LMFDB - Embedded newform 538.3.c.b.187.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,3,Mod(187,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("538.187");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	538.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.6594382226$
Analytic rank:	$0$
Dimension:	$46$
Relative dimension:	$23$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			187.2
Character	$\chi$	$=$	538.187
Dual form			538.3.c.b.351.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.00000i) q^{2} +(-3.73758 - 3.73758i) q^{3} +2.00000i q^{4} +3.56643 q^{5} +7.47516i q^{6} +(0.891381 - 0.891381i) q^{7} +(2.00000 - 2.00000i) q^{8} +18.9390i q^{9} +(-3.56643 - 3.56643i) q^{10} -2.56603i q^{11} +(7.47516 - 7.47516i) q^{12} -6.86363i q^{13} -1.78276 q^{14} +(-13.3298 - 13.3298i) q^{15} -4.00000 q^{16} +(18.2796 + 18.2796i) q^{17} +(18.9390 - 18.9390i) q^{18} +(19.2264 - 19.2264i) q^{19} +7.13285i q^{20} -6.66321 q^{21} +(-2.56603 + 2.56603i) q^{22} +20.7058 q^{23} -14.9503 q^{24} -12.2806 q^{25} +(-6.86363 + 6.86363i) q^{26} +(37.1478 - 37.1478i) q^{27} +(1.78276 + 1.78276i) q^{28} +(33.1609 - 33.1609i) q^{29} +26.6596i q^{30} +(31.1443 - 31.1443i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-9.59075 + 9.59075i) q^{33} -36.5592i q^{34} +(3.17904 - 3.17904i) q^{35} -37.8780 q^{36} +9.51182 q^{37} -38.4528 q^{38} +(-25.6534 + 25.6534i) q^{39} +(7.13285 - 7.13285i) q^{40} -47.9831 q^{41} +(6.66321 + 6.66321i) q^{42} +27.6003i q^{43} +5.13207 q^{44} +67.5445i q^{45} +(-20.7058 - 20.7058i) q^{46} -83.5411 q^{47} +(14.9503 + 14.9503i) q^{48} +47.4109i q^{49} +(12.2806 + 12.2806i) q^{50} -136.643i q^{51} +13.7273 q^{52} +7.49037 q^{53} -74.2956 q^{54} -9.15157i q^{55} -3.56552i q^{56} -143.720 q^{57} -66.3218 q^{58} +(46.0453 - 46.0453i) q^{59} +(26.6596 - 26.6596i) q^{60} -82.0535 q^{61} -62.2886 q^{62} +(16.8819 + 16.8819i) q^{63} -8.00000i q^{64} -24.4786i q^{65} +19.1815 q^{66} +21.7311 q^{67} +(-36.5592 + 36.5592i) q^{68} +(-77.3896 - 77.3896i) q^{69} -6.35809 q^{70} +(-10.9828 + 10.9828i) q^{71} +(37.8780 + 37.8780i) q^{72} +41.5713i q^{73} +(-9.51182 - 9.51182i) q^{74} +(45.8997 + 45.8997i) q^{75} +(38.4528 + 38.4528i) q^{76} +(-2.28731 - 2.28731i) q^{77} +51.3067 q^{78} -61.7849i q^{79} -14.2657 q^{80} -107.235 q^{81} +(47.9831 + 47.9831i) q^{82} +(29.4236 - 29.4236i) q^{83} -13.3264i q^{84} +(65.1928 + 65.1928i) q^{85} +(27.6003 - 27.6003i) q^{86} -247.883 q^{87} +(-5.13207 - 5.13207i) q^{88} -137.457i q^{89} +(67.5445 - 67.5445i) q^{90} +(-6.11811 - 6.11811i) q^{91} +41.4116i q^{92} -232.808 q^{93} +(83.5411 + 83.5411i) q^{94} +(68.5695 - 68.5695i) q^{95} -29.9006i q^{96} +97.9964i q^{97} +(47.4109 - 47.4109i) q^{98} +48.5981 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 46 q^{2} - 6 q^{3} - 32 q^{5} + 4 q^{7} + 92 q^{8} + 32 q^{10} + 12 q^{12} - 8 q^{14} - 10 q^{15} - 184 q^{16} - 50 q^{17} + 118 q^{18} + 10 q^{19} + 16 q^{21} + 8 q^{22} - 124 q^{23} - 24 q^{24}+ \cdots + 508 q^{99}+O(q^{100}) $ 46 * q - 46 * q^2 - 6 * q^3 - 32 * q^5 + 4 * q^7 + 92 * q^8 + 32 * q^10 + 12 * q^12 - 8 * q^14 - 10 * q^15 - 184 * q^16 - 50 * q^17 + 118 * q^18 + 10 * q^19 + 16 * q^21 + 8 * q^22 - 124 * q^23 - 24 * q^24 + 178 * q^25 + 4 * q^26 + 90 * q^27 + 8 * q^28 + 40 * q^29 + 40 * q^31 + 184 * q^32 - 64 * q^33 - 14 * q^35 - 236 * q^36 - 32 * q^37 - 20 * q^38 - 54 * q^39 - 64 * q^40 - 132 * q^41 - 16 * q^42 - 16 * q^44 + 124 * q^46 - 60 * q^47 + 24 * q^48 - 178 * q^50 - 8 * q^52 - 188 * q^53 - 180 * q^54 - 40 * q^57 - 80 * q^58 + 190 * q^59 + 20 * q^60 - 80 * q^62 - 266 * q^63 + 128 * q^66 - 164 * q^67 + 100 * q^68 + 170 * q^69 + 28 * q^70 - 92 * q^71 + 236 * q^72 + 32 * q^74 - 190 * q^75 + 20 * q^76 + 20 * q^77 + 108 * q^78 + 128 * q^80 - 298 * q^81 + 132 * q^82 + 190 * q^83 + 298 * q^85 + 228 * q^86 - 92 * q^87 + 16 * q^88 - 528 * q^90 + 2 * q^91 + 232 * q^93 + 60 * q^94 - 280 * q^95 - 226 * q^98 + 508 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/538\mathbb{Z}\right)^\times$.

$n$	$271$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	−3.73758	−	3.73758i	−1.24586	−	1.24586i	−0.957532	−	0.288328i	$-0.906901\pi$
$3$	−3.73758	−	3.73758i	−1.24586	−	1.24586i	−0.288328	−	0.957532i	$-0.593099\pi$
$4$			2.00000i			0.500000i
$5$	3.56643			0.713285			0.356643	−	0.934241i	$-0.383921\pi$
$5$	3.56643			0.713285			0.356643	+	0.934241i	$0.383921\pi$
$6$			7.47516i			1.24586i
$7$	0.891381	−	0.891381i	0.127340	−	0.127340i	−0.640564	−	0.767904i	$-0.721300\pi$
$7$	0.891381	−	0.891381i	0.127340	−	0.127340i	0.767904	+	0.640564i	$0.221300\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$			18.9390i			2.10433i
$10$	−3.56643	−	3.56643i	−0.356643	−	0.356643i
$11$		−	2.56603i		−	0.233276i	−0.993175	−	0.116638i	$-0.962788\pi$
$11$		−	2.56603i		−	0.233276i	0.993175	−	0.116638i	$-0.0372117\pi$
$12$	7.47516	−	7.47516i	0.622930	−	0.622930i
$13$		−	6.86363i		−	0.527971i	−0.964527	−	0.263986i	$-0.914963\pi$
$13$		−	6.86363i		−	0.527971i	0.964527	−	0.263986i	$-0.0850372\pi$
$14$	−1.78276			−0.127340
$15$	−13.3298	−	13.3298i	−0.888654	−	0.888654i
$16$	−4.00000			−0.250000
$17$	18.2796	+	18.2796i	1.07527	+	1.07527i	0.996926	+	0.0783435i	$0.0249631\pi$
$17$	18.2796	+	18.2796i	1.07527	+	1.07527i	0.0783435	+	0.996926i	$0.475037\pi$
$18$	18.9390	−	18.9390i	1.05217	−	1.05217i
$19$	19.2264	−	19.2264i	1.01191	−	1.01191i	0.0119866	−	0.999928i	$-0.496184\pi$
$19$	19.2264	−	19.2264i	1.01191	−	1.01191i	0.999928	−	0.0119866i	$-0.00381555\pi$
$20$			7.13285i			0.356643i
$21$	−6.66321			−0.317296
$22$	−2.56603	+	2.56603i	−0.116638	+	0.116638i
$23$	20.7058			0.900252			0.450126	−	0.892965i	$-0.351379\pi$
$23$	20.7058			0.900252			0.450126	+	0.892965i	$0.351379\pi$
$24$	−14.9503			−0.622930
$25$	−12.2806			−0.491224
$26$	−6.86363	+	6.86363i	−0.263986	+	0.263986i
$27$	37.1478	−	37.1478i	1.37584	−	1.37584i
$28$	1.78276	+	1.78276i	0.0636700	+	0.0636700i
$29$	33.1609	−	33.1609i	1.14348	−	1.14348i	0.155670	−	0.987809i	$-0.450246\pi$
$29$	33.1609	−	33.1609i	1.14348	−	1.14348i	0.987809	−	0.155670i	$-0.0497535\pi$
$30$			26.6596i			0.888654i
$31$	31.1443	−	31.1443i	1.00465	−	1.00465i	0.00466538	−	0.999989i	$-0.498515\pi$
$31$	31.1443	−	31.1443i	1.00465	−	1.00465i	0.999989	−	0.00466538i	$-0.00148504\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−9.59075	+	9.59075i	−0.290629	+	0.290629i
$34$		−	36.5592i		−	1.07527i
$35$	3.17904	−	3.17904i	0.0908298	−	0.0908298i
$36$	−37.8780			−1.05217
$37$	9.51182			0.257076			0.128538	−	0.991705i	$-0.458972\pi$
$37$	9.51182			0.257076			0.128538	+	0.991705i	$0.458972\pi$
$38$	−38.4528			−1.01191
$39$	−25.6534	+	25.6534i	−0.657778	+	0.657778i
$40$	7.13285	−	7.13285i	0.178321	−	0.178321i
$41$	−47.9831			−1.17032			−0.585159	−	0.810918i	$-0.698968\pi$
$41$	−47.9831			−1.17032			−0.585159	+	0.810918i	$0.698968\pi$
$42$	6.66321	+	6.66321i	0.158648	+	0.158648i
$43$			27.6003i			0.641867i	0.947102	+	0.320933i	$0.103997\pi$
$43$			27.6003i			0.641867i	−0.947102	+	0.320933i	$0.896003\pi$
$44$	5.13207			0.116638
$45$			67.5445i			1.50099i
$46$	−20.7058	−	20.7058i	−0.450126	−	0.450126i
$47$	−83.5411			−1.77747			−0.888735	−	0.458421i	$-0.848415\pi$
$47$	−83.5411			−1.77747			−0.888735	+	0.458421i	$0.848415\pi$
$48$	14.9503	+	14.9503i	0.311465	+	0.311465i
$49$			47.4109i			0.967569i
$50$	12.2806	+	12.2806i	0.245612	+	0.245612i
$51$		−	136.643i		−	2.67927i
$52$	13.7273			0.263986
$53$	7.49037			0.141328			0.0706638	−	0.997500i	$-0.477488\pi$
$53$	7.49037			0.141328			0.0706638	+	0.997500i	$0.477488\pi$
$54$	−74.2956			−1.37584
$55$		−	9.15157i		−	0.166392i
$56$		−	3.56552i		−	0.0636700i
$57$	−143.720			−2.52141
$58$	−66.3218			−1.14348
$59$	46.0453	−	46.0453i	0.780430	−	0.780430i	−0.199474	−	0.979903i	$-0.563923\pi$
$59$	46.0453	−	46.0453i	0.780430	−	0.780430i	0.979903	+	0.199474i	$0.0639232\pi$
$60$	26.6596	−	26.6596i	0.444327	−	0.444327i
$61$	−82.0535			−1.34514			−0.672570	−	0.740034i	$-0.734810\pi$
$61$	−82.0535			−1.34514			−0.672570	+	0.740034i	$0.734810\pi$
$62$	−62.2886			−1.00465
