LMFDB - Embedded newform 87.2.g.b.49.3

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			49.3
Root			$-1.23500 + 1.54863i$ of defining polynomial
Character	$\chi$	$=$	87.49
Dual form			87.2.g.b.16.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.78462 - 0.859427i) q^{2} +(-0.623490 - 0.781831i) q^{3} +(1.19927 - 1.50384i) q^{4} +(-1.09830 + 0.528911i) q^{5} +(-1.78462 - 0.859427i) q^{6} +(0.245180 + 0.307445i) q^{7} +(-0.0337262 + 0.147764i) q^{8} +(-0.222521 + 0.974928i) q^{9} +O(q^{10})$	\(q+(1.78462 - 0.859427i) q^{2} +(-0.623490 - 0.781831i) q^{3} +(1.19927 - 1.50384i) q^{4} +(-1.09830 + 0.528911i) q^{5} +(-1.78462 - 0.859427i) q^{6} +(0.245180 + 0.307445i) q^{7} +(-0.0337262 + 0.147764i) q^{8} +(-0.222521 + 0.974928i) q^{9} +(-1.50548 + 1.88781i) q^{10} +(0.554919 + 2.43126i) q^{11} -1.92348 q^{12} +(-0.735270 - 3.22143i) q^{13} +(0.701779 + 0.337959i) q^{14} +(1.09830 + 0.528911i) q^{15} +(0.922834 + 4.04320i) q^{16} -4.30028 q^{17} +(0.440765 + 1.93112i) q^{18} +(3.34887 - 4.19936i) q^{19} +(-0.521757 + 2.28597i) q^{20} +(0.0875036 - 0.383378i) q^{21} +(3.07981 + 3.86196i) q^{22} +(-2.70461 - 1.30247i) q^{23} +(0.136554 - 0.0657611i) q^{24} +(-2.19094 + 2.74736i) q^{25} +(-4.08076 - 5.11712i) q^{26} +(0.900969 - 0.433884i) q^{27} +0.756386 q^{28} +(-1.86053 - 5.05355i) q^{29} +2.41460 q^{30} +(9.01303 - 4.34044i) q^{31} +(4.93275 + 6.18547i) q^{32} +(1.55485 - 1.94972i) q^{33} +(-7.67437 + 3.69578i) q^{34} +(-0.431891 - 0.207988i) q^{35} +(1.19927 + 1.50384i) q^{36} +(-0.812038 + 3.55777i) q^{37} +(2.36742 - 10.3724i) q^{38} +(-2.06018 + 2.58339i) q^{39} +(-0.0411127 - 0.180127i) q^{40} -7.82011 q^{41} +(-0.173325 - 0.759387i) q^{42} +(-2.11613 - 1.01908i) q^{43} +(4.32172 + 2.08123i) q^{44} +(-0.271257 - 1.18845i) q^{45} -5.94608 q^{46} +(1.90056 + 8.32691i) q^{47} +(2.58572 - 3.24240i) q^{48} +(1.52324 - 6.67374i) q^{49} +(-1.54885 + 6.78594i) q^{50} +(2.68118 + 3.36210i) q^{51} +(-5.72630 - 2.75764i) q^{52} +(9.83963 - 4.73852i) q^{53} +(1.23500 - 1.54863i) q^{54} +(-1.89539 - 2.37674i) q^{55} +(-0.0536983 + 0.0258597i) q^{56} -5.37118 q^{57} +(-7.66351 - 7.41968i) q^{58} +10.2851 q^{59} +(2.11255 - 1.01735i) q^{60} +(2.32106 + 2.91052i) q^{61} +(12.3545 - 15.4921i) q^{62} +(-0.354295 + 0.170619i) q^{63} +(6.64609 + 3.20059i) q^{64} +(2.51140 + 3.14919i) q^{65} +(1.09917 - 4.81578i) q^{66} +(-1.14527 + 5.01776i) q^{67} +(-5.15721 + 6.46693i) q^{68} +(0.667984 + 2.92663i) q^{69} -0.949512 q^{70} +(1.80048 + 7.88840i) q^{71} +(-0.136554 - 0.0657611i) q^{72} +(-7.88943 - 3.79935i) q^{73} +(1.60847 + 7.04716i) q^{74} +3.51400 q^{75} +(-2.29895 - 10.0723i) q^{76} +(-0.611425 + 0.766702i) q^{77} +(-1.45641 + 6.38094i) q^{78} +(-1.62424 + 7.11624i) q^{79} +(-3.15204 - 3.95253i) q^{80} +(-0.900969 - 0.433884i) q^{81} +(-13.9559 + 6.72082i) q^{82} +(-2.33795 + 2.93170i) q^{83} +(-0.471599 - 0.591366i) q^{84} +(4.72298 - 2.27447i) q^{85} -4.65232 q^{86} +(-2.79100 + 4.60546i) q^{87} -0.377968 q^{88} +(-9.38092 + 4.51762i) q^{89} +(-1.50548 - 1.88781i) q^{90} +(0.810141 - 1.01588i) q^{91} +(-5.20227 + 2.50528i) q^{92} +(-9.01303 - 4.34044i) q^{93} +(10.5482 + 13.2270i) q^{94} +(-1.45697 + 6.38339i) q^{95} +(1.76048 - 7.71316i) q^{96} +(-10.1017 + 12.6672i) q^{97} +(-3.01719 - 13.2192i) q^{98} -2.49378 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 $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{6}{7}\right)$	$1$

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 $

$2$	1.78462	−	0.859427i	1.26192	−	0.607707i	0.321236	−	0.946999i	$-0.395902\pi$
$2$	1.78462	−	0.859427i	1.26192	−	0.607707i	0.940681	+	0.339292i	$0.110188\pi$
$3$	−0.623490	−	0.781831i	−0.359972	−	0.451391i
$3$	−0.623490	−	0.781831i	−0.359972	−	0.451391i
$4$	1.19927	−	1.50384i	0.599636	−	0.751920i
$5$	−1.09830	+	0.528911i	−0.491173	+	0.236536i	−0.663040	−	0.748584i	$-0.730734\pi$
$5$	−1.09830	+	0.528911i	−0.491173	+	0.236536i	0.171867	+	0.985120i	$0.445020\pi$
$6$	−1.78462	−	0.859427i	−0.728568	−	0.350860i
$7$	0.245180	+	0.307445i	0.0926692	+	0.116203i	0.826004	−	0.563664i	$-0.190609\pi$
$7$	0.245180	+	0.307445i	0.0926692	+	0.116203i	−0.733335	+	0.679867i	$0.762037\pi$
$8$	−0.0337262	+	0.147764i	−0.0119240	+	0.0522424i
$9$	−0.222521	+	0.974928i	−0.0741736	+	0.324976i
$10$	−1.50548	+	1.88781i	−0.476074	+	0.596978i
$11$	0.554919	+	2.43126i	0.167314	+	0.733052i	0.987064	+	0.160329i	$0.0512557\pi$
$11$	0.554919	+	2.43126i	0.167314	+	0.733052i	−0.819749	+	0.572723i	$0.805887\pi$
$12$	−1.92348			−0.555262
$13$	−0.735270	−	3.22143i	−0.203927	−	0.893464i	−0.968517	−	0.248947i	$-0.919916\pi$
$13$	−0.735270	−	3.22143i	−0.203927	−	0.893464i	0.764590	−	0.644517i	$-0.222942\pi$
$14$	0.701779	+	0.337959i	0.187558	+	0.0903234i
$15$	1.09830	+	0.528911i	0.283579	+	0.136564i
$16$	0.922834	+	4.04320i	0.230709	+	1.01080i
$17$	−4.30028			−1.04297			−0.521486	−	0.853260i	$-0.674622\pi$
$17$	−4.30028			−1.04297			−0.521486	+	0.853260i	$0.674622\pi$
$18$	0.440765	+	1.93112i	0.103889	+	0.455168i
$19$	3.34887	−	4.19936i	0.768284	−	0.963398i	−0.231671	−	0.972794i	$-0.574419\pi$
$19$	3.34887	−	4.19936i	0.768284	−	0.963398i	0.999956	+	0.00939593i	$0.00299086\pi$
$20$	−0.521757	+	2.28597i	−0.116669	+	0.511158i
$21$	0.0875036	−	0.383378i	0.0190948	−	0.0836600i
$22$	3.07981	+	3.86196i	0.656618	+	0.823372i
$23$	−2.70461	−	1.30247i	−0.563951	−	0.271584i	0.130112	−	0.991499i	$-0.458466\pi$
$23$	−2.70461	−	1.30247i	−0.563951	−	0.271584i	−0.694062	+	0.719915i	$0.744181\pi$
$24$	0.136554	−	0.0657611i	0.0278741	−	0.0134234i
$25$	−2.19094	+	2.74736i	−0.438189	+	0.549471i
$26$	−4.08076	−	5.11712i	−0.800304	−	1.00355i
$27$	0.900969	−	0.433884i	0.173392	−	0.0835010i
$28$	0.756386			0.142943
$29$	−1.86053	−	5.05355i	−0.345492	−	0.938422i
$29$	−1.86053	−	5.05355i	−0.345492	−	0.938422i
$30$	2.41460			0.440844
$31$	9.01303	−	4.34044i	1.61879	−	0.779567i	0.618805	−	0.785544i	$-0.287617\pi$
$31$	9.01303	−	4.34044i	1.61879	−	0.779567i	0.999982	+	0.00597750i	$0.00190271\pi$
$32$	4.93275	+	6.18547i	0.871995	+	1.09345i
$33$	1.55485	−	1.94972i	0.270664	−	0.339402i
$34$	−7.67437	+	3.69578i	−1.31614	+	0.633821i
$35$	−0.431891	−	0.207988i	−0.0730029	−	0.0351564i
$36$	1.19927	+	1.50384i	0.199879	+	0.250640i
$37$	−0.812038	+	3.55777i	−0.133498	+	0.584894i	0.863283	+	0.504721i	$0.168405\pi$
$37$	−0.812038	+	3.55777i	−0.133498	+	0.584894i	−0.996781	+	0.0801733i	$0.974453\pi$
$38$	2.36742	−	10.3724i	0.384047	−	1.68262i
$39$	−2.06018	+	2.58339i	−0.329893	+	0.413673i
$40$	−0.0411127	−	0.180127i	−0.00650049	−	0.0284805i
$41$	−7.82011			−1.22130			−0.610648	−	0.791902i	$-0.709091\pi$
$41$	−7.82011			−1.22130			−0.610648	+	0.791902i	$0.709091\pi$
$42$	−0.173325	−	0.759387i	−0.0267447	−	0.117176i
$43$	−2.11613	−	1.01908i	−0.322708	−	0.155408i	0.265515	−	0.964107i	$-0.414458\pi$
$43$	−2.11613	−	1.01908i	−0.322708	−	0.155408i	−0.588223	+	0.808699i	$0.700172\pi$
$44$	4.32172	+	2.08123i	0.651524	+	0.313757i
$45$	−0.271257	−	1.18845i	−0.0404366	−	0.177164i
$46$	−5.94608			−0.876702
$47$	1.90056	+	8.32691i	0.277226	+	1.21461i	0.901284	+	0.433228i	$0.142625\pi$
$47$	1.90056	+	8.32691i	0.277226	+	1.21461i	−0.624059	+	0.781377i	$0.714517\pi$
