LMFDB - Embedded newform 87.2.g.b.16.3

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			16.3
Root			$-1.23500 - 1.54863i$ of defining polynomial
Character	$\chi$	$=$	87.16
Dual form			87.2.g.b.49.3

$q$-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 $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

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

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	0.940681	−	0.339292i	$-0.110188\pi$
$2$	1.78462	+	0.859427i	1.26192	+	0.607707i	0.321236	+	0.946999i	$0.395902\pi$
$3$	−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	0.171867	−	0.985120i	$-0.445020\pi$
$5$	−1.09830	−	0.528911i	−0.491173	−	0.236536i	−0.663040	+	0.748584i	$0.730734\pi$
$6$	−1.78462	+	0.859427i	−0.728568	+	0.350860i
$7$	0.245180	−	0.307445i	0.0926692	−	0.116203i	−0.733335	−	0.679867i	$-0.762037\pi$
$7$	0.245180	−	0.307445i	0.0926692	−	0.116203i	0.826004	+	0.563664i	$0.190609\pi$
$8$	−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	−0.819749	−	0.572723i	$-0.805887\pi$
$11$	0.554919	−	2.43126i	0.167314	−	0.733052i	0.987064	−	0.160329i	$-0.0512557\pi$
$12$	−1.92348			−0.555262
$13$	−0.735270	+	3.22143i	−0.203927	+	0.893464i	0.764590	+	0.644517i	$0.222942\pi$
$13$	−0.735270	+	3.22143i	−0.203927	+	0.893464i	−0.968517	+	0.248947i	$0.919916\pi$
$14$	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	0.999956	−	0.00939593i	$-0.00299086\pi$
$19$	3.34887	+	4.19936i	0.768284	+	0.963398i	−0.231671	+	0.972794i	$0.574419\pi$
$20$	−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	−0.694062	−	0.719915i	$-0.744181\pi$
$23$	−2.70461	+	1.30247i	−0.563951	+	0.271584i	0.130112	+	0.991499i	$0.458466\pi$
$24$	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	0.999982	−	0.00597750i	$-0.00190271\pi$
$31$	9.01303	+	4.34044i	1.61879	+	0.779567i	0.618805	+	0.785544i	$0.287617\pi$
$32$	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	−0.996781	−	0.0801733i	$-0.974453\pi$
$37$	−0.812038	−	3.55777i	−0.133498	−	0.584894i	0.863283	−	0.504721i	$-0.168405\pi$
$38$	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	−0.588223	−	0.808699i	$-0.700172\pi$
$43$	−2.11613	+	1.01908i	−0.322708	+	0.155408i	0.265515	+	0.964107i	$0.414458\pi$
$44$	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	−0.624059	−	0.781377i	$-0.714517\pi$
$47$	1.90056	−	8.32691i	0.277226	−	1.21461i	0.901284	−	0.433228i	$-0.142625\pi$
$48$	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	0.962742	−	0.270422i	$-0.0871632\pi$
$53$	9.83963	+	4.73852i	1.35158	+	0.650885i	0.388836	+	0.921307i	$0.372877\pi$
$54$	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	−0.610713	−	0.791852i	$-0.709117\pi$
$61$	2.32106	−	2.91052i	0.297182	−	0.372654i	0.907895	+	0.419198i	$0.137689\pi$
$62$	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	−0.995451	−	0.0952705i	$-0.969628\pi$
$67$	−1.14527	−	5.01776i	−0.139917	−	0.613017i	0.855534	−	0.517746i	$-0.173229\pi$
$68$	−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	−0.748366	−	0.663285i	$-0.769162\pi$
$71$	1.80048	−	7.88840i	0.213677	−	0.936181i	0.962044	−	0.272896i	$-0.0879813\pi$
$72$	−0.136554	+	0.0657611i	−0.0160931	+	0.00775003i