$63$	16.8819	+	16.8819i	0.267966	+	0.267966i
$64$		−	8.00000i		−	0.125000i
$65$		−	24.4786i		−	0.376594i
$66$	19.1815			0.290629
$67$	21.7311			0.324345			0.162173	−	0.986762i	$-0.448150\pi$
$67$	21.7311			0.324345			0.162173	+	0.986762i	$0.448150\pi$
$68$	−36.5592	+	36.5592i	−0.537635	+	0.537635i
$69$	−77.3896	−	77.3896i	−1.12159	−	1.12159i
$70$	−6.35809			−0.0908298
$71$	−10.9828	+	10.9828i	−0.154688	+	0.154688i	−0.780208	−	0.625520i	$-0.784887\pi$
$71$	−10.9828	+	10.9828i	−0.154688	+	0.154688i	0.625520	+	0.780208i	$0.284887\pi$
$72$	37.8780	+	37.8780i	0.526083	+	0.526083i
$73$			41.5713i			0.569469i	0.958606	+	0.284735i	$0.0919055\pi$
$73$			41.5713i			0.569469i	−0.958606	+	0.284735i	$0.908095\pi$
$74$	−9.51182	−	9.51182i	−0.128538	−	0.128538i
$75$	45.8997	+	45.8997i	0.611996	+	0.611996i
$76$	38.4528	+	38.4528i	0.505957	+	0.505957i
$77$	−2.28731	−	2.28731i	−0.0297053	−	0.0297053i
$78$	51.3067			0.657778
$79$		−	61.7849i		−	0.782087i	−0.920372	−	0.391043i	$-0.872114\pi$
$79$		−	61.7849i		−	0.782087i	0.920372	−	0.391043i	$-0.127886\pi$
$80$	−14.2657			−0.178321
$81$	−107.235			−1.32388
$82$	47.9831	+	47.9831i	0.585159	+	0.585159i
$83$	29.4236	−	29.4236i	0.354501	−	0.354501i	−0.507280	−	0.861781i	$-0.669349\pi$
$83$	29.4236	−	29.4236i	0.354501	−	0.354501i	0.861781	+	0.507280i	$0.169349\pi$
$84$		−	13.3264i		−	0.158648i
$85$	65.1928	+	65.1928i	0.766974	+	0.766974i
$86$	27.6003	−	27.6003i	0.320933	−	0.320933i
$87$	−247.883			−2.84923
$88$	−5.13207	−	5.13207i	−0.0583189	−	0.0583189i
$89$		−	137.457i		−	1.54447i	−0.635340	−	0.772233i	$-0.719140\pi$
$89$		−	137.457i		−	1.54447i	0.635340	−	0.772233i	$-0.280860\pi$
$90$	67.5445	−	67.5445i	0.750495	−	0.750495i
$91$	−6.11811	−	6.11811i	−0.0672319	−	0.0672319i
$92$			41.4116i			0.450126i
$93$	−232.808			−2.50332
$94$	83.5411	+	83.5411i	0.888735	+	0.888735i
$95$	68.5695	−	68.5695i	0.721784	−	0.721784i
$96$		−	29.9006i		−	0.311465i
$97$			97.9964i			1.01027i	0.863040	+	0.505136i	$0.168558\pi$
$97$			97.9964i			1.01027i	−0.863040	+	0.505136i	$0.831442\pi$
$98$	47.4109	−	47.4109i	0.483785	−	0.483785i
$99$	48.5981			0.490890
$100$		−	24.5612i		−	0.245612i
$101$	−30.4105	−	30.4105i	−0.301094	−	0.301094i	0.540348	−	0.841442i	$-0.318293\pi$
$101$	−30.4105	−	30.4105i	−0.301094	−	0.301094i	−0.841442	+	0.540348i	$0.818293\pi$
$102$	−136.643	+	136.643i	−1.33964	+	1.33964i
$103$		−	53.4784i		−	0.519208i	−0.965715	−	0.259604i	$-0.916408\pi$
$103$		−	53.4784i		−	0.519208i	0.965715	−	0.259604i	$-0.0835920\pi$
$104$	−13.7273	−	13.7273i	−0.131993	−	0.131993i
$105$	−23.7639			−0.226322
$106$	−7.49037	−	7.49037i	−0.0706638	−	0.0706638i
$107$	−60.7293	+	60.7293i	−0.567563	+	0.567563i	−0.931445	−	0.363882i	$-0.881451\pi$
$107$	−60.7293	+	60.7293i	−0.567563	+	0.567563i	0.363882	+	0.931445i	$0.381451\pi$
$108$	74.2956	+	74.2956i	0.687922	+	0.687922i
$109$	42.2357	−	42.2357i	0.387484	−	0.387484i	−0.486305	−	0.873789i	$-0.661656\pi$
$109$	42.2357	−	42.2357i	0.387484	−	0.387484i	0.873789	+	0.486305i	$0.161656\pi$
$110$	−9.15157	+	9.15157i	−0.0831961	+	0.0831961i
$111$	−35.5512	−	35.5512i	−0.320281	−	0.320281i
$112$	−3.56552	+	3.56552i	−0.0318350	+	0.0318350i
$113$	152.587	−	152.587i	1.35033	−	1.35033i	0.465037	−	0.885291i	$-0.346041\pi$
$113$	152.587	−	152.587i	1.35033	−	1.35033i	0.885291	−	0.465037i	$-0.153959\pi$
$114$	143.720	+	143.720i	1.26070	+	1.26070i
$115$	73.8457			0.642137
$116$	66.3218	+	66.3218i	0.571739	+	0.571739i
$117$	129.990			1.11103
$118$	−92.0907			−0.780430
$119$	32.5881			0.273850
$120$	−53.3192			−0.444327
$121$	114.415			0.945582
$122$	82.0535	+	82.0535i	0.672570	+	0.672570i
$123$	179.340	+	179.340i	1.45805	+	1.45805i
$124$	62.2886	+	62.2886i	0.502327	+	0.502327i
$125$	−132.959			−1.06367
$126$		−	33.7637i		−	0.267966i
$127$			73.7961i			0.581072i	0.956864	+	0.290536i	$0.0938336\pi$
$127$			73.7961i			0.581072i	−0.956864	+	0.290536i	$0.906166\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$	103.158	−	103.158i	0.799676	−	0.799676i
$130$	−24.4786	+	24.4786i	−0.188297	+	0.188297i
$131$	42.9213			0.327644			0.163822	−	0.986490i	$-0.447618\pi$
$131$	42.9213			0.327644			0.163822	+	0.986490i	$0.447618\pi$
$132$	−19.1815	−	19.1815i	−0.145314	−	0.145314i
$133$		−	34.2760i		−	0.257715i
$134$	−21.7311	−	21.7311i	−0.162173	−	0.162173i
$135$	132.485	−	132.485i	0.981369	−	0.981369i
$136$	73.1184			0.537635
$137$	−78.8845	+	78.8845i	−0.575799	+	0.575799i	−0.933743	−	0.357944i	$-0.883478\pi$
$137$	−78.8845	+	78.8845i	−0.575799	+	0.575799i	0.357944	+	0.933743i	$0.383478\pi$
$138$			154.779i			1.12159i
$139$	−81.8983	−	81.8983i	−0.589196	−	0.589196i	0.348218	−	0.937414i	$-0.386787\pi$
$139$	−81.8983	−	81.8983i	−0.589196	−	0.589196i	−0.937414	+	0.348218i	$0.886787\pi$
$140$	6.35809	+	6.35809i	0.0454149	+	0.0454149i
$141$	312.241	+	312.241i	2.21448	+	2.21448i
$142$	21.9657			0.154688
$143$	−17.6123			−0.123163
$144$		−	75.7560i		−	0.526083i
$145$	118.266	−	118.266i	0.815627	−	0.815627i
$146$	41.5713	−	41.5713i	0.284735	−	0.284735i
$147$	177.202	−	177.202i	1.20546	−	1.20546i
$148$			19.0236i			0.128538i
$149$		−	135.917i		−	0.912192i	−0.889931	−	0.456096i	$-0.849247\pi$
$149$		−	135.917i		−	0.912192i	0.889931	−	0.456096i	$-0.150753\pi$
$150$		−	91.7994i		−	0.611996i
$151$		−	249.028i		−	1.64919i	−0.565724	−	0.824595i	$-0.691403\pi$
$151$		−	249.028i		−	1.64919i	0.565724	−	0.824595i	$-0.308597\pi$
$152$		−	76.9055i		−	0.505957i
$153$	−346.197	+	346.197i	−2.26273	+	2.26273i
$154$			4.57462i			0.0297053i
$155$	111.074	−	111.074i	0.716605	−	0.716605i
$156$	−51.3067	−	51.3067i	−0.328889	−	0.328889i
$157$	−46.5704	−	46.5704i	−0.296627	−	0.296627i	0.543064	−	0.839691i	$-0.317264\pi$
$157$	−46.5704	−	46.5704i	−0.296627	−	0.296627i	−0.839691	+	0.543064i	$0.817264\pi$
$158$	−61.7849	+	61.7849i	−0.391043	+	0.391043i
$159$	−27.9958	−	27.9958i	−0.176074	−	0.176074i
$160$	14.2657	+	14.2657i	0.0891607	+	0.0891607i
$161$	18.4568	−	18.4568i	0.114638	−	0.114638i
$162$	107.235	+	107.235i	0.661942	+	0.661942i
$163$	156.419	−	156.419i	0.959628	−	0.959628i	−0.0395881	−	0.999216i	$-0.512605\pi$
$163$	156.419	−	156.419i	0.959628	−	0.959628i	0.999216	+	0.0395881i	$0.0126046\pi$
$164$		−	95.9661i		−	0.585159i
$165$	−34.2047	+	34.2047i	−0.207301	+	0.207301i
$166$	−58.8472			−0.354501
$167$	−100.759	−	100.759i	−0.603349	−	0.603349i	0.337850	−	0.941200i	$-0.390300\pi$
$167$	−100.759	−	100.759i	−0.603349	−	0.603349i	−0.941200	+	0.337850i	$0.890300\pi$
$168$	−13.3264	+	13.3264i	−0.0793239	+	0.0793239i
$169$	121.891			0.721246
$170$		−	130.386i		−	0.766974i
$171$	364.128	+	364.128i	2.12941	+	2.12941i
$172$	−55.2006			−0.320933
$173$	−74.9613			−0.433303			−0.216651	−	0.976249i	$-0.569513\pi$
$173$	−74.9613			−0.433303			−0.216651	+	0.976249i	$0.569513\pi$
$174$	247.883	+	247.883i	1.42461	+	1.42461i
$175$	−10.9467	+	10.9467i	−0.0625525	+	0.0625525i
$176$			10.2641i			0.0583189i
$177$	−344.196			−1.94461
$178$	−137.457	+	137.457i	−0.772233	+	0.772233i
$179$	11.6583	+	11.6583i	0.0651301	+	0.0651301i	0.738922	−	0.673791i	$-0.235335\pi$
$179$	11.6583	+	11.6583i	0.0651301	+	0.0651301i	−0.673791	+	0.738922i	$0.735335\pi$
$180$	−135.089			−0.750495
$181$	−192.374	+	192.374i	−1.06284	+	1.06284i	−0.0649502	+	0.997889i	$0.520689\pi$
$181$	−192.374	+	192.374i	−1.06284	+	1.06284i	−0.997889	+	0.0649502i	$0.979311\pi$
$182$			12.2362i			0.0672319i
$183$	306.682	+	306.682i	1.67586	+	1.67586i
$184$	41.4116	−	41.4116i	0.225063	−	0.225063i
$185$	33.9232			0.183369
$186$	232.808	+	232.808i	1.25166	+	1.25166i
$187$	46.9060	−	46.9060i	0.250834	−	0.250834i
$188$		−	167.082i		−	0.888735i
$189$		−	66.2256i		−	0.350400i
$190$	−137.139			−0.721784
$191$		−	42.8213i		−	0.224195i	−0.993697	−	0.112098i	$-0.964243\pi$
$191$		−	42.8213i		−	0.224195i	0.993697	−	0.112098i	$-0.0357570\pi$
$192$	−29.9006	+	29.9006i	−0.155732	+	0.155732i
$193$	−224.710	+	224.710i	−1.16430	+	1.16430i	−0.180775	+	0.983524i	$0.557861\pi$
$193$	−224.710	+	224.710i	−1.16430	+	1.16430i	−0.983524	+	0.180775i	$0.942139\pi$
$194$	97.9964	−	97.9964i	0.505136	−	0.505136i
$195$	−91.4908	+	91.4908i	−0.469184	+	0.469184i
