LMFDB - Embedded newform 210.3.p.a.199.1

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			199.1
Character	$\chi$	$=$	210.199
Dual form			210.3.p.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-3.49700 - 3.57365i) q^{5} -2.44949i q^{6} +(0.180689 + 6.99767i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-3.49700 - 3.57365i) q^{5} -2.44949i q^{6} +(0.180689 + 6.99767i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(6.80989 + 1.90405i) 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} +(-0.541928 + 24.9941i) q^{25} +(15.7909 - 9.11687i) q^{26} +5.19615 q^{27} +(12.3010 + 6.68471i) q^{28} +24.4662 q^{29} +(-8.75362 + 8.56588i) q^{30} +(-23.0583 - 13.3127i) q^{31} +(4.89898 + 2.82843i) q^{32} +(12.9880 + 22.4960i) q^{33} +30.9495i q^{34} +(24.3753 - 25.1166i) q^{35} -6.00000 q^{36} +(45.3718 - 26.1954i) q^{37} +(-16.0892 + 27.8673i) q^{38} +(11.1658 - 19.3398i) q^{39} +(10.1078 - 9.89102i) q^{40} +25.5228i q^{41} +(17.1407 - 0.442596i) q^{42} -30.7736i q^{43} +(-14.9973 - 25.9761i) q^{44} +(-4.03911 + 14.4460i) 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} +(4.66396 - 16.6808i) q^{60} +(6.52416 - 3.76672i) q^{61} +37.6540 q^{62} +(17.9094 - 10.9659i) q^{63} -8.00000 q^{64} +(45.0876 + 46.0758i) q^{65} +(-31.8141 - 18.3679i) q^{66} +(98.9190 + 57.1109i) q^{67} +(-21.8846 - 37.9052i) q^{68} +38.6654i q^{69} +(-12.0935 + 47.9974i) q^{70} -114.316 q^{71} +(7.34847 - 4.24264i) q^{72} +(-11.6101 + 20.1092i) q^{73} +(-37.0459 + 64.1654i) q^{74} +(-37.0219 - 22.4584i) q^{75} -45.5071i q^{76} +(92.2409 + 50.1263i) q^{77} +31.5818i q^{78} +(31.4174 + 54.4165i) q^{79} +(-5.38547 + 19.2613i) 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} +(-109.566 - 30.6347i) 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 $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

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

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
$5$	−3.49700	−	3.57365i	−0.699401	−	0.714730i
$5$	−3.49700	−	3.57365i	−0.699401	−	0.714730i
$6$		−	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
$10$	6.80989	+	1.90405i	0.680989	+	0.190405i
$11$	7.49865	−	12.9880i	0.681696	−	1.18073i	−0.292768	−	0.956184i	$-0.594576\pi$
$11$	7.49865	−	12.9880i	0.681696	−	1.18073i	0.974463	−	0.224548i	$-0.0720904\pi$
$12$	1.73205	+	3.00000i	0.144338	+	0.250000i
$13$	−12.8932			−0.991785			−0.495893	−	0.868384i	$-0.665159\pi$
$13$	−12.8932			−0.991785			−0.495893	+	0.868384i	$0.665159\pi$
$14$	−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	−0.340944	−	0.940083i	$-0.610747\pi$
$17$	10.9423	−	18.9526i	0.643664	−	1.11486i	0.984608	−	0.174775i	$-0.0559199\pi$
$18$	3.67423	+	2.12132i	0.204124	+	0.117851i
$19$	19.7051	−	11.3768i	1.03711	−	0.598778i	0.118099	−	0.993002i	$-0.462320\pi$
$19$	19.7051	−	11.3768i	1.03711	−	0.598778i	0.919014	+	0.394224i	$0.128987\pi$
$20$	−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	$-0.505380\pi$
$23$	19.3327	−	11.1617i	0.840553	−	0.485293i	0.857452	+	0.514564i	$0.172046\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$	−0.541928	+	24.9941i	−0.0216771	+	0.999765i
$26$	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	$0.361388\pi$
$30$	−8.75362	+	8.56588i	−0.291787	+	0.285529i
$31$	−23.0583	−	13.3127i	−0.743816	−	0.429442i	0.0796391	−	0.996824i	$-0.474623\pi$
$31$	−23.0583	−	13.3127i	−0.743816	−	0.429442i	−0.823455	+	0.567381i	$0.807957\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$	12.9880	+	22.4960i	0.393577	+	0.681696i
$34$			30.9495i			0.910278i
$35$	24.3753	−	25.1166i	0.696438	−	0.717617i
$36$	−6.00000			−0.166667
$37$	45.3718	−	26.1954i	1.22627	−	0.707985i	0.260019	−	0.965604i	$-0.416271\pi$
$37$	45.3718	−	26.1954i	1.22627	−	0.707985i	0.966247	+	0.257619i	$0.0829379\pi$
$38$	−16.0892	+	27.8673i	−0.423400	+	0.733350i
$39$	11.1658	−	19.3398i	0.286304	−	0.495893i
$40$	10.1078	−	9.89102i	0.252695	−	0.247276i
$41$			25.5228i			0.622507i	0.950327	+	0.311254i	$0.100749\pi$
$41$			25.5228i			0.622507i	−0.950327	+	0.311254i	$0.899251\pi$
$42$	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
$45$	−4.03911	+	14.4460i	−0.0897579	+	0.321021i
$46$	−15.7851	+	27.3406i	−0.343154	+	0.594360i
$47$	−30.3981	−	52.6511i	−0.646769	−	1.12024i	−0.983890	−	0.178775i	$-0.942786\pi$
$47$	−30.3981	−	52.6511i	−0.646769	−	1.12024i	0.337121	−	0.941461i	$-0.390547\pi$
$48$	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	−0.983511	−	0.180849i	$-0.942116\pi$
$53$	−86.4900	−	49.9350i	−1.63189	−	0.942170i	−0.648375	−	0.761321i	$-0.724551\pi$
$54$	−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	0.489445	−	0.872034i	$-0.337199\pi$
$59$	−1.24114	−	0.716573i	−0.0210363	−	0.0121453i	−0.510481	+	0.859889i	$0.670533\pi$
$60$	4.66396	−	16.6808i	0.0777326	−	0.278013i
$61$	6.52416	−	3.76672i	0.106953	−	0.0617496i	−0.445569	−	0.895248i	$-0.646999\pi$
$61$	6.52416	−	3.76672i	0.106953	−	0.0617496i	0.552523	+	0.833498i	$0.313665\pi$
$62$	37.6540			0.607323
$63$	17.9094	−	10.9659i	0.284277	−	0.174063i
$64$	−8.00000			−0.125000
$65$	45.0876	+	46.0758i	0.693655	+	0.708858i
$66$	−31.8141	−	18.3679i	−0.482032	−	0.278301i
$67$	98.9190	+	57.1109i	1.47640	+	0.852402i	0.999645	−	0.0266333i	$-0.00847863\pi$
$67$	98.9190	+	57.1109i	1.47640	+	0.852402i	0.476758	+	0.879035i	$0.341812\pi$
$68$	−21.8846	−	37.9052i	−0.321832	−	0.557429i
$69$			38.6654i			0.560368i
$70$	−12.0935	+	47.9974i	−0.172764	+	0.685677i
$71$	−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	$-0.884174\pi$
