LMFDB - Embedded newform 273.2.cd.d.200.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(44,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("273.44");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cd (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			200.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	273.200
Dual form			273.2.cd.d.86.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(1.62484 + 0.599900i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.151613 - 0.565826i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(-1.15539 - 2.38014i) q^{7} +(-2.12132 + 2.12132i) q^{8} +(2.28024 + 1.94949i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(1.62484 + 0.599900i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.151613 - 0.565826i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(-1.15539 - 2.38014i) q^{7} +(-2.12132 + 2.12132i) q^{8} +(2.28024 + 1.94949i) q^{9} +(0.507306 + 0.292893i) q^{10} +(1.50851 + 5.62983i) q^{11} +(1.10721 + 1.33195i) q^{12} +(2.00000 - 3.00000i) q^{13} +(2.59808 - 0.500000i) q^{14} +(0.585786 - 0.828427i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.914214 - 1.58346i) q^{17} +(-2.47323 + 1.69798i) q^{18} +(-6.43003 - 1.72292i) q^{19} +(0.414214 - 0.414214i) q^{20} +(-0.449490 - 4.56048i) q^{21} -5.82843 q^{22} +(-3.29289 - 5.70346i) q^{23} +(-4.71940 + 2.17423i) q^{24} +(4.03295 + 2.32843i) q^{25} +(2.38014 + 2.70831i) q^{26} +(2.53553 + 4.53553i) q^{27} +(0.189469 - 2.63896i) q^{28} +1.00000i q^{29} +(0.648586 + 0.780239i) q^{30} +(0.214413 + 0.800199i) q^{31} +(-4.82963 + 1.29410i) q^{32} +(-0.926246 + 10.0525i) q^{33} +(1.29289 + 1.29289i) q^{34} +(-1.52192 + 0.292893i) q^{35} +(1.00000 + 2.82843i) q^{36} +(1.03528 - 3.86370i) q^{37} +(3.32843 - 5.76500i) q^{38} +(5.04939 - 3.67473i) q^{39} +(0.878680 + 1.52192i) q^{40} +(-4.00000 - 4.00000i) q^{41} +(4.52142 + 0.746165i) q^{42} -6.00000i q^{43} +(-1.50851 + 5.62983i) q^{44} +(1.44879 - 0.994652i) q^{45} +(6.36138 - 1.70453i) q^{46} +(0.634472 + 0.170006i) q^{47} +(-0.292893 - 1.70711i) q^{48} +(-4.33013 + 5.50000i) q^{49} +(-3.29289 + 3.29289i) q^{50} +(2.43538 - 2.02445i) q^{51} +(3.23205 - 1.59808i) q^{52} +(-7.49706 - 4.32843i) q^{53} +(-5.03723 + 1.27526i) q^{54} +3.41421 q^{55} +(7.50000 + 2.59808i) q^{56} +(-9.41421 - 6.65685i) q^{57} +(-0.965926 - 0.258819i) q^{58} +(-2.45497 - 9.16208i) q^{59} +(0.921519 - 0.424546i) q^{60} +(0.500000 + 0.866025i) q^{61} -0.828427 q^{62} +(2.00548 - 7.67972i) q^{63} -7.00000i q^{64} +(-1.39425 - 1.58649i) q^{65} +(-9.47029 - 3.49648i) q^{66} +(3.49025 + 13.0258i) q^{67} +(1.58346 - 0.914214i) q^{68} +(-1.92893 - 11.2426i) q^{69} +(0.110988 - 1.54587i) q^{70} +(-0.464466 - 0.464466i) q^{71} +(-8.97261 + 0.701625i) q^{72} +(12.3913 - 3.32024i) q^{73} +(3.46410 + 2.00000i) q^{74} +(5.15610 + 6.20270i) q^{75} +(-4.70711 - 4.70711i) q^{76} +(11.6569 - 10.0951i) q^{77} +(2.24264 + 5.82843i) q^{78} +(-0.707107 - 1.22474i) q^{79} +(-0.565826 + 0.151613i) q^{80} +(1.39898 + 8.89060i) q^{81} +(4.89898 - 2.82843i) q^{82} +(-3.07107 - 3.07107i) q^{83} +(1.89097 - 4.17423i) q^{84} +(-0.757359 - 0.757359i) q^{85} +(5.79555 + 1.55291i) q^{86} +(-0.599900 + 1.62484i) q^{87} +(-15.1427 - 8.74264i) q^{88} +(12.0599 + 3.23143i) q^{89} +(0.585786 + 1.65685i) q^{90} +(-9.45121 - 1.29410i) q^{91} -6.58579i q^{92} +(-0.131652 + 1.42883i) q^{93} +(-0.328427 + 0.568852i) q^{94} +(-1.94975 + 3.37706i) q^{95} +(-8.62372 - 0.794593i) q^{96} +(-7.00000 + 7.00000i) q^{97} +(-4.19187 - 5.60609i) q^{98} +(-7.53553 + 15.7782i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{5} - 8 q^{6}+O(q^{10}) $ 8 * q + 4 * q^3 + 4 * q^5 - 8 * q^6	$ 8 q + 4 q^{3} + 4 q^{5} - 8 q^{6} - 8 q^{11} + 4 q^{12} + 16 q^{13} + 16 q^{15} - 4 q^{16} - 4 q^{17} - 8 q^{18} - 16 q^{19} - 8 q^{20} + 16 q^{21} - 24 q^{22} - 32 q^{23} - 8 q^{27} + 4 q^{30} - 8 q^{31} + 16 q^{33} + 16 q^{34} + 8 q^{36} + 4 q^{38} + 20 q^{39} + 24 q^{40} - 32 q^{41} + 20 q^{42} + 8 q^{44} + 12 q^{45} - 4 q^{46} + 16 q^{47} - 8 q^{48} - 32 q^{50} + 12 q^{51} + 12 q^{52} + 16 q^{55} + 60 q^{56} - 64 q^{57} + 24 q^{59} - 8 q^{60} + 4 q^{61} + 16 q^{62} - 8 q^{63} + 20 q^{65} - 4 q^{66} - 24 q^{67} - 72 q^{69} - 16 q^{70} - 32 q^{71} - 24 q^{72} + 8 q^{73} + 12 q^{75} - 32 q^{76} + 48 q^{77} - 16 q^{78} + 4 q^{80} - 28 q^{81} + 32 q^{83} - 40 q^{85} - 4 q^{87} + 24 q^{89} + 16 q^{90} + 16 q^{93} + 20 q^{94} + 24 q^{95} - 20 q^{96} - 56 q^{97} - 32 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^5 - 8 * q^6 - 8 * q^11 + 4 * q^12 + 16 * q^13 + 16 * q^15 - 4 * q^16 - 4 * q^17 - 8 * q^18 - 16 * q^19 - 8 * q^20 + 16 * q^21 - 24 * q^22 - 32 * q^23 - 8 * q^27 + 4 * q^30 - 8 * q^31 + 16 * q^33 + 16 * q^34 + 8 * q^36 + 4 * q^38 + 20 * q^39 + 24 * q^40 - 32 * q^41 + 20 * q^42 + 8 * q^44 + 12 * q^45 - 4 * q^46 + 16 * q^47 - 8 * q^48 - 32 * q^50 + 12 * q^51 + 12 * q^52 + 16 * q^55 + 60 * q^56 - 64 * q^57 + 24 * q^59 - 8 * q^60 + 4 * q^61 + 16 * q^62 - 8 * q^63 + 20 * q^65 - 4 * q^66 - 24 * q^67 - 72 * q^69 - 16 * q^70 - 32 * q^71 - 24 * q^72 + 8 * q^73 + 12 * q^75 - 32 * q^76 + 48 * q^77 - 16 * q^78 + 4 * q^80 - 28 * q^81 + 32 * q^83 - 40 * q^85 - 4 * q^87 + 24 * q^89 + 16 * q^90 + 16 * q^93 + 20 * q^94 + 24 * q^95 - 20 * q^96 - 56 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i	0.812035	+	0.583609i	$0.198360\pi$
