LMFDB - Embedded newform 42.3.c.a.13.3

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			13.3
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	42.13
Dual form			42.3.c.a.13.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -1.01461i q^{5} -2.44949i q^{6} +(-2.24264 + 6.63103i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -1.01461i q^{5} -2.44949i q^{6} +(-2.24264 + 6.63103i) q^{7} +2.82843 q^{8} -3.00000 q^{9} -1.43488i q^{10} -10.2426 q^{11} -3.46410i q^{12} +8.95743i q^{13} +(-3.17157 + 9.37769i) q^{14} -1.75736 q^{15} +4.00000 q^{16} -30.4085i q^{17} -4.24264 q^{18} +16.1318i q^{19} -2.02922i q^{20} +(11.4853 + 3.88437i) q^{21} -14.4853 q^{22} -6.72792 q^{23} -4.89898i q^{24} +23.9706 q^{25} +12.6677i q^{26} +5.19615i q^{27} +(-4.48528 + 13.2621i) q^{28} +30.0000 q^{29} -2.48528 q^{30} -50.1785i q^{31} +5.65685 q^{32} +17.7408i q^{33} -43.0041i q^{34} +(6.72792 + 2.27541i) q^{35} -6.00000 q^{36} +30.9117 q^{37} +22.8138i q^{38} +15.5147 q^{39} -2.86976i q^{40} +7.10228i q^{41} +(16.2426 + 5.49333i) q^{42} -74.4264 q^{43} -20.4853 q^{44} +3.04384i q^{45} -9.51472 q^{46} +58.2954i q^{47} -6.92820i q^{48} +(-38.9411 - 29.7420i) q^{49} +33.8995 q^{50} -52.6690 q^{51} +17.9149i q^{52} -70.9706 q^{53} +7.34847i q^{54} +10.3923i q^{55} +(-6.34315 + 18.7554i) q^{56} +27.9411 q^{57} +42.4264 q^{58} +0.492372i q^{59} -3.51472 q^{60} -2.86976i q^{61} -70.9631i q^{62} +(6.72792 - 19.8931i) q^{63} +8.00000 q^{64} +9.08831 q^{65} +25.0892i q^{66} +27.0294 q^{67} -60.8170i q^{68} +11.6531i q^{69} +(9.51472 + 3.21792i) q^{70} +50.6102 q^{71} -8.48528 q^{72} +70.6149i q^{73} +43.7157 q^{74} -41.5182i q^{75} +32.2636i q^{76} +(22.9706 - 67.9193i) q^{77} +21.9411 q^{78} +133.823 q^{79} -4.05845i q^{80} +9.00000 q^{81} +10.0441i q^{82} +104.415i q^{83} +(22.9706 + 7.76874i) q^{84} -30.8528 q^{85} -105.255 q^{86} -51.9615i q^{87} -28.9706 q^{88} -144.970i q^{89} +4.30463i q^{90} +(-59.3970 - 20.0883i) q^{91} -13.4558 q^{92} -86.9117 q^{93} +82.4421i q^{94} +16.3675 q^{95} -9.79796i q^{96} +100.705i q^{97} +(-55.0711 - 42.0616i) q^{98} +30.7279 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$		−	1.01461i		−	0.202922i	−0.994839	−	0.101461i	$-0.967648\pi$
$5$		−	1.01461i		−	0.202922i	0.994839	−	0.101461i	$-0.0323518\pi$
$6$		−	2.44949i		−	0.408248i
$7$	−2.24264	+	6.63103i	−0.320377	+	0.947290i
$7$	−2.24264	+	6.63103i	−0.320377	+	0.947290i
$8$	2.82843			0.353553
$9$	−3.00000			−0.333333
$10$		−	1.43488i		−	0.143488i
$11$	−10.2426			−0.931149			−0.465575	−	0.885009i	$-0.654152\pi$
$11$	−10.2426			−0.931149			−0.465575	+	0.885009i	$0.654152\pi$
$12$		−	3.46410i		−	0.288675i
$13$			8.95743i			0.689033i	0.938780	+	0.344516i	$0.111957\pi$
$13$			8.95743i			0.689033i	−0.938780	+	0.344516i	$0.888043\pi$
$14$	−3.17157	+	9.37769i	−0.226541	+	0.669835i
$15$	−1.75736			−0.117157
$16$	4.00000			0.250000
$17$		−	30.4085i		−	1.78873i	−0.447333	−	0.894367i	$-0.647626\pi$
$17$		−	30.4085i		−	1.78873i	0.447333	−	0.894367i	$-0.352374\pi$
$18$	−4.24264			−0.235702
$19$			16.1318i			0.849043i	0.905418	+	0.424521i	$0.139558\pi$
$19$			16.1318i			0.849043i	−0.905418	+	0.424521i	$0.860442\pi$
$20$		−	2.02922i		−	0.101461i
$21$	11.4853	+	3.88437i	0.546918	+	0.184970i
$22$	−14.4853			−0.658422
$23$	−6.72792			−0.292518			−0.146259	−	0.989246i	$-0.546723\pi$
$23$	−6.72792			−0.292518			−0.146259	+	0.989246i	$0.546723\pi$
$24$		−	4.89898i		−	0.204124i
$25$	23.9706			0.958823
$26$			12.6677i			0.487220i
$27$			5.19615i			0.192450i
$28$	−4.48528	+	13.2621i	−0.160189	+	0.473645i
$29$	30.0000			1.03448			0.517241	−	0.855840i	$-0.326959\pi$
$29$	30.0000			1.03448			0.517241	+	0.855840i	$0.326959\pi$
$30$	−2.48528			−0.0828427
$31$		−	50.1785i		−	1.61866i	−0.587354	−	0.809330i	$-0.699830\pi$
$31$		−	50.1785i		−	1.61866i	0.587354	−	0.809330i	$-0.300170\pi$
$32$	5.65685			0.176777
$33$			17.7408i			0.537599i
$34$		−	43.0041i		−	1.26483i
$35$	6.72792	+	2.27541i	0.192226	+	0.0650117i
$36$	−6.00000			−0.166667
$37$	30.9117			0.835451			0.417726	−	0.908573i	$-0.362827\pi$
$37$	30.9117			0.835451			0.417726	+	0.908573i	$0.362827\pi$
$38$			22.8138i			0.600364i
$39$	15.5147			0.397813
$40$		−	2.86976i		−	0.0717439i
$41$			7.10228i			0.173226i	0.996242	+	0.0866132i	$0.0276044\pi$
$41$			7.10228i			0.173226i	−0.996242	+	0.0866132i	$0.972396\pi$
$42$	16.2426	+	5.49333i	0.386730	+	0.130793i
$43$	−74.4264			−1.73085			−0.865423	−	0.501041i	$-0.832950\pi$
$43$	−74.4264			−1.73085			−0.865423	+	0.501041i	$0.832950\pi$
$44$	−20.4853			−0.465575
$45$			3.04384i			0.0676408i
$46$	−9.51472			−0.206842
$47$			58.2954i			1.24033i	0.784472	+	0.620164i	$0.212934\pi$
$47$			58.2954i			1.24033i	−0.784472	+	0.620164i	$0.787066\pi$
$48$		−	6.92820i		−	0.144338i
$49$	−38.9411	−	29.7420i	−0.794717	−	0.606980i
$50$	33.8995			0.677990
$51$	−52.6690			−1.03273
$52$			17.9149i			0.344516i
$53$	−70.9706			−1.33907			−0.669534	−	0.742782i	$-0.733506\pi$
$53$	−70.9706			−1.33907			−0.669534	+	0.742782i	$0.733506\pi$
$54$			7.34847i			0.136083i
$55$			10.3923i			0.188951i
$56$	−6.34315	+	18.7554i	−0.113270	+	0.334918i
$57$	27.9411			0.490195
$58$	42.4264			0.731490
$59$			0.492372i			0.00834529i	0.999991	+	0.00417265i	$0.00132820\pi$
$59$			0.492372i			0.00834529i	−0.999991	+	0.00417265i	$0.998672\pi$
$60$	−3.51472			−0.0585786
$61$		−	2.86976i		−	0.0470452i	−0.999723	−	0.0235226i	$-0.992512\pi$
$61$		−	2.86976i		−	0.0470452i	0.999723	−	0.0235226i	$-0.00748816\pi$
$62$		−	70.9631i		−	1.14457i
$63$	6.72792	−	19.8931i	0.106792	−	0.315763i
$64$	8.00000			0.125000
$65$	9.08831			0.139820
$66$			25.0892i			0.380140i
$67$	27.0294			0.403424			0.201712	−	0.979445i	$-0.435349\pi$
$67$	27.0294			0.403424			0.201712	+	0.979445i	$0.435349\pi$
$68$		−	60.8170i		−	0.894367i
$69$			11.6531i			0.168886i
$70$	9.51472	+	3.21792i	0.135925	+	0.0459702i
$71$	50.6102			0.712819			0.356410	−	0.934330i	$-0.384001\pi$
$71$	50.6102			0.712819			0.356410	+	0.934330i	$0.384001\pi$
$72$	−8.48528			−0.117851
$73$			70.6149i			0.967328i	0.875254	+	0.483664i	$0.160694\pi$
$73$			70.6149i			0.967328i	−0.875254	+	0.483664i	$0.839306\pi$
$74$	43.7157			0.590753
$75$		−	41.5182i		−	0.553576i
$76$			32.2636i			0.424521i
$77$	22.9706	−	67.9193i	0.298319	−	0.882068i
$78$	21.9411			0.281296
$79$	133.823			1.69397			0.846983	−	0.531619i	$-0.178416\pi$
$79$	133.823			1.69397			0.846983	+	0.531619i	$0.178416\pi$
$80$		−	4.05845i		−	0.0507306i
$81$	9.00000			0.111111
$82$			10.0441i			0.122490i
$83$			104.415i			1.25802i	0.777398	+	0.629009i	$0.216539\pi$
$83$			104.415i			1.25802i	−0.777398	+	0.629009i	$0.783461\pi$
$84$	22.9706	+	7.76874i	0.273459	+	0.0924849i
$85$	−30.8528			−0.362974
$86$	−105.255			−1.22389
$87$		−	51.9615i		−	0.597259i