$73$	−11.6101	+	20.1092i	−0.159042	+	0.275469i	0.775481	+	0.631370i	$0.217507\pi$
$74$	−37.0459	+	64.1654i	−0.500621	+	0.867101i
$75$	−37.0219	−	22.4584i	−0.493625	−	0.299446i
$76$		−	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	0.993440	−	0.114352i	$-0.0364793\pi$
$79$	31.4174	+	54.4165i	0.397688	+	0.688816i	−0.595752	+	0.803168i	$0.703146\pi$
$80$	−5.38547	+	19.2613i	−0.0673184	+	0.240766i
$81$	−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	$-0.759323\pi$
$83$	−120.767			−1.45502			−0.727512	+	0.686095i	$0.759323\pi$
$84$	−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	−0.235165	−	0.971955i	$-0.575563\pi$
$89$	43.5201	−	25.1263i	0.488990	−	0.282319i	0.724155	+	0.689637i	$0.242230\pi$
$90$	−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
$95$	−109.566	−	30.6347i	−1.15332	−	0.322470i
$96$	−8.48528	+	4.89898i	−0.0883883	+	0.0510310i
$97$	46.0549			0.474793			0.237397	−	0.971413i	$-0.423706\pi$
$97$	46.0549			0.474793			0.237397	+	0.971413i	$0.423706\pi$
$98$	58.1444	−	37.6992i	0.593310	−	0.384686i
$99$	−44.9919			−0.454464
$100$	42.7492	+	25.9328i	0.427492	+	0.259328i
$101$	14.6707	+	8.47013i	0.145254	+	0.0838626i	0.570866	−	0.821043i	$-0.306608\pi$
$101$	14.6707	+	8.47013i	0.145254	+	0.0838626i	−0.425611	+	0.904906i	$0.639941\pi$
$102$	−46.4242	−	26.8030i	−0.455139	−	0.262775i
$103$	−44.5416	−	77.1483i	−0.432442	−	0.749012i	0.564641	−	0.825337i	$-0.309015\pi$
$103$	−44.5416	−	77.1483i	−0.432442	−	0.749012i	−0.997083	+	0.0763247i	$0.975681\pi$
$104$		−	36.4675i		−	0.350649i
$105$	16.5652	+	58.3146i	0.157764	+	0.555377i
$106$	141.238			1.33243
$107$	75.8211	−	43.7753i	0.708608	−	0.409115i	−0.101937	−	0.994791i	$-0.532504\pi$
$107$	75.8211	−	43.7753i	0.708608	−	0.409115i	0.810545	+	0.585676i	$0.199171\pi$
$108$	5.19615	−	9.00000i	0.0481125	−	0.0833333i
$109$	44.7266	−	77.4687i	0.410336	−	0.710722i	−0.584591	−	0.811328i	$-0.698745\pi$
$109$	44.7266	−	77.4687i	0.410336	−	0.710722i	0.994926	+	0.100606i	$0.0320782\pi$
$110$	75.7949	−	74.1693i	0.689045	−	0.674266i
$111$			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
$115$	−107.495	−	30.0556i	−0.934737	−	0.261353i
$116$	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
$130$	−87.8013	−	24.5493i	−0.675395	−	0.188841i
$131$	−31.3118	+	18.0779i	−0.239022	+	0.137999i	−0.614727	−	0.788740i	$-0.710734\pi$
$131$	−31.3118	+	18.0779i	−0.239022	+	0.137999i	0.375705	+	0.926739i	$0.377400\pi$
$132$	51.9522			0.393577
$133$	83.1714	+	135.834i	0.625349	+	1.02131i
$134$	−161.534			−1.20548
$135$	−18.1710	−	18.5692i	−0.134600	−	0.137550i
$136$	53.6060	+	30.9495i	0.394162	+	0.227570i
$137$	152.235	+	87.8927i	1.11120	+	0.641552i	0.939140	−	0.343534i	$-0.111624\pi$
$137$	152.235	+	87.8927i	1.11120	+	0.641552i	0.172061	+	0.985086i	$0.444957\pi$
$138$	−27.3406	−	47.3553i	−0.198120	−	0.343154i
$139$		−	82.2676i		−	0.591853i	−0.955211	−	0.295927i	$-0.904372\pi$
$139$		−	82.2676i		−	0.591853i	0.955211	−	0.295927i	$-0.0956284\pi$
$140$	−19.1279	−	67.3359i	−0.136628	−	0.480971i
$141$	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
$145$	−85.5583	−	87.4335i	−0.590057	−	0.602990i
$146$		−	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	0.908340	−	0.418233i	$-0.137350\pi$
$149$	13.7035	+	23.7351i	0.0919697	+	0.159296i	−0.816370	+	0.577529i	$0.804017\pi$
$150$	61.2229	+	1.32745i	0.408152	+	0.00884964i
$151$	110.576	−	191.523i	0.732292	−	1.26837i	−0.223609	−	0.974679i	$-0.571784\pi$
$151$	110.576	−	191.523i	0.732292	−	1.26837i	0.955901	−	0.293688i	$-0.0948827\pi$
$152$	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	0.0551455	+	0.998478i	$0.482438\pi$
$157$	−131.430	+	227.644i	−0.837135	+	1.44996i	−0.892280	+	0.451482i	$0.850896\pi$
$158$	−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	$-0.452082\pi$
$163$	176.234	−	101.749i	1.08119	−	0.624225i	0.931217	+	0.364466i	$0.118748\pi$
$164$	44.2068	+	25.5228i	0.269553	+	0.155627i
$165$	34.9734	−	125.083i	0.211960	−	0.758080i
$166$	147.909	−	85.3951i	0.891016	−	0.514428i
$167$	−0.444753			−0.00266319			−0.00133160	−	0.999999i	$-0.500424\pi$
$167$	−0.444753			−0.00266319			−0.00133160	+	0.999999i	$0.500424\pi$
$168$	16.3741	−	30.1312i	0.0974650	−	0.179352i
$169$	−2.76518			−0.0163620
$170$	110.603	−	108.230i	0.650603	−	0.636649i
$171$	−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	$-0.0719471\pi$
$173$	50.7233	+	87.8553i	0.293198	+	0.507834i	−0.681366	+	0.731943i	$0.738614\pi$
$174$		−	59.9296i		−	0.344423i
$175$	−174.999	+	0.723931i	−0.999991	+	0.00413675i
$176$	−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	−0.515815	−	0.856700i	$-0.672511\pi$
$179$	86.6390	−	150.063i	0.484017	−	0.838342i	0.999831	+	0.0183584i	$0.00584400\pi$
$180$	20.9820	+	21.4419i	0.116567	+	0.119122i
$181$			222.765i			1.23075i	0.788236	+	0.615373i	$0.210995\pi$
$181$			222.765i			1.23075i	−0.788236	+	0.615373i	$0.789005\pi$
$182$	66.6501	+	108.852i	0.366209	+	0.598088i
$183$			13.0483i			0.0713023i
$184$	31.5702	+	54.6812i	0.171577	+	0.297180i
$185$	−252.279	−	70.5374i	−1.36367	−	0.381283i
$186$	−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	0.973163	−	0.230115i	$-0.0739103\pi$
$191$	54.8736	+	95.0438i	0.287296	+	0.497611i	−0.685867	+	0.727727i	$0.740577\pi$
$192$	6.92820	−	12.0000i	0.0360844	−	0.0625000i
$193$	151.207	+	87.2991i	0.783453	+	0.452327i	0.837653	−	0.546203i	$-0.183927\pi$
$193$	151.207	+	87.2991i	0.783453	+	0.452327i	−0.0541993	+	0.998530i	$0.517261\pi$
