LMFDB - Embedded newform 38.3.f.a.15.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,3,Mod(3,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("38.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	38.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.03542500457$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			15.4
Character	$\chi$	$=$	38.15
Dual form			38.3.f.a.33.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.483690 - 1.32893i) q^{2} +(3.82266 - 0.674039i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(-6.81117 + 5.71525i) q^{5} +(0.953235 - 5.40606i) q^{6} +(2.55329 - 4.42243i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(5.70119 - 2.07506i) q^{9} +O(q^{10})$	\(q+(0.483690 - 1.32893i) q^{2} +(3.82266 - 0.674039i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(-6.81117 + 5.71525i) q^{5} +(0.953235 - 5.40606i) q^{6} +(2.55329 - 4.42243i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(5.70119 - 2.07506i) q^{9} +(4.30065 + 11.8160i) q^{10} +(2.70464 + 4.68458i) q^{11} +(-6.72319 - 3.88163i) q^{12} +(-12.3403 - 2.17592i) q^{13} +(-4.64208 - 5.53221i) q^{14} +(-22.1845 + 26.4385i) q^{15} +(0.694593 + 3.93923i) q^{16} +(24.2154 + 8.81367i) q^{17} -8.58014i q^{18} +(-8.05172 - 17.2096i) q^{19} +17.7827 q^{20} +(6.77948 - 18.6265i) q^{21} +(7.53367 - 1.32839i) q^{22} +(6.41312 + 5.38124i) q^{23} +(-8.41034 + 7.05711i) q^{24} +(9.38676 - 53.2349i) q^{25} +(-8.86051 + 15.3469i) q^{26} +(-9.85929 + 5.69226i) q^{27} +(-9.59723 + 3.49311i) q^{28} +(-16.1666 - 44.4173i) q^{29} +(24.4044 + 42.2696i) q^{30} +(19.0672 + 11.0085i) q^{31} +(5.57091 + 0.982302i) q^{32} +(13.4965 + 16.0845i) q^{33} +(23.4254 - 27.9174i) q^{34} +(7.88439 + 44.7146i) q^{35} +(-11.4024 - 4.15013i) q^{36} +16.7436i q^{37} +(-26.7648 + 2.37604i) q^{38} -48.6394 q^{39} +(8.60131 - 23.6319i) q^{40} +(-5.00714 + 0.882894i) q^{41} +(-21.4740 - 18.0188i) q^{42} +(28.8313 - 24.1924i) q^{43} +(1.87863 - 10.6542i) q^{44} +(-26.9723 + 46.7173i) q^{45} +(10.2532 - 5.91971i) q^{46} +(-42.1962 + 15.3582i) q^{47} +(5.31039 + 14.5902i) q^{48} +(11.4614 + 19.8518i) q^{49} +(-66.2050 - 38.2235i) q^{50} +(98.5079 + 17.3696i) q^{51} +(16.1091 + 19.1981i) q^{52} +(-18.1611 + 21.6435i) q^{53} +(2.79576 + 15.8556i) q^{54} +(-45.1953 - 16.4498i) q^{55} +14.4436i q^{56} +(-42.3789 - 60.3593i) q^{57} -66.8469 q^{58} +(-14.4265 + 39.6364i) q^{59} +(67.9773 - 11.9862i) q^{60} +(37.9655 + 31.8568i) q^{61} +(23.8521 - 20.0143i) q^{62} +(5.37997 - 30.5113i) q^{63} +(4.00000 - 6.92820i) q^{64} +(96.4878 - 55.7072i) q^{65} +(27.9033 - 10.1560i) q^{66} +(-8.84321 - 24.2965i) q^{67} +(-25.7695 - 44.6340i) q^{68} +(28.1424 + 16.2480i) q^{69} +(63.2360 + 11.1502i) q^{70} +(38.5613 + 45.9555i) q^{71} +(-11.0304 + 13.1455i) q^{72} +(5.90643 + 33.4970i) q^{73} +(22.2510 + 8.09869i) q^{74} -209.826i q^{75} +(-9.78827 + 36.7177i) q^{76} +27.6229 q^{77} +(-23.5264 + 64.6382i) q^{78} +(71.9176 - 12.6810i) q^{79} +(-27.2447 - 22.8610i) q^{80} +(-75.6808 + 63.5037i) q^{81} +(-1.24860 + 7.08117i) q^{82} +(-35.5483 + 61.5715i) q^{83} +(-34.3325 + 19.8219i) q^{84} +(-215.307 + 78.3655i) q^{85} +(-18.2045 - 50.0163i) q^{86} +(-91.7383 - 158.895i) q^{87} +(-13.2500 - 7.64989i) q^{88} +(-51.5470 - 9.08913i) q^{89} +(49.0377 + 58.4408i) q^{90} +(-41.1312 + 49.0182i) q^{91} +(-2.90747 - 16.4891i) q^{92} +(80.3078 + 29.2296i) q^{93} +63.5042i q^{94} +(153.199 + 71.1999i) q^{95} +21.9578 q^{96} +(14.8523 - 40.8063i) q^{97} +(31.9253 - 5.62929i) q^{98} +(25.1405 + 21.0954i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} + 12 q^{6} - 18 q^{7} + 6 q^{9}+O(q^{10}) $ 24 * q - 6 * q^3 + 12 * q^6 - 18 * q^7 + 6 * q^9	$ 24 q - 6 q^{3} + 12 q^{6} - 18 q^{7} + 6 q^{9} + 30 q^{11} - 36 q^{12} - 90 q^{13} - 48 q^{14} - 114 q^{15} + 18 q^{17} - 12 q^{19} + 24 q^{20} + 90 q^{21} + 84 q^{22} + 120 q^{23} - 24 q^{24} + 252 q^{25} + 48 q^{26} + 126 q^{27} + 72 q^{28} - 210 q^{29} - 108 q^{31} - 132 q^{33} - 24 q^{34} - 66 q^{35} - 12 q^{36} + 84 q^{38} + 120 q^{39} + 54 q^{41} + 72 q^{42} + 90 q^{43} - 48 q^{44} - 144 q^{45} - 360 q^{46} - 246 q^{47} - 48 q^{48} + 54 q^{49} - 432 q^{50} - 342 q^{51} + 36 q^{52} - 174 q^{53} - 42 q^{55} - 12 q^{57} + 48 q^{58} + 228 q^{59} + 132 q^{60} + 12 q^{61} + 204 q^{62} + 174 q^{63} + 96 q^{64} + 630 q^{65} + 696 q^{66} + 72 q^{67} - 48 q^{68} + 702 q^{69} + 528 q^{70} + 432 q^{71} + 96 q^{72} - 144 q^{74} + 72 q^{76} - 144 q^{77} - 708 q^{78} - 246 q^{79} - 642 q^{81} - 384 q^{82} - 126 q^{83} - 540 q^{84} - 684 q^{85} - 12 q^{86} - 324 q^{87} - 12 q^{89} - 336 q^{90} + 372 q^{91} - 132 q^{92} - 168 q^{93} - 570 q^{95} + 72 q^{97} + 384 q^{98} - 204 q^{99}+O(q^{100}) $ 24 * q - 6 * q^3 + 12 * q^6 - 18 * q^7 + 6 * q^9 + 30 * q^11 - 36 * q^12 - 90 * q^13 - 48 * q^14 - 114 * q^15 + 18 * q^17 - 12 * q^19 + 24 * q^20 + 90 * q^21 + 84 * q^22 + 120 * q^23 - 24 * q^24 + 252 * q^25 + 48 * q^26 + 126 * q^27 + 72 * q^28 - 210 * q^29 - 108 * q^31 - 132 * q^33 - 24 * q^34 - 66 * q^35 - 12 * q^36 + 84 * q^38 + 120 * q^39 + 54 * q^41 + 72 * q^42 + 90 * q^43 - 48 * q^44 - 144 * q^45 - 360 * q^46 - 246 * q^47 - 48 * q^48 + 54 * q^49 - 432 * q^50 - 342 * q^51 + 36 * q^52 - 174 * q^53 - 42 * q^55 - 12 * q^57 + 48 * q^58 + 228 * q^59 + 132 * q^60 + 12 * q^61 + 204 * q^62 + 174 * q^63 + 96 * q^64 + 630 * q^65 + 696 * q^66 + 72 * q^67 - 48 * q^68 + 702 * q^69 + 528 * q^70 + 432 * q^71 + 96 * q^72 - 144 * q^74 + 72 * q^76 - 144 * q^77 - 708 * q^78 - 246 * q^79 - 642 * q^81 - 384 * q^82 - 126 * q^83 - 540 * q^84 - 684 * q^85 - 12 * q^86 - 324 * q^87 - 12 * q^89 - 336 * q^90 + 372 * q^91 - 132 * q^92 - 168 * q^93 - 570 * q^95 + 72 * q^97 + 384 * q^98 - 204 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	0.483690	−	1.32893i	0.241845	−	0.664463i
$2$	0.483690	−	1.32893i	0.241845	−	0.664463i
$3$	3.82266	−	0.674039i	1.27422	−	0.224680i	0.504696	−	0.863297i	$-0.331604\pi$
$3$	3.82266	−	0.674039i	1.27422	−	0.224680i	0.769524	+	0.638617i	$0.220493\pi$
$4$	−1.53209	−	1.28558i	−0.383022	−	0.321394i
$5$	−6.81117	+	5.71525i	−1.36223	+	1.14305i	−0.386949	+	0.922101i	$0.626471\pi$
$5$	−6.81117	+	5.71525i	−1.36223	+	1.14305i	−0.975285	+	0.220949i	$0.929084\pi$
$6$	0.953235	−	5.40606i	0.158872	−	0.901010i
$7$	2.55329	−	4.42243i	0.364756	−	0.631775i	−0.623981	−	0.781439i	$-0.714486\pi$
$7$	2.55329	−	4.42243i	0.364756	−	0.631775i	0.988737	+	0.149664i	$0.0478192\pi$
$8$	−2.44949	+	1.41421i	−0.306186	+	0.176777i
$9$	5.70119	−	2.07506i	0.633465	−	0.230563i
$10$	4.30065	+	11.8160i	0.430065	+	1.18160i
$11$	2.70464	+	4.68458i	0.245877	+	0.425871i	0.962378	−	0.271715i	$-0.0875909\pi$
$11$	2.70464	+	4.68458i	0.245877	+	0.425871i	−0.716501	+	0.697586i	$0.754258\pi$
$12$	−6.72319	−	3.88163i	−0.560266	−	0.323469i
$13$	−12.3403	−	2.17592i	−0.949253	−	0.167379i	−0.322476	−	0.946578i	$-0.604515\pi$
$13$	−12.3403	−	2.17592i	−0.949253	−	0.167379i	−0.626777	+	0.779199i	$0.715626\pi$
$14$	−4.64208	−	5.53221i	−0.331577	−	0.395158i
$15$	−22.1845	+	26.4385i	−1.47897	+	1.76257i
$16$	0.694593	+	3.93923i	0.0434120	+	0.246202i
$17$	24.2154	+	8.81367i	1.42443	+	0.518451i	0.935331	−	0.353775i	$-0.115102\pi$
$17$	24.2154	+	8.81367i	1.42443	+	0.518451i	0.489103	+	0.872226i	$0.337324\pi$
$18$		−	8.58014i		−	0.476675i
$19$	−8.05172	−	17.2096i	−0.423774	−	0.905768i
$19$	−8.05172	−	17.2096i	−0.423774	−	0.905768i
$20$	17.7827			0.889135
$21$	6.77948	−	18.6265i	0.322832	−	0.886974i
$22$	7.53367	−	1.32839i	0.342439	−	0.0603813i
$23$	6.41312	+	5.38124i	0.278831	+	0.233967i	0.771468	−	0.636268i	$-0.219523\pi$
$23$	6.41312	+	5.38124i	0.278831	+	0.233967i	−0.492637	+	0.870235i	$0.663967\pi$
$24$	−8.41034	+	7.05711i	−0.350431	+	0.294046i
$25$	9.38676	−	53.2349i	0.375470	−	2.12940i
$26$	−8.86051	+	15.3469i	−0.340789	+	0.590264i
$27$	−9.85929	+	5.69226i	−0.365159	+	0.210825i
$28$	−9.59723	+	3.49311i	−0.342758	+	0.124754i
$29$	−16.1666	−	44.4173i	−0.557468	−	1.53163i	−0.823297	−	0.567610i	$-0.807868\pi$
$29$	−16.1666	−	44.4173i	−0.557468	−	1.53163i	0.265830	−	0.964020i	$-0.414354\pi$
$30$	24.4044	+	42.2696i	0.813479	+	1.40899i
$31$	19.0672	+	11.0085i	0.615072	+	0.355112i	0.774948	−	0.632025i	$-0.217776\pi$
$31$	19.0672	+	11.0085i	0.615072	+	0.355112i	−0.159876	+	0.987137i	$0.551109\pi$
$32$	5.57091	+	0.982302i	0.174091	+	0.0306970i
$33$	13.4965	+	16.0845i	0.408986	+	0.487410i
$34$	23.4254	−	27.9174i	0.688984	−	0.821099i
$35$	7.88439	+	44.7146i	0.225268	+	1.27756i
$36$	−11.4024	−	4.15013i	−0.316733	−	0.115281i
$37$			16.7436i			0.452529i	0.974066	+	0.226265i	$0.0726514\pi$
$37$			16.7436i			0.452529i	−0.974066	+	0.226265i	$0.927349\pi$
$38$	−26.7648	+	2.37604i	−0.704337	+	0.0625273i
$39$	−48.6394			−1.24716
$40$	8.60131	−	23.6319i	0.215033	−	0.590798i
$41$	−5.00714	+	0.882894i	−0.122125	+	0.0215340i	−0.234377	−	0.972146i	$-0.575305\pi$
$41$	−5.00714	+	0.882894i	−0.122125	+	0.0215340i	0.112251	+	0.993680i	$0.464194\pi$
$42$	−21.4740	−	18.0188i	−0.511286	−	0.429020i
$43$	28.8313	−	24.1924i	0.670496	−	0.562613i	−0.242716	−	0.970097i	$-0.578038\pi$
$43$	28.8313	−	24.1924i	0.670496	−	0.562613i	0.913212	+	0.407484i	$0.133594\pi$
$44$	1.87863	−	10.6542i	0.0426960	−	0.242141i
$45$	−26.9723	+	46.7173i	−0.599384	+	1.03816i
$46$	10.2532	−	5.91971i	0.222896	−	0.128689i
$47$	−42.1962	+	15.3582i	−0.897791	+	0.326769i	−0.749367	−	0.662155i	$-0.769642\pi$
$47$	−42.1962	+	15.3582i	−0.897791	+	0.326769i	−0.148424	+	0.988924i	$0.547420\pi$
$48$	5.31039	+	14.5902i	0.110633	+	0.303962i
$49$	11.4614	+	19.8518i	0.233907	+	0.405138i
$50$	−66.2050	−	38.2235i	−1.32410	−	0.764470i
$51$	98.5079	+	17.3696i	1.93153	+	0.340581i
$52$	16.1091	+	19.1981i	0.309790	+	0.369194i
