LMFDB - Embedded newform 19.3.f.a.10.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,3,Mod(2,19)]

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

lf = mfeigenbasis(mf)

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")

//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);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	19.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:	$0.517712502285$
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			10.2
Root			$0.918492i$ of defining polynomial
Character	$\chi$	$=$	19.10
Dual form			19.3.f.a.2.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.904538 - 0.159494i) q^{2} +(-0.464845 - 0.553981i) q^{3} +(-2.96602 + 1.07954i) q^{4} +(0.295437 + 0.107530i) q^{5} +(-0.508827 - 0.426957i) q^{6} +(-0.328846 + 0.569578i) q^{7} +(-5.69245 + 3.28654i) q^{8} +(1.47202 - 8.34824i) q^{9} +O(q^{10})$	\(q+(0.904538 - 0.159494i) q^{2} +(-0.464845 - 0.553981i) q^{3} +(-2.96602 + 1.07954i) q^{4} +(0.295437 + 0.107530i) q^{5} +(-0.508827 - 0.426957i) q^{6} +(-0.328846 + 0.569578i) q^{7} +(-5.69245 + 3.28654i) q^{8} +(1.47202 - 8.34824i) q^{9} +(0.284385 + 0.0501447i) q^{10} +(5.74398 + 9.94886i) q^{11} +(1.97679 + 1.14130i) q^{12} +(8.87147 - 10.5726i) q^{13} +(-0.206609 + 0.567654i) q^{14} +(-0.0777629 - 0.213652i) q^{15} +(5.04684 - 4.23480i) q^{16} +(2.87674 + 16.3148i) q^{17} -7.78608i q^{18} +(-18.1952 - 5.47110i) q^{19} -0.992357 q^{20} +(0.468398 - 0.0825913i) q^{21} +(6.78243 + 8.08299i) q^{22} +(-32.5643 + 11.8524i) q^{23} +(4.46679 + 1.62578i) q^{24} +(-19.0754 - 16.0062i) q^{25} +(6.33831 - 10.9783i) q^{26} +(-10.9456 + 6.31944i) q^{27} +(0.360480 - 2.04438i) q^{28} +(23.6911 + 4.17738i) q^{29} +(-0.104416 - 0.180853i) q^{30} +(36.6615 + 21.1665i) q^{31} +(20.7900 - 24.7765i) q^{32} +(2.84142 - 7.80673i) q^{33} +(5.20425 + 14.2986i) q^{34} +(-0.158400 + 0.132914i) q^{35} +(4.64624 + 26.3502i) q^{36} -38.2623i q^{37} +(-17.3309 - 2.04678i) q^{38} -9.98089 q^{39} +(-2.03516 + 0.358854i) q^{40} +(19.9806 + 23.8120i) q^{41} +(0.410511 - 0.149414i) q^{42} +(-23.3585 - 8.50180i) q^{43} +(-27.7770 - 23.3076i) q^{44} +(1.33258 - 2.30810i) q^{45} +(-27.5652 + 15.9148i) q^{46} +(0.261302 - 1.48192i) q^{47} +(-4.69200 - 0.827326i) q^{48} +(24.2837 + 42.0606i) q^{49} +(-19.8073 - 11.4358i) q^{50} +(7.70087 - 9.17754i) q^{51} +(-14.8994 + 40.9357i) q^{52} +(-23.9382 - 65.7695i) q^{53} +(-8.89279 + 7.46193i) q^{54} +(0.627180 + 3.55692i) q^{55} -4.32306i q^{56} +(5.42709 + 12.6230i) q^{57} +22.0958 q^{58} +(60.4126 - 10.6524i) q^{59} +(0.461293 + 0.549747i) q^{60} +(7.01185 - 2.55210i) q^{61} +(36.5376 + 13.2986i) q^{62} +(4.27091 + 3.58372i) q^{63} +(1.67726 - 2.90509i) q^{64} +(3.75784 - 2.16959i) q^{65} +(1.32504 - 7.51468i) q^{66} +(-4.76316 - 0.839873i) q^{67} +(-26.1450 - 45.2845i) q^{68} +(21.7034 + 12.5305i) q^{69} +(-0.122080 + 0.145490i) q^{70} +(6.72879 - 18.4872i) q^{71} +(19.0574 + 52.3597i) q^{72} +(-50.3508 + 42.2494i) q^{73} +(-6.10263 - 34.6097i) q^{74} +18.0078i q^{75} +(59.8738 - 3.41515i) q^{76} -7.55554 q^{77} +(-9.02809 + 1.59190i) q^{78} +(-32.2459 - 38.4291i) q^{79} +(1.94639 - 0.708429i) q^{80} +(-63.1033 - 22.9677i) q^{81} +(21.8711 + 18.3520i) q^{82} +(-19.0911 + 33.0668i) q^{83} +(-1.30012 + 0.750623i) q^{84} +(-0.904442 + 5.12935i) q^{85} +(-22.4846 - 3.96465i) q^{86} +(-8.69851 - 15.0663i) q^{87} +(-65.3945 - 37.7556i) q^{88} +(-85.8514 + 102.314i) q^{89} +(0.837240 - 2.30030i) q^{90} +(3.10458 + 8.52976i) q^{91} +(83.7911 - 70.3091i) q^{92} +(-5.31607 - 30.1489i) q^{93} -1.38213i q^{94} +(-4.78725 - 3.57291i) q^{95} -23.3899 q^{96} +(-79.6741 + 14.0487i) q^{97} +(28.6740 + 34.1723i) q^{98} +(91.5107 - 33.3072i) 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}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^5 - 36 * q^6 + 6 * q^7 - 9 * q^8 - 24 * q^9	\( 12 q - 6 q^{2} - 6 q^{5} - 36 q^{6} + 6 q^{7} - 9 q^{8} - 24 q^{9} + 51 q^{10} - 18 q^{11} + 63 q^{12} + 21 q^{13} + 9 q^{14} + 63 q^{15} - 12 q^{16} - 3 q^{17} - 24 q^{19} - 90 q^{20} + 30 q^{21} - 78 q^{22} - 102 q^{23} - 12 q^{24} - 156 q^{25} + 21 q^{26} - 27 q^{27} + 12 q^{28} + 147 q^{29} + 24 q^{30} + 99 q^{31} + 165 q^{32} + 84 q^{33} + 132 q^{34} + 96 q^{35} + 63 q^{36} + 72 q^{38} - 108 q^{39} - 138 q^{40} - 144 q^{41} - 237 q^{42} - 27 q^{43} - 123 q^{44} - 3 q^{45} - 54 q^{46} - 99 q^{47} - 51 q^{48} - 24 q^{49} + 72 q^{50} - 42 q^{51} + 93 q^{52} + 111 q^{53} + 21 q^{54} + 162 q^{55} - 168 q^{57} - 132 q^{58} + 3 q^{59} - 30 q^{60} + 150 q^{61} + 108 q^{62} + 234 q^{63} + 27 q^{64} + 126 q^{65} + 168 q^{66} + 135 q^{67} - 30 q^{68} + 72 q^{69} + 225 q^{70} - 168 q^{71} - 102 q^{72} - 90 q^{73} - 231 q^{74} + 42 q^{76} + 246 q^{77} - 189 q^{78} - 75 q^{79} + 21 q^{80} - 159 q^{81} - 117 q^{82} - 156 q^{83} + 99 q^{84} - 300 q^{85} - 144 q^{86} + 69 q^{87} - 405 q^{88} - 558 q^{89} - 66 q^{90} - 453 q^{91} + 48 q^{92} - 57 q^{93} - 69 q^{95} + 558 q^{96} + 465 q^{97} + 777 q^{98} + 462 q^{99}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

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 $

$2$	0.904538	−	0.159494i	0.452269	−	0.0797472i	0.0571263	−	0.998367i	$-0.481806\pi$
$2$	0.904538	−	0.159494i	0.452269	−	0.0797472i	0.395143	+	0.918620i	$0.370695\pi$
$3$	−0.464845	−	0.553981i	−0.154948	−	0.184660i	0.682986	−	0.730432i	$-0.260681\pi$
$3$	−0.464845	−	0.553981i	−0.154948	−	0.184660i	−0.837934	+	0.545771i	$0.816237\pi$
$4$	−2.96602	+	1.07954i	−0.741505	+	0.269886i
$5$	0.295437	+	0.107530i	0.0590875	+	0.0215061i	0.371395	−	0.928475i	$-0.378880\pi$
$5$	0.295437	+	0.107530i	0.0590875	+	0.0215061i	−0.312307	+	0.949981i	$0.601102\pi$
$6$	−0.508827	−	0.426957i	−0.0848046	−	0.0711595i
$7$	−0.328846	+	0.569578i	−0.0469780	+	0.0813683i	−0.888558	−	0.458764i	$-0.848292\pi$
$7$	−0.328846	+	0.569578i	−0.0469780	+	0.0813683i	0.841580	+	0.540132i	$0.181626\pi$
$8$	−5.69245	+	3.28654i	−0.711556	+	0.410817i
$9$	1.47202	−	8.34824i	0.163558	−	0.927582i
$10$	0.284385	+	0.0501447i	0.0284385	+	0.00501447i
$11$	5.74398	+	9.94886i	0.522180	+	0.904442i	0.999667	+	0.0258030i	$0.00821426\pi$
$11$	5.74398	+	9.94886i	0.522180	+	0.904442i	−0.477487	+	0.878639i	$0.658452\pi$
$12$	1.97679	+	1.14130i	0.164732	+	0.0951082i
$13$	8.87147	−	10.5726i	0.682421	−	0.813277i	−0.307996	−	0.951388i	$-0.599658\pi$
$13$	8.87147	−	10.5726i	0.682421	−	0.813277i	0.990417	+	0.138110i	$0.0441029\pi$
$14$	−0.206609	+	0.567654i	−0.0147578	+	0.0405467i
$15$	−0.0777629	−	0.213652i	−0.00518419	−	0.0142435i
$16$	5.04684	−	4.23480i	0.315427	−	0.264675i
$17$	2.87674	+	16.3148i	0.169220	+	0.959696i	0.944606	+	0.328207i	$0.106445\pi$
$17$	2.87674	+	16.3148i	0.169220	+	0.959696i	−0.775385	+	0.631488i	$0.782444\pi$
$18$		−	7.78608i		−	0.432560i
$19$	−18.1952	−	5.47110i	−0.957645	−	0.287953i
$19$	−18.1952	−	5.47110i	−0.957645	−	0.287953i
$20$	−0.992357			−0.0496178
$21$	0.468398	−	0.0825913i	0.0223047	−	0.00393292i
$22$	6.78243	+	8.08299i	0.308292	+	0.367409i
$23$	−32.5643	+	11.8524i	−1.41584	+	0.515323i	−0.932838	−	0.360297i	$-0.882675\pi$
$23$	−32.5643	+	11.8524i	−1.41584	+	0.515323i	−0.483001	+	0.875620i	$0.660453\pi$
$24$	4.46679	+	1.62578i	0.186116	+	0.0677407i
$25$	−19.0754	−	16.0062i	−0.763016	−	0.640246i
$26$	6.33831	−	10.9783i	0.243781	−	0.422241i
$27$	−10.9456	+	6.31944i	−0.405392	+	0.234053i
$28$	0.360480	−	2.04438i	0.0128743	−	0.0730137i
$29$	23.6911	+	4.17738i	0.816934	+	0.144048i	0.566474	−	0.824079i	$-0.308307\pi$
$29$	23.6911	+	4.17738i	0.816934	+	0.144048i	0.250460	+	0.968127i	$0.419418\pi$
$30$	−0.104416	−	0.180853i	−0.00348053	−	0.00602845i
$31$	36.6615	+	21.1665i	1.18263	+	0.682791i	0.956621	−	0.291335i	$-0.0940995\pi$
$31$	36.6615	+	21.1665i	1.18263	+	0.682791i	0.226007	+	0.974126i	$0.427433\pi$
$32$	20.7900	−	24.7765i	0.649687	−	0.774267i
$33$	2.84142	−	7.80673i	0.0861036	−	0.236568i
$34$	5.20425	+	14.2986i	0.153066	+	0.420546i
$35$	−0.158400	+	0.132914i	−0.00452573	+	0.00379754i
$36$	4.64624	+	26.3502i	0.129062	+	0.731949i
$37$		−	38.2623i		−	1.03412i	−0.855950	−	0.517058i	$-0.827027\pi$
$37$		−	38.2623i		−	1.03412i	0.855950	−	0.517058i	$-0.172973\pi$
$38$	−17.3309	−	2.04678i	−0.456076	−	0.0538626i
$39$	−9.98089			−0.255920
$40$	−2.03516	+	0.358854i	−0.0508791	+	0.00897136i
$41$	19.9806	+	23.8120i	0.487332	+	0.580780i	0.952537	−	0.304423i	$-0.0984638\pi$
$41$	19.9806	+	23.8120i	0.487332	+	0.580780i	−0.465205	+	0.885203i	$0.654019\pi$
$42$	0.410511	−	0.149414i	0.00977408	−	0.00355747i
$43$	−23.3585	−	8.50180i	−0.543221	−	0.197716i	0.0558110	−	0.998441i	$-0.482226\pi$
$43$	−23.3585	−	8.50180i	−0.543221	−	0.197716i	−0.599032	+	0.800725i	$0.704448\pi$
$44$	−27.7770	−	23.3076i	−0.631295	−	0.529719i
$45$	1.33258	−	2.30810i	0.0296129	−	0.0512910i
$46$	−27.5652	+	15.9148i	−0.599244	+	0.345974i
$47$	0.261302	−	1.48192i	0.00555962	−	0.0315302i	−0.981902	−	0.189391i	$-0.939349\pi$
$47$	0.261302	−	1.48192i	0.00555962	−	0.0315302i	0.987461	+	0.157861i	$0.0504597\pi$
$48$	−4.69200	−	0.827326i	−0.0977499	−	0.0172360i
$49$	24.2837	+	42.0606i	0.495586	+	0.858380i
$50$	−19.8073	−	11.4358i	−0.396146	−	0.228715i
$51$	7.70087	−	9.17754i	0.150997	−	0.179952i
$52$	−14.8994	+	40.9357i	−0.286526	+	0.787225i
$53$	−23.9382	−	65.7695i	−0.451663	−	1.24093i	−0.931553	−	0.363606i	$-0.881546\pi$
$53$	−23.9382	−	65.7695i	−0.451663	−	1.24093i	0.479890	−	0.877329i	$-0.340677\pi$
$54$	−8.89279	+	7.46193i	−0.164681	+	0.138184i
$55$	0.627180	+	3.55692i	0.0114033	+	0.0646712i
$56$		−	4.32306i		−	0.0771975i
$57$	5.42709	+	12.6230i	0.0952121	+	0.221457i
$58$	22.0958			0.380962
$59$	60.4126	−	10.6524i	1.02394	−	0.180549i	0.363633	−	0.931542i	$-0.381536\pi$
$59$	60.4126	−	10.6524i	1.02394	−	0.180549i	0.660309	+	0.750994i	$0.270425\pi$