$196$	−94.8218			−0.483785
$197$	40.5886	−	40.5886i	0.206034	−	0.206034i	−0.596546	−	0.802579i	$-0.703460\pi$
$197$	40.5886	−	40.5886i	0.206034	−	0.206034i	0.802579	+	0.596546i	$0.203460\pi$
$198$	−48.5981	−	48.5981i	−0.245445	−	0.245445i
$199$		−	81.1621i		−	0.407850i	−0.978987	−	0.203925i	$-0.934630\pi$
$199$		−	81.1621i		−	0.407850i	0.978987	−	0.203925i	$-0.0653698\pi$
$200$	−24.5612	+	24.5612i	−0.122806	+	0.122806i
$201$	−81.2218	−	81.2218i	−0.404089	−	0.404089i
$202$			60.8210i			0.301094i
$203$		−	59.1179i		−	0.291221i
$204$	273.286			1.33964
$205$	−171.128			−0.834771
$206$	−53.4784	+	53.4784i	−0.259604	+	0.259604i
$207$			392.147i			1.89443i
$208$			27.4545i			0.131993i
$209$	−49.3355	−	49.3355i	−0.236055	−	0.236055i
$210$	23.7639	+	23.7639i	0.113161	+	0.113161i
$211$			221.892i			1.05162i	0.850602	+	0.525810i	$0.176238\pi$
$211$			221.892i			1.05162i	−0.850602	+	0.525810i	$0.823762\pi$
$212$			14.9807i			0.0706638i
$213$	82.0984			0.385438
$214$	121.459			0.567563
$215$			98.4344i			0.457834i
$216$		−	148.591i		−	0.687922i
$217$		−	55.5228i		−	0.255866i
$218$	−84.4714			−0.387484
$219$	155.376	−	155.376i	0.709479	−	0.709479i
$220$	18.3031			0.0831961
$221$	125.464	−	125.464i	0.567712	−	0.567712i
$222$			71.1023i			0.320281i
$223$	−236.861	+	236.861i	−1.06216	+	1.06216i	−0.0642236	+	0.997936i	$0.520457\pi$
$223$	−236.861	+	236.861i	−1.06216	+	1.06216i	−0.997936	+	0.0642236i	$0.979543\pi$
$224$	7.13104			0.0318350
$225$		−	232.582i		−	1.03370i
$226$	−305.174			−1.35033
$227$	237.886	−	237.886i	1.04796	−	1.04796i	0.0491659	−	0.998791i	$-0.484344\pi$
$227$	237.886	−	237.886i	1.04796	−	1.04796i	0.998791	−	0.0491659i	$-0.0156563\pi$
$228$		−	287.440i		−	1.26070i
$229$	106.805	+	106.805i	0.466399	+	0.466399i	0.900746	−	0.434347i	$-0.143021\pi$
$229$	106.805	+	106.805i	0.466399	+	0.466399i	−0.434347	+	0.900746i	$0.643021\pi$
$230$	−73.8457	−	73.8457i	−0.321068	−	0.321068i
$231$			17.0980i			0.0740174i
$232$		−	132.644i		−	0.571739i
$233$			27.8816i			0.119663i	0.998208	+	0.0598317i	$0.0190564\pi$
$233$			27.8816i			0.119663i	−0.998208	+	0.0598317i	$0.980944\pi$
$234$	−129.990	−	129.990i	−0.555514	−	0.555514i
$235$	−297.943			−1.26784
$236$	92.0907	+	92.0907i	0.390215	+	0.390215i
$237$	−230.926	+	230.926i	−0.974370	+	0.974370i
$238$	−32.5881	−	32.5881i	−0.136925	−	0.136925i
$239$	366.238			1.53237			0.766187	−	0.642617i	$-0.222151\pi$
$239$	366.238			1.53237			0.766187	+	0.642617i	$0.222151\pi$
$240$	53.3192	+	53.3192i	0.222163	+	0.222163i
$241$	−20.8243	+	20.8243i	−0.0864077	+	0.0864077i	−0.748990	−	0.662582i	$-0.769461\pi$
$241$	−20.8243	+	20.8243i	−0.0864077	+	0.0864077i	0.662582	+	0.748990i	$0.269461\pi$
$242$	−114.415	−	114.415i	−0.472791	−	0.472791i
$243$	66.4678	+	66.4678i	0.273530	+	0.273530i
$244$		−	164.107i		−	0.672570i
$245$			169.087i			0.690153i
$246$		−	358.681i		−	1.45805i
$247$	−131.963	−	131.963i	−0.534262	−	0.534262i
$248$		−	124.577i		−	0.502327i
$249$	−219.946			−0.883318
$250$	132.959	+	132.959i	0.531834	+	0.531834i
$251$	−169.149	−	169.149i	−0.673902	−	0.673902i	0.284711	−	0.958613i	$-0.408102\pi$
$251$	−169.149	−	169.149i	−0.673902	−	0.673902i	−0.958613	+	0.284711i	$0.908102\pi$
$252$	−33.7637	+	33.7637i	−0.133983	+	0.133983i
$253$		−	53.1318i		−	0.210007i
$254$	73.7961	−	73.7961i	0.290536	−	0.290536i
$255$		−	487.327i		−	1.91108i
$256$	16.0000			0.0625000
$257$	−53.7468	−	53.7468i	−0.209132	−	0.209132i	0.594767	−	0.803898i	$-0.297244\pi$
$257$	−53.7468	−	53.7468i	−0.209132	−	0.209132i	−0.803898	+	0.594767i	$0.797244\pi$
$258$	−206.316			−0.799676
$259$	8.47865	−	8.47865i	0.0327361	−	0.0327361i
$260$	48.9573			0.188297
$261$	628.034	+	628.034i	2.40626	+	2.40626i
$262$	−42.9213	−	42.9213i	−0.163822	−	0.163822i
$263$	−44.7508			−0.170155			−0.0850776	−	0.996374i	$-0.527114\pi$
$263$	−44.7508			−0.170155			−0.0850776	+	0.996374i	$0.527114\pi$
$264$			38.3630i			0.145314i
$265$	26.7138			0.100807
$266$	−34.2760	+	34.2760i	−0.128857	+	0.128857i
$267$	−513.758	+	513.758i	−1.92419	+	1.92419i
$268$			43.4623i			0.162173i
$269$	240.734	+	120.034i	0.894921	+	0.446225i
$269$	240.734	+	120.034i	0.894921	+	0.446225i
$270$	−264.970			−0.981369
$271$	168.597	+	168.597i	0.622131	+	0.622131i	0.946076	−	0.323945i	$-0.105009\pi$
$271$	168.597	+	168.597i	0.622131	+	0.622131i	−0.323945	+	0.946076i	$0.605009\pi$
$272$	−73.1184	−	73.1184i	−0.268817	−	0.268817i
$273$			45.7338i			0.167523i
$274$	157.769			0.575799
$275$			31.5124i			0.114591i
$276$	154.779	−	154.779i	0.560794	−	0.560794i
$277$	137.561	−	137.561i	0.496609	−	0.496609i	−0.413771	−	0.910381i	$-0.635789\pi$
$277$	137.561	−	137.561i	0.496609	−	0.496609i	0.910381	+	0.413771i	$0.135789\pi$
$278$			163.797i			0.589196i
$279$	589.842	+	589.842i	2.11413	+	2.11413i
$280$		−	12.7162i		−	0.0454149i
$281$	229.073	−	229.073i	0.815205	−	0.815205i	−0.170204	−	0.985409i	$-0.554443\pi$
$281$	229.073	−	229.073i	0.815205	−	0.815205i	0.985409	+	0.170204i	$0.0544427\pi$
$282$		−	624.483i		−	2.21448i
$283$	11.2423			0.0397254			0.0198627	−	0.999803i	$-0.493677\pi$
$283$	11.2423			0.0397254			0.0198627	+	0.999803i	$0.493677\pi$
$284$	−21.9657	−	21.9657i	−0.0773439	−	0.0773439i
$285$	−512.568			−1.79848
$286$	17.6123	+	17.6123i	0.0615815	+	0.0615815i
$287$	−42.7712	+	42.7712i	−0.149028	+	0.149028i
$288$	−75.7560	+	75.7560i	−0.263042	+	0.263042i
$289$			379.287i			1.31241i
$290$	−236.532			−0.815627
$291$	366.269	−	366.269i	1.25866	−	1.25866i
$292$	−83.1425			−0.284735
$293$	480.569			1.64017			0.820083	−	0.572244i	$-0.193927\pi$
$293$	480.569			1.64017			0.820083	+	0.572244i	$0.193927\pi$
$294$	−354.404			−1.20546
$295$	164.217	−	164.217i	0.556669	−	0.556669i
$296$	19.0236	−	19.0236i	0.0642690	−	0.0642690i
$297$	−95.3224	−	95.3224i	−0.320951	−	0.320951i
$298$	−135.917	+	135.917i	−0.456096	+	0.456096i
$299$		−	142.117i		−	0.475308i
$300$	−91.7994	+	91.7994i	−0.305998	+	0.305998i
$301$	24.6023	+	24.6023i	0.0817354	+	0.0817354i
$302$	−249.028	+	249.028i	−0.824595	+	0.824595i
$303$			227.323i			0.750242i
$304$	−76.9055	+	76.9055i	−0.252979	+	0.252979i
$305$	−292.638			−0.959469
$306$	692.394			2.26273
$307$	572.021			1.86326			0.931630	−	0.363408i	$-0.118387\pi$
$307$	572.021			1.86326			0.931630	+	0.363408i	$0.118387\pi$
$308$	4.57462	−	4.57462i	0.0148527	−	0.0148527i
$309$	−199.880	+	199.880i	−0.646860	+	0.646860i
$310$	−222.148			−0.716605
$311$	−364.716	−	364.716i	−1.17272	−	1.17272i	−0.981558	−	0.191163i	$-0.938774\pi$
$311$	−364.716	−	364.716i	−1.17272	−	1.17272i	−0.191163	−	0.981558i	$-0.561226\pi$
$312$			102.613i			0.328889i
$313$	354.557			1.13277			0.566385	−	0.824141i	$-0.308341\pi$
$313$	354.557			1.13277			0.566385	+	0.824141i	$0.308341\pi$
$314$			93.1408i			0.296627i
$315$	60.2079	+	60.2079i	0.191136	+	0.191136i
$316$	123.570			0.391043
$317$	−239.526	−	239.526i	−0.755603	−	0.755603i	0.219916	−	0.975519i	$-0.429422\pi$
$317$	−239.526	−	239.526i	−0.755603	−	0.755603i	−0.975519	+	0.219916i	$0.929422\pi$
$318$			55.9917i			0.176074i
$319$	−85.0919	−	85.0919i	−0.266746	−	0.266746i
$320$		−	28.5314i		−	0.0891607i
$321$	453.961			1.41421
$322$	−36.9135			−0.114638
$323$	702.901			2.17616
$324$		−	214.469i		−	0.661942i
$325$			84.2895i			0.259352i
$326$	−312.839			−0.959628
$327$	−315.719			−0.965500
$328$	−95.9661	+	95.9661i	−0.292580	+	0.292580i
$329$	−74.4669	+	74.4669i	−0.226343	+	0.226343i
$330$	68.4094			0.207301
$331$	−521.688			−1.57610			−0.788048	−	0.615614i	$-0.788908\pi$
$331$	−521.688			−1.57610			−0.788048	+	0.615614i	$0.788908\pi$
$332$	58.8472	+	58.8472i	0.177251	+	0.177251i
$333$			180.144i			0.540974i
$334$			201.519i			0.603349i
$335$	77.5025			0.231351
$336$	26.6528			0.0793239
$337$	−285.098	+	285.098i	−0.845988	+	0.845988i	−0.989630	−	0.143641i	$-0.954119\pi$
$337$	−285.098	+	285.098i	−0.845988	+	0.845988i	0.143641	+	0.989630i	$0.454119\pi$
$338$	−121.891	−	121.891i	−0.360623	−	0.360623i
$339$	−1140.61			−3.36464
$340$	−130.386	+	130.386i	−0.383487	+	0.383487i
$341$	−79.9173	−	79.9173i	−0.234361	−	0.234361i
$342$		−	728.257i		−	2.12941i