$48$	2.58572	−	3.24240i	0.373217	−	0.468000i
$49$	1.52324	−	6.67374i	0.217605	−	0.953391i
$50$	−1.54885	+	6.78594i	−0.219040	+	0.959677i
$51$	2.68118	+	3.36210i	0.375440	+	0.470787i
$52$	−5.72630	−	2.75764i	−0.794095	−	0.382416i
$53$	9.83963	−	4.73852i	1.35158	−	0.650885i	0.388836	−	0.921307i	$-0.372877\pi$
$53$	9.83963	−	4.73852i	1.35158	−	0.650885i	0.962742	+	0.270422i	$0.0871632\pi$
$54$	1.23500	−	1.54863i	0.168062	−	0.210743i
$55$	−1.89539	−	2.37674i	−0.255574	−	0.320479i
$56$	−0.0536983	+	0.0258597i	−0.00717574	+	0.00345565i
$57$	−5.37118			−0.711430
$58$	−7.66351	−	7.41968i	−1.00627	−	0.974252i
$59$	10.2851			1.33901			0.669503	−	0.742809i	$-0.266507\pi$
$59$	10.2851			1.33901			0.669503	+	0.742809i	$0.266507\pi$
$60$	2.11255	−	1.01735i	0.272729	−	0.131340i
$61$	2.32106	+	2.91052i	0.297182	+	0.372654i	0.907895	−	0.419198i	$-0.137689\pi$
$61$	2.32106	+	2.91052i	0.297182	+	0.372654i	−0.610713	+	0.791852i	$0.709117\pi$
$62$	12.3545	−	15.4921i	1.56903	−	1.96750i
$63$	−0.354295	+	0.170619i	−0.0446369	+	0.0214960i
$64$	6.64609	+	3.20059i	0.830761	+	0.400073i
$65$	2.51140	+	3.14919i	0.311500	+	0.390609i
$66$	1.09917	−	4.81578i	0.135299	−	0.592782i
$67$	−1.14527	+	5.01776i	−0.139917	+	0.613017i	0.855534	+	0.517746i	$0.173229\pi$
$67$	−1.14527	+	5.01776i	−0.139917	+	0.613017i	−0.995451	+	0.0952705i	$0.969628\pi$
$68$	−5.15721	+	6.46693i	−0.625403	+	0.784231i
$69$	0.667984	+	2.92663i	0.0804158	+	0.352325i
$70$	−0.949512			−0.113488
$71$	1.80048	+	7.88840i	0.213677	+	0.936181i	0.962044	+	0.272896i	$0.0879813\pi$
$71$	1.80048	+	7.88840i	0.213677	+	0.936181i	−0.748366	+	0.663285i	$0.769162\pi$
$72$	−0.136554	−	0.0657611i	−0.0160931	−	0.00775003i
$73$	−7.88943	−	3.79935i	−0.923387	−	0.444680i	−0.0891081	−	0.996022i	$-0.528402\pi$
$73$	−7.88943	−	3.79935i	−0.923387	−	0.444680i	−0.834279	+	0.551342i	$0.814116\pi$
$74$	1.60847	+	7.04716i	0.186981	+	0.819215i
$75$	3.51400			0.405762
$76$	−2.29895	−	10.0723i	−0.263707	−	1.15538i
$77$	−0.611425	+	0.766702i	−0.0696783	+	0.0873738i
$78$	−1.45641	+	6.38094i	−0.164906	+	0.722499i
$79$	−1.62424	+	7.11624i	−0.182741	+	0.800640i	0.797577	+	0.603216i	$0.206115\pi$
$79$	−1.62424	+	7.11624i	−0.182741	+	0.800640i	−0.980318	+	0.197423i	$0.936743\pi$
$80$	−3.15204	−	3.95253i	−0.352409	−	0.441907i
$81$	−0.900969	−	0.433884i	−0.100108	−	0.0482093i
$82$	−13.9559	+	6.72082i	−1.54117	+	0.742190i
$83$	−2.33795	+	2.93170i	−0.256624	+	0.321796i	−0.893408	−	0.449246i	$-0.851693\pi$
$83$	−2.33795	+	2.93170i	−0.256624	+	0.321796i	0.636785	+	0.771042i	$0.280264\pi$
$84$	−0.471599	−	0.591366i	−0.0514556	−	0.0645233i
$85$	4.72298	−	2.27447i	0.512279	−	0.246701i
$86$	−4.65232			−0.501672
$87$	−2.79100	+	4.60546i	−0.299227	+	0.493758i
$88$	−0.377968			−0.0402915
$89$	−9.38092	+	4.51762i	−0.994376	+	0.478866i	−0.859026	−	0.511932i	$-0.828930\pi$
$89$	−9.38092	+	4.51762i	−0.994376	+	0.478866i	−0.135350	+	0.990798i	$0.543216\pi$
$90$	−1.50548	−	1.88781i	−0.158691	−	0.198993i
$91$	0.810141	−	1.01588i	0.0849258	−	0.106494i
$92$	−5.20227	+	2.50528i	−0.542375	+	0.261194i
$93$	−9.01303	−	4.34044i	−0.934607	−	0.450083i
$94$	10.5482	+	13.2270i	1.08796	+	1.36426i
$95$	−1.45697	+	6.38339i	−0.149482	+	0.654922i
$96$	1.76048	−	7.71316i	0.179678	−	0.787221i
$97$	−10.1017	+	12.6672i	−1.02568	+	1.28616i	−0.0681928	+	0.997672i	$0.521723\pi$
$97$	−10.1017	+	12.6672i	−1.02568	+	1.28616i	−0.957484	+	0.288486i	$0.906848\pi$
$98$	−3.01719	−	13.2192i	−0.304783	−	1.33534i
$99$	−2.49378			−0.250635
$100$	1.50404	+	6.58965i	0.150404	+	0.658965i
$101$	2.49049	+	1.19936i	0.247813	+	0.119341i	0.553668	−	0.832738i	$-0.313228\pi$
$101$	2.49049	+	1.19936i	0.247813	+	0.119341i	−0.305854	+	0.952078i	$0.598942\pi$
$102$	7.67437	+	3.69578i	0.759875	+	0.365937i
$103$	−0.842490	−	3.69119i	−0.0830130	−	0.363704i	0.916311	−	0.400467i	$-0.131152\pi$
$103$	−0.842490	−	3.69119i	−0.0830130	−	0.363704i	−0.999324	+	0.0367637i	$0.988295\pi$
$104$	0.500809			0.0491084
$105$	0.106668	+	0.467344i	0.0104098	+	0.0456081i
$106$	13.4876	−	16.9129i	1.31003	−	1.64273i
$107$	2.51363	−	11.0129i	0.243002	−	1.06466i	−0.695266	−	0.718752i	$-0.744714\pi$
$107$	2.51363	−	11.0129i	0.243002	−	1.06466i	0.938268	−	0.345909i	$-0.112429\pi$
$108$	0.428015	−	1.87526i	0.0411858	−	0.180447i
$109$	9.27648	+	11.6323i	0.888526	+	1.11418i	0.992819	+	0.119630i	$0.0381707\pi$
$109$	9.27648	+	11.6323i	0.888526	+	1.11418i	−0.104293	+	0.994547i	$0.533258\pi$
$110$	−5.42518	−	2.61263i	−0.517270	−	0.249104i
$111$	3.28788	−	1.58336i	0.312071	−	0.150286i
$112$	−1.01680	+	1.27503i	−0.0960789	+	0.120479i
$113$	−0.0109212	−	0.0136948i	−0.00102738	−	0.00128830i	0.781318	−	0.624134i	$-0.214548\pi$
$113$	−0.0109212	−	0.0136948i	−0.00102738	−	0.00128830i	−0.782345	+	0.622845i	$0.785977\pi$
$114$	−9.58551	+	4.61614i	−0.897765	+	0.432341i
$115$	3.65936			0.341237
$116$	−9.83102	−	3.26264i	−0.912787	−	0.302929i
$117$	3.30428			0.305480
$118$	18.3550	−	8.83930i	1.68971	−	0.813724i
$119$	−1.05434	−	1.32210i	−0.0966513	−	0.121197i
$120$	−0.115195	+	0.144450i	−0.0105158	+	0.0131865i
$121$	4.30757	−	2.07442i	0.391598	−	0.188583i
$122$	6.64360	+	3.19939i	0.601483	+	0.289659i
$123$	4.87576	+	6.11401i	0.439632	+	0.551281i
$124$	4.28174	−	18.7595i	0.384511	−	1.68465i
$125$	2.30948	−	10.1185i	0.206566	−	0.905025i
$126$	−0.485646	+	0.608981i	−0.0432648	+	0.0542524i
$127$	−2.28217	−	9.99883i	−0.202510	−	0.887253i	−0.969402	−	0.245477i	$-0.921055\pi$
$127$	−2.28217	−	9.99883i	−0.202510	−	0.887253i	0.766893	−	0.641775i	$-0.221802\pi$
$128$	−1.21162			−0.107093
$129$	0.522642	+	2.28984i	0.0460161	+	0.201610i
$130$	7.18839	+	3.46174i	0.630463	+	0.303615i
$131$	−4.46222	−	2.14889i	−0.389866	−	0.187750i	0.228674	−	0.973503i	$-0.426561\pi$
$131$	−4.46222	−	2.14889i	−0.389866	−	0.187750i	−0.618540	+	0.785754i	$0.712275\pi$
$132$	−1.06738	−	4.67648i	−0.0929032	−	0.407036i
$133$	2.11215			0.183146
$134$	2.26853	+	9.93906i	0.195971	+	0.858604i
$135$	−0.760044	+	0.953065i	−0.0654142	+	0.0820268i
$136$	0.145032	−	0.635427i	0.0124364	−	0.0544874i
$137$	3.01935	−	13.2286i	0.257960	−	1.13020i	−0.665468	−	0.746426i	$-0.731768\pi$
$137$	3.01935	−	13.2286i	0.257960	−	1.13020i	0.923428	−	0.383771i	$-0.125375\pi$
$138$	3.70732	+	4.64884i	0.315588	+	0.395735i
$139$	−14.8411	−	7.14709i	−1.25880	−	0.606208i	−0.318946	−	0.947773i	$-0.603329\pi$
$139$	−14.8411	−	7.14709i	−1.25880	−	0.606208i	−0.939858	+	0.341564i	$0.889043\pi$
$140$	−0.830735	+	0.400061i	−0.0702099	+	0.0338113i
$141$	5.32526	−	6.67767i	0.448468	−	0.562361i
$142$	9.99267	+	12.5304i	0.838567	+	1.05153i
$143$	7.42411	−	3.57527i	0.620836	−	0.298979i
$144$	−4.14718			−0.345598
$145$	4.71630	+	4.56624i	0.391667	+	0.379206i
$146$	−17.3449			−1.43547
$147$	−6.16746	+	2.97009i	−0.508684	+	0.244969i
$148$	4.37646	+	5.48791i	0.359743	+	0.451103i
$149$	4.97975	−	6.24440i	0.407957	−	0.511562i	−0.534829	−	0.844960i	$-0.679624\pi$
$149$	4.97975	−	6.24440i	0.407957	−	0.511562i	0.942786	+	0.333399i	$0.108195\pi$
$150$	6.27115	−	3.02003i	0.512037	−	0.246584i
$151$	18.2927	+	8.80931i	1.48864	+	0.716891i	0.988803	−	0.149228i	$-0.0476788\pi$
