LMFDB - Embedded newform 690.3.b.a.599.58

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(599,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("690.599");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.b (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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			599.58
Character	$\chi$	$=$	690.599
Dual form			690.3.b.a.599.57

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +(-1.95499 + 2.27553i) q^{3} +2.00000 q^{4} +(-4.97479 + 0.501484i) q^{5} +(-2.76477 + 3.21808i) q^{6} +8.64527i q^{7} +2.82843 q^{8} +(-1.35605 - 8.89725i) q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +(-1.95499 + 2.27553i) q^{3} +2.00000 q^{4} +(-4.97479 + 0.501484i) q^{5} +(-2.76477 + 3.21808i) q^{6} +8.64527i q^{7} +2.82843 q^{8} +(-1.35605 - 8.89725i) q^{9} +(-7.03541 + 0.709206i) q^{10} -3.45825i q^{11} +(-3.90997 + 4.55106i) q^{12} +8.53030i q^{13} +12.2263i q^{14} +(8.58450 - 12.3007i) q^{15} +4.00000 q^{16} -0.0194686 q^{17} +(-1.91775 - 12.5826i) q^{18} -36.9473 q^{19} +(-9.94958 + 1.00297i) q^{20} +(-19.6725 - 16.9014i) q^{21} -4.89070i q^{22} +4.79583 q^{23} +(-5.52954 + 6.43616i) q^{24} +(24.4970 - 4.98955i) q^{25} +12.0637i q^{26} +(22.8970 + 14.3083i) q^{27} +17.2905i q^{28} -17.7156i q^{29} +(12.1403 - 17.3958i) q^{30} -15.6306 q^{31} +5.65685 q^{32} +(7.86934 + 6.76083i) q^{33} -0.0275328 q^{34} +(-4.33546 - 43.0084i) q^{35} +(-2.71211 - 17.7945i) q^{36} -54.6082i q^{37} -52.2513 q^{38} +(-19.4109 - 16.6766i) q^{39} +(-14.0708 + 1.41841i) q^{40} -31.5460i q^{41} +(-27.8212 - 23.9022i) q^{42} -49.5403i q^{43} -6.91650i q^{44} +(11.2079 + 43.5819i) q^{45} +6.78233 q^{46} -69.5957 q^{47} +(-7.81995 + 9.10211i) q^{48} -25.7406 q^{49} +(34.6440 - 7.05630i) q^{50} +(0.0380609 - 0.0443014i) q^{51} +17.0606i q^{52} -45.7420 q^{53} +(32.3813 + 20.2350i) q^{54} +(1.73426 + 17.2041i) q^{55} +24.4525i q^{56} +(72.2314 - 84.0745i) q^{57} -25.0536i q^{58} -32.1302i q^{59} +(17.1690 - 24.6013i) q^{60} +57.6808 q^{61} -22.1050 q^{62} +(76.9191 - 11.7234i) q^{63} +8.00000 q^{64} +(-4.27781 - 42.4364i) q^{65} +(11.1289 + 9.56126i) q^{66} -36.6983i q^{67} -0.0389373 q^{68} +(-9.37579 + 10.9130i) q^{69} +(-6.13127 - 60.8230i) q^{70} +100.308i q^{71} +(-3.83550 - 25.1652i) q^{72} +130.409i q^{73} -77.2276i q^{74} +(-36.5375 + 65.4982i) q^{75} -73.8945 q^{76} +29.8975 q^{77} +(-27.4512 - 23.5843i) q^{78} -142.738 q^{79} +(-19.8992 + 2.00594i) q^{80} +(-77.3222 + 24.1303i) q^{81} -44.6128i q^{82} -28.0816 q^{83} +(-39.3451 - 33.8028i) q^{84} +(0.0968524 - 0.00976322i) q^{85} -70.0605i q^{86} +(40.3123 + 34.6338i) q^{87} -9.78141i q^{88} -148.287i q^{89} +(15.8504 + 61.6341i) q^{90} -73.7467 q^{91} +9.59166 q^{92} +(30.5576 - 35.5679i) q^{93} -98.4231 q^{94} +(183.805 - 18.5285i) q^{95} +(-11.0591 + 12.8723i) q^{96} +102.899i q^{97} -36.4027 q^{98} +(-30.7689 + 4.68957i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 176 q^{4} + 8 q^{9}+O(q^{10}) $ 88 * q + 176 * q^4 + 8 * q^9	$ 88 q + 176 q^{4} + 8 q^{9} + 32 q^{10} - 12 q^{15} + 352 q^{16} - 16 q^{19} - 176 q^{21} + 72 q^{25} - 72 q^{30} + 32 q^{31} + 160 q^{34} + 16 q^{36} + 144 q^{39} + 64 q^{40} + 92 q^{45} - 360 q^{49} + 48 q^{51} - 144 q^{54} + 16 q^{55} - 24 q^{60} + 208 q^{61} + 704 q^{64} + 512 q^{66} + 304 q^{70} + 536 q^{75} - 32 q^{76} + 448 q^{79} - 24 q^{81} - 352 q^{84} - 96 q^{85} + 32 q^{90} - 64 q^{91} + 160 q^{94} + 296 q^{99}+O(q^{100}) $ 88 * q + 176 * q^4 + 8 * q^9 + 32 * q^10 - 12 * q^15 + 352 * q^16 - 16 * q^19 - 176 * q^21 + 72 * q^25 - 72 * q^30 + 32 * q^31 + 160 * q^34 + 16 * q^36 + 144 * q^39 + 64 * q^40 + 92 * q^45 - 360 * q^49 + 48 * q^51 - 144 * q^54 + 16 * q^55 - 24 * q^60 + 208 * q^61 + 704 * q^64 + 512 * q^66 + 304 * q^70 + 536 * q^75 - 32 * q^76 + 448 * q^79 - 24 * q^81 - 352 * q^84 - 96 * q^85 + 32 * q^90 - 64 * q^91 + 160 * q^94 + 296 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$1$

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
$3$	−1.95499	+	2.27553i	−0.651662	+	0.758509i
$3$	−1.95499	+	2.27553i	−0.651662	+	0.758509i
$4$	2.00000			0.500000
$5$	−4.97479	+	0.501484i	−0.994958	+	0.100297i
$5$	−4.97479	+	0.501484i	−0.994958	+	0.100297i
$6$	−2.76477	+	3.21808i	−0.460795	+	0.536347i
$7$			8.64527i			1.23504i	0.786556	+	0.617519i	$0.211862\pi$
$7$			8.64527i			1.23504i	−0.786556	+	0.617519i	$0.788138\pi$
$8$	2.82843			0.353553
$9$	−1.35605	−	8.89725i	−0.150673	−	0.988584i
$10$	−7.03541	+	0.709206i	−0.703541	+	0.0709206i
$11$		−	3.45825i		−	0.314386i	−0.987568	−	0.157193i	$-0.949755\pi$
$11$		−	3.45825i		−	0.314386i	0.987568	−	0.157193i	$-0.0502445\pi$
$12$	−3.90997	+	4.55106i	−0.325831	+	0.379255i
$13$			8.53030i			0.656177i	0.944647	+	0.328088i	$0.106404\pi$
$13$			8.53030i			0.656177i	−0.944647	+	0.328088i	$0.893596\pi$
$14$			12.2263i			0.873304i
$15$	8.58450	−	12.3007i	0.572300	−	0.820044i
$16$	4.00000			0.250000
$17$	−0.0194686			−0.00114521			−0.000572607	−	1.00000i	$-0.500182\pi$
$17$	−0.0194686			−0.00114521			−0.000572607		1.00000i	$0.500182\pi$
$18$	−1.91775	−	12.5826i	−0.106542	−	0.699034i
$19$	−36.9473			−1.94459			−0.972297	−	0.233751i	$-0.924900\pi$
$19$	−36.9473			−1.94459			−0.972297	+	0.233751i	$0.924900\pi$
$20$	−9.94958	+	1.00297i	−0.497479	+	0.0501484i
$21$	−19.6725	−	16.9014i	−0.936788	−	0.804828i
$22$		−	4.89070i		−	0.222305i
$23$	4.79583			0.208514
$23$	4.79583			0.208514
$24$	−5.52954	+	6.43616i	−0.230397	+	0.268174i
$25$	24.4970	−	4.98955i	0.979881	−	0.199582i
$26$			12.0637i			0.463987i
$27$	22.8970	+	14.3083i	0.848038	+	0.529936i
$28$			17.2905i			0.617519i
$29$		−	17.7156i		−	0.610883i	−0.952211	−	0.305441i	$-0.901196\pi$
$29$		−	17.7156i		−	0.610883i	0.952211	−	0.305441i	$-0.0988040\pi$
$30$	12.1403	−	17.3958i	0.404677	−	0.579859i
$31$	−15.6306			−0.504213			−0.252107	−	0.967699i	$-0.581123\pi$
$31$	−15.6306			−0.504213			−0.252107	+	0.967699i	$0.581123\pi$
$32$	5.65685			0.176777
$33$	7.86934	+	6.76083i	0.238465	+	0.204874i
$34$	−0.0275328			−0.000809789
$35$	−4.33546	−	43.0084i	−0.123870	−	1.22881i
$36$	−2.71211	−	17.7945i	−0.0753363	−	0.494292i
$37$		−	54.6082i		−	1.47590i	−0.674857	−	0.737949i	$-0.735795\pi$
$37$		−	54.6082i		−	1.47590i	0.674857	−	0.737949i	$-0.264205\pi$
$38$	−52.2513			−1.37503
$39$	−19.4109	−	16.6766i	−0.497716	−	0.427606i
$40$	−14.0708	+	1.41841i	−0.351771	+	0.0354603i
$41$		−	31.5460i		−	0.769415i	−0.923039	−	0.384707i	$-0.874302\pi$
$41$		−	31.5460i		−	0.769415i	0.923039	−	0.384707i	$-0.125698\pi$
$42$	−27.8212	−	23.9022i	−0.662409	−	0.569099i
$43$		−	49.5403i		−	1.15210i	−0.817415	−	0.576050i	$-0.804594\pi$
$43$		−	49.5403i		−	1.15210i	0.817415	−	0.576050i	$-0.195406\pi$
$44$		−	6.91650i		−	0.157193i
$45$	11.2079	+	43.5819i	0.249065	+	0.968487i
$46$	6.78233			0.147442
$47$	−69.5957			−1.48076			−0.740379	−	0.672189i	$-0.765354\pi$
$47$	−69.5957			−1.48076			−0.740379	+	0.672189i	$0.765354\pi$
$48$	−7.81995	+	9.10211i	−0.162916	+	0.189627i
$49$	−25.7406			−0.525319
$50$	34.6440	−	7.05630i	0.692881	−	0.141126i
$51$	0.0380609	−	0.0443014i	0.000746293	−	0.000868656i
$52$			17.0606i			0.328088i
$53$	−45.7420			−0.863056			−0.431528	−	0.902100i	$-0.642025\pi$
$53$	−45.7420			−0.863056			−0.431528	+	0.902100i	$0.642025\pi$
$54$	32.3813	+	20.2350i	0.599653	+	0.374721i
$55$	1.73426	+	17.2041i	0.0315319	+	0.312801i
$56$			24.4525i			0.436652i
$57$	72.2314	−	84.0745i	1.26722	−	1.47499i
$58$		−	25.0536i		−	0.431959i
$59$		−	32.1302i		−	0.544580i	−0.962215	−	0.272290i	$-0.912219\pi$
$59$		−	32.1302i		−	0.544580i	0.962215	−	0.272290i	$-0.0877810\pi$
$60$	17.1690	−	24.6013i	0.286150	−	0.410022i
$61$	57.6808			0.945587			0.472793	−	0.881173i	$-0.343246\pi$
$61$	57.6808			0.945587			0.472793	+	0.881173i	$0.343246\pi$
$62$	−22.1050			−0.356533
$63$	76.9191	−	11.7234i	1.22094	−	0.186086i
