LMFDB - Embedded newform 392.3.j.e.117.11

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			117.11
Character	$\chi$	$=$	392.117
Dual form			392.3.j.e.325.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34357 - 1.48149i) q^{2} +(1.93494 + 3.35141i) q^{3} +(-0.389632 - 3.98098i) q^{4} +(2.33882 - 4.05096i) q^{5} +(7.56482 + 1.63627i) q^{6} +(-6.42128 - 4.77149i) q^{8} +(-2.98798 + 5.17534i) q^{9} +O(q^{10})$	\(q+(1.34357 - 1.48149i) q^{2} +(1.93494 + 3.35141i) q^{3} +(-0.389632 - 3.98098i) q^{4} +(2.33882 - 4.05096i) q^{5} +(7.56482 + 1.63627i) q^{6} +(-6.42128 - 4.77149i) q^{8} +(-2.98798 + 5.17534i) q^{9} +(-2.85908 - 8.90769i) q^{10} +(12.6383 - 7.29671i) q^{11} +(12.5880 - 9.00877i) q^{12} -12.7102 q^{13} +18.1019 q^{15} +(-15.6964 + 3.10223i) q^{16} +(16.9068 - 9.76116i) q^{17} +(3.65265 + 11.3801i) q^{18} +(8.86233 - 15.3500i) q^{19} +(-17.0380 - 7.73241i) q^{20} +(6.17041 - 28.5271i) q^{22} +(-4.43038 + 7.67364i) q^{23} +(3.56645 - 30.7529i) q^{24} +(1.55984 + 2.70172i) q^{25} +(-17.0770 + 18.8300i) q^{26} +11.7027 q^{27} +35.4981i q^{29} +(24.3212 - 26.8178i) q^{30} +(-25.1331 + 14.5106i) q^{31} +(-16.4933 + 27.4221i) q^{32} +(48.9086 + 28.2374i) q^{33} +(8.25445 - 38.1621i) q^{34} +(21.7671 + 9.87861i) q^{36} +(10.5802 + 6.10847i) q^{37} +(-10.8337 - 33.7533i) q^{38} +(-24.5934 - 42.5970i) q^{39} +(-34.3473 + 14.8527i) q^{40} +22.0903i q^{41} -79.8001i q^{43} +(-33.9723 - 47.4696i) q^{44} +(13.9767 + 24.2084i) q^{45} +(5.41590 + 16.8736i) q^{46} +(36.5041 + 21.0756i) q^{47} +(-40.7684 - 46.6024i) q^{48} +(6.09833 + 1.31907i) q^{50} +(65.4273 + 37.7745i) q^{51} +(4.95229 + 50.5989i) q^{52} +(-31.3096 + 18.0766i) q^{53} +(15.7234 - 17.3374i) q^{54} -68.2627i q^{55} +68.5923 q^{57} +(52.5901 + 47.6942i) q^{58} +(-1.20348 - 2.08449i) q^{59} +(-7.05308 - 72.0633i) q^{60} +(14.6224 - 25.3268i) q^{61} +(-12.2708 + 56.7306i) q^{62} +(18.4657 + 61.2782i) q^{64} +(-29.7268 + 51.4883i) q^{65} +(107.546 - 34.5187i) q^{66} +(-35.2303 + 20.3402i) q^{67} +(-45.4464 - 63.5024i) q^{68} -34.2900 q^{69} -22.6174 q^{71} +(43.8807 - 18.9752i) q^{72} +(-66.1587 + 38.1967i) q^{73} +(23.2649 - 7.46728i) q^{74} +(-6.03639 + 10.4553i) q^{75} +(-64.5611 - 29.2999i) q^{76} +(-96.1501 - 20.7972i) q^{78} +(-68.4014 + 118.475i) q^{79} +(-24.1440 + 70.8409i) q^{80} +(49.5358 + 85.7985i) q^{81} +(32.7266 + 29.6799i) q^{82} +49.9942 q^{83} -91.3184i q^{85} +(-118.223 - 107.217i) q^{86} +(-118.969 + 68.6866i) q^{87} +(-115.970 - 13.4492i) q^{88} +(-0.970023 - 0.560043i) q^{89} +(54.6432 + 11.8193i) q^{90} +(32.2748 + 14.6473i) q^{92} +(-97.2622 - 56.1544i) q^{93} +(80.2692 - 25.7638i) q^{94} +(-41.4548 - 71.8018i) q^{95} +(-123.816 - 2.21566i) q^{96} +158.827i q^{97} +87.2097i 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 $

$2$	1.34357	−	1.48149i	0.671786	−	0.740746i
$2$	1.34357	−	1.48149i	0.671786	−	0.740746i
$3$	1.93494	+	3.35141i	0.644980	+	1.11714i	0.984306	+	0.176469i	$0.0564676\pi$
$3$	1.93494	+	3.35141i	0.644980	+	1.11714i	−0.339326	+	0.940669i	$0.610199\pi$
$4$	−0.389632	−	3.98098i	−0.0974079	−	0.995245i
$5$	2.33882	−	4.05096i	0.467764	−	0.810191i	−0.531557	−	0.847022i	$-0.678393\pi$
$5$	2.33882	−	4.05096i	0.467764	−	0.810191i	0.999322	+	0.0368311i	$0.0117264\pi$
$6$	7.56482	+	1.63627i	1.26080	+	0.272711i
$7$		0			0
$7$		0			0
$8$	−6.42128	−	4.77149i	−0.802660	−	0.596437i
$9$	−2.98798	+	5.17534i	−0.331998	+	0.575037i
$10$	−2.85908	−	8.90769i	−0.285908	−	0.890769i
$11$	12.6383	−	7.29671i	1.14893	−	0.663337i	0.200306	−	0.979733i	$-0.435806\pi$
$11$	12.6383	−	7.29671i	1.14893	−	0.663337i	0.948627	+	0.316396i	$0.102473\pi$
$12$	12.5880	−	9.00877i	1.04900	−	0.750731i
$13$	−12.7102			−0.977705			−0.488853	−	0.872366i	$-0.662584\pi$
$13$	−12.7102			−0.977705			−0.488853	+	0.872366i	$0.662584\pi$
$14$		0			0
$15$	18.1019			1.20679
$16$	−15.6964	+	3.10223i	−0.981023	+	0.193889i
$17$	16.9068	−	9.76116i	0.994519	−	0.574186i	0.0878969	−	0.996130i	$-0.471985\pi$
$17$	16.9068	−	9.76116i	0.994519	−	0.574186i	0.906622	+	0.421944i	$0.138652\pi$
$18$	3.65265	+	11.3801i	0.202925	+	0.632228i
$19$	8.86233	−	15.3500i	0.466439	−	0.807895i	−0.532827	−	0.846224i	$-0.678870\pi$
$19$	8.86233	−	15.3500i	0.466439	−	0.807895i	0.999265	+	0.0383291i	$0.0122035\pi$
$20$	−17.0380	−	7.73241i	−0.851902	−	0.386621i
$21$		0			0
$22$	6.17041	−	28.5271i	0.280473	−	1.29669i
$23$	−4.43038	+	7.67364i	−0.192625	+	0.333636i	−0.946119	−	0.323818i	$-0.895033\pi$
$23$	−4.43038	+	7.67364i	−0.192625	+	0.333636i	0.753494	+	0.657454i	$0.228367\pi$
$24$	3.56645	−	30.7529i	0.148602	−	1.28137i
$25$	1.55984	+	2.70172i	0.0623936	+	0.108069i
$26$	−17.0770	+	18.8300i	−0.656808	+	0.724231i
$27$	11.7027			0.433432
$28$		0			0
$29$			35.4981i			1.22407i	0.790830	+	0.612036i	$0.209649\pi$
$29$			35.4981i			1.22407i	−0.790830	+	0.612036i	$0.790351\pi$
$30$	24.3212	−	26.8178i	0.810707	−	0.893927i
$31$	−25.1331	+	14.5106i	−0.810747	+	0.468085i	−0.847215	−	0.531250i	$-0.821722\pi$
$31$	−25.1331	+	14.5106i	−0.810747	+	0.468085i	0.0364685	+	0.999335i	$0.488389\pi$
$32$	−16.4933	+	27.4221i	−0.515415	+	0.856941i
$33$	48.9086	+	28.2374i	1.48208	+	0.855678i
$34$	8.25445	−	38.1621i	0.242778	−	1.12242i
$35$		0			0
$36$	21.7671	+	9.87861i	0.604642	+	0.274406i
$37$	10.5802	+	6.10847i	0.285951	+	0.165094i	0.636114	−	0.771595i	$-0.280541\pi$
$37$	10.5802	+	6.10847i	0.285951	+	0.165094i	−0.350163	+	0.936689i	$0.613874\pi$
$38$	−10.8337	−	33.7533i	−0.285098	−	0.888245i
$39$	−24.5934	−	42.5970i	−0.630600	−	1.09223i
$40$	−34.3473	+	14.8527i	−0.858683	+	0.371317i
$41$			22.0903i			0.538788i	0.963030	+	0.269394i	$0.0868233\pi$
$41$			22.0903i			0.538788i	−0.963030	+	0.269394i	$0.913177\pi$
$42$		0			0
$43$		−	79.8001i		−	1.85582i	−0.372809	−	0.927908i	$-0.621605\pi$
$43$		−	79.8001i		−	1.85582i	0.372809	−	0.927908i	$-0.378395\pi$
$44$	−33.9723	−	47.4696i	−0.772098	−	1.07886i
$45$	13.9767	+	24.2084i	0.310593	+	0.537964i
$46$	5.41590	+	16.8736i	0.117737	+	0.366818i
$47$	36.5041	+	21.0756i	0.776682	+	0.448418i	0.835253	−	0.549865i	$-0.185321\pi$
$47$	36.5041	+	21.0756i	0.776682	+	0.448418i	−0.0585708	+	0.998283i	$0.518654\pi$
$48$	−40.7684	−	46.6024i	−0.849342	−	0.970884i
$49$		0			0
$50$	6.09833	+	1.31907i	0.121967	+	0.0263813i
$51$	65.4273	+	37.7745i	1.28289	+	0.740676i
$52$	4.95229	+	50.5989i	0.0952363	+	0.973056i
$53$	−31.3096	+	18.0766i	−0.590748	+	0.341068i	−0.765393	−	0.643563i	$-0.777455\pi$
$53$	−31.3096	+	18.0766i	−0.590748	+	0.341068i	0.174645	+	0.984631i	$0.444122\pi$
$54$	15.7234	−	17.3374i	0.291173	−	0.321063i
$55$		−	68.2627i		−	1.24114i
$56$		0			0
$57$	68.5923			1.20337
$58$	52.5901	+	47.6942i	0.906726	+	0.822314i
$59$	−1.20348	−	2.08449i	−0.0203979	−	0.0353303i	0.855646	−	0.517561i	$-0.173160\pi$
$59$	−1.20348	−	2.08449i	−0.0203979	−	0.0353303i	−0.876044	+	0.482231i	$0.839827\pi$
$60$	−7.05308	−	72.0633i	−0.117551	−	1.20105i
$61$	14.6224	−	25.3268i	0.239712	−	0.415194i	−0.720919	−	0.693019i	$-0.756280\pi$
$61$	14.6224	−	25.3268i	0.239712	−	0.415194i	0.960632	+	0.277825i	$0.0896136\pi$
$62$	−12.2708	+	56.7306i	−0.197916	+	0.915010i
$63$		0			0
$64$	18.4657	+	61.2782i	0.288527	+	0.957472i
$65$	−29.7268	+	51.4883i	−0.457335	+	0.792128i
$66$	107.546	−	34.5187i	1.62948	−	0.523010i
$67$	−35.2303	+	20.3402i	−0.525825	+	0.303585i	−0.739315	−	0.673360i	$-0.764850\pi$
$67$	−35.2303	+	20.3402i	−0.525825	+	0.303585i	0.213490	+	0.976945i	$0.431517\pi$
$68$	−45.4464	−	63.5024i	−0.668329	−	0.933859i
$69$	−34.2900			−0.496957
$70$		0			0
$71$	−22.6174			−0.318554			−0.159277	−	0.987234i	$-0.550916\pi$
$71$	−22.6174			−0.318554			−0.159277	+	0.987234i	$0.550916\pi$
$72$	43.8807	−	18.9752i	0.609455	−	0.263544i
$73$	−66.1587	+	38.1967i	−0.906283	+	0.523243i	−0.879233	−	0.476391i	$-0.841945\pi$
$73$	−66.1587	+	38.1967i	−0.906283	+	0.523243i	−0.0270498	+	0.999634i	$0.508611\pi$
$74$	23.2649	−	7.46728i	0.314390	−	0.100909i
$75$	−6.03639	+	10.4553i	−0.0804852	+	0.139404i
$76$	−64.5611	−	29.2999i	−0.849488	−	0.385525i
$77$		0			0
$78$	−96.1501	−	20.7972i	−1.23269	−	0.266631i
$79$	−68.4014	+	118.475i	−0.865840	+	1.49968i	0.000370612		1.00000i	$0.499882\pi$
$79$	−68.4014	+	118.475i	−0.865840	+	1.49968i	−0.866211	+	0.499679i	$0.833451\pi$
$80$	−24.1440	+	70.8409i	−0.301800	+	0.885511i