$151$	18.2927	+	8.80931i	1.48864	+	0.716891i	0.499837	+	0.866119i	$0.333393\pi$
$152$	0.507569	+	0.636471i	0.0411693	+	0.0516246i
$153$	0.956903	−	4.19246i	0.0773610	−	0.338941i
$154$	−0.432235	+	1.89375i	−0.0348305	+	0.152602i
$155$	−7.60326	+	9.53418i	−0.610708	+	0.765804i
$156$	1.41428	+	6.19636i	0.113233	+	0.496106i
$157$	−4.08988			−0.326408			−0.163204	−	0.986592i	$-0.552183\pi$
$157$	−4.08988			−0.326408			−0.163204	+	0.986592i	$0.552183\pi$
$158$	3.21725	+	14.0957i	0.255951	+	1.12139i
$159$	−9.83963	−	4.73852i	−0.780334	−	0.375789i
$160$	−8.68918	−	4.18449i	−0.686940	−	0.330813i
$161$	−0.262676	−	1.15086i	−0.0207018	−	0.0907005i
$162$	−1.98078			−0.155625
$163$	−4.28966	−	18.7942i	−0.335992	−	1.47208i	−0.807317	−	0.590118i	$-0.799081\pi$
$163$	−4.28966	−	18.7942i	−0.335992	−	1.47208i	0.471325	−	0.881960i	$-0.343776\pi$
$164$	−9.37844	+	11.7602i	−0.732333	+	0.918316i
$165$	−0.676455	+	2.96374i	−0.0526620	+	0.230727i
$166$	−1.65277	+	7.24127i	−0.128280	+	0.562031i
$167$	−2.02456	−	2.53871i	−0.156665	−	0.196452i	0.697304	−	0.716775i	$-0.254383\pi$
$167$	−2.02456	−	2.53871i	−0.156665	−	0.196452i	−0.853969	+	0.520324i	$0.825811\pi$
$168$	0.0536983	+	0.0258597i	0.00414292	+	0.00199512i
$169$	1.87561	−	0.903244i	0.144277	−	0.0694803i
$170$	6.47398	−	8.11812i	0.496532	−	0.622631i
$171$	3.34887	+	4.19936i	0.256095	+	0.321133i
$172$	−4.07035	+	1.96018i	−0.310361	+	0.149462i
$173$	−8.02956			−0.610476			−0.305238	−	0.952276i	$-0.598736\pi$
$173$	−8.02956			−0.610476			−0.305238	+	0.952276i	$0.598736\pi$
$174$	−1.02282	+	10.6177i	−0.0775398	+	0.804923i
$175$	−1.38184			−0.104457
$176$	−9.31797	+	4.48730i	−0.702368	+	0.338243i
$177$	−6.41266	−	8.04122i	−0.482005	−	0.604415i
$178$	−12.8588	+	16.1244i	−0.963809	+	1.20858i
$179$	9.51892	−	4.58407i	0.711478	−	0.342630i	−0.0428918	−	0.999080i	$-0.513657\pi$
$179$	9.51892	−	4.58407i	0.711478	−	0.342630i	0.754369	+	0.656450i	$0.227943\pi$
$180$	−2.11255	−	1.01735i	−0.157460	−	0.0758289i
$181$	−7.63399	−	9.57273i	−0.567430	−	0.711535i	0.412482	−	0.910966i	$-0.364662\pi$
$181$	−7.63399	−	9.57273i	−0.567430	−	0.711535i	−0.979912	+	0.199431i	$0.936091\pi$
$182$	0.572714	−	2.50922i	0.0424524	−	0.185996i
$183$	0.828378	−	3.62936i	0.0612355	−	0.268290i
$184$	0.283675	−	0.355717i	0.0209128	−	0.0262238i
$185$	−0.989888	−	4.33698i	−0.0727780	−	0.318861i
$186$	−19.8151			−1.45292
$187$	−2.38631	−	10.4551i	−0.174504	−	0.764552i
$188$	14.8016	+	7.12809i	1.07952	+	0.519869i
$189$	0.354295	+	0.170619i	0.0257712	+	0.0124107i
$190$	2.88593	+	12.6441i	0.209367	+	0.917298i
$191$	6.79213			0.491461			0.245731	−	0.969338i	$-0.420972\pi$
$191$	6.79213			0.491461			0.245731	+	0.969338i	$0.420972\pi$
$192$	−1.64145	−	7.19165i	−0.118461	−	0.519013i
$193$	−15.2461	+	19.1181i	−1.09744	+	1.37615i	−0.177487	+	0.984123i	$0.556797\pi$
$193$	−15.2461	+	19.1181i	−1.09744	+	1.37615i	−0.919954	+	0.392025i	$0.871775\pi$
$194$	−7.14124	+	31.2878i	−0.512711	+	2.24634i
$195$	0.896307	−	3.92698i	0.0641859	−	0.281217i
$196$	−8.20945	−	10.2943i	−0.586389	−	0.735309i
$197$	6.77867	+	3.26444i	0.482960	+	0.232581i	0.659489	−	0.751714i	$-0.270773\pi$
$197$	6.77867	+	3.26444i	0.482960	+	0.232581i	−0.176529	+	0.984295i	$0.556487\pi$
$198$	−4.45045	+	2.14323i	−0.316280	+	0.152312i
$199$	−14.3765	+	18.0276i	−1.01913	+	1.27794i	−0.0590340	+	0.998256i	$0.518802\pi$
$199$	−14.3765	+	18.0276i	−1.01913	+	1.27794i	−0.960091	+	0.279687i	$0.909769\pi$
$200$	−0.332068	−	0.416400i	−0.0234808	−	0.0294439i
$201$	4.63710	−	2.23311i	0.327076	−	0.157512i
$202$	5.47534			0.385244
$203$	1.09753	−	1.81104i	0.0770313	−	0.127110i
$204$	8.27152			0.579122
$205$	8.58879	−	4.13614i	0.599867	−	0.288881i
$206$	−4.67583	−	5.86331i	−0.325781	−	0.408516i
$207$	1.87165	−	2.34697i	0.130089	−	0.163126i
$208$	12.3464	−	5.94569i	0.856066	−	0.412260i
$209$	12.0681	+	5.81168i	0.834766	+	0.402002i
$210$	0.592011	+	0.742358i	0.0408526	+	0.0512276i
$211$	−1.45370	+	6.36909i	−0.100077	+	0.438466i	0.899920	+	0.436055i	$0.143625\pi$
$211$	−1.45370	+	6.36909i	−0.100077	+	0.438466i	−0.999997	+	0.00241130i	$0.999232\pi$
$212$	4.67443	−	20.4800i	0.321041	−	1.40657i
$213$	5.04482	−	6.32601i	0.345666	−	0.433451i
$214$	−4.97895	−	21.8142i	−0.340354	−	1.49119i
$215$	2.86314			0.195265
$216$	0.0337262	+	0.147764i	0.00229477	+	0.0100541i
$217$	3.54426	+	1.70683i	0.240600	+	0.115867i
$218$	26.5521	+	12.7868i	1.79834	+	0.866034i
$219$	1.94853	+	8.53706i	0.131669	+	0.576881i
$220$	−5.84731			−0.394226
$221$	3.16187	+	13.8531i	0.212690	+	0.931857i
$222$	4.50683	−	5.65138i	0.302478	−	0.379296i
$223$	2.71840	−	11.9101i	0.182038	−	0.797560i	−0.798621	−	0.601834i	$-0.794437\pi$
$223$	2.71840	−	11.9101i	0.182038	−	0.797560i	0.980659	−	0.195725i	$-0.0627061\pi$
$224$	−0.692286	+	3.03310i	−0.0462553	+	0.202658i
$225$	−2.19094	−	2.74736i	−0.146063	−	0.183157i
$226$	−0.0312600	−	0.0150540i	−0.00207938	−	0.00100138i
$227$	13.0371	−	6.27836i	0.865306	−	0.416709i	0.0520700	−	0.998643i	$-0.483418\pi$
$227$	13.0371	−	6.27836i	0.865306	−	0.416709i	0.813236	+	0.581934i	$0.197704\pi$
$228$	−6.44150	+	8.07739i	−0.426599	+	0.534938i
$229$	6.49636	+	8.14618i	0.429292	+	0.538315i	0.948686	−	0.316220i	$-0.102414\pi$
$229$	6.49636	+	8.14618i	0.429292	+	0.538315i	−0.519394	+	0.854535i	$0.673842\pi$
$230$	6.53056	−	3.14495i	0.430612	−	0.207372i
$231$	0.980649			0.0645220
$232$	0.809482	−	0.104483i	0.0531451	−	0.00685963i
$233$	−18.5595			−1.21587			−0.607935	−	0.793987i	$-0.708002\pi$
$233$	−18.5595			−1.21587			−0.607935	+	0.793987i	$0.708002\pi$
$234$	5.89687	−	2.83979i	0.385491	−	0.185643i
$235$	−6.49158	−	8.14018i	−0.423464	−	0.531007i
$236$	12.3346	−	15.4671i	0.802916	−	1.00683i
$237$	6.57640	−	3.16703i	0.427183	−	0.205720i
$238$	−3.01785	−	1.45332i	−0.195618	−	0.0942047i
$239$	−14.8606	−	18.6346i	−0.961252	−	1.20537i	−0.978652	−	0.205523i	$-0.934111\pi$
$239$	−14.8606	−	18.6346i	−0.961252	−	1.20537i	0.0174007	−	0.999849i	$-0.494461\pi$
$240$	−1.12495	+	4.92873i	−0.0726152	+	0.318148i
$241$	−4.06237	+	17.7984i	−0.261680	+	1.14650i	0.657748	+	0.753238i	$0.271509\pi$
$241$	−4.06237	+	17.7984i	−0.261680	+	1.14650i	−0.919428	+	0.393258i	$0.871348\pi$
$242$	5.90457	−	7.40409i	0.379560	−	0.475953i
$243$	0.222521	+	0.974928i	0.0142747	+	0.0625417i
$244$	7.16054			0.458407
$245$	1.85685	+	8.13539i	0.118630	+	0.519751i
$246$	13.9559	+	6.72082i	0.889797	+	0.428504i
$247$	−15.9903	−	7.70050i	−1.01744	−	0.489971i
$248$	0.337387	+	1.47819i	0.0214241	+	0.0938650i
$249$	3.74978			0.237633
$250$	−4.57457	−	20.0425i	−0.289321	−	1.26760i
$251$	−10.6999	+	13.4173i	−0.675372	+	0.846889i	−0.994919	−	0.100681i	$-0.967898\pi$
$251$	−10.6999	+	13.4173i	−0.675372	+	0.846889i	0.319547	+	0.947570i	$0.396469\pi$
$252$	−0.168312	+	0.737421i	−0.0106026	+	0.0464532i
$253$	1.66581	−	7.29838i	0.104728	−	0.458845i
$254$	−12.6661	−	15.8828i	−0.794740	−	0.996573i
$255$	−4.72298	−	2.27447i	−0.295765	−	0.142433i
$256$	−15.4545	+	7.44248i	−0.965904	+	0.465155i
$257$	−1.02439	+	1.28454i	−0.0638996	+	0.0801275i	−0.812754	−	0.582607i	$-0.802033\pi$
$257$	−1.02439	+	1.28454i	−0.0638996	+	0.0801275i	0.748855	+	0.662734i	$0.230604\pi$
$258$	2.90067	+	3.63733i	0.180588	+	0.226450i
