LMFDB - Embedded newform 19.3.d.a.12.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [19,3,Mod(8,19)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("19.8"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(19, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	19.d (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.517712502285$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.6967728.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 $ x^6 - x^5 + 8x^4 + 5x^3 + 50x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			12.1
Root			$1.56632 + 2.71294i$ of defining polynomial
Character	$\chi$	$=$	19.12
Dual form			19.3.d.a.8.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.90671 + 1.67819i) q^{2} +(-3.29225 + 1.90078i) q^{3} +(3.63264 - 6.29191i) q^{4} +(3.47303 + 6.01546i) q^{5} +(6.37974 - 11.0500i) q^{6} -1.22892 q^{7} +10.9595i q^{8} +(2.72593 - 4.72145i) q^{9} +(-20.1902 - 11.6568i) q^{10} -0.0363521 q^{11} +27.6194i q^{12} +(14.6268 + 8.44481i) q^{13} +(3.57212 - 2.06236i) q^{14} +(-22.8681 - 13.2029i) q^{15} +(-3.86156 - 6.68842i) q^{16} +(-4.59329 - 7.95581i) q^{17} +18.2985i q^{18} +(12.7864 - 14.0537i) q^{19} +50.4650 q^{20} +(4.04592 - 2.33591i) q^{21} +(0.105665 - 0.0610058i) q^{22} +(-4.87974 + 8.45195i) q^{23} +(-20.8316 - 36.0814i) q^{24} +(-11.6238 + 20.1331i) q^{25} -56.6879 q^{26} -13.4885i q^{27} +(-4.46423 + 7.73228i) q^{28} +(4.50339 + 2.60003i) q^{29} +88.6280 q^{30} +44.3727i q^{31} +(-15.5160 - 8.95814i) q^{32} +(0.119680 - 0.0690974i) q^{33} +(26.7027 + 15.4168i) q^{34} +(-4.26808 - 7.39254i) q^{35} +(-19.8046 - 34.3026i) q^{36} -45.5661i q^{37} +(-13.5817 + 62.3081i) q^{38} -64.2069 q^{39} +(-65.9264 + 38.0626i) q^{40} +(50.0829 - 28.9153i) q^{41} +(-7.84020 + 13.5796i) q^{42} +(15.1574 + 26.2534i) q^{43} +(-0.132054 + 0.228724i) q^{44} +37.8689 q^{45} -32.7565i q^{46} +(25.5066 - 44.1787i) q^{47} +(25.4264 + 14.6800i) q^{48} -47.4897 q^{49} -78.0280i q^{50} +(30.2445 + 17.4617i) q^{51} +(106.268 - 61.3538i) q^{52} +(10.0847 + 5.82239i) q^{53} +(22.6362 + 39.2071i) q^{54} +(-0.126252 - 0.218675i) q^{55} -13.4684i q^{56} +(-15.3831 + 70.5725i) q^{57} -17.4534 q^{58} +(-17.7409 + 10.2427i) q^{59} +(-166.143 + 95.9229i) q^{60} +(-8.23849 + 14.2695i) q^{61} +(-74.4658 - 128.978i) q^{62} +(-3.34996 + 5.80229i) q^{63} +91.0263 q^{64} +117.316i q^{65} +(-0.231917 + 0.401692i) q^{66} +(-1.83276 - 1.05814i) q^{67} -66.7430 q^{68} -37.1012i q^{69} +(24.8121 + 14.3253i) q^{70} +(-33.7958 + 19.5120i) q^{71} +(51.7447 + 29.8748i) q^{72} +(-28.1064 - 48.6818i) q^{73} +(76.4686 + 132.447i) q^{74} -88.3775i q^{75} +(-41.9762 - 131.503i) q^{76} +0.0446740 q^{77} +(186.631 - 107.751i) q^{78} +(39.8385 - 23.0008i) q^{79} +(26.8226 - 46.4581i) q^{80} +(50.1720 + 86.9004i) q^{81} +(-97.0508 + 168.097i) q^{82} +65.3332 q^{83} -33.9421i q^{84} +(31.9053 - 55.2615i) q^{85} +(-88.1162 - 50.8739i) q^{86} -19.7684 q^{87} -0.398401i q^{88} +(-134.435 - 77.6163i) q^{89} +(-110.074 + 63.5512i) q^{90} +(-17.9753 - 10.3780i) q^{91} +(35.4526 + 61.4058i) q^{92} +(-84.3427 - 146.086i) q^{93} +171.219i q^{94} +(128.947 + 28.1074i) q^{95} +68.1098 q^{96} +(-98.8107 + 57.0484i) q^{97} +(138.039 - 79.6968i) q^{98} +(-0.0990933 + 0.171635i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 9 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 14 q^{9} - 60 q^{10} + 26 q^{11} + 30 q^{13} + 54 q^{14} - 18 q^{15} + q^{16} - 42 q^{17} + 25 q^{19} + 108 q^{20} - 102 q^{21} - 39 q^{22} + 8 q^{23}+ \cdots - 56 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 9 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 14 * q^9 - 60 * q^10 + 26 * q^11 + 30 * q^13 + 54 * q^14 - 18 * q^15 + q^16 - 42 * q^17 + 25 * q^19 + 108 * q^20 - 102 * q^21 - 39 * q^22 + 8 * q^23 - 83 * q^24 - 17 * q^25 - 148 * q^26 + 32 * q^28 - 12 * q^29 + 304 * q^30 + 51 * q^32 + 123 * q^33 - 6 * q^34 - 38 * q^35 - 54 * q^36 - 14 * q^38 - 44 * q^39 - 96 * q^40 + 63 * q^41 - 92 * q^42 - 34 * q^43 - 69 * q^44 - 28 * q^45 + 58 * q^47 - 147 * q^48 + 18 * q^49 + 132 * q^51 + 162 * q^52 - 12 * q^53 + 29 * q^54 - 28 * q^55 - 16 * q^57 + 172 * q^58 - 147 * q^59 - 222 * q^60 + 58 * q^61 - 116 * q^62 + 86 * q^63 + 166 * q^64 + 11 * q^66 + 201 * q^67 - 84 * q^68 - 198 * q^70 - 102 * q^71 + 210 * q^72 + 7 * q^73 + 174 * q^74 - 173 * q^76 - 376 * q^77 + 450 * q^78 + 134 * q^80 + 253 * q^81 - 145 * q^82 + 146 * q^83 - 90 * q^85 - 270 * q^86 - 568 * q^87 - 72 * q^89 - 438 * q^90 - 216 * q^91 + 72 * q^92 - 160 * q^93 + 558 * q^95 + 126 * q^96 + 21 * q^97 + 411 * q^98 - 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.90671	+	1.67819i	−1.45335	+	0.839095i	−0.998670	−	0.0515581i	$-0.983581\pi$
$2$	−2.90671	+	1.67819i	−1.45335	+	0.839095i	−0.454684	+	0.890653i	$0.650248\pi$
$3$	−3.29225	+	1.90078i	−1.09742	+	0.633593i	−0.935541	−	0.353218i	$-0.885087\pi$
$3$	−3.29225	+	1.90078i	−1.09742	+	0.633593i	−0.161875	+	0.986811i	$0.551754\pi$
$4$	3.63264	−	6.29191i	0.908159	−	1.57298i
$5$	3.47303	+	6.01546i	0.694606	+	1.20309i	0.970313	+	0.241851i	$0.0777544\pi$
$5$	3.47303	+	6.01546i	0.694606	+	1.20309i	−0.275708	+	0.961241i	$0.588912\pi$
$6$	6.37974	−	11.0500i	1.06329	−	1.84167i
$7$	−1.22892			−0.175560			−0.0877802	−	0.996140i	$-0.527977\pi$
$7$	−1.22892			−0.175560			−0.0877802	+	0.996140i	$0.527977\pi$
$8$			10.9595i			1.36994i
$9$	2.72593	−	4.72145i	0.302881	−	0.524605i
$10$	−20.1902	−	11.6568i	−2.01902	−	1.16568i
$11$	−0.0363521			−0.00330474			−0.00165237	−	0.999999i	$-0.500526\pi$
$11$	−0.0363521			−0.00330474			−0.00165237	+	0.999999i	$0.500526\pi$
$12$			27.6194i			2.30161i
$13$	14.6268	+	8.44481i	1.12514	+	0.649601i	0.942708	−	0.333618i	$-0.108269\pi$
$13$	14.6268	+	8.44481i	1.12514	+	0.649601i	0.182433	+	0.983218i	$0.441603\pi$
$14$	3.57212	−	2.06236i	0.255151	−	0.147312i
$15$	−22.8681	−	13.2029i	−1.52454	−	0.880195i
$16$	−3.86156	−	6.68842i	−0.241348	−	0.418026i
$17$	−4.59329	−	7.95581i	−0.270194	−	0.467989i	0.698718	−	0.715398i	$-0.253754\pi$
$17$	−4.59329	−	7.95581i	−0.270194	−	0.467989i	−0.968911	+	0.247408i	$0.920421\pi$
$18$			18.2985i			1.01658i
$19$	12.7864	−	14.0537i	0.672971	−	0.739669i
$19$	12.7864	−	14.0537i	0.672971	−	0.739669i
$20$	50.4650			2.52325
$21$	4.04592	−	2.33591i	0.192663	−	0.111234i
$22$	0.105665	−	0.0610058i	0.00480296	−	0.00277299i
$23$	−4.87974	+	8.45195i	−0.212162	+	0.367476i	−0.952391	−	0.304879i	$-0.901384\pi$
$23$	−4.87974	+	8.45195i	−0.212162	+	0.367476i	0.740229	+	0.672355i	$0.234717\pi$
$24$	−20.8316	−	36.0814i	−0.867983	−	1.50339i
$25$	−11.6238	+	20.1331i	−0.464954	+	0.805323i
$26$	−56.6879			−2.18031
$27$		−	13.4885i		−	0.499573i
$28$	−4.46423	+	7.73228i	−0.159437	+	0.276153i
$29$	4.50339	+	2.60003i	0.155289	+	0.0896564i	0.575631	−	0.817710i	$-0.304756\pi$
$29$	4.50339	+	2.60003i	0.155289	+	0.0896564i	−0.420342	+	0.907366i	$0.638090\pi$
$30$	88.6280			2.95427
$31$			44.3727i			1.43138i	0.698420	+	0.715689i	$0.253887\pi$
$31$			44.3727i			1.43138i	−0.698420	+	0.715689i	$0.746113\pi$
$32$	−15.5160	−	8.95814i	−0.484873	−	0.279942i
$33$	0.119680	−	0.0690974i	0.00362667	−	0.00209386i
$34$	26.7027	+	15.4168i	0.785374	+	0.453436i
$35$	−4.26808	−	7.39254i	−0.121945	−	0.211215i
$36$	−19.8046	−	34.3026i	−0.550128	−	0.952850i
$37$		−	45.5661i		−	1.23152i	−0.787935	−	0.615758i	$-0.788850\pi$
$37$		−	45.5661i		−	1.23152i	0.787935	−	0.615758i	$-0.211150\pi$
$38$	−13.5817	+	62.3081i	−0.357413	+	1.63969i
$39$	−64.2069			−1.64633
$40$	−65.9264	+	38.0626i	−1.64816	+	0.951566i
$41$	50.0829	−	28.9153i	1.22153	−	0.705252i	0.256288	−	0.966600i	$-0.417500\pi$
$41$	50.0829	−	28.9153i	1.22153	−	0.705252i	0.965245	+	0.261348i	$0.0841670\pi$
$42$	−7.84020	+	13.5796i	−0.186672	+	0.323325i
$43$	15.1574	+	26.2534i	0.352497	+	0.610543i	0.986686	−	0.162635i	$-0.0519992\pi$
$43$	15.1574	+	26.2534i	0.352497	+	0.610543i	−0.634189	+	0.773178i	$0.718666\pi$
$44$	−0.132054	+	0.228724i	−0.00300123	+	0.00519828i
$45$	37.8689			0.841531
$46$		−	32.7565i		−	0.712097i
$47$	25.5066	−	44.1787i	0.542693	−	0.939972i	−0.456055	−	0.889951i	$-0.650738\pi$
$47$	25.5066	−	44.1787i	0.542693	−	0.939972i	0.998748	−	0.0500204i	$-0.0159286\pi$
$48$	25.4264	+	14.6800i	0.529717	+	0.305832i
$49$	−47.4897			−0.969179
$50$		−	78.0280i		−	1.56056i
$51$	30.2445	+	17.4617i	0.593029	+	0.342386i
$52$	106.268	−	61.3538i	2.04362	−	1.17988i
$53$	10.0847	+	5.82239i	0.190277	+	0.109856i	0.592112	−	0.805856i	$-0.298294\pi$
$53$	10.0847	+	5.82239i	0.190277	+	0.109856i	−0.401835	+	0.915712i	$0.631628\pi$
$54$	22.6362	+	39.2071i	0.419189	+	0.726057i
$55$	−0.126252	−	0.218675i	−0.00229549	−	0.00397591i
$56$		−	13.4684i		−	0.240507i
$57$	−15.3831	+	70.5725i	−0.269879	+	1.23811i
$58$	−17.4534			−0.300921
$59$	−17.7409	+	10.2427i	−0.300694	+	0.173606i	−0.642754	−	0.766072i	$-0.722208\pi$
$59$	−17.7409	+	10.2427i	−0.300694	+	0.173606i	0.342061	+	0.939678i	$0.388875\pi$
