LMFDB - Embedded newform 19.3.f.a.10.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [19,3,Mod(2,19)] 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("19.2"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(19, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	19.f (of order $18$, degree $6$, 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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 24x^{10} + 216x^{8} + 905x^{6} + 1770x^{4} + 1395x^{2} + 361 $ x^12 + 24x^10 + 216x^8 + 905x^6 + 1770x^4 + 1395*x^2 + 361
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			10.1
Root			$-2.88811i$ of defining polynomial
Character	$\chi$	$=$	19.10
Dual form			19.3.f.a.2.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.84423 + 0.501515i) q^{2} +(3.28392 + 3.91363i) q^{3} +(4.07936 - 1.48477i) q^{4} +(-3.00117 - 1.09234i) q^{5} +(-11.3030 - 9.48432i) q^{6} +(3.87208 - 6.70664i) q^{7} +(-0.853313 + 0.492661i) q^{8} +(-2.96949 + 16.8408i) q^{9} +(9.08386 + 1.60173i) q^{10} +(-3.45312 - 5.98097i) q^{11} +(19.2071 + 11.0892i) q^{12} +(3.92326 - 4.67556i) q^{13} +(-7.64961 + 21.0171i) q^{14} +(-5.58062 - 15.3326i) q^{15} +(-11.1222 + 9.33260i) q^{16} +(0.218340 + 1.23827i) q^{17} -49.3885i q^{18} +(-12.9229 + 13.9283i) q^{19} -13.8647 q^{20} +(38.9629 - 6.87021i) q^{21} +(12.8210 + 15.2795i) q^{22} +(-1.77889 + 0.647464i) q^{23} +(-4.73030 - 1.72169i) q^{24} +(-11.3373 - 9.51310i) q^{25} +(-8.81380 + 15.2659i) q^{26} +(-35.8406 + 20.6926i) q^{27} +(5.83782 - 33.1079i) q^{28} +(11.5950 + 2.04451i) q^{29} +(23.5621 + 40.8108i) q^{30} +(-24.9929 - 14.4296i) q^{31} +(29.4870 - 35.1412i) q^{32} +(12.0675 - 33.1553i) q^{33} +(-1.24202 - 3.41242i) q^{34} +(-18.9467 + 15.8982i) q^{35} +(12.8911 + 73.1088i) q^{36} +43.6204i q^{37} +(29.7704 - 46.0964i) q^{38} +31.1821 q^{39} +(3.09909 - 0.546454i) q^{40} +(19.6019 + 23.3607i) q^{41} +(-107.374 + 39.0809i) q^{42} +(-5.57351 - 2.02859i) q^{43} +(-22.9668 - 19.2715i) q^{44} +(27.3079 - 47.2986i) q^{45} +(4.73487 - 2.73368i) q^{46} +(13.9320 - 79.0123i) q^{47} +(-73.0486 - 12.8804i) q^{48} +(-5.48600 - 9.50203i) q^{49} +(37.0168 + 21.3716i) q^{50} +(-4.12911 + 4.92088i) q^{51} +(9.06229 - 24.8984i) q^{52} +(26.8107 + 73.6617i) q^{53} +(91.5612 - 76.8290i) q^{54} +(3.83016 + 21.7219i) q^{55} +7.63048i q^{56} +(-96.9481 - 4.83580i) q^{57} -34.0042 q^{58} +(-74.2124 + 13.0856i) q^{59} +(-45.5307 - 54.2614i) q^{60} +(26.7312 - 9.72936i) q^{61} +(78.3222 + 28.5069i) q^{62} +(101.447 + 85.1244i) q^{63} +(-37.2060 + 64.4427i) q^{64} +(-16.8817 + 9.74665i) q^{65} +(-17.6950 + 100.353i) q^{66} +(126.717 + 22.3436i) q^{67} +(2.72923 + 4.72716i) q^{68} +(-8.37569 - 4.83570i) q^{69} +(45.9156 - 54.7201i) q^{70} +(-1.86033 + 5.11121i) q^{71} +(-5.76291 - 15.8335i) q^{72} +(3.22765 - 2.70832i) q^{73} +(-21.8763 - 124.067i) q^{74} -75.6101i q^{75} +(-32.0368 + 76.0062i) q^{76} -53.4830 q^{77} +(-88.6891 + 15.6383i) q^{78} +(-57.2275 - 68.2011i) q^{79} +(43.5739 - 15.8596i) q^{80} +(-54.0567 - 19.6750i) q^{81} +(-67.4681 - 56.6125i) q^{82} +(10.4759 - 18.1448i) q^{83} +(148.743 - 85.8768i) q^{84} +(0.697331 - 3.95476i) q^{85} +(16.8697 + 2.97458i) q^{86} +(30.0757 + 52.0926i) q^{87} +(5.89318 + 3.40243i) q^{88} +(-94.4270 + 112.534i) q^{89} +(-53.9489 + 148.223i) q^{90} +(-16.1661 - 44.4160i) q^{91} +(-6.29542 + 5.28248i) q^{92} +(-25.6024 - 145.199i) q^{93} +231.716i q^{94} +(53.9983 - 27.6852i) q^{95} +234.362 q^{96} +(68.4359 - 12.0671i) q^{97} +(20.3688 + 24.2746i) q^{98} +(110.979 - 40.3929i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{5} - 36 q^{6} + 6 q^{7} - 9 q^{8} - 24 q^{9} + 51 q^{10} - 18 q^{11} + 63 q^{12} + 21 q^{13} + 9 q^{14} + 63 q^{15} - 12 q^{16} - 3 q^{17} - 24 q^{19} - 90 q^{20} + 30 q^{21} - 78 q^{22}+ \cdots + 462 q^{99}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^5 - 36 * q^6 + 6 * q^7 - 9 * q^8 - 24 * q^9 + 51 * q^10 - 18 * q^11 + 63 * q^12 + 21 * q^13 + 9 * q^14 + 63 * q^15 - 12 * q^16 - 3 * q^17 - 24 * q^19 - 90 * q^20 + 30 * q^21 - 78 * q^22 - 102 * q^23 - 12 * q^24 - 156 * q^25 + 21 * q^26 - 27 * q^27 + 12 * q^28 + 147 * q^29 + 24 * q^30 + 99 * q^31 + 165 * q^32 + 84 * q^33 + 132 * q^34 + 96 * q^35 + 63 * q^36 + 72 * q^38 - 108 * q^39 - 138 * q^40 - 144 * q^41 - 237 * q^42 - 27 * q^43 - 123 * q^44 - 3 * q^45 - 54 * q^46 - 99 * q^47 - 51 * q^48 - 24 * q^49 + 72 * q^50 - 42 * q^51 + 93 * q^52 + 111 * q^53 + 21 * q^54 + 162 * q^55 - 168 * q^57 - 132 * q^58 + 3 * q^59 - 30 * q^60 + 150 * q^61 + 108 * q^62 + 234 * q^63 + 27 * q^64 + 126 * q^65 + 168 * q^66 + 135 * q^67 - 30 * q^68 + 72 * q^69 + 225 * q^70 - 168 * q^71 - 102 * q^72 - 90 * q^73 - 231 * q^74 + 42 * q^76 + 246 * q^77 - 189 * q^78 - 75 * q^79 + 21 * q^80 - 159 * q^81 - 117 * q^82 - 156 * q^83 + 99 * q^84 - 300 * q^85 - 144 * q^86 + 69 * q^87 - 405 * q^88 - 558 * q^89 - 66 * q^90 - 453 * q^91 + 48 * q^92 - 57 * q^93 - 69 * q^95 + 558 * q^96 + 465 * q^97 + 777 * q^98 + 462 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−2.84423	+	0.501515i	−1.42212	+	0.250757i	−0.831199	−	0.555975i	$-0.812345\pi$
$2$	−2.84423	+	0.501515i	−1.42212	+	0.250757i	−0.590917	+	0.806733i	$0.701234\pi$
$3$	3.28392	+	3.91363i	1.09464	+	1.30454i	0.949025	+	0.315201i	$0.102072\pi$
$3$	3.28392	+	3.91363i	1.09464	+	1.30454i	0.145616	+	0.989341i	$0.453484\pi$
$4$	4.07936	−	1.48477i	1.01984	−	0.371191i
$5$	−3.00117	−	1.09234i	−0.600235	−	0.218468i	0.0239902	−	0.999712i	$-0.492363\pi$
$5$	−3.00117	−	1.09234i	−0.600235	−	0.218468i	−0.624225	+	0.781245i	$0.714585\pi$
$6$	−11.3030	−	9.48432i	−1.88383	−	1.58072i
$7$	3.87208	−	6.70664i	0.553154	−	0.958091i	−0.444890	−	0.895585i	$-0.646757\pi$
$7$	3.87208	−	6.70664i	0.553154	−	0.958091i	0.998045	−	0.0625061i	$-0.0199093\pi$
$8$	−0.853313	+	0.492661i	−0.106664	+	0.0615826i
$9$	−2.96949	+	16.8408i	−0.329944	+	1.87120i
$10$	9.08386	+	1.60173i	0.908386	+	0.160173i
$11$	−3.45312	−	5.98097i	−0.313920	−	0.543725i	0.665288	−	0.746587i	$-0.268309\pi$
$11$	−3.45312	−	5.98097i	−0.313920	−	0.543725i	−0.979207	+	0.202862i	$0.934976\pi$
$12$	19.2071	+	11.0892i	1.60059	+	0.924103i
$13$	3.92326	−	4.67556i	0.301789	−	0.359659i	−0.593743	−	0.804655i	$-0.702350\pi$
$13$	3.92326	−	4.67556i	0.301789	−	0.359659i	0.895533	+	0.444996i	$0.146795\pi$
$14$	−7.64961	+	21.0171i	−0.546401	+	1.50122i
$15$	−5.58062	−	15.3326i	−0.372041	−	1.02218i
$16$	−11.1222	+	9.33260i	−0.695135	+	0.583287i
$17$	0.218340	+	1.23827i	0.0128435	+	0.0728393i	0.990556	−	0.137110i	$-0.0437813\pi$
$17$	0.218340	+	1.23827i	0.0128435	+	0.0728393i	−0.977712	+	0.209949i	$0.932670\pi$
$18$		−	49.3885i		−	2.74380i
$19$	−12.9229	+	13.9283i	−0.680153	+	0.733071i
$19$	−12.9229	+	13.9283i	−0.680153	+	0.733071i
$20$	−13.8647			−0.693237
$21$	38.9629	−	6.87021i	1.85538	−	0.327153i
$22$	12.8210	+	15.2795i	0.582773	+	0.694522i
$23$	−1.77889	+	0.647464i	−0.0773432	+	0.0281506i	−0.380402	−	0.924821i	$-0.624214\pi$
$23$	−1.77889	+	0.647464i	−0.0773432	+	0.0281506i	0.303059	+	0.952972i	$0.401992\pi$
$24$	−4.73030	−	1.72169i	−0.197096	−	0.0717371i
$25$	−11.3373	−	9.51310i	−0.453491	−	0.380524i
$26$	−8.81380	+	15.2659i	−0.338992	+	0.587152i
$27$	−35.8406	+	20.6926i	−1.32743	+	0.766391i
$28$	5.83782	−	33.1079i	0.208494	−	1.18243i
$29$	11.5950	+	2.04451i	0.399828	+	0.0705005i	0.369947	−	0.929053i	$-0.379376\pi$
$29$	11.5950	+	2.04451i	0.399828	+	0.0705005i	0.0298814	+	0.999553i	$0.490487\pi$
$30$	23.5621	+	40.8108i	0.785404	+	1.36036i
$31$	−24.9929	−	14.4296i	−0.806222	−	0.465472i	0.0394204	−	0.999223i	$-0.487449\pi$
$31$	−24.9929	−	14.4296i	−0.806222	−	0.465472i	−0.845642	+	0.533750i	$0.820782\pi$
$32$	29.4870	−	35.1412i	0.921467	−	1.09816i
$33$	12.0675	−	33.1553i	0.365683	−	1.00470i
$34$	−1.24202	−	3.41242i	−0.0365300	−	0.100365i
$35$	−18.9467	+	15.8982i	−0.541334	+	0.454233i
$36$	12.8911	+	73.1088i	0.358085	+	2.03080i
$37$			43.6204i			1.17893i	0.807794	+	0.589465i	$0.200662\pi$
$37$			43.6204i			1.17893i	−0.807794	+	0.589465i	$0.799338\pi$
$38$	29.7704	−	46.0964i	0.783432	−	1.21306i
$39$	31.1821			0.799541
$40$	3.09909	−	0.546454i	0.0774773	−	0.0136613i
$41$	19.6019	+	23.3607i	0.478096	+	0.569773i	0.950148	−	0.311798i	$-0.100931\pi$
$41$	19.6019	+	23.3607i	0.478096	+	0.569773i	−0.472053	+	0.881570i	$0.656487\pi$
$42$	−107.374	+	39.0809i	−2.55652	+	0.930498i
$43$	−5.57351	−	2.02859i	−0.129616	−	0.0471765i	0.276398	−	0.961043i	$-0.410859\pi$
$43$	−5.57351	−	2.02859i	−0.129616	−	0.0471765i	−0.406014	+	0.913867i	$0.633082\pi$
$44$	−22.9668	−	19.2715i	−0.521974	−	0.437988i
$45$	27.3079	−	47.2986i	0.606841	−	1.05108i
$46$	4.73487	−	2.73368i	0.102932	−	0.0594278i
$47$	13.9320	−	79.0123i	0.296426	−	1.68111i	−0.364926	−	0.931037i	$-0.618906\pi$
$47$	13.9320	−	79.0123i	0.296426	−	1.68111i	0.661351	−	0.750076i	$-0.269983\pi$
$48$	−73.0486	−	12.8804i	−1.52185	−	0.268343i
$49$	−5.48600	−	9.50203i	−0.111959	−	0.193919i
$50$	37.0168	+	21.3716i	0.740335	+	0.427433i
$51$	−4.12911	+	4.92088i	−0.0809629	+	0.0964879i
$52$	9.06229	−	24.8984i	0.174275	−	0.478816i
$53$	26.8107	+	73.6617i	0.505862	+	1.38984i	0.885470	+	0.464696i	$0.153837\pi$
$53$	26.8107	+	73.6617i	0.505862	+	1.38984i	−0.379608	+	0.925147i	$0.623941\pi$
$54$	91.5612	−	76.8290i	1.69558	−	1.42276i
$55$	3.83016	+	21.7219i	0.0696393	+	0.394944i
$56$			7.63048i			0.136259i
$57$	−96.9481	−	4.83580i	−1.70084	−	0.0848386i
$58$	−34.0042			−0.586280
$59$	−74.2124	+	13.0856i	−1.25784	+	0.221791i	−0.762544	−	0.646936i	$-0.776050\pi$
$59$	−74.2124	+	13.0856i	−1.25784	+	0.221791i	−0.495292	+	0.868726i	$0.664939\pi$
