	+	0.0305495i
$209$			1.09437i			0.00523622i
$210$		0			0
$211$		−	214.045i		−	1.01443i	−0.861819	−	0.507216i	$-0.830675\pi$
$211$		−	214.045i		−	1.01443i	0.861819	−	0.507216i	$-0.169325\pi$
$212$	−226.089	+	116.345i	−1.06646	+	0.548796i
$213$	−7.83624	−	13.5728i	−0.0367899	−	0.0637219i
$214$	−83.1069	+	136.232i	−0.388350	+	0.636598i
$215$	−120.088	−	69.3328i	−0.558549	−	0.322478i
$216$	−41.6185	+	572.949i	−0.192678	+	2.65254i
$217$		0			0
$218$	30.2618	+	55.4692i	0.138816	+	0.254446i
$219$	−61.6494	−	35.5933i	−0.281504	−	0.162526i
$220$	−0.0723826	+	1.49616i	−0.000329012	+	0.00680074i
$221$	−73.4581	+	42.4111i	−0.332390	+	0.191905i
$222$	−322.723	−	7.80193i	−1.45371	−	0.0351438i
$223$			290.270i			1.30166i	0.759224	+	0.650829i	$0.225579\pi$
$223$			290.270i			1.30166i	−0.759224	+	0.650829i	$0.774421\pi$
$224$		0			0
$225$	−342.881			−1.52392
$226$	−2.79377	+	115.563i	−0.0123618	+	0.511341i
$227$	−40.7118	−	70.5149i	−0.179347	−	0.310638i	0.762310	−	0.647212i	$-0.224065\pi$
$227$	−40.7118	−	70.5149i	−0.179347	−	0.310638i	−0.941657	+	0.336574i	$0.890732\pi$
$228$	−198.550	−	9.60560i	−0.870832	−	0.0421298i
$229$	117.111	−	202.842i	0.511400	−	0.885771i	−0.488512	−	0.872557i	$-0.662460\pi$
$229$	117.111	−	202.842i	0.511400	−	0.885771i	0.999913	−	0.0132145i	$-0.00420642\pi$
$230$	−80.7537	+	44.0560i	−0.351103	+	0.191548i
$231$		0			0
$232$	−252.326	−	18.3288i	−1.08761	−	0.0790032i
$233$	30.9903	−	53.6768i	0.133006	−	0.230372i	−0.791828	−	0.610744i	$-0.790871\pi$
$233$	30.9903	−	53.6768i	0.133006	−	0.230372i	0.924834	+	0.380371i	$0.124204\pi$
$234$	−153.937	−	93.9077i	−0.657850	−	0.401315i
$235$	−210.092	+	121.297i	−0.894008	+	0.516156i
$236$	52.1850	+	101.409i	0.221123	+	0.429701i
$237$	−396.086			−1.67125
$238$		0			0
$239$	97.0822			0.406202			0.203101	−	0.979158i	$-0.434898\pi$
$239$	97.0822			0.406202			0.203101	+	0.979158i	$0.434898\pi$
$240$	−270.811	−	26.2645i	−1.12838	−	0.109435i
$241$	207.622	−	119.871i	0.861502	−	0.497388i	−0.00301303	−	0.999995i	$-0.500959\pi$
$241$	207.622	−	119.871i	0.861502	−	0.497388i	0.864515	+	0.502607i	$0.167626\pi$
$242$	−206.567	−	126.014i	−0.853583	−	0.520720i
$243$	238.503	−	413.100i	0.981494	−	1.70000i
$244$	54.6422	−	84.8865i	0.223943	−	0.347895i
$245$		0			0
$246$	−49.3650	−	90.4850i	−0.200671	−	0.367825i
$247$	18.3857	−	31.8450i	0.0744361	−	0.128927i
$248$	92.7510	+	191.477i	0.373996	+	0.772086i
$249$	−83.5475	−	144.709i	−0.335532	−	0.581159i
$250$	6.00883	−	248.552i	0.0240353	−	0.994210i
$251$	136.078			0.542144			0.271072	−	0.962559i	$-0.412622\pi$
$251$	136.078			0.542144			0.271072	+	0.962559i	$0.412622\pi$
$252$		0			0
$253$			1.84138i			0.00727818i
$254$	−3.27751	+	135.573i	−0.0129036	+	0.533751i
$255$	303.628	−	175.300i	1.19070	−	0.687450i
$256$	251.229	+	49.1935i	0.981363	+	0.192162i
$257$	16.4497	+	9.49721i	0.0640064	+	0.0369541i	0.531662	−	0.846957i	$-0.321568\pi$
$257$	16.4497	+	9.49721i	0.0640064	+	0.0369541i	−0.467655	+	0.883911i	$0.654901\pi$
$258$	−241.464	−	442.598i	−0.935906	−	1.71550i
$259$		0			0
$260$	27.2422	−	42.3207i	0.104778	−	0.162772i
$261$	600.181	+	346.515i	2.29954	+	1.32764i
$262$	−191.494	−	116.819i	−0.730893	−	0.445874i
$263$	−123.286	−	213.537i	−0.468767	−	0.811928i	0.530596	−	0.847625i	$-0.321968\pi$
$263$	−123.286	−	213.537i	−0.468767	−	0.811928i	−0.999363	+	0.0356971i	$0.988635\pi$
$264$	−3.05772	+	4.50697i	−0.0115823	+	0.0170719i
$265$			194.414i			0.733638i
$266$		0			0
$267$		−	98.2494i		−	0.367975i
$268$	268.921	−	138.386i	1.00344	−	0.516366i
$269$	−147.121	−	254.821i	−0.546918	−	0.947290i	−0.998483	−	0.0550522i	$-0.982467\pi$
$269$	−147.121	−	254.821i	−0.546918	−	0.947290i	0.451565	−	0.892238i	$-0.350866\pi$
$270$	374.968	+	228.746i	1.38877	+	0.847206i
$271$	−392.032	−	226.340i	−1.44661	−	0.835202i	−0.448335	−	0.893866i	$-0.647983\pi$
$271$	−392.032	−	226.340i	−1.44661	−	0.835202i	−0.998278	+	0.0586635i	$0.981316\pi$
$272$	−300.270	+	136.591i	−1.10393	+	0.502173i
$273$		0			0
$274$	−103.030	+	56.2091i	−0.376022	+	0.205143i
$275$	−1.65908	−	0.957871i	−0.00603302	−	0.00348317i
$276$	−334.078	−	16.1623i	−1.21043	−	0.0585592i
$277$	252.424	−	145.737i	0.911277	−	0.526126i	0.0304353	−	0.999537i	$-0.490311\pi$
$277$	252.424	−	145.737i	0.911277	−	0.526126i	0.880842	+	0.473411i	$0.156977\pi$
$278$	−8.47143	+	350.417i	−0.0304728	+	1.26049i
$279$		−	582.820i		−	2.08896i
$280$		0			0
$281$	495.433			1.76311			0.881553	−	0.472086i	$-0.156499\pi$
$281$	495.433			1.76311			0.881553	+	0.472086i	$0.156499\pi$
$282$	−881.797	−	21.3177i	−3.12694	−	0.0755947i
$283$	−18.3685	−	31.8151i	−0.0649062	−	0.112421i	0.831746	−	0.555156i	$-0.187341\pi$
$283$	−18.3685	−	31.8151i	−0.0649062	−	0.112421i	−0.896652	+	0.442735i	$0.854008\pi$
$284$	11.2618	+	0.544833i	0.0396542	+	0.00191842i
$285$	−75.9946	+	131.626i	−0.266648	+	0.461847i
$286$	−0.482507	−	0.884424i	−0.00168709	−	0.00309239i
$287$		0			0
$288$	−560.617	−	421.296i	−1.94659	−	1.46283i
$289$	68.0371	−	117.844i	0.235423	−	0.407764i
$290$	−100.739	+	165.135i	−0.347377	+	0.569433i
$291$	−126.032	+	72.7644i	−0.433098	+	0.250049i
$292$	45.5368	−	23.4331i	0.155948	−	0.0802505i
$293$	527.984			1.80199			0.900996	−	0.433828i	$-0.142837\pi$
$293$	527.984			1.80199			0.900996	+	0.433828i	$0.142837\pi$
$294$		0			0
$295$	87.2021			0.295600
$296$	130.385	−	192.183i	0.440490	−	0.649268i
$297$	7.61430	−	4.39612i	0.0256374	−	0.0148017i
$298$	74.1971	−	121.627i	0.248984	−	0.408143i
$299$	30.9357	−	53.5822i	0.103464	−	0.179205i
$300$	188.347	−	292.597i	0.627824	−	0.975322i
$301$		0			0
$302$	−303.317	+	165.478i	−1.00436	+	0.547940i
$303$	377.222	−	653.368i	1.24496	−	2.15633i
$304$	83.1241	−	116.366i	0.273435	−	0.382783i
$305$	−38.5944	−	66.8475i	−0.126539	−	0.219172i
$306$	903.383	+	21.8396i	2.95223	+	0.0713711i
$307$	−174.486			−0.568359			−0.284179	−	0.958771i	$-0.591721\pi$
$307$	−174.486			−0.568359			−0.284179	+	0.958771i	$0.591721\pi$
$308$		0			0
$309$		−	707.887i		−	2.29090i
$310$	162.628	+	3.93159i	0.524608	+	0.0126826i
$311$	−11.9119	+	6.87736i	−0.0383020	+	0.0221137i	−0.519029	−	0.854757i	$-0.673706\pi$
$311$	−11.9119	+	6.87736i	−0.0383020	+	0.0221137i	0.480727	+	0.876870i	$0.340373\pi$
$312$	164.695	−	79.7775i	0.527867	−	0.255697i
$313$	365.368	+	210.945i	1.16731	+	0.673947i	0.953045	−	0.302829i	$-0.0979310\pi$