$60$	0.461293	+	0.549747i	0.00768821	+	0.00916245i
$61$	7.01185	−	2.55210i	0.114948	−	0.0418378i	−0.283906	−	0.958852i	$-0.591630\pi$
$61$	7.01185	−	2.55210i	0.114948	−	0.0418378i	0.398854	+	0.917014i	$0.369408\pi$
$62$	36.5376	+	13.2986i	0.589317	+	0.214494i
$63$	4.27091	+	3.58372i	0.0677922	+	0.0568844i
$64$	1.67726	−	2.90509i	0.0262071	−	0.0453921i
$65$	3.75784	−	2.16959i	0.0578129	−	0.0333783i
$66$	1.32504	−	7.51468i	0.0200764	−	0.113859i
$67$	−4.76316	−	0.839873i	−0.0710919	−	0.0125354i	0.137989	−	0.990434i	$-0.455936\pi$
$67$	−4.76316	−	0.839873i	−0.0710919	−	0.0125354i	−0.209081	+	0.977898i	$0.567047\pi$
$68$	−26.1450	−	45.2845i	−0.384486	−	0.665949i
$69$	21.7034	+	12.5305i	0.314542	+	0.181601i
$70$	−0.122080	+	0.145490i	−0.00174400	+	0.00207842i
$71$	6.72879	−	18.4872i	0.0947717	−	0.260383i	−0.883244	−	0.468913i	$-0.844646\pi$
$71$	6.72879	−	18.4872i	0.0947717	−	0.260383i	0.978016	+	0.208530i	$0.0668679\pi$
$72$	19.0574	+	52.3597i	0.264686	+	0.727219i
$73$	−50.3508	+	42.2494i	−0.689738	+	0.578759i	−0.918834	−	0.394645i	$-0.870867\pi$
$73$	−50.3508	+	42.2494i	−0.689738	+	0.578759i	0.229096	+	0.973404i	$0.426423\pi$
$74$	−6.10263	−	34.6097i	−0.0824679	−	0.467699i
$75$			18.0078i			0.240104i
$76$	59.8738	−	3.41515i	0.787813	−	0.0449362i
$77$	−7.55554			−0.0981239
$78$	−9.02809	+	1.59190i	−0.115745	+	0.0204089i
$79$	−32.2459	−	38.4291i	−0.408176	−	0.486445i	0.522319	−	0.852750i	$-0.325067\pi$
$79$	−32.2459	−	38.4291i	−0.408176	−	0.486445i	−0.930495	+	0.366305i	$0.880623\pi$
$80$	1.94639	−	0.708429i	0.0243299	−	0.00885537i
$81$	−63.1033	−	22.9677i	−0.779053	−	0.283552i
$82$	21.8711	+	18.3520i	0.266721	+	0.223805i
$83$	−19.0911	+	33.0668i	−0.230014	+	0.398395i	−0.957812	−	0.287396i	$-0.907210\pi$
$83$	−19.0911	+	33.0668i	−0.230014	+	0.398395i	0.727798	+	0.685791i	$0.240544\pi$
$84$	−1.30012	+	0.750623i	−0.0154776	+	0.00893599i
$85$	−0.904442	+	5.12935i	−0.0106405	+	0.0603453i
$86$	−22.4846	−	3.96465i	−0.261449	−	0.0461006i
$87$	−8.69851	−	15.0663i	−0.0999829	−	0.173175i
$88$	−65.3945	−	37.7556i	−0.743120	−	0.429040i
$89$	−85.8514	+	102.314i	−0.964623	+	1.14959i	0.0240810	+	0.999710i	$0.492334\pi$
$89$	−85.8514	+	102.314i	−0.964623	+	1.14959i	−0.988704	+	0.149883i	$0.952110\pi$
$90$	0.837240	−	2.30030i	0.00930267	−	0.0255589i
$91$	3.10458	+	8.52976i	0.0341162	+	0.0937336i
$92$	83.7911	−	70.3091i	0.910773	−	0.764229i
$93$	−5.31607	−	30.1489i	−0.0571620	−	0.324182i
$94$		−	1.38213i		−	0.0147035i
$95$	−4.78725	−	3.57291i	−0.0503921	−	0.0376096i
$96$	−23.3899			−0.243644
$97$	−79.6741	+	14.0487i	−0.821382	+	0.144832i	−0.568519	−	0.822670i	$-0.692483\pi$
$97$	−79.6741	+	14.0487i	−0.821382	+	0.144832i	−0.252863	+	0.967502i	$0.581372\pi$
$98$	28.6740	+	34.1723i	0.292592	+	0.348697i
$99$	91.5107	−	33.3072i	0.924350	−	0.336436i
$100$	73.8573	+	26.8819i	0.738573	+	0.268819i
$101$	99.4345	+	83.4354i	0.984500	+	0.826093i	0.984762	−	0.173907i	$-0.0556391\pi$
$101$	99.4345	+	83.4354i	0.984500	+	0.826093i	−0.000262465		1.00000i	$0.500084\pi$
$102$	5.50196	−	9.52968i	0.0539408	−	0.0934282i
$103$	162.496	−	93.8172i	1.57763	−	0.910847i	0.582444	−	0.812871i	$-0.302097\pi$
$103$	162.496	−	93.8172i	1.57763	−	0.910847i	0.995189	−	0.0979757i	$-0.0312367\pi$
$104$	−15.7531	+	89.3404i	−0.151472	+	0.859042i
$105$	0.147263	+	0.0259665i	0.00140251	+	0.000247300i
$106$	−32.1428	−	55.6730i	−0.303234	−	0.525217i
$107$	−49.4649	−	28.5586i	−0.462289	−	0.266903i	0.250717	−	0.968060i	$-0.419334\pi$
$107$	−49.4649	−	28.5586i	−0.462289	−	0.266903i	−0.713006	+	0.701158i	$0.752667\pi$
$108$	25.6427	−	30.5598i	0.237433	−	0.282961i
$109$	44.8159	−	123.131i	0.411155	−	1.12964i	−0.545422	−	0.838161i	$-0.683631\pi$
$109$	44.8159	−	123.131i	0.411155	−	1.12964i	0.956578	−	0.291478i	$-0.0941470\pi$
$110$	1.13462	+	3.11733i	0.0103147	+	0.0283394i
$111$	−21.1966	+	17.7861i	−0.190960	+	0.160235i
$112$	0.752416	+	4.26717i	0.00671800	+	0.0380997i
$113$			206.183i			1.82463i	0.409488	+	0.912315i	$0.365707\pi$
$113$			206.183i			1.82463i	−0.409488	+	0.912315i	$0.634293\pi$
$114$	6.92231	+	10.5524i	0.0607220	+	0.0925652i
$115$	−10.8952			−0.0947409
$116$	−74.7779	+	13.1854i	−0.644637	+	0.113667i
$117$	−75.2036	−	89.6242i	−0.642766	−	0.766019i
$118$	52.9465	−	19.2709i	0.448699	−	0.163313i
$119$	−10.2386	−	3.72654i	−0.0860385	−	0.0313154i
$120$	1.14484	+	0.960631i	0.00954029	+	0.00800526i
$121$	−5.48650	+	9.50290i	−0.0453430	+	0.0785364i
$122$	5.93543	−	3.42682i	0.0486511	−	0.0280887i
$123$	3.90349	−	22.1378i	0.0317357	−	0.179982i
$124$	−131.589	−	23.2027i	−1.06120	−	0.187118i
$125$	−7.84441	−	13.5869i	−0.0627553	−	0.108695i
$126$	4.43478	+	2.56042i	0.0351967	+	0.0203208i
$127$	−94.1229	+	112.171i	−0.741125	+	0.883238i	−0.996499	−	0.0836040i	$-0.973357\pi$
$127$	−94.1229	+	112.171i	−0.741125	+	0.883238i	0.255374	+	0.966842i	$0.417801\pi$
$128$	−43.1947	+	118.676i	−0.337458	+	0.927159i
$129$	6.14826	+	16.8922i	0.0476609	+	0.130947i
$130$	3.05307	−	2.56183i	0.0234852	−	0.0197064i
$131$	−34.6271	−	196.380i	−0.264329	−	1.49908i	−0.770940	−	0.636908i	$-0.780213\pi$
$131$	−34.6271	−	196.380i	−0.264329	−	1.49908i	0.506611	−	0.862175i	$-0.330898\pi$
$132$			26.2224i			0.198654i
$133$	9.09966	−	8.56447i	0.0684185	−	0.0643945i
$134$	−4.44241			−0.0331523
$135$	−3.91327	+	0.690015i	−0.0289872	+	0.00511122i
$136$	−69.9950	−	83.4168i	−0.514669	−	0.613359i
$137$	−6.59818	+	2.40154i	−0.0481619	+	0.0175295i	−0.365989	−	0.930619i	$-0.619269\pi$
$137$	−6.59818	+	2.40154i	−0.0481619	+	0.0175295i	0.317827	+	0.948149i	$0.397047\pi$
$138$	21.6301	+	7.87270i	0.156740	+	0.0570486i
$139$	107.440	+	90.1530i	0.772951	+	0.648583i	0.941463	−	0.337117i	$-0.109452\pi$
$139$	107.440	+	90.1530i	0.772951	+	0.648583i	−0.168512	+	0.985700i	$0.553896\pi$
$140$	0.326333	−	0.565225i	0.00233095	−	0.00403732i
$141$	−0.942420	+	0.544106i	−0.00668383	+	0.00385891i
$142$	3.13784	−	17.7956i	0.0220975	−	0.125321i
$143$	156.143	+	27.5322i	1.09191	+	0.192533i
$144$	−27.9241	−	48.3659i	−0.193917	−	0.335874i
$145$	6.55004	+	3.78167i	0.0451727	+	0.0260805i
$146$	−38.8057	+	46.2468i	−0.265793	+	0.316759i
$147$	12.0126	−	33.0044i	0.0817185	−	0.224520i
$148$	41.3058	+	113.487i	0.279093	+	0.766803i
$149$	48.6750	−	40.8432i	0.326678	−	0.274115i	−0.464667	−	0.885486i	$-0.653826\pi$
$149$	48.6750	−	40.8432i	0.326678	−	0.274115i	0.791345	+	0.611370i	$0.209381\pi$
$150$	2.87214	+	16.2887i	0.0191476	+	0.108592i
$151$		−	54.3637i		−	0.360025i	−0.983664	−	0.180012i	$-0.942386\pi$
$151$		−	54.3637i		−	0.360025i	0.983664	−	0.180012i	$-0.0576137\pi$
$152$	121.556	−	28.6554i	0.799713	−	0.188522i
$153$	140.435			0.917874
$154$	−6.83427	+	1.20507i	−0.0443784	+	0.00782511i
$155$	8.55512	+	10.1956i	0.0551944	+	0.0657781i
$156$	29.6035	−	10.7748i	0.189766	−	0.0690692i
$157$	−68.5269	−	24.9417i	−0.436477	−	0.158865i	0.114430	−	0.993431i	$-0.463496\pi$
$157$	−68.5269	−	24.9417i	−0.436477	−	0.158865i	−0.550907	+	0.834567i	$0.685718\pi$
$158$	−35.2969	−	29.6176i	−0.223398	−	0.187453i
$159$	−25.3075	+	43.8340i	−0.159167	+	0.275685i
$160$	8.80637	−	5.08436i	0.0550398	−	0.0317773i
$161$	3.95775	−	22.4455i	0.0245823	−	0.139413i
$162$	−60.7426	−	10.7106i	−0.374954	−	0.0661145i
$163$	57.8449	+	100.190i	0.354877	+	0.614664i	0.987097	−	0.160124i	$-0.0511895\pi$
$163$	57.8449	+	100.190i	0.354877	+	0.614664i	−0.632220	+	0.774789i	$0.717856\pi$
$164$	−84.9689	−	49.0568i	−0.518103	−	0.299127i
$165$	1.67892	−	2.00086i	0.0101753	−	0.0121264i
$166$	−11.9947	+	32.9551i	−0.0722571	+	0.198525i
$167$	−64.4235	−	177.002i	−0.385770	−	1.05989i	−0.968887	−	0.247505i	$-0.920389\pi$
$167$	−64.4235	−	177.002i	−0.385770	−	1.05989i	0.583117	−	0.812388i	$-0.301833\pi$
$168$	−2.39489	+	2.00955i	−0.0142553	+	0.0119616i
$169$	−3.73047	−	21.1565i	−0.0220738	−	0.125187i
$170$			4.78394i			0.0281408i
$171$	−72.4578	+	143.845i	−0.423730	+	0.841197i
$172$	78.4598			0.456162
$173$	85.7770	−	15.1248i	0.495821	−	0.0874266i	0.0798544	−	0.996807i	$-0.474554\pi$
$173$	85.7770	−	15.1248i	0.495821	−	0.0874266i	0.415967	+	0.909380i	$0.363443\pi$
$174$	−10.2711	−	12.2406i	−0.0590294	−	0.0703485i
$175$	15.3896	−	5.60137i	0.0879407	−	0.0320078i
$176$	71.1203	+	25.8857i	0.404093	+	0.147078i
$177$	−33.9837	−	28.5157i	−0.191998	−	0.161106i
$178$	−61.3374	+	106.240i	−0.344592	+	0.596851i
$179$	−152.036	+	87.7779i	−0.849362	+	0.490380i	−0.860436	−	0.509559i	$-0.829808\pi$
$179$	−152.036	+	87.7779i	−0.849362	+	0.490380i	0.0110734	+	0.999939i	$0.496475\pi$
$180$	−1.46077	+	8.28443i	−0.00811538	+	0.0460246i
$181$	−129.156	−	22.7736i	−0.713567	−	0.125821i	−0.194932	−	0.980817i	$-0.562449\pi$
$181$	−129.156	−	22.7736i	−0.713567	−	0.125821i	−0.518635	+	0.854996i	$0.673560\pi$
$182$	4.16866	+	7.22033i	0.0229047	+	0.0396721i
$183$	−4.67324	−	2.69810i	−0.0255368	−	0.0147437i
$184$	146.417	−	174.493i	0.795745	−	0.948331i
$185$	4.11436	−	11.3041i	0.0222398	−	0.0611033i
$186$	−9.61717	−	26.4230i	−0.0517052	−	0.142059i
$187$	−145.790	+	122.332i	−0.779625	+	0.654183i
$188$	0.824767	+	4.67748i	0.00438706	+	0.0248802i
$189$		−	8.31249i		−	0.0439814i
$190$	−4.90011	−	2.46829i	−0.0257900	−	0.0129910i
$191$	−288.456			−1.51024			−0.755119	−	0.655587i	$-0.772421\pi$
$191$	−288.456			−1.51024			−0.755119	+	0.655587i	$0.772421\pi$
$192$	−2.38903	+	0.421251i	−0.0124429	+	0.00219401i
$193$	90.7386	+	108.138i	0.470148	+	0.560301i	0.948054	−	0.318111i	$-0.103048\pi$
$193$	90.7386	+	108.138i	0.470148	+	0.560301i	−0.477905	+	0.878411i	$0.658604\pi$
$194$	−69.8276	+	25.4152i	−0.359936	+	0.131006i
$195$	−2.94873	−	1.07325i	−0.0151217	−	0.00550384i
$196$	−117.432	−	98.5374i	−0.599144	−	0.502742i
$197$	117.725	−	203.905i	0.597587	−	1.03505i	−0.395589	−	0.918428i	$-0.629460\pi$
