LMFDB - Embedded newform 42.3.c.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,3,Mod(13,42)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("42.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	42.c (of order $2$, degree $1$, 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:	$4$
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:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	42.13
Dual form			42.3.c.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +5.91359i q^{5} -2.44949i q^{6} +(6.24264 + 3.16693i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +5.91359i q^{5} -2.44949i q^{6} +(6.24264 + 3.16693i) q^{7} -2.82843 q^{8} -3.00000 q^{9} -8.36308i q^{10} -1.75736 q^{11} +3.46410i q^{12} -18.7554i q^{13} +(-8.82843 - 4.47871i) q^{14} -10.2426 q^{15} +4.00000 q^{16} -23.4803i q^{17} +4.24264 q^{18} +23.0600i q^{19} +11.8272i q^{20} +(-5.48528 + 10.8126i) q^{21} +2.48528 q^{22} +18.7279 q^{23} -4.89898i q^{24} -9.97056 q^{25} +26.5241i q^{26} -5.19615i q^{27} +(12.4853 + 6.33386i) q^{28} +30.0000 q^{29} +14.4853 q^{30} -8.60927i q^{31} -5.65685 q^{32} -3.04384i q^{33} +33.2061i q^{34} +(-18.7279 + 36.9164i) q^{35} -6.00000 q^{36} -70.9117 q^{37} -32.6118i q^{38} +32.4853 q^{39} -16.7262i q^{40} -41.3951i q^{41} +(7.75736 - 15.2913i) q^{42} +10.4264 q^{43} -3.51472 q^{44} -17.7408i q^{45} -26.4853 q^{46} -38.6995i q^{47} +6.92820i q^{48} +(28.9411 + 39.5400i) q^{49} +14.1005 q^{50} +40.6690 q^{51} -37.5108i q^{52} -37.0294 q^{53} +7.34847i q^{54} -10.3923i q^{55} +(-17.6569 - 8.95743i) q^{56} -39.9411 q^{57} -42.4264 q^{58} +97.4872i q^{59} -20.4853 q^{60} -16.7262i q^{61} +12.1753i q^{62} +(-18.7279 - 9.50079i) q^{63} +8.00000 q^{64} +110.912 q^{65} +4.30463i q^{66} +60.9706 q^{67} -46.9606i q^{68} +32.4377i q^{69} +(26.4853 - 52.2077i) q^{70} -110.610 q^{71} +8.48528 q^{72} +56.7585i q^{73} +100.284 q^{74} -17.2695i q^{75} +46.1200i q^{76} +(-10.9706 - 5.56543i) q^{77} -45.9411 q^{78} -69.8234 q^{79} +23.6544i q^{80} +9.00000 q^{81} +58.5416i q^{82} -6.43583i q^{83} +(-10.9706 + 21.6251i) q^{84} +138.853 q^{85} -14.7452 q^{86} +51.9615i q^{87} +4.97056 q^{88} +42.0915i q^{89} +25.0892i q^{90} +(59.3970 - 117.083i) q^{91} +37.4558 q^{92} +14.9117 q^{93} +54.7293i q^{94} -136.368 q^{95} -9.79796i q^{96} -51.7153i q^{97} +(-40.9289 - 55.9180i) q^{98} +5.27208 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{4} + 8 q^{7} - 12 q^{9}+O(q^{10}) $ 4 * q + 8 * q^4 + 8 * q^7 - 12 * q^9	$ 4 q + 8 q^{4} + 8 q^{7} - 12 q^{9} - 24 q^{11} - 24 q^{14} - 24 q^{15} + 16 q^{16} + 12 q^{21} - 24 q^{22} + 24 q^{23} + 28 q^{25} + 16 q^{28} + 120 q^{29} + 24 q^{30} - 24 q^{35} - 24 q^{36} - 80 q^{37} + 96 q^{39} + 48 q^{42} - 128 q^{43} - 48 q^{44} - 72 q^{46} - 20 q^{49} + 96 q^{50} - 24 q^{51} - 216 q^{53} - 48 q^{56} - 24 q^{57} - 48 q^{60} - 24 q^{63} + 32 q^{64} + 240 q^{65} + 176 q^{67} + 72 q^{70} - 120 q^{71} + 288 q^{74} + 24 q^{77} - 48 q^{78} + 128 q^{79} + 36 q^{81} + 24 q^{84} + 216 q^{85} - 240 q^{86} - 48 q^{88} + 48 q^{92} - 144 q^{93} - 240 q^{95} - 192 q^{98} + 72 q^{99}+O(q^{100}) $ 4 * q + 8 * q^4 + 8 * q^7 - 12 * q^9 - 24 * q^11 - 24 * q^14 - 24 * q^15 + 16 * q^16 + 12 * q^21 - 24 * q^22 + 24 * q^23 + 28 * q^25 + 16 * q^28 + 120 * q^29 + 24 * q^30 - 24 * q^35 - 24 * q^36 - 80 * q^37 + 96 * q^39 + 48 * q^42 - 128 * q^43 - 48 * q^44 - 72 * q^46 - 20 * q^49 + 96 * q^50 - 24 * q^51 - 216 * q^53 - 48 * q^56 - 24 * q^57 - 48 * q^60 - 24 * q^63 + 32 * q^64 + 240 * q^65 + 176 * q^67 + 72 * q^70 - 120 * q^71 + 288 * q^74 + 24 * q^77 - 48 * q^78 + 128 * q^79 + 36 * q^81 + 24 * q^84 + 216 * q^85 - 240 * q^86 - 48 * q^88 + 48 * q^92 - 144 * q^93 - 240 * q^95 - 192 * q^98 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$31$
$\chi(n)$	$1$	$-1$

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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	2.00000			0.500000
$5$			5.91359i			1.18272i	0.806408	+	0.591359i	$0.201408\pi$
$5$			5.91359i			1.18272i	−0.806408	+	0.591359i	$0.798592\pi$
$6$		−	2.44949i		−	0.408248i
$7$	6.24264	+	3.16693i	0.891806	+	0.452418i
$7$	6.24264	+	3.16693i	0.891806	+	0.452418i
$8$	−2.82843			−0.353553
$9$	−3.00000			−0.333333
$10$		−	8.36308i		−	0.836308i
$11$	−1.75736			−0.159760			−0.0798800	−	0.996804i	$-0.525454\pi$
$11$	−1.75736			−0.159760			−0.0798800	+	0.996804i	$0.525454\pi$
$12$			3.46410i			0.288675i
$13$		−	18.7554i		−	1.44272i	−0.692559	−	0.721361i	$-0.743517\pi$
$13$		−	18.7554i		−	1.44272i	0.692559	−	0.721361i	$-0.256483\pi$
$14$	−8.82843	−	4.47871i	−0.630602	−	0.319908i
$15$	−10.2426			−0.682843
$16$	4.00000			0.250000
$17$		−	23.4803i		−	1.38119i	−0.723240	−	0.690597i	$-0.757348\pi$
$17$		−	23.4803i		−	1.38119i	0.723240	−	0.690597i	$-0.242652\pi$
$18$	4.24264			0.235702
$19$			23.0600i			1.21369i	0.794822	+	0.606843i	$0.207564\pi$
$19$			23.0600i			1.21369i	−0.794822	+	0.606843i	$0.792436\pi$
$20$			11.8272i			0.591359i
$21$	−5.48528	+	10.8126i	−0.261204	+	0.514884i
$22$	2.48528			0.112967
$23$	18.7279			0.814257			0.407129	−	0.913371i	$-0.366530\pi$
$23$	18.7279			0.814257			0.407129	+	0.913371i	$0.366530\pi$
$24$		−	4.89898i		−	0.204124i
$25$	−9.97056			−0.398823
$26$			26.5241i			1.02016i
$27$		−	5.19615i		−	0.192450i
$28$	12.4853	+	6.33386i	0.445903	+	0.226209i
$29$	30.0000			1.03448			0.517241	−	0.855840i	$-0.326959\pi$
$29$	30.0000			1.03448			0.517241	+	0.855840i	$0.326959\pi$
$30$	14.4853			0.482843
$31$		−	8.60927i		−	0.277718i	−0.990312	−	0.138859i	$-0.955656\pi$
$31$		−	8.60927i		−	0.277718i	0.990312	−	0.138859i	$-0.0443435\pi$
$32$	−5.65685			−0.176777
$33$		−	3.04384i		−	0.0922374i
$34$			33.2061i			0.976651i
$35$	−18.7279	+	36.9164i	−0.535083	+	1.05476i
$36$	−6.00000			−0.166667
$37$	−70.9117			−1.91653			−0.958266	−	0.285878i	$-0.907715\pi$
$37$	−70.9117			−1.91653			−0.958266	+	0.285878i	$0.907715\pi$
$38$		−	32.6118i		−	0.858205i
$39$	32.4853			0.832956
$40$		−	16.7262i		−	0.418154i
$41$		−	41.3951i		−	1.00964i	−0.863225	−	0.504819i	$-0.831559\pi$
$41$		−	41.3951i		−	1.00964i	0.863225	−	0.504819i	$-0.168441\pi$
$42$	7.75736	−	15.2913i	0.184699	−	0.364078i
$43$	10.4264			0.242475			0.121237	−	0.992624i	$-0.461314\pi$
$43$	10.4264			0.242475			0.121237	+	0.992624i	$0.461314\pi$
$44$	−3.51472			−0.0798800
$45$		−	17.7408i		−	0.394239i
$46$	−26.4853			−0.575767
$47$		−	38.6995i		−	0.823393i	−0.911321	−	0.411696i	$-0.864936\pi$
$47$		−	38.6995i		−	0.823393i	0.911321	−	0.411696i	$-0.135064\pi$
$48$			6.92820i			0.144338i
$49$	28.9411	+	39.5400i	0.590635	+	0.806939i
$50$	14.1005			0.282010
$51$	40.6690			0.797432
$52$		−	37.5108i		−	0.721361i
$53$	−37.0294			−0.698669			−0.349334	−	0.936998i	$-0.613592\pi$
$53$	−37.0294			−0.698669			−0.349334	+	0.936998i	$0.613592\pi$
$54$			7.34847i			0.136083i
$55$		−	10.3923i		−	0.188951i
$56$	−17.6569	−	8.95743i	−0.315301	−	0.159954i
$57$	−39.9411			−0.700721
$58$	−42.4264			−0.731490
$59$			97.4872i			1.65233i	0.563431	+	0.826163i	$0.309481\pi$
$59$			97.4872i			1.65233i	−0.563431	+	0.826163i	$0.690519\pi$
$60$	−20.4853			−0.341421
$61$		−	16.7262i		−	0.274199i	−0.990557	−	0.137100i	$-0.956222\pi$