$343$	85.9388	+	85.9388i	0.250550	+	0.250550i
$344$	55.2006	+	55.2006i	0.160467	+	0.160467i
$345$	−276.004	−	276.004i	−0.800012	−	0.800012i
$346$	74.9613	+	74.9613i	0.216651	+	0.216651i
$347$	−126.473			−0.364475			−0.182238	−	0.983255i	$-0.558334\pi$
$347$	−126.473			−0.364475			−0.182238	+	0.983255i	$0.558334\pi$
$348$		−	495.766i		−	1.42461i
$349$	−120.593			−0.345538			−0.172769	−	0.984962i	$-0.555271\pi$
$349$	−120.593			−0.345538			−0.172769	+	0.984962i	$0.555271\pi$
$350$	21.8934			0.0625525
$351$	−254.969	−	254.969i	−0.726406	−	0.726406i
$352$	10.2641	−	10.2641i	0.0291595	−	0.0291595i
$353$		−	362.527i		−	1.02699i	−0.858093	−	0.513494i	$-0.828351\pi$
$353$		−	362.527i		−	1.02699i	0.858093	−	0.513494i	$-0.171649\pi$
$354$	344.196	+	344.196i	0.972306	+	0.972306i
$355$	−39.1694	+	39.1694i	−0.110336	+	0.110336i
$356$	274.915			0.772233
$357$	−121.801	−	121.801i	−0.341179	−	0.341179i
$358$		−	23.3166i		−	0.0651301i
$359$	−129.816	+	129.816i	−0.361606	+	0.361606i	−0.864404	−	0.502798i	$-0.832304\pi$
$359$	−129.816	+	129.816i	−0.361606	+	0.361606i	0.502798	+	0.864404i	$0.332304\pi$
$360$	135.089	+	135.089i	0.375247	+	0.375247i
$361$		−	378.307i		−	1.04794i
$362$	384.748			1.06284
$363$	−427.637	−	427.637i	−1.17806	−	1.17806i
$364$	12.2362	−	12.2362i	0.0336160	−	0.0336160i
$365$			148.261i			0.406194i
$366$		−	613.363i		−	1.67586i
$367$	−446.162	+	446.162i	−1.21570	+	1.21570i	−0.246578	+	0.969123i	$0.579306\pi$
$367$	−446.162	+	446.162i	−1.21570	+	1.21570i	−0.969123	+	0.246578i	$0.920694\pi$
$368$	−82.8232			−0.225063
$369$		−	908.751i		−	2.46274i
$370$	−33.9232	−	33.9232i	−0.0916843	−	0.0916843i
$371$	6.67677	−	6.67677i	0.0179967	−	0.0179967i
$372$		−	465.617i		−	1.25166i
$373$	239.176	+	239.176i	0.641223	+	0.641223i	0.950856	−	0.309633i	$-0.100206\pi$
$373$	239.176	+	239.176i	0.641223	+	0.641223i	−0.309633	+	0.950856i	$0.600206\pi$
$374$	−93.8120			−0.250834
$375$	496.943	+	496.943i	1.32518	+	1.32518i
$376$	−167.082	+	167.082i	−0.444368	+	0.444368i
$377$	−227.604	−	227.604i	−0.603724	−	0.603724i
$378$	−66.2256	+	66.2256i	−0.175200	+	0.175200i
$379$	127.534	−	127.534i	0.336502	−	0.336502i	−0.518547	−	0.855049i	$-0.673527\pi$
$379$	127.534	−	127.534i	0.336502	−	0.336502i	0.855049	+	0.518547i	$0.173527\pi$
$380$	137.139	+	137.139i	0.360892	+	0.360892i
$381$	275.819	−	275.819i	0.723934	−	0.723934i
$382$	−42.8213	+	42.8213i	−0.112098	+	0.112098i
$383$	1.83699	+	1.83699i	0.00479631	+	0.00479631i	0.709501	−	0.704705i	$-0.248920\pi$
$383$	1.83699	+	1.83699i	0.00479631	+	0.00479631i	−0.704705	+	0.709501i	$0.748920\pi$
$384$	59.8013			0.155732
$385$	−8.15753	−	8.15753i	−0.0211884	−	0.0211884i
$386$	449.420			1.16430
$387$	−522.722			−1.35070
$388$	−195.993			−0.505136
$389$	185.801			0.477637			0.238819	−	0.971064i	$-0.423240\pi$
$389$	185.801			0.477637			0.238819	+	0.971064i	$0.423240\pi$
$390$	182.982			0.469184
$391$	378.494	+	378.494i	0.968014	+	0.968014i
$392$	94.8218	+	94.8218i	0.241892	+	0.241892i
$393$	−160.422	−	160.422i	−0.408198	−	0.408198i
$394$	−81.1773			−0.206034
$395$		−	220.351i		−	0.557851i
$396$			97.1962i			0.245445i
$397$	96.1820	−	96.1820i	0.242272	−	0.242272i	−0.575517	−	0.817789i	$-0.695199\pi$
$397$	96.1820	−	96.1820i	0.242272	−	0.242272i	0.817789	+	0.575517i	$0.195199\pi$
$398$	−81.1621	+	81.1621i	−0.203925	+	0.203925i
$399$	−128.109	+	128.109i	−0.321076	+	0.321076i
$400$	49.1224			0.122806
$401$	78.5972	+	78.5972i	0.196003	+	0.196003i	0.798284	−	0.602281i	$-0.205741\pi$
$401$	78.5972	+	78.5972i	0.196003	+	0.196003i	−0.602281	+	0.798284i	$0.705741\pi$
$402$			162.444i			0.404089i
$403$	−213.763	−	213.763i	−0.530429	−	0.530429i
$404$	60.8210	−	60.8210i	0.150547	−	0.150547i
$405$	−382.444			−0.944307
$406$	−59.1179	+	59.1179i	−0.145611	+	0.145611i
$407$		−	24.4076i		−	0.0599696i
$408$	−273.286	−	273.286i	−0.669818	−	0.669818i
$409$	97.1382	+	97.1382i	0.237502	+	0.237502i	0.815815	−	0.578313i	$-0.196289\pi$
$409$	97.1382	+	97.1382i	0.237502	+	0.237502i	−0.578313	+	0.815815i	$0.696289\pi$
$410$	171.128	+	171.128i	0.417386	+	0.417386i
$411$	589.674			1.43473
$412$	106.957			0.259604
$413$		−	82.0879i		−	0.198760i
$414$	392.147	−	392.147i	0.947215	−	0.947215i
$415$	104.937	−	104.937i	0.252861	−	0.252861i
$416$	27.4545	−	27.4545i	0.0659964	−	0.0659964i
$417$			612.203i			1.46811i
$418$			98.6710i			0.236055i
$419$		−	63.9019i		−	0.152511i	−0.997088	−	0.0762553i	$-0.975704\pi$
$419$		−	63.9019i		−	0.152511i	0.997088	−	0.0762553i	$-0.0242964\pi$
$420$		−	47.5277i		−	0.113161i
$421$			524.780i			1.24651i	0.782019	+	0.623254i	$0.214190\pi$
$421$			524.780i			1.24651i	−0.782019	+	0.623254i	$0.785810\pi$
$422$	221.892	−	221.892i	0.525810	−	0.525810i
$423$		−	1582.18i		−	3.74039i
$424$	14.9807	−	14.9807i	0.0353319	−	0.0353319i
$425$	−224.484	−	224.484i	−0.528198	−	0.528198i
$426$	−82.0984	−	82.0984i	−0.192719	−	0.192719i
$427$	−73.1409	+	73.1409i	−0.171290	+	0.171290i
$428$	−121.459	−	121.459i	−0.283782	−	0.283782i
$429$	65.8273	+	65.8273i	0.153444	+	0.153444i
$430$	98.4344	−	98.4344i	0.228917	−	0.228917i
$431$	−82.8266	−	82.8266i	−0.192173	−	0.192173i	0.604461	−	0.796634i	$-0.293388\pi$
$431$	−82.8266	−	82.8266i	−0.192173	−	0.192173i	−0.796634	+	0.604461i	$0.793388\pi$
$432$	−148.591	+	148.591i	−0.343961	+	0.343961i
$433$		−	200.557i		−	0.463180i	−0.972813	−	0.231590i	$-0.925607\pi$
$433$		−	200.557i		−	0.463180i	0.972813	−	0.231590i	$-0.0743928\pi$
$434$	−55.5228	+	55.5228i	−0.127933	+	0.127933i
$435$	−884.056			−2.03231
$436$	84.4714	+	84.4714i	0.193742	+	0.193742i
$437$	398.098	−	398.098i	0.910979	−	0.910979i
$438$	−310.752			−0.709479
$439$			51.1340i			0.116478i	0.998303	+	0.0582392i	$0.0185486\pi$
$439$			51.1340i			0.116478i	−0.998303	+	0.0582392i	$0.981451\pi$
$440$	−18.3031	−	18.3031i	−0.0415980	−	0.0415980i
$441$	−897.915			−2.03609
$442$	−250.929			−0.567712
$443$	307.613	+	307.613i	0.694386	+	0.694386i	0.963194	−	0.268807i	$-0.0866295\pi$
$443$	307.613	+	307.613i	0.694386	+	0.694386i	−0.268807	+	0.963194i	$0.586630\pi$
$444$	71.1023	−	71.1023i	0.160140	−	0.160140i
$445$		−	490.232i		−	1.10164i
$446$	473.723			1.06216
$447$	−507.999	+	507.999i	−1.13646	+	1.13646i
$448$	−7.13104	−	7.13104i	−0.0159175	−	0.0159175i
$449$	−41.1705			−0.0916937			−0.0458468	−	0.998948i	$-0.514599\pi$
$449$	−41.1705			−0.0916937			−0.0458468	+	0.998948i	$0.514599\pi$
$450$	−232.582	+	232.582i	−0.516849	+	0.516849i
$451$			123.126i			0.273007i
$452$	305.174	+	305.174i	0.675164	+	0.675164i
$453$	−930.760	+	930.760i	−2.05466	+	2.05466i
$454$	−475.772			−1.04796
$455$	−21.8198	−	21.8198i	−0.0479556	−	0.0479556i
$456$	−287.440	+	287.440i	−0.630352	+	0.630352i
$457$			339.800i			0.743545i	0.928324	+	0.371772i	$0.121250\pi$
$457$			339.800i			0.743545i	−0.928324	+	0.371772i	$0.878750\pi$
$458$		−	213.611i		−	0.466399i
$459$	1358.09			2.95881
$460$			147.691i			0.321068i
$461$	−214.144	+	214.144i	−0.464520	+	0.464520i	−0.900134	−	0.435614i	$-0.856531\pi$
$461$	−214.144	+	214.144i	−0.464520	+	0.464520i	0.435614	+	0.900134i	$0.356531\pi$
$462$	17.0980	−	17.0980i	0.0370087	−	0.0370087i
$463$	274.915	−	274.915i	0.593769	−	0.593769i	−0.344878	−	0.938647i	$-0.612080\pi$
$463$	274.915	−	274.915i	0.593769	−	0.593769i	0.938647	+	0.344878i	$0.112080\pi$
$464$	−132.644	+	132.644i	−0.285870	+	0.285870i
$465$	−830.294			−1.78558
$466$	27.8816	−	27.8816i	0.0598317	−	0.0598317i
$467$	−74.6671	−	74.6671i	−0.159887	−	0.159887i	0.622630	−	0.782517i	$-0.286064\pi$
$467$	−74.6671	−	74.6671i	−0.159887	−	0.159887i	−0.782517	+	0.622630i	$0.786064\pi$
$468$			259.980i			0.555514i
$469$	19.3707	−	19.3707i	0.0413022	−	0.0413022i
$470$	297.943	+	297.943i	0.633922	+	0.633922i
$471$			348.121i			0.739111i
$472$		−	184.181i		−	0.390215i
$473$	70.8232			0.149732
$474$	461.852			0.974370
$475$	−236.111	+	236.111i	−0.497077	+	0.497077i
$476$			65.1763i			0.136925i
$477$			141.860i			0.297400i
$478$	−366.238	−	366.238i	−0.766187	−	0.766187i
$479$	−240.022	−	240.022i	−0.501089	−	0.501089i	0.410687	−	0.911776i	$-0.365289\pi$