$60$	−166.143	+	95.9229i	−2.76905	+	1.59871i
$61$	−8.23849	+	14.2695i	−0.135057	+	0.233926i	−0.925619	−	0.378456i	$-0.876455\pi$
$61$	−8.23849	+	14.2695i	−0.135057	+	0.233926i	0.790562	+	0.612382i	$0.209788\pi$
$62$	−74.4658	−	128.978i	−1.20106	−	2.08030i
$63$	−3.34996	+	5.80229i	−0.0531739	+	0.0920999i
$64$	91.0263			1.42229
$65$			117.316i			1.80486i
$66$	−0.231917	+	0.401692i	−0.00351389	+	0.00608624i
$67$	−1.83276	−	1.05814i	−0.0273546	−	0.0157932i	0.486260	−	0.873814i	$-0.338361\pi$
$67$	−1.83276	−	1.05814i	−0.0273546	−	0.0157932i	−0.513615	+	0.858021i	$0.671694\pi$
$68$	−66.7430			−0.981515
$69$		−	37.1012i		−	0.537699i
$70$	24.8121	+	14.3253i	0.354459	+	0.204647i
$71$	−33.7958	+	19.5120i	−0.475998	+	0.274817i	−0.718747	−	0.695272i	$-0.755284\pi$
$71$	−33.7958	+	19.5120i	−0.475998	+	0.274817i	0.242749	+	0.970089i	$0.421951\pi$
$72$	51.7447	+	29.8748i	0.718676	+	0.414928i
$73$	−28.1064	−	48.6818i	−0.385020	−	0.666874i	0.606752	−	0.794891i	$-0.292472\pi$
$73$	−28.1064	−	48.6818i	−0.385020	−	0.666874i	−0.991772	+	0.128017i	$0.959139\pi$
$74$	76.4686	+	132.447i	1.03336	+	1.78983i
$75$		−	88.3775i		−	1.17837i
$76$	−41.9762	−	131.503i	−0.552319	−	1.73031i
$77$	0.0446740			0.000580181
$78$	186.631	−	107.751i	2.39270	−	1.38143i
$79$	39.8385	−	23.0008i	0.504285	−	0.291149i	−0.226196	−	0.974082i	$-0.572629\pi$
$79$	39.8385	−	23.0008i	0.504285	−	0.291149i	0.730481	+	0.682933i	$0.239296\pi$
$80$	26.8226	−	46.4581i	0.335283	−	0.580727i
$81$	50.1720	+	86.9004i	0.619407	+	1.07284i
$82$	−97.0508	+	168.097i	−1.18355	+	2.04996i
$83$	65.3332			0.787146			0.393573	−	0.919293i	$-0.371239\pi$
$83$	65.3332			0.787146			0.393573	+	0.919293i	$0.371239\pi$
$84$		−	33.9421i		−	0.404072i
$85$	31.9053	−	55.2615i	0.375356	−	0.650136i
$86$	−88.1162	−	50.8739i	−1.02461	−	0.591557i
$87$	−19.7684			−0.227223
$88$		−	0.398401i		−	0.00452729i
$89$	−134.435	−	77.6163i	−1.51051	−	0.872093i	−0.999925	−	0.0122654i	$-0.996096\pi$
$89$	−134.435	−	77.6163i	−1.51051	−	0.872093i	−0.510585	−	0.859828i	$-0.670571\pi$
$90$	−110.074	+	63.5512i	−1.22304	+	0.706124i
$91$	−17.9753	−	10.3780i	−0.197530	−	0.114044i
$92$	35.4526	+	61.4058i	0.385355	+	0.667454i
$93$	−84.3427	−	146.086i	−0.906911	−	1.57082i
$94$			171.219i			1.82148i
$95$	128.947	+	28.1074i	1.35734	+	0.295868i
$96$	68.1098			0.709477
$97$	−98.8107	+	57.0484i	−1.01867	+	0.588128i	−0.913718	−	0.406350i	$-0.866801\pi$
$97$	−98.8107	+	57.0484i	−1.01867	+	0.588128i	−0.104949	+	0.994478i	$0.533468\pi$
$98$	138.039	−	79.6968i	1.40856	−	0.813232i
$99$	−0.0990933	+	0.171635i	−0.00100094	+	0.00173368i
$100$	84.4504	+	146.272i	0.844504	+	1.46272i
$101$	85.7095	−	148.453i	0.848609	−	1.46983i	−0.0338413	−	0.999427i	$-0.510774\pi$
$101$	85.7095	−	148.453i	0.848609	−	1.46983i	0.882450	−	0.470406i	$-0.155893\pi$
$102$	−117.216			−1.14918
$103$		−	121.297i		−	1.17764i	−0.808264	−	0.588820i	$-0.799593\pi$
$103$		−	121.297i		−	1.17764i	0.808264	−	0.588820i	$-0.200407\pi$
$104$	−92.5508	+	160.303i	−0.889912	+	1.54137i
$105$	28.1032	+	16.2254i	0.267649	+	0.154527i
$106$	−39.0843			−0.368720
$107$			56.0566i			0.523893i	0.965082	+	0.261947i	$0.0843644\pi$
$107$			56.0566i			0.523893i	−0.965082	+	0.261947i	$0.915636\pi$
$108$	−84.8683	−	48.9987i	−0.785818	−	0.453692i
$109$	−46.0431	+	26.5830i	−0.422414	+	0.243881i	−0.696109	−	0.717936i	$-0.745087\pi$
$109$	−46.0431	+	26.5830i	−0.422414	+	0.243881i	0.273696	+	0.961816i	$0.411754\pi$
$110$	0.733955	+	0.423749i	0.00667232	+	0.00385227i
$111$	86.6112	+	150.015i	0.780281	+	1.35149i
$112$	4.74556	+	8.21955i	0.0423711	+	0.0733888i
$113$			136.946i			1.21191i	0.795497	+	0.605957i	$0.207210\pi$
$113$			136.946i			1.21191i	−0.795497	+	0.605957i	$0.792790\pi$
$114$	−73.7198	−	230.950i	−0.646665	−	2.02587i
$115$	−67.7898			−0.589477
$116$	32.7184	−	18.8900i	0.282055	−	0.162845i
$117$	79.7434	−	46.0399i	0.681568	−	0.393503i
$118$	34.3785	−	59.5453i	0.291343	−	0.504621i
$119$	5.64480	+	9.77708i	0.0474353	+	0.0821603i
$120$	144.697	−	250.623i	1.20581	−	2.08853i
$121$	−120.999			−0.999989
$122$		−	55.3030i		−	0.453303i
$123$	−109.923	+	190.393i	−0.893686	+	1.54791i
$124$	279.189	+	161.190i	2.25153	+	1.29992i
$125$	12.1717			0.0973736
$126$		−	22.4874i		−	0.178472i
$127$	136.758	+	78.9573i	1.07684	+	0.621711i	0.930041	−	0.367456i	$-0.119771\pi$
$127$	136.758	+	78.9573i	1.07684	+	0.621711i	0.146794	+	0.989167i	$0.453104\pi$
$128$	−202.523	+	116.927i	−1.58221	+	0.913490i
$129$	−99.8037	−	57.6217i	−0.773672	−	0.446680i
$130$	−196.879	−	341.004i	−1.51445	−	2.62311i
$131$	38.5396	+	66.7525i	0.294195	+	0.509561i	0.974797	−	0.223092i	$-0.0716151\pi$
$131$	38.5396	+	66.7525i	0.294195	+	0.509561i	−0.680602	+	0.732653i	$0.738282\pi$
$132$		−	1.00402i		−	0.00760624i
$133$	−15.7136	+	17.2709i	−0.118147	+	0.129857i
$134$	7.10307			0.0530080
$135$	81.1394	−	46.8459i	0.601033	−	0.347006i
$136$	87.1917	−	50.3402i	0.641116	−	0.370148i
$137$	45.3969	−	78.6298i	0.331364	−	0.573940i	−0.651415	−	0.758721i	$-0.725824\pi$
$137$	45.3969	−	78.6298i	0.331364	−	0.573940i	0.982780	+	0.184781i	$0.0591577\pi$
$138$	62.2629	+	107.842i	0.451180	+	0.781467i
$139$	45.7773	−	79.2886i	0.329333	−	0.570421i	−0.653047	−	0.757318i	$-0.726509\pi$
$139$	45.7773	−	79.2886i	0.329333	−	0.570421i	0.982380	+	0.186896i	$0.0598428\pi$
$140$	−62.0176			−0.442983
$141$			193.930i			1.37539i
$142$	65.4897	−	113.432i	0.461195	−	0.798814i
$143$	−0.531717	−	0.306987i	−0.00371830	−	0.00214676i
$144$	−42.1054			−0.292398
$145$			36.1200i			0.249103i
$146$	163.394	+	94.3358i	1.11914	+	0.646136i
$147$	156.348	−	90.2676i	1.06359	−	0.614065i
$148$	−286.698	−	165.525i	−1.93715	−	1.11841i
$149$	−12.0587	−	20.8863i	−0.0809308	−	0.140176i	0.822719	−	0.568448i	$-0.192456\pi$
$149$	−12.0587	−	20.8863i	−0.0809308	−	0.140176i	−0.903650	+	0.428272i	$0.859123\pi$
$150$	148.314	+	256.888i	0.988761	+	1.71258i
$151$		−	251.451i		−	1.66524i	−0.553848	−	0.832618i	$-0.686841\pi$
$151$		−	251.451i		−	1.66524i	0.553848	−	0.832618i	$-0.313159\pi$
$152$	154.022	+	140.133i	1.01330	+	0.921928i
$153$	−50.0839			−0.327346
$154$	−0.129854	+	0.0749714i	−0.000843209	+	0.000486827i
$155$	−266.922	+	154.108i	−1.72208	+	0.994242i
$156$	−233.240	+	403.984i	−1.49513	+	2.58964i
$157$	44.0172	+	76.2401i	0.280364	+	0.485605i	0.971474	−	0.237144i	$-0.0762113\pi$
$157$	44.0172	+	76.2401i	0.280364	+	0.485605i	−0.691110	+	0.722750i	$0.742878\pi$
$158$	−77.1994	+	133.713i	−0.488604	+	0.846286i
$159$	−44.2684			−0.278417
$160$		−	124.447i		−	0.777797i
$161$	5.99682	−	10.3868i	0.0372473	−	0.0645143i
$162$	−291.671	−	168.396i	−1.80044	−	1.03948i
$163$	−28.3608			−0.173992			−0.0869962	−	0.996209i	$-0.527727\pi$
$163$	−28.3608			−0.173992			−0.0869962	+	0.996209i	$0.527727\pi$
$164$		−	420.156i		−	2.56193i
$165$	0.831305	+	0.479954i	0.00503821	+	0.00290881i
$166$	−189.904	+	109.641i	−1.14400	+	0.660490i
$167$	−52.1162	−	30.0893i	−0.312073	−	0.180176i	0.335781	−	0.941940i	$-0.391000\pi$
$167$	−52.1162	−	30.0893i	−0.312073	−	0.180176i	−0.647854	+	0.761765i	$0.724333\pi$
$168$	25.6004	+	44.3412i	0.152383	+	0.263936i
$169$	58.1295	+	100.683i	0.343962	+	0.595759i
$170$			214.172i			1.25984i
$171$	−31.4989	−	98.6799i	−0.184204	−	0.577076i
$172$	220.245			1.28050
$173$	152.888	−	88.2699i	0.883745	−	0.510230i	0.0118536	−	0.999930i	$-0.496227\pi$
$173$	152.888	−	88.2699i	0.883745	−	0.510230i	0.871891	+	0.489699i	$0.162893\pi$
$174$	57.4609	−	33.1751i	0.330235	−	0.190661i
$175$	14.2848	−	24.7420i	0.0816275	−	0.141383i
$176$	0.140376	+	0.243138i	0.000797591	+	0.00138147i
$177$	38.9383	−	67.4432i	0.219991	−	0.381035i
$178$	521.019			2.92707
$179$			0.226943i			0.00126784i	1.00000		0.000633920i	$0.000201783\pi$
$179$			0.226943i			0.00126784i	−1.00000		0.000633920i	$0.999798\pi$
$180$	137.564	−	238.268i	0.764244	−	1.32371i
$181$	129.410	+	74.7148i	0.714971	+	0.412789i	0.812899	−	0.582405i	$-0.197888\pi$
$181$	129.410	+	74.7148i	0.714971	+	0.412789i	−0.0979279	+	0.995194i	$0.531221\pi$
$182$	69.6651			0.382775
$183$		−	62.6382i		−	0.342285i
$184$	−92.6291	−	53.4795i	−0.503419	−	0.290649i
$185$	274.101	−	158.252i	1.48163	−	0.855418i
$186$	490.319	+	283.086i	2.63613	+	1.52197i
$187$	0.166976	+	0.289211i	0.000892919	+	0.00154658i
$188$	−185.312	−	320.970i	−0.985703	−	1.70729i
$189$			16.5763i			0.0877053i
$190$	−421.982	+	134.698i	−2.22096	+	0.708935i
$191$	−251.306			−1.31574			−0.657870	−	0.753132i	$-0.728542\pi$
$191$	−251.306			−1.31574			−0.657870	+	0.753132i	$0.728542\pi$
$192$	−299.681	+	173.021i	−1.56084	+	0.901151i
$193$	−109.795	+	63.3899i	−0.568884	+	0.328445i	−0.756703	−	0.653758i	$-0.773191\pi$
$193$	−109.795	+	63.3899i	−0.568884	+	0.328445i	0.187820	+	0.982204i	$0.439858\pi$
$194$	191.476	−	331.646i	0.986989	−	1.70952i
$195$	−222.992	−	386.234i	−1.14355	−	1.98069i
$196$	−172.513	+	298.801i	−0.880169	+	1.52450i
$197$	−285.803			−1.45077			−0.725387	−	0.688341i	$-0.758339\pi$