$194$	−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	0.421394	−	0.906878i	$-0.361541\pi$
$199$	−30.5042	−	17.6116i	−0.153288	−	0.0885006i	−0.574682	+	0.818377i	$0.694874\pi$
$200$	−70.6941	−	1.53280i	−0.353470	−	0.00766401i
$201$	−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
$205$	91.2095	−	89.2533i	0.444924	−	0.435382i
$206$	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
$210$	−61.5228	−	59.7071i	−0.292966	−	0.284320i
$211$	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
$215$	−109.974	+	107.616i	−0.511508	+	0.500537i
$216$			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
$220$	−40.3838	+	144.434i	−0.183563	+	0.656516i
$221$	−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	$-0.696127\pi$
$223$	−257.743			−1.15580			−0.577898	+	0.816109i	$0.696127\pi$
$224$	−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	−0.291313	−	0.956628i	$-0.594092\pi$
$227$	154.997	−	268.463i	0.682808	−	1.18266i	0.974120	−	0.226030i	$-0.0725747\pi$
$228$	68.2606	+	39.4103i	0.299389	+	0.172852i
$229$	−258.200	+	149.072i	−1.12751	+	0.650968i	−0.943308	−	0.331920i	$-0.892304\pi$
$229$	−258.200	+	149.072i	−1.12751	+	0.650968i	−0.184203	+	0.982888i	$0.558970\pi$
$230$	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	$-0.733138\pi$
$233$	−83.6641	+	48.3035i	−0.359073	+	0.207311i	0.309601	+	0.950867i	$0.399805\pi$
$234$	−47.3727	−	27.3506i	−0.202447	−	0.116883i
$235$	−81.8542	+	292.753i	−0.348316	+	1.24576i
$236$	−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	$0.728562\pi$
$240$	−24.2280	−	24.7590i	−0.100950	−	0.103162i
$241$	−308.230	−	177.956i	−1.27896	−	0.738408i	−0.302303	−	0.953212i	$-0.597756\pi$
$241$	−308.230	−	177.956i	−1.27896	−	0.738408i	−0.976657	+	0.214803i	$0.931089\pi$
$242$	127.274	+	73.4819i	0.525927	+	0.303644i
$243$	−7.79423	−	13.5000i	−0.0320750	−	0.0555556i
$244$		−	15.0669i		−	0.0617496i
$245$	180.162	+	166.032i	0.735355	+	0.677682i
$246$	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
$250$	−51.2806	+	169.175i	−0.205122	+	0.676701i
$251$			9.10257i			0.0362652i	0.999836	+	0.0181326i	$0.00577210\pi$
$251$			9.10257i			0.0362652i	−0.999836	+	0.0181326i	$0.994228\pi$
$252$	−1.08413	−	41.9860i	−0.00430212	−	0.166611i
$253$		−	334.792i		−	1.32329i
$254$	−24.6118	−	42.6289i	−0.0968968	−	0.167830i
$255$	51.0344	−	182.526i	0.200135	−	0.715787i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−221.792	−	384.155i	−0.863003	−	1.49477i	−0.869016	−	0.494783i	$-0.835247\pi$
$257$	−221.792	−	384.155i	−0.863003	−	1.49477i	0.00601347	−	0.999982i	$-0.498086\pi$
$258$	−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	$-0.273840\pi$
$263$	84.6456	+	48.8702i	0.321846	+	0.185818i	−0.330369	+	0.943852i	$0.607173\pi$
$264$	−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	0.997511	−	0.0705120i	$-0.0224633\pi$
$269$	386.069	+	222.897i	1.43520	+	0.828614i	0.437690	+	0.899126i	$0.355797\pi$
$270$	35.3852	+	9.89375i	0.131056	+	0.0366435i
$271$	356.675	−	205.926i	1.31614	−	0.759875i	0.333037	−	0.942914i	$-0.391927\pi$
$271$	356.675	−	205.926i	1.31614	−	0.759875i	0.983106	+	0.183038i	$0.0585932\pi$
$272$	−87.5383			−0.321832
$273$	137.351	+	74.6404i	0.503118	+	0.273408i
$274$	−248.598			−0.907292
$275$	320.561	+	194.461i	1.16568	+	0.707130i
$276$	66.9705	+	38.6654i	0.242647	+	0.140092i
$277$	−175.978	−	101.601i	−0.635299	−	0.366790i	0.147502	−	0.989062i	$-0.452877\pi$
$277$	−175.978	−	101.601i	−0.635299	−	0.366790i	−0.782801	+	0.622272i	$0.786210\pi$
$278$	58.1720	+	100.757i	0.209252	+	0.362435i
$279$			79.8763i			0.286295i
$280$	71.0404	+	68.9439i	0.253716	+	0.246228i
$281$	−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	$-0.812197\pi$
$283$	18.7783	−	32.5250i	0.0663545	−	0.114929i	0.897294	+	0.441433i	$0.145530\pi$
$284$	−114.316	+	198.001i	−0.402521	+	0.697187i
$285$	140.839	−	137.818i	0.494170	−	0.483572i
$286$		−	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
$290$	166.612	+	46.5849i	0.574524	+	0.160638i
$291$	−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	$-0.226544\pi$
$293$	443.746			1.51449			0.757246	+	0.653129i	$0.226544\pi$
$294$	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
$305$	−36.2760	−	10.1428i	−0.118938	−	0.0332551i
$306$	80.4091	−	46.4242i	0.262775	−	0.151713i
$307$	350.661			1.14222			0.571109	−	0.820874i	$-0.306513\pi$
$307$	350.661			1.14222			0.571109	+	0.820874i	$0.306513\pi$
$308$	179.062	−	109.640i	0.581371	−	0.355973i
$309$	154.297			0.499341
$310$	−131.676	−	134.562i	−0.424762	−	0.434072i
$311$	−324.966	−	187.619i	−1.04491	−	0.603278i	−0.123688	−	0.992321i	$-0.539472\pi$
$311$	−324.966	−	187.619i	−1.04491	−	0.603278i	−0.921219	+	0.389043i	$0.872806\pi$
$312$	54.7012	+	31.5818i	0.175325	+	0.101224i
$313$	61.7457	+	106.947i	0.197271	+	0.341683i	0.947642	−	0.319333i	$-0.103459\pi$
$313$	61.7457	+	106.947i	0.197271	+	0.341683i	−0.750372	+	0.661016i	$0.770126\pi$
$314$		−	371.741i		−	1.18389i
$315$	−101.818	−	25.6541i	−0.323231	−	0.0814416i
$316$	125.669			0.397688
$317$	−321.121	+	185.399i	−1.01300	+	0.584856i	−0.912068	−	0.410038i	$-0.865515\pi$
$317$	−321.121	+	185.399i	−1.01300	+	0.584856i	−0.100931	+	0.994893i	$0.532182\pi$
$318$	−122.315	+	211.856i	−0.384639	+	0.666215i
$319$	183.463	−	317.768i	0.575120	−	0.996137i
$320$	27.9760	+	28.5892i	0.0874251	+	0.0893412i
$321$			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
$325$	6.98719	−	322.254i	0.0214990	−	0.991552i
$326$	−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	0.692214	−	0.721692i	$-0.256635\pi$
