LMFDB - Embedded newform 87.2.g.a.82.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,2,Mod(7,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 6]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("87.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.g (of order $7$, 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:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 18 x^{16} - 37 x^{15} + 71 x^{14} - 83 x^{13} + 225 x^{12} - 237 x^{11} + 485 x^{10} + \cdots + 64 $ x^18 - 6x^17 + 18x^16 - 37x^15 + 71x^14 - 83x^13 + 225x^12 - 237x^11 + 485x^10 - 319x^9 + 1092x^8 - 1080x^7 + 1833x^6 - 4032x^5 + 6004x^4 - 4480x^3 + 3200x^2 - 576*x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			82.2
Root			$0.183119 - 0.802295i$ of defining polynomial
Character	$\chi$	$=$	87.82
Dual form			87.2.g.a.52.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.110403 + 0.138441i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(0.438065 - 1.91929i) q^{4} +(-2.15193 - 2.69844i) q^{5} +(0.110403 - 0.138441i) q^{6} +(0.844514 + 3.70006i) q^{7} +(0.633146 - 0.304907i) q^{8} +(-0.900969 + 0.433884i) q^{9} +O(q^{10})$	\(q+(0.110403 + 0.138441i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(0.438065 - 1.91929i) q^{4} +(-2.15193 - 2.69844i) q^{5} +(0.110403 - 0.138441i) q^{6} +(0.844514 + 3.70006i) q^{7} +(0.633146 - 0.304907i) q^{8} +(-0.900969 + 0.433884i) q^{9} +(0.135995 - 0.595831i) q^{10} +(3.84419 + 1.85126i) q^{11} -1.96865 q^{12} +(4.18329 + 2.01457i) q^{13} +(-0.419003 + 0.525413i) q^{14} +(-2.15193 + 2.69844i) q^{15} +(-3.43526 - 1.65434i) q^{16} -3.07208 q^{17} +(-0.159537 - 0.0768290i) q^{18} +(0.799448 - 3.50261i) q^{19} +(-6.12176 + 2.94808i) q^{20} +(3.41937 - 1.64668i) q^{21} +(0.168119 + 0.736579i) q^{22} +(-0.270347 + 0.339005i) q^{23} +(-0.438150 - 0.549423i) q^{24} +(-1.53815 + 6.73907i) q^{25} +(0.182949 + 0.801554i) q^{26} +(0.623490 + 0.781831i) q^{27} +7.47142 q^{28} +(-1.41466 + 5.19603i) q^{29} -0.611154 q^{30} +(-2.81961 - 3.53568i) q^{31} +(-0.462984 - 2.02846i) q^{32} +(0.949437 - 4.15975i) q^{33} +(-0.339167 - 0.425302i) q^{34} +(8.16704 - 10.2411i) q^{35} +(0.438065 + 1.91929i) q^{36} +(-5.70128 + 2.74559i) q^{37} +(0.573166 - 0.276022i) q^{38} +(1.03319 - 4.52669i) q^{39} +(-2.18526 - 1.05236i) q^{40} -1.97128 q^{41} +(0.605476 + 0.291582i) q^{42} +(-0.156607 + 0.196379i) q^{43} +(5.23711 - 6.56713i) q^{44} +(3.10963 + 1.49752i) q^{45} -0.0767793 q^{46} +(4.33933 + 2.08971i) q^{47} +(-0.848440 + 3.71726i) q^{48} +(-6.67044 + 3.21231i) q^{49} +(-1.10278 + 0.531070i) q^{50} +(0.683602 + 2.99505i) q^{51} +(5.69909 - 7.14643i) q^{52} +(6.83931 + 8.57623i) q^{53} +(-0.0394024 + 0.172633i) q^{54} +(-3.27691 - 14.3571i) q^{55} +(1.66287 + 2.08518i) q^{56} -3.59269 q^{57} +(-0.875526 + 0.377811i) q^{58} -6.06991 q^{59} +(4.23639 + 5.31227i) q^{60} +(-0.843741 - 3.69667i) q^{61} +(0.178190 - 0.780699i) q^{62} +(-2.36628 - 2.96722i) q^{63} +(-4.52484 + 5.67398i) q^{64} +(-3.56598 - 15.6236i) q^{65} +(0.680701 - 0.327808i) q^{66} +(4.74553 - 2.28533i) q^{67} +(-1.34577 + 5.89620i) q^{68} +(0.390663 + 0.188133i) q^{69} +2.31946 q^{70} +(5.25813 + 2.53218i) q^{71} +(-0.438150 + 0.549423i) q^{72} +(-6.57753 + 8.24796i) q^{73} +(-1.00954 - 0.486169i) q^{74} +6.91237 q^{75} +(-6.37230 - 3.06874i) q^{76} +(-3.60331 + 15.7871i) q^{77} +(0.740747 - 0.356725i) q^{78} +(-9.04273 + 4.35475i) q^{79} +(2.92833 + 12.8299i) q^{80} +(0.623490 - 0.781831i) q^{81} +(-0.217635 - 0.272906i) q^{82} +(1.57949 - 6.92019i) q^{83} +(-1.66255 - 7.28410i) q^{84} +(6.61090 + 8.28981i) q^{85} -0.0444768 q^{86} +(5.38055 + 0.222965i) q^{87} +2.99840 q^{88} +(-8.71402 - 10.9270i) q^{89} +(0.135995 + 0.595831i) q^{90} +(-3.92117 + 17.1798i) q^{91} +(0.532218 + 0.667380i) q^{92} +(-2.81961 + 3.53568i) q^{93} +(0.189773 + 0.831452i) q^{94} +(-11.1719 + 5.38012i) q^{95} +(-1.87458 + 0.902751i) q^{96} +(3.18704 - 13.9633i) q^{97} +(-1.18115 - 0.568813i) q^{98} -4.26673 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9}+O(q^{10}) $ 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9} - 14 q^{10} + 26 q^{11} + 22 q^{12} + 9 q^{13} - 10 q^{14} - q^{15} - 14 q^{16} + 4 q^{17} - 4 q^{18} - 10 q^{19} - q^{20} - 4 q^{21} - 8 q^{22} - 8 q^{23} - 8 q^{24} + 16 q^{25} + 5 q^{26} - 3 q^{27} + 80 q^{28} + 8 q^{29} - 12 q^{31} + 9 q^{32} - 16 q^{33} - 22 q^{34} + 9 q^{35} - 6 q^{36} - 16 q^{37} - 32 q^{38} + 2 q^{39} + 33 q^{40} + 24 q^{41} - 3 q^{42} - 31 q^{43} - 52 q^{44} + 6 q^{45} - 44 q^{46} + 5 q^{47} - 47 q^{49} - 7 q^{50} + 11 q^{51} + 80 q^{52} + 5 q^{53} + 3 q^{54} - 17 q^{55} + 45 q^{56} + 18 q^{57} + 54 q^{58} - 32 q^{59} + 27 q^{60} - 28 q^{61} + 69 q^{62} + 3 q^{63} - 75 q^{64} + 22 q^{65} + 34 q^{66} + 6 q^{67} + 38 q^{68} + 20 q^{69} - 12 q^{70} + 46 q^{71} - 8 q^{72} - q^{73} - 35 q^{74} + 2 q^{75} - 45 q^{76} - 36 q^{77} - 51 q^{78} - 15 q^{79} - 86 q^{80} - 3 q^{81} + 47 q^{82} - 16 q^{83} - 25 q^{84} + 19 q^{85} + 116 q^{86} + 43 q^{87} + 54 q^{88} - 72 q^{89} - 14 q^{90} - 47 q^{91} - 121 q^{92} - 12 q^{93} - 22 q^{94} - 72 q^{95} - 12 q^{96} + 43 q^{97} + 31 q^{98} - 2 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9 - 14 * q^10 + 26 * q^11 + 22 * q^12 + 9 * q^13 - 10 * q^14 - q^15 - 14 * q^16 + 4 * q^17 - 4 * q^18 - 10 * q^19 - q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 - 8 * q^24 + 16 * q^25 + 5 * q^26 - 3 * q^27 + 80 * q^28 + 8 * q^29 - 12 * q^31 + 9 * q^32 - 16 * q^33 - 22 * q^34 + 9 * q^35 - 6 * q^36 - 16 * q^37 - 32 * q^38 + 2 * q^39 + 33 * q^40 + 24 * q^41 - 3 * q^42 - 31 * q^43 - 52 * q^44 + 6 * q^45 - 44 * q^46 + 5 * q^47 - 47 * q^49 - 7 * q^50 + 11 * q^51 + 80 * q^52 + 5 * q^53 + 3 * q^54 - 17 * q^55 + 45 * q^56 + 18 * q^57 + 54 * q^58 - 32 * q^59 + 27 * q^60 - 28 * q^61 + 69 * q^62 + 3 * q^63 - 75 * q^64 + 22 * q^65 + 34 * q^66 + 6 * q^67 + 38 * q^68 + 20 * q^69 - 12 * q^70 + 46 * q^71 - 8 * q^72 - q^73 - 35 * q^74 + 2 * q^75 - 45 * q^76 - 36 * q^77 - 51 * q^78 - 15 * q^79 - 86 * q^80 - 3 * q^81 + 47 * q^82 - 16 * q^83 - 25 * q^84 + 19 * q^85 + 116 * q^86 + 43 * q^87 + 54 * q^88 - 72 * q^89 - 14 * q^90 - 47 * q^91 - 121 * q^92 - 12 * q^93 - 22 * q^94 - 72 * q^95 - 12 * q^96 + 43 * q^97 + 31 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{2}{7}\right)$	$1$

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 $

$2$	0.110403	+	0.138441i	0.0780667	+	0.0978926i	0.819331	−	0.573320i	$-0.194345\pi$
$2$	0.110403	+	0.138441i	0.0780667	+	0.0978926i	−0.741264	+	0.671213i	$0.765774\pi$
$3$	−0.222521	−	0.974928i	−0.128473	−	0.562875i
$3$	−0.222521	−	0.974928i	−0.128473	−	0.562875i
$4$	0.438065	−	1.91929i	0.219032	−	0.959644i
$5$	−2.15193	−	2.69844i	−0.962373	−	1.20678i	−0.978361	−	0.206906i	$-0.933661\pi$
$5$	−2.15193	−	2.69844i	−0.962373	−	1.20678i	0.0159877	−	0.999872i	$-0.494911\pi$
$6$	0.110403	−	0.138441i	0.0450718	−	0.0565183i
$7$	0.844514	+	3.70006i	0.319196	+	1.39849i	0.838966	+	0.544184i	$0.183161\pi$
$7$	0.844514	+	3.70006i	0.319196	+	1.39849i	−0.519770	+	0.854306i	$0.673982\pi$
$8$	0.633146	−	0.304907i	0.223851	−	0.107801i
$9$	−0.900969	+	0.433884i	−0.300323	+	0.144628i
$10$	0.135995	−	0.595831i	0.0430053	−	0.188418i
$11$	3.84419	+	1.85126i	1.15907	+	0.558177i	0.911745	−	0.410756i	$-0.134735\pi$
$11$	3.84419	+	1.85126i	1.15907	+	0.558177i	0.247322	+	0.968933i	$0.420450\pi$
$12$	−1.96865			−0.568299
$13$	4.18329	+	2.01457i	1.16024	+	0.558741i	0.912093	−	0.409982i	$-0.134465\pi$
$13$	4.18329	+	2.01457i	1.16024	+	0.558741i	0.248144	+	0.968723i	$0.420179\pi$
$14$	−0.419003	+	0.525413i	−0.111983	+	0.140422i
$15$	−2.15193	+	2.69844i	−0.555626	+	0.696733i
$16$	−3.43526	−	1.65434i	−0.858816	−	0.413584i
$17$	−3.07208			−0.745088			−0.372544	−	0.928014i	$-0.621514\pi$
$17$	−3.07208			−0.745088			−0.372544	+	0.928014i	$0.621514\pi$