$479$	−240.022	−	240.022i	−0.501089	−	0.501089i	−0.911776	+	0.410687i	$0.865289\pi$
$480$		−	106.638i		−	0.222163i
$481$		−	65.2856i		−	0.135729i
$482$	41.6485			0.0864077
$483$	−137.967			−0.285646
$484$			228.831i			0.472791i
$485$			349.497i			0.720613i
$486$		−	132.936i		−	0.273530i
$487$	−421.501			−0.865506			−0.432753	−	0.901513i	$-0.642458\pi$
$487$	−421.501			−0.865506			−0.432753	+	0.901513i	$0.642458\pi$
$488$	−164.107	+	164.107i	−0.336285	+	0.336285i
$489$	−1169.26			−2.39112
$490$	169.087	−	169.087i	0.345076	−	0.345076i
$491$			960.328i			1.95586i	0.208931	+	0.977930i	$0.433002\pi$
$491$			960.328i			1.95586i	−0.208931	+	0.977930i	$0.566998\pi$
$492$	−358.681	+	358.681i	−0.729026	+	0.729026i
$493$	1212.33			2.45910
$494$			263.925i			0.534262i
$495$	173.322			0.350144
$496$	−124.577	+	124.577i	−0.251164	+	0.251164i
$497$			19.5798i			0.0393959i
$498$	219.946	+	219.946i	0.441659	+	0.441659i
$499$	−144.355	−	144.355i	−0.289289	−	0.289289i	0.547510	−	0.836799i	$-0.315576\pi$
$499$	−144.355	−	144.355i	−0.289289	−	0.289289i	−0.836799	+	0.547510i	$0.815576\pi$
$500$		−	265.917i		−	0.531834i
$501$			753.192i			1.50338i
$502$			338.299i			0.673902i
$503$	443.700	+	443.700i	0.882107	+	0.882107i	0.993749	−	0.111642i	$-0.0356108\pi$
$503$	443.700	+	443.700i	0.882107	+	0.882107i	−0.111642	+	0.993749i	$0.535611\pi$
$504$	67.5274			0.133983
$505$	−108.457	−	108.457i	−0.214766	−	0.214766i
$506$	−53.1318	+	53.1318i	−0.105003	+	0.105003i
$507$	−455.576	−	455.576i	−0.898572	−	0.898572i
$508$	−147.592			−0.290536
$509$	308.901	+	308.901i	0.606879	+	0.606879i	0.942129	−	0.335250i	$-0.108821\pi$
$509$	308.901	+	308.901i	0.606879	+	0.606879i	−0.335250	+	0.942129i	$0.608821\pi$
$510$	−487.327	+	487.327i	−0.955542	+	0.955542i
$511$	37.0558	+	37.0558i	0.0725163	+	0.0725163i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$		−	1428.43i		−	2.78447i
$514$			107.494i			0.209132i
$515$		−	190.727i		−	0.370343i
$516$	206.316	+	206.316i	0.399838	+	0.399838i
$517$			214.369i			0.414641i
$518$	−16.9573			−0.0327361
$519$	280.174	+	280.174i	0.539834	+	0.539834i
$520$	−48.9573	−	48.9573i	−0.0941486	−	0.0941486i
$521$	306.825	−	306.825i	0.588916	−	0.588916i	−0.348422	−	0.937338i	$-0.613282\pi$
$521$	306.825	−	306.825i	0.588916	−	0.588916i	0.937338	+	0.348422i	$0.113282\pi$
$522$		−	1256.07i		−	2.40626i
$523$	−430.202	+	430.202i	−0.822567	+	0.822567i	−0.986475	−	0.163909i	$-0.947590\pi$
$523$	−430.202	+	430.202i	−0.822567	+	0.822567i	0.163909	+	0.986475i	$0.447590\pi$
$524$			85.8426i			0.163822i
$525$	81.8282			0.155863
$526$	44.7508	+	44.7508i	0.0850776	+	0.0850776i
$527$	1138.61			2.16055
$528$	38.3630	−	38.3630i	0.0726572	−	0.0726572i
$529$	−100.270			−0.189546
$530$	−26.7138	−	26.7138i	−0.0504035	−	0.0504035i
$531$	872.053	+	872.053i	1.64228	+	1.64228i
$532$	68.5521			0.128857
$533$			329.338i			0.617895i
$534$	1027.52			1.92419
$535$	−216.586	+	216.586i	−0.404835	+	0.404835i
$536$	43.4623	−	43.4623i	0.0810863	−	0.0810863i
$537$		−	87.1476i		−	0.162286i
$538$	−120.699	−	360.768i	−0.224348	−	0.670573i
$539$	121.658			0.225710
$540$	264.970	+	264.970i	0.490685	+	0.490685i
$541$	−136.419	−	136.419i	−0.252161	−	0.252161i	0.569695	−	0.821856i	$-0.307061\pi$
$541$	−136.419	−	136.419i	−0.252161	−	0.252161i	−0.821856	+	0.569695i	$0.807061\pi$
$542$		−	337.195i		−	0.622131i
$543$	1438.02			2.64830
$544$			146.237i			0.268817i
$545$	150.631	−	150.631i	0.276386	−	0.276386i
$546$	45.7338	−	45.7338i	0.0837616	−	0.0837616i
$547$			814.963i			1.48988i	0.667133	+	0.744939i	$0.267521\pi$
$547$			814.963i			1.48988i	−0.667133	+	0.744939i	$0.732479\pi$
$548$	−157.769	−	157.769i	−0.287900	−	0.287900i
$549$		−	1554.01i		−	2.83062i
$550$	31.5124	−	31.5124i	0.0572953	−	0.0572953i
$551$		−	1275.13i		−	2.31421i
$552$	−309.558			−0.560794
$553$	−55.0738	−	55.0738i	−0.0995910	−	0.0995910i
$554$	−275.122			−0.496609
$555$	−126.791	−	126.791i	−0.228452	−	0.228452i
$556$	163.797	−	163.797i	0.294598	−	0.294598i
$557$	473.160	−	473.160i	0.849479	−	0.849479i	−0.140589	−	0.990068i	$-0.544900\pi$
$557$	473.160	−	473.160i	0.849479	−	0.849479i	0.990068	+	0.140589i	$0.0448996\pi$
$558$		−	1179.68i		−	2.11413i
$559$	189.438			0.338887
$560$	−12.7162	+	12.7162i	−0.0227075	+	0.0227075i
$561$	−350.630			−0.625009
$562$	−458.145			−0.815205
$563$	103.066			0.183065			0.0915327	−	0.995802i	$-0.470823\pi$
$563$	103.066			0.183065			0.0915327	+	0.995802i	$0.470823\pi$
$564$	−624.483	+	624.483i	−1.10724	+	1.10724i
$565$	544.191	−	544.191i	0.963169	−	0.963169i
$566$	−11.2423	−	11.2423i	−0.0198627	−	0.0198627i
$567$	−95.5869	+	95.5869i	−0.168584	+	0.168584i
$568$			43.9313i			0.0773439i
$569$	−403.594	+	403.594i	−0.709304	+	0.709304i	−0.966389	−	0.257084i	$-0.917238\pi$
$569$	−403.594	+	403.594i	−0.709304	+	0.709304i	0.257084	+	0.966389i	$0.417238\pi$
$570$	512.568	+	512.568i	0.899242	+	0.899242i
$571$	208.349	−	208.349i	0.364885	−	0.364885i	−0.500723	−	0.865608i	$-0.666932\pi$
$571$	208.349	−	208.349i	0.364885	−	0.364885i	0.865608	+	0.500723i	$0.166932\pi$
$572$		−	35.2246i		−	0.0615815i
$573$	−160.048	+	160.048i	−0.279316	+	0.279316i
$574$	85.5423			0.149028
$575$	−254.280			−0.442226
$576$	151.512			0.263042
$577$	710.572	−	710.572i	1.23149	−	1.23149i	0.268104	−	0.963390i	$-0.413603\pi$
$577$	710.572	−	710.572i	1.23149	−	1.23149i	0.963390	−	0.268104i	$-0.0863972\pi$
$578$	379.287	−	379.287i	0.656205	−	0.656205i
$579$	1679.74			2.90111
$580$	236.532	+	236.532i	0.407813	+	0.407813i
$581$		−	52.4553i		−	0.0902845i
$582$	−732.539			−1.25866
$583$		−	19.2205i		−	0.0329683i
$584$	83.1425	+	83.1425i	0.142367	+	0.142367i
$585$	463.601			0.792480
$586$	−480.569	−	480.569i	−0.820083	−	0.820083i
$587$			745.134i			1.26939i	0.772761	+	0.634697i	$0.218875\pi$
$587$			745.134i			1.26939i	−0.772761	+	0.634697i	$0.781125\pi$
$588$	354.404	+	354.404i	0.602728	+	0.602728i
$589$		−	1197.58i		−	2.03325i
$590$	−328.435			−0.556669
$591$	−303.406			−0.513378
$592$	−38.0473			−0.0642690
$593$		−	166.041i		−	0.280002i	−0.990151	−	0.140001i	$-0.955289\pi$
$593$		−	166.041i		−	0.280002i	0.990151	−	0.140001i	$-0.0447106\pi$
$594$			190.645i			0.320951i
$595$	116.223			0.195333
$596$	271.833			0.456096
$597$	−303.350	+	303.350i	−0.508124	+	0.508124i
$598$	−142.117	+	142.117i	−0.237654	+	0.237654i
$599$	−487.490			−0.813839			−0.406919	−	0.913464i	$-0.633397\pi$
$599$	−487.490			−0.813839			−0.406919	+	0.913464i	$0.633397\pi$
$600$	183.599			0.305998
$601$	556.414	+	556.414i	0.925813	+	0.925813i	0.997432	−	0.0716191i	$-0.0228166\pi$
$601$	556.414	+	556.414i	0.925813	+	0.925813i	−0.0716191	+	0.997432i	$0.522817\pi$
$602$		−	49.2047i		−	0.0817354i
$603$			411.566i			0.682530i
$604$	498.055			0.824595
$605$	408.054			0.674470
$606$	227.323	−	227.323i	0.375121	−	0.375121i
$607$	617.124	+	617.124i	1.01668	+	1.01668i	0.999859	+	0.0168196i	$0.00535409\pi$
$607$	617.124	+	617.124i	1.01668	+	1.01668i	0.0168196	+	0.999859i	$0.494646\pi$
$608$	153.811			0.252979
$609$	−220.958	+	220.958i	−0.362821	+	0.362821i
$610$	292.638	+	292.638i	0.479734	+	0.479734i
$611$			573.395i			0.938453i
$612$	−692.394	−	692.394i	−1.13136	−	1.13136i
$613$	586.008	+	586.008i	0.955967	+	0.955967i	0.999071	−	0.0431036i	$-0.0137246\pi$
$613$	586.008	+	586.008i	0.955967	+	0.955967i	−0.0431036	+	0.999071i	$0.513725\pi$
$614$	−572.021	−	572.021i	−0.931630	−	0.931630i
$615$	639.605	+	639.605i	1.04001	+	1.04001i
$616$	−9.14925			−0.0148527
$617$			381.746i			0.618714i	0.950946	+	0.309357i	$0.100114\pi$
$617$			381.746i			0.618714i	−0.950946	+	0.309357i	$0.899886\pi$
$618$	399.760			0.646860
$619$	−819.066			−1.32321			−0.661604	−	0.749853i	$-0.730124\pi$
$619$	−819.066			−1.32321			−0.661604	+	0.749853i	$0.730124\pi$
$620$	222.148	+	222.148i	0.358303	+	0.358303i
$621$	769.175	−	769.175i	1.23861	−	1.23861i
$622$			729.433i			1.17272i
$623$	−122.527	−	122.527i	−0.196672	−	0.196672i
$624$	102.613	−	102.613i	0.164445	−	0.164445i
$625$	−167.172			−0.267475
$626$	−354.557	−	354.557i	−0.566385	−	0.566385i
$627$			368.791i			0.588183i
$628$	93.1408	−	93.1408i	0.148313	−	0.148313i