$331$	−92.3147	−	159.894i	−0.278896	−	0.483063i	−0.971111	+	0.238629i	$0.923302\pi$
$332$	−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
$340$	−58.9294	+	210.762i	−0.173322	+	0.619889i
$341$	−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
$345$	138.177	−	135.213i	0.400512	−	0.391922i
$346$	−124.246	−	71.7335i	−0.359093	−	0.207322i
$347$	−175.775	−	101.484i	−0.506557	−	0.292461i	0.224861	−	0.974391i	$-0.427807\pi$
$347$	−175.775	−	101.484i	−0.506557	−	0.292461i	−0.731417	+	0.681930i	$0.761141\pi$
$348$	42.3767	+	73.3985i	0.121772	+	0.210915i
$349$			389.811i			1.11694i	0.829526	+	0.558468i	$0.188611\pi$
$349$			389.811i			1.11694i	−0.829526	+	0.558468i	$0.811389\pi$
$350$	213.817	−	124.629i	0.610905	−	0.356084i
$351$	−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	$-0.882259\pi$
$353$	−54.0448	+	93.6083i	−0.153101	+	0.265179i	0.779265	+	0.626695i	$0.215593\pi$
$354$	−1.75524	+	3.04016i	−0.00495830	+	0.00858803i
$355$	399.763	+	408.525i	1.12609	+	1.15077i
$356$		−	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	1.00000		0.000870595i	$0.000277119\pi$
$359$	179.771	+	311.372i	0.500754	+	0.867331i	−0.499246	+	0.866460i	$0.666390\pi$
$360$	−40.8593	−	11.4243i	−0.113498	−	0.0317342i
$361$	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	0.343517	+	0.939147i	$0.388382\pi$
$367$	−235.455	+	407.820i	−0.641566	+	1.11123i	−0.985083	+	0.172079i	$0.944952\pi$
$368$	−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	$-0.910526\pi$
$373$	−447.933	+	258.614i	−1.20089	+	0.693336i	−0.240139	+	0.970739i	$0.577193\pi$
$374$	401.973	+	232.079i	1.07479	+	0.620533i
$375$	49.2070	+	210.840i	0.131219	+	0.562241i
$376$	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	$0.431934\pi$
$380$	−162.626	+	159.138i	−0.427964	+	0.418785i
$381$	−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	$-0.0768940\pi$
$383$	106.591	+	184.621i	0.278305	+	0.482039i	−0.692658	+	0.721266i	$0.743561\pi$
$384$			19.5959i			0.0510310i
$385$	−143.433	−	504.928i	−0.372554	−	1.31150i
$386$	−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	−0.107216	−	0.994236i	$-0.534194\pi$
$389$	314.088	−	544.017i	0.807425	−	1.39850i	0.914642	−	0.404266i	$-0.132473\pi$
$390$	112.862	−	110.442i	0.289390	−	0.283184i
$391$		−	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
$395$	84.5987	−	302.569i	0.214174	−	0.765998i
$396$	−44.9919	+	77.9283i	−0.113616	+	0.196789i
$397$	−90.0752	−	156.015i	−0.226890	−	0.392985i	0.729995	−	0.683453i	$-0.239522\pi$
$397$	−90.0752	−	156.015i	−0.226890	−	0.392985i	−0.956885	+	0.290468i	$0.906189\pi$
$398$	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	0.978355	−	0.206936i	$-0.0663490\pi$
$401$	124.296	+	215.288i	0.309966	+	0.536877i	−0.668389	+	0.743812i	$0.733016\pi$
$402$	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	0.712462	−	0.701711i	$-0.247580\pi$
$409$	188.546	+	108.857i	0.460993	+	0.266154i	−0.251469	+	0.967865i	$0.580914\pi$
$410$	−48.5967	+	173.807i	−0.118529	+	0.423920i
$411$	−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
$415$	422.322	+	431.578i	1.01764	+	1.03995i
$416$	−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	$0.114352\pi$
$419$			294.614i			0.703137i	−0.936162	+	0.351568i	$0.885648\pi$
$420$	117.569	+	29.6228i	0.279926	+	0.0705305i
$421$	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
$425$	467.774	+	283.764i	1.10064	+	0.667680i
$426$			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
$430$	58.5946	−	209.565i	0.136267	−	0.487361i
$431$	−86.1818	+	149.271i	−0.199958	+	0.346337i	−0.948514	−	0.316734i	$-0.897414\pi$
$431$	−86.1818	+	149.271i	−0.199958	+	0.346337i	0.748557	+	0.663071i	$0.230747\pi$
$432$	−10.3923	−	18.0000i	−0.0240563	−	0.0416667i
$433$	258.404			0.596775			0.298388	−	0.954445i	$-0.403551\pi$
$433$	258.404			0.596775			0.298388	+	0.954445i	$0.403551\pi$
$434$	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	−0.249014	−	0.968500i	$-0.580106\pi$
$439$	204.234	−	117.914i	0.465225	−	0.268598i	0.714239	+	0.699902i	$0.246773\pi$
$440$	−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	$-0.655645\pi$
$443$	26.5623	−	15.3357i	0.0599600	−	0.0346179i	0.529680	+	0.848197i	$0.322312\pi$
$444$	157.173	+	90.7436i	0.353992	+	0.204378i
$445$	−241.983	−	67.6586i	−0.543781	−	0.152042i
$446$	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	$0.789023\pi$
$450$	−55.0117	+	90.6847i	−0.122248	+	0.201522i
$451$	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
$455$	−314.276	+	323.833i	−0.690717	+	0.711722i
$456$	−111.469			−0.244450
$457$	−279.381	+	161.301i	−0.611337	+	0.352955i	−0.773488	−	0.633810i	$-0.781490\pi$
$457$	−279.381	+	161.301i	−0.611337	+	0.352955i	0.162152	+	0.986766i	$0.448157\pi$
$458$	210.819	−	365.150i	0.460304	−	0.797270i
$459$	56.8578	−	98.4806i	0.123873	−	0.214555i
$460$	−159.553	+	156.131i	−0.346853	+	0.339414i
$461$			103.910i			0.225400i	0.993629	+	0.112700i	$0.0359500\pi$
$461$			103.910i			0.225400i	−0.993629	+	0.112700i	$0.964050\pi$
$462$	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
$465$	−222.066	−	62.0899i	−0.477562	−	0.133527i
$466$	68.3114	−	118.319i	0.146591	−	0.253903i
$467$	291.820	+	505.448i	0.624883	+	1.08233i	0.988563	+	0.150805i	$0.0481866\pi$
$467$	291.820	+	505.448i	0.624883	+	1.08233i	−0.363681	+	0.931524i	$0.618480\pi$
$468$	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	0.327773	−	0.944757i	$-0.393702\pi$
