LMFDB - Embedded newform 570.2.u.g.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(61,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("570.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.u (of order $9$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			61.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	570.61
Dual form			570.2.u.g.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(0.173648 - 0.984808i) q^{6} +(1.43969 - 2.49362i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(0.173648 - 0.984808i) q^{6} +(1.43969 - 2.49362i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(0.939693 - 0.342020i) q^{10} +(2.26604 + 3.92490i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.368241 - 2.08840i) q^{13} +(2.20574 - 1.85083i) q^{14} +(-0.766044 - 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-4.43242 - 1.61327i) q^{17} -1.00000 q^{18} +(3.37939 - 2.75314i) q^{19} +1.00000 q^{20} +(-2.70574 - 0.984808i) q^{21} +(0.786989 + 4.46324i) q^{22} +(-2.20574 - 1.85083i) q^{23} +(0.766044 - 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(1.06031 - 1.83651i) q^{26} +(0.500000 + 0.866025i) q^{27} +(2.70574 - 0.984808i) q^{28} +(9.33022 - 3.39592i) q^{29} +(-0.500000 - 0.866025i) q^{30} +(-0.0714517 + 0.123758i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(3.47178 - 2.91317i) q^{33} +(-3.61334 - 3.03195i) q^{34} +(-0.500000 - 2.83564i) q^{35} +(-0.939693 - 0.342020i) q^{36} -5.35504 q^{37} +(4.11721 - 1.43128i) q^{38} -2.12061 q^{39} +(0.939693 + 0.342020i) q^{40} +(1.50253 + 8.52125i) q^{41} +(-2.20574 - 1.85083i) q^{42} +(-7.44356 + 6.24589i) q^{43} +(-0.786989 + 4.46324i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-1.43969 - 2.49362i) q^{46} +(4.35844 - 1.58634i) q^{47} +(0.939693 - 0.342020i) q^{48} +(-0.645430 - 1.11792i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.819078 + 4.64522i) q^{51} +(1.62449 - 1.36310i) q^{52} +(10.5287 + 8.83462i) q^{53} +(0.173648 + 0.984808i) q^{54} +(4.25877 + 1.55007i) q^{55} +2.87939 q^{56} +(-3.29813 - 2.84997i) q^{57} +9.92902 q^{58} +(-13.1236 - 4.77660i) q^{59} +(-0.173648 - 0.984808i) q^{60} +(3.42855 + 2.87689i) q^{61} +(-0.109470 + 0.0918566i) q^{62} +(-0.500000 + 2.83564i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.06031 - 1.83651i) q^{65} +(4.25877 - 1.55007i) q^{66} +(-7.23783 + 2.63435i) q^{67} +(-2.35844 - 4.08494i) q^{68} +(-1.43969 + 2.49362i) q^{69} +(0.500000 - 2.83564i) q^{70} +(-10.8610 + 9.11343i) q^{71} +(-0.766044 - 0.642788i) q^{72} +(-2.28059 - 12.9339i) q^{73} +(-5.03209 - 1.83153i) q^{74} -1.00000 q^{75} +(4.35844 + 0.0632028i) q^{76} +13.0496 q^{77} +(-1.99273 - 0.725293i) q^{78} +(-0.481582 - 2.73119i) q^{79} +(0.766044 + 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-1.50253 + 8.52125i) q^{82} +(-0.488856 + 0.846723i) q^{83} +(-1.43969 - 2.49362i) q^{84} +(-4.43242 + 1.61327i) q^{85} +(-9.13088 + 3.32337i) q^{86} +(-4.96451 - 8.59878i) q^{87} +(-2.26604 + 3.92490i) q^{88} +(-2.45811 + 13.9406i) q^{89} +(-0.766044 + 0.642788i) q^{90} +(-4.67752 - 3.92490i) q^{91} +(-0.500000 - 2.83564i) q^{92} +(0.134285 + 0.0488759i) q^{93} +4.63816 q^{94} +(0.819078 - 4.28125i) q^{95} +1.00000 q^{96} +(0.634285 + 0.230861i) q^{97} +(-0.224155 - 1.27125i) q^{98} +(-3.47178 - 2.91317i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q + 3 * q^7 + 3 * q^8	$ 6 q + 3 q^{7} + 3 q^{8} + 9 q^{11} + 3 q^{12} - 3 q^{13} + 3 q^{14} - 3 q^{17} - 6 q^{18} + 9 q^{19} + 6 q^{20} - 6 q^{21} - 3 q^{22} - 3 q^{23} + 12 q^{26} + 3 q^{27} + 6 q^{28} + 33 q^{29} - 3 q^{30} + 6 q^{33} - 15 q^{34} - 3 q^{35} + 18 q^{37} - 6 q^{38} - 24 q^{39} - 6 q^{41} - 3 q^{42} - 15 q^{43} + 3 q^{44} - 3 q^{45} - 3 q^{46} + 18 q^{47} + 12 q^{49} + 3 q^{50} + 12 q^{51} - 3 q^{52} + 12 q^{53} + 3 q^{55} + 6 q^{56} - 6 q^{57} - 6 q^{58} - 9 q^{59} + 21 q^{61} - 18 q^{62} - 3 q^{63} - 3 q^{64} - 12 q^{65} + 3 q^{66} - 24 q^{67} - 6 q^{68} - 3 q^{69} + 3 q^{70} - 42 q^{71} - 45 q^{73} - 21 q^{74} - 6 q^{75} + 18 q^{76} + 24 q^{77} + 6 q^{78} + 9 q^{79} + 6 q^{82} - 9 q^{83} - 3 q^{84} - 3 q^{85} - 3 q^{86} + 3 q^{87} - 9 q^{88} - 21 q^{89} - 3 q^{91} - 3 q^{92} - 9 q^{93} - 6 q^{94} - 12 q^{95} + 6 q^{96} - 6 q^{97} - 3 q^{98} - 6 q^{99}+O(q^{100}) $ 6 * q + 3 * q^7 + 3 * q^8 + 9 * q^11 + 3 * q^12 - 3 * q^13 + 3 * q^14 - 3 * q^17 - 6 * q^18 + 9 * q^19 + 6 * q^20 - 6 * q^21 - 3 * q^22 - 3 * q^23 + 12 * q^26 + 3 * q^27 + 6 * q^28 + 33 * q^29 - 3 * q^30 + 6 * q^33 - 15 * q^34 - 3 * q^35 + 18 * q^37 - 6 * q^38 - 24 * q^39 - 6 * q^41 - 3 * q^42 - 15 * q^43 + 3 * q^44 - 3 * q^45 - 3 * q^46 + 18 * q^47 + 12 * q^49 + 3 * q^50 + 12 * q^51 - 3 * q^52 + 12 * q^53 + 3 * q^55 + 6 * q^56 - 6 * q^57 - 6 * q^58 - 9 * q^59 + 21 * q^61 - 18 * q^62 - 3 * q^63 - 3 * q^64 - 12 * q^65 + 3 * q^66 - 24 * q^67 - 6 * q^68 - 3 * q^69 + 3 * q^70 - 42 * q^71 - 45 * q^73 - 21 * q^74 - 6 * q^75 + 18 * q^76 + 24 * q^77 + 6 * q^78 + 9 * q^79 + 6 * q^82 - 9 * q^83 - 3 * q^84 - 3 * q^85 - 3 * q^86 + 3 * q^87 - 9 * q^88 - 21 * q^89 - 3 * q^91 - 3 * q^92 - 9 * q^93 - 6 * q^94 - 12 * q^95 + 6 * q^96 - 6 * q^97 - 3 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	0.766044	−	0.642788i	0.342585	−	0.287463i
$5$	0.766044	−	0.642788i	0.342585	−	0.287463i
$6$	0.173648	−	0.984808i	0.0708916	−	0.402046i
$7$	1.43969	−	2.49362i	0.544153	−	0.942500i	−0.454507	−	0.890743i	$-0.650185\pi$
$7$	1.43969	−	2.49362i	0.544153	−	0.942500i	0.998660	−	0.0517569i	$-0.0164821\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	0.939693	−	0.342020i	0.297157	−	0.108156i
$11$	2.26604	+	3.92490i	0.683238	+	1.18340i	0.973987	+	0.226604i	$0.0727622\pi$
$11$	2.26604	+	3.92490i	0.683238	+	1.18340i	−0.290749	+	0.956799i	$0.593904\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	0.368241	−	2.08840i	0.102132	−	0.579217i	−0.890196	−	0.455578i	$-0.849432\pi$
$13$	0.368241	−	2.08840i	0.102132	−	0.579217i	0.992327	−	0.123639i	$-0.0394564\pi$
$14$	2.20574	−	1.85083i	0.589508	−	0.494656i
$15$	−0.766044	−	0.642788i	−0.197792	−	0.165967i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−4.43242	−	1.61327i	−1.07502	−	0.391275i	−0.256968	−	0.966420i	$-0.582723\pi$
$17$	−4.43242	−	1.61327i	−1.07502	−	0.391275i	−0.818052	+	0.575145i	$0.804946\pi$
$18$	−1.00000			−0.235702
$19$	3.37939	−	2.75314i	0.775284	−	0.631613i
$19$	3.37939	−	2.75314i	0.775284	−	0.631613i
$20$	1.00000			0.223607
$21$	−2.70574	−	0.984808i	−0.590440	−	0.214903i
$22$	0.786989	+	4.46324i	0.167787	+	0.951565i
$23$	−2.20574	−	1.85083i	−0.459928	−	0.385925i	0.383177	−	0.923675i	$-0.374830\pi$
$23$	−2.20574	−	1.85083i	−0.459928	−	0.385925i	−0.843105	+	0.537750i	$0.819275\pi$
$24$	0.766044	−	0.642788i	0.156368	−	0.131208i
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$	1.06031	−	1.83651i	0.207943	−	0.360169i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	2.70574	−	0.984808i	0.511336	−	0.186111i
$29$	9.33022	−	3.39592i	1.73258	−	0.630607i	0.733770	−	0.679398i	$-0.237759\pi$
$29$	9.33022	−	3.39592i	1.73258	−	0.630607i	0.998809	+	0.0487911i	$0.0155369\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	−0.0714517	+	0.123758i	−0.0128331	+	0.0222276i	−0.872371	−	0.488845i	$-0.837418\pi$
$31$	−0.0714517	+	0.123758i	−0.0128331	+	0.0222276i	0.859538	+	0.511073i	$0.170752\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	3.47178	−	2.91317i	0.604360	−	0.507118i
$34$	−3.61334	−	3.03195i	−0.619683	−	0.519976i
$35$	−0.500000	−	2.83564i	−0.0845154	−	0.479311i
$36$	−0.939693	−	0.342020i	−0.156615	−	0.0570034i
$37$	−5.35504			−0.880363			−0.440181	−	0.897909i	$-0.645086\pi$
$37$	−5.35504			−0.880363			−0.440181	+	0.897909i	$0.645086\pi$
$38$	4.11721	−	1.43128i	0.667900	−	0.232185i
$39$	−2.12061			−0.339570
$40$	0.939693	+	0.342020i	0.148578	+	0.0540781i
$41$	1.50253	+	8.52125i	0.234655	+	1.33080i	0.843339	+	0.537382i	$0.180587\pi$
$41$	1.50253	+	8.52125i	0.234655	+	1.33080i	−0.608683	+	0.793413i	$0.708302\pi$
$42$	−2.20574	−	1.85083i	−0.340353	−	0.285590i
$43$	−7.44356	+	6.24589i	−1.13513	+	0.952489i	−0.999269	−	0.0382380i	$-0.987825\pi$
$43$	−7.44356	+	6.24589i	−1.13513	+	0.952489i	−0.135864	+	0.990727i	$0.543381\pi$
$44$	−0.786989	+	4.46324i	−0.118643	+	0.672858i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	−1.43969	−	2.49362i	−0.212271	−	0.367664i
$47$	4.35844	−	1.58634i	0.635744	−	0.231392i	−0.00398551	−	0.999992i	$-0.501269\pi$
$47$	4.35844	−	1.58634i	0.635744	−	0.231392i	0.639729	+	0.768600i	$0.279046\pi$
$48$	0.939693	−	0.342020i	0.135633	−	0.0493664i
$49$	−0.645430	−	1.11792i	−0.0922042	−	0.159702i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−0.819078	+	4.64522i	−0.114694	+	0.650461i
$52$	1.62449	−	1.36310i	0.225276	−	0.189029i
$53$	10.5287	+	8.83462i	1.44623	+	1.21353i	0.935277	+	0.353917i	$0.115150\pi$
$53$	10.5287	+	8.83462i	1.44623	+	1.21353i	0.510949	+	0.859611i	$0.329294\pi$
$54$	0.173648	+	0.984808i	0.0236305	+	0.134015i
$55$	4.25877	+	1.55007i	0.574252	+	0.209011i
$56$	2.87939			0.384774
$57$	−3.29813	−	2.84997i	−0.436848	−	0.377487i
$58$	9.92902			1.30374
$59$	−13.1236	−	4.77660i	−1.70855	−	0.621861i	−0.711796	−	0.702387i	$-0.752118\pi$
$59$	−13.1236	−	4.77660i	−1.70855	−	0.621861i	−0.996753	+	0.0805259i	$0.974340\pi$
$60$	−0.173648	−	0.984808i	−0.0224179	−	0.127138i
$61$	3.42855	+	2.87689i	0.438981	+	0.368348i	0.835328	−	0.549752i	$-0.185278\pi$
$61$	3.42855	+	2.87689i	0.438981	+	0.368348i	−0.396347	+	0.918101i	$0.629722\pi$
$62$	−0.109470	+	0.0918566i	−0.0139028	+	0.0116658i
