LMFDB - Embedded newform 42.3.h.a.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,3,Mod(11,42)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("42.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	42.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.14441711031$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.2
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	42.23
Dual form			42.3.h.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 + 0.707107i) q^{2} +(2.94949 - 0.548188i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-7.34847 - 4.24264i) q^{5} +(4.00000 + 1.41421i) q^{6} +(-3.50000 + 6.06218i) q^{7} +2.82843i q^{8} +(8.39898 - 3.23375i) q^{9} +O(q^{10})$	\(q+(1.22474 + 0.707107i) q^{2} +(2.94949 - 0.548188i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-7.34847 - 4.24264i) q^{5} +(4.00000 + 1.41421i) q^{6} +(-3.50000 + 6.06218i) q^{7} +2.82843i q^{8} +(8.39898 - 3.23375i) q^{9} +(-6.00000 - 10.3923i) q^{10} +(3.89898 + 4.56048i) q^{12} -1.00000 q^{13} +(-8.57321 + 4.94975i) q^{14} +(-24.0000 - 8.48528i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-7.34847 + 4.24264i) q^{17} +(12.5732 + 1.97846i) q^{18} +(15.5000 - 26.8468i) q^{19} -16.9706i q^{20} +(-7.00000 + 19.7990i) q^{21} +(7.34847 + 4.24264i) q^{23} +(1.55051 + 8.34242i) q^{24} +(23.5000 + 40.7032i) q^{25} +(-1.22474 - 0.707107i) q^{26} +(23.0000 - 14.1421i) q^{27} -14.0000 q^{28} +16.9706i q^{29} +(-23.3939 - 27.3629i) q^{30} +(3.50000 + 6.06218i) q^{31} +(-4.89898 + 2.82843i) q^{32} -12.0000 q^{34} +(51.4393 - 29.6985i) q^{35} +(14.0000 + 11.3137i) q^{36} +(0.500000 - 0.866025i) q^{37} +(37.9671 - 21.9203i) q^{38} +(-2.94949 + 0.548188i) q^{39} +(12.0000 - 20.7846i) q^{40} +33.9411i q^{41} +(-22.5732 + 19.2990i) q^{42} -31.0000 q^{43} +(-75.4393 - 11.8707i) q^{45} +(6.00000 + 10.3923i) q^{46} +(-36.7423 - 21.2132i) q^{47} +(-4.00000 + 11.3137i) q^{48} +(-24.5000 - 42.4352i) q^{49} +66.4680i q^{50} +(-19.3485 + 16.5420i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(22.0454 - 12.7279i) q^{53} +(38.1691 - 1.05705i) q^{54} +(-17.1464 - 9.89949i) q^{56} +(31.0000 - 87.6812i) q^{57} +(-12.0000 + 20.7846i) q^{58} +(-7.34847 + 4.24264i) q^{59} +(-9.30306 - 50.0545i) q^{60} +(-25.0000 + 43.3013i) q^{61} +9.89949i q^{62} +(-9.79286 + 62.2342i) q^{63} -8.00000 q^{64} +(7.34847 + 4.24264i) q^{65} +(-32.5000 - 56.2917i) q^{67} +(-14.6969 - 8.48528i) q^{68} +(24.0000 + 8.48528i) q^{69} +84.0000 q^{70} -59.3970i q^{71} +(9.14643 + 23.7559i) q^{72} +(48.5000 + 84.0045i) q^{73} +(1.22474 - 0.707107i) q^{74} +(91.6260 + 107.171i) q^{75} +62.0000 q^{76} +(-4.00000 - 1.41421i) q^{78} +(51.5000 - 89.2006i) q^{79} +(29.3939 - 16.9706i) q^{80} +(60.0857 - 54.3204i) q^{81} +(-24.0000 + 41.5692i) q^{82} +42.4264i q^{83} +(-41.2929 + 7.67463i) q^{84} +72.0000 q^{85} +(-37.9671 - 21.9203i) q^{86} +(9.30306 + 50.0545i) q^{87} +(-102.879 - 59.3970i) q^{89} +(-84.0000 - 67.8823i) q^{90} +(3.50000 - 6.06218i) q^{91} +16.9706i q^{92} +(13.6464 + 15.9617i) q^{93} +(-30.0000 - 51.9615i) q^{94} +(-227.803 + 131.522i) q^{95} +(-12.8990 + 11.0280i) q^{96} -166.000 q^{97} -69.2965i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 4 q^{4} + 16 q^{6} - 14 q^{7} + 14 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 4 * q^4 + 16 * q^6 - 14 * q^7 + 14 * q^9	$ 4 q + 2 q^{3} + 4 q^{4} + 16 q^{6} - 14 q^{7} + 14 q^{9} - 24 q^{10} - 4 q^{12} - 4 q^{13} - 96 q^{15} - 8 q^{16} + 16 q^{18} + 62 q^{19} - 28 q^{21} + 16 q^{24} + 94 q^{25} + 92 q^{27} - 56 q^{28} + 24 q^{30} + 14 q^{31} - 48 q^{34} + 56 q^{36} + 2 q^{37} - 2 q^{39} + 48 q^{40} - 56 q^{42} - 124 q^{43} - 96 q^{45} + 24 q^{46} - 16 q^{48} - 98 q^{49} - 48 q^{51} - 4 q^{52} + 40 q^{54} + 124 q^{57} - 48 q^{58} - 96 q^{60} - 100 q^{61} + 98 q^{63} - 32 q^{64} - 130 q^{67} + 96 q^{69} + 336 q^{70} - 32 q^{72} + 194 q^{73} - 94 q^{75} + 248 q^{76} - 16 q^{78} + 206 q^{79} - 34 q^{81} - 96 q^{82} - 28 q^{84} + 288 q^{85} + 96 q^{87} - 336 q^{90} + 14 q^{91} - 14 q^{93} - 120 q^{94} - 32 q^{96} - 664 q^{97}+O(q^{100}) $ 4 * q + 2 * q^3 + 4 * q^4 + 16 * q^6 - 14 * q^7 + 14 * q^9 - 24 * q^10 - 4 * q^12 - 4 * q^13 - 96 * q^15 - 8 * q^16 + 16 * q^18 + 62 * q^19 - 28 * q^21 + 16 * q^24 + 94 * q^25 + 92 * q^27 - 56 * q^28 + 24 * q^30 + 14 * q^31 - 48 * q^34 + 56 * q^36 + 2 * q^37 - 2 * q^39 + 48 * q^40 - 56 * q^42 - 124 * q^43 - 96 * q^45 + 24 * q^46 - 16 * q^48 - 98 * q^49 - 48 * q^51 - 4 * q^52 + 40 * q^54 + 124 * q^57 - 48 * q^58 - 96 * q^60 - 100 * q^61 + 98 * q^63 - 32 * q^64 - 130 * q^67 + 96 * q^69 + 336 * q^70 - 32 * q^72 + 194 * q^73 - 94 * q^75 + 248 * q^76 - 16 * q^78 + 206 * q^79 - 34 * q^81 - 96 * q^82 - 28 * q^84 + 288 * q^85 + 96 * q^87 - 336 * q^90 + 14 * q^91 - 14 * q^93 - 120 * q^94 - 32 * q^96 - 664 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$3$	2.94949	−	0.548188i	0.983163	−	0.182729i
$3$	2.94949	−	0.548188i	0.983163	−	0.182729i
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	−7.34847	−	4.24264i	−1.46969	−	0.848528i	−0.470272	−	0.882522i	$-0.655844\pi$
$5$	−7.34847	−	4.24264i	−1.46969	−	0.848528i	−0.999422	+	0.0339935i	$0.989177\pi$
$6$	4.00000	+	1.41421i	0.666667	+	0.235702i
$7$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$7$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$8$			2.82843i			0.353553i
$9$	8.39898	−	3.23375i	0.933220	−	0.359306i
$10$	−6.00000	−	10.3923i	−0.600000	−	1.03923i
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$	3.89898	+	4.56048i	0.324915	+	0.380040i
$13$	−1.00000			−0.0769231			−0.0384615	−	0.999260i	$-0.512246\pi$
$13$	−1.00000			−0.0769231			−0.0384615	+	0.999260i	$0.512246\pi$
$14$	−8.57321	+	4.94975i	−0.612372	+	0.353553i
$15$	−24.0000	−	8.48528i	−1.60000	−	0.565685i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−7.34847	+	4.24264i	−0.432263	+	0.249567i	−0.700310	−	0.713839i	$-0.746955\pi$
$17$	−7.34847	+	4.24264i	−0.432263	+	0.249567i	0.268047	+	0.963406i	$0.413622\pi$
$18$	12.5732	+	1.97846i	0.698512	+	0.109914i
$19$	15.5000	−	26.8468i	0.815789	−	1.41299i	−0.0929702	−	0.995669i	$-0.529636\pi$
$19$	15.5000	−	26.8468i	0.815789	−	1.41299i	0.908760	−	0.417320i	$-0.137031\pi$
$20$		−	16.9706i		−	0.848528i
$21$	−7.00000	+	19.7990i	−0.333333	+	0.942809i
$22$		0			0
$23$	7.34847	+	4.24264i	0.319499	+	0.184463i	0.651169	−	0.758933i	$-0.274279\pi$
$23$	7.34847	+	4.24264i	0.319499	+	0.184463i	−0.331670	+	0.943395i	$0.607612\pi$
$24$	1.55051	+	8.34242i	0.0646046	+	0.347601i
$25$	23.5000	+	40.7032i	0.940000	+	1.62813i
$26$	−1.22474	−	0.707107i	−0.0471056	−	0.0271964i
$27$	23.0000	−	14.1421i	0.851852	−	0.523783i
$28$	−14.0000			−0.500000
$29$			16.9706i			0.585192i	0.956236	+	0.292596i	$0.0945191\pi$
$29$			16.9706i			0.585192i	−0.956236	+	0.292596i	$0.905481\pi$
$30$	−23.3939	−	27.3629i	−0.779796	−	0.912096i
$31$	3.50000	+	6.06218i	0.112903	+	0.195554i	0.916940	−	0.399026i	$-0.130652\pi$
$31$	3.50000	+	6.06218i	0.112903	+	0.195554i	−0.804036	+	0.594580i	$0.797318\pi$
$32$	−4.89898	+	2.82843i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−12.0000			−0.352941
$35$	51.4393	−	29.6985i	1.46969	−	0.848528i
$36$	14.0000	+	11.3137i	0.388889	+	0.314270i
$37$	0.500000	−	0.866025i	0.0135135	−	0.0234061i	−0.859190	−	0.511657i	$-0.829032\pi$
$37$	0.500000	−	0.866025i	0.0135135	−	0.0234061i	0.872703	+	0.488251i	$0.162365\pi$
$38$	37.9671	−	21.9203i	0.999134	−	0.576850i
$39$	−2.94949	+	0.548188i	−0.0756279	+	0.0140561i
$40$	12.0000	−	20.7846i	0.300000	−	0.519615i
$41$			33.9411i			0.827832i	0.910315	+	0.413916i	$0.135839\pi$
$41$			33.9411i			0.827832i	−0.910315	+	0.413916i	$0.864161\pi$
$42$	−22.5732	+	19.2990i	−0.537457	+	0.459499i
$43$	−31.0000			−0.720930			−0.360465	−	0.932773i	$-0.617382\pi$
$43$	−31.0000			−0.720930			−0.360465	+	0.932773i	$0.617382\pi$
$44$		0			0
$45$	−75.4393	−	11.8707i	−1.67643	−	0.263794i
$46$	6.00000	+	10.3923i	0.130435	+	0.225920i
$47$	−36.7423	−	21.2132i	−0.781752	−	0.451345i	0.0552988	−	0.998470i	$-0.482389\pi$
$47$	−36.7423	−	21.2132i	−0.781752	−	0.451345i	−0.837051	+	0.547125i	$0.815722\pi$
$48$	−4.00000	+	11.3137i	−0.0833333	+	0.235702i
$49$	−24.5000	−	42.4352i	−0.500000	−	0.866025i
$50$			66.4680i			1.32936i
$51$	−19.3485	+	16.5420i	−0.379382	+	0.324352i
$52$	−1.00000	−	1.73205i	−0.0192308	−	0.0333087i
$53$	22.0454	−	12.7279i	0.415951	−	0.240149i	−0.277392	−	0.960757i	$-0.589470\pi$
$53$	22.0454	−	12.7279i	0.415951	−	0.240149i	0.693344	+	0.720607i	$0.256137\pi$
$54$	38.1691	−	1.05705i	0.706836	−	0.0195750i
$55$		0			0
$56$	−17.1464	−	9.89949i	−0.306186	−	0.176777i
$57$	31.0000	−	87.6812i	0.543860	−	1.53827i
$58$	−12.0000	+	20.7846i	−0.206897	+	0.358355i
$59$	−7.34847	+	4.24264i	−0.124550	+	0.0719092i	−0.560981	−	0.827829i	$-0.689576\pi$
$59$	−7.34847	+	4.24264i	−0.124550	+	0.0719092i	0.436430	+	0.899738i	$0.356243\pi$