$479$	−156.405	−	90.3006i	−0.326524	−	0.188519i	−0.654297	+	0.756238i	$0.727035\pi$
$480$	47.1803	+	13.1917i	0.0982923	+	0.0274826i
$481$	−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
$485$	−161.054	−	164.584i	−0.332071	−	0.339349i
$486$	19.0919	+	11.0227i	0.0392837	+	0.0226805i
$487$	725.401	+	418.811i	1.48953	+	0.859981i	0.999928	−	0.0119652i	$-0.00380873\pi$
$487$	725.401	+	418.811i	1.48953	+	0.859981i	0.489602	+	0.871946i	$0.337142\pi$
$488$	10.6539	+	18.4531i	0.0218318	+	0.0378137i
$489$			352.468i			0.720793i
$490$	−338.055	−	75.9534i	−0.689908	−	0.155007i
$491$	−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
$495$	157.337	+	160.785i	0.317852	+	0.324819i
$496$			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	0.621382	−	0.783507i	$-0.286571\pi$
$499$	−183.555	−	317.927i	−0.367846	−	0.637128i	−0.989229	+	0.146379i	$0.953238\pi$
$500$	−56.8194	−	243.458i	−0.113639	−	0.486915i
$501$	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	$-0.384751\pi$
$503$	356.332			0.708414			0.354207	+	0.935167i	$0.384751\pi$
$504$	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	−0.729939	−	0.683512i	$-0.760452\pi$
$509$	−256.011	+	147.808i	−0.502969	+	0.290390i	0.226970	+	0.973902i	$0.427118\pi$
$510$	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
$515$	−119.939	+	428.964i	−0.232891	+	0.832939i
$516$	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
$520$	−130.322	+	127.527i	−0.250619	+	0.245244i
$521$	743.226	+	429.101i	1.42654	+	0.823611i	0.996846	−	0.0793648i	$-0.0252892\pi$
$521$	743.226	+	429.101i	1.42654	+	0.823611i	0.429691	+	0.902976i	$0.358623\pi$
$522$	89.8945	+	51.9006i	0.172212	+	0.0994264i
$523$	22.7271	+	39.3644i	0.0434552	+	0.0752666i	0.886935	−	0.461894i	$-0.152830\pi$
$523$	22.7271	+	39.3644i	0.0434552	+	0.0752666i	−0.843480	+	0.537161i	$0.819497\pi$
$524$			72.3116i			0.137999i
$525$	150.467	−	263.125i	0.286604	−	0.501190i
$526$	−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
$530$	−493.908	−	504.733i	−0.931902	−	0.952327i
$531$			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
$535$	−421.584	−	117.875i	−0.788008	−	0.220328i
$536$	−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	0.865578	−	0.500773i	$-0.166951\pi$
$541$	−0.483285	−	0.837075i	−0.000893318	−	0.00154727i	−0.866472	+	0.499226i	$0.833618\pi$
$542$	−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
$550$	−530.110	−	11.4940i	−0.963837	−	0.0208981i
$551$	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
$555$	324.286	−	317.331i	0.584299	−	0.571767i
$556$	−142.492	−	82.2676i	−0.256280	−	0.147963i
$557$	−294.245	−	169.882i	−0.528267	−	0.304995i	0.212044	−	0.977260i	$-0.431988\pi$
$557$	−294.245	−	169.882i	−0.528267	−	0.304995i	−0.740310	+	0.672265i	$0.765321\pi$
$558$	−56.4811	−	97.8281i	−0.101221	−	0.175319i
$559$			396.771i			0.709787i
$560$	−135.757	−	34.2055i	−0.242423	−	0.0610812i
$561$	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	$-0.827227\pi$
$563$	10.8005	−	18.7070i	0.0191838	−	0.0332273i	0.875458	+	0.483294i	$0.160560\pi$
$564$	105.302	−	182.389i	0.186706	−	0.323384i
$565$	70.5694	−	69.0559i	0.124902	−	0.122223i
$566$			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	0.560364	−	0.828247i	$-0.310661\pi$
$569$	−248.710	−	430.779i	−0.437101	−	0.757081i	−0.997464	+	0.0711660i	$0.977328\pi$
$570$	−75.0393	+	268.380i	−0.131648	+	0.470842i
$571$	−38.6915	+	67.0156i	−0.0677609	+	0.117365i	−0.897915	−	0.440168i	$-0.854919\pi$
$571$	−38.6915	+	67.0156i	−0.0677609	+	0.117365i	0.830154	+	0.557533i	$0.188252\pi$
$572$	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	−0.439376	−	0.898303i	$-0.644800\pi$
$577$	322.119	−	557.927i	0.558265	−	0.966944i	0.997641	−	0.0686409i	$-0.0218663\pi$
$578$	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
$585$	52.0770	−	186.255i	0.0890206	−	0.318384i
$586$	−543.476	+	313.776i	−0.927434	+	0.535454i
$587$	899.689			1.53269			0.766345	−	0.642430i	$-0.222074\pi$
$587$	899.689			1.53269			0.766345	+	0.642430i	$0.222074\pi$
$588$	−92.3438	−	142.424i	−0.157047	−	0.242218i
$589$	−605.823			−1.02856
$590$	−7.08764	−	7.24298i	−0.0120129	−	0.0122762i
$591$	−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	$-0.187522\pi$
$593$	−38.8247	−	67.2463i	−0.0654716	−	0.113400i	−0.896903	+	0.442227i	$0.854189\pi$
$594$			110.207i			0.185534i
$595$	−209.303	−	736.809i	−0.351769	−	1.23833i
$596$	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	−0.508108	−	0.861293i	$-0.669655\pi$
$599$	294.617	−	510.291i	0.491848	−	0.851905i	0.999956	+	0.00938786i	$0.00298829\pi$
$600$	63.5221	−	104.714i	0.105870	−	0.174523i
$601$			785.189i			1.30647i	0.757155	+	0.653236i	$0.226589\pi$
$601$			785.189i			1.30647i	−0.757155	+	0.653236i	$0.773411\pi$
$602$	−259.809	+	159.081i	−0.431577	+	0.264254i
$603$		−	342.665i		−	0.568268i
$604$	−221.152	−	383.047i	−0.366146	−	0.634183i
$605$	−139.913	+	500.403i	−0.231262	+	0.827113i
$606$	20.7475	−	35.9357i	0.0342368	−	0.0592998i
$607$	−74.2634	−	128.628i	−0.122345	−	0.211908i	0.798347	−	0.602198i	$-0.205708\pi$
$607$	−74.2634	−	128.628i	−0.122345	−	0.211908i	−0.920692	+	0.390290i	$0.872375\pi$
$608$	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	$-0.329018\pi$
$613$	14.3936	+	8.31014i	0.0234806	+	0.0135565i	−0.488214	+	0.872724i	$0.662351\pi$
$614$	−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	0.830489	−	0.557035i	$-0.188061\pi$
$619$	472.500	+	272.798i	0.763328	+	0.440708i	−0.0671614	+	0.997742i	$0.521394\pi$
$620$	256.420	+	71.6953i	0.413580	+	0.115638i