$60$	−45.5307	−	54.2614i	−0.758846	−	0.904357i
$61$	26.7312	−	9.72936i	0.438216	−	0.159498i	−0.113485	−	0.993540i	$-0.536201\pi$
$61$	26.7312	−	9.72936i	0.438216	−	0.159498i	0.551701	+	0.834042i	$0.313979\pi$
$62$	78.3222	+	28.5069i	1.26326	+	0.459789i
$63$	101.447	+	85.1244i	1.61027	+	1.35118i
$64$	−37.2060	+	64.4427i	−0.581344	+	1.00692i
$65$	−16.8817	+	9.74665i	−0.259718	+	0.149948i
$66$	−17.6950	+	100.353i	−0.268106	+	1.52050i
$67$	126.717	+	22.3436i	1.89130	+	0.333487i	0.994129	−	0.108204i	$-0.0345099\pi$
$67$	126.717	+	22.3436i	1.89130	+	0.333487i	0.897168	+	0.441690i	$0.145621\pi$
$68$	2.72923	+	4.72716i	0.0401357	+	0.0695171i
$69$	−8.37569	−	4.83570i	−0.121387	−	0.0700827i
$70$	45.9156	−	54.7201i	0.655938	−	0.781716i
$71$	−1.86033	+	5.11121i	−0.0262018	+	0.0719889i	−0.952104	−	0.305775i	$-0.901085\pi$
$71$	−1.86033	+	5.11121i	−0.0262018	+	0.0719889i	0.925902	+	0.377764i	$0.123307\pi$
$72$	−5.76291	−	15.8335i	−0.0800404	−	0.219909i
$73$	3.22765	−	2.70832i	0.0442143	−	0.0371002i	−0.620413	−	0.784275i	$-0.713035\pi$
$73$	3.22765	−	2.70832i	0.0442143	−	0.0371002i	0.664627	+	0.747175i	$0.268590\pi$
$74$	−21.8763	−	124.067i	−0.295625	−	1.67658i
$75$		−	75.6101i		−	1.00813i
$76$	−32.0368	+	76.0062i	−0.421537	+	1.00008i
$77$	−53.4830			−0.694584
$78$	−88.6891	+	15.6383i	−1.13704	+	0.200491i
$79$	−57.2275	−	68.2011i	−0.724399	−	0.863305i	0.270652	−	0.962677i	$-0.412761\pi$
$79$	−57.2275	−	68.2011i	−0.724399	−	0.863305i	−0.995050	+	0.0993726i	$0.968316\pi$
$80$	43.5739	−	15.8596i	0.544674	−	0.198245i
$81$	−54.0567	−	19.6750i	−0.667366	−	0.242901i
$82$	−67.4681	−	56.6125i	−0.822782	−	0.690396i
$83$	10.4759	−	18.1448i	0.126215	−	0.218611i	−0.795992	−	0.605307i	$-0.793050\pi$
$83$	10.4759	−	18.1448i	0.126215	−	0.218611i	0.922207	+	0.386696i	$0.126384\pi$
$84$	148.743	−	85.8768i	1.77075	−	1.02234i
$85$	0.697331	−	3.95476i	0.00820390	−	0.0465266i
$86$	16.8697	+	2.97458i	0.196159	+	0.0345882i
$87$	30.0757	+	52.0926i	0.345697	+	0.598765i
$88$	5.89318	+	3.40243i	0.0669679	+	0.0386640i
$89$	−94.4270	+	112.534i	−1.06098	+	1.26442i	−0.0979005	+	0.995196i	$0.531213\pi$
$89$	−94.4270	+	112.534i	−1.06098	+	1.26442i	−0.963077	+	0.269227i	$0.913232\pi$
$90$	−53.9489	+	148.223i	−0.599432	+	1.64693i
$91$	−16.1661	−	44.4160i	−0.177650	−	0.488088i
$92$	−6.29542	+	5.28248i	−0.0684284	+	0.0574183i
$93$	−25.6024	−	145.199i	−0.275295	−	1.56128i
$94$			231.716i			2.46507i
$95$	53.9983	−	27.6852i	0.568403	−	0.291423i
$96$	234.362			2.44128
$97$	68.4359	−	12.0671i	0.705525	−	0.124403i	0.190637	−	0.981661i	$-0.438945\pi$
$97$	68.4359	−	12.0671i	0.705525	−	0.124403i	0.514888	+	0.857257i	$0.327834\pi$
$98$	20.3688	+	24.2746i	0.207845	+	0.247700i
$99$	110.979	−	40.3929i	1.12100	−	0.408009i
$100$	−60.3735	−	21.9742i	−0.603735	−	0.219742i
$101$	−21.1489	−	17.7460i	−0.209395	−	0.175703i	0.532058	−	0.846708i	$-0.321419\pi$
$101$	−21.1489	−	17.7460i	−0.209395	−	0.175703i	−0.741453	+	0.671004i	$0.765863\pi$
$102$	9.27625	−	16.0669i	0.0909436	−	0.157519i
$103$	−112.587	+	65.0023i	−1.09308	+	0.631090i	−0.934395	−	0.356239i	$-0.884059\pi$
$103$	−112.587	+	65.0023i	−1.09308	+	0.631090i	−0.158686	+	0.987329i	$0.550726\pi$
$104$	−1.04431	+	5.92255i	−0.0100414	+	0.0569476i
$105$	−124.439	−	21.9420i	−1.18513	−	0.208971i
$106$	−113.198	−	196.065i	−1.06791	−	1.84967i
$107$	69.4189	+	40.0790i	0.648775	+	0.374570i	0.787987	−	0.615692i	$-0.211124\pi$
$107$	69.4189	+	40.0790i	0.648775	+	0.374570i	−0.139212	+	0.990263i	$0.544457\pi$
$108$	−115.483	+	137.627i	−1.06929	+	1.27433i
$109$	36.3809	−	99.9557i	0.333770	−	0.917025i	−0.653352	−	0.757054i	$-0.726638\pi$
$109$	36.3809	−	99.9557i	0.333770	−	0.917025i	0.987122	−	0.159970i	$-0.0511399\pi$
$110$	−21.7877	−	59.8612i	−0.198070	−	0.544193i
$111$	−170.714	+	143.246i	−1.53797	+	1.29051i
$112$	19.5245	+	110.729i	0.174326	+	0.988651i
$113$		−	37.9540i		−	0.335876i	−0.985798	−	0.167938i	$-0.946289\pi$
$113$		−	37.9540i		−	0.335876i	0.985798	−	0.167938i	$-0.0537109\pi$
$114$	278.168	−	34.8668i	2.44007	−	0.305849i
$115$	6.04602			0.0525741
$116$	50.3359	−	8.87557i	0.433930	−	0.0765136i
$117$	67.0902	+	79.9550i	0.573421	+	0.683376i
$118$	204.514	−	74.4372i	1.73317	−	0.630823i
$119$	9.15005	+	3.33035i	0.0768912	+	0.0279861i
$120$	12.3158	+	10.3342i	0.102632	+	0.0861182i
$121$	36.6520	−	63.4831i	0.302909	−	0.524654i
$122$	−71.1503	+	41.0786i	−0.583199	+	0.336710i
$123$	−27.0537	+	153.429i	−0.219949	+	1.24739i
$124$	−123.380	−	21.7551i	−0.994997	−	0.175445i
$125$	63.5559	+	110.082i	0.508447	+	0.880656i
$126$	−331.231	−	191.236i	−2.62881	−	1.51775i
$127$	46.2134	−	55.0750i	0.363885	−	0.433662i	−0.552774	−	0.833331i	$-0.686431\pi$
$127$	46.2134	−	55.0750i	0.363885	−	0.433662i	0.916659	+	0.399670i	$0.130875\pi$
$128$	10.7448	−	29.5210i	0.0839435	−	0.230633i
$129$	−10.3638	−	28.4744i	−0.0803397	−	0.220732i
$130$	43.1273	−	36.1881i	0.331749	−	0.278370i
$131$	−20.7857	−	117.882i	−0.158670	−	0.899861i	−0.955354	−	0.295465i	$-0.904525\pi$
$131$	−20.7857	−	117.882i	−0.158670	−	0.899861i	0.796684	−	0.604396i	$-0.206586\pi$
$132$		−	153.170i		−	1.16038i
$133$	43.3739	+	140.601i	0.326119	+	1.05715i
$134$	−371.618			−2.77327
$135$	130.167	−	22.9520i	0.964201	−	0.170015i
$136$	−0.796359	−	0.949063i	−0.00585558	−	0.00697841i
$137$	−154.803	+	56.3435i	−1.12995	+	0.411267i	−0.838273	−	0.545251i	$-0.816434\pi$
$137$	−154.803	+	56.3435i	−1.12995	+	0.411267i	−0.291673	+	0.956518i	$0.594212\pi$
$138$	26.2476	+	9.55333i	0.190200	+	0.0692270i
$139$	162.817	+	136.619i	1.17134	+	0.982873i	0.999997	−	0.00233796i	$-0.000744198\pi$
$139$	162.817	+	136.619i	1.17134	+	0.982873i	0.171345	+	0.985211i	$0.445189\pi$
$140$	−53.6854	+	92.9858i	−0.383467	+	0.664184i
$141$	354.976	−	204.946i	2.51756	−	1.45352i
$142$	2.72786	−	15.4704i	0.0192103	−	0.108947i
$143$	−41.5119	−	7.31966i	−0.290293	−	0.0511865i
$144$	−124.142	−	215.020i	−0.862094	−	1.49319i
$145$	−32.5654	−	18.8016i	−0.224589	−	0.129666i
$146$	−7.82191	+	9.32179i	−0.0535747	+	0.0638479i
$147$	19.1718	−	52.6741i	0.130420	−	0.358327i
$148$	64.7661	+	177.943i	0.437609	+	1.20232i
$149$	−44.5956	+	37.4201i	−0.299299	+	0.251142i	−0.780053	−	0.625714i	$-0.784808\pi$
$149$	−44.5956	+	37.4201i	−0.299299	+	0.251142i	0.480753	+	0.876856i	$0.340363\pi$
$150$	37.9196	+	215.053i	0.252797	+	1.43368i
$151$		−	54.6073i		−	0.361638i	−0.983516	−	0.180819i	$-0.942125\pi$
$151$		−	54.6073i		−	0.361638i	0.983516	−	0.180819i	$-0.0578748\pi$
$152$	4.16533	−	18.2518i	0.0274035	−	0.120078i
$153$	−21.5018			−0.140535
$154$	152.118	−	26.8225i	0.987778	−	0.174172i
$155$	59.2459	+	70.6065i	0.382232	+	0.455526i
$156$	127.203	−	46.2981i	0.815404	−	0.296783i
$157$	16.6392	+	6.05619i	0.105982	+	0.0385745i	0.394467	−	0.918910i	$-0.370929\pi$
$157$	16.6392	+	6.05619i	0.105982	+	0.0385745i	−0.288485	+	0.957485i	$0.593151\pi$
$158$	196.972	+	165.279i	1.24666	+	1.04607i
$159$	−200.240	+	346.826i	−1.25937	+	2.18130i
$160$	−126.882	+	73.2551i	−0.793010	+	0.457844i
$161$	−2.54571	+	14.4374i	−0.0158119	+	0.0896735i
$162$	163.617	+	28.8501i	1.00998	+	0.178087i
$163$	−101.967	−	176.611i	−0.625562	−	1.08351i	−0.988432	−	0.151666i	$-0.951536\pi$
$163$	−101.967	−	176.611i	−0.625562	−	1.08351i	0.362869	−	0.931840i	$-0.381797\pi$
$164$	114.648	+	66.1923i	0.699076	+	0.403612i
$165$	−72.4335	+	86.3229i	−0.438991	+	0.523169i
$166$	−20.6960	+	56.8617i	−0.124674	+	0.342540i
$167$	−88.9415	−	244.365i	−0.532584	−	1.46326i	−0.855985	−	0.517000i	$-0.827049\pi$
$167$	−88.9415	−	244.365i	−0.532584	−	1.46326i	0.323402	−	0.946262i	$-0.395173\pi$
$168$	−29.8629	+	25.0579i	−0.177755	+	0.149154i
$169$	22.8777	+	129.746i	0.135371	+	0.767726i
$170$			11.5980i			0.0682234i
$171$	−196.190	−	258.992i	−1.14731	−	1.51458i
$172$	−25.7483			−0.149700
$173$	−82.0048	+	14.4597i	−0.474016	+	0.0835819i	−0.405553	−	0.914072i	$-0.632921\pi$
$173$	−82.0048	+	14.4597i	−0.474016	+	0.0835819i	−0.0684637	+	0.997654i	$0.521810\pi$
$174$	−111.667	−	133.080i	−0.641766	−	0.764827i
$175$	−107.700	+	39.1995i	−0.615427	+	0.223997i
$176$	94.2241	+	34.2948i	0.535364	+	0.194857i
$177$	−294.920	−	247.467i	−1.66621	−	1.39812i
$178$	212.135	−	367.428i	1.19177	−	2.06420i
$179$	196.975	−	113.723i	1.10042	−	0.635327i	0.164087	−	0.986446i	$-0.447532\pi$
$179$	196.975	−	113.723i	1.10042	−	0.635327i	0.936331	+	0.351119i	$0.114199\pi$
$180$	41.1713	−	233.494i	0.228729	−	1.29719i
$181$	37.4457	+	6.60269i	0.206883	+	0.0364790i	0.276129	−	0.961121i	$-0.410948\pi$
$181$	37.4457	+	6.60269i	0.206883	+	0.0364790i	−0.0692463	+	0.997600i	$0.522059\pi$
$182$	68.2555	+	118.222i	0.375030	+	0.649571i
$183$	125.860	+	72.6655i	0.687761	+	0.397079i
$184$	1.19897	−	1.42888i	0.00651616	−	0.00776566i
$185$	47.6483	−	130.913i	0.257558	−	0.707635i
$186$	145.638	+	400.138i	0.783002	+	2.15128i
$187$	6.65210	−	5.58177i	0.0355727	−	0.0298491i
$188$	−60.4811	−	343.005i	−0.321708	−	1.82450i
$189$			320.493i			1.69573i
$190$	−139.699	+	105.824i	−0.735259	+	0.556969i
$191$	217.732			1.13996			0.569979	−	0.821659i	$-0.306951\pi$
$191$	217.732			1.13996			0.569979	+	0.821659i	$0.306951\pi$
$192$	−374.386	+	66.0144i	−1.94993	+	0.343825i
$193$	−108.364	−	129.143i	−0.561469	−	0.669133i	0.408388	−	0.912809i	$-0.366091\pi$
$193$	−108.364	−	129.143i	−0.561469	−	0.669133i	−0.969857	+	0.243676i	$0.921647\pi$
$194$	−188.596	+	68.6432i	−0.972143	+	0.353831i
$195$	−93.5829	−	34.0614i	−0.479912	−	0.174674i
$196$	−36.4876	−	30.6168i	−0.186161	−	0.156208i
$197$	106.287	−	184.094i	0.539527	−	0.934488i	−0.459402	−	0.888228i	$-0.651936\pi$