$197$	117.725	−	203.905i	0.597587	−	1.03505i	0.993176	−	0.116624i	$-0.0372071\pi$
$198$	77.4626	−	44.7230i	0.391225	−	0.225874i
$199$	−10.7594	+	61.0198i	−0.0540675	+	0.306632i	−0.999834	−	0.0182149i	$-0.994202\pi$
$199$	−10.7594	+	61.0198i	−0.0540675	+	0.306632i	0.945767	+	0.324847i	$0.105313\pi$
$200$	161.190	+	28.4222i	0.805952	+	0.142111i
$201$	1.74886	+	3.02911i	0.00870079	+	0.0150702i
$202$	103.250	+	59.6113i	0.511137	+	0.295105i
$203$	−10.1701	+	12.1202i	−0.0500989	+	0.0597055i
$204$	−12.9334	+	35.5342i	−0.0633989	+	0.174187i
$205$	3.34251	+	9.18347i	0.0163049	+	0.0447974i
$206$	132.021	−	110.778i	0.640877	−	0.537760i
$207$	51.0116	+	289.301i	0.246433	+	1.39759i
$208$		−	90.9271i		−	0.437149i
$209$	−50.0818	−	212.448i	−0.239626	−	1.01650i
$210$	0.137347			0.000654033
$211$	145.903	−	25.7266i	0.691483	−	0.121927i	0.183147	−	0.983086i	$-0.441372\pi$
$211$	145.903	−	25.7266i	0.691483	−	0.121927i	0.508337	+	0.861158i	$0.330261\pi$
$212$	142.002	+	169.231i	0.669821	+	0.798262i
$213$	−13.3694	+	4.86607i	−0.0627672	+	0.0228454i
$214$	−49.2979	−	17.9430i	−0.230364	−	0.0838456i
$215$	−5.98677	−	5.02350i	−0.0278455	−	0.0233651i
$216$	41.5381	−	71.9461i	0.192306	−	0.333084i
$217$	−24.1120	+	13.9210i	−0.111115	+	0.0641523i
$218$	20.8990	−	118.524i	0.0958671	−	0.543689i
$219$	46.8107	+	8.25399i	0.213748	+	0.0376895i
$220$	−5.70007	−	9.87282i	−0.0259094	−	0.0448764i
$221$	198.011	+	114.322i	0.895978	+	0.517293i
$222$	−16.3364	+	19.4689i	−0.0735872	+	0.0876978i
$223$	0.702119	−	1.92906i	0.00314852	−	0.00865048i	−0.938108	−	0.346342i	$-0.887424\pi$
$223$	0.702119	−	1.92906i	0.00314852	−	0.00865048i	0.941257	+	0.337691i	$0.109646\pi$
$224$	7.27547	+	19.9892i	0.0324798	+	0.0892375i
$225$	−161.703	+	135.685i	−0.718678	+	0.603042i
$226$	32.8851	+	186.501i	0.145509	+	0.825224i
$227$		−	355.075i		−	1.56421i	−0.623147	−	0.782104i	$-0.714146\pi$
$227$		−	355.075i		−	1.56421i	0.623147	−	0.782104i	$-0.285854\pi$
$228$	−29.7240	−	31.5814i	−0.130368	−	0.138515i
$229$	165.134			0.721111			0.360556	−	0.932738i	$-0.382587\pi$
$229$	165.134			0.721111			0.360556	+	0.932738i	$0.382587\pi$
$230$	−9.85513	+	1.73772i	−0.0428484	+	0.00755533i
$231$	3.51216	+	4.18563i	0.0152041	+	0.0181196i
$232$	−148.589	+	54.0821i	−0.640472	+	0.233113i
$233$	−105.453	−	38.3818i	−0.452588	−	0.164729i	0.105660	−	0.994402i	$-0.466304\pi$
$233$	−105.453	−	38.3818i	−0.452588	−	0.164729i	−0.558249	+	0.829674i	$0.688527\pi$
$234$	−82.3191	−	69.0739i	−0.351791	−	0.295188i
$235$	0.236550	−	0.409716i	0.00100659	−	0.00174347i
$236$	−167.685	+	96.8131i	−0.710531	+	0.410225i
$237$	−6.29967	+	35.7272i	−0.0265809	+	0.150748i
$238$	−9.85554	−	1.73780i	−0.0414099	−	0.00730167i
$239$	−5.26073	−	9.11186i	−0.0220114	−	0.0381249i	0.854810	−	0.518941i	$-0.173674\pi$
$239$	−5.26073	−	9.11186i	−0.0220114	−	0.0381249i	−0.876821	+	0.480816i	$0.840340\pi$
$240$	−1.29723	−	0.748955i	−0.00540512	−	0.00312065i
$241$	194.160	−	231.390i	0.805641	−	0.960126i	−0.194141	−	0.980974i	$-0.562192\pi$
$241$	194.160	−	231.390i	0.805641	−	0.960126i	0.999783	+	0.0208477i	$0.00663651\pi$
$242$	−3.44709	+	9.47080i	−0.0142442	+	0.0391356i
$243$	55.5144	+	152.524i	0.228454	+	0.627673i
$244$	−18.0422	+	15.1392i	−0.0739433	+	0.0620458i
$245$	2.65152	+	15.0375i	0.0108225	+	0.0613777i
$246$		−	20.6470i		−	0.0839310i
$247$	−219.262	+	143.834i	−0.887702	+	0.582326i
$248$	−278.258			−1.12201
$249$	27.1928	−	4.79483i	0.109208	−	0.0192563i
$250$	−9.26260	−	11.0387i	−0.0370504	−	0.0441550i
$251$	−265.516	+	96.6398i	−1.05783	+	0.385019i	−0.811613	−	0.584195i	$-0.801410\pi$
$251$	−265.516	+	96.6398i	−1.05783	+	0.385019i	−0.246218	+	0.969214i	$0.579188\pi$
$252$	−16.5364	−	6.01875i	−0.0656205	−	0.0238839i
$253$	−304.967	−	255.897i	−1.20540	−	1.01145i
$254$	−67.2470	+	116.475i	−0.264752	+	0.458564i
$255$	3.26199	−	1.88331i	0.0127921	−	0.00738553i
$256$	−22.4730	+	127.451i	−0.0877852	+	0.497855i
$257$	243.319	+	42.9037i	0.946765	+	0.166940i	0.625654	−	0.780101i	$-0.284832\pi$
$257$	243.319	+	42.9037i	0.946765	+	0.166940i	0.321112	+	0.947041i	$0.395943\pi$
$258$	8.25554	+	14.2990i	0.0319982	+	0.0554226i
$259$	21.7934	+	12.5824i	0.0841443	+	0.0485807i
$260$	−8.80366	+	10.4918i	−0.0338602	+	0.0403531i
$261$	69.7475	−	191.630i	0.267232	−	0.734214i
$262$	−62.6430	−	172.110i	−0.239095	−	0.656909i
$263$	151.172	−	126.849i	0.574800	−	0.482315i	−0.308435	−	0.951246i	$-0.599805\pi$
$263$	151.172	−	126.849i	0.574800	−	0.482315i	0.883235	+	0.468931i	$0.155361\pi$
$264$	9.48248	+	53.7778i	0.0359185	+	0.203704i
$265$		−	22.0049i		−	0.0830372i
$266$	6.86500	−	9.19823i	0.0258083	−	0.0345798i
$267$	96.5875			0.361751
$268$	15.0343	−	2.65095i	0.0560981	−	0.00989162i
$269$	291.064	+	346.876i	1.08202	+	1.28950i	0.954677	+	0.297644i	$0.0962007\pi$
$269$	291.064	+	346.876i	1.08202	+	1.28950i	0.127344	+	0.991859i	$0.459355\pi$
$270$	−3.42965	+	1.24829i	−0.0127024	+	0.00462329i
$271$	201.193	+	73.2284i	0.742411	+	0.270215i	0.685409	−	0.728159i	$-0.259624\pi$
$271$	201.193	+	73.2284i	0.742411	+	0.270215i	0.0570022	+	0.998374i	$0.481846\pi$
$272$	83.6085	+	70.1558i	0.307384	+	0.257926i
$273$	3.28218	−	5.68490i	0.0120226	−	0.0208238i
$274$	−5.58527	+	3.22466i	−0.0203842	+	0.0117688i
$275$	49.6744	−	281.717i	0.180634	−	1.02443i
$276$	−77.8998	−	13.7358i	−0.282246	−	0.0497675i
$277$	141.224	+	244.608i	0.509835	+	0.883060i	0.999935	+	0.0113941i	$0.00362694\pi$
$277$	141.224	+	244.608i	0.509835	+	0.883060i	−0.490100	+	0.871666i	$0.663040\pi$
$278$	111.563	+	64.4107i	0.401305	+	0.231693i
$279$	230.669	−	274.901i	0.826772	−	0.985309i
$280$	0.464860	−	1.27719i	0.00166022	−	0.00456140i
$281$	−38.5847	−	106.011i	−0.137312	−	0.377262i	0.851909	−	0.523689i	$-0.175445\pi$
$281$	−38.5847	−	106.011i	−0.137312	−	0.377262i	−0.989221	+	0.146428i	$0.953222\pi$
$282$	−0.765673	+	0.642476i	−0.00271515	+	0.00227828i
$283$	2.30006	+	13.0443i	0.00812742	+	0.0460929i	0.988602	−	0.150554i	$-0.0481058\pi$
$283$	2.30006	+	13.0443i	0.00812742	+	0.0460929i	−0.980474	+	0.196647i	$0.936995\pi$
$284$			62.0974i			0.218653i
$285$	0.246004	+	4.31290i	0.000863172	+	0.0151330i
$286$	145.628			0.509190
$287$	−20.1333	+	3.55005i	−0.0701510	+	0.0123695i
$288$	−176.237	−	210.031i	−0.611935	−	0.729275i
$289$	13.6732	−	4.97664i	0.0473121	−	0.0172202i
$290$	6.52792	+	2.37597i	0.0225101	+	0.00819299i
$291$	44.8189	+	37.6075i	0.154017	+	0.129235i
$292$	103.732	−	179.668i	0.355245	−	0.615303i
$293$	−357.705	+	206.521i	−1.22084	+	0.704851i	−0.965096	−	0.261895i	$-0.915653\pi$
$293$	−357.705	+	206.521i	−1.22084	+	0.704851i	−0.255741	+	0.966745i	$0.582319\pi$
$294$	5.60186	−	31.7697i	0.0190539	−	0.108060i
$295$	18.9936	+	3.34908i	0.0643851	+	0.0113528i
$296$	125.750	+	217.806i	0.424833	+	0.735832i
$297$	−125.742	−	72.5974i	−0.423375	−	0.244436i
$298$	37.5141	−	44.7076i	0.125886	−	0.150025i
$299$	−163.582	+	449.438i	−0.547097	+	1.50314i
$300$	−19.4402	−	53.4115i	−0.0648006	−	0.178038i
$301$	12.5238	−	10.5087i	0.0416073	−	0.0349127i
$302$	−8.67071	−	49.1740i	−0.0287110	−	0.162828i
$303$		−	93.8694i		−	0.309800i
$304$	−114.997	+	49.4414i	−0.378281	+	0.162636i
$305$	2.34599			0.00769177
$306$	127.029	−	22.3986i	0.415126	−	0.0731979i
$307$	−297.413	−	354.443i	−0.968773	−	1.15454i	−0.987958	−	0.154723i	$-0.950552\pi$
$307$	−297.413	−	354.443i	−0.968773	−	1.15454i	0.0191851	−	0.999816i	$-0.493893\pi$
$308$	22.4099	−	8.15653i	0.0727593	−	0.0264822i
$309$	−127.509	−	46.4093i	−0.412649	−	0.150192i
$310$	9.36458	+	7.85781i	0.0302083	+	0.0253478i
$311$	−51.7090	+	89.5627i	−0.166267	+	0.287983i	−0.937104	−	0.349049i	$-0.886505\pi$
$311$	−51.7090	+	89.5627i	−0.166267	+	0.287983i	0.770838	+	0.637032i	$0.219838\pi$
$312$	56.8157	−	32.8025i	0.182101	−	0.105136i
$313$	17.8628	−	101.305i	0.0570697	−	0.323659i	−0.942886	−	0.333117i	$-0.891900\pi$
$313$	17.8628	−	101.305i	0.0570697	−	0.323659i	0.999955	+	0.00945832i	$0.00301072\pi$
$314$	−65.9632	−	11.6311i	−0.210074	−	0.0370417i
$315$	0.876427	+	1.51802i	0.00278231	+	0.00481910i
$316$	137.128	+	79.1708i	0.433949	+	0.250540i
$317$	−214.460	+	255.584i	−0.676530	+	0.806257i	−0.989657	−	0.143454i	$-0.954179\pi$
$317$	−214.460	+	255.584i	−0.676530	+	0.806257i	0.313127	+	0.949711i	$0.398624\pi$
$318$	−15.9004	+	43.6859i	−0.0500011	+	0.137377i
$319$	94.5209	+	259.694i	0.296304	+	0.814088i
$320$	0.807910	−	0.677917i	0.00252472	−	0.00211849i
$321$	7.17262	+	40.6780i	0.0223446	+	0.126723i
$322$		−	20.9341i		−	0.0650127i
$323$	36.9170	−	312.591i	0.114294	−	0.967775i
$324$	211.960			0.654199
$325$	−338.453	+	59.6785i	−1.04140	+	0.183626i
$326$	68.3027	+	81.4000i	0.209517	+	0.249693i
$327$	−89.0446	+	32.4096i	−0.272308	+	0.0991118i
$328$	−191.997	−	69.8814i	−0.585358	−	0.213053i
$329$	0.758140	+	0.636155i	0.00230438	+	0.00193360i
$330$	1.19952	−	2.07764i	0.00363492	−	0.00629586i
$331$	110.430	−	63.7569i	0.333626	−	0.192619i	−0.323824	−	0.946117i	$-0.604969\pi$
$331$	110.430	−	63.7569i	0.333626	−	0.192619i	0.657450	+	0.753498i	$0.271635\pi$
$332$	20.9276	−	118.687i	0.0630351	−	0.357490i
$333$	−319.423	−	56.3229i	−0.959228	−	0.169138i
$334$	−86.5044	−	149.830i	−0.258995	−	0.448593i
$335$	−1.31690	−	0.760314i	−0.00393105	−	0.00226960i
$336$	2.01417	−	2.40040i	0.00599456	−	0.00714404i
$337$	28.6484	−	78.7108i	0.0850101	−	0.233563i	−0.889903	−	0.456150i	$-0.849228\pi$
$337$	28.6484	−	78.7108i	0.0850101	−	0.233563i	0.974913	+	0.222587i	$0.0714502\pi$
$338$	−6.74870	−	18.5419i	−0.0199666	−	0.0548577i
$339$	114.222	−	95.8434i	0.336937	−	0.282724i
$340$	−2.85476	−	16.1901i	−0.00839634	−	0.0476180i
$341$			486.320i			1.42616i
$342$	−42.5984	+	141.670i	−0.124557	+	0.414239i
$343$	−64.1694			−0.187083
$344$	160.908	−	28.3725i	0.467757	−	0.0824782i
$345$	5.06459	+	6.03574i	0.0146800	+	0.0174949i