$18$	−0.159537	−	0.0768290i	−0.0376032	−	0.0181088i
$19$	0.799448	−	3.50261i	0.183406	−	0.803554i	−0.796587	−	0.604523i	$-0.793364\pi$
$19$	0.799448	−	3.50261i	0.183406	−	0.803554i	0.979993	−	0.199030i	$-0.0637792\pi$
$20$	−6.12176	+	2.94808i	−1.36887	+	0.659212i
$21$	3.41937	−	1.64668i	0.746167	−	0.359335i
$22$	0.168119	+	0.736579i	0.0358432	+	0.157039i
$23$	−0.270347	+	0.339005i	−0.0563713	+	0.0706873i	−0.809218	−	0.587509i	$-0.800109\pi$
$23$	−0.270347	+	0.339005i	−0.0563713	+	0.0706873i	0.752847	+	0.658196i	$0.228680\pi$
$24$	−0.438150	−	0.549423i	−0.0894371	−	0.112151i
$25$	−1.53815	+	6.73907i	−0.307630	+	1.34781i
$26$	0.182949	+	0.801554i	0.0358793	+	0.157198i
$27$	0.623490	+	0.781831i	0.119991	+	0.150464i
$28$	7.47142			1.41197
$29$	−1.41466	+	5.19603i	−0.262696	+	0.964879i
$29$	−1.41466	+	5.19603i	−0.262696	+	0.964879i
$30$	−0.611154			−0.111581
$31$	−2.81961	−	3.53568i	−0.506417	−	0.635027i	0.461246	−	0.887272i	$-0.347402\pi$
$31$	−2.81961	−	3.53568i	−0.506417	−	0.635027i	−0.967663	+	0.252245i	$0.918831\pi$
$32$	−0.462984	−	2.02846i	−0.0818447	−	0.358585i
$33$	0.949437	−	4.15975i	0.165276	−	0.724120i
$34$	−0.339167	−	0.425302i	−0.0581666	−	0.0729386i
$35$	8.16704	−	10.2411i	1.38048	−	1.73107i
$36$	0.438065	+	1.91929i	0.0730108	+	0.319881i
$37$	−5.70128	+	2.74559i	−0.937284	+	0.451372i	−0.839210	−	0.543807i	$-0.816982\pi$
$37$	−5.70128	+	2.74559i	−0.937284	+	0.451372i	−0.0980737	+	0.995179i	$0.531268\pi$
$38$	0.573166	−	0.276022i	0.0929798	−	0.0447767i
$39$	1.03319	−	4.52669i	0.165443	−	0.724851i
$40$	−2.18526	−	1.05236i	−0.345520	−	0.166394i
$41$	−1.97128			−0.307862			−0.153931	−	0.988082i	$-0.549193\pi$
$41$	−1.97128			−0.307862			−0.153931	+	0.988082i	$0.549193\pi$
$42$	0.605476	+	0.291582i	0.0934270	+	0.0449921i
$43$	−0.156607	+	0.196379i	−0.0238823	+	0.0299475i	−0.793629	−	0.608402i	$-0.791811\pi$
$43$	−0.156607	+	0.196379i	−0.0238823	+	0.0299475i	0.769747	+	0.638349i	$0.220382\pi$
$44$	5.23711	−	6.56713i	0.789524	−	0.990032i
$45$	3.10963	+	1.49752i	0.463557	+	0.223237i
$46$	−0.0767793			−0.0113205
$47$	4.33933	+	2.08971i	0.632956	+	0.304816i	0.722713	−	0.691148i	$-0.242895\pi$
$47$	4.33933	+	2.08971i	0.632956	+	0.304816i	−0.0897569	+	0.995964i	$0.528609\pi$
$48$	−0.848440	+	3.71726i	−0.122462	+	0.536540i
$49$	−6.67044	+	3.21231i	−0.952919	+	0.458902i
$50$	−1.10278	+	0.531070i	−0.155957	+	0.0751047i
$51$	0.683602	+	2.99505i	0.0957234	+	0.419392i
$52$	5.69909	−	7.14643i	0.790322	−	0.991032i
$53$	6.83931	+	8.57623i	0.939452	+	1.17804i	0.983845	+	0.179021i	$0.0572932\pi$
$53$	6.83931	+	8.57623i	0.939452	+	1.17804i	−0.0443931	+	0.999014i	$0.514135\pi$
$54$	−0.0394024	+	0.172633i	−0.00536198	+	0.0234924i
$55$	−3.27691	−	14.3571i	−0.441859	−	1.93591i
$56$	1.66287	+	2.08518i	0.222211	+	0.278644i
$57$	−3.59269			−0.475863
$58$	−0.875526	+	0.377811i	−0.114962	+	0.0496090i
$59$	−6.06991			−0.790234			−0.395117	−	0.918631i	$-0.629296\pi$
$59$	−6.06991			−0.790234			−0.395117	+	0.918631i	$0.629296\pi$
$60$	4.23639	+	5.31227i	0.546916	+	0.685811i
$61$	−0.843741	−	3.69667i	−0.108030	−	0.473310i	−0.999784	−	0.0207897i	$-0.993382\pi$
$61$	−0.843741	−	3.69667i	−0.108030	−	0.473310i	0.891754	−	0.452521i	$-0.149475\pi$
$62$	0.178190	−	0.780699i	0.0226301	−	0.0991489i
$63$	−2.36628	−	2.96722i	−0.298123	−	0.373834i
$64$	−4.52484	+	5.67398i	−0.565606	+	0.709247i
$65$	−3.56598	−	15.6236i	−0.442305	−	1.93787i
$66$	0.680701	−	0.327808i	0.0837885	−	0.0403504i
$67$	4.74553	−	2.28533i	0.579759	−	0.279197i	−0.120934	−	0.992661i	$-0.538589\pi$
$67$	4.74553	−	2.28533i	0.579759	−	0.279197i	0.700693	+	0.713463i	$0.252875\pi$
$68$	−1.34577	+	5.89620i	−0.163198	+	0.715019i
$69$	0.390663	+	0.188133i	0.0470303	+	0.0226486i
$70$	2.31946			0.277228
$71$	5.25813	+	2.53218i	0.624025	+	0.300515i	0.719048	−	0.694960i	$-0.244578\pi$
$71$	5.25813	+	2.53218i	0.624025	+	0.300515i	−0.0950227	+	0.995475i	$0.530292\pi$
$72$	−0.438150	+	0.549423i	−0.0516365	+	0.0647501i
$73$	−6.57753	+	8.24796i	−0.769841	+	0.965350i	−0.999970	−	0.00780984i	$-0.997514\pi$
$73$	−6.57753	+	8.24796i	−0.769841	+	0.965350i	0.230128	+	0.973160i	$0.426085\pi$
$74$	−1.00954	−	0.486169i	−0.117357	−	0.0565160i
$75$	6.91237			0.798172
$76$	−6.37230	−	3.06874i	−0.730953	−	0.352009i
$77$	−3.60331	+	15.7871i	−0.410636	+	1.79911i
$78$	0.740747	−	0.356725i	0.0838731	−	0.0403912i
$79$	−9.04273	+	4.35475i	−1.01739	+	0.489947i	−0.866803	−	0.498650i	$-0.833829\pi$
$79$	−9.04273	+	4.35475i	−1.01739	+	0.489947i	−0.150583	+	0.988597i	$0.548115\pi$
$80$	2.92833	+	12.8299i	0.327397	+	1.43442i
$81$	0.623490	−	0.781831i	0.0692766	−	0.0868702i
$82$	−0.217635	−	0.272906i	−0.0240338	−	0.0301374i
$83$	1.57949	−	6.92019i	0.173371	−	0.759590i	−0.811223	−	0.584737i	$-0.801198\pi$
$83$	1.57949	−	6.92019i	0.173371	−	0.759590i	0.984595	−	0.174853i	$-0.0559451\pi$
$84$	−1.66255	−	7.28410i	−0.181399	−	0.794760i
$85$	6.61090	+	8.28981i	0.717053	+	0.899156i
$86$	−0.0444768			−0.00479606
$87$	5.38055	+	0.222965i	0.576855	+	0.0239044i
$88$	2.99840			0.319630
$89$	−8.71402	−	10.9270i	−0.923684	−	1.15826i	−0.987073	−	0.160274i	$-0.948762\pi$
$89$	−8.71402	−	10.9270i	−0.923684	−	1.15826i	0.0633886	−	0.997989i	$-0.479809\pi$
$90$	0.135995	+	0.595831i	0.0143351	+	0.0628061i
$91$	−3.92117	+	17.1798i	−0.411050	+	1.80093i
$92$	0.532218	+	0.667380i	0.0554875	+	0.0695792i
$93$	−2.81961	+	3.53568i	−0.292380	+	0.366633i
$94$	0.189773	+	0.831452i	0.0195736	+	0.0857577i
$95$	−11.1719	+	5.38012i	−1.14622	+	0.551988i
$96$	−1.87458	+	0.902751i	−0.191324	+	0.0921367i
$97$	3.18704	−	13.9633i	0.323595	−	1.41776i	−0.507510	−	0.861646i	$-0.669434\pi$
$97$	3.18704	−	13.9633i	0.323595	−	1.41776i	0.831105	−	0.556116i	$-0.187709\pi$
$98$	−1.18115	−	0.568813i	−0.119314	−	0.0574588i
$99$	−4.26673			−0.428822
$100$	12.2604	+	5.90430i	1.22604	+	0.590430i
$101$	0.509045	−	0.638322i	0.0506519	−	0.0635154i	−0.755860	−	0.654733i	$-0.772781\pi$
$101$	0.509045	−	0.638322i	0.0506519	−	0.0635154i	0.806512	+	0.591218i	$0.201353\pi$
$102$	−0.339167	+	0.425302i	−0.0335825	+	0.0421111i
$103$	4.46695	+	2.15117i	0.440142	+	0.211961i	0.640812	−	0.767698i	$-0.278598\pi$
$103$	4.46695	+	2.15117i	0.440142	+	0.211961i	−0.200670	+	0.979659i	$0.564312\pi$
$104$	3.26289			0.319953
$105$	−11.8017	−	5.68340i	−1.15173	−	0.554643i
$106$	−0.432221	+	1.89368i	−0.0419810	+	0.183931i
$107$	10.3935	−	5.00522i	1.00477	−	0.483873i	0.142218	−	0.989835i	$-0.454577\pi$
$107$	10.3935	−	5.00522i	1.00477	−	0.483873i	0.862556	+	0.505962i	$0.168862\pi$
$108$	1.77369	−	0.854163i	0.170673	−	0.0821919i
$109$	−1.92418	−	8.43038i	−0.184303	−	0.807484i	−0.979550	−	0.201199i	$-0.935516\pi$
$109$	−1.92418	−	8.43038i	−0.184303	−	0.807484i	0.795247	−	0.606285i	$-0.207341\pi$
$110$	1.62583	−	2.03873i	0.155017	−	0.194385i
$111$	3.94541	+	4.94738i	0.374481	+	0.469585i
$112$	3.22001	−	14.1078i	0.304262	−	1.33306i
$113$	−1.68793	−	7.39532i	−0.158787	−	0.695693i	−0.990156	−	0.139971i	$-0.955299\pi$
$113$	−1.68793	−	7.39532i	−0.158787	−	0.695693i	0.831368	−	0.555722i	$-0.187558\pi$
$114$	−0.396643	−	0.497375i	−0.0371490	−	0.0465834i
$115$	1.49655			0.139554
$116$	9.35296	+	4.99134i	0.868401	+	0.463434i
$117$	−4.64311			−0.429255
$118$	−0.670136	−	0.840324i	−0.0616910	−	0.0773581i
$119$	−2.59441	−	11.3669i	−0.237829	−	1.04200i
$120$	−0.539714	+	2.36464i	−0.0492689	+	0.215861i
$121$	4.49223	+	5.63308i	0.408385	+	0.512098i
$122$	0.418620	−	0.524932i	0.0379000	−	0.0475251i
$123$	0.438650	+	1.92185i	0.0395518	+	0.173288i
$124$	−8.02116	+	3.86279i	−0.720321	+	0.346888i
$125$	5.94678	−	2.86382i	0.531896	−	0.256148i
$126$	0.149540	−	0.655179i	0.0133221	−	0.0583680i
$127$	−1.11242	−	0.535714i	−0.0987114	−	0.0475369i	0.383877	−	0.923384i	$-0.374589\pi$
$127$	−1.11242	−	0.535714i	−0.0987114	−	0.0475369i	−0.482588	+	0.875848i	$0.660303\pi$
$128$	−5.44633			−0.481392