$60$	−9.30306	−	50.0545i	−0.155051	−	0.834242i
$61$	−25.0000	+	43.3013i	−0.409836	+	0.709857i	−0.994871	−	0.101151i	$-0.967747\pi$
$61$	−25.0000	+	43.3013i	−0.409836	+	0.709857i	0.585035	+	0.811008i	$0.301081\pi$
$62$			9.89949i			0.159669i
$63$	−9.79286	+	62.2342i	−0.155442	+	0.987845i
$64$	−8.00000			−0.125000
$65$	7.34847	+	4.24264i	0.113053	+	0.0652714i
$66$		0			0
$67$	−32.5000	−	56.2917i	−0.485075	−	0.840174i	0.514778	−	0.857323i	$-0.327874\pi$
$67$	−32.5000	−	56.2917i	−0.485075	−	0.840174i	−0.999853	+	0.0171494i	$0.994541\pi$
$68$	−14.6969	−	8.48528i	−0.216131	−	0.124784i
$69$	24.0000	+	8.48528i	0.347826	+	0.122975i
$70$	84.0000			1.20000
$71$		−	59.3970i		−	0.836577i	−0.908314	−	0.418289i	$-0.862630\pi$
$71$		−	59.3970i		−	0.836577i	0.908314	−	0.418289i	$-0.137370\pi$
$72$	9.14643	+	23.7559i	0.127034	+	0.329943i
$73$	48.5000	+	84.0045i	0.664384	+	1.15075i	0.979452	+	0.201677i	$0.0646392\pi$
$73$	48.5000	+	84.0045i	0.664384	+	1.15075i	−0.315068	+	0.949069i	$0.602027\pi$
$74$	1.22474	−	0.707107i	0.0165506	−	0.00955550i
$75$	91.6260	+	107.171i	1.22168	+	1.42895i
$76$	62.0000			0.815789
$77$		0			0
$78$	−4.00000	−	1.41421i	−0.0512821	−	0.0181309i
$79$	51.5000	−	89.2006i	0.651899	−	1.12912i	−0.330763	−	0.943714i	$-0.607306\pi$
$79$	51.5000	−	89.2006i	0.651899	−	1.12912i	0.982662	−	0.185408i	$-0.0593606\pi$
$80$	29.3939	−	16.9706i	0.367423	−	0.212132i
$81$	60.0857	−	54.3204i	0.741799	−	0.670622i
$82$	−24.0000	+	41.5692i	−0.292683	+	0.506942i
$83$			42.4264i			0.511162i	0.966788	+	0.255581i	$0.0822667\pi$
$83$			42.4264i			0.511162i	−0.966788	+	0.255581i	$0.917733\pi$
$84$	−41.2929	+	7.67463i	−0.491582	+	0.0913647i
$85$	72.0000			0.847059
$86$	−37.9671	−	21.9203i	−0.441478	−	0.254887i
$87$	9.30306	+	50.0545i	0.106932	+	0.575339i
$88$		0			0
$89$	−102.879	−	59.3970i	−1.15594	−	0.667382i	−0.205612	−	0.978634i	$-0.565918\pi$
$89$	−102.879	−	59.3970i	−1.15594	−	0.667382i	−0.950327	+	0.311252i	$0.899252\pi$
$90$	−84.0000	−	67.8823i	−0.933333	−	0.754247i
$91$	3.50000	−	6.06218i	0.0384615	−	0.0666173i
$92$			16.9706i			0.184463i
$93$	13.6464	+	15.9617i	0.146736	+	0.171631i
$94$	−30.0000	−	51.9615i	−0.319149	−	0.552782i
$95$	−227.803	+	131.522i	−2.39792	+	1.38444i
$96$	−12.8990	+	11.0280i	−0.134364	+	0.114875i
$97$	−166.000			−1.71134			−0.855670	−	0.517522i	$-0.826855\pi$
$97$	−166.000			−1.71134			−0.855670	+	0.517522i	$0.826855\pi$
$98$		−	69.2965i		−	0.707107i
$99$		0			0
$100$	−47.0000	+	81.4064i	−0.470000	+	0.814064i
$101$	117.576	−	67.8823i	1.16411	−	0.672101i	0.211827	−	0.977307i	$-0.432059\pi$
$101$	117.576	−	67.8823i	1.16411	−	0.672101i	0.952286	+	0.305206i	$0.0987252\pi$
$102$	−35.3939	+	6.57826i	−0.346999	+	0.0644927i
$103$	−32.5000	+	56.2917i	−0.315534	+	0.546521i	−0.979551	−	0.201197i	$-0.935517\pi$
$103$	−32.5000	+	56.2917i	−0.315534	+	0.546521i	0.664017	+	0.747718i	$0.268850\pi$
$104$		−	2.82843i		−	0.0271964i
$105$	135.439	−	115.794i	1.28990	−	1.10280i
$106$	36.0000			0.339623
$107$	139.621	+	80.6102i	1.30487	+	0.753366i	0.981235	−	0.192816i	$-0.0617622\pi$
$107$	139.621	+	80.6102i	1.30487	+	0.753366i	0.323634	+	0.946183i	$0.395096\pi$
$108$	47.4949	+	25.6950i	0.439768	+	0.237917i
$109$	−83.5000	−	144.626i	−0.766055	−	1.32685i	−0.939687	−	0.342036i	$-0.888884\pi$
$109$	−83.5000	−	144.626i	−0.766055	−	1.32685i	0.173632	−	0.984811i	$-0.444450\pi$
$110$		0			0
$111$	1.00000	−	2.82843i	0.00900901	−	0.0254813i
$112$	−14.0000	−	24.2487i	−0.125000	−	0.216506i
$113$			161.220i			1.42673i	0.700793	+	0.713364i	$0.252830\pi$
$113$			161.220i			1.42673i	−0.700793	+	0.713364i	$0.747170\pi$
$114$	99.9671	−	85.4668i	0.876904	−	0.749709i
$115$	−36.0000	−	62.3538i	−0.313043	−	0.542207i
$116$	−29.3939	+	16.9706i	−0.253395	+	0.146298i
$117$	−8.39898	+	3.23375i	−0.0717861	+	0.0276389i
$118$	−12.0000			−0.101695
$119$		−	59.3970i		−	0.499134i
$120$	24.0000	−	67.8823i	0.200000	−	0.565685i
$121$	−60.5000	+	104.789i	−0.500000	+	0.866025i
$122$	−61.2372	+	35.3553i	−0.501945	+	0.289798i
$123$	18.6061	+	100.109i	0.151269	+	0.813894i
$124$	−7.00000	+	12.1244i	−0.0564516	+	0.0977771i
$125$		−	186.676i		−	1.49341i
$126$	−56.0000	+	69.2965i	−0.444444	+	0.549972i
$127$	113.000			0.889764			0.444882	−	0.895589i	$-0.353246\pi$
$127$	113.000			0.889764			0.444882	+	0.895589i	$0.353246\pi$
$128$	−9.79796	−	5.65685i	−0.0765466	−	0.0441942i
$129$	−91.4342	+	16.9938i	−0.708792	+	0.131735i
$130$	6.00000	+	10.3923i	0.0461538	+	0.0799408i
$131$	73.4847	+	42.4264i	0.560952	+	0.323866i	0.753527	−	0.657416i	$-0.228351\pi$
$131$	73.4847	+	42.4264i	0.560952	+	0.323866i	−0.192576	+	0.981282i	$0.561684\pi$
$132$		0			0
$133$	108.500	+	187.928i	0.815789	+	1.41299i
$134$		−	91.9239i		−	0.685999i
$135$	−229.015	+	6.34231i	−1.69641	+	0.0469801i
$136$	−12.0000	−	20.7846i	−0.0882353	−	0.152828i
$137$	161.666	−	93.3381i	1.18005	−	0.681300i	0.224021	−	0.974584i	$-0.428082\pi$
$137$	161.666	−	93.3381i	1.18005	−	0.681300i	0.956025	+	0.293284i	$0.0947483\pi$
$138$	23.3939	+	27.3629i	0.169521	+	0.198282i
$139$	113.000			0.812950			0.406475	−	0.913662i	$-0.366758\pi$
$139$	113.000			0.812950			0.406475	+	0.913662i	$0.366758\pi$
$140$	102.879	+	59.3970i	0.734847	+	0.424264i
$141$	−120.000	−	42.4264i	−0.851064	−	0.300897i
$142$	42.0000	−	72.7461i	0.295775	−	0.512297i
$143$		0			0
$144$	−5.59592	+	35.5624i	−0.0388605	+	0.246961i
$145$	72.0000	−	124.708i	0.496552	−	0.860053i
$146$			137.179i			0.939580i
$147$	−95.5250	−	111.732i	−0.649830	−	0.760080i
$148$	2.00000			0.0135135
$149$	−58.7878	−	33.9411i	−0.394549	−	0.227793i	0.289580	−	0.957154i	$-0.406484\pi$
$149$	−58.7878	−	33.9411i	−0.394549	−	0.227793i	−0.684129	+	0.729361i	$0.739818\pi$
$150$	36.4370	+	196.047i	0.242913	+	1.30698i
$151$	29.0000	+	50.2295i	0.192053	+	0.332646i	0.945930	−	0.324370i	$-0.105152\pi$
$151$	29.0000	+	50.2295i	0.192053	+	0.332646i	−0.753877	+	0.657015i	$0.771819\pi$
$152$	75.9342	+	43.8406i	0.499567	+	0.288425i
$153$	−48.0000	+	59.3970i	−0.313725	+	0.388215i
$154$		0			0
$155$		−	59.3970i		−	0.383206i
$156$	−3.89898	−	4.56048i	−0.0249935	−	0.0292338i
$157$	59.0000	+	102.191i	0.375796	+	0.650898i	0.990446	−	0.137902i	$-0.0440359\pi$
$157$	59.0000	+	102.191i	0.375796	+	0.650898i	−0.614650	+	0.788800i	$0.710703\pi$
$158$	126.149	−	72.8320i	0.798410	−	0.460962i
$159$	58.0454	−	49.6259i	0.365065	−	0.312113i
$160$	48.0000			0.300000
$161$	−51.4393	+	29.6985i	−0.319499	+	0.184463i
$162$	112.000	−	24.0416i	0.691358	−	0.148405i
$163$	53.0000	−	91.7987i	0.325153	−	0.563182i	−0.656390	−	0.754422i	$-0.727917\pi$
$163$	53.0000	−	91.7987i	0.325153	−	0.563182i	0.981543	+	0.191240i	$0.0612507\pi$
$164$	−58.7878	+	33.9411i	−0.358462	+	0.206958i
$165$		0			0
$166$	−30.0000	+	51.9615i	−0.180723	+	0.313021i
$167$			144.250i			0.863771i	0.901928	+	0.431886i	$0.142152\pi$
$167$			144.250i			0.863771i	−0.901928	+	0.431886i	$0.857848\pi$
$168$	−56.0000	−	19.7990i	−0.333333	−	0.117851i
$169$	−168.000			−0.994083
$170$	88.1816	+	50.9117i	0.518715	+	0.299481i
$171$	43.3684	−	275.609i	0.253616	−	1.61175i
$172$	−31.0000	−	53.6936i	−0.180233	−	0.312172i
$173$	−66.1362	−	38.1838i	−0.382290	−	0.220715i	0.296524	−	0.955025i	$-0.404173\pi$
$173$	−66.1362	−	38.1838i	−0.382290	−	0.220715i	−0.678814	+	0.734310i	$0.737506\pi$
$174$	−24.0000	+	67.8823i	−0.137931	+	0.390128i
$175$	−329.000			−1.88000
$176$		0			0
$177$	−19.3485	+	16.5420i	−0.109313	+	0.0934575i
$178$	−84.0000	−	145.492i	−0.471910	−	0.817372i
$179$	139.621	−	80.6102i	0.780005	−	0.450336i	−0.0564270	−	0.998407i	$-0.517971\pi$
$179$	139.621	−	80.6102i	0.780005	−	0.450336i	0.836432	+	0.548071i	$0.184637\pi$
$180$	−54.8786	−	142.535i	−0.304881	−	0.791863i
$181$	215.000			1.18785			0.593923	−	0.804522i	$-0.297579\pi$
$181$	215.000			1.18785			0.593923	+	0.804522i	$0.297579\pi$
$182$	8.57321	−	4.94975i	0.0471056	−	0.0271964i
$183$	−50.0000	+	141.421i	−0.273224	+	0.772794i
$184$	−12.0000	+	20.7846i	−0.0652174	+	0.112960i
$185$	−7.34847	+	4.24264i	−0.0397215	+	0.0229332i
$186$	5.42679	+	29.1985i	0.0291763	+	0.156981i
$187$		0			0
$188$		−	84.8528i		−	0.451345i
$189$	5.23214	+	188.928i	0.0276833	+	0.999617i
$190$	−372.000			−1.95789
$191$	−154.318	−	89.0955i	−0.807947	−	0.466468i	0.0382955	−	0.999266i	$-0.487807\pi$
$191$	−154.318	−	89.0955i	−0.807947	−	0.466468i	−0.846242	+	0.532798i	$0.821141\pi$
$192$	−23.5959	+	4.38551i	−0.122895	+	0.0228412i
$193$	48.5000	+	84.0045i	0.251295	+	0.435256i	0.963883	−	0.266327i	$-0.0858101\pi$
$193$	48.5000	+	84.0045i	0.251295	+	0.435256i	−0.712587	+	0.701583i	$0.752477\pi$
$194$	−203.308	−	117.380i	−1.04798	−	0.605050i
$195$	24.0000	+	8.48528i	0.123077	+	0.0435143i
$196$	49.0000	−	84.8705i	0.250000	−	0.433013i
$197$			364.867i			1.85212i	0.377380	+	0.926059i	$0.376825\pi$
$197$			364.867i			1.85212i	−0.377380	+	0.926059i	$0.623175\pi$