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i	−0.995047	+	0.0994033i	$0.968307\pi$
$3$	1.62484	+	0.599900i	0.938104	+	0.346353i
$3$	1.62484	+	0.599900i	0.938104	+	0.346353i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	0.151613	−	0.565826i	0.0678033	−	0.253045i	−0.923702	−	0.383112i	$-0.874852\pi$
$5$	0.151613	−	0.565826i	0.0678033	−	0.253045i	0.991505	+	0.130067i	$0.0415191\pi$
$6$	−1.00000	+	1.41421i	−0.408248	+	0.577350i
$7$	−1.15539	−	2.38014i	−0.436698	−	0.899608i
$7$	−1.15539	−	2.38014i	−0.436698	−	0.899608i
$8$	−2.12132	+	2.12132i	−0.750000	+	0.750000i
$9$	2.28024	+	1.94949i	0.760080	+	0.649830i
$10$	0.507306	+	0.292893i	0.160424	+	0.0926210i
$11$	1.50851	+	5.62983i	0.454832	+	1.69746i	0.688580	+	0.725160i	$0.258234\pi$
$11$	1.50851	+	5.62983i	0.454832	+	1.69746i	−0.233748	+	0.972297i	$0.575099\pi$
$12$	1.10721	+	1.33195i	0.319623	+	0.384501i
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$14$	2.59808	−	0.500000i	0.694365	−	0.133631i
$15$	0.585786	−	0.828427i	0.151249	−	0.213899i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.914214	−	1.58346i	0.221729	−	0.384047i	−0.733604	−	0.679577i	$-0.762163\pi$
$17$	0.914214	−	1.58346i	0.221729	−	0.384047i	0.955333	+	0.295531i	$0.0954965\pi$
$18$	−2.47323	+	1.69798i	−0.582946	+	0.400217i
$19$	−6.43003	−	1.72292i	−1.47515	−	0.395265i	−0.570456	−	0.821328i	$-0.693233\pi$
$19$	−6.43003	−	1.72292i	−1.47515	−	0.395265i	−0.904693	+	0.426063i	$0.859900\pi$
$20$	0.414214	−	0.414214i	0.0926210	−	0.0926210i
$21$	−0.449490	−	4.56048i	−0.0980867	−	0.995178i
$22$	−5.82843			−1.24262
$23$	−3.29289	−	5.70346i	−0.686616	−	1.18925i	−0.972926	−	0.231116i	$-0.925762\pi$
$23$	−3.29289	−	5.70346i	−0.686616	−	1.18925i	0.286310	−	0.958137i	$-0.407571\pi$
$24$	−4.71940	+	2.17423i	−0.963343	+	0.443814i
$25$	4.03295	+	2.32843i	0.806591	+	0.465685i
$26$	2.38014	+	2.70831i	0.466784	+	0.531143i
$27$	2.53553	+	4.53553i	0.487964	+	0.872864i
$28$	0.189469	−	2.63896i	0.0358062	−	0.498716i
$29$			1.00000i			0.185695i	0.995680	+	0.0928477i	$0.0295970\pi$
$29$			1.00000i			0.185695i	−0.995680	+	0.0928477i	$0.970403\pi$
$30$	0.648586	+	0.780239i	0.118415	+	0.142451i
$31$	0.214413	+	0.800199i	0.0385097	+	0.143720i	0.982504	−	0.186242i	$-0.0596308\pi$
$31$	0.214413	+	0.800199i	0.0385097	+	0.143720i	−0.943994	+	0.329962i	$0.892964\pi$
$32$	−4.82963	+	1.29410i	−0.853766	+	0.228766i
$33$	−0.926246	+	10.0525i	−0.161239	+	1.74992i
$34$	1.29289	+	1.29289i	0.221729	+	0.221729i
$35$	−1.52192	+	0.292893i	−0.257251	+	0.0495080i
$36$	1.00000	+	2.82843i	0.166667	+	0.471405i
$37$	1.03528	−	3.86370i	0.170198	−	0.635189i	−0.827121	−	0.562023i	$-0.810023\pi$
$37$	1.03528	−	3.86370i	0.170198	−	0.635189i	0.997320	−	0.0731657i	$-0.0233102\pi$
$38$	3.32843	−	5.76500i	0.539942	−	0.935207i
$39$	5.04939	−	3.67473i	0.808550	−	0.588428i
$40$	0.878680	+	1.52192i	0.138931	+	0.240636i
$41$	−4.00000	−	4.00000i	−0.624695	−	0.624695i	0.322033	−	0.946728i	$-0.395634\pi$
$41$	−4.00000	−	4.00000i	−0.624695	−	0.624695i	−0.946728	+	0.322033i	$0.895634\pi$
$42$	4.52142	+	0.746165i	0.697670	+	0.115136i
$43$		−	6.00000i		−	0.914991i	−0.889212	−	0.457496i	$-0.848747\pi$
$43$		−	6.00000i		−	0.914991i	0.889212	−	0.457496i	$-0.151253\pi$
$44$	−1.50851	+	5.62983i	−0.227416	+	0.848729i
$45$	1.44879	−	0.994652i	0.215972	−	0.148274i
$46$	6.36138	−	1.70453i	0.937934	−	0.251319i
$47$	0.634472	+	0.170006i	0.0925473	+	0.0247980i	0.304796	−	0.952418i	$-0.401412\pi$
$47$	0.634472	+	0.170006i	0.0925473	+	0.0247980i	−0.212248	+	0.977216i	$0.568079\pi$
$48$	−0.292893	−	1.70711i	−0.0422755	−	0.246400i
$49$	−4.33013	+	5.50000i	−0.618590	+	0.785714i
$50$	−3.29289	+	3.29289i	−0.465685	+	0.465685i
$51$	2.43538	−	2.02445i	0.341021	−	0.283479i
$52$	3.23205	−	1.59808i	0.448205	−	0.221613i
$53$	−7.49706	−	4.32843i	−1.02980	−	0.594555i	−0.112872	−	0.993609i	$-0.536005\pi$
$53$	−7.49706	−	4.32843i	−1.02980	−	0.594555i	−0.916927	+	0.399054i	$0.869338\pi$
$54$	−5.03723	+	1.27526i	−0.685481	+	0.173540i
$55$	3.41421			0.460372
$56$	7.50000	+	2.59808i	1.00223	+	0.347183i
$57$	−9.41421	−	6.65685i	−1.24694	−	0.881722i
$58$	−0.965926	−	0.258819i	−0.126832	−	0.0339846i
$59$	−2.45497	−	9.16208i	−0.319610	−	1.19280i	−0.919620	−	0.392809i	$-0.871503\pi$
$59$	−2.45497	−	9.16208i	−0.319610	−	1.19280i	0.600010	−	0.799992i	$-0.295163\pi$
$60$	0.921519	−	0.424546i	0.118968	−	0.0548086i
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	−0.828427			−0.105210
