LMFDB - Embedded newform 19.3.f.a.14.2

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			14.2
Root			$1.89323i$ of defining polynomial
Character	$\chi$	$=$	19.14
Dual form			19.3.f.a.15.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.647524 + 1.77906i) q^{2} +(-1.91357 - 0.337414i) q^{3} +(0.318417 - 0.267183i) q^{4} +(-2.13959 - 1.79533i) q^{5} +(-0.638803 - 3.62283i) q^{6} +(-1.20796 - 2.09224i) q^{7} +(7.23987 + 4.17994i) q^{8} +(-4.90934 - 1.78685i) q^{9} +O(q^{10})$	\(q+(0.647524 + 1.77906i) q^{2} +(-1.91357 - 0.337414i) q^{3} +(0.318417 - 0.267183i) q^{4} +(-2.13959 - 1.79533i) q^{5} +(-0.638803 - 3.62283i) q^{6} +(-1.20796 - 2.09224i) q^{7} +(7.23987 + 4.17994i) q^{8} +(-4.90934 - 1.78685i) q^{9} +(1.80856 - 4.96897i) q^{10} +(-9.60360 + 16.6339i) q^{11} +(-0.699463 + 0.403835i) q^{12} +(14.2961 - 2.52079i) q^{13} +(2.94004 - 3.50380i) q^{14} +(3.48848 + 4.15741i) q^{15} +(-2.45965 + 13.9494i) q^{16} +(16.1226 - 5.86814i) q^{17} -9.89103i q^{18} +(-13.2208 - 13.6459i) q^{19} -1.16096 q^{20} +(1.60556 + 4.41123i) q^{21} +(-35.8113 - 6.31450i) q^{22} +(-5.84413 + 4.90381i) q^{23} +(-12.4436 - 10.4414i) q^{24} +(-2.98657 - 16.9377i) q^{25} +(13.7417 + 23.8013i) q^{26} +(23.9363 + 13.8196i) q^{27} +(-0.943645 - 0.343459i) q^{28} +(2.81743 - 7.74083i) q^{29} +(-5.13740 + 8.89824i) q^{30} +(5.19837 - 3.00128i) q^{31} +(6.52208 - 1.15002i) q^{32} +(23.9897 - 28.5898i) q^{33} +(20.8795 + 24.8832i) q^{34} +(-1.17173 + 6.64521i) q^{35} +(-2.04063 + 0.742729i) q^{36} +59.5153i q^{37} +(15.7160 - 32.3567i) q^{38} -28.2071 q^{39} +(-7.98598 - 21.9413i) q^{40} +(-30.4205 - 5.36396i) q^{41} +(-6.80820 + 5.71276i) q^{42} +(18.8243 + 15.7955i) q^{43} +(1.38636 + 7.86244i) q^{44} +(7.29598 + 12.6370i) q^{45} +(-12.5084 - 7.22171i) q^{46} +(-68.7602 - 25.0267i) q^{47} +(9.41343 - 25.8632i) q^{48} +(21.5817 - 37.3806i) q^{49} +(28.1992 - 16.2808i) q^{50} +(-32.8316 + 5.78910i) q^{51} +(3.87860 - 4.62234i) q^{52} +(-18.0172 - 21.4721i) q^{53} +(-9.08660 + 51.5327i) q^{54} +(50.4111 - 18.3482i) q^{55} -20.1968i q^{56} +(20.6947 + 30.5732i) q^{57} +15.5957 q^{58} +(3.15174 + 8.65934i) q^{59} +(2.22158 + 0.391725i) q^{60} +(-47.2307 + 39.6312i) q^{61} +(8.70552 + 7.30480i) q^{62} +(2.19174 + 12.4300i) q^{63} +(34.5983 + 59.9260i) q^{64} +(-35.1134 - 20.2727i) q^{65} +(66.3968 + 24.1665i) q^{66} +(-4.12065 + 11.3214i) q^{67} +(3.56583 - 6.17619i) q^{68} +(12.8378 - 7.41188i) q^{69} +(-12.5809 + 2.21836i) q^{70} +(24.7209 - 29.4613i) q^{71} +(-28.0740 - 33.4573i) q^{72} +(8.82556 - 50.0523i) q^{73} +(-105.881 + 38.5376i) q^{74} +33.4191i q^{75} +(-7.85568 - 0.812682i) q^{76} +46.4029 q^{77} +(-18.2648 - 50.1821i) q^{78} +(105.834 + 18.6613i) q^{79} +(30.3064 - 25.4301i) q^{80} +(-5.12171 - 4.29762i) q^{81} +(-10.1552 - 57.5932i) q^{82} +(-35.6336 - 61.7192i) q^{83} +(1.68984 + 0.975631i) q^{84} +(-45.0309 - 16.3899i) q^{85} +(-15.9119 + 43.7175i) q^{86} +(-8.00321 + 13.8620i) q^{87} +(-139.058 + 80.2850i) q^{88} +(7.98351 - 1.40771i) q^{89} +(-17.7576 + 21.1627i) q^{90} +(-22.5431 - 26.8659i) q^{91} +(-0.550653 + 3.12291i) q^{92} +(-10.9601 + 3.98915i) q^{93} -138.534i q^{94} +(3.78836 + 52.9323i) q^{95} -12.8685 q^{96} +(40.7412 + 111.936i) q^{97} +(80.4769 + 14.1902i) q^{98} +(76.8697 - 64.5013i) 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 $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	0.647524	+	1.77906i	0.323762	+	0.889529i	0.989653	+	0.143480i	$0.0458293\pi$
$2$	0.647524	+	1.77906i	0.323762	+	0.889529i	−0.665891	+	0.746049i	$0.731948\pi$
$3$	−1.91357	−	0.337414i	−0.637856	−	0.112471i	−0.154638	−	0.987971i	$-0.549421\pi$
$3$	−1.91357	−	0.337414i	−0.637856	−	0.112471i	−0.483218	+	0.875500i	$0.660532\pi$
$4$	0.318417	−	0.267183i	0.0796042	−	0.0667958i
$5$	−2.13959	−	1.79533i	−0.427918	−	0.359066i	0.403248	−	0.915091i	$-0.367881\pi$
$5$	−2.13959	−	1.79533i	−0.427918	−	0.359066i	−0.831165	+	0.556025i	$0.812326\pi$
$6$	−0.638803	−	3.62283i	−0.106467	−	0.603806i
$7$	−1.20796	−	2.09224i	−0.172565	−	0.298892i	0.766751	−	0.641945i	$-0.221872\pi$
$7$	−1.20796	−	2.09224i	−0.172565	−	0.298892i	−0.939316	+	0.343053i	$0.888539\pi$
$8$	7.23987	+	4.17994i	0.904984	+	0.522493i
$9$	−4.90934	−	1.78685i	−0.545482	−	0.198539i
$10$	1.80856	−	4.96897i	0.180856	−	0.496897i
$11$	−9.60360	+	16.6339i	−0.873055	+	1.51218i	−0.0142343	+	0.999899i	$0.504531\pi$
$11$	−9.60360	+	16.6339i	−0.873055	+	1.51218i	−0.858821	+	0.512277i	$0.828802\pi$
$12$	−0.699463	+	0.403835i	−0.0582886	+	0.0336529i
$13$	14.2961	−	2.52079i	1.09970	−	0.193907i	0.405788	−	0.913967i	$-0.366997\pi$
$13$	14.2961	−	2.52079i	1.09970	−	0.193907i	0.693911	+	0.720061i	$0.255886\pi$
$14$	2.94004	−	3.50380i	0.210003	−	0.250272i
$15$	3.48848	+	4.15741i	0.232565	+	0.277161i
$16$	−2.45965	+	13.9494i	−0.153728	+	0.871836i
$17$	16.1226	−	5.86814i	0.948387	−	0.345184i	0.178914	−	0.983865i	$-0.442742\pi$
$17$	16.1226	−	5.86814i	0.948387	−	0.345184i	0.769472	+	0.638680i	$0.220519\pi$
$18$		−	9.89103i		−	0.549501i
$19$	−13.2208	−	13.6459i	−0.695834	−	0.718203i
$19$	−13.2208	−	13.6459i	−0.695834	−	0.718203i
$20$	−1.16096			−0.0580481
$21$	1.60556	+	4.41123i	0.0764550	+	0.210059i
$22$	−35.8113	−	6.31450i	−1.62779	−	0.287023i
$23$	−5.84413	+	4.90381i	−0.254092	+	0.213209i	−0.760932	−	0.648831i	$-0.775258\pi$
$23$	−5.84413	+	4.90381i	−0.254092	+	0.213209i	0.506840	+	0.862040i	$0.330814\pi$
$24$	−12.4436	−	10.4414i	−0.518484	−	0.435060i
$25$	−2.98657	−	16.9377i	−0.119463	−	0.677507i
$26$	13.7417	+	23.8013i	0.528527	+	0.915435i
$27$	23.9363	+	13.8196i	0.886530	+	0.511839i
$28$	−0.943645	−	0.343459i	−0.0337016	−	0.0122664i
$29$	2.81743	−	7.74083i	0.0971528	−	0.266925i	−0.881590	−	0.472015i	$-0.843527\pi$
$29$	2.81743	−	7.74083i	0.0971528	−	0.266925i	0.978743	+	0.205090i	$0.0657489\pi$
$30$	−5.13740	+	8.89824i	−0.171247	+	0.296608i
$31$	5.19837	−	3.00128i	0.167689	−	0.0968155i	−0.413806	−	0.910365i	$-0.635801\pi$
$31$	5.19837	−	3.00128i	0.167689	−	0.0968155i	0.581496	+	0.813549i	$0.302468\pi$
$32$	6.52208	−	1.15002i	0.203815	−	0.0359381i
$33$	23.9897	−	28.5898i	0.726960	−	0.866357i
$34$	20.8795	+	24.8832i	0.614103	+	0.731860i
$35$	−1.17173	+	6.64521i	−0.0334780	+	0.189863i
$36$	−2.04063	+	0.742729i	−0.0566842	+	0.0206314i
$37$			59.5153i			1.60852i	0.594277	+	0.804260i	$0.297438\pi$
$37$			59.5153i			1.60852i	−0.594277	+	0.804260i	$0.702562\pi$
$38$	15.7160	−	32.3567i	0.413578	−	0.851491i
$39$	−28.2071			−0.723259
$40$	−7.98598	−	21.9413i	−0.199650	−	0.548533i
$41$	−30.4205	−	5.36396i	−0.741964	−	0.130828i	−0.210126	−	0.977674i	$-0.567387\pi$
$41$	−30.4205	−	5.36396i	−0.741964	−	0.130828i	−0.531838	+	0.846846i	$0.678498\pi$
$42$	−6.80820	+	5.71276i	−0.162100	+	0.136018i
$43$	18.8243	+	15.7955i	0.437775	+	0.367337i	0.834876	−	0.550438i	$-0.185539\pi$
$43$	18.8243	+	15.7955i	0.437775	+	0.367337i	−0.397101	+	0.917775i	$0.629984\pi$
$44$	1.38636	+	7.86244i	0.0315082	+	0.178692i
$45$	7.29598	+	12.6370i	0.162133	+	0.280822i
$46$	−12.5084	−	7.22171i	−0.271921	−	0.156994i
$47$	−68.7602	−	25.0267i	−1.46298	−	0.532483i	−0.516798	−	0.856107i	$-0.672876\pi$
$47$	−68.7602	−	25.0267i	−1.46298	−	0.532483i	−0.946186	+	0.323625i	$0.895099\pi$
$48$	9.41343	−	25.8632i	0.196113	−	0.538816i
$49$	21.5817	−	37.3806i	0.440443	−	0.762869i
$50$	28.1992	−	16.2808i	0.563984	−	0.325617i
$51$	−32.8316	+	5.78910i	−0.643758	+	0.113512i
$52$	3.87860	−	4.62234i	0.0745885	−	0.0888911i
$53$	−18.0172	−	21.4721i	−0.339947	−	0.405133i	0.568803	−	0.822474i	$-0.307407\pi$
$53$	−18.0172	−	21.4721i	−0.339947	−	0.405133i	−0.908750	+	0.417341i	$0.862962\pi$
$54$	−9.08660	+	51.5327i	−0.168270	+	0.954309i
$55$	50.4111	−	18.3482i	0.916566	−	0.333603i
$56$		−	20.1968i		−	0.360656i
$57$	20.6947	+	30.5732i	0.363065	+	0.536372i
$58$	15.5957			0.268892
$59$	3.15174	+	8.65934i	0.0534194	+	0.146769i	0.963532	−	0.267591i	$-0.0862277\pi$
$59$	3.15174	+	8.65934i	0.0534194	+	0.146769i	−0.910113	+	0.414360i	$0.864005\pi$
$60$	2.22158	+	0.391725i	0.0370264	+	0.00652875i
$61$	−47.2307	+	39.6312i	−0.774273	+	0.649692i	−0.941799	−	0.336175i	$-0.890867\pi$
$61$	−47.2307	+	39.6312i	−0.774273	+	0.649692i	0.167526	+	0.985868i	$0.446422\pi$
$62$	8.70552	+	7.30480i	0.140412	+	0.117819i
$63$	2.19174	+	12.4300i	0.0347895	+	0.197301i
$64$	34.5983	+	59.9260i	0.540598	+	0.936344i
$65$	−35.1134	−	20.2727i	−0.540206	−	0.311888i
$66$	66.3968	+	24.1665i	1.00601	+	0.366158i
$67$	−4.12065	+	11.3214i	−0.0615023	+	0.168976i	−0.966638	−	0.256147i	$-0.917547\pi$
$67$	−4.12065	+	11.3214i	−0.0615023	+	0.168976i	0.905136	+	0.425123i	$0.139769\pi$
$68$	3.56583	−	6.17619i	0.0524386	−	0.0908264i
$69$	12.8378	−	7.41188i	0.186054	−	0.107419i
$70$	−12.5809	+	2.21836i	−0.179728	+	0.0316909i
$71$	24.7209	−	29.4613i	0.348182	−	0.414948i	−0.563322	−	0.826237i	$-0.690477\pi$
$71$	24.7209	−	29.4613i	0.348182	−	0.414948i	0.911505	+	0.411290i	$0.134922\pi$
$72$	−28.0740	−	33.4573i	−0.389917	−	0.464685i
$73$	8.82556	−	50.0523i	0.120898	−	0.685647i	−0.862762	−	0.505611i	$-0.831267\pi$
$73$	8.82556	−	50.0523i	0.120898	−	0.685647i	0.983660	−	0.180037i	$-0.0576217\pi$
$74$	−105.881	+	38.5376i	−1.43083	+	0.520778i
$75$			33.4191i			0.445588i
$76$	−7.85568	−	0.812682i	−0.103364	−	0.0106932i
$77$	46.4029			0.602635
