LMFDB - Embedded newform 87.2.g.b.52.1

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} - 5 x^{17} + 15 x^{16} - 32 x^{15} + 66 x^{14} - 115 x^{13} + 272 x^{12} - 387 x^{11} + 762 x^{10} + \cdots + 49 $ x^18 - 5x^17 + 15x^16 - 32x^15 + 66x^14 - 115x^13 + 272x^12 - 387x^11 + 762x^10 - 822x^9 + 2349x^8 - 3280x^7 + 7428x^6 - 15449x^5 + 23373x^4 - 19712x^3 + 7938x^2 - 392*x + 49
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			52.1
Root			$0.488787 + 2.14152i$ of defining polynomial
Character	$\chi$	$=$	87.52
Dual form			87.2.g.b.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36955 + 1.71736i) q^{2} +(0.222521 - 0.974928i) q^{3} +(-0.628623 - 2.75418i) q^{4} +(-2.54240 + 3.18806i) q^{5} +(1.36955 + 1.71736i) q^{6} +(-0.811607 + 3.55588i) q^{7} +(1.63274 + 0.786286i) q^{8} +(-0.900969 - 0.433884i) q^{9} +O(q^{10})$	\(q+(-1.36955 + 1.71736i) q^{2} +(0.222521 - 0.974928i) q^{3} +(-0.628623 - 2.75418i) q^{4} +(-2.54240 + 3.18806i) q^{5} +(1.36955 + 1.71736i) q^{6} +(-0.811607 + 3.55588i) q^{7} +(1.63274 + 0.786286i) q^{8} +(-0.900969 - 0.433884i) q^{9} +(-1.99312 - 8.73243i) q^{10} +(3.17840 - 1.53064i) q^{11} -2.82501 q^{12} +(-0.834784 + 0.402011i) q^{13} +(-4.99521 - 6.26379i) q^{14} +(2.54240 + 3.18806i) q^{15} +(1.50403 - 0.724302i) q^{16} +1.61861 q^{17} +(1.97906 - 0.953065i) q^{18} +(0.886987 + 3.88614i) q^{19} +(10.3787 + 4.99812i) q^{20} +(3.28613 + 1.58252i) q^{21} +(-1.72433 + 7.55476i) q^{22} +(0.963772 + 1.20853i) q^{23} +(1.12989 - 1.41684i) q^{24} +(-2.58737 - 11.3360i) q^{25} +(0.452881 - 1.98420i) q^{26} +(-0.623490 + 0.781831i) q^{27} +10.3037 q^{28} +(5.19154 - 1.43104i) q^{29} -8.95700 q^{30} +(-1.00241 + 1.25699i) q^{31} +(-1.62246 + 7.10847i) q^{32} +(-0.785001 - 3.43931i) q^{33} +(-2.21677 + 2.77975i) q^{34} +(-9.27296 - 11.6279i) q^{35} +(-0.628623 + 2.75418i) q^{36} +(4.77878 + 2.30134i) q^{37} +(-7.88869 - 3.79899i) q^{38} +(0.206175 + 0.903310i) q^{39} +(-6.65780 + 3.20623i) q^{40} -6.71590 q^{41} +(-7.21828 + 3.47614i) q^{42} +(2.76166 + 3.46301i) q^{43} +(-6.21367 - 7.79170i) q^{44} +(3.67387 - 1.76924i) q^{45} -3.39542 q^{46} +(-3.00732 + 1.44825i) q^{47} +(-0.371464 - 1.62749i) q^{48} +(-5.67882 - 2.73478i) q^{49} +(23.0116 + 11.0818i) q^{50} +(0.360175 - 1.57803i) q^{51} +(1.63197 + 2.04643i) q^{52} +(1.27081 - 1.59355i) q^{53} +(-0.488787 - 2.14152i) q^{54} +(-3.20099 + 14.0244i) q^{55} +(-4.12109 + 5.16768i) q^{56} +3.98608 q^{57} +(-4.65248 + 10.8756i) q^{58} +7.29049 q^{59} +(7.18229 - 9.00630i) q^{60} +(1.33636 - 5.85497i) q^{61} +(-0.785846 - 3.44302i) q^{62} +(2.27407 - 2.85160i) q^{63} +(-7.90414 - 9.91148i) q^{64} +(0.840715 - 3.68341i) q^{65} +(6.98165 + 3.36219i) q^{66} +(-8.54330 - 4.11424i) q^{67} +(-1.01750 - 4.45795i) q^{68} +(1.39269 - 0.670684i) q^{69} +32.6692 q^{70} +(-7.61102 + 3.66527i) q^{71} +(-1.12989 - 1.41684i) q^{72} +(4.71831 + 5.91657i) q^{73} +(-10.4970 + 5.05509i) q^{74} -11.6275 q^{75} +(10.1456 - 4.88584i) q^{76} +(2.86316 + 12.5443i) q^{77} +(-1.83368 - 0.883053i) q^{78} +(-0.259377 - 0.124909i) q^{79} +(-1.51471 + 6.63640i) q^{80} +(0.623490 + 0.781831i) q^{81} +(9.19777 - 11.5336i) q^{82} +(1.44139 + 6.31514i) q^{83} +(2.29280 - 10.0454i) q^{84} +(-4.11515 + 5.16024i) q^{85} -9.72949 q^{86} +(-0.239930 - 5.37982i) q^{87} +6.39303 q^{88} +(10.2934 - 12.9075i) q^{89} +(-1.99312 + 8.73243i) q^{90} +(-0.751987 - 3.29467i) q^{91} +(2.72266 - 3.41411i) q^{92} +(1.00241 + 1.25699i) q^{93} +(1.63151 - 7.14811i) q^{94} +(-14.6443 - 7.05234i) q^{95} +(6.56921 + 3.16357i) q^{96} +(-2.23682 - 9.80015i) q^{97} +(12.4740 - 6.00718i) q^{98} -3.52776 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9	\( 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9} + 6 q^{10} - 6 q^{11} - 22 q^{12} - 11 q^{13} - 2 q^{14} + 7 q^{15} + 18 q^{16} - 32 q^{17} - 2 q^{18} + 2 q^{19} + 51 q^{20} + 4 q^{21} + 20 q^{22} - 6 q^{23} - 4 q^{24} + 4 q^{25} - 3 q^{26} + 3 q^{27} - 48 q^{28} - 10 q^{29} + 8 q^{30} + 8 q^{31} + 55 q^{32} - 8 q^{33} + 6 q^{34} + 31 q^{35} - 6 q^{36} + 20 q^{37} - 20 q^{38} - 10 q^{39} - 59 q^{40} - 68 q^{41} - 19 q^{42} - 3 q^{43} - 10 q^{44} + 14 q^{45} - 12 q^{46} + 19 q^{47} + 24 q^{48} + 17 q^{49} + 23 q^{50} + 11 q^{51} - 4 q^{52} - q^{53} - 5 q^{54} + 3 q^{55} + 7 q^{56} - 2 q^{57} - 30 q^{58} + 20 q^{59} + 47 q^{60} + 24 q^{61} + 79 q^{62} + 3 q^{63} - 23 q^{64} + 6 q^{65} + 50 q^{66} - 14 q^{67} - 8 q^{68} - 8 q^{69} + 28 q^{70} - 28 q^{71} + 4 q^{72} + 43 q^{73} - 47 q^{74} - 18 q^{75} + 19 q^{76} + 26 q^{77} - 11 q^{78} + 9 q^{79} - 74 q^{80} - 3 q^{81} - 17 q^{82} + 8 q^{83} - 15 q^{84} - 21 q^{85} - 140 q^{86} - 11 q^{87} - 58 q^{88} - 6 q^{89} + 6 q^{90} - 15 q^{91} + 11 q^{92} - 8 q^{93} + 6 q^{94} - 16 q^{95} + 36 q^{96} - 81 q^{97} - 11 q^{98} - 6 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9 + 6 * q^10 - 6 * q^11 - 22 * q^12 - 11 * q^13 - 2 * q^14 + 7 * q^15 + 18 * q^16 - 32 * q^17 - 2 * q^18 + 2 * q^19 + 51 * q^20 + 4 * q^21 + 20 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 - 3 * q^26 + 3 * q^27 - 48 * q^28 - 10 * q^29 + 8 * q^30 + 8 * q^31 + 55 * q^32 - 8 * q^33 + 6 * q^34 + 31 * q^35 - 6 * q^36 + 20 * q^37 - 20 * q^38 - 10 * q^39 - 59 * q^40 - 68 * q^41 - 19 * q^42 - 3 * q^43 - 10 * q^44 + 14 * q^45 - 12 * q^46 + 19 * q^47 + 24 * q^48 + 17 * q^49 + 23 * q^50 + 11 * q^51 - 4 * q^52 - q^53 - 5 * q^54 + 3 * q^55 + 7 * q^56 - 2 * q^57 - 30 * q^58 + 20 * q^59 + 47 * q^60 + 24 * q^61 + 79 * q^62 + 3 * q^63 - 23 * q^64 + 6 * q^65 + 50 * q^66 - 14 * q^67 - 8 * q^68 - 8 * q^69 + 28 * q^70 - 28 * q^71 + 4 * q^72 + 43 * q^73 - 47 * q^74 - 18 * q^75 + 19 * q^76 + 26 * q^77 - 11 * q^78 + 9 * q^79 - 74 * q^80 - 3 * q^81 - 17 * q^82 + 8 * q^83 - 15 * q^84 - 21 * q^85 - 140 * q^86 - 11 * q^87 - 58 * q^88 - 6 * q^89 + 6 * q^90 - 15 * q^91 + 11 * q^92 - 8 * q^93 + 6 * q^94 - 16 * q^95 + 36 * q^96 - 81 * q^97 - 11 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{5}{7}\right)$	$1$

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 $

$2$	−1.36955	+	1.71736i	−0.968419	+	1.21436i	0.00832808	+	0.999965i	$0.497349\pi$
$2$	−1.36955	+	1.71736i	−0.968419	+	1.21436i	−0.976747	+	0.214394i	$0.931222\pi$
$3$	0.222521	−	0.974928i	0.128473	−	0.562875i
$3$	0.222521	−	0.974928i	0.128473	−	0.562875i
$4$	−0.628623	−	2.75418i	−0.314312	−	1.37709i
$5$	−2.54240	+	3.18806i	−1.13699	+	1.42575i	−0.247447	+	0.968901i	$0.579592\pi$
$5$	−2.54240	+	3.18806i	−1.13699	+	1.42575i	−0.889547	+	0.456844i	$0.848980\pi$
$6$	1.36955	+	1.71736i	0.559117	+	0.701111i
$7$	−0.811607	+	3.55588i	−0.306759	+	1.34400i	0.552951	+	0.833214i	$0.313502\pi$
$7$	−0.811607	+	3.55588i	−0.306759	+	1.34400i	−0.859709	+	0.510784i	$0.829355\pi$
$8$	1.63274	+	0.786286i	0.577261	+	0.277994i
$9$	−0.900969	−	0.433884i	−0.300323	−	0.144628i
$10$	−1.99312	−	8.73243i	−0.630280	−	2.76144i
$11$	3.17840	−	1.53064i	0.958325	−	0.461505i	0.111728	−	0.993739i	$-0.464362\pi$
$11$	3.17840	−	1.53064i	0.958325	−	0.461505i	0.846597	+	0.532234i	$0.178647\pi$
$12$	−2.82501			−0.815510
$13$	−0.834784	+	0.402011i	−0.231527	+	0.111498i	−0.546051	−	0.837752i	$-0.683870\pi$
$13$	−0.834784	+	0.402011i	−0.231527	+	0.111498i	0.314524	+	0.949250i	$0.398155\pi$
$14$	−4.99521	−	6.26379i	−1.33503	−	1.67407i
$15$	2.54240	+	3.18806i	0.656444	+	0.823154i
$16$	1.50403	−	0.724302i	0.376007	−	0.181075i
$17$	1.61861			0.392571			0.196286	−	0.980547i	$-0.437112\pi$
$17$	1.61861			0.392571			0.196286	+	0.980547i	$0.437112\pi$
$18$	1.97906	−	0.953065i	0.466469	−	0.224640i
$19$	0.886987	+	3.88614i	0.203489	+	0.891542i	0.968793	+	0.247873i	$0.0797316\pi$
$19$	0.886987	+	3.88614i	0.203489	+	0.891542i	−0.765304	+	0.643669i	$0.777411\pi$