$197$	106.287	−	184.094i	0.539527	−	0.934488i	0.998929	−	0.0462599i	$-0.0147302\pi$
$198$	−295.391	+	170.544i	−1.49187	+	0.861334i
$199$	2.18414	−	12.3869i	0.0109756	−	0.0622456i	−0.978828	−	0.204684i	$-0.934383\pi$
$199$	2.18414	−	12.3869i	0.0109756	−	0.0622456i	0.989804	+	0.142439i	$0.0454944\pi$
$200$	14.3610	+	2.53223i	0.0718048	+	0.0126611i
$201$	328.684	+	569.297i	1.63524	+	2.83232i
$202$	69.0522	+	39.8673i	0.341843	+	0.197363i
$203$	58.6086	−	69.8470i	0.288712	−	0.344074i
$204$	−9.53777	+	26.2048i	−0.0467538	+	0.128455i
$205$	−33.3111	−	91.5214i	−0.162493	−	0.446446i
$206$	287.625	−	241.346i	1.39624	−	1.17158i
$207$	−5.62143	−	31.8807i	−0.0271567	−	0.154013i
$208$			88.6166i			0.426041i
$209$	127.929	+	29.1953i	0.612102	+	0.139690i
$210$	364.938			1.73780
$211$	−279.496	+	49.2826i	−1.32462	+	0.233567i	−0.790824	−	0.612044i	$-0.790348\pi$
$211$	−279.496	+	49.2826i	−1.32462	+	0.233567i	−0.533800	+	0.845611i	$0.679236\pi$
$212$	218.741	+	260.685i	1.03180	+	1.22965i
$213$	−26.1126	+	9.50419i	−0.122594	+	0.0446206i
$214$	−217.544	−	79.1794i	−1.01656	−	0.369997i
$215$	14.5112	+	12.1763i	0.0674938	+	0.0566340i
$216$	20.3888	−	35.3145i	0.0943927	−	0.163493i
$217$	−193.549	+	111.745i	−0.891930	+	0.514956i
$218$	−53.3464	+	302.543i	−0.244708	+	1.38781i
$219$	21.1987	+	3.73790i	0.0967976	+	0.0170680i
$220$	47.8766	+	82.9246i	0.217621	+	0.376930i
$221$	6.64621	+	3.83719i	0.0300733	+	0.0173628i
$222$	413.710	−	493.041i	1.86356	−	2.22090i
$223$	−31.9018	+	87.6493i	−0.143057	+	0.393046i	−0.990441	−	0.137934i	$-0.955954\pi$
$223$	−31.9018	+	87.6493i	−0.143057	+	0.393046i	0.847384	+	0.530980i	$0.178176\pi$
$224$	−121.503	−	333.828i	−0.542426	−	1.49030i
$225$	193.874	−	162.680i	0.861664	−	0.723022i
$226$	19.0345	+	107.950i	0.0842234	+	0.477655i
$227$		−	1.80854i		−	0.00796716i	−0.999992	−	0.00398358i	$-0.998732\pi$
$227$		−	1.80854i		−	0.00796716i	0.999992	−	0.00398358i	$-0.00126802\pi$
$228$	−402.666	+	124.218i	−1.76608	+	0.544817i
$229$	111.104			0.485169			0.242584	−	0.970130i	$-0.422005\pi$
$229$	111.104			0.485169			0.242584	+	0.970130i	$0.422005\pi$
$230$	−17.1963	+	3.03217i	−0.0747664	+	0.0131833i
$231$	−175.634	−	209.312i	−0.760320	−	0.906114i
$232$	−10.9014	+	3.96780i	−0.0469889	+	0.0171026i
$233$	136.206	+	49.5749i	0.584575	+	0.212768i	0.617342	−	0.786695i	$-0.288210\pi$
$233$	136.206	+	49.5749i	0.584575	+	0.212768i	−0.0327667	+	0.999463i	$0.510432\pi$
$234$	−230.919	−	193.764i	−0.986832	−	0.828051i
$235$	−128.121	+	221.911i	−0.545194	+	0.944303i
$236$	−283.310	+	163.569i	−1.20047	+	0.693089i
$237$	78.9829	−	447.934i	0.333261	−	1.89002i
$238$	−27.6951	−	4.88339i	−0.116366	−	0.0205184i
$239$	−40.4823	−	70.1174i	−0.169382	−	0.293378i	0.768821	−	0.639464i	$-0.220844\pi$
$239$	−40.4823	−	70.1174i	−0.169382	−	0.293378i	−0.938203	+	0.346086i	$0.887510\pi$
$240$	205.162	+	118.450i	0.854841	+	0.493543i
$241$	−129.396	+	154.208i	−0.536913	+	0.639868i	−0.964493	−	0.264110i	$-0.914922\pi$
$241$	−129.396	+	154.208i	−0.536913	+	0.639868i	0.427580	+	0.903978i	$0.359366\pi$
$242$	−72.4090	+	198.942i	−0.299211	+	0.822075i
$243$	26.8737	+	73.8348i	0.110591	+	0.303847i
$244$	94.6004	−	79.3791i	0.387706	−	0.325324i
$245$	6.08501	+	34.5098i	0.0248368	+	0.140856i
$246$		−	449.956i		−	1.82909i
$247$	14.4229	+	115.066i	0.0583923	+	0.465856i
$248$	28.4357			0.114660
$249$	105.414	−	18.5873i	0.423348	−	0.0746478i
$250$	−235.975	−	281.224i	−0.943901	−	1.12490i
$251$	−238.298	+	86.7332i	−0.949393	+	0.345551i	−0.769868	−	0.638203i	$-0.779678\pi$
$251$	−238.298	+	86.7332i	−0.949393	+	0.345551i	−0.179525	+	0.983753i	$0.557456\pi$
$252$	540.230	+	196.628i	2.14377	+	0.780268i
$253$	10.0152	+	8.40375i	0.0395857	+	0.0332164i
$254$	−103.821	+	179.823i	−0.408743	+	0.707964i
$255$	17.7674	−	10.2580i	0.0696763	−	0.0402276i
$256$	35.9307	−	203.773i	0.140354	−	0.795988i
$257$	220.707	+	38.9165i	0.858780	+	0.151426i	0.585663	−	0.810555i	$-0.300834\pi$
$257$	220.707	+	38.9165i	0.858780	+	0.151426i	0.273117	+	0.961981i	$0.411945\pi$
$258$	43.7574	+	75.7901i	0.169602	+	0.293760i
$259$	292.546	+	168.902i	1.12952	+	0.652130i
$260$	−54.3950	+	64.8254i	−0.209212	+	0.249329i
$261$	−68.8626	+	189.199i	−0.263842	+	0.724899i
$262$	118.239	+	324.859i	0.451294	+	1.23992i
$263$	109.925	−	92.2383i	0.417967	−	0.350716i	−0.409422	−	0.912345i	$-0.634270\pi$
$263$	109.925	−	92.2383i	0.417967	−	0.350716i	0.827389	+	0.561629i	$0.189825\pi$
$264$	6.03691	+	34.2370i	0.0228671	+	0.129686i
$265$		−	250.358i		−	0.944747i
$266$	−193.879	−	378.149i	−0.728867	−	1.42161i
$267$	−750.506			−2.81088
$268$	550.099	−	96.9973i	2.05261	−	0.361930i
$269$	60.6926	+	72.3307i	0.225623	+	0.268887i	0.866966	−	0.498367i	$-0.166067\pi$
$269$	60.6926	+	72.3307i	0.225623	+	0.268887i	−0.641343	+	0.767254i	$0.721622\pi$
$270$	−358.715	+	130.561i	−1.32857	+	0.483561i
$271$	−308.312	−	112.216i	−1.13768	−	0.414082i	−0.296606	−	0.955000i	$-0.595855\pi$
$271$	−308.312	−	112.216i	−1.13768	−	0.414082i	−0.841075	+	0.540918i	$0.818077\pi$
$272$	−13.9847	−	11.7345i	−0.0514143	−	0.0431417i
$273$	120.740	−	209.127i	0.442269	−	0.766033i
$274$	412.037	−	237.890i	1.50379	−	0.868211i
$275$	−17.7487	+	100.658i	−0.0645406	+	0.366028i
$276$	−41.3473	−	7.29065i	−0.149809	−	0.0264154i
$277$	−136.885	−	237.092i	−0.494169	−	0.855927i	0.505808	−	0.862646i	$-0.331194\pi$
$277$	−136.885	−	237.092i	−0.494169	−	0.855927i	−0.999977	+	0.00671948i	$0.997861\pi$
$278$	−531.605	−	306.922i	−1.91225	−	1.10404i
$279$	317.223	−	378.052i	1.13700	−	1.35503i
$280$	8.33507	−	22.9004i	0.0297681	−	0.0817872i
$281$	32.5257	+	89.3636i	0.115750	+	0.318020i	0.984016	−	0.178078i	$-0.0569879\pi$
$281$	32.5257	+	89.3636i	0.115750	+	0.318020i	−0.868267	+	0.496098i	$0.834766\pi$
$282$	−906.851	+	760.939i	−3.21579	+	2.69836i
$283$	79.7073	+	452.042i	0.281651	+	1.59732i	0.717008	+	0.697065i	$0.245511\pi$
$283$	79.7073	+	452.042i	0.281651	+	1.59732i	−0.435357	+	0.900258i	$0.643378\pi$
$284$			23.6126i			0.0831431i
$285$	285.676	+	120.413i	1.00237	+	0.422503i
$286$	121.740			0.425665
$287$	232.572	−	41.0087i	0.810355	−	0.142887i
$288$	504.246	+	600.937i	1.75085	+	2.08659i
$289$	270.086	−	98.3031i	0.934552	−	0.340149i
$290$	102.053	+	37.1441i	0.351906	+	0.128083i
$291$	271.964	+	228.205i	0.934586	+	0.784211i
$292$	9.14552	−	15.8405i	0.0313203	−	0.0542483i
$293$	−186.848	+	107.877i	−0.637708	+	0.368181i	−0.783731	−	0.621100i	$-0.786686\pi$
$293$	−186.848	+	107.877i	−0.637708	+	0.368181i	0.146023	+	0.989281i	$0.453353\pi$
$294$	−28.1122	+	159.432i	−0.0956197	+	0.542286i
$295$	237.018	+	41.7927i	0.803452	+	0.141670i
$296$	−21.4901	−	37.2219i	−0.0726016	−	0.125750i
$297$	247.523	+	142.908i	0.833412	+	0.481171i
$298$	108.073	−	128.797i	0.362662	−	0.432204i
$299$	−3.95181	+	10.8575i	−0.0132167	+	0.0363127i
$300$	−112.263	−	308.441i	−0.374211	−	1.02814i
$301$	−35.1861	+	29.5246i	−0.116897	+	0.0980885i
$302$	27.3864	+	155.316i	0.0906834	+	0.514291i
$303$		−	141.046i		−	0.465497i
$304$	13.7429	−	275.517i	0.0452068	−	0.906307i
$305$	−90.8527			−0.297878
$306$	61.1562	−	10.7835i	0.199857	−	0.0352402i
$307$	101.821	+	121.346i	0.331665	+	0.395262i	0.905944	−	0.423397i	$-0.139162\pi$
$307$	101.821	+	121.346i	0.331665	+	0.395262i	−0.574280	+	0.818659i	$0.694718\pi$
$308$	−218.176	+	79.4097i	−0.708365	+	0.257824i
$309$	−624.123	−	227.162i	−2.01982	−	0.735153i
$310$	−203.919	−	171.109i	−0.657804	−	0.551963i
$311$	−12.3978	+	21.4736i	−0.0398642	+	0.0690469i	−0.885269	−	0.465079i	$-0.846026\pi$
$311$	−12.3978	+	21.4736i	−0.0398642	+	0.0690469i	0.845405	+	0.534126i	$0.179359\pi$
$312$	−26.6081	+	15.3622i	−0.0852823	+	0.0492378i
$313$	−18.9179	+	107.289i	−0.0604405	+	0.342775i	0.939559	+	0.342386i	$0.111235\pi$
$313$	−18.9179	+	107.289i	−0.0604405	+	0.342775i	−1.00000		0.000389330i	$0.999876\pi$
$314$	−50.3631	−	8.88038i	−0.160392	−	0.0282815i
$315$	−211.476	−	366.288i	−0.671354	−	1.16282i
$316$	−334.714	−	193.247i	−1.05922	−	0.611542i
$317$	−309.103	+	368.375i	−0.975090	+	1.16207i	0.0116787	+	0.999932i	$0.496282\pi$
$317$	−309.103	+	368.375i	−0.975090	+	1.16207i	−0.986769	+	0.162135i	$0.948162\pi$
$318$	395.591	−	1086.88i	1.24400	−	3.41785i
$319$	−27.8107	−	76.4094i	−0.0871810	−	0.239528i
$320$	182.055	−	152.762i	0.568922	−	0.477382i
$321$	71.1120	+	403.296i	0.221533	+	1.25637i
$322$		−	42.3401i		−	0.131491i
$323$	−20.0686	−	12.9609i	−0.0621320	−	0.0401266i
$324$	−249.729			−0.770770
$325$	−88.9581	+	15.6857i	−0.273717	+	0.0482637i
$326$	378.590	+	451.186i	1.16132	+	1.38401i
$327$	510.661	−	185.866i	1.56166	−	0.568396i
$328$	−28.2355	−	10.2769i	−0.0860838	−	0.0313319i
$329$	−475.961	−	399.379i	−1.44669	−	1.21392i
$330$	162.725	−	281.849i	0.493107	−	0.854087i
$331$	1.38995	−	0.802488i	0.00419925	−	0.00242444i	−0.497899	−	0.867235i	$-0.665895\pi$
$331$	1.38995	−	0.802488i	0.00419925	−	0.00242444i	0.502098	+	0.864811i	$0.332562\pi$
$332$	15.7942	−	89.5732i	0.0475728	−	0.269799i
$333$	−734.605	−	129.531i	−2.20602	−	0.388981i
$334$	375.523	+	650.424i	1.12432	+	1.94738i
$335$	−355.893	−	205.475i	−1.06237	−	0.613357i
$336$	−369.235	+	440.037i	−1.09891	+	1.30963i
$337$	102.475	−	281.546i	0.304079	−	0.835449i	−0.689702	−	0.724093i	$-0.742258\pi$
$337$	102.475	−	281.546i	0.304079	−	0.835449i	0.993781	−	0.111356i	$-0.0355194\pi$
$338$	−130.139	−	357.553i	−0.385026	−	1.05785i
$339$	148.538	−	124.638i	0.438165	−	0.367664i
$340$	−3.02723	−	17.1683i	−0.00890362	−	0.0504949i
$341$			199.309i			0.584484i
$342$	687.899	+	638.242i	2.01140	+	1.86620i
$343$	294.495			0.858586
$344$	5.75535	−	1.01482i	0.0167307	−	0.00295007i
$345$	19.8547	+	23.6619i	0.0575498	+	0.0685851i