$629$	173.872	+	173.872i	0.276426	+	0.276426i
$630$		−	120.416i		−	0.191136i
$631$	917.988			1.45481			0.727407	−	0.686206i	$-0.240725\pi$
$631$	917.988			1.45481			0.727407	+	0.686206i	$0.240725\pi$
$632$	−123.570	−	123.570i	−0.195522	−	0.195522i
$633$	829.338	−	829.338i	1.31017	−	1.31017i
$634$			479.052i			0.755603i
$635$			263.189i			0.414470i
$636$	55.9917	−	55.9917i	0.0880372	−	0.0880372i
$637$	325.411			0.510849
$638$			170.184i			0.266746i
$639$	−208.004	−	208.004i	−0.325514	−	0.325514i
$640$	−28.5314	+	28.5314i	−0.0445803	+	0.0445803i
$641$			1021.28i			1.59326i	0.604467	+	0.796630i	$0.293386\pi$
$641$			1021.28i			1.59326i	−0.604467	+	0.796630i	$0.706614\pi$
$642$	−453.961	−	453.961i	−0.707104	−	0.707104i
$643$	−671.534			−1.04438			−0.522188	−	0.852830i	$-0.674884\pi$
$643$	−671.534			−1.04438			−0.522188	+	0.852830i	$0.674884\pi$
$644$	36.9135	+	36.9135i	0.0573191	+	0.0573191i
$645$	367.906	−	367.906i	0.570397	−	0.570397i
$646$	−702.901	−	702.901i	−1.08808	−	1.08808i
$647$	407.848	−	407.848i	0.630368	−	0.630368i	−0.317792	−	0.948160i	$-0.602941\pi$
$647$	407.848	−	407.848i	0.630368	−	0.630368i	0.948160	+	0.317792i	$0.102941\pi$
$648$	−214.469	+	214.469i	−0.330971	+	0.330971i
$649$	−118.154	−	118.154i	−0.182055	−	0.182055i
$650$	84.2895	−	84.2895i	0.129676	−	0.129676i
$651$	−207.521	+	207.521i	−0.318773	+	0.318773i
$652$	312.839	+	312.839i	0.479814	+	0.479814i
$653$	395.816			0.606150			0.303075	−	0.952967i	$-0.401987\pi$
$653$	395.816			0.606150			0.303075	+	0.952967i	$0.401987\pi$
$654$	315.719	+	315.719i	0.482750	+	0.482750i
$655$	153.076			0.233703
$656$	191.932			0.292580
$657$	−787.318			−1.19835
$658$	148.934			0.226343
$659$	−981.691			−1.48967			−0.744834	−	0.667250i	$-0.767471\pi$
$659$	−981.691			−1.48967			−0.744834	+	0.667250i	$0.767471\pi$
$660$	−68.4094	−	68.4094i	−0.103651	−	0.103651i
$661$	32.1231	+	32.1231i	0.0485978	+	0.0485978i	0.730988	−	0.682390i	$-0.239060\pi$
$661$	32.1231	+	32.1231i	0.0485978	+	0.0485978i	−0.682390	+	0.730988i	$0.739060\pi$
$662$	521.688	+	521.688i	0.788048	+	0.788048i
$663$	−937.866			−1.41458
$664$		−	117.694i		−	0.177251i
$665$		−	122.243i		−	0.183824i
$666$	180.144	−	180.144i	0.270487	−	0.270487i
$667$	686.623	−	686.623i	1.02942	−	1.02942i
$668$	201.519	−	201.519i	0.301675	−	0.301675i
$669$	1770.58			2.64660
$670$	−77.5025	−	77.5025i	−0.115675	−	0.115675i
$671$			210.552i			0.313788i
$672$	−26.6528	−	26.6528i	−0.0396620	−	0.0396620i
$673$	−777.793	+	777.793i	−1.15571	+	1.15571i	−0.170321	+	0.985389i	$0.554481\pi$
$673$	−777.793	+	777.793i	−1.15571	+	1.15571i	−0.985389	+	0.170321i	$0.945519\pi$
$674$	570.196			0.845988
$675$	−456.197	+	456.197i	−0.675847	+	0.675847i
$676$			243.781i			0.360623i
$677$	−903.696	−	903.696i	−1.33485	−	1.33485i	−0.900968	−	0.433886i	$-0.857142\pi$
$677$	−903.696	−	903.696i	−1.33485	−	1.33485i	−0.433886	−	0.900968i	$-0.642858\pi$
$678$	1140.61	+	1140.61i	1.68232	+	1.68232i
$679$	87.3521	+	87.3521i	0.128648	+	0.128648i
$680$	260.771			0.383487
$681$	−1778.24			−2.61121
$682$			159.835i			0.234361i
$683$	−628.247	+	628.247i	−0.919835	+	0.919835i	−0.997017	−	0.0771823i	$-0.975408\pi$
$683$	−628.247	+	628.247i	−0.919835	+	0.919835i	0.0771823	+	0.997017i	$0.475408\pi$
$684$	−728.257	+	728.257i	−1.06470	+	1.06470i
$685$	−281.336	+	281.336i	−0.410709	+	0.410709i
$686$		−	171.878i		−	0.250550i
$687$		−	798.388i		−	1.16214i
$688$		−	110.401i		−	0.160467i
$689$		−	51.4111i		−	0.0746170i
$690$			552.009i			0.800012i
$691$	467.326	−	467.326i	0.676304	−	0.676304i	−0.282858	−	0.959162i	$-0.591282\pi$
$691$	467.326	−	467.326i	0.676304	−	0.676304i	0.959162	+	0.282858i	$0.0912825\pi$
$692$		−	149.923i		−	0.216651i
$693$	43.3194	−	43.3194i	0.0625099	−	0.0625099i
$694$	126.473	+	126.473i	0.182238	+	0.182238i
$695$	−292.084	−	292.084i	−0.420265	−	0.420265i
$696$	−495.766	+	495.766i	−0.712307	+	0.712307i
$697$	−877.110	−	877.110i	−1.25841	−	1.25841i
$698$	120.593	+	120.593i	0.172769	+	0.172769i
$699$	104.210	−	104.210i	0.149084	−	0.149084i
$700$	−21.8934	−	21.8934i	−0.0312763	−	0.0312763i
$701$	−713.369	+	713.369i	−1.01764	+	1.01764i	−0.0178035	+	0.999842i	$0.505667\pi$
$701$	−713.369	+	713.369i	−1.01764	+	1.01764i	−0.999842	+	0.0178035i	$0.994333\pi$
$702$			509.937i			0.726406i
$703$	182.878	−	182.878i	0.260139	−	0.260139i
$704$	−20.5283			−0.0291595
$705$	1113.59	+	1113.59i	1.57956	+	1.57956i
$706$	−362.527	+	362.527i	−0.513494	+	0.513494i
$707$	−54.2146			−0.0766827
$708$		−	688.393i		−	0.972306i
$709$	417.364	+	417.364i	0.588665	+	0.588665i	0.937270	−	0.348605i	$-0.113344\pi$
$709$	417.364	+	417.364i	0.588665	+	0.588665i	−0.348605	+	0.937270i	$0.613344\pi$
$710$	78.3389			0.110336
$711$	1170.14			1.64577
$712$	−274.915	−	274.915i	−0.386116	−	0.386116i
$713$	644.868	−	644.868i	0.904443	−	0.904443i
$714$			243.602i			0.341179i
$715$	−62.8130			−0.0878503
$716$	−23.3166	+	23.3166i	−0.0325651	+	0.0325651i
$717$	−1368.84	−	1368.84i	−1.90912	−	1.90912i
$718$	259.633			0.361606
$719$	−308.569	+	308.569i	−0.429164	+	0.429164i	−0.888343	−	0.459180i	$-0.848143\pi$
$719$	−308.569	+	308.569i	−0.429164	+	0.429164i	0.459180	+	0.888343i	$0.348143\pi$
$720$		−	270.178i		−	0.375247i
$721$	−47.6696	−	47.6696i	−0.0661160	−	0.0661160i
$722$	−378.307	+	378.307i	−0.523972	+	0.523972i
$723$	155.665			0.215304
$724$	−384.748	−	384.748i	−0.531419	−	0.531419i
$725$	−407.236	+	407.236i	−0.561704	+	0.561704i
$726$			855.274i			1.17806i
$727$			230.505i			0.317063i	0.987354	+	0.158532i	$0.0506760\pi$
$727$			230.505i			0.317063i	−0.987354	+	0.158532i	$0.949324\pi$
$728$	−24.4724			−0.0336160
$729$			468.254i			0.642324i
$730$	148.261	−	148.261i	0.203097	−	0.203097i
$731$	−504.522	+	504.522i	−0.690180	+	0.690180i
$732$	−613.363	+	613.363i	−0.837928	+	0.837928i
$733$	−715.564	+	715.564i	−0.976213	+	0.976213i	−0.999724	−	0.0235111i	$-0.992516\pi$
$733$	−715.564	+	715.564i	−0.976213	+	0.976213i	0.0235111	+	0.999724i	$0.492516\pi$
$734$	892.325			1.21570
$735$	631.978	−	631.978i	0.859834	−	0.859834i
$736$	82.8232	+	82.8232i	0.112532	+	0.112532i
$737$		−	55.7628i		−	0.0756619i
$738$	−908.751	+	908.751i	−1.23137	+	1.23137i
$739$	−195.309	−	195.309i	−0.264288	−	0.264288i	0.562505	−	0.826794i	$-0.309838\pi$
$739$	−195.309	−	195.309i	−0.264288	−	0.264288i	−0.826794	+	0.562505i	$0.809838\pi$
$740$			67.8464i			0.0916843i
$741$			986.442i			1.33123i
$742$	−13.3535			−0.0179967
$743$	149.544			0.201271			0.100635	−	0.994923i	$-0.467912\pi$
$743$	149.544			0.201271			0.100635	+	0.994923i	$0.467912\pi$
$744$	−465.617	+	465.617i	−0.625829	+	0.625829i
$745$		−	484.737i		−	0.650653i
$746$		−	478.352i		−	0.641223i
$747$	557.254	+	557.254i	0.745989	+	0.745989i
$748$	93.8120	+	93.8120i	0.125417	+	0.125417i
$749$			108.266i			0.144547i
$750$		−	993.886i		−	1.32518i
$751$	1082.37			1.44124			0.720622	−	0.693328i	$-0.243856\pi$
$751$	1082.37			1.44124			0.720622	+	0.693328i	$0.243856\pi$
$752$	334.164			0.444368
$753$			1264.42i			1.67917i
$754$			455.208i			0.603724i
$755$		−	888.139i		−	1.17634i
$756$	132.451			0.175200
$757$	−662.151	+	662.151i	−0.874704	+	0.874704i	−0.992981	−	0.118277i	$-0.962263\pi$
$757$	−662.151	+	662.151i	−0.874704	+	0.874704i	0.118277	+	0.992981i	$0.462263\pi$
$758$	−255.069			−0.336502
$759$	−198.584	+	198.584i	−0.261639	+	0.261639i
$760$		−	274.278i		−	0.360892i
$761$	206.058	−	206.058i	0.270773	−	0.270773i	−0.558639	−	0.829411i	$-0.688676\pi$
$761$	206.058	−	206.058i	0.270773	−	0.270773i	0.829411	+	0.558639i	$0.188676\pi$
$762$	−551.638			−0.723934
$763$		−	75.2962i		−	0.0986844i
$764$	85.6426			0.112098
$765$	−1234.69	+	1234.69i	−1.61397	+	1.61397i
$766$		−	3.67397i		−	0.00479631i
$767$	−316.038	−	316.038i	−0.412045	−	0.412045i
$768$	−59.8013	−	59.8013i	−0.0778662	−	0.0778662i
$769$		−	914.612i		−	1.18935i	−0.803965	−	0.594676i	$-0.797280\pi$
$769$		−	914.612i		−	1.18935i	0.803965	−	0.594676i	$-0.202720\pi$
$770$			16.3151i			0.0211884i
$771$			401.766i			0.521097i
$772$	−449.420	−	449.420i	−0.582150	−	0.582150i
$773$	−854.338			−1.10522			−0.552612	−	0.833439i	$-0.686369\pi$