$20$	10.3787	+	4.99812i	2.32075	+	1.11761i
$21$	3.28613	+	1.58252i	0.717093	+	0.345334i
$22$	−1.72433	+	7.55476i	−0.367627	+	1.61068i
$23$	0.963772	+	1.20853i	0.200960	+	0.251996i	0.872092	−	0.489342i	$-0.162763\pi$
$23$	0.963772	+	1.20853i	0.200960	+	0.251996i	−0.671132	+	0.741338i	$0.734192\pi$
$24$	1.12989	−	1.41684i	0.230638	−	0.289211i
$25$	−2.58737	−	11.3360i	−0.517473	−	2.26720i
$26$	0.452881	−	1.98420i	0.0888173	−	0.389134i
$27$	−0.623490	+	0.781831i	−0.119991	+	0.150464i
$28$	10.3037			1.94722
$29$	5.19154	−	1.43104i	0.964046	−	0.265737i
$29$	5.19154	−	1.43104i	0.964046	−	0.265737i
$30$	−8.95700			−1.63532
$31$	−1.00241	+	1.25699i	−0.180039	+	0.225762i	−0.863659	−	0.504076i	$-0.831833\pi$
$31$	−1.00241	+	1.25699i	−0.180039	+	0.225762i	0.683620	+	0.729838i	$0.260404\pi$
$32$	−1.62246	+	7.10847i	−0.286813	+	1.25661i
$33$	−0.785001	−	3.43931i	−0.136651	−	0.598708i
$34$	−2.21677	+	2.77975i	−0.380174	+	0.476723i
$35$	−9.27296	−	11.6279i	−1.56742	−	1.96548i
$36$	−0.628623	+	2.75418i	−0.104771	+	0.459030i
$37$	4.77878	+	2.30134i	0.785626	+	0.378338i	0.783287	−	0.621660i	$-0.213541\pi$
$37$	4.77878	+	2.30134i	0.785626	+	0.378338i	0.00233856	+	0.999997i	$0.499256\pi$
$38$	−7.88869	−	3.79899i	−1.27972	−	0.616278i
$39$	0.206175	+	0.903310i	0.0330143	+	0.144645i
$40$	−6.65780	+	3.20623i	−1.05269	+	0.506949i
$41$	−6.71590			−1.04885			−0.524423	−	0.851458i	$-0.675719\pi$
$41$	−6.71590			−1.04885			−0.524423	+	0.851458i	$0.675719\pi$
$42$	−7.21828	+	3.47614i	−1.11381	+	0.536380i
$43$	2.76166	+	3.46301i	0.421149	+	0.528105i	0.946467	−	0.322802i	$-0.104625\pi$
$43$	2.76166	+	3.46301i	0.421149	+	0.528105i	−0.525317	+	0.850906i	$0.676053\pi$
$44$	−6.21367	−	7.79170i	−0.936747	−	1.17464i
$45$	3.67387	−	1.76924i	0.547668	−	0.263743i
$46$	−3.39542			−0.500628
$47$	−3.00732	+	1.44825i	−0.438663	+	0.211249i	−0.640162	−	0.768240i	$-0.721133\pi$
$47$	−3.00732	+	1.44825i	−0.438663	+	0.211249i	0.201499	+	0.979489i	$0.435419\pi$
$48$	−0.371464	−	1.62749i	−0.0536162	−	0.234908i
$49$	−5.67882	−	2.73478i	−0.811260	−	0.390682i
$50$	23.0116	+	11.0818i	3.25433	+	1.56720i
$51$	0.360175	−	1.57803i	0.0504346	−	0.220969i
$52$	1.63197	+	2.04643i	0.226314	+	0.283789i
$53$	1.27081	−	1.59355i	0.174560	−	0.218891i	−0.686853	−	0.726796i	$-0.741009\pi$
$53$	1.27081	−	1.59355i	0.174560	−	0.218891i	0.861413	+	0.507905i	$0.169580\pi$
$54$	−0.488787	−	2.14152i	−0.0665155	−	0.291424i
$55$	−3.20099	+	14.0244i	−0.431621	+	1.89106i
$56$	−4.12109	+	5.16768i	−0.550703	+	0.690560i
$57$	3.98608			0.527970
$58$	−4.65248	+	10.8756i	−0.610900	+	1.42804i
$59$	7.29049			0.949141			0.474571	−	0.880217i	$-0.342603\pi$
$59$	7.29049			0.949141			0.474571	+	0.880217i	$0.342603\pi$
$60$	7.18229	−	9.00630i	0.927229	−	1.16271i
$61$	1.33636	−	5.85497i	0.171103	−	0.749652i	−0.814443	−	0.580244i	$-0.802957\pi$
$61$	1.33636	−	5.85497i	0.171103	−	0.749652i	0.985546	−	0.169408i	$-0.0541856\pi$
$62$	−0.785846	−	3.44302i	−0.0998026	−	0.437264i
$63$	2.27407	−	2.85160i	0.286506	−	0.359268i
$64$	−7.90414	−	9.91148i	−0.988018	−	1.23893i
$65$	0.840715	−	3.68341i	0.104278	−	0.456871i
$66$	6.98165	+	3.36219i	0.859382	+	0.413857i
$67$	−8.54330	−	4.11424i	−1.04373	−	0.502634i	−0.168178	−	0.985757i	$-0.553788\pi$
$67$	−8.54330	−	4.11424i	−1.04373	−	0.502634i	−0.875553	+	0.483123i	$0.839503\pi$
$68$	−1.01750	−	4.45795i	−0.123390	−	0.540606i
$69$	1.39269	−	0.670684i	0.167660	−	0.0807409i
$70$	32.6692			3.90471
$71$	−7.61102	+	3.66527i	−0.903262	+	0.434988i	−0.827066	−	0.562105i	$-0.809992\pi$
$71$	−7.61102	+	3.66527i	−0.903262	+	0.434988i	−0.0761959	+	0.997093i	$0.524277\pi$
$72$	−1.12989	−	1.41684i	−0.133159	−	0.166976i
$73$	4.71831	+	5.91657i	0.552236	+	0.692482i	0.977101	−	0.212775i	$-0.0682500\pi$
$73$	4.71831	+	5.91657i	0.552236	+	0.692482i	−0.424865	+	0.905257i	$0.639679\pi$
$74$	−10.4970	+	5.05509i	−1.22025	+	0.587643i
$75$	−11.6275			−1.34263
$76$	10.1456	−	4.88584i	1.16377	−	0.560445i
$77$	2.86316	+	12.5443i	0.326287	+	1.42956i
$78$	−1.83368	−	0.883053i	−0.207623	−	0.0999860i
$79$	−0.259377	−	0.124909i	−0.0291822	−	0.0140534i	0.419236	−	0.907877i	$-0.362298\pi$
$79$	−0.259377	−	0.124909i	−0.0291822	−	0.0140534i	−0.448418	+	0.893824i	$0.648012\pi$
$80$	−1.51471	+	6.63640i	−0.169350	+	0.741972i
$81$	0.623490	+	0.781831i	0.0692766	+	0.0868702i
$82$	9.19777	−	11.5336i	1.01572	−	1.27368i
$83$	1.44139	+	6.31514i	0.158213	+	0.693176i	0.990348	+	0.138603i	$0.0442613\pi$
$83$	1.44139	+	6.31514i	0.158213	+	0.693176i	−0.832135	+	0.554573i	$0.812882\pi$
$84$	2.29280	−	10.0454i	0.250165	−	1.09604i
$85$	−4.11515	+	5.16024i	−0.446351	+	0.559707i
$86$	−9.72949			−1.04916
$87$	−0.239930	−	5.37982i	−0.0257232	−	0.576777i
$88$	6.39303			0.681499
$89$	10.2934	−	12.9075i	1.09110	−	1.36819i	0.167036	−	0.985951i	$-0.446580\pi$
$89$	10.2934	−	12.9075i	1.09110	−	1.36819i	0.924062	−	0.382243i	$-0.124848\pi$
$90$	−1.99312	+	8.73243i	−0.210093	+	0.920479i
$91$	−0.751987	−	3.29467i	−0.0788296	−	0.345375i
$92$	2.72266	−	3.41411i	0.283857	−	0.355946i
$93$	1.00241	+	1.25699i	0.103945	+	0.130344i
$94$	1.63151	−	7.14811i	0.168277	−	0.737272i
$95$	−14.6443	−	7.05234i	−1.50248	−	0.723555i
$96$	6.56921	+	3.16357i	0.670467	+	0.322880i
$97$	−2.23682	−	9.80015i	−0.227115	−	0.995054i	−0.951979	−	0.306163i	$-0.900955\pi$
$97$	−2.23682	−	9.80015i	−0.227115	−	0.995054i	0.724864	−	0.688892i	$-0.241902\pi$
$98$	12.4740	−	6.00718i	1.26007	−	0.606817i
$99$	−3.52776			−0.354554
$100$	−29.5949	+	14.2521i	−2.95949	+	1.42521i
$101$	5.13707	+	6.44168i	0.511158	+	0.640971i	0.968705	−	0.248214i	$-0.0798435\pi$
$101$	5.13707	+	6.44168i	0.511158	+	0.640971i	−0.457548	+	0.889185i	$0.651272\pi$
$102$	2.21677	+	2.77975i	0.219493	+	0.275236i
$103$	−6.87172	+	3.30925i	−0.677091	+	0.326070i	−0.740634	−	0.671909i	$-0.765474\pi$
$103$	−6.87172	+	3.30925i	−0.677091	+	0.326070i	0.0635423	+	0.997979i	$0.479760\pi$
$104$	−1.67908			−0.164647
$105$	−13.3998	+	6.45301i	−1.30769	+	0.629749i
$106$	0.996260	+	4.36490i	0.0967653	+	0.423957i
$107$	15.0981	+	7.27087i	1.45959	+	0.702902i	0.984231	−	0.176890i	$-0.0566037\pi$
$107$	15.0981	+	7.27087i	1.45959	+	0.702902i	0.475360	+	0.879792i	$0.342318\pi$
$108$	2.54524	+	1.22573i	0.244916	+	0.117945i
$109$	2.82860	−	12.3929i	0.270931	−	1.18702i	−0.637987	−	0.770047i	$-0.720232\pi$
$109$	2.82860	−	12.3929i	0.270931	−	1.18702i	0.908917	−	0.416977i	$-0.136910\pi$
$110$	−19.7011	−	24.7045i	−1.87843	−	2.35548i
$111$	3.30702	−	4.14687i	0.313888	−	0.393603i
$112$	1.35485	+	5.93600i	0.128022	+	0.560899i
$113$	1.88360	−	8.25259i	0.177194	−	0.776338i	−0.805723	−	0.592292i	$-0.798223\pi$
$113$	1.88360	−	8.25259i	0.177194	−	0.776338i	0.982918	−	0.184046i	$-0.0589196\pi$
$114$	−5.45915	+	6.84555i	−0.511296	+	0.641145i
$115$	−6.30316			−0.587773
$116$	−7.20486	−	13.3989i	−0.668954	−	1.24405i
$117$	0.926540			0.0856587
$118$	−9.98471	+	12.5204i	−0.919167	+	1.15260i
$119$	−1.31368	+	5.75560i	−0.120425	+	0.527615i
$120$	1.64434	+	7.20433i	0.150107	+	0.657662i
$121$	0.901012	−	1.12983i	0.0819101	−	0.102712i
$122$	8.22489	+	10.3137i	0.744647	+	0.933758i
$123$	−1.49443	+	6.54751i	−0.134748	+	0.590370i
$124$	4.09211	+	1.97066i	0.367482	+	0.176970i
$125$	24.3486	+	11.7257i	2.17781	+	1.04878i
$126$	1.78277	+	7.81082i	0.158822	+	0.695843i
$127$	16.0419	−	7.72538i	1.42349	−	0.685516i	0.445715	−	0.895175i	$-0.352950\pi$
$127$	16.0419	−	7.72538i	1.42349	−	0.685516i	0.977775	+	0.209659i	$0.0672354\pi$
$128$	13.2642			1.17240
$129$	3.99072	−	1.92183i	0.351363	−	0.169207i
$130$	5.17436	+	6.48844i	0.453821	+	0.569074i
$131$	7.06407	+	8.85807i	0.617191	+	0.773933i	0.987946	−	0.154798i	$-0.0494726\pi$
$131$	7.06407	+	8.85807i	0.617191	+	0.773933i	−0.370755	+	0.928731i	$0.620901\pi$
