LMFDB - Embedded newform 210.3.p.a.19.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(19,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, 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("210.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.14
Character	$\chi$	$=$	210.19
Dual form			210.3.p.a.199.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 + 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.34637 - 4.81532i) q^{5} +2.44949i q^{6} +(-0.180689 + 6.99767i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.22474 + 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.34637 - 4.81532i) q^{5} +2.44949i q^{6} +(-0.180689 + 6.99767i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(5.05390 - 4.94551i) q^{10} +(7.49865 + 12.9880i) q^{11} +(-1.73205 + 3.00000i) q^{12} +12.8932 q^{13} +(-5.16940 + 8.44259i) q^{14} +(8.38897 - 2.15064i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-10.9423 - 18.9526i) q^{17} +(-3.67423 + 2.12132i) q^{18} +(19.7051 + 11.3768i) q^{19} +(9.68674 - 2.48334i) q^{20} +(-10.6530 + 5.78912i) q^{21} +21.2094i q^{22} +(-19.3327 - 11.1617i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(-21.3746 - 12.9664i) q^{25} +(15.7909 + 9.11687i) q^{26} -5.19615 q^{27} +(-12.3010 + 6.68471i) q^{28} +24.4662 q^{29} +(11.7951 + 3.29792i) q^{30} +(-23.0583 + 13.3127i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(-12.9880 + 22.4960i) q^{33} -30.9495i q^{34} +(33.4527 + 10.2915i) q^{35} -6.00000 q^{36} +(-45.3718 - 26.1954i) q^{37} +(16.0892 + 27.8673i) q^{38} +(11.1658 + 19.3398i) q^{39} +(13.6198 + 3.80811i) q^{40} -25.5228i q^{41} +(-17.1407 - 0.442596i) q^{42} -30.7736i q^{43} +(-14.9973 + 25.9761i) q^{44} +(10.4910 + 10.7209i) q^{45} +(-15.7851 - 27.3406i) q^{46} +(30.3981 - 52.6511i) q^{47} -6.92820 q^{48} +(-48.9347 - 2.52880i) q^{49} +(-17.0098 - 30.9946i) q^{50} +(18.9526 - 32.8269i) q^{51} +(12.8932 + 22.3317i) q^{52} +(86.4900 - 49.9350i) q^{53} +(-6.36396 - 3.67423i) q^{54} +(72.6375 - 18.6217i) q^{55} +(-19.7924 - 0.511065i) q^{56} +39.4103i q^{57} +(29.9648 + 17.3002i) q^{58} +(-1.24114 + 0.716573i) q^{59} +(12.1140 + 12.3795i) q^{60} +(6.52416 + 3.76672i) q^{61} -37.6540 q^{62} +(-17.9094 - 10.9659i) q^{63} -8.00000 q^{64} +(17.3590 - 62.0849i) q^{65} +(-31.8141 + 18.3679i) q^{66} +(-98.9190 + 57.1109i) q^{67} +(21.8846 - 37.9052i) q^{68} -38.6654i q^{69} +(33.6939 + 36.2591i) q^{70} -114.316 q^{71} +(-7.34847 - 4.24264i) q^{72} +(11.6101 + 20.1092i) q^{73} +(-37.0459 - 64.1654i) q^{74} +(0.938646 - 43.2911i) q^{75} +45.5071i q^{76} +(-92.2409 + 50.1263i) q^{77} +31.5818i q^{78} +(31.4174 - 54.4165i) q^{79} +(13.9880 + 14.2946i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(18.0473 - 31.2589i) q^{82} +120.767 q^{83} +(-20.6800 - 12.6624i) q^{84} +(-105.995 + 27.1734i) q^{85} +(21.7603 - 37.6899i) q^{86} +(21.1883 + 36.6993i) q^{87} +(-36.7357 + 21.2094i) q^{88} +(43.5201 + 25.1263i) q^{89} +(5.26796 + 20.5487i) q^{90} +(-2.32966 + 90.2224i) q^{91} -44.6470i q^{92} +(-39.9381 - 23.0583i) q^{93} +(74.4599 - 42.9895i) q^{94} +(81.3132 - 79.5692i) q^{95} +(-8.48528 - 4.89898i) q^{96} -46.0549 q^{97} +(-58.1444 - 37.6992i) q^{98} -44.9919 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} + 12 q^{5} - 48 q^{9}+O(q^{10}) $ 32 * q + 32 * q^4 + 12 * q^5 - 48 * q^9	$ 32 q + 32 q^{4} + 12 q^{5} - 48 q^{9} - 24 q^{10} + 48 q^{11} - 16 q^{14} + 24 q^{15} - 64 q^{16} + 48 q^{19} - 24 q^{21} + 72 q^{25} + 96 q^{26} + 176 q^{29} - 24 q^{30} - 48 q^{31} + 68 q^{35} - 192 q^{36} - 72 q^{39} - 48 q^{40} - 96 q^{44} - 36 q^{45} + 32 q^{46} - 272 q^{49} + 192 q^{50} - 24 q^{51} - 64 q^{56} + 744 q^{59} + 24 q^{60} - 672 q^{61} - 256 q^{64} + 172 q^{65} + 320 q^{70} - 144 q^{71} - 416 q^{74} - 144 q^{75} + 128 q^{79} - 48 q^{80} - 144 q^{81} - 96 q^{84} - 736 q^{85} + 304 q^{86} - 48 q^{89} + 976 q^{91} + 528 q^{94} + 236 q^{95} - 288 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 + 12 * q^5 - 48 * q^9 - 24 * q^10 + 48 * q^11 - 16 * q^14 + 24 * q^15 - 64 * q^16 + 48 * q^19 - 24 * q^21 + 72 * q^25 + 96 * q^26 + 176 * q^29 - 24 * q^30 - 48 * q^31 + 68 * q^35 - 192 * q^36 - 72 * q^39 - 48 * q^40 - 96 * q^44 - 36 * q^45 + 32 * q^46 - 272 * q^49 + 192 * q^50 - 24 * q^51 - 64 * q^56 + 744 * q^59 + 24 * q^60 - 672 * q^61 - 256 * q^64 + 172 * q^65 + 320 * q^70 - 144 * q^71 - 416 * q^74 - 144 * q^75 + 128 * q^79 - 48 * q^80 - 144 * q^81 - 96 * q^84 - 736 * q^85 + 304 * q^86 - 48 * q^89 + 976 * q^91 + 528 * q^94 + 236 * q^95 - 288 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	1.34637	−	4.81532i	0.269274	−	0.963064i
$5$	1.34637	−	4.81532i	0.269274	−	0.963064i
$6$			2.44949i			0.408248i
$7$	−0.180689	+	6.99767i	−0.0258127	+	0.999667i
$7$	−0.180689	+	6.99767i	−0.0258127	+	0.999667i
$8$			2.82843i			0.353553i
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$	5.05390	−	4.94551i	0.505390	−	0.494551i
$11$	7.49865	+	12.9880i	0.681696	+	1.18073i	0.974463	+	0.224548i	$0.0720904\pi$
$11$	7.49865	+	12.9880i	0.681696	+	1.18073i	−0.292768	+	0.956184i	$0.594576\pi$
$12$	−1.73205	+	3.00000i	−0.144338	+	0.250000i
$13$	12.8932			0.991785			0.495893	−	0.868384i	$-0.334841\pi$
$13$	12.8932			0.991785			0.495893	+	0.868384i	$0.334841\pi$
$14$	−5.16940	+	8.44259i	−0.369243	+	0.603042i
$15$	8.38897	−	2.15064i	0.559264	−	0.143376i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−10.9423	−	18.9526i	−0.643664	−	1.11486i	−0.984608	−	0.174775i	$-0.944080\pi$
$17$	−10.9423	−	18.9526i	−0.643664	−	1.11486i	0.340944	−	0.940083i	$-0.389253\pi$
$18$	−3.67423	+	2.12132i	−0.204124	+	0.117851i
$19$	19.7051	+	11.3768i	1.03711	+	0.598778i	0.919014	−	0.394224i	$-0.128987\pi$
$19$	19.7051	+	11.3768i	1.03711	+	0.598778i	0.118099	+	0.993002i	$0.462320\pi$
$20$	9.68674	−	2.48334i	0.484337	−	0.124167i
$21$	−10.6530	+	5.78912i	−0.507285	+	0.275673i
$22$			21.2094i			0.964063i
$23$	−19.3327	−	11.1617i	−0.840553	−	0.485293i	0.0168995	−	0.999857i	$-0.494620\pi$
$23$	−19.3327	−	11.1617i	−0.840553	−	0.485293i	−0.857452	+	0.514564i	$0.827954\pi$
$24$	−4.24264	+	2.44949i	−0.176777	+	0.102062i
$25$	−21.3746	−	12.9664i	−0.854983	−	0.518655i
$26$	15.7909	+	9.11687i	0.607342	+	0.350649i
$27$	−5.19615			−0.192450
$28$	−12.3010	+	6.68471i	−0.439322	+	0.238739i
$29$	24.4662			0.843661			0.421831	−	0.906675i	$-0.361388\pi$
$29$	24.4662			0.843661			0.421831	+	0.906675i	$0.361388\pi$
$30$	11.7951	+	3.29792i	0.393169	+	0.109931i
$31$	−23.0583	+	13.3127i	−0.743816	+	0.429442i	−0.823455	−	0.567381i	$-0.807957\pi$
$31$	−23.0583	+	13.3127i	−0.743816	+	0.429442i	0.0796391	+	0.996824i	$0.474623\pi$
$32$	−4.89898	+	2.82843i	−0.153093	+	0.0883883i
$33$	−12.9880	+	22.4960i	−0.393577	+	0.681696i
$34$		−	30.9495i		−	0.910278i
$35$	33.4527	+	10.2915i	0.955792	+	0.294043i
$36$	−6.00000			−0.166667
$37$	−45.3718	−	26.1954i	−1.22627	−	0.707985i	−0.260019	−	0.965604i	$-0.583729\pi$
$37$	−45.3718	−	26.1954i	−1.22627	−	0.707985i	−0.966247	+	0.257619i	$0.917062\pi$
$38$	16.0892	+	27.8673i	0.423400	+	0.733350i
$39$	11.1658	+	19.3398i	0.286304	+	0.495893i
$40$	13.6198	+	3.80811i	0.340494	+	0.0952026i
$41$		−	25.5228i		−	0.622507i	−0.950327	−	0.311254i	$-0.899251\pi$
$41$		−	25.5228i		−	0.622507i	0.950327	−	0.311254i	$-0.100749\pi$
$42$	−17.1407	−	0.442596i	−0.408112	−	0.0105380i
$43$		−	30.7736i		−	0.715666i	−0.933786	−	0.357833i	$-0.883516\pi$
$43$		−	30.7736i		−	0.715666i	0.933786	−	0.357833i	$-0.116484\pi$
$44$	−14.9973	+	25.9761i	−0.340848	+	0.590366i
$45$	10.4910	+	10.7209i	0.233134	+	0.238243i
$46$	−15.7851	−	27.3406i	−0.343154	−	0.594360i
$47$	30.3981	−	52.6511i	0.646769	−	1.12024i	−0.337121	−	0.941461i	$-0.609453\pi$
$47$	30.3981	−	52.6511i	0.646769	−	1.12024i	0.983890	−	0.178775i	$-0.0572135\pi$
$48$	−6.92820			−0.144338
$49$	−48.9347	−	2.52880i	−0.998667	−	0.0516082i
$50$	−17.0098	−	30.9946i	−0.340196	−	0.619893i
$51$	18.9526	−	32.8269i	0.371620	−	0.643664i
$52$	12.8932	+	22.3317i	0.247946	+	0.429456i
$53$	86.4900	−	49.9350i	1.63189	−	0.942170i	0.648375	−	0.761321i	$-0.275449\pi$
$53$	86.4900	−	49.9350i	1.63189	−	0.942170i	0.983511	−	0.180849i	$-0.0578845\pi$
$54$	−6.36396	−	3.67423i	−0.117851	−	0.0680414i
$55$	72.6375	−	18.6217i	1.32068	−	0.338576i
$56$	−19.7924	−	0.511065i	−0.353436	−	0.00912617i
$57$			39.4103i			0.691409i
$58$	29.9648	+	17.3002i	0.516635	+	0.298279i
$59$	−1.24114	+	0.716573i	−0.0210363	+	0.0121453i	−0.510481	−	0.859889i	$-0.670533\pi$
$59$	−1.24114	+	0.716573i	−0.0210363	+	0.0121453i	0.489445	+	0.872034i	$0.337199\pi$
$60$	12.1140	+	12.3795i	0.201900	+	0.206325i
$61$	6.52416	+	3.76672i	0.106953	+	0.0617496i	0.552523	−	0.833498i	$-0.313665\pi$
$61$	6.52416	+	3.76672i	0.106953	+	0.0617496i	−0.445569	+	0.895248i	$0.646999\pi$
$62$	−37.6540			−0.607323
$63$	−17.9094	−	10.9659i	−0.284277	−	0.174063i
$64$	−8.00000			−0.125000
$65$	17.3590	−	62.0849i	0.267062	−	0.955152i
$66$	−31.8141	+	18.3679i	−0.482032	+	0.278301i
$67$	−98.9190	+	57.1109i	−1.47640	+	0.852402i	−0.999645	−	0.0266333i	$-0.991521\pi$