$61$		−	16.7262i		−	0.274199i	0.990557	−	0.137100i	$-0.0437781\pi$
$62$			12.1753i			0.196376i
$63$	−18.7279	−	9.50079i	−0.297269	−	0.150806i
$64$	8.00000			0.125000
$65$	110.912			1.70633
$66$			4.30463i			0.0652217i
$67$	60.9706			0.910008			0.455004	−	0.890489i	$-0.349638\pi$
$67$	60.9706			0.910008			0.455004	+	0.890489i	$0.349638\pi$
$68$		−	46.9606i		−	0.690597i
$69$			32.4377i			0.470112i
$70$	26.4853	−	52.2077i	0.378361	−	0.745824i
$71$	−110.610			−1.55789			−0.778945	−	0.627092i	$-0.784245\pi$
$71$	−110.610			−1.55789			−0.778945	+	0.627092i	$0.784245\pi$
$72$	8.48528			0.117851
$73$			56.7585i			0.777514i	0.921340	+	0.388757i	$0.127095\pi$
$73$			56.7585i			0.777514i	−0.921340	+	0.388757i	$0.872905\pi$
$74$	100.284			1.35519
$75$		−	17.2695i		−	0.230260i
$76$			46.1200i			0.606843i
$77$	−10.9706	−	5.56543i	−0.142475	−	0.0722783i
$78$	−45.9411			−0.588989
$79$	−69.8234			−0.883840			−0.441920	−	0.897054i	$-0.645703\pi$
$79$	−69.8234			−0.883840			−0.441920	+	0.897054i	$0.645703\pi$
$80$			23.6544i			0.295680i
$81$	9.00000			0.111111
$82$			58.5416i			0.713922i
$83$		−	6.43583i		−	0.0775401i	−0.999248	−	0.0387701i	$-0.987656\pi$
$83$		−	6.43583i		−	0.0775401i	0.999248	−	0.0387701i	$-0.0123440\pi$
$84$	−10.9706	+	21.6251i	−0.130602	+	0.257442i
$85$	138.853			1.63356
$86$	−14.7452			−0.171455
$87$			51.9615i			0.597259i
$88$	4.97056			0.0564837
$89$			42.0915i			0.472938i	0.971639	+	0.236469i	$0.0759901\pi$
$89$			42.0915i			0.472938i	−0.971639	+	0.236469i	$0.924010\pi$
$90$			25.0892i			0.278769i
$91$	59.3970	−	117.083i	0.652714	−	1.28663i
$92$	37.4558			0.407129
$93$	14.9117			0.160341
$94$			54.7293i			0.582227i
$95$	−136.368			−1.43545
$96$		−	9.79796i		−	0.102062i
$97$		−	51.7153i		−	0.533148i	−0.963814	−	0.266574i	$-0.914108\pi$
$97$		−	51.7153i		−	0.533148i	0.963814	−	0.266574i	$-0.0858916\pi$
$98$	−40.9289	−	55.9180i	−0.417642	−	0.570592i
$99$	5.27208			0.0532533
$100$	−19.9411			−0.199411
$101$		−	6.60991i		−	0.0654447i	−0.999464	−	0.0327223i	$-0.989582\pi$
$101$		−	6.60991i		−	0.0654447i	0.999464	−	0.0327223i	$-0.0104177\pi$
$102$	−57.5147			−0.563870
$103$		−	175.871i		−	1.70748i	−0.520696	−	0.853742i	$-0.674327\pi$
$103$		−	175.871i		−	1.70748i	0.520696	−	0.853742i	$-0.325673\pi$
$104$			53.0482i			0.510079i
$105$	−63.9411	−	32.4377i	−0.608963	−	0.308931i
$106$	52.3675			0.494033
$107$	−46.2426			−0.432174			−0.216087	−	0.976374i	$-0.569330\pi$
$107$	−46.2426			−0.432174			−0.216087	+	0.976374i	$0.569330\pi$
$108$		−	10.3923i		−	0.0962250i
$109$	−35.9411			−0.329735			−0.164868	−	0.986316i	$-0.552720\pi$
$109$	−35.9411			−0.329735			−0.164868	+	0.986316i	$0.552720\pi$
$110$			14.6969i			0.133609i
$111$		−	122.823i		−	1.10651i
$112$	24.9706	+	12.6677i	0.222951	+	0.113105i
$113$	−73.0294			−0.646278			−0.323139	−	0.946351i	$-0.604738\pi$
$113$	−73.0294			−0.646278			−0.323139	+	0.946351i	$0.604738\pi$
$114$	56.4853			0.495485
$115$			110.749i			0.963037i
$116$	60.0000			0.517241
$117$			56.2662i			0.480907i
$118$		−	137.868i		−	1.16837i
$119$	74.3604	−	146.579i	0.624877	−	1.23176i
$120$	28.9706			0.241421
$121$	−117.912			−0.974477
$122$			23.6544i			0.193888i
$123$	71.6985			0.582915
$124$		−	17.2185i		−	0.138859i
$125$			88.8780i			0.711024i
$126$	26.4853	+	13.4361i	0.210201	+	0.106636i
$127$	89.9411			0.708198			0.354099	−	0.935208i	$-0.384788\pi$
$127$	89.9411			0.708198			0.354099	+	0.935208i	$0.384788\pi$
$128$	−11.3137			−0.0883883
$129$			18.0591i			0.139993i
$130$	−156.853			−1.20656
$131$		−	12.1753i		−	0.0929415i	−0.998920	−	0.0464708i	$-0.985203\pi$
$131$		−	12.1753i		−	0.0929415i	0.998920	−	0.0464708i	$-0.0147974\pi$
$132$		−	6.08767i		−	0.0461187i
$133$	−73.0294	+	143.955i	−0.549094	+	1.08237i
$134$	−86.2254			−0.643473
$135$	30.7279			0.227614
$136$			66.4123i			0.488326i
$137$	165.765			1.20996			0.604980	−	0.796241i	$-0.293181\pi$
$137$	165.765			1.20996			0.604980	+	0.796241i	$0.293181\pi$
$138$		−	45.8739i		−	0.332419i
$139$			220.514i			1.58643i	0.608941	+	0.793215i	$0.291594\pi$
$139$			220.514i			1.58643i	−0.608941	+	0.793215i	$0.708406\pi$
$140$	−37.4558	+	73.8329i	−0.267542	+	0.527378i
$141$	67.0294			0.475386
$142$	156.426			1.10159
$143$			32.9600i			0.230489i
$144$	−12.0000			−0.0833333
$145$			177.408i			1.22350i
$146$		−	80.2687i		−	0.549786i
$147$	−68.4853	+	50.1275i	−0.465886	+	0.341003i
$148$	−141.823			−0.958266
$149$	210.853			1.41512			0.707560	−	0.706653i	$-0.249796\pi$
$149$	210.853			1.41512			0.707560	+	0.706653i	$0.249796\pi$
$150$			24.4228i			0.162819i
$151$	−72.3675			−0.479255			−0.239628	−	0.970865i	$-0.577025\pi$
$151$	−72.3675			−0.479255			−0.239628	+	0.970865i	$0.577025\pi$
$152$		−	65.2236i		−	0.429103i
$153$			70.4409i			0.460398i
$154$	15.5147	+	7.87071i	0.100745	+	0.0511085i
$155$	50.9117			0.328463
$156$	64.9706			0.416478
$157$		−	233.674i		−	1.48837i	−0.667974	−	0.744184i	$-0.732838\pi$
$157$		−	233.674i		−	1.48837i	0.667974	−	0.744184i	$-0.267162\pi$
$158$	98.7452			0.624969
$159$		−	64.1369i		−	0.403377i
$160$		−	33.4523i		−	0.209077i
$161$	116.912	+	59.3100i	0.726160	+	0.368385i
$162$	−12.7279			−0.0785674
$163$	−73.0883			−0.448395			−0.224197	−	0.974544i	$-0.571976\pi$
$163$	−73.0883			−0.448395			−0.224197	+	0.974544i	$0.571976\pi$
$164$		−	82.7903i		−	0.504819i
$165$	18.0000			0.109091
$166$			9.10164i			0.0548292i
$167$			39.3958i			0.235903i	0.993019	+	0.117951i	$0.0376327\pi$
$167$			39.3958i			0.235903i	−0.993019	+	0.117951i	$0.962367\pi$
$168$	15.5147	−	30.5826i	0.0923495	−	0.182039i
$169$	−182.765			−1.08145
$170$	−196.368			−1.15510
$171$		−	69.1801i		−	0.404562i
$172$	20.8528			0.121237
$173$		−	23.8284i		−	0.137737i	−0.997626	−	0.0688683i	$-0.978061\pi$
$173$		−	23.8284i		−	0.137737i	0.997626	−	0.0688683i	$-0.0219388\pi$
$174$		−	73.4847i		−	0.422326i
$175$	−62.2426	−	31.5761i	−0.355672	−	0.180435i
$176$	−7.02944			−0.0399400
$177$	−168.853			−0.953971
$178$		−	59.5263i		−	0.334417i
$179$	−12.9045			−0.0720924			−0.0360462	−	0.999350i	$-0.511476\pi$
$179$	−12.9045			−0.0720924			−0.0360462	+	0.999350i	$0.511476\pi$
$180$		−	35.4815i		−	0.197120i
$181$		−	65.3678i		−	0.361148i	−0.983561	−	0.180574i	$-0.942204\pi$
$181$		−	65.3678i		−	0.361148i	0.983561	−	0.180574i	$-0.0577955\pi$
$182$	−84.0000	+	165.581i	−0.461538	+	0.909783i
$183$	28.9706			0.158309
$184$	−52.9706			−0.287883
$185$		−	419.343i		−	2.26672i
$186$	−21.0883			−0.113378
$187$			41.2633i			0.220659i
$188$		−	77.3989i		−	0.411696i
$189$	16.4558	−	32.4377i	0.0870680	−	0.171628i
$190$	192.853			1.01501
$191$	−100.066			−0.523906			−0.261953	−	0.965081i	$-0.584367\pi$
$191$	−100.066			−0.523906			−0.261953	+	0.965081i	$0.584367\pi$
$192$			13.8564i			0.0721688i
$193$	78.9117			0.408869			0.204434	−	0.978880i	$-0.434464\pi$
$193$	78.9117			0.408869			0.204434	+	0.978880i	$0.434464\pi$
$194$			73.1365i			0.376992i
$195$			192.105i			0.985152i
$196$	57.8823	+	79.0800i	0.295318	+	0.403469i
$197$	−183.941			−0.933711			−0.466856	−	0.884334i	$-0.654613\pi$
$197$	−183.941			−0.933711			−0.466856	+	0.884334i	$0.654613\pi$
$198$	−7.45584			−0.0376558