$53$	−18.1611	+	21.6435i	−0.342662	+	0.408368i	−0.909662	−	0.415349i	$-0.863659\pi$
$53$	−18.1611	+	21.6435i	−0.342662	+	0.408368i	0.567000	+	0.823718i	$0.308104\pi$
$54$	2.79576	+	15.8556i	0.0517734	+	0.293621i
$55$	−45.1953	−	16.4498i	−0.821734	−	0.299087i
$56$			14.4436i			0.257921i
$57$	−42.3789	−	60.3593i	−0.743490	−	1.05893i
$58$	−66.8469			−1.15253
$59$	−14.4265	+	39.6364i	−0.244516	+	0.671803i	0.755348	+	0.655324i	$0.227468\pi$
$59$	−14.4265	+	39.6364i	−0.244516	+	0.671803i	−0.999864	+	0.0164790i	$0.994754\pi$
$60$	67.9773	−	11.9862i	1.13295	−	0.199771i
$61$	37.9655	+	31.8568i	0.622385	+	0.522243i	0.898552	−	0.438866i	$-0.144620\pi$
$61$	37.9655	+	31.8568i	0.622385	+	0.522243i	−0.276167	+	0.961110i	$0.589064\pi$
$62$	23.8521	−	20.0143i	0.384711	−	0.322811i
$63$	5.37997	−	30.5113i	0.0853964	−	0.484307i
$64$	4.00000	−	6.92820i	0.0625000	−	0.108253i
$65$	96.4878	−	55.7072i	1.48443	−	0.857034i
$66$	27.9033	−	10.1560i	0.422777	−	0.153878i
$67$	−8.84321	−	24.2965i	−0.131988	−	0.362635i	0.856040	−	0.516910i	$-0.172918\pi$
$67$	−8.84321	−	24.2965i	−0.131988	−	0.362635i	−0.988028	+	0.154276i	$0.950696\pi$
$68$	−25.7695	−	44.6340i	−0.378963	−	0.656382i
$69$	28.1424	+	16.2480i	0.407860	+	0.235478i
$70$	63.2360	+	11.1502i	0.903371	+	0.159289i
$71$	38.5613	+	45.9555i	0.543116	+	0.647261i	0.965883	−	0.258977i	$-0.0833855\pi$
$71$	38.5613	+	45.9555i	0.543116	+	0.647261i	−0.422767	+	0.906238i	$0.638941\pi$
$72$	−11.0304	+	13.1455i	−0.153200	+	0.182577i
$73$	5.90643	+	33.4970i	0.0809100	+	0.458863i	0.998164	+	0.0605617i	$0.0192892\pi$
$73$	5.90643	+	33.4970i	0.0809100	+	0.458863i	−0.917254	+	0.398302i	$0.869600\pi$
$74$	22.2510	+	8.09869i	0.300689	+	0.109442i
$75$		−	209.826i		−	2.79768i
$76$	−9.78827	+	36.7177i	−0.128793	+	0.483128i
$77$	27.6229			0.358740
$78$	−23.5264	+	64.6382i	−0.301620	+	0.828694i
$79$	71.9176	−	12.6810i	0.910350	−	0.160519i	0.301188	−	0.953565i	$-0.402617\pi$
$79$	71.9176	−	12.6810i	0.910350	−	0.160519i	0.609162	+	0.793046i	$0.291506\pi$
$80$	−27.2447	−	22.8610i	−0.340559	−	0.285763i
$81$	−75.6808	+	63.5037i	−0.934331	+	0.783997i
$82$	−1.24860	+	7.08117i	−0.0152268	+	0.0863557i
$83$	−35.5483	+	61.5715i	−0.428293	+	0.741825i	−0.996722	−	0.0809077i	$-0.974218\pi$
$83$	−35.5483	+	61.5715i	−0.428293	+	0.741825i	0.568429	+	0.822732i	$0.307551\pi$
$84$	−34.3325	+	19.8219i	−0.408720	+	0.235975i
$85$	−215.307	+	78.3655i	−2.53303	+	0.921947i
$86$	−18.2045	−	50.0163i	−0.211680	−	0.581585i
$87$	−91.7383	−	158.895i	−1.05446	−	1.82638i
$88$	−13.2500	−	7.64989i	−0.150568	−	0.0869305i
$89$	−51.5470	−	9.08913i	−0.579180	−	0.102125i	−0.123619	−	0.992330i	$-0.539450\pi$
$89$	−51.5470	−	9.08913i	−0.579180	−	0.102125i	−0.455561	+	0.890205i	$0.650561\pi$
$90$	49.0377	+	58.4408i	0.544863	+	0.649343i
$91$	−41.1312	+	49.0182i	−0.451991	+	0.538662i
$92$	−2.90747	−	16.4891i	−0.0316030	−	0.179229i
$93$	80.3078	+	29.2296i	0.863525	+	0.314297i
$94$			63.5042i			0.675576i
$95$	153.199	+	71.1999i	1.61262	+	0.749472i
$96$	21.9578			0.228727
$97$	14.8523	−	40.8063i	0.153116	−	0.420683i	−0.839290	−	0.543683i	$-0.817029\pi$
$97$	14.8523	−	40.8063i	0.153116	−	0.420683i	0.992407	+	0.123000i	$0.0392515\pi$
$98$	31.9253	−	5.62929i	0.325769	−	0.0574418i
$99$	25.1405	+	21.0954i	0.253944	+	0.213085i
$100$	−82.8189	+	69.4933i	−0.828189	+	0.694933i
$101$	5.17443	−	29.3457i	0.0512320	−	0.290551i	−0.948418	−	0.317024i	$-0.897316\pi$
$101$	5.17443	−	29.3457i	0.0512320	−	0.290551i	0.999650	+	0.0264728i	$0.00842754\pi$
$102$	70.7302	−	122.508i	0.693433	−	1.20106i
$103$	39.3922	−	22.7431i	0.382449	−	0.220807i	−0.296435	−	0.955053i	$-0.595798\pi$
$103$	39.3922	−	22.7431i	0.382449	−	0.220807i	0.678883	+	0.734246i	$0.262464\pi$
$104$	33.3046	−	12.1219i	0.320237	−	0.116557i
$105$	60.2787	+	165.614i	0.574083	+	1.57728i
$106$	19.9783	+	34.6035i	0.188475	+	0.326448i
$107$	−162.047	−	93.5580i	−1.51446	−	0.874373i	−0.999856	−	0.0169446i	$-0.994606\pi$
$107$	−162.047	−	93.5580i	−1.51446	−	0.874373i	−0.514603	−	0.857429i	$-0.672061\pi$
$108$	22.4231	+	3.95380i	0.207622	+	0.0366093i
$109$	−36.0310	−	42.9401i	−0.330560	−	0.393946i	0.575008	−	0.818148i	$-0.304999\pi$
$109$	−36.0310	−	42.9401i	−0.330560	−	0.393946i	−0.905567	+	0.424202i	$0.860555\pi$
$110$	−43.7210	+	52.1047i	−0.397464	+	0.473679i
$111$	11.2858	+	64.0051i	0.101674	+	0.576622i
$112$	19.1945	+	6.98621i	0.171379	+	0.0623769i
$113$		−	125.823i		−	1.11348i	−0.830687	−	0.556739i	$-0.812052\pi$
$113$		−	125.823i		−	1.11348i	0.830687	−	0.556739i	$-0.187948\pi$
$114$	−100.711	+	27.1233i	−0.883432	+	0.237924i
$115$	−74.4360			−0.647270
$116$	−32.3331	+	88.8345i	−0.278734	+	0.765815i
$117$	−74.8695	+	13.2015i	−0.639910	+	0.112833i
$118$	45.6959	+	38.3434i	0.387253	+	0.324944i
$119$	100.807	−	84.5868i	0.847115	−	0.710814i
$120$	16.9511	−	96.1344i	0.141259	−	0.801120i
$121$	45.8698	−	79.4488i	0.379089	−	0.656602i
$122$	60.6989	−	35.0445i	0.497532	−	0.287250i
$123$	−18.5455	+	6.75001i	−0.150776	+	0.0548782i
$124$	−15.0605	−	41.3783i	−0.121456	−	0.333696i
$125$	129.174	+	223.737i	1.03340	+	1.78989i
$126$	−37.9451	−	21.9076i	−0.301151	−	0.173870i
$127$	1.58597	+	0.279649i	0.0124880	+	0.00220196i	0.179889	−	0.983687i	$-0.442426\pi$
$127$	1.58597	+	0.279649i	0.0124880	+	0.00220196i	−0.167401	+	0.985889i	$0.553537\pi$
$128$	−7.27231	−	8.66680i	−0.0568149	−	0.0677094i
$129$	93.9059	−	111.913i	0.727953	−	0.867541i
$130$	−27.3607	−	155.170i	−0.210467	−	1.19362i
$131$	182.652	+	66.4799i	1.39429	+	0.507480i	0.926478	−	0.376348i	$-0.122820\pi$
$131$	182.652	+	66.4799i	1.39429	+	0.507480i	0.467812	+	0.883828i	$0.345043\pi$
$132$		−	41.9937i		−	0.318134i
$133$	−96.6665	−	8.33293i	−0.726816	−	0.0626536i
$134$	−36.5656			−0.272878
$135$	34.6206	−	95.1193i	0.256449	−	0.704587i
$136$	−71.7797	+	12.6567i	−0.527792	+	0.0930640i
$137$	−139.253	−	116.847i	−1.01644	−	0.852898i	−0.0272675	−	0.999628i	$-0.508681\pi$
$137$	−139.253	−	116.847i	−1.01644	−	0.852898i	−0.989177	+	0.146730i	$0.953125\pi$
$138$	35.2045	−	29.5401i	0.255105	−	0.214059i
$139$	−26.6261	+	151.004i	−0.191555	+	1.08636i	0.725686	+	0.688026i	$0.241523\pi$
$139$	−26.6261	+	151.004i	−0.191555	+	1.08636i	−0.917241	+	0.398334i	$0.869589\pi$
$140$	45.4044	−	78.6427i	0.324317	−	0.561734i
$141$	−150.950	+	87.1509i	−1.07057	+	0.618091i
$142$	79.7232	−	29.0169i	0.561431	−	0.204344i
$143$	−23.1828	−	63.6941i	−0.162117	−	0.445414i
$144$	12.1342	+	21.0170i	0.0842650	+	0.145951i
$145$	363.969	+	210.138i	2.51013	+	1.44923i
$146$	47.3720	+	8.35295i	0.324465	+	0.0572120i
$147$	57.1940	+	68.1612i	0.389075	+	0.463682i
$148$	21.5251	−	25.6527i	0.145440	−	0.173329i
$149$	−21.9985	−	124.760i	−0.147641	−	0.837312i	−0.965209	−	0.261480i	$-0.915789\pi$
$149$	−21.9985	−	124.760i	−0.147641	−	0.837312i	0.817568	−	0.575832i	$-0.195322\pi$
$150$	−278.844	−	101.491i	−1.85896	−	0.676605i
$151$			155.504i			1.02983i	0.857242	+	0.514913i	$0.172176\pi$
$151$			155.504i			1.02983i	−0.857242	+	0.514913i	$0.827824\pi$
$152$	44.0606	+	30.7679i	0.289873	+	0.202420i
$153$	156.345			1.02186
$154$	13.3609	−	36.7088i	0.0867593	−	0.238369i
$155$	−192.787	+	33.9935i	−1.24378	+	0.219313i
$156$	74.5199	+	62.5296i	0.477692	+	0.400831i
$157$	−82.4620	+	69.1938i	−0.525236	+	0.440725i	−0.866452	−	0.499260i	$-0.833605\pi$
$157$	−82.4620	+	69.1938i	−0.525236	+	0.440725i	0.341217	+	0.939985i	$0.389161\pi$
$158$	17.9337	−	101.707i	0.113504	−	0.643714i
$159$	−54.8351	+	94.9772i	−0.344875	+	0.597341i
$160$	−43.5586	+	25.1485i	−0.272241	+	0.157178i
$161$	40.1727	−	14.6217i	0.249520	−	0.0908178i
$162$	47.7858	+	131.290i	0.294974	+	0.810434i
$163$	−50.5731	−	87.5953i	−0.310265	−	0.537394i	0.668155	−	0.744022i	$-0.267084\pi$
$163$	−50.5731	−	87.5953i	−0.310265	−	0.537394i	−0.978420	+	0.206628i	$0.933751\pi$
$164$	8.80641	+	5.08438i	0.0536976	+	0.0310023i
$165$	−183.854	−	32.4185i	−1.11427	−	0.196476i
$166$	64.6296	+	77.0225i	0.389335	+	0.463991i
$167$	−10.9883	+	13.0953i	−0.0657980	+	0.0784150i	−0.797939	−	0.602738i	$-0.794077\pi$
$167$	−10.9883	+	13.0953i	−0.0657980	+	0.0784150i	0.732141	+	0.681153i	$0.238521\pi$
$168$	9.73553	+	55.2130i	0.0579496	+	0.328649i
$169$	−11.2601	−	4.09834i	−0.0666278	−	0.0242505i
$170$			324.032i			1.90607i
$171$	−81.6153	−	81.4073i	−0.477283	−	0.476066i
$172$	−75.2733			−0.437635
$173$	75.4796	−	207.378i	0.436298	−	1.19872i	−0.505584	−	0.862777i	$-0.668723\pi$
$173$	75.4796	−	207.378i	0.436298	−	1.19872i	0.941883	−	0.335942i	$-0.109055\pi$
$174$	−255.533	+	45.0574i	−1.46858	+	0.258950i
$175$	−211.461	−	177.436i	−1.20835	−	1.01392i
$176$	−16.5750	+	13.9081i	−0.0941762	+	0.0790232i
$177$	−28.4310	+	161.240i	−0.160627	+	0.910963i
$178$	−37.0115	+	64.1059i	−0.207930	+	0.360145i
$179$	8.87590	−	5.12450i	0.0495860	−	0.0286285i	−0.475002	−	0.879985i	$-0.657553\pi$
$179$	8.87590	−	5.12450i	0.0495860	−	0.0286285i	0.524588	+	0.851356i	$0.324219\pi$
$180$	101.383	−	36.9002i	0.563237	−	0.205001i
$181$	−64.6251	−	177.556i	−0.357045	−	0.980972i	−0.980049	−	0.198754i	$-0.936310\pi$
$181$	−64.6251	−	177.556i	−0.357045	−	0.980972i	0.623005	−	0.782218i	$-0.285912\pi$
$182$	45.2469	+	78.3699i	0.248609	+	0.430604i
$183$	166.602	+	96.1877i	0.910394	+	0.525616i
$184$	−23.3191	−	4.11179i	−0.126734	−	0.0223467i
$185$	−95.6938	−	114.043i	−0.517264	−	0.616451i
$186$	77.6881	−	92.5850i	0.417678	−	0.497769i
$187$	24.2056	+	137.277i	0.129442	+	0.734100i
$188$	84.3923	+	30.7163i	0.448895	+	0.163385i
$189$			58.1360i			0.307598i
$190$	168.720	−	169.151i	0.888000	−	0.890269i
$191$	1.43003			0.00748707			0.00374354	−	0.999993i	$-0.498808\pi$
$191$	1.43003			0.00748707			0.00374354	+	0.999993i	$0.498808\pi$
$192$	10.6208	−	29.1803i	0.0553165	−	0.151981i