$88$	−28.9706			−0.329211
$89$		−	144.970i		−	1.62888i	−0.580250	−	0.814438i	$-0.697045\pi$
$89$		−	144.970i		−	1.62888i	0.580250	−	0.814438i	$-0.302955\pi$
$90$			4.30463i			0.0478293i
$91$	−59.3970	−	20.0883i	−0.652714	−	0.220750i
$92$	−13.4558			−0.146259
$93$	−86.9117			−0.934534
$94$			82.4421i			0.877044i
$95$	16.3675			0.172290
$96$		−	9.79796i		−	0.102062i
$97$			100.705i			1.03820i	0.854714	+	0.519099i	$0.173732\pi$
$97$			100.705i			1.03820i	−0.854714	+	0.519099i	$0.826268\pi$
$98$	−55.0711	−	42.0616i	−0.561950	−	0.429200i
$99$	30.7279			0.310383
$100$	47.9411			0.479411
$101$			138.882i			1.37507i	0.726150	+	0.687536i	$0.241308\pi$
$101$			138.882i			1.37507i	−0.726150	+	0.687536i	$0.758692\pi$
$102$	−74.4853			−0.730248
$103$		−	78.8760i		−	0.765787i	−0.923793	−	0.382893i	$-0.874928\pi$
$103$		−	78.8760i		−	0.765787i	0.923793	−	0.382893i	$-0.125072\pi$
$104$			25.3354i			0.243610i
$105$	3.94113	−	11.6531i	0.0375345	−	0.110982i
$106$	−100.368			−0.946864
$107$	−37.7574			−0.352873			−0.176436	−	0.984312i	$-0.556457\pi$
$107$	−37.7574			−0.352873			−0.176436	+	0.984312i	$0.556457\pi$
$108$			10.3923i			0.0962250i
$109$	31.9411			0.293038			0.146519	−	0.989208i	$-0.453193\pi$
$109$	31.9411			0.293038			0.146519	+	0.989208i	$0.453193\pi$
$110$			14.6969i			0.133609i
$111$		−	53.5406i		−	0.482348i
$112$	−8.97056	+	26.5241i	−0.0800943	+	0.236823i
$113$	−106.971			−0.946642			−0.473321	−	0.880890i	$-0.656945\pi$
$113$	−106.971			−0.946642			−0.473321	+	0.880890i	$0.656945\pi$
$114$	39.5147			0.346620
$115$			6.82623i			0.0593585i
$116$	60.0000			0.517241
$117$		−	26.8723i		−	0.229678i
$118$			0.696320i			0.00590101i
$119$	201.640	+	68.1953i	1.69445	+	0.573070i
$120$	−4.97056			−0.0414214
$121$	−16.0883			−0.132961
$122$		−	4.05845i		−	0.0332660i
$123$	12.3015			0.100012
$124$		−	100.357i		−	0.809330i
$125$		−	49.6861i		−	0.397489i
$126$	9.51472	−	28.1331i	0.0755136	−	0.223278i
$127$	22.0589			0.173692			0.0868460	−	0.996222i	$-0.472321\pi$
$127$	22.0589			0.173692			0.0868460	+	0.996222i	$0.472321\pi$
$128$	11.3137			0.0883883
$129$			128.910i			0.999305i
$130$	12.8528			0.0988678
$131$			70.9631i			0.541703i	0.962621	+	0.270852i	$0.0873052\pi$
$131$			70.9631i			0.541703i	−0.962621	+	0.270852i	$0.912695\pi$
$132$			35.4815i			0.268800i
$133$	−106.971	−	36.1779i	−0.804290	−	0.272014i
$134$	38.2254			0.285264
$135$	5.27208			0.0390524
$136$		−	86.0082i		−	0.632413i
$137$	−105.765			−0.772004			−0.386002	−	0.922498i	$-0.626144\pi$
$137$	−105.765			−0.772004			−0.386002	+	0.922498i	$0.626144\pi$
$138$			16.4800i			0.119420i
$139$		−	181.322i		−	1.30447i	−0.758015	−	0.652237i	$-0.773831\pi$
$139$		−	181.322i		−	1.30447i	0.758015	−	0.652237i	$-0.226169\pi$
$140$	13.4558	+	4.55082i	0.0961132	+	0.0325059i
$141$	100.971			0.716103
$142$	71.5736			0.504039
$143$		−	91.7477i		−	0.641592i
$144$	−12.0000			−0.0833333
$145$		−	30.4384i		−	0.209920i
$146$			99.8646i			0.684004i
$147$	−51.5147	+	67.4480i	−0.350440	+	0.458830i
$148$	61.8234			0.417726
$149$	41.1472			0.276156			0.138078	−	0.990421i	$-0.455908\pi$
$149$	41.1472			0.276156			0.138078	+	0.990421i	$0.455908\pi$
$150$		−	58.7156i		−	0.391438i
$151$	80.3675			0.532235			0.266118	−	0.963941i	$-0.414259\pi$
$151$	80.3675			0.532235			0.266118	+	0.963941i	$0.414259\pi$
$152$			45.6277i			0.300182i
$153$			91.2255i			0.596245i
$154$	32.4853	−	96.0523i	0.210943	−	0.623716i
$155$	−50.9117			−0.328463
$156$	31.0294			0.198907
$157$			57.3106i			0.365036i	0.983203	+	0.182518i	$0.0584248\pi$
$157$			57.3106i			0.365036i	−0.983203	+	0.182518i	$0.941575\pi$
$158$	189.255			1.19782
$159$			122.925i			0.773111i
$160$		−	5.73951i		−	0.0358719i
$161$	15.0883	−	44.6131i	0.0937162	−	0.277100i
$162$	12.7279			0.0785674
$163$	−174.912			−1.07308			−0.536539	−	0.843876i	$-0.680269\pi$
$163$	−174.912			−1.07308			−0.536539	+	0.843876i	$0.680269\pi$
$164$			14.2046i			0.0866132i
$165$	18.0000			0.109091
$166$			147.666i			0.889552i
$167$		−	196.163i		−	1.17463i	−0.809359	−	0.587315i	$-0.800185\pi$
$167$		−	196.163i		−	1.17463i	0.809359	−	0.587315i	$-0.199815\pi$
$168$	32.4853	+	10.9867i	0.193365	+	0.0653967i
$169$	88.7645			0.525234
$170$	−43.6325			−0.256662
$171$		−	48.3954i		−	0.283014i
$172$	−148.853			−0.865423
$173$			38.5254i			0.222690i	0.993782	+	0.111345i	$0.0355159\pi$
$173$			38.5254i			0.222690i	−0.993782	+	0.111345i	$0.964484\pi$
$174$		−	73.4847i		−	0.422326i
$175$	−53.7574	+	158.950i	−0.307185	+	0.908283i
$176$	−40.9706			−0.232787
$177$	0.852814			0.00481816
$178$		−	205.019i		−	1.15179i
$179$	−191.095			−1.06757			−0.533786	−	0.845619i	$-0.679231\pi$
$179$	−191.095			−1.06757			−0.533786	+	0.845619i	$0.679231\pi$
$180$			6.08767i			0.0338204i
$181$		−	120.793i		−	0.667367i	−0.942685	−	0.333683i	$-0.891708\pi$
$181$		−	120.793i		−	0.667367i	0.942685	−	0.333683i	$-0.108292\pi$
$182$	−84.0000	−	28.4091i	−0.461538	−	0.156094i
$183$	−4.97056			−0.0271615
$184$	−19.0294			−0.103421
$185$		−	31.3634i		−	0.169532i
$186$	−122.912			−0.660816
$187$			311.463i			1.66558i
$188$			116.591i			0.620164i
$189$	−34.4558	−	11.6531i	−0.182306	−	0.0616566i
$190$	23.1472			0.121827
$191$	112.066			0.586733			0.293367	−	0.956000i	$-0.405224\pi$
$191$	112.066			0.586733			0.293367	+	0.956000i	$0.405224\pi$
$192$		−	13.8564i		−	0.0721688i
$193$	−22.9117			−0.118713			−0.0593567	−	0.998237i	$-0.518905\pi$
$193$	−22.9117			−0.118713			−0.0593567	+	0.998237i	$0.518905\pi$
$194$			142.419i			0.734116i
$195$		−	15.7414i		−	0.0807252i
$196$	−77.8823	−	59.4841i	−0.397358	−	0.303490i
$197$	−116.059			−0.589131			−0.294566	−	0.955631i	$-0.595175\pi$
$197$	−116.059			−0.589131			−0.294566	+	0.955631i	$0.595175\pi$
$198$	43.4558			0.219474
$199$		−	163.101i		−	0.819604i	−0.912174	−	0.409802i	$-0.865598\pi$
$199$		−	163.101i		−	0.819604i	0.912174	−	0.409802i	$-0.134402\pi$
$200$	67.7990			0.338995
$201$		−	46.8164i		−	0.232917i
$202$			196.409i			0.972323i
$203$	−67.2792	+	198.931i	−0.331425	+	0.979955i
$204$	−105.338			−0.516363
$205$	7.20606			0.0351515
$206$		−	111.548i		−	0.541493i
$207$	20.1838			0.0975061
$208$			35.8297i			0.172258i
$209$		−	165.232i		−	0.790586i
$210$	5.57359	−	16.4800i	0.0265409	−	0.0784761i
$211$	106.426			0.504391			0.252195	−	0.967676i	$-0.418847\pi$
$211$	106.426			0.504391			0.252195	+	0.967676i	$0.418847\pi$
$212$	−141.941			−0.669534
$213$		−	87.6594i		−	0.411546i
$214$	−53.3970			−0.249519
$215$			75.5139i			0.351228i
$216$			14.6969i			0.0680414i
$217$	332.735	+	112.532i	1.53334	+	0.518582i
$218$	45.1716			0.207209
$219$	122.309			0.558487
$220$			20.7846i			0.0944755i
$221$	272.382			1.23250
$222$		−	75.7179i		−	0.341071i
$223$			57.0047i			0.255627i	0.991798	+	0.127813i	$0.0407958\pi$