$199$		−	170.029i		−	0.854419i	−0.904153	−	0.427210i	$-0.859497\pi$
$199$		−	170.029i		−	0.854419i	0.904153	−	0.427210i	$-0.140503\pi$
$200$	28.2010			0.141005
$201$			105.604i			0.525394i
$202$			9.34783i			0.0462764i
$203$	187.279	+	95.0079i	0.922558	+	0.468019i
$204$	81.3381			0.398716
$205$	244.794			1.19412
$206$			248.719i			1.20737i
$207$	−56.1838			−0.271419
$208$		−	75.0215i		−	0.360680i
$209$		−	40.5247i		−	0.193898i
$210$	90.4264	+	45.8739i	0.430602	+	0.218447i
$211$	21.5736			0.102245			0.0511223	−	0.998692i	$-0.483720\pi$
$211$	21.5736			0.102245			0.0511223	+	0.998692i	$0.483720\pi$
$212$	−74.0589			−0.349334
$213$		−	191.582i		−	0.899448i
$214$	65.3970			0.305593
$215$			61.6575i			0.286779i
$216$			14.6969i			0.0680414i
$217$	27.2649	−	53.7446i	0.125645	−	0.247671i
$218$	50.8284			0.233158
$219$	−98.3087			−0.448898
$220$		−	20.7846i		−	0.0944755i
$221$	−440.382			−1.99268
$222$			173.697i			0.782421i
$223$			119.359i			0.535240i	0.963525	+	0.267620i	$0.0862372\pi$
$223$			119.359i			0.535240i	−0.963525	+	0.267620i	$0.913763\pi$
$224$	−35.3137	−	17.9149i	−0.157650	−	0.0799770i
$225$	29.9117			0.132941
$226$	103.279			0.456988
$227$			169.843i			0.748207i	0.927387	+	0.374103i	$0.122049\pi$
$227$			169.843i			0.748207i	−0.927387	+	0.374103i	$0.877951\pi$
$228$	−79.8823			−0.350361
$229$			110.011i			0.480396i	0.970724	+	0.240198i	$0.0772124\pi$
$229$			110.011i			0.480396i	−0.970724	+	0.240198i	$0.922788\pi$
$230$		−	156.623i		−	0.680970i
$231$	9.63961	−	19.0016i	0.0417299	−	0.0822579i
$232$	−84.8528			−0.365745
$233$	57.2649			0.245772			0.122886	−	0.992421i	$-0.460785\pi$
$233$	57.2649			0.245772			0.122886	+	0.992421i	$0.460785\pi$
$234$		−	79.5724i		−	0.340053i
$235$	228.853			0.973842
$236$			194.974i			0.826163i
$237$		−	120.938i		−	0.510285i
$238$	−105.161	+	207.294i	−0.441855	+	0.870983i
$239$	281.522			1.17792			0.588958	−	0.808164i	$-0.299538\pi$
$239$	281.522			1.17792			0.588958	+	0.808164i	$0.299538\pi$
$240$	−40.9706			−0.170711
$241$		−	168.306i		−	0.698366i	−0.937055	−	0.349183i	$-0.886459\pi$
$241$		−	168.306i		−	0.698366i	0.937055	−	0.349183i	$-0.113541\pi$
$242$	166.752			0.689059
$243$			15.5885i			0.0641500i
$244$		−	33.4523i		−	0.137100i
$245$	−233.823	+	171.146i	−0.954381	+	0.698555i
$246$	−101.397			−0.412183
$247$	432.500			1.75101
$248$			24.3507i			0.0981882i
$249$	11.1472			0.0447678
$250$		−	125.692i		−	0.502770i
$251$		−	106.096i		−	0.422695i	−0.977411	−	0.211348i	$-0.932215\pi$
$251$		−	106.096i		−	0.422695i	0.977411	−	0.211348i	$-0.0677852\pi$
$252$	−37.4558	−	19.0016i	−0.148634	−	0.0754031i
$253$	−32.9117			−0.130086
$254$	−127.196			−0.500771
$255$			240.500i			0.943138i
$256$	16.0000			0.0625000
$257$			290.462i			1.13020i	0.825021	+	0.565102i	$0.191163\pi$
$257$			290.462i			1.13020i	−0.825021	+	0.565102i	$0.808837\pi$
$258$		−	25.5394i		−	0.0989898i
$259$	−442.676	−	224.572i	−1.70917	−	0.867074i
$260$	221.823			0.853167
$261$	−90.0000			−0.344828
$262$			17.2185i			0.0657196i
$263$	−89.0223			−0.338488			−0.169244	−	0.985574i	$-0.554133\pi$
$263$	−89.0223			−0.338488			−0.169244	+	0.985574i	$0.554133\pi$
$264$			8.60927i			0.0326109i
$265$		−	218.977i		−	0.826328i
$266$	103.279	−	203.584i	0.388268	−	0.765352i
$267$	−72.9045			−0.273051
$268$	121.941			0.455004
$269$		−	191.498i		−	0.711888i	−0.934507	−	0.355944i	$-0.884159\pi$
$269$		−	191.498i		−	0.711888i	0.934507	−	0.355944i	$-0.115841\pi$
$270$	−43.4558			−0.160948
$271$			217.440i			0.802362i	0.915999	+	0.401181i	$0.131400\pi$
$271$			217.440i			0.802362i	−0.915999	+	0.401181i	$0.868600\pi$
$272$		−	93.9211i		−	0.345298i
$273$	202.794	+	102.879i	0.742835	+	0.376845i
$274$	−234.426			−0.855571
$275$	17.5219			0.0637159
$276$			64.8754i			0.235056i
$277$	290.676			1.04937			0.524686	−	0.851296i	$-0.324183\pi$
$277$	290.676			1.04937			0.524686	+	0.851296i	$0.324183\pi$
$278$		−	311.854i		−	1.12178i
$279$			25.8278i			0.0925728i
$280$	52.9706	−	104.415i	0.189181	−	0.372912i
$281$	18.8528			0.0670919			0.0335459	−	0.999437i	$-0.489320\pi$
$281$	18.8528			0.0670919			0.0335459	+	0.999437i	$0.489320\pi$
$282$	−94.7939			−0.336149
$283$			401.734i			1.41955i	0.704426	+	0.709777i	$0.251204\pi$
$283$			401.734i			1.41955i	−0.704426	+	0.709777i	$0.748796\pi$
$284$	−221.220			−0.778945
$285$		−	236.195i		−	0.828756i
$286$		−	46.6124i		−	0.162980i
$287$	131.095	−	258.415i	0.456779	−	0.900401i
$288$	16.9706			0.0589256
$289$	−262.324			−0.907695
$290$		−	250.892i		−	0.865146i
$291$	89.5736			0.307813
$292$			113.517i			0.388757i
$293$			280.893i			0.958679i	0.877629	+	0.479340i	$0.159124\pi$
$293$			280.893i			0.958679i	−0.877629	+	0.479340i	$0.840876\pi$
$294$	96.8528	−	70.8910i	0.329431	−	0.241126i
$295$	−576.500			−1.95424
$296$	200.569			0.677596
$297$			9.13151i			0.0307458i
$298$	−298.191			−1.00064
$299$		−	351.249i		−	1.17475i
$300$		−	34.5390i		−	0.115130i
$301$	65.0883	+	33.0197i	0.216240	+	0.109700i
$302$	102.343			0.338885
$303$	11.4487			0.0377845
$304$			92.2401i			0.303421i
$305$	98.9117			0.324301
$306$		−	99.6184i		−	0.325550i
$307$		−	152.318i		−	0.496151i	−0.968741	−	0.248076i	$-0.920202\pi$
$307$		−	152.318i		−	0.496151i	0.968741	−	0.248076i	$-0.0797982\pi$
$308$	−21.9411	−	11.1309i	−0.0712374	−	0.0361392i
$309$	304.617			0.985817
$310$	−72.0000			−0.232258
$311$			283.156i			0.910470i	0.890371	+	0.455235i	$0.150445\pi$
$311$			283.156i			0.910470i	−0.890371	+	0.455235i	$0.849555\pi$
$312$	−91.8823			−0.294494
$313$		−	48.5819i		−	0.155214i	−0.996984	−	0.0776069i	$-0.975272\pi$
$313$		−	48.5819i		−	0.155214i	0.996984	−	0.0776069i	$-0.0247279\pi$
$314$			330.465i			1.05244i
$315$	56.1838	−	110.749i	0.178361	−	0.351585i
$316$	−139.647			−0.441920
$317$	−578.029			−1.82343			−0.911717	−	0.410819i	$-0.865243\pi$
$317$	−578.029			−1.82343			−0.911717	+	0.410819i	$0.865243\pi$
$318$			90.7032i			0.285230i
$319$	−52.7208			−0.165269
$320$			47.3087i			0.147840i
$321$		−	80.0946i		−	0.249516i
$322$	−165.338	−	83.8770i	−0.513472	−	0.260488i
$323$	541.456			1.67633
$324$	18.0000			0.0555556
$325$			187.002i			0.575390i
$326$	103.362			0.317063
$327$		−	62.2519i		−	0.190373i
$328$			117.083i			0.356961i
$329$	122.558	−	241.587i	0.372518	−	0.734307i
$330$	−25.4558			−0.0771389
$331$	332.368			1.00413			0.502066	−	0.864829i	$-0.332574\pi$
$331$	332.368			1.00413			0.502066	+	0.864829i	$0.332574\pi$
$332$		−	12.8717i		−	0.0387701i
$333$	212.735			0.638844
$334$		−	55.7141i		−	0.166809i
$335$			360.555i			1.07628i
$336$	−21.9411	+	43.2503i	−0.0653010	+	0.128721i
$337$	88.1766			0.261652			0.130826	−	0.991405i	$-0.458237\pi$
$337$	88.1766			0.261652			0.130826	+	0.991405i	$0.458237\pi$
$338$	258.468			0.764698
$339$		−	126.491i		−	0.373129i
$340$	277.706			0.816781
$341$			15.1296i			0.0443683i
$342$			97.8354i			0.286068i
$343$	55.4487	+	338.488i	0.161658	+	0.986847i
$344$	−29.4903			−0.0857277
$345$	−191.823			−0.556010
$346$			33.6985i			0.0973945i
$347$	−320.080			−0.922422			−0.461211	−	0.887291i	$-0.652585\pi$
$347$	−320.080			−0.922422			−0.461211	+	0.887291i	$0.652585\pi$
$348$			103.923i			0.298629i