$132$	−8.97902	+	4.32407i	−0.781523	+	0.376362i
$133$	−14.5386			−1.26065
$134$	18.7661	−	9.03729i	1.62115	−	0.780703i
$135$	−0.907370	−	3.97545i	−0.0780940	−	0.342152i
$136$	2.64278	+	1.27269i	0.226616	+	0.109133i
$137$	−7.48927	−	3.60664i	−0.639851	−	0.308136i	0.0856826	−	0.996322i	$-0.472693\pi$
$137$	−7.48927	−	3.60664i	−0.639851	−	0.308136i	−0.725534	+	0.688186i	$0.758407\pi$
$138$	−0.755553	+	3.31029i	−0.0643169	+	0.281791i
$139$	−1.94077	−	2.43365i	−0.164614	−	0.206419i	0.692682	−	0.721243i	$-0.256429\pi$
$139$	−1.94077	−	2.43365i	−0.164614	−	0.206419i	−0.857296	+	0.514824i	$0.827857\pi$
$140$	−26.1962	+	32.8490i	−2.21398	+	2.77624i
$141$	0.742747	+	3.25419i	0.0625506	+	0.274052i
$142$	4.12908	−	18.0907i	0.346504	−	1.51814i
$143$	−2.03795	+	2.55550i	−0.170422	+	0.213702i
$144$	−1.66934			−0.139112
$145$	−8.63673	+	20.1892i	−0.717241	+	1.67662i
$146$	−16.6229			−1.37572
$147$	−3.92987	+	4.92790i	−0.324130	+	0.406446i
$148$	3.33425	−	14.6083i	0.274073	−	1.20079i
$149$	−3.37249	−	14.7758i	−0.276285	−	1.21048i	−0.902450	−	0.430794i	$-0.858234\pi$
$149$	−3.37249	−	14.7758i	−0.276285	−	1.21048i	0.626165	−	0.779691i	$-0.284624\pi$
$150$	15.9245	−	19.9687i	1.30023	−	1.63044i
$151$	0.423281	+	0.530778i	0.0344461	+	0.0431941i	0.798756	−	0.601655i	$-0.205492\pi$
$151$	0.423281	+	0.530778i	0.0344461	+	0.0431941i	−0.764310	+	0.644849i	$0.776920\pi$
$152$	−1.60740	+	7.04249i	−0.130378	+	0.571221i
$153$	−1.45832	−	0.702290i	−0.117898	−	0.0567768i
$154$	−25.4644	−	12.2630i	−2.05198	−	0.988181i
$155$	−1.45882	−	6.39152i	−0.117175	−	0.513379i
$156$	2.35827	−	1.13568i	0.188813	−	0.0909274i
$157$	−6.23584			−0.497674			−0.248837	−	0.968545i	$-0.580048\pi$
$157$	−6.23584			−0.497674			−0.248837	+	0.968545i	$0.580048\pi$
$158$	0.569745	−	0.274375i	0.0453265	−	0.0218281i
$159$	−1.27081	−	1.59355i	−0.100782	−	0.126377i
$160$	−18.5373	−	23.2450i	−1.46550	−	1.83768i
$161$	−5.07960	+	2.44621i	−0.400329	+	0.192788i
$162$	−2.19659			−0.172580
$163$	13.7996	−	6.64551i	1.08086	−	0.520517i	0.193271	−	0.981145i	$-0.438090\pi$
$163$	13.7996	−	6.64551i	1.08086	−	0.520517i	0.887593	+	0.460629i	$0.152376\pi$
$164$	4.22177	+	18.4968i	0.329665	+	1.44436i
$165$	12.9605	+	6.24146i	1.00898	+	0.485897i
$166$	−12.8194	−	6.17352i	−0.994981	−	0.479158i
$167$	3.51273	−	15.3903i	0.271823	−	1.19094i	−0.636036	−	0.771660i	$-0.719427\pi$
$167$	3.51273	−	15.3903i	0.271823	−	1.19094i	0.907859	−	0.419276i	$-0.137716\pi$
$168$	4.12109	+	5.16768i	0.317949	+	0.398695i
$169$	−7.57012	+	9.49263i	−0.582317	+	0.730202i
$170$	−3.22609	−	14.1344i	−0.247430	−	1.08406i
$171$	0.886987	−	3.88614i	0.0678296	−	0.297181i
$172$	7.80172	−	9.78304i	0.594875	−	0.745950i
$173$	−3.44502			−0.261920			−0.130960	−	0.991388i	$-0.541806\pi$
$173$	−3.44502			−0.261920			−0.130960	+	0.991388i	$0.541806\pi$
$174$	9.56770	+	6.95589i	0.725325	+	0.527325i
$175$	42.4094			3.20585
$176$	3.67176	−	4.60425i	0.276770	−	0.347058i
$177$	1.62229	−	7.10771i	0.121939	−	0.534248i
$178$	8.06955	+	35.3550i	0.604838	+	2.64997i
$179$	−7.50542	+	9.41150i	−0.560981	+	0.703448i	−0.978739	−	0.205110i	$-0.934245\pi$
$179$	−7.50542	+	9.41150i	−0.560981	+	0.703448i	0.417758	+	0.908559i	$0.362816\pi$
$180$	−7.18229	−	9.00630i	−0.535336	−	0.671290i
$181$	−0.538337	+	2.35861i	−0.0400143	+	0.175314i	−0.990986	−	0.133963i	$-0.957230\pi$
$181$	−0.538337	+	2.35861i	−0.0400143	+	0.175314i	0.950972	+	0.309277i	$0.100087\pi$
$182$	6.68803	+	3.22078i	0.495750	+	0.238740i
$183$	−5.41080	−	2.60571i	−0.399978	−	0.192619i
$184$	0.623337	+	2.73102i	0.0459530	+	0.201333i
$185$	−19.4863	+	9.38413i	−1.43266	+	0.689935i
$186$	−3.53156			−0.258947
$187$	5.14461	−	2.47751i	0.376211	−	0.181174i
$188$	5.87921	+	7.37230i	0.428785	+	0.537680i
$189$	−2.27407	−	2.85160i	−0.165414	−	0.207423i
$190$	32.1676	−	15.4911i	2.33368	−	1.12384i
$191$	5.83662			0.422323			0.211162	−	0.977451i	$-0.432275\pi$
$191$	5.83662			0.422323			0.211162	+	0.977451i	$0.432275\pi$
$192$	−11.4218	+	5.50046i	−0.824298	+	0.396961i
$193$	−4.44827	−	19.4891i	−0.320193	−	1.40286i	−0.837209	−	0.546883i	$-0.815814\pi$
$193$	−4.44827	−	19.4891i	−0.320193	−	1.40286i	0.517015	−	0.855976i	$-0.327043\pi$
$194$	19.8939	+	9.58038i	1.42830	+	0.687831i
$195$	−3.40399	−	1.63927i	−0.243764	−	0.117391i
$196$	−3.96222	+	17.3596i	−0.283016	+	1.23997i
$197$	−7.30267	−	9.15726i	−0.520294	−	0.652428i	0.450378	−	0.892838i	$-0.351289\pi$
$197$	−7.30267	−	9.15726i	−0.520294	−	0.652428i	−0.970671	+	0.240411i	$0.922718\pi$
$198$	4.83145	−	6.05845i	0.343356	−	0.430555i
$199$	3.70461	+	16.2310i	0.262613	+	1.15058i	0.918405	+	0.395641i	$0.129478\pi$
$199$	3.70461	+	16.2310i	0.262613	+	1.15058i	−0.655792	+	0.754941i	$0.727665\pi$
$200$	4.68884	−	20.5431i	0.331551	−	1.45262i
$201$	−5.91215	+	7.41360i	−0.417011	+	0.522915i
$202$	−18.0982			−1.27338
$203$	0.875104	+	19.6220i	0.0614202	+	1.37719i
$204$	−4.57260			−0.320146
$205$	17.0745	−	21.4107i	1.19253	−	1.49539i
$206$	3.72800	−	16.3334i	0.259742	−	1.13800i
$207$	−0.343966	−	1.50701i	−0.0239073	−	0.104745i
$208$	−0.964361	+	1.20927i	−0.0668664	+	0.0838478i
$209$	8.76749	+	10.9941i	0.606460	+	0.760476i
$210$	7.26957	−	31.8501i	0.501648	−	2.19786i
$211$	21.8426	+	10.5189i	1.50371	+	0.724148i	0.990931	−	0.134373i	$-0.0429019\pi$
$211$	21.8426	+	10.5189i	1.50371	+	0.724148i	0.512778	+	0.858521i	$0.328616\pi$
$212$	−5.18779	−	2.49831i	−0.356299	−	0.171584i
$213$	1.87977	+	8.23580i	0.128799	+	0.564307i
$214$	−33.1644	+	15.9711i	−2.26707	+	1.09176i
$215$	−18.0615			−1.23179
$216$	−1.63274	+	0.786286i	−0.111094	+	0.0535000i
$217$	−3.65613	−	4.58465i	−0.248195	−	0.311226i
$218$	17.4092	+	21.8304i	1.17910	+	1.47854i
$219$	6.81815	−	3.28345i	0.460728	−	0.221875i
$220$	40.6381			2.73982
$221$	−1.35119	+	0.650700i	−0.0908910	+	0.0437708i
$222$	2.59255	+	11.3587i	0.174000	+	0.762346i
$223$	−25.5135	−	12.2867i	−1.70851	−	0.822776i	−0.992151	−	0.125048i	$-0.960092\pi$
$223$	−25.5135	−	12.2867i	−1.70851	−	0.822776i	−0.716362	−	0.697729i	$-0.754194\pi$
$224$	−23.9601	−	11.5386i	−1.60090	−	0.770953i
$225$	−2.58737	+	11.3360i	−0.172491	+	0.755733i
$226$	11.5930	+	14.5372i	0.771155	+	0.966998i
$227$	6.15022	−	7.71213i	0.408204	−	0.511872i	−0.534652	−	0.845073i	$-0.679557\pi$
$227$	6.15022	−	7.71213i	0.408204	−	0.511872i	0.942856	+	0.333201i	$0.108129\pi$
$228$	−2.50575	−	10.9784i	−0.165947	−	0.727061i
$229$	−3.48401	+	15.2644i	−0.230230	+	1.00870i	0.719219	+	0.694783i	$0.244500\pi$
$229$	−3.48401	+	15.2644i	−0.230230	+	1.00870i	−0.949449	+	0.313920i	$0.898358\pi$
$230$	8.63251	−	10.8248i	0.569211	−	0.713768i
$231$	12.8669			0.846581
$232$	9.60165	+	1.74553i	0.630379	+	0.114600i
$233$	−19.7879			−1.29635			−0.648176	−	0.761491i	$-0.724468\pi$
$233$	−19.7879			−1.29635			−0.648176	+	0.761491i	$0.724468\pi$
$234$	−1.26894	+	1.59121i	−0.0829535	+	0.104020i
$235$	3.02869	−	13.2695i	0.197570	−	0.865610i
$236$	−4.58298	−	20.0793i	−0.298326	−	1.30705i
$237$	−0.179495	+	0.225079i	−0.0116594	+	0.0146205i
$238$	−8.08531	−	10.1387i	−0.524093	−	0.657191i
$239$	2.07678	−	9.09899i	0.134336	−	0.588564i	−0.862285	−	0.506424i	$-0.830967\pi$
$239$	2.07678	−	9.09899i	0.134336	−	0.588564i	0.996621	−	0.0821407i	$-0.0261757\pi$
$240$	6.13295	+	2.95347i	0.395880	+	0.190646i
$241$	22.1401	+	10.6621i	1.42617	+	0.686807i	0.978281	−	0.207282i	$-0.0664619\pi$
$241$	22.1401	+	10.6621i	1.42617	+	0.686807i	0.447888	+	0.894089i	$0.352176\pi$
$242$	0.706352	+	3.09473i	0.0454060	+	0.198937i
$243$	0.900969	−	0.433884i	0.0577972	−	0.0278337i
$244$	−16.9657			−1.08612
$245$	23.1564	−	11.1516i	1.47941	−	0.712447i
$246$	−9.19777	−	11.5336i	−0.586428	−	0.735358i
$247$	−2.30271	−	2.88751i	−0.146518	−	0.183728i