$346$	225.989	−	82.2532i	0.653147	−	0.237726i
$347$	363.902	+	132.449i	1.04871	+	0.381699i	0.808175	−	0.588942i	$-0.200455\pi$
$347$	363.902	+	132.449i	1.04871	+	0.381699i	0.240533	+	0.970641i	$0.422678\pi$
$348$	200.035	+	167.849i	0.574813	+	0.482325i
$349$	−118.007	+	204.393i	−0.338128	+	0.585654i	−0.984081	−	0.177723i	$-0.943127\pi$
$349$	−118.007	+	204.393i	−0.338128	+	0.585654i	0.645953	+	0.763377i	$0.276460\pi$
$350$	286.664	−	165.505i	0.819039	−	0.472872i
$351$	−43.8626	+	248.757i	−0.124965	+	0.708710i
$352$	−312.000	−	55.0141i	−0.886365	−	0.156290i
$353$	−151.713	−	262.775i	−0.429782	−	0.744405i	0.567071	−	0.823669i	$-0.308076\pi$
$353$	−151.713	−	262.775i	−0.429782	−	0.744405i	−0.996854	+	0.0792640i	$0.974743\pi$
$354$	962.929	+	555.947i	2.72014	+	1.57047i
$355$	11.1663	−	13.3075i	0.0314545	−	0.0374860i
$356$	−218.115	+	599.267i	−0.612684	+	1.68334i
$357$	17.0143	+	46.7465i	0.0476592	+	0.130943i
$358$	−503.208	+	422.242i	−1.40561	+	1.17945i
$359$	−27.4387	−	155.612i	−0.0764308	−	0.433461i	−0.998879	−	0.0473395i	$-0.984926\pi$
$359$	−27.4387	−	155.612i	−0.0764308	−	0.433461i	0.922448	−	0.386121i	$-0.126185\pi$
$360$			53.8140i			0.149483i
$361$	−26.9974	−	359.989i	−0.0747851	−	0.997200i
$362$	−109.816			−0.303358
$363$	368.811	−	65.0314i	1.01601	−	0.179150i
$364$	−131.895	−	157.186i	−0.362348	−	0.431830i
$365$	−12.6451	+	4.60245i	−0.0346442	+	0.0126095i
$366$	−394.418	−	143.557i	−1.07765	−	0.392231i
$367$	101.679	+	85.3188i	0.277054	+	0.232476i	0.770717	−	0.637177i	$-0.219898\pi$
$367$	101.679	+	85.3188i	0.277054	+	0.232476i	−0.493663	+	0.869653i	$0.664342\pi$
$368$	13.7426	−	23.8029i	0.0373441	−	0.0646818i
$369$	−451.621	+	260.744i	−1.22391	+	0.706622i
$370$	−69.8681	+	396.242i	−0.188833	+	1.07092i
$371$	597.836	+	105.415i	1.61142	+	0.284136i
$372$	−320.027	−	554.304i	−0.860289	−	1.49006i
$373$	−278.822	−	160.978i	−0.747513	−	0.431577i	0.0772818	−	0.997009i	$-0.475376\pi$
$373$	−278.822	−	160.978i	−0.747513	−	0.431577i	−0.824794	+	0.565433i	$0.808709\pi$
$374$	−16.1208	+	19.2120i	−0.0431036	+	0.0513689i
$375$	−222.107	+	610.235i	−0.592286	+	1.62729i
$376$	27.0379	+	74.2860i	0.0719093	+	0.197569i
$377$	55.0495	−	46.1920i	0.146020	−	0.122525i
$378$	−160.732	−	911.556i	−0.425217	−	2.41152i
$379$		−	241.981i		−	0.638471i	−0.947675	−	0.319236i	$-0.896574\pi$
$379$		−	241.981i		−	0.638471i	0.947675	−	0.319236i	$-0.103426\pi$
$380$	179.173	−	193.113i	0.471507	−	0.508192i
$381$	367.305			0.964054
$382$	−619.280	+	109.196i	−1.62115	+	0.285853i
$383$	−265.553	−	316.474i	−0.693350	−	0.826302i	0.298407	−	0.954439i	$-0.403545\pi$
$383$	−265.553	−	316.474i	−0.693350	−	0.826302i	−0.991757	+	0.128137i	$0.959100\pi$
$384$	150.819	−	54.8937i	0.392758	−	0.142952i
$385$	160.512	+	58.4215i	0.416913	+	0.151744i
$386$	372.978	+	312.965i	0.966263	+	0.810791i
$387$	50.7137	−	87.8386i	0.131043	−	0.226973i
$388$	261.258	−	150.837i	0.673345	−	0.388756i
$389$	14.4968	−	82.2154i	0.0372668	−	0.211351i	−0.960488	−	0.278321i	$-0.910222\pi$
$389$	14.4968	−	82.2154i	0.0372668	−	0.211351i	0.997755	+	0.0669702i	$0.0213332\pi$
$390$	283.254	+	49.9453i	0.726291	+	0.128065i
$391$	−1.19014	−	2.06138i	−0.00304383	−	0.00527208i
$392$	9.36255	+	5.40547i	0.0238840	+	0.0137895i
$393$	393.087	−	468.462i	1.00022	−	1.19202i
$394$	−209.978	+	576.911i	−0.532940	+	1.46424i
$395$	97.2511	+	267.195i	0.246205	+	0.676443i
$396$	392.748	−	329.554i	0.991787	−	0.832208i
$397$	−114.052	−	646.820i	−0.287284	−	1.62927i	−0.697010	−	0.717061i	$-0.745487\pi$
$397$	−114.052	−	646.820i	−0.287284	−	1.62927i	0.409726	−	0.912209i	$-0.365624\pi$
$398$			36.3265i			0.0912726i
$399$	−407.823	+	631.472i	−1.02211	+	1.58264i
$400$	214.877			0.537192
$401$	342.020	−	60.3074i	0.852918	−	0.150393i	0.269937	−	0.962878i	$-0.412997\pi$
$401$	342.020	−	60.3074i	0.852918	−	0.150393i	0.582981	+	0.812485i	$0.301886\pi$
$402$	−1220.36	−	1454.37i	−3.03573	−	3.61784i
$403$	−165.520	+	60.2444i	−0.410720	+	0.149490i
$404$	−112.623	−	40.9913i	−0.278769	−	0.101464i
$405$	140.742	+	118.096i	0.347510	+	0.291596i
$406$	−131.667	+	228.054i	−0.324303	+	0.561710i
$407$	260.893	−	150.626i	0.641014	−	0.370089i
$408$	1.09910	−	6.23330i	0.00269387	−	0.0152777i
$409$	−65.6040	−	11.5678i	−0.160401	−	0.0282830i	0.0928709	−	0.995678i	$-0.470396\pi$
$409$	−65.6040	−	11.5678i	−0.160401	−	0.0282830i	−0.253272	+	0.967395i	$0.581507\pi$
$410$	140.644	+	243.602i	0.343033	+	0.594151i
$411$	−728.868	−	420.812i	−1.77340	−	1.02387i
$412$	−362.771	+	432.334i	−0.880512	+	1.04935i
$413$	−199.596	+	548.384i	−0.483282	+	1.32781i
$414$	31.9773	+	87.8568i	0.0772398	+	0.212215i
$415$	−51.2601	+	43.0124i	−0.123518	+	0.103644i
$416$	−48.6197	−	275.736i	−0.116874	−	0.662827i
$417$			1085.85i			2.60396i
$418$	−378.502	−	18.8798i	−0.905508	−	0.0451670i
$419$	−154.857			−0.369586			−0.184793	−	0.982777i	$-0.559161\pi$
$419$	−154.857			−0.369586			−0.184793	+	0.982777i	$0.559161\pi$
$420$	−540.210	+	95.2537i	−1.28622	+	0.226794i
$421$	339.565	+	404.678i	0.806567	+	0.961230i	0.999802	−	0.0199231i	$-0.00634215\pi$
$421$	339.565	+	404.678i	0.806567	+	0.961230i	−0.193234	+	0.981153i	$0.561898\pi$
$422$	770.234	−	280.342i	1.82520	−	0.664318i
$423$	1289.26	+	469.253i	3.04790	+	1.10935i
$424$	−59.1681	−	49.6480i	−0.139547	−	0.117094i
$425$	9.30439	−	16.1157i	0.0218927	−	0.0379192i
$426$	69.5036	−	40.1279i	0.163154	−	0.0941971i
$427$	38.2540	−	216.949i	0.0895879	−	0.508078i
$428$	342.693	+	60.4259i	0.800684	+	0.141182i
$429$	−107.675	−	186.499i	−0.250992	−	0.434730i
$430$	−47.3797	−	27.3547i	−0.110185	−	0.0636155i
$431$	−225.422	+	268.647i	−0.523020	+	0.623311i	−0.961292	−	0.275531i	$-0.911146\pi$
$431$	−225.422	+	268.647i	−0.523020	+	0.623311i	0.438272	+	0.898842i	$0.355591\pi$
$432$	205.509	−	564.632i	0.475716	−	1.30702i
$433$	55.5822	+	152.711i	0.128365	+	0.352681i	0.987181	−	0.159604i	$-0.0510216\pi$
$433$	55.5822	+	152.711i	0.128365	+	0.352681i	−0.858816	+	0.512284i	$0.828799\pi$
$434$	494.455	−	414.897i	1.13930	−	0.955985i
$435$	−33.3596	−	189.192i	−0.0766888	−	0.434924i
$436$		−	461.772i		−	1.05911i
$437$	13.9704	−	33.1442i	0.0319688	−	0.0758448i
$438$	−62.1686			−0.141937
$439$	−423.963	+	74.7562i	−0.965748	+	0.170287i	−0.634215	−	0.773156i	$-0.718677\pi$
$439$	−423.963	+	74.7562i	−0.965748	+	0.170287i	−0.331533	+	0.943444i	$0.607566\pi$
$440$	−13.9699	−	16.6486i	−0.0317497	−	0.0378378i
$441$	176.313	−	64.1726i	0.399802	−	0.145516i
$442$	−20.8278	−	7.58068i	−0.0471216	−	0.0171509i
$443$	−166.191	−	139.451i	−0.375149	−	0.314787i	0.435645	−	0.900118i	$-0.356520\pi$
$443$	−166.191	−	139.451i	−0.375149	−	0.314787i	−0.810794	+	0.585331i	$0.800965\pi$
$444$	−483.718	+	837.823i	−1.08945	+	1.88699i
$445$	406.317	−	234.587i	0.913071	−	0.527162i
$446$	46.7785	−	265.294i	0.104885	−	0.594830i
$447$	−292.897	−	51.6456i	−0.655251	−	0.115538i
$448$	288.129	+	499.054i	0.643145	+	1.11396i
$449$	182.412	+	105.316i	0.406262	+	0.234556i	0.689183	−	0.724588i	$-0.257970\pi$
$449$	182.412	+	105.316i	0.406262	+	0.234556i	−0.282920	+	0.959143i	$0.591303\pi$
$450$	−469.837	+	559.930i	−1.04408	+	1.24429i
$451$	72.0318	−	197.906i	0.159716	−	0.438815i
$452$	−56.3528	−	154.828i	−0.124674	−	0.342540i
$453$	213.713	−	179.326i	0.471772	−	0.395864i
$454$	0.907011	+	5.14392i	0.00199782	+	0.0113302i
$455$			150.959i			0.331778i
$456$	85.1095	−	43.6361i	0.186644	−	0.0956932i
$457$	627.841			1.37383			0.686916	−	0.726737i	$-0.258964\pi$
$457$	627.841			1.37383			0.686916	+	0.726737i	$0.258964\pi$
$458$	−316.004	+	55.7201i	−0.689966	+	0.121660i
$459$	−33.4484	−	39.8623i	−0.0728723	−	0.0868459i
$460$	24.6639	−	8.97693i	0.0536172	−	0.0195151i
$461$	−709.636	−	258.286i	−1.53934	−	0.560274i	−0.573454	−	0.819238i	$-0.694397\pi$
$461$	−709.636	−	258.286i	−1.53934	−	0.560274i	−0.965887	+	0.258964i	$0.916619\pi$
$462$	604.517	+	507.250i	1.30848	+	1.09794i
$463$	−6.58305	+	11.4022i	−0.0142182	+	0.0246267i	−0.873047	−	0.487636i	$-0.837859\pi$
$463$	−6.58305	+	11.4022i	−0.0142182	+	0.0246267i	0.858829	+	0.512263i	$0.171193\pi$
$464$	−148.042	+	85.4722i	−0.319056	+	0.184207i
$465$	−81.7686	+	463.733i	−0.175846	+	0.997275i
$466$	−412.264	−	72.6932i	−0.884686	−	0.155994i
$467$	9.80331	+	16.9798i	0.0209921	+	0.0363594i	0.876331	−	0.481710i	$-0.159984\pi$
$467$	9.80331	+	16.9798i	0.0209921	+	0.0363594i	−0.855339	+	0.518070i	$0.826651\pi$
$468$	392.400	+	226.552i	0.838461	+	0.484086i
$469$	640.508	−	763.328i	1.36569	−	1.62756i
$470$	253.113	−	695.421i	0.538537	−	1.47962i
$471$	30.9403	+	85.0079i	0.0656907	+	0.180484i
$472$	56.8796	−	47.7277i	0.120508	−	0.101118i
$473$	7.11302	+	40.3400i	0.0150381	+	0.0852853i
$474$			1313.64i			2.77139i
$475$	279.012	−	34.9726i	0.587394	−	0.0736264i
$476$	42.2711			0.0888049
$477$	−1320.14	+	232.776i	−2.76759	+	0.488000i
$478$	150.306	+	179.127i	0.314447	+	0.374744i
$479$	−716.826	+	260.903i	−1.49650	+	0.544683i	−0.955153	−	0.296113i	$-0.904309\pi$
$479$	−716.826	+	260.903i	−1.49650	+	0.544683i	−0.541352	+	0.840796i	$0.682087\pi$
$480$	−703.363	−	256.003i	−1.46534	−	0.533340i
$481$	203.950	+	171.134i	0.424012	+	0.355789i
$482$	290.695	−	503.498i	0.603101	−	1.04460i
$483$	−64.8626	+	37.4485i	−0.134291	+	0.0775330i
$484$	55.2591	−	313.390i	0.114172	−	0.647500i
$485$	−218.570	−	38.5397i	−0.450659	−	0.0794633i
$486$	−113.464	−	196.526i	−0.233465	−	0.404374i
$487$	−220.903	−	127.539i	−0.453601	−	0.261886i	0.255749	−	0.966743i	$-0.417678\pi$
$487$	−220.903	−	127.539i	−0.453601	−	0.261886i	−0.709350	+	0.704857i	$0.751011\pi$
$488$	−18.0168	+	21.4716i	−0.0369197	+	0.0439992i