$313$	365.368	+	210.945i	1.16731	+	0.673947i	0.214265	+	0.976776i	$0.431264\pi$
$314$	−473.770	+	258.470i	−1.50882	+	0.823152i
$315$		0			0
$316$	154.233	−	239.600i	0.488078	−	0.758227i
$317$	−408.352	−	235.762i	−1.28818	−	0.743730i	−0.309848	−	0.950786i	$-0.600278\pi$
$317$	−408.352	−	235.762i	−1.28818	−	0.743730i	−0.978329	+	0.207056i	$0.933612\pi$
$318$	−368.131	+	603.454i	−1.15765	+	1.89765i
$319$	1.93605	+	3.35333i	0.00606911	+	0.0105120i
$320$	121.339	−	153.591i	0.379185	−	0.479973i
$321$			443.642i			1.38206i
$322$		0			0
$323$			184.275i			0.570510i
$324$	369.758	+	718.538i	1.14123	+	2.21771i
$325$	32.1850	+	55.7460i	0.0990308	+	0.171526i
$326$	−284.114	+	465.730i	−0.871515	+	1.42862i
$327$	152.129	+	87.8317i	0.465226	+	0.268598i
$328$	73.9583	+	5.37227i	0.225483	+	0.0163789i
$329$		0			0
$330$	1.99437	+	3.65563i	0.00604354	+	0.0110777i
$331$	383.707	+	221.533i	1.15923	+	0.669284i	0.951120	−	0.308820i	$-0.0999342\pi$
$331$	383.707	+	221.533i	1.15923	+	0.669284i	0.208114	+	0.978105i	$0.433268\pi$
$332$	120.070	+	5.80883i	0.361655	+	0.0174965i
$333$	−550.949	+	318.090i	−1.65450	+	0.955227i
$334$	−165.087	−	3.99103i	−0.494272	−	0.0119492i
$335$		−	231.245i		−	0.690284i
$336$		0			0
$337$	556.978			1.65276			0.826378	−	0.563117i	$-0.190398\pi$
$337$	556.978			1.65276			0.826378	+	0.563117i	$0.190398\pi$
$338$	7.35072	−	304.059i	0.0217477	−	0.899583i
$339$	160.683	+	278.311i	0.473990	+	0.820975i
$340$	−12.1881	+	251.930i	−0.0358474	+	0.740972i
$341$	1.62816	−	2.82006i	0.00477467	−	0.00826998i
$342$	−343.893	+	187.615i	−1.00554	+	0.548581i
$343$		0			0
$344$	361.760	+	26.2779i	1.05163	+	0.0763892i
$345$	−127.868	+	221.474i	−0.370632	+	0.641953i
$346$	393.138	+	239.830i	1.13624	+	0.693151i
$347$	−277.806	+	160.392i	−0.800595	+	0.462223i	−0.843679	−	0.536848i	$-0.819615\pi$
$347$	−277.806	+	160.392i	−0.800595	+	0.462223i	0.0430845	+	0.999071i	$0.486282\pi$
$348$	−625.382	+	321.820i	−1.79707	+	0.924770i
$349$	−222.198			−0.636670			−0.318335	−	0.947978i	$-0.603124\pi$
$349$	−222.198			−0.636670			−0.318335	+	0.947978i	$0.603124\pi$
$350$		0			0
$351$	−295.424			−0.841664
$352$	−1.53570	−	3.60465i	−0.00436279	−	0.0102405i
$353$	118.142	−	68.2096i	0.334681	−	0.193228i	−0.323236	−	0.946318i	$-0.604771\pi$
$353$	118.142	−	68.2096i	0.334681	−	0.193228i	0.657918	+	0.753090i	$0.271438\pi$
$354$	270.672	+	165.121i	0.764610	+	0.466443i
$355$	4.31043	−	7.46589i	0.0121421	−	0.0210307i
$356$	59.4329	+	38.2575i	0.166946	+	0.107465i
$357$		0			0
$358$	252.909	+	463.576i	0.706449	+	1.29491i
$359$	−124.441	+	215.538i	−0.346632	+	0.600384i	−0.985649	−	0.168809i	$-0.946008\pi$
$359$	−124.441	+	215.538i	−0.346632	+	0.600384i	0.639017	+	0.769193i	$0.279341\pi$
$360$	−482.561	+	233.751i	−1.34045	+	0.649308i
$361$	140.557	+	243.452i	0.389355	+	0.674383i
$362$	−8.89348	+	367.875i	−0.0245676	+	1.01623i
$363$	−672.689			−1.85314
$364$		0			0
$365$		−	39.1572i		−	0.107280i
$366$	6.78292	−	280.572i	0.0185326	−	0.766591i
$367$	225.916	−	130.432i	0.615574	−	0.355402i	−0.159570	−	0.987187i	$-0.551011\pi$
$367$	225.916	−	130.432i	0.615574	−	0.355402i	0.775144	+	0.631785i	$0.217677\pi$
$368$	139.864	−	195.797i	0.380066	−	0.532056i
$369$	−175.917	−	101.566i	−0.476739	−	0.275245i
$370$	−85.0425	−	155.881i	−0.229845	−	0.421300i
$371$		0			0
$372$	497.348	+	320.147i	1.33696	+	0.860611i
$373$	381.464	+	220.239i	1.02269	+	0.590452i	0.914883	−	0.403720i	$-0.132283\pi$
$373$	381.464	+	220.239i	1.02269	+	0.590452i	0.107810	+	0.994172i	$0.465616\pi$
$374$	4.31015	+	2.62936i	0.0115245	+	0.00703038i
$375$	−345.595	−	598.589i	−0.921588	−	1.59624i
$376$	356.260	−	525.115i	0.947499	−	1.39658i
$377$		−	130.104i		−	0.345104i
$378$		0			0
$379$			283.715i			0.748587i	0.927310	+	0.374294i	$0.122115\pi$
$379$			283.715i			0.748587i	−0.927310	+	0.374294i	$0.877885\pi$
$380$	−50.0316	−	97.2247i	−0.131662	−	0.255855i
$381$	188.505	+	326.500i	0.494763	+	0.856955i
$382$	−506.030	−	308.698i	−1.32468	−	0.808111i
$383$	−138.511	−	79.9691i	−0.361646	−	0.208797i	0.308156	−	0.951336i	$-0.400288\pi$
$383$	−138.511	−	79.9691i	−0.361646	−	0.208797i	−0.669803	+	0.742539i	$0.733621\pi$
$384$	667.464	−	246.980i	1.73819	−	0.643178i
$385$		0			0
$386$	167.907	−	91.6033i	0.434992	−	0.237314i
$387$	−860.479	−	496.798i	−2.22346	−	1.28371i
$388$	5.05911	−	104.573i	0.0130389	−	0.269517i
$389$	430.295	−	248.431i	1.10616	−	0.638640i	0.168326	−	0.985731i	$-0.446164\pi$
$389$	430.295	−	248.431i	1.10616	−	0.638640i	0.937831	+	0.347091i	$0.112830\pi$
$390$	3.38166	−	139.881i	0.00867093	−	0.358669i
$391$			310.060i			0.792992i
$392$		0			0
$393$	−623.604			−1.58678
$394$	322.113	+	7.78719i	0.817547	+	0.0197644i
$395$	−108.936	−	188.683i	−0.275788	−	0.477679i
$396$	−0.518651	+	10.7206i	−0.00130972	+	0.0270722i
$397$	142.186	−	246.273i	0.358150	−	0.620334i	−0.629502	−	0.776999i	$-0.716741\pi$
$397$	142.186	−	246.273i	0.358150	−	0.620334i	0.987652	+	0.156665i	$0.0500743\pi$
$398$	−1.06297	−	1.94841i	−0.00267079	−	0.00489550i
$399$		0			0
$400$	103.656	+	227.869i	0.259141	+	0.569673i
$401$	−70.8759	+	122.761i	−0.176748	+	0.306136i	−0.940765	−	0.339060i	$-0.889891\pi$
$401$	−70.8759	+	122.761i	−0.176748	+	0.306136i	0.764017	+	0.645196i	$0.223224\pi$
$402$	437.873	−	717.776i	1.08924	−	1.78551i
$403$	−94.7556	+	54.7072i	−0.235126	+	0.135750i
$404$	248.347	+	482.605i	0.614721	+	1.19457i
$405$	617.872			1.52561
$406$		0			0
$407$	−3.55447			−0.00873333
$408$	−514.872	+	758.904i	−1.26194	+	1.86006i
$409$	323.318	−	186.668i	0.790508	−	0.456400i	−0.0496336	−	0.998767i	$-0.515805\pi$
$409$	323.318	−	186.668i	0.790508	−	0.456400i	0.840141	+	0.542368i	$0.182472\pi$
$410$	29.5273	−	48.4022i	0.0720178	−	0.118054i
$411$	−163.141	+	282.568i	−0.396937	+	0.687514i
$412$	428.214	+	275.645i	1.03935	+	0.669042i
$413$		0			0
$414$	−578.633	+	315.679i	−1.39766	+	0.762510i
$415$	45.9565	−	79.5989i	0.110738	−	0.191805i
$416$	−15.8718	+	130.692i	−0.0381534	+	0.314162i
$417$	487.231	+	843.908i	1.16842	+	2.02376i
$418$	−2.18810	−	0.0528980i	−0.00523469	−	0.000126550i
$419$	418.864			0.999676			0.499838	−	0.866119i	$-0.333393\pi$
$419$	418.864			0.999676			0.499838	+	0.866119i	$0.333393\pi$
$420$		0			0
$421$		−	315.112i		−	0.748485i	−0.927331	−	0.374243i	$-0.877903\pi$
$421$		−	315.112i		−	0.748485i	0.927331	−	0.374243i	$-0.122097\pi$