$349$			333.046i			0.954287i	0.878825	+	0.477143i	$0.158328\pi$
$349$			333.046i			0.954287i	−0.878825	+	0.477143i	$0.841672\pi$
$350$	88.0244	+	44.6553i	0.251498	+	0.127587i
$351$	−97.4558			−0.277652
$352$	9.94113			0.0282418
$353$			655.712i			1.85754i	0.370654	+	0.928771i	$0.379134\pi$
$353$			655.712i			1.85754i	−0.370654	+	0.928771i	$0.620866\pi$
$354$	238.794			0.674559
$355$		−	654.103i		−	1.84254i
$356$			84.1829i			0.236469i
$357$	253.882	+	128.796i	0.711155	+	0.360773i
$358$	18.2498			0.0509770
$359$	−97.7574			−0.272305			−0.136152	−	0.990688i	$-0.543474\pi$
$359$	−97.7574			−0.272305			−0.136152	+	0.990688i	$0.543474\pi$
$360$			50.1785i			0.139385i
$361$	−170.765			−0.473032
$362$			92.4440i			0.255370i
$363$		−	204.229i		−	0.562614i
$364$	118.794	−	234.166i	0.326357	−	0.643314i
$365$	−335.647			−0.919580
$366$	−40.9706			−0.111941
$367$			321.057i			0.874815i	0.899263	+	0.437408i	$0.144103\pi$
$367$			321.057i			0.874815i	−0.899263	+	0.437408i	$0.855897\pi$
$368$	74.9117			0.203564
$369$			124.185i			0.336546i
$370$			593.040i			1.60281i
$371$	−231.161	−	117.270i	−0.623077	−	0.316091i
$372$	29.8234			0.0801704
$373$	187.470			0.502601			0.251300	−	0.967909i	$-0.419142\pi$
$373$	187.470			0.502601			0.251300	+	0.967909i	$0.419142\pi$
$374$		−	58.3551i		−	0.156030i
$375$	−153.941			−0.410510
$376$			109.459i			0.291113i
$377$		−	562.662i		−	1.49247i
$378$	−23.2721	+	45.8739i	−0.0615663	+	0.121359i
$379$	−357.103			−0.942223			−0.471112	−	0.882074i	$-0.656147\pi$
$379$	−357.103			−0.942223			−0.471112	+	0.882074i	$0.656147\pi$
$380$	−272.735			−0.717724
$381$			155.783i			0.408878i
$382$	141.515			0.370457
$383$		−	622.230i		−	1.62462i	−0.583225	−	0.812311i	$-0.698209\pi$
$383$		−	622.230i		−	1.62462i	0.583225	−	0.812311i	$-0.301791\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	32.9117	−	64.8754i	0.0854849	−	0.168508i
$386$	−111.598			−0.289114
$387$	−31.2792			−0.0808249
$388$		−	103.431i		−	0.266574i
$389$	227.470			0.584756			0.292378	−	0.956303i	$-0.405553\pi$
$389$	227.470			0.584756			0.292378	+	0.956303i	$0.405553\pi$
$390$		−	271.677i		−	0.696608i
$391$		−	439.737i		−	1.12465i
$392$	−81.8579	−	111.836i	−0.208821	−	0.285296i
$393$	21.0883			0.0536598
$394$	260.132			0.660234
$395$		−	412.907i		−	1.04533i
$396$	10.5442			0.0266267
$397$		−	720.329i		−	1.81443i	−0.420666	−	0.907216i	$-0.638204\pi$
$397$		−	720.329i		−	1.81443i	0.420666	−	0.907216i	$-0.361796\pi$
$398$			240.458i			0.604166i
$399$	−249.338	−	126.491i	−0.624908	−	0.317019i
$400$	−39.8823			−0.0997056
$401$	697.176			1.73859			0.869296	−	0.494291i	$-0.164572\pi$
$401$	697.176			1.73859			0.869296	+	0.494291i	$0.164572\pi$
$402$		−	149.347i		−	0.371509i
$403$	−161.470			−0.400670
$404$		−	13.2198i		−	0.0327223i
$405$			53.2223i			0.131413i
$406$	−264.853	−	134.361i	−0.652347	−	0.330939i
$407$	124.617			0.306185
$408$	−115.029			−0.281935
$409$		−	102.386i		−	0.250333i	−0.992136	−	0.125166i	$-0.960053\pi$
$409$		−	102.386i		−	0.250333i	0.992136	−	0.125166i	$-0.0399465\pi$
$410$	−346.191			−0.844368
$411$			287.113i			0.698571i
$412$		−	351.742i		−	0.853742i
$413$	−308.735	+	608.578i	−0.747543	+	1.47355i
$414$	79.4558			0.191922
$415$	38.0589			0.0917081
$416$			106.096i			0.255040i
$417$	−381.941			−0.915926
$418$			57.3106i			0.137107i
$419$		−	391.426i		−	0.934191i	−0.884207	−	0.467095i	$-0.845300\pi$
$419$		−	391.426i		−	0.934191i	0.884207	−	0.467095i	$-0.154700\pi$
$420$	−127.882	−	64.8754i	−0.304482	−	0.154465i
$421$	354.441			0.841902			0.420951	−	0.907083i	$-0.361696\pi$
$421$	354.441			0.841902			0.420951	+	0.907083i	$0.361696\pi$
$422$	−30.5097			−0.0722978
$423$			116.098i			0.274464i
$424$	104.735			0.247017
$425$			234.112i			0.550851i
$426$			270.938i			0.636006i
$427$	52.9706	−	104.415i	0.124053	−	0.244533i
$428$	−92.4853			−0.216087
$429$	−57.0883			−0.133073
$430$		−	87.1969i		−	0.202783i
$431$	585.286			1.35797			0.678987	−	0.734151i	$-0.262419\pi$
$431$	585.286			1.35797			0.678987	+	0.734151i	$0.262419\pi$
$432$		−	20.7846i		−	0.0481125i
$433$			392.207i			0.905789i	0.891564	+	0.452895i	$0.149609\pi$
$433$			392.207i			0.905789i	−0.891564	+	0.452895i	$0.850391\pi$
$434$	−38.5584	+	76.0063i	−0.0888443	+	0.175130i
$435$	−307.279			−0.706389
$436$	−71.8823			−0.164868
$437$			431.866i			0.988252i
$438$	139.029			0.317419
$439$			392.513i			0.894106i	0.894507	+	0.447053i	$0.147527\pi$
$439$			392.513i			0.894106i	−0.894507	+	0.447053i	$0.852473\pi$
$440$			29.3939i			0.0668043i
$441$	−86.8234	−	118.620i	−0.196878	−	0.268980i
$442$	622.794			1.40904
$443$	−814.742			−1.83915			−0.919574	−	0.392918i	$-0.871466\pi$
$443$	−814.742			−1.83915			−0.919574	+	0.392918i	$0.871466\pi$
$444$		−	245.645i		−	0.553255i
$445$	−248.912			−0.559352
$446$		−	168.798i		−	0.378472i
$447$			365.208i			0.817020i
$448$	49.9411	+	25.3354i	0.111476	+	0.0565523i
$449$	180.323			0.401610			0.200805	−	0.979631i	$-0.435644\pi$
$449$	180.323			0.401610			0.200805	+	0.979631i	$0.435644\pi$
$450$	−42.3015			−0.0940034
$451$			72.7461i			0.161300i
$452$	−146.059			−0.323139
$453$		−	125.344i		−	0.276698i
$454$		−	240.194i		−	0.529062i
$455$	692.382	+	351.249i	1.52172	+	0.771977i
$456$	112.971			0.247742
$457$	280.177			0.613078			0.306539	−	0.951858i	$-0.400829\pi$
$457$	280.177			0.613078			0.306539	+	0.951858i	$0.400829\pi$
$458$		−	155.579i		−	0.339691i
$459$	−122.007			−0.265811
$460$			221.499i			0.481519i
$461$		−	406.297i		−	0.881338i	−0.897670	−	0.440669i	$-0.854741\pi$
$461$		−	406.297i		−	0.881338i	0.897670	−	0.440669i	$-0.145259\pi$
$462$	−13.6325	+	26.8723i	−0.0295075	+	0.0581651i
$463$	457.470			0.988056			0.494028	−	0.869446i	$-0.335524\pi$
$463$	457.470			0.988056			0.494028	+	0.869446i	$0.335524\pi$
$464$	120.000			0.258621
$465$			88.1816i			0.189638i
$466$	−80.9848			−0.173787
$467$			643.711i			1.37840i	0.724573	+	0.689198i	$0.242037\pi$
$467$			643.711i			1.37840i	−0.724573	+	0.689198i	$0.757963\pi$
$468$			112.532i			0.240454i
$469$	380.617	+	193.089i	0.811551	+	0.411705i
$470$	−323.647			−0.688610
$471$	404.735			0.859310
$472$		−	275.735i		−	0.584185i
$473$	−18.3229			−0.0387377
$474$			171.032i			0.360826i
$475$		−	229.921i		−	0.484045i
$476$	148.721	−	293.158i	0.312439	−	0.615878i
$477$	111.088			0.232890
$478$	−398.132			−0.832912
$479$		−	168.535i		−	0.351847i	−0.984404	−	0.175924i	$-0.943709\pi$
$479$		−	168.535i		−	0.351847i	0.984404	−	0.175924i	$-0.0562912\pi$
$480$	57.9411			0.120711
$481$			1329.98i			2.76502i
$482$			238.021i			0.493819i
$483$	−102.728	+	202.497i	−0.212687	+	0.419248i
$484$	−235.823			−0.487238
$485$	305.823			0.630564
$486$		−	22.0454i		−	0.0453609i
$487$	−2.77965			−0.00570771			−0.00285385	−	0.999996i	$-0.500908\pi$
$487$	−2.77965			−0.00570771			−0.00285385	+	0.999996i	$0.500908\pi$
$488$			47.3087i			0.0969441i
$489$		−	126.593i		−	0.258881i
$490$	330.676	−	242.037i	0.674849	−	0.493953i
$491$	−247.477			−0.504027			−0.252014	−	0.967724i	$-0.581093\pi$
$491$	−247.477			−0.504027			−0.252014	+	0.967724i	$0.581093\pi$
$492$	143.397			0.291457
$493$		−	704.409i		−	1.42882i