$198$		0			0
$199$	53.0000	+	91.7987i	0.266332	+	0.461300i	0.967912	−	0.251291i	$-0.0808550\pi$
$199$	53.0000	+	91.7987i	0.266332	+	0.461300i	−0.701580	+	0.712591i	$0.747522\pi$
$200$	−115.126	+	66.4680i	−0.575630	+	0.332340i
$201$	−126.717	−	148.216i	−0.630432	−	0.737391i
$202$	192.000			0.950495
$203$	−102.879	−	59.3970i	−0.506791	−	0.292596i
$204$	−48.0000	−	16.9706i	−0.235294	−	0.0831890i
$205$	144.000	−	249.415i	0.702439	−	1.21666i
$206$	−79.6084	+	45.9619i	−0.386449	+	0.223116i
$207$	75.4393	+	11.8707i	0.364441	+	0.0573465i
$208$	2.00000	−	3.46410i	0.00961538	−	0.0166543i
$209$		0			0
$210$	247.757	−	46.0478i	1.17980	−	0.219275i
$211$	62.0000			0.293839			0.146919	−	0.989148i	$-0.453064\pi$
$211$	62.0000			0.293839			0.146919	+	0.989148i	$0.453064\pi$
$212$	44.0908	+	25.4558i	0.207976	+	0.120075i
$213$	−32.5607	−	175.191i	−0.152867	−	0.822492i
$214$	114.000	+	197.454i	0.532710	+	0.922681i
$215$	227.803	+	131.522i	1.05955	+	0.611730i
$216$	40.0000	+	65.0538i	0.185185	+	0.301175i
$217$	−49.0000			−0.225806
$218$		−	236.174i		−	1.08337i
$219$	189.101	+	221.183i	0.863473	+	1.00997i
$220$		0			0
$221$	7.34847	−	4.24264i	0.0332510	−	0.0191975i
$222$	3.22474	−	2.75699i	0.0145259	−	0.0124189i
$223$	−202.000			−0.905830			−0.452915	−	0.891554i	$-0.649616\pi$
$223$	−202.000			−0.905830			−0.452915	+	0.891554i	$0.649616\pi$
$224$		−	39.5980i		−	0.176777i
$225$	329.000	+	265.872i	1.46222	+	1.18165i
$226$	−114.000	+	197.454i	−0.504425	+	0.873689i
$227$	−14.6969	+	8.48528i	−0.0647442	+	0.0373801i	−0.532023	−	0.846730i	$-0.678568\pi$
$227$	−14.6969	+	8.48528i	−0.0647442	+	0.0373801i	0.467278	+	0.884110i	$0.345235\pi$
$228$	182.868	−	33.9877i	0.802054	−	0.149069i
$229$	0.500000	−	0.866025i	0.00218341	−	0.00378177i	−0.864932	−	0.501890i	$-0.832638\pi$
$229$	0.500000	−	0.866025i	0.00218341	−	0.00378177i	0.867115	+	0.498108i	$0.165972\pi$
$230$		−	101.823i		−	0.442710i
$231$		0			0
$232$	−48.0000			−0.206897
$233$	−286.590	−	165.463i	−1.23000	−	0.710142i	−0.262971	−	0.964804i	$-0.584702\pi$
$233$	−286.590	−	165.463i	−1.23000	−	0.710142i	−0.967030	+	0.254662i	$0.918036\pi$
$234$	−12.5732	−	1.97846i	−0.0537317	−	0.00845494i
$235$	180.000	+	311.769i	0.765957	+	1.32668i
$236$	−14.6969	−	8.48528i	−0.0622752	−	0.0359546i
$237$	103.000	−	291.328i	0.434599	−	1.22923i
$238$	42.0000	−	72.7461i	0.176471	−	0.305656i
$239$		−	458.205i		−	1.91718i	−0.284796	−	0.958588i	$-0.591926\pi$
$239$		−	458.205i		−	1.91718i	0.284796	−	0.958588i	$-0.408074\pi$
$240$	77.3939	−	66.1679i	0.322474	−	0.275699i
$241$	11.0000	+	19.0526i	0.0456432	+	0.0790563i	0.887944	−	0.459951i	$-0.152133\pi$
$241$	11.0000	+	19.0526i	0.0456432	+	0.0790563i	−0.842301	+	0.539007i	$0.818800\pi$
$242$	−148.194	+	85.5599i	−0.612372	+	0.353553i
$243$	147.444	−	193.156i	0.606767	−	0.794880i
$244$	−100.000			−0.409836
$245$			415.779i			1.69706i
$246$	−48.0000	+	135.765i	−0.195122	+	0.551888i
$247$	−15.5000	+	26.8468i	−0.0627530	+	0.108691i
$248$	−17.1464	+	9.89949i	−0.0691388	+	0.0399173i
$249$	23.2577	+	125.136i	0.0934042	+	0.502555i
$250$	132.000	−	228.631i	0.528000	−	0.914523i
$251$		−	178.191i		−	0.709924i	−0.934881	−	0.354962i	$-0.884494\pi$
$251$		−	178.191i		−	0.709924i	0.934881	−	0.354962i	$-0.115506\pi$
$252$	−117.586	+	45.2725i	−0.466610	+	0.179653i
$253$		0			0
$254$	138.396	+	79.9031i	0.544867	+	0.314579i
$255$	212.363	−	39.4695i	0.832797	−	0.154783i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	242.499	+	140.007i	0.943578	+	0.544775i	0.891080	−	0.453846i	$-0.149948\pi$
$257$	242.499	+	140.007i	0.943578	+	0.544775i	0.0524977	+	0.998621i	$0.483282\pi$
$258$	−124.000	−	43.8406i	−0.480620	−	0.169925i
$259$	3.50000	+	6.06218i	0.0135135	+	0.0234061i
$260$			16.9706i			0.0652714i
$261$	54.8786	+	142.535i	0.210263	+	0.546113i
$262$	60.0000	+	103.923i	0.229008	+	0.396653i
$263$	−88.1816	+	50.9117i	−0.335291	+	0.193581i	−0.658188	−	0.752854i	$-0.728677\pi$
$263$	−88.1816	+	50.9117i	−0.335291	+	0.193581i	0.322897	+	0.946434i	$0.395343\pi$
$264$		0			0
$265$	−216.000			−0.815094
$266$			306.884i			1.15370i
$267$	−336.000	−	118.794i	−1.25843	−	0.444921i
$268$	65.0000	−	112.583i	0.242537	−	0.420087i
$269$	−367.423	+	212.132i	−1.36589	+	0.788595i	−0.990400	−	0.138233i	$-0.955858\pi$
$269$	−367.423	+	212.132i	−1.36589	+	0.788595i	−0.375487	+	0.926828i	$0.622524\pi$
$270$	−284.969	−	154.170i	−1.05544	−	0.571001i
$271$	125.000	−	216.506i	0.461255	−	0.798916i	−0.537769	−	0.843092i	$-0.680733\pi$
$271$	125.000	−	216.506i	0.461255	−	0.798916i	0.999024	+	0.0441757i	$0.0140661\pi$
$272$		−	33.9411i		−	0.124784i
$273$	7.00000	−	19.7990i	0.0256410	−	0.0725238i
$274$	264.000			0.963504
$275$		0			0
$276$	9.30306	+	50.0545i	0.0337067	+	0.181357i
$277$	−191.500	−	331.688i	−0.691336	−	1.19743i	−0.971400	−	0.237447i	$-0.923689\pi$
$277$	−191.500	−	331.688i	−0.691336	−	1.19743i	0.280065	−	0.959981i	$-0.409644\pi$
$278$	138.396	+	79.9031i	0.497828	+	0.287421i
$279$	49.0000	+	39.5980i	0.175627	+	0.141928i
$280$	84.0000	+	145.492i	0.300000	+	0.519615i
$281$		−	178.191i		−	0.634131i	−0.948404	−	0.317066i	$-0.897302\pi$
$281$		−	178.191i		−	0.634131i	0.948404	−	0.317066i	$-0.102698\pi$
$282$	−116.969	−	136.814i	−0.414785	−	0.485157i
$283$	−152.500	−	264.138i	−0.538869	−	0.933349i	−0.998965	−	0.0454798i	$-0.985518\pi$
$283$	−152.500	−	264.138i	−0.538869	−	0.933349i	0.460096	−	0.887869i	$-0.347815\pi$
$284$	102.879	−	59.3970i	0.362248	−	0.209144i
$285$	−599.803	+	512.801i	−2.10457	+	1.79930i
$286$		0			0
$287$	−205.757	−	118.794i	−0.716924	−	0.413916i
$288$	−32.0000	+	39.5980i	−0.111111	+	0.137493i
$289$	−108.500	+	187.928i	−0.375433	+	0.650268i
$290$	176.363	−	101.823i	0.608149	−	0.351115i
$291$	−489.615	+	90.9992i	−1.68253	+	0.312712i
$292$	−97.0000	+	168.009i	−0.332192	+	0.575373i
$293$		−	135.765i		−	0.463360i	−0.972792	−	0.231680i	$-0.925578\pi$
$293$		−	135.765i		−	0.463360i	0.972792	−	0.231680i	$-0.0744222\pi$
$294$	−37.9875	−	204.389i	−0.129209	−	0.695201i
$295$	72.0000			0.244068
$296$	2.44949	+	1.41421i	0.00827530	+	0.00477775i
$297$		0			0
$298$	−48.0000	−	83.1384i	−0.161074	−	0.278988i
$299$	−7.34847	−	4.24264i	−0.0245768	−	0.0141894i
$300$	−94.0000	+	265.872i	−0.313333	+	0.886240i
$301$	108.500	−	187.928i	0.360465	−	0.624344i
$302$			82.0244i			0.271604i
$303$	309.576	−	264.672i	1.02170	−	0.873503i
$304$	62.0000	+	107.387i	0.203947	+	0.353247i
$305$	367.423	−	212.132i	1.20467	−	0.695515i
$306$	−100.788	+	38.8050i	−0.329372	+	0.126814i
$307$	−199.000			−0.648208			−0.324104	−	0.946021i	$-0.605063\pi$
$307$	−199.000			−0.648208			−0.324104	+	0.946021i	$0.605063\pi$
$308$		0			0
$309$	−65.0000	+	183.848i	−0.210356	+	0.594977i
$310$	42.0000	−	72.7461i	0.135484	−	0.234665i
$311$	382.120	−	220.617i	1.22868	−	0.709380i	0.261929	−	0.965087i	$-0.415642\pi$
$311$	382.120	−	220.617i	1.22868	−	0.709380i	0.966754	+	0.255707i	$0.0823082\pi$
$312$	−1.55051	−	8.34242i	−0.00496958	−	0.0267385i
$313$	−59.5000	+	103.057i	−0.190096	+	0.329256i	−0.945282	−	0.326255i	$-0.894213\pi$
$313$	−59.5000	+	103.057i	−0.190096	+	0.329256i	0.755186	+	0.655511i	$0.227547\pi$
$314$			166.877i			0.531456i
$315$	336.000	−	415.779i	1.06667	−	1.31993i
$316$	206.000			0.651899
$317$	176.363	+	101.823i	0.556351	+	0.321209i	0.751680	−	0.659528i	$-0.229244\pi$
$317$	176.363	+	101.823i	0.556351	+	0.321209i	−0.195329	+	0.980738i	$0.562577\pi$
$318$	106.182	−	19.7348i	0.333904	−	0.0620590i
$319$		0			0
$320$	58.7878	+	33.9411i	0.183712	+	0.106066i
$321$	456.000	+	161.220i	1.42056	+	0.502244i
$322$	−84.0000			−0.260870
$323$			263.044i			0.814377i
$324$	154.171	+	49.7511i	0.475838	+	0.153553i
$325$	−23.5000	−	40.7032i	−0.0723077	−	0.125241i
$326$	129.823	−	74.9533i	0.398230	−	0.229918i
$327$	−325.565	−	380.800i	−0.995611	−	1.16453i
$328$	−96.0000			−0.292683
$329$	257.196	−	148.492i	0.781752	−	0.451345i
$330$		0			0
$331$	−260.500	+	451.199i	−0.787009	+	1.36314i	0.140782	+	0.990041i	$0.455038\pi$
$331$	−260.500	+	451.199i	−0.787009	+	1.36314i	−0.927791	+	0.373099i	$0.878295\pi$
$332$	−73.4847	+	42.4264i	−0.221339	+	0.127790i
$333$	1.39898	−	8.89060i	0.00420114	−	0.0266985i
$334$	−102.000	+	176.669i	−0.305389	+	0.528950i
$335$			551.543i			1.64640i
$336$	−54.5857	−	63.8467i	−0.162457	−	0.190020i
$337$	311.000			0.922849			0.461424	−	0.887180i	$-0.347339\pi$
$337$	311.000			0.922849			0.461424	+	0.887180i	$0.347339\pi$
$338$	−205.757	−	118.794i	−0.608749	−	0.351461i
$339$	88.3791	+	475.518i	0.260705	+	1.40271i
$340$	72.0000	+	124.708i	0.211765	+	0.366787i
$341$		0			0
$342$	248.000	−	306.884i	0.725146	−	0.897323i
$343$	343.000			1.00000
$344$		−	87.6812i		−	0.254887i
$345$	−140.363	−	164.177i	−0.406850	−	0.475876i
$346$	−54.0000	−	93.5307i	−0.156069	−	0.270320i
$347$	−95.5301	+	55.1543i	−0.275303	+	0.158946i	−0.631295	−	0.775543i	$-0.717476\pi$