$63$	2.00548	−	7.67972i	0.252667	−	0.967553i
$64$		−	7.00000i		−	0.875000i
$65$	−1.39425	−	1.58649i	−0.172936	−	0.196780i
$66$	−9.47029	−	3.49648i	−1.16571	−	0.430386i
$67$	3.49025	+	13.0258i	0.426402	+	1.59135i	0.760843	+	0.648936i	$0.224786\pi$
$67$	3.49025	+	13.0258i	0.426402	+	1.59135i	−0.334441	+	0.942417i	$0.608548\pi$
$68$	1.58346	−	0.914214i	0.192023	−	0.110865i
$69$	−1.92893	−	11.2426i	−0.232216	−	1.35345i
$70$	0.110988	−	1.54587i	0.0132656	−	0.184766i
$71$	−0.464466	−	0.464466i	−0.0551220	−	0.0551220i	0.679008	−	0.734130i	$-0.262410\pi$
$71$	−0.464466	−	0.464466i	−0.0551220	−	0.0551220i	−0.734130	+	0.679008i	$0.762410\pi$
$72$	−8.97261	+	0.701625i	−1.05743	+	0.0826873i
$73$	12.3913	−	3.32024i	1.45029	−	0.388605i	0.554167	−	0.832405i	$-0.313037\pi$
$73$	12.3913	−	3.32024i	1.45029	−	0.388605i	0.896126	+	0.443800i	$0.146370\pi$
$74$	3.46410	+	2.00000i	0.402694	+	0.232495i
$75$	5.15610	+	6.20270i	0.595375	+	0.716226i
$76$	−4.70711	−	4.70711i	−0.539942	−	0.539942i
$77$	11.6569	−	10.0951i	1.32842	−	1.15045i
$78$	2.24264	+	5.82843i	0.253929	+	0.659939i
$79$	−0.707107	−	1.22474i	−0.0795557	−	0.137795i	0.823503	−	0.567312i	$-0.192017\pi$
$79$	−0.707107	−	1.22474i	−0.0795557	−	0.137795i	−0.903058	+	0.429518i	$0.858683\pi$
$80$	−0.565826	+	0.151613i	−0.0632613	+	0.0169508i
$81$	1.39898	+	8.89060i	0.155442	+	0.987845i
$82$	4.89898	−	2.82843i	0.541002	−	0.312348i
$83$	−3.07107	−	3.07107i	−0.337093	−	0.337093i	0.518179	−	0.855272i	$-0.326610\pi$
$83$	−3.07107	−	3.07107i	−0.337093	−	0.337093i	−0.855272	+	0.518179i	$0.826610\pi$
$84$	1.89097	−	4.17423i	0.206322	−	0.455446i
$85$	−0.757359	−	0.757359i	−0.0821472	−	0.0821472i
$86$	5.79555	+	1.55291i	0.624951	+	0.167455i
$87$	−0.599900	+	1.62484i	−0.0643161	+	0.174202i
$88$	−15.1427	−	8.74264i	−1.61422	−	0.931969i
$89$	12.0599	+	3.23143i	1.27834	+	0.342531i	0.833221	−	0.552940i	$-0.186494\pi$
$89$	12.0599	+	3.23143i	1.27834	+	0.342531i	0.445121	+	0.895470i	$0.353161\pi$
$90$	0.585786	+	1.65685i	0.0617473	+	0.174648i
$91$	−9.45121	−	1.29410i	−0.990756	−	0.135658i
$92$		−	6.58579i		−	0.686616i
$93$	−0.131652	+	1.42883i	−0.0136517	+	0.148162i
$94$	−0.328427	+	0.568852i	−0.0338747	+	0.0586727i
$95$	−1.94975	+	3.37706i	−0.200040	+	0.346479i
$96$	−8.62372	−	0.794593i	−0.880155	−	0.0810978i
$97$	−7.00000	+	7.00000i	−0.710742	+	0.710742i	−0.966691	−	0.255948i	$-0.917612\pi$
$97$	−7.00000	+	7.00000i	−0.710742	+	0.710742i	0.255948	+	0.966691i	$0.417612\pi$
$98$	−4.19187	−	5.60609i	−0.423443	−	0.566300i
$99$	−7.53553	+	15.7782i	−0.757350	+	1.58577i
$100$	2.32843	+	4.03295i	0.232843	+	0.403295i
$101$	−2.00000	+	3.46410i	−0.199007	+	0.344691i	−0.948207	−	0.317653i	$-0.897105\pi$
$101$	−2.00000	+	3.46410i	−0.199007	+	0.344691i	0.749199	+	0.662344i	$0.230438\pi$
$102$	1.32514	+	2.87636i	0.131209	+	0.284802i
$103$	5.61642	−	3.24264i	0.553402	−	0.319507i	−0.197091	−	0.980385i	$-0.563149\pi$
$103$	5.61642	−	3.24264i	0.553402	−	0.319507i	0.750493	+	0.660878i	$0.229816\pi$
$104$	2.12132	+	10.6066i	0.208013	+	1.04006i
$105$	−2.64859	−	0.437093i	−0.258476	−	0.0426559i
$106$	6.12132	−	6.12132i	0.594555	−	0.594555i
$107$	5.91359	−	3.41421i	0.571688	−	0.330064i	−0.186135	−	0.982524i	$-0.559596\pi$
$107$	5.91359	−	3.41421i	0.571688	−	0.330064i	0.757823	+	0.652460i	$0.226263\pi$
$108$	−0.0719302	+	5.19565i	−0.00692148	+	0.499952i
$109$	−1.91894	−	7.16158i	−0.183801	−	0.685955i	−0.994884	−	0.101024i	$-0.967788\pi$
$109$	−1.91894	−	7.16158i	−0.183801	−	0.685955i	0.811083	−	0.584931i	$-0.198878\pi$
$110$	−0.883663	+	3.29788i	−0.0842540	+	0.314440i
$111$	4.00000	−	5.65685i	0.379663	−	0.536925i
$112$	−1.48356	+	2.19067i	−0.140184	+	0.206999i
$113$			9.00000i			0.846649i	0.905978	+	0.423324i	$0.139137\pi$
$113$			9.00000i			0.846649i	−0.905978	+	0.423324i	$0.860863\pi$
$114$	8.86661	−	7.37051i	0.830434	−	0.690312i
$115$	−3.72641	+	0.998489i	−0.347490	+	0.0931096i
$116$	−0.500000	+	0.866025i	−0.0464238	+	0.0804084i
$117$	10.4089	−	2.94174i	0.962308	−	0.271964i
$118$	9.48528			0.873191
$119$	−4.82514	−	0.346430i	−0.442320	−	0.0317572i
$120$	0.514719	+	3.00000i	0.0469872	+	0.273861i
$121$	−19.8931	+	11.4853i	−1.80846	+	1.04412i
$122$	−0.965926	+	0.258819i	−0.0874508	+	0.0234324i
$123$	−4.09978	−	8.89898i	−0.369664	−	0.802394i
$124$	−0.214413	+	0.800199i	−0.0192548	+	0.0718600i
$125$	4.00000	−	4.00000i	0.357771	−	0.357771i
$126$	6.89898	+	3.92480i	0.614610	+	0.349649i
$127$			16.1421i			1.43238i	0.697904	+	0.716191i	$0.254116\pi$
$127$			16.1421i			1.43238i	−0.697904	+	0.716191i	$0.745884\pi$
$128$	−2.89778	−	0.776457i	−0.256130	−	0.0686298i
$129$	3.59940	−	9.74907i	0.316910	−	0.858357i
$130$	1.89329	−	0.936131i	0.166053	−	0.0821042i
$131$	−11.1097	+	6.41421i	−0.970663	+	0.560412i	−0.899438	−	0.437048i	$-0.856024\pi$
$131$	−11.1097	+	6.41421i	−0.970663	+	0.560412i	−0.0712246	+	0.997460i	$0.522691\pi$
$132$	−5.82843	+	8.24264i	−0.507299	+	0.717430i