$197$	−285.803			−1.45077			−0.725387	+	0.688341i	$0.758339\pi$
$198$		−	0.665189i		−	0.00335954i
$199$	−77.0371	+	133.432i	−0.387121	+	0.670514i	−0.992061	−	0.125757i	$-0.959864\pi$
$199$	−77.0371	+	133.432i	−0.387121	+	0.670514i	0.604940	+	0.796271i	$0.293197\pi$
$200$	−220.648	−	127.391i	−1.10324	−	0.636957i
$201$	8.04520			0.0400259
$202$			575.347i			2.84825i
$203$	−5.53432	−	3.19524i	−0.0272627	−	0.0157401i
$204$	219.735	−	126.864i	1.07713	−	0.621882i
$205$	347.878	+	200.848i	1.69697	+	0.979744i
$206$	203.559	+	352.575i	0.988151	+	1.71153i
$207$	26.6036	+	46.0788i	0.128520	+	0.222603i
$208$		−	130.441i		−	0.627118i
$209$	−0.464815	+	0.510882i	−0.00222399	+	0.00244441i
$210$	−108.917			−0.518652
$211$	−138.091	+	79.7266i	−0.654458	+	0.377851i	−0.790162	−	0.612898i	$-0.790004\pi$
$211$	−138.091	+	79.7266i	−0.654458	+	0.377851i	0.135704	+	0.990749i	$0.456670\pi$
$212$	73.2680	−	42.3013i	0.345604	−	0.199534i
$213$	74.1761	−	128.477i	0.348245	−	0.603178i
$214$	−94.0735	−	162.940i	−0.439596	−	0.761402i
$215$	−105.284	+	182.357i	−0.489693	+	0.848173i
$216$	147.827			0.684384
$217$		−	54.5306i		−	0.251293i
$218$	89.2226	−	154.538i	0.409278	−	0.708890i
$219$	185.067	+	106.848i	0.845053	+	0.487892i
$220$	−1.83451			−0.00833868
$221$		−	155.158i		−	0.702072i
$222$	−503.507	−	290.700i	−2.26805	−	1.30946i
$223$	−161.907	+	93.4771i	−0.726041	+	0.419180i	−0.816972	−	0.576677i	$-0.804349\pi$
$223$	−161.907	+	93.4771i	−0.726041	+	0.419180i	0.0909314	+	0.995857i	$0.471016\pi$
$224$	19.0679	+	11.0089i	0.0851246	+	0.0491467i
$225$	63.3715	+	109.763i	0.281651	+	0.487834i
$226$	−229.822	−	398.063i	−1.01691	−	1.76134i
$227$		−	8.87518i		−	0.0390977i	−0.999809	−	0.0195489i	$-0.993777\pi$
$227$		−	8.87518i		−	0.0390977i	0.999809	−	0.0195489i	$-0.00622299\pi$
$228$	388.155	+	353.154i	1.70243	+	1.54892i
$229$	265.920			1.16122			0.580611	−	0.814181i	$-0.302814\pi$
$229$	265.920			1.16122			0.580611	+	0.814181i	$0.302814\pi$
$230$	197.045	−	113.764i	0.856719	−	0.494627i
$231$	−0.147078	+	0.0849154i	−0.000636700	+	0.000367599i
$232$	−28.4951	+	49.3549i	−0.122824	+	0.212737i
$233$	4.52199	+	7.83232i	0.0194077	+	0.0336151i	0.875566	−	0.483098i	$-0.160489\pi$
$233$	4.52199	+	7.83232i	0.0194077	+	0.0336151i	−0.856158	+	0.516713i	$0.827155\pi$
$234$	−154.527	+	267.649i	−0.660373	+	1.14380i
$235$	354.340			1.50783
$236$			148.832i			0.630646i
$237$	−87.4389	+	151.449i	−0.368940	+	0.639024i
$238$	−32.8156	−	18.9461i	−0.137881	−	0.0796054i
$239$	−48.3793			−0.202424			−0.101212	−	0.994865i	$-0.532272\pi$
$239$	−48.3793			−0.202424			−0.101212	+	0.994865i	$0.532272\pi$
$240$			203.936i			0.849731i
$241$	−120.431	−	69.5306i	−0.499712	−	0.288509i	0.228883	−	0.973454i	$-0.426493\pi$
$241$	−120.431	−	69.5306i	−0.499712	−	0.288509i	−0.728594	+	0.684945i	$0.759826\pi$
$242$	351.708	−	203.059i	1.45334	−	0.839085i
$243$	−225.225	−	130.034i	−0.926851	−	0.535118i
$244$	59.8549	+	103.672i	0.245307	+	0.424884i
$245$	−164.933	−	285.673i	−0.673197	−	1.16601i
$246$		−	737.889i		−	2.99955i
$247$	305.706	−	97.5823i	1.23768	−	0.395070i
$248$	−486.302			−1.96090
$249$	−215.093	+	124.184i	−0.863827	+	0.498731i
$250$	−35.3796	+	20.4264i	−0.141518	+	0.0817056i
$251$	−109.025	+	188.837i	−0.434363	+	0.752340i	−0.997243	−	0.0741991i	$-0.976360\pi$
$251$	−109.025	+	188.837i	−0.434363	+	0.752340i	0.562880	+	0.826539i	$0.309693\pi$
$252$	24.3384	+	42.1553i	0.0965808	+	0.167283i
$253$	0.177389	−	0.307246i	0.000701142	−	0.00121441i
$254$	−530.021			−2.08670
$255$			242.579i			0.951292i
$256$	210.398	−	364.420i	0.821867	−	1.42352i
$257$	192.080	+	110.898i	0.747394	+	0.431508i	0.824751	−	0.565495i	$-0.191315\pi$
$257$	192.080	+	110.898i	0.747394	+	0.431508i	−0.0773578	+	0.997003i	$0.524648\pi$
$258$	386.800			1.49923
$259$			55.9973i			0.216206i
$260$	738.143	+	426.167i	2.83901	+	1.63910i
$261$	24.5518	−	14.1750i	0.0940684	−	0.0543104i
$262$	−224.047	−	129.353i	−0.855139	−	0.493715i
$263$	−160.691	−	278.326i	−0.610994	−	1.05827i	−0.991073	−	0.133319i	$-0.957437\pi$
$263$	−160.691	−	278.326i	−0.610994	−	1.05827i	0.380079	−	0.924954i	$-0.375897\pi$
$264$	0.757273	+	1.31164i	0.00286846	+	0.00496832i
$265$			80.8853i			0.305228i
$266$	16.6908	−	76.5719i	0.0627475	−	0.287864i
$267$	590.126			2.21021
$268$	−13.3155	+	7.68771i	−0.0496847	+	0.0286855i
$269$	−137.447	+	79.3552i	−0.510956	+	0.295001i	−0.733227	−	0.679984i	$-0.761987\pi$
$269$	−137.447	+	79.3552i	−0.510956	+	0.295001i	0.222270	+	0.974985i	$0.428653\pi$
$270$	−157.232	+	272.335i	−0.582342	+	1.00865i
$271$	−244.649	−	423.745i	−0.902765	−	1.56364i	−0.823889	−	0.566751i	$-0.808200\pi$
$271$	−244.649	−	423.745i	−0.902765	−	1.56364i	−0.0788765	−	0.996884i	$-0.525133\pi$
$272$	−35.4745	+	61.4437i	−0.130421	+	0.225896i
$273$	78.9053			0.289030
$274$			304.739i			1.11218i
$275$	0.422551	−	0.731881i	0.00153655	−	0.00266138i
$276$	−233.438	−	134.775i	−0.845789	−	0.488316i
$277$	−183.051			−0.660835			−0.330417	−	0.943835i	$-0.607189\pi$
$277$	−183.051			−0.660835			−0.330417	+	0.943835i	$0.607189\pi$
$278$			307.292i			1.10537i
$279$	209.503	+	120.957i	0.750908	+	0.433537i
$280$	81.0185	−	46.7760i	0.289352	−	0.167057i
$281$	230.908	+	133.315i	0.821736	+	0.474430i	0.851015	−	0.525142i	$-0.175988\pi$
$281$	230.908	+	133.315i	0.821736	+	0.474430i	−0.0292787	+	0.999571i	$0.509321\pi$
$282$	−325.450	−	563.697i	−1.15408	−	1.99892i
$283$	178.014	+	308.329i	0.629025	+	1.08950i	0.987748	+	0.156059i	$0.0498789\pi$
$283$	178.014	+	308.329i	0.629025	+	1.08950i	−0.358723	+	0.933444i	$0.616788\pi$
$284$			283.521i			0.998312i
$285$	−477.952	+	152.564i	−1.67703	+	0.535311i
$286$	2.06073			0.00720534
$287$	−61.5480	+	35.5347i	−0.214453	+	0.123814i
$288$	−84.5908	+	48.8385i	−0.293718	+	0.169578i
$289$	102.303	−	177.195i	0.353991	−	0.613130i
$290$	−60.6161	−	104.990i	−0.209021	−	0.362035i
$291$	216.873	−	375.635i	0.745267	−	1.29084i
$292$	−408.402			−1.39864
$293$		−	357.755i		−	1.22101i	−0.792014	−	0.610503i	$-0.790967\pi$
$293$		−	357.755i		−	1.22101i	0.792014	−	0.610503i	$-0.209033\pi$
$294$	−302.972	+	524.763i	−1.03052	+	1.78491i
$295$	−123.229	−	71.1465i	−0.417727	−	0.241175i
$296$	499.382			1.68710
$297$			0.490335i			0.00165096i
$298$	70.1022	+	40.4735i	0.235242	+	0.135817i
$299$	−142.750	+	82.4169i	−0.477425	+	0.275642i
$300$	−556.063	−	321.043i	−1.85354	−	1.07014i
$301$	−18.6273	−	32.2634i	−0.0618846	−	0.107187i
$302$	421.982	+	730.894i	1.39729	+	2.42018i
$303$			651.659i			2.15069i
$304$	−143.373	−	31.2518i	−0.471621	−	0.102802i
$305$	−114.450			−0.375246
$306$	145.579	−	84.0503i	0.475750	−	0.274674i
$307$	125.866	−	72.6688i	0.409987	−	0.236706i	−0.280797	−	0.959767i	$-0.590599\pi$
$307$	125.866	−	72.6688i	0.409987	−	0.236706i	0.690784	+	0.723061i	$0.257265\pi$
$308$	0.162284	−	0.281085i	0.000526897	−	0.000912613i
$309$	230.559	+	399.339i	0.746145	+	1.29236i
$310$	517.243	−	895.892i	1.66853	−	2.88997i
$311$	−191.291			−0.615084			−0.307542	−	0.951534i	$-0.599506\pi$
$311$	−191.291			−0.615084			−0.307542	+	0.951534i	$0.599506\pi$
$312$		−	703.675i		−	2.25537i
$313$	156.376	−	270.851i	0.499603	−	0.865337i	−0.500397	−	0.865796i	$-0.666813\pi$
$313$	156.376	−	270.851i	0.499603	−	0.865337i	1.00000		0.000458751i	$0.000146025\pi$
$314$	−255.890	−	147.738i	−0.814938	−	0.470505i
$315$	−46.5380			−0.147740
$316$		−	334.214i		−	1.05764i
$317$	78.3676	+	45.2456i	0.247217	+	0.142731i	0.618489	−	0.785793i	$-0.287745\pi$
$317$	78.3676	+	45.2456i	0.247217	+	0.142731i	−0.371273	+	0.928524i	$0.621078\pi$
$318$	128.675	−	74.2907i	0.404639	−	0.233618i
$319$	−0.163708	−	0.0945168i	−0.000513191	−	0.000296291i
$320$	316.137	+	547.565i	0.987928	+	1.71114i
$321$	−106.551	−	184.552i	−0.331935	−	0.574928i
$322$			40.2552i			0.125016i
$323$	−170.541	−	37.1738i	−0.527989	−	0.115089i
$324$	729.027			2.25008
$325$	−340.040	+	196.322i	−1.04628	+	0.604068i
$326$	82.4365	−	47.5947i	0.252873	−	0.145996i
$327$	101.057	−	175.036i	0.309042	−	0.535277i
$328$	316.898	+	548.883i	0.966152	+	1.67342i
$329$	−31.3456	+	54.2922i	−0.0952754	+	0.165022i
$330$	−3.22182			−0.00976308
$331$			251.295i			0.759199i	0.925151	+	0.379599i	$0.123938\pi$
$331$			251.295i			0.759199i	−0.925151	+	0.379599i	$0.876062\pi$
$332$	237.332	−	411.071i	0.714854	−	1.23816i
$333$	−215.138	−	124.210i	−0.646060	−	0.373003i
$334$	201.982			0.604737
$335$		−	14.6999i		−	0.0438802i
$336$	−31.2471	−	18.0405i	−0.0929974	−	0.0536921i
$337$	−225.749	+	130.336i	−0.669879	+	0.386755i	−0.796031	−	0.605256i	$-0.793071\pi$
$337$	−225.749	+	130.336i	−0.669879	+	0.386755i	0.126152	+	0.992011i	$0.459737\pi$
$338$	−337.931	−	195.105i	−0.999797	−	0.577233i
$339$	−260.305	−	450.861i	−0.767861	−	1.32997i
$340$	−231.800	−	401.490i	−0.681766	−	1.18085i
$341$		−	1.61304i		−	0.00473033i
$342$	257.162	+	233.973i	0.751935	+	0.684131i
$343$	118.578			0.345710
$344$	−287.724	+	166.117i	−0.836406	+	0.482899i