$73$	−7.88943	+	3.79935i	−0.923387	+	0.444680i	−0.834279	−	0.551342i	$-0.814116\pi$
$73$	−7.88943	+	3.79935i	−0.923387	+	0.444680i	−0.0891081	+	0.996022i	$0.528402\pi$
$74$	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	−0.980318	−	0.197423i	$-0.936743\pi$
$79$	−1.62424	−	7.11624i	−0.182741	−	0.800640i	0.797577	−	0.603216i	$-0.206115\pi$
$80$	−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	0.636785	−	0.771042i	$-0.280264\pi$
$83$	−2.33795	−	2.93170i	−0.256624	−	0.321796i	−0.893408	+	0.449246i	$0.851693\pi$
$84$	−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	−0.135350	−	0.990798i	$-0.543216\pi$
$89$	−9.38092	−	4.51762i	−0.994376	−	0.478866i	−0.859026	+	0.511932i	$0.828930\pi$
$90$	−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	−0.957484	−	0.288486i	$-0.906848\pi$
$97$	−10.1017	−	12.6672i	−1.02568	−	1.28616i	−0.0681928	−	0.997672i	$-0.521723\pi$
$98$	−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	−0.305854	−	0.952078i	$-0.598942\pi$
$101$	2.49049	−	1.19936i	0.247813	−	0.119341i	0.553668	+	0.832738i	$0.313228\pi$
$102$	7.67437	−	3.69578i	0.759875	−	0.365937i
$103$	−0.842490	+	3.69119i	−0.0830130	+	0.363704i	−0.999324	−	0.0367637i	$-0.988295\pi$
$103$	−0.842490	+	3.69119i	−0.0830130	+	0.363704i	0.916311	+	0.400467i	$0.131152\pi$
$104$	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	0.938268	+	0.345909i	$0.112429\pi$
$107$	2.51363	+	11.0129i	0.243002	+	1.06466i	−0.695266	+	0.718752i	$0.744714\pi$
$108$	0.428015	+	1.87526i	0.0411858	+	0.180447i
$109$	9.27648	−	11.6323i	0.888526	−	1.11418i	−0.104293	−	0.994547i	$-0.533258\pi$
$109$	9.27648	−	11.6323i	0.888526	−	1.11418i	0.992819	−	0.119630i	$-0.0381707\pi$
$110$	−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	−0.782345	−	0.622845i	$-0.785977\pi$
$113$	−0.0109212	+	0.0136948i	−0.00102738	+	0.00128830i	0.781318	+	0.624134i	$0.214548\pi$
$114$	−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	0.766893	+	0.641775i	$0.221802\pi$
$127$	−2.28217	+	9.99883i	−0.202510	+	0.887253i	−0.969402	+	0.245477i	$0.921055\pi$
$128$	−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	−0.618540	−	0.785754i	$-0.712275\pi$
$131$	−4.46222	+	2.14889i	−0.389866	+	0.187750i	0.228674	+	0.973503i	$0.426561\pi$
$132$	−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	0.923428	+	0.383771i	$0.125375\pi$
$137$	3.01935	+	13.2286i	0.257960	+	1.13020i	−0.665468	+	0.746426i	$0.731768\pi$
$138$	3.70732	−	4.64884i	0.315588	−	0.395735i
$139$	−14.8411	+	7.14709i	−1.25880	+	0.606208i	−0.939858	−	0.341564i	$-0.889043\pi$
$139$	−14.8411	+	7.14709i	−1.25880	+	0.606208i	−0.318946	+	0.947773i	$0.603329\pi$
$140$	−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	0.942786	−	0.333399i	$-0.108195\pi$
$149$	4.97975	+	6.24440i	0.407957	+	0.511562i	−0.534829	+	0.844960i	$0.679624\pi$
$150$	6.27115	+	3.02003i	0.512037	+	0.246584i
$151$	18.2927	−	8.80931i	1.48864	−	0.716891i	0.499837	−	0.866119i	$-0.333393\pi$
$151$	18.2927	−	8.80931i	1.48864	−	0.716891i	0.988803	+	0.149228i	$0.0476788\pi$
$152$	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	0.471325	+	0.881960i	$0.343776\pi$
$163$	−4.28966	+	18.7942i	−0.335992	+	1.47208i	−0.807317	+	0.590118i	$0.799081\pi$