$63$	−0.500000	+	2.83564i	−0.0629941	+	0.357257i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−1.06031	−	1.83651i	−0.131515	−	0.227791i
$66$	4.25877	−	1.55007i	0.524218	−	0.190800i
$67$	−7.23783	+	2.63435i	−0.884241	+	0.321837i	−0.743920	−	0.668269i	$-0.767036\pi$
$67$	−7.23783	+	2.63435i	−0.884241	+	0.321837i	−0.140321	+	0.990106i	$0.544813\pi$
$68$	−2.35844	−	4.08494i	−0.286003	−	0.495372i
$69$	−1.43969	+	2.49362i	−0.173319	+	0.300197i
$70$	0.500000	−	2.83564i	0.0597614	−	0.338924i
$71$	−10.8610	+	9.11343i	−1.28896	+	1.08157i	−0.297018	+	0.954872i	$0.595992\pi$
$71$	−10.8610	+	9.11343i	−1.28896	+	1.08157i	−0.991942	+	0.126694i	$0.959564\pi$
$72$	−0.766044	−	0.642788i	−0.0902792	−	0.0757532i
$73$	−2.28059	−	12.9339i	−0.266923	−	1.51380i	−0.763502	−	0.645805i	$-0.776522\pi$
$73$	−2.28059	−	12.9339i	−0.266923	−	1.51380i	0.496579	−	0.867991i	$-0.334589\pi$
$74$	−5.03209	−	1.83153i	−0.584968	−	0.212911i
$75$	−1.00000			−0.115470
$76$	4.35844	+	0.0632028i	0.499947	+	0.00724985i
$77$	13.0496			1.48714
$78$	−1.99273	−	0.725293i	−0.225632	−	0.0821233i
$79$	−0.481582	−	2.73119i	−0.0541822	−	0.307282i	0.945658	−	0.325163i	$-0.105419\pi$
$79$	−0.481582	−	2.73119i	−0.0541822	−	0.307282i	−0.999840	+	0.0178807i	$0.994308\pi$
$80$	0.766044	+	0.642788i	0.0856464	+	0.0718658i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	−1.50253	+	8.52125i	−0.165926	+	0.941015i
$83$	−0.488856	+	0.846723i	−0.0536589	+	0.0929399i	−0.891607	−	0.452810i	$-0.850422\pi$
$83$	−0.488856	+	0.846723i	−0.0536589	+	0.0929399i	0.837948	+	0.545750i	$0.183755\pi$
$84$	−1.43969	−	2.49362i	−0.157083	−	0.272076i
$85$	−4.43242	+	1.61327i	−0.480763	+	0.174984i
$86$	−9.13088	+	3.32337i	−0.984608	+	0.358368i
$87$	−4.96451	−	8.59878i	−0.532251	−	0.921886i
$88$	−2.26604	+	3.92490i	−0.241561	+	0.418396i
$89$	−2.45811	+	13.9406i	−0.260559	+	1.47770i	0.520830	+	0.853661i	$0.325623\pi$
$89$	−2.45811	+	13.9406i	−0.260559	+	1.47770i	−0.781389	+	0.624044i	$0.785488\pi$
$90$	−0.766044	+	0.642788i	−0.0807482	+	0.0677558i
$91$	−4.67752	−	3.92490i	−0.490337	−	0.411442i
$92$	−0.500000	−	2.83564i	−0.0521286	−	0.295636i
$93$	0.134285	+	0.0488759i	0.0139247	+	0.00506819i
$94$	4.63816			0.478389
$95$	0.819078	−	4.28125i	0.0840356	−	0.439247i
$96$	1.00000			0.102062
$97$	0.634285	+	0.230861i	0.0644019	+	0.0234404i	0.374020	−	0.927421i	$-0.377979\pi$
$97$	0.634285	+	0.230861i	0.0644019	+	0.0234404i	−0.309618	+	0.950861i	$0.600201\pi$
$98$	−0.224155	−	1.27125i	−0.0226431	−	0.128415i
$99$	−3.47178	−	2.91317i	−0.348927	−	0.292785i
$100$	0.766044	−	0.642788i	0.0766044	−	0.0642788i
$101$	−1.13088	+	6.41355i	−0.112527	+	0.638172i	0.875418	+	0.483367i	$0.160586\pi$
$101$	−1.13088	+	6.41355i	−0.112527	+	0.638172i	−0.987945	+	0.154805i	$0.950525\pi$
$102$	−2.35844	+	4.08494i	−0.233520	+	0.404469i
$103$	−5.73783	−	9.93821i	−0.565365	−	0.979241i	−0.997016	−	0.0771998i	$-0.975402\pi$
$103$	−5.73783	−	9.93821i	−0.565365	−	0.979241i	0.431651	−	0.902041i	$-0.357931\pi$
$104$	1.99273	−	0.725293i	0.195403	−	0.0711208i
$105$	−2.70574	+	0.984808i	−0.264053	+	0.0961074i
$106$	6.87211	+	11.9028i	0.667478	+	1.15611i
$107$	−5.96451	+	10.3308i	−0.576611	+	0.998719i	0.419254	+	0.907869i	$0.362292\pi$
$107$	−5.96451	+	10.3308i	−0.576611	+	0.998719i	−0.995865	+	0.0908500i	$0.971042\pi$
$108$	−0.173648	+	0.984808i	−0.0167093	+	0.0947632i
$109$	1.62836	−	1.36635i	0.155968	−	0.130873i	−0.561464	−	0.827501i	$-0.689762\pi$
$109$	1.62836	−	1.36635i	0.155968	−	0.130873i	0.717432	+	0.696628i	$0.245317\pi$
$110$	3.47178	+	2.91317i	0.331021	+	0.277760i
$111$	0.929892	+	5.27368i	0.0882615	+	0.500556i
$112$	2.70574	+	0.984808i	0.255668	+	0.0930556i
$113$	−3.14796			−0.296135			−0.148067	−	0.988977i	$-0.547305\pi$
$113$	−3.14796			−0.296135			−0.148067	+	0.988977i	$0.547305\pi$
$114$	−2.12449	−	3.80612i	−0.198976	−	0.356476i
$115$	−2.87939			−0.268504
$116$	9.33022	+	3.39592i	0.866289	+	0.315304i
$117$	0.368241	+	2.08840i	0.0340439	+	0.193072i
$118$	−10.6985	−	8.97708i	−0.984873	−	0.826407i
$119$	−10.4042	+	8.73016i	−0.953751	+	0.800293i
$120$	0.173648	−	0.984808i	0.0158518	−	0.0899002i
$121$	−4.76991	+	8.26173i	−0.433629	+	0.751067i
$122$	2.23783	+	3.87603i	0.202603	+	0.350919i
$123$	8.13088	−	2.95940i	0.733137	−	0.266840i
$124$	−0.134285	+	0.0488759i	−0.0120592	+	0.00438918i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$	−1.43969	+	2.49362i	−0.128258	+	0.222149i
$127$	−2.08765	+	11.8396i	−0.185249	+	1.05060i	0.740386	+	0.672182i	$0.234643\pi$
$127$	−2.08765	+	11.8396i	−0.185249	+	1.05060i	−0.925635	+	0.378417i	$0.876469\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	7.44356	+	6.24589i	0.655369	+	0.549920i
$130$	−0.368241	−	2.08840i	−0.0322969	−	0.183165i
$131$	15.6604	+	5.69994i	1.36826	+	0.498006i	0.918598	−	0.395193i	$-0.129322\pi$
$131$	15.6604	+	5.69994i	1.36826	+	0.498006i	0.449661	+	0.893199i	$0.351545\pi$
$132$	4.53209			0.394468
$133$	−2.00000	−	12.3906i	−0.173422	−	1.07440i
$134$	−7.70233			−0.665380
$135$	0.939693	+	0.342020i	0.0808759	+	0.0294364i
$136$	−0.819078	−	4.64522i	−0.0702353	−	0.398324i
$137$	9.36824	+	7.86089i	0.800383	+	0.671601i	0.948292	−	0.317400i	$-0.102810\pi$
$137$	9.36824	+	7.86089i	0.800383	+	0.671601i	−0.147909	+	0.989001i	$0.547254\pi$
$138$	−2.20574	+	1.85083i	−0.187765	+	0.157553i
$139$	0.837029	−	4.74703i	0.0709959	−	0.402638i	−0.928513	−	0.371300i	$-0.878912\pi$
$139$	0.837029	−	4.74703i	0.0709959	−	0.402638i	0.999509	−	0.0313378i	$-0.00997675\pi$
$140$	1.43969	−	2.49362i	0.121676	−	0.210749i
$141$	−2.31908	−	4.01676i	−0.195302	−	0.338272i
$142$	−13.3229	+	4.84916i	−1.11804	+	0.406932i
$143$	9.03121	−	3.28709i	0.755228	−	0.274880i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	4.96451	−	8.59878i	0.412280	−	0.714090i
$146$	2.28059	−	12.9339i	0.188743	−	1.07042i
$147$	−0.988856	+	0.829748i	−0.0815594	+	0.0684365i
$148$	−4.10220	−	3.44215i	−0.337198	−	0.282943i
$149$	−0.394400	−	2.23675i	−0.0323105	−	0.183242i	0.964381	−	0.264516i	$-0.0852122\pi$
$149$	−0.394400	−	2.23675i	−0.0323105	−	0.183242i	−0.996692	+	0.0812741i	$0.974101\pi$
$150$	−0.939693	−	0.342020i	−0.0767256	−	0.0279258i
$151$	−21.1976			−1.72504			−0.862518	−	0.506027i	$-0.831114\pi$
$151$	−21.1976			−1.72504			−0.862518	+	0.506027i	$0.831114\pi$
$152$	4.07398	+	1.55007i	0.330443	+	0.125727i
$153$	4.71688			0.381337
$154$	12.2626	+	4.46324i	0.988152	+	0.359658i
$155$	0.0248149	+	0.140732i	0.00199318	+	0.0113039i
$156$	−1.62449	−	1.36310i	−0.130063	−	0.109136i
$157$	1.45677	−	1.22237i	0.116263	−	0.0975559i	−0.582803	−	0.812614i	$-0.698044\pi$
$157$	1.45677	−	1.22237i	0.116263	−	0.0975559i	0.699066	+	0.715058i	$0.253600\pi$
$158$	0.481582	−	2.73119i	0.0383126	−	0.217281i
$159$	6.87211	−	11.9028i	0.544994	−	0.943957i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−7.79086	+	2.83564i	−0.614006	+	0.223480i
$162$	0.939693	−	0.342020i	0.0738292	−	0.0268716i
$163$	4.11721	+	7.13122i	0.322485	+	0.558560i	0.981000	−	0.194007i	$-0.0621485\pi$
$163$	4.11721	+	7.13122i	0.322485	+	0.558560i	−0.658515	+	0.752567i	$0.728815\pi$
$164$	−4.32635	+	7.49346i	−0.337831	+	0.585141i
$165$	0.786989	−	4.46324i	0.0612670	−	0.347462i
$166$	−0.748970	+	0.628461i	−0.0581314	+	0.0487780i
$167$	6.86618	+	5.76141i	0.531321	+	0.445831i	0.868557	−	0.495589i	$-0.165048\pi$
$167$	6.86618	+	5.76141i	0.531321	+	0.445831i	−0.337236	+	0.941420i	$0.609492\pi$
$168$	−0.500000	−	2.83564i	−0.0385758	−	0.218774i
$169$	7.99020	+	2.90819i	0.614631	+	0.223707i
$170$	−4.71688			−0.361768
$171$	−2.23396	+	3.74292i	−0.170835	+	0.286228i
$172$	−9.71688			−0.740905
$173$	−9.58899	−	3.49011i	−0.729038	−	0.265348i	−0.0492802	−	0.998785i	$-0.515693\pi$
$173$	−9.58899	−	3.49011i	−0.729038	−	0.265348i	−0.679757	+	0.733437i	$0.737915\pi$
$174$	−1.72416	−	9.77817i	−0.130708	−	0.741281i
$175$	−2.20574	−	1.85083i	−0.166738	−	0.139910i
$176$	−3.47178	+	2.91317i	−0.261695	+	0.219588i
$177$	−2.42514	+	13.7537i	−0.182285	+	1.03379i
$178$	−7.07785	+	12.2592i	−0.530507	+	0.918865i
$179$	−11.5175	−	19.9490i	−0.860861	−	1.49106i	−0.871099	−	0.491108i	$-0.836592\pi$
$179$	−11.5175	−	19.9490i	−0.860861	−	1.49106i	0.0102372	−	0.999948i	$-0.496741\pi$
$180$	−0.939693	+	0.342020i	−0.0700406	+	0.0254927i
$181$	−17.5471	+	6.38662i	−1.30427	+	0.474714i	−0.898384	−	0.439211i	$-0.855258\pi$
$181$	−17.5471	+	6.38662i	−1.30427	+	0.474714i	−0.405882	+	0.913925i	$0.633036\pi$
$182$	−3.05303	−	5.28801i	−0.226306	−	0.391973i
$183$	2.23783	−	3.87603i	0.165425	−	0.286524i
$184$	0.500000	−	2.83564i	0.0368605	−	0.209046i
$185$	−4.10220	+	3.44215i	−0.301599	+	0.253072i
$186$	0.109470	+	0.0918566i	0.00802676	+	0.00673525i
$187$	−3.71213	−	21.0526i	−0.271458	−	1.53952i
$188$	4.35844	+	1.58634i	0.317872	+	0.115696i
$189$	2.87939			0.209444
$190$	2.23396	−	3.74292i	0.162068	−	0.271540i
$191$	2.43376			0.176101			0.0880504	−	0.996116i	$-0.471936\pi$
$191$	2.43376			0.176101			0.0880504	+	0.996116i	$0.471936\pi$
$192$	0.939693	+	0.342020i	0.0678165	+	0.0246832i
$193$	0.267226	+	1.51552i	0.0192354	+	0.109089i	0.992914	−	0.118837i	$-0.0379166\pi$
$193$	0.267226	+	1.51552i	0.0192354	+	0.109089i	−0.973678	+	0.227926i	$0.926805\pi$
$194$	0.517074	+	0.433877i	0.0371238	+	0.0311505i
$195$	−1.62449	+	1.36310i	−0.116332	+	0.0976140i
$196$	0.224155	−	1.27125i	0.0160111	−	0.0908035i
$197$	11.7554	−	20.3609i	0.837535	−	1.45065i	−0.0544143	−	0.998518i	$-0.517329\pi$
$197$	11.7554	−	20.3609i	0.837535	−	1.45065i	0.891949	−	0.452135i	$-0.149338\pi$