$346$	75.1763	−	27.3619i	0.217272	−	0.0790807i
$347$	440.707	+	160.404i	1.27005	+	0.462260i	0.887129	−	0.461521i	$-0.152696\pi$
$347$	440.707	+	160.404i	1.27005	+	0.462260i	0.382920	+	0.923781i	$0.374918\pi$
$348$	42.0646	+	35.2964i	0.120875	+	0.101426i
$349$	37.1655	−	64.3726i	0.106492	−	0.184449i	−0.807855	−	0.589381i	$-0.799372\pi$
$349$	37.1655	−	64.3726i	0.106492	−	0.184449i	0.914347	+	0.404932i	$0.132705\pi$
$350$	13.0271	−	7.52121i	0.0372203	−	0.0214892i
$351$	−30.2905	+	171.786i	−0.0862978	+	0.489419i
$352$	365.915	+	64.5208i	1.03953	+	0.183298i
$353$	−80.6305	−	139.656i	−0.228415	−	0.395627i	0.728923	−	0.684595i	$-0.240021\pi$
$353$	−80.6305	−	139.656i	−0.228415	−	0.395627i	−0.957339	+	0.288969i	$0.906688\pi$
$354$	−35.2877	−	20.3733i	−0.0996827	−	0.0575518i
$355$	3.97587	−	4.73826i	0.0111996	−	0.0133472i
$356$	144.185	−	396.145i	0.405014	−	1.11277i
$357$	2.69492	+	7.40424i	0.00754881	+	0.0207402i
$358$	−123.522	+	103.647i	−0.345034	+	0.289518i
$359$	−96.7186	−	548.519i	−0.269411	−	1.52791i	−0.756173	−	0.654372i	$-0.772933\pi$
$359$	−96.7186	−	548.519i	−0.269411	−	1.52791i	0.486761	−	0.873535i	$-0.338178\pi$
$360$			17.5183i			0.0486619i
$361$	301.134	+	199.096i	0.834166	+	0.551513i
$362$	−120.458			−0.332758
$363$	7.81481	−	1.37796i	0.0215284	−	0.00379604i
$364$	−18.4165	−	21.9479i	−0.0505947	−	0.0602964i
$365$	−19.4186	+	7.06780i	−0.0532017	+	0.0193638i
$366$	−4.65746	−	1.69518i	−0.0127253	−	0.00463163i
$367$	233.112	+	195.604i	0.635182	+	0.532981i	0.902534	−	0.430618i	$-0.141704\pi$
$367$	233.112	+	195.604i	0.635182	+	0.532981i	−0.267352	+	0.963599i	$0.586149\pi$
$368$	−114.154	+	197.720i	−0.310201	+	0.537284i
$369$	228.200	−	131.751i	0.618428	−	0.357049i
$370$	1.91865	−	10.8812i	0.00518555	−	0.0294087i
$371$	45.3329	+	7.99341i	0.122191	+	0.0215456i
$372$	48.3146	+	83.6834i	0.129878	+	0.224955i
$373$	−263.000	−	151.843i	−0.705095	−	0.407087i	0.104147	−	0.994562i	$-0.466789\pi$
$373$	−263.000	−	151.843i	−0.705095	−	0.407087i	−0.809242	+	0.587475i	$0.800122\pi$
$374$	−112.361	+	133.907i	−0.300431	+	0.358040i
$375$	−3.88046	+	10.6615i	−0.0103479	+	0.0284306i
$376$	3.38293	+	9.29452i	0.00899715	+	0.0247195i
$377$	254.341	−	213.417i	0.674644	−	0.566093i
$378$	−1.32580	−	7.51897i	−0.00350740	−	0.0198914i
$379$			5.00631i			0.0132093i	0.999978	+	0.00660463i	$0.00210233\pi$
$379$			5.00631i			0.0132093i	−0.999978	+	0.00660463i	$0.997898\pi$
$380$	18.0562	+	5.42929i	0.0475163	+	0.0142876i
$381$	105.893			0.277935
$382$	−260.919	+	46.0071i	−0.683034	+	0.120437i
$383$	−21.6156	−	25.7605i	−0.0564377	−	0.0672598i	0.737087	−	0.675798i	$-0.236201\pi$
$383$	−21.6156	−	25.7605i	−0.0564377	−	0.0672598i	−0.793525	+	0.608538i	$0.791756\pi$
$384$	85.8233	−	31.2371i	0.223498	−	0.0813467i
$385$	−2.23219	−	0.812450i	−0.00579789	−	0.00211026i
$386$	99.3239	+	83.3427i	0.257316	+	0.215914i
$387$	−105.359	+	182.488i	−0.272246	+	0.471544i
$388$	221.149	−	127.680i	0.569971	−	0.329073i
$389$	−79.7035	+	452.021i	−0.204893	+	1.16201i	0.692714	+	0.721212i	$0.256415\pi$
$389$	−79.7035	+	452.021i	−0.204893	+	1.16201i	−0.897607	+	0.440796i	$0.854696\pi$
$390$	−2.83841	−	0.500489i	−0.00727798	−	0.00128330i
$391$	−287.049	−	497.184i	−0.734142	−	1.27157i
$392$	−276.468	−	159.619i	−0.705274	−	0.407190i
$393$	−92.6945	+	110.469i	−0.235864	+	0.281092i
$394$	73.9647	−	203.216i	0.187728	−	0.515778i
$395$	−5.39434	−	14.8208i	−0.0136565	−	0.0375211i
$396$	−235.466	+	197.579i	−0.594611	+	0.498938i
$397$	85.2334	+	483.383i	0.214694	+	1.21759i	0.881437	+	0.472301i	$0.156577\pi$
$397$	85.2334	+	483.383i	0.214694	+	1.21759i	−0.666744	+	0.745287i	$0.732312\pi$
$398$			56.9108i			0.142992i
$399$	−8.97449	−	1.05989i	−0.0224925	−	0.00265636i
$400$	−164.053			−0.410133
$401$	−322.647	+	56.8913i	−0.804605	+	0.141874i	−0.560801	−	0.827951i	$-0.689507\pi$
$401$	−322.647	+	56.8913i	−0.804605	+	0.141874i	−0.243805	+	0.969824i	$0.578396\pi$
$402$	2.06504	+	2.46101i	0.00513690	+	0.00612192i
$403$	549.026	−	199.829i	1.36235	−	0.495854i
$404$	−384.997	−	140.127i	−0.952962	−	0.346850i
$405$	−16.1733	−	13.5711i	−0.0399342	−	0.0335088i
$406$	−7.26611	+	12.5853i	−0.0178968	+	0.0309982i
$407$	380.666	−	219.778i	0.935298	−	0.539995i
$408$	−13.6745	+	77.5518i	−0.0335159	+	0.190078i
$409$	−644.395	−	113.624i	−1.57554	−	0.277810i	−0.683561	−	0.729893i	$-0.739570\pi$
$409$	−644.395	−	113.624i	−1.57554	−	0.277810i	−0.891976	+	0.452083i	$0.850681\pi$
$410$	4.48814	+	7.77369i	0.0109467	+	0.0189602i
$411$	4.39754	+	2.53892i	0.0106996	+	0.00617742i
$412$	−380.687	+	453.685i	−0.923998	+	1.10118i
$413$	−13.7991	+	37.9127i	−0.0334118	+	0.0917983i
$414$	92.2839	+	253.548i	0.222908	+	0.612435i
$415$	−9.19592	+	7.71630i	−0.0221589	+	0.0185935i
$416$	−77.5148	−	439.609i	−0.186334	−	1.05675i
$417$		−	101.427i		−	0.243230i
$418$	−79.1852	−	184.179i	−0.189438	−	0.440620i
$419$	−433.473			−1.03454			−0.517271	−	0.855822i	$-0.673052\pi$
$419$	−433.473			−1.03454			−0.517271	+	0.855822i	$0.673052\pi$
$420$	−0.464818	+	0.0819600i	−0.00110671	+	0.000195143i
$421$	−36.0724	−	42.9894i	−0.0856826	−	0.102113i	0.721500	−	0.692415i	$-0.243453\pi$
$421$	−36.0724	−	42.9894i	−0.0856826	−	0.102113i	−0.807182	+	0.590302i	$0.799009\pi$
$422$	127.872	−	46.5414i	0.303013	−	0.110288i
$423$	−11.9868	−	4.36282i	−0.0283375	−	0.0103140i
$424$	352.421	+	295.716i	0.831181	+	0.697443i
$425$	206.263	−	357.257i	0.485324	−	0.840605i
$426$	−11.3170	+	6.53389i	−0.0265658	+	0.0153378i
$427$	−0.852196	+	4.83304i	−0.00199578	+	0.0113186i
$428$	177.544	+	31.3058i	0.414823	+	0.0731445i
$429$	−57.3300	−	99.2984i	−0.133636	−	0.231465i
$430$	−6.21648	−	3.58909i	−0.0144569	−	0.00834672i
$431$	−44.8318	+	53.4285i	−0.104018	+	0.123964i	−0.815542	−	0.578698i	$-0.803561\pi$
$431$	−44.8318	+	53.4285i	−0.104018	+	0.123964i	0.711524	+	0.702662i	$0.248005\pi$
$432$	−28.4790	+	78.2455i	−0.0659237	+	0.181124i
$433$	45.7144	+	125.599i	0.105576	+	0.290068i	0.981221	−	0.192888i	$-0.0617854\pi$
$433$	45.7144	+	125.599i	0.105576	+	0.290068i	−0.875645	+	0.482956i	$0.839563\pi$
$434$	−19.5899	+	16.4378i	−0.0451379	+	0.0378752i
$435$	−0.949784	−	5.38649i	−0.00218341	−	0.0123827i
$436$			413.589i			0.948598i
$437$	657.361	−	37.4953i	1.50426	−	0.0858016i
$438$	43.6585			0.0996770
$439$	647.748	−	114.215i	1.47551	−	0.260172i	0.622726	−	0.782440i	$-0.286025\pi$
$439$	647.748	−	114.215i	1.47551	−	0.260172i	0.852781	+	0.522268i	$0.174914\pi$
$440$	−15.2601	−	18.1863i	−0.0346821	−	0.0413325i
$441$	386.878	−	140.812i	0.877275	−	0.319302i
$442$	197.342	+	71.8267i	0.446476	+	0.162504i
$443$	205.636	+	172.549i	0.464190	+	0.389502i	0.844670	−	0.535288i	$-0.179797\pi$
$443$	205.636	+	172.549i	0.464190	+	0.389502i	−0.380480	+	0.924789i	$0.624241\pi$
$444$	43.6687	−	75.6365i	0.0983530	−	0.170352i
$445$	−36.3656	+	20.9957i	−0.0817204	+	0.0471813i
$446$	0.327420	−	1.85689i	0.000734125	−	0.00416343i
$447$	−45.2527	−	7.97927i	−0.101236	−	0.0178507i
$448$	1.10312	+	1.91066i	0.00246232	+	0.00426486i
$449$	−67.7778	−	39.1315i	−0.150953	−	0.0871526i	0.422621	−	0.906306i	$-0.361110\pi$
$449$	−67.7778	−	39.1315i	−0.150953	−	0.0871526i	−0.573574	+	0.819154i	$0.694443\pi$
$450$	−124.625	+	148.522i	−0.276945	+	0.330050i
$451$	−122.134	+	335.560i	−0.270806	+	0.744035i
$452$	−222.584	−	611.544i	−0.492442	−	1.35297i
$453$	−30.1165	+	25.2707i	−0.0664823	+	0.0557853i
$454$	−56.6326	−	321.179i	−0.124741	−	0.707443i
$455$			2.85385i			0.00627219i
$456$	−72.3795	−	54.0197i	−0.158727	−	0.118464i
$457$	346.968			0.759231			0.379615	−	0.925144i	$-0.376056\pi$
$457$	346.968			0.759231			0.379615	+	0.925144i	$0.376056\pi$
$458$	149.370	−	26.3380i	0.326136	−	0.0575066i
$459$	−134.588	−	160.396i	−0.293221	−	0.349447i
$460$	32.3154	−	11.7618i	0.0702509	−	0.0255692i
$461$	263.912	+	96.0562i	0.572478	+	0.208365i	0.612005	−	0.790854i	$-0.290363\pi$
$461$	263.912	+	96.0562i	0.572478	+	0.208365i	−0.0395276	+	0.999218i	$0.512585\pi$
$462$	3.84446	+	3.22589i	0.00832135	+	0.00698244i
$463$	−291.238	+	504.438i	−0.629023	+	1.08950i	0.358725	+	0.933443i	$0.383212\pi$
$463$	−291.238	+	504.438i	−0.629023	+	1.08950i	−0.987748	+	0.156057i	$0.950122\pi$
$464$	137.255	−	79.2445i	0.295809	−	0.170785i
$465$	1.67136	−	9.47876i	0.00359432	−	0.0203844i
$466$	−101.508	−	17.8986i	−0.217828	−	0.0384090i
$467$	−252.648	−	437.600i	−0.541003	−	0.937045i	−0.998847	−	0.0480121i	$-0.984711\pi$
$467$	−252.648	−	437.600i	−0.541003	−	0.937045i	0.457844	−	0.889033i	$-0.348622\pi$
$468$	319.809	+	184.642i	0.683352	+	0.394533i
$469$	2.04472	−	2.43680i	0.00435974	−	0.00519574i
$470$	0.148621	−	0.408332i	0.000316214	−	0.000868792i
$471$	18.0371	+	49.5567i	0.0382954	+	0.105216i
$472$	−308.886	+	259.186i	−0.654420	+	0.549123i
$473$	−49.5875	−	281.225i	−0.104836	−	0.594555i
$474$			33.3214i			0.0702983i
$475$	259.510	+	395.599i	0.546337	+	0.832841i
$476$	34.3908			0.0722495
$477$	−584.297	+	103.027i	−1.22494	+	0.215990i
$478$	−6.21182	−	7.40296i	−0.0129954	−	0.0154874i
$479$	−141.056	+	51.3403i	−0.294481	+	0.107182i	−0.485036	−	0.874494i	$-0.661193\pi$
$479$	−141.056	+	51.3403i	−0.294481	+	0.107182i	0.190555	+	0.981676i	$0.438971\pi$
$480$	−6.91024	−	2.51512i	−0.0143963	−	0.00523984i
$481$	−404.532	−	339.443i	−0.841023	−	0.705702i
$482$	138.719	−	240.269i	0.287799	−	0.498483i
$483$	−14.2741	+	8.24118i	−0.0295531	+	0.0170625i
$484$	6.01429	−	34.1087i	0.0124262	−	0.0704726i
$485$	−25.0494	−	4.41688i	−0.0516482	−	0.00910697i
$486$	74.5416	+	129.110i	0.153378	+	0.265658i
$487$	−506.482	−	292.417i	−1.04000	−	0.600447i	−0.120170	−	0.992753i	$-0.538344\pi$
$487$	−506.482	−	292.417i	−1.04000	−	0.600447i	−0.919834	+	0.392307i	$0.871677\pi$
$488$	−31.5270	+	37.5724i	−0.0646045	+	0.0769926i
$489$	28.6146	−	78.6180i	0.0585166	−	0.160773i