$489$	356.341	−	979.038i	0.728713	−	2.00212i
$490$	−34.6143	−	95.1021i	−0.0706415	−	0.194086i
$491$	177.941	−	149.310i	0.362406	−	0.304095i	−0.443343	−	0.896352i	$-0.646208\pi$
$491$	177.941	−	149.310i	0.362406	−	0.304095i	0.805749	+	0.592257i	$0.201763\pi$
$492$	117.445	+	666.062i	0.238709	+	1.35378i
$493$			14.8041i			0.0300287i
$494$	−98.7295	−	320.042i	−0.199857	−	0.647858i
$495$	−377.189			−0.761997
$496$	412.641	−	72.7597i	0.831937	−	0.146693i
$497$	27.0757	+	32.2676i	0.0544783	+	0.0649247i
$498$	−290.499	+	105.733i	−0.583332	+	0.212315i
$499$	540.500	+	196.726i	1.08317	+	0.394240i	0.821085	−	0.570805i	$-0.193369\pi$
$499$	540.500	+	196.726i	1.08317	+	0.394240i	0.262081	+	0.965046i	$0.415591\pi$
$500$	422.713	+	354.699i	0.845427	+	0.709397i
$501$	664.275	−	1150.56i	1.32590	−	2.29652i
$502$	634.275	−	366.199i	1.26350	−	0.729480i
$503$	19.2056	−	108.920i	0.0381821	−	0.216541i	−0.959747	−	0.280866i	$-0.909378\pi$
$503$	19.2056	−	108.920i	0.0381821	−	0.216541i	0.997929	+	0.0643249i	$0.0204894\pi$
$504$	−128.504	−	22.6587i	−0.254968	−	0.0449577i
$505$	44.0869	+	76.3607i	0.0873007	+	0.151209i
$506$	−32.7001	−	18.8794i	−0.0646247	−	0.0373111i
$507$	−432.648	+	515.609i	−0.853348	+	1.01698i
$508$	106.748	−	293.287i	0.210133	−	0.577337i
$509$	238.556	+	655.427i	0.468676	+	1.28768i	0.918805	+	0.394712i	$0.129156\pi$
$509$	238.556	+	655.427i	0.468676	+	1.28768i	−0.450129	+	0.892964i	$0.648622\pi$
$510$	−45.3902	+	38.0869i	−0.0890003	+	0.0746801i
$511$	−5.66600	−	32.1335i	−0.0110881	−	0.0628835i
$512$			723.259i			1.41262i
$513$	174.951	−	766.608i	0.341035	−	1.49436i
$514$	−647.257			−1.25926
$515$	408.899	−	72.0999i	0.793978	−	0.140000i
$516$	−84.5555	−	100.769i	−0.163867	−	0.195289i
$517$	−520.679	+	189.512i	−1.00712	+	0.366560i
$518$	−916.776	−	333.679i	−1.76984	−	0.644169i
$519$	−325.887	−	273.452i	−0.627914	−	0.526882i
$520$	9.60358	−	16.6339i	0.0184684	−	0.0319882i
$521$	−787.086	+	454.424i	−1.51072	+	0.872215i	−0.510799	+	0.859700i	$0.670650\pi$
$521$	−787.086	+	454.424i	−1.51072	+	0.872215i	−0.999922	+	0.0125152i	$0.996016\pi$
$522$	100.975	−	572.660i	0.193439	−	1.09705i
$523$	−617.615	−	108.902i	−1.18091	−	0.208226i	−0.451479	−	0.892282i	$-0.649103\pi$
$523$	−617.615	−	108.902i	−1.18091	−	0.208226i	−0.729430	+	0.684056i	$0.760215\pi$
$524$	−259.819	−	450.020i	−0.495839	−	0.858818i
$525$	−507.090	−	292.768i	−0.965885	−	0.557654i
$526$	−266.394	+	317.476i	−0.506452	+	0.603567i
$527$	12.4108	−	34.0985i	0.0235500	−	0.0647030i
$528$	175.208	+	481.379i	0.331833	+	0.911704i
$529$	−402.492	+	337.731i	−0.760855	+	0.638433i
$530$	125.558	+	712.076i	0.236902	+	1.34354i
$531$		−	1288.66i		−	2.42685i
$532$	385.697	+	509.162i	0.724994	+	0.957071i
$533$	186.128			0.349208
$534$	2134.61	−	376.390i	3.99740	−	0.704849i
$535$	−164.558	−	196.113i	−0.307586	−	0.366566i
$536$	−119.137	+	43.3623i	−0.222270	+	0.0808998i
$537$	1091.92	+	397.427i	2.03337	+	0.740087i
$538$	−208.899	−	175.287i	−0.388288	−	0.325812i
$539$	−37.8876	+	65.6232i	−0.0702923	+	0.121750i
$540$	496.920	−	286.897i	0.920223	−	0.531291i
$541$	−173.424	+	983.534i	−0.320561	+	1.81799i	0.218629	+	0.975808i	$0.429842\pi$
$541$	−173.424	+	983.534i	−0.320561	+	1.81799i	−0.539190	+	0.842184i	$0.681269\pi$
$542$	933.187	+	164.546i	1.72175	+	0.303591i
$543$	97.1284	+	168.231i	0.178874	+	0.309818i
$544$	49.9524	+	28.8400i	0.0918243	+	0.0530148i
$545$	−218.371	+	260.244i	−0.400680	+	0.477512i
$546$	−238.531	+	655.358i	−0.436870	+	1.20029i
$547$	7.65225	+	21.0244i	0.0139895	+	0.0384358i	0.946491	−	0.322731i	$-0.104601\pi$
$547$	7.65225	+	21.0244i	0.0139895	+	0.0384358i	−0.932501	+	0.361167i	$0.882379\pi$
$548$	−547.839	+	459.691i	−0.999706	+	0.838853i
$549$	84.4724	+	479.067i	0.153866	+	0.872617i
$550$		−	295.195i		−	0.536718i
$551$	−178.318	+	135.078i	−0.323626	+	0.245151i
$552$	9.52944			0.0172635
$553$	−678.989	+	119.724i	−1.22783	+	0.216499i
$554$	508.237	+	605.694i	0.917396	+	1.09331i
$555$	668.816	−	243.429i	1.20507	−	0.438611i
$556$	867.035	+	315.575i	1.55942	+	0.567581i
$557$	725.066	+	608.403i	1.30173	+	1.09229i	0.989843	+	0.142168i	$0.0454072\pi$
$557$	725.066	+	608.403i	1.30173	+	1.09229i	0.311892	+	0.950117i	$0.399037\pi$
$558$	−712.658	+	1234.36i	−1.27716	+	2.21211i
$559$	−31.3511	+	18.1006i	−0.0560843	+	0.0323803i
$560$	62.3570	−	353.644i	0.111352	−	0.631507i
$561$	43.6900	+	7.70372i	0.0778787	+	0.0137321i
$562$	−137.328	−	237.859i	−0.244355	−	0.423236i
$563$	375.791	+	216.963i	0.667479	+	0.385369i	0.795121	−	0.606451i	$-0.207407\pi$
$563$	375.791	+	216.963i	0.667479	+	0.385369i	−0.127642	+	0.991820i	$0.540741\pi$
$564$	1143.78	−	1363.10i	2.02798	−	2.41685i
$565$	−41.4586	+	113.907i	−0.0733781	+	0.201605i
$566$	−453.412	−	1245.74i	−0.801081	−	2.20095i
$567$	−341.265	+	286.355i	−0.601878	+	0.505036i
$568$	−0.930649	−	5.27798i	−0.00163847	−	0.00929221i
$569$		−	966.317i		−	1.69827i	−0.528174	−	0.849136i	$-0.677123\pi$
$569$		−	966.317i		−	1.69827i	0.528174	−	0.849136i	$-0.322877\pi$
$570$	−872.917	−	199.212i	−1.53143	−	0.349495i
$571$	−249.882			−0.437623			−0.218811	−	0.975767i	$-0.570218\pi$
$571$	−249.882			−0.437623			−0.218811	+	0.975767i	$0.570218\pi$
$572$	−180.210	+	31.7759i	−0.315052	+	0.0555522i
$573$	715.015	+	852.122i	1.24785	+	1.48712i
$574$	−640.921	+	233.276i	−1.11659	+	0.406405i
$575$	26.3272	+	9.58231i	0.0457864	+	0.0166649i
$576$	−974.786	−	817.942i	−1.69234	−	1.42004i
$577$	−452.337	+	783.471i	−0.783946	+	1.35783i	0.145680	+	0.989332i	$0.453463\pi$
$577$	−452.337	+	783.471i	−0.783946	+	1.35783i	−0.929626	+	0.368503i	$0.879870\pi$
$578$	−718.885	+	415.049i	−1.24375	+	0.718077i
$579$	149.559	−	848.189i	0.258305	−	1.46492i
$580$	−160.762	−	28.3467i	−0.277176	−	0.0488735i
$581$	−81.1269	−	140.516i	−0.139633	−	0.241852i
$582$	−887.978	−	512.674i	−1.52574	−	0.880884i
$583$	347.988	−	414.716i	0.596893	−	0.711349i
$584$	−1.41991	+	3.90118i	−0.00243136	+	0.00668010i
$585$	−114.012	−	313.244i	−0.194892	−	0.535460i
$586$	477.338	−	400.534i	0.814570	−	0.683506i
$587$	−119.086	−	675.372i	−0.202873	−	1.15055i	−0.900752	−	0.434333i	$-0.856984\pi$
$587$	−119.086	−	675.372i	−0.202873	−	1.15055i	0.697880	−	0.716215i	$-0.254127\pi$
$588$		−	243.342i		−	0.413847i
$589$	523.961	−	161.636i	0.889578	−	0.274425i
$590$	−695.094			−1.17813
$591$	1069.51	−	188.584i	1.80967	−	0.319093i
$592$	−407.092	−	485.153i	−0.687655	−	0.819516i
$593$	1012.42	−	368.492i	1.70729	−	0.621403i	0.710669	−	0.703526i	$-0.248392\pi$
$593$	1012.42	−	368.492i	1.70729	−	0.621403i	0.996622	+	0.0821232i	$0.0261701\pi$
$594$	−775.684	−	282.326i	−1.30586	−	0.475296i
$595$	−23.8230	−	19.9899i	−0.0400387	−	0.0335965i
$596$	−126.361	+	218.864i	−0.212016	+	0.367222i
$597$	55.6502	−	32.1296i	0.0932163	−	0.0538185i
$598$	5.79465	−	32.8631i	0.00969006	−	0.0549551i
$599$	−592.388	−	104.454i	−0.988961	−	0.174381i	−0.344309	−	0.938856i	$-0.611887\pi$
$599$	−592.388	−	104.454i	−0.988961	−	0.174381i	−0.644652	+	0.764476i	$0.722998\pi$
$600$	37.2501	+	64.5191i	0.0620835	+	0.107532i
$601$	450.991	+	260.380i	0.750401	+	0.433244i	0.825839	−	0.563906i	$-0.190702\pi$
$601$	450.991	+	260.380i	0.750401	+	0.433244i	−0.0754379	+	0.997151i	$0.524035\pi$
$602$	85.2703	−	101.621i	0.141645	−	0.168806i
$603$	−752.570	+	2067.67i	−1.24804	+	3.42897i
$604$	−81.0791	−	222.763i	−0.134237	−	0.368813i
$605$	−179.344	+	150.487i	−0.296436	+	0.248740i
$606$	70.7364	+	401.166i	0.116727	+	0.661990i
$607$		−	841.425i		−	1.38620i	−0.720840	−	0.693102i	$-0.756244\pi$
$607$		−	841.425i		−	1.38620i	0.720840	−	0.693102i	$-0.243756\pi$
$608$	108.402	+	864.830i	0.178292	+	1.42242i
$609$	465.822			0.764896
$610$	258.406	−	45.5640i	0.423617	−	0.0746950i
$611$	−314.768	−	375.126i	−0.515169	−	0.613954i
$612$	−87.7138	+	31.9252i	−0.143323	+	0.0521654i
$613$	−691.946	−	251.848i	−1.12879	−	0.410845i	−0.290935	−	0.956743i	$-0.593966\pi$
$613$	−691.946	−	251.848i	−1.12879	−	0.410845i	−0.837852	+	0.545898i	$0.816189\pi$
$614$	−350.459	−	294.070i	−0.570780	−	0.478941i
$615$	248.790	−	430.916i	0.404536	−	0.700677i
$616$	45.6377	−	26.3489i	0.0740872	−	0.0427743i
$617$	40.5128	−	229.760i	0.0656610	−	0.372382i	−0.934216	−	0.356707i	$-0.883899\pi$
$617$	40.5128	−	229.760i	0.0656610	−	0.372382i	0.999877	−	0.0156746i	$-0.00498958\pi$
$618$	1889.07	+	333.095i	3.05676	+	0.538988i
$619$	449.457	+	778.482i	0.726102	+	1.25765i	0.958519	+	0.285029i	$0.0920032\pi$
$619$	449.457	+	778.482i	0.726102	+	1.25765i	−0.232417	+	0.972616i	$0.574663\pi$
$620$	346.520	+	200.063i	0.558903	+	0.322683i
$621$	50.3589	−	60.0154i	0.0810932	−	0.0966431i
$622$	24.4928	−	67.2935i	0.0393775	−	0.108189i
$623$	389.094	+	1069.03i	0.624549	+	1.71593i
$624$	−346.812	+	291.010i	−0.555789	+	0.466362i
$625$	−6.24677	−	35.4272i	−0.00999483	−	0.0566835i
$626$		−	314.641i		−	0.502622i
$627$	305.850	+	596.543i	0.487800	+	0.951424i
$628$	76.8695			0.122404
$629$	−54.0138	+	9.52409i	−0.0858725	+	0.0151416i
$630$	785.186	+	935.749i	1.24633	+	1.48532i
$631$	−164.748	+	59.9632i	−0.261090	+	0.0950289i	−0.469248	−	0.883066i	$-0.655475\pi$
$631$	−164.748	+	59.9632i	−0.261090	+	0.0950289i	0.208159	+	0.978095i	$0.433253\pi$
$632$	82.4330	+	30.0031i	0.130432	+	0.0474733i
$633$	−1110.72	−	932.001i	−1.75469	−	1.47236i
$634$	694.416	−	1202.76i	1.09529	−	1.89710i
$635$	−198.855	+	114.809i	−0.313158	+	0.180802i
$636$	−301.897	+	1712.14i	−0.474680	+	2.69204i
$637$	−65.9503	−	11.6288i	−0.103533	−	0.0182556i
$638$	117.421	+	203.378i	0.184045	+	0.318775i
$639$	−80.5528	−	46.5072i	−0.126061	−	0.0727812i
$640$	−64.4938	+	76.8608i	−0.100772	+	0.120095i