$223$			57.0047i			0.255627i	−0.991798	+	0.127813i	$0.959204\pi$
$224$	−12.6863	+	37.5108i	−0.0566352	+	0.167459i
$225$	−71.9117			−0.319608
$226$	−151.279			−0.669377
$227$		−	287.418i		−	1.26616i	−0.774086	−	0.633080i	$-0.781790\pi$
$227$		−	287.418i		−	1.26616i	0.774086	−	0.633080i	$-0.218210\pi$
$228$	55.8823			0.245098
$229$		−	139.405i		−	0.608754i	−0.952552	−	0.304377i	$-0.901552\pi$
$229$		−	139.405i		−	0.608754i	0.952552	−	0.304377i	$-0.0984482\pi$
$230$			9.65375i			0.0419728i
$231$	−117.640	−	39.7862i	−0.509262	−	0.172235i
$232$	84.8528			0.365745
$233$	362.735			1.55680			0.778401	−	0.627767i	$-0.216031\pi$
$233$	362.735			1.55680			0.778401	+	0.627767i	$0.216031\pi$
$234$		−	38.0031i		−	0.162407i
$235$	59.1472			0.251690
$236$			0.984744i			0.00417265i
$237$		−	231.789i		−	0.978012i
$238$	285.161	+	96.4427i	1.19816	+	0.405222i
$239$	18.4781			0.0773144			0.0386572	−	0.999253i	$-0.487692\pi$
$239$	18.4781			0.0773144			0.0386572	+	0.999253i	$0.487692\pi$
$240$	−7.02944			−0.0292893
$241$			178.104i			0.739021i	0.929227	+	0.369510i	$0.120475\pi$
$241$			178.104i			0.739021i	−0.929227	+	0.369510i	$0.879525\pi$
$242$	−22.7523			−0.0940178
$243$		−	15.5885i		−	0.0641500i
$244$		−	5.73951i		−	0.0235226i
$245$	−30.1766	+	39.5101i	−0.123170	+	0.161266i
$246$	17.3970			0.0707194
$247$	−144.500			−0.585018
$248$		−	141.926i		−	0.572283i
$249$	180.853			0.726317
$250$		−	70.2668i		−	0.281067i
$251$		−	50.6709i		−	0.201876i	−0.994893	−	0.100938i	$-0.967816\pi$
$251$		−	50.6709i		−	0.201876i	0.994893	−	0.100938i	$-0.0321844\pi$
$252$	13.4558	−	39.7862i	0.0533962	−	0.157882i
$253$	68.9117			0.272378
$254$	31.1960			0.122819
$255$			53.4386i			0.209563i
$256$	16.0000			0.0625000
$257$		−	187.584i		−	0.729898i	−0.931028	−	0.364949i	$-0.881086\pi$
$257$		−	187.584i		−	0.729898i	0.931028	−	0.364949i	$-0.118914\pi$
$258$			182.307i			0.706615i
$259$	−69.3238	+	204.976i	−0.267659	+	0.791414i
$260$	18.1766			0.0699101
$261$	−90.0000			−0.344828
$262$			100.357i			0.383042i
$263$	−402.978			−1.53223			−0.766117	−	0.642701i	$-0.777814\pi$
$263$	−402.978			−1.53223			−0.766117	+	0.642701i	$0.777814\pi$
$264$			50.1785i			0.190070i
$265$			72.0076i			0.271727i
$266$	−151.279	−	51.1632i	−0.568719	−	0.192343i
$267$	−251.095			−0.940432
$268$	54.0589			0.201712
$269$			480.538i			1.78639i	0.449674	+	0.893193i	$0.351540\pi$
$269$			480.538i			1.78639i	−0.449674	+	0.893193i	$0.648460\pi$
$270$	7.45584			0.0276142
$271$			37.3068i			0.137664i	0.997628	+	0.0688318i	$0.0219272\pi$
$271$			37.3068i			0.137664i	−0.997628	+	0.0688318i	$0.978073\pi$
$272$		−	121.634i		−	0.447184i
$273$	−34.7939	+	102.879i	−0.127450	+	0.376845i
$274$	−149.574			−0.545889
$275$	−245.522			−0.892807
$276$			23.3062i			0.0844428i
$277$	−82.6762			−0.298470			−0.149235	−	0.988802i	$-0.547681\pi$
$277$	−82.6762			−0.298470			−0.149235	+	0.988802i	$0.547681\pi$
$278$		−	256.428i		−	0.922403i
$279$			150.535i			0.539554i
$280$	19.0294	+	6.43583i	0.0679623	+	0.0229851i
$281$	−150.853			−0.536843			−0.268421	−	0.963302i	$-0.586502\pi$
$281$	−150.853			−0.536843			−0.268421	+	0.963302i	$0.586502\pi$
$282$	142.794			0.506361
$283$		−	284.158i		−	1.00409i	−0.864841	−	0.502046i	$-0.832581\pi$
$283$		−	284.158i		−	1.00409i	0.864841	−	0.502046i	$-0.167419\pi$
$284$	101.220			0.356410
$285$		−	28.3494i		−	0.0994716i
$286$		−	129.751i		−	0.453674i
$287$	−47.0955	−	15.9279i	−0.164096	−	0.0554978i
$288$	−16.9706			−0.0589256
$289$	−635.676			−2.19957
$290$		−	43.0463i		−	0.148436i
$291$	174.426			0.599403
$292$			141.230i			0.483664i
$293$			537.237i			1.83357i	0.399379	+	0.916786i	$0.369226\pi$
$293$			537.237i			1.83357i	−0.399379	+	0.916786i	$0.630774\pi$
$294$	−72.8528	+	95.3859i	−0.247799	+	0.324442i
$295$	0.499567			0.00169345
$296$	87.4315			0.295377
$297$		−	53.2223i		−	0.179200i
$298$	58.1909			0.195272
$299$		−	60.2649i		−	0.201555i
$300$		−	83.0365i		−	0.276788i
$301$	166.912	−	493.524i	0.554524	−	1.63961i
$302$	113.657			0.376347
$303$	240.551			0.793899
$304$			64.5273i			0.212261i
$305$	−2.91169			−0.00954652
$306$			129.012i			0.421609i
$307$			34.7430i			0.113169i	0.998398	+	0.0565847i	$0.0180211\pi$
$307$			34.7430i			0.113169i	−0.998398	+	0.0565847i	$0.981979\pi$
$308$	45.9411	−	135.839i	0.149159	−	0.441034i
$309$	−136.617			−0.442127
$310$	−72.0000			−0.232258
$311$			89.1664i			0.286709i	0.989671	+	0.143354i	$0.0457888\pi$
$311$			89.1664i			0.286709i	−0.989671	+	0.143354i	$0.954211\pi$
$312$	43.8823			0.140648
$313$		−	519.700i		−	1.66038i	−0.557479	−	0.830191i	$-0.688231\pi$
$313$		−	519.700i		−	1.66038i	0.557479	−	0.830191i	$-0.311769\pi$
$314$			81.0495i			0.258119i
$315$	−20.1838	−	6.82623i	−0.0640754	−	0.0216706i
$316$	267.647			0.846983
$317$	542.029			1.70987			0.854935	−	0.518736i	$-0.173597\pi$
$317$	542.029			1.70987			0.854935	+	0.518736i	$0.173597\pi$
$318$			173.842i			0.546672i
$319$	−307.279			−0.963258
$320$		−	8.11689i		−	0.0253653i
$321$			65.3977i			0.203731i
$322$	21.3381	−	63.0924i	0.0662674	−	0.195939i
$323$	490.544			1.51871
$324$	18.0000			0.0555556
$325$			214.715i			0.660660i
$326$	−247.362			−0.758781
$327$		−	55.3237i		−	0.169185i
$328$			20.0883i			0.0612448i
$329$	−386.558	−	130.736i	−1.17495	−	0.397373i
$330$	25.4558			0.0771389
$331$	179.632			0.542696			0.271348	−	0.962481i	$-0.412531\pi$
$331$	179.632			0.542696			0.271348	+	0.962481i	$0.412531\pi$
$332$			208.831i			0.629009i
$333$	−92.7351			−0.278484
$334$		−	277.417i		−	0.830588i
$335$		−	27.4244i		−	0.0818638i
$336$	45.9411	+	15.5375i	0.136730	+	0.0462425i
$337$	291.823			0.865945			0.432972	−	0.901407i	$-0.357465\pi$
$337$	291.823			0.865945			0.432972	+	0.901407i	$0.357465\pi$
$338$	125.532			0.371396
$339$			185.278i			0.546544i
$340$	−61.7056			−0.181487
$341$			513.960i			1.50721i
$342$		−	68.4415i		−	0.200121i
$343$	284.551	−	191.519i	0.829596	−	0.558365i
$344$	−210.510			−0.611947
$345$	11.8234			0.0342707
$346$			54.4831i			0.157466i
$347$	452.080			1.30283			0.651413	−	0.758724i	$-0.274177\pi$
$347$	452.080			1.30283			0.651413	+	0.758724i	$0.274177\pi$
$348$		−	103.923i		−	0.298629i
$349$		−	235.067i		−	0.673543i	−0.941586	−	0.336772i	$-0.890665\pi$
$349$		−	235.067i		−	0.673543i	0.941586	−	0.336772i	$-0.109335\pi$
$350$	−76.0244	+	224.789i	−0.217213	+	0.642253i
$351$	−46.5442			−0.132604
$352$	−57.9411			−0.164605
$353$			25.2458i			0.0715179i	0.999360	+	0.0357590i	$0.0113849\pi$
$353$			25.2458i			0.0715179i	−0.999360	+	0.0357590i	$0.988615\pi$
$354$	1.20606			0.00340695
$355$		−	51.3497i		−	0.144647i
$356$		−	289.940i		−	0.814438i
$357$	118.118	−	349.250i	0.330862	−	0.978291i
$358$	−270.250			−0.754888
$359$	−106.243			−0.295941			−0.147970	−	0.988992i	$-0.547274\pi$
$359$	−106.243			−0.295941			−0.147970	+	0.988992i	$0.547274\pi$