$490$	4.79680	+	13.1791i	0.00978940	+	0.0268961i
$491$	−72.1647	+	60.5534i	−0.146975	+	0.123327i	−0.713311	−	0.700848i	$-0.752805\pi$
$491$	−72.1647	+	60.5534i	−0.146975	+	0.123327i	0.566336	+	0.824175i	$0.308361\pi$
$492$	12.3209	+	69.8750i	0.0250424	+	0.142022i
$493$			398.533i			0.808384i
$494$	−175.390	+	165.075i	−0.355041	+	0.334160i
$495$	30.6172			0.0618529
$496$	274.660	−	48.4300i	0.553751	−	0.0976412i
$497$	8.31717	+	9.91201i	0.0167347	+	0.0199437i
$498$	23.8322	−	8.67421i	0.0478558	−	0.0174181i
$499$	−443.381	−	161.378i	−0.888539	−	0.323402i	−0.142889	−	0.989739i	$-0.545639\pi$
$499$	−443.381	−	161.378i	−0.888539	−	0.323402i	−0.745651	+	0.666337i	$0.767861\pi$
$500$	37.9343	+	31.8307i	0.0758687	+	0.0636614i
$501$	−68.1089	+	117.968i	−0.135946	+	0.235465i
$502$	−224.756	+	129.763i	−0.447720	+	0.258491i
$503$	−90.5918	+	513.771i	−0.180103	+	1.02141i	0.751984	+	0.659181i	$0.229097\pi$
$503$	−90.5918	+	513.771i	−0.180103	+	1.02141i	−0.932087	+	0.362234i	$0.882014\pi$
$504$	−36.0899	−	6.36363i	−0.0716070	−	0.0126262i
$505$	20.4048	+	35.3422i	0.0404056	+	0.0699845i
$506$	−316.668	−	182.828i	−0.625826	−	0.361321i
$507$	−9.98623	+	11.9011i	−0.0196967	+	0.0234736i
$508$	158.077	−	434.312i	0.311174	−	0.854945i
$509$	20.6040	+	56.6089i	0.0404793	+	0.111216i	0.958285	−	0.285813i	$-0.0922636\pi$
$509$	20.6040	+	56.6089i	0.0404793	+	0.111216i	−0.917806	+	0.397029i	$0.870041\pi$
$510$	2.65022	−	2.22379i	0.00519650	−	0.00436038i
$511$	−7.50664	−	42.5723i	−0.0146901	−	0.0833117i
$512$		−	386.303i		−	0.754497i
$513$	233.732	−	55.0993i	0.455618	−	0.107406i
$514$	226.934			0.441506
$515$	58.0956	−	10.2438i	0.112807	−	0.0198909i
$516$	−36.4717	−	43.4653i	−0.0706816	−	0.0842350i
$517$	16.2443	−	5.91244i	0.0314203	−	0.0114361i
$518$	21.7198	+	7.90535i	0.0419301	+	0.0152613i
$519$	−48.2519	−	40.4882i	−0.0929709	−	0.0780119i
$520$	−14.2609	+	24.7005i	−0.0274247	+	0.0475011i
$521$	−75.7727	+	43.7474i	−0.145437	+	0.0839681i	−0.570953	−	0.820983i	$-0.693426\pi$
$521$	−75.7727	+	43.7474i	−0.145437	+	0.0839681i	0.425516	+	0.904951i	$0.360093\pi$
$522$	32.5254	−	184.461i	0.0623092	−	0.353373i
$523$	176.249	+	31.0774i	0.336996	+	0.0594215i	0.339586	−	0.940575i	$-0.389713\pi$
$523$	176.249	+	31.0774i	0.336996	+	0.0594215i	−0.00258959	+	0.999997i	$0.500824\pi$
$524$	314.705	+	545.085i	0.600582	+	1.04024i
$525$	−10.2568	−	5.92179i	−0.0195369	−	0.0112796i
$526$	116.510	−	138.851i	0.221501	−	0.263975i
$527$	−239.862	+	659.016i	−0.455147	+	1.25051i
$528$	−18.7198	−	51.4322i	−0.0354541	−	0.0974094i
$529$	514.715	−	431.897i	0.972996	−	0.816441i
$530$	−3.50965	−	19.9042i	−0.00662199	−	0.0375552i
$531$		−	520.019i		−	0.979320i
$532$	−17.7441	+	35.2258i	−0.0333535	+	0.0662140i
$533$	429.012			0.804900
$534$	87.3671	−	15.4052i	0.163609	−	0.0288486i
$535$	−11.5429	−	13.7563i	−0.0215755	−	0.0257126i
$536$	29.8743	−	10.8734i	0.0557356	−	0.0202861i
$537$	119.300	+	43.4218i	0.222161	+	0.0808600i
$538$	318.603	+	267.340i	0.592199	+	0.496914i
$539$	−278.970	+	483.191i	−0.517570	+	0.896457i
$540$	10.8619	−	6.27114i	0.0201147	−	0.0116132i
$541$	101.717	−	576.866i	0.188017	−	1.06630i	−0.734001	−	0.679148i	$-0.762349\pi$
$541$	101.717	−	576.866i	0.188017	−	1.06630i	0.922018	−	0.387147i	$-0.126540\pi$
$542$	193.667	+	34.1486i	0.357318	+	0.0630049i
$543$	47.4212	+	82.1360i	0.0873319	+	0.151263i
$544$	464.032	+	267.909i	0.853001	+	0.492480i
$545$	26.4806	−	31.5583i	0.0485882	−	0.0579052i
$546$	2.06214	−	5.66569i	0.00377682	−	0.0103767i
$547$	41.8971	+	115.111i	0.0765943	+	0.210441i	0.972080	−	0.234649i	$-0.0753940\pi$
$547$	41.8971	+	115.111i	0.0765943	+	0.210441i	−0.895486	+	0.445090i	$0.853172\pi$
$548$	16.9778	−	14.2460i	0.0309813	−	0.0259964i
$549$	−10.9840	−	62.2933i	−0.0200073	−	0.113467i
$550$		−	262.747i		−	0.477721i
$551$	−408.210	−	205.625i	−0.740854	−	0.373185i
$552$	−164.727			−0.298419
$553$	32.4923	−	5.72928i	0.0587565	−	0.0103604i
$554$	166.756	+	198.732i	0.301004	+	0.358723i
$555$	−8.17481	+	2.97539i	−0.0147294	+	0.00536106i
$556$	−415.994	−	151.409i	−0.748190	−	0.272319i
$557$	−400.488	−	336.049i	−0.719008	−	0.603319i	0.208103	−	0.978107i	$-0.433271\pi$
$557$	−400.488	−	336.049i	−0.719008	−	0.603319i	−0.927111	+	0.374788i	$0.877716\pi$
$558$	164.804	−	285.449i	0.295348	−	0.511557i
$559$	−297.110	+	171.537i	−0.531503	+	0.306864i
$560$	−0.236558	+	1.34159i	−0.000422425	+	0.00239569i
$561$	135.540	+	23.8993i	0.241604	+	0.0426012i
$562$	−51.8094	−	89.7365i	−0.0921876	−	0.159674i
$563$	435.427	+	251.394i	0.773406	+	0.446526i	0.834088	−	0.551631i	$-0.185994\pi$
$563$	435.427	+	251.394i	0.773406	+	0.446526i	−0.0606825	+	0.998157i	$0.519328\pi$
$564$	2.20785	−	2.63121i	0.00391463	−	0.00466527i
$565$	−22.1710	+	60.9143i	−0.0392407	+	0.107813i
$566$	4.16098	+	11.4322i	0.00735156	+	0.0201982i
$567$	33.8332	−	28.3894i	0.0596705	−	0.0500695i
$568$	22.4556	+	127.352i	0.0395344	+	0.224211i
$569$			682.157i			1.19887i	0.800423	+	0.599435i	$0.204608\pi$
$569$			682.157i			1.19887i	−0.800423	+	0.599435i	$0.795392\pi$
$570$	0.910403	+	3.86194i	0.00159720	+	0.00677534i
$571$	−909.575			−1.59295			−0.796476	−	0.604671i	$-0.793305\pi$
$571$	−909.575			−1.59295			−0.796476	+	0.604671i	$0.793305\pi$
$572$	−492.845	+	86.9019i	−0.861617	+	0.151926i
$573$	134.087	+	159.799i	0.234009	+	0.278881i
$574$	−17.6451	+	6.42231i	−0.0307407	+	0.0111887i
$575$	810.888	+	295.139i	1.41024	+	0.513286i
$576$	−21.7835	−	18.2785i	−0.0378185	−	0.0317335i
$577$	520.297	−	901.180i	0.901727	−	1.56184i	0.0764767	−	0.997071i	$-0.475633\pi$
$577$	520.297	−	901.180i	0.901727	−	1.56184i	0.825251	−	0.564766i	$-0.191034\pi$
$578$	11.5742	−	6.68236i	0.0200245	−	0.0115612i
$579$	17.7270	−	100.535i	0.0306166	−	0.173635i
$580$	−23.5100	−	4.14545i	−0.0405345	−	0.00714733i
$581$	−12.5561	−	21.7478i	−0.0216112	−	0.0374317i
$582$	46.5385	+	26.8690i	0.0799631	+	0.0461667i
$583$	516.832	−	615.936i	0.886503	−	1.05649i
$584$	147.765	−	405.982i	0.253023	−	0.695175i
$585$	−12.5806	−	34.5650i	−0.0215054	−	0.0590855i
$586$	−290.619	+	243.858i	−0.495937	+	0.416140i
$587$	176.023	+	998.273i	0.299868	+	1.70064i	0.646729	+	0.762720i	$0.276136\pi$
$587$	176.023	+	998.273i	0.299868	+	1.70064i	−0.346861	+	0.937916i	$0.612753\pi$
$588$			110.860i			0.188537i
$589$	−551.260	−	585.709i	−0.935926	−	0.994412i
$590$	17.7146			0.0300247
$591$	−167.683	+	29.5671i	−0.283728	+	0.0500289i
$592$	−162.033	−	193.104i	−0.273705	−	0.326189i
$593$	−894.267	+	325.486i	−1.50804	+	0.548881i	−0.958127	−	0.286342i	$-0.907561\pi$
$593$	−894.267	+	325.486i	−1.50804	+	0.548881i	−0.549911	+	0.835223i	$0.685338\pi$
$594$	−125.318	−	45.6119i	−0.210972	−	0.0767877i
$595$	−2.62414	−	2.20192i	−0.00441032	−	0.00370070i
$596$	−100.279	+	173.688i	−0.168253	+	0.291423i
$597$	38.8053	−	22.4042i	0.0650005	−	0.0375280i
$598$	−76.2833	+	432.624i	−0.127564	+	0.723451i
$599$	−224.325	−	39.5546i	−0.374500	−	0.0660344i	−0.0167696	−	0.999859i	$-0.505338\pi$
$599$	−224.325	−	39.5546i	−0.374500	−	0.0660344i	−0.357730	+	0.933825i	$0.616449\pi$
$600$	−59.1833	−	102.508i	−0.0986388	−	0.170847i
$601$	443.024	+	255.780i	0.737144	+	0.425590i	0.821030	−	0.570885i	$-0.193400\pi$
$601$	443.024	+	255.780i	0.737144	+	0.425590i	−0.0838858	+	0.996475i	$0.526733\pi$
$602$	9.65217	−	11.5030i	0.0160335	−	0.0191080i
$603$	−14.0229	+	38.5277i	−0.0232553	+	0.0638933i
$604$	58.6880	+	161.244i	0.0971655	+	0.266960i
$605$	−2.64277	+	2.21755i	−0.00436821	+	0.00366537i
$606$	−14.9716	−	84.9084i	−0.0247057	−	0.140113i
$607$		−	561.445i		−	0.924951i	−0.886632	−	0.462475i	$-0.846961\pi$
$607$		−	561.445i		−	0.924951i	0.886632	−	0.462475i	$-0.153039\pi$
$608$	−513.834	+	337.071i	−0.845122	+	0.554393i
$609$	11.4419			0.0187880
$610$	2.12204	−	0.374172i	0.00347875	−	0.000613397i
$611$	−13.3496	−	15.9094i	−0.0218488	−	0.0260383i
$612$	−416.532	+	151.605i	−0.680608	+	0.247721i
$613$	−272.868	−	99.3160i	−0.445136	−	0.162016i	0.109720	−	0.993963i	$-0.465005\pi$
$613$	−272.868	−	99.3160i	−0.445136	−	0.162016i	−0.554856	+	0.831946i	$0.687227\pi$
$614$	−325.553	−	273.172i	−0.530217	−	0.444905i
$615$	3.53372	−	6.12058i	0.00574589	−	0.00995216i
$616$	43.0095	−	24.8315i	0.0698206	−	0.0403109i
$617$	76.6888	−	434.924i	0.124293	−	0.704901i	−0.857432	−	0.514597i	$-0.827942\pi$
$617$	76.6888	−	434.924i	0.124293	−	0.704901i	0.981725	−	0.190304i	$-0.0609473\pi$
$618$	−122.738	−	21.6421i	−0.198606	−	0.0350196i
$619$	116.217	+	201.294i	0.187750	+	0.325193i	0.944500	−	0.328512i	$-0.106547\pi$
$619$	116.217	+	201.294i	0.187750	+	0.325193i	−0.756750	+	0.653705i	$0.773214\pi$
$620$	−36.3813	−	21.0047i	−0.0586795	−	0.0338786i
$621$	281.535	−	335.520i	0.453357	−	0.540290i
$622$	−32.4880	+	89.2601i	−0.0522316	+	0.143505i
$623$	−30.0438	−	82.5446i	−0.0482244	−	0.132495i
$624$	−50.3719	+	42.2670i	−0.0807242	+	0.0677356i
$625$	107.244	+	608.214i	0.171591	+	0.973142i
$626$		−	94.4834i		−	0.150932i
$627$	−94.4118	+	126.500i	−0.150577	+	0.201754i
$628$	230.178			0.366525
$629$	624.243	−	110.071i	0.992437	−	0.174993i
$630$	1.03488	+	1.23332i	0.00164266	+	0.00195765i
$631$	−301.624	+	109.782i	−0.478009	+	0.173981i	−0.569777	−	0.821799i	$-0.692970\pi$
$631$	−301.624	+	109.782i	−0.478009	+	0.173981i	0.0917677	+	0.995780i	$0.470748\pi$
$632$	309.857	+	112.779i	0.490280	+	0.178447i
$633$	−82.0744	−	68.8686i	−0.129659	−	0.108797i
$634$	−153.223	+	265.390i	−0.241677	+	0.418597i
$635$	−39.8692	+	23.0185i	−0.0627862	+	0.0362496i
$636$	27.7420	−	157.333i	0.0436196	−	0.247379i
$637$	660.123	+	116.397i	1.03630	+	0.182728i
$638$	126.918	+	219.828i	0.198930	+	0.344557i
$639$	−144.431	−	83.3870i	−0.226026	−	0.130496i
$640$	−25.5226	+	30.4167i	−0.0398791	+	0.0475261i
$641$	132.895	−	365.125i	0.207324	−	0.569618i	−0.791830	−	0.610742i	$-0.790871\pi$