$64$	8.00000			0.125000
$65$	−4.27781	−	42.4364i	−0.0658125	−	0.652868i
$66$	11.1289	+	9.56126i	0.168620	+	0.144868i
$67$		−	36.6983i		−	0.547736i	−0.961767	−	0.273868i	$-0.911697\pi$
$67$		−	36.6983i		−	0.547736i	0.961767	−	0.273868i	$-0.0883031\pi$
$68$	−0.0389373			−0.000572607
$69$	−9.37579	+	10.9130i	−0.135881	+	0.158160i
$70$	−6.13127	−	60.8230i	−0.0875896	−	0.868900i
$71$			100.308i			1.41279i	0.707816	+	0.706397i	$0.249681\pi$
$71$			100.308i			1.41279i	−0.707816	+	0.706397i	$0.750319\pi$
$72$	−3.83550	−	25.1652i	−0.0532708	−	0.349517i
$73$			130.409i			1.78643i	0.449634	+	0.893213i	$0.351554\pi$
$73$			130.409i			1.78643i	−0.449634	+	0.893213i	$0.648446\pi$
$74$		−	77.2276i		−	1.04362i
$75$	−36.5375	+	65.4982i	−0.487167	+	0.873309i
$76$	−73.8945			−0.972297
$77$	29.8975			0.388279
$78$	−27.4512	−	23.5843i	−0.351939	−	0.302363i
$79$	−142.738			−1.80681			−0.903405	−	0.428788i	$-0.858941\pi$
$79$	−142.738			−1.80681			−0.903405	+	0.428788i	$0.858941\pi$
$80$	−19.8992	+	2.00594i	−0.248739	+	0.0250742i
$81$	−77.3222	+	24.1303i	−0.954596	+	0.297905i
$82$		−	44.6128i		−	0.544058i
$83$	−28.0816			−0.338332			−0.169166	−	0.985588i	$-0.554107\pi$
$83$	−28.0816			−0.338332			−0.169166	+	0.985588i	$0.554107\pi$
$84$	−39.3451	−	33.8028i	−0.468394	−	0.402414i
$85$	0.0968524	−	0.00976322i	0.00113944	−	0.000114861i
$86$		−	70.0605i		−	0.814657i
$87$	40.3123	+	34.6338i	0.463360	+	0.398089i
$88$		−	9.78141i		−	0.111152i
$89$		−	148.287i		−	1.66615i	−0.553163	−	0.833073i	$-0.686579\pi$
$89$		−	148.287i		−	1.66615i	0.553163	−	0.833073i	$-0.313421\pi$
$90$	15.8504	+	61.6341i	0.176115	+	0.684824i
$91$	−73.7467			−0.810403
$92$	9.59166			0.104257
$93$	30.5576	−	35.5679i	0.328577	−	0.382450i
$94$	−98.4231			−1.04705
$95$	183.805	−	18.5285i	1.93479	−	0.195037i
$96$	−11.0591	+	12.8723i	−0.115199	+	0.134087i
$97$			102.899i			1.06081i	0.847744	+	0.530405i	$0.177960\pi$
$97$			102.899i			1.06081i	−0.847744	+	0.530405i	$0.822040\pi$
$98$	−36.4027			−0.371456
$99$	−30.7689	+	4.68957i	−0.310797	+	0.0473694i
$100$	48.9941	−	9.97911i	0.489941	−	0.0997911i
$101$			55.9456i			0.553917i	0.960882	+	0.276958i	$0.0893264\pi$
$101$			55.9456i			0.553917i	−0.960882	+	0.276958i	$0.910674\pi$
$102$	0.0538263	−	0.0626517i	0.000527709	−	0.000614232i
$103$			23.9655i			0.232675i	0.993210	+	0.116337i	$0.0371153\pi$
$103$			23.9655i			0.232675i	−0.993210	+	0.116337i	$0.962885\pi$
$104$			24.1273i			0.231994i
$105$	106.342	+	74.2153i	1.01279	+	0.706812i
$106$	−64.6889			−0.610273
$107$	−57.1522			−0.534132			−0.267066	−	0.963678i	$-0.586054\pi$
$107$	−57.1522			−0.534132			−0.267066	+	0.963678i	$0.586054\pi$
$108$	45.7940	+	28.6165i	0.424019	+	0.264968i
$109$	31.6211			0.290101			0.145051	−	0.989424i	$-0.453665\pi$
$109$	31.6211			0.290101			0.145051	+	0.989424i	$0.453665\pi$
$110$	2.45261	+	24.3302i	0.0222965	+	0.221184i
$111$	124.262	+	106.758i	1.11948	+	0.961786i
$112$			34.5811i			0.308759i
$113$	4.36985			0.0386712			0.0193356	−	0.999813i	$-0.493845\pi$
$113$	4.36985			0.0386712			0.0193356	+	0.999813i	$0.493845\pi$
$114$	102.151	−	118.899i	0.896058	−	1.04298i
$115$	−23.8582	+	2.40503i	−0.207463	+	0.0209133i
$116$		−	35.4312i		−	0.305441i
$117$	75.8962	−	11.5675i	0.648686	−	0.0988679i
$118$		−	45.4390i		−	0.385076i
$119$		−	0.168312i		−	0.00141438i
$120$	24.2806	−	34.7915i	0.202339	−	0.289929i
$121$	109.041			0.901161
$122$	81.5729			0.668631
$123$	71.7838	+	61.6720i	0.583608	+	0.501398i
$124$	−31.2612			−0.252107
$125$	−119.365	+	37.1068i	−0.954923	+	0.296855i
$126$	108.780	−	16.5795i	0.863334	−	0.131583i
$127$			228.985i			1.80303i	0.432748	+	0.901515i	$0.357544\pi$
$127$			228.985i			1.80303i	−0.432748	+	0.901515i	$0.642456\pi$
$128$	11.3137			0.0883883
$129$	112.730	+	96.8506i	0.873878	+	0.750780i
$130$	−6.04974	−	60.0142i	−0.0465364	−	0.461647i
$131$			63.1507i			0.482067i	0.970517	+	0.241033i	$0.0774863\pi$
$131$			63.1507i			0.482067i	−0.970517	+	0.241033i	$0.922514\pi$
$132$	15.7387	+	13.5217i	0.119232	+	0.102437i
$133$		−	319.419i		−	2.40165i
$134$		−	51.8992i		−	0.387308i
$135$	−121.083	−	59.6981i	−0.896912	−	0.442208i
$136$	−0.0550656			−0.000404894
$137$	−50.2871			−0.367059			−0.183530	−	0.983014i	$-0.558752\pi$
$137$	−50.2871			−0.367059			−0.183530	+	0.983014i	$0.558752\pi$
$138$	−13.2594	+	15.4334i	−0.0960824	+	0.111836i
$139$	−66.5047			−0.478451			−0.239225	−	0.970964i	$-0.576893\pi$
$139$	−66.5047			−0.478451			−0.239225	+	0.970964i	$0.576893\pi$
$140$	−8.67093	−	86.0167i	−0.0619352	−	0.614405i
$141$	136.059	−	158.367i	0.964955	−	1.12317i
$142$			141.857i			0.998996i
$143$	29.4999			0.206293
$144$	−5.42422	−	35.5890i	−0.0376682	−	0.247146i
$145$	8.88409	+	88.1313i	0.0612696	+	0.607802i
$146$			184.426i			1.26319i
$147$	50.3226	−	58.5735i	0.342330	−	0.398459i
$148$		−	109.216i		−	0.737949i
$149$		−	202.598i		−	1.35972i	−0.733344	−	0.679858i	$-0.762041\pi$
$149$		−	202.598i		−	1.35972i	0.733344	−	0.679858i	$-0.237959\pi$
$150$	−51.6718	+	92.6284i	−0.344479	+	0.617523i
$151$	−218.749			−1.44867			−0.724335	−	0.689448i	$-0.757853\pi$
$151$	−218.749			−1.44867			−0.724335	+	0.689448i	$0.757853\pi$
$152$	−104.503			−0.687517
$153$	0.0264005	+	0.173217i	0.000172553	+	0.00113214i
$154$	42.2814			0.274555
$155$	77.7590	−	7.83850i	0.501671	−	0.0505710i
$156$	−38.8219	−	33.3532i	−0.248858	−	0.213803i
$157$			170.583i			1.08651i	0.839567	+	0.543256i	$0.182809\pi$
$157$			170.583i			1.08651i	−0.839567	+	0.543256i	$0.817191\pi$
$158$	−201.862			−1.27761
$159$	89.4249	−	104.087i	0.562421	−	0.654636i
$160$	−28.1416	+	2.83682i	−0.175885	+	0.0177301i
$161$			41.4612i			0.257523i
$162$	−109.350	+	34.1254i	−0.675001	+	0.210651i
$163$			40.4431i			0.248117i	0.992275	+	0.124059i	$0.0395911\pi$
$163$			40.4431i			0.248117i	−0.992275	+	0.124059i	$0.960409\pi$
$164$		−	63.0920i		−	0.384707i
$165$	−42.5388	−	29.6873i	−0.257811	−	0.179923i
$166$	−39.7133			−0.239237
$167$	−83.7586			−0.501549			−0.250774	−	0.968046i	$-0.580685\pi$
$167$	−83.7586			−0.501549			−0.250774	+	0.968046i	$0.580685\pi$
$168$	−55.6424	−	47.8043i	−0.331204	−	0.284550i
$169$	96.2340			0.569432
$170$	0.136970	−	0.0138073i	0.000805706	−	8.12193e-5i
$171$	50.1025	+	328.729i	0.292997	+	1.92239i
$172$		−	99.0805i		−	0.576050i
$173$	−145.335			−0.840088			−0.420044	−	0.907504i	$-0.637985\pi$
$173$	−145.335			−0.840088			−0.420044	+	0.907504i	$0.637985\pi$
$174$	57.0102	+	48.9795i	0.327645	+	0.281492i
$175$	43.1360	+	211.783i	0.246492	+	1.21019i
$176$		−	13.8330i		−	0.0785966i
$177$	73.1132	+	62.8142i	0.413069	+	0.354882i
$178$		−	209.709i		−	1.17814i
$179$		−	79.9041i		−	0.446391i	−0.974774	−	0.223196i	$-0.928351\pi$
$179$		−	79.9041i		−	0.446391i	0.974774	−	0.223196i	$-0.0716489\pi$
$180$	22.4158	+	87.1638i	0.124532	+	0.484243i
$181$	−80.0989			−0.442535			−0.221268	−	0.975213i	$-0.571019\pi$
$181$	−80.0989			−0.442535			−0.221268	+	0.975213i	$0.571019\pi$
$182$	−104.294			−0.573042
$183$	−112.765	+	131.254i	−0.616203	+	0.717236i
$184$	13.5647			0.0737210
$185$	27.3851	+	271.664i	0.148028	+	1.46845i
$186$	43.2150	−	50.3006i	0.232339	−	0.270433i
$187$			0.0673274i			0.000360040i
$188$	−139.191			−0.740379
$189$	−123.699	+	197.951i	−0.654491	+	1.04736i
$190$	259.939	−	26.2032i	1.36810	−	0.137912i
$191$			347.688i			1.82035i	0.414219	+	0.910177i	$0.364055\pi$
$191$			347.688i			1.82035i	−0.414219	+	0.910177i	$0.635945\pi$
$192$	−15.6399	+	18.2042i	−0.0814578	+	0.0948137i
$193$		−	71.1299i		−	0.368549i	−0.982875	−	0.184274i	$-0.941007\pi$
$193$		−	71.1299i		−	0.368549i	0.982875	−	0.184274i	$-0.0589935\pi$
$194$			145.521i			0.750106i
$195$	104.928	+	73.2284i	0.538094	+	0.375530i
$196$	−51.4812			−0.262659
$197$	−78.9715			−0.400871			−0.200435	−	0.979707i	$-0.564236\pi$
$197$	−78.9715			−0.400871			−0.200435	+	0.979707i	$0.564236\pi$