$360$			8.60927i			0.0239146i
$361$	100.765			0.279126
$362$		−	170.828i		−	0.471900i
$363$			27.8658i			0.0767652i
$364$	−118.794	−	40.1766i	−0.326357	−	0.110375i
$365$	71.6468			0.196292
$366$	−7.02944			−0.0192061
$367$			286.416i			0.780426i	0.920725	+	0.390213i	$0.127599\pi$
$367$			286.416i			0.780426i	−0.920725	+	0.390213i	$0.872401\pi$
$368$	−26.9117			−0.0731296
$369$		−	21.3068i		−	0.0577421i
$370$		−	44.3545i		−	0.119877i
$371$	159.161	−	470.608i	0.429007	−	1.26849i
$372$	−173.823			−0.467267
$373$	−423.470			−1.13531			−0.567654	−	0.823267i	$-0.692149\pi$
$373$	−423.470			−1.13531			−0.567654	+	0.823267i	$0.692149\pi$
$374$			440.476i			1.17774i
$375$	−86.0589			−0.229490
$376$			164.884i			0.438522i
$377$			268.723i			0.712793i
$378$	−48.7279	−	16.4800i	−0.128910	−	0.0435978i
$379$	101.103			0.266761			0.133381	−	0.991065i	$-0.457417\pi$
$379$	101.103			0.266761			0.133381	+	0.991065i	$0.457417\pi$
$380$	32.7351			0.0861449
$381$		−	38.2071i		−	0.100281i
$382$	158.485			0.414883
$383$		−	220.394i		−	0.575442i	−0.957714	−	0.287721i	$-0.907102\pi$
$383$		−	220.394i		−	0.575442i	0.957714	−	0.287721i	$-0.0928976\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	−68.9117	−	23.3062i	−0.178991	−	0.0605356i
$386$	−32.4020			−0.0839431
$387$	223.279			0.576949
$388$			201.410i			0.519099i
$389$	−383.470			−0.985784			−0.492892	−	0.870090i	$-0.664060\pi$
$389$	−383.470			−0.985784			−0.492892	+	0.870090i	$0.664060\pi$
$390$		−	22.2617i		−	0.0570813i
$391$			204.586i			0.523238i
$392$	−110.142	−	84.1232i	−0.280975	−	0.214600i
$393$	122.912			0.312752
$394$	−164.132			−0.416579
$395$		−	135.779i		−	0.343744i
$396$	61.4558			0.155192
$397$			485.178i			1.22211i	0.791588	+	0.611056i	$0.209255\pi$
$397$			485.178i			1.22211i	−0.791588	+	0.611056i	$0.790745\pi$
$398$		−	230.660i		−	0.579548i
$399$	−62.6619	+	185.278i	−0.157047	+	0.464357i
$400$	95.8823			0.239706
$401$	−253.176			−0.631361			−0.315680	−	0.948866i	$-0.602233\pi$
$401$	−253.176			−0.631361			−0.315680	+	0.948866i	$0.602233\pi$
$402$		−	66.2083i		−	0.164697i
$403$	449.470			1.11531
$404$			277.765i			0.687536i
$405$		−	9.13151i		−	0.0225469i
$406$	−95.1472	+	281.331i	−0.234353	+	0.692933i
$407$	−316.617			−0.777930
$408$	−148.971			−0.365124
$409$		−	5.39135i		−	0.0131818i	−0.999978	−	0.00659089i	$-0.997902\pi$
$409$		−	5.39135i		−	0.0131818i	0.999978	−	0.00659089i	$-0.00209796\pi$
$410$	10.1909			0.0248559
$411$			183.189i			0.445717i
$412$		−	157.752i		−	0.382893i
$413$	−3.26494	−	1.10421i	−0.00790541	−	0.00267364i
$414$	28.5442			0.0689472
$415$	105.941			0.255280
$416$			50.6709i			0.121805i
$417$	−314.059			−0.753139
$418$		−	233.674i		−	0.559028i
$419$		−	294.431i		−	0.702700i	−0.936244	−	0.351350i	$-0.885723\pi$
$419$		−	294.431i		−	0.702700i	0.936244	−	0.351350i	$-0.114277\pi$
$420$	7.88225	−	23.3062i	0.0187673	−	0.0554910i
$421$	−290.441			−0.689883			−0.344941	−	0.938624i	$-0.612101\pi$
$421$	−290.441			−0.689883			−0.344941	+	0.938624i	$0.612101\pi$
$422$	150.510			0.356658
$423$		−	174.886i		−	0.413442i
$424$	−200.735			−0.473432
$425$		−	728.909i		−	1.71508i
$426$		−	123.969i		−	0.291007i
$427$	19.0294	+	6.43583i	0.0445654	+	0.0150722i
$428$	−75.5147			−0.176436
$429$	−158.912			−0.370424
$430$			106.793i			0.248355i
$431$	50.7136			0.117665			0.0588325	−	0.998268i	$-0.481262\pi$
$431$	50.7136			0.117665			0.0588325	+	0.998268i	$0.481262\pi$
$432$			20.7846i			0.0481125i
$433$			724.761i			1.67381i	0.547347	+	0.836906i	$0.315638\pi$
$433$			724.761i			1.67381i	−0.547347	+	0.836906i	$0.684362\pi$
$434$	470.558	+	159.145i	1.08424	+	0.366693i
$435$	−52.7208			−0.121197
$436$	63.8823			0.146519
$437$		−	108.534i		−	0.248361i
$438$	172.971			0.394910
$439$			371.728i			0.846761i	0.905952	+	0.423381i	$0.139157\pi$
$439$			371.728i			0.846761i	−0.905952	+	0.423381i	$0.860843\pi$
$440$			29.3939i			0.0668043i
$441$	116.823	+	89.2261i	0.264906	+	0.202327i
$442$	385.206			0.871507
$443$	−229.258			−0.517512			−0.258756	−	0.965943i	$-0.583313\pi$
$443$	−229.258			−0.517512			−0.258756	+	0.965943i	$0.583313\pi$
$444$		−	107.081i		−	0.241174i
$445$	−147.088			−0.330536
$446$			80.6168i			0.180755i
$447$		−	71.2690i		−	0.159439i
$448$	−17.9411	+	53.0482i	−0.0400472	+	0.118411i
$449$	−600.323			−1.33702			−0.668511	−	0.743702i	$-0.733068\pi$
$449$	−600.323			−1.33702			−0.668511	+	0.743702i	$0.733068\pi$
$450$	−101.698			−0.225997
$451$		−	72.7461i		−	0.161300i
$452$	−213.941			−0.473321
$453$		−	139.201i		−	0.307286i
$454$		−	406.471i		−	0.895311i
$455$	−20.3818	+	60.2649i	−0.0447952	+	0.132450i
$456$	79.0294			0.173310
$457$	483.823			1.05869			0.529347	−	0.848405i	$-0.322437\pi$
$457$	483.823			1.05869			0.529347	+	0.848405i	$0.322437\pi$
$458$		−	197.148i		−	0.430454i
$459$	158.007			0.344242
$460$			13.6525i			0.0296793i
$461$		−	274.661i		−	0.595794i	−0.954598	−	0.297897i	$-0.903715\pi$
$461$		−	274.661i		−	0.595794i	0.954598	−	0.297897i	$-0.0962852\pi$
$462$	−166.368	−	56.2662i	−0.360103	−	0.121788i
$463$	−153.470			−0.331469			−0.165734	−	0.986170i	$-0.552999\pi$
$463$	−153.470			−0.331469			−0.165734	+	0.986170i	$0.552999\pi$
$464$	120.000			0.258621
$465$			88.1816i			0.189638i
$466$	512.985			1.10083
$467$			61.7420i			0.132210i	0.997813	+	0.0661049i	$0.0210572\pi$
$467$			61.7420i			0.132210i	−0.997813	+	0.0661049i	$0.978943\pi$
$468$		−	53.7446i		−	0.114839i
$469$	−60.6173	+	179.233i	−0.129248	+	0.382160i
$470$	83.6468			0.177972
$471$	99.2649			0.210754
$472$			1.39264i			0.00295051i
$473$	762.323			1.61168
$474$		−	327.799i		−	0.691559i
$475$			386.689i			0.814082i
$476$	403.279	+	136.391i	0.847225	+	0.286535i
$477$	212.912			0.446356
$478$	26.1320			0.0546695
$479$		−	556.514i		−	1.16182i	−0.813966	−	0.580912i	$-0.802696\pi$
$479$		−	556.514i		−	1.16182i	0.813966	−	0.580912i	$-0.197304\pi$
$480$	−9.94113			−0.0207107
$481$			276.889i			0.575653i
$482$			251.877i			0.522567i
$483$	−77.2721	−	26.1337i	−0.159984	−	0.0541071i
$484$	−32.1766			−0.0664806
$485$	102.177			0.210673
$486$		−	22.0454i		−	0.0453609i
$487$	−325.220			−0.667804			−0.333902	−	0.942608i	$-0.608365\pi$
$487$	−325.220			−0.667804			−0.333902	+	0.942608i	$0.608365\pi$
$488$		−	8.11689i		−	0.0166330i
$489$			302.956i			0.619542i
$490$	−42.6762	+	55.8758i	−0.0870943	+	0.114032i
$491$	643.477			1.31054			0.655272	−	0.755393i	$-0.272554\pi$
$491$	643.477			1.31054			0.655272	+	0.755393i	$0.272554\pi$
$492$	24.6030			0.0500062
$493$		−	912.255i		−	1.85042i
$494$	−204.353			−0.413671
$495$		−	31.1769i		−	0.0629837i
$496$		−	200.714i		−	0.404665i
$497$	−113.500	+	335.598i	−0.228371	+	0.675247i
$498$	255.765			0.513583
$499$	755.426			1.51388			0.756939	−	0.653485i	$-0.226694\pi$