$422$	427.965	+	10.3462i	1.01414	+	0.0245170i
$423$	−1505.39	+	869.139i	−3.55885	+	2.05470i
$424$	−221.693	−	457.669i	−0.522862	−	1.07941i
$425$	−279.364	−	161.291i	−0.657326	−	0.379507i
$426$	27.5164	−	15.0118i	0.0645925	−	0.0352391i
$427$		0			0
$428$	−268.367	−	172.750i	−0.627026	−	0.403622i
$429$	−2.42561	−	1.40043i	−0.00565410	−	0.00326440i
$430$	144.430	−	236.754i	0.335883	−	0.550592i
$431$	−111.663	−	193.405i	−0.259078	−	0.448736i	0.706917	−	0.707296i	$-0.250085\pi$
$431$	−111.663	−	193.405i	−0.259078	−	0.448736i	−0.965995	+	0.258560i	$0.916752\pi$
$432$	−1143.55	−	110.907i	−2.64711	−	0.256729i
$433$		−	591.725i		−	1.36657i	−0.730151	−	0.683286i	$-0.760550\pi$
$433$		−	591.725i		−	1.36657i	0.730151	−	0.683286i	$-0.239450\pi$
$434$		0			0
$435$			537.767i			1.23625i
$436$	−112.369	+	57.8247i	−0.257726	+	0.132625i
$437$	−67.2074	−	116.407i	−0.153793	−	0.266377i
$438$	74.1457	−	121.542i	0.169282	−	0.277494i
$439$	443.687	+	256.163i	1.01068	+	0.583515i	0.911390	−	0.411544i	$-0.135010\pi$
$439$	443.687	+	256.163i	1.01068	+	0.583515i	0.0992873	+	0.995059i	$0.468344\pi$
$440$	−2.98795	−	0.217042i	−0.00679080	−	0.000493278i
$441$		0			0
$442$	−81.2466	−	148.923i	−0.183816	−	0.336931i
$443$	−134.591	−	77.7063i	−0.303818	−	0.175409i	0.340339	−	0.940303i	$-0.389458\pi$
$443$	−134.591	−	77.7063i	−0.303818	−	0.175409i	−0.644157	+	0.764894i	$0.722792\pi$
$444$	31.1986	−	644.881i	0.0702671	−	1.45243i
$445$	46.8030	−	27.0217i	0.105175	−	0.0607229i
$446$	−580.370	−	14.0306i	−1.30128	−	0.0314588i
$447$		−	396.079i		−	0.886084i
$448$		0			0
$449$	−369.139			−0.822136			−0.411068	−	0.911605i	$-0.634844\pi$
$449$	−369.139			−0.822136			−0.411068	+	0.911605i	$0.634844\pi$
$450$	16.5737	−	685.561i	0.0368303	−	1.52347i
$451$	−0.567467	−	0.982881i	−0.00125824	−	0.00217934i
$452$	−230.924	−	11.1718i	−0.510893	−	0.0247164i
$453$	−480.282	+	831.873i	−1.06023	+	1.83636i
$454$	142.957	−	77.9914i	0.314882	−	0.171787i
$455$		0			0
$456$	28.8028	−	396.519i	0.0631640	−	0.869559i
$457$	214.079	−	370.795i	0.468444	−	0.811369i	−0.530906	−	0.847431i	$-0.678148\pi$
$457$	214.079	−	370.795i	0.468444	−	0.811369i	0.999350	+	0.0360623i	$0.0114815\pi$
$458$	399.904	+	243.958i	0.873153	+	0.532659i
$459$	1282.13	−	740.238i	2.79331	−	1.61272i
$460$	−84.1830	−	163.590i	−0.183006	−	0.355630i
$461$	−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			0
$463$	−605.376			−1.30751			−0.653754	−	0.756708i	$-0.726807\pi$
$463$	−605.376			−1.30751			−0.653754	+	0.756708i	$0.726807\pi$
$464$	48.8434	−	503.619i	0.105266	−	1.08539i
$465$	391.658	−	226.124i	0.842275	−	0.486288i
$466$	105.824	+	64.5570i	0.227091	+	0.138534i
$467$	−286.063	+	495.476i	−0.612555	+	1.06098i	0.378253	+	0.925702i	$0.376525\pi$
$467$	−286.063	+	495.476i	−0.612555	+	1.06098i	−0.990808	+	0.135275i	$0.956808\pi$
$468$	195.201	−	303.245i	0.417097	−	0.647959i
$469$		0			0
$470$	−232.367	−	425.924i	−0.494398	−	0.906221i
$471$	−750.182	+	1299.35i	−1.59274	+	2.75871i
$472$	−205.282	+	99.4378i	−0.434919	+	0.210673i
$473$	−2.77570	−	4.80766i	−0.00586830	−	0.0101642i
$474$	19.1454	−	791.941i	0.0403911	−	1.67076i
$475$	139.843			0.294406
$476$		0			0
$477$			1393.06i			2.92045i
$478$	−4.69261	+	194.108i	−0.00981718	+	0.406083i
$479$	−32.2540	+	18.6218i	−0.0673361	+	0.0388765i	−0.533290	−	0.845932i	$-0.679045\pi$
$479$	−32.2540	+	18.6218i	−0.0673361	+	0.0388765i	0.465954	+	0.884809i	$0.345711\pi$
$480$	65.6037	−	540.194i	0.136674	−	1.12540i
$481$	103.431	+	59.7160i	0.215034	+	0.124150i
$482$	229.635	+	420.917i	0.476422	+	0.873271i
$483$		0			0
$484$	261.939	−	406.922i	0.541197	−	0.840748i
$485$	−69.3254	−	40.0250i	−0.142939	−	0.0825259i
$486$	814.429	+	496.835i	1.67578	+	1.02229i
$487$	−137.172	−	237.589i	−0.281668	−	0.487863i	0.690128	−	0.723688i	$-0.257554\pi$
$487$	−137.172	−	237.589i	−0.281668	−	0.487863i	−0.971796	+	0.235824i	$0.924221\pi$
$488$	167.082	+	113.356i	0.342382	+	0.232286i
$489$			1516.66i			3.10155i
$490$		0			0
$491$			881.994i			1.79632i	0.439667	+	0.898161i	$0.355097\pi$
$491$			881.994i			1.79632i	−0.439667	+	0.898161i	$0.644903\pi$
$492$	183.303	−	94.3274i	0.372567	−	0.191722i
$493$	326.000	+	564.648i	0.661257	+	1.14533i
$494$	62.7827	+	38.3000i	0.127090	+	0.0775303i
$495$	7.10712	+	4.10330i	0.0143578	+	0.00828949i
$496$	−387.326	+	176.192i	−0.780900	+	0.355227i
$497$		0			0
$498$	293.371	−	160.052i	0.589098	−	0.321389i
$499$	305.733	+	176.515i	0.612692	+	0.353738i	0.774018	−	0.633163i	$-0.218244\pi$
$499$	305.733	+	176.515i	0.612692	+	0.353738i	−0.161327	+	0.986901i	$0.551577\pi$
$500$	496.669	+	24.0283i	0.993339	+	0.0480566i
$501$	−397.579	+	229.542i	−0.793570	+	0.458168i
$502$	−6.57754	+	272.077i	−0.0131027	+	0.541986i
$503$		−	291.993i		−	0.580502i	−0.956951	−	0.290251i	$-0.906261\pi$
$503$		−	291.993i		−	0.580502i	0.956951	−	0.290251i	$-0.0937388\pi$
$504$		0			0
$505$	414.993			0.821768
$506$	−3.68168	−	0.0890058i	−0.00727606	−	0.000175901i
$507$	−422.774	−	732.266i	−0.833873	−	1.44431i
$508$	−270.908	−	13.1062i	−0.533284	−	0.0257997i
$509$	41.5606	−	71.9851i	0.0816515	−	0.141425i	−0.822308	−	0.569043i	$-0.807314\pi$
$509$	41.5606	−	71.9851i	0.0816515	−	0.141425i	0.903959	+	0.427618i	$0.140647\pi$
$510$	335.821	+	615.552i	0.658472	+	1.20696i
$511$		0			0
$512$	−110.502	+	499.933i	−0.215824	+	0.976432i
$513$	−320.902	+	555.819i	−0.625541	+	1.08347i
$514$	−19.7840	+	32.4306i	−0.0384903	+	0.0630946i
$515$	337.216	−	194.692i	0.654788	−	0.378042i
$516$	896.609	−	461.393i	1.73761	−	0.894172i
$517$	−9.71210			−0.0187855
$518$		0			0
$519$	1280.26			2.46679
$520$	83.2998	+	56.5141i	0.160192	+	0.108681i
$521$	−513.150	+	296.267i	−0.984933	+	0.568651i	−0.903756	−	0.428048i	$-0.859201\pi$
$521$	−513.150	+	296.267i	−0.984933	+	0.568651i	−0.0811772	+	0.996700i	$0.525868\pi$
$522$	−721.838	+	1183.26i	−1.38283	+	2.26679i
$523$	151.233	−	261.943i	0.289164	−	0.500847i	−0.684446	−	0.729063i	$-0.739956\pi$
$523$	151.233	−	261.943i	0.289164	−	0.500847i	0.973610	+	0.228217i	$0.0732894\pi$
$524$	242.826	−	377.230i	0.463408	−	0.719904i
$525$		0			0
$526$	432.908	−	236.178i	0.823020	−	0.449007i
$527$	274.157	−	474.855i	0.520223	−	0.901052i
$528$	−8.86351	−	6.33150i	−0.0167869	−	0.0119915i
$529$	151.417	+	262.262i	0.286233	+	0.495770i
$530$	−388.715	−	9.39729i	−0.733424	−	0.0177307i