$67$	−98.9190	+	57.1109i	−1.47640	+	0.852402i	−0.476758	+	0.879035i	$0.658188\pi$
$68$	21.8846	−	37.9052i	0.321832	−	0.557429i
$69$		−	38.6654i		−	0.560368i
$70$	33.6939	+	36.2591i	0.481341	+	0.517988i
$71$	−114.316			−1.61008			−0.805042	−	0.593218i	$-0.797857\pi$
$71$	−114.316			−1.61008			−0.805042	+	0.593218i	$0.797857\pi$
$72$	−7.34847	−	4.24264i	−0.102062	−	0.0589256i
$73$	11.6101	+	20.1092i	0.159042	+	0.275469i	0.934524	−	0.355901i	$-0.115826\pi$
$73$	11.6101	+	20.1092i	0.159042	+	0.275469i	−0.775481	+	0.631370i	$0.782493\pi$
$74$	−37.0459	−	64.1654i	−0.500621	−	0.867101i
$75$	0.938646	−	43.2911i	0.0125153	−	0.577215i
$76$			45.5071i			0.598778i
$77$	−92.2409	+	50.1263i	−1.19793	+	0.650991i
$78$			31.5818i			0.404895i
$79$	31.4174	−	54.4165i	0.397688	−	0.688816i	−0.595752	−	0.803168i	$-0.703146\pi$
$79$	31.4174	−	54.4165i	0.397688	−	0.688816i	0.993440	+	0.114352i	$0.0364793\pi$
$80$	13.9880	+	14.2946i	0.174850	+	0.178682i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	18.0473	−	31.2589i	0.220090	−	0.381206i
$83$	120.767			1.45502			0.727512	−	0.686095i	$-0.240677\pi$
$83$	120.767			1.45502			0.727512	+	0.686095i	$0.240677\pi$
$84$	−20.6800	−	12.6624i	−0.246191	−	0.150743i
$85$	−105.995	+	27.1734i	−1.24700	+	0.319687i
$86$	21.7603	−	37.6899i	0.253026	−	0.438254i
$87$	21.1883	+	36.6993i	0.243544	+	0.421831i
$88$	−36.7357	+	21.2094i	−0.417452	+	0.241016i
$89$	43.5201	+	25.1263i	0.488990	+	0.282319i	0.724155	−	0.689637i	$-0.242230\pi$
$89$	43.5201	+	25.1263i	0.488990	+	0.282319i	−0.235165	+	0.971955i	$0.575563\pi$
$90$	5.26796	+	20.5487i	0.0585329	+	0.228319i
$91$	−2.32966	+	90.2224i	−0.0256007	+	0.991455i
$92$		−	44.6470i		−	0.485293i
$93$	−39.9381	−	23.0583i	−0.429442	−	0.247939i
$94$	74.4599	−	42.9895i	0.792127	−	0.457335i
$95$	81.3132	−	79.5692i	0.855928	−	0.837571i
$96$	−8.48528	−	4.89898i	−0.0883883	−	0.0510310i
$97$	−46.0549			−0.474793			−0.237397	−	0.971413i	$-0.576294\pi$
$97$	−46.0549			−0.474793			−0.237397	+	0.971413i	$0.576294\pi$
$98$	−58.1444	−	37.6992i	−0.593310	−	0.384686i
$99$	−44.9919			−0.454464
$100$	1.08386	−	49.9883i	0.0108386	−	0.499883i
$101$	14.6707	−	8.47013i	0.145254	−	0.0838626i	−0.425611	−	0.904906i	$-0.639941\pi$
$101$	14.6707	−	8.47013i	0.145254	−	0.0838626i	0.570866	+	0.821043i	$0.306608\pi$
$102$	46.4242	−	26.8030i	0.455139	−	0.262775i
$103$	44.5416	−	77.1483i	0.432442	−	0.749012i	−0.564641	−	0.825337i	$-0.690985\pi$
$103$	44.5416	−	77.1483i	0.432442	−	0.749012i	0.997083	+	0.0763247i	$0.0243186\pi$
$104$			36.4675i			0.350649i
$105$	13.5336	+	59.0918i	0.128892	+	0.562779i
$106$	141.238			1.33243
$107$	−75.8211	−	43.7753i	−0.708608	−	0.409115i	0.101937	−	0.994791i	$-0.467496\pi$
$107$	−75.8211	−	43.7753i	−0.708608	−	0.409115i	−0.810545	+	0.585676i	$0.800829\pi$
$108$	−5.19615	−	9.00000i	−0.0481125	−	0.0833333i
$109$	44.7266	+	77.4687i	0.410336	+	0.710722i	0.994926	−	0.100606i	$-0.0320782\pi$
$109$	44.7266	+	77.4687i	0.410336	+	0.710722i	−0.584591	+	0.811328i	$0.698745\pi$
$110$	102.130	+	28.5557i	0.928454	+	0.259597i
$111$		−	90.7436i		−	0.817510i
$112$	−23.8793	−	14.6213i	−0.213208	−	0.130547i
$113$			19.7472i			0.174754i	0.996175	+	0.0873768i	$0.0278484\pi$
$113$			19.7472i			0.174754i	−0.996175	+	0.0873768i	$0.972152\pi$
$114$	−27.8673	+	48.2676i	−0.244450	+	0.423400i
$115$	−79.7763	+	78.0653i	−0.693707	+	0.678829i
$116$	24.4662	+	42.3767i	0.210915	+	0.365316i
$117$	−19.3398	+	33.4975i	−0.165298	+	0.286304i
$118$	−2.02677			−0.0171761
$119$	134.601	−	73.1460i	1.13110	−	0.614672i
$120$	6.08292	+	23.7276i	0.0506910	+	0.197730i
$121$	−51.9595	+	89.9965i	−0.429418	+	0.743773i
$122$	5.32695	+	9.22655i	0.0436636	+	0.0756275i
$123$	38.2842	−	22.1034i	0.311254	−	0.179702i
$124$	−46.1166	−	26.6254i	−0.371908	−	0.214721i
$125$	−91.2153	+	85.4679i	−0.729723	+	0.683743i
$126$	−14.1804	−	26.0944i	−0.112543	−	0.207098i
$127$			34.8063i			0.274066i	0.990567	+	0.137033i	$0.0437566\pi$
$127$			34.8063i			0.274066i	−0.990567	+	0.137033i	$0.956243\pi$
$128$	−9.79796	−	5.65685i	−0.0765466	−	0.0441942i
$129$	46.1605	−	26.6508i	0.357833	−	0.206595i
$130$	65.1610	−	63.7635i	0.501239	−	0.490488i
$131$	−31.3118	−	18.0779i	−0.239022	−	0.137999i	0.375705	−	0.926739i	$-0.377400\pi$
$131$	−31.3118	−	18.0779i	−0.239022	−	0.137999i	−0.614727	+	0.788740i	$0.710734\pi$
$132$	−51.9522			−0.393577
$133$	−83.1714	+	135.834i	−0.625349	+	1.02131i
$134$	−161.534			−1.20548
$135$	−6.99594	+	25.0211i	−0.0518217	+	0.185342i
$136$	53.6060	−	30.9495i	0.394162	−	0.227570i
$137$	−152.235	+	87.8927i	−1.11120	+	0.641552i	−0.939140	−	0.343534i	$-0.888376\pi$
$137$	−152.235	+	87.8927i	−1.11120	+	0.641552i	−0.172061	+	0.985086i	$0.555043\pi$
$138$	27.3406	−	47.3553i	0.198120	−	0.343154i
$139$			82.2676i			0.591853i	0.955211	+	0.295927i	$0.0956284\pi$
$139$			82.2676i			0.591853i	−0.955211	+	0.295927i	$0.904372\pi$
$140$	15.6273	+	68.2333i	0.111624	+	0.487381i
$141$	105.302			0.746824
$142$	−140.008	−	80.8336i	−0.985971	−	0.569250i
$143$	96.6817	+	167.458i	0.676096	+	1.17103i
$144$	−6.00000	−	10.3923i	−0.0416667	−	0.0721688i
$145$	32.9405	−	117.812i	0.227176	−	0.812499i
$146$			32.8382i			0.224919i
$147$	−38.5855	−	75.5921i	−0.262486	−	0.514232i
$148$		−	104.782i		−	0.707985i
$149$	13.7035	−	23.7351i	0.0919697	−	0.159296i	−0.816370	−	0.577529i	$-0.804017\pi$
$149$	13.7035	−	23.7351i	0.0919697	−	0.159296i	0.908340	+	0.418233i	$0.137350\pi$
$150$	31.7610	−	52.3568i	0.211740	−	0.349045i
$151$	110.576	+	191.523i	0.732292	+	1.26837i	0.955901	+	0.293688i	$0.0948827\pi$
$151$	110.576	+	191.523i	0.732292	+	1.26837i	−0.223609	+	0.974679i	$0.571784\pi$
$152$	−32.1784	+	55.7346i	−0.211700	+	0.366675i
$153$	65.6537			0.429109
$154$	−148.416	−	3.83230i	−0.963742	−	0.0248851i
$155$	33.0600	+	128.957i	0.213290	+	0.831980i
$156$	−22.3317	+	38.6796i	−0.143152	+	0.247946i
$157$	131.430	+	227.644i	0.837135	+	1.44996i	0.892280	+	0.451482i	$0.149104\pi$
$157$	131.430	+	227.644i	0.837135	+	1.44996i	−0.0551455	+	0.998478i	$0.517562\pi$
$158$	76.9565	−	44.4309i	0.487066	−	0.281208i
$159$	149.805	+	86.4900i	0.942170	+	0.543962i
$160$	7.02395	+	27.3983i	0.0438997	+	0.171239i
$161$	81.5994	−	133.267i	0.506828	−	0.827746i
$162$		−	12.7279i		−	0.0785674i
$163$	−176.234	−	101.749i	−1.08119	−	0.624225i	−0.149972	−	0.988690i	$-0.547918\pi$
$163$	−176.234	−	101.749i	−1.08119	−	0.624225i	−0.931217	+	0.364466i	$0.881252\pi$
$164$	44.2068	−	25.5228i	0.269553	−	0.155627i
$165$	90.8385	+	92.8294i	0.550536	+	0.562602i
$166$	147.909	+	85.3951i	0.891016	+	0.514428i
$167$	0.444753			0.00266319			0.00133160	−	0.999999i	$-0.499576\pi$
$167$	0.444753			0.00266319			0.00133160	+	0.999999i	$0.499576\pi$
$168$	−16.3741	−	30.1312i	−0.0974650	−	0.179352i
$169$	−2.76518			−0.0163620
$170$	−149.032	−	41.6694i	−0.876656	−	0.245114i
$171$	−59.1154	+	34.1303i	−0.345704	+	0.199593i
$172$	53.3015	−	30.7736i	0.309893	−	0.178917i
$173$	−50.7233	+	87.8553i	−0.293198	+	0.507834i	−0.974564	−	0.224109i	$-0.928053\pi$
$173$	−50.7233	+	87.8553i	−0.293198	+	0.507834i	0.681366	+	0.731943i	$0.261386\pi$
$174$			59.9296i			0.344423i
$175$	94.5966	−	147.229i	0.540552	−	0.841311i
$176$	−59.9892			−0.340848
$177$	−2.14972	−	1.24114i	−0.0121453	−	0.00701210i
$178$	35.5340	+	61.5467i	0.199629	+	0.345768i
$179$	86.6390	+	150.063i	0.484017	+	0.838342i	0.999831	−	0.0183584i	$-0.00584400\pi$
$179$	86.6390	+	150.063i	0.484017	+	0.838342i	−0.515815	+	0.856700i	$0.672511\pi$
$180$	−8.07821	+	28.8919i	−0.0448789	+	0.160511i
$181$		−	222.765i		−	1.23075i	−0.788236	−	0.615373i	$-0.789005\pi$
$181$		−	222.765i		−	1.23075i	0.788236	−	0.615373i	$-0.210995\pi$
$182$	−66.6501	+	108.852i	−0.366209	+	0.598088i
$183$			13.0483i			0.0713023i
$184$	31.5702	−	54.6812i	0.171577	−	0.297180i
$185$	−187.227	+	183.211i	−1.01204	+	0.990330i
$186$	−32.6094	−	56.4811i	−0.175319	−	0.303662i
$187$	164.105	−	284.238i	0.877566	−	1.51999i
$188$	121.593			0.646769
$189$	0.938887	−	36.3609i	0.00496766	−	0.192386i
$190$	155.852	−	39.9549i	0.820273	−	0.210289i
$191$	54.8736	−	95.0438i	0.287296	−	0.497611i	−0.685867	−	0.727727i	$-0.740577\pi$
$191$	54.8736	−	95.0438i	0.287296	−	0.497611i	0.973163	+	0.230115i	$0.0739103\pi$
$192$	−6.92820	−	12.0000i	−0.0360844	−	0.0625000i
$193$	−151.207	+	87.2991i	−0.783453	+	0.452327i	−0.837653	−	0.546203i	$-0.816073\pi$
$193$	−151.207	+	87.2991i	−0.783453	+	0.452327i	0.0541993	+	0.998530i	$0.482739\pi$
$194$	−56.4055	−	32.5658i	−0.290750	−	0.167865i
$195$	108.161	−	27.7286i	0.554670	−	0.142198i
$196$	−44.5547	−	87.2862i	−0.227320	−	0.445338i
$197$			158.798i			0.806081i	0.915182	+	0.403041i	$0.132047\pi$
$197$			158.798i			0.806081i	−0.915182	+	0.403041i	$0.867953\pi$
$198$	−55.1036	−	31.8141i	−0.278301	−	0.160677i
$199$	−30.5042	+	17.6116i	−0.153288	+	0.0885006i	−0.574682	−	0.818377i	$-0.694874\pi$
$199$	−30.5042	+	17.6116i	−0.153288	+	0.0885006i	0.421394	+	0.906878i	$0.361541\pi$
$200$	36.6745	−	60.4565i	0.183372	−	0.302282i
$201$	−171.333	−	98.9190i	−0.852402	−	0.492134i
$202$	23.9571			0.118600
$203$	−4.42077	+	171.206i	−0.0217772	+	0.843380i