$193$	59.7448	−	10.5346i	0.309559	−	0.0545835i	−0.0167108	−	0.999860i	$-0.505319\pi$
$193$	59.7448	−	10.5346i	0.309559	−	0.0545835i	0.326269	+	0.945277i	$0.394208\pi$
$194$	−47.0446	−	39.4751i	−0.242498	−	0.203480i
$195$	331.291	−	277.986i	1.69893	−	1.42557i
$196$	7.96102	−	45.1492i	0.0406175	−	0.230353i
$197$	−118.683	+	205.566i	−0.602453	+	1.04348i	0.389995	+	0.920817i	$0.372477\pi$
$197$	−118.683	+	205.566i	−0.602453	+	1.04348i	−0.992448	+	0.122663i	$0.960857\pi$
$198$	40.1944	−	23.2062i	0.203002	−	0.117203i
$199$	239.059	−	87.0105i	1.20130	−	0.437239i	0.337624	−	0.941281i	$-0.390377\pi$
$199$	239.059	−	87.0105i	1.20130	−	0.437239i	0.863679	+	0.504042i	$0.168154\pi$
$200$	52.2928	+	143.673i	0.261464	+	0.718367i
$201$	−50.1814	−	86.9167i	−0.249659	−	0.432421i
$202$	−36.4954	−	21.0706i	−0.180670	−	0.104310i
$203$	−237.710	−	41.9147i	−1.17099	−	0.206476i
$204$	−128.593	−	153.251i	−0.630358	−	0.751231i
$205$	29.0585	−	34.6306i	0.141749	−	0.168930i
$206$	−11.1703	−	63.3499i	−0.0542248	−	0.307524i
$207$	47.7288	+	17.3719i	0.230574	+	0.0839221i
$208$		−	50.1226i		−	0.240974i
$209$	58.8427	−	84.2647i	0.281544	−	0.403180i
$210$	249.246			1.18688
$211$	−23.9637	+	65.8396i	−0.113572	+	0.312036i	−0.983436	−	0.181255i	$-0.941984\pi$
$211$	−23.9637	+	65.8396i	−0.113572	+	0.312036i	0.869864	+	0.493291i	$0.164206\pi$
$212$	55.6488	−	9.81238i	0.262494	−	0.0462848i
$213$	178.383	+	149.681i	0.837477	+	0.702726i
$214$	−202.712	+	170.096i	−0.947253	+	0.794839i
$215$	−58.1098	+	329.557i	−0.270278	+	1.53282i
$216$	16.1002	−	27.8863i	0.0745377	−	0.129103i
$217$	97.3684	−	56.2157i	0.448702	−	0.259058i
$218$	−74.4920	+	27.1129i	−0.341706	+	0.124371i
$219$	45.1566	+	124.067i	0.206194	+	0.566515i
$220$	48.0959	+	83.3045i	0.218618	+	0.378657i
$221$	−279.647	−	161.454i	−1.26537	−	0.730561i
$222$	90.5168	+	15.9606i	0.407733	+	0.0718944i
$223$	−163.747	−	195.146i	−0.734290	−	0.875092i	0.261646	−	0.965164i	$-0.415735\pi$
$223$	−163.747	−	195.146i	−0.734290	−	0.875092i	−0.995935	+	0.0900715i	$0.971290\pi$
$224$	18.5683	−	22.1289i	0.0828943	−	0.0987895i
$225$	−56.9502	−	322.981i	−0.253112	−	1.43547i
$226$	−167.210	−	60.8593i	−0.739865	−	0.269289i
$227$			303.973i			1.33909i	0.742772	+	0.669544i	$0.233511\pi$
$227$			303.973i			1.33909i	−0.742772	+	0.669544i	$0.766489\pi$
$228$	−12.6681	+	146.957i	−0.0555620	+	0.644549i
$229$	397.312			1.73499			0.867493	−	0.497449i	$-0.165730\pi$
$229$	397.312			1.73499			0.867493	+	0.497449i	$0.165730\pi$
$230$	−36.0039	+	98.9200i	−0.156539	+	0.430087i
$231$	105.593	−	18.6189i	0.457113	−	0.0806014i
$232$	102.415	+	85.9367i	0.441445	+	0.370417i
$233$	−78.1429	+	65.5697i	−0.335377	+	0.281415i	−0.794887	−	0.606758i	$-0.792470\pi$
$233$	−78.1429	+	65.5697i	−0.335377	+	0.281415i	0.459509	+	0.888173i	$0.348025\pi$
$234$	−18.6698	+	105.881i	−0.0797853	+	0.452485i
$235$	199.630	−	345.769i	0.849488	−	1.47136i
$236$	73.0582	−	42.1801i	0.309568	−	0.178729i
$237$	266.369	−	96.9505i	1.12392	−	0.409074i
$238$	−63.6505	−	174.878i	−0.267439	−	0.734783i
$239$	−184.028	−	318.746i	−0.769992	−	1.33366i	−0.937567	−	0.347805i	$-0.886927\pi$
$239$	−184.028	−	318.746i	−0.769992	−	1.33366i	0.167575	−	0.985859i	$-0.446406\pi$
$240$	−119.556	−	69.0260i	−0.498152	−	0.287608i
$241$	−65.6864	−	11.5823i	−0.272557	−	0.0480592i	0.0356988	−	0.999363i	$-0.488634\pi$
$241$	−65.6864	−	11.5823i	−0.272557	−	0.0480592i	−0.308256	+	0.951303i	$0.599745\pi$
$242$	−83.3949	−	99.3862i	−0.344607	−	0.410687i
$243$	−180.638	+	215.276i	−0.743365	+	0.885908i
$244$	−17.2122	−	97.6150i	−0.0705416	−	0.400062i
$245$	−191.524	−	69.7089i	−0.781729	−	0.284526i
$246$			27.9105i			0.113457i
$247$	61.9137	+	229.891i	0.250663	+	0.930733i
$248$	−62.2734			−0.251102
$249$	−94.3876	+	259.328i	−0.379067	+	1.04148i
$250$	359.810	−	63.4442i	1.43924	−	0.253777i
$251$	274.637	+	230.448i	1.09417	+	0.918119i	0.997019	−	0.0771501i	$-0.0245821\pi$
$251$	274.637	+	230.448i	1.09417	+	0.918119i	0.0971526	+	0.995269i	$0.469027\pi$
$252$	−47.4672	+	39.8297i	−0.188362	+	0.158054i
$253$	−7.86367	+	44.5971i	−0.0310817	+	0.176273i
$254$	1.13875	−	1.97237i	0.00448327	−	0.00776525i
$255$	−770.226	+	444.690i	−3.02050	+	1.74388i
$256$	−15.0351	+	5.47232i	−0.0587308	+	0.0213763i
$257$	41.0267	+	112.720i	0.159637	+	0.438599i	0.993564	−	0.113276i	$-0.0361345\pi$
$257$	41.0267	+	112.720i	0.159637	+	0.438599i	−0.833926	+	0.551876i	$0.813912\pi$
$258$	−103.302	−	178.925i	−0.400397	−	0.693508i
$259$	74.0472	+	42.7512i	0.285897	+	0.165063i
$260$	−219.444	−	38.6938i	−0.844014	−	0.148822i
$261$	−184.337	−	219.685i	−0.706273	−	0.841704i
$262$	176.694	−	210.575i	0.674403	−	0.803723i
$263$	60.8083	+	344.861i	0.231210	+	1.31126i	0.850449	+	0.526057i	$0.176330\pi$
$263$	60.8083	+	344.861i	0.231210	+	1.31126i	−0.619239	+	0.785203i	$0.712559\pi$
$264$	−55.8066	−	20.3119i	−0.211389	−	0.0769391i
$265$		−	251.213i		−	0.947973i
$266$	−57.8304	+	124.432i	−0.217408	+	0.467790i
$267$	−203.173			−0.760949
$268$	−17.6864	+	48.5930i	−0.0659941	+	0.181317i
$269$	115.424	−	20.3524i	0.429085	−	0.0756593i	0.0450652	−	0.998984i	$-0.485650\pi$
$269$	115.424	−	20.3524i	0.429085	−	0.0756593i	0.384020	+	0.923325i	$0.374539\pi$
$270$	−109.661	−	92.0164i	−0.406151	−	0.340802i
$271$	−203.292	+	170.582i	−0.750156	+	0.629455i	−0.935544	−	0.353210i	$-0.885090\pi$
$271$	−203.292	+	170.582i	−0.750156	+	0.629455i	0.185388	+	0.982665i	$0.440646\pi$
$272$	−17.8993	+	101.512i	−0.0658062	+	0.373205i
$273$	−124.190	+	215.104i	−0.454910	+	0.787927i
$274$	−222.636	+	128.539i	−0.812541	+	0.469121i
$275$	274.771	−	100.009i	0.999168	−	0.363667i
$276$	−22.2286	−	61.0725i	−0.0805383	−	0.221277i
$277$	17.2320	+	29.8467i	0.0622094	+	0.107750i	0.895453	−	0.445157i	$-0.146852\pi$
$277$	17.2320	+	29.8467i	0.0622094	+	0.107750i	−0.833243	+	0.552906i	$0.813519\pi$
$278$	187.794	+	108.423i	0.675519	+	0.390011i
$279$	131.549	+	23.1957i	0.471503	+	0.0831387i
$280$	−82.5487	−	98.3777i	−0.294817	−	0.351349i
$281$	124.089	−	147.883i	0.441597	−	0.526275i	−0.498634	−	0.866813i	$-0.666165\pi$
$281$	124.089	−	147.883i	0.441597	−	0.526275i	0.940231	+	0.340538i	$0.110609\pi$
$282$	42.8043	+	242.755i	0.151788	+	0.860833i
$283$	3.28173	+	1.19445i	0.0115962	+	0.00422068i	0.347812	−	0.937564i	$-0.386925\pi$
$283$	3.28173	+	1.19445i	0.0115962	+	0.00422068i	−0.336216	+	0.941785i	$0.609147\pi$
$284$		−	119.981i		−	0.422470i
$285$	633.619	+	168.911i	2.22322	+	0.592671i
$286$	−95.8581			−0.335168
$287$	−8.88015	+	24.3980i	−0.0309413	+	0.0850104i
$288$	33.7992	−	5.95971i	0.117358	−	0.0206934i
$289$	287.316	+	241.087i	0.994174	+	0.834211i
$290$	455.306	−	382.047i	1.57002	−	1.31740i
$291$	29.2702	−	166.000i	0.100585	−	0.570446i
$292$	34.0138	−	58.9136i	0.116486	−	0.201759i
$293$	406.052	−	234.434i	1.38584	−	0.800117i	0.392999	−	0.919539i	$-0.371438\pi$
$293$	406.052	−	234.434i	1.38584	−	0.800117i	0.992844	+	0.119422i	$0.0381043\pi$
$294$	118.245	−	43.0378i	0.402195	−	0.146387i
$295$	−128.271	−	352.421i	−0.434816	−	1.19465i
$296$	−23.6790	−	41.0132i	−0.0799966	−	0.138558i
$297$	−53.3317	−	30.7911i	−0.179568	−	0.103674i
$298$	−176.437	−	31.1105i	−0.592069	−	0.104398i
$299$	−67.4305	−	80.3606i	−0.225520	−	0.268764i
$300$	−269.747	+	321.473i	−0.899158	+	1.07158i
$301$	−33.3742	−	189.275i	−0.110878	−	0.628819i
$302$	206.653	+	75.2156i	0.684282	+	0.249058i
$303$		−	115.666i		−	0.381737i
$304$	62.1999	−	43.6712i	0.204605	−	0.143655i
$305$	−440.659			−1.44478
$306$	75.6226	−	207.771i	0.247133	−	0.678991i
$307$	52.5650	−	9.26863i	0.171221	−	0.0301910i	−0.0873801	−	0.996175i	$-0.527849\pi$
$307$	52.5650	−	9.26863i	0.171221	−	0.0301910i	0.258602	+	0.965984i	$0.416738\pi$
$308$	−42.3208	−	35.5114i	−0.137405	−	0.115297i
$309$	135.253	−	113.491i	0.437713	−	0.367285i
$310$	−48.0740	+	272.641i	−0.155078	+	0.879488i
$311$	220.320	−	381.606i	0.708426	−	1.22703i	−0.257015	−	0.966407i	$-0.582739\pi$
$311$	220.320	−	381.606i	0.708426	−	1.22703i	0.965441	−	0.260622i	$-0.0839275\pi$
$312$	119.142	−	68.7865i	0.381864	−	0.220470i
$313$	−568.688	+	206.985i	−1.81689	+	0.661295i	−0.820982	+	0.570954i	$0.806574\pi$
$313$	−568.688	+	206.985i	−1.81689	+	0.661295i	−0.995911	+	0.0903411i	$0.971204\pi$
$314$	52.0675	+	143.054i	0.165820	+	0.455587i
$315$	137.736	+	238.566i	0.437257	+	0.757352i
$316$	−126.487	−	73.0271i	−0.400274	−	0.231098i
$317$	151.913	+	26.7863i	0.479220	+	0.0844994i	0.408040	−	0.912964i	$-0.366212\pi$
$317$	151.913	+	26.7863i	0.479220	+	0.0844994i	0.0711799	+	0.997463i	$0.477324\pi$
$318$	99.6945	+	118.811i	0.313505	+	0.373620i
$319$	164.351	−	195.866i	0.515208	−	0.614001i
$320$	12.3517	+	70.0502i	0.0385992	+	0.218907i
$321$	−682.513	−	248.414i	−2.12621	−	0.773877i
$322$		−	60.4589i		−	0.187761i
$323$	−43.2956	−	487.702i	−0.134042	−	1.50991i
$324$	197.589			0.609841
$325$	−231.670	+	636.509i	−0.712832	+	1.95849i
$326$	−140.869	+	24.8391i	−0.432114	+	0.0761934i
$327$	−166.678	−	139.859i	−0.509718	−	0.427704i
$328$	11.0163	−	9.24381i	0.0335864	−	0.0281823i
$329$	−39.8187	+	225.823i	−0.121030	+	0.686393i
$330$	−132.010	+	228.648i	−0.400031	+	0.692874i
$331$	450.525	−	260.110i	1.36110	−	0.785832i	0.371331	−	0.928501i	$-0.378902\pi$
$331$	450.525	−	260.110i	1.36110	−	0.785832i	0.989771	+	0.142668i	$0.0455683\pi$
$332$	133.618	−	48.6329i	0.402463	−	0.146485i
$333$	34.7440	+	95.4583i	0.104336	+	0.286662i
$334$	12.0878	+	20.9367i	0.0361910	+	0.0626846i
$335$	199.093	+	114.947i	0.594308	+	0.343124i
$336$	78.0829	+	13.7681i	0.232390	+	0.0409766i
$337$	−23.1102	−	27.5417i	−0.0685763	−	0.0817260i	0.730666	−	0.682735i	$-0.239210\pi$
$337$	−23.1102	−	27.5417i	−0.0685763	−	0.0817260i	−0.799242	+	0.601009i	$0.794765\pi$