$345$	223.181	−	128.854i	0.646901	−	0.373489i
$346$	−296.267	+	513.150i	−0.856263	+	1.48309i
$347$	169.713	+	293.952i	0.489088	+	0.847125i	0.999921	−	0.0125549i	$-0.00399646\pi$
$347$	169.713	+	293.952i	0.489088	+	0.847125i	−0.510833	+	0.859680i	$0.670663\pi$
$348$	−71.8113	+	124.381i	−0.206354	+	0.357416i
$349$	−76.4095			−0.218938			−0.109469	−	0.993990i	$-0.534915\pi$
$349$	−76.4095			−0.218938			−0.109469	+	0.993990i	$0.534915\pi$
$350$			95.8904i			0.273973i
$351$	113.908	−	197.294i	0.324523	−	0.562090i
$352$	0.564038	+	0.325647i	0.00160238	+	0.000925135i
$353$	635.437			1.80010			0.900052	−	0.435783i	$-0.143528\pi$
$353$	635.437			1.80010			0.900052	+	0.435783i	$0.143528\pi$
$354$			261.384i			0.738372i
$355$	−234.748	−	135.532i	−0.661261	−	0.381779i
$356$	−976.710	+	563.904i	−2.74357	+	1.58400i
$357$	−37.1682	−	21.4590i	−0.104112	−	0.0601094i
$358$	−0.380854	−	0.659658i	−0.00106384	−	0.00184262i
$359$	−2.43138	−	4.21127i	−0.00677264	−	0.0117306i	0.862619	−	0.505854i	$-0.168822\pi$
$359$	−2.43138	−	4.21127i	−0.00677264	−	0.0117306i	−0.869392	+	0.494123i	$0.835489\pi$
$360$			415.024i			1.15284i
$361$	−34.0136	−	359.394i	−0.0942206	−	0.995551i
$362$	−501.542			−1.38548
$363$	398.358	−	229.992i	1.09740	−	0.633586i
$364$	−130.595	+	75.3991i	−0.358778	+	0.207141i
$365$	195.229	−	338.146i	0.534874	−	0.926428i
$366$	105.119	+	182.071i	0.287210	+	0.497462i
$367$	−149.568	+	259.060i	−0.407542	+	0.705884i	−0.994614	−	0.103651i	$-0.966948\pi$
$367$	−149.568	+	259.060i	−0.407542	+	0.705884i	0.587071	+	0.809535i	$0.300281\pi$
$368$	75.3736			0.204820
$369$		−	315.285i		−	0.854430i
$370$	−531.155	+	919.987i	−1.43555	+	2.48645i
$371$	−12.3933	−	7.15527i	−0.0334051	−	0.0192864i
$372$	−1225.55			−3.29448
$373$			286.394i			0.767813i	0.923372	+	0.383907i	$0.125422\pi$
$373$			286.394i			0.767813i	−0.923372	+	0.383907i	$0.874578\pi$
$374$	−0.970701	−	0.560434i	−0.00259546	−	0.00149849i
$375$	−40.0722	+	23.1357i	−0.106859	+	0.0616952i
$376$	484.176	+	279.539i	1.28770	+	0.743455i
$377$	43.9136	+	76.0605i	0.116482	+	0.201752i
$378$	−27.8182	−	48.1825i	−0.0735930	−	0.127467i
$379$		−	638.486i		−	1.68466i	−0.538962	−	0.842330i	$-0.681183\pi$
$379$		−	638.486i		−	1.68466i	0.538962	−	0.842330i	$-0.318817\pi$
$380$	645.268	−	709.221i	1.69807	−	1.86637i
$381$	−600.322			−1.57565
$382$	730.474	−	421.739i	1.91224	−	1.10403i
$383$	297.246	−	171.615i	0.776100	−	0.448082i	−0.0589464	−	0.998261i	$-0.518774\pi$
$383$	297.246	−	171.615i	0.776100	−	0.448082i	0.835046	+	0.550180i	$0.185441\pi$
$384$	444.504	−	769.904i	1.15756	−	2.00496i
$385$	0.155154	+	0.268734i	0.000402997	+	0.000698012i
$386$	212.761	−	368.512i	0.551193	−	0.954694i
$387$	165.272			0.427059
$388$			828.944i			2.13645i
$389$	−176.043	+	304.915i	−0.452552	+	0.783843i	−0.998544	−	0.0539474i	$-0.982820\pi$
$389$	−176.043	+	304.915i	−0.452552	+	0.783843i	0.545992	+	0.837791i	$0.316153\pi$
$390$	1296.35	+	748.446i	3.32397	+	1.91909i
$391$	89.6562			0.229300
$392$		−	520.464i		−	1.32771i
$393$	−253.764	−	146.510i	−0.645709	−	0.372800i
$394$	830.745	−	479.631i	2.10849	−	1.21734i
$395$	276.721	+	159.765i	0.700559	+	0.404468i
$396$	0.719940	+	1.24697i	0.00181803	+	0.00314892i
$397$	205.686	+	356.259i	0.518101	+	0.897378i	0.999779	+	0.0210293i	$0.00669432\pi$
$397$	205.686	+	356.259i	0.518101	+	0.897378i	−0.481678	+	0.876349i	$0.659972\pi$
$398$		−	517.132i		−	1.29933i
$399$	18.9047	−	86.7282i	0.0473801	−	0.217364i
$400$	179.545			0.448862
$401$	−26.8409	+	15.4966i	−0.0669349	+	0.0386449i	−0.533094	−	0.846056i	$-0.678971\pi$
$401$	−26.8409	+	15.4966i	−0.0669349	+	0.0386449i	0.466159	+	0.884701i	$0.345637\pi$
$402$	−23.3851	+	13.5014i	−0.0581718	+	0.0335855i
$403$	−374.719	+	649.032i	−0.929823	+	1.61050i
$404$	−622.703	−	1078.55i	−1.54134	−	2.66969i
$405$	−348.497	+	603.615i	−0.860487	+	1.49041i
$406$	21.4489			0.0528297
$407$			1.65643i			0.00406984i
$408$	−191.371	+	331.465i	−0.469047	+	0.812413i
$409$	−336.926	−	194.525i	−0.823781	−	0.475610i	0.0279377	−	0.999610i	$-0.491106\pi$
$409$	−336.926	−	194.525i	−0.823781	−	0.475610i	−0.851719	+	0.524000i	$0.824439\pi$
$410$	−1348.24			−3.28839
$411$			345.158i			0.839801i
$412$	−763.190	−	440.628i	−1.85240	−	1.06948i
$413$	21.8022	−	12.5875i	0.0527899	−	0.0304783i
$414$	−154.658	−	89.2918i	−0.373570	−	0.215681i
$415$	226.904	+	393.009i	0.546756	+	0.947010i
$416$	−151.300	−	262.058i	−0.363701	−	0.629948i
$417$			348.050i			0.834653i
$418$	0.493723	−	2.26503i	0.00118116	−	0.00541874i
$419$	455.941			1.08817			0.544083	−	0.839032i	$-0.316878\pi$
$419$	455.941			1.08817			0.544083	+	0.839032i	$0.316878\pi$
$420$	204.177	−	117.882i	0.486136	−	0.280671i
$421$	−176.502	+	101.903i	−0.419244	+	0.242051i	−0.694754	−	0.719248i	$-0.744487\pi$
$421$	−176.502	+	101.903i	−0.419244	+	0.242051i	0.275510	+	0.961298i	$0.411153\pi$
$422$	267.593	−	463.484i	0.634106	−	1.09830i
$423$	−139.058	−	240.856i	−0.328743	−	0.569399i
$424$	−63.8105	+	110.523i	−0.150496	+	0.260668i
$425$	213.567			0.502510
$426$			497.926i			1.16884i
$427$	10.1245	−	17.5361i	0.0237107	−	0.0410681i
$428$	352.703	+	203.633i	0.824072	+	0.475778i
$429$	2.33406			0.00544069
$430$		−	706.746i		−	1.64360i
$431$	609.299	+	351.779i	1.41369	+	0.816193i	0.995734	−	0.0922756i	$-0.0294141\pi$
$431$	609.299	+	351.779i	1.41369	+	0.816193i	0.417954	+	0.908468i	$0.362747\pi$
$432$	−90.2166	+	52.0866i	−0.208835	+	0.120571i
$433$	−164.941	−	95.2288i	−0.380927	−	0.219928i	0.297295	−	0.954786i	$-0.403916\pi$
$433$	−164.941	−	95.2288i	−0.380927	−	0.219928i	−0.678221	+	0.734858i	$0.737249\pi$
$434$	91.5127	+	158.505i	0.210859	+	0.365218i
$435$	−68.6561	−	118.916i	−0.157830	−	0.273370i
$436$			386.265i			0.885930i
$437$	56.3868	+	176.649i	0.129032	+	0.404231i
$438$	−717.247			−1.63755
$439$	415.097	−	239.656i	0.945551	−	0.545914i	0.0538552	−	0.998549i	$-0.482849\pi$
$439$	415.097	−	239.656i	0.945551	−	0.545914i	0.891696	+	0.452634i	$0.149516\pi$
$440$	2.39657	−	1.38366i	0.00544674	−	0.00314468i
$441$	−129.454	+	224.220i	−0.293546	+	0.508436i
$442$	260.384	+	450.999i	0.589105	+	1.02036i
$443$	−383.888	+	664.914i	−0.866565	+	1.50094i	−0.00108097	+	0.999999i	$0.500344\pi$
$443$	−383.888	+	664.914i	−0.866565	+	1.50094i	−0.865484	+	0.500936i	$0.832989\pi$
$444$	1258.51			2.83448
$445$		−	1078.25i		−	2.42304i
$446$	313.744	−	543.421i	0.703463	−	1.21843i
$447$	79.4004	+	45.8418i	0.177629	+	0.102554i
$448$	−111.864			−0.249697
$449$		−	392.421i		−	0.873988i	−0.899464	−	0.436994i	$-0.856043\pi$
$449$		−	392.421i		−	0.873988i	0.899464	−	0.436994i	$-0.143957\pi$
$450$	−368.405	−	212.699i	−0.818678	−	0.472664i
$451$	−1.82062	+	1.05113i	−0.00403685	+	0.00233068i
$452$	861.654	+	497.476i	1.90631	+	1.10061i
$453$	477.952	+	827.837i	1.05508	+	1.82746i
$454$	14.8942	+	25.7976i	0.0328067	+	0.0568228i
$455$		−	144.173i		−	0.316863i
$456$	−773.439	−	168.591i	−1.69614	−	0.369718i
$457$	−695.090			−1.52099			−0.760493	−	0.649347i	$-0.775042\pi$
$457$	−695.090			−1.52099			−0.760493	+	0.649347i	$0.775042\pi$
$458$	−772.952	+	446.264i	−1.68767	+	0.974376i
$459$	−107.312	+	61.9565i	−0.233795	+	0.134981i
$460$	−246.256	+	426.528i	−0.535339	+	0.927234i
$461$	351.150	+	608.210i	0.761714	+	1.31933i	0.941967	+	0.335707i	$0.108975\pi$
$461$	351.150	+	608.210i	0.761714	+	1.31933i	−0.180253	+	0.983620i	$0.557692\pi$
$462$	0.285008	−	0.493649i	0.000616901	−	0.00106850i
$463$	−14.4955			−0.0313077			−0.0156538	−	0.999877i	$-0.504983\pi$
$463$	−14.4955			−0.0313077			−0.0156538	+	0.999877i	$0.504983\pi$
$464$		−	40.1608i		−	0.0865534i
$465$	585.849	−	1014.72i	1.25989	−	2.18219i
$466$	−26.2882	−	15.1775i	−0.0564125	−	0.0325698i
$467$	−863.890			−1.84987			−0.924935	−	0.380124i	$-0.875881\pi$
$467$	−863.890			−1.84987			−0.924935	+	0.380124i	$0.875881\pi$
$468$		−	668.985i		−	1.42945i
$469$	2.25232	+	1.30038i	0.00480239	+	0.00277266i
$470$	−1029.96	+	594.650i	−2.19141	+	1.26521i
$471$	−289.831	−	167.334i	−0.615353	−	0.355274i
$472$	−112.255	−	194.432i	−0.237829	−	0.411931i
$473$	−0.551003	−	0.954366i	−0.00116491	−	0.00201769i
$474$		−	586.956i		−	1.23830i
$475$	134.317	+	420.789i	0.282773	+	0.885871i
$476$	82.0221			0.172315
$477$	54.9802	−	31.7429i	0.115263	−	0.0665469i
$478$	140.625	−	81.1897i	0.294194	−	0.169853i
$479$	−198.015	+	342.972i	−0.413393	+	0.716017i	−0.995258	−	0.0972678i	$-0.968990\pi$
$479$	−198.015	+	342.972i	−0.413393	+	0.716017i	0.581866	+	0.813285i	$0.302323\pi$
$480$	236.547	+	409.712i	0.492807	+	0.853566i
$481$	384.797	−	666.488i	0.799994	−	1.38563i
$482$	466.742			0.968344
$483$			45.5945i			0.0943986i
$484$	−439.544	+	761.313i	−0.908149	+	1.57296i
$485$	−686.345	−	396.261i	−1.41514	−	0.817033i
$486$	872.884			1.79606
$487$		−	872.905i		−	1.79241i	−0.443636	−	0.896207i	$-0.646312\pi$
$487$		−	872.905i		−	1.79241i	0.443636	−	0.896207i	$-0.353688\pi$
$488$	−156.386	−	90.2897i	−0.320464	−	0.185020i