$494$	−611.647			−1.23815
$495$			31.1769i			0.0629837i
$496$		−	34.4371i		−	0.0694296i
$497$	−690.500	−	350.295i	−1.38934	−	0.704818i
$498$	−15.7645			−0.0316556
$499$	−483.426			−0.968789			−0.484394	−	0.874850i	$-0.660960\pi$
$499$	−483.426			−0.968789			−0.484394	+	0.874850i	$0.660960\pi$
$500$			177.756i			0.355512i
$501$	−68.2355			−0.136199
$502$			150.043i			0.298891i
$503$		−	58.7033i		−	0.116706i	−0.998296	−	0.0583532i	$-0.981415\pi$
$503$		−	58.7033i		−	0.116706i	0.998296	−	0.0583532i	$-0.0185849\pi$
$504$	52.9706	+	26.8723i	0.105100	+	0.0533180i
$505$	39.0883			0.0774026
$506$	46.5442			0.0919845
$507$		−	316.557i		−	0.624374i
$508$	179.882			0.354099
$509$		−	68.8793i		−	0.135323i	−0.997708	−	0.0676614i	$-0.978446\pi$
$509$		−	68.8793i		−	0.135323i	0.997708	−	0.0676614i	$-0.0215537\pi$
$510$		−	340.119i		−	0.666899i
$511$	−179.750	+	354.323i	−0.351762	+	0.693392i
$512$	−22.6274			−0.0441942
$513$	119.823			0.233574
$514$		−	410.776i		−	0.799175i
$515$	1040.03			2.01947
$516$			36.1181i			0.0699964i
$517$			68.0089i			0.131545i
$518$	626.039	+	317.593i	1.20857	+	0.613114i
$519$	41.2721			0.0795223
$520$	−313.706			−0.603280
$521$		−	292.720i		−	0.561843i	−0.959731	−	0.280922i	$-0.909360\pi$
$521$		−	292.720i		−	0.561843i	0.959731	−	0.280922i	$-0.0906401\pi$
$522$	127.279			0.243830
$523$		−	493.056i		−	0.942746i	−0.881934	−	0.471373i	$-0.843759\pi$
$523$		−	493.056i		−	0.942746i	0.881934	−	0.471373i	$-0.156241\pi$
$524$		−	24.3507i		−	0.0464708i
$525$	54.6913	−	107.807i	0.104174	−	0.205347i
$526$	125.897			0.239347
$527$	−202.148			−0.383583
$528$		−	12.1753i		−	0.0230594i
$529$	−178.265			−0.336985
$530$			309.680i			0.584302i
$531$		−	292.462i		−	0.550775i
$532$	−146.059	+	287.911i	−0.274547	+	0.541186i
$533$	−776.382			−1.45663
$534$	103.103			0.193076
$535$		−	273.460i		−	0.511140i
$536$	−172.451			−0.321737
$537$		−	22.3513i		−	0.0416226i
$538$			270.819i			0.503381i
$539$	−50.8600	−	69.4860i	−0.0943598	−	0.128916i
$540$	61.4558			0.113807
$541$	−1037.85			−1.91840			−0.959198	−	0.282736i	$-0.908758\pi$
$541$	−1037.85			−1.91840			−0.959198	+	0.282736i	$0.908758\pi$
$542$		−	307.507i		−	0.567356i
$543$	113.220			0.208509
$544$			132.825i			0.244163i
$545$		−	212.541i		−	0.389984i
$546$	−286.794	−	145.492i	−0.525264	−	0.266469i
$547$	−130.530			−0.238629			−0.119314	−	0.992857i	$-0.538070\pi$
$547$	−130.530			−0.238629			−0.119314	+	0.992857i	$0.538070\pi$
$548$	331.529			0.604980
$549$			50.1785i			0.0913998i
$550$	−24.7797			−0.0450539
$551$			691.801i			1.25554i
$552$		−	91.7477i		−	0.166210i
$553$	−435.882	−	221.126i	−0.788214	−	0.399866i
$554$	−411.078			−0.742018
$555$	726.323			1.30869
$556$			441.028i			0.793215i
$557$	665.147			1.19416			0.597080	−	0.802182i	$-0.296327\pi$
$557$	665.147			1.19416			0.597080	+	0.802182i	$0.296327\pi$
$558$		−	36.5260i		−	0.0654588i
$559$		−	195.551i		−	0.349823i
$560$	−74.9117	+	147.666i	−0.133771	+	0.263689i
$561$	−71.4701			−0.127398
$562$	−26.6619			−0.0474411
$563$		−	829.295i		−	1.47299i	−0.676441	−	0.736497i	$-0.736479\pi$
$563$		−	829.295i		−	1.47299i	0.676441	−	0.736497i	$-0.263521\pi$
$564$	134.059			0.237693
$565$		−	431.866i		−	0.764365i
$566$		−	568.137i		−	1.00378i
$567$	56.1838	+	28.5024i	0.0990895	+	0.0502687i
$568$	312.853			0.550797
$569$	706.971			1.24248			0.621240	−	0.783621i	$-0.286629\pi$
$569$	706.971			1.24248			0.621240	+	0.783621i	$0.286629\pi$
$570$			334.031i			0.586019i
$571$	−366.912			−0.642577			−0.321289	−	0.946981i	$-0.604116\pi$
$571$	−366.912			−0.642577			−0.321289	+	0.946981i	$0.604116\pi$
$572$			65.9199i			0.115245i
$573$		−	173.319i		−	0.302477i
$574$	−185.397	+	365.454i	−0.322991	+	0.636679i
$575$	−186.728			−0.324744
$576$	−24.0000			−0.0416667
$577$			390.357i			0.676528i	0.941051	+	0.338264i	$0.109840\pi$
$577$			390.357i			0.676528i	−0.941051	+	0.338264i	$0.890160\pi$
$578$	370.982			0.641837
$579$			136.679i			0.236061i
$580$			354.815i			0.611751i
$581$	20.3818	−	40.1766i	0.0350806	−	0.0691507i
$582$	−126.676			−0.217657
$583$	65.0740			0.111619
$584$		−	160.537i		−	0.274893i
$585$	−332.735			−0.568778
$586$		−	397.243i		−	0.677889i
$587$			702.499i			1.19676i	0.801212	+	0.598381i	$0.204189\pi$
$587$			702.499i			1.19676i	−0.801212	+	0.598381i	$0.795811\pi$
$588$	−136.971	+	100.255i	−0.232943	+	0.170502i
$589$	198.530			0.337063
$590$	815.294			1.38185
$591$		−	318.595i		−	0.539078i
$592$	−283.647			−0.479133
$593$		−	942.519i		−	1.58941i	−0.606997	−	0.794704i	$-0.707626\pi$
$593$		−	942.519i		−	1.58941i	0.606997	−	0.794704i	$-0.292374\pi$
$594$		−	12.9139i		−	0.0217406i
$595$	866.808	+	439.737i	1.45682	+	0.739054i
$596$	421.706			0.707560
$597$	294.500			0.493299
$598$			496.742i			0.830672i
$599$	−952.109			−1.58950			−0.794749	−	0.606939i	$-0.792397\pi$
$599$	−952.109			−1.58950			−0.794749	+	0.606939i	$0.792397\pi$
$600$			48.8456i			0.0814093i
$601$		−	729.804i		−	1.21432i	−0.794581	−	0.607158i	$-0.792310\pi$
$601$		−	729.804i		−	1.21432i	0.794581	−	0.607158i	$-0.207690\pi$
$602$	−92.0488	−	46.6969i	−0.152905	−	0.0775696i
$603$	−182.912			−0.303336
$604$	−144.735			−0.239628
$605$		−	697.282i		−	1.15253i
$606$	−16.1909			−0.0267177
$607$			1006.34i			1.65789i	0.559332	+	0.828944i	$0.311058\pi$
$607$			1006.34i			1.65789i	−0.559332	+	0.828944i	$0.688942\pi$
$608$		−	130.447i		−	0.214551i
$609$	−164.558	+	324.377i	−0.270211	+	0.532639i
$610$	−139.882			−0.229315
$611$	−725.823			−1.18793
$612$			140.882i			0.230199i
$613$	−199.588			−0.325592			−0.162796	−	0.986660i	$-0.552051\pi$
$613$	−199.588			−0.325592			−0.162796	+	0.986660i	$0.552051\pi$
$614$			215.411i			0.350832i
$615$			423.996i			0.689424i
$616$	31.0294	+	15.7414i	0.0503725	+	0.0255542i
$617$	−353.294			−0.572599			−0.286299	−	0.958140i	$-0.592425\pi$
$617$	−353.294			−0.572599			−0.286299	+	0.958140i	$0.592425\pi$
$618$	−430.794			−0.697078
$619$			56.2064i			0.0908020i	0.998969	+	0.0454010i	$0.0144566\pi$
$619$			56.2064i			0.0908020i	−0.998969	+	0.0454010i	$0.985543\pi$
$620$	101.823			0.164231
$621$		−	97.3131i		−	0.156704i
$622$		−	400.443i		−	0.643799i
$623$	−133.301	+	262.762i	−0.213966	+	0.421769i
$624$	129.941			0.208239
$625$	−774.852			−1.23976
$626$			68.7052i			0.109753i
$627$	70.1909			0.111947
$628$		−	467.348i		−	0.744184i
$629$			1665.03i			2.64710i
$630$	−79.4558	+	156.623i	−0.126120	+	0.248608i
$631$	807.322			1.27943			0.639716	−	0.768611i	$-0.279052\pi$
$631$	807.322			1.27943			0.639716	+	0.768611i	$0.279052\pi$
$632$	197.490			0.312485
$633$			37.3666i			0.0590309i
$634$	817.456			1.28936
$635$			531.875i			0.837599i
$636$		−	128.274i		−	0.201688i
$637$	741.588	−	542.802i	1.16419	−	0.852122i
$638$	74.5584			0.116863
$639$	331.831			0.519297
$640$		−	66.9046i		−	0.104539i
$641$	1016.35			1.58557			0.792786	−	0.609500i	$-0.208630\pi$
$641$	1016.35			1.58557			0.792786	+	0.609500i	$0.208630\pi$
$642$			113.271i			0.176434i
$643$			404.688i			0.629375i	0.949195	+	0.314687i	$0.101900\pi$
$643$			404.688i			0.629375i	−0.949195	+	0.314687i	$0.898100\pi$
$644$	233.823	+	118.620i	0.363080	+	0.184193i
$645$	−106.794			−0.165572