$133$	3.32843	+	17.2950i	0.288611	+	1.49967i
$134$	−13.4853			−1.16495
$135$	2.95074	−	0.747027i	0.253960	−	0.0642939i
$136$	1.41970	+	5.29837i	0.121738	+	0.454332i
$137$	2.95422	+	11.0253i	0.252396	+	0.941954i	0.969521	+	0.245009i	$0.0787909\pi$
$137$	2.95422	+	11.0253i	0.252396	+	0.941954i	−0.717125	+	0.696944i	$0.754542\pi$
$138$	11.3588	+	1.04660i	0.966925	+	0.0890929i
$139$	2.92893			0.248429			0.124214	−	0.992255i	$-0.460359\pi$
$139$	2.92893			0.248429			0.124214	+	0.992255i	$0.460359\pi$
$140$	−1.46447	−	0.507306i	−0.123770	−	0.0428752i
$141$	0.928932	+	0.656854i	0.0782302	+	0.0553171i
$142$	0.568852	−	0.328427i	0.0477370	−	0.0275610i
$143$	19.9065	+	6.73413i	1.66467	+	0.563136i
$144$	0.548188	−	2.94949i	0.0456823	−	0.245791i
$145$	0.565826	+	0.151613i	0.0469893	+	0.0125907i
$146$			12.8284i			1.06169i
$147$	−10.3352	+	6.33900i	−0.852436	+	0.522832i
$148$	2.82843	−	2.82843i	0.232495	−	0.232495i
$149$	3.74907	−	13.9917i	0.307136	−	1.14625i	−0.623956	−	0.781460i	$-0.714476\pi$
$149$	3.74907	−	13.9917i	0.307136	−	1.14625i	0.931091	−	0.364786i	$-0.118858\pi$
$150$	−7.32585	+	3.37503i	−0.598153	+	0.275570i
$151$	−19.1528	+	5.13197i	−1.55863	+	0.417634i	−0.932230	−	0.361866i	$-0.882140\pi$
$151$	−19.1528	+	5.13197i	−1.55863	+	0.417634i	−0.626402	+	0.779500i	$0.715473\pi$
$152$	17.2950	−	9.98528i	1.40281	−	0.809913i
$153$	5.17157	−	1.82843i	0.418097	−	0.147820i
$154$	6.73413	+	13.8725i	0.542652	+	1.11788i
$155$	0.485281			0.0389787
$156$	6.21027	−	0.657717i	0.497219	−	0.0526595i
$157$	0.914214	−	1.58346i	0.0729622	−	0.126374i	−0.827236	−	0.561854i	$-0.810088\pi$
$157$	0.914214	−	1.58346i	0.0729622	−	0.126374i	0.900198	+	0.435480i	$0.143421\pi$
$158$	1.36603	−	0.366025i	0.108675	−	0.0291194i
$159$	−9.58492	−	11.5305i	−0.760134	−	0.914429i
$160$			2.92893i			0.231552i
$161$	−9.77044	+	14.4273i	−0.770018	+	1.13703i
$162$	−8.94975	−	0.949747i	−0.703159	−	0.0746192i
$163$	0.562044	−	2.09758i	0.0440227	−	0.164295i	−0.940415	−	0.340029i	$-0.889563\pi$
$163$	0.562044	−	2.09758i	0.0440227	−	0.164295i	0.984438	+	0.175734i	$0.0562298\pi$
$164$	−1.46410	−	5.46410i	−0.114327	−	0.426675i
$165$	5.54757	+	2.04819i	0.431877	+	0.159451i
$166$	3.76127	−	2.17157i	0.291932	−	0.168547i
$167$	−15.5355	+	15.5355i	−1.20218	+	1.20218i	−0.228672	+	0.973503i	$0.573438\pi$
$167$	−15.5355	+	15.5355i	−1.20218	+	1.20218i	−0.973503	+	0.228672i	$0.926562\pi$
$168$	10.6277	+	8.72072i	0.819948	+	0.672818i
$169$	−5.00000	−	12.0000i	−0.384615	−	0.923077i
$170$	0.927572	−	0.535534i	0.0711415	−	0.0410736i
$171$	−11.3032	−	16.4639i	−0.864376	−	1.25903i
$172$	3.00000	−	5.19615i	0.228748	−	0.396203i
$173$	7.74264	+	13.4106i	0.588662	+	1.01959i	0.994408	+	0.105607i	$0.0336785\pi$
$173$	7.74264	+	13.4106i	0.588662	+	1.01959i	−0.405746	+	0.913986i	$0.632988\pi$
$174$	−1.41421	−	1.00000i	−0.107211	−	0.0758098i
$175$	0.882328	−	12.2892i	0.0666977	−	0.928980i
$176$	4.12132	−	4.12132i	0.310656	−	0.310656i
$177$	1.50739	−	16.3597i	0.113302	−	1.22967i
$178$	−6.24264	+	10.8126i	−0.467906	+	0.810436i
$179$	−0.757359	+	1.31178i	−0.0566077	+	0.0980474i	−0.892941	−	0.450175i	$-0.851362\pi$
$179$	−0.757359	+	1.31178i	−0.0566077	+	0.0980474i	0.836333	+	0.548222i	$0.184695\pi$
$180$	1.75201	−	0.137001i	0.130587	−	0.0102114i
$181$			9.14214i			0.679530i	0.940510	+	0.339765i	$0.110347\pi$
$181$			9.14214i			0.679530i	−0.940510	+	0.339765i	$0.889653\pi$
$182$	3.69615	−	8.79423i	0.273977	−	0.651872i
$183$	0.292893	+	1.70711i	0.0216513	+	0.126193i
$184$	19.0841	+	5.11358i	1.40690	+	0.376978i
$185$	−2.02922	−	1.17157i	−0.149191	−	0.0861358i
$186$	−1.34607	−	0.496974i	−0.0986983	−	0.0364399i
$187$	10.2937	+	2.75820i	0.752752	+	0.201699i
$188$	0.464466	+	0.464466i	0.0338747	+	0.0338747i
$189$	7.86566	−	11.2753i	0.572143	−	0.820154i
$190$	−2.75736	−	2.75736i	−0.200040	−	0.200040i
$191$	−14.6969	+	8.48528i	−1.06343	+	0.613973i	−0.926380	−	0.376590i	$-0.877096\pi$
$191$	−14.6969	+	8.48528i	−1.06343	+	0.613973i	−0.137053	+	0.990564i	$0.543763\pi$
$192$	4.19930	−	11.3739i	0.303059	−	0.820841i
$193$	2.73205	−	0.732051i	0.196657	−	0.0526942i	−0.159146	−	0.987255i	$-0.550874\pi$
$193$	2.73205	−	0.732051i	0.196657	−	0.0526942i	0.355803	+	0.934561i	$0.384207\pi$
$194$	−4.94975	−	8.57321i	−0.355371	−	0.615521i
$195$	−1.31371	−	3.41421i	−0.0940766	−	0.244497i
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$	5.00000	+	5.00000i	0.356235	+	0.356235i	0.862423	−	0.506188i	$-0.168946\pi$
$197$	5.00000	+	5.00000i	0.356235	+	0.356235i	−0.506188	+	0.862423i	$0.668946\pi$
$198$	−13.2902	−	11.3625i	−0.944494	−	0.807495i
$199$	13.0519	+	7.53553i	0.925227	+	0.534180i	0.885299	−	0.465023i	$-0.153954\pi$
$199$	13.0519	+	7.53553i	0.925227	+	0.534180i	0.0399279	+	0.999203i	$0.487287\pi$
$200$	−13.4945	+	3.61585i	−0.954207	+	0.255679i
$201$	−2.14306	+	23.2587i	−0.151160	+	1.64054i
$202$	−2.82843	−	2.82843i	−0.199007	−	0.199007i