$248$	−2.62503	+	1.26415i	−0.166690	+	0.0802736i
$249$	6.47754			0.410498
$250$	−53.4840	+	25.7565i	−3.38262	+	1.62899i
$251$	−1.03735	−	4.54494i	−0.0654771	−	0.286874i	0.931580	−	0.363536i	$-0.118431\pi$
$251$	−1.03735	−	4.54494i	−0.0654771	−	0.286874i	−0.997057	+	0.0766624i	$0.975574\pi$
$252$	−9.28335	−	4.47062i	−0.584796	−	0.281623i
$253$	4.91308	+	2.36602i	0.308883	+	0.148750i
$254$	−8.70294	+	38.1301i	−0.546071	+	2.39249i
$255$	4.11515	+	5.16024i	0.257701	+	0.323147i
$256$	−2.35770	+	2.95647i	−0.147356	+	0.184779i
$257$	6.30942	+	27.6434i	0.393571	+	1.72435i	0.651915	+	0.758292i	$0.273966\pi$
$257$	6.30942	+	27.6434i	0.393571	+	1.72435i	−0.258344	+	0.966053i	$0.583177\pi$
$258$	−2.16502	+	9.48555i	−0.134788	+	0.590545i
$259$	−12.0618	+	15.1250i	−0.749482	+	0.939821i
$260$	−10.6733			−0.661928
$261$	−5.29832	−	0.963208i	−0.327958	−	0.0596211i
$262$	−24.8871			−1.53753
$263$	−16.6977	+	20.9383i	−1.02963	+	1.29111i	−0.0737713	+	0.997275i	$0.523503\pi$
$263$	−16.6977	+	20.9383i	−1.02963	+	1.29111i	−0.955856	+	0.293836i	$0.905068\pi$
$264$	1.42258	−	6.23274i	0.0875539	−	0.383599i
$265$	1.84943	+	8.10287i	0.113609	+	0.497756i
$266$	19.9113	−	24.9680i	1.22084	−	1.53089i
$267$	−10.2934	−	12.9075i	−0.629946	−	0.789927i
$268$	−5.96083	+	26.1161i	−0.364115	+	1.59529i
$269$	0.707757	+	0.340838i	0.0431527	+	0.0207812i	0.455336	−	0.890320i	$-0.349519\pi$
$269$	0.707757	+	0.340838i	0.0431527	+	0.0207812i	−0.412183	+	0.911101i	$0.635234\pi$
$270$	8.06998	+	3.88630i	0.491123	+	0.236513i
$271$	2.70395	+	11.8468i	0.164253	+	0.719641i	0.988225	+	0.153009i	$0.0488965\pi$
$271$	2.70395	+	11.8468i	0.164253	+	0.719641i	−0.823971	+	0.566631i	$0.808246\pi$
$272$	2.43444	−	1.17236i	0.147610	−	0.0710850i
$273$	−3.37940			−0.204530
$274$	16.4509	−	7.92231i	0.993832	−	0.478604i
$275$	−25.5750	−	32.0701i	−1.54223	−	1.93390i
$276$	−2.72266	−	3.41411i	−0.163885	−	0.205505i
$277$	14.2206	−	6.84830i	0.854435	−	0.411474i	0.0452134	−	0.998977i	$-0.485603\pi$
$277$	14.2206	−	6.84830i	0.854435	−	0.411474i	0.809222	+	0.587503i	$0.199889\pi$
$278$	6.83744			0.410083
$279$	1.44853	−	0.697575i	0.0867212	−	0.0417627i
$280$	−5.99746	−	26.2766i	−0.358417	−	1.57033i
$281$	−18.0845	−	8.70903i	−1.07883	−	0.519537i	−0.191887	−	0.981417i	$-0.561461\pi$
$281$	−18.0845	−	8.70903i	−1.07883	−	0.519537i	−0.886942	+	0.461880i	$0.847175\pi$
$282$	−6.60585	−	3.18121i	−0.393373	−	0.189438i
$283$	0.435154	−	1.90654i	0.0258672	−	0.113332i	−0.960346	−	0.278811i	$-0.910060\pi$
$283$	0.435154	−	1.90654i	0.0258672	−	0.113332i	0.986213	+	0.165479i	$0.0529170\pi$
$284$	14.8793	+	18.6580i	0.882923	+	1.10715i
$285$	−10.1342	+	12.7079i	−0.600298	+	0.752750i
$286$	−1.59766	−	6.99979i	−0.0944714	−	0.413906i
$287$	5.45067	−	23.8809i	0.321743	−	1.40965i
$288$	4.54604	−	5.70055i	0.267878	−	0.335908i
$289$	−14.3801			−0.845888
$290$	−22.8438	−	42.4826i	−1.34143	−	2.49466i
$291$	−10.0522			−0.589269
$292$	13.3293	−	16.7144i	0.780035	−	0.978134i
$293$	0.537209	−	2.35367i	0.0313841	−	0.137503i	−0.956809	−	0.290718i	$-0.906106\pi$
$293$	0.537209	−	2.35367i	0.0313841	−	0.137503i	0.988193	+	0.153216i	$0.0489629\pi$
$294$	−3.08083	−	13.4980i	−0.179678	−	0.787220i
$295$	−18.5353	+	23.2426i	−1.07917	+	1.35323i
$296$	5.99299	+	7.51497i	0.348336	+	0.436799i
$297$	−0.785001	+	3.43931i	−0.0455504	+	0.199569i
$298$	29.9943	+	14.4445i	1.73752	+	0.836747i
$299$	−1.29038	−	0.621416i	−0.0746248	−	0.0359374i
$300$	7.30933	+	32.0243i	0.422005	+	1.84892i
$301$	−14.5555	+	7.00954i	−0.838963	+	0.404023i
$302$	−1.49124			−0.0858114
$303$	7.42328	−	3.57486i	0.426456	−	0.205371i
$304$	4.14879	+	5.20242i	0.237950	+	0.298379i
$305$	15.2685	+	19.1460i	0.874269	+	1.09630i
$306$	3.20333	−	1.54264i	0.183122	−	0.0881870i
$307$	−1.11367			−0.0635606			−0.0317803	−	0.999495i	$-0.510118\pi$
$307$	−1.11367			−0.0635606			−0.0317803	+	0.999495i	$0.510118\pi$
$308$	32.7494	−	15.7713i	1.86607	−	0.898653i
$309$	1.69718	+	7.43581i	0.0965490	+	0.423009i
$310$	12.9745	+	6.24819i	0.736902	+	0.354873i
$311$	−3.99119	−	1.92206i	−0.226320	−	0.108990i	0.317288	−	0.948329i	$-0.397228\pi$
$311$	−3.99119	−	1.92206i	−0.226320	−	0.108990i	−0.543608	+	0.839339i	$0.682942\pi$
$312$	−0.373631	+	1.63698i	−0.0211527	+	0.0926759i
$313$	−18.7672	−	23.5333i	−1.06078	−	1.33018i	−0.941385	−	0.337334i	$-0.890475\pi$
$313$	−18.7672	−	23.5333i	−1.06078	−	1.33018i	−0.119399	−	0.992846i	$-0.538097\pi$
$314$	8.54030	−	10.7092i	0.481957	−	0.604355i
$315$	3.30948	+	14.4998i	0.186468	+	0.816970i
$316$	−0.180973	+	0.792892i	−0.0101805	+	0.0446037i
$317$	−3.87230	+	4.85571i	−0.217490	+	0.272724i	−0.878593	−	0.477571i	$-0.841517\pi$
$317$	−3.87230	+	4.85571i	−0.217490	+	0.272724i	0.661103	+	0.750295i	$0.270089\pi$
$318$	4.47715			0.251066
$319$	14.3104	−	12.4948i	0.801230	−	0.699574i
$320$	51.6939			2.88978
$321$	10.4482	−	13.1017i	0.583163	−	0.731263i
$322$	2.75575	−	12.0737i	0.153572	−	0.672843i
$323$	1.43569	+	6.29016i	0.0798838	+	0.349994i
$324$	1.76136	−	2.20868i	0.0978535	−	0.122704i
$325$	6.71708	+	8.42296i	0.372597	+	0.467221i
$326$	−7.48644	+	32.8002i	−0.414635	+	1.81664i
$327$	−11.4528	−	5.51536i	−0.633339	−	0.305000i
$328$	−10.9653	−	5.28062i	−0.605458	−	0.291573i
$329$	−2.70904	−	11.8691i	−0.149354	−	0.654364i
$330$	−28.4690	+	13.7099i	−1.56717	+	0.754707i
$331$	10.0058			0.549967			0.274984	−	0.961449i	$-0.411328\pi$
$331$	10.0058			0.549967			0.274984	+	0.961449i	$0.411328\pi$
$332$	16.4869	−	7.93969i	0.904838	−	0.435747i
$333$	−3.30702	−	4.14687i	−0.181223	−	0.227247i
$334$	21.6198	+	27.1104i	1.18298	+	1.48342i
$335$	34.8369	−	16.7766i	1.90334	−	0.916602i
$336$	6.08865			0.332163
$337$	24.5924	−	11.8431i	1.33963	−	0.645133i	0.379634	−	0.925137i	$-0.376050\pi$
$337$	24.5924	−	11.8431i	1.33963	−	0.645133i	0.959999	+	0.280004i	$0.0903358\pi$
$338$	−5.93462	−	26.0013i	−0.322801	−	1.41428i
$339$	−7.62654	−	3.67275i	−0.414217	−	0.199476i
$340$	16.7991	+	8.09003i	0.911060	+	0.438743i
$341$	−1.26208	+	5.52955i	−0.0683456	+	0.299442i
$342$	5.45915	+	6.84555i	0.295197	+	0.370165i
$343$	−1.58499	+	1.98752i	−0.0855816	+	0.107316i
$344$	1.78616	+	7.82566i	0.0963030	+	0.421931i
$345$	−1.40259	+	6.14513i	−0.0755127	+	0.330843i
$346$	4.71813	−	5.91635i	0.253648	−	0.318065i
$347$	1.19493			0.0641473			0.0320736	−	0.999486i	$-0.489789\pi$
$347$	1.19493			0.0641473			0.0320736	+	0.999486i	$0.489789\pi$
$348$	−14.6662	+	4.04269i	−0.786189	+	0.216711i
$349$	7.25120			0.388148			0.194074	−	0.980987i	$-0.437830\pi$
$349$	7.25120			0.388148			0.194074	+	0.980987i	$0.437830\pi$
$350$	−58.0819	+	72.8324i	−3.10461	+	3.89305i
$351$	0.206175	−	0.903310i	0.0110048	−	0.0482151i
$352$	5.72366	+	25.0770i	0.305072	+	1.33661i
$353$	−3.28176	+	4.11519i	−0.174670	+	0.219030i	−0.861459	−	0.507828i	$-0.830449\pi$
$353$	−3.28176	+	4.11519i	−0.174670	+	0.219030i	0.686788	+	0.726858i	$0.259020\pi$
$354$	9.98471	+	12.5204i	0.530681	+	0.665453i
$355$	7.66510	−	33.5830i	0.406821	−	1.78240i
$356$	−42.0203	−	20.2359i	−2.22707	−	1.07250i
$357$	5.31897	+	2.56148i	0.281510	+	0.135568i
$358$	−5.88390	−	25.7791i	−0.310974	−	1.36247i
$359$	13.1799	−	6.34711i	0.695609	−	0.334987i	−0.0524468	−	0.998624i	$-0.516702\pi$
$359$	13.1799	−	6.34711i	0.695609	−	0.334987i	0.748055	+	0.663636i	$0.230988\pi$
$360$	7.38960			0.389466
$361$	2.80304	−	1.34988i	0.147529	−	0.0710461i
$362$	−3.31331	−	4.15476i	−0.174144	−	0.218369i
$363$	−0.901012	−	1.12983i	−0.0472908	−	0.0593008i
$364$	−8.60139	+	4.14221i	−0.450835	+	0.217111i
$365$	−30.8582			−1.61519
$366$	11.8853	−	5.72367i	0.621255	−	0.299181i
$367$	−1.23570	−	5.41395i	−0.0645030	−	0.282606i	0.932382	−	0.361474i	$-0.117726\pi$
$367$	−1.23570	−	5.41395i	−0.0645030	−	0.282606i	−0.996885	+	0.0788683i	$0.974869\pi$