$198$	−43.5138	+	6.63206i	−0.219767	+	0.0334952i
$199$	264.366			1.32847			0.664237	−	0.747522i	$-0.268756\pi$
$199$	264.366			1.32847			0.664237	+	0.747522i	$0.268756\pi$
$200$	69.2881	−	14.1126i	0.346440	−	0.0705630i
$201$	83.5080	+	71.7447i	0.415463	+	0.356939i
$202$			79.1190i			0.391678i
$203$	153.156			0.754463
$204$	0.0761219	−	0.0886029i	0.000373147	−	0.000434328i
$205$	15.8198	+	156.935i	0.0771699	+	0.765535i
$206$			33.8923i			0.164526i
$207$	−6.50341	−	42.6697i	−0.0314174	−	0.206134i
$208$			34.1212i			0.164044i
$209$			127.773i			0.611353i
$210$	150.391	+	104.956i	0.716148	+	0.499792i
$211$	213.474			1.01173			0.505863	−	0.862614i	$-0.331174\pi$
$211$	213.474			1.01173			0.505863	+	0.862614i	$0.331174\pi$
$212$	−91.4839			−0.431528
$213$	−228.254	−	196.102i	−1.07162	−	0.920664i
$214$	−80.8254			−0.377689
$215$	24.8437	+	246.452i	0.115552	+	1.14629i
$216$	64.7625	+	40.4699i	0.299827	+	0.187361i
$217$		−	135.131i		−	0.622723i
$218$	44.7189			0.205133
$219$	−296.750	−	254.948i	−1.35502	−	1.16415i
$220$	3.46851	+	34.4081i	0.0157660	+	0.156401i
$221$		−	0.166073i		−	0.000751463i
$222$	175.734	+	150.979i	0.791593	+	0.680086i
$223$		−	93.1696i		−	0.417801i	−0.977937	−	0.208900i	$-0.933012\pi$
$223$		−	93.1696i		−	0.417801i	0.977937	−	0.208900i	$-0.0669884\pi$
$224$			48.9050i			0.218326i
$225$	−77.6126	−	211.190i	−0.344945	−	0.938623i
$226$	6.17990			0.0273447
$227$	128.533			0.566226			0.283113	−	0.959087i	$-0.408633\pi$
$227$	128.533			0.566226			0.283113	+	0.959087i	$0.408633\pi$
$228$	144.463	−	168.149i	0.633609	−	0.737496i
$229$	−176.176			−0.769328			−0.384664	−	0.923057i	$-0.625683\pi$
$229$	−176.176			−0.769328			−0.384664	+	0.923057i	$0.625683\pi$
$230$	−33.7407	+	3.40123i	−0.146698	+	0.0147880i
$231$	−58.4492	+	68.0326i	−0.253027	+	0.294513i
$232$		−	50.1073i		−	0.215980i
$233$	−225.112			−0.966146			−0.483073	−	0.875580i	$-0.660479\pi$
$233$	−225.112			−0.966146			−0.483073	+	0.875580i	$0.660479\pi$
$234$	107.333	−	16.3590i	0.458690	−	0.0699102i
$235$	346.224	−	34.9011i	1.47329	−	0.148515i
$236$		−	64.2604i		−	0.272290i
$237$	279.051	−	324.804i	1.17743	−	1.37048i
$238$		−	0.238029i		−	0.00100012i
$239$			240.154i			1.00483i	0.864627	+	0.502415i	$0.167555\pi$
$239$			240.154i			1.00483i	−0.864627	+	0.502415i	$0.832445\pi$
$240$	34.3380	−	49.2027i	0.143075	−	0.205011i
$241$	−80.5890			−0.334394			−0.167197	−	0.985923i	$-0.553472\pi$
$241$	−80.5890			−0.334394			−0.167197	+	0.985923i	$0.553472\pi$
$242$	154.207			0.637217
$243$	96.2548	−	223.123i	0.396110	−	0.918203i
$244$	115.362			0.472793
$245$	128.054	−	12.9085i	0.522670	−	0.0526878i
$246$	101.518	+	87.2174i	0.412673	+	0.354542i
$247$		−	315.171i		−	1.27600i
$248$	−44.2101			−0.178266
$249$	54.8991	−	63.9004i	0.220478	−	0.256628i
$250$	−168.808	+	52.4770i	−0.675232	+	0.209908i
$251$		−	22.9497i		−	0.0914329i	−0.998954	−	0.0457165i	$-0.985443\pi$
$251$		−	22.9497i		−	0.0914329i	0.998954	−	0.0457165i	$-0.0145571\pi$
$252$	153.838	−	23.4469i	0.610469	−	0.0930432i
$253$		−	16.5852i		−	0.0655541i
$254$			323.833i			1.27493i
$255$	−0.167129	+	0.239477i	−0.000655406	+	0.000939126i
$256$	16.0000			0.0625000
$257$	−412.733			−1.60597			−0.802983	−	0.596002i	$-0.796755\pi$
$257$	−412.733			−1.60597			−0.802983	+	0.596002i	$0.796755\pi$
$258$	159.425	+	136.967i	0.617925	+	0.530881i
$259$	472.102			1.82279
$260$	−8.55562	−	84.8729i	−0.0329062	−	0.326434i
$261$	−157.620	+	24.0233i	−0.603909	+	0.0920433i
$262$			89.3086i			0.340873i
$263$	−327.165			−1.24397			−0.621987	−	0.783027i	$-0.713675\pi$
$263$	−327.165			−1.24397			−0.621987	+	0.783027i	$0.713675\pi$
$264$	22.2579	+	19.1225i	0.0843101	+	0.0724338i
$265$	227.557	−	22.9389i	0.858704	−	0.0865618i
$266$		−	451.727i		−	1.69822i
$267$	337.431	+	289.899i	1.26379	+	1.08576i
$268$		−	73.3966i		−	0.273868i
$269$		−	117.972i		−	0.438559i	−0.975662	−	0.219280i	$-0.929629\pi$
$269$		−	117.972i		−	0.438559i	0.975662	−	0.219280i	$-0.0703707\pi$
$270$	−171.237	−	84.4259i	−0.634213	−	0.312689i
$271$	469.883			1.73389			0.866943	−	0.498407i	$-0.166081\pi$
$271$	469.883			1.73389			0.866943	+	0.498407i	$0.166081\pi$
$272$	−0.0778746			−0.000286304
$273$	144.174	−	167.813i	0.528109	−	0.614698i
$274$	−71.1167			−0.259550
$275$	−17.2551	−	84.7168i	−0.0627459	−	0.308061i
$276$	−18.7516	+	21.8261i	−0.0679405	+	0.0790801i
$277$			149.338i			0.539126i	0.962983	+	0.269563i	$0.0868793\pi$
$277$			149.338i			0.539126i	−0.962983	+	0.269563i	$0.913121\pi$
$278$	−94.0518			−0.338316
$279$	21.1960	+	139.070i	0.0759712	+	0.498457i
$280$	−12.2625	−	121.646i	−0.0437948	−	0.434450i
$281$		−	86.4247i		−	0.307561i	−0.988105	−	0.153781i	$-0.950855\pi$
$281$		−	86.4247i		−	0.307561i	0.988105	−	0.153781i	$-0.0491449\pi$
$282$	192.416	−	223.965i	0.682326	−	0.794201i
$283$		−	223.380i		−	0.789330i	−0.918825	−	0.394665i	$-0.870861\pi$
$283$		−	223.380i		−	0.789330i	0.918825	−	0.394665i	$-0.129139\pi$
$284$			200.617i			0.706397i
$285$	−317.174	+	454.476i	−1.11289	+	1.59465i
$286$	41.7192			0.145871
$287$	272.724			0.950256
$288$	−7.67100	−	50.3305i	−0.0266354	−	0.174759i
$289$	−289.000			−0.999999
$290$	12.5640	+	124.637i	0.0433241	+	0.429781i
$291$	−234.148	−	201.165i	−0.804634	−	0.691290i
$292$			260.818i			0.893213i
$293$	−446.608			−1.52426			−0.762129	−	0.647425i	$-0.775846\pi$
$293$	−446.608			−1.52426			−0.762129	+	0.647425i	$0.775846\pi$
$294$	71.1669	−	82.8354i	0.242064	−	0.281753i
$295$	16.1128	+	159.841i	0.0546197	+	0.541834i
$296$		−	154.455i		−	0.521808i
$297$	49.4816	−	79.1836i	0.166605	−	0.266611i
$298$		−	286.516i		−	0.961464i
$299$			40.9099i			0.136822i
$300$	−73.0750	+	130.996i	−0.243583	+	0.436655i
$301$	428.289			1.42289
$302$	−309.358			−1.02436
$303$	−127.306	−	109.373i	−0.420151	−	0.360967i
$304$	−147.789			−0.486148
$305$	−286.950	+	28.9260i	−0.940819	+	0.0948393i
$306$	0.0373360	+	0.244967i	0.000122013	+	0.000800544i
$307$			117.376i			0.382332i	0.981558	+	0.191166i	$0.0612269\pi$
$307$			117.376i			0.382332i	−0.981558	+	0.191166i	$0.938773\pi$
$308$	59.7950			0.194139
$309$	−54.5341	−	46.8522i	−0.176486	−	0.151625i
$310$	109.968	−	11.0853i	0.354735	−	0.0357591i
$311$		−	370.986i		−	1.19288i	−0.802657	−	0.596441i	$-0.796581\pi$
$311$		−	370.986i		−	1.19288i	0.802657	−	0.596441i	$-0.203419\pi$
$312$	−54.9024	−	47.1686i	−0.175969	−	0.151181i
$313$		−	23.6728i		−	0.0756320i	−0.999285	−	0.0378160i	$-0.987960\pi$
$313$		−	23.6728i		−	0.0756320i	0.999285	−	0.0378160i	$-0.0120401\pi$
$314$			241.240i			0.768281i
$315$	−376.777	+	96.8954i	−1.19612	+	0.307604i
$316$	−285.476			−0.903405
$317$	317.403			1.00127			0.500635	−	0.865658i	$-0.333100\pi$
$317$	317.403			1.00127			0.500635	+	0.865658i	$0.333100\pi$
$318$	126.466	−	147.201i	0.397692	−	0.462898i
$319$	−61.2649			−0.192053
$320$	−39.7983	+	4.01187i	−0.124370	+	0.0125371i
$321$	111.732	−	130.051i	0.348074	−	0.405144i
$322$			58.6350i			0.182096i
$323$	0.719313			0.00222698
$324$	−154.644	+	48.2606i	−0.477298	+	0.148953i
$325$	42.5624	+	208.967i	0.130961	+	0.642975i
$326$			57.1952i			0.175445i
$327$	−61.8188	+	71.9546i	−0.189048	+	0.220045i
$328$		−	89.2256i		−	0.272029i
$329$		−	601.673i		−	1.82879i
$330$	−60.1589	−	41.9843i	−0.182300	−	0.127225i
$331$	133.975			0.404759			0.202379	−	0.979307i	$-0.435133\pi$
$331$	133.975			0.404759			0.202379	+	0.979307i	$0.435133\pi$
$332$	−56.1632			−0.169166
$333$	−485.863	+	74.0516i	−1.45905	+	0.222377i
$334$	−118.453			−0.354648
$335$	18.4036	+	182.566i	0.0549362	+	0.544974i
$336$	−78.6902	−	67.6055i	−0.234197	−	0.201207i
$337$		−	421.306i		−	1.25017i	−0.780558	−	0.625083i	$-0.785065\pi$
$337$		−	421.306i		−	1.25017i	0.780558	−	0.625083i	$-0.214935\pi$
$338$	136.095			0.402649
$339$	−8.54299	+	9.94371i	−0.0252006	+	0.0293325i
$340$	0.193705	−	0.0195264i	0.000569720	−	5.74307e-5i