$204$	75.8104			0.371620
$205$	−122.900	−	34.3631i	−0.599514	−	0.167625i
$206$	109.104	−	62.9913i	0.529632	−	0.305783i
$207$	57.9981	−	33.4852i	0.280184	−	0.161764i
$208$	−25.7864	+	44.6634i	−0.123973	+	0.214728i
$209$			341.242i			1.63274i
$210$	−25.2090	+	81.9421i	−0.120043	+	0.390200i
$211$	324.375			1.53732			0.768661	−	0.639656i	$-0.220923\pi$
$211$	324.375			1.53732			0.768661	+	0.639656i	$0.220923\pi$
$212$	172.980	+	99.8700i	0.815943	+	0.471085i
$213$	−99.0005	−	171.474i	−0.464791	−	0.805042i
$214$	−61.9076	−	107.227i	−0.289288	−	0.501062i
$215$	−148.185	−	41.4327i	−0.689232	−	0.192710i
$216$		−	14.6969i		−	0.0680414i
$217$	−88.9916	−	163.760i	−0.410099	−	0.754653i
$218$			126.506i			0.580302i
$219$	−20.1092	+	34.8302i	−0.0918230	+	0.159042i
$220$	104.891	+	107.190i	0.476778	+	0.487228i
$221$	−141.081	−	244.360i	−0.638376	−	1.10570i
$222$	64.1654	−	111.138i	0.289034	−	0.500621i
$223$	257.743			1.15580			0.577898	−	0.816109i	$-0.303873\pi$
$223$	257.743			1.15580			0.577898	+	0.816109i	$0.303873\pi$
$224$	−18.9072	−	34.7925i	−0.0844071	−	0.155324i
$225$	65.7495	−	36.0832i	0.292220	−	0.160370i
$226$	−13.9633	+	24.1852i	−0.0617847	+	0.107014i
$227$	−154.997	−	268.463i	−0.682808	−	1.18266i	−0.974120	−	0.226030i	$-0.927425\pi$
$227$	−154.997	−	268.463i	−0.682808	−	1.18266i	0.291313	−	0.956628i	$-0.405908\pi$
$228$	−68.2606	+	39.4103i	−0.299389	+	0.172852i
$229$	−258.200	−	149.072i	−1.12751	−	0.650968i	−0.184203	−	0.982888i	$-0.558970\pi$
$229$	−258.200	−	149.072i	−1.12751	−	0.650968i	−0.943308	+	0.331920i	$0.892304\pi$
$230$	−152.906	+	39.1997i	−0.664809	+	0.170434i
$231$	−155.072	−	94.9508i	−0.671309	−	0.411042i
$232$			69.2008i			0.298279i
$233$	83.6641	+	48.3035i	0.359073	+	0.207311i	0.668674	−	0.743556i	$-0.266862\pi$
$233$	83.6641	+	48.3035i	0.359073	+	0.207311i	−0.309601	+	0.950867i	$0.600195\pi$
$234$	−47.3727	+	27.3506i	−0.202447	+	0.116883i
$235$	−212.605	−	217.265i	−0.904701	−	0.924530i
$236$	−2.48228	−	1.43315i	−0.0105181	−	0.00607265i
$237$	108.833			0.459211
$238$	216.574	+	5.59222i	0.909975	+	0.0234967i
$239$	−314.484			−1.31583			−0.657916	−	0.753092i	$-0.728562\pi$
$239$	−314.484			−1.31583			−0.657916	+	0.753092i	$0.728562\pi$
$240$	−9.32791	+	33.3615i	−0.0388663	+	0.139006i
$241$	−308.230	+	177.956i	−1.27896	+	0.738408i	−0.976657	−	0.214803i	$-0.931089\pi$
$241$	−308.230	+	177.956i	−1.27896	+	0.738408i	−0.302303	+	0.953212i	$0.597756\pi$
$242$	−127.274	+	73.4819i	−0.525927	+	0.303644i
$243$	7.79423	−	13.5000i	0.0320750	−	0.0555556i
$244$			15.0669i			0.0617496i
$245$	−78.0611	+	232.231i	−0.318617	+	0.947884i
$246$	62.5178			0.254137
$247$	254.063	+	146.683i	1.02859	+	0.593859i
$248$	−37.6540	−	65.2187i	−0.151831	−	0.262979i
$249$	104.587	+	181.150i	0.420029	+	0.727512i
$250$	−172.150	+	40.1774i	−0.688602	+	0.160710i
$251$		−	9.10257i		−	0.0362652i	−0.999836	−	0.0181326i	$-0.994228\pi$
$251$		−	9.10257i		−	0.0362652i	0.999836	−	0.0181326i	$-0.00577210\pi$
$252$	1.08413	−	41.9860i	0.00430212	−	0.166611i
$253$		−	334.792i		−	1.32329i
$254$	−24.6118	+	42.6289i	−0.0968968	+	0.167830i
$255$	−132.555	−	135.460i	−0.519822	−	0.531215i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	221.792	−	384.155i	0.863003	−	1.49477i	−0.00601347	−	0.999982i	$-0.501914\pi$
$257$	221.792	−	384.155i	0.863003	−	1.49477i	0.869016	−	0.494783i	$-0.164753\pi$
$258$	75.3797			0.292169
$259$	191.505	−	312.764i	0.739402	−	1.20758i
$260$	124.893	−	32.0182i	0.480359	−	0.123147i
$261$	−36.6993	+	63.5650i	−0.140610	+	0.243544i
$262$	−25.5660	−	44.2816i	−0.0975802	−	0.169014i
$263$	−84.6456	+	48.8702i	−0.321846	+	0.185818i	−0.652215	−	0.758034i	$-0.726160\pi$
$263$	−84.6456	+	48.8702i	−0.321846	+	0.185818i	0.330369	+	0.943852i	$0.392827\pi$
$264$	−63.6282	−	36.7357i	−0.241016	−	0.139151i
$265$	−124.006	−	483.708i	−0.467946	−	1.82531i
$266$	−197.913	+	107.551i	−0.744034	+	0.404329i
$267$			87.0402i			0.325993i
$268$	−197.838	−	114.222i	−0.738201	−	0.426201i
$269$	386.069	−	222.897i	1.43520	−	0.828614i	0.437690	−	0.899126i	$-0.355797\pi$
$269$	386.069	−	222.897i	1.43520	−	0.828614i	0.997511	+	0.0705120i	$0.0224633\pi$
$270$	−26.2608	+	25.6976i	−0.0972624	+	0.0951764i
$271$	356.675	+	205.926i	1.31614	+	0.759875i	0.983106	−	0.183038i	$-0.0585932\pi$
$271$	356.675	+	205.926i	1.31614	+	0.759875i	0.333037	+	0.942914i	$0.391927\pi$
$272$	87.5383			0.321832
$273$	−137.351	+	74.6404i	−0.503118	+	0.273408i
$274$	−248.598			−0.907292
$275$	8.12745	−	374.844i	0.0295544	−	1.36307i
$276$	66.9705	−	38.6654i	0.242647	−	0.140092i
$277$	175.978	−	101.601i	0.635299	−	0.366790i	−0.147502	−	0.989062i	$-0.547123\pi$
$277$	175.978	−	101.601i	0.635299	−	0.366790i	0.782801	+	0.622272i	$0.213790\pi$
$278$	−58.1720	+	100.757i	−0.209252	+	0.362435i
$279$		−	79.8763i		−	0.286295i
$280$	−29.1088	+	94.6186i	−0.103960	+	0.337924i
$281$	−75.1279			−0.267359			−0.133680	−	0.991025i	$-0.542679\pi$
$281$	−75.1279			−0.267359			−0.133680	+	0.991025i	$0.542679\pi$
$282$	128.968	+	74.4599i	0.457335	+	0.264042i
$283$	−18.7783	−	32.5250i	−0.0663545	−	0.114929i	0.830940	−	0.556363i	$-0.187803\pi$
$283$	−18.7783	−	32.5250i	−0.0663545	−	0.114929i	−0.897294	+	0.441433i	$0.854470\pi$
$284$	−114.316	−	198.001i	−0.402521	−	0.697187i
$285$	189.773	+	53.0608i	0.665871	+	0.186178i
$286$			273.457i			0.956144i
$287$	178.600	+	4.61169i	0.622300	+	0.0160686i
$288$		−	16.9706i		−	0.0589256i
$289$	−94.9673	+	164.488i	−0.328607	+	0.569163i
$290$	123.650	−	120.998i	0.426378	−	0.417233i
$291$	−39.8847	−	69.0824i	−0.137061	−	0.237397i
$292$	−23.2201	+	40.2185i	−0.0795210	+	0.137734i
$293$	−443.746			−1.51449			−0.757246	−	0.653129i	$-0.773456\pi$
$293$	−443.746			−1.51449			−0.757246	+	0.653129i	$0.773456\pi$
$294$	6.19427	−	119.865i	0.0210690	−	0.407704i
$295$	1.77949	+	6.94126i	0.00603218	+	0.0235297i
$296$	74.0919	−	128.331i	0.250310	−	0.433550i
$297$	−38.9641	−	67.4879i	−0.131192	−	0.227232i
$298$	33.5666	−	19.3797i	0.112639	−	0.0650324i
$299$	−249.261	−	143.911i	−0.833648	−	0.481307i
$300$	75.9210	−	41.6653i	0.253070	−	0.138884i
$301$	215.344	+	5.56046i	0.715428	+	0.0184733i
$302$			312.756i			1.03562i
$303$	25.4104	+	14.6707i	0.0838626	+	0.0484181i
$304$	−78.8206	+	45.5071i	−0.259278	+	0.149694i
$305$	26.9219	−	26.3445i	0.0882685	−	0.0863754i
$306$	80.4091	+	46.4242i	0.262775	+	0.151713i
$307$	−350.661			−1.14222			−0.571109	−	0.820874i	$-0.693487\pi$
$307$	−350.661			−1.14222			−0.571109	+	0.820874i	$0.693487\pi$
$308$	−179.062	−	109.640i	−0.581371	−	0.355973i
$309$	154.297			0.499341
$310$	−50.6962	+	181.316i	−0.163536	+	0.584891i
$311$	−324.966	+	187.619i	−1.04491	+	0.603278i	−0.921219	−	0.389043i	$-0.872806\pi$
$311$	−324.966	+	187.619i	−1.04491	+	0.603278i	−0.123688	+	0.992321i	$0.539472\pi$
$312$	−54.7012	+	31.5818i	−0.175325	+	0.101224i
$313$	−61.7457	+	106.947i	−0.197271	+	0.341683i	−0.947642	−	0.319333i	$-0.896541\pi$
$313$	−61.7457	+	106.947i	−0.197271	+	0.341683i	0.750372	+	0.661016i	$0.229874\pi$
$314$			371.741i			1.18389i
$315$	−76.9172	+	71.4755i	−0.244182	+	0.226906i
$316$	125.669			0.397688
$317$	321.121	+	185.399i	1.01300	+	0.584856i	0.912068	−	0.410038i	$-0.134485\pi$
$317$	321.121	+	185.399i	1.01300	+	0.584856i	0.100931	+	0.994893i	$0.467818\pi$
$318$	122.315	+	211.856i	0.384639	+	0.666215i
$319$	183.463	+	317.768i	0.575120	+	0.996137i
$320$	−10.7709	+	38.5225i	−0.0336592	+	0.120383i
$321$		−	151.642i		−	0.472405i
$322$	194.172	−	105.519i	0.603020	−	0.327698i
$323$		−	497.952i		−	1.54165i
$324$	9.00000	−	15.5885i	0.0277778	−	0.0481125i
$325$	−275.587	−	167.178i	−0.847960	−	0.514395i
$326$	−143.894	−	249.232i	−0.441394	−	0.764516i
$327$	−77.4687	+	134.180i	−0.236907	+	0.410336i
$328$	72.1894			0.220090
$329$	362.942	+	222.230i	1.10317	+	0.675470i
$330$	45.6137	+	177.925i	0.138223	+	0.539166i
$331$	−92.3147	+	159.894i	−0.278896	+	0.483063i	−0.971111	−	0.238629i	$-0.923302\pi$
$331$	−92.3147	+	159.894i	−0.278896	+	0.483063i	0.692214	+	0.721692i	$0.256635\pi$
$332$	120.767	+	209.174i	0.363756	+	0.630043i
$333$	136.115	−	78.5863i	0.408755	−	0.235995i
$334$	0.544709	+	0.314488i	0.00163087	+	0.000941581i
$335$	141.826	+	553.219i	0.423361	+	1.65140i
$336$	1.25185	−	48.4813i	0.00372574	−	0.144289i
$337$			210.806i			0.625538i	0.949829	+	0.312769i	$0.101256\pi$
$337$			210.806i			0.625538i	−0.949829	+	0.312769i	$0.898744\pi$
$338$	−3.38664	−	1.95528i	−0.0100197	−	0.00578485i
$339$	−29.6207	+	17.1015i	−0.0873768	+	0.0504470i
$340$	−153.061	−	156.416i	−0.450179	−	0.460046i
$341$	−345.812	−	199.655i	−1.01411	−	0.585498i
$342$	−96.5351			−0.282266
$343$	26.5377	−	341.972i	0.0773693	−	0.997003i
$344$	87.0410			0.253026
$345$	−186.186	−	52.0579i	−0.539670	−	0.150892i
$346$	−124.246	+	71.7335i	−0.359093	+	0.207322i
$347$	175.775	−	101.484i	0.506557	−	0.292461i	−0.224861	−	0.974391i	$-0.572193\pi$
$347$	175.775	−	101.484i	0.506557	−	0.292461i	0.731417	+	0.681930i	$0.238859\pi$
$348$	−42.3767	+	73.3985i	−0.121772	+	0.210915i
$349$		−	389.811i		−	1.11694i	−0.829526	−	0.558468i	$-0.811389\pi$