$347$	−95.5301	+	55.1543i	−0.275303	+	0.158946i	0.355992	+	0.934489i	$0.384143\pi$
$348$	−77.3939	+	66.1679i	−0.222396	+	0.190138i
$349$	50.0000			0.143266			0.0716332	−	0.997431i	$-0.477179\pi$
$349$	50.0000			0.143266			0.0716332	+	0.997431i	$0.477179\pi$
$350$	−402.941	−	232.638i	−1.15126	−	0.664680i
$351$	−23.0000	+	14.1421i	−0.0655271	+	0.0402910i
$352$		0			0
$353$	−139.621	+	80.6102i	−0.395527	+	0.228357i	−0.684552	−	0.728964i	$-0.740002\pi$
$353$	−139.621	+	80.6102i	−0.395527	+	0.228357i	0.289025	+	0.957321i	$0.406669\pi$
$354$	−35.3939	+	6.57826i	−0.0999827	+	0.0185826i
$355$	−252.000	+	436.477i	−0.709859	+	1.22951i
$356$		−	237.588i		−	0.667382i
$357$	−32.5607	−	175.191i	−0.0912065	−	0.490730i
$358$	228.000			0.636872
$359$	352.727	+	203.647i	0.982525	+	0.567261i	0.903032	−	0.429574i	$-0.141336\pi$
$359$	352.727	+	203.647i	0.982525	+	0.567261i	0.0794936	+	0.996835i	$0.474670\pi$
$360$	33.5755	−	213.375i	0.0932653	−	0.592707i
$361$	−300.000	−	519.615i	−0.831025	−	1.43938i
$362$	263.320	+	152.028i	0.727404	+	0.419967i
$363$	−121.000	+	342.240i	−0.333333	+	0.942809i
$364$	14.0000			0.0384615
$365$		−	823.072i		−	2.25499i
$366$	−161.237	+	137.850i	−0.440539	+	0.376639i
$367$	267.500	+	463.324i	0.728883	+	1.26246i	0.957356	+	0.288912i	$0.0932934\pi$
$367$	267.500	+	463.324i	0.728883	+	1.26246i	−0.228473	+	0.973550i	$0.573373\pi$
$368$	−29.3939	+	16.9706i	−0.0798747	+	0.0461157i
$369$	109.757	+	285.071i	0.297445	+	0.772550i
$370$	−12.0000			−0.0324324
$371$			178.191i			0.480299i
$372$	−14.0000	+	39.5980i	−0.0376344	+	0.106446i
$373$	192.500	−	333.420i	0.516086	−	0.893887i	−0.483740	−	0.875212i	$-0.660722\pi$
$373$	192.500	−	333.420i	0.516086	−	0.893887i	0.999826	−	0.0186750i	$-0.00594477\pi$
$374$		0			0
$375$	−102.334	−	550.600i	−0.272890	−	1.46827i
$376$	60.0000	−	103.923i	0.159574	−	0.276391i
$377$		−	16.9706i		−	0.0450148i
$378$	−127.184	+	235.088i	−0.336465	+	0.621925i
$379$	−55.0000			−0.145119			−0.0725594	−	0.997364i	$-0.523117\pi$
$379$	−55.0000			−0.145119			−0.0725594	+	0.997364i	$0.523117\pi$
$380$	−455.605	−	263.044i	−1.19896	−	0.692220i
$381$	333.292	−	61.9453i	0.874783	−	0.162586i
$382$	−126.000	−	218.238i	−0.329843	−	0.571305i
$383$	360.075	+	207.889i	0.940144	+	0.542792i	0.890005	−	0.455950i	$-0.150700\pi$
$383$	360.075	+	207.889i	0.940144	+	0.542792i	0.0501383	+	0.998742i	$0.484034\pi$
$384$	−32.0000	−	11.3137i	−0.0833333	−	0.0294628i
$385$		0			0
$386$			137.179i			0.355385i
$387$	−260.368	+	100.246i	−0.672786	+	0.259034i
$388$	−166.000	−	287.520i	−0.427835	−	0.741032i
$389$	−330.681	+	190.919i	−0.850080	+	0.490794i	−0.860678	−	0.509150i	$-0.829960\pi$
$389$	−330.681	+	190.919i	−0.850080	+	0.490794i	0.0105979	+	0.999944i	$0.496627\pi$
$390$	23.3939	+	27.3629i	0.0599843	+	0.0701612i
$391$	−72.0000			−0.184143
$392$	120.025	−	69.2965i	0.306186	−	0.176777i
$393$	240.000	+	84.8528i	0.610687	+	0.215910i
$394$	−258.000	+	446.869i	−0.654822	+	1.13419i
$395$	−756.892	+	436.992i	−1.91618	+	1.10631i
$396$		0			0
$397$	240.500	−	416.558i	0.605793	−	1.04927i	−0.386132	−	0.922443i	$-0.626189\pi$
$397$	240.500	−	416.558i	0.605793	−	1.04927i	0.991926	−	0.126822i	$-0.0404776\pi$
$398$			149.907i			0.376650i
$399$	423.039	+	494.812i	1.06025	+	1.24013i
$400$	−188.000			−0.470000
$401$	−66.1362	−	38.1838i	−0.164928	−	0.0952214i	0.415264	−	0.909701i	$-0.363689\pi$
$401$	−66.1362	−	38.1838i	−0.164928	−	0.0952214i	−0.580192	+	0.814480i	$0.697023\pi$
$402$	−50.3916	−	271.129i	−0.125352	−	0.674449i
$403$	−3.50000	−	6.06218i	−0.00868486	−	0.0150426i
$404$	235.151	+	135.765i	0.582057	+	0.336051i
$405$	−672.000	+	144.250i	−1.65926	+	0.356172i
$406$	−84.0000	−	145.492i	−0.206897	−	0.358355i
$407$		0			0
$408$	−46.7878	−	54.7257i	−0.114676	−	0.134132i
$409$	24.5000	+	42.4352i	0.0599022	+	0.103754i	0.894421	−	0.447225i	$-0.147588\pi$
$409$	24.5000	+	42.4352i	0.0599022	+	0.103754i	−0.834519	+	0.550979i	$0.814254\pi$
$410$	352.727	−	203.647i	0.860309	−	0.496699i
$411$	425.666	−	363.923i	1.03568	−	0.885458i
$412$	−130.000			−0.315534
$413$		−	59.3970i		−	0.143818i
$414$	84.0000	+	67.8823i	0.202899	+	0.163967i
$415$	180.000	−	311.769i	0.433735	−	0.751251i
$416$	4.89898	−	2.82843i	0.0117764	−	0.00679910i
$417$	333.292	−	61.9453i	0.799262	−	0.148550i
$418$		0			0
$419$		−	322.441i		−	0.769548i	−0.923011	−	0.384774i	$-0.874279\pi$
$419$		−	322.441i		−	0.769548i	0.923011	−	0.384774i	$-0.125721\pi$
$420$	336.000	+	118.794i	0.800000	+	0.282843i
$421$	−313.000			−0.743468			−0.371734	−	0.928339i	$-0.621237\pi$
$421$	−313.000			−0.743468			−0.371734	+	0.928339i	$0.621237\pi$
$422$	75.9342	+	43.8406i	0.179939	+	0.103888i
$423$	−377.196	−	59.3537i	−0.891717	−	0.140316i
$424$	36.0000	+	62.3538i	0.0849057	+	0.147061i
$425$	−345.378	−	199.404i	−0.812654	−	0.469186i
$426$	84.0000	−	237.588i	0.197183	−	0.557718i
$427$	−175.000	−	303.109i	−0.409836	−	0.709857i
$428$			322.441i			0.753366i
$429$		0			0
$430$	186.000	+	322.161i	0.432558	+	0.749213i
$431$	−301.287	+	173.948i	−0.699042	+	0.403592i	−0.806991	−	0.590564i	$-0.798905\pi$
$431$	−301.287	+	173.948i	−0.699042	+	0.403592i	0.107948	+	0.994157i	$0.465572\pi$
$432$	2.98979	+	107.959i	0.00692082	+	0.249904i
$433$	−97.0000			−0.224018			−0.112009	−	0.993707i	$-0.535729\pi$
$433$	−97.0000			−0.224018			−0.112009	+	0.993707i	$0.535729\pi$
$434$	−60.0125	−	34.6482i	−0.138278	−	0.0798346i
$435$	144.000	−	407.294i	0.331034	−	0.936307i
$436$	167.000	−	289.252i	0.383028	−	0.663423i
$437$	227.803	−	131.522i	0.521287	−	0.300965i
$438$	75.1997	+	404.607i	0.171689	+	0.923761i
$439$	−187.000	+	323.894i	−0.425968	+	0.737798i	−0.996510	−	0.0834699i	$-0.973400\pi$
$439$	−187.000	+	323.894i	−0.425968	+	0.737798i	0.570542	+	0.821268i	$0.306733\pi$
$440$		0			0
$441$	−343.000	−	277.186i	−0.777778	−	0.628539i
$442$	12.0000			0.0271493
$443$	−521.741	−	301.227i	−1.17775	−	0.679972i	−0.222254	−	0.974989i	$-0.571341\pi$
$443$	−521.741	−	301.227i	−1.17775	−	0.679972i	−0.955492	+	0.295017i	$0.904675\pi$
$444$	5.89898	−	1.09638i	0.0132860	−	0.00246932i
$445$	504.000	+	872.954i	1.13258	+	1.96169i
$446$	−247.398	−	142.836i	−0.554705	−	0.320259i
$447$	−192.000	−	67.8823i	−0.429530	−	0.151862i
$448$	28.0000	−	48.4974i	0.0625000	−	0.108253i
$449$			42.4264i			0.0944909i	0.998883	+	0.0472454i	$0.0150443\pi$
$449$			42.4264i			0.0944909i	−0.998883	+	0.0472454i	$0.984956\pi$
$450$	214.941	+	558.264i	0.477647	+	1.24059i
$451$		0			0
$452$	−279.242	+	161.220i	−0.617792	+	0.356682i
$453$	113.070	+	132.254i	0.249604	+	0.291951i
$454$	−24.0000			−0.0528634
$455$	−51.4393	+	29.6985i	−0.113053	+	0.0652714i
$456$	248.000	+	87.6812i	0.543860	+	0.192283i
$457$	−227.500	+	394.042i	−0.497812	+	0.862235i	−0.999997	−	0.00252486i	$-0.999196\pi$
$457$	−227.500	+	394.042i	−0.497812	+	0.862235i	0.502185	+	0.864760i	$0.332530\pi$
$458$	1.22474	−	0.707107i	0.00267412	−	0.00154390i
$459$	−109.015	+	201.504i	−0.237505	+	0.439006i
$460$	72.0000	−	124.708i	0.156522	−	0.271104i
$461$		−	220.617i		−	0.478563i	−0.970950	−	0.239281i	$-0.923088\pi$
$461$		−	220.617i		−	0.478563i	0.970950	−	0.239281i	$-0.0769118\pi$
$462$		0			0
$463$	−7.00000			−0.0151188			−0.00755940	−	0.999971i	$-0.502406\pi$
$463$	−7.00000			−0.0151188			−0.00755940	+	0.999971i	$0.502406\pi$
$464$	−58.7878	−	33.9411i	−0.126698	−	0.0731490i
$465$	−32.5607	−	175.191i	−0.0700230	−	0.376754i
$466$	−234.000	−	405.300i	−0.502146	−	0.869742i
$467$	−536.438	−	309.713i	−1.14869	−	0.663197i	−0.200122	−	0.979771i	$-0.564134\pi$
$467$	−536.438	−	309.713i	−1.14869	−	0.663197i	−0.948568	+	0.316574i	$0.897467\pi$
$468$	−14.0000	−	11.3137i	−0.0299145	−	0.0241746i
$469$	455.000			0.970149
$470$			509.117i			1.08323i
$471$	230.040	+	269.068i	0.488407	+	0.571270i
$472$	−12.0000	−	20.7846i	−0.0254237	−	0.0440352i
$473$		0			0
$474$	332.149	−	283.970i	0.700736	−	0.599094i
$475$	1457.00			3.06737
$476$	102.879	−	59.3970i	0.216131	−	0.124784i
$477$	144.000	−	178.191i	0.301887	−	0.373566i
$478$	324.000	−	561.184i	0.677824	−	1.17403i
$479$	580.529	−	335.169i	1.21196	−	0.699726i	0.248774	−	0.968561i	$-0.419972\pi$
$479$	580.529	−	335.169i	1.21196	−	0.699726i	0.963186	+	0.268836i	$0.0866389\pi$
$480$	141.576	−	26.3130i	0.294949	−	0.0548188i
$481$	−0.500000	+	0.866025i	−0.00103950	+	0.00180047i
$482$			31.1127i			0.0645492i
$483$	−135.439	+	115.794i	−0.280413	+	0.239739i
$484$	−242.000			−0.500000
$485$	1219.85	+	704.278i	2.51515	+	1.45212i
$486$	317.164	−	132.308i	0.652600	−	0.272238i
$487$	231.500	+	400.970i	0.475359	+	0.823347i	0.999602	−	0.0282226i	$-0.00898473\pi$
$487$	231.500	+	400.970i	0.475359	+	0.823347i	−0.524242	+	0.851569i	$0.675651\pi$
$488$	−122.474	−	70.7107i	−0.250972	−	0.144899i
$489$	106.000	−	299.813i	0.216769	−	0.613115i
$490$	−294.000	+	509.223i	−0.600000	+	1.03923i