$164$	−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	−0.853969	−	0.520324i	$-0.825811\pi$
$167$	−2.02456	+	2.53871i	−0.156665	+	0.196452i	0.697304	+	0.716775i	$0.254383\pi$
$168$	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	0.754369	−	0.656450i	$-0.227943\pi$
$179$	9.51892	+	4.58407i	0.711478	+	0.342630i	−0.0428918	+	0.999080i	$0.513657\pi$
$180$	−2.11255	+	1.01735i	−0.157460	+	0.0758289i
$181$	−7.63399	+	9.57273i	−0.567430	+	0.711535i	−0.979912	−	0.199431i	$-0.936091\pi$
$181$	−7.63399	+	9.57273i	−0.567430	+	0.711535i	0.412482	+	0.910966i	$0.364662\pi$
$182$	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	−0.919954	−	0.392025i	$-0.871775\pi$
$193$	−15.2461	−	19.1181i	−1.09744	−	1.37615i	−0.177487	−	0.984123i	$-0.556797\pi$
$194$	−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	−0.176529	−	0.984295i	$-0.556487\pi$
$197$	6.77867	−	3.26444i	0.482960	−	0.232581i	0.659489	+	0.751714i	$0.270773\pi$
$198$	−4.45045	−	2.14323i	−0.316280	−	0.152312i
$199$	−14.3765	−	18.0276i	−1.01913	−	1.27794i	−0.960091	−	0.279687i	$-0.909769\pi$
$199$	−14.3765	−	18.0276i	−1.01913	−	1.27794i	−0.0590340	−	0.998256i	$-0.518802\pi$
$200$	−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	−0.999997	−	0.00241130i	$-0.999232\pi$
$211$	−1.45370	−	6.36909i	−0.100077	−	0.438466i	0.899920	−	0.436055i	$-0.143625\pi$
$212$	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	0.980659	+	0.195725i	$0.0627061\pi$
$223$	2.71840	+	11.9101i	0.182038	+	0.797560i	−0.798621	+	0.601834i	$0.794437\pi$
$224$	−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	0.813236	−	0.581934i	$-0.197704\pi$
$227$	13.0371	+	6.27836i	0.865306	+	0.416709i	0.0520700	+	0.998643i	$0.483418\pi$
$228$	−6.44150	−	8.07739i	−0.426599	−	0.534938i
$229$	6.49636	−	8.14618i	0.429292	−	0.538315i	−0.519394	−	0.854535i	$-0.673842\pi$
$229$	6.49636	−	8.14618i	0.429292	−	0.538315i	0.948686	+	0.316220i	$0.102414\pi$
$230$	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	0.0174007	+	0.999849i	$0.494461\pi$
$239$	−14.8606	+	18.6346i	−0.961252	+	1.20537i	−0.978652	+	0.205523i	$0.934111\pi$
$240$	−1.12495	−	4.92873i	−0.0726152	−	0.318148i
$241$	−4.06237	−	17.7984i	−0.261680	−	1.14650i	−0.919428	−	0.393258i	$-0.871348\pi$
$241$	−4.06237	−	17.7984i	−0.261680	−	1.14650i	0.657748	−	0.753238i	$-0.271509\pi$
$242$	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	0.319547	−	0.947570i	$-0.396469\pi$
$251$	−10.6999	−	13.4173i	−0.675372	−	0.846889i	−0.994919	+	0.100681i	$0.967898\pi$
$252$	−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	0.748855	−	0.662734i	$-0.230604\pi$
$257$	−1.02439	−	1.28454i	−0.0638996	−	0.0801275i	−0.812754	+	0.582607i	$0.802033\pi$
$258$	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	0.233074	−	0.972459i	$-0.425122\pi$
$263$	−6.19347	−	2.98262i	−0.381906	−	0.183916i	−0.614980	+	0.788543i	$0.710836\pi$
$264$	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	0.994904	−	0.100831i	$-0.0321502\pi$
$269$	0.898416	+	3.93622i	0.0547774	+	0.239995i	−0.940126	+	0.340827i	$0.889293\pi$
$270$	−0.537299	−	2.35406i	−0.0326990	−	0.143264i
$271$	8.04210	+	10.0845i	0.488523	+	0.612589i	0.963598	−	0.267357i	$-0.0861503\pi$
$271$	8.04210	+	10.0845i	0.488523	+	0.612589i	−0.475074	+	0.879946i	$0.657579\pi$