$349$		−	389.811i		−	1.11694i	0.829526	−	0.558468i	$-0.188611\pi$
$350$	219.964	−	113.428i	0.628467	−	0.324081i
$351$	−66.9951			−0.190869
$352$	−73.4715	−	42.4188i	−0.208726	−	0.120508i
$353$	54.0448	+	93.6083i	0.153101	+	0.265179i	0.932366	−	0.361516i	$-0.117741\pi$
$353$	54.0448	+	93.6083i	0.153101	+	0.265179i	−0.779265	+	0.626695i	$0.784407\pi$
$354$	−1.75524	−	3.04016i	−0.00495830	−	0.00858803i
$355$	−153.911	+	550.468i	−0.433553	+	1.55061i
$356$			100.505i			0.282319i
$357$	226.287	+	138.555i	0.633857	+	0.388110i
$358$			245.052i			0.684503i
$359$	179.771	−	311.372i	0.500754	−	0.867331i	−0.499246	−	0.866460i	$-0.666390\pi$
$359$	179.771	−	311.372i	0.500754	−	0.867331i	1.00000		0.000870595i	$-0.000277119\pi$
$360$	−30.3234	+	29.6731i	−0.0842317	+	0.0824252i
$361$	78.3619	+	135.727i	0.217069	+	0.375975i
$362$	157.519	−	272.830i	0.435135	−	0.753675i
$363$	−179.993			−0.495849
$364$	−158.599	+	86.1873i	−0.435713	+	0.236778i
$365$	112.464	−	28.8318i	0.308120	−	0.0789911i
$366$	−9.22655	+	15.9809i	−0.0252092	+	0.0436636i
$367$	235.455	+	407.820i	0.641566	+	1.11123i	0.985083	+	0.172079i	$0.0550485\pi$
$367$	235.455	+	407.820i	0.641566	+	1.11123i	−0.343517	+	0.939147i	$0.611618\pi$
$368$	77.3308	−	44.6470i	0.210138	−	0.121323i
$369$	66.3102	+	38.2842i	0.179702	+	0.103751i
$370$	−358.855	+	91.9977i	−0.969877	+	0.248642i
$371$	333.801	+	614.251i	0.899733	+	1.65566i
$372$		−	92.2332i		−	0.247939i
$373$	447.933	+	258.614i	1.20089	+	0.693336i	0.960754	−	0.277403i	$-0.0894737\pi$
$373$	447.933	+	258.614i	1.20089	+	0.693336i	0.240139	+	0.970739i	$0.422807\pi$
$374$	401.973	−	232.079i	1.07479	−	0.620533i
$375$	−207.197	−	62.8056i	−0.552524	−	0.167482i
$376$	148.920	+	85.9789i	0.396063	+	0.228667i
$377$	315.447			0.836731
$378$	26.8610	−	43.8690i	0.0710608	−	0.116056i
$379$	160.856			0.424422			0.212211	−	0.977224i	$-0.431934\pi$
$379$	160.856			0.424422			0.212211	+	0.977224i	$0.431934\pi$
$380$	219.131	+	61.2693i	0.576661	+	0.161235i
$381$	−52.2095	+	30.1432i	−0.137033	+	0.0791159i
$382$	134.412	−	77.6029i	0.351864	−	0.203149i
$383$	−106.591	+	184.621i	−0.278305	+	0.482039i	−0.970964	−	0.239227i	$-0.923106\pi$
$383$	−106.591	+	184.621i	−0.278305	+	0.482039i	0.692658	+	0.721266i	$0.256439\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	117.184	+	511.658i	0.304373	+	1.32898i
$386$	−246.919			−0.639687
$387$	79.9523	+	46.1605i	0.206595	+	0.119278i
$388$	−46.0549	−	79.7695i	−0.118698	−	0.205591i
$389$	314.088	+	544.017i	0.807425	+	1.39850i	0.914642	+	0.404266i	$0.132473\pi$
$389$	314.088	+	544.017i	0.807425	+	1.39850i	−0.107216	+	0.994236i	$0.534194\pi$
$390$	152.076	+	42.5207i	0.389939	+	0.109027i
$391$			488.540i			1.24946i
$392$	7.15253	−	138.408i	0.0182463	−	0.353082i
$393$		−	62.6237i		−	0.159348i
$394$	−112.287	+	194.487i	−0.284993	+	0.493622i
$395$	−219.733	−	224.549i	−0.556287	−	0.568479i
$396$	−44.9919	−	77.9283i	−0.113616	−	0.196789i
$397$	90.0752	−	156.015i	0.226890	−	0.392985i	−0.729995	−	0.683453i	$-0.760478\pi$
$397$	90.0752	−	156.015i	0.226890	−	0.392985i	0.956885	+	0.290468i	$0.0938109\pi$
$398$	−49.8132			−0.125159
$399$	−275.780	−	7.12100i	−0.691178	−	0.0178471i
$400$	87.6660	−	48.1110i	0.219165	−	0.120277i
$401$	124.296	−	215.288i	0.309966	−	0.536877i	−0.668389	−	0.743812i	$-0.733016\pi$
$401$	124.296	−	215.288i	0.309966	−	0.536877i	0.978355	+	0.206936i	$0.0663490\pi$
$402$	−139.893	−	242.301i	−0.347991	−	0.602739i
$403$	−297.295	+	171.644i	−0.737706	+	0.425915i
$404$	29.3414	+	16.9403i	0.0726272	+	0.0419313i
$405$	−43.5904	+	11.1750i	−0.107630	+	0.0275927i
$406$	−126.475	+	206.558i	−0.311516	+	0.508763i
$407$		−	785.722i		−	1.93052i
$408$	92.8484	+	53.6060i	0.227570	+	0.131387i
$409$	188.546	−	108.857i	0.460993	−	0.266154i	−0.251469	−	0.967865i	$-0.580914\pi$
$409$	188.546	−	108.857i	0.460993	−	0.266154i	0.712462	+	0.701711i	$0.247580\pi$
$410$	−126.223	−	128.990i	−0.307862	−	0.314609i
$411$	−263.678	−	152.235i	−0.641552	−	0.370400i
$412$	178.166			0.432442
$413$	−4.79008	−	8.81457i	−0.0115983	−	0.0213428i
$414$	94.7105			0.228769
$415$	162.597	−	581.531i	0.391799	−	1.40128i
$416$	−63.1636	+	36.4675i	−0.151835	+	0.0876623i
$417$	−123.401	+	71.2458i	−0.295927	+	0.170853i
$418$	−241.294	+	417.934i	−0.577259	+	0.999842i
$419$		−	294.614i		−	0.703137i	−0.936162	−	0.351568i	$-0.885648\pi$
$419$		−	294.614i		−	0.703137i	0.936162	−	0.351568i	$-0.114352\pi$
$420$	−88.8164	+	82.5327i	−0.211468	+	0.196507i
$421$	347.454			0.825305			0.412653	−	0.910888i	$-0.364602\pi$
$421$	347.454			0.825305			0.412653	+	0.910888i	$0.364602\pi$
$422$	397.277	+	229.368i	0.941414	+	0.543525i
$423$	91.1944	+	157.953i	0.215590	+	0.373412i
$424$	141.238	+	244.631i	0.333107	+	0.576959i
$425$	−11.8599	+	546.986i	−0.0279055	+	1.28703i
$426$		−	280.016i		−	0.657314i
$427$	−27.5371	+	44.9733i	−0.0644898	+	0.105324i
$428$		−	175.101i		−	0.409115i
$429$	−167.458	+	290.045i	−0.390344	+	0.676096i
$430$	−152.191	−	155.527i	−0.353933	−	0.361691i
$431$	−86.1818	−	149.271i	−0.199958	−	0.346337i	0.748557	−	0.663071i	$-0.230747\pi$
$431$	−86.1818	−	149.271i	−0.199958	−	0.346337i	−0.948514	+	0.316734i	$0.897414\pi$
$432$	10.3923	−	18.0000i	0.0240563	−	0.0416667i
$433$	−258.404			−0.596775			−0.298388	−	0.954445i	$-0.596449\pi$
$433$	−258.404			−0.596775			−0.298388	+	0.954445i	$0.596449\pi$
$434$	6.80367	−	263.490i	0.0156767	−	0.607121i
$435$	205.246	−	52.6178i	0.471830	−	0.120960i
$436$	−89.4532	+	154.937i	−0.205168	+	0.355361i
$437$	−253.969	−	439.888i	−0.581165	−	1.00661i
$438$	−49.2574	+	28.4388i	−0.112460	+	0.0649287i
$439$	204.234	+	117.914i	0.465225	+	0.268598i	0.714239	−	0.699902i	$-0.246773\pi$
$439$	204.234	+	117.914i	0.465225	+	0.268598i	−0.249014	+	0.968500i	$0.580106\pi$
$440$	52.6701	+	205.450i	0.119705	+	0.466932i
$441$	79.9721	−	123.343i	0.181343	−	0.279689i
$442$		−	399.038i		−	0.902801i
$443$	−26.5623	−	15.3357i	−0.0599600	−	0.0346179i	0.469720	−	0.882815i	$-0.344355\pi$
$443$	−26.5623	−	15.3357i	−0.0599600	−	0.0346179i	−0.529680	+	0.848197i	$0.677688\pi$
$444$	157.173	−	90.7436i	0.353992	−	0.204378i
$445$	179.585	−	175.734i	0.403563	−	0.394908i
$446$	315.669	+	182.252i	0.707778	+	0.408636i
$447$	47.4703			0.106198
$448$	1.44551	−	55.9813i	0.00322659	−	0.124958i
$449$	−707.867			−1.57654			−0.788271	−	0.615329i	$-0.789023\pi$
$449$	−707.867			−1.57654			−0.788271	+	0.615329i	$0.789023\pi$
$450$	106.041	+	2.29920i	0.235647	+	0.00510934i
$451$	331.491	−	191.387i	0.735014	−	0.424360i
$452$	−34.2031	+	19.7472i	−0.0756705	+	0.0436884i
$453$	−191.523	+	331.728i	−0.422789	+	0.732292i
$454$		−	438.399i		−	0.965636i
$455$	431.313	+	132.691i	0.947941	+	0.291628i
$456$	−111.469			−0.244450
$457$	279.381	+	161.301i	0.611337	+	0.352955i	0.773488	−	0.633810i	$-0.218510\pi$
$457$	279.381	+	161.301i	0.611337	+	0.352955i	−0.162152	+	0.986766i	$0.551843\pi$
$458$	−210.819	−	365.150i	−0.460304	−	0.797270i
$459$	56.8578	+	98.4806i	0.123873	+	0.214555i
$460$	−214.989	−	60.1113i	−0.467368	−	0.130677i
$461$		−	103.910i		−	0.225400i	−0.993629	−	0.112700i	$-0.964050\pi$
$461$		−	103.910i		−	0.225400i	0.993629	−	0.112700i	$-0.0359500\pi$
$462$	−122.784	−	225.943i	−0.265766	−	0.489055i
$463$			710.215i			1.53394i	0.641682	+	0.766971i	$0.278237\pi$
$463$			710.215i			1.53394i	−0.641682	+	0.766971i	$0.721763\pi$
$464$	−48.9323	+	84.7533i	−0.105458	+	0.182658i
$465$	−164.805	+	161.270i	−0.354418	+	0.346817i
$466$	68.3114	+	118.319i	0.146591	+	0.253903i
$467$	−291.820	+	505.448i	−0.624883	+	1.08233i	0.363681	+	0.931524i	$0.381520\pi$
$467$	−291.820	+	505.448i	−0.624883	+	1.08233i	−0.988563	+	0.150805i	$0.951813\pi$
$468$	−77.3592			−0.165298
$469$	−381.770	−	702.522i	−0.814008	−	1.49791i
$470$	−106.757	−	416.428i	−0.227143	−	0.886017i
$471$	−227.644	+	394.291i	−0.483320	+	0.837135i
$472$	−2.02677	−	3.51048i	−0.00429401	−	0.00743745i
$473$	399.689	−	230.761i	0.845009	−	0.487866i
$474$	133.293	+	76.9565i	0.281208	+	0.162355i
$475$	−273.674	−	498.678i	−0.576155	−	1.04985i
$476$	261.294	+	159.990i	0.548936	+	0.336113i
$477$			299.610i			0.628113i
$478$	−385.162	−	222.374i	−0.805779	−	0.465217i
$479$	−156.405	+	90.3006i	−0.326524	+	0.188519i	−0.654297	−	0.756238i	$-0.727035\pi$
$479$	−156.405	+	90.3006i	−0.326524	+	0.188519i	0.327773	+	0.944757i	$0.393702\pi$
$480$	−35.0145	+	34.2635i	−0.0729468	+	0.0713823i
$481$	−584.988	−	337.743i	−1.21619	−	0.702169i
$482$	−503.337			−1.04427
$483$	270.568	+	6.98641i	0.560182	+	0.0144646i
$484$	−207.838			−0.429418
$485$	−62.0069	+	221.769i	−0.127849	+	0.457256i
$486$	19.0919	−	11.0227i	0.0392837	−	0.0226805i
$487$	−725.401	+	418.811i	−1.48953	+	0.859981i	−0.999928	−	0.0119652i	$-0.996191\pi$
$487$	−725.401	+	418.811i	−1.48953	+	0.859981i	−0.489602	+	0.871946i	$0.662858\pi$
$488$	−10.6539	+	18.4531i	−0.0218318	+	0.0378137i
$489$		−	352.468i		−	0.720793i
$490$	−259.817	+	229.227i	−0.530240	+	0.467810i
$491$	−749.720			−1.52693			−0.763463	−	0.645852i	$-0.776502\pi$
$491$	−749.720			−1.52693			−0.763463	+	0.645852i	$0.776502\pi$
$492$	76.5684	+	44.2068i	0.155627	+	0.0898512i