$491$			356.382i			0.725829i	0.931823	+	0.362914i	$0.118218\pi$
$491$			356.382i			0.725829i	−0.931823	+	0.362914i	$0.881782\pi$
$492$	−154.788	+	132.336i	−0.314609	+	0.268975i
$493$	−72.0000	−	124.708i	−0.146045	−	0.252957i
$494$	−37.9671	+	21.9203i	−0.0768565	+	0.0443731i
$495$		0			0
$496$	−28.0000			−0.0564516
$497$	360.075	+	207.889i	0.724497	+	0.418289i
$498$	−60.0000	+	169.706i	−0.120482	+	0.340774i
$499$	267.500	−	463.324i	0.536072	−	0.928504i	−0.463038	−	0.886338i	$-0.653241\pi$
$499$	267.500	−	463.324i	0.536072	−	0.928504i	0.999111	−	0.0421660i	$-0.0134258\pi$
$500$	323.333	−	186.676i	0.646665	−	0.373352i
$501$	79.0760	+	425.463i	0.157836	+	0.849228i
$502$	126.000	−	218.238i	0.250996	−	0.434738i
$503$		−	627.911i		−	1.24833i	−0.781292	−	0.624166i	$-0.785439\pi$
$503$		−	627.911i		−	1.24833i	0.781292	−	0.624166i	$-0.214561\pi$
$504$	−176.025	−	27.6984i	−0.349256	−	0.0549571i
$505$	−1152.00			−2.28119
$506$		0			0
$507$	−495.514	+	92.0956i	−0.977346	+	0.181648i
$508$	113.000	+	195.722i	0.222441	+	0.385279i
$509$	−551.135	−	318.198i	−1.08278	−	0.625144i	−0.151135	−	0.988513i	$-0.548293\pi$
$509$	−551.135	−	318.198i	−1.08278	−	0.625144i	−0.931645	+	0.363370i	$0.881626\pi$
$510$	288.000	+	101.823i	0.564706	+	0.199654i
$511$	−679.000			−1.32877
$512$		−	22.6274i		−	0.0441942i
$513$	−23.1709	−	836.679i	−0.0451675	−	1.63095i
$514$	198.000	+	342.946i	0.385214	+	0.667210i
$515$	477.650	−	275.772i	0.927477	−	0.535479i
$516$	−120.868	−	141.375i	−0.234241	−	0.273982i
$517$		0			0
$518$			9.89949i			0.0191110i
$519$	−216.000	−	76.3675i	−0.416185	−	0.147144i
$520$	−12.0000	+	20.7846i	−0.0230769	+	0.0399704i
$521$	−558.484	+	322.441i	−1.07195	+	0.618888i	−0.928712	−	0.370801i	$-0.879083\pi$
$521$	−558.484	+	322.441i	−1.07195	+	0.618888i	−0.143233	+	0.989689i	$0.545750\pi$
$522$	−33.5755	+	213.375i	−0.0643209	+	0.408763i
$523$	−344.500	+	596.692i	−0.658700	+	1.14090i	0.322253	+	0.946654i	$0.395560\pi$
$523$	−344.500	+	596.692i	−0.658700	+	1.14090i	−0.980952	+	0.194248i	$0.937773\pi$
$524$			169.706i			0.323866i
$525$	−970.382	+	180.354i	−1.84835	+	0.343531i
$526$	−144.000			−0.273764
$527$	−51.4393	−	29.6985i	−0.0976078	−	0.0563539i
$528$		0			0
$529$	−228.500	−	395.774i	−0.431947	−	0.748154i
$530$	−264.545	−	152.735i	−0.499141	−	0.288179i
$531$	−48.0000	+	59.3970i	−0.0903955	+	0.111859i
$532$	−217.000	+	375.855i	−0.407895	+	0.706494i
$533$		−	33.9411i		−	0.0636794i
$534$	−327.514	−	383.080i	−0.613323	−	0.717379i
$535$	−684.000	−	1184.72i	−1.27850	−	2.21444i
$536$	159.217	−	91.9239i	0.297046	−	0.171500i
$537$	367.621	−	314.297i	0.684583	−	0.585284i
$538$	−600.000			−1.11524
$539$		0			0
$540$	−240.000	−	390.323i	−0.444444	−	0.722820i
$541$	−287.500	+	497.965i	−0.531423	+	0.920452i	0.467904	+	0.883779i	$0.345009\pi$
$541$	−287.500	+	497.965i	−0.531423	+	0.920452i	−0.999327	+	0.0366729i	$0.988324\pi$
$542$	306.186	−	176.777i	0.564919	−	0.326156i
$543$	634.140	−	117.860i	1.16785	−	0.217054i
$544$	24.0000	−	41.5692i	0.0441176	−	0.0764140i
$545$			1417.04i			2.60008i
$546$	22.5732	−	19.2990i	0.0413429	−	0.0353461i
$547$	302.000			0.552102			0.276051	−	0.961143i	$-0.410974\pi$
$547$	302.000			0.552102			0.276051	+	0.961143i	$0.410974\pi$
$548$	323.333	+	186.676i	0.590023	+	0.340650i
$549$	−69.9490	+	444.530i	−0.127412	+	0.809709i
$550$		0			0
$551$	455.605	+	263.044i	0.826869	+	0.477393i
$552$	−24.0000	+	67.8823i	−0.0434783	+	0.122975i
$553$	360.500	+	624.404i	0.651899	+	1.12912i
$554$		−	541.644i		−	0.977696i
$555$	−19.3485	+	16.5420i	−0.0348621	+	0.0298053i
$556$	113.000	+	195.722i	0.203237	+	0.352018i
$557$	117.576	−	67.8823i	0.211087	−	0.121871i	−0.390729	−	0.920506i	$-0.627777\pi$
$557$	117.576	−	67.8823i	0.211087	−	0.121871i	0.601817	+	0.798634i	$0.294444\pi$
$558$	32.0125	+	83.1457i	0.0573701	+	0.149007i
$559$	31.0000			0.0554562
$560$			237.588i			0.424264i
$561$		0			0
$562$	126.000	−	218.238i	0.224199	−	0.388325i
$563$	521.741	−	301.227i	0.926716	−	0.535040i	0.0409448	−	0.999161i	$-0.486963\pi$
$563$	521.741	−	301.227i	0.926716	−	0.535040i	0.885772	+	0.464121i	$0.153630\pi$
$564$	−46.5153	−	250.273i	−0.0824739	−	0.443746i
$565$	684.000	−	1184.72i	1.21062	−	2.09685i
$566$		−	431.335i		−	0.762076i
$567$	119.000	+	554.372i	0.209877	+	0.977728i
$568$	168.000			0.295775
$569$	−573.181	−	330.926i	−1.00735	−	0.581592i	−0.0969334	−	0.995291i	$-0.530903\pi$
$569$	−573.181	−	330.926i	−1.00735	−	0.581592i	−0.910414	+	0.413699i	$0.864237\pi$
$570$	−1097.21	+	203.926i	−1.92493	+	0.357765i
$571$	−56.5000	−	97.8609i	−0.0989492	−	0.171385i	0.812301	−	0.583239i	$-0.198215\pi$
$571$	−56.5000	−	97.8609i	−0.0989492	−	0.171385i	−0.911250	+	0.411854i	$0.864881\pi$
$572$		0			0
$573$	−504.000	−	178.191i	−0.879581	−	0.310979i
$574$	−168.000	−	290.985i	−0.292683	−	0.506942i
$575$			398.808i			0.693580i
$576$	−67.1918	+	25.8700i	−0.116652	+	0.0449132i
$577$	60.5000	+	104.789i	0.104853	+	0.181610i	0.913678	−	0.406439i	$-0.133230\pi$
$577$	60.5000	+	104.789i	0.104853	+	0.181610i	−0.808825	+	0.588049i	$0.799896\pi$
$578$	−265.770	+	153.442i	−0.459809	+	0.265471i
$579$	189.101	+	221.183i	0.326598	+	0.382009i
$580$	288.000			0.496552
$581$	−257.196	−	148.492i	−0.442679	−	0.255581i
$582$	−664.000	−	234.759i	−1.14089	−	0.403367i
$583$		0			0
$584$	−237.601	+	137.179i	−0.406850	+	0.234895i
$585$	75.4393	+	11.8707i	0.128956	+	0.0202919i
$586$	96.0000	−	166.277i	0.163823	−	0.283749i
$587$		−	67.8823i		−	0.115643i	−0.998327	−	0.0578213i	$-0.981585\pi$
$587$		−	67.8823i		−	0.115643i	0.998327	−	0.0578213i	$-0.0184154\pi$
$588$	98.0000	−	277.186i	0.166667	−	0.471405i
$589$	217.000			0.368421
$590$	88.1816	+	50.9117i	0.149460	+	0.0862910i
$591$	200.016	+	1076.17i	0.338436	+	1.82093i
$592$	2.00000	+	3.46410i	0.00337838	+	0.00585152i
$593$	426.211	+	246.073i	0.718737	+	0.414963i	0.814288	−	0.580461i	$-0.197128\pi$
$593$	426.211	+	246.073i	0.718737	+	0.414963i	−0.0955505	+	0.995425i	$0.530461\pi$
$594$		0			0
$595$	−252.000	+	436.477i	−0.423529	+	0.733574i
$596$		−	135.765i		−	0.227793i
$597$	206.646	+	241.705i	0.346141	+	0.404867i
$598$	−6.00000	−	10.3923i	−0.0100334	−	0.0173784i
$599$	88.1816	−	50.9117i	0.147215	−	0.0849945i	−0.424583	−	0.905389i	$-0.639579\pi$
$599$	88.1816	−	50.9117i	0.147215	−	0.0849945i	0.571798	+	0.820394i	$0.306246\pi$
$600$	−303.126	+	259.158i	−0.505210	+	0.431929i
$601$	791.000			1.31614			0.658070	−	0.752957i	$-0.271373\pi$
$601$	791.000			1.31614			0.658070	+	0.752957i	$0.271373\pi$
$602$	265.770	−	153.442i	0.441478	−	0.254887i
$603$	−455.000	−	367.696i	−0.754561	−	0.609777i
$604$	−58.0000	+	100.459i	−0.0960265	+	0.166323i
$605$	889.165	−	513.360i	1.46969	−	0.848528i
$606$	566.302	−	105.252i	0.934492	−	0.173683i
$607$	−56.5000	+	97.8609i	−0.0930807	+	0.161221i	−0.908806	−	0.417219i	$-0.863005\pi$
$607$	−56.5000	+	97.8609i	−0.0930807	+	0.161221i	0.815725	+	0.578440i	$0.196338\pi$
$608$			175.362i			0.288425i
$609$	−336.000	−	118.794i	−0.551724	−	0.195064i
$610$	600.000			0.983607
$611$	36.7423	+	21.2132i	0.0601348	+	0.0347188i
$612$	−150.879	−	23.7415i	−0.246534	−	0.0387933i
$613$	287.000	+	497.099i	0.468189	+	0.810928i	0.999339	−	0.0363503i	$-0.0115732\pi$
$613$	287.000	+	497.099i	0.468189	+	0.810928i	−0.531150	+	0.847278i	$0.678240\pi$
$614$	−243.724	−	140.714i	−0.396945	−	0.229176i
$615$	288.000	−	814.587i	0.468293	−	1.32453i
$616$		0			0
$617$			661.852i			1.07269i	0.843998	+	0.536347i	$0.180196\pi$
$617$			661.852i			1.07269i	−0.843998	+	0.536347i	$0.819804\pi$
$618$	−209.608	+	179.205i	−0.339172	+	0.289975i
$619$	−476.500	−	825.322i	−0.769790	−	1.33332i	−0.937677	−	0.347509i	$-0.887028\pi$
$619$	−476.500	−	825.322i	−0.769790	−	1.33332i	0.167887	−	0.985806i	$-0.446306\pi$
$620$	102.879	−	59.3970i	0.165933	−	0.0958016i
$621$	229.015	−	6.34231i	0.368784	−	0.0102131i
$622$	624.000			1.00322
$623$	720.150	−	415.779i	1.15594	−	0.667382i
$624$	4.00000	−	11.3137i	0.00641026	−	0.0181309i
$625$	−204.500	+	354.204i	−0.327200	+	0.566727i
$626$	−145.745	+	84.1457i	−0.232819	+	0.134418i
$627$		0			0
$628$	−118.000	+	204.382i	−0.187898	+	0.325449i
$629$			8.48528i			0.0134901i
$630$	705.514	−	271.635i	1.11986	−	0.431167i
$631$	758.000			1.20127			0.600634	−	0.799524i	$-0.294915\pi$
$631$	758.000			1.20127			0.600634	+	0.799524i	$0.294915\pi$
$632$	252.297	+	145.664i	0.399205	+	0.230481i
$633$	182.868	−	33.9877i	0.288892	−	0.0536930i
$634$	144.000	+	249.415i	0.227129	+	0.393400i
$635$	−830.377	−	479.418i	−1.30768	−	0.754990i
$636$	144.000	+	50.9117i	0.226415	+	0.0800498i
$637$	24.5000	+	42.4352i	0.0384615	+	0.0666173i
$638$		0			0
$639$	−192.075	−	498.874i	−0.300587	−	0.780710i
$640$	48.0000	+	83.1384i	0.0750000	+	0.129904i
$641$	−933.256	+	538.815i	−1.45594	+	0.840586i	−0.998808	−	0.0488147i	$-0.984456\pi$
$641$	−933.256	+	538.815i	−1.45594	+	0.840586i	−0.457129	+	0.889400i	$0.651122\pi$