$129$	0.226304	+	0.108982i	0.0199249	+	0.00959534i
$130$	1.76925	−	2.21857i	0.155173	−	0.194581i
$131$	−2.49124	+	3.12392i	−0.217661	+	0.272938i	−0.878659	−	0.477449i	$-0.841561\pi$
$131$	−2.49124	+	3.12392i	−0.217661	+	0.272938i	0.660999	+	0.750387i	$0.270133\pi$
$132$	−7.56785	−	3.64448i	−0.658697	−	0.317212i
$133$	13.6350			1.18230
$134$	0.840304	+	0.404669i	0.0725912	+	0.0349581i
$135$	0.768016	−	3.36490i	0.0661003	−	0.289604i
$136$	−1.94507	+	0.936698i	−0.166789	+	0.0803212i
$137$	−15.0046	+	7.22585i	−1.28193	+	0.617346i	−0.945886	−	0.324500i	$-0.894804\pi$
$137$	−15.0046	+	7.22585i	−1.28193	+	0.617346i	−0.336046	+	0.941846i	$0.609090\pi$
$138$	0.0170850	+	0.0748543i	0.00145437	+	0.00637202i
$139$	5.15692	−	6.46658i	0.437405	−	0.548488i	−0.513452	−	0.858118i	$-0.671634\pi$
$139$	5.15692	−	6.46658i	0.437405	−	0.548488i	0.950857	+	0.309630i	$0.100205\pi$
$140$	−16.0780	−	20.1612i	−1.35884	−	1.70393i
$141$	1.07173	−	4.69554i	0.0902556	−	0.395436i
$142$	0.229956	+	1.00750i	0.0192974	+	0.0845476i
$143$	12.3519	+	15.4888i	1.03292	+	1.29524i
$144$	3.81285			0.317738
$145$	17.0654	−	7.36414i	1.41721	−	0.611558i
$146$	−1.86803			−0.154600
$147$	4.61609	+	5.78839i	0.380728	+	0.477418i
$148$	2.77205	+	12.1451i	0.227861	+	0.998324i
$149$	2.08913	−	9.15309i	0.171149	−	0.749851i	−0.814379	−	0.580334i	$-0.802922\pi$
$149$	2.08913	−	9.15309i	0.171149	−	0.749851i	0.985527	−	0.169517i	$-0.0542208\pi$
$150$	0.763147	+	0.956956i	0.0623107	+	0.0781351i
$151$	12.2599	−	15.3734i	0.997693	−	1.25107i	0.0298388	−	0.999555i	$-0.490501\pi$
$151$	12.2599	−	15.3734i	0.997693	−	1.25107i	0.967854	−	0.251513i	$-0.0809280\pi$
$152$	−0.561803	−	2.46142i	−0.0455682	−	0.199647i
$153$	2.76785	−	1.33292i	0.223767	−	0.107761i
$154$	−2.58340	+	1.24410i	−0.208177	+	0.100253i
$155$	−3.47320	+	15.2171i	−0.278974	+	1.22227i
$156$	−8.23542	−	3.96597i	−0.659362	−	0.317532i
$157$	−2.61457			−0.208665			−0.104333	−	0.994542i	$-0.533271\pi$
$157$	−2.61457			−0.208665			−0.104333	+	0.994542i	$0.533271\pi$
$158$	−1.60122	−	0.771107i	−0.127386	−	0.0613460i
$159$	6.83931	−	8.57623i	0.542393	−	0.680139i
$160$	−4.47737	+	5.61445i	−0.353967	+	0.443861i
$161$	−1.48265	−	0.714006i	−0.116849	−	0.0562715i
$162$	0.177073			0.0139121
$163$	0.475531	+	0.229004i	0.0372465	+	0.0179370i	0.452414	−	0.891808i	$-0.350563\pi$
$163$	0.475531	+	0.229004i	0.0372465	+	0.0179370i	−0.415168	+	0.909745i	$0.636277\pi$
$164$	−0.863547	+	3.78345i	−0.0674317	+	0.295437i
$165$	−13.2680	+	6.38951i	−1.03291	+	0.497423i
$166$	1.13242	−	0.545344i	0.0878928	−	0.0423269i
$167$	3.34870	+	14.6716i	0.259131	+	1.13533i	0.922183	+	0.386753i	$0.126403\pi$
$167$	3.34870	+	14.6716i	0.259131	+	1.13533i	−0.663053	+	0.748573i	$0.730740\pi$
$168$	1.66287	−	2.08518i	0.128293	−	0.160875i
$169$	5.33610	+	6.69126i	0.410469	+	0.514712i
$170$	−0.417786	+	1.83044i	−0.0320427	+	0.140388i
$171$	0.799448	+	3.50261i	0.0611353	+	0.267851i
$172$	0.308304	+	0.386601i	0.0235079	+	0.0294780i
$173$	0.103233			0.00784865			0.00392433	−	0.999992i	$-0.498751\pi$
$173$	0.103233			0.00784865			0.00392433	+	0.999992i	$0.498751\pi$
$174$	0.563161	+	0.769504i	0.0426931	+	0.0583360i
$175$	−26.2339			−1.98310
$176$	−10.1432	−	12.7192i	−0.764572	−	0.958743i
$177$	1.35068	+	5.91772i	0.101523	+	0.444803i
$178$	0.550695	−	2.41275i	0.0412764	−	0.180844i
$179$	−2.52461	−	3.16576i	−0.188698	−	0.236620i	0.678479	−	0.734620i	$-0.262640\pi$
$179$	−2.52461	−	3.16576i	−0.188698	−	0.236620i	−0.867177	+	0.498000i	$0.834068\pi$
$180$	4.23639	−	5.31227i	0.315762	−	0.395953i
$181$	2.56394	+	11.2334i	0.190576	+	0.834969i	0.976305	+	0.216398i	$0.0694309\pi$
$181$	2.56394	+	11.2334i	0.190576	+	0.834969i	−0.785729	+	0.618571i	$0.787712\pi$
$182$	−2.81129	+	1.35385i	−0.208387	+	0.100354i
$183$	−3.41624	+	1.64517i	−0.252536	+	0.121615i
$184$	−0.0678043	+	0.297070i	−0.00499860	+	0.0219003i
$185$	19.6776	+	9.47621i	1.44672	+	0.696705i
$186$	−0.800776			−0.0587158
$187$	−11.8097	−	5.68723i	−0.863607	−	0.415891i
$188$	5.91166	−	7.41299i	0.431152	−	0.540648i
$189$	−2.36628	+	2.96722i	−0.172121	+	0.215833i
$190$	−1.97824	−	0.952672i	−0.143517	−	0.0691141i
$191$	1.55942			0.112836			0.0564179	−	0.998407i	$-0.482032\pi$
$191$	1.55942			0.112836			0.0564179	+	0.998407i	$0.482032\pi$
$192$	6.53859	+	3.14882i	0.471882	+	0.227246i
$193$	−2.97677	+	13.0421i	−0.214273	+	0.938790i	0.747354	+	0.664427i	$0.231324\pi$
$193$	−2.97677	+	13.0421i	−0.214273	+	0.938790i	−0.961626	+	0.274363i	$0.911533\pi$
$194$	2.28496	−	1.10038i	0.164050	−	0.0790024i
$195$	−14.4384	+	6.95314i	−1.03395	+	0.497925i
$196$	3.24327	+	14.2097i	0.231662	+	1.01498i
$197$	−7.96548	+	9.98840i	−0.567517	+	0.711644i	−0.979927	−	0.199354i	$-0.936116\pi$
$197$	−7.96548	+	9.98840i	−0.567517	+	0.711644i	0.412411	+	0.910998i	$0.364687\pi$
$198$	−0.471060	−	0.590690i	−0.0334768	−	0.0419785i
$199$	−1.96309	+	8.60088i	−0.139160	+	0.609700i	0.856460	+	0.516213i	$0.172659\pi$
$199$	−1.96309	+	8.60088i	−0.139160	+	0.609700i	−0.995620	+	0.0934873i	$0.970199\pi$
$200$	1.08092	+	4.73580i	0.0764323	+	0.334872i
$201$	−3.28401	−	4.11802i	−0.231636	−	0.290463i
$202$	0.144570			0.0101719
$203$	−20.4203	−	0.846200i	−1.43322	−	0.0593916i
$204$	6.04783			0.423433
$205$	4.24205	+	5.31937i	0.296278	+	0.371521i
$206$	0.195355	+	0.855906i	0.0136110	+	0.0596338i
$207$	0.0964858	−	0.422732i	0.00670623	−	0.0293819i
$208$	−11.0379	−	13.8411i	−0.765344	−	0.959711i
$209$	9.55749	−	11.9847i	0.661105	−	0.829000i
$210$	−0.516128	−	2.26131i	−0.0356162	−	0.156045i
$211$	13.5356	−	6.51841i	0.931830	−	0.448746i	0.0945500	−	0.995520i	$-0.469859\pi$
$211$	13.5356	−	6.51841i	0.931830	−	0.448746i	0.837280	+	0.546774i	$0.184144\pi$
$212$	19.4563	−	9.36966i	1.33626	−	0.643511i
$213$	1.29865	−	5.68976i	0.0889821	−	0.389856i
$214$	1.84040	+	0.886289i	0.125807	+	0.0605854i
$215$	0.866924			0.0591237
$216$	0.633146	+	0.304907i	0.0430801	+	0.0207463i
$217$	10.7010	−	13.4186i	0.726432	−	0.910917i
$218$	0.954675	−	1.19712i	0.0646587	−	0.0810795i
$219$	9.50480	+	4.57727i	0.642275	+	0.309303i
$220$	−28.9909			−1.95457
$221$	−12.8514	−	6.18891i	−0.864479	−	0.416311i
$222$	−0.249336	+	1.09241i	−0.0167343	+	0.0733179i
$223$	−21.5743	+	10.3896i	−1.44472	+	0.695740i	−0.981669	−	0.190592i	$-0.938959\pi$
$223$	−21.5743	+	10.3896i	−1.44472	+	0.695740i	−0.463050	+	0.886332i	$0.653245\pi$
$224$	7.11444	−	3.42613i	0.475353	−	0.228918i
$225$	−1.53815	−	6.73907i	−0.102543	−	0.449271i
$226$	0.837463	−	1.05015i	0.0557072	−	0.0698546i
$227$	−3.21628	−	4.03308i	−0.213472	−	0.267685i	0.663554	−	0.748128i	$-0.269047\pi$
$227$	−3.21628	−	4.03308i	−0.213472	−	0.267685i	−0.877026	+	0.480443i	$0.840476\pi$
$228$	−1.57383	+	6.89539i	−0.104229	+	0.456659i
$229$	1.80280	+	7.89857i	0.119132	+	0.521952i	0.998915	+	0.0465760i	$0.0148310\pi$
$229$	1.80280	+	7.89857i	0.119132	+	0.521952i	−0.879783	+	0.475376i	$0.842312\pi$
$230$	0.165224	+	0.207184i	0.0108945	+	0.0136613i
$231$	16.1931			1.06543
$232$	0.688620	+	3.72118i	0.0452101	+	0.244308i
$233$	24.5153			1.60605			0.803027	−	0.595943i	$-0.203222\pi$
$233$	24.5153			1.60605			0.803027	+	0.595943i	$0.203222\pi$
$234$	−0.512613	−	0.642796i	−0.0335106	−	0.0420209i
$235$	−3.69899	−	16.2063i	−0.241295	−	1.05718i
$236$	−2.65901	+	11.6499i	−0.173087	+	0.758343i
$237$	6.25776	+	7.84699i	0.406485	+	0.509716i
$238$	1.28721	−	1.61411i	0.0834374	−	0.104627i
$239$	6.21741	+	27.2402i	0.402171	+	1.76202i	0.618580	+	0.785722i	$0.287708\pi$
$239$	6.21741	+	27.2402i	0.402171	+	1.76202i	−0.216410	+	0.976303i	$0.569435\pi$
$240$	11.8566	−	5.70982i	0.765339	−	0.368568i
$241$	−3.57537	+	1.72181i	−0.230310	+	0.110911i	−0.545480	−	0.838124i	$-0.683653\pi$
$241$	−3.57537	+	1.72181i	−0.230310	+	0.110911i	0.315170	+	0.949035i	$0.397938\pi$
$242$	−0.283893	+	1.24382i	−0.0182494	+	0.0799557i
$243$	−0.900969	−	0.433884i	−0.0577972	−	0.0278337i