$198$	−2.26604	−	3.92490i	−0.161041	−	0.278931i
$199$	14.4265	−	5.25081i	1.02267	−	0.372220i	0.224382	−	0.974501i	$-0.427964\pi$
$199$	14.4265	−	5.25081i	1.02267	−	0.372220i	0.798284	+	0.602281i	$0.205741\pi$
$200$	0.939693	−	0.342020i	0.0664463	−	0.0241845i
$201$	3.85117	+	6.67042i	0.271640	+	0.470495i
$202$	−3.25624	+	5.63998i	−0.229109	+	0.396828i
$203$	4.96451	−	28.1551i	0.348440	−	1.97610i
$204$	−3.61334	+	3.03195i	−0.252984	+	0.212279i
$205$	6.62836	+	5.56185i	0.462944	+	0.388457i
$206$	−1.99273	−	11.3013i	−0.138840	−	0.787400i
$207$	2.70574	+	0.984808i	0.188062	+	0.0684489i
$208$	2.12061			0.147038
$209$	18.4636	+	7.02504i	1.27716	+	0.485932i
$210$	−2.87939			−0.198696
$211$	−0.868241	−	0.316014i	−0.0597722	−	0.0217553i	0.311961	−	0.950095i	$-0.399014\pi$
$211$	−0.868241	−	0.316014i	−0.0597722	−	0.0217553i	−0.371733	+	0.928340i	$0.621236\pi$
$212$	2.38666	+	13.5354i	0.163916	+	0.929616i
$213$	10.8610	+	9.11343i	0.744181	+	0.624442i
$214$	−9.13816	+	7.66782i	−0.624671	+	0.524162i
$215$	−1.68732	+	9.56926i	−0.115074	+	0.652618i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	0.205737	+	0.356347i	0.0139663	+	0.0241904i
$218$	1.99747	−	0.727021i	0.135286	−	0.0492401i
$219$	−12.3414	+	4.49189i	−0.833952	+	0.303534i
$220$	2.26604	+	3.92490i	0.152777	+	0.264617i
$221$	−5.00134	+	8.66258i	−0.336427	+	0.582708i
$222$	−0.929892	+	5.27368i	−0.0624103	+	0.353946i
$223$	6.82816	−	5.72951i	0.457248	−	0.383676i	−0.384870	−	0.922971i	$-0.625754\pi$
$223$	6.82816	−	5.72951i	0.457248	−	0.383676i	0.842117	+	0.539295i	$0.181309\pi$
$224$	2.20574	+	1.85083i	0.147377	+	0.123664i
$225$	0.173648	+	0.984808i	0.0115765	+	0.0656539i
$226$	−2.95811	−	1.07666i	−0.196771	−	0.0716186i
$227$	8.35504			0.554543			0.277272	−	0.960792i	$-0.410570\pi$
$227$	8.35504			0.554543			0.277272	+	0.960792i	$0.410570\pi$
$228$	−0.694593	−	4.30320i	−0.0460005	−	0.284986i
$229$	18.9564			1.25267			0.626336	−	0.779554i	$-0.284554\pi$
$229$	18.9564			1.25267			0.626336	+	0.779554i	$0.284554\pi$
$230$	−2.70574	−	0.984808i	−0.178411	−	0.0649363i
$231$	−2.26604	−	12.8514i	−0.149095	−	0.845559i
$232$	7.60607	+	6.38225i	0.499363	+	0.419015i
$233$	10.5398	−	8.84397i	0.690487	−	0.579388i	−0.228562	−	0.973529i	$-0.573403\pi$
$233$	10.5398	−	8.84397i	0.690487	−	0.579388i	0.919050	+	0.394142i	$0.128958\pi$
$234$	−0.368241	+	2.08840i	−0.0240727	+	0.136523i
$235$	2.31908	−	4.01676i	0.151280	−	0.262025i
$236$	−6.98293	−	12.0948i	−0.454550	−	0.787303i
$237$	−2.60607	+	0.948531i	−0.169282	+	0.0616137i
$238$	−12.7626	+	4.64522i	−0.827279	+	0.301105i
$239$	5.05556	+	8.75649i	0.327017	+	0.566410i	0.981918	−	0.189304i	$-0.0606232\pi$
$239$	5.05556	+	8.75649i	0.327017	+	0.566410i	−0.654902	+	0.755714i	$0.727290\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	2.04710	−	11.6097i	0.131866	−	0.747847i	−0.845126	−	0.534568i	$-0.820475\pi$
$241$	2.04710	−	11.6097i	0.131866	−	0.747847i	0.976991	−	0.213279i	$-0.0684144\pi$
$242$	−7.30793	+	6.13208i	−0.469772	+	0.394185i
$243$	−0.766044	−	0.642788i	−0.0491418	−	0.0412348i
$244$	0.777189	+	4.40766i	0.0497544	+	0.282171i
$245$	−1.21301	−	0.441500i	−0.0774964	−	0.0282064i
$246$	8.65270			0.551676
$247$	−4.50521	−	8.07132i	−0.286660	−	0.513566i
$248$	−0.142903			−0.00907438
$249$	0.918748	+	0.334397i	0.0582233	+	0.0211915i
$250$	−0.173648	−	0.984808i	−0.0109825	−	0.0622847i
$251$	−16.4454	−	13.7993i	−1.03802	−	0.871005i	−0.0462391	−	0.998930i	$-0.514724\pi$
$251$	−16.4454	−	13.7993i	−1.03802	−	0.871005i	−0.991784	+	0.127926i	$0.959168\pi$
$252$	−2.20574	+	1.85083i	−0.138948	+	0.116592i
$253$	2.26604	−	12.8514i	0.142465	−	0.807959i
$254$	−6.01114	+	10.4116i	−0.377173	+	0.653282i
$255$	2.35844	+	4.08494i	0.147691	+	0.255809i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−5.71941	+	2.08169i	−0.356767	+	0.129853i	−0.514184	−	0.857680i	$-0.671905\pi$
$257$	−5.71941	+	2.08169i	−0.356767	+	0.129853i	0.157418	+	0.987532i	$0.449683\pi$
$258$	4.85844	+	8.41507i	0.302473	+	0.523899i
$259$	−7.70961	+	13.3534i	−0.479052	+	0.829742i
$260$	0.368241	−	2.08840i	0.0228373	−	0.129517i
$261$	−7.60607	+	6.38225i	−0.470804	+	0.395051i
$262$	12.7665	+	10.7124i	0.788718	+	0.661813i
$263$	1.74257	+	9.88263i	0.107452	+	0.609389i	0.990213	+	0.139567i	$0.0445709\pi$
$263$	1.74257	+	9.88263i	0.107452	+	0.609389i	−0.882761	+	0.469822i	$0.844318\pi$
$264$	4.25877	+	1.55007i	0.262109	+	0.0953999i
$265$	13.7442			0.844301
$266$	2.35844	−	12.3274i	0.144605	−	0.755840i
$267$	14.1557			0.866315
$268$	−7.23783	−	2.63435i	−0.442121	−	0.160919i
$269$	−1.94444	−	11.0275i	−0.118555	−	0.672357i	−0.984929	−	0.172961i	$-0.944667\pi$
$269$	−1.94444	−	11.0275i	−0.118555	−	0.672357i	0.866374	−	0.499396i	$-0.166445\pi$
$270$	0.766044	+	0.642788i	0.0466200	+	0.0391188i
$271$	0.639500	−	0.536604i	0.0388469	−	0.0325964i	−0.623158	−	0.782096i	$-0.714150\pi$
$271$	0.639500	−	0.536604i	0.0388469	−	0.0325964i	0.662004	+	0.749500i	$0.269706\pi$
$272$	0.819078	−	4.64522i	0.0496639	−	0.281658i
$273$	−3.05303	+	5.28801i	−0.184778	+	0.320045i
$274$	6.11468	+	10.5909i	0.369402	+	0.639822i
$275$	4.25877	−	1.55007i	0.256814	−	0.0934725i
$276$	−2.70574	+	0.984808i	−0.162866	+	0.0592785i
$277$	−8.72668	−	15.1151i	−0.524335	−	0.908176i	−0.999599	−	0.0283320i	$-0.990980\pi$
$277$	−8.72668	−	15.1151i	−0.524335	−	0.908176i	0.475263	−	0.879844i	$-0.342353\pi$
$278$	2.41013	−	4.17447i	0.144550	−	0.250368i
$279$	0.0248149	−	0.140732i	0.00148563	−	0.00842543i
$280$	2.20574	−	1.85083i	0.131818	−	0.110608i
$281$	13.6138	+	11.4233i	0.812132	+	0.681459i	0.951116	−	0.308835i	$-0.0999392\pi$
$281$	13.6138	+	11.4233i	0.812132	+	0.681459i	−0.138984	+	0.990295i	$0.544384\pi$
$282$	−0.805407	−	4.56769i	−0.0479613	−	0.272002i
$283$	−3.31908	−	1.20805i	−0.197299	−	0.0718109i	0.241481	−	0.970406i	$-0.422367\pi$
$283$	−3.31908	−	1.20805i	−0.197299	−	0.0718109i	−0.438780	+	0.898595i	$0.644589\pi$
$284$	−14.1780			−0.841309
$285$	−4.35844	−	0.0632028i	−0.258172	−	0.00374381i
$286$	9.61081			0.568299
$287$	23.4119	+	8.52125i	1.38196	+	0.502993i
$288$	−0.173648	−	0.984808i	−0.0102323	−	0.0580304i
$289$	4.02094	+	3.37397i	0.236526	+	0.198469i
$290$	7.60607	−	6.38225i	0.446644	−	0.374779i
$291$	0.117211	−	0.664738i	0.00687104	−	0.0389676i
$292$	6.56670	−	11.3739i	0.384287	−	0.665605i
$293$	5.48293	+	9.49671i	0.320316	+	0.554803i	0.980553	−	0.196254i	$-0.0628776\pi$
$293$	5.48293	+	9.49671i	0.320316	+	0.554803i	−0.660237	+	0.751057i	$0.729544\pi$
$294$	−1.21301	+	0.441500i	−0.0707442	+	0.0257488i
$295$	−13.1236	+	4.77660i	−0.764086	+	0.278105i
$296$	−2.67752	−	4.63760i	−0.155628	−	0.269555i
$297$	−2.26604	+	3.92490i	−0.131489	+	0.227746i
$298$	0.394400	−	2.23675i	0.0228470	−	0.129572i
$299$	−4.67752	+	3.92490i	−0.270508	+	0.226983i
$300$	−0.766044	−	0.642788i	−0.0442276	−	0.0371114i
$301$	4.85844	+	27.5536i	0.280036	+	1.58816i
$302$	−19.9192	−	7.25000i	−1.14622	−	0.417191i
$303$	6.51249			0.374133
$304$	3.29813	+	2.84997i	0.189161	+	0.163457i
$305$	4.47565			0.256275
$306$	4.43242	+	1.61327i	0.253385	+	0.0922244i
$307$	−3.55097	−	20.1386i	−0.202665	−	1.14937i	−0.901072	−	0.433669i	$-0.857219\pi$
$307$	−3.55097	−	20.1386i	−0.202665	−	1.14937i	0.698408	−	0.715700i	$-0.253892\pi$
$308$	9.99660	+	8.38814i	0.569609	+	0.477959i
$309$	−8.79086	+	7.37641i	−0.500095	+	0.419629i
$310$	−0.0248149	+	0.140732i	−0.00140939	+	0.00799307i
$311$	−1.18345	+	2.04979i	−0.0671072	+	0.116233i	−0.897627	−	0.440756i	$-0.854710\pi$
$311$	−1.18345	+	2.04979i	−0.0671072	+	0.116233i	0.830520	+	0.556989i	$0.188044\pi$
$312$	−1.06031	−	1.83651i	−0.0600281	−	0.103972i
$313$	−5.75624	+	2.09510i	−0.325362	+	0.118422i	−0.499537	−	0.866293i	$-0.666496\pi$
$313$	−5.75624	+	2.09510i	−0.325362	+	0.118422i	0.174175	+	0.984715i	$0.444274\pi$
$314$	1.78699	−	0.650411i	0.100846	−	0.0367048i
$315$	1.43969	+	2.49362i	0.0811175	+	0.140500i
$316$	1.38666	−	2.40176i	0.0780057	−	0.135110i
$317$	1.10813	−	6.28450i	0.0622386	−	0.352972i	−0.937745	−	0.347323i	$-0.887091\pi$
$317$	1.10813	−	6.28450i	0.0622386	−	0.352972i	0.999984	−	0.00564924i	$-0.00179822\pi$
$318$	10.5287	−	8.83462i	0.590419	−	0.495421i
$319$	34.4714	+	28.9249i	1.93003	+	1.61948i
$320$	0.173648	+	0.984808i	0.00970723	+	0.0550524i
$321$	11.2096	+	4.07996i	0.625659	+	0.227721i
$322$	−8.29086			−0.462032
$323$	−19.4204	+	6.75119i	−1.08058	+	0.375646i
$324$	1.00000			0.0555556
$325$	−1.99273	−	0.725293i	−0.110537	−	0.0402320i
$326$	1.42989	+	8.10932i	0.0791944	+	0.449134i
$327$	−1.62836	−	1.36635i	−0.0900483	−	0.0755595i
$328$	−6.62836	+	5.56185i	−0.365990	+	0.307102i
$329$	2.31908	−	13.1521i	0.127855	−	0.725101i
$330$	2.26604	−	3.92490i	0.124742	−	0.216059i
$331$	−0.789515	−	1.36748i	−0.0433957	−	0.0751635i	0.843512	−	0.537111i	$-0.180484\pi$
$331$	−0.789515	−	1.36748i	−0.0433957	−	0.0751635i	−0.886907	+	0.461947i	$0.847151\pi$
$332$	−0.918748	+	0.334397i	−0.0504229	+	0.0183524i
$333$	5.03209	−	1.83153i	0.275757	−	0.100367i
$334$	4.48158	+	7.76233i	0.245221	+	0.424736i
$335$	−3.85117	+	6.67042i	−0.210412	+	0.364444i
$336$	0.500000	−	2.83564i	0.0272772	−	0.154697i
$337$	12.5398	−	10.5222i	0.683088	−	0.573179i	−0.233819	−	0.972280i	$-0.575122\pi$
$337$	12.5398	−	10.5222i	0.683088	−	0.573179i	0.916907	+	0.399101i	$0.130678\pi$
$338$	6.51367	+	5.46562i	0.354297	+	0.297290i
$339$	0.546637	+	3.10013i	0.0296892	+	0.168376i
$340$	−4.43242	−	1.61327i	−0.240382	−	0.0874918i
$341$	−0.647651			−0.0350723
$342$	−3.37939	+	2.75314i	−0.182736	+	0.148873i