$531$	624.838			1.17672
$532$		0			0
$533$			38.1344i			0.0715467i
$534$	196.441	+	4.74903i	0.367868	+	0.00889331i
$535$	−211.337	+	122.016i	−0.395023	+	0.228067i
$536$	263.692	+	544.373i	0.491964	+	1.01562i
$537$	1271.40	+	734.041i	2.36759	+	1.36693i
$538$	516.605	−	281.839i	0.960232	−	0.523864i
$539$		0			0
$540$	−475.482	+	738.660i	−0.880523	+	1.36789i
$541$	−630.140	−	363.811i	−1.16477	−	0.672480i	−0.212327	−	0.977199i	$-0.568104\pi$
$541$	−630.140	−	363.811i	−1.16477	−	0.672480i	−0.952442	+	0.304719i	$0.901437\pi$
$542$	471.497	−	772.895i	0.869920	−	1.42600i
$543$	511.505	+	885.952i	0.941997	+	1.63159i
$544$	−258.588	−	606.966i	−0.475346	−	1.11575i
$545$			96.6260i			0.177296i
$546$		0			0
$547$		−	1033.51i		−	1.88941i	−0.327921	−	0.944705i	$-0.606348\pi$
$547$		−	1033.51i		−	1.88941i	0.327921	−	0.944705i	$-0.393652\pi$
$548$	−107.405	−	208.717i	−0.195995	−	0.380870i
$549$	−276.545	−	478.990i	−0.503724	−	0.872476i
$550$	1.99538	−	3.27089i	0.00362796	−	0.00594708i
$551$	−244.782	−	141.325i	−0.444250	−	0.256488i
$552$	48.4634	−	667.180i	0.0877960	−	1.20866i
$553$		0			0
$554$	279.187	+	511.745i	0.503948	+	0.923727i
$555$	−427.517	−	246.827i	−0.770301	−	0.444734i
$556$	−700.219	−	33.8758i	−1.25939	−	0.0609277i
$557$	625.736	−	361.269i	1.12340	−	0.648597i	0.181136	−	0.983458i	$-0.442023\pi$
$557$	625.736	−	361.269i	1.12340	−	0.648597i	0.942268	+	0.334861i	$0.108689\pi$
$558$	1165.30	+	28.1714i	2.08835	+	0.0504865i
$559$			186.530i			0.333686i
$560$		0			0
$561$	14.0361			0.0250197
$562$	−23.9475	+	990.576i	−0.0426111	+	1.76259i
$563$	−206.897	−	358.355i	−0.367489	−	0.636510i	0.621683	−	0.783269i	$-0.286449\pi$
$563$	−206.897	−	358.355i	−0.367489	−	0.636510i	−0.989172	+	0.146759i	$0.953116\pi$
$564$	85.2459	−	1762.05i	0.151145	−	3.12420i
$565$	−88.3857	+	153.089i	−0.156435	+	0.270953i
$566$	64.4995	−	35.1884i	0.113957	−	0.0621702i
$567$		0			0
$568$	−1.63370	+	22.4907i	−0.00287624	+	0.0395962i
$569$	258.602	−	447.911i	0.454485	−	0.787190i	−0.544174	−	0.838972i	$-0.683157\pi$
$569$	258.602	−	447.911i	0.454485	−	0.787190i	0.998658	+	0.0517822i	$0.0164901\pi$
$570$	−259.503	−	158.307i	−0.455268	−	0.277732i
$571$	−615.938	+	355.612i	−1.07870	+	0.622788i	−0.930545	−	0.366177i	$-0.880667\pi$
$571$	−615.938	+	355.612i	−1.07870	+	0.622788i	−0.148155	+	0.988964i	$0.547333\pi$
$572$	1.79165	−	0.921982i	0.00313226	−	0.00161186i
$573$	−1647.89			−2.87591
$574$		0			0
$575$	235.299			0.409215
$576$	869.445	−	1100.54i	1.50945	−	1.91067i
$577$	−527.662	+	304.646i	−0.914491	+	0.527982i	−0.881874	−	0.471486i	$-0.843718\pi$
$577$	−527.662	+	304.646i	−0.914491	+	0.527982i	−0.0326179	+	0.999468i	$0.510384\pi$
$578$	232.330	+	141.731i	0.401955	+	0.245209i
$579$	265.869	−	460.499i	0.459187	−	0.795335i
$580$	−325.305	−	209.402i	−0.560871	−	0.361038i
$581$		0			0
$582$	−139.394	−	255.507i	−0.239509	−	0.439015i
$583$	−3.89164	+	6.74051i	−0.00667519	+	0.0115618i
$584$	44.6515	+	92.1797i	0.0764580	+	0.157842i
$585$	−137.873	−	238.803i	−0.235680	−	0.408210i
$586$	−25.5209	+	1055.66i	−0.0435510	+	1.80147i
$587$	972.801			1.65724			0.828621	−	0.559810i	$-0.189126\pi$
$587$	972.801			1.65724			0.828621	+	0.559810i	$0.189126\pi$
$588$		0			0
$589$			237.701i			0.403567i
$590$	−4.21504	+	174.353i	−0.00714414	+	0.295514i
$591$	775.745	−	447.877i	1.31260	−	0.757829i
$592$	377.952	+	269.984i	0.638432	+	0.456053i
$593$	281.520	+	162.536i	0.474739	+	0.274091i	0.718222	−	0.695814i	$-0.244956\pi$
$593$	281.520	+	162.536i	0.474739	+	0.274091i	−0.243482	+	0.969905i	$0.578290\pi$
$594$	8.42162	+	15.4366i	0.0141778	+	0.0259876i
$595$		0			0
$596$	239.596	+	154.230i	0.402006	+	0.258775i
$597$	−5.34367	−	3.08517i	−0.00895088	−	0.00516779i
$598$	105.638	+	64.4433i	0.176652	+	0.107765i
$599$	−231.570	−	401.091i	−0.386595	−	0.669602i	0.605394	−	0.795926i	$-0.293015\pi$
$599$	−231.570	−	401.091i	−0.386595	−	0.669602i	−0.991989	+	0.126324i	$0.959682\pi$
$600$	575.918	+	390.727i	0.959864	+	0.651212i
$601$		−	325.247i		−	0.541176i	−0.962695	−	0.270588i	$-0.912782\pi$
$601$		−	325.247i		−	0.541176i	0.962695	−	0.270588i	$-0.0872182\pi$
$602$		0			0
$603$		−	1656.97i		−	2.74787i
$604$	−316.198	−	614.456i	−0.523506	−	1.01731i
$605$	−185.011	−	320.448i	−0.305803	−	0.529667i
$606$	1288.12	+	785.806i	2.12561	+	1.29671i
$607$	−346.450	−	200.023i	−0.570758	−	0.329527i	0.186694	−	0.982418i	$-0.440223\pi$
$607$	−346.450	−	200.023i	−0.570758	−	0.329527i	−0.757452	+	0.652891i	$0.773556\pi$
$608$	228.646	+	171.824i	0.376063	+	0.282606i
$609$		0			0
$610$	135.522	−	73.9351i	0.222166	−	0.121205i
$611$	282.612	+	163.166i	0.462540	+	0.267047i
$612$	−87.3327	+	1805.18i	−0.142701	+	2.94965i
$613$	−821.365	+	474.215i	−1.33991	+	0.773597i	−0.986794	−	0.161982i	$-0.948211\pi$
$613$	−821.365	+	474.215i	−1.33991	+	0.773597i	−0.353116	+	0.935579i	$0.614878\pi$
$614$	8.43404	−	348.870i	0.0137362	−	0.568193i
$615$		−	157.623i		−	0.256297i
$616$		0			0
$617$	−1066.14			−1.72793			−0.863967	−	0.503548i	$-0.832028\pi$
$617$	−1066.14			−1.72793			−0.863967	+	0.503548i	$0.832028\pi$
$618$	1415.36	+	34.2168i	2.29023	+	0.0553669i
$619$	471.501	+	816.664i	0.761715	+	1.31933i	0.941966	+	0.335708i	$0.108976\pi$
$619$	471.501	+	816.664i	0.761715	+	1.31933i	−0.180251	+	0.983621i	$0.557691\pi$
$620$	−15.7218	+	324.972i	−0.0253577	+	0.524148i
$621$	−539.948	+	935.218i	−0.869482	+	1.50599i
$622$	−13.1749	−	24.1493i	−0.0211815	−	0.0388253i
$623$		0			0
$624$	151.548	+	333.149i	0.242865	+	0.533893i
$625$	−5.47705	+	9.48652i	−0.00876328	+	0.0151784i
$626$	−439.428	+	720.326i	−0.701962	+	1.15068i
$627$	−5.26960	+	3.04240i	−0.00840446	+	0.00485232i
$628$	−493.888	−	959.756i	−0.786447	−	1.52827i
$629$	−598.517			−0.951537
$630$		0			0
$631$	−575.646			−0.912276			−0.456138	−	0.889909i	$-0.650768\pi$
$631$	−575.646			−0.912276			−0.456138	+	0.889909i	$0.650768\pi$
$632$	471.604	+	319.956i	0.746210	+	0.506260i
$633$	1030.67	−	595.056i	1.62823	−	0.940057i
$634$	491.125	−	805.070i	0.774645	−	1.26983i
$635$	−103.690	+	179.596i	−0.163291	+	0.282828i
$636$	−1188.76	−	765.216i	−1.86912	−	1.20317i
$637$		0			0
$638$	−6.79828	+	3.70887i	−0.0106556	+	0.00581328i
$639$	30.8860	−	53.4961i	0.0483349	−	0.0837185i
$640$	301.228	+	250.032i	0.470668	+	0.390675i
$641$	−396.899	−	687.449i	−0.619187	−	1.07246i	−0.989634	−	0.143610i	$-0.954129\pi$