$341$			54.0546i			0.158518i
$342$	70.8556	+	464.893i	0.207180	+	1.35934i
$343$			201.084i			0.586249i
$344$		−	140.121i		−	0.407329i
$345$	41.1698	−	58.9919i	0.119333	−	0.170991i
$346$	−205.535			−0.594032
$347$	347.450			1.00130			0.500649	−	0.865651i	$-0.333095\pi$
$347$	347.450			1.00130			0.500649	+	0.865651i	$0.333095\pi$
$348$	80.6247	+	69.2675i	0.231680	+	0.199045i
$349$	55.8523			0.160035			0.0800177	−	0.996793i	$-0.474502\pi$
$349$	55.8523			0.160035			0.0800177	+	0.996793i	$0.474502\pi$
$350$	61.0036	+	299.507i	0.174296	+	0.855734i
$351$	−122.054	+	195.318i	−0.347732	+	0.556463i
$352$		−	19.5628i		−	0.0555762i
$353$	7.59096			0.0215041			0.0107521	−	0.999942i	$-0.496577\pi$
$353$	7.59096			0.0215041			0.0107521	+	0.999942i	$0.496577\pi$
$354$	103.398	+	88.8326i	0.292084	+	0.250940i
$355$	−50.3031	−	499.013i	−0.141699	−	1.40567i
$356$		−	296.574i		−	0.833073i
$357$	0.382998	+	0.329047i	0.00107282	+	0.000921700i
$358$		−	113.001i		−	0.315646i
$359$		−	6.62640i		−	0.0184579i	−0.999957	−	0.00922897i	$-0.997062\pi$
$359$		−	6.62640i		−	0.0184579i	0.999957	−	0.00922897i	$-0.00293772\pi$
$360$	31.7008	+	123.268i	0.0880577	+	0.342412i
$361$	1004.10			2.78144
$362$	−113.277			−0.312920
$363$	−213.173	+	248.125i	−0.587253	+	0.683539i
$364$	−147.493			−0.405202
$365$	−65.3981	−	648.758i	−0.179173	−	1.77742i
$366$	−159.474	+	185.622i	−0.435721	+	0.507163i
$367$			509.285i			1.38770i	0.720121	+	0.693848i	$0.244086\pi$
$367$			509.285i			1.38770i	−0.720121	+	0.693848i	$0.755914\pi$
$368$	19.1833			0.0521286
$369$	−280.673	+	42.7781i	−0.760631	+	0.115930i
$370$	38.7284	+	384.191i	0.104671	+	1.03835i
$371$		−	395.451i		−	1.06591i
$372$	61.1153	−	71.1358i	0.164288	−	0.191225i
$373$		−	53.5047i		−	0.143444i	−0.997425	−	0.0717221i	$-0.977151\pi$
$373$		−	53.5047i		−	0.143444i	0.997425	−	0.0717221i	$-0.0228495\pi$
$374$			0.0952154i			0.000254587i
$375$	148.920	−	344.163i	0.397120	−	0.917767i
$376$	−196.846			−0.523527
$377$	151.119			0.400847
$378$	−174.937	+	279.945i	−0.462795	+	0.740594i
$379$	−81.6677			−0.215482			−0.107741	−	0.994179i	$-0.534362\pi$
$379$	−81.6677			−0.215482			−0.107741	+	0.994179i	$0.534362\pi$
$380$	367.610	−	37.0569i	0.967394	−	0.0975183i
$381$	−521.061	−	447.662i	−1.36761	−	1.17497i
$382$			491.705i			1.28719i
$383$	−644.750			−1.68342			−0.841710	−	0.539929i	$-0.818451\pi$
$383$	−644.750			−1.68342			−0.841710	+	0.539929i	$0.818451\pi$
$384$	−22.1181	+	25.7447i	−0.0575993	+	0.0670434i
$385$	−148.734	+	14.9931i	−0.386321	+	0.0389432i
$386$		−	100.593i		−	0.260603i
$387$	−440.772	+	67.1793i	−1.13895	+	0.173590i
$388$			205.797i			0.530405i
$389$			749.628i			1.92706i	0.267591	+	0.963532i	$0.413772\pi$
$389$			749.628i			1.92706i	−0.267591	+	0.963532i	$0.586228\pi$
$390$	148.391	+	103.561i	0.380490	+	0.265540i
$391$	−0.0933683			−0.000238794
$392$	−72.8055			−0.185728
$393$	−143.701	−	123.459i	−0.365652	−	0.314145i
$394$	−111.683			−0.283458
$395$	710.091	−	71.5808i	1.79770	−	0.181217i
$396$	−61.5378	+	9.37914i	−0.155399	+	0.0236847i
$397$		−	523.641i		−	1.31899i	−0.751707	−	0.659497i	$-0.770769\pi$
$397$		−	523.641i		−	1.31899i	0.751707	−	0.659497i	$-0.229231\pi$
$398$	373.871			0.939374
$399$	726.847	+	624.460i	1.82167	+	1.56506i
$400$	97.9881	−	19.9582i	0.244970	−	0.0498955i
$401$			572.668i			1.42810i	0.700095	+	0.714050i	$0.253141\pi$
$401$			572.668i			1.42810i	−0.700095	+	0.714050i	$0.746859\pi$
$402$	118.098	+	101.462i	0.293777	+	0.252394i
$403$		−	133.334i		−	0.330853i
$404$			111.891i			0.276958i
$405$	372.561	−	158.819i	0.919903	−	0.392146i
$406$	216.595			0.533486
$407$	−188.849			−0.464002
$408$	0.107653	−	0.125303i	0.000263854	−	0.000307116i
$409$	−641.298			−1.56797			−0.783983	−	0.620783i	$-0.786815\pi$
$409$	−641.298			−1.56797			−0.783983	+	0.620783i	$0.786815\pi$
$410$	22.3726	+	221.939i	0.0545673	+	0.541315i
$411$	98.3106	−	114.430i	0.239199	−	0.278418i
$412$			47.9310i			0.116337i
$413$	277.774			0.672577
$414$	−9.19720	−	60.3441i	−0.0222155	−	0.145759i
$415$	139.700	−	14.0825i	0.336626	−	0.0339337i
$416$			48.2547i			0.115997i
$417$	130.016	−	151.333i	0.311788	−	0.362909i
$418$			180.698i			0.432292i
$419$			315.449i			0.752862i	0.926445	+	0.376431i	$0.122849\pi$
$419$			315.449i			0.752862i	−0.926445	+	0.376431i	$0.877151\pi$
$420$	212.685	+	148.431i	0.506393	+	0.353406i
$421$	−418.127			−0.993176			−0.496588	−	0.867986i	$-0.665414\pi$
$421$	−418.127			−0.993176			−0.496588	+	0.867986i	$0.665414\pi$
$422$	301.898			0.715398
$423$	94.3755	+	619.210i	0.223110	+	1.46385i
$424$	−129.378			−0.305136
$425$	−0.476924	+	0.0971399i	−0.00112217	+	0.000228564i
$426$	−322.801	−	277.329i	−0.757748	−	0.651008i
$427$			498.666i			1.16784i
$428$	−114.304			−0.267066
$429$	−57.6719	+	67.1278i	−0.134433	+	0.156475i
$430$	35.1342	+	348.536i	0.0817075	+	0.810549i
$431$		−	734.406i		−	1.70396i	−0.523576	−	0.851979i	$-0.675402\pi$
$431$		−	734.406i		−	1.70396i	0.523576	−	0.851979i	$-0.324598\pi$
$432$	91.5881	+	57.2331i	0.212009	+	0.132484i
$433$		−	231.531i		−	0.534713i	−0.963598	−	0.267356i	$-0.913850\pi$
$433$		−	231.531i		−	0.534713i	0.963598	−	0.267356i	$-0.0861501\pi$
$434$		−	191.104i		−	0.440331i
$435$	−217.914	−	152.080i	−0.500951	−	0.349608i
$436$	63.2421			0.145051
$437$	−177.193			−0.405476
$438$	−419.667	−	360.551i	−0.958144	−	0.823176i
$439$	−375.664			−0.855726			−0.427863	−	0.903844i	$-0.640733\pi$
$439$	−375.664			−0.855726			−0.427863	+	0.903844i	$0.640733\pi$
$440$	4.90522	+	48.6604i	0.0111482	+	0.110592i
$441$	34.9057	+	229.021i	0.0791512	+	0.519322i
$442$		−	0.234863i		−	0.000531365i
$443$	321.303			0.725288			0.362644	−	0.931928i	$-0.381874\pi$
$443$	321.303			0.725288			0.362644	+	0.931928i	$0.381874\pi$
$444$	248.525	+	213.517i	0.559741	+	0.480893i
$445$	74.3636	+	737.696i	0.167109	+	1.65774i
$446$		−	131.762i		−	0.295430i
$447$	461.017	+	396.076i	1.03136	+	0.886075i
$448$			69.1621i			0.154380i
$449$		−	539.452i		−	1.20145i	−0.799455	−	0.600726i	$-0.794878\pi$
$449$		−	539.452i		−	1.20145i	0.799455	−	0.600726i	$-0.205122\pi$
$450$	−109.761	−	298.668i	−0.243913	−	0.663707i
$451$	−109.094			−0.241893
$452$	8.73969			0.0193356
$453$	427.652	−	497.770i	0.944043	−	1.09883i
$454$	181.773			0.400382
$455$	366.874	−	36.9828i	0.806317	−	0.0812809i
$456$	204.301	−	237.799i	0.448029	−	0.521488i
$457$		−	821.320i		−	1.79720i	−0.438770	−	0.898599i	$-0.644586\pi$
$457$		−	821.320i		−	1.79720i	0.438770	−	0.898599i	$-0.355414\pi$
$458$	−249.151			−0.543997
$459$	−0.445774	−	0.278563i	−0.000971185	−	0.000606890i
$460$	−47.7165	+	4.81007i	−0.103731	+	0.0104567i
$461$		−	289.499i		−	0.627980i	−0.949426	−	0.313990i	$-0.898334\pi$
$461$		−	289.499i		−	0.627980i	0.949426	−	0.313990i	$-0.101666\pi$
$462$	−82.6596	+	96.2126i	−0.178917	+	0.208252i
$463$			155.610i			0.336091i	0.985779	+	0.168045i	$0.0537455\pi$
$463$			155.610i			0.336091i	−0.985779	+	0.168045i	$0.946254\pi$
$464$		−	70.8624i		−	0.152721i
$465$	−134.181	+	192.267i	−0.288561	+	0.413477i
$466$	−318.356			−0.683168
$467$	−674.677			−1.44470			−0.722352	−	0.691525i	$-0.756939\pi$
$467$	−674.677			−1.44470			−0.722352	+	0.691525i	$0.756939\pi$
$468$	151.792	−	23.1351i	0.324343	−	0.0494340i
$469$	317.267			0.676475
$470$	489.634	−	49.3576i	1.04177	−	0.105016i
$471$	−388.165	−	333.487i	−0.824130	−	0.708039i
$472$		−	90.8780i		−	0.192538i
$473$	−171.323			−0.362204
$474$	394.638	−	459.343i	0.832569	−	0.969077i
$475$	−905.098	+	184.350i	−1.90547	+	0.388106i
$476$		−	0.336623i		−	0.000707192i
$477$	62.0286	+	406.978i	0.130039	+	0.853203i
$478$			339.630i			0.710522i
$479$		−	442.952i		−	0.924743i	−0.886686	−	0.462372i	$-0.846999\pi$
$479$		−	442.952i		−	0.924743i	0.886686	−	0.462372i	$-0.153001\pi$
$480$	48.5613	−	69.5831i	0.101169	−	0.144965i
$481$	465.824			0.968449
$482$	−113.970			−0.236452