$343$	16.4388			0.887613
$344$	−9.13088	−	3.32337i	−0.492304	−	0.179184i
$345$	0.500000	+	2.83564i	0.0269191	+	0.152666i
$346$	−7.81702	−	6.55926i	−0.420246	−	0.352628i
$347$	8.19640	−	6.87760i	0.440006	−	0.369209i	−0.395706	−	0.918377i	$-0.629500\pi$
$347$	8.19640	−	6.87760i	0.440006	−	0.369209i	0.835712	+	0.549169i	$0.185055\pi$
$348$	1.72416	−	9.77817i	0.0924244	−	0.524165i
$349$	8.15317	−	14.1217i	0.436429	−	0.755918i	−0.560982	−	0.827828i	$-0.689576\pi$
$349$	8.15317	−	14.1217i	0.436429	−	0.755918i	0.997411	+	0.0719105i	$0.0229096\pi$
$350$	−1.43969	−	2.49362i	−0.0769548	−	0.133290i
$351$	1.99273	−	0.725293i	0.106364	−	0.0387133i
$352$	−4.25877	+	1.55007i	−0.226993	+	0.0826188i
$353$	−14.6878	−	25.4400i	−0.781752	−	1.35403i	−0.930920	−	0.365222i	$-0.880993\pi$
$353$	−14.6878	−	25.4400i	−0.781752	−	1.35403i	0.149168	−	0.988812i	$-0.452340\pi$
$354$	−6.98293	+	12.0948i	−0.371138	+	0.642830i
$355$	−2.46198	+	13.9626i	−0.130668	+	0.741057i
$356$	−10.8439	+	9.09911i	−0.574725	+	0.482252i
$357$	10.4042	+	8.73016i	0.550649	+	0.462049i
$358$	−4.00000	−	22.6851i	−0.211407	−	1.19895i
$359$	−30.9342	−	11.2591i	−1.63265	−	0.594235i	−0.646915	−	0.762562i	$-0.723941\pi$
$359$	−30.9342	−	11.2591i	−1.63265	−	0.594235i	−0.985731	+	0.168327i	$0.946163\pi$
$360$	−1.00000			−0.0527046
$361$	3.84049	−	18.6078i	0.202131	−	0.979358i
$362$	−18.6732			−0.981444
$363$	8.96451	+	3.26281i	0.470515	+	0.171253i
$364$	−1.06031	−	6.01330i	−0.0555752	−	0.315183i
$365$	−10.0608	−	8.44199i	−0.526605	−	0.441874i
$366$	3.42855	−	2.87689i	0.179213	−	0.150378i
$367$	−5.53121	+	31.3691i	−0.288727	+	1.63745i	0.402934	+	0.915229i	$0.367990\pi$
$367$	−5.53121	+	31.3691i	−0.288727	+	1.63745i	−0.691661	+	0.722222i	$0.743121\pi$
$368$	1.43969	−	2.49362i	0.0750492	−	0.129989i
$369$	−4.32635	−	7.49346i	−0.225221	−	0.390094i
$370$	−5.03209	+	1.83153i	−0.261606	+	0.0952167i
$371$	37.1883	−	13.5354i	1.93072	−	0.702724i
$372$	0.0714517	+	0.123758i	0.00370460	+	0.00641655i
$373$	−8.42396	+	14.5907i	−0.436176	+	0.755479i	−0.997391	−	0.0721909i	$-0.977001\pi$
$373$	−8.42396	+	14.5907i	−0.436176	+	0.755479i	0.561215	+	0.827670i	$0.310334\pi$
$374$	3.71213	−	21.0526i	0.191950	−	1.08860i
$375$	−0.766044	+	0.642788i	−0.0395584	+	0.0331934i
$376$	3.55303	+	2.98135i	0.183234	+	0.153751i
$377$	−3.65627	−	20.7357i	−0.188307	−	1.06794i
$378$	2.70574	+	0.984808i	0.139168	+	0.0506530i
$379$	−10.9118			−0.560500			−0.280250	−	0.959927i	$-0.590417\pi$
$379$	−10.9118			−0.560500			−0.280250	+	0.959927i	$0.590417\pi$
$380$	3.37939	−	2.75314i	0.173359	−	0.141233i
$381$	12.0223			0.615921
$382$	2.28699	+	0.832396i	0.117013	+	0.0425891i
$383$	−1.39006	−	7.88344i	−0.0710289	−	0.402825i	−0.999506	−	0.0314347i	$-0.989992\pi$
$383$	−1.39006	−	7.88344i	−0.0710289	−	0.402825i	0.928477	−	0.371390i	$-0.121119\pi$
$384$	0.766044	+	0.642788i	0.0390920	+	0.0328021i
$385$	9.99660	−	8.38814i	0.509474	−	0.427499i
$386$	−0.267226	+	1.51552i	−0.0136015	+	0.0771378i
$387$	4.85844	−	8.41507i	0.246968	−	0.427762i
$388$	0.337496	+	0.584561i	0.0171338	+	0.0296766i
$389$	−12.0706	+	4.39333i	−0.612002	+	0.222751i	−0.629379	−	0.777098i	$-0.716691\pi$
$389$	−12.0706	+	4.39333i	−0.612002	+	0.222751i	0.0173768	+	0.999849i	$0.494469\pi$
$390$	−1.99273	+	0.725293i	−0.100906	+	0.0367266i
$391$	6.79086	+	11.7621i	0.343429	+	0.594836i
$392$	0.645430	−	1.11792i	0.0325991	−	0.0564633i
$393$	2.89393	−	16.4123i	0.145980	−	0.827892i
$394$	18.0103	−	15.1124i	0.907344	−	0.761352i
$395$	−2.12449	−	1.78265i	−0.106894	−	0.0896951i
$396$	−0.786989	−	4.46324i	−0.0395477	−	0.224286i
$397$	10.6429	+	3.87370i	0.534152	+	0.194415i	0.594991	−	0.803732i	$-0.297155\pi$
$397$	10.6429	+	3.87370i	0.534152	+	0.194415i	−0.0608393	+	0.998148i	$0.519378\pi$
$398$	15.3523			0.769544
$399$	−11.8550	+	4.12122i	−0.593494	+	0.206319i
$400$	1.00000			0.0500000
$401$	19.1348	+	6.96448i	0.955544	+	0.347790i	0.772286	−	0.635275i	$-0.219113\pi$
$401$	19.1348	+	6.96448i	0.955544	+	0.347790i	0.183258	+	0.983065i	$0.441336\pi$
$402$	1.33750	+	7.58532i	0.0667082	+	0.378321i
$403$	0.232145	+	0.194792i	0.0115639	+	0.00970330i
$404$	−4.98886	+	4.18615i	−0.248205	+	0.208269i
$405$	0.173648	−	0.984808i	0.00862865	−	0.0489355i
$406$	14.2947	−	24.7592i	0.709436	−	1.22878i
$407$	−12.1348	−	21.0180i	−0.601497	−	1.04182i
$408$	−4.43242	+	1.61327i	−0.219437	+	0.0798687i
$409$	30.9752	−	11.2741i	1.53163	−	0.557467i	0.567608	−	0.823299i	$-0.307869\pi$
$409$	30.9752	−	11.2741i	1.53163	−	0.557467i	0.964019	+	0.265832i	$0.0856468\pi$
$410$	4.32635	+	7.49346i	0.213663	+	0.370076i
$411$	6.11468	−	10.5909i	0.301615	−	0.522413i
$412$	1.99273	−	11.3013i	0.0981746	−	0.556776i
$413$	−30.8050	+	25.8485i	−1.51581	+	1.27192i
$414$	2.20574	+	1.85083i	0.108406	+	0.0909635i
$415$	0.169778	+	0.962858i	0.00833406	+	0.0472648i
$416$	1.99273	+	0.725293i	0.0977014	+	0.0355604i
$417$	−4.82026			−0.236049
$418$	14.9474	+	12.9163i	0.731103	+	0.631757i
$419$	0.494319			0.0241490			0.0120745	−	0.999927i	$-0.496156\pi$
$419$	0.494319			0.0241490			0.0120745	+	0.999927i	$0.496156\pi$
$420$	−2.70574	−	0.984808i	−0.132026	−	0.0480537i
$421$	−5.55778	−	31.5197i	−0.270870	−	1.53618i	−0.751783	−	0.659410i	$-0.770806\pi$
$421$	−5.55778	−	31.5197i	−0.270870	−	1.53618i	0.480914	−	0.876768i	$-0.340305\pi$
$422$	−0.707796	−	0.593912i	−0.0344550	−	0.0289112i
$423$	−3.55303	+	2.98135i	−0.172754	+	0.144958i
$424$	−2.38666	+	13.5354i	−0.115906	+	0.657338i
$425$	−2.35844	+	4.08494i	−0.114401	+	0.198149i
$426$	7.08899	+	12.2785i	0.343463	+	0.594895i
$427$	12.1099	−	4.40766i	0.586041	−	0.213301i
$428$	−11.2096	+	4.07996i	−0.541837	+	0.197212i
$429$	−4.80541	−	8.32321i	−0.232007	−	0.401848i
$430$	−4.85844	+	8.41507i	−0.234295	+	0.405811i
$431$	2.89899	−	16.4410i	0.139639	−	0.791933i	−0.831877	−	0.554960i	$-0.812734\pi$
$431$	2.89899	−	16.4410i	0.139639	−	0.791933i	0.971516	−	0.236973i	$-0.0761554\pi$
$432$	−0.766044	+	0.642788i	−0.0368563	+	0.0309261i
$433$	16.2010	+	13.5942i	0.778570	+	0.653298i	0.942888	−	0.333110i	$-0.108098\pi$
$433$	16.2010	+	13.5942i	0.778570	+	0.653298i	−0.164318	+	0.986407i	$0.552542\pi$
$434$	0.0714517	+	0.405223i	0.00342979	+	0.0194513i
$435$	−9.33022	−	3.39592i	−0.447350	−	0.162822i
$436$	2.12567			0.101801
$437$	−12.5496	−	0.181985i	−0.600330	−	0.00870553i
$438$	−13.1334			−0.627539
$439$	−2.22193	−	0.808718i	−0.106047	−	0.0385980i	0.288452	−	0.957494i	$-0.406860\pi$
$439$	−2.22193	−	0.808718i	−0.106047	−	0.0385980i	−0.394499	+	0.918896i	$0.629082\pi$
$440$	0.786989	+	4.46324i	0.0375182	+	0.212776i
$441$	0.988856	+	0.829748i	0.0470884	+	0.0395118i
$442$	−7.66250	+	6.42960i	−0.364468	+	0.305825i
$443$	3.76991	−	21.3802i	0.179114	−	1.01581i	−0.754173	−	0.656676i	$-0.771962\pi$
$443$	3.76991	−	21.3802i	0.179114	−	1.01581i	0.933287	−	0.359131i	$-0.116927\pi$
$444$	−2.67752	+	4.63760i	−0.127069	+	0.220091i
$445$	7.07785	+	12.2592i	0.335522	+	0.581141i
$446$	8.37598	−	3.04861i	0.396614	−	0.144356i
$447$	−2.13429	+	0.776816i	−0.100948	+	0.0367422i
$448$	1.43969	+	2.49362i	0.0680191	+	0.117813i
$449$	−9.91060	+	17.1657i	−0.467710	+	0.810097i	−0.999319	−	0.0368923i	$-0.988254\pi$
$449$	−9.91060	+	17.1657i	−0.467710	+	0.810097i	0.531609	+	0.846990i	$0.321587\pi$
$450$	−0.173648	+	0.984808i	−0.00818585	+	0.0464243i
$451$	−30.0403	+	25.2068i	−1.41454	+	1.18694i
$452$	−2.41147	−	2.02347i	−0.113426	−	0.0951759i
$453$	3.68092	+	20.8755i	0.172945	+	0.980819i
$454$	7.85117	+	2.85759i	0.368474	+	0.134113i
$455$	−6.10607			−0.286257
$456$	0.819078	−	4.28125i	0.0383568	−	0.200488i
$457$	32.1293			1.50294			0.751472	−	0.659765i	$-0.229344\pi$
$457$	32.1293			1.50294			0.751472	+	0.659765i	$0.229344\pi$
$458$	17.8131	+	6.48346i	0.832354	+	0.302952i
$459$	−0.819078	−	4.64522i	−0.0382313	−	0.216820i
$460$	−2.20574	−	1.85083i	−0.102843	−	0.0862955i
$461$	−28.4447	+	23.8680i	−1.32480	+	1.11164i	−0.339542	+	0.940591i	$0.610272\pi$
$461$	−28.4447	+	23.8680i	−1.32480	+	1.11164i	−0.985262	+	0.171051i	$0.945284\pi$
$462$	2.26604	−	12.8514i	0.105426	−	0.597900i
$463$	4.41534	−	7.64760i	0.205198	−	0.355414i	−0.744997	−	0.667067i	$-0.767549\pi$
$463$	4.41534	−	7.64760i	0.205198	−	0.355414i	0.950196	+	0.311653i	$0.100883\pi$
$464$	4.96451	+	8.59878i	0.230471	+	0.399188i
$465$	0.134285	−	0.0488759i	0.00622733	−	0.00226656i
$466$	12.9290	−	4.70578i	0.598925	−	0.217991i
$467$	−11.2430	−	19.4735i	−0.520266	−	0.901127i	−0.999722	−	0.0235613i	$-0.992500\pi$
$467$	−11.2430	−	19.4735i	−0.520266	−	0.901127i	0.479457	−	0.877566i	$-0.340834\pi$
$468$	−1.06031	+	1.83651i	−0.0490127	+	0.0848925i
$469$	−3.85117	+	21.8411i	−0.177830	+	1.00853i
$470$	3.55303	−	2.98135i	0.163889	−	0.137519i
$471$	−1.45677	−	1.22237i	−0.0671243	−	0.0563239i
$472$	−2.42514	−	13.7537i	−0.111626	−	0.633064i
$473$	−41.3820	−	15.0618i	−1.90274	−	0.692543i
$474$	−2.77332			−0.127383
$475$	−2.12449	−	3.80612i	−0.0974781	−	0.174637i
$476$	−13.5817			−0.622517
$477$	−12.9153	−	4.70080i	−0.591353	−	0.215235i
$478$	1.75578	+	9.95751i	0.0803074	+	0.455446i
$479$	−13.3439	−	11.1969i	−0.609698	−	0.511597i	0.284848	−	0.958573i	$-0.408057\pi$
$479$	−13.3439	−	11.1969i	−0.609698	−	0.511597i	−0.894546	+	0.446975i	$0.852501\pi$
$480$	0.766044	−	0.642788i	0.0349650	−	0.0293391i
$481$	−1.97194	+	11.1834i	−0.0899129	+	0.509921i
$482$	5.89440	−	10.2094i	0.268483	−	0.465025i
$483$	4.14543	+	7.18009i	0.188624	+	0.326706i
$484$	−8.96451	+	3.26281i	−0.407478	+	0.148310i