$641$	−396.899	−	687.449i	−0.619187	−	1.07246i	0.370447	−	0.928854i	$-0.379204\pi$
$642$	−887.024	−	21.4441i	−1.38166	−	0.0334020i
$643$	−841.343			−1.30847			−0.654233	−	0.756293i	$-0.727008\pi$
$643$	−841.343			−1.30847			−0.654233	+	0.756293i	$0.727008\pi$
$644$		0			0
$645$		−	770.995i		−	1.19534i
$646$	−368.442	−	8.90720i	−0.570344	−	0.0137882i
$647$	−476.604	+	275.167i	−0.736637	+	0.425297i	−0.820845	−	0.571151i	$-0.806497\pi$
$647$	−476.604	+	275.167i	−0.736637	+	0.425297i	0.0842084	+	0.996448i	$0.473164\pi$
$648$	−1454.53	+	704.568i	−2.24464	+	1.08730i
$649$	3.02337	+	1.74555i	0.00465851	+	0.00268959i
$650$	−113.015	+	61.6566i	−0.173870	+	0.0948563i
$651$		0			0
$652$	−917.454	−	590.573i	−1.40714	−	0.905787i
$653$	−713.506	−	411.943i	−1.09266	−	0.630847i	−0.158375	−	0.987379i	$-0.550626\pi$
$653$	−713.506	−	411.943i	−1.09266	−	0.630847i	−0.934283	+	0.356532i	$0.883959\pi$
$654$	−182.965	+	299.924i	−0.279764	+	0.458599i
$655$	−171.511	−	297.066i	−0.261849	−	0.453535i
$656$	−14.3163	+	147.614i	−0.0218236	+	0.225021i
$657$		−	280.577i		−	0.427058i
$658$		0			0
$659$			354.257i			0.537567i	0.963201	+	0.268784i	$0.0866217\pi$
$659$			354.257i			0.537567i	−0.963201	+	0.268784i	$0.913378\pi$
$660$	−7.40553	+	3.81087i	−0.0112205	+	0.00577405i
$661$	84.3031	+	146.017i	0.127539	+	0.220904i	0.922722	−	0.385465i	$-0.125959\pi$
$661$	84.3031	+	146.017i	0.127539	+	0.220904i	−0.795184	+	0.606369i	$0.792626\pi$
$662$	−461.484	+	756.481i	−0.697105	+	1.14272i
$663$	−408.435	−	235.810i	−0.616040	−	0.355671i
$664$	−17.4180	+	239.788i	−0.0262319	+	0.361127i
$665$		0			0
$666$	−609.364	−	1116.95i	−0.914961	−	1.67710i
$667$	−411.869	−	237.793i	−0.617494	−	0.356511i
$668$	15.9594	−	329.885i	0.0238914	−	0.493839i
$669$	−1397.70	+	806.965i	−2.08924	+	1.20623i
$670$	462.355	+	11.1776i	0.690083	+	0.0166830i
$671$		−	3.09022i		−	0.00460539i
$672$		0			0
$673$	514.054			0.763824			0.381912	−	0.924199i	$-0.375266\pi$
$673$	514.054			0.763824			0.381912	+	0.924199i	$0.375266\pi$
$674$	−26.9224	+	1113.63i	−0.0399442	+	1.65227i
$675$	−561.753	−	972.986i	−0.832227	−	1.44146i
$676$	607.586	+	29.3943i	0.898795	+	0.0434827i
$677$	260.650	−	451.460i	0.385008	−	0.666853i	−0.606762	−	0.794883i	$-0.707532\pi$
$677$	260.650	−	451.460i	0.385008	−	0.666853i	0.991770	+	0.128030i	$0.0408654\pi$
$678$	−564.226	+	307.819i	−0.832191	+	0.454010i
$679$		0			0
$680$	−503.125	−	36.5465i	−0.739889	−	0.0537449i
$681$	226.362	−	392.070i	0.332396	−	0.575727i
$682$	5.55978	+	3.39169i	0.00815216	+	0.00497315i
$683$	441.591	−	254.953i	0.646547	−	0.373284i	−0.140585	−	0.990069i	$-0.544898\pi$
$683$	441.591	−	254.953i	0.646547	−	0.373284i	0.787132	+	0.616785i	$0.211565\pi$
$684$	−358.497	−	696.655i	−0.524118	−	1.01850i
$685$	−179.476			−0.262009
$686$		0			0
$687$	1302.30			1.89563
$688$	−70.0266	+	722.038i	−0.101783	+	1.04947i
$689$	226.485	−	130.761i	0.328715	−	0.189784i
$690$	−436.638	−	266.367i	−0.632808	−	0.386039i
$691$	−467.402	+	809.565i	−0.676415	+	1.17158i	0.299639	+	0.954053i	$0.403134\pi$
$691$	−467.402	+	809.565i	−0.676415	+	1.17158i	−0.976053	+	0.217532i	$0.930199\pi$
$692$	−498.523	+	774.455i	−0.720409	+	1.11915i
$693$		0			0
$694$	−307.261	−	563.203i	−0.442739	−	0.811532i
$695$	−268.008	+	464.203i	−0.385623	+	0.667919i
$696$	−613.223	−	1265.95i	−0.881068	−	1.81890i
$697$	−95.5526	−	165.502i	−0.137091	−	0.237449i
$698$	10.7403	−	444.266i	0.0153872	−	0.636484i
$699$	344.619			0.493017
$700$		0			0
$701$			364.276i			0.519651i	0.965656	+	0.259826i	$0.0836651\pi$
$701$			364.276i			0.519651i	−0.965656	+	0.259826i	$0.916335\pi$
$702$	14.2798	−	590.676i	0.0203415	−	0.841418i
$703$	224.703	−	129.732i	0.319634	−	0.184541i
$704$	7.28142	−	2.89627i	0.0103429	−	0.00411402i
$705$	−1168.13	−	674.422i	−1.65693	−	0.956626i
$706$	130.669	+	239.513i	0.185083	+	0.339253i
$707$		0			0
$708$	−343.228	+	533.204i	−0.484786	+	0.753113i
$709$	−429.168	−	247.780i	−0.605315	−	0.349479i	0.165815	−	0.986157i	$-0.446975\pi$
$709$	−429.168	−	247.780i	−0.605315	−	0.349479i	−0.771130	+	0.636678i	$0.780308\pi$
$710$	14.7191	+	8.97922i	0.0207311	+	0.0126468i
$711$	−780.572	−	1351.99i	−1.09785	−	1.90153i
$712$	−79.3654	+	116.982i	−0.111468	+	0.164300i
$713$			399.955i			0.560946i
$714$		0			0
$715$		−	1.54065i		−	0.00215475i
$716$	−939.106	+	483.262i	−1.31160	+	0.674947i
$717$	269.894	+	467.470i	0.376421	+	0.651980i
$718$	−424.935	−	259.227i	−0.591831	−	0.361041i
$719$	582.836	+	336.500i	0.810620	+	0.468012i	0.847171	−	0.531320i	$-0.178304\pi$
$719$	582.836	+	336.500i	0.810620	+	0.468012i	−0.0365511	+	0.999332i	$0.511637\pi$
$720$	−444.040	−	976.139i	−0.616722	−	1.35575i
$721$		0			0
$722$	−493.557	+	269.265i	−0.683596	+	0.372943i
$723$	1154.40	+	666.493i	1.59668	+	0.921844i
$724$	−735.104	−	35.5635i	−1.01534	−	0.0491209i
$725$	428.502	−	247.395i	0.591037	−	0.341235i
$726$	32.5154	−	1344.99i	0.0447871	−	1.85260i
$727$		−	165.434i		−	0.227557i	−0.993506	−	0.113778i	$-0.963705\pi$
$727$		−	165.434i		−	0.227557i	0.993506	−	0.113778i	$-0.0362954\pi$
$728$		0			0
$729$	833.991			1.14402
$730$	78.2914	+	1.89272i	0.107249	+	0.00259277i
$731$	−467.386	−	809.536i	−0.639378	−	1.10744i
$732$	560.653	+	27.1237i	0.765919	+	0.0370543i
$733$	474.614	−	822.055i	0.647495	−	1.12149i	−0.336225	−	0.941782i	$-0.609150\pi$
$733$	474.614	−	822.055i	0.647495	−	1.12149i	0.983719	−	0.179712i	$-0.0575165\pi$
$734$	249.869	+	458.004i	0.340421	+	0.623984i
$735$		0			0
$736$	384.719	+	289.111i	0.522715	+	0.392814i
$737$	4.62889	−	8.01748i	0.00628073	−	0.0108785i
$738$	211.575	−	346.821i	0.286687	−	0.469948i
$739$	−62.4587	+	36.0605i	−0.0845178	+	0.0487964i	−0.541663	−	0.840596i	$-0.682205\pi$
$739$	−62.4587	+	36.0605i	−0.0845178	+	0.0487964i	0.457145	+	0.889392i	$0.348872\pi$
$740$	315.782	−	162.501i	0.426732	−	0.219595i
$741$	204.453			0.275915
$742$		0			0
$743$	159.310			0.214415			0.107208	−	0.994237i	$-0.465809\pi$
$743$	159.310			0.214415			0.107208	+	0.994237i	$0.465809\pi$
$744$	−664.148	+	978.931i	−0.892672	+	1.31577i
$745$	188.680	−	108.934i	0.253262	−	0.146221i
$746$	−458.787	+	752.060i	−0.614996	+	1.00812i
$747$	329.297	−	570.358i	0.440825	−	0.763532i
$748$	−5.46553	+	8.49068i	−0.00730686	+	0.0113512i
$749$		0			0
$750$	1213.53	−	662.055i	1.61804	−	0.882740i