$78$	−18.2648	−	50.1821i	−0.234164	−	0.643360i
$79$	105.834	+	18.6613i	1.33967	+	0.236219i	0.797127	−	0.603812i	$-0.206352\pi$
$79$	105.834	+	18.6613i	1.33967	+	0.236219i	0.542538	+	0.840031i	$0.317463\pi$
$80$	30.3064	−	25.4301i	0.378830	−	0.317876i
$81$	−5.12171	−	4.29762i	−0.0632310	−	0.0530571i
$82$	−10.1552	−	57.5932i	−0.123844	−	0.702356i
$83$	−35.6336	−	61.7192i	−0.429321	−	0.743605i	0.567492	−	0.823379i	$-0.307914\pi$
$83$	−35.6336	−	61.7192i	−0.429321	−	0.743605i	−0.996813	+	0.0797735i	$0.974580\pi$
$84$	1.68984	+	0.975631i	0.0201172	+	0.0116147i
$85$	−45.0309	−	16.3899i	−0.529775	−	0.192822i
$86$	−15.9119	+	43.7175i	−0.185022	+	0.508343i
$87$	−8.00321	+	13.8620i	−0.0919909	+	0.159333i
$88$	−139.058	+	80.2850i	−1.58020	+	0.912330i
$89$	7.98351	−	1.40771i	0.0897024	−	0.0158169i	−0.128617	−	0.991694i	$-0.541054\pi$
$89$	7.98351	−	1.40771i	0.0897024	−	0.0158169i	0.218319	+	0.975877i	$0.429943\pi$
$90$	−17.7576	+	21.1627i	−0.197307	+	0.235141i
$91$	−22.5431	−	26.8659i	−0.247727	−	0.295229i
$92$	−0.550653	+	3.12291i	−0.00598535	+	0.0339446i
$93$	−10.9601	+	3.98915i	−0.117851	+	0.0428941i
$94$		−	138.534i		−	1.47376i
$95$	3.78836	+	52.9323i	0.0398775	+	0.557182i
$96$	−12.8685			−0.134047
$97$	40.7412	+	111.936i	0.420013	+	1.15398i	0.951699	+	0.307034i	$0.0993364\pi$
$97$	40.7412	+	111.936i	0.420013	+	1.15398i	−0.531686	+	0.846941i	$0.678441\pi$
$98$	80.4769	+	14.1902i	0.821193	+	0.144798i
$99$	76.8697	−	64.5013i	0.776462	−	0.651529i
$100$	−5.47643	−	4.59527i	−0.0547643	−	0.0459527i
$101$	22.8186	+	129.411i	0.225926	+	1.28129i	0.860906	+	0.508764i	$0.169897\pi$
$101$	22.8186	+	129.411i	0.225926	+	1.28129i	−0.634980	+	0.772529i	$0.718992\pi$
$102$	−31.5584	−	54.6608i	−0.309396	−	0.535890i
$103$	11.4431	+	6.60670i	0.111098	+	0.0641427i	0.554520	−	0.832171i	$-0.312902\pi$
$103$	11.4431	+	6.60670i	0.111098	+	0.0641427i	−0.443421	+	0.896313i	$0.646235\pi$
$104$	114.039	+	41.5067i	1.09653	+	0.399102i
$105$	4.48437	−	12.3207i	0.0427083	−	0.117340i
$106$	26.5335	−	45.9573i	0.250316	−	0.433560i
$107$	94.8683	−	54.7722i	0.886620	−	0.511890i	0.0137844	−	0.999905i	$-0.495612\pi$
$107$	94.8683	−	54.7722i	0.886620	−	0.511890i	0.872835	+	0.488015i	$0.162279\pi$
$108$	11.3141	−	1.99498i	0.104760	−	0.0184720i
$109$	−132.479	+	157.882i	−1.21540	+	1.44846i	−0.358071	+	0.933694i	$0.616565\pi$
$109$	−132.479	+	157.882i	−1.21540	+	1.44846i	−0.857331	+	0.514766i	$0.827879\pi$
$110$	65.2849	+	77.8035i	0.593499	+	0.707304i
$111$	20.0813	−	113.887i	0.180912	−	1.02600i
$112$	32.1566	−	11.7041i	0.287113	−	0.104500i
$113$		−	18.3671i		−	0.162541i	−0.996692	−	0.0812705i	$-0.974102\pi$
$113$		−	18.3671i		−	0.162541i	0.996692	−	0.0812705i	$-0.0258978\pi$
$114$	−40.9912	+	56.6139i	−0.359572	+	0.496613i
$115$	21.3080			0.185287
$116$	−1.17110	−	3.21758i	−0.0100957	−	0.0277377i
$117$	−74.6886	−	13.1696i	−0.638364	−	0.112561i
$118$	−13.3646	+	11.2143i	−0.113260	+	0.0950362i
$119$	−31.7529	−	26.6439i	−0.266831	−	0.223898i
$120$	7.87843	+	44.6808i	0.0656536	+	0.372340i
$121$	−123.958	−	214.702i	−1.02445	−	1.77440i
$122$	−101.089	−	58.3639i	−0.828601	−	0.478393i
$123$	56.4019	+	20.5286i	0.458552	+	0.166899i
$124$	0.853356	−	2.34458i	0.00688190	−	0.0189079i
$125$	−58.9316	+	102.072i	−0.471453	+	0.816580i
$126$	−20.6944	+	11.9479i	−0.164241	+	0.0948248i
$127$	−11.1586	+	1.96757i	−0.0878634	+	0.0154927i	−0.217407	−	0.976081i	$-0.569760\pi$
$127$	−11.1586	+	1.96757i	−0.0878634	+	0.0154927i	0.129544	+	0.991574i	$0.458649\pi$
$128$	−67.1807	+	80.0628i	−0.524849	+	0.625491i
$129$	−30.6920	−	36.5773i	−0.237922	−	0.283545i
$130$	13.3296	−	75.5959i	0.102535	−	0.581507i
$131$	−10.5473	+	3.83890i	−0.0805137	+	0.0293046i	−0.381963	−	0.924178i	$-0.624752\pi$
$131$	−10.5473	+	3.83890i	−0.0805137	+	0.0293046i	0.301449	+	0.953482i	$0.402530\pi$
$132$		−	15.5131i		−	0.117523i
$133$	−12.5802	+	44.1448i	−0.0945883	+	0.331916i
$134$	−22.8097			−0.170221
$135$	−26.4031	−	72.5419i	−0.195578	−	0.537347i
$136$	141.254	+	24.9069i	1.03863	+	0.183139i
$137$	123.899	−	103.964i	0.904374	−	0.758860i	−0.0666667	−	0.997775i	$-0.521236\pi$
$137$	123.899	−	103.964i	0.904374	−	0.758860i	0.971040	+	0.238916i	$0.0767920\pi$
$138$	21.4989	+	18.0397i	0.155789	+	0.130723i
$139$	−33.3504	−	189.139i	−0.239931	−	1.36071i	−0.831977	−	0.554810i	$-0.812791\pi$
$139$	−33.3504	−	189.139i	−0.239931	−	1.36071i	0.592046	−	0.805904i	$-0.298320\pi$
$140$	1.40239	+	2.42901i	0.0100171	+	0.0173501i
$141$	123.133	+	71.0909i	0.873284	+	0.504191i
$142$	68.4208	+	24.9031i	0.481836	+	0.175374i
$143$	−95.3634	+	262.009i	−0.666877	+	1.83223i
$144$	37.0007	−	64.0872i	0.256950	−	0.445050i
$145$	−19.9255	+	11.5040i	−0.137417	+	0.0793378i
$146$	94.7607	−	16.7089i	0.649046	−	0.114444i
$147$	−53.9108	+	64.2483i	−0.366740	+	0.437064i
$148$	15.9015	+	18.9506i	0.107442	+	0.128045i
$149$	24.4090	−	138.430i	0.163819	−	0.929063i	−0.786455	−	0.617648i	$-0.788086\pi$
$149$	24.4090	−	138.430i	0.163819	−	0.929063i	0.950274	−	0.311415i	$-0.100803\pi$
$150$	−59.4545	+	21.6397i	−0.396363	+	0.144264i
$151$			101.605i			0.672880i	0.941705	+	0.336440i	$0.109223\pi$
$151$			101.605i			0.672880i	−0.941705	+	0.336440i	$0.890777\pi$
$152$	−38.6783	−	154.057i	−0.254462	−	1.01353i
$153$	−89.6366			−0.585860
$154$	30.0470	+	82.5535i	0.195111	+	0.536062i
$155$	−16.5107	−	2.91127i	−0.106520	−	0.0187824i
$156$	−8.98161	+	7.53646i	−0.0575744	+	0.0483107i
$157$	128.198	+	107.571i	0.816551	+	0.685167i	0.952162	−	0.305595i	$-0.0988553\pi$
$157$	128.198	+	107.571i	0.816551	+	0.685167i	−0.135611	+	0.990762i	$0.543300\pi$
$158$	35.3302	+	200.368i	0.223609	+	1.26815i
$159$	27.2322	+	47.1675i	0.171272	+	0.296651i
$160$	−16.0192	−	9.24871i	−0.100120	−	0.0578044i
$161$	17.3194	+	6.30374i	0.107574	+	0.0391537i
$162$	4.32929	−	11.8946i	0.0267240	−	0.0734237i
$163$	16.9195	−	29.3054i	0.103801	−	0.179788i	−0.809447	−	0.587193i	$-0.800233\pi$
$163$	16.9195	−	29.3054i	0.103801	−	0.179788i	0.913248	+	0.407405i	$0.133566\pi$
$164$	−11.1196	+	6.41988i	−0.0678022	+	0.0391456i
$165$	−102.656	+	18.1010i	−0.622158	+	0.109703i
$166$	86.7285	−	103.359i	0.522461	−	0.622644i
$167$	−31.0323	−	36.9829i	−0.185822	−	0.221454i	0.665089	−	0.746764i	$-0.268394\pi$
$167$	−31.0323	−	36.9829i	−0.185822	−	0.221454i	−0.850911	+	0.525310i	$0.823949\pi$
$168$	−6.81466	+	38.6479i	−0.0405635	+	0.230047i
$169$	39.2157	−	14.2733i	0.232046	−	0.0844577i
$170$		−	90.7255i		−	0.533679i
$171$	40.5224	+	90.6158i	0.236973	+	0.529917i
$172$	10.2143			0.0593852
$173$	17.6894	+	48.6013i	0.102251	+	0.280932i	0.980260	−	0.197711i	$-0.0633509\pi$
$173$	17.6894	+	48.6013i	0.102251	+	0.280932i	−0.878009	+	0.478643i	$0.841129\pi$
$174$	−29.8435	−	5.26222i	−0.171514	−	0.0302426i
$175$	−31.8300	+	26.7086i	−0.181886	+	0.152620i
$176$	−208.411	−	174.878i	−1.18416	−	0.993625i
$177$	−3.10930	−	17.6337i	−0.0175666	−	0.0996254i
$178$	7.67391	+	13.2916i	0.0431119	+	0.0746719i
$179$	−200.919	−	116.001i	−1.12245	−	0.648048i	−0.180426	−	0.983589i	$-0.557748\pi$
$179$	−200.919	−	116.001i	−1.12245	−	0.648048i	−0.942026	+	0.335541i	$0.891081\pi$
$180$	5.69956	+	2.07447i	0.0316642	+	0.0115248i
$181$	92.4816	−	254.091i	0.510948	−	1.40382i	−0.369303	−	0.929309i	$-0.620404\pi$
$181$	92.4816	−	254.091i	0.510948	−	1.40382i	0.880251	−	0.474509i	$-0.157374\pi$
$182$	33.1987	−	57.5019i	0.182411	−	0.315944i
$183$	103.751	−	59.9008i	0.566947	−	0.327327i
$184$	−62.8084	+	11.0748i	−0.341350	+	0.0601892i
$185$	106.849	−	127.338i	0.577564	−	0.688315i
$186$	−14.1939	−	16.9156i	−0.0763112	−	0.0909441i
$187$	−57.2246	+	324.537i	−0.306014	+	1.73549i
$188$	−28.5811	+	10.4027i	−0.152027	+	0.0553334i
$189$		−	66.7741i		−	0.353302i
$190$	−91.7166	+	41.0146i	−0.482719	+	0.215867i
$191$	81.4552			0.426467			0.213233	−	0.977001i	$-0.431601\pi$
$191$	81.4552			0.426467			0.213233	+	0.977001i	$0.431601\pi$
$192$	−45.9864	−	126.346i	−0.239512	−	0.658055i
$193$	−29.3774	−	5.18002i	−0.152214	−	0.0268395i	0.0970217	−	0.995282i	$-0.469068\pi$
$193$	−29.3774	−	5.18002i	−0.152214	−	0.0268395i	−0.249236	+	0.968443i	$0.580179\pi$
$194$	−172.759	+	144.962i	−0.890510	+	0.747227i
$195$	60.3516	+	50.6410i	0.309495	+	0.259697i
$196$	−3.11550	−	17.6689i	−0.0158954	−	0.0901472i
$197$	90.0191	+	155.918i	0.456950	+	0.791461i	0.998798	−	0.0490159i	$-0.0156085\pi$
$197$	90.0191	+	155.918i	0.456950	+	0.791461i	−0.541848	+	0.840476i	$0.682275\pi$
$198$	164.527	+	94.9895i	0.830943	+	0.479745i
$199$	−103.486	−	37.6658i	−0.520030	−	0.189276i	0.0686510	−	0.997641i	$-0.478130\pi$
$199$	−103.486	−	37.6658i	−0.520030	−	0.189276i	−0.588681	+	0.808365i	$0.700353\pi$
$200$	49.1761	−	135.110i	0.245880	−	0.675551i
$201$	11.7051	−	20.2739i	0.0582346	−	0.100865i
$202$	−215.453	+	124.392i	−1.06660	+	0.615802i
$203$	−19.5990	+	3.45583i	−0.0965468	+	0.0170238i
$204$	−8.90739	+	10.6154i	−0.0436637	+	0.0520363i
$205$	55.4573	+	66.0915i	0.270524	+	0.322397i
$206$	−4.34399	+	24.6360i	−0.0210874	+	0.119592i
$207$	37.4532	−	13.6318i	0.180933	−	0.0658543i
$208$			205.622i			0.988566i
$209$	353.952	−	88.8650i	1.69355	−	0.425192i
$210$	24.8230			0.118205
$211$	−52.6404	−	144.628i	−0.249480	−	0.685442i	−0.999706	−	0.0242596i	$-0.992277\pi$
$211$	−52.6404	−	144.628i	−0.249480	−	0.685442i	0.750225	−	0.661182i	$-0.229945\pi$