$485$	0.634285	−	0.230861i	0.0288014	−	0.0104829i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−15.1074	+	26.1668i	−0.684582	+	1.18573i	0.288986	+	0.957333i	$0.406682\pi$
$487$	−15.1074	+	26.1668i	−0.684582	+	1.18573i	−0.973568	+	0.228398i	$0.926651\pi$
$488$	−0.777189	+	4.40766i	−0.0351817	+	0.199525i
$489$	6.30793	−	5.29298i	0.285255	−	0.239357i
$490$	−0.988856	−	0.829748i	−0.0446719	−	0.0374842i
$491$	−2.09462	−	11.8792i	−0.0945288	−	0.536099i	−0.994891	−	0.100958i	$-0.967809\pi$
$491$	−2.09462	−	11.8792i	−0.0945288	−	0.536099i	0.900362	−	0.435142i	$-0.143302\pi$
$492$	8.13088	+	2.95940i	0.366568	+	0.133420i
$493$	−46.8340			−2.10930
$494$	−1.47296	−	9.12543i	−0.0662718	−	0.410573i
$495$	−4.53209			−0.203702
$496$	−0.134285	−	0.0488759i	−0.00602959	−	0.00219459i
$497$	7.08899	+	40.2037i	0.317985	+	1.80338i
$498$	0.748970	+	0.628461i	0.0335622	+	0.0281620i
$499$	−0.676803	+	0.567905i	−0.0302979	+	0.0254229i	−0.657811	−	0.753183i	$-0.728517\pi$
$499$	−0.676803	+	0.567905i	−0.0302979	+	0.0254229i	0.627513	+	0.778606i	$0.284073\pi$
$500$	0.173648	−	0.984808i	0.00776578	−	0.0440419i
$501$	4.48158	−	7.76233i	0.200222	−	0.346795i
$502$	−10.7340	−	18.5918i	−0.479080	−	0.829791i
$503$	6.18227	−	2.25016i	0.275654	−	0.100330i	−0.200494	−	0.979695i	$-0.564255\pi$
$503$	6.18227	−	2.25016i	0.275654	−	0.100330i	0.476148	+	0.879365i	$0.342033\pi$
$504$	−2.70574	+	0.984808i	−0.120523	+	0.0438668i
$505$	3.25624	+	5.63998i	0.144901	+	0.250976i
$506$	6.52481	−	11.3013i	0.290063	−	0.502405i
$507$	1.47653	−	8.37381i	0.0655750	−	0.371894i
$508$	−9.20961	+	7.72778i	−0.408610	+	0.342865i
$509$	2.90941	+	2.44129i	0.128958	+	0.108208i	0.704985	−	0.709222i	$-0.250954\pi$
$509$	2.90941	+	2.44129i	0.128958	+	0.108208i	−0.576028	+	0.817430i	$0.695398\pi$
$510$	0.819078	+	4.64522i	0.0362694	+	0.205694i
$511$	−35.5355	−	12.9339i	−1.57200	−	0.572161i
$512$	−1.00000			−0.0441942
$513$	4.07398	+	1.55007i	0.179871	+	0.0684371i
$514$	−6.08647			−0.268463
$515$	−10.7836	−	3.92490i	−0.475182	−	0.172952i
$516$	1.68732	+	9.56926i	0.0742801	+	0.421263i
$517$	16.1027	+	13.5117i	0.708194	+	0.594246i
$518$	−11.8118	+	9.91128i	−0.518981	+	0.435477i
$519$	−1.77197	+	10.0494i	−0.0777810	+	0.441118i
$520$	1.06031	−	1.83651i	0.0464976	−	0.0805361i
$521$	−2.61381	−	4.52725i	−0.114513	−	0.198342i	0.803072	−	0.595882i	$-0.203197\pi$
$521$	−2.61381	−	4.52725i	−0.114513	−	0.198342i	−0.917585	+	0.397540i	$0.869864\pi$
$522$	−9.33022	+	3.39592i	−0.408373	+	0.148636i
$523$	−9.73277	+	3.54244i	−0.425584	+	0.154900i	−0.545928	−	0.837832i	$-0.683823\pi$
$523$	−9.73277	+	3.54244i	−0.425584	+	0.154900i	0.120343	+	0.992732i	$0.461600\pi$
$524$	8.33275	+	14.4327i	0.364018	+	0.630497i
$525$	−1.43969	+	2.49362i	−0.0628333	+	0.108831i
$526$	−1.74257	+	9.88263i	−0.0759798	+	0.430903i
$527$	0.516359	−	0.433277i	0.0224929	−	0.0188738i
$528$	3.47178	+	2.91317i	0.151090	+	0.126779i
$529$	−2.55422	−	14.4857i	−0.111053	−	0.629812i
$530$	12.9153	+	4.70080i	0.561007	+	0.204190i
$531$	13.9659			0.606066
$532$	6.43242	−	10.7773i	0.278881	−	0.467255i
$533$	18.3491			0.794786
$534$	13.3020	+	4.84153i	0.575634	+	0.209514i
$535$	2.07145	+	11.7478i	0.0895567	+	0.507901i
$536$	−5.90033	−	4.95096i	−0.254855	−	0.213849i
$537$	−17.6459	+	14.8067i	−0.761477	+	0.638955i
$538$	1.94444	−	11.0275i	0.0838308	−	0.475428i
$539$	2.92514	−	5.06650i	0.125995	−	0.218230i
$540$	0.500000	+	0.866025i	0.0215166	+	0.0372678i
$541$	20.8564	−	7.59110i	0.896686	−	0.326367i	0.147762	−	0.989023i	$-0.452793\pi$
$541$	20.8564	−	7.59110i	0.896686	−	0.326367i	0.748924	+	0.662656i	$0.230571\pi$
$542$	0.784463	−	0.285521i	0.0336956	−	0.0122642i
$543$	9.33662	+	16.1715i	0.400673	+	0.693985i
$544$	2.35844	−	4.08494i	0.101117	−	0.175140i
$545$	0.369118	−	2.09337i	0.0158113	−	0.0896703i
$546$	−4.67752	+	3.92490i	−0.200179	+	0.167970i
$547$	−19.5221	−	16.3810i	−0.834706	−	0.700401i	0.121660	−	0.992572i	$-0.461178\pi$
$547$	−19.5221	−	16.3810i	−0.834706	−	0.700401i	−0.956366	+	0.292170i	$0.905623\pi$
$548$	2.12361	+	12.0436i	0.0907160	+	0.514476i
$549$	−4.20574	−	1.53076i	−0.179496	−	0.0653314i
$550$	4.53209			0.193249
$551$	22.1810	−	37.1635i	0.944941	−	1.58322i
$552$	−2.87939			−0.122555
$553$	−7.50387	−	2.73119i	−0.319097	−	0.116142i
$554$	−3.03074	−	17.1882i	−0.128764	−	0.730257i
$555$	4.10220	+	3.44215i	0.174129	+	0.146111i
$556$	3.69253	−	3.09840i	0.156598	−	0.131402i
$557$	2.07573	−	11.7721i	0.0879516	−	0.498798i	−0.908729	−	0.417387i	$-0.862946\pi$
$557$	2.07573	−	11.7721i	0.0879516	−	0.498798i	0.996681	−	0.0814116i	$-0.0259428\pi$
$558$	0.0714517	−	0.123758i	0.00302479	−	0.00523910i
$559$	10.3029	+	17.8451i	0.435765	+	0.754768i
$560$	2.70574	−	0.984808i	0.114338	−	0.0416157i
$561$	−20.0881	+	7.31148i	−0.848121	+	0.308691i
$562$	8.88578	+	15.3906i	0.374824	+	0.649214i
$563$	−13.1348	+	22.7501i	−0.553564	+	0.958801i	0.444450	+	0.895804i	$0.353399\pi$
$563$	−13.1348	+	22.7501i	−0.553564	+	0.958801i	−0.998014	+	0.0629969i	$0.979934\pi$
$564$	0.805407	−	4.56769i	0.0339138	−	0.192335i
$565$	−2.41147	+	2.02347i	−0.101451	+	0.0851279i
$566$	−2.70574	−	2.27038i	−0.113731	−	0.0954313i
$567$	−0.500000	−	2.83564i	−0.0209980	−	0.119086i
$568$	−13.3229	−	4.84916i	−0.559018	−	0.203466i
$569$	5.88032			0.246516			0.123258	−	0.992375i	$-0.460666\pi$
$569$	5.88032			0.246516			0.123258	+	0.992375i	$0.460666\pi$
$570$	−4.07398	−	1.55007i	−0.170640	−	0.0649251i
$571$	−0.738236			−0.0308942			−0.0154471	−	0.999881i	$-0.504917\pi$
$571$	−0.738236			−0.0308942			−0.0154471	+	0.999881i	$0.504917\pi$
$572$	9.03121	+	3.28709i	0.377614	+	0.137440i
$573$	−0.422618	−	2.39679i	−0.0176551	−	0.100127i
$574$	19.0856	+	16.0147i	0.796617	+	0.668441i
$575$	−2.20574	+	1.85083i	−0.0919856	+	0.0771851i
$576$	0.173648	−	0.984808i	0.00723534	−	0.0410337i
$577$	−21.8897	+	37.9140i	−0.911278	+	1.57838i	−0.0990173	+	0.995086i	$0.531570\pi$
$577$	−21.8897	+	37.9140i	−0.911278	+	1.57838i	−0.812261	+	0.583294i	$0.801763\pi$
$578$	2.62449	+	4.54574i	0.109164	+	0.189078i
$579$	1.44609	−	0.526333i	0.0600974	−	0.0218737i
$580$	9.33022	−	3.39592i	0.387416	−	0.141008i
$581$	1.40760	+	2.43804i	0.0583972	+	0.101147i
$582$	0.337496	−	0.584561i	0.0139897	−	0.0242308i
$583$	−10.8166	+	61.3437i	−0.447976	+	2.54060i
$584$	10.0608	−	8.44199i	0.416318	−	0.349332i
$585$	1.62449	+	1.36310i	0.0671642	+	0.0563575i
$586$	1.90420	+	10.7993i	0.0786618	+	0.446113i
$587$	−12.0697	−	4.39301i	−0.498170	−	0.181319i	0.0807009	−	0.996738i	$-0.474284\pi$
$587$	−12.0697	−	4.39301i	−0.498170	−	0.181319i	−0.578871	+	0.815419i	$0.696506\pi$
$588$	−1.29086			−0.0532341
$589$	0.0992597	+	0.614942i	0.00408992	+	0.0253383i
$590$	−13.9659			−0.574965
$591$	−22.0929	−	8.04114i	−0.908779	−	0.330768i
$592$	−0.929892	−	5.27368i	−0.0382183	−	0.216747i
$593$	14.8780	+	12.4842i	0.610968	+	0.512663i	0.894950	−	0.446167i	$-0.147211\pi$
$593$	14.8780	+	12.4842i	0.610968	+	0.512663i	−0.283982	+	0.958830i	$0.591656\pi$
$594$	−3.47178	+	2.91317i	−0.142449	+	0.119529i
$595$	−2.35844	+	13.3754i	−0.0966866	+	0.548337i
$596$	1.13563	−	1.96697i	0.0465172	−	0.0805701i
$597$	−7.67617	−	13.2955i	−0.314165	−	0.544150i
$598$	−5.73783	+	2.08840i	−0.234637	+	0.0854009i
$599$	−37.1327	+	13.5152i	−1.51720	+	0.552216i	−0.960447	−	0.278462i	$-0.910175\pi$
$599$	−37.1327	+	13.5152i	−1.51720	+	0.552216i	−0.556753	+	0.830678i	$0.687953\pi$
$600$	−0.500000	−	0.866025i	−0.0204124	−	0.0353553i
$601$	−5.98158	+	10.3604i	−0.243994	+	0.422610i	−0.961848	−	0.273584i	$-0.911791\pi$
$601$	−5.98158	+	10.3604i	−0.243994	+	0.422610i	0.717854	+	0.696193i	$0.245124\pi$
$602$	−4.85844	+	27.5536i	−0.198015	+	1.12300i
$603$	5.90033	−	4.95096i	0.240280	−	0.201619i
$604$	−16.2383	−	13.6255i	−0.660727	−	0.554416i
$605$	1.65657	+	9.39490i	0.0673493	+	0.381957i
$606$	6.11974	+	2.22740i	0.248597	+	0.0904820i
$607$	13.7638			0.558656			0.279328	−	0.960196i	$-0.409888\pi$
$607$	13.7638			0.558656			0.279328	+	0.960196i	$0.409888\pi$
$608$	2.12449	+	3.80612i	0.0861593	+	0.154359i
$609$	−28.5895			−1.15850
$610$	4.20574	+	1.53076i	0.170285	+	0.0619788i
$611$	−1.70796	−	9.68631i	−0.0690966	−	0.391866i
$612$	3.61334	+	3.03195i	0.146061	+	0.122559i
$613$	−25.2139	+	21.1570i	−1.01838	+	0.854524i	−0.989423	−	0.145057i	$-0.953663\pi$
$613$	−25.2139	+	21.1570i	−1.01838	+	0.854524i	−0.0289583	+	0.999581i	$0.509219\pi$
$614$	3.55097	−	20.1386i	0.143306	−	0.812727i
$615$	4.32635	−	7.49346i	0.174455	−	0.302166i
$616$	6.52481	+	11.3013i	0.262892	+	0.455343i
$617$	−19.0783	+	6.94394i	−0.768064	+	0.279552i	−0.696186	−	0.717861i	$-0.745121\pi$
$617$	−19.0783	+	6.94394i	−0.768064	+	0.279552i	−0.0718776	+	0.997413i	$0.522899\pi$
$618$	−10.7836	+	3.92490i	−0.433779	+	0.157883i
$619$	−4.75402	−	8.23421i	−0.191080	−	0.330961i	0.754528	−	0.656268i	$-0.227866\pi$
$619$	−4.75402	−	8.23421i	−0.191080	−	0.330961i	−0.945609	+	0.325307i	$0.894532\pi$
$620$	−0.0714517	+	0.123758i	−0.00286957	+	0.00497024i
$621$	0.500000	−	2.83564i	0.0200643	−	0.113790i
$622$	−1.81315	+	1.52141i	−0.0727006	+	0.0610031i
$623$	31.2237	+	26.1998i	1.25095	+	1.04967i
$624$	−0.368241	−	2.08840i	−0.0147414	−	0.0836028i
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$	−6.12567			−0.244831
$627$	3.71213	−	19.4030i	0.148248	−	0.774882i
$628$	1.90167			0.0758851
$629$	23.7358	+	8.63911i	0.946407	+	0.344464i
$630$	0.500000	+	2.83564i	0.0199205	+	0.112975i
$631$	28.8273	+	24.1890i	1.14760	+	0.962947i	0.999661	−	0.0260495i	$-0.00829276\pi$
$631$	28.8273	+	24.1890i	1.14760	+	0.962947i	0.147935	+	0.988997i	$0.452737\pi$