$751$	−382.562	+	662.616i	−0.509403	+	0.882312i	0.490538	+	0.871420i	$0.336800\pi$
$751$	−382.562	+	662.616i	−0.509403	+	0.882312i	−0.999941	+	0.0108919i	$0.996533\pi$
$752$	1032.70	+	737.694i	1.37327	+	0.980976i
$753$	378.305	+	655.243i	0.502397	+	0.870176i
$754$	260.133	+	6.28879i	0.345004	+	0.00834056i
$755$	−528.371			−0.699830
$756$		0			0
$757$			950.822i			1.25604i	0.778197	+	0.628020i	$0.216134\pi$
$757$			950.822i			1.25604i	−0.778197	+	0.628020i	$0.783866\pi$
$758$	−567.263	−	13.7138i	−0.748369	−	0.0180920i
$759$	−8.86660	+	5.11913i	−0.0116819	+	0.00674457i
$760$	196.811	−	95.3346i	0.258962	−	0.125440i
$761$	−529.627	−	305.781i	−0.695962	−	0.401814i	0.109879	−	0.993945i	$-0.464954\pi$
$761$	−529.627	−	305.781i	−0.695962	−	0.401814i	−0.805842	+	0.592131i	$0.798287\pi$
$762$	−661.921	+	361.118i	−0.868662	+	0.473908i
$763$		0			0
$764$	641.676	−	996.842i	0.839890	−	1.30477i
$765$	1196.73	+	690.931i	1.56435	+	0.903178i
$766$	166.587	−	273.075i	0.217476	−	0.356495i
$767$	−58.6513	−	101.587i	−0.0764685	−	0.132447i
$768$	461.554	+	1346.48i	0.600981	+	1.75322i
$769$		−	979.152i		−	1.27328i	−0.771161	−	0.636640i	$-0.780324\pi$
$769$		−	979.152i		−	1.27328i	0.771161	−	0.636640i	$-0.219676\pi$
$770$		0			0
$771$			105.611i			0.136979i
$772$	175.037	+	340.143i	0.226732	+	0.440600i
$773$	228.660	+	396.051i	0.295809	+	0.512356i	0.975173	−	0.221445i	$-0.0710774\pi$
$773$	228.660	+	396.051i	0.295809	+	0.512356i	−0.679364	+	0.733802i	$0.737744\pi$
$774$	1034.90	−	1696.44i	1.33708	−	2.19178i
$775$	−360.359	−	208.053i	−0.464979	−	0.268456i
$776$	208.840	+	15.1699i	0.269123	+	0.0195489i
$777$		0			0
$778$	475.918	+	872.348i	0.611720	+	1.12127i
$779$	71.7471	+	41.4232i	0.0921015	+	0.0531748i
$780$	279.517	+	13.5227i	0.358355	+	0.0173368i
$781$	0.298893	−	0.172566i	0.000382706	−	0.000220955i
$782$	−619.939	−	14.9872i	−0.792760	−	0.0191652i
$783$			2270.83i			2.90016i
$784$		0			0
$785$	−825.296			−1.05133
$786$	30.1428	−	1246.84i	0.0383496	−	1.58631i
$787$	−91.5206	−	158.518i	−0.116290	−	0.201421i	0.802004	−	0.597318i	$-0.203767\pi$
$787$	−91.5206	−	158.518i	−0.116290	−	0.201421i	−0.918295	+	0.395897i	$0.870434\pi$
$788$	−31.1397	+	643.662i	−0.0395173	+	0.816830i
$789$	685.481	−	1187.29i	0.868797	−	1.50480i
$790$	382.522	−	208.689i	0.484205	−	0.264163i
$791$		0			0
$792$	−21.4099	−	1.55519i	−0.0270327	−	0.00196363i
$793$	−51.9165	+	89.9220i	−0.0654685	+	0.113395i
$794$	485.528	+	296.192i	0.611497	+	0.373038i
$795$	−936.141	+	540.481i	−1.17754	+	0.679851i
$796$	3.94706	−	2.03115i	0.00495862	−	0.00255169i
$797$	619.727			0.777575			0.388787	−	0.921328i	$-0.372894\pi$
$797$	619.727			0.777575			0.388787	+	0.921328i	$0.372894\pi$
$798$		0			0
$799$	−1635.37			−2.04677
$800$	−460.616	+	196.238i	−0.575770	+	0.245297i
$801$	335.362	−	193.621i	0.418679	−	0.241725i
$802$	−242.024	−	147.644i	−0.301775	−	0.184095i
$803$	0.783819	−	1.35761i	0.000976113	−	0.00169068i
$804$	1413.97	+	910.184i	1.75867	+	1.13207i
$805$		0			0
$806$	−104.802	−	192.100i	−0.130028	−	0.238338i
$807$	818.008	−	1416.83i	1.01364	−	1.75568i
$808$	−976.932	+	473.222i	−1.20907	+	0.585671i
$809$	335.874	+	581.750i	0.415171	+	0.719098i	0.995446	−	0.0953227i	$-0.0303883\pi$
$809$	335.874	+	581.750i	0.415171	+	0.719098i	−0.580275	+	0.814421i	$0.697055\pi$
$810$	−29.8657	+	1235.38i	−0.0368713	+	1.52516i
$811$	−1133.22			−1.39732			−0.698658	−	0.715456i	$-0.746219\pi$
$811$	−1133.22			−1.39732			−0.698658	+	0.715456i	$0.746219\pi$
$812$		0			0
$813$		−	2516.95i		−	3.09587i
$814$	0.171810	−	7.10686i	0.000211069	−	0.00873078i
$815$	−722.489	+	417.129i	−0.886489	+	0.511815i
$816$	−1492.48	−	1066.13i	−1.82902	−	1.30653i
$817$	350.944	+	202.617i	0.429551	+	0.248002i
$818$	357.598	+	655.469i	0.437161	+	0.801307i
$819$		0			0
$820$	95.3489	+	61.3769i	0.116279	+	0.0748499i
$821$	620.954	+	358.508i	0.756338	+	0.436672i	0.827979	−	0.560758i	$-0.189490\pi$
$821$	620.954	+	358.508i	0.756338	+	0.436672i	−0.0716414	+	0.997430i	$0.522824\pi$
$822$	−557.086	−	339.845i	−0.677720	−	0.413437i
$823$	362.895	+	628.553i	0.440942	+	0.763734i	0.997760	−	0.0669009i	$-0.0213111\pi$
$823$	362.895	+	628.553i	0.440942	+	0.763734i	−0.556818	+	0.830635i	$0.687978\pi$
$824$	−571.828	+	842.855i	−0.693966	+	1.02288i
$825$		−	10.6517i		−	0.0129112i
$826$		0			0
$827$		−	436.858i		−	0.528244i	−0.964489	−	0.264122i	$-0.914918\pi$
$827$		−	436.858i		−	0.528244i	0.964489	−	0.264122i	$-0.0850822\pi$
$828$	−603.205	−	1172.19i	−0.728508	−	1.41568i
$829$	−588.361	−	1019.07i	−0.709724	−	1.22928i	−0.964959	−	0.262399i	$-0.915486\pi$
$829$	−588.361	−	1019.07i	−0.709724	−	1.22928i	0.255235	−	0.966879i	$-0.417847\pi$
$830$	156.930	+	95.7336i	0.189072	+	0.115342i
$831$	1403.50	+	810.313i	1.68893	+	0.975105i
$832$	−260.540	−	38.0515i	−0.313148	−	0.0457350i
$833$		0			0
$834$	−1710.87	+	933.385i	−2.05141	+	1.11917i
$835$	−218.694	−	126.263i	−0.261909	−	0.151213i
$836$	0.211530	−	4.37237i	0.000253026	−	0.00523010i
$837$	1653.85	−	954.853i	1.97593	−	1.14080i
$838$	−20.2464	+	837.484i	−0.0241604	+	0.999384i
$839$		−	1551.16i		−	1.84881i	−0.381407	−	0.924407i	$-0.624560\pi$
$839$		−	1551.16i		−	1.84881i	0.381407	−	0.924407i	$-0.375440\pi$
$840$		0			0
$841$	−159.070			−0.189143
$842$	630.040	+	15.2314i	0.748267	+	0.0180896i
$843$	1377.33	+	2385.60i	1.63384	+	2.82990i
$844$	−41.3726	+	855.180i	−0.0490197	+	1.01325i
$845$	232.552	−	402.793i	0.275210	−	0.476678i
$846$	−1665.01	−	3051.92i	−1.96809	−	3.60747i
$847$		0			0
$848$	925.787	−	421.135i	1.09173	−	0.496622i
$849$	102.131	−	176.895i	0.120295	−	0.208357i
$850$	335.990	−	550.768i	0.395283	−	0.647962i
$851$	378.084	−	218.287i	0.444282	−	0.256506i
$852$	28.6849	+	55.7423i	0.0336677	+	0.0654253i
$853$	138.736			0.162645			0.0813225	−	0.996688i	$-0.474086\pi$
$853$	138.736			0.162645			0.0813225	+	0.996688i	$0.474086\pi$
$854$		0			0
$855$	−599.054			−0.700648
$856$	358.372	−	528.227i	0.418658	−	0.617088i
$857$	−1475.23	+	851.725i	−1.72139	+	0.993844i	−0.805302	+	0.592865i	$0.797997\pi$
$857$	−1475.23	+	851.725i	−1.72139	+	0.993844i	−0.916087	+	0.400980i	$0.868670\pi$
$858$	2.91728	−	4.78211i	0.00340009	−	0.00557355i
$859$	256.796	−	444.784i	0.298948	−	0.517793i	−0.676948	−	0.736031i	$-0.736698\pi$
$859$	256.796	−	444.784i	0.298948	−	0.517793i	0.975896	+	0.218238i	$0.0700310\pi$
$860$	466.389	+	300.219i	0.542313	+	0.349092i