$621$	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
$625$	−624.413	−	27.0900i	−0.999060	−	0.0433440i
$626$	−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
$630$	142.841	−	40.5763i	0.226732	−	0.0644069i
$631$	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
$635$	124.386	−	121.718i	0.195883	−	0.191682i
$636$		−	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
$640$	−54.4791	−	15.2324i	−0.0851236	−	0.0238007i
$641$	−243.379	+	421.546i	−0.379687	+	0.657637i	−0.991017	−	0.133739i	$-0.957302\pi$
$641$	−243.379	+	421.546i	−0.379687	+	0.657637i	0.611329	+	0.791376i	$0.290635\pi$
$642$	−107.227	−	185.723i	−0.167021	−	0.289288i
$643$	533.132			0.829133			0.414566	−	0.910019i	$-0.363933\pi$
$643$	533.132			0.829133			0.414566	+	0.910019i	$0.363933\pi$
$644$	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	$-0.853275\pi$
$647$	−40.5066	+	70.1594i	−0.0626068	+	0.108438i	0.833023	+	0.553238i	$0.186608\pi$
$648$	−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	$-0.649071\pi$
$653$	62.4895	−	36.0783i	0.0956960	−	0.0552501i	0.547084	+	0.837078i	$0.315738\pi$
$654$	−189.759	−	109.557i	−0.290151	−	0.167519i
$655$	174.102	+	48.6790i	0.265804	+	0.0743191i
$656$	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	$0.832908\pi$
$660$	−181.677	−	185.659i	−0.275268	−	0.281301i
$661$	335.898	+	193.931i	0.508166	+	0.293390i	0.732079	−	0.681219i	$-0.238550\pi$
$661$	335.898	+	193.931i	0.508166	+	0.293390i	−0.223914	+	0.974609i	$0.571883\pi$
$662$	226.124	+	130.553i	0.341577	+	0.197210i
$663$	−244.360	−	423.244i	−0.368567	−	0.638376i
$664$		−	341.580i		−	0.514428i
$665$	194.574	−	772.239i	0.292592	−	1.16126i
$666$	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
$670$	564.885	+	577.266i	0.843112	+	0.861591i
$671$		−	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
$675$	−2.81594	+	129.873i	−0.00417176	+	0.192405i
$676$	−2.76518	+	4.78944i	−0.00409051	+	0.00708496i
$677$	338.153	+	585.699i	0.499488	+	0.865138i	1.00000		0.000591359i	$-0.000188235\pi$
$677$	338.153	+	585.699i	0.499488	+	0.865138i	−0.500512	+	0.865730i	$0.666855\pi$
$678$	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	$-0.122476\pi$
$683$	727.579	+	420.068i	1.06527	+	0.615034i	0.138384	+	0.990379i	$0.455809\pi$
$684$	−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
$690$	−73.6210	+	263.307i	−0.106697	+	0.381605i
$691$	880.089	−	508.120i	1.27365	−	0.735340i	0.297973	−	0.954574i	$-0.403689\pi$
$691$	880.089	−	508.120i	1.27365	−	0.735340i	0.975672	+	0.219235i	$0.0703560\pi$
$692$	202.893			0.293198
$693$	−8.12954	−	314.838i	−0.0117309	−	0.454312i
$694$	287.040			0.413602
$695$	−293.995	+	287.690i	−0.423015	+	0.413943i
$696$	−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
$700$	−173.745	+	303.830i	−0.248207	+	0.434043i
$701$	−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
$705$	−368.242	−	376.313i	−0.522330	−	0.533778i
$706$		−	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	−0.864449	−	0.502721i	$-0.832332\pi$
$709$	−615.124	−	1065.43i	−0.867593	−	1.50272i	−0.00314433	−	0.999995i	$-0.501001\pi$
$710$	−778.479	−	217.664i	−1.09645	−	0.306568i
$711$	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	−0.624025	−	0.781405i	$-0.714504\pi$
$719$	−186.452	+	107.648i	−0.259321	+	0.149719i	0.364704	+	0.931124i	$0.381170\pi$
$720$	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
$725$	−13.2589	+	611.511i	−0.0182881	+	0.843463i
$726$	−220.446	+	127.274i	−0.303644	+	0.175309i
$727$	−83.4871			−0.114838			−0.0574189	−	0.998350i	$-0.518287\pi$
$727$	−83.4871			−0.114838			−0.0574189	+	0.998350i	$0.518287\pi$
$728$	255.187	−	6.58927i	0.350532	−	0.00905120i
$729$	27.0000			0.0370370
$730$	−117.352	+	114.835i	−0.160757	+	0.157309i
$731$	−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	−0.774374	−	0.632728i	$-0.781935\pi$
$733$	−685.462	−	1187.25i	−0.935146	−	1.61972i	−0.160771	−	0.986992i	$-0.551398\pi$
$734$		−	665.967i		−	0.907312i
$735$	−405.073	+	126.455i	−0.551120	+	0.172047i
$736$	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	−0.757592	−	0.652728i	$-0.773624\pi$
$739$	137.811	−	238.695i	0.186483	−	0.322998i	0.944075	+	0.329730i	$0.106958\pi$
$740$	−374.453	+	366.422i	−0.506018	+	0.495165i
$741$		−	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
$745$	36.8999	−	131.973i	0.0495301	−	0.177145i
$746$	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	0.748216	−	0.663455i	$-0.230911\pi$
$751$	−150.546	−	260.754i	−0.200461	−	0.347209i	−0.948677	+	0.316246i	$0.897577\pi$
$752$	−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
$760$	86.6479	−	309.898i	0.114010	−	0.407761i
$761$	321.453	−	185.591i	0.422408	−	0.243878i	−0.273699	−	0.961815i	$-0.588247\pi$
$761$	321.453	−	185.591i	0.422408	−	0.243878i	0.696107	+	0.717938i	$0.254914\pi$
$762$	85.2577			0.111887
$763$	550.182	+	298.984i	0.721077	+	0.391853i
$764$	219.494			0.287296
$765$	229.591	+	234.623i	0.300119	+	0.306697i
$766$	−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	$-0.638092\pi$
$769$		−	1395.52i		−	1.81473i	0.420347	−	0.907363i	$-0.361908\pi$
$770$	532.707	+	516.986i	0.691828	+	0.671410i
$771$	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	$-0.883241\pi$
$773$	−120.703	+	209.064i	−0.156149	+	0.270458i	0.777328	+	0.629096i	$0.216575\pi$
$774$	65.2808	−	113.070i	0.0843421	−	0.146085i
$775$	345.236	−	569.107i	0.445465	−	0.734332i
$776$			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