$338$	−10.8928	+	12.9815i	−0.0322272	+	0.0384068i
$339$	−84.8096	−	480.979i	−0.250176	−	1.41882i
$340$	430.615	+	156.731i	1.26651	+	0.460973i
$341$			119.096i			0.349255i
$342$	−147.661	+	69.0849i	−0.431757	+	0.202003i
$343$	367.280			1.07079
$344$	−36.4089	+	100.033i	−0.105840	+	0.290793i
$345$	−284.544	+	50.1728i	−0.824765	+	0.145428i
$346$	−239.082	−	200.614i	−0.690988	−	0.579808i
$347$	26.1505	−	21.9429i	0.0753617	−	0.0632360i	−0.604329	−	0.796735i	$-0.706559\pi$
$347$	26.1505	−	21.9429i	0.0753617	−	0.0632360i	0.679690	+	0.733499i	$0.262114\pi$
$348$	−63.7207	+	361.378i	−0.183106	+	1.03844i
$349$	−282.963	+	490.107i	−0.810783	+	1.40432i	0.101534	+	0.994832i	$0.467625\pi$
$349$	−282.963	+	490.107i	−0.810783	+	1.40432i	−0.912317	+	0.409485i	$0.865709\pi$
$350$	−338.081	+	195.191i	−0.965946	+	0.557689i
$351$	134.052	−	48.7911i	0.381916	−	0.139006i
$352$	10.4657	+	28.7542i	0.0297320	+	0.0816880i
$353$	105.283	+	182.356i	0.298253	+	0.516590i	0.975736	−	0.218948i	$-0.0702627\pi$
$353$	105.283	+	182.356i	0.298253	+	0.516590i	−0.677483	+	0.735538i	$0.736929\pi$
$354$	200.525	+	115.773i	0.566454	+	0.327043i
$355$	−525.295	−	92.6237i	−1.47970	−	0.260912i
$356$	67.2898	+	80.1929i	0.189016	+	0.225261i
$357$	328.335	−	391.295i	0.919706	−	1.09606i
$358$	−2.51691	−	14.2741i	−0.00703047	−	0.0398718i
$359$	−171.635	−	62.4700i	−0.478092	−	0.174011i	0.0917228	−	0.995785i	$-0.470763\pi$
$359$	−171.635	−	62.4700i	−0.478092	−	0.174011i	−0.569814	+	0.821773i	$0.692985\pi$
$360$		−	152.578i		−	0.423828i
$361$	−231.340	+	277.133i	−0.640830	+	0.767683i
$362$	−267.217			−0.738169
$363$	121.793	−	334.624i	0.335519	−	0.921830i
$364$	126.033	−	22.2231i	0.346245	−	0.0610524i
$365$	−231.674	−	194.397i	−0.634723	−	0.532595i
$366$	208.410	−	174.877i	0.569426	−	0.477805i
$367$	101.549	−	575.911i	0.276699	−	1.56924i	−0.456813	−	0.889563i	$-0.651009\pi$
$367$	101.549	−	575.911i	0.276699	−	1.56924i	0.733512	−	0.679676i	$-0.237880\pi$
$368$	−16.7435	+	29.0005i	−0.0454985	+	0.0788058i
$369$	−26.7146	+	15.4237i	−0.0723973	+	0.0417986i
$370$	−197.841	+	72.0084i	−0.534706	+	0.194617i
$371$	49.3464	+	135.578i	0.133009	+	0.365440i
$372$	−85.4618	−	148.024i	−0.229736	−	0.397914i
$373$	121.339	+	70.0550i	0.325305	+	0.187815i	0.653755	−	0.756707i	$-0.273193\pi$
$373$	121.339	+	70.0550i	0.325305	+	0.187815i	−0.328450	+	0.944521i	$0.606526\pi$
$374$	194.139	+	34.2319i	0.519087	+	0.0915290i
$375$	644.597	+	768.201i	1.71893	+	2.04854i
$376$	81.6394	−	97.2940i	0.217126	−	0.258761i
$377$	102.851	+	583.299i	0.272815	+	1.54721i
$378$	77.2584	+	28.1198i	0.204387	+	0.0743909i
$379$			656.903i			1.73325i	0.498957	+	0.866627i	$0.333716\pi$
$379$			656.903i			1.73325i	−0.498957	+	0.866627i	$0.666284\pi$
$380$	−143.181	−	306.033i	−0.376793	−	0.805350i
$381$	6.25113			0.0164072
$382$	0.691691	−	1.90040i	0.00181071	−	0.00497488i
$383$	−553.246	+	97.5522i	−1.44451	+	0.254706i	−0.840300	−	0.542122i	$-0.817621\pi$
$383$	−553.246	+	97.5522i	−1.44451	+	0.254706i	−0.604207	+	0.796827i	$0.706510\pi$
$384$	−33.6414	−	28.2284i	−0.0876077	−	0.0735116i
$385$	−188.145	+	157.872i	−0.488687	+	0.410057i
$386$	14.8982	−	84.4919i	0.0385964	−	0.218891i
$387$	114.172	−	197.752i	0.295019	−	0.510988i
$388$	−75.2146	+	43.4251i	−0.193852	+	0.111920i
$389$	−90.7497	+	33.0302i	−0.233290	+	0.0849105i	−0.456020	−	0.889970i	$-0.650725\pi$
$389$	−90.7497	+	33.0302i	−0.233290	+	0.0849105i	0.222730	+	0.974880i	$0.428503\pi$
$390$	−209.181	−	574.721i	−0.536362	−	1.47364i
$391$	107.867	+	186.832i	0.275876	+	0.477831i
$392$	−56.1493	−	32.4178i	−0.143238	−	0.0826985i
$393$	743.027	+	131.016i	1.89065	+	0.333373i
$394$	215.776	+	257.151i	0.547654	+	0.652668i
$395$	−417.368	+	497.400i	−1.05663	+	1.25924i
$396$	−11.3978	−	64.6400i	−0.0287822	−	0.163232i
$397$	−386.969	−	140.845i	−0.974733	−	0.354774i	−0.194943	−	0.980815i	$-0.562452\pi$
$397$	−386.969	−	140.845i	−0.974733	−	0.354774i	−0.779790	+	0.626041i	$0.784674\pi$
$398$		−	359.778i		−	0.903966i
$399$	−375.140	+	33.3030i	−0.940201	+	0.0834661i
$400$	216.225			0.540562
$401$	202.368	−	556.000i	0.504657	−	1.38653i	−0.382024	−	0.924152i	$-0.624773\pi$
$401$	202.368	−	556.000i	0.504657	−	1.38653i	0.886681	−	0.462382i	$-0.153005\pi$
$402$	−139.778	+	24.6466i	−0.347707	+	0.0613101i
$403$	−211.342	−	177.337i	−0.524421	−	0.440041i
$404$	−45.6538	+	38.3080i	−0.113004	+	0.0948219i
$405$	152.535	−	865.070i	0.376630	−	2.13597i
$406$	−170.679	+	295.625i	−0.420393	+	0.728141i
$407$	−78.4366	+	45.2854i	−0.192719	+	0.111266i
$408$	−265.859	+	96.7646i	−0.651614	+	0.237168i
$409$	229.898	+	631.639i	0.562097	+	1.54435i	0.816557	+	0.577265i	$0.195880\pi$
$409$	229.898	+	631.639i	0.562097	+	1.54435i	−0.254460	+	0.967083i	$0.581898\pi$
$410$	−31.9662	−	55.3671i	−0.0779664	−	0.135042i
$411$	−611.076	−	352.805i	−1.48680	−	0.858406i
$412$	−89.5903	−	15.7972i	−0.217452	−	0.0383427i
$413$	138.454	+	165.003i	0.335240	+	0.399523i
$414$	46.1719	−	55.0255i	0.111526	−	0.132912i
$415$	−109.771	−	622.541i	−0.264508	−	1.50010i
$416$	−66.6092	−	24.2438i	−0.160118	−	0.0582783i
$417$			595.184i			1.42730i
$418$	−83.5200	−	118.955i	−0.199809	−	0.284583i
$419$	−121.024			−0.288839			−0.144420	−	0.989517i	$-0.546131\pi$
$419$	−121.024			−0.288839			−0.144420	+	0.989517i	$0.546131\pi$
$420$	120.557	−	331.229i	0.287042	−	0.788640i
$421$	262.699	−	46.3210i	0.623989	−	0.110026i	0.147291	−	0.989093i	$-0.452945\pi$
$421$	262.699	−	46.3210i	0.623989	−	0.110026i	0.476698	+	0.879067i	$0.341834\pi$
$422$	75.9050	+	63.6918i	0.179870	+	0.150929i
$423$	−208.699	+	175.119i	−0.493379	+	0.413994i
$424$	13.8768	−	78.6992i	0.0327283	−	0.185611i
$425$	696.499	−	1206.37i	1.63882	−	2.83852i
$426$	285.196	−	164.658i	0.669475	−	0.386522i
$427$	237.821	−	86.5599i	0.556959	−	0.202716i
$428$	127.995	+	351.663i	0.299053	+	0.821642i
$429$	−131.552	−	227.855i	−0.306649	−	0.531131i
$430$	409.850	+	236.627i	0.953139	+	0.550295i
$431$	712.000	+	125.545i	1.65197	+	0.291287i	0.920546	−	0.390634i	$-0.127744\pi$
$431$	712.000	+	125.545i	1.65197	+	0.291287i	0.731426	+	0.681921i	$0.238855\pi$
$432$	−29.2713	−	34.8842i	−0.0677577	−	0.0807505i
$433$	−69.8599	+	83.2558i	−0.161339	+	0.192277i	−0.840657	−	0.541567i	$-0.817831\pi$
$433$	−69.8599	+	83.2558i	−0.161339	+	0.192277i	0.679318	+	0.733844i	$0.262276\pi$
$434$	−27.6104	−	156.586i	−0.0636184	−	0.360798i
$435$	1532.97	+	557.956i	3.52407	+	1.28266i
$436$			112.109i			0.257130i
$437$	40.9724	−	153.695i	0.0937584	−	0.351706i
$438$	186.717			0.426295
$439$	24.9171	−	68.4591i	0.0567587	−	0.155943i	−0.908073	−	0.418812i	$-0.862447\pi$
$439$	24.9171	−	68.4591i	0.0567587	−	0.155943i	0.964832	+	0.262869i	$0.0846687\pi$
$440$	133.969	−	23.6223i	0.304475	−	0.0536872i
$441$	106.537	+	89.3955i	0.241582	+	0.202711i
$442$	−349.823	+	293.536i	−0.791454	+	0.664109i
$443$	−78.6832	+	446.235i	−0.177614	+	1.00730i	0.757468	+	0.652872i	$0.226436\pi$
$443$	−78.6832	+	446.235i	−0.177614	+	1.00730i	−0.935083	+	0.354430i	$0.884675\pi$
$444$	64.9924	−	112.570i	0.146379	−	0.253536i
$445$	403.042	−	232.697i	0.905713	−	0.522914i
$446$	−338.537	+	123.217i	−0.759051	+	0.276272i
$447$	−168.185	−	462.086i	−0.376254	−	1.03375i
$448$	−20.4263	−	35.3794i	−0.0455944	−	0.0789719i
$449$	−453.771	−	261.985i	−1.01063	−	0.583485i	−0.0992513	−	0.995062i	$-0.531645\pi$
$449$	−453.771	−	261.985i	−1.01063	−	0.583485i	−0.911375	+	0.411577i	$0.864978\pi$
$450$	−456.764	−	80.5397i	−1.01503	−	0.178977i
$451$	−17.6785	−	21.0684i	−0.0391985	−	0.0467149i
$452$	−161.755	+	192.772i	−0.357865	+	0.426487i
$453$	104.816	+	594.439i	0.231381	+	1.31223i
$454$	403.958	+	147.029i	0.889775	+	0.323852i
$455$		−	568.947i		−	1.25043i
$456$	189.168	+	87.9166i	0.414841	+	0.192800i
$457$	−234.737			−0.513647			−0.256823	−	0.966458i	$-0.582676\pi$
$457$	−234.737			−0.513647			−0.256823	+	0.966458i	$0.582676\pi$
$458$	192.176	−	527.998i	0.419597	−	1.15283i
$459$	−288.916	+	50.9437i	−0.629447	+	0.110988i
$460$	114.043	+	95.6931i	0.247919	+	0.208028i
$461$	−244.641	+	205.279i	−0.530676	+	0.445290i	−0.868335	−	0.495979i	$-0.834809\pi$
$461$	−244.641	+	205.279i	−0.530676	+	0.445290i	0.337659	+	0.941268i	$0.390365\pi$
$462$	26.3311	−	149.331i	0.0569938	−	0.323228i
$463$	−347.408	+	601.728i	−0.750341	+	1.29963i	0.197317	+	0.980340i	$0.436777\pi$
$463$	−347.408	+	601.728i	−0.750341	+	1.29963i	−0.947658	+	0.319288i	$0.896556\pi$
$464$	163.741	−	94.5358i	0.352889	−	0.203741i
$465$	−714.045	+	259.891i	−1.53558	+	0.558906i
$466$	49.3403	+	135.561i	0.105881	+	0.290904i
$467$	217.856	+	377.338i	0.466501	+	0.808004i	0.999268	−	0.0382582i	$-0.0121809\pi$
$467$	217.856	+	377.338i	0.466501	+	0.808004i	−0.532767	+	0.846262i	$0.678848\pi$
$468$	131.678	+	76.0245i	0.281364	+	0.162445i
$469$	−130.029	−	22.9276i	−0.277247	−	0.0488861i
$470$	−362.942	−	432.538i	−0.772218	−	0.920293i
$471$	−268.585	+	320.087i	−0.570244	+	0.679591i
$472$	−20.7168	−	117.491i	−0.0438916	−	0.248922i
$473$	191.310	+	69.6310i	0.404460	+	0.147211i
$474$		−	400.879i		−	0.845737i
$475$	−991.731	+	267.090i	−2.08785	+	0.562296i
$476$	−263.188			−0.552915
$477$	−58.6280	+	161.079i	−0.122910	+	0.337692i
$478$	−512.602	+	90.3856i	−1.07239	+	0.189091i
$479$	84.4817	+	70.8886i	0.176371	+	0.147993i	0.726700	−	0.686955i	$-0.241053\pi$
$479$	84.4817	+	70.8886i	0.176371	+	0.147993i	−0.550329	+	0.834948i	$0.685498\pi$
$480$	−149.559	+	125.495i	−0.311580	+	0.261447i
$481$	36.4328	−	206.621i	0.0757438	−	0.429564i
$482$	−47.1638	+	81.6901i	−0.0978502	+	0.169481i
$483$	143.711	−	82.9717i	0.297539	−	0.171784i
$484$	−172.414	+	62.7536i	−0.356227	+	0.129656i
$485$	132.057	+	362.823i	0.272282	+	0.748089i
$486$	198.713	+	344.181i	0.408874	+	0.708191i