$259$	−1.29292	+	0.622636i	−0.0803379	+	0.0386887i
$260$	7.74772			0.480493
$261$	5.34086	−	0.689364i	0.330591	−	0.0426706i
$262$	−9.81019			−0.606075
$263$	−6.19347	+	2.98262i	−0.381906	+	0.183916i	−0.614980	−	0.788543i	$-0.710836\pi$
$263$	−6.19347	+	2.98262i	−0.381906	+	0.183916i	0.233074	+	0.972459i	$0.425122\pi$
$264$	0.235659	+	0.295507i	0.0145038	+	0.0181872i
$265$	−8.30057	+	10.4086i	−0.509900	+	0.639394i
$266$	3.76938	−	1.81524i	0.231116	−	0.111299i
$267$	9.38092	+	4.51762i	0.574103	+	0.276474i
$268$	6.17241	+	7.73996i	0.377040	+	0.472793i
$269$	0.898416	−	3.93622i	0.0547774	−	0.239995i	−0.940126	−	0.340827i	$-0.889293\pi$
$269$	0.898416	−	3.93622i	0.0547774	−	0.239995i	0.994904	+	0.100831i	$0.0321502\pi$
$270$	−0.537299	+	2.35406i	−0.0326990	+	0.143264i
$271$	8.04210	−	10.0845i	0.488523	−	0.612589i	−0.475074	−	0.879946i	$-0.657579\pi$
$271$	8.04210	−	10.0845i	0.488523	−	0.612589i	0.963598	+	0.267357i	$0.0861503\pi$
$272$	−3.96845	−	17.3869i	−0.240622	−	1.05424i
$273$	−1.29936			−0.0786411
$274$	−5.98066	−	26.2030i	−0.361305	−	1.58298i
$275$	−7.89533	−	3.80219i	−0.476106	−	0.229281i
$276$	5.20227	+	2.50528i	0.313140	+	0.150800i
$277$	0.712674	+	3.12243i	0.0428204	+	0.187608i	0.991815	−	0.127684i	$-0.0407544\pi$
$277$	0.712674	+	3.12243i	0.0428204	+	0.187608i	−0.948994	+	0.315293i	$0.897897\pi$
$278$	−32.6281			−1.95690
$279$	2.22603	+	9.75289i	0.133269	+	0.583890i
$280$	0.0452991	−	0.0568033i	0.00270714	−	0.00339465i
$281$	−4.28030	+	18.7532i	−0.255341	+	1.11872i	0.670828	+	0.741613i	$0.265939\pi$
$281$	−4.28030	+	18.7532i	−0.255341	+	1.11872i	−0.926169	+	0.377109i	$0.876918\pi$
$282$	3.76460	−	16.4938i	0.224178	−	0.982190i
$283$	17.6050	+	22.0760i	1.04651	+	1.31228i	0.948390	+	0.317105i	$0.102711\pi$
$283$	17.6050	+	22.0760i	1.04651	+	1.31228i	0.0981179	+	0.995175i	$0.468718\pi$
$284$	14.0221	+	6.75271i	0.832061	+	0.400700i
$285$	5.89914	−	2.84088i	0.349435	−	0.168279i
$286$	10.1765	−	12.7610i	0.601751	−	0.754572i
$287$	−1.91733	−	2.40426i	−0.113176	−	0.141919i
$288$	−7.12803	+	3.43268i	−0.420023	+	0.202272i
$289$	1.49242			0.0877892
$290$	12.3412	+	4.09569i	0.724697	+	0.240507i
$291$	16.2019			0.949775
$292$	−15.1752	+	7.30798i	−0.888060	+	0.427667i
$293$	−20.7774	−	26.0541i	−1.21383	−	1.52210i	−0.785986	−	0.618245i	$-0.787844\pi$
$293$	−20.7774	−	26.0541i	−1.21383	−	1.52210i	−0.427846	−	0.903852i	$-0.640727\pi$
$294$	−8.45399	+	10.6010i	−0.493047	+	0.618261i
$295$	−11.2961	+	5.43991i	−0.657683	+	0.316724i
$296$	−0.498323	−	0.239980i	−0.0289645	−	0.0139486i
$297$	1.55485	+	1.94972i	0.0902214	+	0.113134i
$298$	3.52034	−	15.4236i	0.203928	−	0.893466i
$299$	−2.20720	+	9.67039i	−0.127646	+	0.559253i
$300$	4.21424	−	5.28449i	0.243309	−	0.305100i
$301$	−0.205522	−	0.900453i	−0.0118461	−	0.0519012i
$302$	40.2165			2.31420
$303$	−0.615101	−	2.69493i	−0.0353366	−	0.154820i
$304$	20.0693	+	9.66486i	1.15105	+	0.554318i
$305$	−4.08862	−	1.96898i	−0.234114	−	0.112743i
$306$	−1.89541	−	8.30434i	−0.108353	−	0.474728i
$307$	−0.940065			−0.0536523			−0.0268262	−	0.999640i	$-0.508540\pi$
$307$	−0.940065			−0.0536523			−0.0268262	+	0.999640i	$0.508540\pi$
$308$	0.419733	+	1.83897i	0.0239165	+	0.104785i
$309$	−2.36060	+	2.96010i	−0.134290	+	0.168394i
$310$	−5.37498	+	23.5493i	−0.305279	+	1.33751i
$311$	−1.94755	+	8.53276i	−0.110435	+	0.483848i	0.889217	+	0.457485i	$0.151250\pi$
$311$	−1.94755	+	8.53276i	−0.110435	+	0.483848i	−0.999652	+	0.0263630i	$0.991607\pi$
$312$	−0.312249	−	0.391548i	−0.0176776	−	0.0221671i
$313$	29.6754	+	14.2909i	1.67735	+	0.807771i	0.997206	+	0.0746966i	$0.0237988\pi$
$313$	29.6754	+	14.2909i	1.67735	+	0.807771i	0.680148	+	0.733075i	$0.261915\pi$
$314$	−7.29888	+	3.51496i	−0.411900	+	0.198361i
$315$	0.298878	−	0.374781i	0.0168399	−	0.0211165i
$316$	8.75378	+	10.9769i	0.492439	+	0.617499i
$317$	21.1355	−	10.1783i	1.18709	−	0.571672i	0.267120	−	0.963663i	$-0.413928\pi$
$317$	21.1355	−	10.1783i	1.18709	−	0.571672i	0.919969	+	0.391991i	$0.128214\pi$
$318$	−21.6324			−1.21309
$319$	11.2541	−	7.32775i	0.630106	−	0.410275i
$320$	−8.99219			−0.502679
$321$	−10.1775	+	4.90122i	−0.568052	+	0.273559i
$322$	−1.45786	−	1.82810i	−0.0812433	−	0.101876i
$323$	−14.4011	+	18.0584i	−0.801299	+	1.00480i
$324$	−1.73300	+	0.834568i	−0.0962777	+	0.0463649i
$325$	10.4613	+	5.03792i	0.580291	+	0.279454i
$326$	−23.8077	−	29.8539i	−1.31859	−	1.65345i
$327$	3.31074	−	14.5053i	0.183084	−	0.802145i
$328$	0.263742	−	1.15553i	0.0145627	−	0.0638035i
$329$	−2.09409	+	2.62591i	−0.115451	+	0.144771i
$330$	1.33991	+	5.87052i	0.0737595	+	0.323161i
$331$	−26.4233			−1.45236			−0.726178	−	0.687506i	$-0.758705\pi$
$331$	−26.4233			−1.45236			−0.726178	+	0.687506i	$0.758705\pi$
$332$	1.60496	+	7.03181i	0.0880839	+	0.385921i
$333$	−3.28788	−	1.58336i	−0.180174	−	0.0867674i
$334$	−5.79490	−	2.79068i	−0.317083	−	0.152699i
$335$	−1.39610	−	6.11673i	−0.0762773	−	0.334192i
$336$	1.63083			0.0889689
$337$	1.42909	+	6.26127i	0.0778476	+	0.341073i	0.998821	−	0.0485537i	$-0.0154612\pi$
$337$	1.42909	+	6.26127i	0.0778476	+	0.341073i	−0.920973	+	0.389627i	$0.872604\pi$
$338$	2.57097	−	3.22389i	0.139842	−	0.175357i
$339$	−0.00389775	+	0.0170771i	−0.000211697	+	0.000927503i
$340$	2.24370	−	9.83031i	0.121682	−	0.533123i
$341$	15.5542	+	19.5044i	0.842310	+	1.05622i
$342$	9.58551	+	4.61614i	0.518325	+	0.249612i
$343$	4.90534	−	2.36229i	0.264863	−	0.127552i
$344$	0.221952	−	0.278319i	0.0119668	−	0.0150059i
$345$	−2.28157	−	2.86100i	−0.122836	−	0.154031i
$346$	−14.3297	+	6.90082i	−0.770370	+	0.370990i
$347$	−5.30429			−0.284749			−0.142375	−	0.989813i	$-0.545474\pi$
$347$	−5.30429			−0.284749			−0.142375	+	0.989813i	$0.545474\pi$
$348$	3.57870	+	9.72042i	0.191839	+	0.521069i
$349$	13.3972			0.717134			0.358567	−	0.933504i	$-0.383265\pi$
$349$	13.3972			0.717134			0.358567	+	0.933504i	$0.383265\pi$
$350$	−2.46605	+	1.18759i	−0.131816	+	0.0634793i
$351$	−2.06018	−	2.58339i	−0.109964	−	0.137891i
$352$	−12.3012	+	15.4252i	−0.655657	+	0.822167i
$353$	14.4975	−	6.98162i	0.771623	−	0.371594i	−0.00627832	−	0.999980i	$-0.501998\pi$
$353$	14.4975	−	6.98162i	0.771623	−	0.371594i	0.777902	+	0.628386i	$0.216284\pi$
$354$	−18.3550	−	8.83930i	−0.975557	−	0.469803i
$355$	−6.14972	−	7.71151i	−0.326393	−	0.409284i
$356$	−4.45651	+	19.5253i	−0.236195	+	1.03484i
$357$	−0.376290	+	1.64863i	−0.0199154	+	0.0872550i
$358$	13.0480	−	16.3616i	0.689607	−	0.864740i
$359$	2.68955	+	11.7837i	0.141949	+	0.621920i	0.994981	+	0.100061i	$0.0319039\pi$
$359$	2.68955	+	11.7837i	0.141949	+	0.621920i	−0.853032	+	0.521858i	$0.825239\pi$
$360$	0.184759			0.00973765
$361$	−2.19173	−	9.60259i	−0.115354	−	0.505400i
$362$	−21.8508	−	10.5228i	−1.14845	−	0.553067i
$363$	−4.30757	−	2.07442i	−0.226089	−	0.108879i
$364$	−0.556148	−	2.43664i	−0.0291501	−	0.127715i
$365$	10.6744			0.558726
$366$	−1.64083	−	7.18896i	−0.0857677	−	0.375773i
$367$	−4.56482	+	5.72410i	−0.238282	+	0.298796i	−0.886566	−	0.462603i	$-0.846916\pi$
$367$	−4.56482	+	5.72410i	−0.238282	+	0.298796i	0.648284	+	0.761399i	$0.275487\pi$
$368$	2.77025	−	12.1373i	0.144409	−	0.632698i
$369$	1.74014	−	7.62404i	0.0905880	−	0.396892i