$499$	755.426			1.51388			0.756939	+	0.653485i	$0.226694\pi$
$500$		−	99.3722i		−	0.198744i
$501$	−339.765			−0.678173
$502$		−	71.6594i		−	0.142748i
$503$			509.409i			1.01274i	0.862316	+	0.506371i	$0.169013\pi$
$503$			509.409i			1.01274i	−0.862316	+	0.506371i	$0.830987\pi$
$504$	19.0294	−	56.2662i	0.0377568	−	0.111639i
$505$	140.912			0.279033
$506$	97.4558			0.192600
$507$		−	153.745i		−	0.303244i
$508$	44.1177			0.0868460
$509$			769.433i			1.51166i	0.654770	+	0.755828i	$0.272766\pi$
$509$			769.433i			1.51166i	−0.654770	+	0.755828i	$0.727234\pi$
$510$			75.5737i			0.148184i
$511$	−468.250	−	158.364i	−0.916340	−	0.309910i
$512$	22.6274			0.0441942
$513$	−83.8234			−0.163398
$514$		−	265.283i		−	0.516116i
$515$	−80.0286			−0.155395
$516$			257.821i			0.499652i
$517$		−	597.099i		−	1.15493i
$518$	−98.0387	+	289.880i	−0.189264	+	0.559615i
$519$	66.7279			0.128570
$520$	25.7056			0.0494339
$521$		−	535.207i		−	1.02727i	−0.858009	−	0.513635i	$-0.828299\pi$
$521$		−	535.207i		−	1.02727i	0.858009	−	0.513635i	$-0.171701\pi$
$522$	−127.279			−0.243830
$523$		−	839.466i		−	1.60510i	−0.596586	−	0.802549i	$-0.703477\pi$
$523$		−	839.466i		−	1.60510i	0.596586	−	0.802549i	$-0.296523\pi$
$524$			141.926i			0.270852i
$525$	275.309	+	93.1105i	0.524397	+	0.177353i
$526$	−569.897			−1.08345
$527$	−1525.85			−2.89535
$528$			70.9631i			0.134400i
$529$	−483.735			−0.914433
$530$			101.834i			0.192140i
$531$		−	1.47712i		−	0.00278176i
$532$	−213.941	−	72.3557i	−0.402145	−	0.136007i
$533$	−63.6182			−0.119359
$534$	−355.103			−0.664986
$535$			38.3091i			0.0716057i
$536$	76.4508			0.142632
$537$			330.987i			0.616363i
$538$			679.583i			1.26317i
$539$	398.860	+	304.637i	0.740000	+	0.565189i
$540$	10.5442			0.0195262
$541$	285.852			0.528377			0.264188	−	0.964471i	$-0.414896\pi$
$541$	285.852			0.528377			0.264188	+	0.964471i	$0.414896\pi$
$542$			52.7598i			0.0973428i
$543$	−209.220			−0.385305
$544$		−	172.016i		−	0.316207i
$545$		−	32.4078i		−	0.0594639i
$546$	−49.2061	+	145.492i	−0.0901210	+	0.266469i
$547$	−741.470			−1.35552			−0.677761	−	0.735283i	$-0.737049\pi$
$547$	−741.470			−1.35552			−0.677761	+	0.735283i	$0.737049\pi$
$548$	−211.529			−0.386002
$549$			8.60927i			0.0156817i
$550$	−347.220			−0.631310
$551$			483.954i			0.878320i
$552$			32.9600i			0.0597101i
$553$	−300.118	+	887.387i	−0.542708	+	1.60468i
$554$	−116.922			−0.211050
$555$	−54.3229			−0.0978792
$556$		−	362.644i		−	0.652237i
$557$	834.853			1.49884			0.749419	−	0.662096i	$-0.230333\pi$
$557$	834.853			1.49884			0.749419	+	0.662096i	$0.230333\pi$
$558$			212.889i			0.381522i
$559$		−	666.669i		−	1.19261i
$560$	26.9117	+	9.10164i	0.0480566	+	0.0162529i
$561$	539.470			0.961622
$562$	−213.338			−0.379605
$563$			417.781i			0.742062i	0.928620	+	0.371031i	$0.120996\pi$
$563$			417.781i			0.742062i	−0.928620	+	0.371031i	$0.879004\pi$
$564$	201.941			0.358052
$565$			108.534i			0.192095i
$566$		−	401.861i		−	0.710001i
$567$	−20.1838	+	59.6793i	−0.0355975	+	0.105254i
$568$	143.147			0.252020
$569$	673.029			1.18283			0.591414	−	0.806368i	$-0.298570\pi$
$569$	673.029			1.18283			0.591414	+	0.806368i	$0.298570\pi$
$570$		−	40.0921i		−	0.0703370i
$571$	−265.088			−0.464253			−0.232126	−	0.972686i	$-0.574568\pi$
$571$	−265.088			−0.464253			−0.232126	+	0.972686i	$0.574568\pi$
$572$		−	183.495i		−	0.320796i
$573$		−	194.104i		−	0.338750i
$574$	−66.6030	−	22.5254i	−0.116033	−	0.0392429i
$575$	−161.272			−0.280473
$576$	−24.0000			−0.0416667
$577$		−	468.740i		−	0.812375i	−0.913790	−	0.406188i	$-0.866858\pi$
$577$		−	468.740i		−	0.812375i	0.913790	−	0.406188i	$-0.133142\pi$
$578$	−898.982			−1.55533
$579$			39.6842i			0.0685392i
$580$		−	60.8767i		−	0.104960i
$581$	−692.382	−	234.166i	−1.19171	−	0.403040i
$582$	246.676			0.423842
$583$	726.926			1.24687
$584$			199.729i			0.342002i
$585$	−27.2649			−0.0466067
$586$			759.767i			1.29653i
$587$			120.530i			0.205332i	0.994716	+	0.102666i	$0.0327372\pi$
$587$			120.530i			0.205332i	−0.994716	+	0.102666i	$0.967263\pi$
$588$	−103.029	+	134.896i	−0.175220	+	0.229415i
$589$	809.470			1.37431
$590$	0.706494			0.00119745
$591$			201.020i			0.340135i
$592$	123.647			0.208863
$593$		−	561.468i		−	0.946826i	−0.880841	−	0.473413i	$-0.843022\pi$
$593$		−	561.468i		−	0.946826i	0.880841	−	0.473413i	$-0.156978\pi$
$594$		−	75.2677i		−	0.126713i
$595$	69.1918	−	204.586i	0.116289	−	0.343842i
$596$	82.2944			0.138078
$597$	−282.500			−0.473199
$598$		−	85.2274i		−	0.142521i
$599$	940.109			1.56946			0.784732	−	0.619835i	$-0.212801\pi$
$599$	940.109			1.56946			0.784732	+	0.619835i	$0.212801\pi$
$600$		−	117.431i		−	0.195719i
$601$		−	563.527i		−	0.937649i	−0.883291	−	0.468824i	$-0.844678\pi$
$601$		−	563.527i		−	0.937649i	0.883291	−	0.468824i	$-0.155322\pi$
$602$	236.049	−	697.948i	0.392108	−	1.15938i
$603$	−81.0883			−0.134475
$604$	160.735			0.266118
$605$			16.3234i			0.0269808i
$606$	340.191			0.561371
$607$			306.589i			0.505089i	0.967585	+	0.252544i	$0.0812674\pi$
$607$			306.589i			0.505089i	−0.967585	+	0.252544i	$0.918733\pi$
$608$			91.2553i			0.150091i
$609$	344.558	+	116.531i	0.565777	+	0.191348i
$610$	−4.11775			−0.00675041
$611$	−522.177			−0.854626
$612$			182.451i			0.298122i
$613$	275.588			0.449572			0.224786	−	0.974408i	$-0.427832\pi$
$613$	275.588			0.449572			0.224786	+	0.974408i	$0.427832\pi$
$614$			49.1340i			0.0800228i
$615$		−	12.4813i		−	0.0202947i
$616$	64.9706	−	192.105i	0.105472	−	0.311858i
$617$	461.294			0.747639			0.373820	−	0.927501i	$-0.378048\pi$
$617$	461.294			0.747639			0.373820	+	0.927501i	$0.378048\pi$
$618$	−193.206			−0.312631
$619$			374.904i			0.605660i	0.953045	+	0.302830i	$0.0979315\pi$
$619$			374.904i			0.605660i	−0.953045	+	0.302830i	$0.902068\pi$
$620$	−101.823			−0.164231
$621$		−	34.9593i		−	0.0562952i
$622$			126.100i			0.202734i
$623$	961.301	+	325.116i	1.54302	+	0.521855i
$624$	62.0589			0.0994533
$625$	548.852			0.878163
$626$		−	734.966i		−	1.17407i
$627$	−286.191			−0.456445
$628$			114.621i			0.182518i
$629$		−	939.978i		−	1.49440i
$630$	−28.5442	−	9.65375i	−0.0453082	−	0.0153234i
$631$	−1127.32			−1.78656			−0.893282	−	0.449496i	$-0.851603\pi$
$631$	−1127.32			−1.78656			−0.893282	+	0.449496i	$0.851603\pi$
$632$	378.510			0.598908
$633$		−	184.336i		−	0.291210i
$634$	766.544			1.20906
$635$		−	22.3812i		−	0.0352460i
$636$			245.849i			0.386555i
$637$	266.412	−	348.812i	0.418229	−	0.547586i
$638$	−434.558			−0.681126
$639$	−151.831			−0.237606
$640$		−	11.4790i		−	0.0179360i
$641$	−884.352			−1.37964			−0.689822	−	0.723979i	$-0.742311\pi$
$641$	−884.352			−1.37964			−0.689822	+	0.723979i	$0.742311\pi$
$642$			92.4863i			0.144060i
$643$			300.765i			0.467753i	0.972266	+	0.233876i	$0.0751411\pi$