$483$	−94.3462	−	81.0562i	−0.195334	−	0.167818i
$484$	218.081			0.450581
$485$	−51.6020	−	511.898i	−0.106396	−	1.05546i
$486$	136.125	−	315.544i	0.280092	−	0.649268i
$487$			98.6922i			0.202653i	0.994853	+	0.101327i	$0.0323087\pi$
$487$			98.6922i			0.202653i	−0.994853	+	0.101327i	$0.967691\pi$
$488$	163.146			0.334315
$489$	−92.0294	−	79.0657i	−0.188199	−	0.161689i
$490$	181.096	−	18.2554i	0.369583	−	0.0372559i
$491$			816.906i			1.66376i	0.554956	+	0.831880i	$0.312735\pi$
$491$			816.906i			1.66376i	−0.554956	+	0.831880i	$0.687265\pi$
$492$	143.568	+	123.344i	0.291804	+	0.250699i
$493$			0.344899i			0.000699592i
$494$		−	445.719i		−	0.902266i
$495$	150.717	−	38.7598i	0.304479	−	0.0783025i
$496$	−62.5225			−0.126053
$497$	−867.192			−1.74485
$498$	77.6391	−	90.3688i	0.155902	−	0.181464i
$499$	−658.367			−1.31937			−0.659686	−	0.751541i	$-0.729311\pi$
$499$	−658.367			−1.31937			−0.659686	+	0.751541i	$0.729311\pi$
$500$	−238.731	+	74.2137i	−0.477461	+	0.148427i
$501$	163.747	−	190.595i	0.326840	−	0.380429i
$502$		−	32.4557i		−	0.0646528i
$503$	577.585			1.14828			0.574140	−	0.818757i	$-0.305336\pi$
$503$	577.585			1.14828			0.574140	+	0.818757i	$0.305336\pi$
$504$	217.560	−	33.1589i	0.431667	−	0.0657915i
$505$	−28.0558	−	278.318i	−0.0555561	−	0.551124i
$506$		−	23.4550i		−	0.0463537i
$507$	−188.136	+	218.983i	−0.371077	+	0.431919i
$508$			457.970i			0.901515i
$509$			12.2945i			0.0241543i	0.999927	+	0.0120771i	$0.00384436\pi$
$509$			12.2945i			0.0241543i	−0.999927	+	0.0120771i	$0.996156\pi$
$510$	−0.236356	+	0.338672i	−0.000463442	+	0.000664063i
$511$	−1127.42			−2.20630
$512$	22.6274			0.0441942
$513$	−845.982	−	528.652i	−1.64909	−	1.03051i
$514$	−583.693			−1.13559
$515$	−12.0183	−	119.223i	−0.0233365	−	0.231501i
$516$	225.461	+	193.701i	0.436939	+	0.375390i
$517$			240.679i			0.465530i
$518$	667.653			1.28891
$519$	284.129	−	330.715i	0.547454	−	0.637215i
$520$	−12.0995	−	120.028i	−0.0232682	−	0.230824i
$521$			544.215i			1.04456i	0.852774	+	0.522279i	$0.174918\pi$
$521$			544.215i			1.04456i	−0.852774	+	0.522279i	$0.825082\pi$
$522$	−222.909	+	33.9741i	−0.427028	+	0.0650844i
$523$			355.011i			0.678798i	0.940643	+	0.339399i	$0.110224\pi$
$523$			355.011i			0.678798i	−0.940643	+	0.339399i	$0.889776\pi$
$524$			126.301i			0.241033i
$525$	−566.249	−	315.876i	−1.07857	−	0.601669i
$526$	−462.682			−0.879623
$527$	0.304307			0.000577432
$528$	31.4774	+	27.0433i	0.0596162	+	0.0512184i
$529$	23.0000			0.0434783
$530$	321.814	−	32.4405i	0.607196	−	0.0612084i
$531$	−285.871	+	43.5703i	−0.538363	+	0.0820533i
$532$		−	638.838i		−	1.20082i
$533$	269.097			0.504872
$534$	477.200	+	409.979i	0.893632	+	0.767751i
$535$	284.320	−	28.6609i	0.531439	−	0.0535718i
$536$		−	103.798i		−	0.193654i
$537$	181.824	+	156.211i	0.338592	+	0.290896i
$538$		−	166.838i		−	0.310108i
$539$			89.0175i			0.165153i
$540$	−242.166	−	119.396i	−0.448456	−	0.221104i
$541$	289.494			0.535108			0.267554	−	0.963543i	$-0.413785\pi$
$541$	289.494			0.535108			0.267554	+	0.963543i	$0.413785\pi$
$542$	664.515			1.22604
$543$	156.592	−	182.267i	0.288383	−	0.335667i
$544$	−0.110131			−0.000202447
$545$	−157.308	+	15.8575i	−0.288639	+	0.0290963i
$546$	203.893	−	237.323i	0.373430	−	0.434657i
$547$		−	673.608i		−	1.23146i	−0.787957	−	0.615730i	$-0.788861\pi$
$547$		−	673.608i		−	1.23146i	0.787957	−	0.615730i	$-0.211139\pi$
$548$	−100.574			−0.183530
$549$	−78.2183	−	513.201i	−0.142474	−	0.934792i
$550$	−24.4024	−	119.808i	−0.0443681	−	0.217832i
$551$			654.543i			1.18792i
$552$	−26.5187	+	30.8668i	−0.0480412	+	0.0559180i
$553$		−	1234.01i		−	2.23148i
$554$			211.196i			0.381220i
$555$	−671.717	−	468.784i	−1.21030	−	0.844656i
$556$	−133.009			−0.239225
$557$	−265.811			−0.477220			−0.238610	−	0.971115i	$-0.576692\pi$
$557$	−265.811			−0.477220			−0.238610	+	0.971115i	$0.576692\pi$
$558$	29.9756	+	196.674i	0.0537197	+	0.352462i
$559$	422.593			0.755981
$560$	−17.3419	−	172.033i	−0.0309676	−	0.307203i
$561$	−0.153205	−	0.131624i	−0.000273093	−	0.000234624i
$562$		−	122.223i		−	0.217479i
$563$	234.857			0.417152			0.208576	−	0.978006i	$-0.433117\pi$
$563$	234.857			0.417152			0.208576	+	0.978006i	$0.433117\pi$
$564$	272.117	−	316.734i	0.482477	−	0.561585i
$565$	−21.7391	+	2.19141i	−0.0384762	+	0.00387860i
$566$		−	315.908i		−	0.558141i
$567$	−208.613	−	668.471i	−0.367924	−	1.17896i
$568$			283.715i			0.499498i
$569$			71.9504i			0.126451i	0.997999	+	0.0632253i	$0.0201387\pi$
$569$			71.9504i			0.126451i	−0.997999	+	0.0632253i	$0.979861\pi$
$570$	−448.552	+	642.726i	−0.786933	+	1.12759i
$571$	−121.228			−0.212308			−0.106154	−	0.994350i	$-0.533854\pi$
$571$	−121.228			−0.212308			−0.106154	+	0.994350i	$0.533854\pi$
$572$	58.9998			0.103146
$573$	−791.173	−	679.725i	−1.38076	−	1.18626i
$574$	385.689			0.671933
$575$	117.484	−	23.9291i	0.204319	−	0.0416158i
$576$	−10.8484	−	71.1780i	−0.0188341	−	0.123573i
$577$			74.5471i			0.129198i	0.997911	+	0.0645989i	$0.0205768\pi$
$577$			74.5471i			0.129198i	−0.997911	+	0.0645989i	$0.979423\pi$
$578$	−408.707			−0.707106
$579$	161.858	+	139.058i	0.279548	+	0.240169i
$580$	17.7682	+	176.263i	0.0306348	+	0.303901i
$581$		−	242.773i		−	0.417853i
$582$	−331.136	−	284.491i	−0.568962	−	0.488816i
$583$			158.187i			0.271333i
$584$			368.853i			0.631597i
$585$	−371.767	+	95.6068i	−0.635499	+	0.163430i
$586$	−631.599			−1.07781
$587$	−270.303			−0.460482			−0.230241	−	0.973134i	$-0.573951\pi$
$587$	−270.303			−0.460482			−0.230241	+	0.973134i	$0.573951\pi$
$588$	100.645	−	117.147i	0.171165	−	0.199230i
$589$	577.508			0.980490
$590$	22.7869	+	226.049i	0.0386219	+	0.383135i
$591$	154.388	−	179.702i	0.261232	−	0.304064i
$592$		−	218.433i		−	0.368974i
$593$	−79.9886			−0.134888			−0.0674440	−	0.997723i	$-0.521484\pi$
$593$	−79.9886			−0.134888			−0.0674440	+	0.997723i	$0.521484\pi$
$594$	69.9775	−	111.982i	0.117807	−	0.188523i
$595$	0.0844056	+	0.837315i	0.000141858	+	0.00140725i
$596$		−	405.195i		−	0.679858i
$597$	−516.833	+	601.573i	−0.865717	+	1.00766i
$598$			57.8553i			0.0967480i
$599$			865.493i			1.44490i	0.691425	+	0.722448i	$0.256983\pi$
$599$			865.493i			1.44490i	−0.691425	+	0.722448i	$0.743017\pi$
$600$	−103.344	+	185.257i	−0.172239	+	0.308761i
$601$	−99.7983			−0.166054			−0.0830269	−	0.996547i	$-0.526459\pi$
$601$	−99.7983			−0.166054			−0.0830269	+	0.996547i	$0.526459\pi$
$602$	605.692			1.00613
$603$	−326.514	+	49.7649i	−0.541483	+	0.0825288i
$604$	−437.498			−0.724335
$605$	−542.453	+	54.6821i	−0.896617	+	0.0903836i
$606$	−180.038	−	154.677i	−0.297092	−	0.255242i
$607$			100.195i			0.165066i	0.996588	+	0.0825328i	$0.0263009\pi$
$607$			100.195i			0.165066i	−0.996588	+	0.0825328i	$0.973699\pi$
$608$	−209.005			−0.343759
$609$	−299.418	+	348.511i	−0.491655	+	0.572267i
$610$	−405.808	+	40.9075i	−0.665259	+	0.0670615i
$611$		−	593.672i		−	0.971640i
$612$	0.0528011	+	0.346435i	8.62763e−5	+	0.000566070i
$613$		−	1046.00i		−	1.70637i	−0.521612	−	0.853183i	$-0.674669\pi$
$613$		−	1046.00i		−	1.70637i	0.521612	−	0.853183i	$-0.325331\pi$
$614$			165.995i			0.270350i
$615$	−388.037	−	270.807i	−0.630954	−	0.440336i
$616$	84.5628			0.137277
$617$	555.615			0.900511			0.450255	−	0.892900i	$-0.351333\pi$
$617$	555.615			0.900511			0.450255	+	0.892900i	$0.351333\pi$
$618$	−77.1229	−	66.2590i	−0.124794	−	0.107215i
$619$	−156.807			−0.253323			−0.126661	−	0.991946i	$-0.540426\pi$
$619$	−156.807			−0.253323			−0.126661	+	0.991946i	$0.540426\pi$
$620$	155.518	−	15.6770i	0.250835	−	0.0252855i
$621$	109.810	+	68.6201i	0.176828	+	0.110499i
$622$		−	524.653i		−	0.843494i
$623$	1281.98			2.05775
$624$	−77.6437	−	66.7065i	−0.124429	−	0.106901i
$625$	575.209	−	244.459i	0.920334	−	0.391134i
$626$		−	33.4784i		−	0.0534799i
$627$	−290.751	−	249.794i	−0.463717	−	0.398396i
$628$			341.165i			0.543256i