$81$	49.5358	+	85.7985i	0.611553	+	1.05924i
$82$	32.7266	+	29.6799i	0.399105	+	0.361950i
$83$	49.9942			0.602340			0.301170	−	0.953571i	$-0.402623\pi$
$83$	49.9942			0.602340			0.301170	+	0.953571i	$0.402623\pi$
$84$		0			0
$85$		−	91.3184i		−	1.07433i
$86$	−118.223	−	107.217i	−1.37469	−	1.24671i
$87$	−118.969	+	68.6866i	−1.36746	+	0.789502i
$88$	−115.970	−	13.4492i	−1.31784	−	0.152832i
$89$	−0.970023	−	0.560043i	−0.0108991	−	0.00629262i	0.494541	−	0.869155i	$-0.335336\pi$
$89$	−0.970023	−	0.560043i	−0.0108991	−	0.00629262i	−0.505440	+	0.862862i	$0.668670\pi$
$90$	54.6432	+	11.8193i	0.607146	+	0.131326i
$91$		0			0
$92$	32.2748	+	14.6473i	0.350813	+	0.159210i
$93$	−97.2622	−	56.1544i	−1.04583	−	0.603810i
$94$	80.2692	−	25.7638i	0.853928	−	0.274083i
$95$	−41.4548	−	71.8018i	−0.436366	−	0.755809i
$96$	−123.816	−	2.21566i	−1.28975	−	0.0230797i
$97$			158.827i			1.63740i	0.574225	+	0.818698i	$0.305304\pi$
$97$			158.827i			1.63740i	−0.574225	+	0.818698i	$0.694696\pi$
$98$		0			0
$99$			87.2097i			0.880906i
$100$	10.1477	−	7.26236i	0.101477	−	0.0726236i
$101$	−34.8122	−	60.2965i	−0.344675	−	0.596995i	0.640620	−	0.767858i	$-0.278678\pi$
$101$	−34.8122	−	60.2965i	−0.344675	−	0.596995i	−0.985295	+	0.170864i	$0.945344\pi$
$102$	143.869	−	46.1773i	1.41048	−	0.452719i
$103$	−16.9911	−	9.80983i	−0.164962	−	0.0952411i	0.415246	−	0.909709i	$-0.363696\pi$
$103$	−16.9911	−	9.80983i	−0.164962	−	0.0952411i	−0.580208	+	0.814468i	$0.697029\pi$
$104$	81.6156	+	60.6465i	0.784765	+	0.583139i
$105$		0			0
$106$	−15.2864	+	70.6722i	−0.144211	+	0.666718i
$107$	−38.7540	−	22.3747i	−0.362187	−	0.209109i	0.307852	−	0.951434i	$-0.400390\pi$
$107$	−38.7540	−	22.3747i	−0.362187	−	0.209109i	−0.670040	+	0.742325i	$0.733723\pi$
$108$	−4.55973	−	46.5880i	−0.0422197	−	0.431371i
$109$	49.0210	−	28.3023i	0.449734	−	0.259654i	−0.257984	−	0.966149i	$-0.583058\pi$
$109$	49.0210	−	28.3023i	0.449734	−	0.259654i	0.707718	+	0.706495i	$0.249725\pi$
$110$	−101.131	−	91.7159i	−0.919369	−	0.833781i
$111$			47.2781i			0.425929i
$112$		0			0
$113$	−188.632			−1.66931			−0.834657	−	0.550770i	$-0.814334\pi$
$113$	−188.632			−1.66931			−0.834657	+	0.550770i	$0.814334\pi$
$114$	92.1587	−	101.619i	0.808409	−	0.891394i
$115$	20.7237	+	35.8945i	0.180206	+	0.312126i
$116$	141.317	−	13.8312i	1.21825	−	0.119234i
$117$	37.9777	−	65.7794i	0.324596	−	0.562217i
$118$	−4.70511	−	1.01771i	−0.0398738	−	0.00862469i
$119$		0			0
$120$	−116.237	−	86.3731i	−0.968645	−	0.719776i
$121$	45.9838	−	79.6463i	0.380032	−	0.658234i
$122$	−17.8752	−	55.6914i	−0.146518	−	0.456487i
$123$	−74.0337	+	42.7434i	−0.601900	+	0.347507i
$124$	67.5592	+	94.4007i	0.544832	+	0.761296i
$125$	131.534			1.05227
$126$		0			0
$127$	45.8547			0.361060			0.180530	−	0.983569i	$-0.442219\pi$
$127$	45.8547			0.361060			0.180530	+	0.983569i	$0.442219\pi$
$128$	115.593	+	54.9748i	0.903071	+	0.429491i
$129$	267.443	−	154.408i	2.07320	−	1.19696i
$130$	36.3394	+	113.218i	0.279534	+	0.870909i
$131$	−60.4982	+	104.786i	−0.461818	+	0.799893i	−0.999052	−	0.0435409i	$-0.986136\pi$
$131$	−60.4982	+	104.786i	−0.461818	+	0.799893i	0.537233	+	0.843434i	$0.319469\pi$
$132$	93.3560	−	205.706i	0.707243	−	1.55838i
$133$		0			0
$134$	−17.2006	+	79.5219i	−0.128362	+	0.593447i
$135$	27.3704	−	47.4069i	0.202744	−	0.351163i
$136$	−155.139	−	17.9916i	−1.14073	−	0.132291i
$137$	72.6207	+	125.783i	0.530078	+	0.918122i	0.999384	+	0.0350869i	$0.0111708\pi$
$137$	72.6207	+	125.783i	0.530078	+	0.918122i	−0.469306	+	0.883036i	$0.655496\pi$
$138$	−46.0711	+	50.8004i	−0.333849	+	0.368119i
$139$	−86.3503			−0.621225			−0.310613	−	0.950537i	$-0.600534\pi$
$139$	−86.3503			−0.621225			−0.310613	+	0.950537i	$0.600534\pi$
$140$		0			0
$141$			163.120i			1.15688i
$142$	−30.3880	+	33.5074i	−0.214000	+	0.235968i
$143$	−160.634	+	92.7424i	−1.12332	+	0.648548i
$144$	30.8454	−	90.5034i	0.214204	−	0.628496i
$145$	143.801	+	83.0236i	0.991732	+	0.572577i
$146$	−32.3008	+	149.334i	−0.221238	+	1.02283i
$147$		0			0
$148$	20.1953	−	44.4996i	0.136455	−	0.300673i
$149$	189.536	+	109.429i	1.27205	+	0.734421i	0.975374	−	0.220556i	$-0.0707873\pi$
$149$	189.536	+	109.429i	1.27205	+	0.734421i	0.296680	+	0.954977i	$0.404121\pi$
$150$	7.37916	+	22.9903i	0.0491944	+	0.153269i
$151$	−41.6552	−	72.1490i	−0.275862	−	0.477808i	0.694490	−	0.719502i	$-0.255630\pi$
$151$	−41.6552	−	72.1490i	−0.275862	−	0.477808i	−0.970352	+	0.241695i	$0.922297\pi$
$152$	−130.150	+	56.2802i	−0.856250	+	0.370264i
$153$			116.665i			0.762514i
$154$		0			0
$155$			135.751i			0.875813i
$156$	−159.995	+	114.503i	−1.02561	+	0.733993i
$157$	17.7207	+	30.6932i	0.112871	+	0.195498i	0.916927	−	0.399056i	$-0.130662\pi$
$157$	17.7207	+	30.6932i	0.112871	+	0.195498i	−0.804056	+	0.594554i	$0.797329\pi$
$158$	83.6170	+	260.515i	0.529222	+	1.64883i
$159$	−121.164	−	69.9543i	−0.762041	−	0.439964i
$160$	72.5109	+	130.949i	0.453193	+	0.818431i
$161$		0			0
$162$	193.664	+	41.8896i	1.19546	+	0.258578i
$163$	−9.05412	−	5.22740i	−0.0555468	−	0.0320699i	0.471969	−	0.881615i	$-0.343543\pi$
$163$	−9.05412	−	5.22740i	−0.0555468	−	0.0320699i	−0.527516	+	0.849545i	$0.676877\pi$
$164$	87.9410	−	8.60708i	0.536226	−	0.0524822i
$165$	228.777	−	132.084i	1.38653	−	0.800511i
$166$	67.1708	−	74.0659i	0.404643	−	0.446180i
$167$		−	78.8843i		−	0.472361i	−0.971709	−	0.236181i	$-0.924104\pi$
$167$		−	78.8843i		−	0.472361i	0.971709	−	0.236181i	$-0.0758957\pi$
$168$		0			0
$169$	−7.45163			−0.0440925
$170$	−135.287	−	122.693i	−0.795808	−	0.721722i
$171$	52.9610	+	91.7311i	0.309713	+	0.536439i
$172$	−317.682	+	31.0926i	−1.84699	+	0.180771i
$173$	−95.9208	+	166.140i	−0.554456	+	0.960345i	0.443490	+	0.896279i	$0.353740\pi$
$173$	−95.9208	+	166.140i	−0.554456	+	0.960345i	−0.997946	+	0.0640660i	$0.979593\pi$
$174$	−58.0844	+	268.537i	−0.333818	+	1.54331i
$175$		0			0
$176$	−175.739	+	153.739i	−0.998516	+	0.873515i
$177$	4.65732	−	8.06671i	0.0263125	−	0.0455746i
$178$	−2.13299	+	0.684623i	−0.0119831	+	0.00384620i
$179$	60.5426	−	34.9543i	0.338227	−	0.195275i	−0.321261	−	0.946991i	$-0.604107\pi$
$179$	60.5426	−	34.9543i	0.338227	−	0.195275i	0.659488	+	0.751715i	$0.270773\pi$
$180$	90.9272	−	65.0733i	0.505151	−	0.361518i
$181$	343.635			1.89853			0.949267	−	0.314472i	$-0.101827\pi$
$181$	343.635			1.89853			0.949267	+	0.314472i	$0.101827\pi$
$182$		0			0
$183$	113.174			0.618438
$184$	65.0634	−	28.1351i	0.353605	−	0.152908i
$185$	49.4903	−	28.5732i	0.267515	−	0.154450i
$186$	−213.871	+	68.6457i	−1.14984	+	0.369063i
$187$	142.449	−	246.728i	0.761757	−	1.31940i
$188$	69.6785	−	153.534i	0.370630	−	0.816668i
$189$		0			0
$190$	−162.071	−	35.0560i	−0.853007	−	0.184505i
$191$	69.8895	−	121.052i	0.365913	−	0.633781i	−0.623009	−	0.782215i	$-0.714090\pi$
$191$	69.8895	−	121.052i	0.365913	−	0.633781i	0.988922	+	0.148434i	$0.0474233\pi$
$192$	−169.639	+	180.456i	−0.883534	+	0.939874i
$193$	−11.4616	−	19.8521i	−0.0593867	−	0.102861i	0.834804	−	0.550548i	$-0.185581\pi$
$193$	−11.4616	−	19.8521i	−0.0593867	−	0.102861i	−0.894190	+	0.447687i	$0.852248\pi$
$194$	235.301	+	213.396i	1.21289	+	1.09998i
$195$	−230.078			−1.17989
$196$		0			0
$197$		−	287.788i		−	1.46085i	−0.682992	−	0.730426i	$-0.739322\pi$
$197$		−	287.788i		−	1.46085i	0.682992	−	0.730426i	$-0.260678\pi$
$198$	129.200	+	117.172i	0.652527	+	0.591780i
$199$	56.7091	−	32.7410i	0.284970	−	0.164528i	−0.350701	−	0.936487i	$-0.614057\pi$
$199$	56.7091	−	32.7410i	0.284970	−	0.164528i	0.635671	+	0.771960i	$0.280723\pi$
$200$	2.87507	−	24.7913i	0.0143754	−	0.123956i
$201$	−136.337	−	78.7141i	−0.678293	−	0.391613i
$202$	−136.101	−	29.4387i	−0.673769	−	0.145736i
$203$		0			0
$204$	124.887	−	275.183i	0.612191	−	1.34894i
$205$	89.4868	+	51.6652i	0.436521	+	0.252026i
$206$	−37.3620	+	11.9920i	−0.181369	+	0.0582135i
$207$	−26.4758	−	45.8574i	−0.127902	−	0.221533i
$208$	199.504	−	39.4299i	0.959152	−	0.189567i
$209$		−	258.663i		−	1.23762i
$210$		0			0
$211$		−	17.8985i		−	0.0848270i	−0.999100	−	0.0424135i	$-0.986495\pi$
$211$		−	17.8985i		−	0.0848270i	0.999100	−	0.0424135i	$-0.0135047\pi$
$212$	84.1618	+	117.600i	0.396990	+	0.554716i
$213$	−43.7632	−	75.8001i	−0.205461	−	0.355869i
$214$	−85.2167	+	27.3518i	−0.398209	+	0.127812i
$215$	−323.267	−	186.638i	−1.50357	−	0.868084i