$244$	−7.46459			−0.477871
$245$	23.0225	+	11.0871i	1.47086	+	0.708327i
$246$	−0.217635	+	0.272906i	−0.0138759	+	0.0173998i
$247$	10.4006	−	13.0419i	0.661773	−	0.829837i
$248$	−2.86328	−	1.37888i	−0.181818	−	0.0875591i
$249$	−7.09816			−0.449828
$250$	1.05301	+	0.507104i	0.0665983	+	0.0320721i
$251$	7.03374	−	30.8168i	0.443965	−	1.94514i	0.154218	−	0.988037i	$-0.450714\pi$
$251$	7.03374	−	30.8168i	0.443965	−	1.94514i	0.289748	−	0.957103i	$-0.406429\pi$
$252$	−6.73152	+	3.24173i	−0.424046	+	0.204210i
$253$	−1.66685	+	0.802714i	−0.104794	+	0.0504662i
$254$	−0.0486499	−	0.213149i	−0.00305256	−	0.0133742i
$255$	6.61090	−	8.28981i	0.413991	−	0.519128i
$256$	8.44840	+	10.5940i	0.528025	+	0.662122i
$257$	0.901269	−	3.94872i	0.0562196	−	0.246314i	−0.939008	−	0.343895i	$-0.888253\pi$
$257$	0.901269	−	3.94872i	0.0562196	−	0.246314i	0.995228	+	0.0975812i	$0.0311106\pi$
$258$	0.00989702	+	0.0433617i	0.000616161	+	0.00269958i
$259$	−14.9736	−	18.7764i	−0.930417	−	1.16671i
$260$	−31.5483			−1.95654
$261$	−0.979909	−	5.29526i	−0.0606549	−	0.327768i
$262$	−0.707518			−0.0437106
$263$	−8.91597	−	11.1803i	−0.549782	−	0.689405i	0.426850	−	0.904322i	$-0.359623\pi$
$263$	−8.91597	−	11.1803i	−0.549782	−	0.689405i	−0.976632	+	0.214917i	$0.931052\pi$
$264$	−0.667206	−	2.92322i	−0.0410637	−	0.179912i
$265$	8.42468	−	36.9109i	0.517524	−	2.26742i
$266$	1.50534	+	1.88764i	0.0922986	+	0.115739i
$267$	−8.71402	+	10.9270i	−0.533289	+	0.668723i
$268$	−2.30735	−	10.1092i	−0.140944	−	0.617515i
$269$	−19.3865	+	9.33606i	−1.18202	+	0.569230i	−0.918498	−	0.395425i	$-0.870597\pi$
$269$	−19.3865	+	9.33606i	−1.18202	+	0.569230i	−0.263519	+	0.964654i	$0.584883\pi$
$270$	0.550631	−	0.265170i	0.0335103	−	0.0161377i
$271$	4.40370	−	19.2939i	0.267506	−	1.17202i	−0.645399	−	0.763846i	$-0.723309\pi$
$271$	4.40370	−	19.2939i	0.267506	−	1.17202i	0.912904	−	0.408174i	$-0.133834\pi$
$272$	10.5534	+	5.08225i	0.639894	+	0.308157i
$273$	17.6216			1.06651
$274$	−2.65691	−	1.27950i	−0.160510	−	0.0772974i
$275$	−18.3887	+	23.0587i	−1.10888	+	1.39049i
$276$	0.532218	−	0.667380i	0.0320357	−	0.0401715i
$277$	−5.04862	−	2.43129i	−0.303342	−	0.146082i	0.276020	−	0.961152i	$-0.410984\pi$
$277$	−5.04862	−	2.43129i	−0.303342	−	0.146082i	−0.579363	+	0.815070i	$0.696699\pi$
$278$	1.46458			0.0878397
$279$	4.07445	+	1.96215i	0.243931	+	0.117471i
$280$	2.04833	−	8.97432i	0.122411	−	0.536318i
$281$	9.74719	−	4.69400i	0.581469	−	0.280021i	−0.119939	−	0.992781i	$-0.538270\pi$
$281$	9.74719	−	4.69400i	0.581469	−	0.280021i	0.701407	+	0.712761i	$0.252555\pi$
$282$	0.768377	−	0.370031i	0.0457562	−	0.0220350i
$283$	1.65442	+	7.24849i	0.0983451	+	0.430878i	0.999999	−	0.00158078i	$-0.000503178\pi$
$283$	1.65442	+	7.24849i	0.0983451	+	0.430878i	−0.901654	+	0.432459i	$0.857646\pi$
$284$	7.16339	−	8.98260i	0.425069	−	0.533019i
$285$	7.73121	+	9.69464i	0.457958	+	0.574261i
$286$	−0.780596	+	3.42001i	−0.0461576	+	0.202230i
$287$	−1.66477	−	7.29384i	−0.0982683	−	0.430542i
$288$	1.29725	+	1.62670i	0.0764413	+	0.0958543i
$289$	−7.56234			−0.444843
$290$	2.90357	+	1.54953i	0.170504	+	0.0909916i
$291$	−14.3224			−0.839595
$292$	12.9488	+	16.2373i	0.757772	+	0.950216i
$293$	−2.76291	−	12.1051i	−0.161411	−	0.707186i	−0.989252	−	0.146223i	$-0.953288\pi$
$293$	−2.76291	−	12.1051i	−0.161411	−	0.707186i	0.827841	−	0.560963i	$-0.189569\pi$
$294$	−0.291720	+	1.27811i	−0.0170135	+	0.0745409i
$295$	13.0620	+	16.3793i	0.760500	+	0.953637i
$296$	−2.77259	+	3.47672i	−0.161153	+	0.202080i
$297$	0.949437	+	4.15975i	0.0550919	+	0.241373i
$298$	1.49781	−	0.721307i	0.0867658	−	0.0417842i
$299$	−1.81389	+	0.873523i	−0.104900	+	0.0505172i
$300$	3.02807	−	13.2668i	0.174826	−	0.765961i
$301$	−0.858870	−	0.413610i	−0.0495045	−	0.0238401i
$302$	3.48183			0.200357
$303$	−0.735591	−	0.354242i	−0.0422586	−	0.0203507i
$304$	−8.54080	+	10.7098i	−0.489849	+	0.614251i
$305$	−8.15957	+	10.2318i	−0.467215	+	0.585870i
$306$	0.490110	+	0.236025i	0.0280177	+	0.0134926i
$307$	24.0387			1.37196			0.685981	−	0.727620i	$-0.259373\pi$
$307$	24.0387			1.37196			0.685981	+	0.727620i	$0.259373\pi$
$308$	28.7216	+	13.8316i	1.63656	+	0.788128i
$309$	1.10325	−	4.83364i	0.0627615	−	0.274976i
$310$	−2.49012	+	1.19918i	−0.141429	+	0.0681088i
$311$	28.1593	−	13.5608i	1.59677	−	0.768963i	0.597314	−	0.802007i	$-0.296234\pi$
$311$	28.1593	−	13.5608i	1.59677	−	0.768963i	0.999454	+	0.0330440i	$0.0105201\pi$
$312$	−0.726062	−	3.18108i	−0.0411051	−	0.180093i
$313$	−13.1250	+	16.4582i	−0.741867	+	0.930272i	−0.999351	−	0.0360104i	$-0.988535\pi$
$313$	−13.1250	+	16.4582i	−0.741867	+	0.930272i	0.257484	+	0.966283i	$0.417106\pi$
$314$	−0.288656	−	0.361964i	−0.0162898	−	0.0204268i
$315$	−2.91478	+	12.7705i	−0.164229	+	0.719536i
$316$	4.39671	+	19.2633i	0.247334	+	1.08364i
$317$	−9.75852	−	12.2368i	−0.548093	−	0.687287i	0.428214	−	0.903677i	$-0.359143\pi$
$317$	−9.75852	−	12.2368i	−0.548093	−	0.687287i	−0.976307	+	0.216390i	$0.930572\pi$
$318$	1.94238			0.108923
$319$	−15.0574	+	17.3556i	−0.843055	+	0.971728i
$320$	25.0480			1.40023
$321$	−7.19249	−	9.01910i	−0.401446	−	0.503397i
$322$	−0.0648412	−	0.284088i	−0.00361346	−	0.0158316i
$323$	−2.45597	+	10.7603i	−0.136654	+	0.598718i
$324$	−1.22743	−	1.53915i	−0.0681906	−	0.0855083i
$325$	−20.0108	+	25.0928i	−1.11000	+	1.39190i
$326$	0.0207966	+	0.0911157i	0.00115181	+	0.00504643i
$327$	−7.79084	+	3.75187i	−0.430835	+	0.207479i
$328$	−1.24811	+	0.601056i	−0.0689151	+	0.0331878i
$329$	−4.06743	+	17.8206i	−0.224244	+	0.982479i
$330$	−2.34939	−	1.13141i	−0.129330	−	0.0622820i
$331$	−19.4595			−1.06959			−0.534796	−	0.844981i	$-0.679612\pi$
$331$	−19.4595			−1.06959			−0.534796	+	0.844981i	$0.679612\pi$
$332$	−12.5899	−	6.06299i	−0.690962	−	0.332750i
$333$	3.94541	−	4.94738i	0.216207	−	0.271115i
$334$	−1.66145	+	2.08339i	−0.0909104	+	0.113998i
$335$	−16.3789	−	7.88765i	−0.894873	−	0.430948i
$336$	−14.4706			−0.789435
$337$	−18.1797	−	8.75489i	−0.990312	−	0.476909i	−0.132672	−	0.991160i	$-0.542356\pi$
$337$	−18.1797	−	8.75489i	−0.990312	−	0.476909i	−0.857640	+	0.514251i	$0.828070\pi$
$338$	−0.337223	+	1.47747i	−0.0183425	+	0.0803638i
$339$	−6.83431	+	3.29123i	−0.371189	+	0.178755i
$340$	18.8065	−	9.05675i	1.01993	−	0.491171i
$341$	−4.29364	−	18.8117i	−0.232514	−	1.01871i
$342$	−0.396643	+	0.497375i	−0.0214480	+	0.0268950i
$343$	−0.955090	−	1.19764i	−0.0515700	−	0.0646667i
$344$	−0.0392777	+	0.172087i	−0.00211771	+	0.00927831i
$345$	−0.333014	−	1.45903i	−0.0179289	−	0.0785515i
$346$	0.0113972	+	0.0142917i	0.000612719	+	0.000768325i
$347$	0.788354			0.0423211			0.0211605	−	0.999776i	$-0.493264\pi$
$347$	0.788354			0.0423211			0.0211605	+	0.999776i	$0.493264\pi$
$348$	2.78496	−	10.2291i	0.149290	−	0.548340i
$349$	20.9417			1.12098			0.560491	−	0.828161i	$-0.310613\pi$
$349$	20.9417			1.12098			0.560491	+	0.828161i	$0.310613\pi$
$350$	−2.89630	−	3.63185i	−0.154814	−	0.194131i
$351$	1.03319	+	4.52669i	0.0551475	+	0.241617i
$352$	1.97543	−	8.65491i	0.105291	−	0.461308i
$353$	−22.5006	−	28.2149i	−1.19759	−	1.50173i	−0.816658	−	0.577122i	$-0.804176\pi$
$353$	−22.5006	−	28.2149i	−1.19759	−	1.50173i	−0.380929	−	0.924604i	$-0.624396\pi$
$354$	−0.670136	+	0.840324i	−0.0356173	+	0.0446627i
$355$	−4.48220	−	19.6378i	−0.237891	−	1.04227i
$356$	−24.7894	+	11.9380i	−1.31384	+	0.632710i
$357$	−10.5046	+	5.05873i	−0.555960	+	0.267736i
$358$	0.159547	−	0.699020i	0.00843230	−	0.0369443i
$359$	−16.7787	−	8.08019i	−0.885545	−	0.426456i	−0.0648984	−	0.997892i	$-0.520672\pi$
$359$	−16.7787	−	8.08019i	−0.885545	−	0.426456i	−0.820647	+	0.571436i	$0.806387\pi$
$360$	2.42545			0.127833
$361$	5.48925	+	2.64349i	0.288908	+	0.139131i
$362$	−1.27209	+	1.59515i	−0.0668596	+	0.0838393i
$363$	4.49223	−	5.63308i	0.235781	−	0.295660i
$364$	31.2552	+	15.0517i	1.63822	+	0.788923i
$365$	36.4110			1.90584
$366$	−0.604923	−	0.291315i	−0.0316198	−	0.0152273i