$629$			1.06315i			0.00169022i
$630$	−532.843	+	137.031i	−0.845783	+	0.217509i
$631$	539.810			0.855483			0.427741	−	0.903901i	$-0.359309\pi$
$631$	539.810			0.855483			0.427741	+	0.903901i	$0.359309\pi$
$632$	−403.724			−0.638804
$633$	−417.339	+	485.767i	−0.659304	+	0.767404i
$634$	448.875			0.708005
$635$	−114.832	−	1139.15i	−0.180838	−	1.79394i
$636$	178.850	−	208.174i	0.281211	−	0.327318i
$637$		−	219.575i		−	0.344702i
$638$	−86.6417			−0.135802
$639$	892.469	−	136.024i	1.39666	−	0.212869i
$640$	−56.2833	+	5.67365i	−0.0879427	+	0.00886507i
$641$			474.949i			0.740950i	0.928842	+	0.370475i	$0.120805\pi$
$641$			474.949i			0.740950i	−0.928842	+	0.370475i	$0.879195\pi$
$642$	158.013	−	183.920i	0.246125	−	0.286480i
$643$		−	999.589i		−	1.55457i	−0.629149	−	0.777285i	$-0.716596\pi$
$643$		−	999.589i		−	1.55457i	0.629149	−	0.777285i	$-0.283404\pi$
$644$			82.9225i			0.128762i
$645$	−609.378	−	425.279i	−0.944772	−	0.659347i
$646$	1.01726			0.00157471
$647$	1042.01			1.61052			0.805262	−	0.592919i	$-0.202025\pi$
$647$	1042.01			1.61052			0.805262	+	0.592919i	$0.202025\pi$
$648$	−218.700	+	68.2508i	−0.337500	+	0.105325i
$649$	−111.114			−0.171209
$650$	60.1923	+	295.524i	0.0926036	+	0.454652i
$651$	307.494	+	264.179i	0.472341	+	0.405805i
$652$			80.8862i			0.124059i
$653$	554.768			0.849568			0.424784	−	0.905295i	$-0.360350\pi$
$653$	554.768			0.849568			0.424784	+	0.905295i	$0.360350\pi$
$654$	−87.4249	+	101.759i	−0.133677	+	0.155595i
$655$	−31.6691	−	314.162i	−0.0483498	−	0.479636i
$656$		−	126.184i		−	0.192354i
$657$	1160.28	−	176.842i	1.76603	−	0.269166i
$658$		−	850.894i		−	1.29315i
$659$		−	1132.00i		−	1.71775i	−0.512186	−	0.858875i	$-0.671164\pi$
$659$		−	1132.00i		−	1.71775i	0.512186	−	0.858875i	$-0.328836\pi$
$660$	−85.0775	−	59.3747i	−0.128905	−	0.0899617i
$661$	761.422			1.15192			0.575962	−	0.817476i	$-0.304628\pi$
$661$	761.422			1.15192			0.575962	+	0.817476i	$0.304628\pi$
$662$	189.469			0.286208
$663$	0.377905	+	0.324671i	0.000569992	+	0.000489700i
$664$	−79.4267			−0.119619
$665$	160.184	+	1589.04i	0.240878	+	2.38954i
$666$	−687.114	+	104.725i	−1.03170	+	0.157245i
$667$		−	84.9610i		−	0.127378i
$668$	−167.517			−0.250774
$669$	212.010	+	182.145i	0.316906	+	0.272265i
$670$	26.0266	+	258.188i	0.0388457	+	0.385355i
$671$		−	199.475i		−	0.297279i
$672$	−111.285	−	95.6086i	−0.165602	−	0.142275i
$673$			507.194i			0.753631i	0.926288	+	0.376816i	$0.122981\pi$
$673$			507.194i			0.753631i	−0.926288	+	0.376816i	$0.877019\pi$
$674$		−	595.816i		−	0.884001i
$675$	632.301	+	236.264i	0.936742	+	0.350021i
$676$	192.468			0.284716
$677$	34.2348			0.0505684			0.0252842	−	0.999680i	$-0.491951\pi$
$677$	34.2348			0.0505684			0.0252842	+	0.999680i	$0.491951\pi$
$678$	−12.0816	+	14.0625i	−0.0178195	+	0.0207412i
$679$	−889.585			−1.31014
$680$	0.273940	−	0.0276145i	0.000402853	−	4.06096e-5i
$681$	−251.281	+	292.481i	−0.368988	+	0.429487i
$682$			76.4447i			0.112089i
$683$	−1014.79			−1.48578			−0.742891	−	0.669413i	$-0.766546\pi$
$683$	−1014.79			−1.48578			−0.742891	+	0.669413i	$0.766546\pi$
$684$	100.205	+	657.458i	0.146498	+	0.961196i
$685$	250.168	−	25.2182i	0.365208	−	0.0368149i
$686$			284.375i			0.414541i
$687$	344.422	−	400.894i	0.501342	−	0.583542i
$688$		−	198.161i		−	0.288025i
$689$		−	390.193i		−	0.566317i
$690$	58.2229	−	83.4272i	0.0843811	−	0.120909i
$691$	646.662			0.935835			0.467917	−	0.883772i	$-0.345004\pi$
$691$	646.662			0.935835			0.467917	+	0.883772i	$0.345004\pi$
$692$	−290.671			−0.420044
$693$	−40.5426	−	266.005i	−0.0585030	−	0.383846i
$694$	491.369			0.708024
$695$	330.847	−	33.3510i	0.476038	−	0.0479871i
$696$	114.020	+	97.9590i	0.163823	+	0.140746i
$697$			0.614158i			0.000881145i
$698$	78.9871			0.113162
$699$	440.091	−	512.249i	0.629601	−	0.732831i
$700$	86.2720	+	423.567i	0.123246	+	0.605095i
$701$			1136.36i			1.62105i	0.585701	+	0.810527i	$0.300819\pi$
$701$			1136.36i			1.62105i	−0.585701	+	0.810527i	$0.699181\pi$
$702$	−172.610	+	276.222i	−0.245883	+	0.393478i
$703$			2017.62i			2.87002i
$704$		−	27.6660i		−	0.0392983i
$705$	−597.444	+	856.073i	−0.847439	+	1.21429i
$706$	10.7352			0.0152057
$707$	−483.665			−0.684108
$708$	146.226	+	125.628i	0.206535	+	0.177441i
$709$	−674.376			−0.951164			−0.475582	−	0.879671i	$-0.657763\pi$
$709$	−674.376			−0.951164			−0.475582	+	0.879671i	$0.657763\pi$
$710$	−71.1393	−	705.711i	−0.100196	−	0.993959i
$711$	193.560	+	1269.98i	0.272237	+	1.78618i
$712$		−	419.419i		−	0.589072i
$713$	−74.9618			−0.105136
$714$	0.541641	+	0.465343i	0.000758600	+	0.000651740i
$715$	−146.756	+	14.7937i	−0.205253	+	0.0206905i
$716$		−	159.808i		−	0.223196i
$717$	−546.478	−	469.499i	−0.762173	−	0.654810i
$718$		−	9.37115i		−	0.0130517i
$719$			104.843i			0.145818i	0.997339	+	0.0729091i	$0.0232283\pi$
$719$			104.843i			0.145818i	−0.997339	+	0.0729091i	$0.976772\pi$
$720$	44.8316	+	174.328i	0.0622662	+	0.242122i
$721$	−207.188			−0.287362
$722$	1420.01			1.96678
$723$	157.550	−	183.383i	0.217912	−	0.253641i
$724$	−160.198			−0.221268
$725$	−88.3929	−	433.979i	−0.121921	−	0.598592i
$726$	−301.472	+	350.901i	−0.415250	+	0.483335i
$727$			309.330i			0.425489i	0.977108	+	0.212744i	$0.0682402\pi$
$727$			309.330i			0.425489i	−0.977108	+	0.212744i	$0.931760\pi$
$728$	−208.587			−0.286521
$729$	319.547	+	655.234i	0.438336	+	0.898811i
$730$	−92.4869	−	917.482i	−0.126694	−	1.25682i
$731$			0.964482i			0.00131940i
$732$	−225.530	+	262.508i	−0.308102	+	0.358618i
$733$		−	176.441i		−	0.240711i	−0.992731	−	0.120356i	$-0.961597\pi$
$733$		−	176.441i		−	0.240711i	0.992731	−	0.120356i	$-0.0384035\pi$
$734$			720.237i			0.981250i
$735$	−220.970	+	316.627i	−0.300640	+	0.430785i
$736$	27.1293			0.0368605
$737$	−126.912			−0.172201
$738$	−396.931	+	60.4973i	−0.537847	+	0.0819747i
$739$	−304.308			−0.411783			−0.205892	−	0.978575i	$-0.566009\pi$
$739$	−304.308			−0.411783			−0.205892	+	0.978575i	$0.566009\pi$
$740$	54.7703	+	543.328i	0.0740139	+	0.734227i
$741$	717.181	+	616.156i	0.967855	+	0.831519i
$742$		−	559.253i		−	0.753710i
$743$	−108.852			−0.146504			−0.0732519	−	0.997313i	$-0.523338\pi$
$743$	−108.852			−0.146504			−0.0732519	+	0.997313i	$0.523338\pi$
$744$	86.4301	−	100.601i	0.116169	−	0.135217i
$745$	101.599	+	1007.88i	0.136375	+	1.35286i
$746$		−	75.6670i		−	0.101430i
$747$	38.0801	+	249.849i	0.0509774	+	0.334470i
$748$			0.134655i			0.000180020i
$749$		−	494.096i		−	0.659674i
$750$	210.605	−	486.719i	0.280806	−	0.648959i
$751$	−125.886			−0.167624			−0.0838121	−	0.996482i	$-0.526710\pi$
$751$	−125.886			−0.167624			−0.0838121	+	0.996482i	$0.526710\pi$
$752$	−278.383			−0.370190
$753$	52.2226	+	44.8663i	0.0693527	+	0.0595834i
$754$	213.715			0.283442
$755$	1088.23	−	109.699i	1.44137	−	0.145297i
$756$	−247.398	+	395.902i	−0.327246	+	0.523679i
$757$			711.339i			0.939682i	0.882751	+	0.469841i	$0.155689\pi$
$757$			711.339i			0.939682i	−0.882751	+	0.469841i	$0.844311\pi$
$758$	−115.496			−0.152369
$759$	37.7400	+	32.4238i	0.0497234	+	0.0427191i
$760$	519.879	−	52.4064i	0.684051	−	0.0689558i
$761$			1304.52i			1.71421i	0.515140	+	0.857106i	$0.327740\pi$
$761$			1304.52i			1.71421i	−0.515140	+	0.857106i	$0.672260\pi$
$762$	−736.892	−	633.090i	−0.967050	−	0.830827i
$763$			273.372i			0.358286i
$764$			695.376i			0.910177i
$765$	−0.218203	−	0.848481i	−0.000285233	−	0.00110913i
$766$	−911.814			−1.19036
$767$	274.080			0.357341
$768$	−31.2798	+	36.4084i	−0.0407289	+	0.0474068i
$769$	718.227			0.933976			0.466988	−	0.884264i	$-0.345339\pi$
$769$	718.227			0.933976			0.466988	+	0.884264i	$0.345339\pi$
$770$	−210.341	+	21.2035i	−0.273170	+	0.0275370i
$771$	806.888	−	939.186i	1.04655	−	1.21814i
$772$		−	142.260i		−	0.184274i
$773$	1410.80			1.82510			0.912552	−	0.408962i	$-0.134109\pi$
$773$	1410.80			1.82510			0.912552	+	0.408962i	$0.134109\pi$