$216$	−75.1461	−	55.8391i	−0.347898	−	0.258515i
$217$		0			0
$218$	23.9336	−	110.650i	0.109787	−	0.507570i
$219$	−256.026	−	147.817i	−1.16907	−	0.674962i
$220$	−271.752	+	26.5973i	−1.23524	+	0.120897i
$221$	−214.889	+	124.066i	−0.972346	+	0.561384i
$222$	70.0421	+	63.5215i	0.315505	+	0.286133i
$223$		−	258.973i		−	1.16132i	−0.814148	−	0.580658i	$-0.802795\pi$
$223$		−	258.973i		−	1.16132i	0.814148	−	0.580658i	$-0.197205\pi$
$224$		0			0
$225$	−18.6431			−0.0828581
$226$	−253.441	+	279.457i	−1.12142	+	1.23654i
$227$	58.6721	+	101.623i	0.258468	+	0.447679i	0.965832	−	0.259171i	$-0.0834492\pi$
$227$	58.6721	+	101.623i	0.258468	+	0.447679i	−0.707364	+	0.706849i	$0.750116\pi$
$228$	−26.7257	−	273.065i	−0.117218	−	1.19765i
$229$	−43.5475	+	75.4264i	−0.190164	+	0.329373i	−0.945304	−	0.326190i	$-0.894235\pi$
$229$	−43.5475	+	75.4264i	−0.190164	+	0.329373i	0.755141	+	0.655563i	$0.227569\pi$
$230$	81.0212	+	17.5249i	0.352266	+	0.0761950i
$231$		0			0
$232$	169.379	−	227.943i	0.730081	−	0.982514i
$233$	155.825	−	269.897i	0.668778	−	1.15836i	−0.309468	−	0.950910i	$-0.600151\pi$
$233$	155.825	−	269.897i	0.668778	−	1.15836i	0.978246	−	0.207448i	$-0.0665159\pi$
$234$	−46.4258	−	144.643i	−0.198401	−	0.618132i
$235$	170.753	−	98.5843i	0.726608	−	0.419507i
$236$	−7.82938	+	5.60320i	−0.0331753	+	0.0237424i
$237$	−529.410			−2.23380
$238$		0			0
$239$	−140.823			−0.589218			−0.294609	−	0.955618i	$-0.595189\pi$
$239$	−140.823			−0.589218			−0.294609	+	0.955618i	$0.595189\pi$
$240$	−284.134	+	56.1563i	−1.18389	+	0.233985i
$241$	41.6447	−	24.0436i	0.172799	−	0.0997658i	−0.411106	−	0.911588i	$-0.634857\pi$
$241$	41.6447	−	24.0436i	0.172799	−	0.0997658i	0.583905	+	0.811822i	$0.301524\pi$
$242$	−56.2128	−	175.135i	−0.232284	−	0.723699i
$243$	−139.035	+	240.816i	−0.572162	+	0.991014i
$244$	−106.523	−	48.3435i	−0.436569	−	0.198129i
$245$		0			0
$246$	−36.1456	+	167.109i	−0.146934	+	0.679305i
$247$	−112.642	+	195.101i	−0.456039	+	0.789883i
$248$	230.624	+	26.7458i	0.929937	+	0.107846i
$249$	96.7357	+	167.551i	0.388497	+	0.672896i
$250$	176.725	−	194.866i	0.706900	−	0.779464i
$251$	−152.080			−0.605895			−0.302947	−	0.953007i	$-0.597971\pi$
$251$	−152.080			−0.605895			−0.302947	+	0.953007i	$0.597971\pi$
$252$		0			0
$253$			129.309i			0.511101i
$254$	61.6090	−	67.9333i	0.242555	−	0.267454i
$255$	306.046	−	176.696i	1.20018	−	0.692924i
$256$	236.752	−	97.3876i	0.924814	−	0.380420i
$257$	−126.153	−	72.8347i	−0.490869	−	0.283403i	0.234066	−	0.972221i	$-0.424797\pi$
$257$	−126.153	−	72.8347i	−0.490869	−	0.283403i	−0.724935	+	0.688817i	$0.758130\pi$
$258$	130.574	−	603.673i	0.506102	−	2.33982i
$259$		0			0
$260$	216.556	+	98.2803i	0.832909	+	0.378001i
$261$	−183.714	−	106.068i	−0.703887	−	0.406389i
$262$	73.9558	+	230.415i	0.282274	+	0.879446i
$263$	−176.696	−	306.047i	−0.671850	−	1.16368i	−0.977379	−	0.211495i	$-0.932167\pi$
$263$	−176.696	−	306.047i	−0.671850	−	1.16368i	0.305529	−	0.952183i	$-0.401167\pi$
$264$	−179.321	−	414.687i	−0.679247	−	1.57078i
$265$			169.112i			0.638158i
$266$		0			0
$267$		−	4.33460i		−	0.0162345i
$268$	94.7008	+	132.326i	0.353361	+	0.493753i
$269$	−66.6490	−	115.439i	−0.247766	−	0.429143i	0.715140	−	0.698981i	$-0.246363\pi$
$269$	−66.6490	−	115.439i	−0.247766	−	0.429143i	−0.962906	+	0.269838i	$0.913030\pi$
$270$	−33.4589	−	104.244i	−0.123922	−	0.386088i
$271$	326.342	+	188.414i	1.20421	+	0.695253i	0.961489	−	0.274842i	$-0.0886255\pi$
$271$	326.342	+	188.414i	1.20421	+	0.695253i	0.242725	+	0.970095i	$0.421959\pi$
$272$	−235.094	+	205.664i	−0.864318	+	0.756116i
$273$		0			0
$274$	283.917	+	61.4112i	1.03619	+	0.224128i
$275$	39.4273	+	22.7634i	0.143372	+	0.0827759i
$276$	13.3605	+	136.508i	0.0484076	+	0.494594i
$277$	−67.4788	+	38.9589i	−0.243606	+	0.140646i	−0.616833	−	0.787094i	$-0.711585\pi$
$277$	−67.4788	+	38.9589i	−0.243606	+	0.140646i	0.373227	+	0.927740i	$0.378251\pi$
$278$	−116.018	+	127.927i	−0.417330	+	0.460170i
$279$		−	173.430i		−	0.621613i
$280$		0			0
$281$	324.564			1.15503			0.577516	−	0.816380i	$-0.304022\pi$
$281$	324.564			1.15503			0.577516	+	0.816380i	$0.304022\pi$
$282$	241.661	+	219.164i	0.856955	+	0.777177i
$283$	−149.741	−	259.359i	−0.529119	−	0.916462i	−0.999423	−	0.0339572i	$-0.989189\pi$
$283$	−149.741	−	259.359i	−0.529119	−	0.916462i	0.470304	−	0.882505i	$-0.344144\pi$
$284$	8.81244	+	90.0392i	0.0310297	+	0.317040i
$285$	160.425	−	277.864i	0.562895	−	0.974963i
$286$	−78.4269	+	362.585i	−0.274220	+	1.26778i
$287$		0			0
$288$	−92.6370	−	167.295i	−0.321656	−	0.580885i
$289$	46.0604	−	79.7789i	0.159378	−	0.276052i
$290$	316.206	−	101.492i	1.09037	−	0.349972i
$291$	−532.296	+	307.321i	−1.82920	+	1.05609i
$292$	177.838	+	248.494i	0.609034	+	0.851005i
$293$	81.7250			0.278925			0.139463	−	0.990227i	$-0.455463\pi$
$293$	81.7250			0.278925			0.139463	+	0.990227i	$0.455463\pi$
$294$		0			0
$295$	−11.2589			−0.0381657
$296$	−38.7918	−	89.7075i	−0.131053	−	0.303066i
$297$	147.901	−	85.3908i	0.497984	−	0.287511i
$298$	416.773	−	133.771i	1.39857	−	0.448895i
$299$	56.3108	−	97.5332i	0.188331	−	0.326198i
$300$	43.9744	+	19.9570i	0.146581	+	0.0665233i
$301$		0			0
$302$	−162.855	−	35.2254i	−0.539254	−	0.116641i
$303$	134.719	−	233.340i	0.444617	−	0.770099i
$304$	−91.4872	+	268.433i	−0.300945	+	0.883002i
$305$	−68.3986	−	118.470i	−0.224258	−	0.388425i
$306$	172.838	+	156.747i	0.564829	+	0.512246i
$307$	361.930			1.17892			0.589462	−	0.807796i	$-0.299340\pi$
$307$	361.930			1.17892			0.589462	+	0.807796i	$0.299340\pi$
$308$		0			0
$309$		−	75.9257i		−	0.245714i
$310$	201.114	+	182.391i	0.648755	+	0.588359i
$311$	−163.508	+	94.4017i	−0.525751	+	0.303542i	−0.739284	−	0.673393i	$-0.764836\pi$
$311$	−163.508	+	94.4017i	−0.525751	+	0.303542i	0.213534	+	0.976936i	$0.431503\pi$
$312$	−45.3302	+	390.875i	−0.145289	+	1.25280i
$313$	22.2463	+	12.8439i	0.0710745	+	0.0410349i	0.535116	−	0.844779i	$-0.320268\pi$
$313$	22.2463	+	12.8439i	0.0710745	+	0.0410349i	−0.464042	+	0.885813i	$0.653601\pi$
$314$	69.2808	+	14.9854i	0.220639	+	0.0477242i
$315$		0			0
$316$	498.296	+	226.143i	1.57689	+	0.715642i
$317$	−432.257	−	249.564i	−1.36359	−	0.787268i	−0.373489	−	0.927635i	$-0.621838\pi$
$317$	−432.257	−	249.564i	−1.36359	−	0.787268i	−0.990100	+	0.140367i	$0.955172\pi$
$318$	−266.430	+	85.5154i	−0.837830	+	0.268916i
$319$	259.019	+	448.634i	0.811972	+	1.40638i
$320$	291.423	+	68.5149i	0.910698	+	0.214109i
$321$		−	173.174i		−	0.539484i
$322$		0			0
$323$		−	346.027i		−	1.07129i
$324$	322.261	−	230.631i	0.994633	−	0.711823i
$325$	−19.8258	−	34.3393i	−0.0610025	−	0.105659i
$326$	−19.9092	+	6.39022i	−0.0610712	+	0.0196019i
$327$	189.705	+	109.526i	0.580138	+	0.334943i
$328$	105.404	−	141.848i	0.321353	−	0.432464i
$329$		0			0
$330$	111.696	−	516.395i	0.338473	−	1.56483i
$331$	216.384	+	124.930i	0.653729	+	0.377431i	0.789883	−	0.613257i	$-0.210141\pi$
$331$	216.384	+	124.930i	0.653729	+	0.377431i	−0.136154	+	0.990688i	$0.543474\pi$
$332$	−19.4793	−	199.026i	−0.0586727	−	0.599475i
$333$	−63.2268	+	36.5040i	−0.189870	+	0.109622i
$334$	−116.866	−	105.987i	−0.349899	−	0.317326i
$335$			190.288i			0.568025i
$336$		0			0
$337$	−84.4039			−0.250457			−0.125228	−	0.992128i	$-0.539966\pi$
$337$	−84.4039			−0.250457			−0.125228	+	0.992128i	$0.539966\pi$
$338$	−10.0118	+	11.0395i	−0.0296207	+	0.0326613i
$339$	−364.992	−	632.185i	−1.07667	−	1.86485i
$340$	−363.536	+	35.5805i	−1.06922	+	0.104649i
$341$	−211.760	+	366.778i	−0.620996	+	1.07560i
$342$	207.056	+	44.7861i	0.605426	+	0.130953i
$343$		0			0
$344$	−380.766	+	512.419i	−1.10688	+	1.48959i
$345$	−80.1982	+	138.907i	−0.232459	+	0.402630i
$346$	117.258	+	365.326i	0.338896	+	1.05586i
$347$	326.707	−	188.624i	0.941518	−	0.543586i	0.0510824	−	0.998694i	$-0.483733\pi$
$347$	326.707	−	188.624i	0.941518	−	0.543586i	0.890436	+	0.455109i	$0.150400\pi$
$348$	319.794	+	446.849i	0.918948	+	1.28405i
$349$	−400.193			−1.14668			−0.573342	−	0.819316i	$-0.694353\pi$
$349$	−400.193			−1.14668			−0.573342	+	0.819316i	$0.694353\pi$
$350$		0			0
$351$	−148.743			−0.423768
$352$	−8.35529	+	466.914i	−0.0237366	+	1.32646i
$353$	−256.293	+	147.971i	−0.726043	+	0.419181i	−0.816973	−	0.576676i	$-0.804350\pi$
$353$	−256.293	+	147.971i	−0.726043	+	0.419181i	0.0909296	+	0.995857i	$0.471016\pi$