$861$		0			0
$862$	392.095	−	213.911i	0.454866	−	0.248157i
$863$	−117.938	+	204.275i	−0.136661	+	0.236703i	−0.926231	−	0.376958i	$-0.876970\pi$
$863$	−117.938	+	204.275i	−0.136661	+	0.236703i	0.789570	+	0.613660i	$0.210304\pi$
$864$	277.025	−	2281.08i	0.320631	−	2.64013i
$865$	352.113	+	609.878i	0.407067	+	0.705061i
$866$	1183.11	+	28.6019i	1.36617	+	0.0330276i
$867$	756.587			0.872649
$868$		0			0
$869$		−	8.72242i		−	0.0100373i
$870$	−1075.22	−	25.9937i	−1.23588	−	0.0298779i
$871$	−269.392	+	155.533i	−0.309290	+	0.178569i
$872$	−110.184	−	227.467i	−0.126358	−	0.260857i
$873$	−496.745	−	286.796i	−0.569009	−	0.328517i
$874$	235.994	−	128.749i	0.270016	−	0.147310i
$875$		0			0
$876$	239.430	+	154.123i	0.273322	+	0.175940i
$877$	384.546	+	222.017i	0.438478	+	0.253156i	0.702952	−	0.711237i	$-0.251865\pi$
$877$	384.546	+	222.017i	0.438478	+	0.253156i	−0.264474	+	0.964393i	$0.585198\pi$
$878$	−533.623	+	874.733i	−0.607771	+	0.996279i
$879$	1467.82	+	2542.34i	1.66988	+	2.89231i
$880$	0.578384	−	5.96367i	0.000657255	−	0.00677689i
$881$		−	71.7252i		−	0.0814134i	−0.999171	−	0.0407067i	$-0.987039\pi$
$881$		−	71.7252i		−	0.0814134i	0.999171	−	0.0407067i	$-0.0129609\pi$
$882$		0			0
$883$			973.840i			1.10288i	0.834216	+	0.551438i	$0.185921\pi$
$883$			973.840i			1.10288i	−0.834216	+	0.551438i	$0.814079\pi$
$884$	301.687	−	155.247i	0.341275	−	0.175619i
$885$	242.426	+	419.895i	0.273928	+	0.474457i
$886$	161.873	−	265.348i	0.182701	−	0.299490i
$887$	−715.042	−	412.830i	−0.806135	−	0.465422i	0.0394767	−	0.999220i	$-0.487431\pi$
$887$	−715.042	−	412.830i	−0.806135	−	0.465422i	−0.845612	+	0.533798i	$0.820764\pi$
$888$	1287.88	+	93.5502i	1.45031	+	0.105349i
$889$		0			0
$890$	51.7653	+	94.8847i	0.0581633	+	0.106612i
$891$	21.4222	+	12.3681i	0.0240428	+	0.0138811i
$892$	56.1061	−	1159.72i	0.0628992	−	1.30014i
$893$	613.970	−	354.476i	0.687536	−	0.396949i
$894$	791.927	+	19.1451i	0.885825	+	0.0214151i
$895$			807.539i			0.902278i
$896$		0			0
$897$	344.011			0.383513
$898$	17.8429	−	738.063i	0.0198696	−	0.821896i
$899$	420.516	+	728.355i	0.467760	+	0.810184i
$900$	1369.92	+	66.2752i	1.52213	+	0.0736392i
$901$	−655.291	+	1135.00i	−0.727293	+	1.25971i
$902$	1.99262	−	1.08709i	0.00220911	−	0.00120520i
$903$		0			0
$904$	33.4992	−	461.173i	0.0370566	−	0.510147i
$905$	−281.360	+	487.330i	−0.310895	+	0.538486i
$906$	−1640.04	−	1000.49i	−1.81020	−	1.10430i
$907$	637.046	−	367.799i	0.702366	−	0.405511i	−0.105862	−	0.994381i	$-0.533760\pi$
$907$	637.046	−	367.799i	0.702366	−	0.405511i	0.808228	+	0.588870i	$0.200427\pi$
$908$	149.027	+	289.599i	0.164127	+	0.318942i
$909$	2973.59			3.27128
$910$		0			0
$911$	235.528			0.258538			0.129269	−	0.991610i	$-0.458737\pi$
$911$	235.528			0.258538			0.129269	+	0.991610i	$0.458737\pi$
$912$	791.414	+	76.7551i	0.867778	+	0.0841612i
$913$	3.18670	−	1.83984i	0.00349036	−	0.00201516i
$914$	731.027	+	445.956i	0.799810	+	0.487916i
$915$	214.589	−	371.679i	0.234524	−	0.406207i
$916$	−507.103	+	787.783i	−0.553606	+	0.860025i
$917$		0			0
$918$	1418.07	+	2599.29i	1.54474	+	2.83147i
$919$	717.115	−	1242.08i	0.780321	−	1.35156i	−0.151434	−	0.988467i	$-0.548389\pi$
$919$	717.115	−	1242.08i	0.780321	−	1.35156i	0.931755	−	0.363088i	$-0.118278\pi$
$920$	331.153	−	160.409i	0.359949	−	0.174358i
$921$	−485.080	−	840.184i	−0.526689	−	0.912252i
$922$	8.00345	−	331.059i	0.00868054	−	0.359066i
$923$	−11.5966			−0.0125641
$924$		0			0
$925$			454.204i			0.491031i
$926$	29.2617	−	1210.40i	0.0316001	−	1.30713i
$927$	2416.29	−	1395.04i	2.60657	−	1.50490i
$928$	1004.58	+	122.001i	1.08252	+	0.131467i
$929$	1194.57	+	689.687i	1.28587	+	0.742397i	0.977915	−	0.209003i	$-0.0670220\pi$
$929$	1194.57	+	689.687i	1.28587	+	0.742397i	0.307955	+	0.951401i	$0.400355\pi$
$930$	433.184	+	794.017i	0.465790	+	0.853782i
$931$		0			0
$932$	−134.192	+	208.466i	−0.143982	+	0.223676i
$933$	−66.2316	−	38.2388i	−0.0709878	−	0.0409848i
$934$	−976.836	−	595.909i	−1.04586	−	0.638018i
$935$	3.86037	+	6.68635i	0.00412874	+	0.00715118i
$936$	596.877	+	404.946i	0.637689	+	0.432635i
$937$		−	541.545i		−	0.577956i	−0.957336	−	0.288978i	$-0.906685\pi$
$937$		−	541.545i		−	0.577956i	0.957336	−	0.288978i	$-0.0933154\pi$
$938$		0			0
$939$			2345.76i			2.49814i
$940$	862.831	−	444.011i	0.917905	−	0.472352i
$941$	48.9285	+	84.7467i	0.0519963	+	0.0900603i	0.890852	−	0.454294i	$-0.150108\pi$
$941$	48.9285	+	84.7467i	0.0519963	+	0.0900603i	−0.838856	+	0.544354i	$0.816775\pi$
$942$	−2561.69	−	1562.73i	−2.71941	−	1.65895i
$943$	120.721	+	69.6984i	0.128018	+	0.0739114i
$944$	−188.895	−	415.250i	−0.200101	−	0.439884i
$945$		0			0
$946$	9.74668	−	5.31740i	0.0103030	−	0.00562093i
$947$	−674.176	−	389.236i	−0.711907	−	0.411020i	0.0998594	−	0.995002i	$-0.468161\pi$
$947$	−674.176	−	389.236i	−0.711907	−	0.411020i	−0.811767	+	0.583982i	$0.801494\pi$
$948$	1582.49	+	76.5592i	1.66930	+	0.0807587i
$949$	−45.6166	+	26.3367i	−0.0480680	+	0.0277521i
$950$	−6.75951	+	279.604i	−0.00711528	+	0.294320i
$951$		−	2621.73i		−	2.75681i
$952$		0			0
$953$	348.435			0.365620			0.182810	−	0.983148i	$-0.441481\pi$
$953$	348.435			0.365620			0.182810	+	0.983148i	$0.441481\pi$
$954$	−2785.30	−	67.3354i	−2.91960	−	0.0705822i
$955$	−453.224	−	785.006i	−0.474580	−	0.821996i
$956$	−387.875	−	18.7650i	−0.405727	−	0.0196286i
$957$	−10.7646	+	18.6449i	−0.0112483	+	0.0194826i
$958$	−35.6738	−	65.3892i	−0.0372377	−	0.0682560i
$959$		0			0
$960$	1076.90	+	157.280i	1.12177	+	0.163833i
$961$	−126.857	+	219.722i	−0.132005	+	0.228639i
$962$	−124.397	+	203.915i	−0.129310	+	0.211970i
$963$	−1514.32	+	874.291i	−1.57250	+	0.907883i
$964$	−852.687	+	438.791i	−0.884530	+	0.455178i
$965$	292.490			0.303098
$966$		0			0
$967$	−1055.75			−1.09177			−0.545887	−	0.837859i	$-0.683807\pi$
$967$	−1055.75			−1.09177			−0.545887	+	0.837859i	$0.683807\pi$
$968$	800.945	+	543.395i	0.827423	+	0.561359i
$969$	−887.319	+	512.294i	−0.915706	+	0.528683i
$970$	83.3776	−	136.676i	0.0859563	−	0.140903i
$971$	426.302	−	738.377i	0.439034	−	0.760429i	−0.558581	−	0.829450i	$-0.688654\pi$
$971$	426.302	−	738.377i	0.439034	−	0.760429i	0.997615	+	0.0690206i	$0.0219874\pi$
$972$	−1032.75	+	1604.37i	−1.06250	+	1.65058i
$973$		0			0
$974$	481.670	−	262.780i	0.494528	−	0.269795i
$975$	−178.952	+	309.954i	−0.183540	+	0.317901i