$493$	−267.716	−	463.697i	−0.543034	−	0.940563i
$494$	207.441	+	359.299i	0.419922	+	0.727325i
$495$	−60.5757	+	216.650i	−0.122375	+	0.437677i
$496$		−	106.502i		−	0.214721i
$497$	20.6556	−	799.945i	0.0415606	−	1.60955i
$498$			295.817i			0.594011i
$499$	−183.555	+	317.927i	−0.367846	+	0.637128i	−0.989229	−	0.146379i	$-0.953238\pi$
$499$	−183.555	+	317.927i	−0.367846	+	0.637128i	0.621382	+	0.783507i	$0.286571\pi$
$500$	−239.250	−	72.5217i	−0.478500	−	0.145043i
$501$	0.385168	+	0.667130i	0.000768798	+	0.00133160i
$502$	6.43649	−	11.1483i	0.0128217	−	0.0222078i
$503$	−356.332			−0.708414			−0.354207	−	0.935167i	$-0.615249\pi$
$503$	−356.332			−0.708414			−0.354207	+	0.935167i	$0.615249\pi$
$504$	31.0164	−	50.6555i	0.0615404	−	0.100507i
$505$	−21.0342	−	82.0480i	−0.0416519	−	0.162471i
$506$	236.734	−	410.035i	0.467853	−	0.810346i
$507$	−2.39472	−	4.14777i	−0.00472331	−	0.00818101i
$508$	−60.2863	+	34.8063i	−0.118674	+	0.0685164i
$509$	−256.011	−	147.808i	−0.502969	−	0.290390i	0.226970	−	0.973902i	$-0.427118\pi$
$509$	−256.011	−	147.808i	−0.502969	−	0.290390i	−0.729939	+	0.683512i	$0.760452\pi$
$510$	−66.5610	−	259.634i	−0.130512	−	0.509086i
$511$	−142.816	+	77.6099i	−0.279483	+	0.151879i
$512$		−	22.6274i		−	0.0441942i
$513$	−102.391	−	59.1154i	−0.199593	−	0.115235i
$514$	543.277	−	313.661i	1.05696	−	0.610235i
$515$	−311.524	−	318.352i	−0.604901	−	0.618159i
$516$	92.3209	+	53.3015i	0.178917	+	0.103298i
$517$	911.780			1.76360
$518$	455.702	−	247.641i	0.879734	−	0.478072i
$519$	−175.711			−0.338556
$520$	175.603	+	49.0987i	0.337697	+	0.0944206i
$521$	743.226	−	429.101i	1.42654	−	0.823611i	0.429691	−	0.902976i	$-0.358623\pi$
$521$	743.226	−	429.101i	1.42654	−	0.823611i	0.996846	+	0.0793648i	$0.0252892\pi$
$522$	−89.8945	+	51.9006i	−0.172212	+	0.0994264i
$523$	−22.7271	+	39.3644i	−0.0434552	+	0.0752666i	−0.886935	−	0.461894i	$-0.847170\pi$
$523$	−22.7271	+	39.3644i	−0.0434552	+	0.0752666i	0.843480	+	0.537161i	$0.180503\pi$
$524$		−	72.3116i		−	0.137999i
$525$	302.767	+	14.3906i	0.576699	+	0.0274106i
$526$	−138.226			−0.262786
$527$	504.621	+	291.343i	0.957535	+	0.552833i
$528$	−51.9522	−	89.9838i	−0.0983943	−	0.170424i
$529$	−15.3309	−	26.5539i	−0.0289809	−	0.0501965i
$530$	190.158	−	680.104i	0.358788	−	1.28321i
$531$		−	4.29944i		−	0.00809687i
$532$	−318.444	−	8.22263i	−0.598578	−	0.0154561i
$533$		−	329.071i		−	0.617393i
$534$	−61.5467	+	106.602i	−0.115256	+	0.199629i
$535$	−312.875	+	306.165i	−0.584813	+	0.572271i
$536$	−161.534	−	279.785i	−0.301369	−	0.521987i
$537$	−150.063	+	259.917i	−0.279447	+	0.484017i
$538$	630.448			1.17184
$539$	−334.100	−	654.529i	−0.619852	−	1.21434i
$540$	−50.3338	+	12.9038i	−0.0932107	+	0.0238959i
$541$	−0.483285	+	0.837075i	−0.000893318	+	0.00154727i	−0.866472	−	0.499226i	$-0.833618\pi$
$541$	−0.483285	+	0.837075i	−0.000893318	+	0.00154727i	0.865578	+	0.500773i	$0.166951\pi$
$542$	291.224	+	504.414i	0.537313	+	0.930654i
$543$	334.148	−	192.920i	0.615373	−	0.355286i
$544$	107.212	+	61.8989i	0.197081	+	0.113785i
$545$	433.255	−	111.071i	0.794964	−	0.203801i
$546$	−220.999	−	5.70648i	−0.404760	−	0.0104514i
$547$			335.996i			0.614252i	0.951669	+	0.307126i	$0.0993674\pi$
$547$			335.996i			0.614252i	−0.951669	+	0.307126i	$0.900633\pi$
$548$	−304.469	−	175.785i	−0.555601	−	0.320776i
$549$	−19.5725	+	11.3002i	−0.0356511	+	0.0205832i
$550$	275.009	−	453.342i	0.500017	−	0.824258i
$551$	482.110	+	278.346i	0.874972	+	0.505165i
$552$	109.362			0.198120
$553$	375.112	+	229.681i	0.678321	+	0.415336i
$554$	287.371			0.518720
$555$	−436.960	−	122.174i	−0.787314	−	0.220134i
$556$	−142.492	+	82.2676i	−0.256280	+	0.147963i
$557$	294.245	−	169.882i	0.528267	−	0.304995i	−0.212044	−	0.977260i	$-0.568012\pi$
$557$	294.245	−	169.882i	0.528267	−	0.304995i	0.740310	+	0.672265i	$0.234679\pi$
$558$	56.4811	−	97.8281i	0.101221	−	0.175319i
$559$		−	396.771i		−	0.709787i
$560$	−102.556	+	95.3006i	−0.183136	+	0.170180i
$561$	568.476			1.01333
$562$	−92.0125	−	53.1234i	−0.163723	−	0.0945257i
$563$	−10.8005	−	18.7070i	−0.0191838	−	0.0332273i	0.856274	−	0.516522i	$-0.172773\pi$
$563$	−10.8005	−	18.7070i	−0.0191838	−	0.0332273i	−0.875458	+	0.483294i	$0.839440\pi$
$564$	105.302	+	182.389i	0.186706	+	0.323384i
$565$	95.0888	+	26.5869i	0.168299	+	0.0470565i
$566$		−	53.1131i		−	0.0938394i
$567$	55.3545	−	30.0812i	0.0976270	−	0.0530532i
$568$		−	323.334i		−	0.569250i
$569$	−248.710	+	430.779i	−0.437101	+	0.757081i	−0.997464	−	0.0711660i	$-0.977328\pi$
$569$	−248.710	+	430.779i	−0.437101	+	0.757081i	0.560364	+	0.828247i	$0.310661\pi$
$570$	194.904	+	199.176i	0.341937	+	0.349431i
$571$	−38.6915	−	67.0156i	−0.0677609	−	0.117365i	0.830154	−	0.557533i	$-0.188252\pi$
$571$	−38.6915	−	67.0156i	−0.0677609	−	0.117365i	−0.897915	+	0.440168i	$0.854919\pi$
$572$	−193.363	+	334.915i	−0.338048	+	0.585516i
$573$	190.088			0.331741
$574$	215.479	+	131.937i	0.375398	+	0.229856i
$575$	268.501	+	489.253i	0.466958	+	0.850875i
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	−322.119	−	557.927i	−0.558265	−	0.966944i	−0.997641	−	0.0686409i	$-0.978134\pi$
$577$	−322.119	−	557.927i	−0.558265	−	0.966944i	0.439376	−	0.898303i	$-0.355200\pi$
$578$	−232.621	+	134.304i	−0.402459	+	0.232360i
$579$	−261.897	−	151.207i	−0.452327	−	0.261151i
$580$	236.998	−	60.7578i	0.408616	−	0.104755i
$581$	−21.8212	+	845.087i	−0.0375581	+	1.45454i
$582$		−	112.811i		−	0.193833i
$583$	1297.12	+	748.890i	2.22490	+	1.28455i
$584$	−56.8775	+	32.8382i	−0.0973930	+	0.0562299i
$585$	135.263	+	138.227i	0.231218	+	0.236286i
$586$	−543.476	−	313.776i	−0.927434	−	0.535454i
$587$	−899.689			−1.53269			−0.766345	−	0.642430i	$-0.777926\pi$
$587$	−899.689			−1.53269			−0.766345	+	0.642430i	$0.777926\pi$
$588$	92.3438	−	142.424i	0.157047	−	0.242218i
$589$	−605.823			−1.02856
$590$	−2.72879	+	9.75957i	−0.00462506	+	0.0165416i
$591$	−238.197	+	137.523i	−0.403041	+	0.232696i
$592$	181.487	−	104.782i	0.306566	−	0.176996i
$593$	38.8247	−	67.2463i	0.0654716	−	0.113400i	−0.831431	−	0.555627i	$-0.812478\pi$
$593$	38.8247	−	67.2463i	0.0654716	−	0.113400i	0.896903	+	0.442227i	$0.145811\pi$
$594$		−	110.207i		−	0.185534i
$595$	−170.998	−	746.629i	−0.287392	−	1.25484i
$596$	54.8140			0.0919697
$597$	−52.8349	−	30.5042i	−0.0885006	−	0.0510959i
$598$	−203.520	−	352.508i	−0.340335	−	0.589478i
$599$	294.617	+	510.291i	0.491848	+	0.851905i	0.999956	−	0.00938786i	$-0.00298829\pi$
$599$	294.617	+	510.291i	0.491848	+	0.851905i	−0.508108	+	0.861293i	$0.669655\pi$
$600$	122.446	+	2.65489i	0.204076	+	0.00442482i
$601$		−	785.189i		−	1.30647i	−0.757155	−	0.653236i	$-0.773411\pi$
$601$		−	785.189i		−	1.30647i	0.757155	−	0.653236i	$-0.226589\pi$
$602$	259.809	+	159.081i	0.431577	+	0.264254i
$603$		−	342.665i		−	0.568268i
$604$	−221.152	+	383.047i	−0.366146	+	0.634183i
$605$	363.405	+	371.370i	0.600670	+	0.613835i
$606$	20.7475	+	35.9357i	0.0342368	+	0.0592998i
$607$	74.2634	−	128.628i	0.122345	−	0.211908i	−0.798347	−	0.602198i	$-0.794292\pi$
$607$	74.2634	−	128.628i	0.122345	−	0.211908i	0.920692	+	0.390290i	$0.127625\pi$
$608$	−128.713			−0.211700
$609$	−260.638	+	141.638i	−0.427977	+	0.232574i
$610$	51.6008	−	13.2286i	0.0845915	−	0.0216863i
$611$	391.930	−	678.842i	0.641456	−	1.11103i
$612$	65.6537	+	113.716i	0.107277	+	0.185810i
$613$	−14.3936	+	8.31014i	−0.0234806	+	0.0135565i	−0.511694	−	0.859168i	$-0.670982\pi$
$613$	−14.3936	+	8.31014i	−0.0234806	+	0.0135565i	0.488214	+	0.872724i	$0.337649\pi$
$614$	−429.470	−	247.955i	−0.699463	−	0.403835i
$615$	−54.8902	−	214.110i	−0.0892524	−	0.348146i
$616$	−141.779	−	260.897i	−0.230160	−	0.423534i
$617$			262.167i			0.424906i	0.977171	+	0.212453i	$0.0681453\pi$
$617$			262.167i			0.424906i	−0.977171	+	0.212453i	$0.931855\pi$
$618$	188.974	+	109.104i	0.305783	+	0.176544i
$619$	472.500	−	272.798i	0.763328	−	0.440708i	−0.0671614	−	0.997742i	$-0.521394\pi$
$619$	472.500	−	272.798i	0.763328	−	0.440708i	0.830489	+	0.557035i	$0.188061\pi$
$620$	−190.300	+	186.218i	−0.306935	+	0.300352i
$621$	100.456	+	57.9981i	0.161764	+	0.0933947i
$622$	−530.668			−0.853164
$623$	−183.689	+	299.999i	−0.294847	+	0.481540i
$624$	−89.3268			−0.143152
$625$	288.746	+	554.302i	0.461993	+	0.886884i
$626$	−151.245	+	87.3216i	−0.241606	+	0.139491i
$627$	−511.863	+	295.524i	−0.816368	+	0.471330i
$628$	−262.860	+	455.287i	−0.418567	+	0.724980i
$629$			1146.55i			1.82282i
$630$	−144.745	+	33.1505i	−0.229754	+	0.0526199i
$631$	393.964			0.624348			0.312174	−	0.950025i	$-0.398943\pi$
$631$	393.964			0.624348			0.312174	+	0.950025i	$0.398943\pi$
$632$	153.913	+	88.8617i	0.243533	+	0.140604i
$633$	280.917	+	486.562i	0.443787	+	0.768661i
$634$	262.194	+	454.133i	0.413555	+	0.716299i
$635$	167.604	+	46.8621i	0.263943	+	0.0737986i
$636$			345.960i			0.543962i
$637$	−630.925	−	32.6044i	−0.990464	−	0.0511842i
$638$			518.913i			0.813342i
$639$	171.474	−	297.001i	0.268347	−	0.464791i
$640$	−40.4312	+	39.5641i	−0.0631738	+	0.0618189i
$641$	−243.379	−	421.546i	−0.379687	−	0.657637i	0.611329	−	0.791376i	$-0.290635\pi$