$489$	93.3707	−	53.9076i	0.190942	−	0.110240i
$490$	958.826	+	553.578i	1.95679	+	1.12975i
$491$	−350.193	−	606.552i	−0.713224	−	1.23534i	−0.963641	−	0.267201i	$-0.913901\pi$
$491$	−350.193	−	606.552i	−0.713224	−	1.23534i	0.250417	−	0.968138i	$-0.419432\pi$
$492$	798.624	+	1383.26i	1.62322	+	2.81150i
$493$		−	47.7709i		−	0.0968983i
$494$	−724.837	+	796.676i	−1.46728	+	1.61270i
$495$	−1.37662			−0.00278104
$496$	296.783	−	171.348i	0.598353	−	0.345459i
$497$	41.5325	−	23.9788i	0.0835663	−	0.0482470i
$498$	416.808	−	721.933i	0.836965	−	1.44967i
$499$	−76.5488	−	132.586i	−0.153404	−	0.265704i	0.779073	−	0.626934i	$-0.215690\pi$
$499$	−76.5488	−	132.586i	−0.153404	−	0.265704i	−0.932477	+	0.361230i	$0.882357\pi$
$500$	44.2154	−	76.5832i	0.0884307	−	0.153166i
$501$	228.773			0.456632
$502$		−	731.860i		−	1.45789i
$503$	203.824	−	353.033i	0.405216	−	0.701855i	−0.589130	−	0.808038i	$-0.700530\pi$
$503$	203.824	−	353.033i	0.405216	−	0.701855i	0.994347	+	0.106183i	$0.0338628\pi$
$504$	−63.5902	−	36.7138i	−0.126171	−	0.0728449i
$505$	1190.69			2.35779
$506$			1.19077i			0.00235330i
$507$	−382.754	−	220.983i	−0.754938	−	0.435864i
$508$	993.585	−	573.647i	1.95588	−	1.12923i
$509$	−171.070	−	98.7673i	−0.336090	−	0.194042i	0.322452	−	0.946586i	$-0.395493\pi$
$509$	−171.070	−	98.7673i	−0.336090	−	0.194042i	−0.658542	+	0.752544i	$0.728826\pi$
$510$	−407.094	−	705.108i	−0.798224	−	1.38256i
$511$	34.5406	+	59.8261i	0.0675942	+	0.117077i
$512$			476.936i			0.931515i
$513$	−189.563	−	172.470i	−0.369519	−	0.336198i
$514$	−744.428			−1.44830
$515$	729.657	−	421.268i	1.41681	−	0.817995i
$516$	−725.102	+	418.638i	−1.40524	+	0.811313i
$517$	−0.927218	+	1.60599i	−0.00179346	+	0.00310636i
$518$	−93.9740	−	162.768i	−0.181417	−	0.314223i
$519$	−335.563	+	581.212i	−0.646557	+	1.11987i
$520$	−1285.73			−2.47255
$521$			698.844i			1.34135i	0.741751	+	0.670676i	$0.233996\pi$
$521$			698.844i			1.34135i	−0.741751	+	0.670676i	$0.766004\pi$
$522$	−47.5767	+	82.4053i	−0.0911431	+	0.157865i
$523$	−381.571	−	220.300i	−0.729582	−	0.421224i	0.0886874	−	0.996060i	$-0.471733\pi$
$523$	−381.571	−	220.300i	−0.729582	−	0.421224i	−0.818269	+	0.574835i	$0.805066\pi$
$524$	560.001			1.06870
$525$			108.609i			0.206874i
$526$	934.166	+	539.341i	1.77598	+	1.02536i
$527$	353.021	−	203.817i	0.669869	−	0.386749i
$528$	−0.924305	−	0.533648i	−0.00175058	−	0.00101070i
$529$	216.876	+	375.641i	0.409974	+	0.710096i
$530$	−135.741	−	235.110i	−0.256115	−	0.443604i
$531$			111.684i			0.210327i
$532$	51.5855	+	161.607i	0.0969653	+	0.303773i
$533$	976.738			1.83253
$534$	−1715.32	+	990.343i	−3.21222	+	1.85457i
$535$	−337.206	+	194.686i	−0.630292	+	0.363899i
$536$	11.5967	−	20.0861i	0.0216357	−	0.0374741i
$537$	−0.431369	−	0.747153i	−0.000803295	−	0.00139135i
$538$	266.346	−	461.325i	0.495067	−	0.857481i
$539$	1.72635			0.00320288
$540$		−	680.696i		−	1.26055i
$541$	−442.696	+	766.772i	−0.818292	+	1.41732i	0.0886479	+	0.996063i	$0.471745\pi$
$541$	−442.696	+	766.772i	−0.818292	+	1.41732i	−0.906940	+	0.421260i	$0.861588\pi$
$542$	1422.25	+	821.136i	2.62408	+	1.51501i
$543$	−568.065			−1.04616
$544$			164.589i			0.302554i
$545$	−319.818	−	184.647i	−0.586822	−	0.338802i
$546$	−229.355	+	132.418i	−0.420064	+	0.242524i
$547$	−801.617	−	462.814i	−1.46548	−	0.846095i	−0.466223	−	0.884667i	$-0.654386\pi$
$547$	−801.617	−	462.814i	−1.46548	−	0.846095i	−0.999256	+	0.0385725i	$0.987719\pi$
$548$	−329.821	−	571.267i	−0.601863	−	1.04246i
$549$	44.9151	+	77.7952i	0.0818125	+	0.141703i
$550$			2.83648i			0.00515725i
$551$	94.1225	−	30.0442i	0.170821	−	0.0545266i
$552$	406.611			0.736614
$553$	−48.9585	+	28.2662i	−0.0885325	+	0.0511143i
$554$	532.077	−	307.195i	0.960427	−	0.554503i
$555$	−601.606	+	1042.01i	−1.08397	+	1.87750i
$556$	−332.585	−	576.053i	−0.598174	−	1.03607i
$557$	176.665	−	305.992i	0.317172	−	0.549358i	−0.662725	−	0.748863i	$-0.730600\pi$
$557$	176.665	−	305.992i	0.317172	−	0.549358i	0.979897	+	0.199505i	$0.0639335\pi$
$558$	−811.954			−1.45511
$559$			512.005i			0.915930i
$560$	−32.9629	+	57.0935i	−0.0588624	+	0.101953i
$561$	−1.09945	−	0.634769i	−0.00195981	−	0.00113150i
$562$	−894.909			−1.59236
$563$		−	21.4065i		−	0.0380221i	−0.999819	−	0.0190111i	$-0.993948\pi$
$563$		−	21.4065i		−	0.0380221i	0.999819	−	0.0190111i	$-0.00605177\pi$
$564$	1220.19	+	704.476i	2.16345	+	1.24907i
$565$	−823.795	+	475.618i	−1.45804	+	0.841802i
$566$	−1034.87	−	597.482i	−1.82839	−	1.05562i
$567$	−61.6575	−	106.794i	−0.108743	−	0.188349i
$568$	−213.842	−	370.385i	−0.376482	−	0.652087i
$569$			378.852i			0.665821i	0.942958	+	0.332911i	$0.108031\pi$
$569$			378.852i			0.665821i	−0.942958	+	0.332911i	$0.891969\pi$
$570$	1133.24	−	1245.55i	1.98814	−	2.18518i
$571$	−38.5842			−0.0675730			−0.0337865	−	0.999429i	$-0.510757\pi$
$571$	−38.5842			−0.0675730			−0.0337865	+	0.999429i	$0.510757\pi$
$572$	−3.86307	+	2.23034i	−0.00675362	+	0.00389920i
$573$	827.362	−	477.678i	1.44391	−	0.833644i
$574$	119.268	−	206.578i	0.207784	−	0.359892i
$575$	−113.443	−	196.488i	−0.197291	−	0.341719i
$576$	248.131	−	429.776i	0.430783	−	0.746139i
$577$	399.348			0.692112			0.346056	−	0.938214i	$-0.387521\pi$
$577$	399.348			0.692112			0.346056	+	0.938214i	$0.387521\pi$
$578$			686.737i			1.18813i
$579$	240.981	−	417.391i	0.416201	−	0.720882i
$580$	227.264	+	131.211i	0.391834	+	0.226225i
$581$	−80.2894			−0.138192
$582$			1455.81i			2.50140i
$583$	−0.366600	−	0.211656i	−0.000628816	−	0.000363047i
$584$	533.528	−	308.032i	0.913575	−	0.527453i
$585$	553.902	+	319.796i	0.946841	+	0.546659i
$586$	600.380	+	1039.89i	1.02454	+	1.77455i
$587$	−247.769	−	429.148i	−0.422093	−	0.731087i	0.574051	−	0.818820i	$-0.305371\pi$
$587$	−247.769	−	429.148i	−0.422093	−	0.731087i	−0.996144	+	0.0877330i	$0.972038\pi$
$588$		−	1311.64i		−	2.23068i
$589$	623.601	+	567.369i	1.05875	+	0.963275i
$590$	477.589			0.809474
$591$	940.933	−	543.248i	1.59210	−	0.919201i
$592$	−304.765	+	175.956i	−0.514806	+	0.297224i
$593$	−114.717	+	198.696i	−0.193452	+	0.335069i	−0.946392	−	0.323020i	$-0.895302\pi$
$593$	−114.717	+	198.696i	−0.193452	+	0.335069i	0.752940	+	0.658089i	$0.228635\pi$
$594$	−0.822875	−	1.42526i	−0.00138531	−	0.00239943i
$595$	−39.2091	+	67.9121i	−0.0658976	+	0.114138i
$596$	−175.219			−0.293992
$597$		−	585.723i		−	0.981110i
$598$	276.622	−	479.124i	0.462579	−	0.801210i
$599$	−26.4546	−	15.2736i	−0.0441646	−	0.0254984i	0.477755	−	0.878493i	$-0.341451\pi$
$599$	−26.4546	−	15.2736i	−0.0441646	−	0.0254984i	−0.521920	+	0.852995i	$0.674784\pi$
$600$	968.573			1.61429
$601$			962.490i			1.60148i	0.599012	+	0.800740i	$0.295560\pi$
$601$			962.490i			1.60148i	−0.599012	+	0.800740i	$0.704440\pi$
$602$	108.288	+	62.5201i	0.179880	+	0.103854i
$603$	−9.99195	+	5.76885i	−0.0165704	+	0.00956692i
$604$	−1582.10	−	913.429i	−2.61938	−	1.51230i
$605$	−420.232	−	727.863i	−0.694598	−	1.20308i
$606$	−1093.61	−	1894.18i	−1.80463	−	3.12572i
$607$			249.770i			0.411483i	0.978606	+	0.205741i	$0.0659606\pi$
$607$			249.770i			0.411483i	−0.978606	+	0.205741i	$0.934039\pi$
$608$	−324.289	+	103.514i	−0.533370	+	0.170253i
$609$	24.2938			0.0398913
$610$	332.673	−	192.069i	0.545365	−	0.314867i
$611$	746.161	−	430.796i	1.22121	−	0.705067i
$612$	−181.937	+	315.124i	−0.297282	+	0.514908i
$613$	−189.015	−	327.384i	−0.308345	−	0.534069i	0.669655	−	0.742672i	$-0.266442\pi$
$613$	−189.015	−	327.384i	−0.308345	−	0.534069i	−0.978000	+	0.208603i	$0.933108\pi$
$614$	−243.904	+	422.454i	−0.397238	+	0.688036i
$615$	−1527.07			−2.48304
$616$			0.489604i			0.000794812i
$617$	−259.371	+	449.243i	−0.420374	+	0.728109i	−0.995976	−	0.0896208i	$-0.971434\pi$
$617$	−259.371	+	449.243i	−0.420374	+	0.728109i	0.575602	+	0.817730i	$0.304768\pi$
$618$	−1340.33	−	773.842i	−2.16883	−	1.25217i
$619$	1035.34			1.67261			0.836303	−	0.548267i	$-0.184712\pi$
$619$	1035.34			1.67261			0.836303	+	0.548267i	$0.184712\pi$
$620$			2239.27i			3.61172i
$621$	114.004	+	65.8202i	0.183581	+	0.105991i
$622$	556.028	−	321.023i	0.893935	−	0.516114i
$623$	165.211	+	95.3844i	0.265186	+	0.153105i
$624$	247.939	+	429.443i	0.397338	+	0.688209i
$625$	332.869	+	576.545i	0.532590	+	0.922473i
$626$			1049.71i			1.67686i
$627$	0.559210	−	2.56546i	0.000891881	−	0.00409165i
$628$	639.594			1.01846
$629$	−362.516	+	209.298i	−0.576336	+	0.332748i
$630$	135.272	−	78.0995i	0.214718	−	0.123967i
$631$	528.945	−	916.160i	0.838265	−	1.45192i	−0.0530794	−	0.998590i	$-0.516904\pi$
$631$	528.945	−	916.160i	0.838265	−	1.45192i	0.891344	−	0.453327i	$-0.149763\pi$
$632$	252.077	+	436.610i	0.398856	+	0.690839i
$633$	303.086	−	524.960i	0.478808	−	0.829320i
$634$	−303.723			−0.479058
$635$			1096.88i			1.72738i
$636$	−160.811	+	278.533i	−0.252847	+	0.437944i
$637$	−694.625	−	401.042i	−1.09046	−	0.629579i
$638$	0.634468			0.000994464
$639$			212.754i			0.332948i
$640$	−1406.74	−	812.180i	−2.19803	−	1.26903i