$354$	−5.69332	−	17.7380i	−0.0160828	−	0.0501073i
$355$	−52.8980	+	91.6220i	−0.149008	+	0.258090i
$356$	−1.85157	+	4.07985i	−0.00520103	+	0.0114603i
$357$		0			0
$358$	29.5588	−	136.657i	0.0825666	−	0.381723i
$359$	102.587	−	177.686i	0.285757	−	0.494946i	−0.687035	−	0.726624i	$-0.741088\pi$
$359$	102.587	−	177.686i	0.285757	−	0.494946i	0.972793	+	0.231678i	$0.0744215\pi$
$360$	25.7617	−	222.138i	0.0715602	−	0.617051i
$361$	23.4181	+	40.5613i	0.0648701	+	0.112358i
$362$	461.698	−	509.092i	1.27541	−	1.40633i
$363$	355.904			0.980451
$364$		0			0
$365$			357.341i			0.979017i
$366$	152.058	−	167.667i	0.415458	−	0.458105i
$367$	306.216	−	176.794i	0.834377	−	0.481728i	−0.0209719	−	0.999780i	$-0.506676\pi$
$367$	306.216	−	176.794i	0.834377	−	0.481728i	0.855349	+	0.518052i	$0.173343\pi$
$368$	45.7355	−	134.192i	0.124281	−	0.364653i
$369$	−114.325	−	66.0054i	−0.309823	−	0.178876i
$370$	24.1628	−	111.710i	0.0653048	−	0.301918i
$371$		0			0
$372$	−185.653	+	409.078i	−0.499067	+	1.09967i
$373$	310.062	+	179.014i	0.831264	+	0.479931i	0.854285	−	0.519804i	$-0.173995\pi$
$373$	310.062	+	179.014i	0.831264	+	0.479931i	−0.0230210	+	0.999735i	$0.507328\pi$
$374$	−174.136	−	542.533i	−0.465604	−	1.45062i
$375$	254.510	+	440.824i	0.678693	+	1.17553i
$376$	−133.841	−	309.512i	−0.355959	−	0.823169i
$377$		−	451.187i		−	1.19678i
$378$		0			0
$379$		−	514.679i		−	1.35799i	−0.734142	−	0.678996i	$-0.762415\pi$
$379$		−	514.679i		−	1.35799i	0.734142	−	0.678996i	$-0.237585\pi$
$380$	−269.689	+	193.007i	−0.709709	+	0.507913i
$381$	88.7260	+	153.678i	0.232877	+	0.403354i
$382$	−85.4361	−	266.183i	−0.223655	−	0.696813i
$383$	−450.193	−	259.919i	−1.17544	−	0.678639i	−0.220483	−	0.975391i	$-0.570763\pi$
$383$	−450.193	−	259.919i	−1.17544	−	0.678639i	−0.954955	+	0.296752i	$0.904097\pi$
$384$	39.4223	+	493.773i	0.102662	+	1.28587i
$385$		0			0
$386$	−44.8103	−	9.69244i	−0.116089	−	0.0251100i
$387$	412.992	+	238.441i	1.06716	+	0.616127i
$388$	632.288	−	61.8842i	1.62961	−	0.159495i
$389$	91.3278	−	52.7281i	0.234776	−	0.135548i	−0.377997	−	0.925807i	$-0.623387\pi$
$389$	91.3278	−	52.7281i	0.234776	−	0.135548i	0.612773	+	0.790259i	$0.290054\pi$
$390$	−309.127	+	340.859i	−0.792632	+	0.873997i
$391$			172.982i			0.442410i
$392$		0			0
$393$	−468.241			−1.19145
$394$	−426.355	−	386.663i	−1.08212	−	0.981379i
$395$	319.957	+	554.182i	0.810018	+	1.40299i
$396$	347.180	−	33.9797i	0.876717	−	0.0858072i
$397$	185.762	−	321.749i	0.467914	−	0.810450i	−0.531414	−	0.847112i	$-0.678339\pi$
$397$	185.762	−	321.749i	0.467914	−	0.810450i	0.999328	+	0.0366619i	$0.0116725\pi$
$398$	27.6872	−	128.004i	0.0695659	−	0.321618i
$399$		0			0
$400$	−32.8652	−	37.5682i	−0.0821629	−	0.0939206i
$401$	−149.636	+	259.177i	−0.373157	+	0.646327i	−0.990049	−	0.140721i	$-0.955058\pi$
$401$	−149.636	+	259.177i	−0.373157	+	0.646327i	0.616893	+	0.787047i	$0.288391\pi$
$402$	−299.793	+	96.2238i	−0.745753	+	0.239363i
$403$	319.446	−	184.433i	0.792671	−	0.457649i
$404$	−226.475	+	162.080i	−0.560582	+	0.401188i
$405$	463.421			1.14425
$406$		0			0
$407$	178.287			0.438052
$408$	−239.887	−	554.747i	−0.587958	−	1.35967i
$409$	17.6410	−	10.1850i	0.0431320	−	0.0249023i	−0.478279	−	0.878208i	$-0.658739\pi$
$409$	17.6410	−	10.1850i	0.0431320	−	0.0249023i	0.521411	+	0.853306i	$0.325406\pi$
$410$	196.774	−	63.1580i	0.479935	−	0.154044i
$411$	−281.033	+	486.764i	−0.683780	+	1.18434i
$412$	−32.4324	+	71.4635i	−0.0787195	+	0.173455i
$413$		0			0
$414$	−103.509	−	22.3890i	−0.250023	−	0.0540798i
$415$	116.927	−	202.524i	0.281753	−	0.488010i
$416$	209.632	−	348.540i	0.503924	−	0.837836i
$417$	−167.083	−	289.396i	−0.400678	−	0.693994i
$418$	−383.207	−	347.533i	−0.916764	−	0.831418i
$419$	183.085			0.436956			0.218478	−	0.975842i	$-0.429891\pi$
$419$	183.085			0.436956			0.218478	+	0.975842i	$0.429891\pi$
$420$		0			0
$421$			293.022i			0.696014i	0.937492	+	0.348007i	$0.113141\pi$
$421$			293.022i			0.696014i	−0.937492	+	0.348007i	$0.886859\pi$
$422$	−26.5165	−	24.0479i	−0.0628352	−	0.0569856i
$423$	−218.147	+	125.947i	−0.515714	+	0.297748i
$424$	287.300	+	33.3186i	0.677595	+	0.0785815i
$425$	52.7438	+	30.4517i	0.124103	+	0.0716510i
$426$	−171.096	−	37.0081i	−0.401634	−	0.0868734i
$427$		0			0
$428$	−73.9732	+	162.997i	−0.172835	+	0.380834i
$429$	−621.636	−	358.902i	−1.44903	−	0.836601i
$430$	−710.834	+	228.155i	−1.65310	+	0.530593i
$431$	37.6108	+	65.1439i	0.0872641	+	0.151146i	0.906354	−	0.422520i	$-0.138854\pi$
$431$	37.6108	+	65.1439i	0.0872641	+	0.151146i	−0.819090	+	0.573666i	$0.805521\pi$
$432$	−183.689	+	36.3043i	−0.425207	+	0.0840378i
$433$			506.209i			1.16907i	0.811367	+	0.584536i	$0.198724\pi$
$433$			506.209i			1.16907i	−0.811367	+	0.584536i	$0.801276\pi$
$434$		0			0
$435$			642.583i			1.47720i
$436$	−131.771	−	184.124i	−0.302227	−	0.422303i
$437$	78.5269	+	136.013i	0.179696	+	0.311242i
$438$	−562.978	+	180.698i	−1.28534	+	0.412553i
$439$	141.358	+	81.6130i	0.322000	+	0.185907i	0.652284	−	0.757975i	$-0.273811\pi$
$439$	141.358	+	81.6130i	0.322000	+	0.185907i	−0.330284	+	0.943882i	$0.607144\pi$
$440$	−325.715	+	438.334i	−0.740262	+	0.996214i
$441$		0			0
$442$	−104.915	+	485.047i	−0.237365	+	1.09739i
$443$	−98.4732	−	56.8535i	−0.222287	−	0.128338i	0.384722	−	0.923033i	$-0.374297\pi$
$443$	−98.4732	−	56.8535i	−0.222287	−	0.128338i	−0.607009	+	0.794695i	$0.707631\pi$
$444$	188.213	−	18.4211i	0.423903	−	0.0414889i
$445$	−4.53742	+	2.61968i	−0.0101964	+	0.00588692i
$446$	−383.667	−	347.949i	−0.860239	−	0.780155i
$447$			846.952i			1.89475i
$448$		0			0
$449$	391.120			0.871091			0.435546	−	0.900167i	$-0.356555\pi$
$449$	391.120			0.871091			0.435546	+	0.900167i	$0.356555\pi$
$450$	−25.0483	+	27.6196i	−0.0556629	+	0.0613768i
$451$	161.186	+	279.183i	0.357398	+	0.619031i
$452$	73.4972	+	750.942i	0.162604	+	1.66138i
$453$	161.201	−	279.208i	0.355851	−	0.616353i
$454$	229.384	+	49.6157i	0.505251	+	0.109286i
$455$		0			0
$456$	−440.451	−	327.288i	−0.965900	−	0.717736i
$457$	−286.893	+	496.913i	−0.627774	+	1.08734i	0.360223	+	0.932866i	$0.382701\pi$
$457$	−286.893	+	496.913i	−0.627774	+	1.08734i	−0.987997	+	0.154471i	$0.950633\pi$
$458$	53.2345	+	165.856i	0.116232	+	0.362131i
$459$	197.855	−	114.231i	0.431056	−	0.248870i
$460$	134.821	−	96.4863i	0.293088	−	0.209753i
$461$	−847.131			−1.83759			−0.918797	−	0.394729i	$-0.870838\pi$
$461$	−847.131			−1.83759			−0.918797	+	0.394729i	$0.870838\pi$
$462$		0			0
$463$	109.055			0.235539			0.117770	−	0.993041i	$-0.462426\pi$
$463$	109.055			0.235539			0.117770	+	0.993041i	$0.462426\pi$
$464$	−110.123	−	557.191i	−0.237335	−	1.20084i
$465$	−454.958	+	262.670i	−0.978404	+	0.564882i
$466$	−190.488	−	593.480i	−0.408773	−	1.27356i
$467$	321.205	−	556.343i	0.687805	−	1.19131i	−0.284741	−	0.958604i	$-0.591908\pi$
$467$	321.205	−	556.343i	0.687805	−	1.19131i	0.972546	−	0.232709i	$-0.0747590\pi$
$468$	−276.664	−	125.559i	−0.591162	−	0.268288i
$469$		0			0
$470$	83.3671	−	385.424i	0.177377	−	0.820051i
$471$	−68.5771	+	118.779i	−0.145599	+	0.252185i
$472$	−2.21823	+	19.1275i	−0.00469965	+	0.0405243i
$473$	−582.278	−	1008.53i	−1.23103	−	2.13221i
$474$	−711.300	+	784.316i	−1.50063	+	1.65468i
$475$	55.2952			0.116411
$476$		0			0
$477$		−	216.050i		−	0.452936i
$478$	−189.206	+	208.628i	−0.395828	+	0.436461i
$479$	367.909	−	212.412i	0.768077	−	0.443449i	−0.0641112	−	0.997943i	$-0.520421\pi$
$479$	367.909	−	212.412i	0.768077	−	0.443449i	0.832188	+	0.554493i	$0.187088\pi$
$480$	−298.560	+	496.392i	−0.621999	+	1.03415i
$481$	−134.476	−	77.6397i	−0.279576	−	0.161413i
$482$	20.3323	−	94.0004i	0.0421831	−	0.195022i
$483$		0			0
$484$	−334.987	−	152.028i	−0.692122	−	0.314107i
$485$	643.403	+	371.469i	1.32660	+	0.765915i
$486$	169.963	+	529.534i	0.349719	+	1.08958i
$487$	−388.616	−	673.103i	−0.797980	−	1.38214i	−0.920929	−	0.389729i	$-0.872569\pi$
$487$	−388.616	−	673.103i	−0.797980	−	1.38214i	0.122949	−	0.992413i	$-0.460765\pi$
$488$	−214.742	+	92.8598i	−0.440044	+	0.190286i
$489$		−	40.4588i		−	0.0827379i
$490$		0			0
$491$			476.370i			0.970203i	0.874458	+	0.485102i	$0.161217\pi$
$491$			476.370i			0.970203i	−0.874458	+	0.485102i	$0.838783\pi$
$492$	199.006	+	278.072i	0.404485	+	0.565188i
$493$	346.502	+	600.160i	0.702845	+	1.21736i