$641$	132.895	−	365.125i	0.207324	−	0.569618i	0.999154	+	0.0411233i	$0.0130936\pi$
$642$	12.9758	+	35.6508i	0.0202116	+	0.0555308i
$643$	752.813	−	631.685i	1.17078	−	0.982403i	0.170786	−	0.985308i	$-0.445369\pi$
$643$	752.813	−	631.685i	1.17078	−	0.982403i	0.999996	+	0.00290542i	$0.000924826\pi$
$644$	12.4921	+	70.8465i	0.0193977	+	0.110010i
$645$			5.65171i			0.00876234i
$646$	−16.4637	−	288.639i	−0.0254856	−	0.446809i
$647$	401.585			0.620688			0.310344	−	0.950624i	$-0.399556\pi$
$647$	401.585			0.620688			0.310344	+	0.950624i	$0.399556\pi$
$648$	434.696	−	76.6487i	0.670828	−	0.118285i
$649$	452.987	+	539.849i	0.697977	+	0.831817i
$650$	−296.626	+	107.963i	−0.456347	+	0.166097i
$651$	18.9203	+	6.88644i	0.0290635	+	0.0105782i
$652$	−279.729	−	234.720i	−0.429032	−	0.360000i
$653$	108.727	−	188.321i	0.166504	−	0.288394i	−0.770684	−	0.637217i	$-0.780085\pi$
$653$	108.727	−	188.321i	0.166504	−	0.288394i	0.937188	+	0.348823i	$0.113419\pi$
$654$	−75.3750	+	43.5178i	−0.115252	+	0.0665410i
$655$	10.8867	−	61.7414i	0.0166209	−	0.0942617i
$656$	201.678	+	35.5612i	0.307436	+	0.0542092i
$657$	278.590	+	482.533i	0.424034	+	0.734449i
$658$	0.787230	+	0.454507i	0.00119640	+	0.000690740i
$659$	497.244	−	592.592i	0.754543	−	0.899230i	−0.242947	−	0.970040i	$-0.578114\pi$
$659$	497.244	−	592.592i	0.754543	−	0.899230i	0.997490	+	0.0708101i	$0.0225584\pi$
$660$	−2.81970	+	7.74707i	−0.00427228	+	0.0117380i
$661$	107.876	+	296.386i	0.163201	+	0.448390i	0.994157	−	0.107948i	$-0.0344280\pi$
$661$	107.876	+	296.386i	0.163201	+	0.448390i	−0.830956	+	0.556338i	$0.812206\pi$
$662$	89.7194	−	75.2835i	0.135528	−	0.113721i
$663$	−28.7125	−	162.836i	−0.0433069	−	0.245605i
$664$		−	250.975i		−	0.377974i
$665$	3.60932	−	1.55177i	0.00542755	−	0.00233349i
$666$	−297.913			−0.447317
$667$	−820.996	+	144.764i	−1.23088	+	0.217037i
$668$	382.163	+	455.444i	0.572100	+	0.681802i
$669$	−1.39504	+	0.507752i	−0.00208526	+	0.000758972i
$670$	−1.31245	−	0.477695i	−0.00195889	−	0.000712977i
$671$	65.6664	+	55.1006i	0.0978634	+	0.0821172i
$672$	7.69167	−	13.3224i	0.0114459	−	0.0198249i
$673$	−699.452	+	403.829i	−1.03930	+	0.600043i	−0.919636	−	0.392771i	$-0.871516\pi$
$673$	−699.452	+	403.829i	−1.03930	+	0.600043i	−0.119668	+	0.992814i	$0.538183\pi$
$674$	13.3596	−	75.7662i	0.0198214	−	0.112413i
$675$	309.941	+	54.6510i	0.459172	+	0.0809645i
$676$	33.9040	+	58.7235i	0.0501539	+	0.0868691i
$677$	86.9458	+	50.1982i	0.128428	+	0.0741479i	0.562838	−	0.826567i	$-0.309710\pi$
$677$	86.9458	+	50.1982i	0.128428	+	0.0741479i	−0.434410	+	0.900715i	$0.643043\pi$
$678$	88.0314	−	104.912i	0.129840	−	0.154737i
$679$	18.1987	−	50.0005i	0.0268022	−	0.0736384i
$680$	−11.7093	−	32.1710i	−0.0172196	−	0.0473103i
$681$	−196.705	+	165.055i	−0.288847	+	0.242372i
$682$	77.5653	+	439.895i	0.113732	+	0.645007i
$683$		−	935.160i		−	1.36919i	−0.728922	−	0.684597i	$-0.759978\pi$
$683$		−	935.160i		−	1.36919i	0.728922	−	0.684597i	$-0.240022\pi$
$684$	59.6249	−	504.868i	0.0871709	−	0.738110i
$685$	−2.20759			−0.00322275
$686$	−58.0436	+	10.2347i	−0.0846117	+	0.0149193i
$687$	−76.7620	−	91.4814i	−0.111735	−	0.133161i
$688$	−153.890	+	56.0114i	−0.223677	+	0.0814119i
$689$	−907.722	−	330.384i	−1.31745	−	0.479512i
$690$	5.54378	+	4.65178i	0.00803446	+	0.00674171i
$691$	−137.359	+	237.913i	−0.198784	+	0.344303i	−0.948134	−	0.317870i	$-0.897032\pi$
$691$	−137.359	+	237.913i	−0.198784	+	0.344303i	0.749351	+	0.662173i	$0.230366\pi$
$692$	−238.088	+	137.460i	−0.344059	+	0.198642i
$693$	−11.1219	+	63.0754i	−0.0160489	+	0.0910179i
$694$	424.220	+	74.8014i	0.611268	+	0.107783i
$695$	22.0477	+	38.1877i	0.0317233	+	0.0549463i
$696$	99.0316	+	57.1759i	0.142287	+	0.0821493i
$697$	−331.009	+	394.481i	−0.474905	+	0.565970i
$698$	23.3506	−	64.1552i	0.0334535	−	0.0919128i
$699$	27.7566	+	76.2606i	0.0397090	+	0.109100i
$700$	−39.5990	+	33.2275i	−0.0565700	+	0.0474679i
$701$	39.6502	+	224.868i	0.0565624	+	0.320781i	0.999940	−	0.0109391i	$-0.00348209\pi$
$701$	39.6502	+	224.868i	0.0565624	+	0.320781i	−0.943378	+	0.331720i	$0.892371\pi$
$702$			160.218i			0.228231i
$703$	−209.337	+	696.192i	−0.297777	+	0.990316i
$704$	38.5365			0.0547393
$705$	−0.336934	+	0.0594106i	−0.000477921	+	8.42703e-5i
$706$	−95.2078	−	113.464i	−0.134855	−	0.160714i
$707$	−80.2216	+	29.1983i	−0.113468	+	0.0412989i
$708$	131.580	+	47.8913i	0.185848	+	0.0676431i
$709$	−505.264	−	423.967i	−0.712643	−	0.597978i	0.212697	−	0.977118i	$-0.431775\pi$
$709$	−505.264	−	423.967i	−0.712643	−	0.597978i	−0.925339	+	0.379140i	$0.876220\pi$
$710$	2.84060	−	4.92007i	0.00400085	−	0.00692967i
$711$	−368.282	+	212.628i	−0.517978	+	0.299055i
$712$	152.447	−	864.569i	0.214111	−	1.21428i
$713$	−1444.73	−	254.745i	−2.02627	−	0.357286i
$714$	3.61860	+	6.26759i	0.00506806	+	0.00877814i
$715$	43.1699	+	24.9241i	0.0603775	+	0.0348589i
$716$	356.181	−	424.480i	0.497460	−	0.592850i
$717$	−2.60237	+	7.14995i	−0.00362953	+	0.00997204i
$718$	−174.971	−	480.730i	−0.243693	−	0.669540i
$719$	−677.401	+	568.407i	−0.942143	+	0.790552i	−0.977957	−	0.208807i	$-0.933042\pi$
$719$	−677.401	+	568.407i	−0.942143	+	0.790552i	0.0358142	+	0.999358i	$0.488598\pi$
$720$	−3.04901	−	17.2918i	−0.00423473	−	0.0240164i
$721$			123.406i			0.171159i
$722$	304.142	+	132.061i	0.421249	+	0.182910i
$723$	−218.440			−0.302130
$724$	407.663	−	71.8820i	0.563071	−	0.0992846i
$725$	−385.053	−	458.888i	−0.531108	−	0.632950i
$726$	6.84901	−	2.49284i	0.00943390	−	0.00343366i
$727$	861.704	+	313.635i	1.18529	+	0.431409i	0.858067	−	0.513539i	$-0.171666\pi$
$727$	861.704	+	313.635i	1.18529	+	0.431409i	0.327221	+	0.944948i	$0.393888\pi$
$728$	−45.7060	−	38.3519i	−0.0627829	−	0.0526811i
$729$	−243.499	+	421.753i	−0.334018	+	0.578536i
$730$	−16.4376	+	9.49025i	−0.0225173	+	0.0130003i
$731$	71.5090	−	405.547i	0.0978235	−	0.554784i
$732$	16.7736	+	2.95764i	0.0229148	+	0.00404050i
$733$	128.863	+	223.198i	0.175803	+	0.304499i	0.940439	−	0.339963i	$-0.110415\pi$
$733$	128.863	+	223.198i	0.175803	+	0.304499i	−0.764636	+	0.644462i	$0.777081\pi$
$734$	242.056	+	139.751i	0.329777	+	0.190397i
$735$	7.09796	−	8.45902i	0.00965709	−	0.0115089i
$736$	−383.349	+	1053.24i	−0.520854	+	1.43104i
$737$	−19.0037	−	52.2122i	−0.0257852	−	0.0708442i
$738$	185.402	−	155.571i	0.251222	−	0.210800i
$739$	−90.9919	−	516.040i	−0.123128	−	0.698296i	−0.982402	−	0.186779i	$-0.940195\pi$
$739$	−90.9919	−	516.040i	−0.123128	−	0.698296i	0.859274	−	0.511516i	$-0.170916\pi$
$740$			37.9699i			0.0513106i
$741$	181.605	+	54.6065i	0.245081	+	0.0736929i
$742$	42.2802			0.0569814
$743$	1062.18	−	187.292i	1.42959	−	0.252075i	0.595345	−	0.803470i	$-0.297015\pi$
$743$	1062.18	−	187.292i	1.42959	−	0.252075i	0.834244	+	0.551395i	$0.185904\pi$
$744$	129.347	+	154.150i	0.173853	+	0.207190i
$745$	18.7723	−	6.83255i	0.0251977	−	0.00917121i
$746$	−262.112	−	95.4010i	−0.351357	−	0.127883i
$747$	247.947	+	208.052i	0.331924	+	0.278517i
$748$	300.353	−	520.227i	0.401541	−	0.695490i
$749$	32.5327	−	18.7828i	0.0434349	−	0.0250771i
$750$	−1.80958	+	10.2626i	−0.00241277	+	0.0136835i
$751$	600.458	+	105.877i	0.799544	+	0.140981i	0.558469	−	0.829525i	$-0.311389\pi$
$751$	600.458	+	105.877i	0.799544	+	0.140981i	0.241075	+	0.970507i	$0.422500\pi$
$752$	−4.95687	−	8.58556i	−0.00659159	−	0.0114170i
$753$	176.960	+	102.168i	0.235007	+	0.135681i
$754$	196.022	−	233.610i	0.259976	−	0.309827i
$755$	5.84575	−	16.0611i	0.00774272	−	0.0212729i
$756$	8.97369	+	24.6550i	0.0118700	+	0.0326125i
$757$	−478.951	+	401.888i	−0.632696	+	0.530895i	−0.901765	−	0.432226i	$-0.857728\pi$
$757$	−478.951	+	401.888i	−0.632696	+	0.530895i	0.269069	+	0.963121i	$0.413284\pi$
$758$	0.798479	+	4.52840i	0.00105340	+	0.00597414i
$759$			287.898i			0.379313i
$760$	38.9936	+	4.60515i	0.0513074	+	0.00605941i
$761$	671.396			0.882255			0.441128	−	0.897444i	$-0.354579\pi$
$761$	671.396			0.882255			0.441128	+	0.897444i	$0.354579\pi$
$762$	95.7846	−	16.8894i	0.125702	−	0.0221646i
$763$	55.3950	+	66.0172i	0.0726016	+	0.0865232i
$764$	855.565	−	311.400i	1.11985	−	0.407592i
$765$	41.4897	+	15.1010i	0.0542349	+	0.0197399i
$766$	−23.6608	−	19.8538i	−0.0308888	−	0.0259188i
$767$	423.325	−	733.221i	0.551923	−	0.955959i
$768$	81.0518	−	46.7953i	0.105536	−	0.0609314i
$769$	−236.349	+	1340.40i	−0.307346	+	1.74305i	0.304905	+	0.952383i	$0.401375\pi$
$769$	−236.349	+	1340.40i	−0.307346	+	1.74305i	−0.612251	+	0.790663i	$0.709736\pi$
$770$	−2.14868	−	0.378870i	−0.00279049	−	0.000492039i
$771$	−89.3378	−	154.738i	−0.115873	−	0.200697i
$772$	−385.872	−	222.783i	−0.499834	−	0.288580i
$773$	−60.0113	+	71.5186i	−0.0776342	+	0.0925209i	−0.803463	−	0.595354i	$-0.797012\pi$
$773$	−60.0113	+	71.5186i	−0.0776342	+	0.0925209i	0.725829	+	0.687875i	$0.241456\pi$
$774$	−66.1957	+	181.871i	−0.0855241	+	0.234976i
$775$	−360.537	−	990.568i	−0.465210	−	1.27815i
$776$	407.369	−	341.823i	0.524960	−	0.440494i
$777$	−3.16013	−	17.9220i	−0.00406709	−	0.0230656i
$778$			421.583i			0.541880i
$779$	−233.274	−	542.581i	−0.299454	−	0.696509i
$780$	9.90460			0.0126982
$781$	222.576	−	39.2462i	0.284989	−	0.0502513i
$782$	−338.945	−	403.939i	−0.433434	−	0.516546i
$783$	−285.712	+	103.991i	−0.364894	+	0.132810i
$784$	300.674	+	109.436i	0.383513	+	0.139587i
$785$	−17.5634	−	14.7374i	−0.0223738	−	0.0187738i
$786$	−66.2265	+	114.708i	−0.0842576	+	0.145938i
$787$	584.642	−	337.543i	0.742874	−	0.428898i	−0.0802395	−	0.996776i	$-0.525569\pi$
$787$	584.642	−	337.543i	0.742874	−	0.428898i	0.823113	+	0.567877i	$0.192235\pi$
$788$	−129.049	+	731.875i	−0.163768	+	0.928776i
$789$	−140.544	−	24.7816i	−0.178129	−	0.0314089i
$790$	−7.24322	−	12.5456i	−0.00916864	−	0.0158805i
$791$	−117.438	−	67.8026i	−0.148467	−	0.0857175i