$368$	2.32488	+	1.11960i	0.121193	+	0.0583634i
$369$	6.05081	+	2.91392i	0.314993	+	0.151693i
$370$	10.5716	−	46.3172i	0.549591	−	2.40792i
$371$	4.63508	+	5.81221i	0.240641	+	0.301755i
$372$	2.83183	−	3.55100i	0.146823	−	0.184111i
$373$	−6.61909	−	29.0001i	−0.342724	−	1.50157i	−0.793299	−	0.608832i	$-0.791638\pi$
$373$	−6.61909	−	29.0001i	−0.342724	−	1.50157i	0.450575	−	0.892738i	$-0.351219\pi$
$374$	−2.79102	+	12.2282i	−0.144320	+	0.632307i
$375$	16.8498	−	21.1290i	0.870119	−	1.09109i
$376$	−6.04891			−0.311949
$377$	−3.75852	+	3.28166i	−0.193574	+	0.169014i
$378$	8.01169			0.412077
$379$	−1.22348	+	1.53420i	−0.0628460	+	0.0788064i	−0.812261	−	0.583294i	$-0.801763\pi$
$379$	−1.22348	+	1.53420i	−0.0628460	+	0.0788064i	0.749415	+	0.662101i	$0.230335\pi$
$380$	−10.2176	+	44.7664i	−0.524154	+	2.29647i
$381$	−3.96202	−	17.3588i	−0.202981	−	0.889316i
$382$	−7.99356	+	10.0236i	−0.408986	+	0.512852i
$383$	−7.36748	−	9.23852i	−0.376460	−	0.472067i	0.557121	−	0.830431i	$-0.311906\pi$
$383$	−7.36748	−	9.23852i	−0.376460	−	0.472067i	−0.933582	+	0.358365i	$0.883334\pi$
$384$	2.95156	−	12.9316i	0.150621	−	0.659914i
$385$	−47.2713	−	22.7647i	−2.40917	−	1.16020i
$386$	39.5621	+	19.0521i	2.01366	+	0.969726i
$387$	−0.985625	−	4.31831i	−0.0501022	−	0.219512i
$388$	−25.5853	+	12.3212i	−1.29889	+	0.625515i
$389$	11.9013			0.603422			0.301711	−	0.953399i	$-0.402442\pi$
$389$	11.9013			0.603422			0.301711	+	0.953399i	$0.402442\pi$
$390$	7.47716	−	3.60081i	0.378621	−	0.182334i
$391$	1.55997	+	1.95614i	0.0788912	+	0.0989265i
$392$	−7.12172	−	8.93036i	−0.359701	−	0.451051i
$393$	10.2079	−	4.91586i	0.514919	−	0.247972i
$394$	25.7277			1.29614
$395$	1.05766	−	0.509342i	0.0532166	−	0.0256278i
$396$	2.21763	+	9.71609i	0.111440	+	0.488252i
$397$	−17.7291	−	8.53790i	−0.889799	−	0.428505i	−0.0676053	−	0.997712i	$-0.521536\pi$
$397$	−17.7291	−	8.53790i	−0.889799	−	0.428505i	−0.822194	+	0.569207i	$0.807250\pi$
$398$	−32.9481	−	15.8670i	−1.65154	−	0.795340i
$399$	−3.23513	+	14.1740i	−0.161959	+	0.709590i
$400$	−12.1022	−	15.1756i	−0.605108	−	0.758781i
$401$	−12.7980	+	16.0482i	−0.639102	+	0.801408i	−0.990890	−	0.134671i	$-0.957002\pi$
$401$	−12.7980	+	16.0482i	−0.639102	+	0.801408i	0.351789	+	0.936079i	$0.385574\pi$
$402$	−4.63485	−	20.3066i	−0.231165	−	1.01280i
$403$	0.331477	−	1.45229i	0.0165120	−	0.0723439i
$404$	14.5123	−	18.1978i	0.722012	−	0.905375i
$405$	−4.07769			−0.202622
$406$	−34.8965	−	25.3704i	−1.73189	−	1.25911i
$407$	18.7114			0.927490
$408$	1.82886	−	2.29331i	0.0905419	−	0.113536i
$409$	−7.16116	+	31.3751i	−0.354097	+	1.55140i	0.413524	+	0.910493i	$0.364298\pi$
$409$	−7.16116	+	31.3751i	−0.354097	+	1.55140i	−0.767620	+	0.640905i	$0.778559\pi$
$410$	13.3856	+	58.6461i	0.661067	+	2.89633i
$411$	−5.18273	+	6.49894i	−0.255645	+	0.320569i
$412$	13.4340	+	16.8457i	0.661845	+	0.829928i
$413$	−5.91702	+	25.9241i	−0.291157	+	1.27564i
$414$	3.05917	+	1.47322i	0.150350	+	0.0724047i
$415$	−23.7976	−	11.4603i	−1.16818	−	0.562566i
$416$	−1.50328	−	6.58628i	−0.0737041	−	0.322919i
$417$	−2.80449	+	1.35057i	−0.137337	+	0.0661379i
$418$	−30.8884			−1.51080
$419$	−1.42979	+	0.688551i	−0.0698499	+	0.0336379i	−0.468483	−	0.883473i	$-0.655199\pi$
$419$	−1.42979	+	0.688551i	−0.0698499	+	0.0336379i	0.398633	+	0.917111i	$0.369485\pi$
$420$	26.1962	+	32.8490i	1.27824	+	1.60287i
$421$	3.65562	+	4.58401i	0.178164	+	0.223411i	0.862892	−	0.505388i	$-0.168650\pi$
$421$	3.65562	+	4.58401i	0.178164	+	0.223411i	−0.684728	+	0.728799i	$0.740079\pi$
$422$	−47.9793	+	23.1056i	−2.33560	+	1.12476i
$423$	3.33787			0.162293
$424$	3.32790	−	1.60263i	0.161617	−	0.0778306i
$425$	−4.18795	−	18.3486i	−0.203145	−	0.890037i
$426$	−16.7183	−	8.05110i	−0.810004	−	0.390077i
$427$	19.7350	+	9.50387i	0.955043	+	0.459924i
$428$	10.5343	−	46.1536i	0.509192	−	2.23092i
$429$	2.03795	+	2.55550i	0.0983930	+	0.123381i
$430$	24.7362	−	31.0182i	1.19289	−	1.49583i
$431$	1.88305	+	8.25019i	0.0907034	+	0.397397i	0.999817	−	0.0191516i	$-0.00609653\pi$
$431$	1.88305	+	8.25019i	0.0907034	+	0.397397i	−0.909113	+	0.416549i	$0.863239\pi$
$432$	−0.371464	+	1.62749i	−0.0178721	+	0.0783027i
$433$	7.92985	−	9.94372i	0.381084	−	0.477864i	−0.553885	−	0.832593i	$-0.686855\pi$
$433$	7.92985	−	9.94372i	0.381084	−	0.477864i	0.934969	+	0.354729i	$0.115427\pi$
$434$	12.8808			0.618297
$435$	17.7612	+	12.9127i	0.851584	+	0.619117i
$436$	−35.9104			−1.71980
$437$	−3.84167	+	4.81731i	−0.183772	+	0.230443i
$438$	−3.69893	+	16.2061i	−0.176742	+	0.774357i
$439$	1.67011	+	7.31721i	0.0797098	+	0.349232i	0.999018	−	0.0443069i	$-0.0141080\pi$
$439$	1.67011	+	7.31721i	0.0797098	+	0.349232i	−0.919308	+	0.393538i	$0.871251\pi$
$440$	−16.2536	+	20.3814i	−0.774860	+	0.971644i
$441$	3.92987	+	4.92790i	0.187136	+	0.234662i
$442$	0.733039	−	3.21165i	0.0348671	−	0.152763i
$443$	10.5038	+	5.05834i	0.499048	+	0.240329i	0.666436	−	0.745562i	$-0.267819\pi$
$443$	10.5038	+	5.05834i	0.499048	+	0.240329i	−0.167388	+	0.985891i	$0.553533\pi$
$444$	−13.5001	−	6.50130i	−0.640686	−	0.308538i
$445$	14.9801	+	65.6320i	0.710124	+	3.11126i
$446$	56.0428	−	26.9888i	2.65370	−	1.27796i
$447$	−15.1558			−0.716847
$448$	41.6591	−	20.0620i	1.96821	−	0.947839i
$449$	−12.1276	−	15.2075i	−0.572337	−	0.717687i	0.408448	−	0.912782i	$-0.366070\pi$
$449$	−12.1276	−	15.2075i	−0.572337	−	0.717687i	−0.980784	+	0.195094i	$0.937499\pi$
$450$	−15.9245	−	19.9687i	−0.750688	−	0.941333i
$451$	−21.3458	+	10.2796i	−1.00514	+	0.484048i
$452$	−23.9132			−1.12478
$453$	0.611659	−	0.294559i	0.0287383	−	0.0138396i
$454$	4.82149	+	21.1243i	0.226284	+	0.991413i
$455$	12.4155	+	5.97897i	0.582046	+	0.280298i
$456$	6.50824	+	3.13420i	0.304776	+	0.146772i
$457$	−3.80789	+	16.6835i	−0.178126	+	0.780419i	0.804369	+	0.594130i	$0.202503\pi$
$457$	−3.80789	+	16.6835i	−0.178126	+	0.780419i	−0.982495	+	0.186290i	$0.940354\pi$
$458$	−21.4431	−	26.8888i	−1.00197	−	1.25643i
$459$	−1.00919	+	1.26548i	−0.0471049	+	0.0590677i
$460$	3.96232	+	17.3600i	0.184744	+	0.809416i
$461$	−1.89815	+	8.31633i	−0.0884056	+	0.387330i	−0.999702	−	0.0244213i	$-0.992226\pi$
$461$	−1.89815	+	8.31633i	−0.0884056	+	0.387330i	0.911296	+	0.411752i	$0.135083\pi$
$462$	−17.6219	+	22.0972i	−0.819845	+	1.02805i
$463$	1.49772			0.0696050			0.0348025	−	0.999394i	$-0.488920\pi$
$463$	1.49772			0.0696050			0.0348025	+	0.999394i	$0.488920\pi$
$464$	6.77172	−	5.91256i	0.314369	−	0.274484i
$465$	−6.55589			−0.304022
$466$	27.1006	−	33.9831i	1.25541	−	1.57424i
$467$	4.76878	−	20.8934i	0.220673	−	0.966831i	−0.736300	−	0.676655i	$-0.763429\pi$
$467$	4.76878	−	20.8934i	0.220673	−	0.966831i	0.956973	−	0.290176i	$-0.0937140\pi$
$468$	−0.582445	−	2.55186i	−0.0269235	−	0.117960i
$469$	21.5636	−	27.0398i	0.995712	−	1.24858i
$470$	18.6407	+	23.3747i	0.859831	+	1.07819i
$471$	−1.38760	+	6.07949i	−0.0639374	+	0.280128i
$472$	11.9035	+	5.73242i	0.547902	+	0.263856i
$473$	14.0783	+	6.77975i	0.647321	+	0.311733i
$474$	−0.140715	−	0.616515i	−0.00646328	−	0.0283175i
$475$	41.7583	−	20.1098i	1.91600	−	0.922699i
$476$	16.6778			0.764424
$477$	−1.83638	+	0.884354i	−0.0840821	+	0.0404918i
$478$	12.7820	+	16.0281i	0.584635	+	0.733109i
$479$	−17.8030	−	22.3242i	−0.813439	−	1.02002i	−0.999299	−	0.0374436i	$-0.988079\pi$
$479$	−17.8030	−	22.3242i	−0.813439	−	1.02002i	0.185860	−	0.982576i	$-0.440493\pi$
$480$	−26.7872	+	12.9000i	−1.22266	+	0.588803i
$481$	−4.91441			−0.224078
$482$	−48.6327	+	23.4203i	−2.21516	+	1.06677i
$483$	1.25456	+	5.49658i	0.0570844	+	0.250103i
$484$	−3.67816	−	1.77131i	−0.167189	−	0.0805140i
$485$	36.9304	+	17.7847i	1.67692	+	0.807563i
$486$	−0.488787	+	2.14152i	−0.0221718	+	0.0971412i
$487$	15.6842	+	19.6674i	0.710720	+	0.891214i	0.997773	−	0.0667002i	$-0.0212471\pi$