$487$	387.961	+	223.989i	0.796635	+	0.459937i	0.842293	−	0.539020i	$-0.181205\pi$
$487$	387.961	+	223.989i	0.796635	+	0.459937i	−0.0456583	+	0.998957i	$0.514539\pi$
$488$	−138.048	−	24.3417i	−0.282886	−	0.0498805i
$489$	−252.367	−	300.759i	−0.516087	−	0.615049i
$490$	−185.276	+	220.803i	−0.378114	+	0.450619i
$491$	−41.6210	−	236.044i	−0.0847678	−	0.480742i	−0.997406	−	0.0719749i	$-0.977070\pi$
$491$	−41.6210	−	236.044i	−0.0847678	−	0.480742i	0.912639	−	0.408767i	$-0.134041\pi$
$492$	37.0910	+	13.5000i	0.0753882	+	0.0274391i
$493$		−	1218.07i		−	2.47073i
$494$	335.455	+	28.9172i	0.679059	+	0.0585369i
$495$	−291.801			−0.589498
$496$	−30.1210	+	82.7567i	−0.0607278	+	0.166848i
$497$	301.693	−	53.1966i	0.607028	−	0.107035i
$498$	298.973	+	250.868i	0.600348	+	0.503752i
$499$	−346.239	+	290.529i	−0.693865	+	0.582222i	−0.920021	−	0.391869i	$-0.871829\pi$
$499$	−346.239	+	290.529i	−0.693865	+	0.582222i	0.226156	+	0.974091i	$0.427384\pi$
$500$	89.7236	−	508.848i	0.179447	−	1.01770i
$501$	−33.1777	+	57.4655i	−0.0662230	+	0.114702i
$502$	439.087	−	253.507i	0.874676	−	0.504995i
$503$	410.210	−	149.304i	0.815528	−	0.296828i	0.0996224	−	0.995025i	$-0.468237\pi$
$503$	410.210	−	149.304i	0.815528	−	0.296828i	0.715905	+	0.698198i	$0.246014\pi$
$504$	29.9714	+	82.3456i	0.0594670	+	0.163384i
$505$	132.474	+	229.452i	0.262325	+	0.454360i
$506$	55.4627	+	32.0214i	0.109610	+	0.0632834i
$507$	−45.8060	−	8.07683i	−0.0903471	−	0.0159306i
$508$	−2.07034	−	2.46733i	−0.00407547	−	0.00485695i
$509$	−56.1612	+	66.9303i	−0.110336	+	0.131494i	−0.818386	−	0.574669i	$-0.805131\pi$
$509$	−56.1612	+	66.9303i	−0.110336	+	0.131494i	0.708050	+	0.706163i	$0.249575\pi$
$510$	218.410	+	1238.67i	0.428255	+	2.42876i
$511$	163.219	+	59.4069i	0.319411	+	0.116256i
$512$			22.6274i			0.0441942i
$513$	177.346	+	123.842i	0.345703	+	0.241407i
$514$	169.641			0.330040
$515$	−138.325	+	380.043i	−0.268591	+	0.737949i
$516$	−287.744	+	50.7371i	−0.557644	+	0.0983277i
$517$	−186.072	−	156.133i	−0.359907	−	0.301998i
$518$	92.6291	−	77.7250i	0.178821	−	0.150048i
$519$	148.752	−	843.614i	0.286613	−	1.62546i
$520$	−157.564	+	272.909i	−0.303007	+	0.524824i
$521$	−718.337	+	414.732i	−1.37877	+	0.796031i	−0.992011	−	0.126151i	$-0.959738\pi$
$521$	−718.337	+	414.732i	−1.37877	+	0.796031i	−0.386756	+	0.922182i	$0.626404\pi$
$522$	−381.107	+	138.711i	−0.730089	+	0.265731i
$523$	−332.878	−	914.574i	−0.636477	−	1.74871i	−0.662518	−	0.749046i	$-0.730512\pi$
$523$	−332.878	−	914.574i	−0.636477	−	1.74871i	0.0260404	−	0.999661i	$-0.491710\pi$
$524$	−194.374	−	336.666i	−0.370943	−	0.642492i
$525$	−927.941	−	535.747i	−1.76751	−	1.02047i
$526$	487.708	+	85.9960i	0.927201	+	0.163490i
$527$	364.695	+	434.627i	0.692021	+	0.824719i
$528$	−53.9861	+	64.3381i	−0.102246	+	0.121853i
$529$	−79.6896	−	451.942i	−0.150642	−	0.854333i
$530$	−333.843	−	121.509i	−0.629893	−	0.229262i
$531$			255.910i			0.481940i
$532$	137.389	+	137.039i	0.258250	+	0.257592i
$533$	63.7107			0.119532
$534$	−98.2728	+	270.002i	−0.184031	+	0.505622i
$535$	1638.44	−	288.901i	3.06250	−	0.540002i
$536$	56.0218	+	47.0079i	0.104518	+	0.0877013i
$537$	30.4755	−	25.5720i	0.0567513	−	0.0476200i
$538$	28.7826	−	163.234i	0.0534992	−	0.303409i
$539$	−61.9981	+	107.384i	−0.115024	+	0.199228i
$540$	−175.325	+	101.224i	−0.324676	+	0.187452i
$541$	430.483	−	156.683i	0.795717	−	0.289617i	0.0880063	−	0.996120i	$-0.471950\pi$
$541$	430.483	−	156.683i	0.795717	−	0.289617i	0.707710	+	0.706503i	$0.249728\pi$
$542$	128.361	+	352.669i	0.236829	+	0.650681i
$543$	−366.720	−	635.177i	−0.675358	−	1.16975i
$544$	126.244	+	72.8870i	0.232066	+	0.133984i
$545$	490.827	+	86.5460i	0.900600	+	0.158800i
$546$	225.788	+	269.084i	0.413531	+	0.492827i
$547$	139.282	−	165.989i	0.254628	−	0.303454i	−0.623554	−	0.781780i	$-0.714312\pi$
$547$	139.282	−	165.989i	0.254628	−	0.303454i	0.878182	+	0.478326i	$0.158756\pi$
$548$	63.1321	+	358.040i	0.115205	+	0.653358i
$549$	282.553	+	102.841i	0.514669	+	0.187324i
$550$		−	413.524i		−	0.751861i
$551$	−634.234	+	635.855i	−1.15106	+	1.15400i
$552$	−91.9125			−0.166508
$553$	127.546	−	350.429i	0.230643	−	0.633687i
$554$	47.9990	−	8.46351i	0.0866407	−	0.0152771i
$555$	−442.675	−	371.448i	−0.797612	−	0.669276i
$556$	234.921	−	197.122i	0.422519	−	0.354535i
$557$	50.3849	−	285.747i	0.0904576	−	0.513011i	−0.905587	−	0.424160i	$-0.860569\pi$
$557$	50.3849	−	285.747i	0.0904576	−	0.513011i	0.996045	−	0.0888508i	$-0.0283194\pi$
$558$	94.4544	−	163.600i	0.169273	−	0.293189i
$559$	−408.428	+	235.806i	−0.730640	+	0.421835i
$560$	−170.665	+	62.1169i	−0.304758	+	0.110923i
$561$	185.060	+	508.447i	0.329874	+	0.906322i
$562$	−136.505	−	236.434i	−0.242892	−	0.420702i
$563$	135.430	+	78.1905i	0.240550	+	0.138882i	0.615430	−	0.788192i	$-0.288983\pi$
$563$	135.430	+	78.1905i	0.240550	+	0.138882i	−0.374879	+	0.927074i	$0.622316\pi$
$564$	343.307	+	60.5344i	0.608701	+	0.107330i
$565$	719.110	+	857.002i	1.27276	+	1.51682i
$566$	3.17468	−	3.78344i	0.00560897	−	0.00668451i
$567$	87.6056	+	496.836i	0.154507	+	0.876254i
$568$	−159.446	−	58.0337i	−0.280715	−	0.102172i
$569$		−	469.455i		−	0.825053i	−0.910946	−	0.412527i	$-0.864646\pi$
$569$		−	469.455i		−	0.825053i	0.910946	−	0.412527i	$-0.135354\pi$
$570$	530.945	−	760.332i	0.931483	−	1.33392i
$571$	−112.970			−0.197846			−0.0989230	−	0.995095i	$-0.531540\pi$
$571$	−112.970			−0.197846			−0.0989230	+	0.995095i	$0.531540\pi$
$572$	−46.3655	+	127.388i	−0.0810586	+	0.222707i
$573$	5.46652	−	0.963896i	0.00954018	−	0.00168219i
$574$	28.1279	+	23.6021i	0.0490033	+	0.0411187i
$575$	346.669	−	290.890i	0.602902	−	0.505895i
$576$	8.42830	−	47.7992i	0.0146325	−	0.0829848i
$577$	−65.0229	+	112.623i	−0.112691	+	0.195187i	−0.916855	−	0.399221i	$-0.869280\pi$
$577$	−65.0229	+	112.623i	−0.112691	+	0.195187i	0.804163	+	0.594409i	$0.202614\pi$
$578$	459.359	−	265.211i	0.794739	−	0.458843i
$579$	221.284	−	80.5406i	0.382182	−	0.139103i
$580$	−287.485	−	789.859i	−0.495664	−	1.36183i
$581$	181.530	+	314.419i	0.312444	+	0.541169i
$582$	−206.444	−	119.190i	−0.354714	−	0.204794i
$583$	−150.510	−	26.5390i	−0.258165	−	0.0455214i
$584$	−61.8397	−	73.6977i	−0.105890	−	0.126195i
$585$	434.499	−	517.816i	0.742733	−	0.885155i
$586$	−115.143	−	653.006i	−0.196489	−	1.11435i
$587$	−801.822	−	291.839i	−1.36597	−	0.497171i	−0.448072	−	0.893998i	$-0.647889\pi$
$587$	−801.822	−	291.839i	−1.36597	−	0.497171i	−0.917894	+	0.396827i	$0.870111\pi$
$588$		−	177.956i		−	0.302647i
$589$	35.9273	−	416.777i	0.0609972	−	0.707600i
$590$	−530.385			−0.898957
$591$	−315.127	+	865.805i	−0.533210	+	1.46498i
$592$	−65.9568	+	11.6300i	−0.111414	+	0.0196452i
$593$	177.032	+	148.547i	0.298536	+	0.250501i	0.779735	−	0.626110i	$-0.215354\pi$
$593$	177.032	+	148.547i	0.298536	+	0.250501i	−0.481199	+	0.876612i	$0.659798\pi$
$594$	−66.7151	+	55.9806i	−0.112315	+	0.0942434i
$595$	−203.176	+	1152.27i	−0.341473	+	1.93659i
$596$	−126.684	+	219.423i	−0.212557	+	0.368160i
$597$	855.195	−	493.747i	1.43249	−	0.827047i
$598$	−139.409	+	50.7406i	−0.233125	+	0.0848505i
$599$	−128.583	−	353.278i	−0.214662	−	0.589779i	0.784892	−	0.619632i	$-0.212718\pi$
$599$	−128.583	−	353.278i	−0.214662	−	0.589779i	−0.999554	+	0.0298532i	$0.990496\pi$
$600$	296.739	+	513.967i	0.494565	+	0.856612i
$601$	−663.945	−	383.329i	−1.10473	−	0.637818i	−0.167273	−	0.985911i	$-0.553496\pi$
$601$	−663.945	−	383.329i	−1.10473	−	0.637818i	−0.937460	+	0.348092i	$0.886830\pi$
$602$	−267.675	−	47.1983i	−0.444642	−	0.0784025i
$603$	−100.834	−	120.169i	−0.167220	−	0.199285i
$604$	199.912	−	238.246i	0.330980	−	0.394446i
$605$	141.643	+	803.297i	0.234121	+	1.32776i
$606$	−153.712	−	55.9466i	−0.253650	−	0.0923211i
$607$			504.411i			0.830990i	0.909596	+	0.415495i	$0.136392\pi$
$607$			504.411i			0.830990i	−0.909596	+	0.415495i	$0.863608\pi$
$608$	−27.9504	−	103.782i	−0.0459710	−	0.170695i
$609$	−936.937			−1.53849
$610$	−213.142	+	585.604i	−0.349414	+	0.960006i
$611$	554.131	−	97.7082i	0.906925	−	0.159915i
$612$	−239.535	−	200.994i	−0.391397	−	0.328421i
$613$	736.614	−	618.093i	1.20165	−	1.00831i	0.202073	−	0.979370i	$-0.435232\pi$
$613$	736.614	−	618.093i	1.20165	−	1.00831i	0.999581	−	0.0289371i	$-0.00921225\pi$
$614$	13.1078	−	74.3381i	0.0213482	−	0.121072i
$615$	87.7386	−	151.968i	0.142664	−	0.247102i
$616$	−67.6621	+	39.0647i	−0.109841	+	0.0634168i
$617$	−120.801	+	43.9680i	−0.195788	+	0.0712609i	−0.438053	−	0.898949i	$-0.644332\pi$
$617$	−120.801	+	43.9680i	−0.195788	+	0.0712609i	0.242265	+	0.970210i	$0.422110\pi$
$618$	−85.4006	−	234.636i	−0.138189	−	0.379670i
$619$	371.077	+	642.724i	0.599478	+	1.03833i	0.992898	+	0.118968i	$0.0379585\pi$
$619$	371.077	+	642.724i	0.599478	+	1.03833i	−0.393420	+	0.919359i	$0.628708\pi$
$620$	339.067	+	195.761i	0.546883	+	0.315743i
$621$	−93.8602	−	16.5501i	−0.151144	−	0.0266507i
$622$	−400.560	−	477.368i	−0.643986	−	0.767473i
$623$	−171.810	+	204.756i	−0.275779	+	0.328661i
$624$	−33.7846	−	191.602i	−0.0541419	−	0.307054i
$625$	−888.635	−	323.437i	−1.42182	−	0.517499i
$626$			855.860i			1.36719i
$627$	168.138	−	361.778i	0.268163	−	0.576998i
$628$	215.293			0.342823
$629$	−147.572	+	405.452i	−0.234614	+	0.644598i
$630$	383.658	−	67.6492i	0.608981	−	0.107380i
$631$	426.786	+	358.116i	0.676365	+	0.567538i	0.914942	−	0.403586i	$-0.132236\pi$
$631$	426.786	+	358.116i	0.676365	+	0.567538i	−0.238577	+	0.971124i	$0.576681\pi$
$632$	−158.228	+	132.769i	−0.250360	+	0.210077i
$633$	−47.2265	+	267.835i	−0.0746075	+	0.423120i
$634$	109.076	−	188.924i	0.172044	−	0.297988i
$635$	−12.4006	+	7.15948i	−0.0195285	+	0.0112748i
$636$	206.113	−	75.0188i	0.324076	−	0.117954i
$637$	−98.2413	−	269.916i	−0.154225	−	0.423730i