$792$	−411.454	+	490.352i	−0.519513	+	0.619132i
$793$	35.2230	−	96.7744i	0.0444174	−	0.122036i
$794$	154.194	+	423.644i	0.194199	+	0.533556i
$795$	−12.1903	+	10.2289i	−0.0153337	+	0.0128665i
$796$	−33.9608	−	192.601i	−0.0426643	−	0.241961i
$797$		−	547.797i		−	0.687323i	−0.939094	−	0.343662i	$-0.888333\pi$
$797$		−	547.797i		−	0.687323i	0.939094	−	0.343662i	$-0.111667\pi$
$798$	−8.28681	+	0.472673i	−0.0103845	+	0.000592322i
$799$	24.9289			0.0312002
$800$	−793.154	+	139.854i	−0.991443	+	0.174818i
$801$	727.765	+	867.316i	0.908570	+	1.08279i
$802$	−282.772	+	102.921i	−0.352584	+	0.128330i
$803$	−709.547	−	258.254i	−0.883620	−	0.321611i
$804$	−8.45720	−	7.09644i	−0.0105189	−	0.00882641i
$805$	3.58285	−	6.20567i	0.00445074	−	0.00770891i
$806$	464.743	−	268.320i	0.576605	−	0.332903i
$807$	56.8633	−	322.488i	0.0704625	−	0.399613i
$808$	−840.239	−	148.157i	−1.03990	−	0.183362i
$809$	−211.477	−	366.289i	−0.261405	−	0.452767i	0.705210	−	0.708998i	$-0.250853\pi$
$809$	−211.477	−	366.289i	−0.261405	−	0.452767i	−0.966616	+	0.256231i	$0.917519\pi$
$810$	−16.7939	−	9.69597i	−0.0207332	−	0.0119703i
$811$	−696.147	+	829.636i	−0.858382	+	1.02298i	0.141074	+	0.989999i	$0.454944\pi$
$811$	−696.147	+	829.636i	−0.858382	+	1.02298i	−0.999456	+	0.0329804i	$0.989500\pi$
$812$	17.0803	−	46.9278i	0.0210349	−	0.0577929i
$813$	−52.9567	−	145.497i	−0.0651373	−	0.178963i
$814$	309.274	−	259.512i	0.379943	−	0.318810i
$815$	6.31604	+	35.8200i	0.00774974	+	0.0439510i
$816$		−	78.9291i		−	0.0967269i
$817$	378.499	+	282.489i	0.463280	+	0.345764i
$818$	−601.002			−0.734721
$819$	75.7784	−	13.3618i	0.0925256	−	0.0163148i
$820$	−19.8279	−	23.6300i	−0.0241804	−	0.0288170i
$821$	1033.93	−	376.319i	1.25935	−	0.458367i	0.375801	−	0.926700i	$-0.377368\pi$
$821$	1033.93	−	376.319i	1.25935	−	0.458367i	0.883552	+	0.468334i	$0.155145\pi$
$822$	4.38269	+	1.59517i	0.00533173	+	0.00194059i
$823$	492.234	+	413.033i	0.598097	+	0.501863i	0.890833	−	0.454330i	$-0.150121\pi$
$823$	492.234	+	413.033i	0.598097	+	0.501863i	−0.292736	+	0.956193i	$0.594566\pi$
$824$	−616.667	+	1068.10i	−0.748382	+	1.29624i
$825$	−179.157	+	103.436i	−0.217160	+	0.125377i
$826$	−6.43494	+	36.4943i	−0.00779048	+	0.0441820i
$827$	1088.98	+	192.017i	1.31679	+	0.232185i	0.787531	−	0.616275i	$-0.211359\pi$
$827$	1088.98	+	192.017i	1.31679	+	0.232185i	0.529258	+	0.848461i	$0.322470\pi$
$828$	−463.615	−	803.004i	−0.559921	−	0.969812i
$829$	−207.502	−	119.801i	−0.250304	−	0.144513i	0.369599	−	0.929191i	$-0.379495\pi$
$829$	−207.502	−	119.801i	−0.250304	−	0.144513i	−0.619903	+	0.784678i	$0.712828\pi$
$830$	−7.08736	+	8.44638i	−0.00853898	+	0.0101764i
$831$	69.8606	−	191.940i	0.0840681	−	0.230975i
$832$	−15.8347	−	43.5054i	−0.0190321	−	0.0522902i
$833$	−616.354	+	517.182i	−0.739921	+	0.620867i
$834$	−16.1771	−	91.7447i	−0.0193970	−	0.110006i
$835$		−	59.2206i		−	0.0709228i
$836$	377.890	+	576.059i	0.452022	+	0.689066i
$837$	−535.042			−0.639238
$838$	−392.093	+	69.1366i	−0.467891	+	0.0825019i
$839$	−685.765	−	817.263i	−0.817360	−	0.974092i	0.182598	−	0.983188i	$-0.441549\pi$
$839$	−685.765	−	817.263i	−0.817360	−	0.974092i	−0.999959	+	0.00909544i	$0.997105\pi$
$840$	−0.923629	+	0.336174i	−0.00109956	+	0.000400207i
$841$	−246.464	−	89.7055i	−0.293061	−	0.106665i
$842$	−39.4854	−	33.1322i	−0.0468948	−	0.0393494i
$843$	−40.7919	+	70.6537i	−0.0483890	+	0.0838122i
$844$	−404.978	+	233.814i	−0.479832	+	0.277031i
$845$	1.17285	−	6.65157i	0.00138799	−	0.00787168i
$846$	−11.5383	−	2.03452i	−0.0136387	−	0.00240487i
$847$	−3.60843	−	6.24999i	−0.00426025	−	0.00737897i
$848$	−399.333	−	230.555i	−0.470911	−	0.271881i
$849$	6.15712	−	7.33777i	0.00725220	−	0.00864283i
$850$	129.592	−	356.051i	0.152461	−	0.418883i
$851$	453.501	+	1245.98i	0.532904	+	1.46414i
$852$	34.4008	−	28.8657i	0.0403765	−	0.0338799i
$853$	−252.439	−	1431.65i	−0.295942	−	1.67837i	−0.663347	−	0.748312i	$-0.730865\pi$
$853$	−252.439	−	1431.65i	−0.295942	−	1.67837i	0.367405	−	0.930061i	$-0.380246\pi$
$854$			4.50759i			0.00527821i
$855$	−36.8744	+	34.7057i	−0.0431280	+	0.0405914i
$856$	375.435			0.438593
$857$	−964.961	+	170.149i	−1.12598	+	0.198540i	−0.705463	−	0.708747i	$-0.749261\pi$
$857$	−964.961	+	170.149i	−1.12598	+	0.198540i	−0.420513	+	0.907287i	$0.638150\pi$
$858$	−67.6947	−	80.6754i	−0.0788982	−	0.0940272i
$859$	854.588	−	311.045i	0.994864	−	0.362101i	0.207262	−	0.978285i	$-0.433545\pi$
$859$	854.588	−	311.045i	0.994864	−	0.362101i	0.787602	+	0.616185i	$0.211323\pi$
$860$	23.1800	+	8.43682i	0.0269535	+	0.00981025i
$861$	11.3255	+	9.50326i	0.0131539	+	0.0110375i
$862$	−32.0305	+	55.4785i	−0.0371584	+	0.0643602i
$863$	912.338	−	526.738i	1.05717	−	0.610357i	0.132522	−	0.991180i	$-0.457692\pi$
$863$	912.338	−	526.738i	1.05717	−	0.610357i	0.924648	+	0.380823i	$0.124359\pi$
$864$	−70.9848	+	402.575i	−0.0821583	+	0.465943i
$865$	26.9681	+	4.75521i	0.0311770	+	0.00549735i
$866$	61.3828	+	106.318i	0.0708809	+	0.122769i
$867$	−9.11289	−	5.26133i	−0.0105108	−	0.00606843i
$868$	56.4882	−	67.3200i	0.0650786	−	0.0775576i
$869$	197.107	−	541.546i	0.226820	−	0.623183i
$870$	−1.71823	−	4.72080i	−0.00197498	−	0.00542621i
$871$	−51.1359	+	42.9081i	−0.0587094	+	0.0492630i
$872$	149.561	+	848.204i	0.171515	+	0.972711i
$873$			685.818i			0.785588i
$874$	588.628	−	138.761i	0.673487	−	0.158766i
$875$	10.3184			0.0117925
$876$	−147.752	+	26.0527i	−0.168667	+	0.0297405i
$877$	456.823	+	544.420i	0.520893	+	0.620776i	0.960792	−	0.277272i	$-0.0894302\pi$
$877$	456.823	+	544.420i	0.520893	+	0.620776i	−0.439899	+	0.898047i	$0.644986\pi$
$878$	567.696	−	206.624i	0.646578	−	0.235335i
$879$	280.687	+	102.162i	0.319325	+	0.116225i
$880$	18.2281	+	15.2952i	0.0207138	+	0.0173809i
$881$	205.259	−	355.518i	0.232984	−	0.403540i	−0.725701	−	0.688010i	$-0.758484\pi$
$881$	205.259	−	355.518i	0.232984	−	0.403540i	0.958685	+	0.284470i	$0.0918178\pi$
$882$	327.487	−	189.075i	0.371301	−	0.214371i
$883$	2.48474	−	14.0916i	0.00281397	−	0.0159588i	−0.983368	−	0.181622i	$-0.941865\pi$
$883$	2.48474	−	14.0916i	0.00281397	−	0.0159588i	0.986182	+	0.165663i	$0.0529764\pi$
$884$	−710.720	−	125.319i	−0.803982	−	0.141764i
$885$	−6.97376	−	12.0789i	−0.00787995	−	0.0136485i
$886$	213.526	+	123.280i	0.241000	+	0.139142i
$887$	−667.053	+	794.963i	−0.752032	+	0.896237i	−0.997316	−	0.0732139i	$-0.976674\pi$
$887$	−667.053	+	794.963i	−0.752032	+	0.896237i	0.245284	+	0.969451i	$0.421119\pi$
$888$	62.2060	−	170.910i	0.0700518	−	0.192466i
$889$	−32.9384	−	90.4974i	−0.0370510	−	0.101797i
$890$	−29.5453	+	24.7915i	−0.0331970	+	0.0278556i
$891$	−133.961	−	759.732i	−0.150349	−	0.852673i
$892$			6.47959i			0.00726411i
$893$	−12.8622	+	25.5343i	−0.0144033	+	0.0285938i
$894$	−42.2054			−0.0472096
$895$	−54.3559	+	9.58441i	−0.0607328	+	0.0107088i
$896$	−53.3911	−	63.6290i	−0.0595883	−	0.0710145i
$897$	325.020	−	118.298i	0.362342	−	0.131882i
$898$	−67.5488	−	24.5858i	−0.0752214	−	0.0273784i
$899$	780.130	+	654.607i	0.867775	+	0.728150i
$900$	333.136	−	577.008i	0.370151	−	0.641120i
$901$	1004.15	−	579.749i	1.11449	−	0.643451i
$902$	−56.9547	+	323.006i	−0.0631427	+	0.358100i
$903$	−11.6433	−	2.05302i	−0.0128940	−	0.00227355i
$904$	−677.629	−	1173.69i	−0.749589	−	1.29833i
$905$	−35.7085	−	20.6163i	−0.0394569	−	0.0227805i
$906$	−23.2110	+	27.6617i	−0.0256192	+	0.0305317i
$907$	128.766	−	353.782i	0.141969	−	0.390058i	−0.848247	−	0.529602i	$-0.822341\pi$
$907$	128.766	−	353.782i	0.141969	−	0.390058i	0.990216	+	0.139544i	$0.0445637\pi$
$908$	383.319	+	1053.16i	0.422158	+	1.15987i
$909$	842.908	−	707.284i	0.927292	−	0.778090i
$910$	0.455173	+	2.58141i	0.000500190	+	0.00283672i
$911$			1313.91i			1.44227i	0.692796	+	0.721134i	$0.256379\pi$
$911$			1313.91i			1.44227i	−0.692796	+	0.721134i	$0.743621\pi$
$912$	80.8457	+	40.7238i	0.0886466	+	0.0446533i
$913$	−438.636			−0.480434
$914$	313.846	−	55.3395i	0.343376	−	0.0605465i
$915$	−1.09052	−	1.29963i	−0.00119183	−	0.00142037i
$916$	−489.792	+	178.270i	−0.534707	+	0.194618i
$917$	123.241	+	44.8559i	0.134395	+	0.0489159i
$918$	−147.322	−	123.618i	−0.160482	−	0.134660i
$919$	−448.379	+	776.615i	−0.487899	+	0.845065i	−0.999903	−	0.0139174i	$-0.995570\pi$
$919$	−448.379	+	776.615i	−0.487899	+	0.845065i	0.512004	+	0.858983i	$0.328903\pi$
$920$	62.0204	−	35.8075i	0.0674134	−	0.0389212i
$921$	−58.1037	+	329.523i	−0.0630877	+	0.357788i
$922$	254.039	+	44.7939i	0.275530	+	0.0485834i
$923$	−135.764	−	235.149i	−0.147089	−	0.254766i
$924$	−14.9357	−	8.62312i	−0.0161642	−	0.00933239i
$925$	−612.432	+	729.869i	−0.662089	+	0.789047i
$926$	−182.980	+	502.735i	−0.197603	+	0.542910i
$927$	−544.011	−	1494.66i	−0.586851	−	1.61236i
$928$	596.038	−	500.136i	0.642283	−	0.538939i
$929$	−45.4679	−	257.861i	−0.0489428	−	0.277568i	0.950508	−	0.310699i	$-0.100563\pi$
$929$	−45.4679	−	257.861i	−0.0489428	−	0.277568i	−0.999451	+	0.0331310i	$0.989452\pi$
$930$		−	8.84047i		−	0.00950588i
$931$	−211.730	−	898.162i	−0.227422	−	0.964729i
$932$	354.211			0.380054
$933$	73.6527	−	12.9870i	0.0789418	−	0.0139196i
$934$	−298.325	−	355.530i	−0.319406	−	0.380653i
$935$	−56.2262	+	20.4647i	−0.0601350	+	0.0218874i
$936$	722.646	+	263.022i	0.772058	+	0.281006i
$937$	1099.91	+	922.937i	1.17387	+	0.984991i	1.00000		0.000221721i	$7.05759e-5\pi$
$937$	1099.91	+	922.937i	1.17387	+	0.984991i	0.173867	+	0.984769i	$0.444374\pi$
$938$	1.46087	−	2.53030i	0.00155743	−	0.00269755i
$939$	−64.4246	+	37.1956i	−0.0686098	+	0.0396119i
$940$	−0.259305	+	1.47059i	−0.000275856	+	0.00156446i
$941$	−592.336	−	104.445i	−0.629475	−	0.110994i	−0.150197	−	0.988656i	$-0.547991\pi$
$941$	−592.336	−	104.445i	−0.629475	−	0.110994i	−0.479279	+	0.877663i	$0.659102\pi$
$942$	24.2193	+	41.9491i	0.0257105	+	0.0445319i
$943$	−932.884	−	538.601i	−0.989273	−	0.571157i