$272$	−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	−0.948994	−	0.315293i	$-0.897897\pi$
$277$	0.712674	−	3.12243i	0.0428204	−	0.187608i	0.991815	+	0.127684i	$0.0407544\pi$
$278$	−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	−0.926169	−	0.377109i	$-0.876918\pi$
$281$	−4.28030	−	18.7532i	−0.255341	−	1.11872i	0.670828	−	0.741613i	$-0.265939\pi$
$282$	3.76460	+	16.4938i	0.224178	+	0.982190i
$283$	17.6050	−	22.0760i	1.04651	−	1.31228i	0.0981179	−	0.995175i	$-0.468718\pi$
$283$	17.6050	−	22.0760i	1.04651	−	1.31228i	0.948390	−	0.317105i	$-0.102711\pi$
$284$	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	−0.427846	+	0.903852i	$0.640727\pi$
$293$	−20.7774	+	26.0541i	−1.21383	+	1.52210i	−0.785986	+	0.618245i	$0.787844\pi$
$294$	−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	−0.999652	−	0.0263630i	$-0.991607\pi$
$311$	−1.94755	−	8.53276i	−0.110435	−	0.483848i	0.889217	−	0.457485i	$-0.151250\pi$
$312$	−0.312249	+	0.391548i	−0.0176776	+	0.0221671i
$313$	29.6754	−	14.2909i	1.67735	−	0.807771i	0.680148	−	0.733075i	$-0.261915\pi$
$313$	29.6754	−	14.2909i	1.67735	−	0.807771i	0.997206	−	0.0746966i	$-0.0237988\pi$
$314$	−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	0.919969	−	0.391991i	$-0.128214\pi$
$317$	21.1355	+	10.1783i	1.18709	+	0.571672i	0.267120	+	0.963663i	$0.413928\pi$
$318$	−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	−0.920973	−	0.389627i	$-0.872604\pi$
$337$	1.42909	−	6.26127i	0.0778476	−	0.341073i	0.998821	+	0.0485537i	$0.0154612\pi$
$338$	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	0.777902	−	0.628386i	$-0.216284\pi$
$353$	14.4975	+	6.98162i	0.771623	+	0.371594i	−0.00627832	+	0.999980i	$0.501998\pi$
$354$	−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	−0.853032	−	0.521858i	$-0.825239\pi$
$359$	2.68955	−	11.7837i	0.141949	−	0.621920i	0.994981	−	0.100061i	$-0.0319039\pi$
$360$	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	0.648284	−	0.761399i	$-0.275487\pi$
$367$	−4.56482	−	5.72410i	−0.238282	−	0.298796i	−0.886566	+	0.462603i	$0.846916\pi$
$368$	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	0.630096	−	0.776517i	$-0.283015\pi$
$373$	−5.15974	−	6.47011i	−0.267161	−	0.335010i	−0.897258	+	0.441507i	$0.854444\pi$
$374$	−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	0.521024	−	0.853542i	$-0.325550\pi$
$379$	3.47602	+	1.67396i	0.178551	+	0.0859858i	−0.342473	+	0.939528i	$0.611264\pi$
$380$	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	−0.302212	−	0.953241i	$-0.597725\pi$
$383$	4.98332	−	2.39984i	0.254636	−	0.122626i	0.556848	+	0.830615i	$0.312011\pi$
$384$	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	0.998534	−	0.0541277i	$-0.0172378\pi$
$397$	1.50235	+	6.58223i	0.0754008	+	0.330353i	−0.923133	+	0.384480i	$0.874381\pi$
$398$	−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	0.879873	−	0.475209i	$-0.157627\pi$
$401$	21.1650	+	10.1925i	1.05693	+	0.508992i	0.177059	+	0.984200i	$0.443342\pi$
$402$	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	−0.999675	−	0.0255111i	$-0.991879\pi$
$409$	−15.2154	+	19.0795i	−0.752355	+	0.943423i	0.247320	+	0.968934i	$0.420450\pi$
$410$	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	0.799019	+	0.601306i	$0.205353\pi$