$643$			300.765i			0.467753i	−0.972266	+	0.233876i	$0.924859\pi$
$644$	30.1766	−	89.2261i	0.0468581	−	0.138550i
$645$	130.794			0.202781
$646$	693.734			1.07389
$647$			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
$649$		−	5.04319i		−	0.00777071i
$650$			303.652i			0.467157i
$651$	194.912	−	576.314i	0.299404	−	0.885275i
$652$	−349.823			−0.536539
$653$	−455.970			−0.698269			−0.349135	−	0.937073i	$-0.613524\pi$
$653$	−455.970			−0.698269			−0.349135	+	0.937073i	$0.613524\pi$
$654$		−	78.2395i		−	0.119632i
$655$	72.0000			0.109924
$656$			28.4091i			0.0433066i
$657$		−	211.845i		−	0.322443i
$658$	−546.676	−	184.888i	−0.830815	−	0.280985i
$659$	403.684			0.612571			0.306285	−	0.951940i	$-0.400914\pi$
$659$	403.684			0.612571			0.306285	+	0.951940i	$0.400914\pi$
$660$	36.0000			0.0545455
$661$			1153.41i			1.74495i	0.488663	+	0.872473i	$0.337485\pi$
$661$			1153.41i			1.74495i	−0.488663	+	0.872473i	$0.662515\pi$
$662$	254.039			0.383744
$663$		−	471.779i		−	0.711582i
$664$			295.331i			0.444776i
$665$	−36.7065	+	108.534i	−0.0551977	+	0.163208i
$666$	−131.147			−0.196918
$667$	−201.838			−0.302605
$668$		−	392.326i		−	0.587315i
$669$	98.7351			0.147586
$670$		−	38.7839i		−	0.0578865i
$671$			29.3939i			0.0438061i
$672$	64.9706	+	21.9733i	0.0966824	+	0.0326984i
$673$	−607.440			−0.902585			−0.451293	−	0.892376i	$-0.649037\pi$
$673$	−607.440			−0.902585			−0.451293	+	0.892376i	$0.649037\pi$
$674$	412.701			0.612315
$675$			124.555i			0.184525i
$676$	177.529			0.262617
$677$			1137.59i			1.68034i	0.542326	+	0.840168i	$0.317544\pi$
$677$			1137.59i			1.68034i	−0.542326	+	0.840168i	$0.682456\pi$
$678$			262.023i			0.386465i
$679$	−667.779	−	225.845i	−0.983474	−	0.332615i
$680$	−87.2649			−0.128331
$681$	−497.823			−0.731018
$682$			726.849i			1.06576i
$683$	−818.111			−1.19782			−0.598910	−	0.800817i	$-0.704399\pi$
$683$	−818.111			−1.19782			−0.598910	+	0.800817i	$0.704399\pi$
$684$		−	96.7909i		−	0.141507i
$685$			107.310i			0.156657i
$686$	402.416	−	270.849i	0.586613	−	0.394823i
$687$	−241.456			−0.351464
$688$	−297.706			−0.432712
$689$		−	635.714i		−	0.922661i
$690$	16.7208			0.0242330
$691$		−	204.280i		−	0.295630i	−0.989015	−	0.147815i	$-0.952776\pi$
$691$		−	204.280i		−	0.295630i	0.989015	−	0.147815i	$-0.0472239\pi$
$692$			77.0508i			0.111345i
$693$	−68.9117	+	203.758i	−0.0994397	+	0.294023i
$694$	639.338			0.921236
$695$	−183.971			−0.264707
$696$		−	146.969i		−	0.211163i
$697$	215.970			0.309856
$698$		−	332.434i		−	0.476267i
$699$		−	628.276i		−	0.898821i
$700$	−107.515	+	317.899i	−0.153592	+	0.454142i
$701$	−318.853			−0.454854			−0.227427	−	0.973795i	$-0.573031\pi$
$701$	−318.853			−0.454854			−0.227427	+	0.973795i	$0.573031\pi$
$702$	−65.8234			−0.0937655
$703$			498.662i			0.709334i
$704$	−81.9411			−0.116394
$705$		−	102.446i		−	0.145313i
$706$			35.7030i			0.0505708i
$707$	−920.933	−	311.463i	−1.30259	−	0.440542i
$708$	1.70563			0.00240908
$709$	−217.647			−0.306977			−0.153489	−	0.988150i	$-0.549051\pi$
$709$	−217.647			−0.306977			−0.153489	+	0.988150i	$0.549051\pi$
$710$		−	72.6194i		−	0.102281i
$711$	−401.470			−0.564656
$712$		−	410.037i		−	0.575895i
$713$			337.597i			0.473488i
$714$	167.044	−	493.914i	0.233955	−	0.691757i
$715$	−93.0883			−0.130193
$716$	−382.191			−0.533786
$717$		−	32.0051i		−	0.0446375i
$718$	−150.250			−0.209262
$719$		−	1207.36i		−	1.67922i	−0.543192	−	0.839609i	$-0.682784\pi$
$719$		−	1207.36i		−	1.67922i	0.543192	−	0.839609i	$-0.317216\pi$
$720$			12.1753i			0.0169102i
$721$	523.029	+	176.891i	0.725422	+	0.245341i
$722$	142.503			0.197372
$723$	308.485			0.426674
$724$		−	241.587i		−	0.333683i
$725$	719.117			0.991885
$726$			39.4082i			0.0542812i
$727$		−	123.231i		−	0.169506i	−0.996402	−	0.0847528i	$-0.972990\pi$
$727$		−	123.231i		−	0.169506i	0.996402	−	0.0847528i	$-0.0270100\pi$
$728$	−168.000	−	56.8183i	−0.230769	−	0.0780471i
$729$	−27.0000			−0.0370370
$730$	101.324			0.138800
$731$			2263.19i			3.09603i
$732$	−9.94113			−0.0135808
$733$			375.779i			0.512659i	0.966589	+	0.256330i	$0.0825133\pi$
$733$			375.779i			0.512659i	−0.966589	+	0.256330i	$0.917487\pi$
$734$			405.054i			0.551844i
$735$	68.4335	+	52.2674i	0.0931069	+	0.0711122i
$736$	−38.0589			−0.0517104
$737$	−276.853			−0.375648
$738$		−	30.1324i		−	0.0408299i
$739$	722.530			0.977713			0.488856	−	0.872364i	$-0.337414\pi$
$739$	722.530			0.977713			0.488856	+	0.872364i	$0.337414\pi$
$740$		−	62.7267i		−	0.0847659i
$741$			250.281i			0.337761i
$742$	225.088	−	665.540i	0.303354	−	0.896954i
$743$	1268.48			1.70724			0.853618	−	0.520899i	$-0.174403\pi$
$743$	1268.48			1.70724			0.853618	+	0.520899i	$0.174403\pi$
$744$	−245.823			−0.330408
$745$		−	41.7484i		−	0.0560382i
$746$	−598.877			−0.802784
$747$		−	313.246i		−	0.419339i
$748$			622.926i			0.832789i
$749$	84.6762	−	250.370i	0.113052	−	0.334273i
$750$	−121.706			−0.162274
$751$	439.161			0.584769			0.292384	−	0.956301i	$-0.405551\pi$
$751$	439.161			0.584769			0.292384	+	0.956301i	$0.405551\pi$
$752$			233.182i			0.310082i
$753$	−87.7645			−0.116553
$754$			380.031i			0.504020i
$755$		−	81.5419i		−	0.108002i
$756$	−68.9117	−	23.3062i	−0.0911530	−	0.0308283i
$757$	−668.530			−0.883131			−0.441565	−	0.897229i	$-0.645577\pi$
$757$	−668.530			−0.883131			−0.441565	+	0.897229i	$0.645577\pi$
$758$	142.981			0.188629
$759$		−	119.359i		−	0.157258i
$760$	46.2944			0.0609136
$761$		−	880.116i		−	1.15653i	−0.815851	−	0.578263i	$-0.803731\pi$
$761$		−	880.116i		−	1.15653i	0.815851	−	0.578263i	$-0.196269\pi$
$762$		−	54.0330i		−	0.0709094i
$763$	−71.6325	+	211.803i	−0.0938827	+	0.277592i
$764$	224.132			0.293367
$765$	92.5584			0.120991
$766$		−	311.685i		−	0.406899i
$767$	−4.41039			−0.00575018
$768$		−	27.7128i		−	0.0360844i
$769$			1163.41i			1.51289i	0.654059	+	0.756444i	$0.273065\pi$
$769$			1163.41i			1.51289i	−0.654059	+	0.756444i	$0.726935\pi$
$770$	−97.4558	−	32.9600i	−0.126566	−	0.0428051i
$771$	−324.905			−0.421407
$772$	−45.8234			−0.0593567
$773$		−	536.371i		−	0.693883i	−0.937887	−	0.346941i	$-0.887220\pi$
$773$		−	536.371i		−	0.693883i	0.937887	−	0.346941i	$-0.112780\pi$
$774$	315.765			0.407964
$775$		−	1202.81i		−	1.55201i
$776$			284.837i			0.367058i
$777$	355.029	+	120.072i	0.456923	+	0.154533i
$778$	−542.309			−0.697055
$779$	−114.573			−0.147077
$780$		−	31.4828i		−	0.0403626i
$781$	−518.382			−0.663741
$782$			289.328i			0.369985i
$783$			155.885i			0.199086i
$784$	−155.765	−	118.968i	−0.198679	−	0.151745i
$785$	58.1481			0.0740740
$786$	173.823			0.221149
$787$			83.9192i			0.106632i	0.998578	+	0.0533159i	$0.0169790\pi$
$787$			83.9192i			0.106632i	−0.998578	+	0.0533159i	$0.983021\pi$
$788$	−232.118			−0.294566
$789$			697.978i			0.884636i
$790$		−	192.020i		−	0.243064i
$791$	239.897	−	709.325i	0.303283	−	0.896745i