$494$	137.698	+	429.010i	0.278742	+	0.868442i
$495$	353.283	+	203.968i	0.713702	+	0.412056i
$496$	349.484	−	305.733i	0.704605	−	0.616397i
$497$		0			0
$498$	378.197	+	81.8039i	0.759432	+	0.164265i
$499$	−377.065	−	217.698i	−0.755641	−	0.436269i	0.0720876	−	0.997398i	$-0.477034\pi$
$499$	−377.065	−	217.698i	−0.755641	−	0.436269i	−0.827728	+	0.561129i	$0.810367\pi$
$500$	−51.2497	−	523.633i	−0.102499	−	1.04727i
$501$	264.374	−	152.636i	0.527693	−	0.304663i
$502$	−204.330	+	225.305i	−0.407031	+	0.448814i
$503$		−	375.404i		−	0.746329i	−0.927765	−	0.373165i	$-0.878273\pi$
$503$		−	375.404i		−	0.746329i	0.927765	−	0.373165i	$-0.121727\pi$
$504$		0			0
$505$	−325.678			−0.644907
$506$	191.570	+	173.735i	0.378596	+	0.343351i
$507$	−14.4185	−	24.9735i	−0.0284388	−	0.0492574i
$508$	−17.8664	−	182.546i	−0.0351701	−	0.359343i
$509$	−73.9117	+	128.019i	−0.145210	+	0.251510i	−0.929451	−	0.368945i	$-0.879719\pi$
$509$	−73.9117	+	128.019i	−0.145210	+	0.251510i	0.784242	+	0.620456i	$0.213052\pi$
$510$	149.421	−	690.807i	0.292983	−	1.35452i
$511$		0			0
$512$	173.815	−	481.594i	0.339482	−	0.940613i
$513$	103.713	−	179.636i	0.202169	−	0.350167i
$514$	−277.400	+	89.0365i	−0.539689	+	0.173223i
$515$	−79.4784	+	45.8869i	−0.154327	+	0.0891007i
$516$	−718.901	−	1004.52i	−1.39322	−	1.94675i
$517$	615.131			1.18981
$518$		0			0
$519$	−742.404			−1.43045
$520$	436.560	−	188.780i	0.839539	−	0.363038i
$521$	−755.302	+	436.074i	−1.44972	+	0.836994i	−0.998464	−	0.0554019i	$-0.982356\pi$
$521$	−755.302	+	436.074i	−1.44972	+	0.836994i	−0.451253	+	0.892396i	$0.649023\pi$
$522$	−403.972	+	129.662i	−0.773892	+	0.248395i
$523$	178.600	−	309.344i	0.341491	−	0.591480i	−0.643219	−	0.765683i	$-0.722401\pi$
$523$	178.600	−	309.344i	0.341491	−	0.591480i	0.984710	+	0.174202i	$0.0557347\pi$
$524$	440.723	+	200.014i	0.841074	+	0.381706i
$525$		0			0
$526$	−690.811	−	149.422i	−1.31333	−	0.284072i
$527$	−283.281	+	490.657i	−0.537535	+	0.931038i
$528$	−855.286	−	291.499i	−1.61986	−	0.552081i
$529$	225.244	+	390.133i	0.425791	+	0.737492i
$530$	250.538	+	227.214i	0.472713	+	0.428705i
$531$	14.3839			0.0270883
$532$		0			0
$533$		−	280.771i		−	0.526776i
$534$	−6.42167	−	5.82384i	−0.0120256	−	0.0109061i
$535$	−181.278	+	104.661i	−0.338836	+	0.195627i
$536$	323.277	+	37.4908i	0.603128	+	0.0699455i
$537$	234.293	+	135.269i	0.436299	+	0.251897i
$538$	−260.570	−	56.3613i	−0.484331	−	0.104761i
$539$		0			0
$540$	−199.390	−	90.4898i	−0.369241	−	0.167574i
$541$	807.198	+	466.036i	1.49205	+	0.861434i	0.999958	−	0.00911085i	$-0.00290011\pi$
$541$	807.198	+	466.036i	1.49205	+	0.861434i	0.492089	+	0.870545i	$0.336233\pi$
$542$	717.597	−	230.326i	1.32398	−	0.424955i
$543$	664.912	+	1151.66i	1.22452	+	2.12092i
$544$	−11.1773	+	624.614i	−0.0205465	+	1.14819i
$545$		−	264.776i		−	0.485827i
$546$		0			0
$547$			151.397i			0.276778i	0.990378	+	0.138389i	$0.0441924\pi$
$547$			151.397i			0.276778i	−0.990378	+	0.138389i	$0.955808\pi$
$548$	472.443	−	338.110i	0.862123	−	0.616990i
$549$	87.3832	+	151.352i	0.159168	+	0.275687i
$550$	86.6971	−	27.8270i	0.157631	−	0.0505945i
$551$	544.896	+	314.596i	0.988922	+	0.570954i
$552$	220.186	+	163.615i	0.398888	+	0.296403i
$553$		0			0
$554$	−32.9453	+	152.313i	−0.0594681	+	0.274934i
$555$	191.522	+	110.575i	0.345084	+	0.199234i
$556$	33.6448	+	343.759i	0.0605123	+	0.618271i
$557$	−775.593	+	447.789i	−1.39245	+	0.803929i	−0.993586	−	0.113082i	$-0.963928\pi$
$557$	−775.593	+	447.789i	−1.39245	+	0.803929i	−0.398861	+	0.917011i	$0.630594\pi$
$558$	−256.935	−	233.016i	−0.460457	−	0.417591i
$559$			1014.27i			1.81444i
$560$		0			0
$561$	1102.52			1.96527
$562$	436.075	−	480.838i	0.775933	−	0.855584i
$563$	139.958	+	242.414i	0.248592	+	0.430575i	0.963136	−	0.269017i	$-0.0866987\pi$
$563$	139.958	+	242.414i	0.248592	+	0.430575i	−0.714543	+	0.699591i	$0.753365\pi$
$564$	649.378	−	63.5569i	1.15138	−	0.112689i
$565$	−441.177	+	764.142i	−0.780845	+	1.35246i
$566$	−585.425	−	126.627i	−1.03432	−	0.223723i
$567$		0			0
$568$	145.232	+	107.919i	0.255691	+	0.189998i
$569$	−160.963	+	278.796i	−0.282887	+	0.489975i	−0.972095	−	0.234589i	$-0.924626\pi$
$569$	−160.963	+	278.796i	−0.282887	+	0.489975i	0.689207	+	0.724564i	$0.257959\pi$
$570$	−196.111	−	610.999i	−0.344055	−	1.07193i
$571$	−712.583	+	411.410i	−1.24796	+	0.720508i	−0.970702	−	0.240288i	$-0.922758\pi$
$571$	−712.583	+	411.410i	−1.24796	+	0.720508i	−0.277255	+	0.960796i	$0.589425\pi$
$572$	431.794	+	603.347i	0.754884	+	1.05480i
$573$	540.928			0.944027
$574$		0			0
$575$	−27.6427			−0.0480742
$576$	−372.310	−	87.5318i	−0.646372	−	0.151965i
$577$	−833.162	+	481.027i	−1.44396	+	0.833668i	−0.998111	−	0.0614420i	$-0.980430\pi$
$577$	−833.162	+	481.027i	−1.44396	+	0.833668i	−0.445845	+	0.895110i	$0.647097\pi$
$578$	−56.3064	−	175.427i	−0.0974158	−	0.303506i
$579$	44.3551	−	76.8253i	0.0766064	−	0.132686i
$580$	274.486	−	604.818i	0.473251	−	1.04279i
$581$		0			0
$582$	−259.884	+	1201.50i	−0.446536	+	2.06443i
$583$	−263.800	+	456.914i	−0.452486	+	0.783729i
$584$	607.079	+	70.4037i	1.03952	+	0.120554i
$585$	−177.646	−	307.692i	−0.303669	−	0.525970i
$586$	109.803	−	121.075i	0.187378	−	0.206612i
$587$	−885.638			−1.50875			−0.754377	−	0.656442i	$-0.772061\pi$
$587$	−885.638			−1.50875			−0.754377	+	0.656442i	$0.772061\pi$
$588$		0			0
$589$			514.392i			0.873331i
$590$	−15.1271	+	16.6799i	−0.0256392	+	0.0282711i
$591$	964.496	−	556.852i	1.63197	−	0.942220i
$592$	−185.020	−	63.0587i	−0.312535	−	0.106518i
$593$	−290.818	−	167.904i	−0.490418	−	0.283143i	0.234330	−	0.972157i	$-0.424710\pi$
$593$	−290.818	−	167.904i	−0.490418	−	0.283143i	−0.724748	+	0.689014i	$0.758044\pi$
$594$	72.2102	−	333.843i	0.121566	−	0.562025i
$595$		0			0
$596$	361.784	−	797.176i	0.607020	−	1.33754i
$597$	219.457	+	126.704i	0.367600	+	0.212234i
$598$	−68.8370	−	214.467i	−0.115112	−	0.358640i
$599$	30.1532	+	52.2269i	0.0503393	+	0.0871902i	0.890097	−	0.455771i	$-0.150636\pi$
$599$	30.1532	+	52.2269i	0.0503393	+	0.0871902i	−0.839758	+	0.542961i	$0.817303\pi$
$600$	88.6489	−	38.3340i	0.147748	−	0.0638901i
$601$		−	509.153i		−	0.847176i	−0.905855	−	0.423588i	$-0.860770\pi$
$601$		−	509.153i		−	0.847176i	0.905855	−	0.423588i	$-0.139230\pi$
$602$		0			0
$603$		−	243.105i		−	0.403159i
$604$	−270.993	+	193.940i	−0.448664	+	0.321093i
$605$	−215.096	−	372.557i	−0.355530	−	0.615797i
$606$	−164.687	−	513.094i	−0.271760	−	0.846690i
$607$	900.363	+	519.825i	1.48330	+	0.856384i	0.999820	−	0.0189717i	$-0.00603923\pi$
$607$	900.363	+	519.825i	1.48330	+	0.856384i	0.483480	+	0.875355i	$0.339373\pi$
$608$	274.761	+	496.196i	0.451909	+	0.816111i
$609$		0			0
$610$	−267.410	−	57.8407i	−0.438377	−	0.0948209i
$611$	−463.973	−	267.875i	−0.759366	−	0.438420i
$612$	464.439	−	45.4562i	0.758888	−	0.0742749i
$613$	−172.277	+	99.4641i	−0.281039	+	0.162258i	−0.633894	−	0.773420i	$-0.718544\pi$
$613$	−172.277	+	99.4641i	−0.281039	+	0.162258i	0.352855	+	0.935678i	$0.385211\pi$
$614$	486.278	−	536.196i	0.791984	−	0.873283i
$615$			399.876i			0.650206i
$616$		0			0
$617$	136.689			0.221538			0.110769	−	0.993846i	$-0.464669\pi$
$617$	136.689			0.221538			0.110769	+	0.993846i	$0.464669\pi$
$618$	−112.483	−	102.012i	−0.182012	−	0.165067i
$619$	−230.938	−	399.997i	−0.373083	−	0.646199i	0.616955	−	0.786998i	$-0.288366\pi$
$619$	−230.938	−	399.997i	−0.373083	−	0.646199i	−0.990038	+	0.140799i	$0.955033\pi$
$620$	540.422	−	52.8929i	0.871648	−	0.0853111i
$621$	−51.8472	+	89.8019i	−0.0834898	+	0.144609i
$622$	−79.8301	+	369.072i	−0.128344	+	0.593363i
$623$		0			0
$624$	518.173	+	592.324i	0.830406	+	0.949238i
$625$	268.638	−	465.294i	0.429821	−	0.744471i
$626$	48.9177	−	15.7010i	0.0781432	−	0.0250815i
$627$	866.888	−	500.498i	1.38260	−	0.798242i
$628$	115.284	−	82.5049i	0.183574	−	0.131377i
$629$	238.503			0.379178
$630$		0			0
$631$	1042.33			1.65187			0.825933	−	0.563768i	$-0.190649\pi$
$631$	1042.33			1.65187			0.825933	+	0.563768i	$0.190649\pi$
$632$	1004.53	−	434.382i	1.58944	−	0.687314i
$633$	59.9853	−	34.6325i	0.0947635	−	0.0547117i
$634$	−950.495	+	305.079i	−1.49920	+	0.481196i
$635$	107.246	−	185.755i	0.168891	−	0.292528i
$636$	−231.277	+	509.609i	−0.363643	+	0.801273i
$637$		0			0
$638$	1012.66	+	219.038i	1.58724	+	0.343319i