$419$	−3.72073	+	16.3016i	−0.181769	+	0.796384i	−0.980788	+	0.195077i	$0.937504\pi$
$420$	0.830735	−	0.400061i	0.0405357	−	0.0195210i
$421$	20.8550	−	10.0432i	1.01641	−	0.489478i	0.149935	−	0.988696i	$-0.452094\pi$
$421$	20.8550	−	10.0432i	1.01641	−	0.489478i	0.866476	+	0.499218i	$0.166379\pi$
$422$	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	0.897490	+	0.441035i	$0.145389\pi$
$431$	23.4128	+	29.3588i	1.12776	+	1.41416i	0.230267	+	0.973127i	$0.426040\pi$
$432$	2.58572	−	3.24240i	0.124406	−	0.156000i
$433$	−15.4657	−	7.44790i	−0.743235	−	0.357923i	0.0236390	−	0.999721i	$-0.492475\pi$
$433$	−15.4657	−	7.44790i	−0.743235	−	0.357923i	−0.766874	+	0.641797i	$0.778189\pi$
$434$	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	0.854390	−	0.519632i	$-0.173931\pi$
$439$	3.30350	+	4.14245i	0.157667	+	0.197709i	−0.696723	+	0.717340i	$0.745359\pi$
$440$	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	−0.993966	−	0.109684i	$-0.965016\pi$
$443$	−3.07345	−	13.4656i	−0.146024	−	0.639772i	0.847943	−	0.530088i	$-0.177841\pi$
$444$	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	−0.764036	−	0.645173i	$-0.776785\pi$
$449$	−15.5953	+	7.51031i	−0.735989	+	0.354433i	0.0280478	+	0.999607i	$0.491071\pi$
$450$	−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	−0.984624	−	0.174686i	$-0.944109\pi$
$457$	−12.7243	+	15.9558i	−0.595219	+	0.746381i	0.389406	+	0.921066i	$0.372680\pi$
$458$	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	−0.472457	−	0.881354i	$-0.656633\pi$
$461$	10.5622	−	13.2446i	0.491931	−	0.616861i	0.964388	+	0.264492i	$0.0852043\pi$
$462$	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	−0.181026	−	0.983478i	$-0.557942\pi$
$467$	17.6788	−	22.1685i	0.818077	−	1.02584i	0.999103	−	0.0423574i	$-0.0134868\pi$
$468$	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	−0.970273	−	0.242014i	$-0.922192\pi$
$479$	−30.3344	+	14.6083i	−1.38601	+	0.667469i	−0.415741	+	0.909483i	$0.636478\pi$
$480$	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	0.106843	−	0.994276i	$-0.465926\pi$
$487$	20.9826	−	10.1047i	0.950814	−	0.457888i	0.843971	+	0.536388i	$0.180212\pi$
$488$	−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	0.710420	−	0.703778i	$-0.248505\pi$
$491$	13.3643	+	6.43593i	0.603124	+	0.290449i	−0.107296	+	0.994227i	$0.534219\pi$
$492$	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	−0.838220	−	0.545332i	$-0.816404\pi$
$499$	−20.8748	+	10.0528i	−0.934484	+	0.450024i	−0.0962638	+	0.995356i	$0.530689\pi$
$500$	−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	0.517742	−	0.855537i	$-0.326773\pi$
$503$	−9.67873	−	12.1367i	−0.431553	−	0.541151i	−0.949295	+	0.314386i	$0.898201\pi$
$504$	−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	0.521006	+	0.853553i	$0.325557\pi$
$509$	−7.19126	+	31.5070i	−0.318747	+	1.39652i	−0.839753	+	0.542969i	$0.817300\pi$
$510$	−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	0.526194	−	0.850365i	$-0.323619\pi$
$541$	−9.76755	−	12.2481i	−0.419940	−	0.526588i	−0.946133	+	0.323777i	$0.895047\pi$
$542$	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	0.578881	−	0.815412i	$-0.303490\pi$