$641$	−560.504	+	323.607i	−0.874421	+	0.504847i	−0.868815	−	0.495137i	$-0.835118\pi$
$641$	−560.504	+	323.607i	−0.874421	+	0.504847i	−0.00560636	+	0.999984i	$0.501785\pi$
$642$	619.426	+	357.626i	0.964839	+	0.557050i
$643$	157.333	+	272.508i	0.244685	+	0.423807i	0.962043	−	0.272898i	$-0.0879820\pi$
$643$	157.333	+	272.508i	0.244685	+	0.423807i	−0.717358	+	0.696705i	$0.754649\pi$
$644$	−43.5685	−	75.4629i	−0.0676530	−	0.117178i
$645$		−	800.487i		−	1.24107i
$646$	558.096	−	178.146i	0.863926	−	0.275768i
$647$	−320.116			−0.494769			−0.247384	−	0.968917i	$-0.579571\pi$
$647$	−320.116			−0.494769			−0.247384	+	0.968917i	$0.579571\pi$
$648$	−952.385	+	549.860i	−1.46973	+	0.848549i
$649$	0.644920	−	0.372345i	0.000993714	−	0.000573721i
$650$	658.932	−	1141.30i	1.01374	−	1.75585i
$651$	103.651	+	179.528i	0.159218	+	0.275773i
$652$	−103.024	+	178.443i	−0.158013	+	0.273686i
$653$	131.969			0.202097			0.101049	−	0.994881i	$-0.467780\pi$
$653$	131.969			0.202097			0.101049	+	0.994881i	$0.467780\pi$
$654$			678.370i			1.03726i
$655$	−267.698	+	463.666i	−0.408699	+	0.707888i
$656$	−386.796	−	223.317i	−0.589628	−	0.340422i
$657$	−306.465			−0.466460
$658$		−	210.415i		−	0.319780i
$659$	−635.205	−	366.736i	−0.963892	−	0.556503i	−0.0665235	−	0.997785i	$-0.521191\pi$
$659$	−635.205	−	366.736i	−0.963892	−	0.556503i	−0.897369	+	0.441281i	$0.854524\pi$
$660$	6.03966	−	3.48700i	0.00915100	−	0.00528333i
$661$	590.038	+	340.659i	0.892644	+	0.515368i	0.874807	−	0.484472i	$-0.160988\pi$
$661$	590.038	+	340.659i	0.892644	+	0.515368i	0.0178378	+	0.999841i	$0.494322\pi$
$662$	−421.720	−	730.441i	−0.637040	−	1.10338i
$663$	294.921	+	510.818i	0.444828	+	0.770465i
$664$			716.019i			1.07834i
$665$	−158.466	−	34.5419i	−0.238295	−	0.0519426i
$666$	833.792			1.25194
$667$	−43.9507	+	25.3750i	−0.0658931	+	0.0380434i
$668$	−378.639	+	218.607i	−0.566824	+	0.327256i
$669$	355.359	−	615.499i	0.531179	−	0.920029i
$670$	24.6692	+	42.7282i	0.0368196	+	0.0637735i
$671$	0.299487	−	0.518726i	0.000446329	−	0.000773064i
$672$	−83.7017			−0.124556
$673$		−	710.831i		−	1.05621i	−0.849178	−	0.528107i	$-0.822902\pi$
$673$		−	710.831i		−	1.05621i	0.849178	−	0.528107i	$-0.177098\pi$
$674$	437.458	−	757.700i	0.649048	−	1.12418i
$675$	271.565	+	156.788i	0.402318	+	0.232278i
$676$	844.654			1.24949
$677$		−	493.970i		−	0.729645i	−0.931077	−	0.364823i	$-0.881130\pi$
$677$		−	493.970i		−	0.729645i	0.931077	−	0.364823i	$-0.118870\pi$
$678$	1513.26	+	873.681i	2.23195	+	1.28862i
$679$	121.431	−	70.1081i	0.178838	−	0.103252i
$680$	605.639	+	349.666i	0.890645	+	0.514214i
$681$	16.8698	+	29.2193i	0.0247721	+	0.0429065i
$682$	2.70699	+	4.68864i	0.00396919	+	0.00687484i
$683$			442.962i			0.648553i	0.945962	+	0.324276i	$0.105121\pi$
$683$			442.962i			0.648553i	−0.945962	+	0.324276i	$0.894879\pi$
$684$	−735.310	−	160.280i	−1.07501	−	0.234327i
$685$	630.659			0.920670
$686$	−344.673	+	198.997i	−0.502439	+	0.290083i
$687$	−875.474	+	505.455i	−1.27434	+	0.735743i
$688$	117.062	−	202.758i	0.170149	−	0.294706i
$689$	98.3380	+	170.326i	0.142726	+	0.247208i
$690$	−432.481	+	749.080i	−0.626784	+	1.08562i
$691$	924.711			1.33822			0.669110	−	0.743163i	$-0.266675\pi$
$691$	924.711			1.33822			0.669110	+	0.743163i	$0.266675\pi$
$692$		−	1282.61i		−	1.85348i
$693$	0.121778	−	0.210926i	0.000175726	−	0.000304366i
$694$	−986.615	−	569.622i	−1.42164	−	0.820782i
$695$	635.943			0.915026
$696$		−	216.651i		−	0.311281i
$697$	−460.090	−	265.633i	−0.660101	−	0.381109i
$698$	222.100	−	128.230i	0.318195	−	0.183710i
$699$	−29.7750	−	17.1906i	−0.0425966	−	0.0245932i
$700$	−103.783	−	179.757i	−0.148261	−	0.256796i
$701$	−277.112	−	479.973i	−0.395310	−	0.684697i	0.597831	−	0.801622i	$-0.296030\pi$
$701$	−277.112	−	479.973i	−0.395310	−	0.684697i	−0.993141	+	0.116925i	$0.962696\pi$
$702$			764.634i			1.08922i
$703$	−640.373	−	582.629i	−0.910915	−	0.828775i
$704$	−3.30900			−0.00470028
$705$	−1166.58	+	673.523i	−1.65472	+	0.955351i
$706$	−1847.03	+	1066.38i	−2.61619	+	1.51046i
$707$	−105.330	+	182.437i	−0.148982	+	0.258045i
$708$	−282.898	−	489.993i	−0.399573	−	0.692081i
$709$	249.802	−	432.670i	0.352331	−	0.610254i	−0.634327	−	0.773065i	$-0.718723\pi$
$709$	249.802	−	432.670i	0.352331	−	0.610254i	0.986657	+	0.162811i	$0.0520560\pi$
$710$	909.791			1.28140
$711$		−	250.794i		−	0.352734i
$712$	850.635	−	1473.34i	1.19471	−	2.06930i
$713$	−375.036	−	216.527i	−0.525997	−	0.303684i
$714$	144.049			0.201750
$715$		−	4.26469i		−	0.00596461i
$716$	1.42791	+	0.824403i	0.00199428	+	0.00115140i
$717$	159.277	−	91.9584i	0.222143	−	0.128254i
$718$	14.1346	+	8.16063i	0.0196861	+	0.0113658i
$719$	174.396	+	302.062i	0.242553	+	0.420114i	0.961441	−	0.275012i	$-0.0886818\pi$
$719$	174.396	+	302.062i	0.242553	+	0.420114i	−0.718888	+	0.695126i	$0.755348\pi$
$720$	−146.233	−	253.283i	−0.203101	−	0.351782i
$721$			149.065i			0.206747i
$722$	701.999	+	987.573i	0.972298	+	1.36783i
$723$	528.649			0.731189
$724$	940.198	−	542.823i	1.29862	−	0.749756i
$725$	−104.693	+	60.4448i	−0.144405	+	0.0833721i
$726$	−771.940	+	1337.04i	−1.06328	+	1.84165i
$727$	41.3116	+	71.5538i	0.0568247	+	0.0984233i	0.893038	−	0.449980i	$-0.148569\pi$
$727$	41.3116	+	71.5538i	0.0568247	+	0.0984233i	−0.836214	+	0.548404i	$0.815236\pi$
$728$	113.738	−	197.000i	0.156233	−	0.270604i
$729$	85.5657			0.117374
$730$			1310.52i			1.79524i
$731$	139.245	−	241.179i	0.190485	−	0.329930i
$732$	−394.114	−	227.542i	−0.538407	−	0.310850i
$733$	−981.828			−1.33947			−0.669733	−	0.742602i	$-0.733591\pi$
$733$	−981.828			−1.33947			−0.669733	+	0.742602i	$0.733591\pi$
$734$		−	1004.01i		−	1.36787i
$735$	1086.00	+	627.003i	1.47755	+	0.853066i
$736$	151.428	−	87.4267i	0.205744	−	0.118786i
$737$	0.0666248	+	0.0384658i	9.03999e−5	+	5.21924e-5i
$738$	529.107	+	916.441i	0.716948	+	1.24179i
$739$	−64.8765	−	112.369i	−0.0877895	−	0.152056i	0.818787	−	0.574097i	$-0.194647\pi$
$739$	−64.8765	−	112.369i	−0.0877895	−	0.152056i	−0.906576	+	0.422042i	$0.861314\pi$
$740$		−	2299.49i		−	3.10743i
$741$	−820.978	+	902.345i	−1.10793	+	1.21774i
$742$	48.0316			0.0647326
$743$	−450.862	+	260.306i	−0.606814	+	0.350344i	−0.771717	−	0.635966i	$-0.780602\pi$
$743$	−450.862	+	260.306i	−0.606814	+	0.350344i	0.164904	+	0.986310i	$0.447269\pi$
$744$	1601.03	−	924.354i	2.15192	−	1.24241i
$745$	83.7603	−	145.077i	0.112430	−	0.194734i
$746$	−480.624	−	832.465i	−0.644268	−	1.11590i
$747$	178.094	−	308.467i	0.238412	−	0.412941i
$748$	2.42625			0.00324365
$749$		−	68.8892i		−	0.0919749i
$750$	77.6522	−	134.498i	0.103536	−	0.179330i
$751$	880.913	+	508.595i	1.17299	+	0.677224i	0.954382	−	0.298590i	$-0.0965161\pi$
$751$	880.913	+	508.595i	1.17299	+	0.677224i	0.218605	+	0.975813i	$0.429849\pi$
$752$	−393.981			−0.523910
$753$		−	828.932i		−	1.10084i
$754$	−255.288	−	147.391i	−0.338578	−	0.195478i
$755$	1512.59	−	873.295i	2.00343	−	1.15668i
$756$	104.297	+	60.2157i	0.137958	+	0.0796504i
$757$	155.490	+	269.317i	0.205403	+	0.355768i	0.950261	−	0.311455i	$-0.100816\pi$
$757$	155.490	+	269.317i	0.205403	+	0.355768i	−0.744858	+	0.667223i	$0.767483\pi$
$758$	1071.50	+	1855.89i	1.41359	+	2.44841i
$759$			1.34871i			0.00177695i
$760$	−308.043	+	1413.20i	−0.405320	+	1.85947i
$761$	−1402.51			−1.84298			−0.921489	−	0.388404i	$-0.873027\pi$
$761$	−1402.51			−1.84298			−0.921489	+	0.388404i	$0.873027\pi$
$762$	1744.96	−	1007.45i	2.28998	−	1.32212i
$763$	56.5834	−	32.6684i	0.0741591	−	0.0428158i
$764$	−912.904	+	1581.20i	−1.19490	+	2.06963i
$765$	−173.943	−	301.278i	−0.227376	−	0.393827i
$766$	−576.006	+	997.671i	−0.751966	+	1.30244i
$767$	−345.991			−0.451097
$768$			1599.68i			2.08292i
$769$	196.711	−	340.714i	0.255802	−	0.443061i	−0.709311	−	0.704895i	$-0.750994\pi$
$769$	196.711	−	340.714i	0.255802	−	0.443061i	0.965113	+	0.261834i	$0.0843273\pi$
$770$	−0.901975	−	0.520755i	−0.00117140	−	0.000676306i
$771$	−843.167			−1.09360
$772$			921.090i			1.19312i
$773$	201.825	+	116.524i	0.261093	+	0.150742i	0.624833	−	0.780758i	$-0.285167\pi$
$773$	201.825	+	116.524i	0.261093	+	0.150742i	−0.363740	+	0.931501i	$0.618500\pi$
$774$	−480.397	+	277.357i	−0.620668	+	0.358343i
$775$	−893.359	−	515.781i	−1.15272	−	0.665524i
$776$	−625.222	−	1082.92i	−0.805698	−	1.39551i
$777$	−106.438	−	184.357i	−0.136986	−	0.237267i
$778$		−	1181.73i		−	1.51894i
$779$	234.014	−	1073.57i	0.300403	−	1.37814i
$780$	−3240.20			−4.15410
$781$	1.22855	−	0.709304i	0.00157305	−	0.000908200i
$782$	−260.604	+	150.460i	−0.333254	+	0.192404i
$783$	35.0705	−	60.7439i	0.0447899	−	0.0775784i
$784$	183.385	+	317.631i	0.233909	+	0.405142i
$785$	−305.746	+	529.568i	−0.389485	+	0.674609i
$786$	983.489			1.25126
$787$		−	193.205i		−	0.245495i	−0.992438	−	0.122748i	$-0.960829\pi$
$787$		−	193.205i		−	0.245495i	0.992438	−	0.122748i	$-0.0391706\pi$
$788$	−1038.22	+	1798.25i	−1.31753	+	2.28204i
$789$	1058.07	+	610.878i	1.34103	+	0.774243i
$790$	−1072.46			−1.35755
$791$		−	168.296i		−	0.212764i