$642$	444.484	+	519.894i	0.692342	+	0.809804i
$643$	−1111.00			−1.72784			−0.863919	−	0.503631i	$-0.831997\pi$
$643$	−1111.00			−1.72784			−0.863919	+	0.503631i	$0.831997\pi$
$644$	−102.879	−	59.3970i	−0.159749	−	0.0922313i
$645$	744.000	+	263.044i	1.15349	+	0.407820i
$646$	−186.000	+	322.161i	−0.287926	+	0.498702i
$647$	−293.939	+	169.706i	−0.454310	+	0.262296i	−0.709649	−	0.704556i	$-0.751146\pi$
$647$	−293.939	+	169.706i	−0.454310	+	0.262296i	0.255339	+	0.966852i	$0.417813\pi$
$648$	153.641	+	169.948i	0.237101	+	0.262266i
$649$		0			0
$650$		−	66.4680i		−	0.102259i
$651$	−144.525	+	26.8612i	−0.222005	+	0.0412615i
$652$	212.000			0.325153
$653$	−558.484	−	322.441i	−0.855258	−	0.493784i	0.00716327	−	0.999974i	$-0.497720\pi$
$653$	−558.484	−	322.441i	−0.855258	−	0.493784i	−0.862422	+	0.506191i	$0.831053\pi$
$654$	−129.468	−	696.592i	−0.197963	−	1.06513i
$655$	−360.000	−	623.538i	−0.549618	−	0.951967i
$656$	−117.576	−	67.8823i	−0.179231	−	0.103479i
$657$	679.000	+	548.715i	1.03349	+	0.835182i
$658$	420.000			0.638298
$659$			873.984i			1.32623i	0.748519	+	0.663114i	$0.230765\pi$
$659$			873.984i			1.32623i	−0.748519	+	0.663114i	$0.769235\pi$
$660$		0			0
$661$	432.500	+	749.112i	0.654312	+	1.13330i	0.982066	+	0.188538i	$0.0603749\pi$
$661$	432.500	+	749.112i	0.654312	+	1.13330i	−0.327754	+	0.944763i	$0.606292\pi$
$662$	−638.092	+	368.403i	−0.963885	+	0.556499i
$663$	19.3485	−	16.5420i	0.0291832	−	0.0249502i
$664$	−120.000			−0.180723
$665$		−	1841.31i		−	2.76888i
$666$	8.00000	−	9.89949i	0.0120120	−	0.0148641i
$667$	−72.0000	+	124.708i	−0.107946	+	0.186968i
$668$	−249.848	+	144.250i	−0.374024	+	0.215943i
$669$	−595.797	+	110.734i	−0.890578	+	0.165522i
$670$	−390.000	+	675.500i	−0.582090	+	1.00821i
$671$		0			0
$672$	−21.7071	−	116.794i	−0.0323023	−	0.173800i
$673$	−505.000			−0.750371			−0.375186	−	0.926950i	$-0.622421\pi$
$673$	−505.000			−0.750371			−0.375186	+	0.926950i	$0.622421\pi$
$674$	380.896	+	219.910i	0.565127	+	0.326276i
$675$	1116.13	+	603.833i	1.65353	+	0.894568i
$676$	−168.000	−	290.985i	−0.248521	−	0.430450i
$677$	−279.242	−	161.220i	−0.412469	−	0.238139i	0.279381	−	0.960180i	$-0.409871\pi$
$677$	−279.242	−	161.220i	−0.412469	−	0.238139i	−0.691850	+	0.722041i	$0.743204\pi$
$678$	−228.000	+	644.881i	−0.336283	+	0.951152i
$679$	581.000	−	1006.32i	0.855670	−	1.48206i
$680$			203.647i			0.299481i
$681$	−38.6969	+	33.0839i	−0.0568237	+	0.0485814i
$682$		0			0
$683$	683.408	−	394.566i	1.00060	−	0.577695i	0.0921720	−	0.995743i	$-0.470619\pi$
$683$	683.408	−	394.566i	1.00060	−	0.577695i	0.908425	+	0.418048i	$0.137286\pi$
$684$	520.737	−	200.493i	0.761311	−	0.293118i
$685$	−1584.00			−2.31241
$686$	420.087	+	242.538i	0.612372	+	0.353553i
$687$	1.00000	−	2.82843i	0.00145560	−	0.00411707i
$688$	62.0000	−	107.387i	0.0901163	−	0.156086i
$689$	−22.0454	+	12.7279i	−0.0319962	+	0.0184730i
$690$	−55.8184	−	300.327i	−0.0808962	−	0.435257i
$691$	−92.5000	+	160.215i	−0.133864	+	0.231859i	−0.925163	−	0.379570i	$-0.876072\pi$
$691$	−92.5000	+	160.215i	−0.133864	+	0.231859i	0.791299	+	0.611429i	$0.209405\pi$
$692$		−	152.735i		−	0.220715i
$693$		0			0
$694$	−156.000			−0.224784
$695$	−830.377	−	479.418i	−1.19479	−	0.689811i
$696$	−141.576	+	26.3130i	−0.203413	+	0.0378061i
$697$	−144.000	−	249.415i	−0.206600	−	0.357841i
$698$	61.2372	+	35.3553i	0.0877324	+	0.0506523i
$699$	−936.000	−	330.926i	−1.33906	−	0.473428i
$700$	−329.000	−	569.845i	−0.470000	−	0.814064i
$701$			93.3381i			0.133150i	0.997781	+	0.0665750i	$0.0212072\pi$
$701$			93.3381i			0.133150i	−0.997781	+	0.0665750i	$0.978793\pi$
$702$	−38.1691	+	1.05705i	−0.0543720	+	0.00150577i
$703$	−15.5000	−	26.8468i	−0.0220484	−	0.0381889i
$704$		0			0
$705$	701.816	+	820.886i	0.995484	+	1.16438i
$706$	−228.000			−0.322946
$707$			950.352i			1.34420i
$708$	−48.0000	−	16.9706i	−0.0677966	−	0.0239697i
$709$	−97.0000	+	168.009i	−0.136812	+	0.236966i	−0.926288	−	0.376815i	$-0.877019\pi$
$709$	−97.0000	+	168.009i	−0.136812	+	0.236966i	0.789476	+	0.613782i	$0.210352\pi$
$710$	−617.271	+	356.382i	−0.869396	+	0.501946i
$711$	144.095	−	915.732i	0.202665	−	1.28795i
$712$	168.000	−	290.985i	0.235955	−	0.408686i
$713$			59.3970i			0.0833057i
$714$	84.0000	−	237.588i	0.117647	−	0.332756i
$715$		0			0
$716$	279.242	+	161.220i	0.390003	+	0.225168i
$717$	−251.183	−	1351.47i	−0.350324	−	1.88490i
$718$	288.000	+	498.831i	0.401114	+	0.694750i
$719$	−338.030	−	195.161i	−0.470139	−	0.271435i	0.246159	−	0.969229i	$-0.420831\pi$
$719$	−338.030	−	195.161i	−0.470139	−	0.271435i	−0.716298	+	0.697795i	$0.754165\pi$
$720$	192.000	−	237.588i	0.266667	−	0.329983i
$721$	−227.500	−	394.042i	−0.315534	−	0.546521i
$722$		−	848.528i		−	1.17525i
$723$	42.8888	+	50.1653i	0.0593206	+	0.0693849i
$724$	215.000	+	372.391i	0.296961	+	0.514352i
$725$	−690.756	+	398.808i	−0.952767	+	0.550080i
$726$	−390.194	+	333.596i	−0.537457	+	0.459499i
$727$	425.000			0.584594			0.292297	−	0.956328i	$-0.405580\pi$
$727$	425.000			0.584594			0.292297	+	0.956328i	$0.405580\pi$
$728$	17.1464	+	9.89949i	0.0235528	+	0.0135982i
$729$	329.000	−	650.538i	0.451303	−	0.892371i
$730$	582.000	−	1008.05i	0.797260	−	1.38090i
$731$	227.803	−	131.522i	0.311631	−	0.179920i
$732$	−294.949	+	54.8188i	−0.402936	+	0.0748891i
$733$	−203.500	+	352.472i	−0.277626	+	0.480863i	−0.970794	−	0.239913i	$-0.922881\pi$
$733$	−203.500	+	352.472i	−0.277626	+	0.480863i	0.693168	+	0.720776i	$0.256214\pi$
$734$			756.604i			1.03080i
$735$	227.925	+	1226.34i	0.310102	+	1.66848i
$736$	−48.0000			−0.0652174
$737$		0			0
$738$	−67.1510	+	426.749i	−0.0909905	+	0.578251i
$739$	−380.500	−	659.045i	−0.514885	−	0.891807i	−0.999851	−	0.0172738i	$-0.994501\pi$
$739$	−380.500	−	659.045i	−0.514885	−	0.891807i	0.484966	−	0.874533i	$-0.338832\pi$
$740$	−14.6969	−	8.48528i	−0.0198607	−	0.0114666i
$741$	−31.0000	+	87.6812i	−0.0418354	+	0.118328i
$742$	−126.000	+	218.238i	−0.169811	+	0.294122i
$743$			576.999i			0.776580i	0.921537	+	0.388290i	$0.126934\pi$
$743$			576.999i			0.776580i	−0.921537	+	0.388290i	$0.873066\pi$
$744$	−45.1464	+	38.5979i	−0.0606807	+	0.0518789i
$745$	288.000	+	498.831i	0.386577	+	0.669571i
$746$	471.527	−	272.236i	0.632073	−	0.364928i
$747$	137.196	+	356.339i	0.183663	+	0.477026i
$748$		0			0
$749$	−977.346	+	564.271i	−1.30487	+	0.753366i
$750$	264.000	−	746.705i	0.352000	−	0.995606i
$751$	−344.500	+	596.692i	−0.458722	+	0.794529i	−0.998894	−	0.0470253i	$-0.985026\pi$
$751$	−344.500	+	596.692i	−0.458722	+	0.794529i	0.540172	+	0.841555i	$0.318359\pi$
$752$	146.969	−	84.8528i	0.195438	−	0.112836i
$753$	−97.6821	−	525.572i	−0.129724	−	0.697971i
$754$	12.0000	−	20.7846i	0.0159151	−	0.0275658i
$755$		−	492.146i		−	0.651849i
$756$	−322.000	+	197.990i	−0.425926	+	0.261891i
$757$	−142.000			−0.187583			−0.0937913	−	0.995592i	$-0.529899\pi$
$757$	−142.000			−0.187583			−0.0937913	+	0.995592i	$0.529899\pi$
$758$	−67.3610	−	38.8909i	−0.0888667	−	0.0513072i
$759$		0			0
$760$	−372.000	−	644.323i	−0.489474	−	0.847793i
$761$	962.649	+	555.786i	1.26498	+	0.730336i	0.974034	−	0.226403i	$-0.0726967\pi$
$761$	962.649	+	555.786i	1.26498	+	0.730336i	0.290946	+	0.956740i	$0.406030\pi$
$762$	452.000	+	159.806i	0.593176	+	0.209719i
$763$	1169.00			1.53211
$764$		−	356.382i		−	0.466468i
$765$	604.727	−	232.830i	0.790492	−	0.304353i
$766$	294.000	+	509.223i	0.383812	+	0.664782i
$767$	7.34847	−	4.24264i	0.00958079	−	0.00553147i
$768$	−31.1918	−	36.4838i	−0.0406144	−	0.0475050i
$769$	1127.00			1.46554			0.732770	−	0.680477i	$-0.238227\pi$
$769$	1127.00			1.46554			0.732770	+	0.680477i	$0.238227\pi$
$770$		0			0
$771$	792.000	+	280.014i	1.02724	+	0.363183i
$772$	−97.0000	+	168.009i	−0.125648	+	0.217628i
$773$	396.817	−	229.103i	0.513347	−	0.296381i	−0.220861	−	0.975305i	$-0.570887\pi$
$773$	396.817	−	229.103i	0.513347	−	0.296381i	0.734208	+	0.678924i	$0.237553\pi$
$774$	−389.770	−	61.3321i	−0.503578	−	0.0792405i
$775$	−164.500	+	284.922i	−0.212258	+	0.367642i
$776$		−	469.519i		−	0.605050i
$777$	13.6464	+	15.9617i	0.0175630	+	0.0205427i
$778$	−540.000			−0.694087
$779$	911.210	+	526.087i	1.16972	+	0.675337i
$780$	9.30306	+	50.0545i	0.0119270	+	0.0641724i
$781$		0			0
$782$	−88.1816	−	50.9117i	−0.112764	−	0.0651045i
$783$	240.000	+	390.323i	0.306513	+	0.498497i
$784$	196.000			0.250000
$785$		−	1001.26i		−	1.27549i
$786$	233.939	+	273.629i	0.297632	+	0.348128i
$787$	293.000	+	507.491i	0.372300	+	0.644842i	0.989919	−	0.141635i	$-0.0452360\pi$
$787$	293.000	+	507.491i	0.372300	+	0.644842i	−0.617619	+	0.786477i	$0.711903\pi$
$788$	−631.968	+	364.867i	−0.801990	+	0.463029i
$789$	−232.182	+	198.504i	−0.294273	+	0.251589i
$790$	−1236.00			−1.56456
$791$	−977.346	−	564.271i	−1.23558	−	0.713364i
$792$		0			0
$793$	25.0000	−	43.3013i	0.0315259	−	0.0546044i
$794$	589.102	−	340.118i	0.741942	−	0.428361i