$212$	−11.4740	−	2.02317i	−0.0541224	−	0.00954324i
$213$	−57.2459	+	48.0350i	−0.268760	+	0.225516i
$214$	158.873	+	133.310i	0.742395	+	0.622944i
$215$	−11.9182	−	67.5916i	−0.0554336	−	0.314380i
$216$	115.531	+	200.105i	0.534864	+	0.926412i
$217$	−12.5588	−	7.25083i	−0.0578747	−	0.0334140i
$218$	−366.665	−	133.455i	−1.68195	−	0.612179i
$219$	−33.7766	+	92.8006i	−0.154231	+	0.423747i
$220$	11.1494	−	19.3114i	0.0506792	−	0.0877789i
$221$	215.697	−	124.533i	0.976006	−	0.563497i
$222$	215.614	−	38.0185i	0.971234	−	0.171255i
$223$	100.038	−	119.221i	0.448602	−	0.534623i	−0.493591	−	0.869694i	$-0.664316\pi$
$223$	100.038	−	119.221i	0.448602	−	0.534623i	0.942193	+	0.335071i	$0.108760\pi$
$224$	−10.2845	−	12.2566i	−0.0459129	−	0.0547169i
$225$	−15.6030	+	88.4892i	−0.0693468	+	0.393286i
$226$	32.6762	−	11.8932i	0.144585	−	0.0526247i
$227$			67.0830i			0.295520i	0.989023	+	0.147760i	$0.0472063\pi$
$227$			67.0830i			0.295520i	−0.989023	+	0.147760i	$0.952794\pi$
$228$	14.7582	+	4.20574i	0.0647288	+	0.0184462i
$229$	69.2740			0.302506			0.151253	−	0.988495i	$-0.451669\pi$
$229$	69.2740			0.302506			0.151253	+	0.988495i	$0.451669\pi$
$230$	13.7974	+	37.9081i	0.0599888	+	0.164818i
$231$	−88.7952	−	15.6570i	−0.384395	−	0.0677792i
$232$	52.7541	−	44.2659i	0.227388	−	0.190801i
$233$	−125.028	−	104.911i	−0.536601	−	0.450261i	0.333773	−	0.942654i	$-0.391678\pi$
$233$	−125.028	−	104.911i	−0.536601	−	0.450261i	−0.870373	+	0.492392i	$0.836123\pi$
$234$	−24.9332	−	141.403i	−0.106552	−	0.604286i
$235$	102.188	+	176.994i	0.434841	+	0.753166i
$236$	3.31720	+	1.91519i	0.0140559	+	0.00811519i
$237$	−196.223	−	71.4194i	−0.827946	−	0.301348i
$238$	26.8402	−	73.7428i	0.112774	−	0.309844i
$239$	−152.816	+	264.685i	−0.639397	+	1.10747i	0.346168	+	0.938172i	$0.387483\pi$
$239$	−152.816	+	264.685i	−0.639397	+	1.10747i	−0.985565	+	0.169296i	$0.945851\pi$
$240$	−66.5738	+	38.4364i	−0.277391	+	0.160152i
$241$	−236.403	+	41.6842i	−0.980925	+	0.172963i	−0.641043	−	0.767505i	$-0.721498\pi$
$241$	−236.403	+	41.6842i	−0.980925	+	0.172963i	−0.339881	+	0.940468i	$0.610387\pi$
$242$	301.702	−	359.554i	1.24670	−	1.48576i
$243$	−151.545	−	180.604i	−0.623642	−	0.743228i
$244$	−4.45023	+	25.2385i	−0.0182386	+	0.103436i
$245$	−113.286	+	41.2329i	−0.462393	+	0.168297i
$246$			113.635i			0.461931i
$247$	−223.405	−	161.755i	−0.904472	−	0.654881i
$248$	50.1807			0.202342
$249$	47.3624	+	130.127i	0.190211	+	0.522599i
$250$	−219.753	−	38.7483i	−0.879010	−	0.154993i
$251$	−244.652	+	205.287i	−0.974708	+	0.817877i	−0.983283	−	0.182086i	$-0.941715\pi$
$251$	−244.652	+	205.287i	−0.974708	+	0.817877i	0.00857425	+	0.999963i	$0.497271\pi$
$252$	4.01896	+	3.37231i	0.0159483	+	0.0133822i
$253$	−25.4449	−	144.305i	−0.100573	−	0.570375i
$254$	−10.7259	−	18.5778i	−0.0422280	−	0.0731411i
$255$	80.6396	+	46.5573i	0.316234	+	0.182578i
$256$	74.1565	+	26.9908i	0.289674	+	0.105433i
$257$	39.3775	−	108.189i	0.153220	−	0.420968i	−0.839206	−	0.543814i	$-0.816980\pi$
$257$	39.3775	−	108.189i	0.153220	−	0.420968i	0.992426	+	0.122846i	$0.0392021\pi$
$258$	45.1993	−	78.2875i	0.175191	−	0.303440i
$259$	124.520	−	71.8918i	0.480773	−	0.277575i
$260$	−16.5972	+	2.92654i	−0.0638355	+	0.0112559i
$261$	−27.6634	+	32.9680i	−0.105990	+	0.126314i
$262$	−13.6593	−	16.2785i	−0.0521346	−	0.0621315i
$263$	−3.94528	+	22.3748i	−0.0150011	+	0.0850752i	−0.991389	−	0.130949i	$-0.958198\pi$
$263$	−3.94528	+	22.3748i	−0.0150011	+	0.0850752i	0.976388	+	0.216024i	$0.0693088\pi$
$264$	293.186	−	106.711i	1.11055	−	0.404208i
$265$			78.2882i			0.295427i
$266$	−86.6822	+	6.20384i	−0.325873	+	0.0233227i
$267$	−15.7520			−0.0589962
$268$	1.71280	+	4.70589i	0.00639106	+	0.0175593i
$269$	−273.598	−	48.2428i	−1.01709	−	0.179341i	−0.359843	−	0.933013i	$-0.617170\pi$
$269$	−273.598	−	48.2428i	−1.01709	−	0.179341i	−0.657251	+	0.753672i	$0.728281\pi$
$270$	111.960	−	93.9453i	0.414665	−	0.347946i
$271$	2.59209	+	2.17502i	0.00956490	+	0.00802590i	0.647558	−	0.762017i	$-0.275791\pi$
$271$	2.59209	+	2.17502i	0.00956490	+	0.00802590i	−0.637993	+	0.770042i	$0.720235\pi$
$272$	42.2009	+	239.333i	0.155151	+	0.879902i
$273$	34.0729	+	59.0161i	0.124809	+	0.216176i
$274$	265.185	+	153.105i	0.967830	+	0.558777i
$275$	310.422	+	112.984i	1.12881	+	0.410852i
$276$	2.10742	−	5.79010i	0.00763559	−	0.0209786i
$277$	67.8848	−	117.580i	0.245072	−	0.424476i	−0.717080	−	0.696991i	$-0.754522\pi$
$277$	67.8848	−	117.580i	0.245072	−	0.424476i	0.962152	+	0.272514i	$0.0878552\pi$
$278$	314.895	−	181.804i	1.13271	−	0.653973i
$279$	−30.8834	+	5.44558i	−0.110693	+	0.0195182i
$280$	−36.2598	+	43.2127i	−0.129499	+	0.154331i
$281$	317.040	+	377.834i	1.12826	+	1.34460i	0.931326	+	0.364188i	$0.118653\pi$
$281$	317.040	+	377.834i	1.12826	+	1.34460i	0.196932	+	0.980417i	$0.436902\pi$
$282$	−46.7432	+	265.094i	−0.165756	+	0.940050i
$283$	352.072	−	128.144i	1.24407	−	0.452804i	0.365676	−	0.930742i	$-0.380838\pi$
$283$	352.072	−	128.144i	1.24407	−	0.452804i	0.878393	+	0.477938i	$0.158616\pi$
$284$		−	15.9860i		−	0.0562887i
$285$	10.6108	−	102.568i	0.0372309	−	0.359887i
$286$	−527.879			−1.84573
$287$	25.5240	+	70.1265i	0.0889336	+	0.244343i
$288$	−34.0740	−	6.00816i	−0.118312	−	0.0208617i
$289$	4.11543	−	3.45325i	0.0142402	−	0.0119490i
$290$	−33.3685	−	27.9995i	−0.115064	−	0.0965499i
$291$	−40.1925	−	227.943i	−0.138119	−	0.783310i
$292$	−10.5629	−	18.2955i	−0.0361744	−	0.0626559i
$293$	−63.5500	−	36.6906i	−0.216894	−	0.125224i	0.387617	−	0.921820i	$-0.373298\pi$
$293$	−63.5500	−	36.6906i	−0.216894	−	0.125224i	−0.604511	+	0.796597i	$0.706632\pi$
$294$	−149.210	−	54.3080i	−0.507517	−	0.184721i
$295$	8.80293	−	24.1859i	0.0298404	−	0.0819859i
$296$	−248.770	+	430.883i	−0.840440	+	1.45569i
$297$	−459.750	+	265.437i	−1.54798	+	0.893726i
$298$	262.081	−	46.2120i	0.879467	−	0.155074i
$299$	−71.1867	+	84.8370i	−0.238083	+	0.283736i
$300$	8.92902	+	10.6412i	0.0297634	+	0.0354706i
$301$	10.3090	−	58.4652i	0.0342492	−	0.194237i
$302$	−180.761	+	65.7916i	−0.598547	+	0.217853i
$303$		−	255.335i		−	0.842691i
$304$	222.870	−	150.858i	0.733125	−	0.496245i
$305$	172.205			0.564607
$306$	−58.0419	−	159.469i	−0.189679	−	0.521140i
$307$	−91.0288	−	16.0508i	−0.296511	−	0.0522829i	0.0234138	−	0.999726i	$-0.492546\pi$
$307$	−91.0288	−	16.0508i	−0.296511	−	0.0522829i	−0.319925	+	0.947443i	$0.603658\pi$
$308$	14.7755	−	12.3981i	0.0479723	−	0.0402535i
$309$	−19.6680	−	16.5035i	−0.0636506	−	0.0534092i
$310$	−5.51173	−	31.2585i	−0.0177798	−	0.100834i
$311$	−99.6155	−	172.539i	−0.320307	−	0.554788i	0.660244	−	0.751051i	$-0.270453\pi$
$311$	−99.6155	−	172.539i	−0.320307	−	0.554788i	−0.980551	+	0.196263i	$0.937119\pi$
$312$	−204.216	−	117.904i	−0.654538	−	0.377898i
$313$	−28.7523	−	10.4650i	−0.0918605	−	0.0334345i	0.295681	−	0.955287i	$-0.404453\pi$
$313$	−28.7523	−	10.4650i	−0.0918605	−	0.0334345i	−0.387542	+	0.921852i	$0.626676\pi$
$314$	−108.364	+	297.728i	−0.345108	+	0.948177i
$315$	17.6264	−	30.5299i	0.0559569	−	0.0969203i
$316$	38.6852	−	22.3349i	0.122421	−	0.0706800i
$317$	561.248	−	98.9631i	1.77050	−	0.312186i	0.809166	−	0.587581i	$-0.199919\pi$
$317$	561.248	−	98.9631i	1.77050	−	0.312186i	0.961331	+	0.275394i	$0.0888084\pi$
$318$	−66.2803	+	78.9897i	−0.208429	+	0.248395i
$319$	101.703	+	121.205i	0.318818	+	0.379952i
$320$	33.5607	−	190.332i	0.104877	−	0.594789i
$321$	−200.018	+	72.8006i	−0.623109	+	0.226793i
$322$			34.8940i			0.108367i
$323$	−293.230	−	142.425i	−0.907832	−	0.440943i
$324$	−2.77909			−0.00857744
$325$	−85.3924	−	234.614i	−0.262746	−	0.721889i
$326$	63.0919	+	11.1248i	0.193533	+	0.0341251i
$327$	306.779	−	257.418i	0.938162	−	0.787211i
$328$	−197.820	−	165.990i	−0.603109	−	0.506068i
$329$	30.6975	+	174.094i	0.0933055	+	0.529162i
$330$	−98.6751	−	170.910i	−0.299015	−	0.517910i
$331$	383.016	+	221.134i	1.15715	+	0.668079i	0.950619	−	0.310361i	$-0.100450\pi$
$331$	383.016	+	221.134i	1.15715	+	0.668079i	0.206529	+	0.978441i	$0.433783\pi$
$332$	−27.8367	−	10.1317i	−0.0838454	−	0.0305172i
$333$	106.345	−	292.180i	0.319354	−	0.877419i
$334$	45.7005	−	79.1556i	0.136828	−	0.236993i
$335$	29.1421	−	16.8252i	0.0869915	−	0.0502245i
$336$	−65.4830	+	11.5464i	−0.194890	+	0.0343644i
$337$	−284.270	+	338.780i	−0.843531	+	1.00528i	0.156314	+	0.987707i	$0.450039\pi$
$337$	−284.270	+	338.780i	−0.843531	+	1.00528i	−0.999846	+	0.0175740i	$0.994406\pi$
$338$	50.7862	+	60.5247i	0.150255	+	0.179067i
$339$	−6.19733	+	35.1468i	−0.0182812	+	0.103678i
$340$	−18.7177	+	6.81269i	−0.0550521	+	0.0200373i
$341$			115.292i			0.338101i
$342$	−134.972	+	130.768i	−0.394654	+	0.382362i
$343$	−222.659			−0.649150
$344$	70.2614	+	193.042i	0.204248	+	0.561168i
$345$	−40.7743	−	7.18960i	−0.118186	−	0.0208394i
$346$	−75.0102	+	62.9410i	−0.216792	+	0.181910i
$347$	2.68547	+	2.25337i	0.00773910	+	0.00649387i	0.646649	−	0.762788i	$-0.276170\pi$
$347$	2.68547	+	2.25337i	0.00773910	+	0.00649387i	−0.638910	+	0.769282i	$0.720614\pi$
$348$	1.15533	+	6.55220i	0.00331991	+	0.0188282i
$349$	−44.1774	−	76.5174i	−0.126583	−	0.219248i	0.795768	−	0.605602i	$-0.207068\pi$
$349$	−44.1774	−	76.5174i	−0.126583	−	0.219248i	−0.922350	+	0.386354i	$0.873734\pi$
$350$	−68.1268	−	39.3330i	−0.194648	−	0.112380i
$351$	377.032	+	137.228i	1.07417	+	0.390964i
$352$	−43.5061	+	119.532i	−0.123597	+	0.339580i