$646$	−765.734			−1.18535
$647$			940.604i			1.45379i	0.686747	+	0.726896i	$0.259038\pi$
$647$			940.604i			1.45379i	−0.686747	+	0.726896i	$0.740962\pi$
$648$	−25.4558			−0.0392837
$649$		−	171.320i		−	0.263975i
$650$		−	264.460i		−	0.406862i
$651$	93.0883	+	47.2243i	0.142993	+	0.0725411i
$652$	−146.177			−0.224197
$653$	731.970			1.12093			0.560467	−	0.828177i	$-0.310622\pi$
$653$	731.970			1.12093			0.560467	+	0.828177i	$0.310622\pi$
$654$			88.0374i			0.134614i
$655$	72.0000			0.109924
$656$		−	165.581i		−	0.252409i
$657$		−	170.276i		−	0.259171i
$658$	−173.324	+	341.655i	−0.263410	+	0.519233i
$659$	904.316			1.37225			0.686127	−	0.727481i	$-0.259309\pi$
$659$	904.316			1.37225			0.686127	+	0.727481i	$0.259309\pi$
$660$	36.0000			0.0545455
$661$			335.881i			0.508141i	0.967186	+	0.254070i	$0.0817695\pi$
$661$			335.881i			0.508141i	−0.967186	+	0.254070i	$0.918231\pi$
$662$	−470.039			−0.710028
$663$		−	762.764i		−	1.15047i
$664$			18.2033i			0.0274146i
$665$	−851.294	−	431.866i	−1.28014	−	0.649423i
$666$	−300.853			−0.451731
$667$	561.838			0.842335
$668$			78.7916i			0.117951i
$669$	−206.735			−0.309021
$670$		−	509.902i		−	0.761047i
$671$			29.3939i			0.0438061i
$672$	31.0294	−	61.1651i	0.0461748	−	0.0910195i
$673$	1191.44			1.77034			0.885171	−	0.465266i	$-0.154041\pi$
$673$	1191.44			1.77034			0.885171	+	0.465266i	$0.154041\pi$
$674$	−124.701			−0.185016
$675$			51.8086i			0.0767534i
$676$	−365.529			−0.540723
$677$		−	1211.07i		−	1.78888i	−0.447186	−	0.894441i	$-0.647574\pi$
$677$		−	1211.07i		−	1.78888i	0.447186	−	0.894441i	$-0.352426\pi$
$678$			178.885i			0.263842i
$679$	163.779	−	322.840i	0.241206	−	0.475464i
$680$	−392.735			−0.577552
$681$	−294.177			−0.431977
$682$		−	21.3965i		−	0.0313731i
$683$	−1233.89			−1.80657			−0.903287	−	0.429038i	$-0.858853\pi$
$683$	−1233.89			−1.80657			−0.903287	+	0.429038i	$0.858853\pi$
$684$		−	138.360i		−	0.202281i
$685$			980.264i			1.43104i
$686$	−78.4163	−	478.695i	−0.114309	−	0.697806i
$687$	−190.544			−0.277357
$688$	41.7056			0.0606186
$689$			694.501i			1.00798i
$690$	271.279			0.393158
$691$			86.7045i			0.125477i	0.998030	+	0.0627384i	$0.0199834\pi$
$691$			86.7045i			0.125477i	−0.998030	+	0.0627384i	$0.980017\pi$
$692$		−	47.6569i		−	0.0688683i
$693$	32.9117	+	16.6963i	0.0474916	+	0.0240928i
$694$	452.662			0.652251
$695$	−1304.03			−1.87630
$696$		−	146.969i		−	0.211163i
$697$	−971.970			−1.39450
$698$		−	470.998i		−	0.674783i
$699$			99.1858i			0.141897i
$700$	−124.485	−	63.1521i	−0.177836	−	0.0902173i
$701$	−149.147			−0.212763			−0.106382	−	0.994325i	$-0.533927\pi$
$701$	−149.147			−0.212763			−0.106382	+	0.994325i	$0.533927\pi$
$702$	137.823			0.196330
$703$		−	1635.22i		−	2.32607i
$704$	−14.0589			−0.0199700
$705$			396.385i			0.562248i
$706$		−	927.317i		−	1.31348i
$707$	20.9331	−	41.2633i	0.0296084	−	0.0583639i
$708$	−337.706			−0.476985
$709$	189.647			0.267485			0.133742	−	0.991016i	$-0.457301\pi$
$709$	189.647			0.267485			0.133742	+	0.991016i	$0.457301\pi$
$710$			925.042i			1.30288i
$711$	209.470			0.294613
$712$		−	119.053i		−	0.167209i
$713$		−	161.234i		−	0.226134i
$714$	−359.044	−	182.145i	−0.502862	−	0.255105i
$715$	−194.912			−0.272604
$716$	−25.8091			−0.0360462
$717$			487.610i			0.680070i
$718$	138.250			0.192548
$719$			12.0064i			0.0166987i	0.999965	+	0.00834937i	$0.00265772\pi$
$719$			12.0064i			0.0166987i	−0.999965	+	0.00834937i	$0.997342\pi$
$720$		−	70.9631i		−	0.0985599i
$721$	556.971	−	1097.90i	0.772497	−	1.52274i
$722$	241.497			0.334484
$723$	291.515			0.403202
$724$		−	130.736i		−	0.180574i
$725$	−299.117			−0.412575
$726$			288.823i			0.397828i
$727$			417.169i			0.573823i	0.957957	+	0.286911i	$0.0926286\pi$
$727$			417.169i			0.573823i	−0.957957	+	0.286911i	$0.907371\pi$
$728$	−168.000	+	331.161i	−0.230769	+	0.454892i
$729$	−27.0000			−0.0370370
$730$	474.676			0.650241
$731$		−	244.815i		−	0.334904i
$732$	57.9411			0.0791545
$733$		−	1286.99i		−	1.75578i	−0.478859	−	0.877892i	$-0.658949\pi$
$733$		−	1286.99i		−	1.75578i	0.478859	−	0.877892i	$-0.341051\pi$
$734$		−	454.043i		−	0.618588i
$735$	−296.434	−	404.994i	−0.403311	−	0.551012i
$736$	−105.941			−0.143942
$737$	−107.147			−0.145383
$738$		−	175.625i		−	0.237974i
$739$	1333.47			1.80443			0.902213	−	0.431292i	$-0.141942\pi$
$739$	1333.47			1.80443			0.902213	+	0.431292i	$0.141942\pi$
$740$		−	838.685i		−	1.13336i
$741$			749.111i			1.01095i
$742$	326.912	+	165.844i	0.440582	+	0.223510i
$743$	−776.476			−1.04506			−0.522528	−	0.852622i	$-0.675011\pi$
$743$	−776.476			−1.04506			−0.522528	+	0.852622i	$0.675011\pi$
$744$	−42.1766			−0.0566890
$745$			1246.90i			1.67369i
$746$	−265.123			−0.355392
$747$			19.3075i			0.0258467i
$748$			82.5266i			0.110330i
$749$	−288.676	−	146.447i	−0.385415	−	0.195524i
$750$	217.706			0.290274
$751$	48.8385			0.0650313			0.0325157	−	0.999471i	$-0.489648\pi$
$751$	48.8385			0.0650313			0.0325157	+	0.999471i	$0.489648\pi$
$752$		−	154.798i		−	0.205848i
$753$	183.765			0.244043
$754$			795.724i			1.05534i
$755$		−	427.952i		−	0.566824i
$756$	32.9117	−	64.8754i	0.0435340	−	0.0858141i
$757$	−1279.47			−1.69019			−0.845093	−	0.534620i	$-0.820455\pi$
$757$	−1279.47			−1.69019			−0.845093	+	0.534620i	$0.820455\pi$
$758$	505.019			0.666252
$759$		−	57.0047i		−	0.0751050i
$760$	385.706			0.507507
$761$			1316.12i			1.72947i	0.502231	+	0.864734i	$0.332513\pi$
$761$			1316.12i			1.72947i	−0.502231	+	0.864734i	$0.667487\pi$
$762$		−	220.310i		−	0.289121i
$763$	−224.368	−	113.823i	−0.294060	−	0.149178i
$764$	−200.132			−0.261953
$765$	−416.558			−0.544521
$766$			879.966i			1.14878i
$767$	1828.41			2.38385
$768$			27.7128i			0.0360844i
$769$			110.324i			0.143464i	0.997424	+	0.0717320i	$0.0228526\pi$
$769$			110.324i			0.143464i	−0.997424	+	0.0717320i	$0.977147\pi$
$770$	−46.5442	+	91.7477i	−0.0604470	+	0.119153i
$771$	−503.095			−0.652523
$772$	157.823			0.204434
$773$			717.634i			0.928375i	0.885737	+	0.464187i	$0.153654\pi$
$773$			717.634i			0.928375i	−0.885737	+	0.464187i	$0.846346\pi$
$774$	44.2355			0.0571518
$775$			85.8392i			0.110760i
$776$			146.273i			0.188496i
$777$	388.971	−	766.738i	0.500606	−	0.986792i
$778$	−321.691			−0.413485
$779$	954.573			1.22538
$780$			384.209i			0.492576i
$781$	194.382			0.248888
$782$			621.882i			0.795245i
$783$		−	155.885i		−	0.199086i
$784$	115.765	+	158.160i	0.147659	+	0.201735i
$785$	1381.85			1.76032
$786$	−29.8234			−0.0379432
$787$			347.191i			0.441158i	0.975369	+	0.220579i	$0.0707946\pi$
$787$			347.191i			0.441158i	−0.975369	+	0.220579i	$0.929205\pi$
$788$	−367.882			−0.466856
$789$		−	154.191i		−	0.195426i
$790$			583.939i			0.739163i
$791$	−455.897	−	231.279i	−0.576355	−	0.292388i
$792$	−14.9117			−0.0188279
$793$	−313.706			−0.395593
$794$			1018.70i			1.28300i
$795$	379.279			0.477081
$796$		−	340.059i		−	0.427210i
$797$		−	361.246i		−	0.453257i	−0.973981	−	0.226629i	$-0.927230\pi$
$797$		−	361.246i		−	0.453257i	0.973981	−	0.226629i	$-0.0727704\pi$
$798$	352.617	+	178.885i	0.441876	+	0.224166i
$799$	−908.674			−1.13726
$800$	56.4020			0.0705025
$801$		−	126.274i		−	0.157646i
$802$	−985.955			−1.22937