$641$	−243.379	−	421.546i	−0.379687	−	0.657637i	−0.991017	+	0.133739i	$0.957302\pi$
$642$	107.227	−	185.723i	0.167021	−	0.289288i
$643$	−533.132			−0.829133			−0.414566	−	0.910019i	$-0.636067\pi$
$643$	−533.132			−0.829133			−0.414566	+	0.910019i	$0.636067\pi$
$644$	312.425	+	8.06721i	0.485132	+	0.0125267i
$645$	−66.1829	−	258.159i	−0.102609	−	0.400247i
$646$	352.105	−	609.864i	0.545054	−	0.944062i
$647$	40.5066	+	70.1594i	0.0626068	+	0.108438i	0.895630	−	0.444800i	$-0.146725\pi$
$647$	40.5066	+	70.1594i	0.0626068	+	0.108438i	−0.833023	+	0.553238i	$0.813392\pi$
$648$	22.0454	−	12.7279i	0.0340207	−	0.0196419i
$649$	−18.6138	−	10.7467i	−0.0286807	−	0.0165588i
$650$	−219.311	−	399.620i	−0.337401	−	0.614800i
$651$	168.571	−	275.307i	0.258941	−	0.422899i
$652$		−	406.995i		−	0.624225i
$653$	−62.4895	−	36.0783i	−0.0956960	−	0.0552501i	0.451388	−	0.892328i	$-0.350929\pi$
$653$	−62.4895	−	36.0783i	−0.0956960	−	0.0552501i	−0.547084	+	0.837078i	$0.684262\pi$
$654$	−189.759	+	109.557i	−0.290151	+	0.167519i
$655$	−129.208	+	126.437i	−0.197264	+	0.193034i
$656$	88.4135	+	51.0456i	0.134777	+	0.0778134i
$657$	−69.6604			−0.106028
$658$	287.372	+	528.814i	0.436735	+	0.803668i
$659$	−1140.54			−1.73071			−0.865357	−	0.501156i	$-0.832908\pi$
$659$	−1140.54			−1.73071			−0.865357	+	0.501156i	$0.832908\pi$
$660$	−69.9468	+	250.166i	−0.105980	+	0.379040i
$661$	335.898	−	193.931i	0.508166	−	0.293390i	−0.223914	−	0.974609i	$-0.571883\pi$
$661$	335.898	−	193.931i	0.508166	−	0.293390i	0.732079	+	0.681219i	$0.238550\pi$
$662$	−226.124	+	130.553i	−0.341577	+	0.197210i
$663$	244.360	−	423.244i	0.368567	−	0.638376i
$664$			341.580i			0.514428i
$665$	542.107	+	583.380i	0.815198	+	0.877263i
$666$	222.276			0.333747
$667$	−472.997	−	273.085i	−0.709141	−	0.409423i
$668$	0.444753	+	0.770335i	0.000665798	+	0.00115320i
$669$	223.212	+	386.614i	0.333650	+	0.577898i
$670$	−217.484	+	777.838i	−0.324603	+	1.16095i
$671$			112.981i			0.168378i
$672$	35.8146	−	58.4920i	0.0532956	−	0.0870416i
$673$		−	792.610i		−	1.17773i	−0.808233	−	0.588863i	$-0.799576\pi$
$673$		−	792.610i		−	1.17773i	0.808233	−	0.588863i	$-0.200424\pi$
$674$	−149.062	+	258.184i	−0.221161	+	0.383062i
$675$	111.066	+	67.3753i	0.164542	+	0.0998153i
$676$	−2.76518	−	4.78944i	−0.00409051	−	0.00708496i
$677$	−338.153	+	585.699i	−0.499488	+	0.865138i	−1.00000		0.000591359i	$-0.999812\pi$
$677$	−338.153	+	585.699i	−0.499488	+	0.865138i	0.500512	+	0.865730i	$0.333145\pi$
$678$	−48.3705			−0.0713429
$679$	8.32162	−	322.277i	0.0122557	−	0.474635i
$680$	−76.8580	−	299.800i	−0.113027	−	0.440882i
$681$	268.463	−	464.992i	0.394219	−	0.682808i
$682$	−282.355	−	489.052i	−0.414010	−	0.717086i
$683$	−727.579	+	420.068i	−1.06527	+	0.615034i	−0.926885	−	0.375345i	$-0.877524\pi$
$683$	−727.579	+	420.068i	−1.06527	+	0.615034i	−0.138384	+	0.990379i	$0.544191\pi$
$684$	−118.231	−	68.2606i	−0.172852	−	0.0997963i
$685$	218.267	+	851.394i	0.318638	+	1.24291i
$686$	274.312	−	400.063i	0.399872	−	0.583183i
$687$		−	516.400i		−	0.751674i
$688$	106.603	+	61.5473i	0.154946	+	0.0894583i
$689$	1115.13	−	643.822i	1.61848	−	0.934430i
$690$	−191.220	−	195.411i	−0.277131	−	0.283205i
$691$	880.089	+	508.120i	1.27365	+	0.735340i	0.975672	−	0.219235i	$-0.0703560\pi$
$691$	880.089	+	508.120i	1.27365	+	0.735340i	0.297973	+	0.954574i	$0.403689\pi$
$692$	−202.893			−0.293198
$693$	8.12954	−	314.838i	0.0117309	−	0.454312i
$694$	287.040			0.413602
$695$	396.145	+	110.762i	0.569992	+	0.159370i
$696$	−103.801	+	59.9296i	−0.149140	+	0.0861058i
$697$	−483.723	+	279.278i	−0.694007	+	0.400685i
$698$	275.638	−	477.419i	0.394897	−	0.683981i
$699$			167.328i			0.239382i
$700$	349.605	+	16.6168i	0.499436	+	0.0237383i
$701$	−447.888			−0.638927			−0.319464	−	0.947599i	$-0.603503\pi$
$701$	−447.888			−0.638927			−0.319464	+	0.947599i	$0.603503\pi$
$702$	−82.0519	−	47.3727i	−0.116883	−	0.0674824i
$703$	−596.039	−	1032.37i	−0.847851	−	1.46852i
$704$	−59.9892	−	103.904i	−0.0852119	−	0.147591i
$705$	141.776	−	507.064i	0.201100	−	0.719239i
$706$			152.862i			0.216518i
$707$	56.6203	+	104.191i	0.0800853	+	0.147371i
$708$		−	4.96456i		−	0.00701210i
$709$	−615.124	+	1065.43i	−0.867593	+	1.50272i	−0.00314433	+	0.999995i	$0.501001\pi$
$709$	−615.124	+	1065.43i	−0.867593	+	1.50272i	−0.864449	+	0.502721i	$0.832332\pi$
$710$	−577.742	+	565.351i	−0.813720	+	0.796268i
$711$	94.2521	+	163.249i	0.132563	+	0.229605i
$712$	−71.0680	+	123.093i	−0.0998147	+	0.172884i
$713$	594.372			0.833622
$714$	179.170	+	329.704i	0.250939	+	0.461770i
$715$	936.531	−	240.093i	1.30983	−	0.335795i
$716$	−173.278	+	300.126i	−0.242008	+	0.419171i
$717$	−272.351	−	471.725i	−0.379848	−	0.657916i
$718$	440.346	−	254.234i	0.613296	−	0.354086i
$719$	−186.452	−	107.648i	−0.259321	−	0.149719i	0.364704	−	0.931124i	$-0.381170\pi$
$719$	−186.452	−	107.648i	−0.259321	−	0.149719i	−0.624025	+	0.781405i	$0.714504\pi$
$720$	−58.1205	+	14.9000i	−0.0807229	+	0.0206945i
$721$	531.810	+	325.627i	0.737600	+	0.451632i
$722$			221.641i			0.306982i
$723$	−533.869	−	308.230i	−0.738408	−	0.426320i
$724$	385.841	−	222.765i	0.532929	−	0.307687i
$725$	−522.954	−	317.238i	−0.721316	−	0.437569i
$726$	−220.446	−	127.274i	−0.303644	−	0.175309i
$727$	83.4871			0.114838			0.0574189	−	0.998350i	$-0.481713\pi$
$727$	83.4871			0.114838			0.0574189	+	0.998350i	$0.481713\pi$
$728$	−255.187	−	6.58927i	−0.350532	−	0.00905120i
$729$	27.0000			0.0370370
$730$	158.127	+	44.2124i	0.216612	+	0.0605649i
$731$	−583.240	+	336.734i	−0.797867	+	0.460648i
$732$	−22.6003	+	13.0483i	−0.0308748	+	0.0178256i
$733$	685.462	−	1187.25i	0.935146	−	1.61972i	0.160771	−	0.986992i	$-0.448602\pi$
$733$	685.462	−	1187.25i	0.935146	−	1.61972i	0.774374	−	0.632728i	$-0.218065\pi$
$734$			665.967i			0.907312i
$735$	−415.950	+	84.0267i	−0.565919	+	0.114322i
$736$	126.281			0.171577
$737$	−1483.52	−	856.509i	−2.01291	−	1.16216i
$738$	54.1420	+	93.7767i	0.0733632	+	0.127069i
$739$	137.811	+	238.695i	0.186483	+	0.322998i	0.944075	−	0.329730i	$-0.106958\pi$
$739$	137.811	+	238.695i	0.186483	+	0.322998i	−0.757592	+	0.652728i	$0.773624\pi$
$740$	−504.557	−	141.075i	−0.681834	−	0.190642i
$741$			508.125i			0.685729i
$742$	−25.5201	+	988.333i	−0.0343936	+	1.33199i
$743$			511.392i			0.688280i	0.938918	+	0.344140i	$0.111830\pi$
$743$			511.392i			0.688280i	−0.938918	+	0.344140i	$0.888170\pi$
$744$	65.2187	−	112.962i	0.0876596	−	0.151831i
$745$	−95.8423	−	97.9429i	−0.128647	−	0.131467i
$746$	365.736	+	633.473i	0.490262	+	0.849159i
$747$	−181.150	+	313.762i	−0.242504	+	0.420029i
$748$	656.419			0.877566
$749$	320.025	−	522.661i	0.427270	−	0.697812i
$750$	−209.353	−	223.431i	−0.279137	−	0.297908i
$751$	−150.546	+	260.754i	−0.200461	+	0.347209i	−0.948677	−	0.316246i	$-0.897577\pi$
$751$	−150.546	+	260.754i	−0.200461	+	0.347209i	0.748216	+	0.663455i	$0.230911\pi$
$752$	121.593	+	210.604i	0.161692	+	0.280059i
$753$	13.6539	−	7.88306i	0.0181326	−	0.0104689i
$754$	386.343	+	223.055i	0.512391	+	0.295829i
$755$	1071.12	−	274.598i	1.41871	−	0.363706i
$756$	63.9179	−	34.7347i	0.0845475	−	0.0459454i
$757$			1311.93i			1.73306i	0.499126	+	0.866529i	$0.333654\pi$
$757$			1311.93i			1.73306i	−0.499126	+	0.866529i	$0.666346\pi$
$758$	197.008	+	113.742i	0.259904	+	0.150056i
$759$	502.188	−	289.938i	0.661644	−	0.382001i
$760$	225.056	+	229.988i	0.296126	+	0.302616i
$761$	321.453	+	185.591i	0.422408	+	0.243878i	0.696107	−	0.717938i	$-0.254914\pi$
$761$	321.453	+	185.591i	0.422408	+	0.243878i	−0.273699	+	0.961815i	$0.588247\pi$
$762$	−85.2577			−0.111887
$763$	−550.182	+	298.984i	−0.721077	+	0.391853i
$764$	219.494			0.287296
$765$	88.3941	−	316.144i	0.115548	−	0.413260i
$766$	−261.093	+	150.742i	−0.340853	+	0.196792i
$767$	−16.0023	+	9.23893i	−0.0208635	+	0.0120455i
$768$	13.8564	−	24.0000i	0.0180422	−	0.0312500i
$769$			1395.52i			1.81473i	0.420347	+	0.907363i	$0.361908\pi$
$769$			1395.52i			1.81473i	−0.420347	+	0.907363i	$0.638092\pi$
$770$	−218.277	+	709.512i	−0.283476	+	0.921444i
$771$	768.309			0.996510
$772$	−302.413	−	174.598i	−0.391727	−	0.226164i
$773$	120.703	+	209.064i	0.156149	+	0.270458i	0.933477	−	0.358638i	$-0.116759\pi$
$773$	120.703	+	209.064i	0.156149	+	0.270458i	−0.777328	+	0.629096i	$0.783425\pi$
$774$	65.2808	+	113.070i	0.0843421	+	0.146085i
$775$	665.479	+	14.4291i	0.858683	+	0.0186181i
$776$		−	130.263i		−	0.167865i
$777$	634.994	+	16.3964i	0.817238	+	0.0211021i
$778$			888.376i			1.14187i
$779$	290.367	−	502.930i	0.372743	−	0.645610i
$780$	156.188	+	159.611i	0.200241	+	0.204630i
$781$	−857.215	−	1484.74i	−1.09759	−	1.90108i
$782$	−345.450	+	598.337i	−0.441752	+	0.765137i
$783$	−127.130			−0.162363
$784$	106.629	−	164.457i	0.136007	−	0.209767i
$785$	1273.13	−	326.386i	1.62182	−	0.415778i
$786$	44.2816	−	76.6980i	0.0563380	−	0.0975802i
$787$	144.868	+	250.919i	0.184077	+	0.318830i	0.943265	−	0.332041i	$-0.107737\pi$
$787$	144.868	+	250.919i	0.184077	+	0.318830i	−0.759188	+	0.650871i	$0.774404\pi$
$788$	−275.046	+	158.798i	−0.349043	+	0.201520i
$789$	−146.610	−	84.6456i	−0.185818	−	0.107282i