$353$	62.9423	−	109.019i	0.178307	−	0.308837i	−0.762994	−	0.646406i	$-0.776271\pi$
$353$	62.9423	−	109.019i	0.178307	−	0.308837i	0.941301	+	0.337569i	$0.109605\pi$
$354$	29.3580	−	16.9499i	0.0829323	−	0.0478810i
$355$	−105.785	+	18.6528i	−0.297987	+	0.0525431i
$356$	2.16597	−	2.58130i	0.00608418	−	0.00725084i
$357$	51.7714	+	61.6987i	0.145018	+	0.172826i
$358$	76.2719	−	432.559i	0.213050	−	1.20827i
$359$	56.5579	−	20.5854i	0.157543	−	0.0573409i	−0.262045	−	0.965056i	$-0.584397\pi$
$359$	56.5579	−	20.5854i	0.157543	−	0.0573409i	0.419588	+	0.907715i	$0.362175\pi$
$360$			121.987i			0.338853i
$361$	−11.4190	+	360.819i	−0.0316314	+	0.999500i
$362$	511.927			1.41416
$363$	164.759	+	452.673i	0.453883	+	1.24703i
$364$	−14.3562	−	2.53139i	−0.0394402	−	0.00695437i
$365$	−108.743	+	91.2465i	−0.297927	+	0.249990i
$366$	173.748	+	145.792i	0.474723	+	0.398340i
$367$	26.6342	+	151.050i	0.0725729	+	0.411581i	0.999353	+	0.0359761i	$0.0114540\pi$
$367$	26.6342	+	151.050i	0.0725729	+	0.411581i	−0.926780	+	0.375605i	$0.877435\pi$
$368$	−54.0305	−	93.5836i	−0.146822	−	0.254303i
$369$	139.760	+	80.6904i	0.378753	+	0.218673i
$370$	295.730	+	107.637i	0.799269	+	0.290910i
$371$	−23.1607	+	63.6336i	−0.0624279	+	0.171519i
$372$	−2.42405	+	4.19857i	−0.00651625	+	0.0112865i
$373$	−230.727	+	133.210i	−0.618571	+	0.357132i	−0.776313	−	0.630348i	$-0.782912\pi$
$373$	−230.727	+	133.210i	−0.618571	+	0.357132i	0.157741	+	0.987480i	$0.449579\pi$
$374$	−614.425	+	108.340i	−1.64285	+	0.289678i
$375$	147.210	−	175.438i	0.392561	−	0.467836i
$376$	−393.205	−	468.604i	−1.04576	−	1.24629i
$377$	20.7653	−	117.766i	0.0550803	−	0.312376i
$378$	118.795	−	43.2378i	0.314272	−	0.114386i
$379$		−	670.093i		−	1.76806i	−0.467435	−	0.884028i	$-0.654822\pi$
$379$		−	670.093i		−	1.76806i	0.467435	−	0.884028i	$-0.345178\pi$
$380$	15.3489	+	15.8423i	0.0403918	+	0.0416903i
$381$	22.0167			0.0577867
$382$	52.7442	+	144.914i	0.138074	+	0.379355i
$383$	679.414	+	119.799i	1.77393	+	0.312791i	0.962423	−	0.271556i	$-0.0875382\pi$
$383$	679.414	+	119.799i	1.77393	+	0.312791i	0.811504	+	0.584347i	$0.198649\pi$
$384$	155.569	−	130.538i	0.405128	−	0.339943i
$385$	−99.2832	−	83.3085i	−0.257878	−	0.216386i
$386$	−9.80699	−	55.6182i	−0.0254067	−	0.144089i
$387$	−64.1907	−	111.182i	−0.165867	−	0.287291i
$388$	42.8800	+	24.7568i	0.110515	+	0.0638061i
$389$	−212.211	−	77.2383i	−0.545528	−	0.198556i	0.0545302	−	0.998512i	$-0.482634\pi$
$389$	−212.211	−	77.2383i	−0.545528	−	0.198556i	−0.600059	+	0.799956i	$0.704856\pi$
$390$	−51.0142	+	140.160i	−0.130806	+	0.359385i
$391$	−65.4462	+	113.356i	−0.167381	+	0.289913i
$392$	312.497	−	180.420i	0.797187	−	0.460256i
$393$	21.4783	−	3.78720i	0.0546521	−	0.00963663i
$394$	−219.097	+	261.110i	−0.556084	+	0.662715i
$395$	−192.937	−	229.934i	−0.488448	−	0.582110i
$396$	7.24291	−	41.0766i	0.0182902	−	0.103729i
$397$	−568.125	+	206.781i	−1.43105	+	0.520858i	−0.937231	−	0.348709i	$-0.886620\pi$
$397$	−568.125	+	206.781i	−1.43105	+	0.520858i	−0.493815	+	0.869567i	$0.664398\pi$
$398$		−	208.497i		−	0.523862i
$399$	38.9682	−	80.2293i	0.0976647	−	0.201076i
$400$	243.616			0.609039
$401$	−110.875	−	304.626i	−0.276495	−	0.759665i	−0.997753	−	0.0669980i	$-0.978658\pi$
$401$	−110.875	−	304.626i	−0.276495	−	0.759665i	0.721258	−	0.692667i	$-0.243564\pi$
$402$	43.6478	+	7.69629i	0.108577	+	0.0191450i
$403$	66.7508	−	56.0105i	0.165635	−	0.138984i
$404$	41.8421	+	35.1097i	0.103570	+	0.0869053i
$405$	3.24271	+	18.3903i	0.00800668	+	0.0454082i
$406$	−18.8390	−	32.6300i	−0.0464014	−	0.0803696i
$407$	−989.972	−	571.561i	−2.43236	−	1.40433i
$408$	−261.895	−	95.3220i	−0.641900	−	0.233632i
$409$	−89.4166	+	245.670i	−0.218623	+	0.600660i	−0.999718	−	0.0237513i	$-0.992439\pi$
$409$	−89.4166	+	245.670i	−0.218623	+	0.600660i	0.781095	+	0.624412i	$0.214661\pi$
$410$	−81.6706	+	141.458i	−0.199197	+	0.345019i
$411$	−272.168	+	157.137i	−0.662210	+	0.382327i
$412$	5.40889	−	0.953733i	0.0131284	−	0.00231489i
$413$	14.3103	−	17.0543i	0.0346496	−	0.0412937i
$414$	48.5037	+	57.8044i	0.117159	+	0.139624i
$415$	−34.5650	+	196.028i	−0.0832891	+	0.472356i
$416$	90.3412	−	32.8815i	0.217166	−	0.0790421i
$417$			373.184i			0.894925i
$418$	387.289	+	572.159i	0.926528	+	1.36880i
$419$	−242.808			−0.579495			−0.289747	−	0.957103i	$-0.593571\pi$
$419$	−242.808			−0.579495			−0.289747	+	0.957103i	$0.593571\pi$
$420$	−1.86399	−	5.12127i	−0.00443807	−	0.0121935i
$421$	547.350	+	96.5126i	1.30012	+	0.229246i	0.780502	−	0.625154i	$-0.214964\pi$
$421$	547.350	+	96.5126i	1.30012	+	0.229246i	0.519617	+	0.854399i	$0.326075\pi$
$422$	223.216	−	187.301i	0.528948	−	0.443840i
$423$	292.848	+	245.729i	0.692312	+	0.580919i
$424$	−40.6902	−	230.766i	−0.0959676	−	0.544259i
$425$	−147.544	−	255.553i	−0.347162	−	0.601301i
$426$	−122.525	−	70.7399i	−0.287618	−	0.166056i
$427$	139.971	+	50.9452i	0.327800	+	0.119309i
$428$	15.5734	−	42.7876i	0.0363865	−	0.0999711i
$429$	270.890	−	469.195i	0.631445	−	1.09369i
$430$	112.532	−	64.9704i	0.261703	−	0.151094i
$431$	6.30702	−	1.11210i	0.0146335	−	0.00258028i	−0.166327	−	0.986071i	$-0.553191\pi$
$431$	6.30702	−	1.11210i	0.0146335	−	0.00258028i	0.180960	+	0.983490i	$0.442080\pi$
$432$	−251.650	+	299.905i	−0.582524	+	0.694225i
$433$	−36.8103	−	43.8687i	−0.0850121	−	0.101314i	0.721862	−	0.692037i	$-0.243287\pi$
$433$	−36.8103	−	43.8687i	−0.0850121	−	0.101314i	−0.806874	+	0.590724i	$0.798842\pi$
$434$	4.76752	−	27.0379i	0.0109851	−	0.0622994i
$435$	42.0104	−	15.2905i	0.0965755	−	0.0351506i
$436$			85.6684i			0.196487i
$437$	144.181	+	14.9157i	0.329933	+	0.0341321i
$438$	−186.969			−0.426870
$439$	−179.069	−	491.987i	−0.407901	−	1.12070i	−0.958292	−	0.285792i	$-0.907744\pi$
$439$	−179.069	−	491.987i	−0.407901	−	1.12070i	0.550391	−	0.834907i	$-0.314479\pi$
$440$	441.664	+	77.8774i	1.00378	+	0.176994i
$441$	−172.745	+	144.951i	−0.391713	+	0.328686i
$442$	361.221	+	303.100i	0.817241	+	0.685747i
$443$	75.4553	+	427.928i	0.170328	+	0.965978i	0.943399	+	0.331659i	$0.107608\pi$
$443$	75.4553	+	427.928i	0.170328	+	0.965978i	−0.773071	+	0.634319i	$0.781281\pi$
$444$	−24.0344	−	41.6287i	−0.0541315	−	0.0937584i
$445$	−19.6087	−	11.3211i	−0.0440646	−	0.0254407i
$446$	276.878	+	100.775i	0.620803	+	0.225954i
$447$	−93.4166	+	256.660i	−0.208986	+	0.574184i
$448$	83.5864	−	144.776i	0.186577	−	0.323161i
$449$	−272.280	+	157.201i	−0.606415	+	0.350114i	−0.771561	−	0.636155i	$-0.780524\pi$
$449$	−272.280	+	157.201i	−0.606415	+	0.350114i	0.165146	+	0.986269i	$0.447190\pi$
$450$	−167.531	+	29.5402i	−0.372291	+	0.0656449i
$451$	381.370	−	454.499i	0.845610	−	1.00776i
$452$	−4.90739	−	5.84840i	−0.0108571	−	0.0129389i
$453$	34.2829	−	194.428i	0.0756797	−	0.429201i
$454$	−119.345	+	43.4379i	−0.262873	+	0.0956781i
$455$			97.9543i			0.215284i
$456$	22.0327	+	307.849i	0.0483173	+	0.675106i
$457$	525.189			1.14921			0.574606	−	0.818431i	$-0.305155\pi$
$457$	525.189			1.14921			0.574606	+	0.818431i	$0.305155\pi$
$458$	44.8566	+	123.242i	0.0979401	+	0.269088i
$459$	467.011	+	82.3466i	1.01745	+	0.179404i
$460$	6.78481	−	5.69313i	0.0147496	−	0.0123764i
$461$	−466.982	−	391.845i	−1.01298	−	0.849988i	−0.0242478	−	0.999706i	$-0.507719\pi$
$461$	−466.982	−	391.845i	−1.01298	−	0.849988i	−0.988729	+	0.149718i	$0.952164\pi$
$462$	−29.6423	−	168.110i	−0.0641609	−	0.363875i
$463$	381.720	+	661.158i	0.824449	+	1.42799i	0.902340	+	0.431025i	$0.141848\pi$
$463$	381.720	+	661.158i	0.824449	+	1.42799i	−0.0778909	+	0.996962i	$0.524819\pi$
$464$	101.050	+	58.3411i	0.217780	+	0.125735i
$465$	30.6120	+	11.1418i	0.0658322	+	0.0239610i
$466$	105.684	−	290.364i	0.226790	−	0.623099i
$467$	224.311	−	388.519i	0.480324	−	0.831946i	−0.519421	−	0.854519i	$-0.673852\pi$
$467$	224.311	−	388.519i	0.480324	−	0.831946i	0.999745	+	0.0225724i	$0.00718563\pi$
$468$	−27.3008	+	15.7621i	−0.0583350	+	0.0336797i
$469$	28.6647	−	5.05436i	0.0611187	−	0.0107769i
$470$	−248.714	+	296.406i	−0.529178	+	0.630650i
$471$	−209.021	−	249.101i	−0.443780	−	0.528877i
$472$	−13.3773	+	75.8667i	−0.0283418	+	0.160734i
$473$	−443.522	+	161.429i	−0.937678	+	0.341287i
$474$		−	395.338i		−	0.834047i
$475$	−191.644	+	264.684i	−0.403461	+	0.557230i
$476$	−17.2294			−0.0361963
$477$	50.0851	+	137.608i	0.105000	+	0.288486i
$478$	−569.842	−	100.478i	−1.19214	−	0.210206i
$479$	−533.676	+	447.807i	−1.11415	+	0.934879i	−0.998294	−	0.0583874i	$-0.981404\pi$
$479$	−533.676	+	447.807i	−1.11415	+	0.934879i	−0.115852	+	0.993267i	$0.536960\pi$
$480$	27.5333	+	23.1031i	0.0573609	+	0.0481315i
$481$	150.025	+	850.835i	0.311903	+	1.76889i
$482$	−227.235	−	393.583i	−0.471442	−	0.816562i
$483$	−31.0149	−	17.9064i	−0.0642130	−	0.0370734i
$484$	−96.8353	−	35.2451i	−0.200073	−	0.0728206i
$485$	113.792	−	312.640i	0.234622	−	0.644619i
$486$	223.177	−	386.553i	0.459211	−	0.795377i
$487$	16.8247	−	9.71373i	0.0345476	−	0.0199461i	−0.482627	−	0.875826i	$-0.660317\pi$
$487$	16.8247	−	9.71373i	0.0345476	−	0.0199461i	0.517174	+	0.855880i	$0.326984\pi$
$488$	−507.600	+	89.5036i	−1.04016	+	0.183409i
$489$	−42.2647	+	50.3691i	−0.0864308	+	0.103004i
$490$	−146.711	−	174.844i	−0.299411	−	0.356824i
$491$	115.016	−	652.286i	0.234248	−	1.32848i	−0.609944	−	0.792444i	$-0.708808\pi$
$491$	115.016	−	652.286i	0.234248	−	1.32848i	0.844192	−	0.536041i	$-0.180081\pi$