$774$	−623.346	+	95.0058i	−0.805357	+	0.122747i
$775$	−382.904	+	77.9898i	−0.494069	+	0.100632i
$776$			291.041i			0.375053i
$777$	−922.954	+	1074.28i	−1.18784	+	1.38260i
$778$			1060.13i			1.36264i
$779$			1165.54i			1.49620i
$780$	209.857	+	146.457i	0.269047	+	0.187765i
$781$	346.891			0.444163
$782$	−0.132043			−0.000168853
$783$	253.480	−	405.634i	0.323729	−	0.518051i
$784$	−102.962			−0.131330
$785$	−85.5444	−	848.612i	−0.108974	−	1.08103i
$786$	−203.224	−	174.597i	−0.258555	−	0.222134i
$787$			815.494i			1.03621i	0.855318	+	0.518103i	$0.173362\pi$
$787$			815.494i			1.03621i	−0.855318	+	0.518103i	$0.826638\pi$
$788$	−157.943			−0.200435
$789$	639.604	−	744.474i	0.810652	−	0.943567i
$790$	1004.22	−	101.231i	1.27117	−	0.128140i
$791$			37.7785i			0.0477604i
$792$	−87.0276	+	13.2641i	−0.109883	+	0.0167476i
$793$			492.034i			0.620472i
$794$		−	740.540i		−	0.932669i
$795$	−392.672	+	562.657i	−0.493927	+	0.707744i
$796$	528.733			0.664237
$797$	−561.711			−0.704781			−0.352391	−	0.935853i	$-0.614631\pi$
$797$	−561.711			−0.704781			−0.352391	+	0.935853i	$0.614631\pi$
$798$	1027.92	+	883.120i	1.28812	+	1.10667i
$799$	1.35493			0.00169579
$800$	138.576	−	28.2252i	0.173220	−	0.0352815i
$801$	−1319.35	+	201.085i	−1.64712	+	0.251043i
$802$			809.874i			1.00982i
$803$	450.987			0.561628
$804$	167.016	+	143.489i	0.207731	+	0.178469i
$805$	−20.7922	−	206.261i	−0.0258288	−	0.256225i
$806$		−	188.562i		−	0.233948i
$807$	268.450	+	230.635i	0.332651	+	0.285793i
$808$			158.238i			0.195839i
$809$			439.521i			0.543289i	0.962398	+	0.271645i	$0.0875675\pi$
$809$			439.521i			0.543289i	−0.962398	+	0.271645i	$0.912433\pi$
$810$	526.880	−	224.604i	0.650470	−	0.277289i
$811$	278.570			0.343490			0.171745	−	0.985141i	$-0.445060\pi$
$811$	278.570			0.343490			0.171745	+	0.985141i	$0.445060\pi$
$812$	306.312			0.377232
$813$	−918.616	+	1069.23i	−1.12991	+	1.31517i
$814$	−267.072			−0.328099
$815$	−20.2816	−	201.196i	−0.0248854	−	0.246866i
$816$	0.152244	−	0.177206i	0.000186573	−	0.000217164i
$817$			1830.38i			2.24036i
$818$	−906.932			−1.10872
$819$	100.004	+	656.143i	0.122106	+	0.801151i
$820$	31.6396	+	313.869i	0.0385849	+	0.382767i
$821$		−	631.571i		−	0.769271i	−0.923069	−	0.384635i	$-0.874327\pi$
$821$		−	631.571i		−	0.769271i	0.923069	−	0.384635i	$-0.125673\pi$
$822$	139.032	−	161.828i	0.169139	−	0.196871i
$823$			473.500i			0.575334i	0.957730	+	0.287667i	$0.0928797\pi$
$823$			473.500i			0.575334i	−0.957730	+	0.287667i	$0.907120\pi$
$824$			67.7846i			0.0822629i
$825$	226.509	+	126.356i	0.274556	+	0.153158i
$826$	392.832			0.475584
$827$	−665.814			−0.805096			−0.402548	−	0.915399i	$-0.631875\pi$
$827$	−665.814			−0.805096			−0.402548	+	0.915399i	$0.631875\pi$
$828$	−13.0068	−	85.3395i	−0.0157087	−	0.103067i
$829$	871.132			1.05082			0.525411	−	0.850849i	$-0.323912\pi$
$829$	871.132			1.05082			0.525411	+	0.850849i	$0.323912\pi$
$830$	197.565	−	19.9156i	0.238031	−	0.0239947i
$831$	−339.823	−	291.954i	−0.408932	−	0.351328i
$832$			68.2424i			0.0820221i
$833$	0.501135			0.000601603
$834$	183.870	−	214.017i	0.220468	−	0.256616i
$835$	416.681	−	42.0036i	0.499020	−	0.0503037i
$836$			255.546i			0.305677i
$837$	−357.894	−	223.647i	−0.427592	−	0.267201i
$838$			446.113i			0.532354i
$839$			101.589i			0.121083i	0.998166	+	0.0605417i	$0.0192828\pi$
$839$			101.589i			0.121083i	−0.998166	+	0.0605417i	$0.980717\pi$
$840$	300.782	+	209.913i	0.358074	+	0.249896i
$841$	527.158			0.626822
$842$	−591.321			−0.702282
$843$	196.662	+	168.959i	0.233288	+	0.200426i
$844$	426.948			0.505863
$845$	−478.744	+	48.2598i	−0.566561	+	0.0571122i
$846$	133.467	+	875.696i	0.157762	+	1.03510i
$847$			942.684i			1.11297i
$848$	−182.968			−0.215764
$849$	508.308	+	436.706i	0.598714	+	0.514377i
$850$	−0.674472	+	0.137377i	−0.000793497	+	0.000161619i
$851$		−	261.892i		−	0.307746i
$852$	−456.509	−	392.203i	−0.535809	−	0.460332i
$853$		−	1081.50i		−	1.26788i	−0.773381	−	0.633942i	$-0.781436\pi$
$853$		−	1081.50i		−	1.26788i	0.773381	−	0.633942i	$-0.218564\pi$
$854$			705.220i			0.825784i
$855$	−414.102	−	1610.23i	−0.484329	−	1.88331i
$856$	−161.651			−0.188844
$857$	35.9893			0.0419945			0.0209973	−	0.999780i	$-0.493316\pi$
$857$	35.9893			0.0419945			0.0209973	+	0.999780i	$0.493316\pi$
$858$	−81.5604	+	94.9331i	−0.0950587	+	0.110645i
$859$	−1178.88			−1.37238			−0.686191	−	0.727422i	$-0.740718\pi$
$859$	−1178.88			−1.37238			−0.686191	+	0.727422i	$0.740718\pi$
$860$	49.6873	+	492.905i	0.0577760	+	0.573145i
$861$	−533.171	+	620.590i	−0.619246	+	0.720778i
$862$		−	1038.61i		−	1.20488i
$863$	1595.97			1.84932			0.924662	−	0.380790i	$-0.124348\pi$
$863$	1595.97			1.84932			0.924662	+	0.380790i	$0.124348\pi$
$864$	129.525	+	80.9398i	0.149913	+	0.0936803i
$865$	723.012	−	72.8834i	0.835852	−	0.0842582i
$866$		−	327.434i		−	0.378099i
$867$	564.990	−	657.627i	0.651661	−	0.758508i
$868$		−	270.262i		−	0.311361i
$869$			493.624i			0.568036i
$870$	−308.176	−	215.073i	−0.354226	−	0.247210i
$871$	313.048			0.359412
$872$	89.4379			0.102566
$873$	915.514	−	139.536i	1.04870	−	0.159835i
$874$	−250.589			−0.286715
$875$	−320.799	−	1031.94i	−0.366627	−	1.17937i
$876$	−593.499	−	509.896i	−0.677510	−	0.582073i
$877$		−	147.243i		−	0.167894i	−0.996470	−	0.0839472i	$-0.973247\pi$
$877$		−	147.243i		−	0.167894i	0.996470	−	0.0839472i	$-0.0267527\pi$
$878$	−531.268			−0.605089
$879$	873.112	−	1016.27i	0.993301	−	1.15616i
$880$	6.93703	+	68.8162i	0.00788299	+	0.0782003i
$881$			746.933i			0.847824i	0.905703	+	0.423912i	$0.139343\pi$
$881$			746.933i			0.847824i	−0.905703	+	0.423912i	$0.860657\pi$
$882$	49.3641	+	323.884i	0.0559683	+	0.367216i
$883$			1333.87i			1.51061i	0.655375	+	0.755303i	$0.272511\pi$
$883$			1333.87i			1.51061i	−0.655375	+	0.755303i	$0.727489\pi$
$884$		−	0.332147i		−	0.000375732i
$885$	−395.223	−	275.822i	−0.446580	−	0.311663i
$886$	454.391			0.512856
$887$	839.382			0.946315			0.473158	−	0.880978i	$-0.343114\pi$
$887$	839.382			0.946315			0.473158	+	0.880978i	$0.343114\pi$
$888$	351.467	+	301.958i	0.395797	+	0.340043i
$889$	−1979.63			−2.22681
$890$	105.166	+	1043.26i	0.118164	+	1.17220i
$891$	83.4486	+	267.400i	0.0936573	+	0.300112i
$892$		−	186.339i		−	0.208900i
$893$	2571.37			2.87947
$894$	651.976	+	560.136i	0.729279	+	0.626550i
$895$	40.0706	+	397.506i	0.0447717	+	0.444141i
$896$			97.8100i			0.109163i
$897$	−93.0916	−	79.9783i	−0.103781	−	0.0891619i
$898$		−	762.900i		−	0.849555i
$899$			276.906i			0.308015i
$900$	−155.225	−	422.380i	−0.172472	−	0.469311i
$901$	0.890534			0.000988384
$902$	−154.282			−0.171044
$903$	−837.299	+	974.583i	−0.927241	+	1.07927i
$904$	12.3598			0.0136723
$905$	398.475	−	40.1683i	0.440304	−	0.0443849i
$906$	604.791	−	703.953i	0.667540	−	0.776990i
$907$		−	954.042i		−	1.05187i	−0.850526	−	0.525933i	$-0.823716\pi$
$907$		−	954.042i		−	1.05187i	0.850526	−	0.525933i	$-0.176284\pi$
$908$	257.066			0.283113
$909$	497.762	−	75.8653i	0.547593	−	0.0834601i
$910$	518.838	−	52.3016i	0.570152	−	0.0574743i
$911$			150.009i			0.164664i	0.996605	+	0.0823318i	$0.0262367\pi$
$911$			150.009i			0.164664i	−0.996605	+	0.0823318i	$0.973763\pi$
$912$	288.926	−	336.298i	0.316804	−	0.368748i
$913$			97.1131i			0.106367i
$914$		−	1161.52i		−	1.27081i
$915$	495.161	−	709.512i	0.541159	−	0.775423i
$916$	−352.352			−0.384664
$917$	−545.955			−0.595371
$918$	−0.630419	−	0.393947i	−0.000686731	−	0.000429136i
$919$	232.592			0.253093			0.126546	−	0.991961i	$-0.459611\pi$
$919$	232.592			0.253093			0.126546	+	0.991961i	$0.459611\pi$
$920$	−67.4813	+	6.80246i	−0.0733492	+	0.00739398i
$921$	−267.092	−	229.468i	−0.290002	−	0.249151i
$922$		−	409.413i		−	0.444049i
$923$	−855.660			−0.927043
$924$	−116.898	+	136.065i	−0.126513	+	0.147257i
$925$	−272.471	−	1337.74i	−0.294563	−	1.44620i
$926$			220.066i			0.237652i