$367$	−3.58975	+	15.7277i	−0.187383	+	0.820981i	0.790606	+	0.612325i	$0.209766\pi$
$367$	−3.58975	+	15.7277i	−0.187383	+	0.820981i	−0.977989	+	0.208655i	$0.933091\pi$
$368$	1.48954	−	0.717325i	0.0776477	−	0.0373932i
$369$	1.77606	−	0.855305i	0.0924579	−	0.0445254i
$370$	0.860566	+	3.77038i	0.0447387	+	0.196013i
$371$	−25.9566	+	32.5486i	−1.34760	+	1.68984i
$372$	5.55081	+	6.96050i	0.287796	+	0.360885i
$373$	−0.252766	+	1.10744i	−0.0130877	+	0.0573410i	−0.981050	−	0.193754i	$-0.937934\pi$
$373$	−0.252766	+	1.10744i	−0.0130877	+	0.0573410i	0.967962	+	0.251095i	$0.0807907\pi$
$374$	−0.516476	−	2.26283i	−0.0267063	−	0.117008i
$375$	−4.11530	−	5.16042i	−0.212513	−	0.266483i
$376$	3.38460			0.174547
$377$	−16.3857	+	18.8866i	−0.843906	+	0.972709i
$378$	−0.672028			−0.0345654
$379$	18.8590	+	23.6485i	0.968723	+	1.21474i	0.976664	+	0.214772i	$0.0689008\pi$
$379$	18.8590	+	23.6485i	0.968723	+	1.21474i	−0.00794116	+	0.999968i	$0.502528\pi$
$380$	5.43196	+	23.7990i	0.278654	+	1.22086i
$381$	−0.274745	+	1.20374i	−0.0140756	+	0.0616693i
$382$	0.172165	+	0.215888i	0.00880873	+	0.0110458i
$383$	−10.9608	+	13.7443i	−0.560068	+	0.702303i	−0.978570	−	0.205912i	$-0.933984\pi$
$383$	−10.9608	+	13.7443i	−0.560068	+	0.702303i	0.418502	+	0.908216i	$0.362555\pi$
$384$	1.21192	+	5.30978i	0.0618456	+	0.270963i
$385$	50.3547	−	24.2495i	2.56631	−	1.23587i
$386$	−2.13420	+	1.02778i	−0.108628	+	0.0523125i
$387$	0.0558924	−	0.244881i	0.00284117	−	0.0124480i
$388$	−25.4035	−	12.2337i	−1.28967	−	0.621071i
$389$	38.5442			1.95427			0.977134	−	0.212625i	$-0.0682014\pi$
$389$	38.5442			1.95427			0.977134	+	0.212625i	$0.0682014\pi$
$390$	−2.55664	−	1.23121i	−0.129460	−	0.0623448i
$391$	0.830527	−	1.04145i	0.0420016	−	0.0526683i
$392$	−3.24390	+	4.06772i	−0.163842	+	0.205451i
$393$	3.59995	+	1.73364i	0.181593	+	0.0874507i
$394$	−2.26222			−0.113969
$395$	31.2103	+	15.0301i	1.57036	+	0.756247i
$396$	−1.86910	+	8.18908i	−0.0939260	+	0.411517i
$397$	18.9872	−	9.14373i	0.952938	−	0.458911i	0.108223	−	0.994127i	$-0.465484\pi$
$397$	18.9872	−	9.14373i	0.952938	−	0.458911i	0.844715	+	0.535216i	$0.179770\pi$
$398$	−1.40745	+	0.677790i	−0.0705489	+	0.0339745i
$399$	−3.03407	−	13.2931i	−0.151894	−	0.665489i
$400$	16.4326	−	20.6059i	0.821631	−	1.03029i
$401$	−21.6506	−	27.1490i	−1.08118	−	1.35576i	−0.930130	−	0.367231i	$-0.880306\pi$
$401$	−21.6506	−	27.1490i	−1.08118	−	1.35576i	−0.151051	−	0.988526i	$-0.548266\pi$
$402$	0.207538	−	0.909283i	0.0103511	−	0.0453509i
$403$	−4.67239	−	20.4711i	−0.232748	−	1.01974i
$404$	−1.00213	−	1.25663i	−0.0498578	−	0.0625197i
$405$	−3.45143			−0.171503
$406$	−2.13732	−	2.92043i	−0.106073	−	0.144939i
$407$	−26.9996			−1.33832
$408$	1.34603	+	1.68787i	0.0666385	+	0.0835621i
$409$	0.697528	+	3.05607i	0.0344905	+	0.151113i	0.989241	−	0.146295i	$-0.0467349\pi$
$409$	0.697528	+	3.05607i	0.0344905	+	0.151113i	−0.954750	+	0.297408i	$0.903878\pi$
$410$	−0.268083	+	1.17455i	−0.0132397	+	0.0580068i
$411$	10.3835	+	13.0205i	0.512181	+	0.642255i
$412$	6.08553	−	7.63102i	0.299813	−	0.375953i
$413$	−5.12612	−	22.4590i	−0.252240	−	1.10514i
$414$	0.0691757	−	0.0333133i	0.00339980	−	0.00163726i
$415$	−22.0727	+	10.6296i	−1.08350	+	0.521788i
$416$	2.14968	−	9.41838i	0.105397	−	0.461774i
$417$	−7.45197	−	3.58868i	−0.364925	−	0.175738i
$418$	2.71435			0.132763
$419$	7.82316	+	3.76744i	0.382186	+	0.184051i	0.615105	−	0.788445i	$-0.289113\pi$
$419$	7.82316	+	3.76744i	0.382186	+	0.184051i	−0.232919	+	0.972496i	$0.574828\pi$
$420$	−16.0780	+	20.1612i	−0.784526	+	0.983764i
$421$	17.6965	−	22.1907i	0.862475	−	1.08151i	−0.133426	−	0.991059i	$-0.542598\pi$
$421$	17.6965	−	22.1907i	0.862475	−	1.08151i	0.995901	−	0.0904508i	$-0.0288308\pi$
$422$	2.39679	+	1.15423i	0.116674	+	0.0561871i
$423$	−4.81629			−0.234176
$424$	6.94523	+	3.34465i	0.337290	+	0.162430i
$425$	4.72531	−	20.7029i	0.229211	−	1.00424i
$426$	0.931071	−	0.448380i	0.0451106	−	0.0217241i
$427$	12.9653	−	6.24378i	0.627437	−	0.302158i
$428$	−5.05346	−	22.1406i	−0.244268	−	1.07021i
$429$	12.3519	−	15.4888i	0.596355	−	0.747805i
$430$	0.0957110	+	0.120018i	0.00461560	+	0.00578777i
$431$	−0.0183247	+	0.0802859i	−0.000882671	+	0.00386723i	−0.975367	−	0.220587i	$-0.929203\pi$
$431$	−0.0183247	+	0.0802859i	−0.000882671	+	0.00386723i	0.974485	+	0.224454i	$0.0720599\pi$
$432$	−0.848440	−	3.71726i	−0.0408206	−	0.178847i
$433$	0.788400	+	0.988623i	0.0378881	+	0.0475102i	0.800415	−	0.599447i	$-0.204613\pi$
$433$	0.788400	+	0.988623i	0.0378881	+	0.0475102i	−0.762526	+	0.646957i	$0.776041\pi$
$434$	3.03912			0.145882
$435$	−10.9769	−	14.9989i	−0.526303	−	0.719141i
$436$	−17.0232			−0.815265
$437$	0.971272	+	1.21794i	0.0464623	+	0.0582618i
$438$	0.415677	+	1.82120i	0.0198618	+	0.0870202i
$439$	−6.49242	+	28.4451i	−0.309866	+	1.35761i	0.544857	+	0.838529i	$0.316584\pi$
$439$	−6.49242	+	28.4451i	−0.309866	+	1.35761i	−0.854723	+	0.519084i	$0.826273\pi$
$440$	−6.45234	−	8.09098i	−0.307603	−	0.385722i
$441$	4.61609	−	5.78839i	0.219814	−	0.275638i
$442$	−0.562035	−	2.46244i	−0.0267333	−	0.117126i
$443$	16.4847	−	7.93860i	0.783211	−	0.377174i	0.000849826	−	1.00000i	$-0.499729\pi$
$443$	16.4847	−	7.93860i	0.783211	−	0.377174i	0.782361	+	0.622825i	$0.214015\pi$
$444$	11.2238	−	5.40509i	0.532658	−	0.256514i
$445$	−10.7339	+	47.0285i	−0.508837	+	2.22936i
$446$	−3.82021	−	1.83972i	−0.180892	−	0.0871131i
$447$	−9.38848			−0.444060
$448$	−24.8153	−	11.9504i	−1.17241	−	0.564605i
$449$	−6.63592	+	8.32119i	−0.313169	+	0.392701i	−0.913358	−	0.407157i	$-0.866520\pi$
$449$	−6.63592	+	8.32119i	−0.313169	+	0.392701i	0.600190	+	0.799858i	$0.295092\pi$
$450$	0.763147	−	0.956956i	0.0359751	−	0.0451113i
$451$	−7.57796	−	3.64935i	−0.356832	−	0.171841i
$452$	−14.9332			−0.702397
$453$	−17.7160	−	8.53158i	−0.832370	−	0.400848i
$454$	0.203257	−	0.890529i	0.00953934	−	0.0417946i
$455$	54.7966	−	26.3886i	2.56890	−	1.23712i
$456$	−2.27469	+	1.09543i	−0.106522	+	0.0512984i
$457$	−6.72070	−	29.4453i	−0.314381	−	1.37739i	−0.847249	−	0.531196i	$-0.821743\pi$
$457$	−6.72070	−	29.4453i	−0.314381	−	1.37739i	0.532868	−	0.846199i	$-0.321114\pi$
$458$	−0.894452	+	1.12161i	−0.0417950	+	0.0524093i
$459$	−1.91541	−	2.40185i	−0.0894036	−	0.112109i
$460$	0.655586	−	2.87231i	0.0305669	−	0.133922i
$461$	8.11297	+	35.5452i	0.377859	+	1.65551i	0.704011	+	0.710189i	$0.251391\pi$
$461$	8.11297	+	35.5452i	0.377859	+	1.65551i	−0.326152	+	0.945317i	$0.605752\pi$
$462$	1.78777	+	2.24179i	0.0831747	+	0.104298i
$463$	18.1919			0.845450			0.422725	−	0.906258i	$-0.361074\pi$
$463$	18.1919			0.845450			0.422725	+	0.906258i	$0.361074\pi$
$464$	13.4557	−	15.5094i	0.624666	−	0.720006i
$465$	15.6084			0.723823
$466$	2.70657	+	3.39393i	0.125379	+	0.157221i
$467$	−2.20583	−	9.66436i	−0.102074	−	0.447213i	−0.999975	−	0.00701766i	$-0.997766\pi$
$467$	−2.20583	−	9.66436i	−0.102074	−	0.447213i	0.897902	−	0.440196i	$-0.145091\pi$
$468$	−2.03398	+	8.91146i	−0.0940208	+	0.411932i
$469$	12.4635	+	15.6287i	0.575511	+	0.721669i
$470$	1.83524	−	2.30132i	0.0846533	−	0.106152i
$471$	0.581796	+	2.54902i	0.0268078	+	0.117452i
$472$	−3.84313	+	1.85076i	−0.176895	+	0.0851880i
$473$	−0.965577	+	0.464997i	−0.0443973	+	0.0213806i
$474$	−0.395469	+	1.73266i	−0.0181645	+	0.0795838i
$475$	22.3746	+	10.7751i	1.02662	+	0.494394i
$476$	−22.9528			−1.05204
$477$	−9.88310	−	4.75945i	−0.452516	−	0.217920i
$478$	−3.08475	+	3.86815i	−0.141093	+	0.176925i
$479$	26.6415	−	33.4074i	1.21728	−	1.52642i	0.439027	−	0.898474i	$-0.355323\pi$
$479$	26.6415	−	33.4074i	1.21728	−	1.52642i	0.778255	−	0.627949i	$-0.216105\pi$
$480$	6.46999	+	3.11578i	0.295313	+	0.142215i
$481$	−29.3813			−1.33967
$482$	−0.633101	−	0.304885i	−0.0288369	−	0.0138871i
$483$	−0.366184	+	1.60436i	−0.0166619	+	0.0730007i
$484$	12.7794	−	6.15423i	0.580881	−	0.279738i