$203$	2.38014	−	1.15539i	0.167053	−	0.0810928i
$204$	3.12132	−	0.535534i	0.218536	−	0.0374949i
$205$	−2.86976	+	1.65685i	−0.200432	+	0.115720i
$206$	1.67851	+	6.26430i	0.116948	+	0.436455i
$207$	3.61025	−	19.4247i	0.250930	−	1.35011i
$208$	−3.59808	−	0.232051i	−0.249482	−	0.0160898i
$209$		−	38.7990i		−	2.68378i
$210$	1.10770	−	2.44521i	0.0764389	−	0.168736i
$211$	−15.0711			−1.03754			−0.518768	−	0.854915i	$-0.673609\pi$
$211$	−15.0711			−1.03754			−0.518768	+	0.854915i	$0.673609\pi$
$212$	−4.32843	−	7.49706i	−0.297278	−	0.514900i
$213$	−0.476052	−	1.03332i	−0.0326185	−	0.0708018i
$214$	1.76733	+	6.59575i	0.120812	+	0.450876i
$215$	−3.39496	−	0.909676i	−0.231534	−	0.0620394i
$216$	−15.0000	−	4.24264i	−1.02062	−	0.288675i
$217$	1.65685	−	1.43488i	0.112475	−	0.0974059i
$218$	7.41421			0.502154
$219$	22.1258	+	2.03868i	1.49512	+	0.137761i
$220$	2.95680	+	1.70711i	0.199347	+	0.115093i
$221$	−2.92197	−	5.90957i	−0.196553	−	0.397521i
$222$	4.42883	+	5.32780i	0.297243	+	0.357579i
$223$	−3.53553	+	3.53553i	−0.236757	+	0.236757i	−0.815506	−	0.578749i	$-0.803541\pi$
$223$	−3.53553	+	3.53553i	−0.236757	+	0.236757i	0.578749	+	0.815506i	$0.303541\pi$
$224$	8.66025	+	10.0000i	0.578638	+	0.668153i
$225$	4.65685	+	13.1716i	0.310457	+	0.878105i
$226$	−8.69333	−	2.32937i	−0.578272	−	0.154947i
$227$	−5.79555	+	1.55291i	−0.384664	+	0.103071i	−0.445969	−	0.895049i	$-0.647141\pi$
$227$	−5.79555	+	1.55291i	−0.384664	+	0.103071i	0.0613041	+	0.998119i	$0.480474\pi$
$228$	−4.82452	−	10.4721i	−0.319512	−	0.693533i
$229$	−1.42731	+	5.32681i	−0.0943196	+	0.352005i	−0.996915	−	0.0784835i	$-0.974992\pi$
$229$	−1.42731	+	5.32681i	−0.0943196	+	0.352005i	0.902596	+	0.430489i	$0.141659\pi$
$230$		−	3.85786i		−	0.254380i
$231$	24.9966	−	9.41007i	1.64466	−	0.619137i
$232$	−2.12132	−	2.12132i	−0.139272	−	0.139272i
$233$	0.671573	+	1.16320i	0.0439962	+	0.0762037i	0.887185	−	0.461414i	$-0.152658\pi$
$233$	0.671573	+	1.16320i	0.0439962	+	0.0762037i	−0.843189	+	0.537618i	$0.819324\pi$
$234$	0.147466	+	10.8156i	0.00964018	+	0.707041i
$235$	0.192388	−	0.333226i	0.0125500	−	0.0217373i
$236$	2.45497	−	9.16208i	0.159805	−	0.596400i
$237$	−0.414214	−	2.41421i	−0.0269061	−	0.156820i
$238$	1.58346	−	4.57107i	0.102641	−	0.296298i
$239$	4.46447	+	4.46447i	0.288782	+	0.288782i	0.836599	−	0.547816i	$-0.184541\pi$
$239$	4.46447	+	4.46447i	0.288782	+	0.288782i	−0.547816	+	0.836599i	$0.684541\pi$
$240$	−1.01033	−	0.0930924i	−0.0652167	−	0.00600909i
$241$	21.4847	−	5.75682i	1.38395	−	0.370829i	0.511398	−	0.859344i	$-0.329128\pi$
$241$	21.4847	−	5.75682i	1.38395	−	0.370829i	0.872556	+	0.488515i	$0.162461\pi$
$242$	−5.94522	−	22.1879i	−0.382173	−	1.42629i
$243$	−3.06035	+	15.2851i	−0.196322	+	0.980540i
$244$			1.00000i			0.0640184i
$245$	2.45554	+	3.28397i	0.156879	+	0.209805i
$246$	9.65685	−	1.65685i	0.615699	−	0.105637i
$247$	−18.0288	+	15.8442i	−1.14715	+	1.00814i
$248$	−2.15232	−	1.24264i	−0.136672	−	0.0789078i
$249$	−3.14767	−	6.83234i	−0.199476	−	0.432982i
$250$	2.82843	+	4.89898i	0.178885	+	0.309839i
$251$	2.00000			0.126239			0.0631194	−	0.998006i	$-0.479895\pi$
$251$	2.00000			0.126239			0.0631194	+	0.998006i	$0.479895\pi$
$252$	5.57666	−	5.64809i	0.351296	−	0.355796i
$253$	27.1421	−	27.1421i	1.70641	−	1.70641i
$254$	−15.5921	−	4.17789i	−0.978336	−	0.262144i
$255$	−0.776251	−	1.68493i	−0.0486107	−	0.105514i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−9.41421	−	16.3059i	−0.587243	−	1.01713i	−0.994592	−	0.103861i	$-0.966880\pi$
$257$	−9.41421	−	16.3059i	−0.587243	−	1.01713i	0.407349	−	0.913272i	$-0.366453\pi$
$258$	8.48528	+	6.00000i	0.528271	+	0.373544i
$259$	−10.3923	+	2.00000i	−0.645746	+	0.124274i
$260$	−0.414214	−	2.07107i	−0.0256884	−	0.128442i
$261$	−1.94949	+	2.28024i	−0.120670	+	0.141143i
$262$	−3.32024	−	12.3913i	−0.205125	−	0.765538i
$263$	17.7408	+	10.2426i	1.09394	+	0.631588i	0.934623	−	0.355639i	$-0.115737\pi$
$263$	17.7408	+	10.2426i	1.09394	+	0.631588i	0.159320	+	0.987227i	$0.449070\pi$
$264$	−19.3598	−	23.2895i	−1.19151	−	1.43337i
$265$	−3.58579	+	3.58579i	−0.220273	+	0.220273i
$266$	−17.5672	−	1.26127i	−1.07711	−	0.0773331i
$267$	17.6569	+	12.4853i	1.08058	+	0.764087i
$268$	−3.49025	+	13.0258i	−0.213201	+	0.795676i
$269$	−6.06218	−	3.50000i	−0.369618	−	0.213399i	0.303674	−	0.952776i	$-0.401787\pi$
$269$	−6.06218	−	3.50000i	−0.369618	−	0.213399i	−0.673291	+	0.739377i	$0.735120\pi$
$270$	−0.0421357	+	3.04354i	−0.00256430	+	0.185224i
$271$	−1.07968	+	4.02943i	−0.0655860	+	0.244770i	−0.990934	−	0.134348i	$-0.957106\pi$
$271$	−1.07968	+	4.02943i	−0.0655860	+	0.244770i	0.925348	+	0.379118i	$0.123773\pi$
$272$	−1.82843			−0.110865
$273$	−14.5804	−	7.77249i	−0.882447	−	0.470412i
$274$	−11.4142			−0.689558
$275$	−7.02490	+	26.2173i	−0.423618	+	1.58096i
$276$	3.95082	−	10.7009i	0.237811	−	0.644117i
$277$	3.31552	+	1.91421i	0.199210	+	0.115014i	0.596287	−	0.802771i	$-0.296642\pi$