$492$	23.4442	−	8.53299i	0.0476508	−	0.0173435i
$493$		−	141.335i		−	0.286684i
$494$	143.113	−	502.190i	0.289702	−	1.01658i
$495$	−280.271			−0.566203
$496$	29.0798	+	79.8961i	0.0586287	+	0.161081i
$497$	−91.5019	−	16.1343i	−0.184109	−	0.0324633i
$498$	−200.836	+	168.521i	−0.403284	+	0.338396i
$499$	−102.346	−	85.8785i	−0.205102	−	0.172101i	0.534451	−	0.845200i	$-0.320519\pi$
$499$	−102.346	−	85.8785i	−0.205102	−	0.172101i	−0.739553	+	0.673098i	$0.764963\pi$
$500$	8.50727	+	48.2471i	0.0170145	+	0.0964942i
$501$	46.9040	+	81.2400i	0.0936207	+	0.162156i
$502$	−523.636	−	302.321i	−1.04310	−	0.602234i
$503$	305.161	+	111.070i	0.606682	+	0.220814i	0.627051	−	0.778978i	$-0.284262\pi$
$503$	305.161	+	111.070i	0.606682	+	0.220814i	−0.0203686	+	0.999793i	$0.506484\pi$
$504$	−36.0886	+	99.1526i	−0.0716044	+	0.196731i
$505$	183.512	−	317.852i	0.363390	−	0.629410i
$506$	240.251	−	138.709i	0.474804	−	0.274128i
$507$	−79.8580	+	14.0811i	−0.157511	+	0.0277734i
$508$	−3.02740	+	3.60791i	−0.00595944	+	0.00710219i
$509$	314.036	+	374.253i	0.616966	+	0.735271i	0.980545	−	0.196292i	$-0.0628900\pi$
$509$	314.036	+	374.253i	0.616966	+	0.735271i	−0.363580	+	0.931563i	$0.618446\pi$
$510$	−30.6120	+	173.609i	−0.0600236	+	0.340411i
$511$	−115.382	+	41.9957i	−0.225797	+	0.0821834i
$512$			567.464i			1.10833i
$513$	−127.877	−	509.339i	−0.249274	−	0.992863i
$514$	217.972			0.424070
$515$	−12.6224	−	34.6798i	−0.0245096	−	0.0673395i
$516$	−19.5457	−	3.44643i	−0.0378792	−	0.00667913i
$517$	1076.64	−	903.407i	2.08247	−	1.74740i
$518$	208.530	+	174.977i	0.402567	+	0.337794i
$519$	−17.4512	−	98.9705i	−0.0336246	−	0.190695i
$520$	−169.478	−	293.544i	−0.325919	−	0.564508i
$521$	539.718	+	311.606i	1.03593	+	0.598093i	0.918677	−	0.395010i	$-0.129259\pi$
$521$	539.718	+	311.606i	1.03593	+	0.598093i	0.117250	+	0.993102i	$0.462592\pi$
$522$	−76.5647	−	27.8673i	−0.146676	−	0.0533856i
$523$	−224.813	+	617.668i	−0.429853	+	1.18101i	0.516050	+	0.856559i	$0.327402\pi$
$523$	−224.813	+	617.668i	−0.429853	+	1.18101i	−0.945902	+	0.324452i	$0.894820\pi$
$524$	−2.33274	+	4.04043i	−0.00445180	+	0.00771074i
$525$	69.9208	−	40.3688i	0.133182	−	0.0768929i
$526$	−42.3607	+	7.46933i	−0.0805336	+	0.0142003i
$527$	66.1992	−	78.8931i	0.125615	−	0.149702i
$528$	339.803	+	404.962i	0.643567	+	0.766973i
$529$	−81.7534	+	463.646i	−0.154543	+	0.876458i
$530$	−139.279	+	50.6935i	−0.262791	+	0.0956481i
$531$		−	48.1433i		−	0.0906654i
$532$	7.78899	+	17.4177i	0.0146410	+	0.0327400i
$533$	−448.416			−0.841305
$534$	−10.1998	−	28.0237i	−0.0191007	−	0.0524788i
$535$	−301.313	−	53.1297i	−0.563203	−	0.0993078i
$536$	−77.1558	+	64.7414i	−0.143947	+	0.120786i
$537$	345.332	+	289.768i	0.643076	+	0.539605i
$538$	−91.3349	−	517.986i	−0.169767	−	0.962799i
$539$	414.524	+	717.976i	0.769061	+	1.33205i
$540$	−27.7892	−	16.0441i	−0.0514614	−	0.0297113i
$541$	−84.0065	−	30.5759i	−0.155280	−	0.0565173i	0.263211	−	0.964738i	$-0.415219\pi$
$541$	−84.0065	−	30.5759i	−0.155280	−	0.0565173i	−0.418491	+	0.908221i	$0.637441\pi$
$542$	−2.19105	+	6.01985i	−0.00404252	+	0.0111067i
$543$	−262.704	+	455.016i	−0.483800	+	0.837967i
$544$	98.4042	−	56.8137i	0.180890	−	0.104437i
$545$	566.901	−	99.9599i	1.04018	−	0.183413i
$546$	−82.9299	+	98.8321i	−0.151886	+	0.181011i
$547$	−450.474	−	536.854i	−0.823535	−	0.981451i	0.176461	−	0.984308i	$-0.443535\pi$
$547$	−450.474	−	536.854i	−0.823535	−	0.981451i	−0.999996	+	0.00285665i	$0.999091\pi$
$548$	11.6742	−	66.2076i	0.0213033	−	0.120817i
$549$	302.686	−	110.169i	0.551341	−	0.200672i
$550$			625.418i			1.13712i
$551$	−142.879	+	63.8939i	−0.259309	+	0.115960i
$552$	123.925			0.224502
$553$	−88.7983	−	243.971i	−0.160576	−	0.441178i
$554$	253.139	+	44.6352i	0.456929	+	0.0805689i
$555$	−247.429	+	207.618i	−0.445819	+	0.374086i
$556$	−61.1541	−	51.3144i	−0.109989	−	0.0922921i
$557$	−36.5801	−	207.456i	−0.0656733	−	0.372452i	−0.999877	−	0.0157108i	$-0.994999\pi$
$557$	−36.5801	−	207.456i	−0.0656733	−	0.372452i	0.934203	−	0.356741i	$-0.116112\pi$
$558$	−29.6857	−	51.4172i	−0.0532003	−	0.0921455i
$559$	308.931	+	178.361i	0.552649	+	0.319072i
$560$	−89.8146	−	32.6898i	−0.160383	−	0.0583747i
$561$	219.006	−	601.715i	0.390386	−	1.07258i
$562$	−466.897	+	808.690i	−0.830778	+	1.43895i
$563$	−461.855	+	266.652i	−0.820347	+	0.473627i	−0.850536	−	0.525917i	$-0.823722\pi$
$563$	−461.855	+	266.652i	−0.820347	+	0.473627i	0.0301894	+	0.999544i	$0.490389\pi$
$564$	58.2019	−	10.2626i	0.103195	−	0.0181960i
$565$	−32.9751	+	39.2981i	−0.0583629	+	0.0695542i
$566$	455.950	+	543.380i	0.805565	+	0.960035i
$567$	−2.80487	+	15.9072i	−0.00494686	+	0.0280550i
$568$	302.123	−	109.964i	0.531907	−	0.193598i
$569$		−	610.046i		−	1.07214i	−0.844174	−	0.536068i	$-0.819909\pi$
$569$		−	610.046i		−	1.07214i	0.844174	−	0.536068i	$-0.180091\pi$
$570$	189.345	−	47.5379i	0.332184	−	0.0833999i
$571$	−678.976			−1.18910			−0.594550	−	0.804059i	$-0.702670\pi$
$571$	−678.976			−1.18910			−0.594550	+	0.804059i	$0.702670\pi$
$572$	39.6391	+	108.907i	0.0692991	+	0.190398i
$573$	−155.870	−	27.4841i	−0.272025	−	0.0479653i
$574$	−108.232	+	90.8172i	−0.188557	+	0.158218i
$575$	100.513	+	84.3403i	0.174805	+	0.146679i
$576$	−62.7757	−	356.019i	−0.108986	−	0.618088i
$577$	−363.669	−	629.894i	−0.630276	−	1.09167i	−0.987495	−	0.157649i	$-0.949608\pi$
$577$	−363.669	−	629.894i	−0.630276	−	1.09167i	0.357219	−	0.934021i	$-0.383725\pi$
$578$	8.80838	+	5.08552i	0.0152394	+	0.00879847i
$579$	54.4678	+	19.8247i	0.0940722	+	0.0342395i
$580$	−3.27093	+	8.98681i	−0.00563954	+	0.0154945i
$581$	−86.0877	+	149.108i	−0.148172	+	0.256641i
$582$	379.498	−	219.104i	0.652059	−	0.376467i
$583$	530.195	−	93.4876i	0.909425	−	0.160356i
$584$	273.112	−	325.482i	0.467657	−	0.557332i
$585$	136.159	+	162.268i	0.232751	+	0.277381i
$586$	24.1246	−	136.817i	0.0411682	−	0.233477i
$587$	920.712	−	335.112i	1.56850	−	0.570889i	0.595840	−	0.803103i	$-0.296819\pi$
$587$	920.712	−	335.112i	1.56850	−	0.570889i	0.972665	+	0.232214i	$0.0745971\pi$
$588$			34.8618i			0.0592888i
$589$	−109.682	−	31.2568i	−0.186217	−	0.0530676i
$590$	48.7282			0.0825901
$591$	−119.649	−	328.733i	−0.202452	−	0.556232i
$592$	−830.201	−	146.387i	−1.40237	−	0.247275i
$593$	−267.014	+	224.051i	−0.450277	+	0.377827i	−0.839538	−	0.543300i	$-0.817175\pi$
$593$	−267.014	+	224.051i	−0.450277	+	0.377827i	0.389262	+	0.921127i	$0.372730\pi$
$594$	−769.927	−	646.045i	−1.29617	−	1.08762i
$595$	20.1037	+	114.014i	0.0337878	+	0.191620i
$596$	−29.2140	−	50.6002i	−0.0490169	−	0.0848997i
$597$	185.319	+	106.994i	0.310417	+	0.179219i
$598$	−197.025	−	71.7113i	−0.329473	−	0.119919i
$599$	−144.781	+	397.783i	−0.241705	+	0.664078i	0.758222	+	0.651996i	$0.226068\pi$
$599$	−144.781	+	397.783i	−0.241705	+	0.664078i	−0.999927	+	0.0120820i	$0.996154\pi$
$600$	−139.690	+	241.950i	−0.232817	+	0.403250i
$601$	437.051	−	252.331i	0.727206	−	0.419853i	−0.0901931	−	0.995924i	$-0.528748\pi$
$601$	437.051	−	252.331i	0.727206	−	0.419853i	0.817399	+	0.576072i	$0.195415\pi$
$602$	110.688	−	19.5173i	0.183868	−	0.0324208i
$603$	40.4593	−	48.2176i	0.0670968	−	0.0799628i
$604$	27.1471	+	32.3527i	0.0449456	+	0.0535641i
$605$	−120.241	+	681.921i	−0.198745	+	1.12714i
$606$	454.256	−	165.336i	0.749598	−	0.272831i
$607$			73.0072i			0.120275i	0.998190	+	0.0601377i	$0.0191540\pi$
$607$			73.0072i			0.120275i	−0.998190	+	0.0601377i	$0.980846\pi$
$608$	−101.920	−	73.7952i	−0.167632	−	0.121374i
$609$	38.6701			0.0634977
$610$	111.507	+	306.363i	0.182799	+	0.502235i
$611$	−1046.09	−	184.454i	−1.71209	−	0.301888i
$612$	−28.5418	+	23.9494i	−0.0466369	+	0.0391330i
$613$	−786.854	−	660.249i	−1.28361	−	1.07708i	−0.992735	−	0.120317i	$-0.961609\pi$
$613$	−786.854	−	660.249i	−1.28361	−	1.07708i	−0.290876	−	0.956761i	$-0.593947\pi$
$614$	−30.3880	−	172.339i	−0.0494919	−	0.280682i
$615$	−83.8212	−	145.183i	−0.136295	−	0.236069i
$616$	335.951	+	193.962i	0.545376	+	0.314873i
$617$	−398.587	−	145.074i	−0.646007	−	0.235127i	−0.00182377	−	0.999998i	$-0.500581\pi$
$617$	−398.587	−	145.074i	−0.646007	−	0.235127i	−0.644184	+	0.764871i	$0.722803\pi$
$618$	16.6251	−	45.6770i	0.0269014	−	0.0739110i
$619$	−164.352	+	284.665i	−0.265512	+	0.459879i	−0.967698	−	0.252114i	$-0.918874\pi$
$619$	−164.352	+	284.665i	−0.265512	+	0.459879i	0.702186	+	0.711994i	$0.252208\pi$
$620$	−6.03511	+	3.48437i	−0.00973405	+	0.00561996i
$621$	−207.656	+	36.6153i	−0.334389	+	0.0589619i
$622$	242.454	−	288.945i	0.389797	−	0.464542i
$623$	−12.5890	−	15.0030i	−0.0202071	−	0.0240818i
$624$	69.3796	−	393.471i	0.111185	−	0.630563i
$625$	−94.7002	+	34.4681i	−0.151520	+	0.0551489i
$626$		−	57.9284i		−	0.0925375i
$627$	−707.296	+	50.6211i	−1.12806	+	0.0807354i
$628$	69.5618			0.110767
$629$	349.244	+	959.539i	0.555236	+	1.52550i
$630$	65.7280	+	11.5896i	0.104330	+	0.0183962i
$631$	90.2242	−	75.7071i	0.142986	−	0.119980i	−0.568489	−	0.822691i	$-0.692472\pi$
$631$	90.2242	−	75.7071i	0.142986	−	0.119980i	0.711475	+	0.702711i	$0.248027\pi$
$632$	688.218	+	577.484i	1.08895	+	0.913740i
$633$	51.9314	+	294.518i	0.0820401	+	0.465273i
$634$	539.483	+	934.411i	0.850919	+	1.47383i
$635$	27.4074	+	15.8236i	0.0431612	+	0.0249191i
$636$	21.2735	+	7.74294i	0.0334490	+	0.0121744i
$637$	214.305	−	588.799i	0.336429	−	0.924331i