$485$	−44.5375	+	21.4481i	−2.02234	+	0.973908i
$486$	−0.0394024	−	0.172633i	−0.00178733	−	0.00783080i
$487$	−15.8593	+	19.8869i	−0.718654	+	0.901163i	−0.998261	−	0.0589511i	$-0.981224\pi$
$487$	−15.8593	+	19.8869i	−0.718654	+	0.901163i	0.279607	+	0.960115i	$0.409796\pi$
$488$	−1.66135	−	2.08327i	−0.0752059	−	0.0943052i
$489$	0.117446	−	0.514567i	0.00531111	−	0.0232695i
$490$	1.00685	+	4.41131i	0.0454850	+	0.199283i
$491$	19.5910	+	24.5664i	0.884131	+	1.10867i	0.993406	+	0.114654i	$0.0365759\pi$
$491$	19.5910	+	24.5664i	0.884131	+	1.10867i	−0.109274	+	0.994012i	$0.534853\pi$
$492$	3.88074			0.174957
$493$	4.34594	−	15.9626i	0.195731	−	0.718920i
$494$	2.95379			0.132897
$495$	9.18171	+	11.5135i	0.412687	+	0.517493i
$496$	3.83690	+	16.8106i	0.172282	+	0.754817i
$497$	−4.92865	+	21.5938i	−0.221080	+	0.968616i
$498$	−0.783658	−	0.982676i	−0.0351166	−	0.0440348i
$499$	−4.33114	+	5.43107i	−0.193888	+	0.243128i	−0.869267	−	0.494343i	$-0.835409\pi$
$499$	−4.33114	+	5.43107i	−0.193888	+	0.243128i	0.675379	+	0.737471i	$0.263980\pi$
$500$	−2.89141	−	12.6681i	−0.129308	−	0.566535i
$501$	13.5586	−	6.52949i	0.605755	−	0.291716i
$502$	5.04286	−	2.42851i	0.225074	−	0.108390i
$503$	−5.90822	+	25.8856i	−0.263434	+	1.15418i	0.654063	+	0.756440i	$0.273063\pi$
$503$	−5.90822	+	25.8856i	−0.263434	+	1.15418i	−0.917497	+	0.397742i	$0.869794\pi$
$504$	−2.40292	−	1.15719i	−0.107035	−	0.0515452i
$505$	−2.81790			−0.125395
$506$	−0.295154	−	0.142139i	−0.0131212	−	0.00631884i
$507$	5.33610	−	6.69126i	0.236985	−	0.297169i
$508$	−1.51550	+	1.90038i	−0.0672395	+	0.0843156i
$509$	1.24379	+	0.598977i	0.0551299	+	0.0265492i	0.461246	−	0.887273i	$-0.347403\pi$
$509$	1.24379	+	0.598977i	0.0551299	+	0.0265492i	−0.406116	+	0.913822i	$0.633117\pi$
$510$	1.87751			0.0831377
$511$	−36.0727	−	17.3717i	−1.59576	−	0.768479i
$512$	−2.95775	+	12.9588i	−0.130715	+	0.572702i
$513$	3.23690	−	1.55881i	0.142913	−	0.0688230i
$514$	0.646167	−	0.311178i	0.0285012	−	0.0137255i
$515$	−3.80778	−	16.6830i	−0.167791	−	0.735140i
$516$	0.308304	−	0.386601i	0.0135723	−	0.0170191i
$517$	12.8126	+	16.0665i	0.563498	+	0.706604i
$518$	0.946282	−	4.14593i	0.0415773	−	0.182162i
$519$	−0.0229715	−	0.100645i	−0.00100834	−	0.00441781i
$520$	−7.02152	−	8.80471i	−0.307914	−	0.386112i
$521$	8.46722			0.370956			0.185478	−	0.982648i	$-0.440617\pi$
$521$	8.46722			0.370956			0.185478	+	0.982648i	$0.440617\pi$
$522$	0.624896	−	0.720272i	0.0273510	−	0.0315255i
$523$	4.74716			0.207579			0.103789	−	0.994599i	$-0.466903\pi$
$523$	4.74716			0.207579			0.103789	+	0.994599i	$0.466903\pi$
$524$	4.90437	+	6.14988i	0.214248	+	0.268659i
$525$	5.83760	+	25.5762i	0.254774	+	1.11624i
$526$	0.563458	−	2.46867i	0.0245679	−	0.107639i
$527$	8.66206	+	10.8619i	0.377325	+	0.473151i
$528$	−10.1432	+	12.7192i	−0.441426	+	0.553531i
$529$	5.07614	+	22.2400i	0.220702	+	0.966958i
$530$	6.04009	−	2.90876i	0.262365	−	0.126348i
$531$	5.46880	−	2.63363i	0.237326	−	0.114290i
$532$	5.97301	−	26.1695i	0.258963	−	1.13459i
$533$	−8.24643	−	3.97127i	−0.357193	−	0.172015i
$534$	−2.47480			−0.107095
$535$	−35.8723	−	17.2752i	−1.55089	−	0.746871i
$536$	2.30780	−	2.89389i	0.0996818	−	0.124997i
$537$	−2.52461	+	3.16576i	−0.108945	+	0.136613i
$538$	−3.43282	−	1.65316i	−0.148000	−	0.0712728i
$539$	−31.5893			−1.36065
$540$	−6.12176	−	2.94808i	−0.263439	−	0.126865i
$541$	−0.543856	+	2.38279i	−0.0233822	+	0.102444i	−0.985273	−	0.170992i	$-0.945303\pi$
$541$	−0.543856	+	2.38279i	−0.0233822	+	0.102444i	0.961890	+	0.273436i	$0.0881601\pi$
$542$	3.15725	−	1.52045i	0.135615	−	0.0653089i
$543$	10.3812	−	4.99932i	0.445499	−	0.214541i
$544$	1.42232	+	6.23160i	0.0609816	+	0.267178i
$545$	−18.6081	+	23.3339i	−0.797085	+	0.999513i
$546$	1.94547	+	2.43955i	0.0832586	+	0.104403i
$547$	−1.37369	+	6.01855i	−0.0587350	+	0.257335i	−0.995768	−	0.0919072i	$-0.970704\pi$
$547$	−1.37369	+	6.01855i	−0.0587350	+	0.257335i	0.937033	+	0.349242i	$0.113561\pi$
$548$	7.29548	+	31.9636i	0.311647	+	1.36542i
$549$	2.36411	+	2.96450i	0.100898	+	0.126522i
$550$	−5.22245			−0.222686
$551$	17.0687	+	9.10895i	0.727152	+	0.388054i
$552$	0.304710			0.0129693
$553$	−23.7495	−	29.7810i	−1.00993	−	1.26642i
$554$	−0.220793	−	0.967358i	−0.00938060	−	0.0410991i
$555$	4.85996	−	21.2929i	0.206294	−	0.903832i
$556$	−10.1522	−	12.7304i	−0.430547	−	0.539889i
$557$	−7.76642	+	9.73879i	−0.329074	+	0.412646i	−0.918653	−	0.395065i	$-0.870722\pi$
$557$	−7.76642	+	9.73879i	−0.329074	+	0.412646i	0.589579	+	0.807710i	$0.299294\pi$
$558$	0.178190	+	0.780699i	0.00754336	+	0.0330496i
$559$	−1.05075	+	0.506016i	−0.0444421	+	0.0214022i
$560$	−44.9982	+	21.6700i	−1.90152	+	0.915724i
$561$	−2.91674	+	12.7791i	−0.123145	+	0.539534i
$562$	1.72596	+	0.831179i	0.0728053	+	0.0350612i
$563$	−3.58213			−0.150969			−0.0754843	−	0.997147i	$-0.524050\pi$
$563$	−3.58213			−0.150969			−0.0754843	+	0.997147i	$0.524050\pi$
$564$	−8.54260	−	4.11390i	−0.359708	−	0.173226i
$565$	−16.3235	+	20.4690i	−0.686735	+	0.861138i
$566$	−0.820836	+	1.02930i	−0.0345023	+	0.0432645i
$567$	3.41937	+	1.64668i	0.143600	+	0.0691541i
$568$	4.10124			0.172084
$569$	24.2253	+	11.6663i	1.01558	+	0.489076i	0.866197	−	0.499703i	$-0.166558\pi$
$569$	24.2253	+	11.6663i	1.01558	+	0.489076i	0.149381	+	0.988780i	$0.452272\pi$
$570$	−0.488586	+	2.14063i	−0.0204646	+	0.0896613i
$571$	27.0389	−	13.0212i	1.13154	−	0.544922i	0.228103	−	0.973637i	$-0.426748\pi$
$571$	27.0389	−	13.0212i	1.13154	−	0.544922i	0.903440	+	0.428715i	$0.141033\pi$
$572$	35.1383	−	16.9217i	1.46921	−	0.707533i
$573$	−0.347004	−	1.52033i	−0.0144963	−	0.0635125i
$574$	0.825970	−	1.03573i	0.0344753	−	0.0432307i
$575$	−1.86874	−	2.34333i	−0.0779319	−	0.0977235i
$576$	1.61490	−	7.07533i	0.0672874	−	0.294805i
$577$	0.637724	+	2.79405i	0.0265488	+	0.116318i	0.986466	−	0.163966i	$-0.0524286\pi$
$577$	0.637724	+	2.79405i	0.0265488	+	0.116318i	−0.959917	+	0.280284i	$0.909571\pi$
$578$	−0.834905	−	1.04694i	−0.0347275	−	0.0435469i
$579$	13.3775			0.555949
$580$	−6.65813	−	35.9794i	−0.276464	−	1.49396i
$581$	26.9390			1.11762
$582$	−1.58124	−	1.98281i	−0.0655444	−	0.0821901i
$583$	10.4148	+	45.6300i	0.431335	+	1.88980i
$584$	−1.64967	+	7.22769i	−0.0682640	+	0.299084i
$585$	9.99165	+	12.5291i	0.413104	+	0.518016i
$586$	1.37081	−	1.71894i	0.0566275	−	0.0710086i
$587$	−4.85992	−	21.2927i	−0.200591	−	0.878844i	−0.970578	−	0.240786i	$-0.922595\pi$
$587$	−4.85992	−	21.2927i	−0.200591	−	0.878844i	0.769988	−	0.638059i	$-0.220262\pi$
$588$	13.1317	−	6.32390i	0.541543	−	0.260793i
$589$	−14.6382	+	7.04940i	−0.603158	+	0.290466i
$590$	−0.825474	+	3.61664i	−0.0339842	+	0.148895i
$591$	11.5105	+	5.54314i	0.473477	+	0.228014i
$592$	24.1275			0.991635
$593$	−17.9895	−	8.66330i	−0.738741	−	0.355759i	0.0263741	−	0.999652i	$-0.491604\pi$
$593$	−17.9895	−	8.66330i	−0.738741	−	0.355759i	−0.765116	+	0.643893i	$0.777318\pi$
$594$	−0.471060	+	0.590690i	−0.0193278	+	0.0242363i
$595$	−25.0898	+	31.4616i	−1.02858	+	1.28980i
$596$	−16.6522	−	8.01930i	−0.682102	−	0.328483i
$597$	8.82206			0.361063
$598$	−0.321190	−	0.154677i	−0.0131345	−	0.00632522i
$599$	5.76162	−	25.2433i	0.235413	−	1.03141i	−0.709657	−	0.704547i	$-0.751150\pi$
$599$	5.76162	−	25.2433i	0.235413	−	1.03141i	0.945071	−	0.326866i	$-0.105993\pi$
$600$	4.37654	−	2.10763i	0.178671	−	0.0860436i
$601$	−21.7322	+	10.4657i	−0.886473	+	0.426903i	−0.820985	−	0.570950i	$-0.806575\pi$
$601$	−21.7322	+	10.4657i	−0.886473	+	0.426903i	−0.0654886	+	0.997853i	$0.520861\pi$
$602$	−0.0375613	−	0.164567i	−0.00153088	−	0.00670724i
$603$	−3.28401	+	4.11802i	−0.133735	+	0.167699i
$604$	−24.1353	−	30.2647i	−0.982052	−	1.23145i
$605$	5.53354	−	24.2440i	0.224970	−	0.985659i
$606$	−0.0321699	−	0.140945i	−0.00130681	−	0.00572552i
$607$	−3.54000	−	4.43901i	−0.143684	−	0.180174i	0.704782	−	0.709424i	$-0.251045\pi$
$607$	−3.54000	−	4.43901i	−0.143684	−	0.180174i	−0.848466	+	0.529250i	$0.822473\pi$