$639$	67.5803	−	117.052i	0.105759	−	0.183181i
$640$	493.052	−	339.686i	0.770394	−	0.530760i
$641$	−61.3334	−	106.233i	−0.0956840	−	0.165730i	0.814210	−	0.580571i	$-0.197170\pi$
$641$	−61.3334	−	106.233i	−0.0956840	−	0.165730i	−0.909894	+	0.414841i	$0.863837\pi$
$642$	−256.556	−	232.672i	−0.399621	−	0.362418i
$643$	−720.813			−1.12102			−0.560508	−	0.828149i	$-0.689394\pi$
$643$	−720.813			−1.12102			−0.560508	+	0.828149i	$0.689394\pi$
$644$		0			0
$645$		−	1444.53i		−	2.23959i
$646$	−512.635	−	464.911i	−0.793553	−	0.719677i
$647$	−510.825	+	294.925i	−0.789528	+	0.455834i	−0.839796	−	0.542901i	$-0.817326\pi$
$647$	−510.825	+	294.925i	−0.789528	+	0.455834i	0.0502683	+	0.998736i	$0.483992\pi$
$648$	91.3036	−	787.296i	0.140901	−	1.21496i
$649$	−30.4198	−	17.5629i	−0.0468717	−	0.0270614i
$650$	−77.5108	−	16.7656i	−0.119247	−	0.0257932i
$651$		0			0
$652$	−17.2824	+	38.0810i	−0.0265067	+	0.0584065i
$653$	−215.294	−	124.300i	−0.329700	−	0.190352i	0.326008	−	0.945367i	$-0.394296\pi$
$653$	−215.294	−	124.300i	−0.329700	−	0.190352i	−0.655708	+	0.755015i	$0.727630\pi$
$654$	417.145	−	133.890i	0.637836	−	0.204725i
$655$	282.989	+	490.151i	0.432044	+	0.748322i
$656$	−68.5292	−	346.738i	−0.104465	−	0.528563i
$657$		−	456.524i		−	0.694862i
$658$		0			0
$659$		−	640.918i		−	0.972562i	−0.873802	−	0.486281i	$-0.838353\pi$
$659$		−	640.918i		−	0.972562i	0.873802	−	0.486281i	$-0.161647\pi$
$660$	−614.963	−	859.291i	−0.931762	−	1.30196i
$661$	−483.321	−	837.137i	−0.731197	−	1.26647i	−0.956372	−	0.292152i	$-0.905629\pi$
$661$	−483.321	−	837.137i	−0.731197	−	1.26647i	0.225175	−	0.974318i	$-0.427705\pi$
$662$	475.810	−	152.720i	0.718746	−	0.230694i
$663$	−831.593	−	480.120i	−1.25429	−	0.724163i
$664$	−321.027	−	238.547i	−0.483474	−	0.359257i
$665$		0			0
$666$	−30.8694	+	142.716i	−0.0463504	+	0.214288i
$667$	−272.399	−	157.270i	−0.408395	−	0.235787i
$668$	−314.037	+	30.7358i	−0.470115	+	0.0460117i
$669$	867.927	−	501.098i	1.29735	−	0.749025i
$670$	281.911	+	255.666i	0.420762	+	0.381591i
$671$		−	426.783i		−	0.636040i
$672$		0			0
$673$	−754.537			−1.12115			−0.560577	−	0.828102i	$-0.689421\pi$
$673$	−754.537			−1.12115			−0.560577	+	0.828102i	$0.689421\pi$
$674$	−113.403	+	125.044i	−0.168253	+	0.185525i
$675$	18.2543	+	31.6173i	0.0270433	+	0.0468404i
$676$	2.90339	+	29.6648i	0.00429496	+	0.0438828i
$677$	380.978	−	659.874i	0.562745	−	0.974703i	−0.434511	−	0.900667i	$-0.643079\pi$
$677$	380.978	−	659.874i	0.562745	−	0.974703i	0.997256	−	0.0740362i	$-0.0235880\pi$
$678$	−1426.97	−	308.653i	−2.10468	−	0.455241i
$679$		0			0
$680$	−435.725	+	586.381i	−0.640772	+	0.862325i
$681$	−227.054	+	393.269i	−0.333413	+	0.577488i
$682$	258.865	+	806.513i	0.379567	+	1.18257i
$683$	−657.604	+	379.668i	−0.962817	+	0.555883i	−0.897039	−	0.441952i	$-0.854286\pi$
$683$	−657.604	+	379.668i	−0.962817	+	0.555883i	−0.0657781	+	0.997834i	$0.520953\pi$
$684$	344.544	−	246.578i	0.503720	−	0.360494i
$685$	679.387			0.991806
$686$		0			0
$687$	−337.047			−0.490607
$688$	247.558	+	1252.57i	0.359823	+	1.82060i
$689$	397.951	−	229.757i	0.577577	−	0.333464i
$690$	98.0381	+	305.445i	0.142084	+	0.442674i
$691$	245.076	−	424.484i	0.354669	−	0.614304i	−0.632393	−	0.774648i	$-0.717927\pi$
$691$	245.076	−	424.484i	0.354669	−	0.614304i	0.987061	+	0.160344i	$0.0512604\pi$
$692$	698.773	+	317.125i	1.00979	+	0.458274i
$693$		0			0
$694$	159.509	−	737.443i	0.229840	−	1.06260i
$695$	−201.958	+	349.801i	−0.290587	+	0.503311i
$696$	1091.67	+	126.602i	1.56849	+	0.181900i
$697$	215.627	+	373.477i	0.309364	+	0.535835i
$698$	−537.687	+	592.882i	−0.770326	+	0.849401i
$699$	1206.05			1.72539
$700$		0			0
$701$		−	577.533i		−	0.823870i	−0.911213	−	0.411935i	$-0.864853\pi$
$701$		−	577.533i		−	0.823870i	0.911213	−	0.411935i	$-0.135147\pi$
$702$	−199.846	+	220.361i	−0.284682	+	0.313905i
$703$	187.530	−	108.271i	0.266757	−	0.154012i
$704$	680.504	+	639.711i	0.966624	+	0.908681i
$705$	660.793	+	381.509i	0.937295	+	0.541148i
$706$	−125.131	+	578.506i	−0.177239	+	0.819413i
$707$		0			0
$708$	−33.9280	−	15.3976i	−0.0479209	−	0.0217481i
$709$	−615.814	−	355.540i	−0.868567	−	0.501467i	−0.00169497	−	0.999999i	$-0.500540\pi$
$709$	−615.814	−	355.540i	−0.868567	−	0.501467i	−0.866872	+	0.498531i	$0.833873\pi$
$710$	64.6649	+	201.468i	0.0910774	+	0.283758i
$711$	−408.764	−	708.000i	−0.574914	−	0.995781i
$712$	3.55655	+	8.22465i	0.00499516	+	0.0115515i
$713$		−	257.150i		−	0.360659i
$714$		0			0
$715$			867.631i			1.21347i
$716$	−162.742	−	227.399i	−0.227293	−	0.317597i
$717$	−272.484	−	471.957i	−0.380034	−	0.658238i
$718$	−125.407	−	390.715i	−0.174662	−	0.544171i
$719$	150.440	+	86.8564i	0.209235	+	0.120802i	0.600956	−	0.799282i	$-0.294787\pi$
$719$	150.440	+	86.8564i	0.209235	+	0.120802i	−0.391721	+	0.920084i	$0.628120\pi$
$720$	−294.484	−	336.625i	−0.409005	−	0.467534i
$721$		0			0
$722$	91.5551	+	19.8033i	0.126808	+	0.0274285i
$723$	161.160	+	93.0457i	0.222904	+	0.128694i
$724$	−133.891	−	1368.00i	−0.184932	−	1.88951i
$725$	−95.9059	+	55.3713i	−0.132284	+	0.0763742i
$726$	478.182	−	527.268i	0.658653	−	0.726265i
$727$		−	1056.57i		−	1.45333i	−0.686993	−	0.726664i	$-0.741070\pi$
$727$		−	1056.57i		−	1.45333i	0.686993	−	0.726664i	$-0.258930\pi$
$728$		0			0
$729$	−184.457			−0.253028
$730$	529.398	+	480.113i	0.725202	+	0.657689i
$731$	−778.941	−	1349.17i	−1.06558	−	1.84564i
$732$	−44.0963	−	450.544i	−0.0602408	−	0.615497i
$733$	−115.299	+	199.703i	−0.157297	+	0.272446i	−0.933893	−	0.357553i	$-0.883611\pi$
$733$	−115.299	+	199.703i	−0.157297	+	0.272446i	0.776596	+	0.629999i	$0.216945\pi$
$734$	149.505	−	691.192i	0.203685	−	0.941679i
$735$		0			0
$736$	−137.356	−	248.054i	−0.186625	−	0.337029i
$737$	−296.833	+	514.130i	−0.402758	+	0.697598i
$738$	−251.390	+	80.6881i	−0.340637	+	0.109333i
$739$	77.4971	−	44.7430i	0.104868	−	0.0605453i	−0.446649	−	0.894709i	$-0.647383\pi$
$739$	77.4971	−	44.7430i	0.104868	−	0.0605453i	0.551517	+	0.834164i	$0.314049\pi$
$740$	−133.032	−	185.887i	−0.179774	−	0.251198i
$741$	−871.820			−1.17654
$742$		0			0
$743$	−236.120			−0.317793			−0.158897	−	0.987295i	$-0.550794\pi$
$743$	−236.120			−0.317793			−0.158897	+	0.987295i	$0.550794\pi$
$744$	356.608	+	824.669i	0.479312	+	1.10843i
$745$	886.581	−	511.868i	1.19004	−	0.687071i
$746$	681.798	−	218.835i	0.913938	−	0.293345i
$747$	−149.382	+	258.737i	−0.199976	+	0.346368i
$748$	−1037.72	−	470.952i	−1.38733	−	0.629614i
$749$		0			0
$750$	995.029	+	215.224i	1.32671	+	0.286966i
$751$	717.692	−	1243.08i	0.955649	−	1.65523i	0.222772	−	0.974871i	$-0.428490\pi$
$751$	717.692	−	1243.08i	0.955649	−	1.65523i	0.732877	−	0.680361i	$-0.238177\pi$
$752$	−638.363	−	217.567i	−0.848887	−	0.289318i
$753$	−294.265	−	509.682i	−0.390790	−	0.676868i
$754$	−668.429	−	606.201i	−0.886510	−	0.803981i
$755$	−389.696			−0.516154
$756$		0			0
$757$		−	692.645i		−	0.914987i	−0.889213	−	0.457494i	$-0.848747\pi$
$757$		−	692.645i		−	0.914987i	0.889213	−	0.457494i	$-0.151253\pi$
$758$	−762.493	−	691.508i	−1.00593	−	0.912280i
$759$	−433.367	+	250.204i	−0.570971	+	0.329650i
$760$	−76.4089	+	658.861i	−0.100538	+	0.866923i
$761$	999.810	+	577.241i	1.31381	+	0.758529i	0.982725	−	0.185071i	$-0.0592516\pi$
$761$	999.810	+	577.241i	1.31381	+	0.758529i	0.331086	+	0.943601i	$0.392585\pi$
$762$	346.882	+	75.0305i	0.455226	+	0.0984652i
$763$		0			0
$764$	−509.137	−	231.063i	−0.666410	−	0.302438i
$765$	472.603	+	272.858i	0.617782	+	0.356677i
$766$	−989.933	+	317.737i	−1.29234	+	0.414800i
$767$	15.2964	+	26.4942i	0.0199432	+	0.0345426i
$768$	784.487	+	605.016i	1.02147	+	0.787781i
$769$			894.095i			1.16267i	0.813663	+	0.581336i	$0.197470\pi$
$769$			894.095i			1.16267i	−0.813663	+	0.581336i	$0.802530\pi$
$770$		0			0
$771$		−	563.723i		−	0.731158i
$772$	−74.5650	+	53.3635i	−0.0965868	+	0.0691237i
$773$	464.538	+	804.603i	0.600954	+	1.04088i	0.992677	+	0.120800i	$0.0385460\pi$
$773$	464.538	+	804.603i	0.600954	+	1.04088i	−0.391722	+	0.920083i	$0.628121\pi$
$774$	908.133	−	291.482i	1.17330	−	0.376591i
$775$	−78.4073	−	45.2685i	−0.101171	−	0.0584109i
$776$	757.844	−	1019.88i	0.976603	−	1.31427i
$777$		0			0
$778$	44.5892	−	206.145i	0.0573126	−	0.264968i
$779$	339.086	+	195.772i	0.435284	+	0.251311i
$780$	89.6458	+	915.936i	0.114930	+	1.17428i