$638$	−149.775	+	259.418i	−0.234757	+	0.406612i
$639$	−174.006	+	100.463i	−0.272310	+	0.157219i
$640$	287.478	−	50.6902i	0.449185	−	0.0792034i
$641$	47.8317	−	57.0036i	0.0746204	−	0.0889292i	−0.727443	−	0.686168i	$-0.759291\pi$
$641$	47.8317	−	57.0036i	0.0746204	−	0.0889292i	0.802063	+	0.597239i	$0.203736\pi$
$642$	−259.033	−	308.703i	−0.403478	−	0.480847i
$643$	−85.6026	+	485.476i	−0.133130	+	0.755018i	0.843014	+	0.537892i	$0.180779\pi$
$643$	−85.6026	+	485.476i	−0.133130	+	0.755018i	−0.976144	+	0.217126i	$0.930332\pi$
$644$	7.19904	−	2.62024i	0.0111786	−	0.00406869i
$645$			133.363i			0.206764i
$646$	63.5085	−	613.896i	0.0983103	−	0.950304i
$647$	989.083			1.52872			0.764361	−	0.644789i	$-0.223055\pi$
$647$	989.083			1.52872			0.764361	+	0.644789i	$0.223055\pi$
$648$	−19.1167	−	52.5227i	−0.0295011	−	0.0810536i
$649$	−174.307	−	30.7350i	−0.268578	−	0.0473575i
$650$	362.098	−	303.836i	0.557074	−	0.467440i
$651$	21.5856	+	18.1125i	0.0331576	+	0.0278225i
$652$	−2.44247	−	13.8519i	−0.00374612	−	0.0212453i
$653$	79.5099	+	137.715i	0.121761	+	0.210896i	0.920462	−	0.390832i	$-0.127813\pi$
$653$	79.5099	+	137.715i	0.121761	+	0.210896i	−0.798701	+	0.601728i	$0.794479\pi$
$654$	656.609	+	379.093i	1.00399	+	0.579653i
$655$	29.4590	+	10.7222i	0.0449755	+	0.0163697i
$656$	149.648	−	411.154i	0.228122	−	0.626759i
$657$	−132.764	+	229.953i	−0.202076	+	0.350005i
$658$	−289.846	+	167.343i	−0.440496	+	0.254320i
$659$	733.027	−	129.252i	1.11233	−	0.196134i	0.412860	−	0.910794i	$-0.364530\pi$
$659$	733.027	−	129.252i	1.11233	−	0.196134i	0.699472	+	0.714660i	$0.253419\pi$
$660$	−27.8511	+	33.1917i	−0.0421986	+	0.0502904i
$661$	492.719	+	587.200i	0.745414	+	0.888350i	0.996833	−	0.0795282i	$-0.0253414\pi$
$661$	492.719	+	587.200i	0.745414	+	0.888350i	−0.251418	+	0.967879i	$0.580897\pi$
$662$	−145.399	+	824.597i	−0.219636	+	1.24562i
$663$	−454.771	+	165.523i	−0.685929	+	0.249658i
$664$		−	595.786i		−	0.897268i
$665$	106.171	−	71.8660i	0.159656	−	0.108069i
$666$	588.667			0.883884
$667$	21.4941	+	59.0545i	0.0322250	+	0.0885375i
$668$	−19.7624	−	3.48465i	−0.0295845	−	0.00521654i
$669$	−231.657	+	194.383i	−0.346273	+	0.290558i
$670$	48.8033	+	40.9508i	0.0728407	+	0.0611206i
$671$	−205.639	−	1166.23i	−0.306466	−	1.73805i
$672$	15.5446	+	26.9240i	0.0231318	+	0.0400654i
$673$	695.119	+	401.327i	1.03287	+	0.596326i	0.917804	−	0.397033i	$-0.129960\pi$
$673$	695.119	+	401.327i	1.03287	+	0.596326i	0.115062	+	0.993358i	$0.463293\pi$
$674$	−786.781	−	286.365i	−1.16733	−	0.424874i
$675$	162.585	−	446.699i	0.240867	−	0.661776i
$676$	8.67333	−	15.0227i	0.0128304	−	0.0222229i
$677$	−432.884	+	249.926i	−0.639415	+	0.369166i	−0.784389	−	0.620269i	$-0.787023\pi$
$677$	−432.884	+	249.926i	−0.639415	+	0.369166i	0.144974	+	0.989435i	$0.453690\pi$
$678$	−66.5411	+	11.7330i	−0.0981432	+	0.0173053i
$679$	184.983	−	220.454i	0.272434	−	0.324674i
$680$	−257.509	−	306.888i	−0.378690	−	0.451305i
$681$	22.6347	−	128.368i	0.0332375	−	0.188499i
$682$	−205.112	+	74.6546i	−0.300751	+	0.109464i
$683$		−	52.2603i		−	0.0765159i	−0.999268	−	0.0382579i	$-0.987819\pi$
$683$		−	52.2603i		−	0.0765159i	0.999268	−	0.0382579i	$-0.0121808\pi$
$684$	37.1140	+	18.0267i	0.0542603	+	0.0263548i
$685$	−451.742			−0.659478
$686$	−144.177	−	396.123i	−0.210170	−	0.577438i
$687$	−132.560	−	23.3740i	−0.192956	−	0.0340233i
$688$	−266.638	+	223.736i	−0.387556	+	0.325198i
$689$	−311.702	−	261.549i	−0.452398	−	0.379607i
$690$	−13.6116	−	77.1953i	−0.0197270	−	0.111877i
$691$	130.083	+	225.311i	0.188253	+	0.326065i	0.944668	−	0.328028i	$-0.106384\pi$
$691$	130.083	+	225.311i	0.188253	+	0.326065i	−0.756415	+	0.654093i	$0.773051\pi$
$692$	18.6180	+	10.7491i	0.0269047	+	0.0155334i
$693$	−227.808	−	82.9152i	−0.328727	−	0.119647i
$694$	−2.26998	+	6.23672i	−0.00327086	+	0.00898662i
$695$	−268.211	+	464.555i	−0.385915	+	0.668425i
$696$	−115.884	+	66.9059i	−0.166501	+	0.0961292i
$697$	−521.933	+	92.0309i	−0.748828	+	0.132039i
$698$	107.523	−	128.141i	0.154044	−	0.183583i
$699$	203.851	+	242.940i	0.291633	+	0.347554i
$700$	−2.99913	+	17.0089i	−0.00428447	+	0.0242984i
$701$	−451.101	+	164.187i	−0.643511	+	0.234219i	−0.643101	−	0.765781i	$-0.722353\pi$
$701$	−451.101	+	164.187i	−0.643511	+	0.234219i	−0.000409474		1.00000i	$0.500130\pi$
$702$			759.621i			1.08208i
$703$	812.137	−	786.841i	1.15524	−	1.11926i
$704$	−1329.07			−1.88789
$705$	−135.823	−	373.170i	−0.192656	−	0.529319i
$706$	234.708	+	41.3854i	0.332448	+	0.0586196i
$707$	243.194	−	204.064i	0.343981	−	0.288634i
$708$	−5.70148	−	4.78411i	−0.00805294	−	0.00675722i
$709$	73.9347	+	419.305i	0.104280	+	0.591403i	0.991505	+	0.130066i	$0.0415189\pi$
$709$	73.9347	+	419.305i	0.104280	+	0.591403i	−0.887225	+	0.461337i	$0.847370\pi$
$710$	−101.683	−	176.120i	−0.143216	−	0.248057i
$711$	−486.227	−	280.724i	−0.683864	−	0.394829i
$712$	63.6837	+	23.1790i	0.0894435	+	0.0325548i
$713$	−15.6622	+	43.0317i	−0.0219667	+	0.0603530i
$714$	−76.2424	+	132.056i	−0.106782	+	0.184952i
$715$	674.430	−	389.382i	0.943259	−	0.544591i
$716$	−94.9693	+	16.7456i	−0.132639	+	0.0233878i
$717$	381.732	−	454.930i	0.532402	−	0.634492i
$718$	73.2452	+	87.2903i	0.102013	+	0.121574i
$719$	97.6030	−	553.534i	0.135748	−	0.769866i	−0.838588	−	0.544767i	$-0.816618\pi$
$719$	97.6030	−	553.534i	0.135748	−	0.769866i	0.974336	−	0.225100i	$-0.0722707\pi$
$720$	−194.224	+	70.6917i	−0.269755	+	0.0981829i
$721$		−	31.9224i		−	0.0442752i
$722$	−649.313	+	213.324i	−0.899325	+	0.295463i
$723$	466.438			0.645142
$724$	−38.4412	−	105.616i	−0.0530956	−	0.145879i
$725$	−139.526	−	24.6022i	−0.192450	−	0.0339341i
$726$	−698.646	+	586.233i	−0.962322	+	0.807484i
$727$	203.608	+	170.848i	0.280067	+	0.235004i	0.771990	−	0.635635i	$-0.219262\pi$
$727$	203.608	+	170.848i	0.280067	+	0.235004i	−0.491923	+	0.870638i	$0.663706\pi$
$728$	−50.9117	−	288.735i	−0.0699336	−	0.396613i
$729$	259.140	+	448.844i	0.355473	+	0.615698i
$730$	−232.747	−	134.376i	−0.318831	−	0.184077i
$731$	396.186	+	144.200i	0.541978	+	0.197264i
$732$	17.0316	−	46.7940i	0.0232672	−	0.0639262i
$733$	354.455	−	613.934i	0.483567	−	0.837563i	−0.516255	−	0.856435i	$-0.672674\pi$
$733$	354.455	−	613.934i	0.483567	−	0.837563i	0.999822	+	0.0188721i	$0.00600753\pi$
$734$	−251.481	+	145.193i	−0.342617	+	0.197810i
$735$	230.694	−	40.6775i	0.313869	−	0.0553436i
$736$	−32.4764	+	38.7039i	−0.0441255	+	0.0525868i
$737$	−148.746	−	177.269i	−0.201827	−	0.240528i
$738$	−53.0550	+	300.890i	−0.0718903	+	0.407710i
$739$	584.475	−	212.732i	0.790901	−	0.287864i	0.0851902	−	0.996365i	$-0.472850\pi$
$739$	584.475	−	212.732i	0.790901	−	0.287864i	0.705710	+	0.708500i	$0.250628\pi$
$740$		−	69.0950i		−	0.0933716i
$741$	372.921	+	384.910i	0.503268	+	0.519447i
$742$	−128.205			−0.172783
$743$	−174.096	−	478.325i	−0.234315	−	0.643775i	−1.00000		0.000559205i	$-0.999822\pi$
$743$	−174.096	−	478.325i	−0.234315	−	0.643775i	0.765685	−	0.643216i	$-0.222400\pi$
$744$	−96.0243	−	16.9317i	−0.129065	−	0.0227576i
$745$	−300.753	+	252.362i	−0.403696	+	0.338741i
$746$	−386.390	−	324.220i	−0.517950	−	0.434611i
$747$	64.6542	+	366.672i	0.0865519	+	0.490860i
$748$	68.4896	+	118.627i	0.0915636	+	0.158593i
$749$	−229.194	−	132.325i	−0.305999	−	0.176669i
$750$	407.437	+	148.295i	0.543250	+	0.197727i
$751$	−185.743	+	510.324i	−0.247327	+	0.679525i	0.752455	+	0.658644i	$0.228870\pi$
$751$	−185.743	+	510.324i	−0.247327	+	0.679525i	−0.999782	+	0.0208816i	$0.993353\pi$
$752$	518.233	−	897.606i	0.689140	−	1.19362i
$753$	537.425	−	310.282i	0.713712	−	0.412062i
$754$	222.958	−	39.3135i	0.295700	−	0.0521399i
$755$	182.414	−	217.393i	0.241608	−	0.287937i
$756$	−17.8409	−	21.2620i	−0.0235991	−	0.0281243i
$757$	−106.917	+	606.358i	−0.141238	+	0.801001i	0.829073	+	0.559140i	$0.188869\pi$
$757$	−106.917	+	606.358i	−0.141238	+	0.801001i	−0.970311	+	0.241860i	$0.922242\pi$
$758$	1192.13	−	433.901i	1.57274	−	0.572429i
$759$			284.723i			0.375129i
$760$	−193.827	+	399.058i	−0.255035	+	0.525076i
$761$	841.391			1.10564			0.552819	−	0.833301i	$-0.313552\pi$
$761$	841.391			1.10564			0.552819	+	0.833301i	$0.313552\pi$
$762$	14.2564	+	39.1690i	0.0187091	+	0.0514029i
$763$	490.356	+	86.4630i	0.642669	+	0.113320i
$764$	25.9367	−	21.7635i	0.0339485	−	0.0284862i
$765$	191.786	+	160.927i	0.250700	+	0.210362i
$766$	226.808	+	1286.29i	0.296093	+	1.67923i
$767$	66.8860	+	115.850i	0.0872046	+	0.151043i
$768$	−132.797	−	76.6701i	−0.172912	−	0.0998309i
$769$	−735.497	−	267.699i	−0.956434	−	0.348113i	−0.183799	−	0.982964i	$-0.558839\pi$
$769$	−735.497	−	267.699i	−0.956434	−	0.348113i	−0.772635	+	0.634851i	$0.781062\pi$
$770$	83.9224	−	230.575i	0.108990	−	0.299448i
$771$	−111.856	+	193.740i	−0.145079	+	0.251284i
$772$	−10.7383	+	6.19973i	−0.0139097	+	0.00803074i
$773$	−950.278	+	167.560i	−1.22934	+	0.216765i	−0.750341	−	0.661051i	$-0.770111\pi$
$773$	−950.278	+	167.560i	−1.22934	+	0.216765i	−0.478997	+	0.877816i	$0.659000\pi$
$774$	156.233	−	186.192i	0.201852	−	0.240558i
$775$	−66.3600	−	79.0847i	−0.0856257	−	0.102045i
$776$	−172.923	+	980.695i	−0.222839	+	1.26378i
$777$	−262.535	+	95.5551i	−0.337883	+	0.122980i
$778$		−	427.549i		−	0.549548i
$779$	328.989	+	486.030i	0.422322	+	0.623915i
$780$	32.7474			0.0419838
$781$	252.647	+	694.141i	0.323491	+	0.888785i