$780$	−60.1334	+	215.068i	−0.0770941	+	0.275729i
$781$	−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	$-0.892263\pi$
$787$	−144.868	+	250.919i	−0.184077	+	0.318830i	0.759188	+	0.650871i	$0.225596\pi$
$788$	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
$795$	−832.953	−	232.895i	−1.04774	−	0.292949i
$796$	−61.0084	+	35.2232i	−0.0766438	+	0.0442503i
$797$	1017.53			1.27670			0.638348	−	0.769748i	$-0.279618\pi$
$797$	1017.53			1.27670			0.638348	+	0.769748i	$0.279618\pi$
$798$	332.725	−	203.727i	0.416949	−	0.255298i
$799$	−1330.50			−1.66521
$800$	−73.3490	+	120.913i	−0.0916862	+	0.151141i
$801$	−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
$805$	190.896	−	757.643i	0.237138	−	0.941171i
$806$	−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	−0.339838	+	0.940484i	$0.610372\pi$
$809$	−796.381	+	1379.37i	−0.984402	+	1.70503i	−0.644564	+	0.764551i	$0.722961\pi$
$810$	−45.4851	+	44.5096i	−0.0561545	+	0.0549501i
$811$		−	1195.23i		−	1.47377i	−0.676017	−	0.736886i	$-0.736296\pi$
$811$		−	1195.23i		−	1.47377i	0.676017	−	0.736886i	$-0.263704\pi$
$812$	300.958	+	163.549i	0.370639	+	0.201415i
$813$			713.349i			0.877429i
$814$	555.589	+	962.309i	0.682542	+	1.18220i
$815$	−979.904	−	273.982i	−1.20234	−	0.336175i
$816$	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	0.737561	−	0.675281i	$-0.235977\pi$
$821$	−177.360	−	307.197i	−0.216030	−	0.374174i	−0.953591	+	0.301106i	$0.902644\pi$
$822$	215.292	−	372.897i	0.261913	−	0.453646i
$823$	−1150.19	−	664.063i	−1.39756	−	0.806881i	−0.403423	−	0.915014i	$-0.632180\pi$
$823$	−1150.19	−	664.063i	−1.39756	−	0.806881i	−0.994137	+	0.108132i	$0.965513\pi$
$824$	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	0.679918	−	0.733288i	$-0.262015\pi$
$829$	319.026	+	184.190i	0.384832	+	0.222183i	−0.295087	+	0.955471i	$0.595348\pi$
$830$	−822.409	−	229.947i	−0.990854	−	0.277044i
$831$	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
$835$	1.55530	+	1.58939i	0.00186264	+	0.00190346i
$836$	−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	$0.0183639\pi$
$839$			96.7533i			0.115320i	−0.998336	+	0.0576599i	$0.981636\pi$
$840$	−164.939	+	46.8535i	−0.196355	+	0.0557780i
$841$	−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
$845$	9.66985	+	9.88179i	0.0114436	+	0.0116944i
$846$		−	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
$850$	−773.555	−	16.7724i	−0.910064	−	0.0197322i
$851$	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	$-0.306445\pi$
$853$	974.612			1.14257			0.571285	+	0.820752i	$0.306445\pi$
$854$	−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	0.457216	+	0.889356i	$0.348847\pi$
$857$	−464.149	+	803.929i	−0.541597	+	0.938074i	−0.998813	+	0.0487177i	$0.984487\pi$
$858$	410.186	+	236.821i	0.478072	+	0.276015i
$859$	−290.783	+	167.884i	−0.338514	+	0.195441i	−0.659615	−	0.751604i	$-0.729280\pi$
$859$	−290.783	+	167.884i	−0.338514	+	0.195441i	0.321101	+	0.947045i	$0.395947\pi$
$860$	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	$-0.719002\pi$
$863$	−244.657	+	141.253i	−0.283497	+	0.163677i	0.351509	+	0.936185i	$0.385669\pi$
$864$	25.4558	+	14.6969i	0.0294628	+	0.0170103i
$865$	136.584	−	488.497i	0.157901	−	0.564737i
$866$	−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
$870$	−214.167	+	209.574i	−0.246169	+	0.240890i
$871$	−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
$875$	614.558	+	622.852i	0.702351	+	0.711830i
$876$	−80.4369			−0.0918230
$877$	1068.45	−	616.870i	1.21830	−	0.703387i	0.253747	−	0.967271i	$-0.418337\pi$
$877$	1068.45	−	616.870i	1.21830	−	0.703387i	0.964554	+	0.263884i	$0.0850036\pi$
$878$	−166.756	+	288.830i	−0.189927	+	0.328964i
$879$	−384.296	+	665.620i	−0.437196	+	0.757246i
$880$	209.782	+	214.380i	0.238389	+	0.243614i
$881$			714.078i			0.810531i	0.914199	+	0.405266i	$0.132821\pi$
$881$			714.078i			0.810531i	−0.914199	+	0.405266i	$0.867179\pi$
$882$	−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
$885$	−11.9530	−	3.34207i	−0.0135062	−	0.00377635i
$886$	−21.6880	+	37.5647i	−0.0244786	+	0.0423981i
$887$	−276.489	−	478.892i	−0.311712	−	0.539901i	0.667021	−	0.745039i	$-0.267569\pi$
$887$	−276.489	−	478.892i	−0.311712	−	0.539901i	−0.978733	+	0.205138i	$0.934236\pi$
$888$	−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
$900$	3.25157	−	149.965i	0.00361285	−	0.166628i
$901$	−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
$905$	796.084	−	779.010i	0.879651	−	0.860785i
$906$	−469.135	−	270.855i	−0.517809	−	0.298957i
$907$	−1188.49	−	686.177i	−1.31036	−	0.756534i	−0.328201	−	0.944608i	$-0.606442\pi$
$907$	−1188.49	−	686.177i	−1.31036	−	0.756534i	−0.982155	+	0.188074i	$0.939776\pi$
$908$	−309.995	−	536.927i	−0.341404	−	0.591329i
$909$		−	50.8208i		−	0.0559084i
$910$	155.923	−	618.840i	0.171344	−	0.680044i
$911$	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
$915$	46.6301	−	45.6300i	0.0509619	−	0.0498689i
$916$			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	0.996498	+	0.0836219i	$0.0266488\pi$
$919$	524.443	+	908.363i	0.570667	+	0.988425i	−0.425830	+	0.904803i	$0.640018\pi$
$920$	85.0102	−	304.041i	0.0924024	−	0.330479i
$921$	−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	−0.927300	−	0.374320i	$-0.877876\pi$
$929$	−991.037	+	572.176i	−1.06678	+	0.615905i	−0.139479	+	0.990225i	$0.544543\pi$
$930$	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
$935$	−441.891	+	1580.43i	−0.472611	+	1.69030i
$936$	−94.7453	+	54.7012i	−0.101224	+	0.0584415i