$803$		−	99.7451i		−	0.124216i
$804$			211.208i			0.262697i
$805$	−350.735	+	691.368i	−0.435696	+	0.858842i
$806$	228.353			0.283317
$807$	331.684			0.411009
$808$			18.6957i			0.0231382i
$809$	−113.147			−0.139861			−0.0699303	−	0.997552i	$-0.522278\pi$
$809$	−113.147			−0.139861			−0.0699303	+	0.997552i	$0.522278\pi$
$810$		−	75.2677i		−	0.0929231i
$811$		−	134.182i		−	0.165453i	−0.996572	−	0.0827264i	$-0.973637\pi$
$811$		−	134.182i		−	0.165453i	0.996572	−	0.0827264i	$-0.0263628\pi$
$812$	374.558	+	190.016i	0.461279	+	0.234010i
$813$	−376.617			−0.463244
$814$	−176.235			−0.216506
$815$		−	432.214i		−	0.530324i
$816$	162.676			0.199358
$817$			240.433i			0.294288i
$818$			144.796i			0.177012i
$819$	−178.191	+	351.249i	−0.217571	+	0.428876i
$820$	489.588			0.597058
$821$	491.677			0.598876			0.299438	−	0.954116i	$-0.403201\pi$
$821$	491.677			0.598876			0.299438	+	0.954116i	$0.403201\pi$
$822$		−	406.038i		−	0.493964i
$823$	−941.852			−1.14441			−0.572207	−	0.820110i	$-0.693912\pi$
$823$	−941.852			−1.14441			−0.572207	+	0.820110i	$0.693912\pi$
$824$			497.438i			0.603687i
$825$			30.3488i			0.0367864i
$826$	436.617	−	860.659i	0.528592	−	1.04196i
$827$	966.978			1.16926			0.584630	−	0.811300i	$-0.301240\pi$
$827$	966.978			1.16926			0.584630	+	0.811300i	$0.301240\pi$
$828$	−112.368			−0.135710
$829$			1185.53i			1.43007i	0.699088	+	0.715035i	$0.253589\pi$
$829$			1185.53i			1.43007i	−0.699088	+	0.715035i	$0.746411\pi$
$830$	−53.8234			−0.0648474
$831$			503.466i			0.605856i
$832$		−	150.043i		−	0.180340i
$833$	928.410	−	679.546i	1.11454	−	0.815781i
$834$	540.146			0.647657
$835$	−232.971			−0.279007
$836$		−	81.0495i		−	0.0969491i
$837$	−44.7351			−0.0534469
$838$			553.560i			0.660573i
$839$		−	1376.91i		−	1.64113i	−0.571550	−	0.820567i	$-0.693658\pi$
$839$		−	1376.91i		−	1.64113i	0.571550	−	0.820567i	$-0.306342\pi$
$840$	180.853	+	91.7477i	0.215301	+	0.109223i
$841$	59.0000			0.0701546
$842$	−501.255			−0.595315
$843$			32.6540i			0.0387355i
$844$	43.1472			0.0511223
$845$		−	1080.79i		−	1.27905i
$846$		−	164.188i		−	0.194076i
$847$	−736.080	−	373.418i	−0.869044	−	0.440871i
$848$	−148.118			−0.174667
$849$	−695.823			−0.819580
$850$		−	331.084i		−	0.389510i
$851$	−1328.03			−1.56055
$852$		−	383.165i		−	0.449724i
$853$			175.006i			0.205165i	0.994725	+	0.102582i	$0.0327105\pi$
$853$			175.006i			0.205165i	−0.994725	+	0.102582i	$0.967289\pi$
$854$	−74.9117	+	147.666i	−0.0877186	+	0.172911i
$855$	409.103			0.478483
$856$	130.794			0.152797
$857$			61.7471i			0.0720503i	0.999351	+	0.0360252i	$0.0114696\pi$
$857$			61.7471i			0.0720503i	−0.999351	+	0.0360252i	$0.988530\pi$
$858$	80.7351			0.0940968
$859$			191.306i			0.222708i	0.993781	+	0.111354i	$0.0355188\pi$
$859$			191.306i			0.222708i	−0.993781	+	0.111354i	$0.964481\pi$
$860$			123.315i			0.143390i
$861$	447.588	+	227.064i	0.519847	+	0.263721i
$862$	−827.720			−0.960232
$863$	−494.507			−0.573009			−0.286504	−	0.958079i	$-0.592493\pi$
$863$	−494.507			−0.573009			−0.286504	+	0.958079i	$0.592493\pi$
$864$			29.3939i			0.0340207i
$865$	140.912			0.162904
$866$		−	554.664i		−	0.640490i
$867$		−	454.358i		−	0.524058i
$868$	54.5299	−	107.489i	0.0628224	−	0.123835i
$869$	122.705			0.141202
$870$	434.558			0.499492
$871$		−	1143.53i		−	1.31289i
$872$	101.657			0.116579
$873$			155.146i			0.177716i
$874$		−	610.751i		−	0.698800i
$875$	−281.470	+	554.833i	−0.321680	+	0.634095i
$876$	−196.617			−0.224449
$877$	−454.353			−0.518077			−0.259038	−	0.965867i	$-0.583406\pi$
$877$	−454.353			−0.518077			−0.259038	+	0.965867i	$0.583406\pi$
$878$		−	555.097i		−	0.632229i
$879$	−486.521			−0.553494
$880$		−	41.5692i		−	0.0472377i
$881$		−	143.493i		−	0.162875i	−0.996678	−	0.0814375i	$-0.974049\pi$
$881$		−	143.493i		−	0.162875i	0.996678	−	0.0814375i	$-0.0259511\pi$
$882$	122.787	+	167.754i	0.139214	+	0.190197i
$883$	−927.986			−1.05095			−0.525473	−	0.850810i	$-0.676112\pi$
$883$	−927.986			−1.05095			−0.525473	+	0.850810i	$0.676112\pi$
$884$	−880.764			−0.996339
$885$		−	998.527i		−	1.12828i
$886$	1152.22			1.30047
$887$		−	958.265i		−	1.08034i	−0.841555	−	0.540172i	$-0.818359\pi$
$887$		−	958.265i		−	1.08034i	0.841555	−	0.540172i	$-0.181641\pi$
$888$			347.395i			0.391210i
$889$	561.470	+	284.837i	0.631575	+	0.320402i
$890$	352.014			0.395522
$891$	−15.8162			−0.0177511
$892$			238.717i			0.267620i
$893$	892.410			0.999340
$894$		−	516.482i		−	0.577720i
$895$		−	76.3122i		−	0.0852650i
$896$	−70.6274	−	35.8297i	−0.0788252	−	0.0399885i
$897$	608.382			0.678241
$898$	−255.015			−0.283981
$899$		−	258.278i		−	0.287295i
$900$	59.8234			0.0664704
$901$			869.462i			0.964996i
$902$		−	102.879i		−	0.114056i
$903$	−57.1918	+	112.736i	−0.0633353	+	0.124846i
$904$	206.558			0.228494
$905$	386.558			0.427136
$906$			177.264i			0.195655i
$907$	−552.721			−0.609394			−0.304697	−	0.952449i	$-0.598555\pi$
$907$	−552.721			−0.609394			−0.304697	+	0.952449i	$0.598555\pi$
$908$			339.686i			0.374103i
$909$			19.8297i			0.0218149i
$910$	−979.176	−	496.742i	−1.07602	−	0.545870i
$911$	142.742			0.156687			0.0783437	−	0.996926i	$-0.475037\pi$
$911$	142.742			0.156687			0.0783437	+	0.996926i	$0.475037\pi$
$912$	−159.765			−0.175180
$913$			11.3101i			0.0123878i
$914$	−396.230			−0.433512
$915$			171.320i			0.187235i
$916$			220.021i			0.240198i
$917$	38.5584	−	76.0063i	0.0420485	−	0.0828858i
$918$	172.544			0.187957
$919$	1086.45			1.18221			0.591107	−	0.806593i	$-0.298691\pi$
$919$	1086.45			1.18221			0.591107	+	0.806593i	$0.298691\pi$
$920$		−	313.246i		−	0.340485i
$921$	263.823			0.286453
$922$			574.591i			0.623200i
$923$			2074.54i			2.24760i
$924$	19.2792	−	38.0031i	0.0208650	−	0.0411289i
$925$	707.029			0.764356
$926$	−646.960			−0.698661
$927$			527.613i			0.569161i
$928$	−169.706			−0.182872
$929$			1550.75i			1.66927i	0.550806	+	0.834633i	$0.314320\pi$
$929$			1550.75i			1.66927i	−0.550806	+	0.834633i	$0.685680\pi$
$930$		−	124.708i		−	0.134094i
$931$	−911.793	+	667.383i	−0.979370	+	0.716845i
$932$	114.530			0.122886
$933$	−490.441			−0.525660
$934$		−	910.345i		−	0.974673i
$935$	−244.014			−0.260978
$936$		−	159.145i		−	0.170026i
$937$		−	759.317i		−	0.810370i	−0.914235	−	0.405185i	$-0.867207\pi$
$937$		−	759.317i		−	0.810370i	0.914235	−	0.405185i	$-0.132793\pi$
$938$	−538.274	−	273.070i	−0.573853	−	0.291119i
$939$	84.1463			0.0896127
$940$	457.706			0.486921
$941$		−	36.3519i		−	0.0386312i	−0.999813	−	0.0193156i	$-0.993851\pi$
$941$		−	36.3519i		−	0.0386312i	0.999813	−	0.0193156i	$-0.00614873\pi$
$942$	−572.382			−0.607624
$943$		−	775.245i		−	0.822105i
$944$			389.949i			0.413081i
$945$	191.823	+	97.3131i	0.202988	+	0.102977i
$946$	25.9126			0.0273917
$947$	92.5370			0.0977160			0.0488580	−	0.998806i	$-0.484442\pi$
$947$	92.5370			0.0977160			0.0488580	+	0.998806i	$0.484442\pi$
$948$		−	241.875i		−	0.255143i
$949$	1064.53			1.12174
$950$			325.158i			0.342271i
$951$		−	1001.17i		−	1.05276i
$952$	−210.323	+	414.588i	−0.220927	+	0.435492i
$953$	−1361.29			−1.42843			−0.714215	−	0.699927i	$-0.753216\pi$
$953$	−1361.29			−1.42843			−0.714215	+	0.699927i	$0.753216\pi$