$790$	−110.337	−	430.390i	−0.139667	−	0.544798i
$791$	−138.184	−	3.56809i	−0.174695	−	0.00451086i
$792$		−	127.256i		−	0.160677i
$793$	84.1173	+	48.5652i	0.106075	+	0.0612423i
$794$	220.638	−	127.386i	0.277882	−	0.160435i
$795$	618.169	−	604.911i	0.777572	−	0.760895i
$796$	−61.0084	−	35.2232i	−0.0766438	−	0.0442503i
$797$	−1017.53			−1.27670			−0.638348	−	0.769748i	$-0.720382\pi$
$797$	−1017.53			−1.27670			−0.638348	+	0.769748i	$0.720382\pi$
$798$	−332.725	−	203.727i	−0.416949	−	0.255298i
$799$	−1330.50			−1.66521
$800$	141.388	+	3.06561i	0.176735	+	0.00383201i
$801$	−130.560	+	75.3790i	−0.162997	+	0.0941062i
$802$	304.463	−	175.782i	0.379629	−	0.219179i
$803$	−174.120	+	301.584i	−0.216837	+	0.375572i
$804$		−	395.676i		−	0.492134i
$805$	−531.861	−	572.354i	−0.660696	−	0.710998i
$806$	−485.481			−0.602334
$807$	668.691	+	386.069i	0.828614	+	0.478400i
$808$	23.9571	+	41.4950i	0.0296499	+	0.0513552i
$809$	−796.381	−	1379.37i	−0.984402	−	1.70503i	−0.644564	−	0.764551i	$-0.722961\pi$
$809$	−796.381	−	1379.37i	−0.984402	−	1.70503i	−0.339838	−	0.940484i	$-0.610372\pi$
$810$	−61.2890	−	17.1365i	−0.0756654	−	0.0211561i
$811$			1195.23i			1.47377i	0.676017	+	0.736886i	$0.263704\pi$
$811$			1195.23i			1.47377i	−0.676017	+	0.736886i	$0.736296\pi$
$812$	−300.958	+	163.549i	−0.370639	+	0.201415i
$813$			713.349i			0.877429i
$814$	555.589	−	962.309i	0.682542	−	1.18220i
$815$	−727.228	+	711.631i	−0.892304	+	0.873167i
$816$	75.8104	+	131.307i	0.0929049	+	0.160916i
$817$	350.105	−	606.399i	0.428525	−	0.742227i
$818$	307.895			0.376399
$819$	−230.910	−	141.386i	−0.281942	−	0.172633i
$820$	−63.3818	−	247.233i	−0.0772948	−	0.301503i
$821$	−177.360	+	307.197i	−0.216030	+	0.374174i	−0.953591	−	0.301106i	$-0.902644\pi$
$821$	−177.360	+	307.197i	−0.216030	+	0.374174i	0.737561	+	0.675281i	$0.235977\pi$
$822$	−215.292	−	372.897i	−0.261913	−	0.453646i
$823$	1150.19	−	664.063i	1.39756	−	0.806881i	0.403423	−	0.915014i	$-0.367820\pi$
$823$	1150.19	−	664.063i	1.39756	−	0.806881i	0.994137	+	0.108132i	$0.0344870\pi$
$824$	218.208	+	125.983i	0.264816	+	0.152891i
$825$	569.305	−	312.434i	0.690067	−	0.378707i
$826$	0.366216	−	14.1827i	0.000443360	−	0.0171703i
$827$		−	831.788i		−	1.00579i	−0.864348	−	0.502895i	$-0.832268\pi$
$827$		−	831.788i		−	1.00579i	0.864348	−	0.502895i	$-0.167732\pi$
$828$	115.996	+	66.9705i	0.140092	+	0.0808822i
$829$	319.026	−	184.190i	0.384832	−	0.222183i	−0.295087	−	0.955471i	$-0.595348\pi$
$829$	319.026	−	184.190i	0.384832	−	0.222183i	0.679918	+	0.733288i	$0.262015\pi$
$830$	610.344	−	597.254i	0.735354	−	0.719583i
$831$	304.803	+	175.978i	0.366790	+	0.211766i
$832$	−103.146			−0.123973
$833$	487.530	+	955.111i	0.585270	+	1.14659i
$834$	−201.514			−0.241623
$835$	0.598802	−	2.14163i	0.000717128	−	0.00256483i
$836$	−591.048	+	341.242i	−0.706995	+	0.408184i
$837$	119.814	−	69.1749i	0.143147	−	0.0826462i
$838$	208.324	−	360.827i	0.248596	−	0.430582i
$839$		−	96.7533i		−	0.115320i	−0.998336	−	0.0576599i	$-0.981636\pi$
$839$		−	96.7533i		−	0.115320i	0.998336	−	0.0576599i	$-0.0183639\pi$
$840$	−167.137	+	38.2789i	−0.198972	+	0.0455701i
$841$	−242.406			−0.288236
$842$	425.542	+	245.687i	0.505394	+	0.291790i
$843$	−65.0627	−	112.692i	−0.0771799	−	0.133680i
$844$	324.375	+	561.834i	0.384330	+	0.665680i
$845$	−3.72295	+	13.3152i	−0.00440586	+	0.0157577i
$846$			257.937i			0.304890i
$847$	−620.377	−	379.857i	−0.732441	−	0.448473i
$848$			399.480i			0.471085i
$849$	32.5250	−	56.3350i	0.0383098	−	0.0663545i
$850$	−401.303	+	661.532i	−0.472121	+	0.778273i
$851$	584.773	+	1012.86i	0.687160	+	1.19020i
$852$	198.001	−	342.948i	0.232396	−	0.402521i
$853$	−974.612			−1.14257			−0.571285	−	0.820752i	$-0.693555\pi$
$853$	−974.612			−1.14257			−0.571285	+	0.820752i	$0.693555\pi$
$854$	−65.5269	+	35.6091i	−0.0767294	+	0.0416969i
$855$	84.7572	+	330.612i	0.0991312	+	0.386680i
$856$	123.815	−	214.454i	0.144644	−	0.250531i
$857$	464.149	+	803.929i	0.541597	+	0.938074i	0.998813	+	0.0487177i	$0.0155135\pi$
$857$	464.149	+	803.929i	0.541597	+	0.938074i	−0.457216	+	0.889356i	$0.651153\pi$
$858$	−410.186	+	236.821i	−0.478072	+	0.276015i
$859$	−290.783	−	167.884i	−0.338514	−	0.195441i	0.321101	−	0.947045i	$-0.395947\pi$
$859$	−290.783	−	167.884i	−0.338514	−	0.195441i	−0.659615	+	0.751604i	$0.729280\pi$
$860$	−76.4214	−	298.096i	−0.0888621	−	0.346624i
$861$	147.755	+	271.894i	0.171608	+	0.315788i
$862$		−	243.759i		−	0.282783i
$863$	244.657	+	141.253i	0.283497	+	0.163677i	0.635005	−	0.772508i	$-0.280998\pi$
$863$	244.657	+	141.253i	0.283497	+	0.163677i	−0.351509	+	0.936185i	$0.614331\pi$
$864$	25.4558	−	14.6969i	0.0294628	−	0.0170103i
$865$	354.759	+	362.534i	0.410126	+	0.419115i
$866$	−316.479	−	182.719i	−0.365449	−	0.210992i
$867$	−328.976			−0.379442
$868$	194.649	−	317.898i	0.224250	−	0.366242i
$869$	942.351			1.08441
$870$	288.580	+	80.6874i	0.331701	+	0.0927441i
$871$	−1275.38	+	736.343i	−1.46427	+	0.845399i
$872$	−219.115	+	126.506i	−0.251278	+	0.145076i
$873$	69.0824	−	119.654i	0.0791322	−	0.137061i
$874$		−	718.334i		−	0.821892i
$875$	−581.594	−	653.738i	−0.664679	−	0.747129i
$876$	−80.4369			−0.0918230
$877$	−1068.45	−	616.870i	−1.21830	−	0.703387i	−0.253747	−	0.967271i	$-0.581663\pi$
$877$	−1068.45	−	616.870i	−1.21830	−	0.703387i	−0.964554	+	0.263884i	$0.914996\pi$
$878$	166.756	+	288.830i	0.189927	+	0.328964i
$879$	−384.296	−	665.620i	−0.437196	−	0.757246i
$880$	−80.7676	+	288.867i	−0.0917813	+	0.328258i
$881$		−	714.078i		−	0.810531i	−0.914199	−	0.405266i	$-0.867179\pi$
$881$		−	714.078i		−	0.810531i	0.914199	−	0.405266i	$-0.132821\pi$
$882$	185.162	−	94.5148i	0.209934	−	0.107160i
$883$		−	497.402i		−	0.563310i	−0.959516	−	0.281655i	$-0.909117\pi$
$883$		−	497.402i		−	0.563310i	0.959516	−	0.281655i	$-0.0908833\pi$
$884$	282.162	−	488.720i	0.319188	−	0.552850i
$885$	−8.87080	+	8.68055i	−0.0100235	+	0.00980853i
$886$	−21.6880	−	37.5647i	−0.0244786	−	0.0423981i
$887$	276.489	−	478.892i	0.311712	−	0.539901i	−0.667021	−	0.745039i	$-0.732431\pi$
$887$	276.489	−	478.892i	0.311712	−	0.539901i	0.978733	+	0.205138i	$0.0657643\pi$
$888$	256.662			0.289034
$889$	−243.563	−	6.28912i	−0.273974	−	0.00707437i
$890$	344.209	−	88.2431i	0.386752	−	0.0991495i
$891$	67.4879	−	116.892i	0.0757439	−	0.131192i
$892$	257.743	+	446.423i	0.288949	+	0.500475i
$893$	1198.00	−	691.665i	1.34155	−	0.774541i
$894$	58.1390	+	33.5666i	0.0650324	+	0.0375465i
$895$	839.250	−	215.154i	0.937710	−	0.240396i
$896$	41.3552	−	67.5407i	0.0461553	−	0.0753803i
$897$		−	498.521i		−	0.555765i
$898$	−866.957	−	500.538i	−0.965430	−	0.557392i
$899$	−564.148	+	325.711i	−0.627529	+	0.362304i
$900$	128.248	+	77.7983i	0.142497	+	0.0864426i
$901$	−1892.80	−	1092.81i	−2.10077	−	1.21288i
$902$	541.323			0.600136
$903$	178.152	+	327.831i	0.197290	+	0.363047i
$904$	−55.8534			−0.0617847
$905$	−1072.68	−	299.924i	−1.18529	−	0.331408i
$906$	−469.135	+	270.855i	−0.517809	+	0.298957i
$907$	1188.49	−	686.177i	1.31036	−	0.756534i	0.328201	−	0.944608i	$-0.393558\pi$
$907$	1188.49	−	686.177i	1.31036	−	0.756534i	0.982155	+	0.188074i	$0.0602244\pi$
$908$	309.995	−	536.927i	0.341404	−	0.591329i
$909$			50.8208i			0.0559084i
$910$	434.422	+	467.496i	0.477387	+	0.513732i
$911$	1114.92			1.22384			0.611920	−	0.790920i	$-0.290398\pi$
$911$	1114.92			1.22384			0.611920	+	0.790920i	$0.290398\pi$
$912$	−136.521	−	78.8206i	−0.149694	−	0.0864261i
$913$	905.589	+	1568.53i	0.991883	+	1.71799i
$914$	228.113	+	395.104i	0.249577	+	0.432280i
$915$	62.8318	+	17.5678i	0.0686686	+	0.0191998i
$916$		−	596.287i		−	0.650968i
$917$	132.161	−	215.843i	0.144123	−	0.235380i
$918$			160.818i			0.175183i
$919$	524.443	−	908.363i	0.570667	−	0.988425i	−0.425830	−	0.904803i	$-0.640018\pi$
$919$	524.443	−	908.363i	0.570667	−	0.988425i	0.996498	−	0.0836219i	$-0.0266488\pi$
$920$	−220.802	−	225.641i	−0.240002	−	0.245262i
$921$	−303.681	−	525.992i	−0.329730	−	0.571109i
$922$	73.4752	−	127.263i	0.0796911	−	0.138029i
$923$	−1473.90			−1.59686
$924$	9.38718	−	363.544i	0.0101593	−	0.393446i
$925$	630.144	+	1148.23i	0.681236	+	1.24132i
$926$	−502.198	+	869.833i	−0.542331	+	0.939344i
$927$	133.625	+	231.445i	0.144147	+	0.249671i
$928$	−119.859	+	69.2008i	−0.129159	+	0.0745698i
$929$	−991.037	−	572.176i	−1.06678	−	0.615905i	−0.139479	−	0.990225i	$-0.544543\pi$
$929$	−991.037	−	572.176i	−1.06678	−	0.615905i	−0.927300	+	0.374320i	$0.877876\pi$
$930$	−315.879	+	80.9801i	−0.339654	+	0.0870754i
$931$	−935.496	−	606.549i	−1.00483	−	0.651503i
$932$			193.214i			0.207311i
$933$	−562.858	−	324.966i	−0.603278	−	0.348303i
$934$	−714.811	+	412.696i	−0.765322	+	0.441859i
$935$	−1147.75	−	1172.91i	−1.22754	−	1.25444i
$936$	−94.7453	−	54.7012i	−0.101224	−	0.0584415i
$937$	255.103			0.272255			0.136127	−	0.990691i	$-0.456534\pi$
$937$	255.103			0.272255			0.136127	+	0.990691i	$0.456534\pi$
$938$	29.1874	−	1130.36i	0.0311166	−	1.20508i
$939$	−213.893			−0.227788
$940$	163.708	−	585.507i	0.174158	−	0.622880i
$941$	1505.34	−	869.107i	1.59972	−	0.923600i	0.608181	−	0.793798i	$-0.291899\pi$