$487$	15.6842	+	19.6674i	0.710720	+	0.891214i	−0.287053	+	0.957915i	$0.592676\pi$
$488$	6.78561	−	8.50888i	0.307170	−	0.385179i
$489$	−3.40821	−	14.9323i	−0.154124	−	0.675263i
$490$	−12.5627	+	55.0407i	−0.567524	+	2.48648i
$491$	−13.5202	+	16.9537i	−0.610156	+	0.765111i	−0.986922	−	0.161197i	$-0.948465\pi$
$491$	−13.5202	+	16.9537i	−0.610156	+	0.765111i	0.376766	+	0.926308i	$0.377036\pi$
$492$	18.9725			0.855345
$493$	8.40310	−	2.31629i	0.378457	−	0.104321i
$494$	8.11259			0.365003
$495$	8.96897	−	11.2467i	0.403125	−	0.505503i
$496$	−0.597221	+	2.61659i	−0.0268160	+	0.117489i
$497$	−6.85613	−	30.0387i	−0.307539	−	1.34742i
$498$	−8.87133	+	11.1243i	−0.397534	+	0.498491i
$499$	3.54720	+	4.44805i	0.158795	+	0.199122i	0.854864	−	0.518853i	$-0.173641\pi$
$499$	3.54720	+	4.44805i	0.158795	+	0.199122i	−0.696069	+	0.717975i	$0.745069\pi$
$500$	16.9885	−	74.4316i	0.759750	−	3.32868i
$501$	−14.2228	−	6.84932i	−0.635426	−	0.306005i
$502$	9.22602	+	4.44302i	0.411778	+	0.198302i
$503$	2.10721	+	9.23230i	0.0939560	+	0.411648i	0.999932	−	0.0116814i	$-0.00371840\pi$
$503$	2.10721	+	9.23230i	0.0939560	+	0.411648i	−0.905976	+	0.423330i	$0.860861\pi$
$504$	5.95514	−	2.86785i	0.265263	−	0.127744i
$505$	−33.5970			−1.49505
$506$	−10.7920	+	5.19717i	−0.479764	+	0.231042i
$507$	7.57012	+	9.49263i	0.336201	+	0.421582i
$508$	−31.3614	−	39.3259i	−1.39144	−	1.74481i
$509$	27.5641	−	13.2742i	1.22176	−	0.588368i	0.291957	−	0.956431i	$-0.405693\pi$
$509$	27.5641	−	13.2742i	1.22176	−	0.588368i	0.929801	+	0.368064i	$0.119979\pi$
$510$	−14.4979			−0.641979
$511$	−24.8680	+	11.9758i	−1.10010	+	0.529779i
$512$	4.05479	+	17.7652i	0.179198	+	0.785117i
$513$	−3.59134	−	1.72950i	−0.158561	−	0.0763591i
$514$	−56.1148	−	27.0234i	−2.47512	−	1.19195i
$515$	6.92055	−	30.3209i	0.304956	−	1.33610i
$516$	−7.80172	−	9.78304i	−0.343451	−	0.430674i
$517$	−7.34173	+	9.20624i	−0.322889	+	0.404890i
$518$	−9.45588	−	41.4289i	−0.415467	−	1.82028i
$519$	−0.766589	+	3.35865i	−0.0336495	+	0.147428i
$520$	4.26889	−	5.35301i	0.187203	−	0.234745i
$521$	8.99098			0.393902			0.196951	−	0.980413i	$-0.436896\pi$
$521$	8.99098			0.393902			0.196951	+	0.980413i	$0.436896\pi$
$522$	8.91050	−	7.77998i	0.390002	−	0.340521i
$523$	−1.43930			−0.0629362			−0.0314681	−	0.999505i	$-0.510018\pi$
$523$	−1.43930			−0.0629362			−0.0314681	+	0.999505i	$0.510018\pi$
$524$	19.9561	−	25.0241i	0.871785	−	1.09318i
$525$	9.43698	−	41.3461i	0.411864	−	1.80449i
$526$	−13.0903	−	57.3522i	−0.570763	−	2.50067i
$527$	−1.62252	+	2.03458i	−0.0706781	+	0.0886275i
$528$	−3.67176	−	4.60425i	−0.159793	−	0.200374i
$529$	4.58629	−	20.0938i	0.199404	−	0.873645i
$530$	−16.4485	−	7.92116i	−0.714476	−	0.344073i
$531$	−6.56851	−	3.16323i	−0.285049	−	0.137272i
$532$	9.13928	+	40.0418i	0.396238	+	1.73603i
$533$	5.60632	−	2.69986i	0.242837	−	0.116944i
$534$	36.2642			1.56931
$535$	−61.5654	+	29.6483i	−2.66170	+	1.28181i
$536$	−10.7140	−	13.4350i	−0.462775	−	0.580302i
$537$	7.50542	+	9.41150i	0.323883	+	0.406136i
$538$	−1.55465	+	0.748681i	−0.0670258	+	0.0322779i
$539$	−22.2355			−0.957753
$540$	−10.3787	+	4.99812i	−0.446628	+	0.215085i
$541$	6.01572	+	26.3566i	0.258636	+	1.13316i	0.922711	+	0.385493i	$0.125969\pi$
$541$	6.01572	+	26.3566i	0.258636	+	1.13316i	−0.664075	+	0.747666i	$0.731174\pi$
$542$	−24.0484	−	11.5811i	−1.03297	−	0.497451i
$543$	2.17968	+	1.04968i	0.0935391	+	0.0450461i
$544$	−2.62614	+	11.5059i	−0.112595	+	0.493310i
$545$	32.3179	+	40.5254i	1.38435	+	1.73592i
$546$	4.62826	−	5.80365i	0.198071	−	0.248373i
$547$	8.29422	+	36.3394i	0.354635	+	1.55376i	0.766336	+	0.642440i	$0.222078\pi$
$547$	8.29422	+	36.3394i	0.354635	+	1.55376i	−0.411701	+	0.911319i	$0.635065\pi$
$548$	−5.22541	+	22.8940i	−0.223218	+	0.977984i
$549$	−3.74439	+	4.69532i	−0.159807	+	0.200391i
$550$	90.1022			3.84197
$551$	10.1660	+	18.9058i	0.433088	+	0.805413i
$552$	2.80125			0.119229
$553$	0.654676	−	0.820938i	0.0278397	−	0.0349098i
$554$	−7.71488	+	33.8011i	−0.327774	+	1.43607i
$555$	4.81273	+	21.0860i	0.204289	+	0.895049i
$556$	−5.48269	+	6.87508i	−0.232518	+	0.291568i
$557$	19.8070	+	24.8372i	0.839249	+	1.05239i	0.997882	+	0.0650476i	$0.0207199\pi$
$557$	19.8070	+	24.8372i	0.839249	+	1.05239i	−0.158633	+	0.987338i	$0.550709\pi$
$558$	−0.785846	+	3.44302i	−0.0332675	+	0.145755i
$559$	−3.69756	−	1.78065i	−0.156390	−	0.0753135i
$560$	−22.3689	−	10.7723i	−0.945259	−	0.455213i
$561$	−1.27061	−	5.56692i	−0.0536453	−	0.235036i
$562$	39.7242	−	19.1302i	1.67566	−	0.806957i
$563$	13.4735			0.567842			0.283921	−	0.958848i	$-0.408365\pi$
$563$	13.4735			0.567842			0.283921	+	0.958848i	$0.408365\pi$
$564$	8.49570	−	4.09132i	0.357734	−	0.172275i
$565$	21.5209	+	26.9864i	0.905392	+	1.13533i
$566$	2.67825	+	3.35842i	0.112575	+	0.141165i
$567$	−3.28613	+	1.58252i	−0.138005	+	0.0664595i
$568$	−15.3088			−0.642342
$569$	4.98991	−	2.40302i	0.209188	−	0.100740i	−0.326356	−	0.945247i	$-0.605821\pi$
$569$	4.98991	−	2.40302i	0.209188	−	0.100740i	0.535544	+	0.844507i	$0.320107\pi$
$570$	−7.94475	−	34.8082i	−0.332769	−	1.45796i
$571$	−37.2132	−	17.9209i	−1.55732	−	0.749968i	−0.560392	−	0.828228i	$-0.689349\pi$
$571$	−37.2132	−	17.9209i	−1.55732	−	0.749968i	−0.996933	+	0.0782596i	$0.975064\pi$
$572$	8.31942	+	4.00642i	0.347852	+	0.167517i
$573$	1.29877	−	5.69029i	0.0542569	−	0.237715i
$574$	33.5473	+	42.0670i	1.40024	+	1.75584i
$575$	11.2063	−	14.0522i	0.467334	−	0.586018i
$576$	2.82095	+	12.3594i	0.117540	+	0.514975i
$577$	8.85347	−	38.7896i	0.368575	−	1.61483i	−0.362123	−	0.932130i	$-0.617948\pi$
$577$	8.85347	−	38.7896i	0.368575	−	1.61483i	0.730698	−	0.682701i	$-0.239195\pi$
$578$	19.6943	−	24.6958i	0.819174	−	1.02721i
$579$	−19.9903			−0.830770
$580$	61.0340	+	11.0957i	2.53430	+	0.460722i
$581$	−23.6257			−0.980161
$582$	13.7670	−	17.2632i	0.570660	−	0.715584i
$583$	1.60001	−	7.01011i	0.0662657	−	0.290329i
$584$	3.05165	+	13.3702i	0.126278	+	0.553261i
$585$	−2.35563	+	2.95387i	−0.0973934	+	0.122127i
$586$	3.30637	+	4.14605i	0.136585	+	0.171272i
$587$	−8.61390	+	37.7400i	−0.355534	+	1.55769i	0.408647	+	0.912692i	$0.366001\pi$
$587$	−8.61390	+	37.7400i	−0.355534	+	1.55769i	−0.764181	+	0.645002i	$0.776856\pi$
$588$	16.0427	+	7.72577i	0.661590	+	0.318605i
$589$	−5.77396	−	2.78059i	−0.237912	−	0.114572i
$590$	−14.5308	−	63.6638i	−0.598225	−	2.62100i
$591$	−10.5527	+	5.08189i	−0.434079	+	0.209041i
$592$	8.85427			0.363908
$593$	1.26777	−	0.610524i	0.0520610	−	0.0250712i	−0.407672	−	0.913128i	$-0.633659\pi$
$593$	1.26777	−	0.610524i	0.0520610	−	0.0250712i	0.459733	+	0.888057i	$0.347945\pi$
$594$	−4.83145	−	6.05845i	−0.198237	−	0.248581i
$595$	−15.0093	−	18.8211i	−0.615322	−	0.771590i
$596$	−38.5753	+	18.5769i	−1.58011	+	0.760939i
$597$	16.6484			0.681373
$598$	2.83444	−	1.36500i	0.115909	−	0.0558188i
$599$	−6.84151	−	29.9746i	−0.279537	−	1.22473i	−0.898381	−	0.439217i	$-0.855256\pi$
$599$	−6.84151	−	29.9746i	−0.279537	−	1.22473i	0.618845	−	0.785513i	$-0.287601\pi$
$600$	−18.9847	−	9.14256i	−0.775048	−	0.373244i
$601$	11.9409	+	5.75041i	0.487078	+	0.234564i	0.661271	−	0.750147i	$-0.270017\pi$
$601$	11.9409	+	5.75041i	0.487078	+	0.234564i	−0.174193	+	0.984712i	$0.555732\pi$
$602$	7.89652	−	34.5969i	0.321838	−	1.41007i
$603$	5.91215	+	7.41360i	0.240761	+	0.301905i
$604$	1.19577	−	1.49945i	0.0486553	−	0.0610118i
$605$	1.31125	+	5.74496i	0.0533099	+	0.233566i
$606$	−4.02723	+	17.6444i	−0.163595	+	0.716756i
$607$	6.14313	−	7.70324i	0.249342	−	0.312665i	−0.641371	−	0.767231i	$-0.721634\pi$
$607$	6.14313	−	7.70324i	0.249342	−	0.312665i	0.890713	+	0.454566i	$0.150206\pi$
$608$	−29.0636			−1.17869
$609$	19.3247	+	3.51314i	0.783078	+	0.142359i