$792$	86.9117			0.109737
$793$	25.7056			0.0324157
$794$			686.146i			0.864163i
$795$	124.721			0.156881
$796$		−	326.202i		−	0.409802i
$797$		−	1005.57i		−	1.26169i	−0.775908	−	0.630846i	$-0.782708\pi$
$797$		−	1005.57i		−	1.26169i	0.775908	−	0.630846i	$-0.217292\pi$
$798$	−88.6173	+	262.023i	−0.111049	+	0.328350i
$799$	1772.67			2.21862
$800$	135.598			0.169497
$801$			434.910i			0.542959i
$802$	−358.045			−0.446440
$803$		−	723.283i		−	0.900727i
$804$		−	93.6327i		−	0.116459i
$805$	−45.2649	−	15.3088i	−0.0562297	−	0.0190171i
$806$	635.647			0.788644
$807$	832.316			1.03137
$808$			392.819i			0.486162i
$809$	−282.853			−0.349633			−0.174816	−	0.984601i	$-0.555933\pi$
$809$	−282.853			−0.349633			−0.174816	+	0.984601i	$0.555933\pi$
$810$		−	12.9139i		−	0.0159431i
$811$		−	923.997i		−	1.13933i	−0.821877	−	0.569665i	$-0.807073\pi$
$811$		−	923.997i		−	1.13933i	0.821877	−	0.569665i	$-0.192927\pi$
$812$	−134.558	+	397.862i	−0.165712	+	0.489978i
$813$	64.6173			0.0794801
$814$	−447.765			−0.550079
$815$			177.467i			0.217752i
$816$	−210.676			−0.258182
$817$		−	1200.63i		−	1.46956i
$818$		−	7.62452i		−	0.00932093i
$819$	178.191	+	60.2649i	0.217571	+	0.0735835i
$820$	14.4121			0.0175758
$821$	1272.32			1.54972			0.774862	−	0.632131i	$-0.217819\pi$
$821$	1272.32			1.54972			0.774862	+	0.632131i	$0.217819\pi$
$822$			259.069i			0.315169i
$823$	381.852			0.463976			0.231988	−	0.972719i	$-0.425477\pi$
$823$	381.852			0.463976			0.231988	+	0.972719i	$0.425477\pi$
$824$		−	223.095i		−	0.270747i
$825$			425.256i			0.515462i
$826$	−4.61732	−	1.56159i	−0.00558997	−	0.00189055i
$827$	653.022			0.789628			0.394814	−	0.918761i	$-0.370809\pi$
$827$	653.022			0.789628			0.394814	+	0.918761i	$0.370809\pi$
$828$	40.3675			0.0487531
$829$			215.580i			0.260048i	0.991511	+	0.130024i	$0.0415054\pi$
$829$			215.580i			0.260048i	−0.991511	+	0.130024i	$0.958495\pi$
$830$	149.823			0.180510
$831$			143.199i			0.172322i
$832$			71.6594i			0.0861291i
$833$	−904.410	+	1184.14i	−1.08573	+	1.42154i
$834$	−444.146			−0.532550
$835$	−199.029			−0.238359
$836$		−	330.465i		−	0.395293i
$837$	260.735			0.311511
$838$		−	416.389i		−	0.496884i
$839$			632.267i			0.753596i	0.926295	+	0.376798i	$0.122975\pi$
$839$			632.267i			0.753596i	−0.926295	+	0.376798i	$0.877025\pi$
$840$	11.1472	−	32.9600i	0.0132705	−	0.0392380i
$841$	59.0000			0.0701546
$842$	−410.745			−0.487821
$843$			261.285i			0.309946i
$844$	212.853			0.252195
$845$		−	90.0615i		−	0.106582i
$846$		−	247.326i		−	0.292348i
$847$	36.0803	−	106.682i	0.0425978	−	0.125953i
$848$	−283.882			−0.334767
$849$	−492.177			−0.579713
$850$		−	1030.83i		−	1.21274i
$851$	−207.971			−0.244385
$852$		−	175.319i		−	0.205773i
$853$		−	919.650i		−	1.07814i	−0.842262	−	0.539068i	$-0.818776\pi$
$853$		−	919.650i		−	1.07814i	0.842262	−	0.539068i	$-0.181224\pi$
$854$	26.9117	+	9.10164i	0.0315125	+	0.0106577i
$855$	−49.1026			−0.0574299
$856$	−106.794			−0.124759
$857$		−	527.150i		−	0.615111i	−0.951530	−	0.307556i	$-0.900489\pi$
$857$		−	527.150i		−	0.615111i	0.951530	−	0.307556i	$-0.0995110\pi$
$858$	−224.735			−0.261929
$859$			239.804i			0.279166i	0.990210	+	0.139583i	$0.0445762\pi$
$859$			239.804i			0.279166i	−0.990210	+	0.139583i	$0.955424\pi$
$860$			151.028i			0.175614i
$861$	−27.5879	+	81.5717i	−0.0320417	+	0.0947407i
$862$	71.7199			0.0832018
$863$	362.507			0.420054			0.210027	−	0.977696i	$-0.432645\pi$
$863$	362.507			0.420054			0.210027	+	0.977696i	$0.432645\pi$
$864$			29.3939i			0.0340207i
$865$	39.0883			0.0451888
$866$			1024.97i			1.18356i
$867$			1101.02i			1.26992i
$868$	665.470	+	225.065i	0.766671	+	0.259291i
$869$	−1370.70			−1.57734
$870$	−74.5584			−0.0856994
$871$			242.114i			0.277973i
$872$	90.3431			0.103605
$873$		−	302.115i		−	0.346066i
$874$		−	153.490i		−	0.175617i
$875$	329.470	+	111.428i	0.376537	+	0.127346i
$876$	244.617			0.279244
$877$	−861.647			−0.982493			−0.491247	−	0.871020i	$-0.663459\pi$
$877$	−861.647			−0.982493			−0.491247	+	0.871020i	$0.663459\pi$
$878$			525.703i			0.598750i
$879$	930.521			1.05861
$880$			41.5692i			0.0472377i
$881$			334.553i			0.379742i	0.981809	+	0.189871i	$0.0608071\pi$
$881$			334.553i			0.379742i	−0.981809	+	0.189871i	$0.939193\pi$
$882$	165.213	+	126.185i	0.187317	+	0.143067i
$883$	−1488.01			−1.68518			−0.842590	−	0.538555i	$-0.818970\pi$
$883$	−1488.01			−1.68518			−0.842590	+	0.538555i	$0.818970\pi$
$884$	544.764			0.616248
$885$		−	0.865275i		−	0.000977712i
$886$	−324.219			−0.365936
$887$			801.498i			0.903606i	0.892118	+	0.451803i	$0.149219\pi$
$887$			801.498i			0.903606i	−0.892118	+	0.451803i	$0.850781\pi$
$888$		−	151.436i		−	0.170536i
$889$	−49.4701	+	146.273i	−0.0556469	+	0.164537i
$890$	−208.014			−0.233724
$891$	−92.1838			−0.103461
$892$			114.009i			0.127813i
$893$	−940.410			−1.05309
$894$		−	100.790i		−	0.112740i
$895$			193.888i			0.216634i
$896$	−25.3726	+	75.0215i	−0.0283176	+	0.0837294i
$897$	−104.382			−0.116368
$898$	−848.985			−0.945417
$899$		−	1505.35i		−	1.67448i
$900$	−143.823			−0.159804
$901$			2158.11i			2.39524i
$902$		−	102.879i		−	0.114056i
$903$	−854.808	−	289.100i	−0.946631	−	0.320155i
$904$	−302.558			−0.334689
$905$	−122.558			−0.135424
$906$		−	196.859i		−	0.217284i
$907$	−807.279			−0.890054			−0.445027	−	0.895517i	$-0.646806\pi$
$907$	−807.279			−0.890054			−0.445027	+	0.895517i	$0.646806\pi$
$908$		−	574.837i		−	0.633080i
$909$		−	416.647i		−	0.458358i
$910$	−28.8242	+	85.2274i	−0.0316750	+	0.0936565i
$911$	−442.742			−0.485996			−0.242998	−	0.970027i	$-0.578131\pi$
$911$	−442.742			−0.485996			−0.242998	+	0.970027i	$0.578131\pi$
$912$	111.765			0.122549
$913$		−	1069.49i		−	1.17140i
$914$	684.230			0.748610
$915$			5.04319i			0.00551169i
$916$		−	278.809i		−	0.304377i
$917$	−470.558	−	159.145i	−0.513150	−	0.173549i
$918$	223.456			0.243416
$919$	−118.455			−0.128896			−0.0644478	−	0.997921i	$-0.520529\pi$
$919$	−118.455			−0.128896			−0.0644478	+	0.997921i	$0.520529\pi$
$920$			19.3075i			0.0209864i
$921$	60.1766			0.0653384
$922$		−	388.430i		−	0.421290i
$923$			453.337i			0.491156i
$924$	−235.279	−	79.5724i	−0.254631	−	0.0861173i
$925$	740.971			0.801049
$926$	−217.040			−0.234384
$927$			236.628i			0.255262i
$928$	169.706			0.182872
$929$			629.297i			0.677392i	0.940896	+	0.338696i	$0.109986\pi$
$929$			629.297i			0.677392i	−0.940896	+	0.338696i	$0.890014\pi$
$930$			124.708i			0.134094i
$931$	479.793	−	628.191i	0.515352	−	0.674749i
$932$	725.470			0.778401
$933$	154.441			0.165531
$934$			87.3164i			0.0934865i
$935$	316.014			0.337983
$936$		−	76.0063i		−	0.0812033i
$937$			210.631i			0.224793i	0.993663	+	0.112397i	$0.0358527\pi$
$937$			210.631i			0.224793i	−0.993663	+	0.112397i	$0.964147\pi$