$641$	133.795	−	367.598i	0.208728	−	0.573476i	−0.790512	−	0.612446i	$-0.790186\pi$
$641$	133.795	−	367.598i	0.208728	−	0.573476i	0.999240	+	0.0389705i	$0.0124078\pi$
$642$	−404.518	−	1111.40i	−0.630090	−	1.73116i
$643$	17.1208	−	14.3661i	0.0266265	−	0.0223423i	−0.629377	−	0.777100i	$-0.716690\pi$
$643$	17.1208	−	14.3661i	0.0266265	−	0.0223423i	0.656004	+	0.754758i	$0.272246\pi$
$644$	11.0513	+	62.6753i	0.0171605	+	0.0973219i
$645$			96.7773i			0.150042i
$646$	63.5799	+	26.7991i	0.0984208	+	0.0414847i
$647$	−599.186			−0.926100			−0.463050	−	0.886332i	$-0.653245\pi$
$647$	−599.186			−0.926100			−0.463050	+	0.886332i	$0.653245\pi$
$648$	55.8204	−	9.84264i	0.0861426	−	0.0151893i
$649$	334.529	+	398.676i	0.515453	+	0.614293i
$650$	245.151	−	89.2276i	0.377155	−	0.137273i
$651$	−1072.93	−	390.514i	−1.64812	−	0.599868i
$652$	−678.186	−	569.065i	−1.04016	−	0.872799i
$653$	152.832	−	264.713i	0.234046	−	0.405380i	−0.724949	−	0.688803i	$-0.758137\pi$
$653$	152.832	−	264.713i	0.234046	−	0.405380i	0.958995	+	0.283423i	$0.0914700\pi$
$654$	−1359.22	+	784.749i	−2.07832	+	1.19992i
$655$	−66.3852	+	376.489i	−0.101351	+	0.574792i
$656$	−436.032	−	76.8841i	−0.664682	−	0.117201i
$657$	36.0258	+	62.3986i	0.0548338	+	0.0949750i
$658$	1554.04	+	897.224i	2.36176	+	1.36356i
$659$	28.8290	−	34.3571i	0.0437466	−	0.0521351i	−0.743727	−	0.668483i	$-0.766944\pi$
$659$	28.8290	−	34.3571i	0.0437466	−	0.0521351i	0.787474	+	0.616348i	$0.211388\pi$
$660$	−167.313	+	459.689i	−0.253505	+	0.696499i
$661$	−331.740	−	911.447i	−0.501875	−	1.37889i	−0.889441	−	0.457049i	$-0.848906\pi$
$661$	−331.740	−	911.447i	−0.501875	−	1.37889i	0.387566	−	0.921842i	$-0.373316\pi$
$662$	−3.55088	+	2.97954i	−0.00536387	+	0.00450082i
$663$	6.80830	+	38.6118i	0.0102689	+	0.0582380i
$664$			20.6442i			0.0310907i
$665$	23.4111	−	469.347i	0.0352047	−	0.705784i
$666$	2154.35			3.23475
$667$	−21.9501	+	3.87039i	−0.0329086	+	0.00580268i
$668$	−725.649	−	864.794i	−1.08630	−	1.29460i
$669$	−447.790	+	162.982i	−0.669342	+	0.243621i
$670$	1115.29	+	405.932i	1.66461	+	0.605869i
$671$	−150.497	−	126.282i	−0.224288	−	0.188200i
$672$	907.470	−	1571.78i	1.35040	−	2.33896i
$673$	−374.338	+	216.124i	−0.556224	+	0.321136i	−0.751628	−	0.659587i	$-0.770731\pi$
$673$	−374.338	+	216.124i	−0.556224	+	0.321136i	0.195405	+	0.980723i	$0.437398\pi$
$674$	−150.262	+	852.175i	−0.222940	+	1.26436i
$675$	603.185	+	106.358i	0.893607	+	0.157567i
$676$	285.968	+	495.311i	0.423030	+	0.732709i
$677$	1085.71	+	626.838i	1.60371	+	0.925905i	0.990735	+	0.135806i	$0.0433625\pi$
$677$	1085.71	+	626.838i	1.60371	+	0.925905i	0.612980	+	0.790099i	$0.289971\pi$
$678$	−359.968	+	428.993i	−0.530927	+	0.632734i
$679$	184.060	−	505.700i	0.271075	−	0.744771i
$680$	1.35331	+	3.71820i	0.00199017	+	0.00546794i
$681$	7.07797	−	5.93912i	0.0103935	−	0.00872118i
$682$	−99.9563	−	566.880i	−0.146564	−	0.831203i
$683$			708.508i			1.03735i	0.854972	+	0.518674i	$0.173574\pi$
$683$			708.508i			1.03735i	−0.854972	+	0.518674i	$0.826426\pi$
$684$	−1184.87	−	765.227i	−1.73227	−	1.11875i
$685$	526.136			0.768082
$686$	−837.611	+	147.693i	−1.22101	+	0.215297i
$687$	364.856	+	434.818i	0.531086	+	0.632923i
$688$	80.9215	−	29.4530i	0.117618	−	0.0428096i
$689$	449.595	+	163.639i	0.652533	+	0.237503i
$690$	−68.3380	−	57.3424i	−0.0990406	−	0.0831050i
$691$	−272.140	+	471.360i	−0.393835	+	0.682142i	−0.992952	−	0.118520i	$-0.962185\pi$
$691$	−272.140	+	471.360i	−0.393835	+	0.682142i	0.599117	+	0.800661i	$0.295518\pi$
$692$	−313.058	+	180.744i	−0.452396	+	0.261191i
$693$	158.817	−	900.698i	0.229174	−	1.29971i
$694$	−1101.45	−	194.215i	−1.58710	−	0.279848i
$695$	−339.407	−	587.869i	−0.488355	−	0.845855i
$696$	−51.3279	−	29.6342i	−0.0737470	−	0.0425779i
$697$	−24.6469	+	29.3730i	−0.0353614	+	0.0421421i
$698$	233.132	−	640.524i	0.333999	−	0.917656i
$699$	253.272	+	695.860i	0.362335	+	0.995507i
$700$	−381.144	+	319.818i	−0.544491	+	0.456882i
$701$	54.0234	+	306.382i	0.0770663	+	0.437064i	0.998788	+	0.0492134i	$0.0156714\pi$
$701$	54.0234	+	306.382i	0.0770663	+	0.437064i	−0.921722	+	0.387851i	$0.873217\pi$
$702$		−	729.520i		−	1.03920i
$703$	−607.560	−	563.702i	−0.864239	−	0.801853i
$704$	513.906			0.729981
$705$	−1289.22	+	227.324i	−1.82868	+	0.322445i
$706$	563.292	+	671.306i	0.797865	+	0.950858i
$707$	−200.906	+	73.1240i	−0.284168	+	0.103429i
$708$	−1570.52	−	571.621i	−2.21824	−	0.807375i
$709$	59.7767	+	50.1586i	0.0843112	+	0.0707455i	0.683969	−	0.729511i	$-0.260252\pi$
$709$	59.7767	+	50.1586i	0.0843112	+	0.0707455i	−0.599658	+	0.800256i	$0.704697\pi$
$710$	−25.0857	+	43.4498i	−0.0353320	+	0.0611969i
$711$	1318.50	−	761.236i	1.85443	−	1.07066i
$712$	25.1349	−	142.547i	0.0353018	−	0.200206i
$713$	53.8023	+	9.48680i	0.0754591	+	0.0133055i
$714$	−71.8367	−	124.425i	−0.100612	−	0.174265i
$715$	116.589	+	67.3126i	0.163061	+	0.0941435i
$716$	634.679	−	756.381i	0.886423	−	1.05640i
$717$	141.473	−	388.693i	0.197312	−	0.542110i
$718$	156.084	+	428.837i	0.217387	+	0.597266i
$719$	418.687	−	351.320i	0.582318	−	0.488623i	−0.303390	−	0.952867i	$-0.598118\pi$
$719$	418.687	−	351.320i	0.582318	−	0.488623i	0.885707	+	0.464244i	$0.153674\pi$
$720$	137.697	+	780.916i	0.191245	+	1.08461i
$721$			1006.78i			1.39636i
$722$	257.327	+	1010.35i	0.356408	+	1.39938i
$723$	−1028.44			−1.42246
$724$	162.558	−	28.6634i	0.224528	−	0.0395903i
$725$	−112.006	−	133.484i	−0.154491	−	0.184115i
$726$	−1016.37	+	369.929i	−1.39996	+	0.509544i
$727$	339.338	+	123.509i	0.466765	+	0.169889i	0.564686	−	0.825306i	$-0.308997\pi$
$727$	339.338	+	123.509i	0.466765	+	0.169889i	−0.0979214	+	0.995194i	$0.531219\pi$
$728$	35.6768	+	29.9364i	0.0490066	+	0.0411214i
$729$	−459.577	+	796.012i	−0.630422	+	1.09192i
$730$	33.6575	−	19.4321i	0.0461061	−	0.0266194i
$731$	1.29502	−	7.34442i	0.00177157	−	0.0100471i
$732$	621.321	+	109.556i	0.848799	+	0.149666i
$733$	−333.779	−	578.122i	−0.455360	−	0.788707i	0.543349	−	0.839507i	$-0.317156\pi$
$733$	−333.779	−	578.122i	−0.455360	−	0.788707i	−0.998709	+	0.0508002i	$0.983823\pi$
$734$	−331.987	−	191.673i	−0.452298	−	0.261135i
$735$	−115.076	+	137.142i	−0.156566	+	0.186588i
$736$	−29.7015	+	81.6042i	−0.0403553	+	0.110875i
$737$	−303.932	−	835.045i	−0.412390	−	1.13303i
$738$	1153.75	−	968.109i	1.56334	−	1.31180i
$739$	−219.072	−	1242.42i	−0.296443	−	1.68121i	−0.661277	−	0.750142i	$-0.729985\pi$
$739$	−219.072	−	1242.42i	−0.296443	−	1.68121i	0.364834	−	0.931073i	$-0.381126\pi$
$740$		−	604.786i		−	0.817278i
$741$	−402.963	+	434.315i	−0.543810	+	0.586120i
$742$	−1753.25			−2.36287
$743$	1295.69	−	228.465i	1.74386	−	0.307490i	0.791209	−	0.611546i	$-0.209452\pi$
$743$	1295.69	−	228.465i	1.74386	−	0.307490i	0.952654	+	0.304056i	$0.0983410\pi$
$744$	93.3805	+	111.287i	0.125511	+	0.149579i
$745$	174.715	−	63.5909i	0.234516	−	0.0853569i
$746$	873.768	+	318.025i	1.17127	+	0.426307i
$747$	274.465	+	230.303i	0.367423	+	0.308304i
$748$	18.8487	−	32.6469i	0.0251988	−	0.0436455i
$749$	537.591	−	310.378i	0.717745	−	0.414390i
$750$	325.683	−	1847.04i	0.434244	−	2.46272i
$751$	931.147	+	164.186i	1.23988	+	0.218624i	0.754862	−	0.655883i	$-0.227704\pi$
$751$	931.147	+	164.186i	1.23988	+	0.218624i	0.485013	+	0.874507i	$0.338815\pi$
$752$	582.436	+	1008.81i	0.774516	+	1.34150i
$753$	−1121.99	−	647.783i	−1.49003	−	0.860269i
$754$	−133.408	+	158.989i	−0.176933	+	0.210861i
$755$	−59.6497	+	163.886i	−0.0790062	+	0.217068i
$756$	475.857	+	1307.41i	0.629441	+	1.72937i
$757$	−227.801	+	191.148i	−0.300926	+	0.252507i	−0.780730	−	0.624869i	$-0.785152\pi$
$757$	−227.801	+	191.148i	−0.300926	+	0.252507i	0.479804	+	0.877376i	$0.340708\pi$
$758$	121.357	+	688.248i	0.160101	+	0.907979i
$759$			66.7930i			0.0880013i
$760$	−32.4381	+	50.2270i	−0.0426817	+	0.0660882i
$761$	−402.072			−0.528348			−0.264174	−	0.964475i	$-0.585099\pi$
$761$	−402.072			−0.528348			−0.264174	+	0.964475i	$0.585099\pi$
$762$	−1044.70	+	184.209i	−1.37100	+	0.241744i
$763$	−529.497	−	631.030i	−0.693967	−	0.827038i
$764$	888.208	−	323.281i	1.16258	−	0.423143i
$765$	64.5308	+	23.4873i	0.0843540	+	0.0307023i
$766$	914.010	+	766.945i	1.19322	+	1.00123i
$767$	−229.972	+	398.323i	−0.299833	+	0.519326i
$768$	915.485	−	528.555i	1.19204	−	0.688223i
$769$	−151.090	+	856.875i	−0.196476	+	1.11427i	0.713824	+	0.700325i	$0.246961\pi$
$769$	−151.090	+	856.875i	−0.196476	+	1.11427i	−0.910301	+	0.413948i	$0.864150\pi$
$770$	−485.831	−	85.6652i	−0.630950	−	0.111254i
$771$	572.479	+	991.562i	0.742514	+	1.28607i
$772$	−633.800	−	365.925i	−0.820985	−	0.473996i
$773$	684.938	−	816.277i	0.886078	−	1.05599i	−0.111981	−	0.993710i	$-0.535720\pi$
$773$	684.938	−	816.277i	0.886078	−	1.05599i	0.998059	−	0.0622759i	$-0.0198359\pi$
$774$	−100.189	+	275.267i	−0.129443	+	0.355642i
$775$	146.080	+	401.352i	0.188491	+	0.517874i
$776$	−52.4523	+	44.0127i	−0.0675932	+	0.0567174i
$777$	299.682	+	1699.58i	0.385691	+	2.18736i
$778$			241.110i			0.309910i
$779$	−578.689	−	28.8652i	−0.742862	−	0.0370541i
$780$	−432.332			−0.554271
$781$	36.9939	−	6.52303i	0.0473674	−	0.00835215i
$782$	4.41884	+	5.26617i	0.00565069	+	0.00673424i
$783$	−457.878	+	166.654i	−0.584774	+	0.212840i
$784$	149.695	+	54.4844i	0.190937	+	0.0694954i
$785$	−43.3219	−	36.3514i	−0.0551871	−	0.0463075i
$786$	−883.088	+	1529.55i	−1.12352	+	1.94600i
$787$	−686.096	+	396.118i	−0.871786	+	0.503326i	−0.867941	−	0.496667i	$-0.834557\pi$
$787$	−686.096	+	396.118i	−0.871786	+	0.503326i	−0.00384484	+	0.999993i	$0.501224\pi$
$788$	160.246	−	908.797i	0.203357	−	1.15330i
$789$	721.972	+	127.303i	0.915047	+	0.161348i