$277$	3.31552	+	1.91421i	0.199210	+	0.115014i	−0.397077	+	0.917785i	$0.629975\pi$
$278$	−0.758063	+	2.82913i	−0.0454656	+	0.169680i
$279$	−1.07107	+	2.24264i	−0.0641232	+	0.134263i
$280$	2.60715	−	3.84980i	0.155807	−	0.230069i
$281$	8.07107	−	8.07107i	0.481480	−	0.481480i	−0.424124	−	0.905604i	$-0.639418\pi$
$281$	8.07107	−	8.07107i	0.481480	−	0.481480i	0.905604	+	0.424124i	$0.139418\pi$
$282$	−0.874898	+	0.727273i	−0.0520994	+	0.0433085i
$283$	−15.4144	−	8.89949i	−0.916290	−	0.529020i	−0.0338402	−	0.999427i	$-0.510774\pi$
$283$	−15.4144	−	8.89949i	−0.916290	−	0.529020i	−0.882449	+	0.470407i	$0.844107\pi$
$284$	−0.170006	−	0.634472i	−0.0100880	−	0.0376490i
$285$	−5.19394	+	4.31755i	−0.307662	+	0.255749i
$286$	−11.6569	+	17.4853i	−0.689284	+	1.03393i
$287$	−4.89898	+	14.1421i	−0.289178	+	0.834784i
$288$	−13.5355	−	6.46447i	−0.797589	−	0.380922i
$289$	6.82843	+	11.8272i	0.401672	+	0.695717i
$290$	−0.292893	+	0.507306i	−0.0171993	+	0.0297900i
$291$	−15.5732	+	7.17461i	−0.912918	+	0.420583i
$292$	12.3913	+	3.32024i	0.725147	+	0.194302i
$293$	9.14214	−	9.14214i	0.534089	−	0.534089i	−0.387697	−	0.921787i	$-0.626729\pi$
$293$	9.14214	−	9.14214i	0.534089	−	0.534089i	0.921787	+	0.387697i	$0.126729\pi$
$294$	−3.44805	−	11.6237i	−0.201094	−	0.677909i
$295$	−5.55635			−0.323503
$296$	6.00000	+	10.3923i	0.348743	+	0.604040i
$297$	−21.7094	+	21.1165i	−1.25971	+	1.22530i
$298$	12.5446	+	7.24264i	0.726690	+	0.419555i
$299$	−23.6962	−	1.52824i	−1.37038	−	0.0883802i
$300$	1.36396	+	7.94975i	0.0787483	+	0.458979i
$301$	−14.2808	+	6.93237i	−0.823134	+	0.399575i
$302$		−	19.8284i		−	1.14100i
$303$	−5.32780	+	4.42883i	−0.306074	+	0.254429i
$304$	1.72292	+	6.43003i	0.0988163	+	0.368787i
$305$	0.565826	−	0.151613i	0.0323991	−	0.00868132i
$306$	0.427623	+	5.46859i	0.0244456	+	0.312618i
$307$	3.53553	+	3.53553i	0.201784	+	0.201784i	0.800764	−	0.598980i	$-0.204427\pi$
$307$	3.53553	+	3.53553i	0.201784	+	0.201784i	−0.598980	+	0.800764i	$0.704427\pi$
$308$	15.1427	−	2.91421i	0.862835	−	0.166053i
$309$	11.0711	−	1.89949i	0.629811	−	0.108058i
$310$	−0.125600	+	0.468746i	−0.00713360	+	0.0266230i
$311$	0.928932	−	1.60896i	0.0526749	−	0.0912356i	−0.838486	−	0.544924i	$-0.816559\pi$
$311$	0.928932	−	1.60896i	0.0526749	−	0.0912356i	0.891161	+	0.453688i	$0.149892\pi$
$312$	−2.91609	+	18.5067i	−0.165091	+	1.04773i
$313$	−11.8284	−	20.4874i	−0.668582	−	1.15802i	−0.978301	−	0.207190i	$-0.933568\pi$
$313$	−11.8284	−	20.4874i	−0.668582	−	1.15802i	0.309718	−	0.950828i	$-0.399765\pi$
$314$	1.29289	+	1.29289i	0.0729622	+	0.0729622i
$315$	−4.04133	−	2.29910i	−0.227703	−	0.129539i
$316$		−	1.41421i		−	0.0795557i
$317$	4.38153	−	16.3521i	0.246091	−	0.918425i	−0.726741	−	0.686912i	$-0.758966\pi$
$317$	4.38153	−	16.3521i	0.246091	−	0.918425i	0.972832	−	0.231513i	$-0.0743676\pi$
$318$	13.6184	−	6.27401i	0.763681	−	0.351829i
$319$	−5.62983	+	1.50851i	−0.315210	+	0.0844602i
$320$	−3.96078	−	1.06129i	−0.221415	−	0.0593278i
$321$	11.6569	−	2.00000i	0.650622	−	0.111629i
$322$	−11.4069	−	13.1716i	−0.635683	−	0.734023i
$323$	−8.60660	+	8.60660i	−0.478884	+	0.478884i
$324$	−3.23375	+	8.39898i	−0.179653	+	0.466610i
$325$	15.0512	−	7.44201i	0.834890	−	0.412808i
$326$	1.88064	+	1.08579i	0.104159	+	0.0601361i
$327$	1.17826	−	12.7876i	0.0651577	−	0.707157i
$328$	16.9706			0.937043
$329$	−0.328427	−	1.70656i	−0.0181068	−	0.0940856i
$330$	−3.41421	+	4.82843i	−0.187946	+	0.265796i
$331$	22.6566	+	6.07082i	1.24532	+	0.333682i	0.820527	−	0.571608i	$-0.193680\pi$
$331$	22.6566	+	6.07082i	1.24532	+	0.333682i	0.424793	+	0.905291i	$0.360347\pi$
$332$	−1.12409	−	4.19516i	−0.0616924	−	0.230239i
$333$	9.89293	−	6.79191i	0.542129	−	0.372194i
$334$	−10.9853	−	19.0271i	−0.601088	−	1.04111i
$335$	7.89949			0.431596
$336$	−3.72474	+	2.66951i	−0.203201	+	0.145634i
$337$		−	17.1421i		−	0.933792i	−0.884312	−	0.466896i	$-0.845372\pi$
$337$		−	17.1421i		−	0.933792i	0.884312	−	0.466896i	$-0.154628\pi$
$338$	12.8852	−	1.72380i	0.700863	−	0.0937624i
$339$	−5.39910	+	14.6236i	−0.293239	+	0.794245i
$340$	−0.277213	−	1.03457i	−0.0150340	−	0.0561075i
$341$	−4.18154	+	2.41421i	−0.226443	+	0.130737i
$342$	18.8284	−	6.65685i	1.01812	−	0.359961i
$343$	18.0938	+	3.95164i	0.976972	+	0.213368i
$344$	12.7279	+	12.7279i	0.686244	+	0.686244i
$345$	−6.65383	−	0.613086i	−0.358230	−	0.0330075i
$346$	−14.9576	+	4.00789i	−0.804127	+	0.215465i
$347$	4.05845	+	2.34315i	0.217869	+	0.125787i	0.604963	−	0.796254i	$-0.293188\pi$
$347$	4.05845	+	2.34315i	0.217869	+	0.125787i	−0.387094	+	0.922040i	$0.626521\pi$
$348$	−1.33195	+	1.10721i	−0.0714001	+	0.0593525i
$349$	3.00000	+	3.00000i	0.160586	+	0.160586i	0.782826	−	0.622240i	$-0.213777\pi$
$349$	3.00000	+	3.00000i	0.160586	+	0.160586i	−0.622240	+	0.782826i	$0.713777\pi$
$350$	11.6421	+	4.03295i	0.622298	+	0.215570i
$351$	18.6777	+	1.46447i	0.996940	+	0.0781674i
$352$	−14.5711	−	25.2378i	−0.776641	−	1.34518i