$638$	−180.797	−	313.149i	−0.283381	−	0.490830i
$639$	315.206	+	181.984i	0.493280	+	0.284795i
$640$	99.0659	+	17.4680i	0.154791	+	0.0272937i
$641$	−47.3994	−	56.4884i	−0.0739460	−	0.0881254i	0.727803	−	0.685786i	$-0.240541\pi$
$641$	−47.3994	−	56.4884i	−0.0739460	−	0.0881254i	−0.801749	+	0.597661i	$0.796097\pi$
$642$	−660.249	+	786.854i	−1.02843	+	1.22563i
$643$	−61.7979	−	350.473i	−0.0961087	−	0.545059i	−0.994402	−	0.105663i	$-0.966304\pi$
$643$	−61.7979	−	350.473i	−0.0961087	−	0.545059i	0.898293	−	0.439396i	$-0.144808\pi$
$644$	−80.3454	−	29.2433i	−0.124760	−	0.0454089i
$645$			1298.95i			2.01388i
$646$	−669.061	−	178.360i	−1.03570	−	0.276098i
$647$	−23.7607			−0.0367245			−0.0183622	−	0.999831i	$-0.505845\pi$
$647$	−23.7607			−0.0367245			−0.0183622	+	0.999831i	$0.505845\pi$
$648$	95.5715	−	262.581i	0.147487	−	0.405217i
$649$	−224.698	+	39.6203i	−0.346222	+	0.0610483i
$650$	733.817	+	615.746i	1.12895	+	0.947301i
$651$	334.315	−	280.524i	0.513541	−	0.430912i
$652$	−35.1277	+	199.219i	−0.0538769	+	0.305551i
$653$	−558.832	+	967.926i	−0.855792	+	1.48228i	0.0201159	+	0.999798i	$0.493596\pi$
$653$	−558.832	+	967.926i	−0.855792	+	1.48228i	−0.875908	+	0.482478i	$0.839737\pi$
$654$	−266.483	+	153.854i	−0.407466	+	0.235251i
$655$	−1624.02	+	591.096i	−2.47943	+	0.902437i
$656$	−6.95585	−	19.1110i	−0.0106034	−	0.0291327i
$657$	103.182	+	178.717i	0.157050	+	0.272019i
$658$	280.843	+	162.145i	0.426812	+	0.246420i
$659$	1024.08	+	180.573i	1.55399	+	0.274011i	0.883688	−	0.468076i	$-0.155053\pi$
$659$	1024.08	+	180.573i	1.55399	+	0.274011i	0.670304	+	0.742087i	$0.266164\pi$
$660$	240.005	+	286.027i	0.363644	+	0.433374i
$661$	245.426	−	292.488i	0.371296	−	0.442493i	−0.547751	−	0.836641i	$-0.684516\pi$
$661$	245.426	−	292.488i	0.371296	−	0.442493i	0.919047	+	0.394148i	$0.128960\pi$
$662$	−127.754	−	724.527i	−0.192981	−	1.09445i
$663$	−1177.82	−	428.692i	−1.77650	−	0.646594i
$664$		−	201.092i		−	0.302849i
$665$	706.037	−	495.716i	1.06171	−	0.745438i
$666$	143.662			0.215709
$667$	135.342	−	371.849i	0.202912	−	0.557495i
$668$	33.6700	−	5.93693i	0.0504042	−	0.00888762i
$669$	−757.484	−	635.604i	−1.13226	−	0.950081i
$670$	249.055	−	208.982i	0.371724	−	0.311913i
$671$	−46.5527	+	264.014i	−0.0693782	+	0.393463i
$672$	56.0647	−	97.1069i	0.0834296	−	0.144504i
$673$	−564.575	+	325.958i	−0.838893	+	0.484335i	−0.856888	−	0.515503i	$-0.827605\pi$
$673$	−564.575	+	325.958i	−0.838893	+	0.484335i	0.0179948	+	0.999838i	$0.494272\pi$
$674$	−47.7790	+	17.3901i	−0.0708887	+	0.0258014i
$675$	210.481	+	578.291i	0.311823	+	0.856727i
$676$	11.9827	+	20.7547i	0.0177260	+	0.0307023i
$677$	−666.881	−	385.024i	−0.985052	−	0.568720i	−0.0812607	−	0.996693i	$-0.525895\pi$
$677$	−666.881	−	385.024i	−0.985052	−	0.568720i	−0.903792	+	0.427973i	$0.859228\pi$
$678$	−680.207	−	119.939i	−1.00326	−	0.176901i
$679$	−142.541	−	169.873i	−0.209927	−	0.250182i
$680$	416.568	−	496.446i	0.612600	−	0.730068i
$681$	204.890	+	1161.99i	0.300866	+	1.70629i
$682$	158.270	+	57.6055i	0.232067	+	0.0844656i
$683$		−	794.510i		−	1.16327i	−0.813452	−	0.581633i	$-0.802414\pi$
$683$		−	794.510i		−	1.16327i	0.813452	−	0.581633i	$-0.197586\pi$
$684$	20.3867	+	229.646i	0.0298052	+	0.335740i
$685$	1616.29			2.35954
$686$	177.649	−	488.088i	0.258964	−	0.711498i
$687$	1518.79	−	267.803i	2.21076	−	0.389816i
$688$	115.325	+	96.7695i	0.167624	+	0.140653i
$689$	271.207	−	227.570i	0.393625	−	0.330290i
$690$	−70.9550	+	402.406i	−0.102833	+	0.583197i
$691$	235.437	−	407.789i	0.340719	−	0.590143i	−0.643847	−	0.765154i	$-0.722663\pi$
$691$	235.437	−	407.789i	0.340719	−	0.590143i	0.984566	+	0.175011i	$0.0559962\pi$
$692$	−382.242	+	220.688i	−0.552373	+	0.318913i
$693$	157.484	−	57.3194i	0.227249	−	0.0827119i
$694$	−16.5117	−	45.3657i	−0.0237921	−	0.0653684i
$695$	−681.671	−	1180.69i	−0.980822	−	1.69883i
$696$	449.424	+	259.475i	0.645724	+	0.372809i
$697$	−129.031	−	22.7517i	−0.185124	−	0.0326423i
$698$	514.449	+	613.096i	0.737033	+	0.878362i
$699$	−254.517	+	303.322i	−0.364116	+	0.433937i
$700$	95.8684	+	543.697i	0.136955	+	0.776710i
$701$	453.072	+	164.905i	0.646322	+	0.235242i	0.644320	−	0.764756i	$-0.277140\pi$
$701$	453.072	+	164.905i	0.646322	+	0.235242i	0.00200220	+	0.999998i	$0.499363\pi$
$702$		−	201.745i		−	0.287387i
$703$	288.150	−	134.815i	0.409886	−	0.191770i
$704$	43.2743			0.0614692
$705$	530.056	−	1456.32i	0.751852	−	2.06570i
$706$	293.262	−	51.7101i	0.415386	−	0.0732437i
$707$	−116.567	−	97.8115i	−0.164876	−	0.138347i
$708$	250.846	−	210.484i	0.354302	−	0.297294i
$709$	142.393	−	807.549i	0.200836	−	1.13900i	−0.703023	−	0.711167i	$-0.748167\pi$
$709$	142.393	−	807.549i	0.200836	−	1.13900i	0.903859	−	0.427830i	$-0.140722\pi$
$710$	−377.170	+	653.277i	−0.531225	+	0.920108i
$711$	383.702	−	221.531i	0.539665	−	0.311576i
$712$	139.118	−	50.6348i	0.195390	−	0.0711162i
$713$	63.0412	+	173.204i	0.0884168	+	0.242923i
$714$	−361.189	−	625.598i	−0.505867	−	0.876188i
$715$	521.930	+	301.336i	0.729972	+	0.421449i
$716$	−20.1866	−	3.55944i	−0.0281936	−	0.00497129i
$717$	−918.324	−	1094.42i	−1.28079	−	1.52638i
$718$	−166.036	+	197.874i	−0.231248	+	0.275590i
$719$	−74.1833	−	420.714i	−0.103176	−	0.585138i	−0.991933	−	0.126761i	$-0.959542\pi$
$719$	−74.1833	−	420.714i	−0.103176	−	0.585138i	0.888758	−	0.458377i	$-0.151569\pi$
$720$	−202.765	−	73.8005i	−0.281618	−	0.102501i
$721$		−	232.279i		−	0.322162i
$722$	256.393	+	441.480i	0.355115	+	0.611468i
$723$	−258.904			−0.358096
$724$	−129.250	+	355.112i	−0.178522	+	0.490486i
$725$	−2516.30	+	443.692i	−3.47076	+	0.611989i
$726$	−385.781	−	323.708i	−0.531378	−	0.445879i
$727$	−661.153	+	554.773i	−0.909426	+	0.763099i	−0.972010	−	0.234940i	$-0.924511\pi$
$727$	−661.153	+	554.773i	−0.909426	+	0.763099i	0.0625833	+	0.998040i	$0.480066\pi$
$728$	31.4282	−	178.238i	0.0431705	−	0.244832i
$729$	−100.839	+	174.658i	−0.138325	+	0.239586i
$730$	−370.398	+	213.849i	−0.507394	+	0.292944i
$731$	911.385	−	331.717i	1.24677	−	0.453785i
$732$	−131.593	−	361.548i	−0.179771	−	0.493917i
$733$	386.858	+	670.058i	0.527774	+	0.914132i	0.999476	+	0.0323734i	$0.0103066\pi$
$733$	386.858	+	670.058i	0.527774	+	0.914132i	−0.471702	+	0.881758i	$0.656360\pi$
$734$	−716.225	−	413.513i	−0.975783	−	0.563369i
$735$	−779.117	−	137.379i	−1.06002	−	0.186911i
$736$	30.4409	+	36.2781i	0.0413599	+	0.0492909i
$737$	89.9012	−	107.140i	0.121983	−	0.145373i
$738$	7.57536	+	42.9620i	0.0102647	+	0.0582141i
$739$	862.926	+	314.079i	1.16769	+	0.425006i	0.851840	−	0.523802i	$-0.175487\pi$
$739$	862.926	+	314.079i	1.16769	+	0.425006i	0.315854	+	0.948808i	$0.397709\pi$
$740$			297.746i			0.402360i
$741$	391.631	+	837.064i	0.528516	+	1.12964i
$742$	204.042			0.274989
$743$	−193.556	+	531.791i	−0.260506	+	0.715736i	0.738627	+	0.674114i	$0.235474\pi$
$743$	−193.556	+	531.791i	−0.260506	+	0.715736i	−0.999133	+	0.0416212i	$0.986748\pi$
$744$	−238.050	+	41.9747i	−0.319960	+	0.0564175i
$745$	862.868	+	724.032i	1.15821	+	0.971855i
$746$	151.788	−	127.365i	0.203469	−	0.170731i
$747$	−74.9029	+	424.795i	−0.100272	+	0.568669i
$748$	139.394	−	241.438i	0.186356	−	0.322778i
$749$	−827.506	+	477.761i	−1.10481	+	0.637865i
$750$	1332.67	−	485.051i	1.77689	−	0.646735i
$751$	−156.364	−	429.606i	−0.208207	−	0.572045i	0.791002	−	0.611814i	$-0.209560\pi$
$751$	−156.364	−	429.606i	−0.208207	−	0.572045i	−0.999209	+	0.0397693i	$0.987338\pi$
$752$	−89.8085	−	155.553i	−0.119426	−	0.206852i
$753$	1205.18	+	695.809i	1.60050	+	0.924049i
$754$	824.909	+	145.454i	1.09404	+	0.192910i
$755$	−888.743	−	1059.16i	−1.17714	−	1.40287i
$756$	74.7382	−	89.0695i	0.0988600	−	0.117817i
$757$	−252.597	−	1432.55i	−0.333681	−	1.89240i	−0.439882	−	0.898056i	$-0.644980\pi$
$757$	−252.597	−	1432.55i	−0.333681	−	1.89240i	0.106201	−	0.994345i	$-0.466131\pi$
$758$	872.975	+	317.737i	1.15168	+	0.419178i
$759$			175.780i			0.231594i
$760$	−475.951	+	42.2524i	−0.626251	+	0.0555952i
$761$	1394.79			1.83284			0.916422	−	0.400213i	$-0.131064\pi$
$761$	1394.79			1.83284			0.916422	+	0.400213i	$0.131064\pi$
$762$	3.02360	−	8.30728i	0.00396798	−	0.0109019i
$763$	−281.897	+	49.7060i	−0.369459	+	0.0651455i
$764$	−2.19093	−	1.83841i	−0.00286771	−	0.00240630i
$765$	−1064.89	+	893.553i	−1.39202	+	1.16804i
$766$	−137.960	+	782.408i	−0.180104	+	1.02142i
$767$	264.272	−	457.733i	0.344553	−	0.596784i
$768$	−53.7855	+	31.0531i	−0.0700332	+	0.0404337i
$769$	840.058	−	305.756i	1.09240	−	0.397602i	0.267893	−	0.963449i	$-0.413673\pi$
$769$	840.058	−	305.756i	1.09240	−	0.397602i	0.824511	+	0.565846i	$0.191450\pi$
$770$	118.797	+	326.391i	0.154281	+	0.423885i
$771$	232.809	+	403.237i	0.301957	+	0.523005i
$772$	−105.077	−	60.6665i	−0.136111	−	0.0785835i
$773$	−1243.52	−	219.266i	−1.60869	−	0.283656i	−0.704155	−	0.710047i	$-0.748674\pi$
$773$	−1243.52	−	219.266i	−1.60869	−	0.283656i	−0.904539	+	0.426391i	$0.859785\pi$
$774$	−207.574	−	247.377i	−0.268184	−	0.319609i
$775$	765.015	−	911.710i	0.987117	−	1.17640i
$776$	21.3283	+	120.959i	0.0274849	+	0.155875i
$777$	311.874	+	113.513i	0.401382	+	0.146091i
$778$			136.576i			0.175548i
$779$	55.5103	+	79.0620i	0.0712584	+	0.101492i
$780$	−864.940			−1.10890
$781$	−110.988	+	304.937i	−0.142110	+	0.390444i
$782$	300.460	−	52.9792i	0.384220	−	0.0677484i
$783$	412.226	+	345.898i	0.526470	+	0.441760i
$784$	−70.2397	+	58.9381i	−0.0895915	+	0.0751762i
$785$	166.203	−	942.582i	0.211723	−	1.20074i
$786$	533.504	−	924.057i	0.678759	−	1.17564i
$787$	558.566	−	322.488i	0.709741	−	0.409769i	−0.101224	−	0.994864i	$-0.532276\pi$
$787$	558.566	−	322.488i	0.709741	−	0.409769i	0.810965	+	0.585094i	$0.198943\pi$
$788$	446.103	−	162.368i	0.566121	−	0.206051i
$789$	464.900	+	1277.30i	0.589226	+	1.61889i