$610$	−53.7916			−2.17796
$611$	1.92825	−	2.41795i	0.0780087	−	0.0978198i
$612$	−1.01750	+	4.45795i	−0.0411299	+	0.180202i
$613$	5.13236	+	22.4863i	0.207294	+	0.908214i	0.966358	+	0.257199i	$0.0827996\pi$
$613$	5.13236	+	22.4863i	0.207294	+	0.908214i	−0.759064	+	0.651015i	$0.774343\pi$
$614$	1.52523	−	1.91258i	0.0615533	−	0.0771854i
$615$	−17.0745	−	21.4107i	−0.688509	−	0.863363i
$616$	−5.18863	+	22.7329i	−0.209056	+	0.915933i
$617$	1.93195	+	0.930376i	0.0777772	+	0.0374555i	0.472368	−	0.881401i	$-0.343399\pi$
$617$	1.93195	+	0.930376i	0.0777772	+	0.0374555i	−0.394591	+	0.918857i	$0.629114\pi$
$618$	−15.0944	−	7.26906i	−0.607184	−	0.292405i
$619$	−6.61917	−	29.0005i	−0.266047	−	1.16563i	−0.914569	−	0.404431i	$-0.867470\pi$
$619$	−6.61917	−	29.0005i	−0.266047	−	1.16563i	0.648522	−	0.761196i	$-0.275388\pi$
$620$	−16.6863	+	8.03572i	−0.670140	+	0.322722i
$621$	−1.54577			−0.0620296
$622$	8.76701	−	4.22197i	0.351525	−	0.169286i
$623$	37.5434	+	47.0780i	1.50415	+	1.88614i
$624$	0.964361	+	1.20927i	0.0386053	+	0.0484096i
$625$	−46.9059	+	22.5887i	−1.87624	+	0.903548i
$626$	66.1178			2.64260
$627$	12.6694	−	6.10125i	0.505966	−	0.243661i
$628$	3.91999	+	17.1746i	0.156425	+	0.685342i
$629$	7.73499	+	3.72497i	0.308414	+	0.148524i
$630$	−29.4339	−	14.1746i	−1.17267	−	0.564730i
$631$	1.00667	−	4.41052i	0.0400750	−	0.175580i	−0.950930	−	0.309407i	$-0.899869\pi$
$631$	1.00667	−	4.41052i	0.0400750	−	0.175580i	0.991005	+	0.133827i	$0.0427266\pi$
$632$	−0.325281	−	0.407889i	−0.0129390	−	0.0162250i
$633$	15.1156	−	18.9543i	0.600790	−	0.753367i
$634$	−3.03571	−	13.3003i	−0.120563	−	0.528222i
$635$	−16.1559	+	70.7836i	−0.641127	+	2.80896i
$636$	−3.59006	+	4.50179i	−0.142355	+	0.178508i
$637$	5.84000			0.231389
$638$	1.85923	+	41.6885i	0.0736076	+	1.65046i
$639$	8.44759			0.334182
$640$	−33.7228	+	42.2871i	−1.33301	+	1.67154i
$641$	6.84340	−	29.9829i	0.270298	−	1.18425i	−0.639364	−	0.768904i	$-0.720802\pi$
$641$	6.84340	−	29.9829i	0.270298	−	1.18425i	0.909662	−	0.415349i	$-0.136340\pi$
$642$	8.19093	+	35.8868i	0.323270	+	1.41634i
$643$	10.5190	−	13.1905i	0.414831	−	0.520181i	−0.529886	−	0.848069i	$-0.677765\pi$
$643$	10.5190	−	13.1905i	0.414831	−	0.520181i	0.944717	+	0.327888i	$0.106337\pi$
$644$	9.93045	+	12.4524i	0.391315	+	0.490693i
$645$	−4.01907	+	17.6087i	−0.158251	+	0.693342i
$646$	−12.7687	−	6.14910i	−0.502380	−	0.241933i
$647$	−12.7316	−	6.13122i	−0.500531	−	0.241043i	0.166543	−	0.986034i	$-0.446739\pi$
$647$	−12.7316	−	6.13122i	−0.500531	−	0.241043i	−0.667075	+	0.744991i	$0.732454\pi$
$648$	0.403254	+	1.76677i	0.0158413	+	0.0694053i
$649$	23.1721	−	11.1591i	0.909586	−	0.438034i
$650$	−23.6647			−0.928205
$651$	−5.28327	+	2.54429i	−0.207068	+	0.0997185i
$652$	−26.9777	−	33.8289i	−1.05653	−	1.32484i
$653$	−24.1439	−	30.2755i	−0.944823	−	1.18477i	−0.982647	−	0.185486i	$-0.940614\pi$
$653$	−24.1439	−	30.2755i	−0.944823	−	1.18477i	0.0378238	−	0.999284i	$-0.487957\pi$
$654$	25.1570	−	12.1150i	0.983717	−	0.473733i
$655$	−46.1997			−1.80517
$656$	−10.1009	+	4.86433i	−0.394374	+	0.189920i
$657$	−1.68394	−	7.37784i	−0.0656969	−	0.287837i
$658$	24.0937	+	11.6029i	0.939271	+	0.452329i
$659$	−15.6609	−	7.54188i	−0.610061	−	0.293790i	0.103231	−	0.994657i	$-0.467082\pi$
$659$	−15.6609	−	7.54188i	−0.610061	−	0.293790i	−0.713291	+	0.700868i	$0.752796\pi$
$660$	9.04282	−	39.6192i	0.351991	−	1.54217i
$661$	0.597977	+	0.749840i	0.0232586	+	0.0291654i	0.793325	−	0.608799i	$-0.208348\pi$
$661$	0.597977	+	0.749840i	0.0232586	+	0.0291654i	−0.770066	+	0.637964i	$0.779777\pi$
$662$	−13.7034	+	17.1835i	−0.532599	+	0.667858i
$663$	0.333717	+	1.46211i	0.0129605	+	0.0567836i
$664$	−2.61209	+	11.4443i	−0.101369	+	0.444126i
$665$	36.9628	−	46.3498i	1.43335	−	1.79737i
$666$	11.6508			0.451460
$667$	6.73292	+	4.89495i	0.260700	+	0.189533i
$668$	−44.5958			−1.72546
$669$	−17.6559	+	22.1398i	−0.682617	+	0.855975i
$670$	−18.8995	+	82.8040i	−0.730150	+	3.19900i
$671$	−4.71435	−	20.6549i	−0.181996	−	0.797375i
$672$	−16.5809	+	20.7918i	−0.639622	+	0.802061i
$673$	−18.7737	−	23.5415i	−0.723673	−	0.907458i	0.274866	−	0.961483i	$-0.411366\pi$
$673$	−18.7737	−	23.5415i	−0.723673	−	0.907458i	−0.998540	+	0.0540246i	$0.982795\pi$
$674$	−13.3417	+	58.4537i	−0.513903	+	2.25155i
$675$	10.4760	+	5.04499i	0.403223	+	0.194182i
$676$	30.9031	+	14.8822i	1.18858	+	0.572391i
$677$	−9.29384	−	40.7190i	−0.357191	−	1.56496i	−0.760155	−	0.649742i	$-0.774877\pi$
$677$	−9.29384	−	40.7190i	−0.357191	−	1.56496i	0.402964	−	0.915216i	$-0.367980\pi$
$678$	16.7524	−	8.06752i	0.643371	−	0.309831i
$679$	36.6636			1.40702
$680$	−10.7764	+	5.18964i	−0.413256	+	0.199014i
$681$	−6.15022	−	7.71213i	−0.235677	−	0.295529i
$682$	−7.76776	−	9.74046i	−0.297443	−	0.372981i
$683$	−36.2797	+	17.4714i	−1.38820	+	0.668524i	−0.970732	−	0.240165i	$-0.922798\pi$
$683$	−36.2797	+	17.4714i	−1.38820	+	0.668524i	−0.417473	+	0.908689i	$0.637084\pi$
$684$	−11.2607			−0.430564
$685$	30.5389	−	14.7068i	1.16683	−	0.561916i
$686$	−1.24256	−	5.44402i	−0.0474412	−	0.207854i
$687$	14.1065	+	6.79332i	0.538195	+	0.259181i
$688$	6.66188	+	3.20819i	0.253982	+	0.122311i
$689$	−0.420231	+	1.84115i	−0.0160095	+	0.0701423i
$690$	−8.63251	−	10.8248i	−0.328634	−	0.412094i
$691$	25.7995	−	32.3515i	0.981458	−	1.23071i	0.00844425	−	0.999964i	$-0.497312\pi$
$691$	25.7995	−	32.3515i	0.981458	−	1.23071i	0.973014	−	0.230746i	$-0.0741165\pi$
$692$	2.16562	+	9.48820i	0.0823245	+	0.360687i
$693$	2.86316	−	12.5443i	0.108762	−	0.476519i
$694$	−1.63652	+	2.05213i	−0.0621215	+	0.0778978i
$695$	12.6928			0.481467
$696$	3.83833	−	8.97250i	0.145492	−	0.340102i
$697$	−10.8704			−0.411747
$698$	−9.93089	+	12.4529i	−0.375890	+	0.471351i
$699$	−4.40323	+	19.2918i	−0.166545	+	0.729684i
$700$	−26.6596	−	116.803i	−1.00764	−	4.41474i
$701$	1.42703	−	1.78944i	0.0538981	−	0.0675861i	−0.754152	−	0.656700i	$-0.771952\pi$
$701$	1.42703	−	1.78944i	0.0538981	−	0.0675861i	0.808050	+	0.589114i	$0.200523\pi$
$702$	1.26894	+	1.59121i	0.0478932	+	0.0600562i
$703$	−4.70462	+	20.6123i	−0.177438	+	0.777406i
$704$	−40.2934	−	19.4043i	−1.51862	−	0.731327i
$705$	−12.2629	−	5.90551i	−0.461848	−	0.222414i
$706$	−2.57275	−	11.2719i	−0.0968266	−	0.424225i
$707$	−27.0752	+	13.0387i	−1.01827	+	0.490371i
$708$	−20.5957			−0.774034
$709$	24.6036	−	11.8485i	0.924009	−	0.444979i	0.0895083	−	0.995986i	$-0.471470\pi$
$709$	24.6036	−	11.8485i	0.924009	−	0.444979i	0.834501	+	0.551007i	$0.185756\pi$
$710$	47.1764	+	59.1574i	1.77050	+	2.22014i
$711$	0.179495	+	0.225079i	0.00673157	+	0.00844113i
$712$	26.9554	−	12.9811i	1.01020	−	0.486486i
$713$	−2.48521			−0.0930717
$714$	−11.6836	+	5.62653i	−0.437248	+	0.210568i
$715$	−2.96584	−	12.9942i	−0.110916	−	0.485956i
$716$	30.6390	+	14.7550i	1.14503	+	0.551420i
$717$	−8.40873	−	4.04943i	−0.314030	−	0.151229i
$718$	−7.15027	+	31.3274i	−0.266846	+	1.16913i
$719$	−11.8932	−	14.9135i	−0.443540	−	0.556181i	0.508933	−	0.860806i	$-0.330040\pi$
$719$	−11.8932	−	14.9135i	−0.443540	−	0.556181i	−0.952472	+	0.304625i	$0.901469\pi$
$720$	4.24413	−	5.32198i	0.158170	−	0.198338i
$721$	−6.19016	−	27.1209i	−0.230534	−	1.01003i
$722$	−1.52069	+	6.66257i	−0.0565941	+	0.247955i
$723$	15.3214	−	19.2125i	0.569810	−	0.714519i
$724$	6.83444			0.254000
$725$	−29.6547	−	55.1487i	−1.10135	−	2.04817i
$726$	3.17432			0.117810
$727$	−18.2417	+	22.8744i	−0.676547	+	0.848363i	−0.995031	−	0.0995652i	$-0.968255\pi$
$727$	−18.2417	+	22.8744i	−0.676547	+	0.848363i	0.318484	+	0.947928i	$0.396826\pi$
$728$	1.36275	−	5.97062i	0.0505070	−	0.221286i
$729$	−0.222521	−	0.974928i	−0.00824152	−	0.0361084i
$730$	42.2619	−	52.9947i	1.56418	−	1.96142i
$731$	4.47006	+	5.60528i	0.165331	+	0.207319i
$732$	−3.77522	+	16.5403i	−0.139536	+	0.611348i