$792$	−1.88103	−	1.08601i	−0.00237504	−	0.00137123i
$793$	−241.006	+	139.145i	−0.303917	+	0.175466i
$794$	−1195.74	−	690.361i	−1.50597	−	0.869472i
$795$	−153.745	−	266.295i	−0.193390	−	0.334962i
$796$	559.696	+	969.422i	0.703136	+	1.21787i
$797$			255.622i			0.320730i	0.987058	+	0.160365i	$0.0512672\pi$
$797$			255.622i			0.320730i	−0.987058	+	0.160365i	$0.948733\pi$
$798$	90.5959	+	283.819i	0.113529	+	0.355663i
$799$	−468.636			−0.586529
$800$	360.710	−	208.256i	0.450887	−	0.260320i
$801$	−732.922	+	423.153i	−0.915009	+	0.528281i
$802$	52.0124	−	90.0882i	0.0648534	−	0.112329i
$803$	1.02173	+	1.76969i	0.00127239	+	0.00220384i
$804$	29.2253	−	50.6197i	0.0363499	−	0.0629598i
$805$	83.3085			0.103489
$806$		−	2515.40i		−	3.12084i
$807$	301.674	−	522.514i	0.373821	−	0.647477i
$808$	1626.97	+	939.333i	2.01358	+	1.16254i
$809$	478.346			0.591281			0.295641	−	0.955299i	$-0.404467\pi$
$809$	478.346			0.591281			0.295641	+	0.955299i	$0.404467\pi$
$810$		−	2339.38i		−	2.88812i
$811$	810.296	+	467.825i	0.999132	+	0.576849i	0.907991	−	0.418989i	$-0.137615\pi$
$811$	810.296	+	467.825i	0.999132	+	0.576849i	0.0911409	+	0.995838i	$0.470949\pi$
$812$	−40.2084	+	23.2143i	−0.0495177	+	0.0285890i
$813$	1610.89	+	930.049i	1.98142	+	1.14397i
$814$	−2.77980	−	4.81475i	−0.00341498	−	0.00591492i
$815$	−98.4977	−	170.603i	−0.120856	−	0.209329i
$816$		−	269.717i		−	0.330536i
$817$	562.766	+	122.670i	0.688820	+	0.150146i
$818$	1305.80			1.59633
$819$	−97.9985	+	56.5795i	−0.119656	+	0.0690836i
$820$	2527.43	−	1459.21i	3.08223	−	1.77953i
$821$	207.851	−	360.008i	0.253168	−	0.438500i	−0.711228	−	0.702961i	$-0.751861\pi$
$821$	207.851	−	360.008i	0.253168	−	0.438500i	0.964396	+	0.264461i	$0.0851941\pi$
$822$	−579.241	−	1003.27i	−0.704673	−	1.22053i
$823$	−571.455	+	989.790i	−0.694356	+	1.20266i	0.276041	+	0.961146i	$0.410978\pi$
$823$	−571.455	+	989.790i	−0.694356	+	1.20266i	−0.970397	+	0.241515i	$0.922356\pi$
$824$	1329.35			1.61329
$825$			3.21271i			0.00389419i
$826$	−42.2485	+	73.1765i	−0.0511483	+	0.0885914i
$827$	943.619	+	544.799i	1.14101	+	0.658765i	0.946682	−	0.322170i	$-0.104412\pi$
$827$	943.619	+	544.799i	1.14101	+	0.658765i	0.194333	+	0.980936i	$0.437746\pi$
$828$	386.565			0.466866
$829$		−	242.265i		−	0.292237i	−0.989267	−	0.146119i	$-0.953322\pi$
$829$		−	242.265i		−	0.292237i	0.989267	−	0.146119i	$-0.0466781\pi$
$830$	−1319.09	−	761.575i	−1.58926	−	0.917560i
$831$	602.650	−	347.940i	0.725210	−	0.418700i
$832$	1331.43	+	768.699i	1.60027	+	0.923918i
$833$	218.134	+	377.820i	0.261866	+	0.453565i
$834$	−584.094	−	1011.68i	−0.700352	−	1.21305i
$835$		−	418.004i		−	0.500604i
$836$	1.52592	+	4.78042i	0.00182527	+	0.00571821i
$837$	598.520			0.715078
$838$	−1325.29	+	765.156i	−1.58149	+	0.913074i
$839$	−1272.95	+	734.939i	−1.51723	+	0.875971i	−0.517431	+	0.855725i	$0.673112\pi$
$839$	−1272.95	+	734.939i	−1.51723	+	0.875971i	−0.999795	+	0.0202457i	$0.993555\pi$
$840$	−177.822	+	307.997i	−0.211693	+	0.366663i
$841$	−406.980	−	704.909i	−0.483923	−	0.838180i
$842$	342.026	−	592.407i	0.406207	−	0.703571i
$843$	−1013.61			−1.20238
$844$			1158.47i			1.37260i
$845$	−403.771	+	699.352i	−0.477836	+	0.827635i
$846$	808.403	+	466.732i	0.955560	+	0.551693i
$847$	148.698			0.175558
$848$		−	89.9341i		−	0.106054i
$849$	−1172.13	−	676.731i	−1.38060	−	0.797092i
$850$	−620.776	+	358.405i	−0.730325	+	0.421653i
$851$	385.123	+	222.351i	0.452553	+	0.261282i
$852$	−538.910	−	933.420i	−0.632524	−	1.09556i
$853$	−493.706	−	855.124i	−0.578788	−	1.00249i	−0.995619	−	0.0935062i	$-0.970192\pi$
$853$	−493.706	−	855.124i	−0.578788	−	1.00249i	0.416831	−	0.908984i	$-0.363141\pi$
$854$			67.9631i			0.0795821i
$855$	484.209	−	532.199i	0.566326	−	0.622455i
$856$	−614.352			−0.717701
$857$	−1279.05	+	738.461i	−1.49248	+	0.861681i	−0.999963	−	0.00862354i	$-0.997255\pi$
$857$	−1279.05	+	738.461i	−1.49248	+	0.861681i	−0.492513	+	0.870305i	$0.663922\pi$
$858$	−6.78442	+	3.91699i	−0.00790726	+	0.00456526i
$859$	466.025	−	807.179i	0.542520	−	0.939673i	−0.456238	−	0.889858i	$-0.650803\pi$
$859$	466.025	−	807.179i	0.542520	−	0.939673i	0.998758	−	0.0498150i	$-0.0158632\pi$
$860$	764.917	+	1324.88i	0.889439	+	1.54055i
$861$	135.087	−	233.978i	0.156896	−	0.271752i
$862$	−2361.41			−2.73945
$863$		−	1088.87i		−	1.26172i	−0.775896	−	0.630861i	$-0.782702\pi$
$863$		−	1088.87i		−	1.26172i	0.775896	−	0.630861i	$-0.217298\pi$
$864$	−120.832	+	209.287i	−0.139851	+	0.242230i
$865$	1061.97	+	613.127i	1.22771	+	0.708818i
$866$	639.248			0.738162
$867$			777.825i			0.897145i
$868$	−343.102	−	198.090i	−0.395279	−	0.228214i
$869$	−1.44822	+	0.836128i	−0.00166653	+	0.000962172i
$870$	399.127	+	230.436i	0.458766	+	0.264869i
$871$	−17.8717	−	30.9546i	−0.0205185	−	0.0355392i
$872$	−291.336	−	504.609i	−0.334101	−	0.578680i
$873$			622.039i			0.712531i
$874$	−460.350	−	418.839i	−0.526716	−	0.479221i
$875$	−14.9581			−0.0170949
$876$	1344.56	−	776.282i	1.53489	−	0.886167i
$877$	−202.296	+	116.796i	−0.230669	+	0.133177i	−0.610881	−	0.791723i	$-0.709184\pi$
$877$	−202.296	+	116.796i	−0.230669	+	0.133177i	0.380212	+	0.924899i	$0.375851\pi$
$878$	−804.378	+	1393.22i	−0.916148	+	1.58681i
$879$	680.013	+	1177.82i	0.773621	+	1.33995i
$880$	−0.975059	+	1.68885i	−0.00110802	+	0.00191915i
$881$	488.267			0.554220			0.277110	−	0.960838i	$-0.410623\pi$
$881$	488.267			0.554220			0.277110	+	0.960838i	$0.410623\pi$
$882$		−	868.991i		−	0.985251i
$883$	−833.774	+	1444.14i	−0.944252	+	1.63549i	−0.187009	+	0.982358i	$0.559879\pi$
$883$	−833.774	+	1444.14i	−0.944252	+	1.63549i	−0.757243	+	0.653134i	$0.773454\pi$
$884$	−976.240	−	563.632i	−1.10434	−	0.637593i
$885$	540.936			0.611227
$886$		−	2576.95i		−	2.90852i
$887$	544.718	+	314.493i	0.614113	+	0.354558i	0.774573	−	0.632484i	$-0.217965\pi$
$887$	544.718	+	314.493i	0.614113	+	0.354558i	−0.160460	+	0.987042i	$0.551298\pi$
$888$	−1644.09	+	949.215i	−1.85145	+	1.06894i
$889$	−168.065	−	97.0325i	−0.189050	−	0.109148i
$890$	1809.51	+	3134.17i	2.03316	+	3.52154i
$891$	−1.82386	−	3.15902i	−0.00204698	−	0.00354547i
$892$			1358.27i			1.52273i
$893$	−294.736	−	923.350i	−0.330052	−	1.03399i
$894$	−307.725			−0.344211
$895$	−1.36517	+	0.788180i	−0.00152533	+	0.000880648i
$896$	248.885	−	143.694i	0.277774	−	0.160373i
$897$	313.313	−	542.673i	0.349289	−	0.604987i
$898$	658.556	+	1140.65i	0.733359	+	1.27021i
$899$	−115.371	+	199.828i	−0.128332	+	0.222278i
$900$	920.823			1.02314
$901$		−	106.976i		−	0.118730i
$902$	3.52801	−	6.11068i	0.00391131	−	0.00677460i
$903$	122.651	+	70.8126i	0.135826	+	0.0784193i
$904$	−1500.86			−1.66025
$905$			1037.95i			1.14690i
$906$	−2778.54	−	1604.19i	−3.06682	−	1.77063i
$907$	−1402.39	+	809.670i	−1.54619	+	0.892690i	−0.547757	+	0.836637i	$0.684518\pi$
$907$	−1402.39	+	809.670i	−1.54619	+	0.892690i	−0.998428	+	0.0560533i	$0.982148\pi$
$908$	−55.8419	−	32.2403i	−0.0614999	−	0.0355070i
$909$	−467.276	−	809.346i	−0.514055	−	0.890369i
$910$	241.949	+	419.068i	0.265878	+	0.460514i
$911$		−	895.922i		−	0.983449i	−0.870751	−	0.491725i	$-0.836367\pi$
$911$		−	895.922i		−	0.983449i	0.870751	−	0.491725i	$-0.163633\pi$
$912$	531.421	−	169.631i	0.582699	−	0.185999i
$913$	−2.37500			−0.00260131
$914$	2020.42	−	1166.49i	2.21053	−	1.27625i
$915$	376.798	−	217.544i	0.411801	−	0.237753i
$916$	965.991	−	1673.15i	1.05458	−	1.82658i
$917$	−47.3621	−	82.0336i	−0.0516490	−	0.0894587i
$918$	207.949	−	360.179i	0.226524	−	0.392352i
$919$	741.588			0.806951			0.403476	−	0.914990i	$-0.367802\pi$
$919$	741.588			0.806951			0.403476	+	0.914990i	$0.367802\pi$
$920$		−	742.943i		−	0.807546i
$921$	−276.255	+	478.487i	−0.299951	+	0.519530i
$922$	−2041.38	−	1178.59i	−2.21408	−	1.27830i
$923$	−659.101			−0.714086
$924$			1.23387i			0.00133535i
$925$	917.387	+	529.653i	0.991769	+	0.572598i
$926$	42.1341	−	24.3261i	0.0455012	−	0.0262701i
$927$	−572.697	−	330.647i	−0.617796	−	0.356685i
$928$	−46.5829	−	80.6840i	−0.0501971	−	0.0869440i
$929$	657.059	+	1138.06i	0.707275	+	1.22504i	0.965864	+	0.259049i	$0.0834093\pi$
$929$	657.059	+	1138.06i	0.707275	+	1.22504i	−0.258589	+	0.965988i	$0.583257\pi$
$930$			3932.66i			4.22867i
$931$	−607.225	+	667.407i	−0.652229	+	0.716871i
$932$	65.7070			0.0705011
$933$	629.778	−	363.602i	0.675003	−	0.389713i
$934$	2511.08	−	1449.77i	2.68852	−	1.55222i
$935$	−1.15982	+	2.00887i	−0.00124045	+	0.00214853i
$936$	504.574	+	873.948i	0.539075	+	0.933705i
$937$	392.873	−	680.475i	0.419288	−	0.726228i	−0.576580	−	0.817041i	$-0.695613\pi$
$937$	392.873	−	680.475i	0.419288	−	0.726228i	0.995868	+	0.0908128i	$0.0289465\pi$
$938$	−8.72912			−0.00930610
$939$			1188.94i			1.26618i
$940$	1287.19	−	2229.48i	1.36935	−	2.37178i
$941$	−224.279	−	129.487i	−0.238341	−	0.137606i	0.376073	−	0.926590i	$-0.377274\pi$
$941$	−224.279	−	129.487i	−0.238341	−	0.137606i	−0.614414	+	0.788984i	$0.710608\pi$
$942$	1123.27			1.19243
$943$			564.397i			0.598512i