$976$	−234.721	+	328.588i	−0.240493	+	0.336668i
$977$	−169.835	−	294.163i	−0.173834	−	0.301089i	0.765923	−	0.642932i	$-0.222282\pi$
$977$	−169.835	−	294.163i	−0.173834	−	0.301089i	−0.939757	+	0.341843i	$0.888949\pi$
$978$	−3032.43	−	73.3098i	−3.10064	−	0.0749589i
$979$	2.16360			0.00221001
$980$		0			0
$981$			692.365i			0.705774i
$982$	−1763.47	−	42.6325i	−1.79580	−	0.0434139i
$983$	905.444	−	522.759i	0.921103	−	0.531799i	0.0371164	−	0.999311i	$-0.488183\pi$
$983$	905.444	−	522.759i	0.921103	−	0.531799i	0.883987	+	0.467512i	$0.154849\pi$
$984$	179.740	+	371.059i	0.182662	+	0.377092i
$985$	426.709	+	246.361i	0.433208	+	0.250112i
$986$	−1144.72	+	624.516i	−1.16098	+	0.633384i
$987$		0			0
$988$	−79.6122	+	123.677i	−0.0805792	+	0.125180i
$989$	590.496	+	340.923i	0.597063	+	0.344715i
$990$	−8.54773	+	14.0117i	−0.00863407	+	0.0141533i
$991$	409.911	+	709.987i	0.413634	+	0.716435i	0.995284	−	0.0970040i	$-0.0309260\pi$
$991$	409.911	+	709.987i	0.413634	+	0.716435i	−0.581650	+	0.813439i	$0.697593\pi$
$992$	−333.560	−	782.943i	−0.336250	−	0.789257i
$993$			2463.49i			2.48086i
$994$		0			0
$995$		−	3.39408i		−	0.00341114i
$996$	305.829	+	594.307i	0.307057	+	0.596694i
$997$	380.211	+	658.545i	0.381355	+	0.660526i	0.991256	−	0.131951i	$-0.0421242\pi$
$997$	380.211	+	658.545i	0.381355	+	0.660526i	−0.609901	+	0.792478i	$0.708791\pi$
$998$	−367.705	+	602.755i	−0.368442	+	0.603963i
$999$	−1805.28	−	1042.28i	−1.80708	−	1.04332i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.3	✓	28	56.13	odd	2
56.3.j.a.5.8	yes	28	7.6	odd	2
56.3.j.a.45.3	yes	28	7.4	even	3
56.3.j.a.45.8	yes	28	56.53	even	6
224.3.n.a.17.1		28	28.11	odd	6
224.3.n.a.17.14		28	56.11	odd	6
224.3.n.a.145.1		28	56.27	even	2
224.3.n.a.145.14		28	28.27	even	2
392.3.h.a.293.21		28	7.2	even	3
392.3.h.a.293.22		28	7.5	odd	6
392.3.h.a.293.23		28	56.5	odd	6
392.3.h.a.293.24		28	56.37	even	6
392.3.j.e.117.3		28	8.5	even	2	inner
392.3.j.e.117.8		28	1.1	even	1	trivial
392.3.j.e.325.3		28	7.3	odd	6	inner
392.3.j.e.325.8		28	56.45	odd	6	inner
1568.3.h.a.881.1		28	28.19	even	6
1568.3.h.a.881.2		28	56.51	odd	6
1568.3.h.a.881.27		28	28.23	odd	6
1568.3.h.a.881.28		28	56.19	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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0483365 + 1.99942i) q^{2} +(2.78005 + 4.81519i) q^{3} +(-3.99533 - 0.193289i) q^{4} +(-1.52921 + 2.64866i) q^{5} +(-9.76195 + 5.32573i) q^{6} +(0.579586 - 7.97898i) q^{8} +(-10.9574 + 18.9787i) q^{9} +O(q^{10})\)	\(q+(-0.0483365 + 1.99942i) q^{2} +(2.78005 + 4.81519i) q^{3} +(-3.99533 - 0.193289i) q^{4} +(-1.52921 + 2.64866i) q^{5} +(-9.76195 + 5.32573i) q^{6} +(0.579586 - 7.97898i) q^{8} +(-10.9574 + 18.9787i) q^{9} +(-5.22186 - 3.18554i) q^{10} +(-0.106038 + 0.0612210i) q^{11} +(-10.1765 - 19.7756i) q^{12} +4.11412 q^{13} -17.0051 q^{15} +(15.9253 + 1.54451i) q^{16} +(-17.8551 + 10.3087i) q^{17} +(-37.4167 - 22.8257i) q^{18} +(4.46893 - 7.74042i) q^{19} +(6.62164 - 10.2867i) q^{20} +(-0.117281 - 0.214973i) q^{22} +(7.51940 - 13.0240i) q^{23} +(40.0316 - 19.3912i) q^{24} +(7.82306 + 13.5499i) q^{25} +(-0.198862 + 8.22583i) q^{26} -71.8074 q^{27} -31.6239i q^{29} +(0.821966 - 34.0002i) q^{30} +(-23.0318 + 13.2974i) q^{31} +(-3.85789 + 31.7666i) q^{32} +(-0.589582 - 0.340395i) q^{33} +(-19.7483 - 36.1981i) q^{34} +(47.4467 - 73.7083i) q^{36} +(25.1405 + 14.5149i) q^{37} +(15.2603 + 9.30940i) q^{38} +(11.4375 + 19.8103i) q^{39} +(20.2473 + 13.7366i) q^{40} +9.26915i q^{41} +45.3391i q^{43} +(0.435489 - 0.224102i) q^{44} +(-33.5122 - 58.0448i) q^{45} +(25.6769 + 15.6639i) q^{46} +(68.6931 + 39.6600i) q^{47} +(36.8360 + 80.9771i) q^{48} +(-27.4701 + 14.9866i) q^{50} +(-99.2764 - 57.3172i) q^{51} +(-16.4372 - 0.795215i) q^{52} +(55.0507 - 31.7835i) q^{53} +(3.47092 - 143.573i) q^{54} -0.374478i q^{55} +49.6955 q^{57} +(63.2293 + 1.52859i) q^{58} +(-14.2561 - 24.6923i) q^{59} +(67.9409 + 3.28690i) q^{60} +(-12.6191 + 21.8569i) q^{61} +(-25.4738 - 46.6929i) q^{62} +(-63.3282 - 9.24901i) q^{64} +(-6.29133 + 10.8969i) q^{65} +(0.709090 - 1.16237i) q^{66} +(-65.4798 + 37.8048i) q^{67} +(73.3296 - 37.7353i) q^{68} +83.6173 q^{69} -2.81874 q^{71} +(145.080 + 98.4285i) q^{72} +(-11.0878 + 6.40155i) q^{73} +(-30.2365 + 49.5648i) q^{74} +(-43.4970 + 75.3391i) q^{75} +(-19.3510 + 30.0617i) q^{76} +(-40.1618 + 21.9107i) q^{78} +(-35.6186 + 61.6932i) q^{79} +(-28.4439 + 39.8188i) q^{80} +(-101.012 - 174.958i) q^{81} +(-18.5329 - 0.448038i) q^{82} -30.0525 q^{83} -63.0563i q^{85} +(-90.6517 - 2.19153i) q^{86} +(152.275 - 87.9160i) q^{87} +(0.427023 + 0.881557i) q^{88} +(-15.3030 - 8.83521i) q^{89} +(117.676 - 64.1991i) q^{90} +(-32.5599 + 50.5816i) q^{92} +(-128.059 - 73.9351i) q^{93} +(-82.6172 + 135.429i) q^{94} +(13.6678 + 23.6734i) q^{95} +(-163.687 + 69.7363i) q^{96} +26.1737i q^{97} -2.68329i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 4 q^{4} - 20 q^{8} - 32 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 4 * q^4 - 20 * q^8 - 32 * q^9	\( 28 q - 2 q^{2} - 4 q^{4} - 20 q^{8} - 32 q^{9} - 24 q^{10} + 18 q^{12} + 28 q^{15} + 16 q^{16} + 6 q^{17} - 42 q^{18} - 92 q^{22} + 30 q^{23} + 30 q^{24} - 32 q^{25} + 30 q^{26} + 22 q^{30} + 6 q^{31} + 88 q^{32} + 6 q^{33} + 256 q^{36} - 6 q^{38} - 20 q^{39} - 102 q^{40} - 42 q^{44} + 68 q^{46} + 294 q^{47} + 400 q^{50} + 168 q^{52} - 330 q^{54} + 124 q^{57} - 22 q^{58} - 62 q^{60} - 520 q^{64} - 52 q^{65} + 306 q^{66} + 456 q^{68} - 136 q^{71} + 96 q^{72} - 234 q^{73} - 138 q^{74} - 956 q^{78} - 162 q^{79} - 276 q^{80} - 18 q^{81} + 642 q^{82} + 168 q^{86} - 48 q^{87} + 50 q^{88} + 150 q^{89} + 1020 q^{92} - 618 q^{94} + 290 q^{95} - 1044 q^{96}+O(q^{100}) \) 28 * q - 2 * q^2 - 4 * q^4 - 20 * q^8 - 32 * q^9 - 24 * q^10 + 18 * q^12 + 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 + 22 * q^30 + 6 * q^31 + 88 * q^32 + 6 * q^33 + 256 * q^36 - 6 * q^38 - 20 * q^39 - 102 * q^40 - 42 * q^44 + 68 * q^46 + 294 * q^47 + 400 * q^50 + 168 * q^52 - 330 * q^54 + 124 * q^57 - 22 * q^58 - 62 * q^60 - 520 * q^64 - 52 * q^65 + 306 * q^66 + 456 * q^68 - 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 + 168 * q^86 - 48 * q^87 + 50 * q^88 + 150 * q^89 + 1020 * q^92 - 618 * q^94 + 290 * q^95 - 1044 * q^96

Introduction

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