$370$	−5.49389	−	6.88913i	−0.285614	−	0.358149i
$371$	3.86931	+	1.86336i	0.200885	+	0.0967410i
$372$	−17.3364	+	8.34877i	−0.898850	+	0.432864i
$373$	−5.15974	+	6.47011i	−0.267161	+	0.335010i	−0.897258	−	0.441507i	$-0.854444\pi$
$373$	−5.15974	+	6.47011i	−0.267161	+	0.335010i	0.630096	+	0.776517i	$0.283015\pi$
$374$	−13.2440	−	16.6075i	−0.684833	−	0.858754i
$375$	−9.35089	+	4.50315i	−0.482878	+	0.232542i
$376$	−1.29452			−0.0667596
$377$	−14.9117	+	9.70931i	−0.767991	+	0.500055i
$378$	0.778916			0.0400631
$379$	3.47602	−	1.67396i	0.178551	−	0.0859858i	−0.342473	−	0.939528i	$-0.611264\pi$
$379$	3.47602	−	1.67396i	0.178551	−	0.0859858i	0.521024	+	0.853542i	$0.325550\pi$
$380$	7.85229	+	9.84647i	0.402814	+	0.505113i
$381$	−6.39449	+	8.01844i	−0.327600	+	0.410797i
$382$	12.1214	−	5.83734i	0.620183	−	0.298665i
$383$	4.98332	+	2.39984i	0.254636	+	0.122626i	0.556848	−	0.830615i	$-0.312011\pi$
$383$	4.98332	+	2.39984i	0.254636	+	0.122626i	−0.302212	+	0.953241i	$0.597725\pi$
$384$	0.755435	+	0.947286i	0.0385507	+	0.0483410i
$385$	0.266008	−	1.16546i	0.0135570	−	0.0593971i
$386$	−10.7780	+	47.2214i	−0.548585	+	2.40351i
$387$	1.46441	−	1.83631i	0.0744402	−	0.0933450i
$388$	6.93468	+	30.3828i	0.352055	+	1.54245i
$389$	8.73816			0.443042			0.221521	−	0.975156i	$-0.428898\pi$
$389$	8.73816			0.443042			0.221521	+	0.975156i	$0.428898\pi$
$390$	−1.77538	−	7.77847i	−0.0899001	−	0.393878i
$391$	11.6306	+	5.60100i	0.588184	+	0.283255i
$392$	0.934765	+	0.450159i	0.0472128	+	0.0227365i
$393$	1.10208	+	4.82852i	0.0555925	+	0.243567i
$394$	14.9029			0.750797
$395$	−1.97997	−	8.67482i	−0.0996231	−	0.436477i
$396$	−2.99072	+	3.75025i	−0.150290	+	0.188457i
$397$	1.50235	−	6.58223i	0.0754008	−	0.330353i	−0.923133	−	0.384480i	$-0.874381\pi$
$397$	1.50235	−	6.58223i	0.0754008	−	0.330353i	0.998534	+	0.0541277i	$0.0172378\pi$
$398$	−10.1632	+	44.5280i	−0.509436	+	2.23199i
$399$	−1.31690	−	1.65134i	−0.0659276	−	0.0826706i
$400$	−13.1300	−	6.32307i	−0.656499	−	0.316153i
$401$	21.1650	−	10.1925i	1.05693	−	0.508992i	0.177059	−	0.984200i	$-0.443342\pi$
$401$	21.1650	−	10.1925i	1.05693	−	0.508992i	0.879873	+	0.475209i	$0.157627\pi$
$402$	6.35627	−	7.97051i	0.317022	−	0.397533i
$403$	−20.6095	−	25.8434i	−1.02663	−	1.28735i
$404$	4.79042	−	2.30694i	0.238332	−	0.114775i
$405$	1.21902			0.0605734
$406$	0.402211	−	4.17526i	0.0199614	−	0.207215i
$407$	−9.10048			−0.451094
$408$	−0.587222	+	0.282791i	−0.0290718	+	0.0140003i
$409$	−15.2154	−	19.0795i	−0.752355	−	0.943423i	0.247320	−	0.968934i	$-0.420450\pi$
$409$	−15.2154	−	19.0795i	−0.752355	−	0.943423i	−0.999675	+	0.0255111i	$0.991879\pi$
$410$	11.7730	−	14.7629i	0.581428	−	0.729087i
$411$	−12.2251	+	5.88729i	−0.603019	+	0.290399i
$412$	−6.56133	−	3.15977i	−0.323254	−	0.155671i
$413$	2.52170	+	3.16211i	0.124085	+	0.155597i
$414$	1.32313	−	5.79700i	0.0650282	−	0.284907i
$415$	1.01715	−	4.45644i	0.0499301	−	0.218758i
$416$	16.2992	−	20.4385i	0.799132	−	1.00208i
$417$	3.66545	+	16.0594i	0.179498	+	0.786431i
$418$	26.5316			1.29770
$419$	−3.72073	−	16.3016i	−0.181769	−	0.796384i	−0.980788	−	0.195077i	$-0.937504\pi$
$419$	−3.72073	−	16.3016i	−0.181769	−	0.796384i	0.799019	−	0.601306i	$-0.205353\pi$
$420$	0.830735	+	0.400061i	0.0405357	+	0.0195210i
$421$	20.8550	+	10.0432i	1.01641	+	0.489478i	0.866476	−	0.499218i	$-0.166379\pi$
$421$	20.8550	+	10.0432i	1.01641	+	0.489478i	0.149935	+	0.988696i	$0.452094\pi$
$422$	2.87946	+	12.6158i	0.140170	+	0.614125i
$423$	−8.54106			−0.415280
$424$	0.368329	+	1.61375i	0.0178876	+	0.0783709i
$425$	9.42167	−	11.8144i	0.457018	−	0.573083i
$426$	3.56634	−	15.6252i	0.172790	−	0.757042i
$427$	−0.325749	+	1.42720i	−0.0157641	+	0.0690671i
$428$	−13.5472	−	16.9876i	−0.654827	−	0.821127i
$429$	−7.42411	−	3.57527i	−0.358440	−	0.172615i
$430$	5.10962	−	2.46066i	0.246408	−	0.118664i
$431$	23.4128	−	29.3588i	1.12776	−	1.41416i	0.230267	−	0.973127i	$-0.426040\pi$
$431$	23.4128	−	29.3588i	1.12776	−	1.41416i	0.897490	−	0.441035i	$-0.145389\pi$
$432$	2.58572	+	3.24240i	0.124406	+	0.156000i
$433$	−15.4657	+	7.44790i	−0.743235	+	0.357923i	−0.766874	−	0.641797i	$-0.778189\pi$
$433$	−15.4657	+	7.44790i	−0.743235	+	0.357923i	0.0236390	+	0.999721i	$0.492475\pi$
$434$	7.79205			0.374030
$435$	0.629467	−	6.53435i	0.0301806	−	0.313298i
$436$	28.6182			1.37056
$437$	−14.5270	+	6.99581i	−0.694918	+	0.334655i
$438$	10.8144	+	13.5608i	0.516730	+	0.647959i
$439$	3.30350	−	4.14245i	0.157667	−	0.197709i	−0.696723	−	0.717340i	$-0.745359\pi$
$439$	3.30350	−	4.14245i	0.157667	−	0.197709i	0.854390	+	0.519632i	$0.173931\pi$
$440$	0.415120	−	0.199911i	0.0197901	−	0.00953040i
$441$	6.16746	+	2.97009i	0.293689	+	0.141433i
$442$	17.5484	+	22.0050i	0.834694	+	1.04667i
$443$	−3.07345	+	13.4656i	−0.146024	+	0.639772i	0.847943	+	0.530088i	$0.177841\pi$
$443$	−3.07345	+	13.4656i	−0.146024	+	0.639772i	−0.993966	+	0.109684i	$0.965016\pi$
$444$	1.56194	−	6.84331i	0.0741265	−	0.324769i
$445$	7.91361	−	9.92336i	0.375141	−	0.470412i
$446$	−5.38456	−	23.5913i	−0.254966	−	1.11708i
$447$	−7.98689			−0.377767
$448$	0.645479	+	2.82803i	0.0304960	+	0.133612i
$449$	−15.5953	−	7.51031i	−0.735989	−	0.354433i	0.0280478	−	0.999607i	$-0.491071\pi$
$449$	−15.5953	−	7.51031i	−0.735989	−	0.354433i	−0.764036	+	0.645173i	$0.776785\pi$
$450$	−6.27115	−	3.02003i	−0.295625	−	0.142365i
$451$	−4.33953	−	19.0127i	−0.204340	−	0.895273i
$452$	−0.0336923			−0.00158475
$453$	−4.51793	−	19.7943i	−0.212271	−	0.930019i
$454$	17.8706	−	22.4090i	0.838707	−	1.05171i
$455$	−0.352461	+	1.54423i	−0.0165236	+	0.0723948i
$456$	0.181149	−	0.793666i	0.00848309	−	0.0371668i
$457$	−12.7243	−	15.9558i	−0.595219	−	0.746381i	0.389406	−	0.921066i	$-0.372680\pi$
$457$	−12.7243	−	15.9558i	−0.595219	−	0.746381i	−0.984624	+	0.174686i	$0.944109\pi$
$458$	18.5946	+	8.95468i	0.868868	+	0.418425i
$459$	−3.87442	+	1.86582i	−0.180842	+	0.0870891i
$460$	4.38856	−	5.50308i	0.204618	−	0.256583i
$461$	10.5622	+	13.2446i	0.491931	+	0.616861i	0.964388	−	0.264492i	$-0.0852043\pi$
$461$	10.5622	+	13.2446i	0.491931	+	0.616861i	−0.472457	+	0.881354i	$0.656633\pi$
$462$	1.75009	−	0.842797i	0.0814213	−	0.0392105i
$463$	26.1995			1.21759			0.608796	−	0.793327i	$-0.291653\pi$
$463$	26.1995			1.21759			0.608796	+	0.793327i	$0.291653\pi$
$464$	18.7156	−	12.1861i	0.868849	−	0.565726i
$465$	12.1947			0.565515
$466$	−33.1216	+	15.9505i	−1.53433	+	0.738893i
$467$	17.6788	+	22.1685i	0.818077	+	1.02584i	0.999103	+	0.0423574i	$0.0134868\pi$
$467$	17.6788	+	22.1685i	0.818077	+	1.02584i	−0.181026	+	0.983478i	$0.557942\pi$
$468$	3.96272	−	4.96910i	0.183177	−	0.229697i
$469$	−1.82348	+	0.878143i	−0.0842006	+	0.0405489i
$470$	−18.5809	−	8.94809i	−0.857073	−	0.412745i
$471$	2.55000	+	3.19760i	0.117498	+	0.147338i
$472$	−0.346877	+	1.51977i	−0.0159663	+	0.0699530i
$473$	1.30336	−	5.71038i	0.0599284	−	0.262563i
$474$	9.01454	−	11.3039i	0.414051	−	0.519204i
$475$	4.19993	+	18.4011i	0.192706	+	0.844300i
$476$	−3.25267			−0.149086
$477$	2.43019	+	10.6474i	0.111271	+	0.487509i
$478$	−42.5356	−	20.4841i	−1.94553	−	0.936919i
$479$	−30.3344	−	14.6083i	−1.38601	−	0.667469i	−0.415741	−	0.909483i	$-0.636478\pi$