$790$	−410.607	−	711.192i	−0.519755	−	0.900243i
$791$	−254.544	−	146.961i	−0.321800	−	0.185791i
$792$	−74.7995	+	89.1426i	−0.0944438	+	0.112554i
$793$	59.3833	−	163.154i	0.0748843	−	0.205743i
$794$	648.780	+	1782.51i	0.817103	+	2.24497i
$795$	979.808	−	822.156i	1.23246	−	1.03416i
$796$	−9.48171	−	53.7735i	−0.0119117	−	0.0675546i
$797$			194.822i			0.244444i	0.992503	+	0.122222i	$0.0390019\pi$
$797$			194.822i			0.244444i	−0.992503	+	0.122222i	$0.960998\pi$
$798$	843.250	−	2000.58i	1.05670	−	2.50699i
$799$	100.880			0.126258
$800$	−668.603	+	117.893i	−0.835754	+	0.147366i
$801$	−1614.76	−	1924.40i	−2.01593	−	2.40249i
$802$	−942.539	+	343.056i	−1.17524	+	0.427751i
$803$	−27.3438	−	9.95233i	−0.0340521	−	0.0123939i
$804$	2186.09	+	1834.35i	2.71902	+	2.28153i
$805$	23.4107	−	40.5485i	0.0290816	−	0.0503708i
$806$	440.564	−	254.360i	0.546606	−	0.315583i
$807$	−83.7653	+	475.057i	−0.103798	+	0.588670i
$808$	26.7894	+	4.72369i	0.0331552	+	0.00584616i
$809$	−304.775	−	527.886i	−0.376731	−	0.652517i	0.613854	−	0.789420i	$-0.289618\pi$
$809$	−304.775	−	527.886i	−0.376731	−	0.652517i	−0.990584	+	0.136903i	$0.956285\pi$
$810$	−459.529	−	265.309i	−0.567320	−	0.327542i
$811$	348.318	−	415.109i	0.429492	−	0.511848i	−0.507284	−	0.861779i	$-0.669350\pi$
$811$	348.318	−	415.109i	0.429492	−	0.511848i	0.936776	+	0.349931i	$0.113795\pi$
$812$	135.379	−	371.951i	0.166723	−	0.458068i
$813$	−573.299	−	1575.13i	−0.705165	−	1.93742i
$814$	−666.497	+	559.258i	−0.818793	+	0.687049i
$815$	113.100	+	641.424i	0.138773	+	0.787023i
$816$		−	93.2662i		−	0.114297i
$817$	100.281	−	51.4144i	0.122743	−	0.0629308i
$818$	192.394			0.235201
$819$	796.008	−	140.358i	0.971927	−	0.171377i
$820$	−271.776	−	323.890i	−0.331434	−	0.394987i
$821$	−1424.58	+	518.505i	−1.73518	+	0.631554i	−0.998978	−	0.0452088i	$-0.985605\pi$
$821$	−1424.58	+	518.505i	−1.73518	+	0.631554i	−0.736202	+	0.676762i	$0.763382\pi$
$822$	2284.11	+	831.348i	2.77872	+	1.01137i
$823$	513.192	+	430.619i	0.623563	+	0.523231i	0.898921	−	0.438110i	$-0.144352\pi$
$823$	513.192	+	430.619i	0.623563	+	0.523231i	−0.275358	+	0.961342i	$0.588797\pi$
$824$	64.0482	−	110.935i	0.0777283	−	0.134629i
$825$	−452.222	+	261.090i	−0.548148	+	0.316473i
$826$	292.673	−	1659.83i	0.354326	−	2.00948i
$827$	−671.710	−	118.441i	−0.812224	−	0.143217i	−0.247916	−	0.968781i	$-0.579746\pi$
$827$	−671.710	−	118.441i	−0.812224	−	0.143217i	−0.564308	+	0.825564i	$0.690857\pi$
$828$	−70.2672	−	121.706i	−0.0848638	−	0.146988i
$829$	−373.918	−	215.882i	−0.451047	−	0.260412i	0.257225	−	0.966352i	$-0.417192\pi$
$829$	−373.918	−	215.882i	−0.451047	−	0.260412i	−0.708272	+	0.705939i	$0.750525\pi$
$830$	124.224	−	148.045i	0.149668	−	0.178367i
$831$	478.369	−	1314.31i	0.575654	−	1.58160i
$832$	155.337	+	426.784i	0.186703	+	0.512962i
$833$	10.5682	−	8.86781i	0.0126870	−	0.0106456i
$834$	−544.570	−	3088.41i	−0.652962	−	3.70313i
$835$			830.535i			0.994653i
$836$	565.218	−	70.8468i	0.676098	−	0.0847450i
$837$	1194.35			1.42694
$838$	440.448	−	77.6628i	0.525594	−	0.0926764i
$839$	108.202	+	128.950i	0.128966	+	0.153695i	0.826663	−	0.562697i	$-0.190236\pi$
$839$	108.202	+	128.950i	0.128966	+	0.153695i	−0.697697	+	0.716393i	$0.745792\pi$
$840$	116.995	−	42.5828i	0.139280	−	0.0506939i
$841$	−660.017	−	240.227i	−0.784800	−	0.285644i
$842$	−1168.75	−	980.700i	−1.38807	−	1.16473i
$843$	−242.924	+	420.757i	−0.288166	+	0.499118i
$844$	−1066.99	+	616.027i	−1.26421	+	0.729890i
$845$	73.0663	−	414.379i	0.0864689	−	0.490390i
$846$	−3902.30	−	688.080i	−4.61264	−	0.813334i
$847$	−283.839	−	491.623i	−0.335111	−	0.580429i
$848$	−985.648	−	569.064i	−1.16232	−	0.671066i
$849$	−1507.37	+	1796.42i	−1.77547	+	2.11592i
$850$	−18.3816	+	50.5030i	−0.0216254	+	0.0594153i
$851$	−28.2427	−	77.5961i	−0.0331876	−	0.0911823i
$852$	−92.4110	+	77.5421i	−0.108464	+	0.0910118i
$853$	89.0407	+	504.975i	0.104385	+	0.591999i	0.991464	+	0.130380i	$0.0416199\pi$
$853$	89.0407	+	504.975i	0.104385	+	0.591999i	−0.887079	+	0.461618i	$0.847269\pi$
$854$			636.239i			0.745010i
$855$	305.894	+	991.588i	0.357771	+	1.15975i
$856$	−78.9814			−0.0922680
$857$	850.500	−	149.966i	0.992415	−	0.174990i	0.346213	−	0.938156i	$-0.387467\pi$
$857$	850.500	−	149.966i	0.992415	−	0.174990i	0.646202	+	0.763166i	$0.276356\pi$
$858$	399.786	+	476.446i	0.465951	+	0.555298i
$859$	813.260	−	296.002i	0.946751	−	0.344589i	0.177923	−	0.984044i	$-0.443062\pi$
$859$	813.260	−	296.002i	0.946751	−	0.344589i	0.768828	+	0.639455i	$0.220840\pi$
$860$	77.2752	+	28.1259i	0.0898549	+	0.0327045i
$861$	924.241	+	775.530i	1.07345	+	0.900732i
$862$	506.421	−	877.147i	0.587495	−	1.01757i
$863$	1358.98	−	784.608i	1.57472	−	0.909163i	0.579138	−	0.815229i	$-0.303389\pi$
$863$	1358.98	−	784.608i	1.57472	−	0.909163i	0.995578	−	0.0939340i	$-0.0299443\pi$
$864$	−329.668	+	1869.64i	−0.381560	+	2.16394i
$865$	261.906	+	46.1810i	0.302781	+	0.0533885i
$866$	−234.675	−	406.470i	−0.270988	−	0.469364i
$867$	1271.66	+	734.194i	1.46674	+	0.846822i
$868$	−623.639	+	743.224i	−0.718479	+	0.856249i
$869$	−210.296	+	577.782i	−0.241997	+	0.664882i
$870$	189.765	+	521.375i	0.218121	+	0.599281i
$871$	601.612	−	504.813i	0.690714	−	0.579578i
$872$	18.1999	+	103.217i	0.0208715	+	0.118368i
$873$			1188.35i			1.36123i
$874$	−23.1126	+	101.276i	−0.0264447	+	0.115876i
$875$	984.374			1.12500
$876$	92.0270	−	16.2268i	0.105054	−	0.0185238i
$877$	702.724	+	837.474i	0.801282	+	0.954931i	0.999683	−	0.0251902i	$-0.00801913\pi$
$877$	702.724	+	837.474i	0.801282	+	0.954931i	−0.198401	+	0.980121i	$0.563575\pi$
$878$	1168.36	−	425.248i	1.33070	−	0.484337i
$879$	−1035.79	−	376.995i	−1.17837	−	0.428891i
$880$	−245.322	−	205.849i	−0.278774	−	0.233920i
$881$	800.040	−	1385.71i	0.908104	−	1.57288i	0.0914086	−	0.995813i	$-0.470863\pi$
$881$	800.040	−	1385.71i	0.908104	−	1.57288i	0.816695	−	0.577069i	$-0.195804\pi$
$882$	−469.290	+	270.945i	−0.532075	+	0.307194i
$883$	295.798	−	1677.55i	0.334992	−	1.89984i	−0.0923160	−	0.995730i	$-0.529427\pi$
$883$	295.798	−	1677.55i	0.334992	−	1.89984i	0.427308	−	0.904106i	$-0.359462\pi$
$884$	32.8096	+	5.78522i	0.0371149	+	0.00654436i
$885$	614.789	+	1064.84i	0.694676	+	1.20321i
$886$	542.622	+	313.283i	0.612440	+	0.353593i
$887$	−276.588	+	329.625i	−0.311824	+	0.371618i	−0.899081	−	0.437783i	$-0.855764\pi$
$887$	−276.588	+	329.625i	−0.311824	+	0.371618i	0.587256	+	0.809401i	$0.300208\pi$
$888$	75.1009	−	206.338i	0.0845731	−	0.232363i
$889$	−190.426	−	523.192i	−0.214203	−	0.588517i
$890$	−1038.01	+	870.993i	−1.16630	+	0.978644i
$891$	68.9882	+	391.252i	0.0774278	+	0.439115i
$892$			404.920i			0.453946i
$893$	920.469	+	1215.12i	1.03076	+	1.36071i
$894$	858.968			0.960814
$895$	−715.380	+	126.141i	−0.799308	+	0.140940i
$896$	−156.382	−	186.369i	−0.174534	−	0.208001i
$897$	−55.4696	+	20.1893i	−0.0618391	+	0.0225076i
$898$	−571.639	−	208.059i	−0.636569	−	0.231692i
$899$	−260.291	−	218.410i	−0.289534	−	0.242948i
$900$	549.342	−	951.488i	0.610380	−	1.05721i
$901$	−85.3592	+	49.2821i	−0.0947383	+	0.0546972i
$902$	−105.622	+	599.015i	−0.117098	+	0.664096i
$903$	−231.097	−	40.7486i	−0.255921	−	0.0451258i
$904$	18.6984	+	32.3867i	0.0206841	+	0.0358260i
$905$	−105.169	−	60.7192i	−0.116209	−	0.0670931i
$906$	−517.914	+	617.226i	−0.571649	+	0.681264i
$907$	−110.421	+	303.380i	−0.121743	+	0.334487i	−0.985562	−	0.169316i	$-0.945844\pi$
$907$	−110.421	+	303.380i	−0.121743	+	0.334487i	0.863818	+	0.503803i	$0.168066\pi$
$908$	−2.68527	−	7.37771i	−0.00295734	−	0.00812523i
$909$	361.660	−	303.468i	0.397865	−	0.333849i
$910$	−75.7082	−	429.363i	−0.0831958	−	0.471827i
$911$			1176.87i			1.29185i	0.763401	+	0.645924i	$0.223528\pi$
$911$			1176.87i			1.29185i	−0.763401	+	0.645924i	$0.776472\pi$
$912$	1123.40	−	850.994i	1.23180	−	0.933107i
$913$	−144.698			−0.158486
$914$	−1785.72	+	314.871i	−1.95375	+	0.344498i
$915$	−298.353	−	355.564i	−0.326069	−	0.388594i
$916$	453.232	−	164.963i	0.494795	−	0.180091i
$917$	−871.075	−	317.045i	−0.949918	−	0.345742i
$918$	115.126	+	96.6026i	0.125410	+	0.105232i
$919$	−227.393	+	393.857i	−0.247436	+	0.428571i	−0.962814	−	0.270167i	$-0.912921\pi$
$919$	−227.393	+	393.857i	−0.247436	+	0.428571i	0.715378	+	0.698738i	$0.246255\pi$
$920$	−5.15915	+	2.97864i	−0.00560777	+	0.00323765i
$921$	−140.529	+	796.979i	−0.152583	+	0.865341i
$922$	2147.90	+	378.733i	2.32961	+	0.410774i
$923$	16.5992	+	28.7507i	0.0179840	+	0.0311492i
$924$	−1027.25	−	593.085i	−1.11175	−	0.641867i
$925$	414.965	−	494.536i	0.448611	−	0.534634i
$926$	13.0054	−	35.7319i	0.0140447	−	0.0385874i
$927$	−760.366	−	2089.09i	−0.820244	−	2.25360i
$928$	413.748	−	347.176i	0.445850	−	0.374112i
$929$	−226.600	−	1285.11i	−0.243918	−	1.38333i	−0.822991	−	0.568054i	$-0.807696\pi$
$929$	−226.600	−	1285.11i	−0.243918	−	1.38333i	0.579073	−	0.815276i	$-0.303415\pi$
$930$		−	1359.97i		−	1.46233i
$931$	203.242	+	46.3829i	0.218306	+	0.0498205i
$932$	629.240			0.675151
$933$	−124.753	+	21.9973i	−0.133712	+	0.0235770i
$934$	−36.3985	−	43.3781i	−0.0389706	−	0.0464433i
$935$	−26.0613	+	9.48553i	−0.0278730	+	0.0101450i
$936$	−96.6397	−	35.1740i	−0.103248	−	0.0375790i
$937$	−502.126	−	421.334i	−0.535887	−	0.449662i	0.334242	−	0.942487i	$-0.391520\pi$
$937$	−502.126	−	421.334i	−0.535887	−	0.449662i	−0.870128	+	0.492825i	$0.835964\pi$
$938$	−1438.93	+	2492.30i	−1.53404	+	2.65704i
$939$	−482.013	+	278.290i	−0.513326	+	0.296369i
$940$	−193.164	+	1095.49i	−0.205493	+	1.16541i
$941$	−218.980	−	38.6121i	−0.232710	−	0.0410331i	0.0560769	−	0.998426i	$-0.482141\pi$
$941$	−218.980	−	38.6121i	−0.232710	−	0.0410331i	−0.288787	+	0.957393i	$0.593252\pi$