$632$	2.12449	−	1.78265i	0.0845075	−	0.0709102i
$633$	−0.160444	+	0.909926i	−0.00637709	+	0.0361663i
$634$	3.19072	−	5.52649i	0.126720	−	0.219485i
$635$	6.01114	+	10.4116i	0.238545	+	0.413172i
$636$	12.9153	−	4.70080i	0.512127	−	0.186399i
$637$	−2.57233	+	0.936251i	−0.101919	+	0.0370956i
$638$	22.4996	+	38.9704i	0.890767	+	1.54285i
$639$	7.08899	−	12.2785i	0.280436	−	0.485730i
$640$	−0.173648	+	0.984808i	−0.00686405	+	0.0389279i
$641$	−8.86618	+	7.43961i	−0.350193	+	0.293847i	−0.800868	−	0.598841i	$-0.795628\pi$
$641$	−8.86618	+	7.43961i	−0.350193	+	0.293847i	0.450674	+	0.892688i	$0.351184\pi$
$642$	9.13816	+	7.66782i	0.360654	+	0.302625i
$643$	0.922152	+	5.22978i	0.0363661	+	0.206242i	0.997577	−	0.0695723i	$-0.0221635\pi$
$643$	0.922152	+	5.22978i	0.0363661	+	0.206242i	−0.961211	+	0.275815i	$0.911052\pi$
$644$	−7.79086	−	2.83564i	−0.307003	−	0.111740i
$645$	9.71688			0.382602
$646$	−20.5582	−	0.298120i	−0.808853	−	0.0117294i
$647$	26.7674			1.05234			0.526168	−	0.850380i	$-0.323628\pi$
$647$	26.7674			1.05234			0.526168	+	0.850380i	$0.323628\pi$
$648$	0.939693	+	0.342020i	0.0369146	+	0.0134358i
$649$	−10.9910	−	62.3329i	−0.431433	−	2.44678i
$650$	−1.62449	−	1.36310i	−0.0637175	−	0.0534654i
$651$	0.315207	−	0.264490i	0.0123540	−	0.0103662i
$652$	−1.42989	+	8.10932i	−0.0559989	+	0.317586i
$653$	−16.3473	+	28.3143i	−0.639719	+	1.10803i	0.345775	+	0.938317i	$0.387616\pi$
$653$	−16.3473	+	28.3143i	−0.639719	+	1.10803i	−0.985494	+	0.169709i	$0.945717\pi$
$654$	−1.06283	−	1.84088i	−0.0415601	−	0.0719842i
$655$	15.6604	−	5.69994i	0.611904	−	0.222715i
$656$	−8.13088	+	2.95940i	−0.317458	+	0.115545i
$657$	6.56670	+	11.3739i	0.256192	+	0.443737i
$658$	6.67752	−	11.5658i	0.260317	−	0.450882i
$659$	2.30747	−	13.0863i	0.0898861	−	0.509770i	−0.906309	−	0.422616i	$-0.861112\pi$
$659$	2.30747	−	13.0863i	0.0898861	−	0.509770i	0.996195	−	0.0871535i	$-0.0277770\pi$
$660$	3.47178	−	2.91317i	0.135139	−	0.113395i
$661$	−10.5615	−	8.86214i	−0.410794	−	0.344697i	0.413854	−	0.910343i	$-0.364182\pi$
$661$	−10.5615	−	8.86214i	−0.410794	−	0.344697i	−0.824648	+	0.565646i	$0.808627\pi$
$662$	−0.274196	−	1.55504i	−0.0106569	−	0.0604384i
$663$	9.39945	+	3.42112i	0.365044	+	0.132865i
$664$	−0.977711			−0.0379426
$665$	−9.49660	−	8.20616i	−0.368262	−	0.318221i
$666$	5.35504			0.207503
$667$	−26.8653	−	9.77817i	−1.04023	−	0.378612i
$668$	1.55644	+	8.82699i	0.0602204	+	0.341527i
$669$	−6.82816	−	5.72951i	−0.263992	−	0.221516i
$670$	−5.90033	+	4.95096i	−0.227950	+	0.191272i
$671$	−3.52229	+	19.9759i	−0.135976	+	0.771161i
$672$	1.43969	−	2.49362i	0.0555373	−	0.0961935i
$673$	−9.09017	−	15.7446i	−0.350400	−	0.606911i	0.635919	−	0.771756i	$-0.280621\pi$
$673$	−9.09017	−	15.7446i	−0.350400	−	0.606911i	−0.986320	+	0.164844i	$0.947288\pi$
$674$	15.3824	−	5.59873i	0.592507	−	0.215655i
$675$	0.939693	−	0.342020i	0.0361688	−	0.0131644i
$676$	4.25150	+	7.36381i	0.163519	+	0.283223i
$677$	−11.5903	+	20.0751i	−0.445453	+	0.771547i	−0.998084	−	0.0618792i	$-0.980291\pi$
$677$	−11.5903	+	20.0751i	−0.445453	+	0.771547i	0.552631	+	0.833426i	$0.313624\pi$
$678$	−0.546637	+	3.10013i	−0.0209935	+	0.119060i
$679$	1.48886	−	1.24930i	0.0571370	−	0.0479437i
$680$	−3.61334	−	3.03195i	−0.138565	−	0.116270i
$681$	−1.45084	−	8.22811i	−0.0555962	−	0.315302i
$682$	−0.608593	−	0.221510i	−0.0233042	−	0.00848205i
$683$	−39.7529			−1.52110			−0.760551	−	0.649278i	$-0.775071\pi$
$683$	−39.7529			−1.52110			−0.760551	+	0.649278i	$0.775071\pi$
$684$	−4.11721	+	1.43128i	−0.157426	+	0.0547265i
$685$	12.2294			0.467260
$686$	15.4474	+	5.62241i	0.589786	+	0.214664i
$687$	−3.29174	−	18.6684i	−0.125588	−	0.712243i
$688$	−7.44356	−	6.24589i	−0.283783	−	0.238122i
$689$	22.3273	−	18.7348i	0.850602	−	0.713740i
$690$	−0.500000	+	2.83564i	−0.0190347	+	0.107951i
$691$	5.37211	−	9.30477i	0.204365	−	0.353970i	−0.745565	−	0.666432i	$-0.767820\pi$
$691$	5.37211	−	9.30477i	0.204365	−	0.353970i	0.949930	+	0.312462i	$0.101154\pi$
$692$	−5.10220	−	8.83726i	−0.193956	−	0.335942i
$693$	−12.2626	+	4.46324i	−0.465819	+	0.169544i
$694$	10.0544	−	3.65949i	0.381659	−	0.138912i
$695$	−2.41013	−	4.17447i	−0.0914214	−	0.158347i
$696$	4.96451	−	8.59878i	0.188179	−	0.325936i
$697$	7.08724	−	40.1937i	0.268448	−	1.52245i
$698$	12.4914	−	10.4815i	0.472806	−	0.396731i
$699$	−10.5398	−	8.84397i	−0.398653	−	0.334510i
$700$	−0.500000	−	2.83564i	−0.0188982	−	0.107177i
$701$	−37.2067	−	13.5421i	−1.40528	−	0.511479i	−0.475537	−	0.879696i	$-0.657746\pi$
$701$	−37.2067	−	13.5421i	−1.40528	−	0.511479i	−0.929740	+	0.368217i	$0.879968\pi$
$702$	2.12061			0.0800374
$703$	−18.0967	+	14.7431i	−0.682531	+	0.556048i
$704$	−4.53209			−0.170810
$705$	−4.35844	−	1.58634i	−0.164148	−	0.0597451i
$706$	−5.10101	−	28.9293i	−0.191979	−	1.08877i
$707$	14.3648	+	12.0535i	0.540245	+	0.453320i
$708$	−10.6985	+	8.97708i	−0.402073	+	0.337379i
$709$	2.32800	−	13.2027i	0.0874299	−	0.495840i	−0.909376	−	0.415975i	$-0.863440\pi$
$709$	2.32800	−	13.2027i	0.0874299	−	0.495840i	0.996806	−	0.0798642i	$-0.0254487\pi$
$710$	−7.08899	+	12.2785i	−0.266045	+	0.460804i
$711$	1.38666	+	2.40176i	0.0520038	+	0.0900732i
$712$	−13.3020	+	4.84153i	−0.498514	+	0.181444i
$713$	0.386659	−	0.140732i	0.0144805	−	0.00527047i
$714$	6.79086	+	11.7621i	0.254142	+	0.440186i
$715$	4.80541	−	8.32321i	0.179712	−	0.311270i
$716$	4.00000	−	22.6851i	0.149487	−	0.847783i
$717$	7.74557	−	6.49930i	0.289263	−	0.242721i
$718$	−25.2178	−	21.1603i	−0.941120	−	0.789694i
$719$	4.87417	+	27.6428i	0.181776	+	1.03090i	0.930028	+	0.367488i	$0.119782\pi$
$719$	4.87417	+	27.6428i	0.181776	+	1.03090i	−0.748252	+	0.663414i	$0.769107\pi$
$720$	−0.939693	−	0.342020i	−0.0350203	−	0.0127463i
$721$	−33.0428			−1.23058
$722$	9.97313	−	16.1721i	0.371161	−	0.601863i
$723$	−11.7888			−0.438430
$724$	−17.5471	−	6.38662i	−0.652133	−	0.237357i
$725$	−1.72416	−	9.77817i	−0.0640335	−	0.363152i
$726$	7.30793	+	6.13208i	0.271223	+	0.227583i
$727$	28.8837	−	24.2363i	1.07124	−	0.898875i	0.0760739	−	0.997102i	$-0.475762\pi$
$727$	28.8837	−	24.2363i	1.07124	−	0.898875i	0.995164	+	0.0982268i	$0.0313171\pi$
$728$	1.06031	−	6.01330i	0.0392976	−	0.222868i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−6.56670	−	11.3739i	−0.243045	−	0.420966i
$731$	43.0693	−	15.6759i	1.59298	−	0.579796i
$732$	4.20574	−	1.53076i	0.155449	−	0.0565786i
$733$	8.38191	+	14.5179i	0.309593	+	0.536231i	0.978273	−	0.207319i	$-0.0664739\pi$
$733$	8.38191	+	14.5179i	0.309593	+	0.536231i	−0.668680	+	0.743550i	$0.733141\pi$
$734$	−15.9265	+	27.5855i	−0.587857	+	1.01820i
$735$	−0.224155	+	1.27125i	−0.00826810	+	0.0468907i
$736$	2.20574	−	1.85083i	0.0813045	−	0.0682226i
$737$	−26.7408	−	22.4382i	−0.985011	−	0.826522i
$738$	−1.50253	−	8.52125i	−0.0553088	−	0.313672i
$739$	−30.7075	−	11.1766i	−1.12960	−	0.411139i	−0.291450	−	0.956586i	$-0.594138\pi$
$739$	−30.7075	−	11.1766i	−1.12960	−	0.411139i	−0.838145	+	0.545447i	$0.816360\pi$
$740$	−5.35504			−0.196855
$741$	−7.16637	+	5.83834i	−0.263263	+	0.214477i
$742$	39.5749			1.45284
$743$	30.6126	+	11.1421i	1.12307	+	0.408763i	0.835771	−	0.549078i	$-0.185021\pi$
$743$	30.6126	+	11.1421i	1.12307	+	0.408763i	0.287297	+	0.957841i	$0.407243\pi$
$744$	0.0248149	+	0.140732i	0.000909759	+	0.00515950i
$745$	−1.73989	−	1.45994i	−0.0637445	−	0.0534880i
$746$	−12.9063	+	10.8296i	−0.472532	+	0.396501i
$747$	0.169778	−	0.962858i	0.00621184	−	0.0352291i
$748$	10.6887	−	18.5133i	0.390816	−	0.676914i
$749$	17.1741	+	29.7464i	0.627529	+	1.08691i
$750$	−0.939693	+	0.342020i	−0.0343127	+	0.0124888i
$751$	49.7781	−	18.1178i	1.81643	−	0.661126i	0.820432	−	0.571744i	$-0.193733\pi$
$751$	49.7781	−	18.1178i	1.81643	−	0.661126i	0.995997	−	0.0893823i	$-0.0284893\pi$
$752$	2.31908	+	4.01676i	0.0845681	+	0.146476i
$753$	−10.7340	+	18.5918i	−0.391167	+	0.677521i
$754$	3.65627	−	20.7357i	0.133153	−	0.755151i
$755$	−16.2383	+	13.6255i	−0.590972	+	0.495884i
$756$	2.20574	+	1.85083i	0.0802219	+	0.0673142i
$757$	−4.43226	−	25.1366i	−0.161093	−	0.913604i	−0.953002	−	0.302965i	$-0.902024\pi$
$757$	−4.43226	−	25.1366i	−0.161093	−	0.913604i	0.791909	−	0.610640i	$-0.209088\pi$
$758$	−10.2537	−	3.73205i	−0.372432	−	0.135554i
$759$	−13.0496			−0.473672
$760$	4.11721	−	1.43128i	0.149347	−	0.0519181i
$761$	36.6827			1.32975			0.664874	−	0.746956i	$-0.268485\pi$
$761$	36.6827			1.32975			0.664874	+	0.746956i	$0.268485\pi$
$762$	11.2973	+	4.11186i	0.409256	+	0.148957i
$763$	−1.06283	−	6.02763i	−0.0384772	−	0.218215i
$764$	1.86437	+	1.56439i	0.0674506	+	0.0565977i
$765$	3.61334	−	3.03195i	0.130641	−	0.109620i
$766$	1.39006	−	7.88344i	0.0502250	−	0.284840i
$767$	−14.8081	+	25.6484i	−0.534689	+	0.926109i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	26.0551	−	9.48330i	0.939573	−	0.341976i	0.173576	−	0.984821i	$-0.444468\pi$
$769$	26.0551	−	9.48330i	0.939573	−	0.341976i	0.765997	+	0.642844i	$0.222246\pi$
$770$	12.2626	−	4.46324i	0.441915	−	0.160844i
$771$	3.04323	+	5.27103i	0.109599	+	0.189832i
$772$	−0.769448	+	1.33272i	−0.0276930	+	0.0479658i
$773$	5.95858	−	33.7928i	0.214315	−	1.21544i	−0.667776	−	0.744362i	$-0.732754\pi$
$773$	5.95858	−	33.7928i	0.214315	−	1.21544i	0.882091	−	0.471079i	$-0.156135\pi$
$774$	7.44356	−	6.24589i	0.267553	−	0.224504i
$775$	0.109470	+	0.0918566i	0.00393229	+	0.00329959i
$776$	0.117211	+	0.664738i	0.00420764	+	0.0238627i
$777$	14.4893	+	5.27368i	0.519802	+	0.189192i
$778$	−12.8452			−0.460524
$779$	28.5378	+	24.6599i	1.02247	+	0.883534i