$479$	−30.3344	−	14.6083i	−1.38601	−	0.667469i	−0.970273	+	0.242014i	$0.922192\pi$
$480$	2.14605	+	9.40246i	0.0979534	+	0.429162i
$481$	12.0582			0.549806
$482$	8.04666	+	35.2547i	0.366515	+	1.60581i
$483$	−0.736003	+	0.922918i	−0.0334893	+	0.0419942i
$484$	2.04636	−	8.96569i	0.0930164	−	0.407531i
$485$	4.39488	−	19.2552i	0.199561	−	0.874336i
$486$	1.23500	+	1.54863i	0.0560205	+	0.0702475i
$487$	20.9826	+	10.1047i	0.950814	+	0.457888i	0.843971	−	0.536388i	$-0.180212\pi$
$487$	20.9826	+	10.1047i	0.950814	+	0.457888i	0.106843	+	0.994276i	$0.465926\pi$
$488$	−0.508351	+	0.244809i	−0.0230120	+	0.0110820i
$489$	−12.0194	+	15.0718i	−0.543534	+	0.681570i
$490$	10.3056	+	12.9228i	0.465557	+	0.583791i
$491$	13.3643	−	6.43593i	0.603124	−	0.290449i	−0.107296	−	0.994227i	$-0.534219\pi$
$491$	13.3643	−	6.43593i	0.603124	−	0.290449i	0.710420	+	0.703778i	$0.248505\pi$
$492$	15.0418			0.678139
$493$	8.00082	+	21.7317i	0.360339	+	0.978747i
$494$	−35.1545			−1.58168
$495$	2.73891	−	1.31899i	0.123105	−	0.0592842i
$496$	25.8668	+	32.4360i	1.16145	+	1.45642i
$497$	−1.98381	+	2.48762i	−0.0889862	+	0.111585i
$498$	6.69194	−	3.22267i	0.299873	−	0.144411i
$499$	−20.8748	−	10.0528i	−0.934484	−	0.450024i	−0.0962638	−	0.995356i	$-0.530689\pi$
$499$	−20.8748	−	10.0528i	−0.934484	−	0.450024i	−0.838220	+	0.545332i	$0.816404\pi$
$500$	−12.4469	−	15.6079i	−0.556642	−	0.698007i
$501$	−0.722556	+	3.16572i	−0.0322814	+	0.141434i
$502$	−7.56410	+	33.1405i	−0.337602	+	1.47913i
$503$	−9.67873	+	12.1367i	−0.431553	+	0.541151i	−0.949295	−	0.314386i	$-0.898201\pi$
$503$	−9.67873	+	12.1367i	−0.431553	+	0.541151i	0.517742	+	0.855537i	$0.326773\pi$
$504$	−0.0132624	−	0.0581063i	−0.000590754	−	0.00258826i
$505$	−3.36965			−0.149948
$506$	−3.29960	−	14.4565i	−0.146685	−	0.642668i
$507$	−1.87561	−	0.903244i	−0.0832986	−	0.0401145i
$508$	−17.7736	−	8.55930i	−0.788575	−	0.379758i
$509$	−7.19126	−	31.5070i	−0.318747	−	1.39652i	−0.839753	−	0.542969i	$-0.817300\pi$
$509$	−7.19126	−	31.5070i	−0.318747	−	1.39652i	0.521006	−	0.853553i	$-0.325557\pi$
$510$	−10.3835			−0.459787
$511$	−0.766234	−	3.35709i	−0.0338962	−	0.148509i
$512$	−19.6732	+	24.6694i	−0.869441	+	1.09024i
$513$	1.19520	−	5.23651i	0.0527693	−	0.231198i
$514$	−0.724172	+	3.17281i	−0.0319419	+	0.139946i
$515$	2.87762	+	3.60842i	0.126803	+	0.159006i
$516$	4.07035	+	1.96018i	0.179187	+	0.0862920i
$517$	−19.1902	+	9.24152i	−0.843985	+	0.406442i
$518$	−1.77225	+	2.22234i	−0.0778683	+	0.0976438i
$519$	5.00635	+	6.27776i	0.219754	+	0.275563i
$520$	−0.550037	+	0.264884i	−0.0241207	+	0.0116159i
$521$	−0.674556			−0.0295529			−0.0147764	−	0.999891i	$-0.504704\pi$
$521$	−0.674556			−0.0295529			−0.0147764	+	0.999891i	$0.504704\pi$
$522$	8.93894	−	5.82033i	0.391247	−	0.254749i
$523$	−6.73109			−0.294330			−0.147165	−	0.989112i	$-0.547015\pi$
$523$	−6.73109			−0.294330			−0.147165	+	0.989112i	$0.547015\pi$
$524$	−8.58301	+	4.13336i	−0.374950	+	0.180567i
$525$	0.861561	+	1.08036i	0.0376016	+	0.0471509i
$526$	−8.48964	+	10.6457i	−0.370166	+	0.464173i
$527$	−38.7585	+	18.6651i	−1.68835	+	0.813066i
$528$	9.31797	+	4.48730i	0.405513	+	0.195285i
$529$	−8.72177	−	10.9368i	−0.379208	−	0.475511i
$530$	−5.86794	+	25.7091i	−0.254887	+	1.11673i
$531$	−2.28865	+	10.0272i	−0.0993190	+	0.435145i
$532$	2.53304	−	3.17633i	0.109821	−	0.137711i
$533$	5.74989	+	25.1919i	0.249056	+	1.09118i
$534$	20.6239			0.892485
$535$	3.06416	+	13.4250i	0.132475	+	0.580411i
$536$	−0.702818	−	0.338459i	−0.0303571	−	0.0146192i
$537$	−9.51892	−	4.58407i	−0.410772	−	0.197817i
$538$	−1.77956	−	7.79678i	−0.0767224	−	0.336143i
$539$	17.0709			0.735294
$540$	0.521757	+	2.28597i	0.0224529	+	0.0983724i
$541$	−9.76755	+	12.2481i	−0.419940	+	0.526588i	−0.946133	−	0.323777i	$-0.895047\pi$
$541$	−9.76755	+	12.2481i	−0.419940	+	0.526588i	0.526194	+	0.850365i	$0.323619\pi$
$542$	5.68522	−	24.9086i	0.244201	−	1.06991i
$543$	−2.72454	+	11.9370i	−0.116921	+	0.512265i
$544$	−21.2122	−	26.5993i	−0.909466	−	1.14043i
$545$	−16.3408	−	7.86931i	−0.699963	−	0.337084i
$546$	−2.31887	+	1.11671i	−0.0992386	+	0.0477908i
$547$	−8.06654	+	10.1151i	−0.344901	+	0.432492i	−0.923781	−	0.382921i	$-0.874918\pi$
$547$	−8.06654	+	10.1151i	−0.344901	+	0.432492i	0.578881	+	0.815412i	$0.303490\pi$
$548$	−16.2727	−	20.4053i	−0.695136	−	0.871673i
$549$	−3.35403	+	1.61522i	−0.143147	+	0.0689358i
$550$	−17.3579			−0.740142
$551$	−27.4524	−	9.11068i	−1.16951	−	0.388128i
$552$	−0.454979			−0.0193652
$553$	−2.58609	+	1.24539i	−0.109972	+	0.0529595i
$554$	3.95535	+	4.95985i	0.168047	+	0.210724i
$555$	−2.77360	+	3.47799i	−0.117733	+	0.147632i
$556$	−28.5466	+	13.7473i	−1.21064	+	0.583016i
$557$	−8.78368	−	4.23000i	−0.372177	−	0.179231i	0.238440	−	0.971157i	$-0.423364\pi$
$557$	−8.78368	−	4.23000i	−0.372177	−	0.179231i	−0.610616	+	0.791926i	$0.709078\pi$
$558$	12.3545	+	15.4921i	0.523009	+	0.655832i
$559$	−1.72695	+	7.56628i	−0.0730424	+	0.320019i
$560$	0.442373	−	1.93816i	0.0186937	−	0.0819022i
$561$	−6.68628	+	8.38434i	−0.282295	+	0.353987i
$562$	8.47832	+	37.1459i	0.357636	+	1.56691i
$563$	39.5811			1.66814			0.834072	−	0.551656i	$-0.186004\pi$
$563$	39.5811			1.66814			0.834072	+	0.551656i	$0.186004\pi$
$564$	−3.65570	−	16.0167i	−0.153933	−	0.674424i
$565$	0.0192381	+	0.00926458i	0.000809353	+	0.000389764i
$566$	50.3909	+	24.2670i	2.11809	+	1.02002i
$567$	−0.0875036	−	0.383378i	−0.00367480	−	0.0161004i
$568$	−1.22634			−0.0514563
$569$	6.44938	+	28.2566i	0.270372	+	1.18458i	0.909575	+	0.415540i	$0.136407\pi$
$569$	6.44938	+	28.2566i	0.270372	+	1.18458i	−0.639203	+	0.769038i	$0.720736\pi$
$570$	8.08619	−	10.1398i	0.338693	−	0.424708i
$571$	6.72499	−	29.4641i	0.281432	−	1.23303i	−0.614526	−	0.788897i	$-0.710653\pi$
$571$	6.72499	−	29.4641i	0.281432	−	1.23303i	0.895958	−	0.444138i	$-0.146490\pi$
$572$	3.52691	−	15.4524i	0.147467	−	0.646097i
$573$	−4.23482	−	5.31030i	−0.176912	−	0.221841i
$574$	−5.48799	−	2.64288i	−0.229064	−	0.110312i
$575$	9.50401	−	4.57689i	0.396344	−	0.190869i
$576$	−4.59923	+	5.76726i	−0.191635	+	0.240302i
$577$	−16.1799	−	20.2889i	−0.673577	−	0.844639i	0.321168	−	0.947022i	$-0.395925\pi$
$577$	−16.1799	−	20.2889i	−0.673577	−	0.844639i	−0.994745	+	0.102383i	$0.967353\pi$
$578$	2.66340	−	1.28262i	0.110783	−	0.0533501i
$579$	24.4529			1.01623
$580$	12.5230	−	1.61639i	0.519990	−	0.0671170i
$581$	−1.47456			−0.0611749
$582$	28.9143	−	13.9244i	1.19854	−	0.577185i
$583$	16.9808	+	21.2932i	0.703271	+	0.881874i
$584$	0.827487	−	1.03764i	0.0342416	−	0.0429377i
$585$	−3.62907	+	1.74767i	−0.150044	+	0.0722572i
$586$	−59.4714	−	28.6399i	−2.45674	−	1.18310i
$587$	0.483492	+	0.606280i	0.0199559	+	0.0250239i	0.791709	−	0.610898i	$-0.209191\pi$
$587$	0.483492	+	0.606280i	0.0199559	+	0.0250239i	−0.771753	+	0.635922i	$0.780620\pi$
$588$	−2.92992	+	12.8368i	−0.120828	+	0.529381i
$589$	11.9564	−	52.3845i	0.492656	−	2.15847i
$590$	−15.4840	+	19.4163i	−0.637466	+	0.799358i
$591$	−1.67419	−	7.33512i	−0.0688671	−	0.301727i
$592$	−15.1342			−0.622010
$593$	6.10600	+	26.7521i	0.250743	+	1.09858i	0.930832	+	0.365449i	$0.119084\pi$
$593$	6.10600	+	26.7521i	0.250743	+	1.09858i	−0.680088	+	0.733130i	$0.738058\pi$
$594$	4.45045	+	2.14323i	0.182604	+	0.0879376i