$790$	459.131	+	795.239i	0.581179	+	1.00663i
$791$	−556.443	−	321.263i	−0.703468	−	0.406147i
$792$	−91.4147	−	16.1189i	−0.115423	−	0.0203521i
$793$	−399.187	−	475.732i	−0.503388	−	0.599915i
$794$	−374.346	+	446.128i	−0.471468	+	0.561874i
$795$	−169.327	−	960.302i	−0.212990	−	1.20793i
$796$	−478.119	−	174.021i	−0.600652	−	0.218619i
$797$			1189.87i			1.49294i	0.665420	+	0.746469i	$0.268252\pi$
$797$			1189.87i			1.49294i	−0.665420	+	0.746469i	$0.731748\pi$
$798$	−137.194	+	514.642i	−0.171923	+	0.644914i
$799$	−1157.16			−1.44826
$800$	104.586	−	287.347i	0.130732	−	0.359183i
$801$	−312.740	+	55.1445i	−0.390437	+	0.0688445i
$802$	−641.000	−	537.863i	−0.799252	−	0.670652i
$803$	−140.945	+	118.267i	−0.175523	+	0.147281i
$804$	−34.8556	+	197.676i	−0.0433528	+	0.245866i
$805$	−190.057	+	329.188i	−0.236095	+	0.408929i
$806$	−337.891	+	195.081i	−0.419220	+	0.242037i
$807$	427.508	−	155.600i	0.529750	−	0.192813i
$808$	28.8263	+	79.1997i	0.0356761	+	0.0980194i
$809$	−18.1339	−	31.4088i	−0.0224152	−	0.0388242i	0.854600	−	0.519286i	$-0.173802\pi$
$809$	−18.1339	−	31.4088i	−0.0224152	−	0.0388242i	−0.877015	+	0.480462i	$0.840469\pi$
$810$	−1075.83	−	621.133i	−1.32819	−	0.766831i
$811$	−1479.98	−	260.960i	−1.82488	−	0.321775i	−0.847102	−	0.531431i	$-0.821655\pi$
$811$	−1479.98	−	260.960i	−1.82488	−	0.321775i	−0.977775	+	0.209656i	$0.932766\pi$
$812$	310.308	+	369.811i	0.382153	+	0.455433i
$813$	−662.138	+	789.106i	−0.814438	+	0.970610i
$814$	22.2420	+	126.141i	0.0273243	+	0.154964i
$815$	845.091	+	307.588i	1.03692	+	0.377409i
$816$			400.110i			0.490331i
$817$	−648.483	−	301.385i	−0.793736	−	0.368893i
$818$	950.600			1.16210
$819$	−132.781	+	364.812i	−0.162125	+	0.445436i
$820$	−89.0405	+	15.7002i	−0.108586	+	0.0191466i
$821$	−250.228	−	209.966i	−0.304784	−	0.255744i	0.477548	−	0.878606i	$-0.341526\pi$
$821$	−250.228	−	209.966i	−0.304784	−	0.255744i	−0.782332	+	0.622861i	$0.785970\pi$
$822$	−764.423	+	641.427i	−0.929955	+	0.780325i
$823$	−276.459	+	1567.88i	−0.335917	+	1.90508i	0.0820738	+	0.996626i	$0.473846\pi$
$823$	−276.459	+	1567.88i	−0.335917	+	1.90508i	−0.417990	+	0.908451i	$0.637265\pi$
$824$	−64.3272	+	111.418i	−0.0780670	+	0.135216i
$825$	982.948	−	567.505i	1.19145	−	0.687885i
$826$	286.246	−	104.185i	0.346544	−	0.126132i
$827$	−369.722	−	1015.80i	−0.447064	−	1.22830i	−0.934759	−	0.355284i	$-0.884384\pi$
$827$	−369.722	−	1015.80i	−0.447064	−	1.22830i	0.487695	−	0.873014i	$-0.337838\pi$
$828$	−50.7920	−	87.9742i	−0.0613429	−	0.106249i
$829$	647.255	+	373.693i	0.780766	+	0.450775i	0.836702	−	0.547659i	$-0.184481\pi$
$829$	647.255	+	373.693i	0.780766	+	0.450775i	−0.0559357	+	0.998434i	$0.517814\pi$
$830$	−880.406	−	155.239i	−1.06073	−	0.187035i
$831$	85.9899	+	102.479i	0.103478	+	0.123320i
$832$	−64.4364	+	76.7923i	−0.0774476	+	0.0922984i
$833$	102.576	+	581.735i	0.123140	+	0.698362i
$834$	790.956	+	287.884i	0.948389	+	0.345185i
$835$		−	151.995i		−	0.182030i
$836$	−198.481	+	53.4543i	−0.237417	+	0.0639406i
$837$	−250.653			−0.299466
$838$	−58.5378	+	160.831i	−0.0698542	+	0.191923i
$839$	−621.162	+	109.528i	−0.740360	+	0.130545i	−0.531094	−	0.847313i	$-0.678219\pi$
$839$	−621.162	+	109.528i	−0.740360	+	0.130545i	−0.209267	+	0.977859i	$0.567108\pi$
$840$	−381.866	−	320.424i	−0.454603	−	0.381457i
$841$	−1067.29	+	895.565i	−1.26908	+	1.06488i
$842$	65.5078	−	371.513i	0.0778002	−	0.441227i
$843$	374.671	−	648.948i	0.444449	−	0.769808i
$844$	121.356	−	70.0650i	0.143787	−	0.0830154i
$845$	100.118	−	36.4398i	0.118482	−	0.0431240i
$846$	131.775	+	362.049i	0.155763	+	0.427954i
$847$	−234.238	−	405.712i	−0.276550	−	0.478999i
$848$	−97.8734	−	56.5072i	−0.115417	−	0.0666359i
$849$	13.3501	+	2.35398i	0.0157245	+	0.00277265i
$850$	−1266.29	−	1509.11i	−1.48975	−	1.77542i
$851$	−90.1013	+	107.379i	−0.105877	+	0.126179i
$852$	−80.8721	−	458.648i	−0.0949203	−	0.538320i
$853$	−445.774	−	162.248i	−0.522595	−	0.190209i	0.0672338	−	0.997737i	$-0.478583\pi$
$853$	−445.774	−	162.248i	−0.522595	−	0.190209i	−0.589829	+	0.807528i	$0.700805\pi$
$854$		−	357.915i		−	0.419104i
$855$	1021.16	+	88.0269i	1.19434	+	0.102955i
$856$	529.244			0.618275
$857$	224.222	−	616.044i	0.261636	−	0.718838i	−0.737422	−	0.675433i	$-0.763957\pi$
$857$	224.222	−	616.044i	0.261636	−	0.718838i	0.999058	−	0.0434057i	$-0.0138208\pi$
$858$	−366.433	+	64.6120i	−0.427078	+	0.0753054i
$859$	1024.32	+	859.510i	1.19246	+	1.00059i	0.999813	+	0.0193257i	$0.00615196\pi$
$859$	1024.32	+	859.510i	1.19246	+	1.00059i	0.192648	+	0.981268i	$0.438292\pi$
$860$	512.699	−	430.206i	0.596162	−	0.500239i
$861$	−17.5006	+	99.2509i	−0.0203259	+	0.115274i
$862$	511.227	−	885.471i	0.593070	−	1.02723i
$863$	−278.578	+	160.837i	−0.322801	+	0.186369i	−0.652641	−	0.757668i	$-0.726339\pi$
$863$	−278.578	+	160.837i	−0.322801	+	0.186369i	0.329839	+	0.944037i	$0.393005\pi$
$864$	−60.5168	+	22.0263i	−0.0700426	+	0.0254934i
$865$	671.116	+	1843.88i	0.775856	+	2.13165i
$866$	76.8503	+	133.109i	0.0887417	+	0.153705i
$867$	1260.82	+	727.932i	1.45423	+	0.839599i
$868$	−221.446	−	39.0470i	−0.255123	−	0.0449850i
$869$	253.917	+	302.606i	0.292194	+	0.348223i
$870$	1482.97	−	1767.33i	1.70456	−	2.03141i
$871$	56.2603	+	319.068i	0.0645928	+	0.366324i
$872$	148.984	+	54.2257i	0.170853	+	0.0621855i
$873$		−	263.464i		−	0.301791i
$874$	−184.432	−	128.790i	−0.211020	−	0.147357i
$875$	1319.28			1.50775
$876$	90.3132	−	248.133i	0.103097	−	0.283257i
$877$	−1422.91	+	250.898i	−1.62248	+	0.286087i	−0.909689	−	0.415290i	$-0.863680\pi$
$877$	−1422.91	+	250.898i	−1.62248	+	0.286087i	−0.712791	+	0.701377i	$0.752569\pi$
$878$	−78.9249	−	66.2259i	−0.0898917	−	0.0754281i
$879$	1394.18	−	1169.86i	1.58610	−	1.33090i
$880$	33.4070	−	189.461i	0.0379626	−	0.215296i
$881$	437.607	−	757.958i	0.496716	−	0.860338i	−0.503276	−	0.864125i	$-0.667872\pi$
$881$	437.607	−	757.958i	0.496716	−	0.860338i	0.999993	+	0.00378748i	$0.00120559\pi$
$882$	170.331	−	98.3407i	0.193119	−	0.111497i
$883$	373.459	−	135.928i	0.422943	−	0.153939i	−0.121775	−	0.992558i	$-0.538859\pi$
$883$	373.459	−	135.928i	0.422943	−	0.153939i	0.544719	+	0.838619i	$0.316637\pi$
$884$	220.882	+	606.869i	0.249867	+	0.686503i
$885$	−727.881	−	1260.73i	−0.822465	−	1.42455i
$886$	554.955	+	320.403i	0.626360	+	0.361629i
$887$	331.705	+	58.4885i	0.373962	+	0.0659396i	0.357471	−	0.933924i	$-0.383639\pi$
$887$	331.705	+	58.4885i	0.373962	+	0.0659396i	0.0164916	+	0.999864i	$0.494750\pi$
$888$	−118.161	−	140.819i	−0.133065	−	0.158580i
$889$	5.28617	−	6.29981i	0.00594620	−	0.00708640i
$890$	−114.289	−	648.166i	−0.128415	−	0.728277i
$891$	−502.178	−	182.778i	−0.563611	−	0.205138i
$892$			509.489i			0.571176i
$893$	604.059	+	602.519i	0.676438	+	0.674714i
$894$	−695.427			−0.777883
$895$	−31.1675	+	85.6319i	−0.0348240	+	0.0956781i
$896$	−56.8966	+	10.0324i	−0.0635007	+	0.0111969i
$897$	−311.930	−	261.741i	−0.347748	−	0.291795i
$898$	−567.643	+	476.309i	−0.632119	+	0.530411i
$899$	180.715	−	1024.88i	0.201018	−	1.14003i
$900$	−327.963	+	568.049i	−0.364403	+	0.631165i
$901$	−630.536	+	364.040i	−0.699818	+	0.404040i
$902$	−36.5493	+	13.3029i	−0.0405203	+	0.0147482i
$903$	−255.157	−	701.038i	−0.282566	−	0.776343i
$904$	177.941	+	308.202i	0.196837	+	0.340932i
$905$	1454.95	+	840.016i	1.60768	+	0.928194i
$906$	840.663	+	148.232i	0.927884	+	0.163611i
$907$	1053.26	+	1255.23i	1.16126	+	1.38394i	0.909271	+	0.416205i	$0.136640\pi$
$907$	1053.26	+	1255.23i	1.16126	+	1.38394i	0.251989	+	0.967730i	$0.418915\pi$
$908$	390.780	−	465.714i	0.430375	−	0.512901i
$909$	−31.3937	−	178.042i	−0.0345365	−	0.195866i
$910$	−756.088	−	275.194i	−0.830866	−	0.302411i
$911$		−	396.810i		−	0.435577i	−0.975996	−	0.217788i	$-0.930116\pi$
$911$		−	396.810i		−	0.435577i	0.975996	−	0.217788i	$-0.0698843\pi$
$912$	208.333	−	208.865i	0.228435	−	0.229019i
$913$	−384.582			−0.421229
$914$	−113.540	+	311.948i	−0.124223	+	0.341299i
$915$	−1684.49	+	297.021i	−1.84098	+	0.324614i
$916$	−608.717	−	510.774i	−0.664538	−	0.557614i
$917$	760.366	−	638.023i	0.829188	−	0.695772i
$918$	−72.0453	+	408.589i	−0.0784807	+	0.445086i
$919$	−267.955	+	464.111i	−0.291572	+	0.505018i	−0.974182	−	0.225766i	$-0.927512\pi$
$919$	−267.955	+	464.111i	−0.291572	+	0.505018i	0.682610	+	0.730783i	$0.260845\pi$
$920$	182.330	−	105.268i	0.198185	−	0.114422i
$921$	194.691	−	70.8617i	0.211391	−	0.0769399i
$922$	154.470	+	424.401i	0.167537	+	0.460305i
$923$	−375.861	−	651.011i	−0.407217	−	0.705320i
$924$	−185.714	−	107.222i	−0.200989	−	0.116041i
$925$	891.343	+	157.168i	0.963615	+	0.169911i
$926$	631.614	+	752.729i	0.682089	+	0.812882i
$927$	177.389	−	211.404i	0.191358	−	0.228052i
$928$	−46.4313	−	263.325i	−0.0500338	−	0.283756i
$929$	−41.9597	−	15.2721i	−0.0451665	−	0.0164393i	0.319338	−	0.947641i	$-0.396539\pi$
$929$	−41.9597	−	15.2721i	−0.0451665	−	0.0164393i	−0.364505	+	0.931202i	$0.618762\pi$
$930$			1074.62i			1.15551i
$931$	249.357	−	357.087i	0.267838	−	0.383552i
$932$	204.017			0.218902
$933$	584.993	−	1607.26i	0.627002	−	1.72267i
$934$	606.829	−	107.000i	0.649710	−	0.114561i
$935$	−949.439	−	796.674i	−1.01544	−	0.852058i
$936$	164.722	−	138.218i	0.175985	−	0.147669i
$937$	−285.568	+	1619.53i	−0.304768	+	1.72843i	0.319826	+	0.947476i	$0.396375\pi$
$937$	−285.568	+	1619.53i	−0.304768	+	1.72843i	−0.624594	+	0.780949i	$0.714736\pi$
$938$	−93.3626	+	161.709i	−0.0995337	+	0.172397i
$939$	−2034.38	+	1174.55i	−2.16654	+	1.25085i
$940$	−750.362	+	273.110i	−0.798258	+	0.290542i
$941$	−545.476	−	1498.68i	−0.579677	−	1.59265i	−0.788726	−	0.614745i	$-0.789259\pi$
$941$	−545.476	−	1498.68i	−0.579677	−	1.59265i	0.209049	−	0.977905i	$-0.432963\pi$
$942$	295.460	+	511.752i	0.313652	+	0.543262i