$353$	−6.92721	+	1.85614i	−0.368698	+	0.0987923i	−0.438411	−	0.898775i	$-0.644458\pi$
$353$	−6.92721	+	1.85614i	−0.368698	+	0.0987923i	0.0697126	+	0.997567i	$0.477792\pi$
$354$	15.4121	+	5.69022i	0.819144	+	0.302432i
$355$	−0.333226	+	0.192388i	−0.0176858	+	0.0102109i
$356$	8.82843	+	8.82843i	0.467906	+	0.467906i
$357$	−7.63228	−	3.45750i	−0.403943	−	0.182990i
$358$	−1.07107	−	1.07107i	−0.0566077	−	0.0566077i
$359$	21.7191	+	5.81962i	1.14629	+	0.307148i	0.781478	−	0.623933i	$-0.214466\pi$
$359$	21.7191	+	5.81962i	1.14629	+	0.307148i	0.364813	+	0.931081i	$0.381133\pi$
$360$	−0.963364	+	5.18331i	−0.0507737	+	0.273185i
$361$	21.9223	+	12.6569i	1.15381	+	0.666150i
$362$	−8.83062	−	2.36616i	−0.464127	−	0.124363i
$363$	−39.2132	+	6.72792i	−2.05816	+	0.353124i
$364$	−7.53794	−	5.84632i	−0.395095	−	0.306431i
$365$		−	7.51472i		−	0.393338i
$366$	−1.72474	−	0.158919i	−0.0901539	−	0.00830681i
$367$	−7.19239	+	12.4576i	−0.375440	+	0.650280i	−0.990393	−	0.138283i	$-0.955842\pi$
$367$	−7.19239	+	12.4576i	−0.375440	+	0.650280i	0.614953	+	0.788564i	$0.289175\pi$
$368$	−3.29289	+	5.70346i	−0.171654	+	0.297313i
$369$	−1.32300	−	16.9189i	−0.0688725	−	0.880764i
$370$	1.65685	−	1.65685i	0.0861358	−	0.0861358i
$371$	−1.64020	+	22.8451i	−0.0851551	+	1.18606i
$372$	−0.828427	+	1.17157i	−0.0429519	+	0.0607432i
$373$	−11.3995	−	19.7445i	−0.590243	−	1.02233i	−0.994199	−	0.107553i	$-0.965698\pi$
$373$	−11.3995	−	19.7445i	−0.590243	−	1.02233i	0.403956	−	0.914778i	$-0.367635\pi$
$374$	−5.32843	+	9.22911i	−0.275526	+	0.477226i
$375$	8.89898	−	4.09978i	0.459541	−	0.211712i
$376$	−1.70656	+	0.985281i	−0.0880090	+	0.0508120i
$377$	3.00000	+	2.00000i	0.154508	+	0.103005i
$378$	8.85528	+	10.5159i	0.455466	+	0.540879i
$379$	−0.928932	+	0.928932i	−0.0477160	+	0.0477160i	−0.730562	−	0.682846i	$-0.760742\pi$
$379$	−0.928932	+	0.928932i	−0.0477160	+	0.0477160i	0.682846	+	0.730562i	$0.260742\pi$
$380$	−3.37706	+	1.94975i	−0.173240	+	0.100020i
$381$	−9.68367	+	26.2285i	−0.496110	+	1.34372i
$382$	−4.39230	−	16.3923i	−0.224730	−	0.838703i
$383$	1.85614	−	6.92721i	0.0948443	−	0.353964i	−0.902151	−	0.431419i	$-0.858013\pi$
$383$	1.85614	−	6.92721i	0.0948443	−	0.353964i	0.996996	+	0.0774556i	$0.0246796\pi$
$384$	−4.24264	−	3.00000i	−0.216506	−	0.153093i
$385$	−3.94476	−	8.12630i	−0.201044	−	0.414155i
$386$			2.82843i			0.143963i
$387$	11.6969	−	13.6814i	0.594589	−	0.695466i
$388$	−9.56218	+	2.56218i	−0.485446	+	0.130075i
$389$	4.67157	−	8.09140i	0.236858	−	0.410250i	−0.722953	−	0.690897i	$-0.757216\pi$
$389$	4.67157	−	8.09140i	0.236858	−	0.410250i	0.959811	+	0.280647i	$0.0905490\pi$
$390$	3.63789	−	0.385281i	0.184212	−	0.0195095i
$391$	−12.0416			−0.608971
$392$	−2.48168	−	20.8528i	−0.125344	−	1.05323i
$393$	−21.8995	+	3.75736i	−1.10468	+	0.189534i
$394$	−6.12372	+	3.53553i	−0.308509	+	0.178118i
$395$	−0.800199	+	0.214413i	−0.0402624	+	0.0107883i
$396$	−14.4151	+	9.89653i	−0.724384	+	0.497319i
$397$	7.28372	−	27.1832i	0.365559	−	1.36429i	−0.501101	−	0.865389i	$-0.667072\pi$
$397$	7.28372	−	27.1832i	0.365559	−	1.36429i	0.866661	−	0.498898i	$-0.166262\pi$
$398$	−10.6569	+	10.6569i	−0.534180	+	0.534180i
$399$	−4.96711	+	30.0984i	−0.248667	+	1.50681i
$400$		−	4.65685i		−	0.232843i
$401$	11.8255	+	3.16863i	0.590536	+	0.158234i	0.541698	−	0.840573i	$-0.317782\pi$
$401$	11.8255	+	3.16863i	0.590536	+	0.158234i	0.0488381	+	0.998807i	$0.484448\pi$
$402$	−21.9115	−	8.08983i	−1.09285	−	0.403484i
$403$	2.82942	+	0.957160i	0.140944	+	0.0476795i
$404$	−3.46410	+	2.00000i	−0.172345	+	0.0995037i
$405$	5.24264	+	0.556349i	0.260509	+	0.0276452i
$406$	0.500000	+	2.59808i	0.0248146	+	0.128940i
$407$	23.3137			1.15562
$408$	−0.871713	+	9.46071i	−0.0431562	+	0.468375i
$409$	6.91770	+	25.8172i	0.342058	+	1.27658i	0.896012	+	0.444030i	$0.146452\pi$
$409$	6.91770	+	25.8172i	0.342058	+	1.27658i	−0.553954	+	0.832547i	$0.686882\pi$
$410$	−0.857651	−	3.20080i	−0.0423564	−	0.158076i
$411$	−1.81393	+	19.6866i	−0.0894746	+	0.971069i
$412$	6.48528			0.319507
$413$	−18.9706	+	16.4290i	−0.933480	+	0.808418i
$414$	17.8284	+	8.51472i	0.876219	+	0.418476i
$415$	−2.20330	+	1.27208i	−0.108156	+	0.0624439i
$416$	−5.77697	+	17.0771i	−0.283239	+	0.837273i
$417$	4.75906	+	1.75707i	0.233052	+	0.0860440i
$418$	37.4769	+	10.0419i	1.83306	+	0.491166i
$419$		−	16.9289i		−	0.827032i	−0.910497	−	0.413516i	$-0.864300\pi$
$419$		−	16.9289i		−	0.827032i	0.910497	−	0.413516i	$-0.135700\pi$
$420$	−2.07520	−	1.70283i	−0.101259	−	0.0830895i
$421$	−11.0711	+	11.0711i	−0.539571	+	0.539571i	−0.923403	−	0.383832i	$-0.874604\pi$
$421$	−11.0711	+	11.0711i	−0.539571	+	0.539571i	0.383832	+	0.923403i	$0.374604\pi$
$422$	3.90068	−	14.5575i	0.189882	−	0.708650i
$423$	1.11532	+	1.62455i	0.0542289	+	0.0789885i
$424$	25.0856	−	6.72168i	1.21827	−	0.326433i
$425$	7.37396	−	4.25736i	0.357690	−	0.206512i
$426$	1.12132	−	0.192388i	0.0543281	−	0.00932124i
$427$	1.48356	−	2.19067i	0.0717947	−	0.106014i