$595$	1.85725	+	0.894406i	0.0761400	+	0.0366671i
$596$	−3.41851	−	14.9775i	−0.140028	−	0.613501i
$597$	23.0582			0.943708
$598$	4.37198	+	19.1549i	0.178784	+	0.783302i
$599$	26.9705	−	33.8200i	1.10199	−	1.38185i	0.185090	−	0.982722i	$-0.440742\pi$
$599$	26.9705	−	33.8200i	1.10199	−	1.38185i	0.916896	−	0.399125i	$-0.130686\pi$
$600$	−0.118514	+	0.519242i	−0.00483830	+	0.0211980i
$601$	7.35145	−	32.2088i	0.299872	−	1.31382i	−0.570447	−	0.821335i	$-0.693230\pi$
$601$	7.35145	−	32.2088i	0.299872	−	1.31382i	0.870318	−	0.492490i	$-0.163913\pi$
$602$	−1.14065	−	1.43033i	−0.0464896	−	0.0582961i
$603$	−4.63710	−	2.23311i	−0.188837	−	0.0909393i
$604$	35.1857	−	16.9446i	1.43169	−	0.689464i
$605$	−3.63381	+	4.55665i	−0.147735	+	0.185254i
$606$	−3.41382	−	4.28079i	−0.138677	−	0.173895i
$607$	15.8783	−	7.64658i	0.644480	−	0.310365i	−0.0829433	−	0.996554i	$-0.526432\pi$
$607$	15.8783	−	7.64658i	0.644480	−	0.310365i	0.727423	+	0.686189i	$0.240718\pi$
$608$	42.4942			1.72337
$609$	−2.10023	+	0.271084i	−0.0851055	+	0.0109849i
$610$	−8.98883			−0.363947
$611$	25.4271	−	12.2451i	1.02867	−	0.495382i
$612$	−5.15721	−	6.46693i	−0.208468	−	0.261410i
$613$	23.7282	−	29.7542i	0.958371	−	1.20176i	−0.0210185	−	0.999779i	$-0.506691\pi$
$613$	23.7282	−	29.7542i	0.958371	−	1.20176i	0.979390	−	0.201980i	$-0.0647377\pi$
$614$	−1.67766	+	0.807917i	−0.0677048	+	0.0326049i
$615$	−8.58879	−	4.13614i	−0.346334	−	0.166785i
$616$	−0.0926700	−	0.116204i	−0.00373378	−	0.00468201i
$617$	1.14817	−	5.03046i	0.0462235	−	0.202519i	−0.946543	−	0.322577i	$-0.895451\pi$
$617$	1.14817	−	5.03046i	0.0462235	−	0.202519i	0.992767	+	0.120058i	$0.0383081\pi$
$618$	−1.66879	+	7.31143i	−0.0671284	+	0.294109i
$619$	−18.4979	+	23.1956i	−0.743494	+	0.932312i	−0.999409	−	0.0343876i	$-0.989052\pi$
$619$	−18.4979	+	23.1956i	−0.743494	+	0.932312i	0.255915	+	0.966699i	$0.417623\pi$
$620$	5.21951	+	22.8682i	0.209620	+	0.918407i
$621$	−3.00189			−0.120462
$622$	3.85766	+	16.9015i	0.154678	+	0.677688i
$623$	−3.68893	−	1.77650i	−0.147794	−	0.0711738i
$624$	−12.3464	−	5.94569i	−0.494250	−	0.238018i
$625$	−1.09440	−	4.79488i	−0.0437760	−	0.191795i
$626$	65.2414			2.60757
$627$	−2.98057	−	13.0587i	−0.119032	−	0.521515i
$628$	−4.90488	+	6.15053i	−0.195726	+	0.245433i
$629$	3.49199	−	15.2994i	0.139235	−	0.610028i
$630$	0.211286	−	0.925705i	0.00841784	−	0.0368810i
$631$	6.21623	+	7.79490i	0.247464	+	0.310310i	0.890014	−	0.455934i	$-0.150695\pi$
$631$	6.21623	+	7.79490i	0.247464	+	0.310310i	−0.642550	+	0.766244i	$0.722123\pi$
$632$	−0.996745	−	0.480007i	−0.0396484	−	0.0190937i
$633$	5.88592	−	2.83451i	0.233945	−	0.112662i
$634$	28.9713	−	36.3289i	1.15060	−	1.44281i
$635$	7.79499	+	9.77461i	0.309335	+	0.387894i
$636$	−18.9264	+	9.11446i	−0.750479	+	0.361412i
$637$	−22.6190			−0.896196
$638$	13.7865	−	22.7493i	0.545814	−	0.900653i
$639$	−8.09127			−0.320086
$640$	1.33072	−	0.640842i	0.0526014	−	0.0253315i
$641$	13.9528	+	17.4963i	0.551104	+	0.691063i	0.976886	−	0.213763i	$-0.0685721\pi$
$641$	13.9528	+	17.4963i	0.551104	+	0.691063i	−0.425781	+	0.904826i	$0.640001\pi$
$642$	−13.9507	+	17.4936i	−0.550590	+	0.690418i
$643$	5.33870	−	2.57098i	0.210538	−	0.101390i	−0.325643	−	0.945493i	$-0.605581\pi$
$643$	5.33870	−	2.57098i	0.210538	−	0.101390i	0.536181	+	0.844103i	$0.319866\pi$
$644$	−2.04573	−	0.985171i	−0.0806130	−	0.0388212i
$645$	−1.78514	−	2.23850i	−0.0702898	−	0.0881407i
$646$	−10.1806	+	44.6041i	−0.400550	+	1.75492i
$647$	−3.42464	+	15.0043i	−0.134636	+	0.589881i	0.861926	+	0.507034i	$0.169258\pi$
$647$	−3.42464	+	15.0043i	−0.134636	+	0.589881i	−0.996562	+	0.0828464i	$0.973599\pi$
$648$	0.0944986	−	0.118497i	0.00371226	−	0.00465502i
$649$	5.70740	+	25.0057i	0.224035	+	0.981561i
$650$	22.9993			0.902105
$651$	−0.875360	−	3.83520i	−0.0343081	−	0.150313i
$652$	−33.4080	−	16.0884i	−1.30836	−	0.630071i
$653$	−30.2207	−	14.5535i	−1.18263	−	0.569523i	−0.263951	−	0.964536i	$-0.585026\pi$
$653$	−30.2207	−	14.5535i	−1.18263	−	0.569523i	−0.918675	+	0.395013i	$0.870740\pi$
$654$	−6.55784	−	28.7318i	−0.256432	−	1.12350i
$655$	6.03741			0.235901
$656$	−7.21667	−	31.6183i	−0.281763	−	1.23449i
$657$	5.45965	−	6.84619i	0.213001	−	0.267095i
$658$	−1.48038	+	6.48597i	−0.0577112	+	0.252849i
$659$	−2.27680	+	9.97530i	−0.0886914	+	0.388582i	−0.999718	−	0.0237662i	$-0.992434\pi$
$659$	−2.27680	+	9.97530i	−0.0886914	+	0.388582i	0.911026	+	0.412349i	$0.135291\pi$
$660$	3.64574	+	4.57161i	0.141910	+	0.177950i
$661$	−12.0033	−	5.78051i	−0.466876	−	0.224836i	0.185629	−	0.982620i	$-0.440568\pi$
$661$	−12.0033	−	5.78051i	−0.466876	−	0.224836i	−0.652505	+	0.757784i	$0.726282\pi$
$662$	−47.1556	+	22.7089i	−1.83275	+	0.882607i
$663$	8.85936	−	11.1093i	0.344069	−	0.431449i
$664$	−0.354349	−	0.444340i	−0.0137514	−	0.0172437i
$665$	−2.31976	+	1.11714i	−0.0899566	+	0.0433208i
$666$	−7.22839			−0.280094
$667$	−1.55010	+	16.0912i	−0.0600199	+	0.623054i
$668$	−6.24581			−0.241658
$669$	−11.0066	+	5.30050i	−0.425539	+	0.204929i
$670$	−7.74840	−	9.71618i	−0.299347	−	0.375369i
$671$	−5.78823	+	7.25821i	−0.223452	+	0.280200i
$672$	2.80301	−	1.34986i	0.108128	−	0.0520719i
$673$	−34.2673	−	16.5022i	−1.32091	−	0.636115i	−0.365335	−	0.930876i	$-0.619046\pi$
$673$	−34.2673	−	16.5022i	−1.32091	−	0.636115i	−0.955571	+	0.294761i	$0.904760\pi$
$674$	7.93149	+	9.94577i	0.305510	+	0.383097i
$675$	−0.781938	+	3.42590i	−0.0300968	+	0.131863i
$676$	0.891027	−	3.90384i	0.0342703	−	0.150148i
$677$	5.49590	−	6.89164i	0.211224	−	0.264867i	−0.664921	−	0.746913i	$-0.731535\pi$
$677$	5.49590	−	6.89164i	0.211224	−	0.264867i	0.876146	+	0.482046i	$0.160106\pi$
$678$	0.00772057	+	0.0338260i	0.000296507	+	0.00129908i
$679$	−6.37121			−0.244505
$680$	0.176796	+	0.774595i	0.00677983	+	0.0297044i
$681$	−13.0371	−	6.27836i	−0.499585	−	0.240587i
$682$	44.5210	+	21.4402i	1.70480	+	0.820988i
$683$	2.25860	+	9.89559i	0.0864231	+	0.378644i	0.999580	−	0.0289628i	$-0.00922044\pi$
$683$	2.25860	+	9.89559i	0.0864231	+	0.378644i	−0.913157	+	0.407607i	$0.866363\pi$
$684$	10.3314			0.395030
$685$	3.68063	+	16.1259i	0.140630	+	0.616139i
$686$	6.72395	−	8.43157i	0.256722	−	0.321919i
$687$	2.31852	−	10.1581i	0.0884572	−	0.387556i
$688$	2.16749	−	9.49640i	0.0826348	−	0.362047i
$689$	−22.4996	−	28.2136i	−0.857166	−	1.07485i
$690$	−6.53056	−	3.14495i	−0.248614	−	0.119726i
$691$	0.129926	−	0.0625692i	0.00494263	−	0.00238024i	−0.431411	−	0.902156i	$-0.641984\pi$
$691$	0.129926	−	0.0625692i	0.00494263	−	0.00238024i	0.436353	+	0.899775i	$0.356270\pi$
$692$	−9.62962	+	12.0752i	−0.366063	+	0.459029i
$693$	−0.611425	−	0.766702i	−0.0232261	−	0.0291246i
$694$	−9.46614	+	4.55865i	−0.359330	+	0.173044i
$695$	20.0801			0.761681
$696$	−0.586392	−	0.567734i	−0.0222271	−	0.0215199i
$697$	33.6287			1.27378
$698$	23.9088	−	11.5139i	0.904963	−	0.435807i
$699$	11.5716	+	14.5104i	0.437679	+	0.548832i
$700$	−1.65720	+	2.07806i	−0.0626362	+	0.0785433i
$701$	−43.4549	+	20.9268i	−1.64127	+	0.790393i	−0.641539	+	0.767090i	$0.721704\pi$
$701$	−43.4549	+	20.9268i	−1.64127	+	0.790393i	−0.999728	+	0.0233027i	$0.992582\pi$
$702$	−5.89687	−	2.83979i	−0.222563	−	0.107181i
$703$	12.2209	+	15.3246i	0.460921	+	0.577977i