$927$	213.227	−	32.4985i	0.230018	−	0.0350577i
$928$		−	100.215i		−	0.107990i
$929$		−	25.5380i		−	0.0274898i	−0.999906	−	0.0137449i	$-0.995625\pi$
$929$		−	25.5380i		−	0.0274898i	0.999906	−	0.0137449i	$-0.00437527\pi$
$930$	−189.761	+	271.906i	−0.204044	+	0.292373i
$931$	951.045			1.02153
$932$	−450.224			−0.483073
$933$	844.189	+	725.273i	0.904811	+	0.777356i
$934$	−954.137			−1.02156
$935$	−0.0337636	−	0.334940i	−3.61108e−5	−	0.000358224i
$936$	214.667	−	32.7180i	0.229345	−	0.0349551i
$937$		−	1286.01i		−	1.37248i	−0.727377	−	0.686238i	$-0.759261\pi$
$937$		−	1286.01i		−	1.37248i	0.727377	−	0.686238i	$-0.240739\pi$
$938$	448.683			0.478340
$939$	53.8681	+	46.2800i	0.0573676	+	0.0492865i
$940$	692.447	−	69.8022i	0.736646	−	0.0742577i
$941$			416.771i			0.442902i	0.975172	+	0.221451i	$0.0710792\pi$
$941$			416.771i			0.442902i	−0.975172	+	0.221451i	$0.928921\pi$
$942$	−548.949	−	471.621i	−0.582748	−	0.500660i
$943$		−	151.289i		−	0.160434i
$944$		−	128.521i		−	0.136145i
$945$	516.106	−	1046.80i	0.546144	−	1.10772i
$946$	−242.287			−0.256117
$947$	−937.680			−0.990158			−0.495079	−	0.868848i	$-0.664861\pi$
$947$	−937.680			−0.990158			−0.495079	+	0.868848i	$0.664861\pi$
$948$	558.102	−	649.609i	0.588715	−	0.685241i
$949$	−1112.43			−1.17221
$950$	−1280.00	+	260.711i	−1.34737	+	0.274432i
$951$	−620.518	+	722.258i	−0.652490	+	0.759473i
$952$		−	0.476057i		−	0.000500060i
$953$	−209.129			−0.219443			−0.109721	−	0.993962i	$-0.534996\pi$
$953$	−209.129			−0.219443			−0.109721	+	0.993962i	$0.534996\pi$
$954$	87.7217	+	575.554i	0.0919514	+	0.603306i
$955$	−174.360	−	1729.67i	−0.182576	−	1.81118i
$956$			480.309i			0.502415i
$957$	119.772	−	139.410i	0.125154	−	0.145674i
$958$		−	626.429i		−	0.653892i
$959$		−	434.745i		−	0.453332i
$960$	68.6760	−	98.4053i	0.0715375	−	0.102506i
$961$	−716.684			−0.745769
$962$	658.775			0.684797
$963$	77.5014	+	508.497i	0.0804791	+	0.528035i
$964$	−161.178			−0.167197
$965$	35.6705	+	353.856i	0.0369643	+	0.366690i
$966$	−133.426	−	114.631i	−0.138122	−	0.118665i
$967$			791.766i			0.818786i	0.912358	+	0.409393i	$0.134260\pi$
$967$			791.766i			0.818786i	−0.912358	+	0.409393i	$0.865740\pi$
$968$	308.413			0.318609
$969$	−1.40625	+	1.63682i	−0.00145124	+	0.00168918i
$970$	−72.9762	−	723.934i	−0.0752332	−	0.746323i
$971$			1458.97i			1.50255i	0.659990	+	0.751274i	$0.270560\pi$
$971$			1458.97i			1.50255i	−0.659990	+	0.751274i	$0.729440\pi$
$972$	192.510	−	446.247i	0.198055	−	0.459102i
$973$		−	574.950i		−	0.590905i
$974$			139.572i			0.143298i
$975$	−558.719	−	311.676i	−0.573045	−	0.319667i
$976$	230.723			0.236397
$977$	−508.585			−0.520557			−0.260279	−	0.965534i	$-0.583814\pi$
$977$	−508.585			−0.520557			−0.260279	+	0.965534i	$0.583814\pi$
$978$	−130.149	−	111.816i	−0.133077	−	0.114331i
$979$	−512.813			−0.523813
$980$	256.108	−	25.8170i	0.261335	−	0.0263439i
$981$	−42.8799	−	281.341i	−0.0437104	−	0.286790i
$982$			1155.28i			1.17646i
$983$	198.158			0.201585			0.100792	−	0.994907i	$-0.467862\pi$
$983$	198.158			0.201585			0.100792	+	0.994907i	$0.467862\pi$
$984$	203.035	+	174.435i	0.206337	+	0.177271i
$985$	392.867	−	39.6030i	0.398849	−	0.0402061i
$986$			0.487760i			0.000494686i
$987$	1369.12	+	1176.26i	1.38716	+	1.19176i
$988$		−	630.342i		−	0.637998i
$989$		−	237.587i		−	0.240229i
$990$	213.146	−	54.8146i	0.215299	−	0.0553682i
$991$	−113.735			−0.114768			−0.0573842	−	0.998352i	$-0.518276\pi$
$991$	−113.735			−0.114768			−0.0573842	+	0.998352i	$0.518276\pi$
$992$	−88.4201			−0.0891332
$993$	−261.920	+	304.864i	−0.263766	+	0.307013i
$994$	−1226.40			−1.23380
$995$	−1315.17	+	132.576i	−1.32178	+	0.133242i
$996$	109.798	−	127.801i	0.110239	−	0.128314i
$997$			1309.80i			1.31374i	0.754003	+	0.656872i	$0.228121\pi$
$997$			1309.80i			1.31374i	−0.754003	+	0.656872i	$0.771879\pi$
$998$	−931.072			−0.932938
$999$	781.349	−	1250.36i	0.782131	−	1.25162i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.b.a.599.58	yes	88
3.2	odd	2	inner	690.3.b.a.599.32	yes	88
5.4	even	2	inner	690.3.b.a.599.31	✓	88
15.14	odd	2	inner	690.3.b.a.599.57	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.b.a.599.31	✓	88	5.4	even	2	inner
690.3.b.a.599.32	yes	88	3.2	odd	2	inner
690.3.b.a.599.57	yes	88	15.14	odd	2	inner
690.3.b.a.599.58	yes	88	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +(-1.95499 + 2.27553i) q^{3} +2.00000 q^{4} +(-4.97479 + 0.501484i) q^{5} +(-2.76477 + 3.21808i) q^{6} +8.64527i q^{7} +2.82843 q^{8} +(-1.35605 - 8.89725i) q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +(-1.95499 + 2.27553i) q^{3} +2.00000 q^{4} +(-4.97479 + 0.501484i) q^{5} +(-2.76477 + 3.21808i) q^{6} +8.64527i q^{7} +2.82843 q^{8} +(-1.35605 - 8.89725i) q^{9} +(-7.03541 + 0.709206i) q^{10} -3.45825i q^{11} +(-3.90997 + 4.55106i) q^{12} +8.53030i q^{13} +12.2263i q^{14} +(8.58450 - 12.3007i) q^{15} +4.00000 q^{16} -0.0194686 q^{17} +(-1.91775 - 12.5826i) q^{18} -36.9473 q^{19} +(-9.94958 + 1.00297i) q^{20} +(-19.6725 - 16.9014i) q^{21} -4.89070i q^{22} +4.79583 q^{23} +(-5.52954 + 6.43616i) q^{24} +(24.4970 - 4.98955i) q^{25} +12.0637i q^{26} +(22.8970 + 14.3083i) q^{27} +17.2905i q^{28} -17.7156i q^{29} +(12.1403 - 17.3958i) q^{30} -15.6306 q^{31} +5.65685 q^{32} +(7.86934 + 6.76083i) q^{33} -0.0275328 q^{34} +(-4.33546 - 43.0084i) q^{35} +(-2.71211 - 17.7945i) q^{36} -54.6082i q^{37} -52.2513 q^{38} +(-19.4109 - 16.6766i) q^{39} +(-14.0708 + 1.41841i) q^{40} -31.5460i q^{41} +(-27.8212 - 23.9022i) q^{42} -49.5403i q^{43} -6.91650i q^{44} +(11.2079 + 43.5819i) q^{45} +6.78233 q^{46} -69.5957 q^{47} +(-7.81995 + 9.10211i) q^{48} -25.7406 q^{49} +(34.6440 - 7.05630i) q^{50} +(0.0380609 - 0.0443014i) q^{51} +17.0606i q^{52} -45.7420 q^{53} +(32.3813 + 20.2350i) q^{54} +(1.73426 + 17.2041i) q^{55} +24.4525i q^{56} +(72.2314 - 84.0745i) q^{57} -25.0536i q^{58} -32.1302i q^{59} +(17.1690 - 24.6013i) q^{60} +57.6808 q^{61} -22.1050 q^{62} +(76.9191 - 11.7234i) q^{63} +8.00000 q^{64} +(-4.27781 - 42.4364i) q^{65} +(11.1289 + 9.56126i) q^{66} -36.6983i q^{67} -0.0389373 q^{68} +(-9.37579 + 10.9130i) q^{69} +(-6.13127 - 60.8230i) q^{70} +100.308i q^{71} +(-3.83550 - 25.1652i) q^{72} +130.409i q^{73} -77.2276i q^{74} +(-36.5375 + 65.4982i) q^{75} -73.8945 q^{76} +29.8975 q^{77} +(-27.4512 - 23.5843i) q^{78} -142.738 q^{79} +(-19.8992 + 2.00594i) q^{80} +(-77.3222 + 24.1303i) q^{81} -44.6128i q^{82} -28.0816 q^{83} +(-39.3451 - 33.8028i) q^{84} +(0.0968524 - 0.00976322i) q^{85} -70.0605i q^{86} +(40.3123 + 34.6338i) q^{87} -9.78141i q^{88} -148.287i q^{89} +(15.8504 + 61.6341i) q^{90} -73.7467 q^{91} +9.59166 q^{92} +(30.5576 - 35.5679i) q^{93} -98.4231 q^{94} +(183.805 - 18.5285i) q^{95} +(-11.0591 + 12.8723i) q^{96} +102.899i q^{97} -36.4027 q^{98} +(-30.7689 + 4.68957i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 176 q^{4} + 8 q^{9}+O(q^{10}) \) 88 * q + 176 * q^4 + 8 * q^9	\( 88 q + 176 q^{4} + 8 q^{9} + 32 q^{10} - 12 q^{15} + 352 q^{16} - 16 q^{19} - 176 q^{21} + 72 q^{25} - 72 q^{30} + 32 q^{31} + 160 q^{34} + 16 q^{36} + 144 q^{39} + 64 q^{40} + 92 q^{45} - 360 q^{49} + 48 q^{51} - 144 q^{54} + 16 q^{55} - 24 q^{60} + 208 q^{61} + 704 q^{64} + 512 q^{66} + 304 q^{70} + 536 q^{75} - 32 q^{76} + 448 q^{79} - 24 q^{81} - 352 q^{84} - 96 q^{85} + 32 q^{90} - 64 q^{91} + 160 q^{94} + 296 q^{99}+O(q^{100}) \) 88 * q + 176 * q^4 + 8 * q^9 + 32 * q^10 - 12 * q^15 + 352 * q^16 - 16 * q^19 - 176 * q^21 + 72 * q^25 - 72 * q^30 + 32 * q^31 + 160 * q^34 + 16 * q^36 + 144 * q^39 + 64 * q^40 + 92 * q^45 - 360 * q^49 + 48 * q^51 - 144 * q^54 + 16 * q^55 - 24 * q^60 + 208 * q^61 + 704 * q^64 + 512 * q^66 + 304 * q^70 + 536 * q^75 - 32 * q^76 + 448 * q^79 - 24 * q^81 - 352 * q^84 - 96 * q^85 + 32 * q^90 - 64 * q^91 + 160 * q^94 + 296 * q^99

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