$547$	−8.06654	−	10.1151i	−0.344901	−	0.432492i	−0.923781	+	0.382921i	$0.874918\pi$
$548$	−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	−0.610616	−	0.791926i	$-0.709078\pi$
$557$	−8.78368	+	4.23000i	−0.372177	+	0.179231i	0.238440	+	0.971157i	$0.423364\pi$
$558$	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	−0.639203	−	0.769038i	$-0.720736\pi$
$569$	6.44938	−	28.2566i	0.270372	−	1.18458i	0.909575	−	0.415540i	$-0.136407\pi$
$570$	8.08619	+	10.1398i	0.338693	+	0.424708i
$571$	6.72499	+	29.4641i	0.281432	+	1.23303i	0.895958	+	0.444138i	$0.146490\pi$
$571$	6.72499	+	29.4641i	0.281432	+	1.23303i	−0.614526	+	0.788897i	$0.710653\pi$
$572$	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	−0.994745	−	0.102383i	$-0.967353\pi$
$577$	−16.1799	+	20.2889i	−0.673577	+	0.844639i	0.321168	+	0.947022i	$0.395925\pi$
$578$	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	−0.771753	−	0.635922i	$-0.780620\pi$
$587$	0.483492	−	0.606280i	0.0199559	−	0.0250239i	0.791709	+	0.610898i	$0.209191\pi$
$588$	−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	−0.680088	−	0.733130i	$-0.738058\pi$
$593$	6.10600	−	26.7521i	0.250743	−	1.09858i	0.930832	−	0.365449i	$-0.119084\pi$
$594$	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	0.916896	+	0.399125i	$0.130686\pi$
$599$	26.9705	+	33.8200i	1.10199	+	1.38185i	0.185090	+	0.982722i	$0.440742\pi$
$600$	−0.118514	−	0.519242i	−0.00483830	−	0.0211980i
$601$	7.35145	+	32.2088i	0.299872	+	1.31382i	0.870318	+	0.492490i	$0.163913\pi$
$601$	7.35145	+	32.2088i	0.299872	+	1.31382i	−0.570447	+	0.821335i	$0.693230\pi$
$602$	−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	0.727423	−	0.686189i	$-0.240718\pi$
$607$	15.8783	+	7.64658i	0.644480	+	0.310365i	−0.0829433	+	0.996554i	$0.526432\pi$
$608$	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	0.979390	+	0.201980i	$0.0647377\pi$
$613$	23.7282	+	29.7542i	0.958371	+	1.20176i	−0.0210185	+	0.999779i	$0.506691\pi$
$614$	−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	0.992767	−	0.120058i	$-0.0383081\pi$
$617$	1.14817	+	5.03046i	0.0462235	+	0.202519i	−0.946543	+	0.322577i	$0.895451\pi$
$618$	−1.66879	−	7.31143i	−0.0671284	−	0.294109i
$619$	−18.4979	−	23.1956i	−0.743494	−	0.932312i	0.255915	−	0.966699i	$-0.417623\pi$
$619$	−18.4979	−	23.1956i	−0.743494	−	0.932312i	−0.999409	+	0.0343876i	$0.989052\pi$
$620$	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	−0.642550	−	0.766244i	$-0.722123\pi$
$631$	6.21623	−	7.79490i	0.247464	−	0.310310i	0.890014	+	0.455934i	$0.150695\pi$
$632$	−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	−0.425781	−	0.904826i	$-0.640001\pi$
$641$	13.9528	−	17.4963i	0.551104	−	0.691063i	0.976886	+	0.213763i	$0.0685721\pi$
$642$	−13.9507	−	17.4936i	−0.550590	−	0.690418i
$643$	5.33870	+	2.57098i	0.210538	+	0.101390i	0.536181	−	0.844103i	$-0.319866\pi$
$643$	5.33870	+	2.57098i	0.210538	+	0.101390i	−0.325643	+	0.945493i	$0.605581\pi$
$644$	−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	−0.996562	−	0.0828464i	$-0.973599\pi$
$647$	−3.42464	−	15.0043i	−0.134636	−	0.589881i	0.861926	−	0.507034i	$-0.169258\pi$
$648$	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	−0.918675	−	0.395013i	$-0.870740\pi$