$942$	−130.634	−	226.265i	−0.138677	−	0.240196i
$943$	−49.9950	−	28.8646i	−0.0530169	−	0.0306093i
$944$	703.279	−	838.135i	0.744999	−	0.887855i
$945$	350.087	−	961.856i	0.370462	−	1.01784i
$946$	−40.4622	−	111.169i	−0.0427718	−	0.117515i
$947$	−1082.21	+	908.079i	−1.14277	+	0.958901i	−0.999526	−	0.0307861i	$-0.990199\pi$
$947$	−1082.21	+	908.079i	−1.14277	+	0.958901i	−0.143247	+	0.989687i	$0.545754\pi$
$948$	−342.878	−	1944.56i	−0.361685	−	2.05122i
$949$		−	25.7165i		−	0.0270985i
$950$	−776.035	+	239.399i	−0.816879	+	0.251999i
$951$	−2456.76			−2.58334
$952$	−9.44859	+	1.66604i	−0.00992499	+	0.00175004i
$953$	−367.047	−	437.430i	−0.385149	−	0.459003i	0.538283	−	0.842764i	$-0.319073\pi$
$953$	−367.047	−	437.430i	−0.385149	−	0.459003i	−0.923432	+	0.383761i	$0.874629\pi$
$954$	3638.04	−	1324.14i	3.81346	−	1.38799i
$955$	−653.452	−	237.837i	−0.684243	−	0.249044i
$956$	−269.250	−	225.927i	−0.281642	−	0.236326i
$957$	207.710	−	359.764i	0.217042	−	0.375928i
$958$	1907.97	−	1101.57i	1.99162	−	1.14986i
$959$	−221.532	+	1256.37i	−0.231003	+	1.31009i
$960$	1195.71	+	210.836i	1.24553	+	0.219621i
$961$	−64.0710	−	110.974i	−0.0666712	−	0.115478i
$962$	−665.907	−	384.462i	−0.692211	−	0.399648i
$963$	−881.103	+	1050.06i	−0.914956	+	1.09040i
$964$	−298.890	+	821.194i	−0.310052	+	0.851861i
$965$	184.150	+	505.949i	0.190829	+	0.524300i
$966$	165.703	−	139.042i	0.171536	−	0.143935i
$967$	274.705	+	1557.93i	0.284080	+	1.61110i	0.708554	+	0.705657i	$0.249348\pi$
$967$	274.705	+	1557.93i	0.284080	+	1.61110i	−0.424474	+	0.905440i	$0.639541\pi$
$968$			72.2279i			0.0746156i
$969$	−15.1797	−	121.104i	−0.0156653	−	0.124978i
$970$	640.990			0.660815
$971$	−802.138	+	141.439i	−0.826095	+	0.145663i	−0.570684	−	0.821170i	$-0.693322\pi$
$971$	−802.138	+	141.439i	−0.826095	+	0.145663i	−0.255411	+	0.966833i	$0.582211\pi$
$972$	219.255	+	261.298i	0.225571	+	0.268825i
$973$	1546.70	−	562.951i	1.58962	−	0.578573i
$974$	692.263	+	251.963i	0.710742	+	0.258689i
$975$	−353.520	−	296.638i	−0.362584	−	0.304244i
$976$	−206.508	+	357.683i	−0.211586	+	0.366478i
$977$	818.544	−	472.586i	0.837813	−	0.483712i	−0.0187071	−	0.999825i	$-0.505955\pi$
$977$	818.544	−	472.586i	0.837813	−	0.483712i	0.856520	+	0.516113i	$0.172622\pi$
$978$	−522.513	+	2963.32i	−0.534267	+	3.02998i
$979$	999.128	+	176.173i	1.02056	+	0.179952i
$980$	76.0619	+	131.743i	0.0776142	+	0.134432i
$981$	1575.30	+	909.502i	1.60581	+	0.927118i
$982$	−431.225	+	513.914i	−0.439129	+	0.523334i
$983$	−5.72777	+	15.7369i	−0.00582683	+	0.0160091i	−0.942572	−	0.334003i	$-0.891600\pi$
$983$	−5.72777	+	15.7369i	−0.00582683	+	0.0160091i	0.936745	+	0.350012i	$0.113823\pi$
$984$	−52.5033	−	144.252i	−0.0533570	−	0.146597i
$985$	−520.078	+	436.398i	−0.527998	+	0.443043i
$986$	−7.42449	−	42.1064i	−0.00752991	−	0.0427043i
$987$		−	3174.26i		−	3.21607i
$988$	229.683	+	447.982i	0.232472	+	0.453423i
$989$	11.2281			0.0113530
$990$	1072.81	−	189.166i	1.08365	−	0.191076i
$991$	249.716	+	297.600i	0.251984	+	0.300302i	0.877177	−	0.480168i	$-0.159424\pi$
$991$	249.716	+	297.600i	0.251984	+	0.300302i	−0.625193	+	0.780470i	$0.714980\pi$
$992$	−1244.04	+	452.793i	−1.25407	+	0.456444i
$993$	7.70513	+	2.80444i	0.00775945	+	0.00282421i
$994$	−93.1922	−	78.1976i	−0.0937547	−	0.0786696i
$995$	−20.0856	+	34.7893i	−0.0201866	+	0.0349642i
$996$	402.423	−	232.339i	0.404039	−	0.233272i
$997$	255.596	−	1449.56i	0.256366	−	1.45392i	−0.536177	−	0.844105i	$-0.680132\pi$
$997$	255.596	−	1449.56i	0.256366	−	1.45392i	0.792543	−	0.609816i	$-0.208757\pi$
$998$	−1635.97	−	288.465i	−1.63925	−	0.289043i
$999$	−902.619	−	1563.38i	−0.903522	−	1.56495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.3.f.a.10.1	yes	12
3.2	odd	2		171.3.ba.b.10.2		12
4.3	odd	2		304.3.z.a.257.1		12
19.2	odd	18	inner	19.3.f.a.2.1	✓	12
19.3	odd	18		361.3.f.e.299.2		12
19.4	even	9		361.3.d.d.293.1		12
19.5	even	9		361.3.f.b.307.1		12
19.6	even	9		361.3.b.c.360.12		12
19.7	even	3		361.3.f.e.262.2		12
19.8	odd	6		361.3.f.b.127.1		12
19.9	even	9		361.3.d.f.69.6		12
19.10	odd	18		361.3.d.d.69.1		12
19.11	even	3		361.3.f.f.127.2		12
19.12	odd	6		361.3.f.c.262.1		12
19.13	odd	18		361.3.b.c.360.1		12
19.14	odd	18		361.3.f.f.307.2		12
19.15	odd	18		361.3.d.f.293.6		12
19.16	even	9		361.3.f.c.299.1		12
19.17	even	9		361.3.f.g.116.2		12
19.18	odd	2		361.3.f.g.333.2		12
57.2	even	18		171.3.ba.b.154.2		12
76.59	even	18		304.3.z.a.97.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.3.f.a.2.1	✓	12	19.2	odd	18	inner
19.3.f.a.10.1	yes	12	1.1	even	1	trivial
171.3.ba.b.10.2		12	3.2	odd	2
171.3.ba.b.154.2		12	57.2	even	18
304.3.z.a.97.1		12	76.59	even	18
304.3.z.a.257.1		12	4.3	odd	2
361.3.b.c.360.1		12	19.13	odd	18
361.3.b.c.360.12		12	19.6	even	9
361.3.d.d.69.1		12	19.10	odd	18
361.3.d.d.293.1		12	19.4	even	9
361.3.d.f.69.6		12	19.9	even	9
361.3.d.f.293.6		12	19.15	odd	18
361.3.f.b.127.1		12	19.8	odd	6
361.3.f.b.307.1		12	19.5	even	9
361.3.f.c.262.1		12	19.12	odd	6
361.3.f.c.299.1		12	19.16	even	9
361.3.f.e.262.2		12	19.7	even	3
361.3.f.e.299.2		12	19.3	odd	18
361.3.f.f.127.2		12	19.11	even	3
361.3.f.f.307.2		12	19.14	odd	18
361.3.f.g.116.2		12	19.17	even	9
361.3.f.g.333.2		12	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-2.84423 + 0.501515i) q^{2} +(3.28392 + 3.91363i) q^{3} +(4.07936 - 1.48477i) q^{4} +(-3.00117 - 1.09234i) q^{5} +(-11.3030 - 9.48432i) q^{6} +(3.87208 - 6.70664i) q^{7} +(-0.853313 + 0.492661i) q^{8} +(-2.96949 + 16.8408i) q^{9} +(9.08386 + 1.60173i) q^{10} +(-3.45312 - 5.98097i) q^{11} +(19.2071 + 11.0892i) q^{12} +(3.92326 - 4.67556i) q^{13} +(-7.64961 + 21.0171i) q^{14} +(-5.58062 - 15.3326i) q^{15} +(-11.1222 + 9.33260i) q^{16} +(0.218340 + 1.23827i) q^{17} -49.3885i q^{18} +(-12.9229 + 13.9283i) q^{19} -13.8647 q^{20} +(38.9629 - 6.87021i) q^{21} +(12.8210 + 15.2795i) q^{22} +(-1.77889 + 0.647464i) q^{23} +(-4.73030 - 1.72169i) q^{24} +(-11.3373 - 9.51310i) q^{25} +(-8.81380 + 15.2659i) q^{26} +(-35.8406 + 20.6926i) q^{27} +(5.83782 - 33.1079i) q^{28} +(11.5950 + 2.04451i) q^{29} +(23.5621 + 40.8108i) q^{30} +(-24.9929 - 14.4296i) q^{31} +(29.4870 - 35.1412i) q^{32} +(12.0675 - 33.1553i) q^{33} +(-1.24202 - 3.41242i) q^{34} +(-18.9467 + 15.8982i) q^{35} +(12.8911 + 73.1088i) q^{36} +43.6204i q^{37} +(29.7704 - 46.0964i) q^{38} +31.1821 q^{39} +(3.09909 - 0.546454i) q^{40} +(19.6019 + 23.3607i) q^{41} +(-107.374 + 39.0809i) q^{42} +(-5.57351 - 2.02859i) q^{43} +(-22.9668 - 19.2715i) q^{44} +(27.3079 - 47.2986i) q^{45} +(4.73487 - 2.73368i) q^{46} +(13.9320 - 79.0123i) q^{47} +(-73.0486 - 12.8804i) q^{48} +(-5.48600 - 9.50203i) q^{49} +(37.0168 + 21.3716i) q^{50} +(-4.12911 + 4.92088i) q^{51} +(9.06229 - 24.8984i) q^{52} +(26.8107 + 73.6617i) q^{53} +(91.5612 - 76.8290i) q^{54} +(3.83016 + 21.7219i) q^{55} +7.63048i q^{56} +(-96.9481 - 4.83580i) q^{57} -34.0042 q^{58} +(-74.2124 + 13.0856i) q^{59} +(-45.5307 - 54.2614i) q^{60} +(26.7312 - 9.72936i) q^{61} +(78.3222 + 28.5069i) q^{62} +(101.447 + 85.1244i) q^{63} +(-37.2060 + 64.4427i) q^{64} +(-16.8817 + 9.74665i) q^{65} +(-17.6950 + 100.353i) q^{66} +(126.717 + 22.3436i) q^{67} +(2.72923 + 4.72716i) q^{68} +(-8.37569 - 4.83570i) q^{69} +(45.9156 - 54.7201i) q^{70} +(-1.86033 + 5.11121i) q^{71} +(-5.76291 - 15.8335i) q^{72} +(3.22765 - 2.70832i) q^{73} +(-21.8763 - 124.067i) q^{74} -75.6101i q^{75} +(-32.0368 + 76.0062i) q^{76} -53.4830 q^{77} +(-88.6891 + 15.6383i) q^{78} +(-57.2275 - 68.2011i) q^{79} +(43.5739 - 15.8596i) q^{80} +(-54.0567 - 19.6750i) q^{81} +(-67.4681 - 56.6125i) q^{82} +(10.4759 - 18.1448i) q^{83} +(148.743 - 85.8768i) q^{84} +(0.697331 - 3.95476i) q^{85} +(16.8697 + 2.97458i) q^{86} +(30.0757 + 52.0926i) q^{87} +(5.89318 + 3.40243i) q^{88} +(-94.4270 + 112.534i) q^{89} +(-53.9489 + 148.223i) q^{90} +(-16.1661 - 44.4160i) q^{91} +(-6.29542 + 5.28248i) q^{92} +(-25.6024 - 145.199i) q^{93} +231.716i q^{94} +(53.9983 - 27.6852i) q^{95} +234.362 q^{96} +(68.4359 - 12.0671i) q^{97} +(20.3688 + 24.2746i) q^{98} +(110.979 - 40.3929i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{5} - 36 q^{6} + 6 q^{7} - 9 q^{8} - 24 q^{9} + 51 q^{10} - 18 q^{11} + 63 q^{12} + 21 q^{13} + 9 q^{14} + 63 q^{15} - 12 q^{16} - 3 q^{17} - 24 q^{19} - 90 q^{20} + 30 q^{21} - 78 q^{22}+ \cdots + 462 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^5 - 36 * q^6 + 6 * q^7 - 9 * q^8 - 24 * q^9 + 51 * q^10 - 18 * q^11 + 63 * q^12 + 21 * q^13 + 9 * q^14 + 63 * q^15 - 12 * q^16 - 3 * q^17 - 24 * q^19 - 90 * q^20 + 30 * q^21 - 78 * q^22 - 102 * q^23 - 12 * q^24 - 156 * q^25 + 21 * q^26 - 27 * q^27 + 12 * q^28 + 147 * q^29 + 24 * q^30 + 99 * q^31 + 165 * q^32 + 84 * q^33 + 132 * q^34 + 96 * q^35 + 63 * q^36 + 72 * q^38 - 108 * q^39 - 138 * q^40 - 144 * q^41 - 237 * q^42 - 27 * q^43 - 123 * q^44 - 3 * q^45 - 54 * q^46 - 99 * q^47 - 51 * q^48 - 24 * q^49 + 72 * q^50 - 42 * q^51 + 93 * q^52 + 111 * q^53 + 21 * q^54 + 162 * q^55 - 168 * q^57 - 132 * q^58 + 3 * q^59 - 30 * q^60 + 150 * q^61 + 108 * q^62 + 234 * q^63 + 27 * q^64 + 126 * q^65 + 168 * q^66 + 135 * q^67 - 30 * q^68 + 72 * q^69 + 225 * q^70 - 168 * q^71 - 102 * q^72 - 90 * q^73 - 231 * q^74 + 42 * q^76 + 246 * q^77 - 189 * q^78 - 75 * q^79 + 21 * q^80 - 159 * q^81 - 117 * q^82 - 156 * q^83 + 99 * q^84 - 300 * q^85 - 144 * q^86 + 69 * q^87 - 405 * q^88 - 558 * q^89 - 66 * q^90 - 453 * q^91 + 48 * q^92 - 57 * q^93 - 69 * q^95 + 558 * q^96 + 465 * q^97 + 777 * q^98 + 462 * q^99

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