$944$	137.015	+	79.1058i	0.145143	+	0.0837985i
$945$	−99.7141	+	57.5699i	−0.105518	+	0.0609206i
$946$	3.20321	+	1.84938i	0.00338606	+	0.00195494i
$947$	−211.830	−	366.901i	−0.223686	−	0.387435i	0.732239	−	0.681048i	$-0.238476\pi$
$947$	−211.830	−	366.901i	−0.223686	−	0.387435i	−0.955924	+	0.293613i	$0.905142\pi$
$948$	635.268	+	1100.32i	0.670113	+	1.16067i
$949$		−	949.414i		−	1.00044i
$950$	−1096.58	−	997.701i	−1.15430	−	1.05021i
$951$	−344.008			−0.361732
$952$	−107.152	+	61.8642i	−0.112555	+	0.0649834i
$953$	1077.21	−	621.927i	1.13034	−	0.652599i	0.186316	−	0.982490i	$-0.440345\pi$
$953$	1077.21	−	621.927i	1.13034	−	0.652599i	0.944019	+	0.329891i	$0.107012\pi$
$954$	−106.541	+	184.534i	−0.111678	+	0.193432i
$955$	−872.794	−	1511.72i	−0.913920	−	1.58296i
$956$	−175.745	+	304.398i	−0.183833	+	0.318408i
$957$	0.718623			0.000750912
$958$		−	1329.23i		−	1.38750i
$959$	−55.7893	+	96.6299i	−0.0581745	+	0.100761i
$960$	−2081.60	−	1201.81i	−2.16833	−	1.25189i
$961$	−1007.94			−1.04884
$962$			2583.05i			2.68508i
$963$	264.668	+	152.806i	0.274837	+	0.158677i
$964$	−874.961	+	505.159i	−0.907636	+	0.524024i
$965$	−762.639	−	440.310i	−0.790300	−	0.456280i
$966$	−76.5163	−	132.530i	−0.0792094	−	0.137195i
$967$	120.498	+	208.709i	0.124610	+	0.215832i	0.921581	−	0.388187i	$-0.126899\pi$
$967$	120.498	+	208.709i	0.124610	+	0.215832i	−0.796970	+	0.604019i	$0.793565\pi$
$968$		−	1326.08i		−	1.36992i
$969$	632.121	−	201.775i	0.652344	−	0.208230i
$970$	2660.00			2.74227
$971$	94.1758	−	54.3724i	0.0969885	−	0.0559963i	−0.450721	−	0.892665i	$-0.648833\pi$
$971$	94.1758	−	54.3724i	0.0969885	−	0.0559963i	0.547710	+	0.836668i	$0.315500\pi$
$972$	−1636.32	+	944.730i	−1.68346	+	0.971945i
$973$	−56.2567	+	97.4395i	−0.0578178	+	0.100143i
$974$	1464.90	+	2537.28i	1.50400	+	2.60501i
$975$	746.331	−	1292.68i	0.765467	−	1.32583i
$976$	127.254			0.130383
$977$			1730.59i			1.77133i	0.464323	+	0.885666i	$0.346298\pi$
$977$			1730.59i			1.77133i	−0.464323	+	0.885666i	$0.653702\pi$
$978$	−180.934	+	313.387i	−0.185004	+	0.320437i
$979$	4.88701	+	2.82152i	0.00499184	+	0.00288204i
$980$	−2396.57			−2.44548
$981$			289.853i			0.295467i
$982$	2035.82	+	1175.38i	2.07313	+	1.19692i
$983$	1505.59	−	869.256i	1.53163	−	0.884288i	0.532346	−	0.846527i	$-0.321311\pi$
$983$	1505.59	−	869.256i	1.53163	−	0.884288i	0.999287	−	0.0377615i	$-0.0120227\pi$
$984$	−2086.61	−	1204.71i	−2.12054	−	1.22429i
$985$	−992.600	−	1719.23i	−1.00772	−	1.74542i
$986$	80.1685	+	138.856i	0.0813068	+	0.140828i
$987$		−	238.324i		−	0.241463i
$988$	496.540	−	2277.96i	0.502571	−	2.30562i
$989$	−295.856			−0.299147
$990$	4.00142	−	2.31022i	0.00404184	−	0.00233356i
$991$	−273.421	+	157.860i	−0.275904	+	0.159293i	−0.631568	−	0.775321i	$-0.717588\pi$
$991$	−273.421	+	157.860i	−0.275904	+	0.159293i	0.355663	+	0.934614i	$0.384255\pi$
$992$	397.497	−	688.485i	0.400702	−	0.694037i
$993$	−477.656	−	827.325i	−0.481023	−	0.833157i
$994$	−80.4818	+	139.399i	−0.0809677	+	0.140240i
$995$	−1070.21			−1.07559
$996$			1804.46i			1.81171i
$997$	637.836	−	1104.76i	0.639755	−	1.10809i	−0.345731	−	0.938334i	$-0.612369\pi$
$997$	637.836	−	1104.76i	0.639755	−	1.10809i	0.985486	−	0.169755i	$-0.0542976\pi$
$998$	445.010	+	256.927i	0.445902	+	0.257442i
$999$	−614.618			−0.615233

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.3.d.a.12.1	yes	6
3.2	odd	2		171.3.p.d.145.3		6
4.3	odd	2		304.3.r.b.145.2		6
19.2	odd	18		361.3.f.h.333.1		18
19.3	odd	18		361.3.f.h.127.3		18
19.4	even	9		361.3.f.h.116.1		18
19.5	even	9		361.3.f.i.262.1		18
19.6	even	9		361.3.f.h.299.3		18
19.7	even	3		361.3.b.b.360.1		6
19.8	odd	6	inner	19.3.d.a.8.1	✓	6
19.9	even	9		361.3.f.h.307.3		18
19.10	odd	18		361.3.f.i.307.1		18
19.11	even	3		361.3.d.c.293.3		6
19.12	odd	6		361.3.b.b.360.6		6
19.13	odd	18		361.3.f.i.299.1		18
19.14	odd	18		361.3.f.h.262.3		18
19.15	odd	18		361.3.f.i.116.3		18
19.16	even	9		361.3.f.i.127.1		18
19.17	even	9		361.3.f.i.333.3		18
19.18	odd	2		361.3.d.c.69.3		6
57.8	even	6		171.3.p.d.46.3		6
76.27	even	6		304.3.r.b.65.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.3.d.a.8.1	✓	6	19.8	odd	6	inner
19.3.d.a.12.1	yes	6	1.1	even	1	trivial
171.3.p.d.46.3		6	57.8	even	6
171.3.p.d.145.3		6	3.2	odd	2
304.3.r.b.65.2		6	76.27	even	6
304.3.r.b.145.2		6	4.3	odd	2
361.3.b.b.360.1		6	19.7	even	3
361.3.b.b.360.6		6	19.12	odd	6
361.3.d.c.69.3		6	19.18	odd	2
361.3.d.c.293.3		6	19.11	even	3
361.3.f.h.116.1		18	19.4	even	9
361.3.f.h.127.3		18	19.3	odd	18
361.3.f.h.262.3		18	19.14	odd	18
361.3.f.h.299.3		18	19.6	even	9
361.3.f.h.307.3		18	19.9	even	9
361.3.f.h.333.1		18	19.2	odd	18
361.3.f.i.116.3		18	19.15	odd	18
361.3.f.i.127.1		18	19.16	even	9
361.3.f.i.262.1		18	19.5	even	9
361.3.f.i.299.1		18	19.13	odd	18
361.3.f.i.307.1		18	19.10	odd	18
361.3.f.i.333.3		18	19.17	even	9

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	19.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.90671 + 1.67819i) q^{2} +(-3.29225 + 1.90078i) q^{3} +(3.63264 - 6.29191i) q^{4} +(3.47303 + 6.01546i) q^{5} +(6.37974 - 11.0500i) q^{6} -1.22892 q^{7} +10.9595i q^{8} +(2.72593 - 4.72145i) q^{9} +(-20.1902 - 11.6568i) q^{10} -0.0363521 q^{11} +27.6194i q^{12} +(14.6268 + 8.44481i) q^{13} +(3.57212 - 2.06236i) q^{14} +(-22.8681 - 13.2029i) q^{15} +(-3.86156 - 6.68842i) q^{16} +(-4.59329 - 7.95581i) q^{17} +18.2985i q^{18} +(12.7864 - 14.0537i) q^{19} +50.4650 q^{20} +(4.04592 - 2.33591i) q^{21} +(0.105665 - 0.0610058i) q^{22} +(-4.87974 + 8.45195i) q^{23} +(-20.8316 - 36.0814i) q^{24} +(-11.6238 + 20.1331i) q^{25} -56.6879 q^{26} -13.4885i q^{27} +(-4.46423 + 7.73228i) q^{28} +(4.50339 + 2.60003i) q^{29} +88.6280 q^{30} +44.3727i q^{31} +(-15.5160 - 8.95814i) q^{32} +(0.119680 - 0.0690974i) q^{33} +(26.7027 + 15.4168i) q^{34} +(-4.26808 - 7.39254i) q^{35} +(-19.8046 - 34.3026i) q^{36} -45.5661i q^{37} +(-13.5817 + 62.3081i) q^{38} -64.2069 q^{39} +(-65.9264 + 38.0626i) q^{40} +(50.0829 - 28.9153i) q^{41} +(-7.84020 + 13.5796i) q^{42} +(15.1574 + 26.2534i) q^{43} +(-0.132054 + 0.228724i) q^{44} +37.8689 q^{45} -32.7565i q^{46} +(25.5066 - 44.1787i) q^{47} +(25.4264 + 14.6800i) q^{48} -47.4897 q^{49} -78.0280i q^{50} +(30.2445 + 17.4617i) q^{51} +(106.268 - 61.3538i) q^{52} +(10.0847 + 5.82239i) q^{53} +(22.6362 + 39.2071i) q^{54} +(-0.126252 - 0.218675i) q^{55} -13.4684i q^{56} +(-15.3831 + 70.5725i) q^{57} -17.4534 q^{58} +(-17.7409 + 10.2427i) q^{59} +(-166.143 + 95.9229i) q^{60} +(-8.23849 + 14.2695i) q^{61} +(-74.4658 - 128.978i) q^{62} +(-3.34996 + 5.80229i) q^{63} +91.0263 q^{64} +117.316i q^{65} +(-0.231917 + 0.401692i) q^{66} +(-1.83276 - 1.05814i) q^{67} -66.7430 q^{68} -37.1012i q^{69} +(24.8121 + 14.3253i) q^{70} +(-33.7958 + 19.5120i) q^{71} +(51.7447 + 29.8748i) q^{72} +(-28.1064 - 48.6818i) q^{73} +(76.4686 + 132.447i) q^{74} -88.3775i q^{75} +(-41.9762 - 131.503i) q^{76} +0.0446740 q^{77} +(186.631 - 107.751i) q^{78} +(39.8385 - 23.0008i) q^{79} +(26.8226 - 46.4581i) q^{80} +(50.1720 + 86.9004i) q^{81} +(-97.0508 + 168.097i) q^{82} +65.3332 q^{83} -33.9421i q^{84} +(31.9053 - 55.2615i) q^{85} +(-88.1162 - 50.8739i) q^{86} -19.7684 q^{87} -0.398401i q^{88} +(-134.435 - 77.6163i) q^{89} +(-110.074 + 63.5512i) q^{90} +(-17.9753 - 10.3780i) q^{91} +(35.4526 + 61.4058i) q^{92} +(-84.3427 - 146.086i) q^{93} +171.219i q^{94} +(128.947 + 28.1074i) q^{95} +68.1098 q^{96} +(-98.8107 + 57.0484i) q^{97} +(138.039 - 79.6968i) q^{98} +(-0.0990933 + 0.171635i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 9 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 14 q^{9} - 60 q^{10} + 26 q^{11} + 30 q^{13} + 54 q^{14} - 18 q^{15} + q^{16} - 42 q^{17} + 25 q^{19} + 108 q^{20} - 102 q^{21} - 39 q^{22} + 8 q^{23}+ \cdots - 56 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 9 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 14 * q^9 - 60 * q^10 + 26 * q^11 + 30 * q^13 + 54 * q^14 - 18 * q^15 + q^16 - 42 * q^17 + 25 * q^19 + 108 * q^20 - 102 * q^21 - 39 * q^22 + 8 * q^23 - 83 * q^24 - 17 * q^25 - 148 * q^26 + 32 * q^28 - 12 * q^29 + 304 * q^30 + 51 * q^32 + 123 * q^33 - 6 * q^34 - 38 * q^35 - 54 * q^36 - 14 * q^38 - 44 * q^39 - 96 * q^40 + 63 * q^41 - 92 * q^42 - 34 * q^43 - 69 * q^44 - 28 * q^45 + 58 * q^47 - 147 * q^48 + 18 * q^49 + 132 * q^51 + 162 * q^52 - 12 * q^53 + 29 * q^54 - 28 * q^55 - 16 * q^57 + 172 * q^58 - 147 * q^59 - 222 * q^60 + 58 * q^61 - 116 * q^62 + 86 * q^63 + 166 * q^64 + 11 * q^66 + 201 * q^67 - 84 * q^68 - 198 * q^70 - 102 * q^71 + 210 * q^72 + 7 * q^73 + 174 * q^74 - 173 * q^76 - 376 * q^77 + 450 * q^78 + 134 * q^80 + 253 * q^81 - 145 * q^82 + 146 * q^83 - 90 * q^85 - 270 * q^86 - 568 * q^87 - 72 * q^89 - 438 * q^90 - 216 * q^91 + 72 * q^92 - 160 * q^93 + 558 * q^95 + 126 * q^96 + 21 * q^97 + 411 * q^98 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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