$781$	−285.844	+	165.032i	−0.365998	+	0.211309i
$782$	256.272	+	232.414i	0.327713	+	0.297205i
$783$			415.422i			0.530552i
$784$		0			0
$785$	165.782			0.211188
$786$	−629.116	+	693.695i	−0.800402	+	0.882564i
$787$	693.013	+	1200.33i	0.880576	+	1.52520i	0.850702	+	0.525649i	$0.176177\pi$
$787$	693.013	+	1200.33i	0.880576	+	1.52520i	0.0298746	+	0.999554i	$0.490489\pi$
$788$	−1145.68	+	112.131i	−1.45390	+	0.142299i
$789$	683.794	−	1184.37i	0.866659	−	1.50110i
$790$	1250.90	+	270.569i	1.58342	+	0.342493i
$791$		0			0
$792$	416.120	−	559.998i	0.525405	−	0.707068i
$793$	−185.854	+	321.908i	−0.234368	+	0.405937i
$794$	−227.084	−	707.497i	−0.286000	−	0.891054i
$795$	−566.764	+	327.221i	−0.712910	+	0.411599i
$796$	−152.437	−	213.001i	−0.191504	−	0.267589i
$797$	−388.524			−0.487484			−0.243742	−	0.969840i	$-0.578375\pi$
$797$	−388.524			−0.487484			−0.243742	+	0.969840i	$0.578375\pi$
$798$		0			0
$799$	822.890			1.02990
$800$	−99.8137	−	1.78614i	−0.124767	−	0.00223267i
$801$	5.79682	−	3.34680i	0.00723698	−	0.00417827i
$802$	182.922	+	569.907i	0.228082	+	0.710607i
$803$	−557.421	+	965.481i	−0.694173	+	1.20234i
$804$	−260.238	+	573.424i	−0.323679	+	0.713214i
$805$		0			0
$806$	155.964	−	721.055i	0.193504	−	0.894610i
$807$	257.924	−	446.737i	0.319608	−	0.553577i
$808$	−64.1653	+	553.287i	−0.0794125	+	0.684761i
$809$	−255.112	−	441.867i	−0.315342	−	0.546189i	0.664168	−	0.747583i	$-0.268786\pi$
$809$	−255.112	−	441.867i	−0.315342	−	0.546189i	−0.979510	+	0.201395i	$0.935453\pi$
$810$	622.639	−	686.554i	0.768690	−	0.847598i
$811$	−54.8689			−0.0676558			−0.0338279	−	0.999428i	$-0.510770\pi$
$811$	−54.8689			−0.0676558			−0.0338279	+	0.999428i	$0.510770\pi$
$812$		0			0
$813$			1458.28i			1.79370i
$814$	239.541	−	264.131i	0.294277	−	0.324485i
$815$	−42.3519	+	24.4519i	−0.0519656	+	0.0300023i
$816$	−1144.16	−	389.952i	−1.40215	−	0.477882i
$817$	−1224.93	−	707.215i	−1.49931	−	0.865624i
$818$	8.61291	−	39.8193i	0.0105292	−	0.0486789i
$819$		0			0
$820$	170.811	−	376.375i	0.208306	−	0.458995i
$821$	167.045	+	96.4438i	0.203466	+	0.117471i	0.598271	−	0.801294i	$-0.295855\pi$
$821$	167.045	+	96.4438i	0.203466	+	0.117471i	−0.394805	+	0.918765i	$0.629188\pi$
$822$	343.548	+	1070.35i	0.417942	+	1.30213i
$823$	−71.3241	−	123.537i	−0.0866636	−	0.150106i	0.819435	−	0.573172i	$-0.194287\pi$
$823$	−71.3241	−	123.537i	−0.0866636	−	0.150106i	−0.906099	+	0.423066i	$0.860954\pi$
$824$	62.2973	+	144.065i	0.0756035	+	0.174836i
$825$			176.183i			0.213555i
$826$		0			0
$827$		−	91.3639i		−	0.110476i	−0.998473	−	0.0552382i	$-0.982408\pi$
$827$		−	91.3639i		−	0.110476i	0.998473	−	0.0552382i	$-0.0175918\pi$
$828$	−172.241	+	123.267i	−0.208021	+	0.148873i
$829$	232.999	+	403.567i	0.281061	+	0.486812i	0.971646	−	0.236439i	$-0.0759804\pi$
$829$	232.999	+	403.567i	0.281061	+	0.486812i	−0.690586	+	0.723251i	$0.742647\pi$
$830$	−142.938	−	445.333i	−0.172214	−	0.536545i
$831$	−261.135	−	150.766i	−0.314242	−	0.181428i
$832$	−234.702	−	778.856i	−0.282094	−	0.936125i
$833$		0			0
$834$	−653.224	−	141.292i	−0.783243	−	0.169415i
$835$	−319.557	−	184.496i	−0.382703	−	0.220954i
$836$	−1029.73	+	100.783i	−1.23174	+	0.120554i
$837$	−294.125	+	169.813i	−0.351403	+	0.202883i
$838$	245.987	−	271.238i	0.293541	−	0.323674i
$839$		−	24.9426i		−	0.0297289i	−0.999890	−	0.0148645i	$-0.995268\pi$
$839$		−	24.9426i		−	0.0297289i	0.999890	−	0.0148645i	$-0.00473168\pi$
$840$		0			0
$841$	−419.114			−0.498352
$842$	434.109	+	393.696i	0.515569	+	0.467572i
$843$	628.011	+	1087.75i	0.744972	+	1.29033i
$844$	−71.2535	+	6.97382i	−0.0844236	+	0.00826282i
$845$	−17.4280	+	30.1862i	−0.0206249	+	0.0357234i
$846$	−106.506	+	492.402i	−0.125894	+	0.582035i
$847$		0			0
$848$	435.370	−	380.867i	0.513408	−	0.449136i
$849$	579.479	−	1003.69i	0.682543	−	1.18220i
$850$	115.979	−	37.2255i	0.136446	−	0.0437947i
$851$	−93.7484	+	54.1257i	−0.110163	+	0.0636025i
$852$	−284.707	+	203.755i	−0.334163	+	0.239149i
$853$	−1642.90			−1.92603			−0.963016	−	0.269445i	$-0.913160\pi$
$853$	−1642.90			−1.92603			−0.963016	+	0.269445i	$0.913160\pi$
$854$		0			0
$855$	495.465			0.579491
$856$	142.090	+	328.589i	0.165993	+	0.383865i
$857$	130.888	−	75.5681i	0.152728	−	0.0881775i	−0.421688	−	0.906741i	$-0.638562\pi$
$857$	130.888	−	75.5681i	0.152728	−	0.0881775i	0.574416	+	0.818563i	$0.305229\pi$
$858$	−1366.92	+	438.738i	−1.59315	+	0.511350i
$859$	−450.007	+	779.435i	−0.523873	+	0.907374i	0.475741	+	0.879585i	$0.342180\pi$
$859$	−450.007	+	779.435i	−0.523873	+	0.907374i	−0.999614	+	0.0277890i	$0.991153\pi$
$860$	−617.047	+	1359.64i	−0.717497	+	1.58097i
$861$		0			0
$862$	147.043	+	31.8053i	0.170583	+	0.0368971i
$863$	−207.932	+	360.149i	−0.240941	+	0.417322i	−0.960983	−	0.276609i	$-0.910789\pi$
$863$	−207.932	+	360.149i	−0.240941	+	0.417322i	0.720042	+	0.693931i	$0.244123\pi$
$864$	−193.015	+	320.911i	−0.223397	+	0.371425i
$865$	448.683	+	777.142i	0.518709	+	0.898430i
$866$	749.943	+	680.127i	0.865986	+	0.785366i
$867$	356.496			0.411184
$868$		0			0
$869$			1996.42i			2.29737i
$870$	951.981	+	863.356i	1.09423	+	0.992363i
$871$	447.783	−	258.527i	0.514102	−	0.296817i
$872$	−449.821	−	52.1663i	−0.515850	−	0.0598238i
$873$	−821.985	−	474.573i	−0.941564	−	0.543612i
$874$	307.008	+	66.4058i	0.351268	+	0.0759791i
$875$		0			0
$876$	−488.699	+	1076.83i	−0.557876	+	1.22926i
$877$	−1488.56	−	859.419i	−1.69733	−	0.979954i	−0.948278	−	0.317442i	$-0.897176\pi$
$877$	−1488.56	−	859.419i	−1.69733	−	0.979954i	−0.749052	−	0.662511i	$-0.769491\pi$
$878$	310.833	−	99.7675i	0.354024	−	0.113630i
$879$	158.133	+	273.894i	0.179901	+	0.311598i
$880$	211.767	+	1071.48i	0.240644	+	1.21759i
$881$		−	1094.47i		−	1.24231i	−0.783689	−	0.621153i	$-0.786664\pi$
$881$		−	1094.47i		−	1.24231i	0.783689	−	0.621153i	$-0.213336\pi$
$882$		0			0
$883$			527.301i			0.597170i	0.954383	+	0.298585i	$0.0965146\pi$
$883$			527.301i			0.597170i	−0.954383	+	0.298585i	$0.903485\pi$
$884$	577.631	+	807.126i	0.653429	+	0.913039i
$885$	−21.7853	−	37.7332i	−0.0246161	−	0.0426363i
$886$	−216.534	+	69.5004i	−0.244395	+	0.0784429i
$887$	−1459.99	−	842.925i	−1.64599	−	0.950310i	−0.978645	−	0.205558i	$-0.934099\pi$
$887$	−1459.99	−	842.925i	−1.64599	−	0.950310i	−0.667341	−	0.744752i	$-0.732568\pi$
$888$	225.587	−	303.586i	0.254040	−	0.341876i
$889$		0			0
$890$	−2.21531	+	10.2419i	−0.00248912	+	0.0115077i
$891$	1252.09	+	722.896i	1.40527	+	0.811331i
$892$	−1030.97	+	100.904i	−1.15579	+	0.113121i
$893$	647.023	−	373.559i	0.724549	−	0.418319i
$894$	1254.75	+	1137.94i	1.40352	+	1.27286i
$895$		−	327.007i		−	0.365371i
$896$		0			0
$897$	435.832			0.485878
$898$	525.498	−	579.441i	0.585187	−	0.645257i
$899$	−515.099	−	892.178i	−0.572969	−	0.992412i
$900$	7.26394	+	74.2177i	0.00807104	+	0.0824641i
$901$	−352.897	+	611.236i	−0.391673	+	0.678398i
$902$	630.173	+	136.306i	0.698639	+	0.151115i
$903$		0			0
$904$	1211.26	+	900.058i	1.33989	+	0.995640i
$905$	803.700	−	1392.05i	0.888066	−	1.53818i
$906$	−197.059	−	613.953i	−0.217505	−	0.677652i
$907$	1439.38	−	831.024i	1.58696	−	0.916234i	0.593160	−	0.805085i	$-0.297880\pi$
$907$	1439.38	−	831.024i	1.58696	−	0.916234i	0.993804	−	0.111149i	$-0.0354530\pi$
$908$	381.699	−	273.168i	0.420373	−	0.300846i
$909$	416.073			0.457726
$910$		0			0
$911$	−1220.19			−1.33940			−0.669698	−	0.742633i	$-0.733577\pi$
$911$	−1220.19			−1.33940			−0.669698	+	0.742633i	$0.733577\pi$
$912$	−1076.65	+	212.789i	−1.18054	+	0.233321i
$913$	631.840	−	364.793i	0.692048	−	0.399554i
$914$	350.711	+	1092.67i	0.383710	+	1.19548i
$915$	264.694	−	458.464i	0.289283	−	0.501053i
$916$	317.238	+	143.973i	0.346330	+	0.157176i
$917$		0			0
$918$	96.5990	−	446.598i	0.105228	−	0.486490i
$919$	38.1217	−	66.0288i	0.0414817	−	0.0718485i	−0.844539	−	0.535494i	$-0.820125\pi$
$919$	38.1217	−	66.0288i	0.0414817	−	0.0718485i	0.886021	+	0.463645i	$0.153459\pi$
$920$	38.1976	−	329.372i	0.0415192	−	0.358013i
$921$	700.312	+	1212.98i	0.760382	+	1.31702i
$922$	−1138.18	+	1255.02i	−1.23447	+	1.36119i
$923$	287.471			0.311452
$924$		0			0
$925$			38.1129i			0.0412032i
$926$	146.523	−	161.564i	0.158232	−	0.174475i
$927$	101.538	−	58.6232i	0.109534	−	0.0632397i
$928$	−973.432	−	585.479i	−1.04896	−	0.630905i