$941$	1505.34	−	869.107i	1.59972	−	0.923600i	0.991540	−	0.129801i	$-0.0414340\pi$
$942$	−557.611	+	321.937i	−0.591944	+	0.341759i
$943$	−284.879	+	493.425i	−0.302099	+	0.523250i
$944$		−	5.73258i		−	0.00607265i
$945$	−173.825	−	53.4763i	−0.183942	−	0.0565886i
$946$	652.690			0.689947
$947$	−583.714	−	337.007i	−0.616382	−	0.355868i	0.159077	−	0.987266i	$-0.449148\pi$
$947$	−583.714	−	337.007i	−0.616382	−	0.355868i	−0.775459	+	0.631398i	$0.782482\pi$
$948$	108.833	+	188.504i	0.114803	+	0.198844i
$949$	149.691	+	259.273i	0.157736	+	0.273206i
$950$	17.4384	−	804.270i	0.0183562	−	0.846600i
$951$			642.242i			0.675333i
$952$	206.888	+	380.709i	0.217319	+	0.399905i
$953$			521.170i			0.546873i	0.961890	+	0.273437i	$0.0881603\pi$
$953$			521.170i			0.546873i	−0.961890	+	0.273437i	$0.911840\pi$
$954$	−211.856	+	366.946i	−0.222072	+	0.384639i
$955$	−383.786	−	392.198i	−0.401870	−	0.410678i
$956$	−314.484	−	544.702i	−0.328958	−	0.569772i
$957$	−317.768	+	550.390i	−0.332046	+	0.575120i
$958$	−255.409			−0.266606
$959$	−587.536	−	1081.17i	−0.612655	−	1.12739i
$960$	−67.1117	+	17.2051i	−0.0699081	+	0.0179220i
$961$	−126.043	+	218.313i	−0.131158	+	0.227173i
$962$	−477.641	−	827.298i	−0.496508	−	0.859978i
$963$	227.463	−	131.326i	0.236203	−	0.136372i
$964$	−616.459	−	355.913i	−0.639480	−	0.369204i
$965$	216.793	+	845.644i	0.224656	+	0.876315i
$966$	326.436	+	199.877i	0.337926	+	0.206912i
$967$			1249.98i			1.29264i	0.763067	+	0.646320i	$0.223693\pi$
$967$			1249.98i			1.29264i	−0.763067	+	0.646320i	$0.776307\pi$
$968$	−254.549	−	146.964i	−0.262963	−	0.151822i
$969$	746.928	−	431.239i	0.770823	−	0.445035i
$970$	−232.757	+	227.765i	−0.239956	+	0.234809i
$971$	988.758	+	570.859i	1.01829	+	0.587909i	0.913608	−	0.406597i	$-0.133285\pi$
$971$	988.758	+	570.859i	1.01829	+	0.587909i	0.104680	+	0.994506i	$0.466618\pi$
$972$	31.1769			0.0320750
$973$	−575.681	−	14.8648i	−0.591656	−	0.0152773i
$974$	−1184.58			−1.21620
$975$	12.1022	−	558.161i	0.0124125	−	0.572473i
$976$	−26.0966	+	15.0669i	−0.0267384	+	0.0154374i
$977$	−297.549	+	171.790i	−0.304554	+	0.175834i	−0.644487	−	0.764615i	$-0.722929\pi$
$977$	−297.549	+	171.790i	−0.304554	+	0.175834i	0.339933	+	0.940450i	$0.389596\pi$
$978$	249.232	−	431.683i	0.254839	−	0.441394i
$979$			753.655i			0.769821i
$980$	−480.298	+	97.0256i	−0.490100	+	0.0990058i
$981$	−268.360			−0.273557
$982$	−918.216	−	530.132i	−0.935047	−	0.539850i
$983$	337.362	+	584.329i	0.343197	+	0.594434i	0.985024	−	0.172415i	$-0.0551569\pi$
$983$	337.362	+	584.329i	0.343197	+	0.594434i	−0.641828	+	0.766849i	$0.721824\pi$
$984$	62.5178	+	108.284i	0.0635344	+	0.110045i
$985$	764.663	+	213.801i	0.776308	+	0.217056i
$986$		−	757.215i		−	0.767966i
$987$	−19.0269	+	736.870i	−0.0192776	+	0.746576i
$988$			586.732i			0.593859i
$989$	−343.488	+	594.938i	−0.347308	+	0.601555i
$990$	−227.385	+	222.508i	−0.229682	+	0.224755i
$991$	−398.425	−	690.093i	−0.402044	−	0.696360i	0.591929	−	0.805990i	$-0.298367\pi$
$991$	−398.425	−	690.093i	−0.402044	−	0.696360i	−0.993972	+	0.109630i	$0.965033\pi$
$992$	75.3081	−	130.437i	0.0759154	−	0.131489i
$993$	−319.788			−0.322042
$994$	590.944	−	965.123i	0.594511	−	0.970948i
$995$	43.7356	+	170.599i	0.0439554	+	0.171457i
$996$	−209.174	+	362.301i	−0.210014	+	0.363756i
$997$	557.272	+	965.224i	0.558949	+	0.968128i	0.997585	+	0.0694633i	$0.0221287\pi$
$997$	557.272	+	965.224i	0.558949	+	0.968128i	−0.438635	+	0.898665i	$0.644538\pi$
$998$	−449.617	+	259.586i	−0.450518	+	0.260106i
$999$	235.759	+	136.115i	0.235995	+	0.136252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.p.a.19.14	yes	32
3.2	odd	2		630.3.bc.b.19.1		32
5.2	odd	4		1050.3.p.h.901.1		16
5.3	odd	4		1050.3.p.g.901.8		16
5.4	even	2	inner	210.3.p.a.19.1	✓	32
7.2	even	3		1470.3.h.a.979.1		32
7.3	odd	6	inner	210.3.p.a.199.1	yes	32
7.5	odd	6		1470.3.h.a.979.27		32
15.14	odd	2		630.3.bc.b.19.12		32
21.17	even	6		630.3.bc.b.199.12		32
35.3	even	12		1050.3.p.g.451.8		16
35.9	even	6		1470.3.h.a.979.28		32
35.17	even	12		1050.3.p.h.451.1		16
35.19	odd	6		1470.3.h.a.979.2		32
35.24	odd	6	inner	210.3.p.a.199.14	yes	32
105.59	even	6		630.3.bc.b.199.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.p.a.19.1	✓	32	5.4	even	2	inner
210.3.p.a.19.14	yes	32	1.1	even	1	trivial
210.3.p.a.199.1	yes	32	7.3	odd	6	inner
210.3.p.a.199.14	yes	32	35.24	odd	6	inner
630.3.bc.b.19.1		32	3.2	odd	2
630.3.bc.b.19.12		32	15.14	odd	2
630.3.bc.b.199.1		32	105.59	even	6
630.3.bc.b.199.12		32	21.17	even	6
1050.3.p.g.451.8		16	35.3	even	12
1050.3.p.g.901.8		16	5.3	odd	4
1050.3.p.h.451.1		16	35.17	even	12
1050.3.p.h.901.1		16	5.2	odd	4
1470.3.h.a.979.1		32	7.2	even	3
1470.3.h.a.979.2		32	35.19	odd	6
1470.3.h.a.979.27		32	7.5	odd	6
1470.3.h.a.979.28		32	35.9	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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.34637 - 4.81532i) q^{5} +2.44949i q^{6} +(-0.180689 + 6.99767i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.22474 + 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.34637 - 4.81532i) q^{5} +2.44949i q^{6} +(-0.180689 + 6.99767i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(5.05390 - 4.94551i) q^{10} +(7.49865 + 12.9880i) q^{11} +(-1.73205 + 3.00000i) q^{12} +12.8932 q^{13} +(-5.16940 + 8.44259i) q^{14} +(8.38897 - 2.15064i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-10.9423 - 18.9526i) q^{17} +(-3.67423 + 2.12132i) q^{18} +(19.7051 + 11.3768i) q^{19} +(9.68674 - 2.48334i) q^{20} +(-10.6530 + 5.78912i) q^{21} +21.2094i q^{22} +(-19.3327 - 11.1617i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(-21.3746 - 12.9664i) q^{25} +(15.7909 + 9.11687i) q^{26} -5.19615 q^{27} +(-12.3010 + 6.68471i) q^{28} +24.4662 q^{29} +(11.7951 + 3.29792i) q^{30} +(-23.0583 + 13.3127i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(-12.9880 + 22.4960i) q^{33} -30.9495i q^{34} +(33.4527 + 10.2915i) q^{35} -6.00000 q^{36} +(-45.3718 - 26.1954i) q^{37} +(16.0892 + 27.8673i) q^{38} +(11.1658 + 19.3398i) q^{39} +(13.6198 + 3.80811i) q^{40} -25.5228i q^{41} +(-17.1407 - 0.442596i) q^{42} -30.7736i q^{43} +(-14.9973 + 25.9761i) q^{44} +(10.4910 + 10.7209i) q^{45} +(-15.7851 - 27.3406i) q^{46} +(30.3981 - 52.6511i) q^{47} -6.92820 q^{48} +(-48.9347 - 2.52880i) q^{49} +(-17.0098 - 30.9946i) q^{50} +(18.9526 - 32.8269i) q^{51} +(12.8932 + 22.3317i) q^{52} +(86.4900 - 49.9350i) q^{53} +(-6.36396 - 3.67423i) q^{54} +(72.6375 - 18.6217i) q^{55} +(-19.7924 - 0.511065i) q^{56} +39.4103i q^{57} +(29.9648 + 17.3002i) q^{58} +(-1.24114 + 0.716573i) q^{59} +(12.1140 + 12.3795i) q^{60} +(6.52416 + 3.76672i) q^{61} -37.6540 q^{62} +(-17.9094 - 10.9659i) q^{63} -8.00000 q^{64} +(17.3590 - 62.0849i) q^{65} +(-31.8141 + 18.3679i) q^{66} +(-98.9190 + 57.1109i) q^{67} +(21.8846 - 37.9052i) q^{68} -38.6654i q^{69} +(33.6939 + 36.2591i) q^{70} -114.316 q^{71} +(-7.34847 - 4.24264i) q^{72} +(11.6101 + 20.1092i) q^{73} +(-37.0459 - 64.1654i) q^{74} +(0.938646 - 43.2911i) q^{75} +45.5071i q^{76} +(-92.2409 + 50.1263i) q^{77} +31.5818i q^{78} +(31.4174 - 54.4165i) q^{79} +(13.9880 + 14.2946i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(18.0473 - 31.2589i) q^{82} +120.767 q^{83} +(-20.6800 - 12.6624i) q^{84} +(-105.995 + 27.1734i) q^{85} +(21.7603 - 37.6899i) q^{86} +(21.1883 + 36.6993i) q^{87} +(-36.7357 + 21.2094i) q^{88} +(43.5201 + 25.1263i) q^{89} +(5.26796 + 20.5487i) q^{90} +(-2.32966 + 90.2224i) q^{91} -44.6470i q^{92} +(-39.9381 - 23.0583i) q^{93} +(74.4599 - 42.9895i) q^{94} +(81.3132 - 79.5692i) q^{95} +(-8.48528 - 4.89898i) q^{96} -46.0549 q^{97} +(-58.1444 - 37.6992i) q^{98} -44.9919 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} + 12 q^{5} - 48 q^{9}+O(q^{10}) \) 32 * q + 32 * q^4 + 12 * q^5 - 48 * q^9	\( 32 q + 32 q^{4} + 12 q^{5} - 48 q^{9} - 24 q^{10} + 48 q^{11} - 16 q^{14} + 24 q^{15} - 64 q^{16} + 48 q^{19} - 24 q^{21} + 72 q^{25} + 96 q^{26} + 176 q^{29} - 24 q^{30} - 48 q^{31} + 68 q^{35} - 192 q^{36} - 72 q^{39} - 48 q^{40} - 96 q^{44} - 36 q^{45} + 32 q^{46} - 272 q^{49} + 192 q^{50} - 24 q^{51} - 64 q^{56} + 744 q^{59} + 24 q^{60} - 672 q^{61} - 256 q^{64} + 172 q^{65} + 320 q^{70} - 144 q^{71} - 416 q^{74} - 144 q^{75} + 128 q^{79} - 48 q^{80} - 144 q^{81} - 96 q^{84} - 736 q^{85} + 304 q^{86} - 48 q^{89} + 976 q^{91} + 528 q^{94} + 236 q^{95} - 288 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 + 12 * q^5 - 48 * q^9 - 24 * q^10 + 48 * q^11 - 16 * q^14 + 24 * q^15 - 64 * q^16 + 48 * q^19 - 24 * q^21 + 72 * q^25 + 96 * q^26 + 176 * q^29 - 24 * q^30 - 48 * q^31 + 68 * q^35 - 192 * q^36 - 72 * q^39 - 48 * q^40 - 96 * q^44 - 36 * q^45 + 32 * q^46 - 272 * q^49 + 192 * q^50 - 24 * q^51 - 64 * q^56 + 744 * q^59 + 24 * q^60 - 672 * q^61 - 256 * q^64 + 172 * q^65 + 320 * q^70 - 144 * q^71 - 416 * q^74 - 144 * q^75 + 128 * q^79 - 48 * q^80 - 144 * q^81 - 96 * q^84 - 736 * q^85 + 304 * q^86 - 48 * q^89 + 976 * q^91 + 528 * q^94 + 236 * q^95 - 288 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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