$938$	−85.7258	+	253.474i	−0.0913921	+	0.270228i
$939$	−900.146			−0.958622
$940$	118.294			0.125845
$941$			178.422i			0.189609i	0.995496	+	0.0948047i	$0.0302226\pi$
$941$			178.422i			0.189609i	−0.995496	+	0.0948047i	$0.969777\pi$
$942$	140.382			0.149025
$943$		−	47.7836i		−	0.0506719i
$944$			1.96949i			0.00208632i
$945$	−11.8234	+	34.9593i	−0.0125115	+	0.0369940i
$946$	1078.09			1.13963
$947$	423.463			0.447163			0.223581	−	0.974685i	$-0.428225\pi$
$947$	423.463			0.447163			0.223581	+	0.974685i	$0.428225\pi$
$948$		−	463.578i		−	0.489006i
$949$	−632.528			−0.666521
$950$			546.860i			0.575643i
$951$		−	938.821i		−	0.987194i
$952$	570.323	+	192.885i	0.599079	+	0.202611i
$953$	−546.706			−0.573669			−0.286834	−	0.957980i	$-0.592603\pi$
$953$	−546.706			−0.573669			−0.286834	+	0.957980i	$0.592603\pi$
$954$	301.103			0.315621
$955$		−	113.704i		−	0.119061i
$956$	36.9563			0.0386572
$957$			532.223i			0.556137i
$958$		−	787.030i		−	0.821534i
$959$	237.192	−	701.328i	0.247332	−	0.731311i
$960$	−14.0589			−0.0146447
$961$	−1556.88			−1.62006
$962$			391.580i			0.407048i
$963$	113.272			0.117624
$964$			356.208i			0.369510i
$965$			23.2465i			0.0240896i
$966$	−109.279	−	36.9587i	−0.113125	−	0.0382595i
$967$	1262.32			1.30540			0.652701	−	0.757616i	$-0.273636\pi$
$967$	1262.32			1.30540			0.652701	+	0.757616i	$0.273636\pi$
$968$	−45.5046			−0.0470089
$969$		−	849.647i		−	0.876829i
$970$	144.500			0.148969
$971$			1080.93i			1.11322i	0.830775	+	0.556608i	$0.187898\pi$
$971$			1080.93i			1.11322i	−0.830775	+	0.556608i	$0.812102\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	1202.35	+	406.640i	1.23572	+	0.417924i
$974$	−459.931			−0.472208
$975$	371.897			0.381432
$976$		−	11.4790i		−	0.0117613i
$977$	1800.26			1.84264			0.921322	−	0.388801i	$-0.127111\pi$
$977$	1800.26			1.84264			0.921322	+	0.388801i	$0.127111\pi$
$978$			428.444i			0.438082i
$979$			1484.88i			1.51673i
$980$	−60.3532	+	79.0203i	−0.0615849	+	0.0806329i
$981$	−95.8234			−0.0976793
$982$	910.014			0.926695
$983$		−	996.810i		−	1.01405i	−0.861932	−	0.507025i	$-0.830745\pi$
$983$		−	996.810i		−	1.01405i	0.861932	−	0.507025i	$-0.169255\pi$
$984$	34.7939			0.0353597
$985$			117.755i			0.119548i
$986$		−	1290.12i		−	1.30844i
$987$	−226.441	+	669.539i	−0.229423	+	0.678358i
$988$	−288.999			−0.292509
$989$	500.735			0.506304
$990$		−	44.0908i		−	0.0445362i
$991$	788.721			0.795884			0.397942	−	0.917411i	$-0.369725\pi$
$991$	788.721			0.795884			0.397942	+	0.917411i	$0.369725\pi$
$992$		−	283.852i		−	0.286142i
$993$		−	311.133i		−	0.313326i
$994$	−160.514	+	474.607i	−0.161483	+	0.477471i
$995$	−165.484			−0.166316
$996$	361.706			0.363158
$997$		−	1942.70i		−	1.94854i	−0.225379	−	0.974271i	$-0.572362\pi$
$997$		−	1942.70i		−	1.94854i	0.225379	−	0.974271i	$-0.427638\pi$
$998$	1068.33			1.07047
$999$			160.622i			0.160783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.3.c.a.13.3	✓	4
3.2	odd	2		126.3.c.b.55.2		4
4.3	odd	2		336.3.f.c.97.4		4
5.2	odd	4		1050.3.h.a.349.5		8
5.3	odd	4		1050.3.h.a.349.4		8
5.4	even	2		1050.3.f.a.601.2		4
7.2	even	3		294.3.g.c.31.1		4
7.3	odd	6		294.3.g.c.19.1		4
7.4	even	3		294.3.g.b.19.1		4
7.5	odd	6		294.3.g.b.31.1		4
7.6	odd	2	inner	42.3.c.a.13.4	yes	4
8.3	odd	2		1344.3.f.e.769.1		4
8.5	even	2		1344.3.f.f.769.3		4
12.11	even	2		1008.3.f.g.433.3		4
21.2	odd	6		882.3.n.d.325.2		4
21.5	even	6		882.3.n.a.325.2		4
21.11	odd	6		882.3.n.a.19.2		4
21.17	even	6		882.3.n.d.19.2		4
21.20	even	2		126.3.c.b.55.1		4
28.27	even	2		336.3.f.c.97.1		4
35.13	even	4		1050.3.h.a.349.1		8
35.27	even	4		1050.3.h.a.349.8		8
35.34	odd	2		1050.3.f.a.601.1		4
56.13	odd	2		1344.3.f.f.769.2		4
56.27	even	2		1344.3.f.e.769.4		4
84.83	odd	2		1008.3.f.g.433.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.c.a.13.3	✓	4	1.1	even	1	trivial
42.3.c.a.13.4	yes	4	7.6	odd	2	inner
126.3.c.b.55.1		4	21.20	even	2
126.3.c.b.55.2		4	3.2	odd	2
294.3.g.b.19.1		4	7.4	even	3
294.3.g.b.31.1		4	7.5	odd	6
294.3.g.c.19.1		4	7.3	odd	6
294.3.g.c.31.1		4	7.2	even	3
336.3.f.c.97.1		4	28.27	even	2
336.3.f.c.97.4		4	4.3	odd	2
882.3.n.a.19.2		4	21.11	odd	6
882.3.n.a.325.2		4	21.5	even	6
882.3.n.d.19.2		4	21.17	even	6
882.3.n.d.325.2		4	21.2	odd	6
1008.3.f.g.433.2		4	84.83	odd	2
1008.3.f.g.433.3		4	12.11	even	2
1050.3.f.a.601.1		4	35.34	odd	2
1050.3.f.a.601.2		4	5.4	even	2
1050.3.h.a.349.1		8	35.13	even	4
1050.3.h.a.349.4		8	5.3	odd	4
1050.3.h.a.349.5		8	5.2	odd	4
1050.3.h.a.349.8		8	35.27	even	4
1344.3.f.e.769.1		4	8.3	odd	2
1344.3.f.e.769.4		4	56.27	even	2
1344.3.f.f.769.2		4	56.13	odd	2
1344.3.f.f.769.3		4	8.5	even	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)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -1.01461i q^{5} -2.44949i q^{6} +(-2.24264 + 6.63103i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -1.01461i q^{5} -2.44949i q^{6} +(-2.24264 + 6.63103i) q^{7} +2.82843 q^{8} -3.00000 q^{9} -1.43488i q^{10} -10.2426 q^{11} -3.46410i q^{12} +8.95743i q^{13} +(-3.17157 + 9.37769i) q^{14} -1.75736 q^{15} +4.00000 q^{16} -30.4085i q^{17} -4.24264 q^{18} +16.1318i q^{19} -2.02922i q^{20} +(11.4853 + 3.88437i) q^{21} -14.4853 q^{22} -6.72792 q^{23} -4.89898i q^{24} +23.9706 q^{25} +12.6677i q^{26} +5.19615i q^{27} +(-4.48528 + 13.2621i) q^{28} +30.0000 q^{29} -2.48528 q^{30} -50.1785i q^{31} +5.65685 q^{32} +17.7408i q^{33} -43.0041i q^{34} +(6.72792 + 2.27541i) q^{35} -6.00000 q^{36} +30.9117 q^{37} +22.8138i q^{38} +15.5147 q^{39} -2.86976i q^{40} +7.10228i q^{41} +(16.2426 + 5.49333i) q^{42} -74.4264 q^{43} -20.4853 q^{44} +3.04384i q^{45} -9.51472 q^{46} +58.2954i q^{47} -6.92820i q^{48} +(-38.9411 - 29.7420i) q^{49} +33.8995 q^{50} -52.6690 q^{51} +17.9149i q^{52} -70.9706 q^{53} +7.34847i q^{54} +10.3923i q^{55} +(-6.34315 + 18.7554i) q^{56} +27.9411 q^{57} +42.4264 q^{58} +0.492372i q^{59} -3.51472 q^{60} -2.86976i q^{61} -70.9631i q^{62} +(6.72792 - 19.8931i) q^{63} +8.00000 q^{64} +9.08831 q^{65} +25.0892i q^{66} +27.0294 q^{67} -60.8170i q^{68} +11.6531i q^{69} +(9.51472 + 3.21792i) q^{70} +50.6102 q^{71} -8.48528 q^{72} +70.6149i q^{73} +43.7157 q^{74} -41.5182i q^{75} +32.2636i q^{76} +(22.9706 - 67.9193i) q^{77} +21.9411 q^{78} +133.823 q^{79} -4.05845i q^{80} +9.00000 q^{81} +10.0441i q^{82} +104.415i q^{83} +(22.9706 + 7.76874i) q^{84} -30.8528 q^{85} -105.255 q^{86} -51.9615i q^{87} -28.9706 q^{88} -144.970i q^{89} +4.30463i q^{90} +(-59.3970 - 20.0883i) q^{91} -13.4558 q^{92} -86.9117 q^{93} +82.4421i q^{94} +16.3675 q^{95} -9.79796i q^{96} +100.705i q^{97} +(-55.0711 - 42.0616i) q^{98} +30.7279 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4} + 8 q^{7} - 12 q^{9}+O(q^{10}) \) 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

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