$773$	−854.338			−1.10522			−0.552612	+	0.833439i	$0.686369\pi$
$774$	522.722	+	522.722i	0.675351	+	0.675351i
$775$	−382.471	+	382.471i	−0.493510	+	0.493510i
$776$	195.993	+	195.993i	0.252568	+	0.252568i
$777$	−63.3792			−0.0815692
$778$	−185.801	−	185.801i	−0.238819	−	0.238819i
$779$	−922.540	+	922.540i	−1.18426	+	1.18426i
$780$	−182.982	−	182.982i	−0.234592	−	0.234592i
$781$	28.1823	+	28.1823i	0.0360849	+	0.0360849i
$782$		−	756.987i		−	0.968014i
$783$		−	2463.71i		−	3.14650i
$784$		−	189.644i		−	0.241892i
$785$	−166.090	−	166.090i	−0.211580	−	0.211580i
$786$			320.844i			0.408198i
$787$	315.408			0.400773			0.200386	−	0.979717i	$-0.435780\pi$
$787$	315.408			0.400773			0.200386	+	0.979717i	$0.435780\pi$
$788$	81.1773	+	81.1773i	0.103017	+	0.103017i
$789$	167.260	+	167.260i	0.211989	+	0.211989i
$790$	−220.351	+	220.351i	−0.278926	+	0.278926i
$791$		−	272.026i		−	0.343902i
$792$	97.1962	−	97.1962i	0.122722	−	0.122722i
$793$			563.185i			0.710195i
$794$	−192.364			−0.242272
$795$	−99.8451	−	99.8451i	−0.125591	−	0.125591i
$796$	162.324			0.203925
$797$	434.738	−	434.738i	0.545468	−	0.545468i	−0.379658	−	0.925127i	$-0.623958\pi$
$797$	434.738	−	434.738i	0.545468	−	0.545468i	0.925127	+	0.379658i	$0.123958\pi$
$798$	256.219			0.321076
$799$	−1527.10	−	1527.10i	−1.91126	−	1.91126i
$800$	−49.1224	−	49.1224i	−0.0614030	−	0.0614030i
$801$	2603.31			3.25007
$802$		−	157.194i		−	0.196003i
$803$	106.673			0.132843
$804$	162.444	−	162.444i	0.202044	−	0.202044i
$805$	65.8247	−	65.8247i	0.0817698	−	0.0817698i
$806$			427.526i			0.530429i
$807$	−451.123	−	1348.40i	−0.559012	−	1.67088i
$808$	−121.642			−0.150547
$809$	424.674	+	424.674i	0.524937	+	0.524937i	0.919058	−	0.394121i	$-0.128951\pi$
$809$	424.674	+	424.674i	0.524937	+	0.524937i	−0.394121	+	0.919058i	$0.628951\pi$
$810$	382.444	+	382.444i	0.472154	+	0.472154i
$811$		−	119.913i		−	0.147858i	−0.997263	−	0.0739292i	$-0.976446\pi$
$811$		−	119.913i		−	0.147858i	0.997263	−	0.0739292i	$-0.0235539\pi$
$812$	118.236			0.145611
$813$		−	1260.29i		−	1.55018i
$814$	−24.4076	+	24.4076i	−0.0299848	+	0.0299848i
$815$	557.858	−	557.858i	0.684489	−	0.684489i
$816$			546.571i			0.669818i
$817$	530.653	+	530.653i	0.649515	+	0.649515i
$818$		−	194.276i		−	0.237502i
$819$	115.871	−	115.871i	0.141478	−	0.141478i
$820$		−	342.256i		−	0.417386i
$821$	1398.26			1.70311			0.851557	−	0.524262i	$-0.175659\pi$
$821$	1398.26			1.70311			0.851557	+	0.524262i	$0.175659\pi$
$822$	−589.674	−	589.674i	−0.717365	−	0.717365i
$823$	−278.835			−0.338804			−0.169402	−	0.985547i	$-0.554184\pi$
$823$	−278.835			−0.338804			−0.169402	+	0.985547i	$0.554184\pi$
$824$	−106.957	−	106.957i	−0.129802	−	0.129802i
$825$	117.780	−	117.780i	0.142764	−	0.142764i
$826$	−82.0879	+	82.0879i	−0.0993800	+	0.0993800i
$827$			132.422i			0.160124i	0.996790	+	0.0800618i	$0.0255118\pi$
$827$			132.422i			0.160124i	−0.996790	+	0.0800618i	$0.974488\pi$
$828$	−784.294			−0.947215
$829$	51.8265	−	51.8265i	0.0625169	−	0.0625169i	−0.675157	−	0.737674i	$-0.735924\pi$
$829$	51.8265	−	51.8265i	0.0625169	−	0.0625169i	0.737674	+	0.675157i	$0.235924\pi$
$830$	−209.874			−0.252861
$831$	−1028.29			−1.23741
$832$	−54.9090			−0.0659964
$833$	−866.651	+	866.651i	−1.04040	+	1.04040i
$834$	612.203	−	612.203i	0.734056	−	0.734056i
$835$	−359.351	−	359.351i	−0.430360	−	0.430360i
$836$	98.6710	−	98.6710i	0.118028	−	0.118028i
$837$		−	2313.88i		−	2.76450i
$838$	−63.9019	+	63.9019i	−0.0762553	+	0.0762553i
$839$	−326.817	−	326.817i	−0.389531	−	0.389531i	0.484989	−	0.874520i	$-0.338824\pi$
$839$	−326.817	−	326.817i	−0.389531	−	0.389531i	−0.874520	+	0.484989i	$0.838824\pi$
$840$	−47.5277	+	47.5277i	−0.0565806	+	0.0565806i
$841$		−	1358.29i		−	1.61509i
$842$	524.780	−	524.780i	0.623254	−	0.623254i
$843$	−1712.35			−2.03126
$844$	−443.784			−0.525810
$845$	434.714			0.514454
$846$	−1582.18	+	1582.18i	−1.87019	+	1.87019i
$847$	101.988	−	101.988i	0.120411	−	0.120411i
$848$	−29.9615			−0.0353319
$849$	−42.0190	−	42.0190i	−0.0494923	−	0.0494923i
$850$			448.969i			0.528198i
$851$	196.950			0.231433
$852$			164.197i			0.192719i
$853$	663.796	+	663.796i	0.778190	+	0.778190i	0.979523	−	0.201333i	$-0.0645273\pi$
$853$	663.796	+	663.796i	0.778190	+	0.778190i	−0.201333	+	0.979523i	$0.564527\pi$
$854$	146.282			0.171290
$855$	1298.64	+	1298.64i	1.51887	+	1.51887i
$856$			242.917i			0.283782i
$857$	176.448	+	176.448i	0.205890	+	0.205890i	0.802518	−	0.596628i	$-0.203493\pi$
$857$	176.448	+	176.448i	0.205890	+	0.205890i	−0.596628	+	0.802518i	$0.703493\pi$
$858$		−	131.655i		−	0.153444i
$859$	1508.88			1.75656			0.878278	−	0.478151i	$-0.158693\pi$
$859$	1508.88			1.75656			0.878278	+	0.478151i	$0.158693\pi$
$860$	−196.869			−0.228917
$861$	319.721			0.371337
$862$			165.653i			0.192173i
$863$		−	699.998i		−	0.811121i	−0.914068	−	0.405561i	$-0.867076\pi$
$863$		−	699.998i		−	0.811121i	0.914068	−	0.405561i	$-0.132924\pi$
$864$	297.182			0.343961
$865$	−267.344			−0.309068
$866$	−200.557	+	200.557i	−0.231590	+	0.231590i
$867$	1417.61	−	1417.61i	1.63508	−	1.63508i
$868$	111.046			0.127933
$869$	−158.542			−0.182442
$870$	884.056	+	884.056i	1.01616	+	1.01616i
$871$		−	149.154i		−	0.171245i
$872$		−	168.943i		−	0.193742i
$873$	−1855.95			−2.12595
$874$	−796.195			−0.910979
$875$	−118.517	+	118.517i	−0.135448	+	0.135448i
$876$	310.752	+	310.752i	0.354739	+	0.354739i
$877$	−1280.46			−1.46004			−0.730021	−	0.683424i	$-0.760490\pi$
$877$	−1280.46			−1.46004			−0.730021	+	0.683424i	$0.760490\pi$
$878$	51.1340	−	51.1340i	0.0582392	−	0.0582392i
$879$	−1796.16	−	1796.16i	−2.04342	−	2.04342i
$880$			36.6063i			0.0415980i
$881$	1094.10	+	1094.10i	1.24188	+	1.24188i	0.959218	+	0.282667i	$0.0912191\pi$
$881$	1094.10	+	1094.10i	1.24188	+	1.24188i	0.282667	+	0.959218i	$0.408781\pi$
$882$	897.915	+	897.915i	1.01804	+	1.01804i
$883$	636.432	+	636.432i	0.720761	+	0.720761i	0.968760	−	0.247999i	$-0.0797730\pi$
$883$	636.432	+	636.432i	0.720761	+	0.720761i	−0.247999	+	0.968760i	$0.579773\pi$
$884$	250.929	+	250.929i	0.283856	+	0.283856i
$885$	−1227.55			−1.38706
$886$		−	615.226i		−	0.694386i
$887$	−961.847			−1.08438			−0.542191	−	0.840255i	$-0.682405\pi$
$887$	−961.847			−1.08438			−0.542191	+	0.840255i	$0.682405\pi$
$888$	−142.205			−0.160140
$889$	65.7804	+	65.7804i	0.0739938	+	0.0739938i
$890$	−490.232	+	490.232i	−0.550822	+	0.550822i
$891$			275.168i			0.308830i
$892$	−473.723	−	473.723i	−0.531080	−	0.531080i
$893$	−1606.19	+	1606.19i	−1.79865	+	1.79865i
$894$	1016.00			1.13646
$895$	41.5784	+	41.5784i	0.0464564	+	0.0464564i
$896$			14.2621i			0.0159175i
$897$	−531.173	+	531.173i	−0.592167	+	0.592167i
$898$	41.1705	+	41.1705i	0.0458468	+	0.0458468i
$899$		−	2065.54i		−	2.29760i
$900$	465.164			0.516849
$901$	136.921	+	136.921i	0.151965	+	0.151965i
$902$	123.126	−	123.126i	0.136503	−	0.136503i
$903$		−	183.906i		−	0.203662i
$904$		−	610.348i		−	0.675164i
$905$	−686.087	+	686.087i	−0.758107	+	0.758107i
$906$	1861.52			2.05466
$907$		−	74.5646i		−	0.0822102i	−0.999155	−	0.0411051i	$-0.986912\pi$
$907$		−	74.5646i		−	0.0822102i	0.999155	−	0.0411051i	$-0.0130878\pi$
$908$	475.772	+	475.772i	0.523978	+	0.523978i
$909$	575.944	−	575.944i	0.633602	−	0.633602i
$910$			43.6396i			0.0479556i
$911$	−968.971	−	968.971i	−1.06363	−	1.06363i	−0.997833	−	0.0658019i	$-0.979039\pi$
$911$	−968.971	−	968.971i	−1.06363	−	1.06363i	−0.0658019	−	0.997833i	$-0.520961\pi$
$912$	574.881			0.630352
$913$	−75.5020	−	75.5020i	−0.0826966	−	0.0826966i
$914$	339.800	−	339.800i	0.371772	−	0.371772i
$915$	1093.76	+	1093.76i	1.19536	+	1.19536i
$916$	−213.611	+	213.611i	−0.233200	+	0.233200i
$917$	38.2592	−	38.2592i	0.0417222	−	0.0417222i
$918$	−1358.09	−	1358.09i	−1.47940	−	1.47940i
$919$	529.117	−	529.117i	0.575753	−	0.575753i	−0.357977	−	0.933730i	$-0.616533\pi$
$919$	529.117	−	529.117i	0.575753	−	0.575753i	0.933730	+	0.357977i	$0.116533\pi$
$920$	147.691	−	147.691i	0.160534	−	0.160534i
$921$	−2137.97	−	2137.97i	−2.32136	−	2.32136i
$922$	428.287			0.464520
$923$	75.3820	+	75.3820i	0.0816707	+	0.0816707i
$924$	−34.1960			−0.0370087