$733$	−18.8742	−	9.08933i	−0.697134	−	0.335722i	0.0515302	−	0.998671i	$-0.483590\pi$
$733$	−18.8742	−	9.08933i	−0.697134	−	0.335722i	−0.748664	+	0.662949i	$0.769304\pi$
$734$	10.9901	+	5.29254i	0.405651	+	0.195351i
$735$	−5.71917	−	25.0573i	−0.210955	−	0.924253i
$736$	−10.1545	+	4.89014i	−0.374299	+	0.180253i
$737$	−33.4515			−1.23220
$738$	−13.2912	+	6.40068i	−0.489254	+	0.235612i
$739$	−21.0504	−	26.3964i	−0.774353	−	0.971008i	0.225642	−	0.974210i	$-0.427552\pi$
$739$	−21.0504	−	26.3964i	−0.774353	−	0.971008i	−0.999995	+	0.00320223i	$0.998981\pi$
$740$	38.0952	+	47.7698i	1.40041	+	1.75605i
$741$	−3.32752	+	1.60245i	−0.122239	+	0.0588674i
$742$	−16.3297			−0.599480
$743$	39.9078	−	19.2186i	1.46407	−	0.705061i	0.479099	−	0.877761i	$-0.340963\pi$
$743$	39.9078	−	19.2186i	1.46407	−	0.705061i	0.984974	+	0.172700i	$0.0552491\pi$
$744$	0.648330	+	2.84052i	0.0237689	+	0.104138i
$745$	55.6805	+	26.8143i	2.03998	+	0.982401i
$746$	58.8690	+	28.3498i	2.15535	+	1.03796i
$747$	1.44139	−	6.31514i	0.0527377	−	0.231059i
$748$	−10.0575	−	12.6117i	−0.367740	−	0.461131i
$749$	−38.1081	+	47.7861i	−1.39244	+	1.74606i
$750$	13.2095	+	57.8744i	0.482341	+	2.11327i
$751$	1.70282	−	7.46053i	0.0621367	−	0.272239i	−0.934310	−	0.356461i	$-0.883983\pi$
$751$	1.70282	−	7.46053i	0.0621367	−	0.272239i	0.996447	+	0.0842221i	$0.0268405\pi$
$752$	−3.47412	+	4.35641i	−0.126688	+	0.158862i
$753$	−4.66182			−0.169886
$754$	−0.488312	−	10.9492i	−0.0177833	−	0.398745i
$755$	−2.76830			−0.100749
$756$	−6.42428	+	8.05579i	−0.233649	+	0.292986i
$757$	−3.62389	+	15.8773i	−0.131713	+	0.577070i	0.865397	+	0.501088i	$0.167067\pi$
$757$	−3.62389	+	15.8773i	−0.131713	+	0.577070i	−0.997109	+	0.0759828i	$0.975791\pi$
$758$	−0.959153	−	4.20232i	−0.0348380	−	0.152635i
$759$	3.39996	−	4.26341i	0.123411	−	0.154752i
$760$	−18.3652	−	23.0293i	−0.666178	−	0.835360i
$761$	6.35279	−	27.8334i	0.230288	−	1.00896i	−0.719113	−	0.694894i	$-0.755451\pi$
$761$	6.35279	−	27.8334i	0.230288	−	1.00896i	0.949401	−	0.314066i	$-0.101691\pi$
$762$	35.2375	+	16.9695i	1.27652	+	0.614740i
$763$	41.7720	+	20.1163i	1.51225	+	0.728260i
$764$	−3.66904	−	16.0751i	−0.132741	−	0.581577i
$765$	5.94657	−	2.86372i	0.214999	−	0.103538i
$766$

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)

\(f(q)\)	\(=\)	\(q+(-1.36955 + 1.71736i) q^{2} +(0.222521 - 0.974928i) q^{3} +(-0.628623 - 2.75418i) q^{4} +(-2.54240 + 3.18806i) q^{5} +(1.36955 + 1.71736i) q^{6} +(-0.811607 + 3.55588i) q^{7} +(1.63274 + 0.786286i) q^{8} +(-0.900969 - 0.433884i) q^{9} +O(q^{10})\)	\(q+(-1.36955 + 1.71736i) q^{2} +(0.222521 - 0.974928i) q^{3} +(-0.628623 - 2.75418i) q^{4} +(-2.54240 + 3.18806i) q^{5} +(1.36955 + 1.71736i) q^{6} +(-0.811607 + 3.55588i) q^{7} +(1.63274 + 0.786286i) q^{8} +(-0.900969 - 0.433884i) q^{9} +(-1.99312 - 8.73243i) q^{10} +(3.17840 - 1.53064i) q^{11} -2.82501 q^{12} +(-0.834784 + 0.402011i) q^{13} +(-4.99521 - 6.26379i) q^{14} +(2.54240 + 3.18806i) q^{15} +(1.50403 - 0.724302i) q^{16} +1.61861 q^{17} +(1.97906 - 0.953065i) q^{18} +(0.886987 + 3.88614i) q^{19} +(10.3787 + 4.99812i) q^{20} +(3.28613 + 1.58252i) q^{21} +(-1.72433 + 7.55476i) q^{22} +(0.963772 + 1.20853i) q^{23} +(1.12989 - 1.41684i) q^{24} +(-2.58737 - 11.3360i) q^{25} +(0.452881 - 1.98420i) q^{26} +(-0.623490 + 0.781831i) q^{27} +10.3037 q^{28} +(5.19154 - 1.43104i) q^{29} -8.95700 q^{30} +(-1.00241 + 1.25699i) q^{31} +(-1.62246 + 7.10847i) q^{32} +(-0.785001 - 3.43931i) q^{33} +(-2.21677 + 2.77975i) q^{34} +(-9.27296 - 11.6279i) q^{35} +(-0.628623 + 2.75418i) q^{36} +(4.77878 + 2.30134i) q^{37} +(-7.88869 - 3.79899i) q^{38} +(0.206175 + 0.903310i) q^{39} +(-6.65780 + 3.20623i) q^{40} -6.71590 q^{41} +(-7.21828 + 3.47614i) q^{42} +(2.76166 + 3.46301i) q^{43} +(-6.21367 - 7.79170i) q^{44} +(3.67387 - 1.76924i) q^{45} -3.39542 q^{46} +(-3.00732 + 1.44825i) q^{47} +(-0.371464 - 1.62749i) q^{48} +(-5.67882 - 2.73478i) q^{49} +(23.0116 + 11.0818i) q^{50} +(0.360175 - 1.57803i) q^{51} +(1.63197 + 2.04643i) q^{52} +(1.27081 - 1.59355i) q^{53} +(-0.488787 - 2.14152i) q^{54} +(-3.20099 + 14.0244i) q^{55} +(-4.12109 + 5.16768i) q^{56} +3.98608 q^{57} +(-4.65248 + 10.8756i) q^{58} +7.29049 q^{59} +(7.18229 - 9.00630i) q^{60} +(1.33636 - 5.85497i) q^{61} +(-0.785846 - 3.44302i) q^{62} +(2.27407 - 2.85160i) q^{63} +(-7.90414 - 9.91148i) q^{64} +(0.840715 - 3.68341i) q^{65} +(6.98165 + 3.36219i) q^{66} +(-8.54330 - 4.11424i) q^{67} +(-1.01750 - 4.45795i) q^{68} +(1.39269 - 0.670684i) q^{69} +32.6692 q^{70} +(-7.61102 + 3.66527i) q^{71} +(-1.12989 - 1.41684i) q^{72} +(4.71831 + 5.91657i) q^{73} +(-10.4970 + 5.05509i) q^{74} -11.6275 q^{75} +(10.1456 - 4.88584i) q^{76} +(2.86316 + 12.5443i) q^{77} +(-1.83368 - 0.883053i) q^{78} +(-0.259377 - 0.124909i) q^{79} +(-1.51471 + 6.63640i) q^{80} +(0.623490 + 0.781831i) q^{81} +(9.19777 - 11.5336i) q^{82} +(1.44139 + 6.31514i) q^{83} +(2.29280 - 10.0454i) q^{84} +(-4.11515 + 5.16024i) q^{85} -9.72949 q^{86} +(-0.239930 - 5.37982i) q^{87} +6.39303 q^{88} +(10.2934 - 12.9075i) q^{89} +(-1.99312 + 8.73243i) q^{90} +(-0.751987 - 3.29467i) q^{91} +(2.72266 - 3.41411i) q^{92} +(1.00241 + 1.25699i) q^{93} +(1.63151 - 7.14811i) q^{94} +(-14.6443 - 7.05234i) q^{95} +(6.56921 + 3.16357i) q^{96} +(-2.23682 - 9.80015i) q^{97} +(12.4740 - 6.00718i) q^{98} -3.52776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9	\( 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9} + 6 q^{10} - 6 q^{11} - 22 q^{12} - 11 q^{13} - 2 q^{14} + 7 q^{15} + 18 q^{16} - 32 q^{17} - 2 q^{18} + 2 q^{19} + 51 q^{20} + 4 q^{21} + 20 q^{22} - 6 q^{23} - 4 q^{24} + 4 q^{25} - 3 q^{26} + 3 q^{27} - 48 q^{28} - 10 q^{29} + 8 q^{30} + 8 q^{31} + 55 q^{32} - 8 q^{33} + 6 q^{34} + 31 q^{35} - 6 q^{36} + 20 q^{37} - 20 q^{38} - 10 q^{39} - 59 q^{40} - 68 q^{41} - 19 q^{42} - 3 q^{43} - 10 q^{44} + 14 q^{45} - 12 q^{46} + 19 q^{47} + 24 q^{48} + 17 q^{49} + 23 q^{50} + 11 q^{51} - 4 q^{52} - q^{53} - 5 q^{54} + 3 q^{55} + 7 q^{56} - 2 q^{57} - 30 q^{58} + 20 q^{59} + 47 q^{60} + 24 q^{61} + 79 q^{62} + 3 q^{63} - 23 q^{64} + 6 q^{65} + 50 q^{66} - 14 q^{67} - 8 q^{68} - 8 q^{69} + 28 q^{70} - 28 q^{71} + 4 q^{72} + 43 q^{73} - 47 q^{74} - 18 q^{75} + 19 q^{76} + 26 q^{77} - 11 q^{78} + 9 q^{79} - 74 q^{80} - 3 q^{81} - 17 q^{82} + 8 q^{83} - 15 q^{84} - 21 q^{85} - 140 q^{86} - 11 q^{87} - 58 q^{88} - 6 q^{89} + 6 q^{90} - 15 q^{91} + 11 q^{92} - 8 q^{93} + 6 q^{94} - 16 q^{95} + 36 q^{96} - 81 q^{97} - 11 q^{98} - 6 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9 + 6 * q^10 - 6 * q^11 - 22 * q^12 - 11 * q^13 - 2 * q^14 + 7 * q^15 + 18 * q^16 - 32 * q^17 - 2 * q^18 + 2 * q^19 + 51 * q^20 + 4 * q^21 + 20 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 - 3 * q^26 + 3 * q^27 - 48 * q^28 - 10 * q^29 + 8 * q^30 + 8 * q^31 + 55 * q^32 - 8 * q^33 + 6 * q^34 + 31 * q^35 - 6 * q^36 + 20 * q^37 - 20 * q^38 - 10 * q^39 - 59 * q^40 - 68 * q^41 - 19 * q^42 - 3 * q^43 - 10 * q^44 + 14 * q^45 - 12 * q^46 + 19 * q^47 + 24 * q^48 + 17 * q^49 + 23 * q^50 + 11 * q^51 - 4 * q^52 - q^53 - 5 * q^54 + 3 * q^55 + 7 * q^56 - 2 * q^57 - 30 * q^58 + 20 * q^59 + 47 * q^60 + 24 * q^61 + 79 * q^62 + 3 * q^63 - 23 * q^64 + 6 * q^65 + 50 * q^66 - 14 * q^67 - 8 * q^68 - 8 * q^69 + 28 * q^70 - 28 * q^71 + 4 * q^72 + 43 * q^73 - 47 * q^74 - 18 * q^75 + 19 * q^76 + 26 * q^77 - 11 * q^78 + 9 * q^79 - 74 * q^80 - 3 * q^81 - 17 * q^82 + 8 * q^83 - 15 * q^84 - 21 * q^85 - 140 * q^86 - 11 * q^87 - 58 * q^88 - 6 * q^89 + 6 * q^90 - 15 * q^91 + 11 * q^92 - 8 * q^93 + 6 * q^94 - 16 * q^95 + 36 * q^96 - 81 * q^97 - 11 * q^98 - 6 * q^99

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