$608$	−7.47505			−0.303153
$609$	3.71896	+	20.0966i	0.150700	+	0.814356i
$610$	−2.31734			−0.0938262
$611$	13.9428	+	17.4838i	0.564067	+	0.707317i
$612$	−1.34577	−	5.89620i	−0.0543995	−	0.238340i
$613$	9.97427	−	43.7001i	0.402857	−	1.76503i	−0.212878	−	0.977079i	$-0.568284\pi$
$613$	9.97427	−	43.7001i	0.402857	−	1.76503i	0.615735	−	0.787953i	$-0.288859\pi$
$614$	2.65395	+	3.32794i	0.107105	+	0.134305i
$615$	4.24205	−	5.31937i	0.171056	−	0.214498i
$616$	2.53219	+	11.0942i	0.102025	+	0.447000i
$617$	26.1672	−	12.6015i	1.05345	−	0.507316i	0.174714	−	0.984619i	$-0.444100\pi$
$617$	26.1672	−	12.6015i	1.05345	−	0.507316i	0.878739	+	0.477303i	$0.158386\pi$
$618$	0.790976	−	0.380914i	0.0318177	−	0.0153226i
$619$	1.69406	−	7.42218i	0.0680901	−	0.298322i	−0.929405	−	0.369062i	$-0.879679\pi$
$619$	1.69406	−	7.42218i	0.0680901	−	0.298322i	0.997495	+	0.0707399i	$0.0225360\pi$
$620$	27.6845	+	13.3321i	1.11183	+	0.535431i
$621$	−0.433603			−0.0173999
$622$	4.98625	+	2.40125i	0.199930	+	0.0962813i
$623$	33.0715	−	41.4704i	1.32498	−	1.66148i
$624$	−11.0379	+	13.8411i	−0.441872	+	0.554089i
$625$	10.6143	+	5.11157i	0.424571	+	0.204463i
$626$	−3.72753			−0.148982
$627$	−13.8110	−	6.65101i	−0.551557	−	0.265616i
$628$	−1.14535	+	5.01811i	−0.0457045	+	0.200244i
$629$	17.5148	−	8.43467i	0.698359	−	0.336312i
$630$	−2.08976	+	1.00638i	−0.0832580	+	0.0400950i
$631$	−9.73830	−	42.6663i	−0.387676	−	1.69852i	−0.672632	−	0.739977i	$-0.734836\pi$
$631$	−9.73830	−	42.6663i	−0.387676	−	1.69852i	0.284957	−	0.958540i	$-0.408021\pi$
$632$	−4.39757	+	5.51438i	−0.174926	+	0.219350i
$633$	−9.36693	−	11.7458i	−0.372302	−	0.466852i
$634$	0.616705	−	2.70196i	0.0244925	−	0.107309i
$635$	0.948264	+	4.15462i	0.0376307	+	0.164871i
$636$	−13.4642	−	16.8836i	−0.533890	−	0.669476i
$637$	−34.3758			−1.36202
$638$	−4.06512	−	0.168455i	−0.160940	−	0.00666920i
$639$	−5.83609			−0.230872
$640$	11.7201	+	14.6966i	0.463279	+	0.580933i
$641$	−3.41266	−	14.9519i	−0.134792	−	0.590563i	−0.996532	−	0.0832123i	$-0.973482\pi$
$641$	−3.41266	−	14.9519i	−0.134792	−	0.590563i	0.861740	−	0.507351i	$-0.169375\pi$
$642$	0.454541	−	1.99147i	0.0179393	−	0.0785971i
$643$	17.0010	+	21.3185i	0.670453	+	0.840721i	0.994436	−	0.105342i	$-0.0335937\pi$
$643$	17.0010	+	21.3185i	0.670453	+	0.840721i	−0.323984	+	0.946063i	$0.605022\pi$
$644$	−2.01988	+	2.53285i	−0.0795943	+	0.0998082i
$645$	−0.192909	−	0.845188i	−0.00759577	−	0.0332793i
$646$	−1.76081	+	0.847962i	−0.0692782	+	0.0333626i
$647$	21.7872	−	10.4921i	0.856542	−	0.412489i	0.0465402	−	0.998916i	$-0.485180\pi$
$647$	21.7872	−	10.4921i	0.856542	−	0.412489i	0.810002	+	0.586428i	$0.199466\pi$
$648$	0.156374	−	0.685120i	0.00614295	−	0.0269140i
$649$	−23.3339	−	11.2370i	−0.915935	−	0.441091i
$650$	−5.68313			−0.222911
$651$	−15.4634	−	7.44679i	−0.606059	−	0.291863i
$652$	0.647837	−	0.812362i	0.0253713	−	0.0318146i
$653$	−15.6696	+	19.6491i	−0.613200	+	0.768929i	−0.987370	−	0.158432i	$-0.949356\pi$
$653$	−15.6696	+	19.6491i	−0.613200	+	0.768929i	0.374170	+	0.927360i	$0.377928\pi$
$654$	−1.37955	−	0.664354i	−0.0539445	−	0.0259783i
$655$	13.7907			0.538846
$656$	6.77185	+	3.26115i	0.264396	+	0.127327i
$657$	2.34749	−	10.2850i	0.0915844	−	0.401257i
$658$	−2.91615	+	1.40434i	−0.113683	+	0.0547471i
$659$	−8.69220	+	4.18594i	−0.338600	+	0.163061i	−0.595455	−	0.803389i	$-0.703028\pi$
$659$	−8.69220	+	4.18594i	−0.338600	+	0.163061i	0.256855	+	0.966450i	$0.417314\pi$
$660$	6.45108	+	28.2640i	0.251108	+	1.10018i
$661$	9.84536	−	12.3457i	0.382940	−	0.480192i	−0.552583	−	0.833458i	$-0.686358\pi$
$661$	9.84536	−	12.3457i	0.382940	−	0.480192i	0.935523	+	0.353266i	$0.114929\pi$
$662$	−2.14839	−	2.69400i	−0.0834996	−	0.104705i
$663$	−3.17404	+	13.9064i	−0.123269	+	0.540078i
$664$	−1.10997	−	4.86309i	−0.0430751	−	0.188724i
$665$	−29.3416	−	36.7932i	−1.13782	−	1.42678i
$666$	1.12051			0.0434187
$667$	−1.37903	−	1.88431i	−0.0533962	−	0.0729607i
$668$	29.6260			1.14627
$669$	14.9299	+	18.7214i	0.577221	+	0.723813i
$670$	−0.716303	−	3.13833i	−0.0276732	−	0.121244i
$671$	3.60002	−	15.7727i	0.138977	−	0.608898i
$672$	−4.92334	−	6.17368i	−0.189922	−	0.238155i
$673$	−10.1812	+	12.7668i	−0.392456	+	0.492124i	−0.938329	−	0.345744i	$-0.887627\pi$
$673$	−10.1812	+	12.7668i	−0.392456	+	0.492124i	0.545873	+	0.837868i	$0.316198\pi$
$674$	−0.795060	−	3.48338i	−0.0306246	−	0.134175i
$675$	−6.22783	+	2.99917i	−0.239709	+	0.115438i
$676$	15.1800	−	7.31031i	0.583846	−	0.281166i
$677$	−2.52618	+	11.0679i	−0.0970889	+	0.425374i	−0.999990	−	0.00447406i	$-0.998576\pi$
$677$	−2.52618	+	11.0679i	−0.0970889	+	0.425374i	0.902901	+	0.429848i	$0.141433\pi$
$678$	−1.21017	−	0.582787i	−0.0464763	−	0.0223818i
$679$	54.3566			2.08602
$680$	6.71328	+	3.23295i	0.257443	+	0.123978i
$681$	−3.21628	+	4.03308i	−0.123248	+	0.154548i
$682$	2.13028	−	2.67128i	0.0815725	−	0.102289i
$683$	−18.9882	−	9.14425i	−0.726565	−	0.349895i	0.0337673	−	0.999430i	$-0.489250\pi$
$683$	−18.9882	−	9.14425i	−0.726565	−	0.349895i	−0.760332	+	0.649535i	$0.774964\pi$
$684$	7.07272			0.270432
$685$	51.7874	+	24.9395i	1.97870	+	0.952890i
$686$	0.0603583	−	0.264447i	0.00230449	−	0.0100966i
$687$	7.29938	−	3.51520i	0.278489	−	0.134113i
$688$	0.862863	−	0.415533i	0.0328963	−	0.0158420i
$689$	11.3335	+	49.6552i	0.431771	+	1.89171i
$690$	0.165224	−	0.207184i	0.00628996	−	0.00788736i
$691$	3.48847	+	4.37440i	0.132708	+	0.166410i	0.843745	−	0.536744i	$-0.180346\pi$
$691$	3.48847	+	4.37440i	0.132708	+	0.166410i	−0.711038	+	0.703154i	$0.751774\pi$
$692$	0.0452227	−	0.198134i	0.00171911	−	0.00753191i
$693$	−3.60331	−	15.7871i	−0.136879	−	0.599704i
$694$	0.0870367	+	0.109141i	0.00330387	+	0.00414292i
$695$	−28.5470			−1.08285
$696$	3.47465	−	1.49940i	0.131706	−	0.0568345i
$697$	6.05592			0.229384
$698$	2.31202	+	2.89918i	0.0875113	+	0.109736i
$699$	−5.45518	−	23.9007i	−0.206334	−	0.904007i
$700$	−11.4922	+	50.3504i	−0.434363	+	1.90307i
$701$	−10.7892	−	13.5292i	−0.407502	−	0.510991i	0.535155	−	0.844754i	$-0.320253\pi$
$701$	−10.7892	−	13.5292i	−0.407502	−	0.510991i	−0.942657	+	0.333762i	$0.891682\pi$
$702$	−0.512613	+	0.642796i	−0.0193473	+	0.0242608i
$703$	5.05886	+	22.1643i	0.190798	+	0.835942i
$704$	−27.8984	+	13.4352i	−1.05146	+	0.506357i
$705$	−14.9769	+	7.21249i	−0.564063	+	0.271638i
$706$	1.42196	−	6.23002i	0.0535162	−	0.234470i
$707$	2.79172	+	1.34442i	0.104994	+	0.0505623i
$708$	11.9495			0.449089
$709$	−16.8452	−	8.11221i	−0.632634	−	0.304660i	0.0899473	−	0.995947i	$-0.471330\pi$
$709$	−16.8452	−	8.11221i	−0.632634	−	0.304660i	−0.722581	+	0.691286i	$0.757044\pi$
$710$	2.22383	−	2.78860i	0.0834589	−	0.104654i
$711$	6.25776	−	7.84699i	0.234684	−	0.294285i
$712$	−8.84897	−	4.26144i	−0.331629	−	0.159704i
$713$	1.96089			0.0734357
$714$	−1.86007	−	0.895763i	−0.0696114	−	0.0335231i
$715$	15.2151	−	66.6616i	0.569011	−	2.49300i
$716$	−7.18195	+	3.45865i	−0.268402	+	0.129256i
$717$	25.1738	−	12.1230i	0.940131	−	0.452743i
$718$	−0.733788	−	3.21494i	−0.0273847	−	0.119980i
$719$	−10.7768	+	13.5137i	−0.401908	+	0.503977i	−0.941064	−	0.338229i	$-0.890172\pi$
$719$	−10.7768	+	13.5137i	−0.401908	+	0.503977i	0.539156	+	0.842206i	$0.318743\pi$
$720$	−8.20500	−	10.2887i	−0.305782	−	0.383439i
$721$	−4.18705	+	18.3447i	−0.155934	+	0.683192i
$722$	0.240063	+	1.05179i	0.00893424	+	0.0391434i
$723$	2.47423	+	3.10259i	0.0920177	+	0.115387i
$724$	22.6832			0.843015
$725$	−32.8404	−	17.5257i	−1.21966	−	0.650890i
$726$	1.27581			0.0473496
$727$	1.79057	+	2.24531i	0.0664086	+	0.0832738i	0.813926	−	0.580968i	$-0.197326\pi$
$727$	1.79057	+	2.24531i	0.0664086	+	0.0832738i	−0.747518	+	0.664242i	$0.768754\pi$
$728$	2.75556	+	12.0729i	0.102128	+	0.447451i
$729$	−0.222521	+	0.974928i	−0.00824152	+	0.0361084i
$730$	4.01988	+	5.04077i	0.148783	+	0.186567i
$731$	0.481109	−	0.603292i	0.0177945	−	0.0223135i