$954$	−157.103			−0.164678
$955$		−	591.750i		−	0.619633i
$956$	563.044			0.588958
$957$		−	91.3151i		−	0.0954180i
$958$			238.344i			0.248794i
$959$	1034.81	+	524.964i	1.07905	+	0.547408i
$960$	−81.9411			−0.0853553
$961$	886.881			0.922873
$962$		−	1880.87i		−	1.95517i
$963$	138.728			0.144058
$964$		−	336.612i		−	0.349183i
$965$			466.651i			0.483577i
$966$	145.279	−	286.374i	0.150393	−	0.296453i
$967$	481.677			0.498115			0.249057	−	0.968489i	$-0.419879\pi$
$967$	481.677			0.498115			0.249057	+	0.968489i	$0.419879\pi$
$968$	333.505			0.344530
$969$			937.829i			0.967832i
$970$	−432.500			−0.445876
$971$			1427.34i			1.46997i	0.678082	+	0.734987i	$0.262812\pi$
$971$			1427.34i			1.46997i	−0.678082	+	0.734987i	$0.737188\pi$
$972$			31.1769i			0.0320750i
$973$	−698.352	+	1376.59i	−0.717730	+	1.41479i
$974$	3.93102			0.00403596
$975$	−323.897			−0.332202
$976$		−	66.9046i		−	0.0685498i
$977$	−1356.26			−1.38819			−0.694095	−	0.719883i	$-0.744195\pi$
$977$	−1356.26			−1.38819			−0.694095	+	0.719883i	$0.744195\pi$
$978$			179.029i			0.183056i
$979$		−	73.9698i		−	0.0755565i
$980$	−467.647	+	342.292i	−0.477191	+	0.349278i
$981$	107.823			0.109912
$982$	349.986			0.356401
$983$		−	1315.51i		−	1.33826i	−0.743146	−	0.669129i	$-0.766667\pi$
$983$		−	1315.51i		−	1.33826i	0.743146	−	0.669129i	$-0.233333\pi$
$984$	−202.794			−0.206091
$985$		−	1087.75i		−	1.10432i
$986$			996.184i			1.01033i
$987$	418.441	+	212.277i	0.423952	+	0.215073i
$988$	864.999			0.875505
$989$	195.265			0.197437
$990$		−	44.0908i		−	0.0445362i
$991$	1043.28			1.05275			0.526377	−	0.850251i	$-0.323550\pi$
$991$	1043.28			1.05275			0.526377	+	0.850251i	$0.323550\pi$
$992$			48.7014i			0.0490941i
$993$			575.677i			0.579736i
$994$	976.514	+	495.391i	0.982408	+	0.498382i
$995$	1005.48			1.01054
$996$	22.2944			0.0223839
$997$		−	820.328i		−	0.822796i	−0.911456	−	0.411398i	$-0.865041\pi$
$997$		−	820.328i		−	0.822796i	0.911456	−	0.411398i	$-0.134959\pi$
$998$	683.667			0.685037
$999$			368.468i			0.368837i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.3.c.a.13.2	yes	4
3.2	odd	2		126.3.c.b.55.3		4
4.3	odd	2		336.3.f.c.97.2		4
5.2	odd	4		1050.3.h.a.349.3		8
5.3	odd	4		1050.3.h.a.349.6		8
5.4	even	2		1050.3.f.a.601.3		4
7.2	even	3		294.3.g.b.31.2		4
7.3	odd	6		294.3.g.b.19.2		4
7.4	even	3		294.3.g.c.19.2		4
7.5	odd	6		294.3.g.c.31.2		4
7.6	odd	2	inner	42.3.c.a.13.1	✓	4
8.3	odd	2		1344.3.f.e.769.3		4
8.5	even	2		1344.3.f.f.769.1		4
12.11	even	2		1008.3.f.g.433.1		4
21.2	odd	6		882.3.n.a.325.1		4
21.5	even	6		882.3.n.d.325.1		4
21.11	odd	6		882.3.n.d.19.1		4
21.17	even	6		882.3.n.a.19.1		4
21.20	even	2		126.3.c.b.55.4		4
28.27	even	2		336.3.f.c.97.3		4
35.13	even	4		1050.3.h.a.349.7		8
35.27	even	4		1050.3.h.a.349.2		8
35.34	odd	2		1050.3.f.a.601.4		4
56.13	odd	2		1344.3.f.f.769.4		4
56.27	even	2		1344.3.f.e.769.2		4
84.83	odd	2		1008.3.f.g.433.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.c.a.13.1	✓	4	7.6	odd	2	inner
42.3.c.a.13.2	yes	4	1.1	even	1	trivial
126.3.c.b.55.3		4	3.2	odd	2
126.3.c.b.55.4		4	21.20	even	2
294.3.g.b.19.2		4	7.3	odd	6
294.3.g.b.31.2		4	7.2	even	3
294.3.g.c.19.2		4	7.4	even	3
294.3.g.c.31.2		4	7.5	odd	6
336.3.f.c.97.2		4	4.3	odd	2
336.3.f.c.97.3		4	28.27	even	2
882.3.n.a.19.1		4	21.17	even	6
882.3.n.a.325.1		4	21.2	odd	6
882.3.n.d.19.1		4	21.11	odd	6
882.3.n.d.325.1		4	21.5	even	6
1008.3.f.g.433.1		4	12.11	even	2
1008.3.f.g.433.4		4	84.83	odd	2
1050.3.f.a.601.3		4	5.4	even	2
1050.3.f.a.601.4		4	35.34	odd	2
1050.3.h.a.349.2		8	35.27	even	4
1050.3.h.a.349.3		8	5.2	odd	4
1050.3.h.a.349.6		8	5.3	odd	4
1050.3.h.a.349.7		8	35.13	even	4
1344.3.f.e.769.2		4	56.27	even	2
1344.3.f.e.769.3		4	8.3	odd	2
1344.3.f.f.769.1		4	8.5	even	2
1344.3.f.f.769.4		4	56.13	odd	2

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +5.91359i q^{5} -2.44949i q^{6} +(6.24264 + 3.16693i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +5.91359i q^{5} -2.44949i q^{6} +(6.24264 + 3.16693i) q^{7} -2.82843 q^{8} -3.00000 q^{9} -8.36308i q^{10} -1.75736 q^{11} +3.46410i q^{12} -18.7554i q^{13} +(-8.82843 - 4.47871i) q^{14} -10.2426 q^{15} +4.00000 q^{16} -23.4803i q^{17} +4.24264 q^{18} +23.0600i q^{19} +11.8272i q^{20} +(-5.48528 + 10.8126i) q^{21} +2.48528 q^{22} +18.7279 q^{23} -4.89898i q^{24} -9.97056 q^{25} +26.5241i q^{26} -5.19615i q^{27} +(12.4853 + 6.33386i) q^{28} +30.0000 q^{29} +14.4853 q^{30} -8.60927i q^{31} -5.65685 q^{32} -3.04384i q^{33} +33.2061i q^{34} +(-18.7279 + 36.9164i) q^{35} -6.00000 q^{36} -70.9117 q^{37} -32.6118i q^{38} +32.4853 q^{39} -16.7262i q^{40} -41.3951i q^{41} +(7.75736 - 15.2913i) q^{42} +10.4264 q^{43} -3.51472 q^{44} -17.7408i q^{45} -26.4853 q^{46} -38.6995i q^{47} +6.92820i q^{48} +(28.9411 + 39.5400i) q^{49} +14.1005 q^{50} +40.6690 q^{51} -37.5108i q^{52} -37.0294 q^{53} +7.34847i q^{54} -10.3923i q^{55} +(-17.6569 - 8.95743i) q^{56} -39.9411 q^{57} -42.4264 q^{58} +97.4872i q^{59} -20.4853 q^{60} -16.7262i q^{61} +12.1753i q^{62} +(-18.7279 - 9.50079i) q^{63} +8.00000 q^{64} +110.912 q^{65} +4.30463i q^{66} +60.9706 q^{67} -46.9606i q^{68} +32.4377i q^{69} +(26.4853 - 52.2077i) q^{70} -110.610 q^{71} +8.48528 q^{72} +56.7585i q^{73} +100.284 q^{74} -17.2695i q^{75} +46.1200i q^{76} +(-10.9706 - 5.56543i) q^{77} -45.9411 q^{78} -69.8234 q^{79} +23.6544i q^{80} +9.00000 q^{81} +58.5416i q^{82} -6.43583i q^{83} +(-10.9706 + 21.6251i) q^{84} +138.853 q^{85} -14.7452 q^{86} +51.9615i q^{87} +4.97056 q^{88} +42.0915i q^{89} +25.0892i q^{90} +(59.3970 - 117.083i) q^{91} +37.4558 q^{92} +14.9117 q^{93} +54.7293i q^{94} -136.368 q^{95} -9.79796i q^{96} -51.7153i q^{97} +(-40.9289 - 55.9180i) q^{98} +5.27208 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4} + 8 q^{7} - 12 q^{9}+O(q^{10}) \) 4 * q + 8 * q^4 + 8 * q^7 - 12 * q^9	\( 4 q + 8 q^{4} + 8 q^{7} - 12 q^{9} - 24 q^{11} - 24 q^{14} - 24 q^{15} + 16 q^{16} + 12 q^{21} - 24 q^{22} + 24 q^{23} + 28 q^{25} + 16 q^{28} + 120 q^{29} + 24 q^{30} - 24 q^{35} - 24 q^{36} - 80 q^{37} + 96 q^{39} + 48 q^{42} - 128 q^{43} - 48 q^{44} - 72 q^{46} - 20 q^{49} + 96 q^{50} - 24 q^{51} - 216 q^{53} - 48 q^{56} - 24 q^{57} - 48 q^{60} - 24 q^{63} + 32 q^{64} + 240 q^{65} + 176 q^{67} + 72 q^{70} - 120 q^{71} + 288 q^{74} + 24 q^{77} - 48 q^{78} + 128 q^{79} + 36 q^{81} + 24 q^{84} + 216 q^{85} - 240 q^{86} - 48 q^{88} + 48 q^{92} - 144 q^{93} - 240 q^{95} - 192 q^{98} + 72 q^{99}+O(q^{100}) \) 4 * q + 8 * q^4 + 8 * q^7 - 12 * q^9 - 24 * q^11 - 24 * q^14 - 24 * q^15 + 16 * q^16 + 12 * q^21 - 24 * q^22 + 24 * q^23 + 28 * q^25 + 16 * q^28 + 120 * q^29 + 24 * q^30 - 24 * q^35 - 24 * q^36 - 80 * q^37 + 96 * q^39 + 48 * q^42 - 128 * q^43 - 48 * q^44 - 72 * q^46 - 20 * q^49 + 96 * q^50 - 24 * q^51 - 216 * q^53 - 48 * q^56 - 24 * q^57 - 48 * q^60 - 24 * q^63 + 32 * q^64 + 240 * q^65 + 176 * q^67 + 72 * q^70 - 120 * q^71 + 288 * q^74 + 24 * q^77 - 48 * q^78 + 128 * q^79 + 36 * q^81 + 24 * q^84 + 216 * q^85 - 240 * q^86 - 48 * q^88 + 48 * q^92 - 144 * q^93 - 240 * q^95 - 192 * q^98 + 72 * q^99

Introduction

L-functions

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