$929$	−200.762	−	115.910i	−0.216106	−	0.124769i	0.388040	−	0.921643i	$-0.373152\pi$
$929$	−200.762	−	115.910i	−0.216106	−	0.124769i	−0.604146	+	0.796874i	$0.706486\pi$
$930$	−222.125	+	1026.93i	−0.238844	+	1.10423i
$931$		0			0
$932$	−1135.17	−	515.177i	−1.21799	−	0.552765i
$933$	−632.758	−	365.323i	−0.678197	−	0.391557i
$934$	−392.656	−	1223.35i	−0.420403	−	1.30980i
$935$	−666.323	−	1154.11i	−0.712645	−	1.23434i
$936$	−557.732	+	241.177i	−0.595867	+	0.257668i
$937$			985.061i			1.05129i	0.850703	+	0.525646i	$0.176176\pi$
$937$			985.061i			1.05129i	−0.850703	+	0.525646i	$0.823824\pi$
$938$		0			0
$939$			99.4088i			0.105867i
$940$	−458.993	−	641.352i	−0.488290	−	0.682290i
$941$	704.239	+	1219.78i	0.748394	+	1.29626i	0.948592	+	0.316501i	$0.102508\pi$
$941$	704.239	+	1219.78i	0.748394	+	1.29626i	−0.200198	+	0.979756i	$0.564158\pi$
$942$	83.8318	+	261.184i	0.0889934	+	0.277266i
$943$	−169.513	−	97.8683i	−0.179759	−	0.103784i
$944$	25.3568	+	28.9854i	0.0268610	+	0.0307049i
$945$		0			0
$946$	−2276.47	−	492.399i	−2.40641	−	0.520506i
$947$	144.121	+	83.2085i	0.152187	+	0.0878654i	0.574160	−	0.818743i	$-0.305329\pi$
$947$	144.121	+	83.2085i	0.152187	+	0.0878654i	−0.421972	+	0.906609i	$0.638662\pi$
$948$	206.275	+	2107.57i	0.217590	+	2.22317i
$949$	840.888	−	485.487i	0.886078	−	0.511577i
$950$	74.2931	−	81.9194i	0.0782033	−	0.0862310i
$951$		−	1931.56i		−	2.03109i
$952$		0			0
$953$	815.618			0.855843			0.427921	−	0.903816i	$-0.359246\pi$
$953$	815.618			0.855843			0.427921	+	0.903816i	$0.359246\pi$
$954$	−320.077	−	290.279i	−0.335510	−	0.304276i
$955$	−326.918	−	566.238i	−0.342322	−	0.592920i
$956$	54.8692	+	560.614i	0.0573945	+	0.586416i
$957$	−1002.37	+	1736.16i	−1.04741	+	1.81417i
$958$	179.625	−	830.445i	0.187500	−	0.866853i
$959$		0			0
$960$	334.265	+	1109.25i	0.348192	+	1.15547i
$961$	−59.3833	+	102.855i	−0.0617933	+	0.107029i
$962$	−295.701	+	94.9104i	−0.307381	+	0.0986595i
$963$	231.593	−	133.710i	0.240491	−	0.138848i
$964$	−111.943	−	156.418i	−0.116123	−	0.162260i
$965$	−107.227			−0.111116
$966$		0			0
$967$	−86.3395			−0.0892860			−0.0446430	−	0.999003i	$-0.514215\pi$
$967$	−86.3395			−0.0892860			−0.0446430	+	0.999003i	$0.514215\pi$
$968$	−675.307	+	292.020i	−0.697631	+	0.301674i
$969$	1159.68	−	669.540i	1.19678	−	0.690960i
$970$	1414.78	−	454.101i	1.45854	−	0.468145i
$971$	−339.651	+	588.292i	−0.349795	+	0.605862i	−0.986213	−	0.165482i	$-0.947082\pi$
$971$	−339.651	+	588.292i	−0.349795	+	0.605862i	0.636418	+	0.771344i	$0.280415\pi$
$972$	1012.86	+	459.667i	1.04203	+	0.472909i
$973$		0			0
$974$	−1519.33	−	328.631i	−1.55989	−	0.337403i
$975$	76.7235	−	132.889i	0.0786908	−	0.136296i
$976$	−150.950	+	442.901i	−0.154662	+	0.453792i
$977$	107.029	+	185.379i	0.109548	+	0.189743i	0.915587	−	0.402119i	$-0.131726\pi$
$977$	107.029	+	185.379i	0.109548	+	0.189743i	−0.806039	+	0.591862i	$0.798393\pi$
$978$	−59.9394	−	54.3593i	−0.0612877	−	0.0555821i
$979$	−16.3459			−0.0166965
$980$		0			0
$981$			338.267i			0.344818i
$982$	705.738	+	640.037i	0.718674	+	0.651769i
$983$	−1559.10	+	900.146i	−1.58606	+	0.915713i	−0.592114	+	0.805854i	$0.701707\pi$
$983$	−1559.10	+	900.146i	−1.58606	+	0.915713i	−0.993947	+	0.109859i	$0.964960\pi$
$984$	679.341	+	78.7840i	0.690387	+	0.0800650i
$985$	−1165.82	−	673.084i	−1.18357	−	0.683334i
$986$	1354.68	+	293.017i	1.37392	+	0.297178i
$987$		0			0
$988$	820.583	+	372.407i	0.830549	+	0.376930i
$989$	612.357	+	353.544i	0.619168	+	0.357477i
$990$	776.837	−	249.340i	0.784684	−	0.251858i
$991$	−205.714	−	356.306i	−0.207582	−	0.359542i	0.743370	−	0.668880i	$-0.233226\pi$
$991$	−205.714	−	356.306i	−0.207582	−	0.359542i	−0.950952	+	0.309338i	$0.899893\pi$
$992$	16.6158	−	928.532i	0.0167498	−	0.936020i
$993$			966.925i			0.973741i
$994$		0			0
$995$		−	306.302i		−	0.307841i
$996$	629.326	−	450.386i	0.631854	−	0.452195i
$997$	−806.000	−	1396.03i	−0.808425	−	1.40023i	−0.913954	−	0.405817i	$-0.866987\pi$
$997$	−806.000	−	1396.03i	−0.808425	−	1.40023i	0.105529	−	0.994416i	$-0.466346\pi$
$998$	−829.132	+	266.125i	−0.830793	+	0.266658i
$999$	123.816	+	71.4854i	0.123940	+	0.0715569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.j.e.117.11		28
7.2	even	3		392.3.h.a.293.1		28
7.3	odd	6	inner	392.3.j.e.325.9		28
7.4	even	3		56.3.j.a.45.9	yes	28
7.5	odd	6		392.3.h.a.293.2		28
7.6	odd	2		56.3.j.a.5.11	yes	28
8.5	even	2	inner	392.3.j.e.117.9		28
28.11	odd	6		224.3.n.a.17.3		28
28.19	even	6		1568.3.h.a.881.6		28
28.23	odd	6		1568.3.h.a.881.24		28
28.27	even	2		224.3.n.a.145.12		28
56.5	odd	6		392.3.h.a.293.3		28
56.11	odd	6		224.3.n.a.17.12		28
56.13	odd	2		56.3.j.a.5.9	✓	28
56.19	even	6		1568.3.h.a.881.23		28
56.27	even	2		224.3.n.a.145.3		28
56.37	even	6		392.3.h.a.293.4		28
56.45	odd	6	inner	392.3.j.e.325.11		28
56.51	odd	6		1568.3.h.a.881.5		28
56.53	even	6		56.3.j.a.45.11	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.9	✓	28	56.13	odd	2
56.3.j.a.5.11	yes	28	7.6	odd	2
56.3.j.a.45.9	yes	28	7.4	even	3
56.3.j.a.45.11	yes	28	56.53	even	6
224.3.n.a.17.3		28	28.11	odd	6
224.3.n.a.17.12		28	56.11	odd	6
224.3.n.a.145.3		28	56.27	even	2
224.3.n.a.145.12		28	28.27	even	2
392.3.h.a.293.1		28	7.2	even	3
392.3.h.a.293.2		28	7.5	odd	6
392.3.h.a.293.3		28	56.5	odd	6
392.3.h.a.293.4		28	56.37	even	6
392.3.j.e.117.9		28	8.5	even	2	inner
392.3.j.e.117.11		28	1.1	even	1	trivial
392.3.j.e.325.9		28	7.3	odd	6	inner
392.3.j.e.325.11		28	56.45	odd	6	inner
1568.3.h.a.881.5		28	56.51	odd	6
1568.3.h.a.881.6		28	28.19	even	6
1568.3.h.a.881.23		28	56.19	even	6
1568.3.h.a.881.24		28	28.23	odd	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)

\(f(q)\)	\(=\)	\(q+(1.34357 - 1.48149i) q^{2} +(1.93494 + 3.35141i) q^{3} +(-0.389632 - 3.98098i) q^{4} +(2.33882 - 4.05096i) q^{5} +(7.56482 + 1.63627i) q^{6} +(-6.42128 - 4.77149i) q^{8} +(-2.98798 + 5.17534i) q^{9} +O(q^{10})\)	\(q+(1.34357 - 1.48149i) q^{2} +(1.93494 + 3.35141i) q^{3} +(-0.389632 - 3.98098i) q^{4} +(2.33882 - 4.05096i) q^{5} +(7.56482 + 1.63627i) q^{6} +(-6.42128 - 4.77149i) q^{8} +(-2.98798 + 5.17534i) q^{9} +(-2.85908 - 8.90769i) q^{10} +(12.6383 - 7.29671i) q^{11} +(12.5880 - 9.00877i) q^{12} -12.7102 q^{13} +18.1019 q^{15} +(-15.6964 + 3.10223i) q^{16} +(16.9068 - 9.76116i) q^{17} +(3.65265 + 11.3801i) q^{18} +(8.86233 - 15.3500i) q^{19} +(-17.0380 - 7.73241i) q^{20} +(6.17041 - 28.5271i) q^{22} +(-4.43038 + 7.67364i) q^{23} +(3.56645 - 30.7529i) q^{24} +(1.55984 + 2.70172i) q^{25} +(-17.0770 + 18.8300i) q^{26} +11.7027 q^{27} +35.4981i q^{29} +(24.3212 - 26.8178i) q^{30} +(-25.1331 + 14.5106i) q^{31} +(-16.4933 + 27.4221i) q^{32} +(48.9086 + 28.2374i) q^{33} +(8.25445 - 38.1621i) q^{34} +(21.7671 + 9.87861i) q^{36} +(10.5802 + 6.10847i) q^{37} +(-10.8337 - 33.7533i) q^{38} +(-24.5934 - 42.5970i) q^{39} +(-34.3473 + 14.8527i) q^{40} +22.0903i q^{41} -79.8001i q^{43} +(-33.9723 - 47.4696i) q^{44} +(13.9767 + 24.2084i) q^{45} +(5.41590 + 16.8736i) q^{46} +(36.5041 + 21.0756i) q^{47} +(-40.7684 - 46.6024i) q^{48} +(6.09833 + 1.31907i) q^{50} +(65.4273 + 37.7745i) q^{51} +(4.95229 + 50.5989i) q^{52} +(-31.3096 + 18.0766i) q^{53} +(15.7234 - 17.3374i) q^{54} -68.2627i q^{55} +68.5923 q^{57} +(52.5901 + 47.6942i) q^{58} +(-1.20348 - 2.08449i) q^{59} +(-7.05308 - 72.0633i) q^{60} +(14.6224 - 25.3268i) q^{61} +(-12.2708 + 56.7306i) q^{62} +(18.4657 + 61.2782i) q^{64} +(-29.7268 + 51.4883i) q^{65} +(107.546 - 34.5187i) q^{66} +(-35.2303 + 20.3402i) q^{67} +(-45.4464 - 63.5024i) q^{68} -34.2900 q^{69} -22.6174 q^{71} +(43.8807 - 18.9752i) q^{72} +(-66.1587 + 38.1967i) q^{73} +(23.2649 - 7.46728i) q^{74} +(-6.03639 + 10.4553i) q^{75} +(-64.5611 - 29.2999i) q^{76} +(-96.1501 - 20.7972i) q^{78} +(-68.4014 + 118.475i) q^{79} +(-24.1440 + 70.8409i) q^{80} +(49.5358 + 85.7985i) q^{81} +(32.7266 + 29.6799i) q^{82} +49.9942 q^{83} -91.3184i q^{85} +(-118.223 - 107.217i) q^{86} +(-118.969 + 68.6866i) q^{87} +(-115.970 - 13.4492i) q^{88} +(-0.970023 - 0.560043i) q^{89} +(54.6432 + 11.8193i) q^{90} +(32.2748 + 14.6473i) q^{92} +(-97.2622 - 56.1544i) q^{93} +(80.2692 - 25.7638i) q^{94} +(-41.4548 - 71.8018i) q^{95} +(-123.816 - 2.21566i) q^{96} +158.827i q^{97} +87.2097i 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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