$732$	1.66103	+	7.27744i	0.0613933	+	0.268982i
$733$	−42.1829	+	20.3142i	−1.55806	+	0.750323i	−0.996996	−	0.0774484i	$-0.975323\pi$
$733$	−42.1829	+	20.3142i	−1.55806	+	0.750323i	−0.561065	+	0.827771i	$0.689608\pi$
$734$	−2.57368	+	1.23942i	−0.0949963	+	0.0457478i
$735$	5.68610	−	24.9124i	0.209735	−	0.918909i
$736$	0.812825	+	0.391436i	0.0299611	+	0.0144285i
$737$	22.4735			0.827821
$738$	0.314492	+	0.151451i	0.0115766	+	0.00557499i
$739$	15.6343	−	19.6048i	0.575116	−	0.721173i	−0.406155	−	0.913804i	$-0.633131\pi$
$739$	15.6343	−	19.6048i	0.575116	−	0.721173i	0.981271	+	0.192631i	$0.0617021\pi$
$740$	26.8076	−	33.6157i	0.985468	−	1.23574i
$741$	−15.0293	−	7.23771i	−0.552114	−	0.265884i
$742$	−7.37175			−0.270626
$743$	−25.3667	−	12.2160i	−0.930616	−	0.448161i	−0.0937664	−	0.995594i	$-0.529891\pi$
$743$	−25.3667	−	12.2160i	−0.930616	−	0.448161i	−0.836849	+	0.547433i	$0.815605\pi$
$744$	−0.707171	+	3.09832i	−0.0259261	+	0.113590i
$745$	−29.1947	+	14.0594i	−1.06961	+	0.515098i
$746$	−0.181221	+	0.0872714i	−0.00663497	+	0.00319523i
$747$	1.57949	+	6.92019i	0.0577905	+	0.253197i
$748$	−16.0888	+	20.1747i	−0.588265	+	0.737662i
$749$	27.2970	+	34.2294i	0.997412	+	1.25071i
$750$	0.260072	−	1.13945i	0.00949650	−	0.0416069i
$751$	9.07997	+	39.7820i	0.331333	+	1.45166i	0.816552	+	0.577272i	$0.195883\pi$
$751$	9.07997	+	39.7820i	0.331333	+	1.45166i	−0.485219	+	0.874393i	$0.661260\pi$
$752$	−11.4497	−	14.3574i	−0.417526	−	0.523561i
$753$	−31.6093			−1.15191
$754$	−4.42371	−	0.183315i	−0.161102	−	0.00667593i
$755$	−67.8664			−2.46991
$756$	4.65836	+	5.84139i	0.169423	+	0.212449i
$757$	−9.07919	−	39.7785i	−0.329989	−	1.44578i	−0.819149	−	0.573581i	$-0.805554\pi$
$757$	−9.07919	−	39.7785i	−0.329989	−	1.44578i	0.489160	−	0.872194i	$-0.337303\pi$
$758$	−1.19182	+	5.22172i	−0.0432890	+	0.189662i
$759$	1.15350	+	1.44644i	0.0418693	+	0.0525025i
$760$	−5.43302	+	6.81280i	−0.197076	+	0.247126i
$761$	9.26200	+	40.5795i	0.335747	+	1.47100i	0.807812	+	0.589441i	$0.200652\pi$
$761$	9.26200	+	40.5795i	0.335747	+	1.47100i	−0.472064	+	0.881564i	$0.656491\pi$
$762$	−0.196979	+	0.0948602i	−0.00713581	+	0.00343642i
$763$	29.5679	−	14.2391i	1.07043	−	0.515492i
$764$	0.683128	−	2.99298i	0.0247147	−	0.108282i

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:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.g (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.110403 + 0.138441i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(0.438065 - 1.91929i) q^{4} +(-2.15193 - 2.69844i) q^{5} +(0.110403 - 0.138441i) q^{6} +(0.844514 + 3.70006i) q^{7} +(0.633146 - 0.304907i) q^{8} +(-0.900969 + 0.433884i) q^{9} +O(q^{10})\)	\(q+(0.110403 + 0.138441i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(0.438065 - 1.91929i) q^{4} +(-2.15193 - 2.69844i) q^{5} +(0.110403 - 0.138441i) q^{6} +(0.844514 + 3.70006i) q^{7} +(0.633146 - 0.304907i) q^{8} +(-0.900969 + 0.433884i) q^{9} +(0.135995 - 0.595831i) q^{10} +(3.84419 + 1.85126i) q^{11} -1.96865 q^{12} +(4.18329 + 2.01457i) q^{13} +(-0.419003 + 0.525413i) q^{14} +(-2.15193 + 2.69844i) q^{15} +(-3.43526 - 1.65434i) q^{16} -3.07208 q^{17} +(-0.159537 - 0.0768290i) q^{18} +(0.799448 - 3.50261i) q^{19} +(-6.12176 + 2.94808i) q^{20} +(3.41937 - 1.64668i) q^{21} +(0.168119 + 0.736579i) q^{22} +(-0.270347 + 0.339005i) q^{23} +(-0.438150 - 0.549423i) q^{24} +(-1.53815 + 6.73907i) q^{25} +(0.182949 + 0.801554i) q^{26} +(0.623490 + 0.781831i) q^{27} +7.47142 q^{28} +(-1.41466 + 5.19603i) q^{29} -0.611154 q^{30} +(-2.81961 - 3.53568i) q^{31} +(-0.462984 - 2.02846i) q^{32} +(0.949437 - 4.15975i) q^{33} +(-0.339167 - 0.425302i) q^{34} +(8.16704 - 10.2411i) q^{35} +(0.438065 + 1.91929i) q^{36} +(-5.70128 + 2.74559i) q^{37} +(0.573166 - 0.276022i) q^{38} +(1.03319 - 4.52669i) q^{39} +(-2.18526 - 1.05236i) q^{40} -1.97128 q^{41} +(0.605476 + 0.291582i) q^{42} +(-0.156607 + 0.196379i) q^{43} +(5.23711 - 6.56713i) q^{44} +(3.10963 + 1.49752i) q^{45} -0.0767793 q^{46} +(4.33933 + 2.08971i) q^{47} +(-0.848440 + 3.71726i) q^{48} +(-6.67044 + 3.21231i) q^{49} +(-1.10278 + 0.531070i) q^{50} +(0.683602 + 2.99505i) q^{51} +(5.69909 - 7.14643i) q^{52} +(6.83931 + 8.57623i) q^{53} +(-0.0394024 + 0.172633i) q^{54} +(-3.27691 - 14.3571i) q^{55} +(1.66287 + 2.08518i) q^{56} -3.59269 q^{57} +(-0.875526 + 0.377811i) q^{58} -6.06991 q^{59} +(4.23639 + 5.31227i) q^{60} +(-0.843741 - 3.69667i) q^{61} +(0.178190 - 0.780699i) q^{62} +(-2.36628 - 2.96722i) q^{63} +(-4.52484 + 5.67398i) q^{64} +(-3.56598 - 15.6236i) q^{65} +(0.680701 - 0.327808i) q^{66} +(4.74553 - 2.28533i) q^{67} +(-1.34577 + 5.89620i) q^{68} +(0.390663 + 0.188133i) q^{69} +2.31946 q^{70} +(5.25813 + 2.53218i) q^{71} +(-0.438150 + 0.549423i) q^{72} +(-6.57753 + 8.24796i) q^{73} +(-1.00954 - 0.486169i) q^{74} +6.91237 q^{75} +(-6.37230 - 3.06874i) q^{76} +(-3.60331 + 15.7871i) q^{77} +(0.740747 - 0.356725i) q^{78} +(-9.04273 + 4.35475i) q^{79} +(2.92833 + 12.8299i) q^{80} +(0.623490 - 0.781831i) q^{81} +(-0.217635 - 0.272906i) q^{82} +(1.57949 - 6.92019i) q^{83} +(-1.66255 - 7.28410i) q^{84} +(6.61090 + 8.28981i) q^{85} -0.0444768 q^{86} +(5.38055 + 0.222965i) q^{87} +2.99840 q^{88} +(-8.71402 - 10.9270i) q^{89} +(0.135995 + 0.595831i) q^{90} +(-3.92117 + 17.1798i) q^{91} +(0.532218 + 0.667380i) q^{92} +(-2.81961 + 3.53568i) q^{93} +(0.189773 + 0.831452i) q^{94} +(-11.1719 + 5.38012i) q^{95} +(-1.87458 + 0.902751i) q^{96} +(3.18704 - 13.9633i) q^{97} +(-1.18115 - 0.568813i) q^{98} -4.26673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9}+O(q^{10}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9} - 14 q^{10} + 26 q^{11} + 22 q^{12} + 9 q^{13} - 10 q^{14} - q^{15} - 14 q^{16} + 4 q^{17} - 4 q^{18} - 10 q^{19} - q^{20} - 4 q^{21} - 8 q^{22} - 8 q^{23} - 8 q^{24} + 16 q^{25} + 5 q^{26} - 3 q^{27} + 80 q^{28} + 8 q^{29} - 12 q^{31} + 9 q^{32} - 16 q^{33} - 22 q^{34} + 9 q^{35} - 6 q^{36} - 16 q^{37} - 32 q^{38} + 2 q^{39} + 33 q^{40} + 24 q^{41} - 3 q^{42} - 31 q^{43} - 52 q^{44} + 6 q^{45} - 44 q^{46} + 5 q^{47} - 47 q^{49} - 7 q^{50} + 11 q^{51} + 80 q^{52} + 5 q^{53} + 3 q^{54} - 17 q^{55} + 45 q^{56} + 18 q^{57} + 54 q^{58} - 32 q^{59} + 27 q^{60} - 28 q^{61} + 69 q^{62} + 3 q^{63} - 75 q^{64} + 22 q^{65} + 34 q^{66} + 6 q^{67} + 38 q^{68} + 20 q^{69} - 12 q^{70} + 46 q^{71} - 8 q^{72} - q^{73} - 35 q^{74} + 2 q^{75} - 45 q^{76} - 36 q^{77} - 51 q^{78} - 15 q^{79} - 86 q^{80} - 3 q^{81} + 47 q^{82} - 16 q^{83} - 25 q^{84} + 19 q^{85} + 116 q^{86} + 43 q^{87} + 54 q^{88} - 72 q^{89} - 14 q^{90} - 47 q^{91} - 121 q^{92} - 12 q^{93} - 22 q^{94} - 72 q^{95} - 12 q^{96} + 43 q^{97} + 31 q^{98} - 2 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9 - 14 * q^10 + 26 * q^11 + 22 * q^12 + 9 * q^13 - 10 * q^14 - q^15 - 14 * q^16 + 4 * q^17 - 4 * q^18 - 10 * q^19 - q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 - 8 * q^24 + 16 * q^25 + 5 * q^26 - 3 * q^27 + 80 * q^28 + 8 * q^29 - 12 * q^31 + 9 * q^32 - 16 * q^33 - 22 * q^34 + 9 * q^35 - 6 * q^36 - 16 * q^37 - 32 * q^38 + 2 * q^39 + 33 * q^40 + 24 * q^41 - 3 * q^42 - 31 * q^43 - 52 * q^44 + 6 * q^45 - 44 * q^46 + 5 * q^47 - 47 * q^49 - 7 * q^50 + 11 * q^51 + 80 * q^52 + 5 * q^53 + 3 * q^54 - 17 * q^55 + 45 * q^56 + 18 * q^57 + 54 * q^58 - 32 * q^59 + 27 * q^60 - 28 * q^61 + 69 * q^62 + 3 * q^63 - 75 * q^64 + 22 * q^65 + 34 * q^66 + 6 * q^67 + 38 * q^68 + 20 * q^69 - 12 * q^70 + 46 * q^71 - 8 * q^72 - q^73 - 35 * q^74 + 2 * q^75 - 45 * q^76 - 36 * q^77 - 51 * q^78 - 15 * q^79 - 86 * q^80 - 3 * q^81 + 47 * q^82 - 16 * q^83 - 25 * q^84 + 19 * q^85 + 116 * q^86 + 43 * q^87 + 54 * q^88 - 72 * q^89 - 14 * q^90 - 47 * q^91 - 121 * q^92 - 12 * q^93 - 22 * q^94 - 72 * q^95 - 12 * q^96 + 43 * q^97 + 31 * q^98 - 2 * q^99

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