$925$	−116.811			−0.126282
$926$	−549.830			−0.593769
$927$	1012.83			1.09259
$928$	265.287			0.285870
$929$	690.119	+	690.119i	0.742862	+	0.742862i	0.973128	−	0.230265i	$-0.0739595\pi$
$929$	690.119	+	690.119i	0.742862	+	0.742862i	−0.230265	+	0.973128i	$0.573959\pi$
$930$	830.294	+	830.294i	0.892790	+	0.892790i
$931$	911.540	+	911.540i	0.979097	+	0.979097i
$932$	−55.7632			−0.0598317
$933$			2726.31i			2.92209i
$934$			149.334i			0.159887i
$935$	167.287	−	167.287i	0.178916	−	0.178916i
$936$	259.980	−	259.980i	0.277757	−	0.277757i
$937$	313.024	−	313.024i	0.334071	−	0.334071i	−0.520060	−	0.854130i	$-0.674090\pi$
$937$	313.024	−	313.024i	0.334071	−	0.334071i	0.854130	+	0.520060i	$0.174090\pi$
$938$	−38.7414			−0.0413022
$939$	−1325.19	−	1325.19i	−1.41127	−	1.41127i
$940$		−	595.886i		−	0.633922i
$941$	−235.189	−	235.189i	−0.249935	−	0.249935i	0.571009	−	0.820944i	$-0.306552\pi$
$941$	−235.189	−	235.189i	−0.249935	−	0.249935i	−0.820944	+	0.571009i	$0.806552\pi$
$942$	348.121	−	348.121i	0.369555	−	0.369555i
$943$	−993.528			−1.05358
$944$	−184.181	+	184.181i	−0.195107	+	0.195107i
$945$		−	236.189i		−	0.249935i
$946$	−70.8232	−	70.8232i	−0.0748660	−	0.0748660i
$947$	268.643	+	268.643i	0.283678	+	0.283678i	0.834574	−	0.550896i	$-0.185714\pi$
$947$	268.643	+	268.643i	0.283678	+	0.283678i	−0.550896	+	0.834574i	$0.685714\pi$
$948$	−461.852	−	461.852i	−0.487185	−	0.487185i
$949$	285.330			0.300664
$950$	472.223			0.497077
$951$			1790.50i			1.88275i
$952$	65.1763	−	65.1763i	0.0684625	−	0.0684625i
$953$	956.368	−	956.368i	1.00353	−	1.00353i	0.00354000	−	0.999994i	$-0.498873\pi$
$953$	956.368	−	956.368i	1.00353	−	1.00353i	0.999994	−	0.00354000i	$-0.00112682\pi$
$954$	141.860	−	141.860i	0.148700	−	0.148700i
$955$		−	152.719i		−	0.159915i
$956$			732.475i			0.766187i
$957$			636.076i			0.664656i
$958$			480.043i			0.501089i
$959$			140.632i			0.146645i
$960$	−106.638	+	106.638i	−0.111082	+	0.111082i
$961$		−	978.934i		−	1.01866i
$962$	−65.2856	+	65.2856i	−0.0678644	+	0.0678644i
$963$	−1150.15	−	1150.15i	−1.19434	−	1.19434i
$964$	−41.6485	−	41.6485i	−0.0432038	−	0.0432038i
$965$	−801.411	+	801.411i	−0.830478	+	0.830478i
$966$	137.967	+	137.967i	0.142823	+	0.142823i
$967$	−545.790	−	545.790i	−0.564415	−	0.564415i	0.366143	−	0.930559i	$-0.380678\pi$
$967$	−545.790	−	545.790i	−0.564415	−	0.564415i	−0.930559	+	0.366143i	$0.880678\pi$
$968$	228.831	−	228.831i	0.236396	−	0.236396i
$969$	−2627.15	−	2627.15i	−2.71119	−	2.71119i
$970$	349.497	−	349.497i	0.360306	−	0.360306i
$971$		−	14.0166i		−	0.0144352i	−0.999974	−	0.00721760i	$-0.997703\pi$
$971$		−	14.0166i		−	0.0144352i	0.999974	−	0.00721760i	$-0.00229745\pi$
$972$	−132.936	+	132.936i	−0.136765	+	0.136765i
$973$	−146.005			−0.150057
$974$	421.501	+	421.501i	0.432753	+	0.432753i
$975$	315.039	−	315.039i	0.323117	−	0.323117i
$976$	328.214			0.336285
$977$		−	1638.23i		−	1.67680i	−0.545057	−	0.838399i	$-0.683492\pi$
$977$		−	1638.23i		−	1.67680i	0.545057	−	0.838399i	$-0.316508\pi$
$978$	1169.26	+	1169.26i	1.19556	+	1.19556i
$979$	−352.720			−0.360286
$980$	−338.175			−0.345076
$981$	799.902	+	799.902i	0.815394	+	0.815394i
$982$	960.328	−	960.328i	0.977930	−	0.977930i
$983$		−	385.358i		−	0.392022i	−0.980602	−	0.196011i	$-0.937201\pi$
$983$		−	385.358i		−	0.392022i	0.980602	−	0.196011i	$-0.0627989\pi$
$984$	717.362			0.729026
$985$	144.756	−	144.756i	0.146961	−	0.146961i
$986$	−1212.33	−	1212.33i	−1.22955	−	1.22955i
$987$	556.652			0.563984
$988$	263.925	−	263.925i	0.267131	−	0.267131i
$989$			571.486i			0.577842i
$990$	−173.322	−	173.322i	−0.175072	−	0.175072i
$991$	359.520	−	359.520i	0.362785	−	0.362785i	−0.502052	−	0.864837i	$-0.667422\pi$
$991$	359.520	−	359.520i	0.362785	−	0.362785i	0.864837	+	0.502052i	$0.167422\pi$
$992$	249.154			0.251164
$993$	1949.85	+	1949.85i	1.96359	+	1.96359i
$994$	19.5798	−	19.5798i	0.0196979	−	0.0196979i
$995$		−	289.459i		−	0.290913i
$996$		−	439.892i		−	0.441659i
$997$	592.073			0.593854			0.296927	−	0.954900i	$-0.404038\pi$
$997$	592.073			0.593854			0.296927	+	0.954900i	$0.404038\pi$
$998$			288.711i			0.289289i
$999$	353.343	−	353.343i	0.353697	−	0.353697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.3.c.b.187.2	✓	46
269.82	odd	4	inner	538.3.c.b.351.2	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.3.c.b.187.2	✓	46	1.1	even	1	trivial
538.3.c.b.351.2	yes	46	269.82	odd	4	inner

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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	538.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-3.73758 - 3.73758i) q^{3} +2.00000i q^{4} +3.56643 q^{5} +7.47516i q^{6} +(0.891381 - 0.891381i) q^{7} +(2.00000 - 2.00000i) q^{8} +18.9390i q^{9} +(-3.56643 - 3.56643i) q^{10} -2.56603i q^{11} +(7.47516 - 7.47516i) q^{12} -6.86363i q^{13} -1.78276 q^{14} +(-13.3298 - 13.3298i) q^{15} -4.00000 q^{16} +(18.2796 + 18.2796i) q^{17} +(18.9390 - 18.9390i) q^{18} +(19.2264 - 19.2264i) q^{19} +7.13285i q^{20} -6.66321 q^{21} +(-2.56603 + 2.56603i) q^{22} +20.7058 q^{23} -14.9503 q^{24} -12.2806 q^{25} +(-6.86363 + 6.86363i) q^{26} +(37.1478 - 37.1478i) q^{27} +(1.78276 + 1.78276i) q^{28} +(33.1609 - 33.1609i) q^{29} +26.6596i q^{30} +(31.1443 - 31.1443i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-9.59075 + 9.59075i) q^{33} -36.5592i q^{34} +(3.17904 - 3.17904i) q^{35} -37.8780 q^{36} +9.51182 q^{37} -38.4528 q^{38} +(-25.6534 + 25.6534i) q^{39} +(7.13285 - 7.13285i) q^{40} -47.9831 q^{41} +(6.66321 + 6.66321i) q^{42} +27.6003i q^{43} +5.13207 q^{44} +67.5445i q^{45} +(-20.7058 - 20.7058i) q^{46} -83.5411 q^{47} +(14.9503 + 14.9503i) q^{48} +47.4109i q^{49} +(12.2806 + 12.2806i) q^{50} -136.643i q^{51} +13.7273 q^{52} +7.49037 q^{53} -74.2956 q^{54} -9.15157i q^{55} -3.56552i q^{56} -143.720 q^{57} -66.3218 q^{58} +(46.0453 - 46.0453i) q^{59} +(26.6596 - 26.6596i) q^{60} -82.0535 q^{61} -62.2886 q^{62} +(16.8819 + 16.8819i) q^{63} -8.00000i q^{64} -24.4786i q^{65} +19.1815 q^{66} +21.7311 q^{67} +(-36.5592 + 36.5592i) q^{68} +(-77.3896 - 77.3896i) q^{69} -6.35809 q^{70} +(-10.9828 + 10.9828i) q^{71} +(37.8780 + 37.8780i) q^{72} +41.5713i q^{73} +(-9.51182 - 9.51182i) q^{74} +(45.8997 + 45.8997i) q^{75} +(38.4528 + 38.4528i) q^{76} +(-2.28731 - 2.28731i) q^{77} +51.3067 q^{78} -61.7849i q^{79} -14.2657 q^{80} -107.235 q^{81} +(47.9831 + 47.9831i) q^{82} +(29.4236 - 29.4236i) q^{83} -13.3264i q^{84} +(65.1928 + 65.1928i) q^{85} +(27.6003 - 27.6003i) q^{86} -247.883 q^{87} +(-5.13207 - 5.13207i) q^{88} -137.457i q^{89} +(67.5445 - 67.5445i) q^{90} +(-6.11811 - 6.11811i) q^{91} +41.4116i q^{92} -232.808 q^{93} +(83.5411 + 83.5411i) q^{94} +(68.5695 - 68.5695i) q^{95} -29.9006i q^{96} +97.9964i q^{97} +(47.4109 - 47.4109i) q^{98} +48.5981 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 46 q^{2} - 6 q^{3} - 32 q^{5} + 4 q^{7} + 92 q^{8} + 32 q^{10} + 12 q^{12} - 8 q^{14} - 10 q^{15} - 184 q^{16} - 50 q^{17} + 118 q^{18} + 10 q^{19} + 16 q^{21} + 8 q^{22} - 124 q^{23} - 24 q^{24}+ \cdots + 508 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 - 6 * q^3 - 32 * q^5 + 4 * q^7 + 92 * q^8 + 32 * q^10 + 12 * q^12 - 8 * q^14 - 10 * q^15 - 184 * q^16 - 50 * q^17 + 118 * q^18 + 10 * q^19 + 16 * q^21 + 8 * q^22 - 124 * q^23 - 24 * q^24 + 178 * q^25 + 4 * q^26 + 90 * q^27 + 8 * q^28 + 40 * q^29 + 40 * q^31 + 184 * q^32 - 64 * q^33 - 14 * q^35 - 236 * q^36 - 32 * q^37 - 20 * q^38 - 54 * q^39 - 64 * q^40 - 132 * q^41 - 16 * q^42 - 16 * q^44 + 124 * q^46 - 60 * q^47 + 24 * q^48 - 178 * q^50 - 8 * q^52 - 188 * q^53 - 180 * q^54 - 40 * q^57 - 80 * q^58 + 190 * q^59 + 20 * q^60 - 80 * q^62 - 266 * q^63 + 128 * q^66 - 164 * q^67 + 100 * q^68 + 170 * q^69 + 28 * q^70 - 92 * q^71 + 236 * q^72 + 32 * q^74 - 190 * q^75 + 20 * q^76 + 20 * q^77 + 108 * q^78 + 128 * q^80 - 298 * q^81 + 132 * q^82 + 190 * q^83 + 298 * q^85 + 228 * q^86 - 92 * q^87 + 16 * q^88 - 528 * q^90 + 2 * q^91 + 232 * q^93 + 60 * q^94 - 280 * q^95 - 226 * q^98 + 508 * q^99

Introduction

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