$795$	−637.090	+	118.409i	−0.801371	+	0.148942i
$796$	−106.000	+	183.597i	−0.133166	+	0.230650i
$797$		−	483.661i		−	0.606852i	−0.952855	−	0.303426i	$-0.901869\pi$
$797$		−	483.661i		−	0.606852i	0.952855	−	0.303426i	$-0.0981305\pi$
$798$	168.230	+	905.152i	0.210815	+	1.13428i
$799$	360.000			0.450563
$800$	−230.252	−	132.936i	−0.287815	−	0.166170i
$801$	−1056.15	−	166.190i	−1.31854	−	0.207479i
$802$	−54.0000	−	93.5307i	−0.0673317	−	0.116622i
$803$		0			0
$804$	130.000	−	367.696i	0.161692	−	0.457333i
$805$	504.000			0.626087
$806$		−	9.89949i		−	0.0122823i
$807$	−967.423	+	827.098i	−1.19879	+	1.02491i
$808$	192.000	+	332.554i	0.237624	+	0.411576i
$809$	698.105	−	403.051i	0.862923	−	0.498209i	−0.00206714	−	0.999998i	$-0.500658\pi$
$809$	698.105	−	403.051i	0.862923	−	0.498209i	0.864990	+	0.501789i	$0.167325\pi$
$810$	−925.029	−	298.507i	−1.14201	−	0.368527i
$811$	398.000			0.490752			0.245376	−	0.969428i	$-0.421089\pi$
$811$	398.000			0.490752			0.245376	+	0.969428i	$0.421089\pi$
$812$		−	237.588i		−	0.292596i
$813$	250.000	−	707.107i	0.307503	−	0.869750i
$814$		0			0
$815$	−778.938	+	449.720i	−0.955752	+	0.551804i
$816$	−18.6061	−	100.109i	−0.0228016	−	0.122683i
$817$	−480.500	+	832.250i	−0.588127	+	1.01867i
$818$			69.2965i			0.0847145i
$819$	9.79286	−	62.2342i	0.0119571	−	0.0759881i
$820$	576.000			0.702439
$821$	1403.56	+	810.344i	1.70957	+	0.987021i	0.935081	+	0.354435i	$0.115327\pi$
$821$	1403.56	+	810.344i	1.70957	+	0.987021i	0.774490	+	0.632586i	$0.218006\pi$
$822$	778.665	−	144.722i	0.947281	−	0.176060i
$823$	581.000	+	1006.32i	0.705954	+	1.22275i	0.966346	+	0.257245i	$0.0828147\pi$
$823$	581.000	+	1006.32i	0.705954	+	1.22275i	−0.260392	+	0.965503i	$0.583852\pi$
$824$	−159.217	−	91.9239i	−0.193224	−	0.111558i
$825$		0			0
$826$	42.0000	−	72.7461i	0.0508475	−	0.0880704i
$827$		−	144.250i		−	0.174425i	−0.996190	−	0.0872127i	$-0.972204\pi$
$827$		−	144.250i		−	0.174425i	0.996190	−	0.0872127i	$-0.0277960\pi$
$828$	54.8786	+	142.535i	0.0662785	+	0.172144i
$829$	−623.500	−	1079.93i	−0.752111	−	1.30269i	−0.946798	−	0.321829i	$-0.895702\pi$
$829$	−623.500	−	1079.93i	−0.752111	−	1.30269i	0.194687	−	0.980865i	$-0.437631\pi$
$830$	440.908	−	254.558i	0.531215	−	0.306697i
$831$	−746.655	−	873.332i	−0.898501	−	1.05094i
$832$	8.00000			0.00961538
$833$	360.075	+	207.889i	0.432263	+	0.249567i
$834$	452.000	+	159.806i	0.541966	+	0.191614i
$835$	612.000	−	1060.02i	0.732934	−	1.26948i
$836$		0			0
$837$	166.232	+	89.9326i	0.198605	+	0.107446i
$838$	228.000	−	394.908i	0.272076	−	0.471250i
$839$			1001.26i			1.19340i	0.802464	+	0.596700i	$0.203522\pi$
$839$			1001.26i			1.19340i	−0.802464	+	0.596700i	$0.796478\pi$
$840$	327.514	+	383.080i	0.389898	+	0.456048i
$841$	553.000			0.657551
$842$	−383.345	−	221.324i	−0.455279	−	0.262856i
$843$	−97.6821	−	525.572i	−0.115874	−	0.623455i
$844$	62.0000	+	107.387i	0.0734597	+	0.127236i
$845$	1234.54	+	712.764i	1.46100	+	0.843507i
$846$	−420.000	−	339.411i	−0.496454	−	0.401195i
$847$	−423.500	−	733.524i	−0.500000	−	0.866025i
$848$			101.823i			0.120075i
$849$	−594.594	−	695.473i	−0.700347	−	0.819167i
$850$	−282.000	−	488.438i	−0.331765	−	0.574633i
$851$	7.34847	−	4.24264i	0.00863510	−	0.00498548i
$852$	270.879	−	231.588i	0.317933	−	0.271816i
$853$	−337.000			−0.395076			−0.197538	−	0.980295i	$-0.563295\pi$
$853$	−337.000			−0.395076			−0.197538	+	0.980295i	$0.563295\pi$
$854$		−	494.975i		−	0.579596i
$855$	−1488.00	+	1841.31i	−1.74035	+	2.15357i
$856$	−228.000	+	394.908i	−0.266355	+	0.461341i
$857$	969.998	−	560.029i	1.13185	−	0.653476i	0.187453	−	0.982274i	$-0.439977\pi$
$857$	969.998	−	560.029i	1.13185	−	0.653476i	0.944400	+	0.328798i	$0.106644\pi$
$858$		0			0
$859$	545.000	−	943.968i	0.634459	−	1.09891i	−0.352171	−	0.935936i	$-0.614556\pi$
$859$	545.000	−	943.968i	0.634459	−	1.09891i	0.986630	−	0.162979i	$-0.0521103\pi$
$860$			526.087i			0.611730i
$861$	−672.000	−	237.588i	−0.780488	−	0.275944i
$862$	−492.000			−0.570766
$863$	999.392	+	576.999i	1.15804	+	0.668597i	0.950834	−	0.309700i	$-0.100229\pi$
$863$	999.392	+	576.999i	1.15804	+	0.668597i	0.207209	+	0.978297i	$0.433562\pi$
$864$	−72.6765	+	134.336i	−0.0841164	+	0.155481i
$865$	324.000	+	561.184i	0.374566	+	0.648768i
$866$	−118.800	−	68.5894i	−0.137183	−	0.0792025i
$867$	−217.000	+	613.769i	−0.250288	+	0.707922i
$868$	−49.0000	−	84.8705i	−0.0564516	−	0.0977771i
$869$		0			0
$870$	464.363	−	397.007i	0.533751	−	0.456330i
$871$	32.5000	+	56.2917i	0.0373134	+	0.0646288i
$872$	409.065	−	236.174i	0.469111	−	0.270841i
$873$	−1394.23	+	536.803i	−1.59706	+	0.614894i
$874$	372.000			0.425629
$875$	1131.66	+	653.367i	1.29333	+	0.746705i
$876$	−194.000	+	548.715i	−0.221461	+	0.626387i
$877$	23.0000	−	39.8372i	0.0262258	−	0.0454244i	−0.852615	−	0.522540i	$-0.824984\pi$
$877$	23.0000	−	39.8372i	0.0262258	−	0.0454244i	0.878840	+	0.477116i	$0.158318\pi$
$878$	−458.055	+	264.458i	−0.521702	+	0.301205i
$879$	−74.4245	−	400.436i	−0.0846695	−	0.455559i
$880$		0			0
$881$		−	924.896i		−	1.04982i	−0.851156	−	0.524912i	$-0.824098\pi$
$881$		−	924.896i		−	1.04982i	0.851156	−	0.524912i	$-0.175902\pi$
$882$	−224.087	−	582.020i	−0.254067	−	0.659886i
$883$	329.000			0.372593			0.186297	−	0.982494i	$-0.440351\pi$
$883$	329.000			0.372593			0.186297	+	0.982494i	$0.440351\pi$
$884$	14.6969	+	8.48528i	0.0166255	+	0.00959873i
$885$	212.363	−	39.4695i	0.239958	−	0.0445984i
$886$	−426.000	−	737.854i	−0.480813	−	0.832792i
$887$	−1219.85	−	704.278i	−1.37525	−	0.794000i	−0.383666	−	0.923472i	$-0.625339\pi$
$887$	−1219.85	−	704.278i	−1.37525	−	0.794000i	−0.991583	+	0.129472i	$0.958672\pi$
$888$	8.00000	+	2.82843i	0.00900901	+	0.00318517i
$889$	−395.500	+	685.026i	−0.444882	+	0.770558i
$890$			1425.53i			1.60172i
$891$		0			0
$892$	−202.000	−	349.874i	−0.226457	−	0.392236i
$893$	−1139.01	+	657.609i	−1.27549	+	0.736405i
$894$	−187.151	−	218.903i	−0.209341	−	0.244858i
$895$	−1368.00			−1.52849
$896$	68.5857	−	39.5980i	0.0765466	−	0.0441942i
$897$	−24.0000	−	8.48528i	−0.0267559	−	0.00945962i
$898$	−30.0000	+	51.9615i	−0.0334076	+	0.0578636i
$899$	−102.879	+	59.3970i	−0.114437	+	0.0660700i
$900$	−131.504	+	835.717i	−0.146116	+	0.928574i
$901$	−108.000	+	187.061i	−0.119867	+	0.207615i
$902$		0			0
$903$	217.000	−	613.769i	0.240310	−	0.679700i
$904$	−456.000			−0.504425
$905$	−1579.92	−	912.168i	−1.74577	−	1.00792i
$906$	44.9648	+	241.930i	0.0496300	+	0.267031i
$907$	87.5000	+	151.554i	0.0964719	+	0.167094i	0.910222	−	0.414121i	$-0.135911\pi$
$907$	87.5000	+	151.554i	0.0964719	+	0.167094i	−0.813750	+	0.581215i	$0.802578\pi$
$908$	−29.3939	−	16.9706i	−0.0323721	−	0.0186900i
$909$	768.000	−	950.352i	0.844884	−	1.04549i
$910$	−84.0000			−0.0923077
$911$		−	1450.98i		−	1.59274i	−0.604812	−	0.796368i	$-0.706752\pi$
$911$		−	1450.98i		−	1.59274i	0.604812	−	0.796368i	$-0.293248\pi$
$912$	241.737	+	282.750i	0.265062	+	0.310032i
$913$		0			0
$914$	−557.259	+	321.734i	−0.609692	+	0.352006i
$915$	967.423	−	827.098i	1.05729	−	0.903933i
$916$	2.00000			0.00218341
$917$	−514.393	+	296.985i	−0.560952	+	0.323866i
$918$	−276.000	+	169.706i	−0.300654	+	0.184865i
$919$	−548.500	+	950.030i	−0.596844	+	1.03376i	0.396439	+	0.918061i	$0.370246\pi$
$919$	−548.500	+	950.030i	−0.596844	+	1.03376i	−0.993284	+	0.115704i	$0.963088\pi$
$920$	176.363	−	101.823i	0.191699	−	0.110678i
$921$	−586.948	+	109.089i	−0.637295	+	0.118447i
$922$	156.000	−	270.200i	0.169197	−	0.293058i
$923$			59.3970i			0.0643521i
$924$		0			0
$925$	47.0000			0.0508108
$926$	−8.57321	−	4.94975i	−0.00925833	−	0.00534530i
$927$	−90.9337	+	577.889i	−0.0980946	+	0.623397i
$928$	−48.0000	−	83.1384i	−0.0517241	−	0.0895888i
$929$	492.347	+	284.257i	0.529976	+	0.305982i	0.741007	−	0.671498i	$-0.234349\pi$
$929$	492.347	+	284.257i	0.529976	+	0.305982i	−0.211031	+	0.977479i	$0.567682\pi$
$930$	84.0000	−	237.588i	0.0903226	−	0.255471i
$931$	−1519.00			−1.63158
$932$		−	661.852i		−	0.710142i
$933$	1006.12	−	860.182i	1.07837	−	0.921953i
$934$	−438.000	−	758.638i	−0.468951	−	0.812247i
$935$		0			0
$936$	−9.14643	−	23.7559i	−0.00977182	−	0.0253802i
$937$	−1.00000			−0.00106724			−0.000533618	−	1.00000i	$-0.500170\pi$
$937$	−1.00000			−0.00106724			−0.000533618		1.00000i	$0.500170\pi$
$938$	557.259	+	321.734i	0.594093	+	0.343000i
$939$	−119.000	+	336.583i	−0.126731	+	0.358448i
$940$	−360.000	+	623.538i	−0.382979	+	0.663339i
$941$	−330.681	+	190.919i	−0.351415	+	0.202889i	−0.665308	−	0.746569i	$-0.731700\pi$
$941$	−330.681	+	190.919i	−0.351415	+	0.202889i	0.313894	+	0.949458i	$0.398366\pi$
$942$	91.4801	+	492.203i	0.0971126	+	0.522508i
$943$	−144.000	+	249.415i	−0.152704	+	0.264491i
$944$		−	33.9411i		−	0.0359546i
$945$	763.104	−	1410.53i	0.807517	−	1.49262i
$946$		0			0
$947$	−1455.00	−	840.043i	−1.53643	−	0.887057i	−0.999044	−	0.0437190i	$-0.986079\pi$