$782$	−244.045	−	43.0317i	−0.312078	−	0.0550278i
$783$	174.414	−	146.351i	0.222751	−	0.186911i
$784$	468.352	+	392.994i	0.597388	+	0.501268i
$785$	−81.1662	−	460.317i	−0.103396	−	0.586391i
$786$	20.6453	+	35.7588i	0.0262663	+	0.0454946i
$787$	−1163.29	−	671.627i	−1.47814	−	0.853402i	−0.478441	−	0.878120i	$-0.658798\pi$
$787$	−1163.29	−	671.627i	−1.47814	−	0.853402i	−0.999694	+	0.0247177i	$0.992131\pi$
$788$	70.3222	+	25.5952i	0.0892414	+	0.0324812i
$789$	15.0991	−	41.4845i	0.0191370	−	0.0525786i
$790$	284.134	−	492.134i	0.359663	−	0.622954i
$791$	−38.4285	+	22.1867i	−0.0485822	+	0.0280489i
$792$	826.139	−	145.671i	1.04310	−	0.183927i
$793$	−575.312	+	685.630i	−0.725488	+	0.864603i
$794$	−735.750	−	876.833i	−0.926637	−	1.10432i
$795$	26.4155	−	149.810i	0.0332271	−	0.188440i
$796$	−43.0154	+	15.6563i	−0.0540394	+	0.0196687i
$797$			1393.79i			1.74880i	0.485209	+	0.874398i	$0.338743\pi$
$797$			1393.79i			1.74880i	−0.485209	+	0.874398i	$0.661257\pi$
$798$	167.966	+	17.3763i	0.210483	+	0.0217748i
$799$	−1255.45			−1.57128
$800$	−38.9572	−	107.034i	−0.0486966	−	0.133793i
$801$	−41.7091	−	7.35444i	−0.0520713	−	0.00918157i
$802$	470.153	−	394.505i	0.586225	−	0.491901i
$803$	747.809	+	627.486i	0.931268	+	0.781427i
$804$	−1.68974	−	9.58297i	−0.00210166	−	0.0119191i
$805$	−25.7391	−	44.5814i	−0.0319740	−	0.0553806i
$806$	142.869	+	82.4853i	0.177257	+	0.102339i
$807$	507.271	+	184.632i	0.628589	+	0.228788i
$808$	−375.725	+	1032.30i	−0.465006	+	1.27759i
$809$	650.512	−	1126.72i	0.804095	−	1.39273i	−0.112806	−	0.993617i	$-0.535984\pi$
$809$	650.512	−	1126.72i	0.804095	−	1.39273i	0.916901	−	0.399116i	$-0.130683\pi$
$810$	−30.6177	+	17.6771i	−0.0377996	+	0.0218236i
$811$	−1454.46	+	256.460i	−1.79341	+	0.316227i	−0.968497	−	0.249027i	$-0.919889\pi$
$811$	−1454.46	+	256.460i	−1.79341	+	0.316227i	−0.824917	+	0.565254i	$0.808778\pi$
$812$	−5.31731	+	6.33692i	−0.00654841	+	0.00780409i
$813$	−4.22626	−	5.03666i	−0.00519835	−	0.00619515i
$814$	375.809	−	2131.32i	0.461682	−	2.61833i
$815$	−88.8136	+	32.3255i	−0.108974	+	0.0396632i
$816$		−	472.220i		−	0.578701i
$817$	−33.3303	−	465.703i	−0.0407960	−	0.570016i
$818$	−494.961			−0.605087
$819$	62.6665	+	172.175i	0.0765159	+	0.210226i
$820$	35.3171	+	6.22735i	0.0430696	+	0.00759433i
$821$	−91.1195	+	76.4583i	−0.110986	+	0.0931283i	−0.696592	−	0.717468i	$-0.745301\pi$
$821$	−91.1195	+	76.4583i	−0.110986	+	0.0931283i	0.585606	+	0.810596i	$0.300857\pi$
$822$	−455.791	−	382.454i	−0.554490	−	0.465272i
$823$	−182.307	−	1033.92i	−0.221516	−	1.25628i	−0.869235	−	0.494398i	$-0.835388\pi$
$823$	−182.307	−	1033.92i	−0.221516	−	1.25628i	0.647720	−	0.761879i	$-0.275723\pi$
$824$	55.2313	+	95.6634i	0.0670282	+	0.116096i
$825$	−555.891	−	320.944i	−0.673807	−	0.389023i
$826$	39.6069	+	14.4157i	0.0479502	+	0.0174524i
$827$	125.480	−	344.754i	0.151729	−	0.416873i	−0.840419	−	0.541937i	$-0.817691\pi$
$827$	125.480	−	344.754i	0.151729	−	0.416873i	0.992149	+	0.125064i	$0.0399135\pi$
$828$	8.28351	−	14.3475i	0.0100042	−	0.0173279i
$829$	290.861	−	167.929i	0.350858	−	0.202568i	−0.314205	−	0.949355i	$-0.601738\pi$
$829$	290.861	−	167.929i	0.350858	−	0.202568i	0.665063	+	0.746787i	$0.268405\pi$
$830$	−371.127	+	65.4396i	−0.447141	+	0.0788429i
$831$	−169.575	+	202.092i	−0.204062	+	0.243191i
$832$	645.681	+	769.492i	0.776059	+	0.924871i
$833$	128.598	−	729.315i	0.154379	−	0.875528i
$834$	−663.916	+	241.646i	−0.796062	+	0.289743i
$835$			134.841i			0.161487i
$836$	88.9609	−	122.866i	0.106413	−	0.146969i
$837$	165.906			0.198216
$838$	−157.224	−	431.970i	−0.187619	−	0.515478i
$839$	1038.92	+	183.189i	1.23828	+	0.218342i	0.754178	−	0.656670i	$-0.228035\pi$
$839$	1038.92	+	183.189i	1.23828	+	0.218342i	0.484102	+	0.875012i	$0.339147\pi$
$840$	83.9662	−	70.4560i	0.0999598	−	0.0838762i
$841$	592.261	+	496.966i	0.704234	+	0.590923i
$842$	182.721	+	1036.26i	0.217008	+	1.23071i
$843$	−479.192	−	829.985i	−0.568437	−	0.984561i
$844$	−55.4038	−	31.9874i	−0.0656443	−	0.0378998i
$845$	−109.531	−	39.8660i	−0.129622	−	0.0471787i
$846$	−247.540	+	680.109i	−0.292600	+	0.803912i
$847$	−299.473	+	518.702i	−0.353569	+	0.612399i
$848$	343.838	−	198.515i	0.405469	−	0.234098i
$849$	−716.951	+	126.418i	−0.844465	+	0.148902i
$850$	359.106	−	427.966i	0.422477	−	0.503489i
$851$	−291.851	−	347.815i	−0.342951	−	0.408713i
$852$	−5.39389	+	30.5903i	−0.00633086	+	0.0359041i
$853$	−504.478	+	183.615i	−0.591417	+	0.215258i	−0.620352	−	0.784323i	$-0.713010\pi$
$853$	−504.478	+	183.615i	−0.591417	+	0.215258i	0.0289358	+	0.999581i	$0.490788\pi$
$854$			282.004i			0.330216i
$855$	75.9838	−	266.632i	0.0888700	−	0.311850i
$856$	915.780			1.06984
$857$	−426.906	−	1172.91i	−0.498140	−	1.36863i	−0.893070	−	0.449917i	$-0.851454\pi$
$857$	−426.906	−	1172.91i	−0.498140	−	1.36863i	0.394930	−	0.918711i	$-0.370769\pi$
$858$	1010.13	+	178.114i	1.17731	+	0.207592i
$859$	−387.840	+	325.436i	−0.451502	+	0.378855i	−0.839993	−	0.542598i	$-0.817441\pi$
$859$	−387.840	+	325.436i	−0.451502	+	0.378855i	0.388491	+	0.921453i	$0.372996\pi$
$860$	−21.8543	−	18.3379i	−0.0254120	−	0.0213232i
$861$	−25.1802	−	142.804i	−0.0292453	−	0.165858i
$862$	6.06244	+	10.5005i	0.00703299	+	0.0121815i
$863$	1102.47	+	636.511i	1.27748	+	0.737556i	0.976385	−	0.216037i	$-0.0693131\pi$
$863$	1102.47	+	636.511i	1.27748	+	0.737556i	0.301099	+	0.953593i	$0.402646\pi$
$864$	172.007	+	62.6056i	0.199083	+	0.0724601i
$865$	49.4072	−	135.745i	0.0571181	−	0.156931i
$866$	54.2095	−	93.8937i	0.0625976	−	0.108422i
$867$	−9.04032	+	5.21943i	−0.0104271	+	0.00602011i
$868$	−5.93623	+	1.04672i	−0.00683898	+	0.00120590i
$869$	−1326.79	+	1581.21i	−1.52681	+	1.81958i
$870$	54.4055	+	64.8379i	0.0625350	+	0.0745263i
$871$	−30.3704	+	172.239i	−0.0348684	+	0.197749i
$872$	−1619.07	+	589.293i	−1.85673	+	0.675794i
$873$		−	622.328i		−	0.712861i
$874$	66.8247	+	266.165i	0.0764584	+	0.304536i
$875$	284.747			0.325425
$876$	14.0397	+	38.5738i	0.0160271	+	0.0440340i
$877$	303.148	+	53.4532i	0.345665	+	0.0609500i	0.343785	−	0.939048i	$-0.388291\pi$
$877$	303.148	+	53.4532i	0.345665	+	0.0609500i	0.00187921	+	0.999998i	$0.499402\pi$
$878$	759.322	−	637.147i	0.864831	−	0.725680i
$879$	109.227	+	91.6527i	0.124263	+	0.104269i
$880$	131.951	+	748.334i	0.149945	+	0.850380i
$881$	−117.273	−	203.123i	−0.133113	−	0.230559i	0.791762	−	0.610830i	$-0.209164\pi$
$881$	−117.273	−	203.123i	−0.133113	−	0.230559i	−0.924875	+	0.380271i	$0.875831\pi$
$882$	−369.732	−	213.465i	−0.419198	−	0.242024i
$883$	258.816	+	94.2012i	0.293110	+	0.106683i	0.484390	−	0.874852i	$-0.339042\pi$
$883$	258.816	+	94.2012i	0.293110	+	0.106683i	−0.191280	+	0.981535i	$0.561264\pi$
$884$	35.4085	−	97.2841i	0.0400549	−	0.110050i
$885$	−25.0057	+	43.3111i	−0.0282550	+	0.0489391i
$886$	−712.450	+	411.333i	−0.804120	+	0.464259i
$887$	332.187	−	58.5735i	0.374506	−	0.0660355i	0.0167728	−	0.999859i	$-0.494661\pi$
$887$	332.187	−	58.5735i	0.374506	−	0.0660355i	0.357733	+	0.933824i	$0.383550\pi$
$888$	621.425	−	740.586i	0.699803	−	0.833993i
$889$	17.5958	+	20.9698i	0.0197928	+	0.0235881i
$890$	7.44378	−	42.2158i	0.00836380	−	0.0474334i
$891$	120.673	−	43.9215i	0.135436	−	0.0492946i
$892$		−	64.6905i		−	0.0725230i
$893$	567.557	+	1269.17i	0.635563	+	1.42124i
$894$	−517.103			−0.578415
$895$	221.625	+	608.909i	0.247625	+	0.680345i
$896$	248.662	+	43.8458i	0.277525	+	0.0489351i
$897$	164.846	−	138.322i	0.183775	−	0.154205i
$898$	−455.978	−	382.611i	−0.507770	−	0.426070i
$899$	−8.58634	−	48.6956i	−0.00955099	−	0.0541664i
$900$	18.6746	+	32.3453i	0.0207495	+	0.0359392i
$901$	−416.485	−	240.457i	−0.462247	−	0.266878i
$902$	1055.53	+	384.181i	1.17021	+	0.425921i
$903$	−39.4540	+	108.399i	−0.0436921	+	0.120043i
$904$	76.7736	−	132.976i	0.0849266	−	0.147097i
$905$	−654.049	+	377.616i	−0.722706	+	0.417255i
$906$	368.098	−	64.9056i	0.406289	−	0.0716397i
$907$	−164.258	+	195.755i	−0.181100	+	0.215827i	−0.848956	−	0.528464i	$-0.822768\pi$
$907$	−164.258	+	195.755i	−0.181100	+	0.215827i	0.667855	+	0.744291i	$0.267212\pi$
$908$	17.9235	+	21.3603i	0.0197395	+	0.0235246i
$909$	119.213	−	676.093i	0.131148	−	0.743777i
$910$	−174.266	+	63.4278i	−0.191501	+	0.0697008i
$911$		−	598.961i		−	0.657477i	−0.944421	−	0.328738i	$-0.893377\pi$
$911$		−	598.961i		−	0.657477i	0.944421	−	0.328738i	$-0.106623\pi$
$912$	−477.379	+	213.479i	−0.523441	+	0.234077i
$913$	1368.84			1.49928
$914$	340.073	+	934.343i	0.372071	+	1.02226i
$915$	−329.527	−	58.1044i	−0.360138	−	0.0635021i
$916$	22.0580	−	18.5088i	0.0240808	−	0.0202062i
$917$	20.7726	+	17.4303i	0.0226527	+	0.0190079i
$918$	155.901	+	884.160i	0.169827	+	0.963138i
$919$	−724.843	−	1255.46i	−0.788730	−	1.36612i	−0.926745	−	0.375691i	$-0.877406\pi$
$919$	−724.843	−	1255.46i	−0.788730	−	1.36612i	0.138015	−	0.990430i	$-0.455928\pi$
$920$	154.267	+	89.0661i	0.167682	+	0.0968110i
$921$	168.774	+	61.4288i	0.183251	+	0.0666979i
$922$	394.732	−	1084.52i	0.428126	−	1.17627i
$923$	279.147	−	483.497i	0.302435	−	0.523832i
$924$	−32.4571	+	18.7391i	−0.0351268	+	0.0202805i
$925$	1008.05	−	177.746i	1.08978	−	0.192158i
$926$	−929.066	+	1107.22i	−1.00331	+	1.19570i
$927$	−44.3730	−	52.8817i	−0.0478673	−	0.0570461i
$928$	9.47341	−	53.7264i	0.0102084	−	0.0578948i
$929$	1664.16	−	605.703i	1.79134	−	0.651995i	0.792212	−	0.610246i	$-0.208929\pi$