$944$	259.782	−	309.596i	0.275193	−	0.327962i
$945$	0.893846	−	2.45582i	0.000945869	−	0.00259875i
$946$	−89.7075	−	246.469i	−0.0948282	−	0.260538i
$947$	−1350.53	+	1133.23i	−1.42612	+	1.19665i	−0.478152	+	0.878277i	$0.658693\pi$
$947$	−1350.53	+	1133.23i	−1.42612	+	1.19665i	−0.947964	+	0.318376i	$0.896862\pi$
$948$	−19.8841	−	112.768i	−0.0209748	−	0.118954i
$949$			907.154i			0.955905i
$950$	297.833	+	316.444i	0.313508	+	0.333099i
$951$	241.279			0.253711
$952$	70.5300	−	12.4363i	0.0740861	−	0.0130634i
$953$	−1018.58	−	1213.89i	−1.06881	−	1.27376i	−0.960092	−	0.279686i	$-0.909770\pi$
$953$	−1018.58	−	1213.89i	−1.06881	−	1.27376i	−0.108718	−	0.994073i	$-0.534675\pi$
$954$	−512.087	+	186.384i	−0.536779	+	0.195371i
$955$	−85.2206	−	31.0178i	−0.0892362	−	0.0324793i
$956$	25.4401	+	21.3468i	0.0266110	+	0.0223293i
$957$	99.9280	−	173.080i	0.104418	−	0.180857i
$958$	−119.402	+	68.9369i	−0.124637	+	0.0719592i
$959$	0.801920	−	4.54791i	0.000836204	−	0.00474235i
$960$	−0.751107	−	0.132440i	−0.000782403	−	0.000137959i
$961$	415.542	+	719.740i	0.432406	+	0.748949i
$962$	−420.054	−	242.518i	−0.436647	−	0.252098i
$963$	−311.227	+	370.906i	−0.323185	+	0.385157i
$964$	−326.085	+	895.912i	−0.338263	+	0.929369i
$965$	15.1794	+	41.7052i	0.0157300	+	0.0432178i
$966$	−11.5971	+	9.73111i	−0.0120053	+	0.0100736i
$967$	−57.0793	−	323.713i	−0.0590272	−	0.334760i	0.940966	−	0.338502i	$-0.109920\pi$
$967$	−57.0793	−	323.713i	−0.0590272	−	0.334760i	−0.999993	+	0.00374165i	$0.998809\pi$
$968$		−	72.1264i		−	0.0745107i
$969$	−190.330	+	124.855i	−0.196419	+	0.128850i
$970$	−23.3626			−0.0240851
$971$	−120.355	+	21.2219i	−0.123950	+	0.0218557i	−0.235279	−	0.971928i	$-0.575600\pi$
$971$	−120.355	+	21.2219i	−0.123950	+	0.0218557i	0.111329	+	0.993784i	$0.464489\pi$
$972$	−329.313	−	392.460i	−0.338800	−	0.403766i
$973$	−86.6805	+	31.5491i	−0.0890858	+	0.0324246i
$974$	−504.771	−	183.722i	−0.518246	−	0.188626i
$975$	190.389	+	159.756i	0.195271	+	0.163852i
$976$	24.5800	−	42.5738i	0.0251844	−	0.0436207i
$977$	−7.80882	+	4.50842i	−0.00799265	+	0.00461456i	−0.503991	−	0.863709i	$-0.668136\pi$
$977$	−7.80882	+	4.50842i	−0.00799265	+	0.00461456i	0.495998	+	0.868323i	$0.334802\pi$
$978$	13.3439	−	75.6768i	0.0136440	−	0.0773792i
$979$	−1511.03	−	266.436i	−1.54345	−	0.272151i
$980$	−24.0981	−	41.7392i	−0.0245899	−	0.0425910i
$981$	−961.955	−	555.385i	−0.980586	−	0.566141i
$982$	−55.6178	+	66.2827i	−0.0566373	+	0.0674977i
$983$	−26.6388	+	73.1895i	−0.0270995	+	0.0744553i	−0.952505	−	0.304524i	$-0.901503\pi$
$983$	−26.6388	+	73.1895i	−0.0270995	+	0.0744553i	0.925405	+	0.378979i	$0.123725\pi$
$984$	50.5362	+	138.847i	0.0513579	+	0.141105i
$985$	56.7063	−	47.5822i	0.0575698	−	0.0483068i
$986$	63.5639	+	360.489i	0.0644664	+	0.365607i
$987$		−	0.715709i		−	0.000725136i
$988$	495.061	−	663.319i	0.501074	−	0.671375i
$989$	861.420			0.871001
$990$	27.6944	−	4.88328i	0.0279742	−	0.00493260i
$991$	−30.2173	−	36.0116i	−0.0304917	−	0.0363386i	0.750583	−	0.660776i	$-0.229773\pi$
$991$	−30.2173	−	36.0116i	−0.0304917	−	0.0363386i	−0.781075	+	0.624437i	$0.785328\pi$
$992$	1286.62	−	468.293i	1.29700	−	0.472069i
$993$	−86.6530	−	31.5391i	−0.0872639	−	0.0317615i
$994$	9.10411	+	7.63925i	0.00915906	+	0.00768536i
$995$	−9.74022	+	16.8706i	−0.00978917	+	0.0169553i
$996$	−75.4782	+	43.5774i	−0.0757813	+	0.0437524i
$997$	180.602	−	1024.24i	0.181145	−	1.02733i	−0.749663	−	0.661820i	$-0.769785\pi$
$997$	180.602	−	1024.24i	0.181145	−	1.02733i	0.930809	−	0.365507i	$-0.119104\pi$
$998$	−426.794	−	75.2553i	−0.427649	−	0.0754061i
$999$	241.796	+	418.804i	0.242038	+	0.419223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.3.f.a.10.2	yes	12
3.2	odd	2		171.3.ba.b.10.1		12
4.3	odd	2		304.3.z.a.257.2		12
19.2	odd	18	inner	19.3.f.a.2.2	✓	12
19.3	odd	18		361.3.f.e.299.1		12
19.4	even	9		361.3.d.d.293.4		12
19.5	even	9		361.3.f.b.307.2		12
19.6	even	9		361.3.b.c.360.5		12
19.7	even	3		361.3.f.e.262.1		12
19.8	odd	6		361.3.f.b.127.2		12
19.9	even	9		361.3.d.f.69.3		12
19.10	odd	18		361.3.d.d.69.4		12
19.11	even	3		361.3.f.f.127.1		12
19.12	odd	6		361.3.f.c.262.2		12
19.13	odd	18		361.3.b.c.360.8		12
19.14	odd	18		361.3.f.f.307.1		12
19.15	odd	18		361.3.d.f.293.3		12
19.16	even	9		361.3.f.c.299.2		12
19.17	even	9		361.3.f.g.116.1		12
19.18	odd	2		361.3.f.g.333.1		12
57.2	even	18		171.3.ba.b.154.1		12
76.59	even	18		304.3.z.a.97.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.3.f.a.2.2	✓	12	19.2	odd	18	inner
19.3.f.a.10.2	yes	12	1.1	even	1	trivial
171.3.ba.b.10.1		12	3.2	odd	2
171.3.ba.b.154.1		12	57.2	even	18
304.3.z.a.97.2		12	76.59	even	18
304.3.z.a.257.2		12	4.3	odd	2
361.3.b.c.360.5		12	19.6	even	9
361.3.b.c.360.8		12	19.13	odd	18
361.3.d.d.69.4		12	19.10	odd	18
361.3.d.d.293.4		12	19.4	even	9
361.3.d.f.69.3		12	19.9	even	9
361.3.d.f.293.3		12	19.15	odd	18
361.3.f.b.127.2		12	19.8	odd	6
361.3.f.b.307.2		12	19.5	even	9
361.3.f.c.262.2		12	19.12	odd	6
361.3.f.c.299.2		12	19.16	even	9
361.3.f.e.262.1		12	19.7	even	3
361.3.f.e.299.1		12	19.3	odd	18
361.3.f.f.127.1		12	19.11	even	3
361.3.f.f.307.1		12	19.14	odd	18
361.3.f.g.116.1		12	19.17	even	9
361.3.f.g.333.1		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.904538 - 0.159494i) q^{2} +(-0.464845 - 0.553981i) q^{3} +(-2.96602 + 1.07954i) q^{4} +(0.295437 + 0.107530i) q^{5} +(-0.508827 - 0.426957i) q^{6} +(-0.328846 + 0.569578i) q^{7} +(-5.69245 + 3.28654i) q^{8} +(1.47202 - 8.34824i) q^{9} +O(q^{10})\)	\(q+(0.904538 - 0.159494i) q^{2} +(-0.464845 - 0.553981i) q^{3} +(-2.96602 + 1.07954i) q^{4} +(0.295437 + 0.107530i) q^{5} +(-0.508827 - 0.426957i) q^{6} +(-0.328846 + 0.569578i) q^{7} +(-5.69245 + 3.28654i) q^{8} +(1.47202 - 8.34824i) q^{9} +(0.284385 + 0.0501447i) q^{10} +(5.74398 + 9.94886i) q^{11} +(1.97679 + 1.14130i) q^{12} +(8.87147 - 10.5726i) q^{13} +(-0.206609 + 0.567654i) q^{14} +(-0.0777629 - 0.213652i) q^{15} +(5.04684 - 4.23480i) q^{16} +(2.87674 + 16.3148i) q^{17} -7.78608i q^{18} +(-18.1952 - 5.47110i) q^{19} -0.992357 q^{20} +(0.468398 - 0.0825913i) q^{21} +(6.78243 + 8.08299i) q^{22} +(-32.5643 + 11.8524i) q^{23} +(4.46679 + 1.62578i) q^{24} +(-19.0754 - 16.0062i) q^{25} +(6.33831 - 10.9783i) q^{26} +(-10.9456 + 6.31944i) q^{27} +(0.360480 - 2.04438i) q^{28} +(23.6911 + 4.17738i) q^{29} +(-0.104416 - 0.180853i) q^{30} +(36.6615 + 21.1665i) q^{31} +(20.7900 - 24.7765i) q^{32} +(2.84142 - 7.80673i) q^{33} +(5.20425 + 14.2986i) q^{34} +(-0.158400 + 0.132914i) q^{35} +(4.64624 + 26.3502i) q^{36} -38.2623i q^{37} +(-17.3309 - 2.04678i) q^{38} -9.98089 q^{39} +(-2.03516 + 0.358854i) q^{40} +(19.9806 + 23.8120i) q^{41} +(0.410511 - 0.149414i) q^{42} +(-23.3585 - 8.50180i) q^{43} +(-27.7770 - 23.3076i) q^{44} +(1.33258 - 2.30810i) q^{45} +(-27.5652 + 15.9148i) q^{46} +(0.261302 - 1.48192i) q^{47} +(-4.69200 - 0.827326i) q^{48} +(24.2837 + 42.0606i) q^{49} +(-19.8073 - 11.4358i) q^{50} +(7.70087 - 9.17754i) q^{51} +(-14.8994 + 40.9357i) q^{52} +(-23.9382 - 65.7695i) q^{53} +(-8.89279 + 7.46193i) q^{54} +(0.627180 + 3.55692i) q^{55} -4.32306i q^{56} +(5.42709 + 12.6230i) q^{57} +22.0958 q^{58} +(60.4126 - 10.6524i) q^{59} +(0.461293 + 0.549747i) q^{60} +(7.01185 - 2.55210i) q^{61} +(36.5376 + 13.2986i) q^{62} +(4.27091 + 3.58372i) q^{63} +(1.67726 - 2.90509i) q^{64} +(3.75784 - 2.16959i) q^{65} +(1.32504 - 7.51468i) q^{66} +(-4.76316 - 0.839873i) q^{67} +(-26.1450 - 45.2845i) q^{68} +(21.7034 + 12.5305i) q^{69} +(-0.122080 + 0.145490i) q^{70} +(6.72879 - 18.4872i) q^{71} +(19.0574 + 52.3597i) q^{72} +(-50.3508 + 42.2494i) q^{73} +(-6.10263 - 34.6097i) q^{74} +18.0078i q^{75} +(59.8738 - 3.41515i) q^{76} -7.55554 q^{77} +(-9.02809 + 1.59190i) q^{78} +(-32.2459 - 38.4291i) q^{79} +(1.94639 - 0.708429i) q^{80} +(-63.1033 - 22.9677i) q^{81} +(21.8711 + 18.3520i) q^{82} +(-19.0911 + 33.0668i) q^{83} +(-1.30012 + 0.750623i) q^{84} +(-0.904442 + 5.12935i) q^{85} +(-22.4846 - 3.96465i) q^{86} +(-8.69851 - 15.0663i) q^{87} +(-65.3945 - 37.7556i) q^{88} +(-85.8514 + 102.314i) q^{89} +(0.837240 - 2.30030i) q^{90} +(3.10458 + 8.52976i) q^{91} +(83.7911 - 70.3091i) q^{92} +(-5.31607 - 30.1489i) q^{93} -1.38213i q^{94} +(-4.78725 - 3.57291i) q^{95} -23.3899 q^{96} +(-79.6741 + 14.0487i) q^{97} +(28.6740 + 34.1723i) q^{98} +(91.5107 - 33.3072i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{5} - 36 q^{6} + 6 q^{7} - 9 q^{8} - 24 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^5 - 36 * q^6 + 6 * q^7 - 9 * q^8 - 24 * q^9	\( 12 q - 6 q^{2} - 6 q^{5} - 36 q^{6} + 6 q^{7} - 9 q^{8} - 24 q^{9} + 51 q^{10} - 18 q^{11} + 63 q^{12} + 21 q^{13} + 9 q^{14} + 63 q^{15} - 12 q^{16} - 3 q^{17} - 24 q^{19} - 90 q^{20} + 30 q^{21} - 78 q^{22} - 102 q^{23} - 12 q^{24} - 156 q^{25} + 21 q^{26} - 27 q^{27} + 12 q^{28} + 147 q^{29} + 24 q^{30} + 99 q^{31} + 165 q^{32} + 84 q^{33} + 132 q^{34} + 96 q^{35} + 63 q^{36} + 72 q^{38} - 108 q^{39} - 138 q^{40} - 144 q^{41} - 237 q^{42} - 27 q^{43} - 123 q^{44} - 3 q^{45} - 54 q^{46} - 99 q^{47} - 51 q^{48} - 24 q^{49} + 72 q^{50} - 42 q^{51} + 93 q^{52} + 111 q^{53} + 21 q^{54} + 162 q^{55} - 168 q^{57} - 132 q^{58} + 3 q^{59} - 30 q^{60} + 150 q^{61} + 108 q^{62} + 234 q^{63} + 27 q^{64} + 126 q^{65} + 168 q^{66} + 135 q^{67} - 30 q^{68} + 72 q^{69} + 225 q^{70} - 168 q^{71} - 102 q^{72} - 90 q^{73} - 231 q^{74} + 42 q^{76} + 246 q^{77} - 189 q^{78} - 75 q^{79} + 21 q^{80} - 159 q^{81} - 117 q^{82} - 156 q^{83} + 99 q^{84} - 300 q^{85} - 144 q^{86} + 69 q^{87} - 405 q^{88} - 558 q^{89} - 66 q^{90} - 453 q^{91} + 48 q^{92} - 57 q^{93} - 69 q^{95} + 558 q^{96} + 465 q^{97} + 777 q^{98} + 462 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

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