$653$	−30.2207	+	14.5535i	−1.18263	+	0.569523i	−0.263951	+	0.964536i	$0.585026\pi$
$654$	−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	0.911026	−	0.412349i	$-0.135291\pi$
$659$	−2.27680	−	9.97530i	−0.0886914	−	0.388582i	−0.999718	+	0.0237662i	$0.992434\pi$
$660$	3.64574	−	4.57161i	0.141910	−	0.177950i
$661$	−12.0033	+	5.78051i	−0.466876	+	0.224836i	−0.652505	−	0.757784i	$-0.726282\pi$
$661$	−12.0033	+	5.78051i	−0.466876	+	0.224836i	0.185629	+	0.982620i	$0.440568\pi$
$662$	−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	−0.955571	−	0.294761i	$-0.904760\pi$
$673$	−34.2673	+	16.5022i	−1.32091	+	0.636115i	−0.365335	+	0.930876i	$0.619046\pi$
$674$	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	0.876146	−	0.482046i	$-0.160106\pi$
$677$	5.49590	+	6.89164i	0.211224	+	0.264867i	−0.664921	+	0.746913i	$0.731535\pi$
$678$	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	−0.913157	−	0.407607i	$-0.866363\pi$
$683$	2.25860	−	9.89559i	0.0864231	−	0.378644i	0.999580	+	0.0289628i	$0.00922044\pi$
$684$	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	0.436353	−	0.899775i	$-0.356270\pi$
$691$	0.129926	+	0.0625692i	0.00494263	+	0.00238024i	−0.431411	+	0.902156i	$0.641984\pi$
$692$	−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	−0.999728	−	0.0233027i	$-0.992582\pi$
$701$	−43.4549	−	20.9268i	−1.64127	−	0.790393i	−0.641539	−	0.767090i	$-0.721704\pi$
$702$	−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	−0.999693	−	0.0247883i	$-0.992109\pi$
$709$	−2.34972	+	10.2948i	−0.0882454	+	0.386629i	0.911447	+	0.411417i	$0.134966\pi$
$710$	−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	0.0423980	−	0.999101i	$-0.486500\pi$
$719$	22.7910	−	10.9756i	0.849961	−	0.409320i	0.807563	+	0.589781i	$0.200786\pi$
$720$	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	0.999767	+	0.0215952i	$0.00687451\pi$
$727$	44.2191	+	21.2948i	1.64000	+	0.789780i	0.640228	+	0.768185i	$0.278840\pi$
$728$	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	0.986980	−	0.160841i	$-0.0514207\pi$
$733$	0.756862	+	3.31603i	0.0279553	+	0.122480i	−0.959025	+	0.283322i	$0.908564\pi$
$734$	−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	−0.549806	−	0.835293i	$-0.685298\pi$
$739$	−6.51194	+	3.13599i	−0.239546	+	0.115359i	0.310260	+	0.950652i	$0.399584\pi$
$740$	−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	0.799248	+	0.601001i	$0.205231\pi$
$743$	−4.95044	+	21.6893i	−0.181614	+	0.795703i	−0.980862	+	0.194702i	$0.937626\pi$
$744$	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	−0.397700	−	0.917515i	$-0.630192\pi$
$751$	16.0400	−	20.1135i	0.585308	−	0.733953i	0.983008	+	0.183563i	$0.0587630\pi$
$752$	−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	−0.985770	−	0.168101i	$-0.946237\pi$
$757$	−16.5778	+	20.7879i	−0.602529	+	0.755548i	0.383240	+	0.923649i	$0.374808\pi$
$758$	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	−0.865924	−	0.500175i	$-0.833269\pi$
$761$	−5.12010	+	6.42041i	−0.185604	+	0.232740i	0.680321	+	0.732914i	$0.261840\pi$
$762$	−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	−	5.11068i	0.0421742	−

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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