$704$	−4.09341	+	17.9344i	−0.154276	+	0.675929i
$705$	−2.31682	+	10.1506i	−0.0872564	+	0.382295i
$706$	19.8723	−	24.9191i	0.747904	−	0.937842i
$707$	0.241881	+	1.05975i	0.00909686	+	0.0398559i
$708$	−19.7832			−0.743499
$709$	−2.34972	−	10.2948i	−0.0882454	−	0.386629i	0.911447	−	0.411417i	$-0.134966\pi$
$709$	−2.34972	−	10.2948i	−0.0882454	−	0.386629i	−0.999693	+	0.0247883i	$0.992109\pi$
$710$	−17.6024	−	8.47686i	−0.660606	−	0.318131i
$711$	−6.57640	−	3.16703i	−0.246634	−	0.118773i
$712$	−0.351158	−	1.53852i	−0.0131602	−	0.0576586i
$713$	−30.0301			−1.12463
$714$	0.745347	+	3.26558i	0.0278939	+	0.122211i
$715$	−6.26288	+	7.85340i	−0.234218	+	0.293700i
$716$	4.52207	−	19.8125i	0.168998	−	0.740427i
$717$	−5.30368	+	23.2370i	−0.198070	+	0.867800i
$718$	14.9271	+	18.7179i	0.557073	+	0.698547i
$719$	22.7910	+	10.9756i	0.849961	+	0.409320i	0.807563	−	0.589781i	$-0.200786\pi$
$719$	22.7910	+	10.9756i	0.849961	+	0.409320i	0.0423980	+	0.999101i	$0.486500\pi$
$720$	4.55483	−	2.19349i	0.169748	−	0.0817466i
$721$	0.928278	−	1.16402i	0.0345709	−	0.0433505i
$722$	−12.1641	−	15.2533i	−0.452702	−	0.567671i
$723$	16.4482	−	7.92104i	0.611715	−	0.294587i
$724$	−23.5511			−0.875269
$725$	17.9602	+	5.96050i	0.667026	+	0.221368i
$726$	−9.47019			−0.351472
$727$	44.2191	−	21.2948i	1.64000	−	0.789780i	0.640228	−	0.768185i	$-0.278840\pi$
$727$	44.2191	−	21.2948i	1.64000	−	0.789780i	0.999767	−	0.0215952i	$-0.00687451\pi$
$728$	0.122788	+	0.153971i	0.00455083	+	0.00570656i
$729$	0.623490	−	0.781831i	0.0230922	−	0.0289567i
$730$	19.0498	−	9.17391i	0.705065	−	0.339542i
$731$	9.09997	+	4.38232i	0.336575	+	0.162086i
$732$	−4.46452	−	5.59834i	−0.165014	−	0.206920i
$733$	0.756862	−	3.31603i	0.0279553	−	0.122480i	−0.959025	−	0.283322i	$-0.908564\pi$
$733$	0.756862	−	3.31603i	0.0279553	−	0.122480i	0.986980	+	0.160841i	$0.0514207\pi$
$734$	−3.22701	+	14.1385i	−0.119111	+	0.521860i
$735$	5.20278	−	6.52408i	0.191907	−	0.240644i
$736$	−5.28477	−	23.1541i	−0.194799	−	0.853471i
$737$	−12.8350			−0.472783
$738$	−3.44683	−	15.1015i	−0.126879	−	0.555895i
$739$	−6.51194	−	3.13599i	−0.239546	−	0.115359i	0.310260	−	0.950652i	$-0.399584\pi$
$739$	−6.51194	−	3.13599i	−0.239546	−	0.115359i	−0.549806	+	0.835293i	$0.685298\pi$
$740$	−7.70927	−	3.71259i	−0.283398	−	0.136477i
$741$	3.94927	+	17.3029i	0.145080	+	0.635637i
$742$	8.50668			0.312290
$743$	−4.95044	−	21.6893i	−0.181614	−	0.795703i	−0.980862	−	0.194702i	$-0.937626\pi$
$743$	−4.95044	−	21.6893i	−0.181614	−	0.795703i	0.799248	−	0.601001i	$-0.205231\pi$
$744$	0.945336	−	1.18541i	0.0346577	−	0.0434594i
$745$	−2.16650	+	9.49205i	−0.0793743	+	0.347762i
$746$	−3.64758	+	15.9811i	−0.133548	+	0.585110i
$747$	−2.33795	−	2.93170i	−0.0855412	−	0.107265i
$748$	−18.5846	−	8.94988i	−0.679521	−	0.327240i
$749$	4.00217	−	1.92734i	0.146236	−	0.0704236i
$750$	−12.8176	+	16.0728i	−0.468034	+	0.586896i
$751$	16.0400	+	20.1135i	0.585308	+	0.733953i	0.983008	−	0.183563i	$-0.0587630\pi$
$751$	16.0400	+	20.1135i	0.585308	+	0.733953i	−0.397700	+	0.917515i	$0.630192\pi$
$752$	−31.9135	+	15.3687i	−1.16377	+	0.560440i
$753$	17.1613			0.625393
$754$	−18.2672	+	30.1429i	−0.665253	+	1.09774i
$755$	−24.7502			−0.900750
$756$	0.681480	−	0.328183i	0.0247852	−	0.0119359i
$757$	−16.5778	−	20.7879i	−0.602529	−	0.755548i	0.383240	−	0.923649i	$-0.374808\pi$
$757$	−16.5778	−	20.7879i	−0.602529	−	0.755548i	−0.985770	+	0.168101i	$0.946237\pi$
$758$	4.76473	−	5.97478i	0.173063	−	0.217014i
$759$	−6.74472	+	3.24808i	−0.244818	+	0.117898i
$760$	−0.894097	−	0.430575i	−0.0324323	−	0.0156186i
$761$	−5.12010	−	6.42041i	−0.185604	−	0.232740i	0.680321	−	0.732914i	$-0.261840\pi$
$761$	−5.12010	−	6.42041i	−0.185604	−	0.232740i	−0.865924	+	0.500175i	$0.833269\pi$
$762$	−4.52047	+	19.8055i	−0.163759	+	0.717476i
$763$	−1.30191	+	5.70403i	−0.0471322	+	0.206500i
$764$	8.14561	−	10.2143i	0.294698	−	0.369539i
$765$	1.16648	+

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)

\(f(q)\)	\(=\)	\(q+(1.78462 - 0.859427i) q^{2} +(-0.623490 - 0.781831i) q^{3} +(1.19927 - 1.50384i) q^{4} +(-1.09830 + 0.528911i) q^{5} +(-1.78462 - 0.859427i) q^{6} +(0.245180 + 0.307445i) q^{7} +(-0.0337262 + 0.147764i) q^{8} +(-0.222521 + 0.974928i) q^{9} +O(q^{10})\)	\(q+(1.78462 - 0.859427i) q^{2} +(-0.623490 - 0.781831i) q^{3} +(1.19927 - 1.50384i) q^{4} +(-1.09830 + 0.528911i) q^{5} +(-1.78462 - 0.859427i) q^{6} +(0.245180 + 0.307445i) q^{7} +(-0.0337262 + 0.147764i) q^{8} +(-0.222521 + 0.974928i) q^{9} +(-1.50548 + 1.88781i) q^{10} +(0.554919 + 2.43126i) q^{11} -1.92348 q^{12} +(-0.735270 - 3.22143i) q^{13} +(0.701779 + 0.337959i) q^{14} +(1.09830 + 0.528911i) q^{15} +(0.922834 + 4.04320i) q^{16} -4.30028 q^{17} +(0.440765 + 1.93112i) q^{18} +(3.34887 - 4.19936i) q^{19} +(-0.521757 + 2.28597i) q^{20} +(0.0875036 - 0.383378i) q^{21} +(3.07981 + 3.86196i) q^{22} +(-2.70461 - 1.30247i) q^{23} +(0.136554 - 0.0657611i) q^{24} +(-2.19094 + 2.74736i) q^{25} +(-4.08076 - 5.11712i) q^{26} +(0.900969 - 0.433884i) q^{27} +0.756386 q^{28} +(-1.86053 - 5.05355i) q^{29} +2.41460 q^{30} +(9.01303 - 4.34044i) q^{31} +(4.93275 + 6.18547i) q^{32} +(1.55485 - 1.94972i) q^{33} +(-7.67437 + 3.69578i) q^{34} +(-0.431891 - 0.207988i) q^{35} +(1.19927 + 1.50384i) q^{36} +(-0.812038 + 3.55777i) q^{37} +(2.36742 - 10.3724i) q^{38} +(-2.06018 + 2.58339i) q^{39} +(-0.0411127 - 0.180127i) q^{40} -7.82011 q^{41} +(-0.173325 - 0.759387i) q^{42} +(-2.11613 - 1.01908i) q^{43} +(4.32172 + 2.08123i) q^{44} +(-0.271257 - 1.18845i) q^{45} -5.94608 q^{46} +(1.90056 + 8.32691i) q^{47} +(2.58572 - 3.24240i) q^{48} +(1.52324 - 6.67374i) q^{49} +(-1.54885 + 6.78594i) q^{50} +(2.68118 + 3.36210i) q^{51} +(-5.72630 - 2.75764i) q^{52} +(9.83963 - 4.73852i) q^{53} +(1.23500 - 1.54863i) q^{54} +(-1.89539 - 2.37674i) q^{55} +(-0.0536983 + 0.0258597i) q^{56} -5.37118 q^{57} +(-7.66351 - 7.41968i) q^{58} +10.2851 q^{59} +(2.11255 - 1.01735i) q^{60} +(2.32106 + 2.91052i) q^{61} +(12.3545 - 15.4921i) q^{62} +(-0.354295 + 0.170619i) q^{63} +(6.64609 + 3.20059i) q^{64} +(2.51140 + 3.14919i) q^{65} +(1.09917 - 4.81578i) q^{66} +(-1.14527 + 5.01776i) q^{67} +(-5.15721 + 6.46693i) q^{68} +(0.667984 + 2.92663i) q^{69} -0.949512 q^{70} +(1.80048 + 7.88840i) q^{71} +(-0.136554 - 0.0657611i) q^{72} +(-7.88943 - 3.79935i) q^{73} +(1.60847 + 7.04716i) q^{74} +3.51400 q^{75} +(-2.29895 - 10.0723i) q^{76} +(-0.611425 + 0.766702i) q^{77} +(-1.45641 + 6.38094i) q^{78} +(-1.62424 + 7.11624i) q^{79} +(-3.15204 - 3.95253i) q^{80} +(-0.900969 - 0.433884i) q^{81} +(-13.9559 + 6.72082i) q^{82} +(-2.33795 + 2.93170i) q^{83} +(-0.471599 - 0.591366i) q^{84} +(4.72298 - 2.27447i) q^{85} -4.65232 q^{86} +(-2.79100 + 4.60546i) q^{87} -0.377968 q^{88} +(-9.38092 + 4.51762i) q^{89} +(-1.50548 - 1.88781i) q^{90} +(0.810141 - 1.01588i) q^{91} +(-5.20227 + 2.50528i) q^{92} +(-9.01303 - 4.34044i) q^{93} +(10.5482 + 13.2270i) q^{94} +(-1.45697 + 6.38339i) q^{95} +(1.76048 - 7.71316i) q^{96} +(-10.1017 + 12.6672i) q^{97} +(-3.01719 - 13.2192i) q^{98} -2.49378 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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