$943$	−36.8625	−	21.2825i	−0.0390906	−	0.0225690i
$944$	−166.157	−	29.2980i	−0.176014	−	0.0310360i
$945$	−332.262	−	395.974i	−0.351600	−	0.419020i
$946$	185.069	−	220.557i	0.195633	−	0.233146i
$947$	35.7341	+	202.658i	0.0377340	+	0.214000i	0.997845	−	0.0656202i	$-0.0209026\pi$
$947$	35.7341	+	202.658i	0.0377340	+	0.214000i	−0.960111	+	0.279620i	$0.909791\pi$
$948$	−532.739	−	193.901i	−0.561961	−	0.204537i
$949$		−	426.215i		−	0.449120i
$950$	−124.746	+	1447.13i	−0.131312	+	1.52329i
$951$	598.766			0.629617
$952$	−127.301	+	349.757i	−0.133720	+	0.367392i
$953$	161.981	−	28.5616i	0.169970	−	0.0299702i	−0.0880155	−	0.996119i	$-0.528053\pi$
$953$	161.981	−	28.5616i	0.169970	−	0.0299702i	0.257985	+	0.966149i	$0.416941\pi$
$954$	185.705	+	155.825i	0.194659	+	0.163338i
$955$	−9.74019	+	8.17299i	−0.0101991	+	0.00855810i
$956$	−127.825	+	724.929i	−0.133708	+	0.758294i
$957$	496.239	−	859.511i	0.518536	−	0.898130i
$958$	135.069	−	77.9819i	0.140990	−	0.0814007i
$959$	−872.300	+	317.491i	−0.909593	+	0.331065i
$960$	94.4331	+	259.453i	0.0983678	+	0.270263i
$961$	−238.127	−	412.448i	−0.247791	−	0.429186i
$962$	−256.961	−	148.357i	−0.267111	−	0.154217i
$963$	−1118.00	−	197.134i	−1.16096	−	0.204708i
$964$	85.7474	+	102.190i	0.0889496	+	0.106006i
$965$	−346.724	+	413.210i	−0.359300	+	0.428197i
$966$	−40.7516	−	231.114i	−0.0421860	−	0.239248i
$967$	−130.875	−	47.6346i	−0.135341	−	0.0492602i	0.273462	−	0.961883i	$-0.411831\pi$
$967$	−130.875	−	47.6346i	−0.135341	−	0.0492602i	−0.408803	+	0.912623i	$0.634054\pi$
$968$			259.479i			0.268057i
$969$	−494.234	−	1835.14i	−0.510046	−	1.89385i
$970$	546.040			0.562927
$971$	−80.4039	+	220.908i	−0.0828053	+	0.227506i	−0.974185	−	0.225752i	$-0.927516\pi$
$971$	−80.4039	+	220.908i	−0.0828053	+	0.227506i	0.891380	+	0.453258i	$0.149738\pi$
$972$	553.506	−	97.5981i	0.569451	−	0.100410i
$973$	599.820	+	503.309i	0.616465	+	0.517275i
$974$	485.318	−	407.230i	0.498273	−	0.418101i
$975$	−456.566	+	2589.32i	−0.468273	+	2.65571i
$976$	−99.1209	+	171.682i	−0.101558	+	0.175904i
$977$	186.217	−	107.512i	0.190601	−	0.110043i	−0.401663	−	0.915788i	$-0.631568\pi$
$977$	186.217	−	107.512i	0.190601	−	0.110043i	0.592264	+	0.805744i	$0.298234\pi$
$978$	−521.753	+	189.903i	−0.533490	+	0.194175i
$979$	−96.8375	−	266.059i	−0.0989147	−	0.271766i
$980$	203.815	+	353.018i	0.207975	+	0.360223i
$981$	−294.523	−	170.043i	−0.300227	−	0.173336i
$982$	−333.817	−	58.8610i	−0.339936	−	0.0599399i
$983$	426.057	+	507.756i	0.433426	+	0.516537i	0.937907	−	0.346886i	$-0.112761\pi$
$983$	426.057	+	507.756i	0.433426	+	0.516537i	−0.504482	+	0.863422i	$0.668316\pi$
$984$	35.8811	−	42.7614i	0.0364645	−	0.0434567i
$985$	−366.486	−	2078.45i	−0.372067	−	2.11010i
$986$	−1618.72	−	589.167i	−1.64171	−	0.597532i
$987$			890.086i			0.901809i
$988$	200.685	−	431.808i	0.203123	−	0.437053i
$989$	315.084			0.318588
$990$	−141.141	+	387.783i	−0.142567	+	0.391700i
$991$	251.249	−	44.3020i	0.253531	−	0.0447044i	−0.0454380	−	0.998967i	$-0.514468\pi$
$991$	251.249	−	44.3020i	0.253531	−	0.0447044i	0.298969	+	0.954263i	$0.403357\pi$
$992$	95.4083	+	80.0571i	0.0961778	+	0.0807027i
$993$	1546.88	−	1297.99i	1.55778	−	1.30714i
$994$	75.2314	−	426.658i	0.0756855	−	0.429234i
$995$	−1130.99	+	1958.93i	−1.13667	+	1.96877i
$996$	477.996	−	275.971i	0.479915	−	0.277079i
$997$	−1394.81	+	507.668i	−1.39900	+	0.509196i	−0.927882	−	0.372873i	$-0.878373\pi$
$997$	−1394.81	+	507.668i	−1.39900	+	0.509196i	−0.471121	+	0.882069i	$0.656150\pi$
$998$	218.619	+	600.651i	0.219057	+	0.601855i
$999$	−95.3088	−	165.080i	−0.0954043	−	0.165245i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.3.f.a.15.4	✓	24
3.2	odd	2		342.3.z.b.91.2		24
4.3	odd	2		304.3.z.c.129.1		24
19.9	even	9		722.3.b.f.721.14		24
19.10	odd	18		722.3.b.f.721.11		24
19.14	odd	18	inner	38.3.f.a.33.4	yes	24
57.14	even	18		342.3.z.b.109.2		24
76.71	even	18		304.3.z.c.33.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.3.f.a.15.4	✓	24	1.1	even	1	trivial
38.3.f.a.33.4	yes	24	19.14	odd	18	inner
304.3.z.c.33.1		24	76.71	even	18
304.3.z.c.129.1		24	4.3	odd	2
342.3.z.b.91.2		24	3.2	odd	2
342.3.z.b.109.2		24	57.14	even	18
722.3.b.f.721.11		24	19.10	odd	18
722.3.b.f.721.14		24	19.9	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	38.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.483690 - 1.32893i) q^{2} +(3.82266 - 0.674039i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(-6.81117 + 5.71525i) q^{5} +(0.953235 - 5.40606i) q^{6} +(2.55329 - 4.42243i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(5.70119 - 2.07506i) q^{9} +O(q^{10})\)	\(q+(0.483690 - 1.32893i) q^{2} +(3.82266 - 0.674039i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(-6.81117 + 5.71525i) q^{5} +(0.953235 - 5.40606i) q^{6} +(2.55329 - 4.42243i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(5.70119 - 2.07506i) q^{9} +(4.30065 + 11.8160i) q^{10} +(2.70464 + 4.68458i) q^{11} +(-6.72319 - 3.88163i) q^{12} +(-12.3403 - 2.17592i) q^{13} +(-4.64208 - 5.53221i) q^{14} +(-22.1845 + 26.4385i) q^{15} +(0.694593 + 3.93923i) q^{16} +(24.2154 + 8.81367i) q^{17} -8.58014i q^{18} +(-8.05172 - 17.2096i) q^{19} +17.7827 q^{20} +(6.77948 - 18.6265i) q^{21} +(7.53367 - 1.32839i) q^{22} +(6.41312 + 5.38124i) q^{23} +(-8.41034 + 7.05711i) q^{24} +(9.38676 - 53.2349i) q^{25} +(-8.86051 + 15.3469i) q^{26} +(-9.85929 + 5.69226i) q^{27} +(-9.59723 + 3.49311i) q^{28} +(-16.1666 - 44.4173i) q^{29} +(24.4044 + 42.2696i) q^{30} +(19.0672 + 11.0085i) q^{31} +(5.57091 + 0.982302i) q^{32} +(13.4965 + 16.0845i) q^{33} +(23.4254 - 27.9174i) q^{34} +(7.88439 + 44.7146i) q^{35} +(-11.4024 - 4.15013i) q^{36} +16.7436i q^{37} +(-26.7648 + 2.37604i) q^{38} -48.6394 q^{39} +(8.60131 - 23.6319i) q^{40} +(-5.00714 + 0.882894i) q^{41} +(-21.4740 - 18.0188i) q^{42} +(28.8313 - 24.1924i) q^{43} +(1.87863 - 10.6542i) q^{44} +(-26.9723 + 46.7173i) q^{45} +(10.2532 - 5.91971i) q^{46} +(-42.1962 + 15.3582i) q^{47} +(5.31039 + 14.5902i) q^{48} +(11.4614 + 19.8518i) q^{49} +(-66.2050 - 38.2235i) q^{50} +(98.5079 + 17.3696i) q^{51} +(16.1091 + 19.1981i) q^{52} +(-18.1611 + 21.6435i) q^{53} +(2.79576 + 15.8556i) q^{54} +(-45.1953 - 16.4498i) q^{55} +14.4436i q^{56} +(-42.3789 - 60.3593i) q^{57} -66.8469 q^{58} +(-14.4265 + 39.6364i) q^{59} +(67.9773 - 11.9862i) q^{60} +(37.9655 + 31.8568i) q^{61} +(23.8521 - 20.0143i) q^{62} +(5.37997 - 30.5113i) q^{63} +(4.00000 - 6.92820i) q^{64} +(96.4878 - 55.7072i) q^{65} +(27.9033 - 10.1560i) q^{66} +(-8.84321 - 24.2965i) q^{67} +(-25.7695 - 44.6340i) q^{68} +(28.1424 + 16.2480i) q^{69} +(63.2360 + 11.1502i) q^{70} +(38.5613 + 45.9555i) q^{71} +(-11.0304 + 13.1455i) q^{72} +(5.90643 + 33.4970i) q^{73} +(22.2510 + 8.09869i) q^{74} -209.826i q^{75} +(-9.78827 + 36.7177i) q^{76} +27.6229 q^{77} +(-23.5264 + 64.6382i) q^{78} +(71.9176 - 12.6810i) q^{79} +(-27.2447 - 22.8610i) q^{80} +(-75.6808 + 63.5037i) q^{81} +(-1.24860 + 7.08117i) q^{82} +(-35.5483 + 61.5715i) q^{83} +(-34.3325 + 19.8219i) q^{84} +(-215.307 + 78.3655i) q^{85} +(-18.2045 - 50.0163i) q^{86} +(-91.7383 - 158.895i) q^{87} +(-13.2500 - 7.64989i) q^{88} +(-51.5470 - 9.08913i) q^{89} +(49.0377 + 58.4408i) q^{90} +(-41.1312 + 49.0182i) q^{91} +(-2.90747 - 16.4891i) q^{92} +(80.3078 + 29.2296i) q^{93} +63.5042i q^{94} +(153.199 + 71.1999i) q^{95} +21.9578 q^{96} +(14.8523 - 40.8063i) q^{97} +(31.9253 - 5.62929i) q^{98} +(25.1405 + 21.0954i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} + 12 q^{6} - 18 q^{7} + 6 q^{9}+O(q^{10}) \) 24 * q - 6 * q^3 + 12 * q^6 - 18 * q^7 + 6 * q^9	\( 24 q - 6 q^{3} + 12 q^{6} - 18 q^{7} + 6 q^{9} + 30 q^{11} - 36 q^{12} - 90 q^{13} - 48 q^{14} - 114 q^{15} + 18 q^{17} - 12 q^{19} + 24 q^{20} + 90 q^{21} + 84 q^{22} + 120 q^{23} - 24 q^{24} + 252 q^{25} + 48 q^{26} + 126 q^{27} + 72 q^{28} - 210 q^{29} - 108 q^{31} - 132 q^{33} - 24 q^{34} - 66 q^{35} - 12 q^{36} + 84 q^{38} + 120 q^{39} + 54 q^{41} + 72 q^{42} + 90 q^{43} - 48 q^{44} - 144 q^{45} - 360 q^{46} - 246 q^{47} - 48 q^{48} + 54 q^{49} - 432 q^{50} - 342 q^{51} + 36 q^{52} - 174 q^{53} - 42 q^{55} - 12 q^{57} + 48 q^{58} + 228 q^{59} + 132 q^{60} + 12 q^{61} + 204 q^{62} + 174 q^{63} + 96 q^{64} + 630 q^{65} + 696 q^{66} + 72 q^{67} - 48 q^{68} + 702 q^{69} + 528 q^{70} + 432 q^{71} + 96 q^{72} - 144 q^{74} + 72 q^{76} - 144 q^{77} - 708 q^{78} - 246 q^{79} - 642 q^{81} - 384 q^{82} - 126 q^{83} - 540 q^{84} - 684 q^{85} - 12 q^{86} - 324 q^{87} - 12 q^{89} - 336 q^{90} + 372 q^{91} - 132 q^{92} - 168 q^{93} - 570 q^{95} + 72 q^{97} + 384 q^{98} - 204 q^{99}+O(q^{100}) \) 24 * q - 6 * q^3 + 12 * q^6 - 18 * q^7 + 6 * q^9 + 30 * q^11 - 36 * q^12 - 90 * q^13 - 48 * q^14 - 114 * q^15 + 18 * q^17 - 12 * q^19 + 24 * q^20 + 90 * q^21 + 84 * q^22 + 120 * q^23 - 24 * q^24 + 252 * q^25 + 48 * q^26 + 126 * q^27 + 72 * q^28 - 210 * q^29 - 108 * q^31 - 132 * q^33 - 24 * q^34 - 66 * q^35 - 12 * q^36 + 84 * q^38 + 120 * q^39 + 54 * q^41 + 72 * q^42 + 90 * q^43 - 48 * q^44 - 144 * q^45 - 360 * q^46 - 246 * q^47 - 48 * q^48 + 54 * q^49 - 432 * q^50 - 342 * q^51 + 36 * q^52 - 174 * q^53 - 42 * q^55 - 12 * q^57 + 48 * q^58 + 228 * q^59 + 132 * q^60 + 12 * q^61 + 204 * q^62 + 174 * q^63 + 96 * q^64 + 630 * q^65 + 696 * q^66 + 72 * q^67 - 48 * q^68 + 702 * q^69 + 528 * q^70 + 432 * q^71 + 96 * q^72 - 144 * q^74 + 72 * q^76 - 144 * q^77 - 708 * q^78 - 246 * q^79 - 642 * q^81 - 384 * q^82 - 126 * q^83 - 540 * q^84 - 684 * q^85 - 12 * q^86 - 324 * q^87 - 12 * q^89 - 336 * q^90 + 372 * q^91 - 132 * q^92 - 168 * q^93 - 570 * q^95 + 72 * q^97 + 384 * q^98 - 204 * q^99

Introduction

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