$937$	−255.103			−0.272255			−0.136127	−	0.990691i	$-0.543466\pi$
$937$	−255.103			−0.272255			−0.136127	+	0.990691i	$0.543466\pi$
$938$	−29.1874	−	1130.36i	−0.0311166	−	1.20508i
$939$	−213.893			−0.227788
$940$	425.210	+	434.529i	0.452351	+	0.462265i
$941$	1505.34	+	869.107i	1.59972	+	0.923600i	0.991540	+	0.129801i	$0.0414340\pi$
$941$	1505.34	+	869.107i	1.59972	+	0.923600i	0.608181	+	0.793798i	$0.291899\pi$
$942$	557.611	+	321.937i	0.591944	+	0.341759i
$943$	284.879	+	493.425i	0.302099	+	0.523250i
$944$			5.73258i			0.00607265i
$945$	126.658	−	130.510i	0.134030	−	0.138105i
$946$	652.690			0.689947
$947$	583.714	−	337.007i	0.616382	−	0.355868i	−0.159077	−	0.987266i	$-0.550852\pi$
$947$	583.714	−	337.007i	0.616382	−	0.355868i	0.775459	+	0.631398i	$0.217518\pi$
$948$	−108.833	+	188.504i	−0.114803	+	0.198844i
$949$	149.691	−	259.273i	0.157736	−	0.273206i
$950$	−687.799	−	417.237i	−0.723999	−	0.439197i
$951$		−	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
$955$	147.760	−	528.467i	0.154723	−	0.553369i
$956$	−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
$970$	313.629	+	87.6910i	0.323329	+	0.0904031i
$971$	988.758	−	570.859i	1.01829	−	0.587909i	0.104680	−	0.994506i	$-0.466618\pi$
$971$	988.758	−	570.859i	1.01829	−	0.587909i	0.913608	+	0.406597i	$0.133285\pi$
$972$	−31.1769			−0.0320750
$973$	575.681	−	14.8648i	0.591656	−	0.0152773i
$974$	−1184.58			−1.21620
$975$	477.331	+	289.561i	0.489570	+	0.296986i
$976$	−26.0966	−	15.0669i	−0.0267384	−	0.0154374i
$977$	297.549	+	171.790i	0.304554	+	0.175834i	0.644487	−	0.764615i	$-0.277071\pi$
$977$	297.549	+	171.790i	0.304554	+	0.175834i	−0.339933	+	0.940450i	$0.610404\pi$
$978$	−249.232	−	431.683i	−0.254839	−	0.441394i
$979$		−	753.655i		−	0.769821i
$980$	467.738	−	146.017i	0.477284	−	0.148997i
$981$	−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	$-0.944843\pi$
$983$	−337.362	+	584.329i	−0.343197	+	0.594434i	0.641828	+	0.766849i	$0.278176\pi$
$984$	62.5178	−	108.284i	0.0635344	−	0.110045i
$985$	567.488	−	555.317i	0.576130	−	0.563774i
$986$			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
$990$	−306.390	−	85.6670i	−0.309485	−	0.0865323i
$991$	−398.425	+	690.093i	−0.402044	+	0.696360i	−0.993972	−	0.109630i	$-0.965033\pi$
$991$	−398.425	+	690.093i	−0.402044	+	0.696360i	0.591929	+	0.805990i	$0.298367\pi$
$992$	−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	0.438635	+	0.898665i	$0.355462\pi$
$997$	−557.272	+	965.224i	−0.558949	+	0.968128i	−0.997585	+	0.0694633i	$0.977871\pi$
$998$	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.199.1	yes	32
3.2	odd	2		630.3.bc.b.199.12		32
5.2	odd	4		1050.3.p.h.451.1		16
5.3	odd	4		1050.3.p.g.451.8		16
5.4	even	2	inner	210.3.p.a.199.14	yes	32
7.3	odd	6		1470.3.h.a.979.1		32
7.4	even	3		1470.3.h.a.979.27		32
7.5	odd	6	inner	210.3.p.a.19.14	yes	32
15.14	odd	2		630.3.bc.b.199.1		32
21.5	even	6		630.3.bc.b.19.1		32
35.4	even	6		1470.3.h.a.979.2		32
35.12	even	12		1050.3.p.h.901.1		16
35.19	odd	6	inner	210.3.p.a.19.1	✓	32
35.24	odd	6		1470.3.h.a.979.28		32
35.33	even	12		1050.3.p.g.901.8		16
105.89	even	6		630.3.bc.b.19.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.p.a.19.1	✓	32	35.19	odd	6	inner
210.3.p.a.19.14	yes	32	7.5	odd	6	inner
210.3.p.a.199.1	yes	32	1.1	even	1	trivial
210.3.p.a.199.14	yes	32	5.4	even	2	inner
630.3.bc.b.19.1		32	21.5	even	6
630.3.bc.b.19.12		32	105.89	even	6
630.3.bc.b.199.1		32	15.14	odd	2
630.3.bc.b.199.12		32	3.2	odd	2
1050.3.p.g.451.8		16	5.3	odd	4
1050.3.p.g.901.8		16	35.33	even	12
1050.3.p.h.451.1		16	5.2	odd	4
1050.3.p.h.901.1		16	35.12	even	12
1470.3.h.a.979.1		32	7.3	odd	6
1470.3.h.a.979.2		32	35.4	even	6
1470.3.h.a.979.27		32	7.4	even	3
1470.3.h.a.979.28		32	35.24	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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-3.49700 - 3.57365i) q^{5} -2.44949i q^{6} +(0.180689 + 6.99767i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-3.49700 - 3.57365i) q^{5} -2.44949i q^{6} +(0.180689 + 6.99767i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(6.80989 + 1.90405i) 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} +(-0.541928 + 24.9941i) q^{25} +(15.7909 - 9.11687i) q^{26} +5.19615 q^{27} +(12.3010 + 6.68471i) q^{28} +24.4662 q^{29} +(-8.75362 + 8.56588i) q^{30} +(-23.0583 - 13.3127i) q^{31} +(4.89898 + 2.82843i) q^{32} +(12.9880 + 22.4960i) q^{33} +30.9495i q^{34} +(24.3753 - 25.1166i) q^{35} -6.00000 q^{36} +(45.3718 - 26.1954i) q^{37} +(-16.0892 + 27.8673i) q^{38} +(11.1658 - 19.3398i) q^{39} +(10.1078 - 9.89102i) q^{40} +25.5228i q^{41} +(17.1407 - 0.442596i) q^{42} -30.7736i q^{43} +(-14.9973 - 25.9761i) q^{44} +(-4.03911 + 14.4460i) 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} +(4.66396 - 16.6808i) q^{60} +(6.52416 - 3.76672i) q^{61} +37.6540 q^{62} +(17.9094 - 10.9659i) q^{63} -8.00000 q^{64} +(45.0876 + 46.0758i) q^{65} +(-31.8141 - 18.3679i) q^{66} +(98.9190 + 57.1109i) q^{67} +(-21.8846 - 37.9052i) q^{68} +38.6654i q^{69} +(-12.0935 + 47.9974i) q^{70} -114.316 q^{71} +(7.34847 - 4.24264i) q^{72} +(-11.6101 + 20.1092i) q^{73} +(-37.0459 + 64.1654i) q^{74} +(-37.0219 - 22.4584i) q^{75} -45.5071i q^{76} +(92.2409 + 50.1263i) q^{77} +31.5818i q^{78} +(31.4174 + 54.4165i) q^{79} +(-5.38547 + 19.2613i) 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} +(-109.566 - 30.6347i) 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

Groups

Database

Properties

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