$780$	−2.12061			−0.0759302
$781$	−60.3808	−	21.9768i	−2.16059	−	0.786392i
$782$	2.35844	+	13.3754i	0.0843377	+	0.478303i
$783$	7.60607	+	6.38225i	0.271819	+	0.228083i
$784$	0.988856	−	0.829748i	0.0353163	−	0.0296339i
$785$	0.330222	−	1.87278i	0.0117861	−	0.0668425i
$786$	8.33275	−	14.4327i	0.297219	−	0.514799i
$787$	−2.09967	−	3.63674i	−0.0748452	−	0.129636i	0.826174	−	0.563415i	$-0.190513\pi$
$787$	−2.09967	−	3.63674i	−0.0748452	−	0.129636i	−0.901019	+	0.433780i	$0.857180\pi$
$788$	22.0929	−	8.04114i	0.787026	−	0.286454i
$789$	9.42989	−	3.43220i	0.335713	−	0.122190i
$790$	−1.38666	−	2.40176i	−0.0493351	−	0.0854509i
$791$	−4.53209	+	7.84981i	−0.161143	+	0.279107i
$792$	0.786989	−	4.46324i	0.0279644	−	0.158594i
$793$	7.27063	−	6.10078i	0.258188	−	0.216645i
$794$	8.67617	+	7.28017i	0.307906	+	0.258364i
$795$	−2.38666	−	13.5354i	−0.0846461	−	0.480052i
$796$	14.4265	+	5.25081i	0.511333	+	0.186110i
$797$	47.4311			1.68009			0.840047	−	0.542513i	$-0.182527\pi$
$797$	47.4311			1.68009			0.840047	+	0.542513i	$0.182527\pi$
$798$	−12.5496	−	0.181985i	−0.444252	−	0.00644220i
$799$	−21.8776			−0.773975
$800$	0.939693	+	0.342020i	0.0332232	+	0.0120922i
$801$	−2.45811	−	13.9406i	−0.0868531	−	0.492568i
$802$	15.5988	+	13.0889i	0.550813	+	0.462187i
$803$	45.5963	−	38.2599i	1.60906	−	1.35016i
$804$	−1.33750	+	7.58532i	−0.0471699	+	0.267514i
$805$	−4.14543	+	7.18009i	−0.146107	+	0.253065i
$806$	0.151522	+	0.262443i	0.00533712	+	0.00924416i
$807$	−10.5223	+	3.82980i	−0.370402	+	0.134815i
$808$	−6.11974	+	2.22740i	−0.215292	+	0.0783597i
$809$	−14.2981	−	24.7651i	−0.502696	−	0.870694i	−0.999995	−	0.00311541i	$-0.999008\pi$
$809$	−14.2981	−	24.7651i	−0.502696	−	0.870694i	0.497300	−	0.867579i	$-0.334325\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	−1.55051	+	8.79336i	−0.0544457	+	0.308777i	−0.999854	−	0.0171127i	$-0.994553\pi$
$811$	−1.55051	+	8.79336i	−0.0544457	+	0.308777i	0.945408	+	0.325889i	$0.105664\pi$
$812$	21.9008	−	18.3770i	0.768567	−	0.644905i
$813$	−0.639500	−	0.536604i	−0.0224282	−	0.0188195i
$814$	−4.21436	−	23.9008i	−0.147713	−	0.837722i
$815$	7.73783	+	2.81634i	0.271044	+	0.0986520i
$816$	−4.71688			−0.165124
$817$	−7.95888	+	41.6004i	−0.278446	+	1.45541i
$818$	32.9632			1.15253
$819$	5.73783	+	2.08840i	0.200496	+	0.0729745i
$820$	1.50253	+	8.52125i	0.0524705	+	0.297575i
$821$	23.5385	+	19.7511i	0.821499	+	0.689319i	0.953323	−	0.301954i	$-0.0976388\pi$
$821$	23.5385	+	19.7511i	0.821499	+	0.689319i	−0.131824	+	0.991273i	$0.542083\pi$
$822$	9.36824	−	7.86089i	0.326755	−	0.274180i
$823$	−6.44878	+	36.5728i	−0.224790	+	1.27485i	0.638295	+	0.769791i	$0.279640\pi$
$823$	−6.44878	+	36.5728i	−0.224790	+	1.27485i	−0.863086	+	0.505057i	$0.831471\pi$
$824$	5.73783	−	9.93821i	0.199887	−	0.346214i
$825$	−2.26604	−	3.92490i	−0.0788935	−	0.136648i
$826$	−37.7879	+	13.7537i	−1.31481	+	0.478552i
$827$	−37.2438	+	13.5556i	−1.29509	+	0.471376i	−0.895396	−	0.445271i	$-0.853107\pi$
$827$	−37.2438	+	13.5556i	−1.29509	+	0.471376i	−0.399698	+	0.916647i	$0.630885\pi$
$828$	1.43969	+	2.49362i	0.0500328	+	0.0866593i
$829$	16.6117	−	28.7724i	0.576950	−	0.999306i	−0.418877	−	0.908043i	$-0.637576\pi$
$829$	16.6117	−	28.7724i	0.576950	−	0.999306i	0.995827	−	0.0912635i	$-0.0290905\pi$
$830$	−0.169778	+	0.962858i	−0.00589307	+	0.0334213i
$831$	−13.3701	+	11.2188i	−0.463802	+	0.389176i
$832$	1.62449	+	1.36310i	0.0563189	+	0.0472572i
$833$	1.05731	+	5.99633i	0.0366338	+	0.207760i
$834$	−4.52956	−	1.64863i	−0.156846	−	0.0570872i
$835$	8.96316			0.310183
$836$	9.62836	+	17.2497i	0.333004	+	0.596593i
$837$	−0.142903			−0.00493947
$838$	0.464508	+	0.169067i	0.0160461	+	0.00584032i
$839$	−3.57239	−	20.2600i	−0.123332	−	0.699453i	−0.982284	−	0.187397i	$-0.939995\pi$
$839$	−3.57239	−	20.2600i	−0.123332	−	0.699453i	0.858952	−	0.512056i	$-0.171116\pi$
$840$	−2.20574	−	1.85083i	−0.0761052	−	0.0638598i
$841$	53.3055	−	44.7286i	1.83812	−	1.54237i
$842$	5.55778	−	31.5197i	0.191534	−	1.08624i
$843$	8.88578	−	15.3906i	0.306043	−	0.530081i
$844$	−0.461981	−	0.800175i	−0.0159021	−	0.0275432i
$845$	7.99020	−	2.90819i	0.274871	−	0.100045i
$846$	−4.35844	+	1.58634i	−0.149846	+	0.0545396i
$847$	13.7344	+	23.7887i	0.471920	+	0.817390i
$848$	−6.87211	+	11.9028i	−0.235989	+	0.408745i
$849$	−0.613341	+	3.47843i	−0.0210498	+	0.119379i
$850$	−3.61334	+	3.03195i	−0.123937	+	0.103995i
$851$	11.8118	+	9.91128i	0.404903	+	0.339754i
$852$	2.46198	+	13.9626i	0.0843461	+	0.478350i
$853$	22.7433	+	8.27790i	0.778717	+	0.283430i	0.700638	−	0.713517i	$-0.252899\pi$
$853$	22.7433	+	8.27790i	0.778717	+	0.283430i	0.0780796	+	0.996947i	$0.475121\pi$
$854$	12.8871			0.440988
$855$	0.694593	+	4.30320i	0.0237546	+	0.147166i
$856$	−11.9290			−0.407725
$857$	−36.4381	−	13.2624i	−1.24470	−	0.453034i	−0.366094	−	0.930578i	$-0.619305\pi$
$857$	−36.4381	−	13.2624i	−1.24470	−	0.453034i	−0.878608	+	0.477544i	$0.841527\pi$
$858$	−1.66890	−	9.46480i	−0.0569753	−	0.323123i
$859$	30.4504	+	25.5509i	1.03896	+	0.871787i	0.991889	−	0.127105i	$-0.0405685\pi$
$859$	30.4504	+	25.5509i	1.03896	+	0.871787i	0.0470659	+	0.998892i	$0.485013\pi$
$860$	−7.44356	+	6.24589i	−0.253823	+	0.212983i
$861$	4.32635	−	24.5360i	0.147442	−	0.836183i
$862$	8.34730	−	14.4579i	0.284310	−	0.492439i
$863$	−12.2071	−	21.1433i	−0.415534	−	0.719726i	0.579950	−	0.814652i	$-0.303072\pi$
$863$	−12.2071	−	21.1433i	−0.415534	−	0.719726i	−0.995484	+	0.0949260i	$0.969739\pi$
$864$	−0.939693	+	0.342020i	−0.0319690	+	0.0116358i
$865$	−9.58899	+	3.49011i	−0.326036	+	0.118667i
$866$	10.5744	+	18.3155i	0.359334	+	0.622385i
$867$	2.62449	−	4.54574i	0.0891322	−	0.154381i
$868$	−0.0714517	+	0.405223i	−0.00242523	+	0.0137542i
$869$	9.62836	−	8.07915i	0.326620	−	0.274066i
$870$	−7.60607	−	6.38225i	−0.257870	−	0.216378i
$871$	2.83631	+	16.0855i	0.0961048	+	0.545038i
$872$	1.99747	+	0.727021i	0.0676430	+	0.0246200i
$873$	−0.674992			−0.0228450
$874$	−11.7306	−	4.46324i	−0.396792	−	0.150971i
$875$	−2.87939			−0.0973410
$876$	−12.3414	−	4.49189i	−0.416976	−	0.151767i
$877$	3.59523	+	20.3895i	0.121402	+	0.688506i	0.983380	+	0.181560i	$0.0581146\pi$
$877$	3.59523	+	20.3895i	0.121402	+	0.688506i	−0.861978	+	0.506946i	$0.830774\pi$
$878$	−1.81134	−	1.51989i	−0.0611297	−	0.0512939i
$879$	8.40033	−	7.04871i	0.283336	−	0.237747i
$880$	−0.786989	+	4.46324i	−0.0265294	+	0.150456i
$881$	4.06893	−	7.04759i	0.137086	−	0.237439i	−0.789307	−	0.613999i	$-0.789560\pi$
$881$	4.06893	−	7.04759i	0.137086	−	0.237439i	0.926392	+	0.376560i	$0.122893\pi$
$882$	0.645430	+	1.11792i	0.0217327	+	0.0376422i
$883$	41.2251	−	15.0047i	1.38733	−	0.504949i	0.462941	−	0.886389i	$-0.346794\pi$
$883$	41.2251	−	15.0047i	1.38733	−	0.504949i	0.924393	+	0.381440i	$0.124572\pi$
$884$	−9.39945	+	3.42112i	−0.316138	+	0.115065i
$885$	6.98293	+	12.0948i	0.234728	+	0.406562i
$886$	10.8550	−	18.8015i	0.364682	−	0.631648i
$887$	−4.46942	+	25.3473i	−0.150068	+	0.851080i	0.813089	+	0.582140i	$0.197784\pi$
$887$	−4.46942	+	25.3473i	−0.150068	+	0.851080i	−0.963157	+	0.268940i	$0.913327\pi$
$888$	−4.10220	+	3.44215i	−0.137661	+	0.115511i
$889$	26.5180	+	22.2513i	0.889385	+	0.746283i
$890$	2.45811	+	13.9406i	0.0823961	+	0.467291i
$891$	4.25877	+	1.55007i	0.142674	+	0.0519292i
$892$	8.91353			0.298447
$893$	10.3614	−	17.3602i	0.346732	−	0.580938i
$894$	−2.27126			−0.0759623
$895$	−21.6459	−	7.87846i	−0.723543	−	0.263348i
$896$	0.500000	+	2.83564i	0.0167038	+	0.0947321i
$897$	4.67752	+	3.92490i	0.156178	+	0.131049i
$898$	−15.1839	+	12.7408i	−0.506694	+	0.425167i
$899$	−0.246388	+	1.39733i	−0.00821749	+	0.0466037i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−32.4149	−	56.1443i	−1.07990	−	1.87044i
$902$	−36.8499	+	13.4123i	−1.22697	+	0.446579i
$903$	26.2913	−	9.56926i	0.874921	−	0.318445i
$904$	−1.57398	−	2.72621i	−0.0523497	−	0.0906724i
$905$	−9.33662	+	16.1715i	−0.310360	+	0.537559i
$906$	−3.68092	+	20.8755i	−0.122290	+	0.693544i
$907$	9.40941	−	7.89544i	0.312434	−	0.262164i	−0.473063	−	0.881029i	$-0.656852\pi$
$907$	9.40941	−	7.89544i	0.312434	−	0.262164i	0.785497	+	0.618865i	$0.212407\pi$
$908$	6.40033	+	5.37051i	0.212402	+	0.178227i
$909$	−1.13088	−	6.41355i	−0.0375090	−	0.212724i
$910$	−5.73783	−	2.08840i	−0.190207	−	0.0692297i
$911$	45.0164			1.49146			0.745730	−	0.666248i	$-0.232101\pi$
$911$	45.0164			1.49146			0.745730	+	0.666248i	$0.232101\pi$
$912$	2.23396	−	3.74292i	0.0739737	−	0.123940i
$913$	−4.43107			−0.146647
$914$	30.1917	+	10.9889i	0.998651	+	0.363479i
$915$	−0.777189	−	4.40766i	−0.0256931	−	0.145713i
$916$	14.5214	+	12.1849i	0.479801	+	0.402601i
$917$	36.7597	−	30.8451i	1.21391	−	1.01859i
$918$	0.819078	−	4.64522i	0.0270336	−	0.153315i
$919$	−13.3414	+	23.1079i	−0.440091	+	0.762260i	−0.997696	−	0.0678465i	$-0.978387\pi$
$919$	−13.3414	+	23.1079i	−0.440091	+	0.762260i	0.557605	+	0.830107i	$0.311721\pi$
$920$	−1.43969	−	2.49362i	−0.0474653	−	0.0822122i
$921$	−19.2160	+	6.99405i	−0.633189	+	0.230462i
$922$	−34.8926	+	12.6999i	−1.14913	+	0.418248i
$923$	15.0330	+	26.0380i	0.494818	+	0.857050i
$924$	6.52481	−	11.3013i	0.214651	−	0.371786i
$925$	−0.929892	+	5.27368i	−0.0305747	+	0.173398i
$926$	6.76470	−	5.67626i	0.222302	−	0.186533i
$927$	8.79086	+	7.37641i	0.288730	+	0.242273i
$928$	1.72416	+	9.77817i	0.0565982	+	0.320984i
$929$	−46.7614	−	17.0197i	−1.53419	−	0.558400i	−0.569547	−	0.821959i	$-0.692881\pi$
$929$	−46.7614	−	17.0197i	−1.53419	−	0.558400i	−0.964643	+	0.263559i	$0.915104\pi$
$930$	0.142903			0.00468599
$931$	−5.25893	−	2.00092i	−0.172355	−	0.0655774i