$947$	−1455.00	−	840.043i	−1.53643	−	0.887057i	−0.537384	−	0.843338i	$-0.680587\pi$
$948$	607.595	−	112.927i	0.640923	−	0.119121i
$949$	−48.5000	−	84.0045i	−0.0511064	−	0.0885189i
$950$	1784.45	+	1030.25i	1.87837	+	1.08448i
$951$	576.000	+	203.647i	0.605678	+	0.214140i
$952$	168.000			0.176471
$953$			195.161i			0.204786i	0.994744	+	0.102393i	$0.0326500\pi$
$953$			195.161i			0.204786i	−0.994744	+	0.102393i	$0.967350\pi$
$954$	302.363	−	116.415i	0.316943	−	0.122028i
$955$	756.000	+	1309.43i	0.791623	+	1.37113i
$956$	793.635	−	458.205i	0.830162	−	0.479294i
$957$		0			0
$958$	948.000			0.989562
$959$			1306.73i			1.36260i
$960$	192.000	+	67.8823i	0.200000	+	0.0707107i
$961$	456.000	−	789.815i	0.474506	−	0.821868i
$962$	−1.22474	+	0.707107i	−0.00127312	+	0.000735038i
$963$	1433.35	+	225.544i	1.48842	+	0.234210i
$964$	−22.0000	+	38.1051i	−0.0228216	+	0.0395281i
$965$		−	823.072i		−	0.852925i
$966$	−247.757	+	46.0478i	−0.256477	+	0.0476685i
$967$	−223.000			−0.230610			−0.115305	−	0.993330i	$-0.536785\pi$
$967$	−223.000			−0.230610			−0.115305	+	0.993330i	$0.536785\pi$
$968$	−296.388	−	171.120i	−0.306186	−	0.176777i
$969$	144.197	+	775.845i	0.148811	+	0.800665i
$970$	996.000	+	1725.12i	1.02680	+	1.77848i
$971$	492.347	+	284.257i	0.507052	+	0.292747i	0.731621	−	0.681712i	$-0.238764\pi$
$971$	492.347	+	284.257i	0.507052	+	0.292747i	−0.224569	+	0.974458i	$0.572097\pi$
$972$	482.000	+	62.2254i	0.495885	+	0.0640179i
$973$	−395.500	+	685.026i	−0.406475	+	0.704035i
$974$			654.781i			0.672260i
$975$	−91.6260	−	107.171i	−0.0939754	−	0.109919i
$976$	−100.000	−	173.205i	−0.102459	−	0.177464i
$977$	1396.21	−	806.102i	1.42908	−	0.825079i	0.432030	−	0.901859i	$-0.357797\pi$
$977$	1396.21	−	806.102i	1.42908	−	0.825079i	0.997048	+	0.0767807i	$0.0244641\pi$
$978$	341.823	−	292.241i	0.349512	−	0.298815i
$979$		0			0
$980$	−720.150	+	415.779i	−0.734847	+	0.424264i
$981$	−1169.00	−	944.695i	−1.19164	−	0.962991i
$982$	−252.000	+	436.477i	−0.256619	+	0.444477i
$983$	−1491.74	+	861.256i	−1.51754	+	0.876151i	−0.517750	+	0.855532i	$0.673230\pi$
$983$	−1491.74	+	861.256i	−1.51754	+	0.876151i	−0.999787	+	0.0206186i	$0.993436\pi$
$984$	−283.151	+	52.6261i	−0.287755	+	0.0534818i
$985$	1548.00	−	2681.21i	1.57157	−	2.72205i
$986$		−	203.647i		−	0.206538i
$987$	677.196	−	578.969i	0.686116	−	0.586595i
$988$	−62.0000			−0.0627530
$989$	−227.803	−	131.522i	−0.230336	−	0.132985i
$990$		0			0
$991$	447.500	+	775.093i	0.451564	+	0.782132i	0.998483	−	0.0550534i	$-0.0175329\pi$
$991$	447.500	+	775.093i	0.451564	+	0.782132i	−0.546919	+	0.837185i	$0.684200\pi$
$992$	−34.2929	−	19.7990i	−0.0345694	−	0.0199587i
$993$	−521.000	+	1473.61i	−0.524673	+	1.48400i
$994$	294.000	+	509.223i	0.295775	+	0.512297i
$995$		−	899.440i		−	0.903960i
$996$	−193.485	+	165.420i	−0.194262	+	0.166084i
$997$	−203.500	−	352.472i	−0.204112	−	0.353533i	0.745737	−	0.666240i	$-0.232097\pi$
$997$	−203.500	−	352.472i	−0.204112	−	0.353533i	−0.949850	+	0.312707i	$0.898764\pi$
$998$	655.239	−	378.302i	0.656552	−	0.379060i
$999$	−0.747449	−	26.9897i	−0.000748197	−	0.0270167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.3.h.a.23.2	yes	4
3.2	odd	2	inner	42.3.h.a.23.1	yes	4
4.3	odd	2		336.3.bn.c.65.1		4
7.2	even	3		294.3.b.b.197.1		2
7.3	odd	6		294.3.h.b.263.1		4
7.4	even	3	inner	42.3.h.a.11.1	✓	4
7.5	odd	6		294.3.b.c.197.1		2
7.6	odd	2		294.3.h.b.275.2		4
12.11	even	2		336.3.bn.c.65.2		4
21.2	odd	6		294.3.b.b.197.2		2
21.5	even	6		294.3.b.c.197.2		2
21.11	odd	6	inner	42.3.h.a.11.2	yes	4
21.17	even	6		294.3.h.b.263.2		4
21.20	even	2		294.3.h.b.275.1		4
28.11	odd	6		336.3.bn.c.305.2		4
84.11	even	6		336.3.bn.c.305.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.h.a.11.1	✓	4	7.4	even	3	inner
42.3.h.a.11.2	yes	4	21.11	odd	6	inner
42.3.h.a.23.1	yes	4	3.2	odd	2	inner
42.3.h.a.23.2	yes	4	1.1	even	1	trivial
294.3.b.b.197.1		2	7.2	even	3
294.3.b.b.197.2		2	21.2	odd	6
294.3.b.c.197.1		2	7.5	odd	6
294.3.b.c.197.2		2	21.5	even	6
294.3.h.b.263.1		4	7.3	odd	6
294.3.h.b.263.2		4	21.17	even	6
294.3.h.b.275.1		4	21.20	even	2
294.3.h.b.275.2		4	7.6	odd	2
336.3.bn.c.65.1		4	4.3	odd	2
336.3.bn.c.65.2		4	12.11	even	2
336.3.bn.c.305.1		4	84.11	even	6
336.3.bn.c.305.2		4	28.11	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:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	42.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(2.94949 - 0.548188i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-7.34847 - 4.24264i) q^{5} +(4.00000 + 1.41421i) q^{6} +(-3.50000 + 6.06218i) q^{7} +2.82843i q^{8} +(8.39898 - 3.23375i) q^{9} +O(q^{10})\)	\(q+(1.22474 + 0.707107i) q^{2} +(2.94949 - 0.548188i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-7.34847 - 4.24264i) q^{5} +(4.00000 + 1.41421i) q^{6} +(-3.50000 + 6.06218i) q^{7} +2.82843i q^{8} +(8.39898 - 3.23375i) q^{9} +(-6.00000 - 10.3923i) q^{10} +(3.89898 + 4.56048i) q^{12} -1.00000 q^{13} +(-8.57321 + 4.94975i) q^{14} +(-24.0000 - 8.48528i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-7.34847 + 4.24264i) q^{17} +(12.5732 + 1.97846i) q^{18} +(15.5000 - 26.8468i) q^{19} -16.9706i q^{20} +(-7.00000 + 19.7990i) q^{21} +(7.34847 + 4.24264i) q^{23} +(1.55051 + 8.34242i) q^{24} +(23.5000 + 40.7032i) q^{25} +(-1.22474 - 0.707107i) q^{26} +(23.0000 - 14.1421i) q^{27} -14.0000 q^{28} +16.9706i q^{29} +(-23.3939 - 27.3629i) q^{30} +(3.50000 + 6.06218i) q^{31} +(-4.89898 + 2.82843i) q^{32} -12.0000 q^{34} +(51.4393 - 29.6985i) q^{35} +(14.0000 + 11.3137i) q^{36} +(0.500000 - 0.866025i) q^{37} +(37.9671 - 21.9203i) q^{38} +(-2.94949 + 0.548188i) q^{39} +(12.0000 - 20.7846i) q^{40} +33.9411i q^{41} +(-22.5732 + 19.2990i) q^{42} -31.0000 q^{43} +(-75.4393 - 11.8707i) q^{45} +(6.00000 + 10.3923i) q^{46} +(-36.7423 - 21.2132i) q^{47} +(-4.00000 + 11.3137i) q^{48} +(-24.5000 - 42.4352i) q^{49} +66.4680i q^{50} +(-19.3485 + 16.5420i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(22.0454 - 12.7279i) q^{53} +(38.1691 - 1.05705i) q^{54} +(-17.1464 - 9.89949i) q^{56} +(31.0000 - 87.6812i) q^{57} +(-12.0000 + 20.7846i) q^{58} +(-7.34847 + 4.24264i) q^{59} +(-9.30306 - 50.0545i) q^{60} +(-25.0000 + 43.3013i) q^{61} +9.89949i q^{62} +(-9.79286 + 62.2342i) q^{63} -8.00000 q^{64} +(7.34847 + 4.24264i) q^{65} +(-32.5000 - 56.2917i) q^{67} +(-14.6969 - 8.48528i) q^{68} +(24.0000 + 8.48528i) q^{69} +84.0000 q^{70} -59.3970i q^{71} +(9.14643 + 23.7559i) q^{72} +(48.5000 + 84.0045i) q^{73} +(1.22474 - 0.707107i) q^{74} +(91.6260 + 107.171i) q^{75} +62.0000 q^{76} +(-4.00000 - 1.41421i) q^{78} +(51.5000 - 89.2006i) q^{79} +(29.3939 - 16.9706i) q^{80} +(60.0857 - 54.3204i) q^{81} +(-24.0000 + 41.5692i) q^{82} +42.4264i q^{83} +(-41.2929 + 7.67463i) q^{84} +72.0000 q^{85} +(-37.9671 - 21.9203i) q^{86} +(9.30306 + 50.0545i) q^{87} +(-102.879 - 59.3970i) q^{89} +(-84.0000 - 67.8823i) q^{90} +(3.50000 - 6.06218i) q^{91} +16.9706i q^{92} +(13.6464 + 15.9617i) q^{93} +(-30.0000 - 51.9615i) q^{94} +(-227.803 + 131.522i) q^{95} +(-12.8990 + 11.0280i) q^{96} -166.000 q^{97} -69.2965i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 4 q^{4} + 16 q^{6} - 14 q^{7} + 14 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 4 * q^4 + 16 * q^6 - 14 * q^7 + 14 * q^9	\( 4 q + 2 q^{3} + 4 q^{4} + 16 q^{6} - 14 q^{7} + 14 q^{9} - 24 q^{10} - 4 q^{12} - 4 q^{13} - 96 q^{15} - 8 q^{16} + 16 q^{18} + 62 q^{19} - 28 q^{21} + 16 q^{24} + 94 q^{25} + 92 q^{27} - 56 q^{28} + 24 q^{30} + 14 q^{31} - 48 q^{34} + 56 q^{36} + 2 q^{37} - 2 q^{39} + 48 q^{40} - 56 q^{42} - 124 q^{43} - 96 q^{45} + 24 q^{46} - 16 q^{48} - 98 q^{49} - 48 q^{51} - 4 q^{52} + 40 q^{54} + 124 q^{57} - 48 q^{58} - 96 q^{60} - 100 q^{61} + 98 q^{63} - 32 q^{64} - 130 q^{67} + 96 q^{69} + 336 q^{70} - 32 q^{72} + 194 q^{73} - 94 q^{75} + 248 q^{76} - 16 q^{78} + 206 q^{79} - 34 q^{81} - 96 q^{82} - 28 q^{84} + 288 q^{85} + 96 q^{87} - 336 q^{90} + 14 q^{91} - 14 q^{93} - 120 q^{94} - 32 q^{96} - 664 q^{97}+O(q^{100}) \) 4 * q + 2 * q^3 + 4 * q^4 + 16 * q^6 - 14 * q^7 + 14 * q^9 - 24 * q^10 - 4 * q^12 - 4 * q^13 - 96 * q^15 - 8 * q^16 + 16 * q^18 + 62 * q^19 - 28 * q^21 + 16 * q^24 + 94 * q^25 + 92 * q^27 - 56 * q^28 + 24 * q^30 + 14 * q^31 - 48 * q^34 + 56 * q^36 + 2 * q^37 - 2 * q^39 + 48 * q^40 - 56 * q^42 - 124 * q^43 - 96 * q^45 + 24 * q^46 - 16 * q^48 - 98 * q^49 - 48 * q^51 - 4 * q^52 + 40 * q^54 + 124 * q^57 - 48 * q^58 - 96 * q^60 - 100 * q^61 + 98 * q^63 - 32 * q^64 - 130 * q^67 + 96 * q^69 + 336 * q^70 - 32 * q^72 + 194 * q^73 - 94 * q^75 + 248 * q^76 - 16 * q^78 + 206 * q^79 - 34 * q^81 - 96 * q^82 - 28 * q^84 + 288 * q^85 + 96 * q^87 - 336 * q^90 + 14 * q^91 - 14 * q^93 - 120 * q^94 - 32 * q^96 - 664 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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