$929$	1664.16	−	605.703i	1.79134	−	0.651995i	0.999128	−	0.0417491i	$-0.0132930\pi$
$930$			61.6751i			0.0663173i
$931$	−795.418	+	199.702i	−0.854369	+	0.214503i
$932$	−67.8414			−0.0727912
$933$	132.404	+	363.777i	0.141912	+	0.389900i
$934$	836.445	+	147.488i	0.895551	+	0.157910i
$935$	705.088	−	591.639i	0.754104	−	0.632769i
$936$	−485.688	−	407.540i	−0.518897	−	0.435406i
$937$	−112.461	−	637.796i	−0.120022	−	0.680678i	−0.984141	−	0.177390i	$-0.943235\pi$
$937$	−112.461	−	637.796i	−0.120022	−	0.680678i	0.864119	−	0.503288i	$-0.167877\pi$
$938$	27.5531	+	47.7233i	0.0293743	+	0.0508777i
$939$	51.4886	+	29.7269i	0.0548334	+	0.0316581i
$940$	79.8281	+	29.0550i	0.0849235	+	0.0309096i
$941$	−463.502	+	1273.46i	−0.492563	+	1.35331i	0.405764	+	0.913978i	$0.367005\pi$
$941$	−463.502	+	1273.46i	−0.492563	+	1.35331i	−0.898327	+	0.439328i	$0.855217\pi$
$942$	307.819	−	533.159i	0.326772	−	0.565986i
$943$	204.085	−	117.829i	0.216421	−	0.124951i
$944$	−128.545	+	22.6659i	−0.136170	+	0.0240105i
$945$	−119.881	+	142.869i	−0.126859	+	0.151184i
$946$	−574.382	−	684.522i	−0.607170	−	0.723597i
$947$	−55.2366	+	313.263i	−0.0583280	+	0.330795i	−0.999983	−	0.00578427i	$-0.998159\pi$
$947$	−55.2366	+	313.263i	−0.0583280	+	0.330795i	0.941655	+	0.336579i	$0.109270\pi$
$948$	−81.5628	+	29.6864i	−0.0860367	+	0.0313148i
$949$		−	737.799i		−	0.777449i
$950$	−594.983	−	169.556i	−0.626298	−	0.178480i
$951$	−1107.38			−1.16443
$952$	−118.517	−	325.624i	−0.124493	−	0.342042i
$953$	−904.106	−	159.418i	−0.948694	−	0.167280i	−0.322170	−	0.946682i	$-0.604412\pi$
$953$	−904.106	−	159.418i	−0.948694	−	0.167280i	−0.626525	+	0.779401i	$0.715523\pi$
$954$	−212.381	+	178.209i	−0.222621	+	0.186801i
$955$	−174.281	−	146.239i	−0.182493	−	0.153130i
$956$	22.0602	+	125.110i	0.0230756	+	0.130868i
$957$	−153.719	−	266.250i	−0.160626	−	0.278213i
$958$	−1142.24	−	659.474i	−1.19232	−	0.688387i
$959$	−367.182	−	133.643i	−0.382880	−	0.139357i
$960$	−128.442	+	352.890i	−0.133793	+	0.367594i
$961$	−462.485	+	801.047i	−0.481254	+	0.833556i
$962$	−1416.54	+	817.840i	−1.47250	+	0.850146i
$963$	−563.610	+	99.3797i	−0.585265	+	0.103198i
$964$	−64.1373	+	76.4358i	−0.0665324	+	0.0792903i
$965$	53.5556	+	63.8251i	0.0554981	+	0.0661400i
$966$	11.7737	−	66.7721i	0.0121881	−	0.0691223i
$967$	−368.728	+	134.206i	−0.381311	+	0.138786i	−0.525562	−	0.850755i	$-0.676145\pi$
$967$	−368.728	+	134.206i	−0.381311	+	0.138786i	0.144251	+	0.989541i	$0.453923\pi$
$968$		−	2072.56i		−	2.14107i
$969$	513.059	+	371.479i	0.529473	+	0.383363i
$970$	629.888			0.649369
$971$	161.114	+	442.657i	0.165926	+	0.455877i	0.994591	−	0.103867i	$-0.0331217\pi$
$971$	161.114	+	442.657i	0.165926	+	0.455877i	−0.828666	+	0.559744i	$0.810899\pi$
$972$	−96.5089	−	17.0171i	−0.0992890	−	0.0175073i
$973$	−355.439	+	298.249i	−0.365302	+	0.306525i
$974$	28.1757	+	23.6422i	0.0289278	+	0.0242733i
$975$	84.2424	+	477.762i	0.0864024	+	0.490013i
$976$	−436.660	−	756.317i	−0.447398	−	0.774915i
$977$	170.882	+	98.6590i	0.174905	+	0.100982i	0.584897	−	0.811108i	$-0.301135\pi$
$977$	170.882	+	98.6590i	0.174905	+	0.100982i	−0.409991	+	0.912089i	$0.634468\pi$
$978$	−116.977	−	42.5761i	−0.119608	−	0.0435339i
$979$	−53.2547	+	146.316i	−0.0543971	+	0.149455i
$980$	−25.0555	+	43.3974i	−0.0255669	+	0.0442831i
$981$	932.495	−	538.376i	0.950556	−	0.548804i
$982$	1234.93	−	217.752i	1.25757	−	0.221743i
$983$	−494.260	+	589.036i	−0.502808	+	0.599223i	−0.956427	−	0.291973i	$-0.905688\pi$
$983$	−494.260	+	589.036i	−0.502808	+	0.599223i	0.453619	+	0.891196i	$0.350133\pi$
$984$	322.534	+	384.381i	0.327779	+	0.390631i
$985$	87.3196	−	495.214i	0.0886493	−	0.502755i
$986$	251.443	−	91.5179i	0.255014	−	0.0928173i
$987$		−	343.499i		−	0.348023i
$988$	−114.354	+	8.18431i	−0.115743	+	0.00828372i
$989$	−187.470			−0.189555
$990$	−181.482	−	498.618i	−0.183315	−	0.503654i
$991$	1718.71	+	303.054i	1.73431	+	0.305806i	0.949463	−	0.313878i	$-0.101628\pi$
$991$	1718.71	+	303.054i	1.73431	+	0.305806i	0.784851	+	0.619685i	$0.212740\pi$
$992$	30.4526	−	25.5528i	0.0306982	−	0.0257589i
$993$	−658.313	−	552.390i	−0.662954	−	0.556284i
$994$	−30.5459	−	173.235i	−0.0307303	−	0.174280i
$995$	153.795	+	266.381i	0.154568	+	0.267719i
$996$	49.8488	+	28.7802i	0.0500490	+	0.0288958i
$997$	1158.78	+	421.762i	1.16227	+	0.423031i	0.849908	−	0.526932i	$-0.176658\pi$
$997$	1158.78	+	421.762i	1.16227	+	0.423031i	0.312362	+	0.949963i	$0.398880\pi$
$998$	86.5114	−	237.688i	0.0866847	−	0.238164i
$999$	−822.479	+	1424.58i	−0.823303	+	1.42600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.3.f.a.14.2	✓	12
3.2	odd	2		171.3.ba.b.109.1		12
4.3	odd	2		304.3.z.a.33.2		12
19.2	odd	18		361.3.b.c.360.9		12
19.3	odd	18		361.3.d.f.69.5		12
19.4	even	9		361.3.f.g.262.1		12
19.5	even	9		361.3.d.f.293.5		12
19.6	even	9		361.3.f.b.333.2		12
19.7	even	3		361.3.f.f.116.1		12
19.8	odd	6		361.3.f.c.307.1		12
19.9	even	9		361.3.f.c.127.1		12
19.10	odd	18		361.3.f.e.127.2		12
19.11	even	3		361.3.f.e.307.2		12
19.12	odd	6		361.3.f.b.116.2		12
19.13	odd	18		361.3.f.f.333.1		12
19.14	odd	18		361.3.d.d.293.2		12
19.15	odd	18	inner	19.3.f.a.15.2	yes	12
19.16	even	9		361.3.d.d.69.2		12
19.17	even	9		361.3.b.c.360.4		12
19.18	odd	2		361.3.f.g.299.1		12
57.53	even	18		171.3.ba.b.91.1		12
76.15	even	18		304.3.z.a.129.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.3.f.a.14.2	✓	12	1.1	even	1	trivial
19.3.f.a.15.2	yes	12	19.15	odd	18	inner
171.3.ba.b.91.1		12	57.53	even	18
171.3.ba.b.109.1		12	3.2	odd	2
304.3.z.a.33.2		12	4.3	odd	2
304.3.z.a.129.2		12	76.15	even	18
361.3.b.c.360.4		12	19.17	even	9
361.3.b.c.360.9		12	19.2	odd	18
361.3.d.d.69.2		12	19.16	even	9
361.3.d.d.293.2		12	19.14	odd	18
361.3.d.f.69.5		12	19.3	odd	18
361.3.d.f.293.5		12	19.5	even	9
361.3.f.b.116.2		12	19.12	odd	6
361.3.f.b.333.2		12	19.6	even	9
361.3.f.c.127.1		12	19.9	even	9
361.3.f.c.307.1		12	19.8	odd	6
361.3.f.e.127.2		12	19.10	odd	18
361.3.f.e.307.2		12	19.11	even	3
361.3.f.f.116.1		12	19.7	even	3
361.3.f.f.333.1		12	19.13	odd	18
361.3.f.g.262.1		12	19.4	even	9
361.3.f.g.299.1		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)

\(f(q)\)	\(=\)	\(q+(0.647524 + 1.77906i) q^{2} +(-1.91357 - 0.337414i) q^{3} +(0.318417 - 0.267183i) q^{4} +(-2.13959 - 1.79533i) q^{5} +(-0.638803 - 3.62283i) q^{6} +(-1.20796 - 2.09224i) q^{7} +(7.23987 + 4.17994i) q^{8} +(-4.90934 - 1.78685i) q^{9} +O(q^{10})\)	\(q+(0.647524 + 1.77906i) q^{2} +(-1.91357 - 0.337414i) q^{3} +(0.318417 - 0.267183i) q^{4} +(-2.13959 - 1.79533i) q^{5} +(-0.638803 - 3.62283i) q^{6} +(-1.20796 - 2.09224i) q^{7} +(7.23987 + 4.17994i) q^{8} +(-4.90934 - 1.78685i) q^{9} +(1.80856 - 4.96897i) q^{10} +(-9.60360 + 16.6339i) q^{11} +(-0.699463 + 0.403835i) q^{12} +(14.2961 - 2.52079i) q^{13} +(2.94004 - 3.50380i) q^{14} +(3.48848 + 4.15741i) q^{15} +(-2.45965 + 13.9494i) q^{16} +(16.1226 - 5.86814i) q^{17} -9.89103i q^{18} +(-13.2208 - 13.6459i) q^{19} -1.16096 q^{20} +(1.60556 + 4.41123i) q^{21} +(-35.8113 - 6.31450i) q^{22} +(-5.84413 + 4.90381i) q^{23} +(-12.4436 - 10.4414i) q^{24} +(-2.98657 - 16.9377i) q^{25} +(13.7417 + 23.8013i) q^{26} +(23.9363 + 13.8196i) q^{27} +(-0.943645 - 0.343459i) q^{28} +(2.81743 - 7.74083i) q^{29} +(-5.13740 + 8.89824i) q^{30} +(5.19837 - 3.00128i) q^{31} +(6.52208 - 1.15002i) q^{32} +(23.9897 - 28.5898i) q^{33} +(20.8795 + 24.8832i) q^{34} +(-1.17173 + 6.64521i) q^{35} +(-2.04063 + 0.742729i) q^{36} +59.5153i q^{37} +(15.7160 - 32.3567i) q^{38} -28.2071 q^{39} +(-7.98598 - 21.9413i) q^{40} +(-30.4205 - 5.36396i) q^{41} +(-6.80820 + 5.71276i) q^{42} +(18.8243 + 15.7955i) q^{43} +(1.38636 + 7.86244i) q^{44} +(7.29598 + 12.6370i) q^{45} +(-12.5084 - 7.22171i) q^{46} +(-68.7602 - 25.0267i) q^{47} +(9.41343 - 25.8632i) q^{48} +(21.5817 - 37.3806i) q^{49} +(28.1992 - 16.2808i) q^{50} +(-32.8316 + 5.78910i) q^{51} +(3.87860 - 4.62234i) q^{52} +(-18.0172 - 21.4721i) q^{53} +(-9.08660 + 51.5327i) q^{54} +(50.4111 - 18.3482i) q^{55} -20.1968i q^{56} +(20.6947 + 30.5732i) q^{57} +15.5957 q^{58} +(3.15174 + 8.65934i) q^{59} +(2.22158 + 0.391725i) q^{60} +(-47.2307 + 39.6312i) q^{61} +(8.70552 + 7.30480i) q^{62} +(2.19174 + 12.4300i) q^{63} +(34.5983 + 59.9260i) q^{64} +(-35.1134 - 20.2727i) q^{65} +(66.3968 + 24.1665i) q^{66} +(-4.12065 + 11.3214i) q^{67} +(3.56583 - 6.17619i) q^{68} +(12.8378 - 7.41188i) q^{69} +(-12.5809 + 2.21836i) q^{70} +(24.7209 - 29.4613i) q^{71} +(-28.0740 - 33.4573i) q^{72} +(8.82556 - 50.0523i) q^{73} +(-105.881 + 38.5376i) q^{74} +33.4191i q^{75} +(-7.85568 - 0.812682i) q^{76} +46.4029 q^{77} +(-18.2648 - 50.1821i) q^{78} +(105.834 + 18.6613i) q^{79} +(30.3064 - 25.4301i) q^{80} +(-5.12171 - 4.29762i) q^{81} +(-10.1552 - 57.5932i) q^{82} +(-35.6336 - 61.7192i) q^{83} +(1.68984 + 0.975631i) q^{84} +(-45.0309 - 16.3899i) q^{85} +(-15.9119 + 43.7175i) q^{86} +(-8.00321 + 13.8620i) q^{87} +(-139.058 + 80.2850i) q^{88} +(7.98351 - 1.40771i) q^{89} +(-17.7576 + 21.1627i) q^{90} +(-22.5431 - 26.8659i) q^{91} +(-0.550653 + 3.12291i) q^{92} +(-10.9601 + 3.98915i) q^{93} -138.534i q^{94} +(3.78836 + 52.9323i) q^{95} -12.8685 q^{96} +(40.7412 + 111.936i) q^{97} +(80.4769 + 14.1902i) q^{98} +(76.8697 - 64.5013i) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more