$932$	13.7588			0.450684
$933$	2.22416	+	0.809526i	0.0728156	+	0.0265027i
$934$	−3.90467	−	22.1445i	−0.127765	−	0.724589i
$935$	−16.3760	−	13.7411i	−0.535552	−	0.449381i
$936$	−1.62449	+	1.36310i	−0.0530980	+	0.0445545i
$937$	9.50939	−	53.9304i	0.310658	−	1.76183i	−0.284938	−	0.958546i	$-0.591973\pi$
$937$	9.50939	−	53.9304i	0.310658	−	1.76183i	0.595596	−	0.803284i	$-0.296916\pi$
$938$	−11.0890	+	19.2067i	−0.362068	+	0.627121i
$939$	3.06283	+	5.30498i	0.0999518	+	0.173122i
$940$	4.35844	−	1.58634i	0.142157	−	0.0517408i
$941$	26.1227	−	9.50790i	0.851577	−	0.309949i	0.120894	−	0.992665i	$-0.461424\pi$
$941$	26.1227	−	9.50790i	0.851577	−	0.309949i	0.730683	+	0.682717i	$0.239202\pi$
$942$	−0.950837	−	1.64690i	−0.0309799	−	0.0536588i
$943$	12.4572	−	21.5766i	0.405663	−	0.702630i
$944$	2.42514	−	13.7537i	0.0789317	−	0.447644i
$945$	2.20574	−	1.85083i	0.0717526	−	0.0602076i
$946$	−33.7349	−	28.3069i	−1.09682	−	0.920338i
$947$	4.14867	+	23.5283i	0.134814	+	0.764566i	0.974989	+	0.222252i	$0.0713408\pi$
$947$	4.14867	+	23.5283i	0.134814	+	0.764566i	−0.840176	+	0.542315i	$0.817548\pi$
$948$	−2.60607	−	0.948531i	−0.0846411	−	0.0308068i
$949$	−27.8509			−0.904078
$950$	−0.694593	−	4.30320i	−0.0225356	−	0.139614i
$951$	−6.38144			−0.206933
$952$	−12.7626	−	4.64522i	−0.413640	−	0.150552i
$953$	5.68021	+	32.2141i	0.184000	+	1.04352i	0.927234	+	0.374484i	$0.122180\pi$
$953$	5.68021	+	32.2141i	0.184000	+	1.04352i	−0.743234	+	0.669032i	$0.766709\pi$
$954$	−10.5287	−	8.83462i	−0.340879	−	0.286031i
$955$	1.86437	−	1.56439i	0.0603296	−	0.0506226i
$956$	−1.75578	+	9.95751i	−0.0567859	+	0.322049i
$957$	22.4996	−	38.9704i	0.727308	−	1.25974i
$958$	−8.70961	−	15.0855i	−0.281395	−	0.487390i
$959$	33.0895	−	12.0436i	1.06851	−	0.388907i
$960$	0.939693	−	0.342020i	0.0303284	−	0.0110387i
$961$	15.4898	+	26.8291i	0.499671	+	0.865455i
$962$	−5.67799	+	9.83456i	−0.183066	+	0.317079i
$963$	2.07145	−	11.7478i	0.0667516	−	0.378567i
$964$	9.03074	−	7.57769i	0.290861	−	0.244061i
$965$	1.17886	+	0.989183i	0.0379489	+	0.0318429i
$966$	1.43969	+	8.16490i	0.0463214	+	0.262701i
$967$	39.3320	+	14.3157i	1.26483	+	0.460362i	0.885388	−	0.464853i	$-0.153893\pi$
$967$	39.3320	+	14.3157i	1.26483	+	0.460362i	0.379445	+	0.925214i	$0.376115\pi$
$968$	−9.53983			−0.306622
$969$	10.0209	+	17.9530i	0.321919	+	0.576734i
$970$	0.674992			0.0216727
$971$	−17.1018	−	6.22454i	−0.548822	−	0.199755i	0.0527008	−	0.998610i	$-0.483217\pi$
$971$	−17.1018	−	6.22454i	−0.548822	−	0.199755i	−0.601523	+	0.798855i	$0.705439\pi$
$972$	−0.173648	−	0.984808i	−0.00556977	−	0.0315877i
$973$	−10.6322	−	8.92150i	−0.340854	−	0.286010i
$974$	−23.1459	+	19.4217i	−0.741642	+	0.622312i
$975$	−0.368241	+	2.08840i	−0.0117931	+	0.0668823i
$976$	−2.23783	+	3.87603i	−0.0716311	+	0.124069i
$977$	0.180512	+	0.312655i	0.00577508	+	0.0100027i	0.868899	−	0.494990i	$-0.164828\pi$
$977$	0.180512	+	0.312655i	0.00577508	+	0.0100027i	−0.863123	+	0.504993i	$0.831495\pi$
$978$	7.73783	−	2.81634i	0.247428	−	0.0900566i
$979$	−60.2859	+	21.9423i	−1.92674	+	0.701278i
$980$	−0.645430	−	1.11792i	−0.0206175	−	0.0357105i
$981$	−1.06283	+	1.84088i	−0.0339337	+	0.0587748i
$982$	2.09462	−	11.8792i	0.0668419	−	0.379079i
$983$	−8.44041	+	7.08234i	−0.269207	+	0.225892i	−0.767390	−	0.641180i	$-0.778445\pi$
$983$	−8.44041	+	7.08234i	−0.269207	+	0.225892i	0.498183	+	0.867072i	$0.334001\pi$
$984$	6.62836	+	5.56185i	0.211304	+	0.177305i
$985$	−4.08260	−	23.1536i	−0.130082	−	0.737734i
$986$	−44.0096	−	16.0182i	−1.40155	−	0.510122i
$987$	−13.3550			−0.425096
$988$	1.73695	−	9.07888i	0.0552597	−	0.288838i
$989$	27.9786			0.889669
$990$	−4.25877	−	1.55007i	−0.135353	−	0.0492643i
$991$	9.93557	+	56.3474i	0.315614	+	1.78994i	0.568756	+	0.822506i	$0.307425\pi$
$991$	9.93557	+	56.3474i	0.315614	+	1.78994i	−0.253142	+	0.967429i	$0.581464\pi$
$992$	−0.109470	−	0.0918566i	−0.00347569	−	0.00291645i
$993$	−1.20961	+	1.01498i	−0.0383857	+	0.0322095i
$994$	−7.08899	+	40.2037i	−0.224849	+	1.27518i
$995$	7.67617	−	13.2955i	0.243351	−	0.421496i
$996$	0.488856	+	0.846723i	0.0154900	+	0.0268294i
$997$	−29.6587	+	10.7949i	−0.939300	+	0.341877i	−0.765889	−	0.642972i	$-0.777701\pi$
$997$	−29.6587	+	10.7949i	−0.939300	+	0.341877i	−0.173411	+	0.984850i	$0.555479\pi$
$998$	−0.830222	+	0.302176i	−0.0262802	+	0.00956522i
$999$	−2.67752	−	4.63760i	−0.0847129	−	0.146727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.u.g.61.1	✓	6
19.5	even	9	inner	570.2.u.g.271.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.g.61.1	✓	6	1.1	even	1	trivial
570.2.u.g.271.1	yes	6	19.5	even	9	inner

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(0.173648 - 0.984808i) q^{6} +(1.43969 - 2.49362i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(0.173648 - 0.984808i) q^{6} +(1.43969 - 2.49362i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(0.939693 - 0.342020i) q^{10} +(2.26604 + 3.92490i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.368241 - 2.08840i) q^{13} +(2.20574 - 1.85083i) q^{14} +(-0.766044 - 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-4.43242 - 1.61327i) q^{17} -1.00000 q^{18} +(3.37939 - 2.75314i) q^{19} +1.00000 q^{20} +(-2.70574 - 0.984808i) q^{21} +(0.786989 + 4.46324i) q^{22} +(-2.20574 - 1.85083i) q^{23} +(0.766044 - 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(1.06031 - 1.83651i) q^{26} +(0.500000 + 0.866025i) q^{27} +(2.70574 - 0.984808i) q^{28} +(9.33022 - 3.39592i) q^{29} +(-0.500000 - 0.866025i) q^{30} +(-0.0714517 + 0.123758i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(3.47178 - 2.91317i) q^{33} +(-3.61334 - 3.03195i) q^{34} +(-0.500000 - 2.83564i) q^{35} +(-0.939693 - 0.342020i) q^{36} -5.35504 q^{37} +(4.11721 - 1.43128i) q^{38} -2.12061 q^{39} +(0.939693 + 0.342020i) q^{40} +(1.50253 + 8.52125i) q^{41} +(-2.20574 - 1.85083i) q^{42} +(-7.44356 + 6.24589i) q^{43} +(-0.786989 + 4.46324i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-1.43969 - 2.49362i) q^{46} +(4.35844 - 1.58634i) q^{47} +(0.939693 - 0.342020i) q^{48} +(-0.645430 - 1.11792i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.819078 + 4.64522i) q^{51} +(1.62449 - 1.36310i) q^{52} +(10.5287 + 8.83462i) q^{53} +(0.173648 + 0.984808i) q^{54} +(4.25877 + 1.55007i) q^{55} +2.87939 q^{56} +(-3.29813 - 2.84997i) q^{57} +9.92902 q^{58} +(-13.1236 - 4.77660i) q^{59} +(-0.173648 - 0.984808i) q^{60} +(3.42855 + 2.87689i) q^{61} +(-0.109470 + 0.0918566i) q^{62} +(-0.500000 + 2.83564i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.06031 - 1.83651i) q^{65} +(4.25877 - 1.55007i) q^{66} +(-7.23783 + 2.63435i) q^{67} +(-2.35844 - 4.08494i) q^{68} +(-1.43969 + 2.49362i) q^{69} +(0.500000 - 2.83564i) q^{70} +(-10.8610 + 9.11343i) q^{71} +(-0.766044 - 0.642788i) q^{72} +(-2.28059 - 12.9339i) q^{73} +(-5.03209 - 1.83153i) q^{74} -1.00000 q^{75} +(4.35844 + 0.0632028i) q^{76} +13.0496 q^{77} +(-1.99273 - 0.725293i) q^{78} +(-0.481582 - 2.73119i) q^{79} +(0.766044 + 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-1.50253 + 8.52125i) q^{82} +(-0.488856 + 0.846723i) q^{83} +(-1.43969 - 2.49362i) q^{84} +(-4.43242 + 1.61327i) q^{85} +(-9.13088 + 3.32337i) q^{86} +(-4.96451 - 8.59878i) q^{87} +(-2.26604 + 3.92490i) q^{88} +(-2.45811 + 13.9406i) q^{89} +(-0.766044 + 0.642788i) q^{90} +(-4.67752 - 3.92490i) q^{91} +(-0.500000 - 2.83564i) q^{92} +(0.134285 + 0.0488759i) q^{93} +4.63816 q^{94} +(0.819078 - 4.28125i) q^{95} +1.00000 q^{96} +(0.634285 + 0.230861i) q^{97} +(-0.224155 - 1.27125i) q^{98} +(-3.47178 - 2.91317i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q + 3 * q^7 + 3 * q^8	\( 6 q + 3 q^{7} + 3 q^{8} + 9 q^{11} + 3 q^{12} - 3 q^{13} + 3 q^{14} - 3 q^{17} - 6 q^{18} + 9 q^{19} + 6 q^{20} - 6 q^{21} - 3 q^{22} - 3 q^{23} + 12 q^{26} + 3 q^{27} + 6 q^{28} + 33 q^{29} - 3 q^{30} + 6 q^{33} - 15 q^{34} - 3 q^{35} + 18 q^{37} - 6 q^{38} - 24 q^{39} - 6 q^{41} - 3 q^{42} - 15 q^{43} + 3 q^{44} - 3 q^{45} - 3 q^{46} + 18 q^{47} + 12 q^{49} + 3 q^{50} + 12 q^{51} - 3 q^{52} + 12 q^{53} + 3 q^{55} + 6 q^{56} - 6 q^{57} - 6 q^{58} - 9 q^{59} + 21 q^{61} - 18 q^{62} - 3 q^{63} - 3 q^{64} - 12 q^{65} + 3 q^{66} - 24 q^{67} - 6 q^{68} - 3 q^{69} + 3 q^{70} - 42 q^{71} - 45 q^{73} - 21 q^{74} - 6 q^{75} + 18 q^{76} + 24 q^{77} + 6 q^{78} + 9 q^{79} + 6 q^{82} - 9 q^{83} - 3 q^{84} - 3 q^{85} - 3 q^{86} + 3 q^{87} - 9 q^{88} - 21 q^{89} - 3 q^{91} - 3 q^{92} - 9 q^{93} - 6 q^{94} - 12 q^{95} + 6 q^{96} - 6 q^{97} - 3 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q + 3 * q^7 + 3 * q^8 + 9 * q^11 + 3 * q^12 - 3 * q^13 + 3 * q^14 - 3 * q^17 - 6 * q^18 + 9 * q^19 + 6 * q^20 - 6 * q^21 - 3 * q^22 - 3 * q^23 + 12 * q^26 + 3 * q^27 + 6 * q^28 + 33 * q^29 - 3 * q^30 + 6 * q^33 - 15 * q^34 - 3 * q^35 + 18 * q^37 - 6 * q^38 - 24 * q^39 - 6 * q^41 - 3 * q^42 - 15 * q^43 + 3 * q^44 - 3 * q^45 - 3 * q^46 + 18 * q^47 + 12 * q^49 + 3 * q^50 + 12 * q^51 - 3 * q^52 + 12 * q^53 + 3 * q^55 + 6 * q^56 - 6 * q^57 - 6 * q^58 - 9 * q^59 + 21 * q^61 - 18 * q^62 - 3 * q^63 - 3 * q^64 - 12 * q^65 + 3 * q^66 - 24 * q^67 - 6 * q^68 - 3 * q^69 + 3 * q^70 - 42 * q^71 - 45 * q^73 - 21 * q^74 - 6 * q^75 + 18 * q^76 + 24 * q^77 + 6 * q^78 + 9 * q^79 + 6 * q^82 - 9 * q^83 - 3 * q^84 - 3 * q^85 - 3 * q^86 + 3 * q^87 - 9 * q^88 - 21 * q^89 - 3 * q^91 - 3 * q^92 - 9 * q^93 - 6 * q^94 - 12 * q^95 + 6 * q^96 - 6 * q^97 - 3 * q^98 - 6 * q^99

Introduction

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