$428$	6.82843			0.330064
$429$	28.3052	+	22.8838i	1.36659	+	1.10484i
$430$	1.75736	−	3.04384i	0.0847474	−	0.146787i
$431$	14.6546	−	3.92669i	0.705888	−	0.189142i	0.112022	−	0.993706i	$-0.464267\pi$
$431$	14.6546	−	3.92669i	0.705888	−	0.189142i	0.593866	+	0.804564i	$0.297601\pi$
$432$	2.66012	−	4.46360i	0.127985	−	0.214755i
$433$		−	5.14214i		−	0.247115i	−0.992337	−	0.123558i	$-0.960570\pi$
$433$		−	5.14214i		−	0.247115i	0.992337	−	0.123558i	$-0.0394304\pi$
$434$	0.957160	+	1.97177i	0.0459452	+	0.0946481i
$435$	0.828427	+	0.585786i	0.0397200	+	0.0280863i
$436$	1.91894	−	7.16158i	0.0919005	−	0.342977i
$437$	11.3468	+	42.3468i	0.542790	+	2.02572i
$438$	−7.69578	+	20.8442i	−0.367719	+	0.995974i
$439$	−27.8359	+	16.0711i	−1.32854	+	0.767030i	−0.985073	−	0.172136i	$-0.944933\pi$
$439$	−27.8359	+	16.0711i	−1.32854	+	0.767030i	−0.343462	+	0.939167i	$0.611600\pi$
$440$	−7.24264	+	7.24264i	−0.345279	+	0.345279i
$441$	−20.5959	+	4.09978i	−0.980758	+	0.195227i
$442$	6.46447	−	1.29289i	0.307483	−	0.0614967i
$443$	4.56575	−	2.63604i	0.216925	−	0.125242i	−0.387600	−	0.921828i	$-0.626696\pi$
$443$	4.56575	−	2.63604i	0.216925	−	0.125242i	0.604526	+	0.796586i	$0.293363\pi$
$444$	6.29253	−	2.89898i	0.298630	−	0.137579i
$445$	3.65685	−	6.33386i	0.173352	−	0.300254i
$446$	−2.50000	−	4.33013i	−0.118378	−	0.205037i
$447$	14.4853	−	20.4853i	0.685130	−	0.968921i
$448$	−16.6610	+	8.08776i	−0.787157	+	0.382111i
$449$	2.00000	−	2.00000i	0.0943858	−	0.0943858i	−0.658337	−	0.752723i	$-0.728740\pi$
$449$	2.00000	−	2.00000i	0.0943858	−	0.0943858i	0.752723	+	0.658337i	$0.228740\pi$
$450$	−13.9280	+	1.08912i	−0.656574	+	0.0513417i
$451$	16.4853	−	28.5533i	0.776262	−	1.34452i
$452$	−4.50000	+	7.79423i	−0.211662	+	0.366610i
$453$	−34.1990	−	3.15111i	−1.60681	−	0.148052i
$454$		−	6.00000i		−	0.281594i
$455$	−2.16516	+	5.15154i	−0.101504	+	0.241508i
$456$	34.0919	−	5.84924i	1.59650	−	0.273916i
$457$	4.29224	+	1.15010i	0.200782	+	0.0537995i	0.357809	−	0.933795i	$-0.383524\pi$
$457$	4.29224	+	1.15010i	0.200782	+	0.0537995i	−0.157026	+	0.987594i	$0.550191\pi$
$458$	−4.77589	−	2.75736i	−0.223163	−	0.128843i
$459$	9.49988	+	0.131519i	0.443416	+	0.00613879i
$460$	−3.72641	−	0.998489i	−0.173745	−	0.0465548i
$461$	28.0711	+	28.0711i	1.30740	+	1.30740i	0.923285	+	0.384115i	$0.125493\pi$
$461$	28.0711	+	28.0711i	1.30740	+	1.30740i	0.384115	+	0.923285i	$0.374507\pi$
$462$	2.61982	+	26.5804i	0.121885	+	1.23663i
$463$	4.00000	+	4.00000i	0.185896	+	0.185896i	0.793919	−	0.608023i	$-0.208037\pi$
$463$	4.00000	+	4.00000i	0.185896	+	0.185896i	−0.608023	+	0.793919i	$0.708037\pi$
$464$	0.866025	−	0.500000i	0.0402042	−	0.0232119i
$465$	0.788507	+	0.291121i	0.0365661	+	0.0135004i
$466$	−1.29738	+	0.347632i	−0.0600999	+	0.0161037i
$467$	−11.4853	−	19.8931i	−0.531475	−	0.920542i	−0.999325	−	0.0367344i	$-0.988304\pi$
$467$	−11.4853	−	19.8931i	−0.531475	−	0.920542i	0.467850	−	0.883808i	$-0.345029\pi$
$468$	10.4853	+	2.65685i	0.484682	+	0.122813i
$469$	26.9706	−	23.3572i	1.24538	−	1.07853i
$470$	0.272078	+	0.272078i	0.0125500	+	0.0125500i
$471$	2.43538	−	2.02445i	0.112216	−	0.0932816i
$472$	24.6435	+	14.2279i	1.13431	+	0.654893i
$473$	33.7790	−	9.05105i	1.55316	−	0.416168i
$474$	2.43916	+	0.224745i	0.112034	+	0.0103229i
$475$	−21.9203	−	21.9203i	−1.00577	−	1.00577i
$476$	−4.00548	−	2.71259i	−0.183591	−	0.124331i
$477$	−8.65685	−	24.4853i	−0.396370	−	1.12110i
$478$	−5.46783	+	3.15685i	−0.250093	+	0.144391i
$479$	−7.63135	−	28.4806i	−0.348685	−	1.30131i	−0.888247	−	0.459366i	$-0.848077\pi$
$479$	−7.63135	−	28.4806i	−0.348685	−	1.30131i	0.539562	−	0.841946i	$-0.318590\pi$
$480$	−1.75707	+	4.75906i	−0.0801988	+	0.217220i
$481$	−9.52056	−	10.8332i	−0.434100	−	0.493953i
$482$			22.2426i			1.01312i
$483$	−24.5304	+	17.5808i	−1.11617	+	0.799955i
$484$	−22.9706			−1.04412
$485$	2.89949	+	5.02207i	0.131659	+	0.228041i
$486$	−13.9722	−	6.91215i	−0.633792	−	0.313541i
$487$	2.41818	+	9.02479i	0.109578	+	0.408952i	0.998824	−	0.0484774i	$-0.0154369\pi$
$487$	2.41818	+	9.02479i	0.109578	+	0.408952i	−0.889246	+	0.457429i	$0.848770\pi$
$488$	−2.89778	−	0.776457i	−0.131176	−	0.0351486i
$489$	2.17157	−	3.07107i	0.0982019	−	0.138878i
$490$	−3.80761	+	1.52192i	−0.172010	+	0.0687532i
$491$	−9.21320			−0.415786			−0.207893	−	0.978152i	$-0.566661\pi$
$491$	−9.21320			−0.415786			−0.207893	+	0.978152i	$0.566661\pi$
$492$	0.898979	−	9.75663i	0.0405291	−	0.439863i
$493$	1.58346	+	0.914214i	0.0713156	+	0.0411741i
$494$	−10.6382	−	21.5153i	−0.478633	−	0.968019i
$495$	7.78522	+	6.65597i	0.349920	+	0.299164i
$496$	0.585786	−	0.585786i	0.0263026	−	0.0263026i
$497$	−0.568852	+	1.64214i	−0.0255165	+	0.0736598i
$498$	7.41421	−	1.27208i	0.332239	−	0.0570032i
$499$	17.7181	+	4.74756i	0.793172	+	0.212530i	0.632584	−	0.774492i	$-0.281994\pi$
$499$	17.7181	+	4.74756i	0.793172	+	0.212530i	0.160588	+	0.987022i	$0.448661\pi$
$500$	5.46410	−	1.46410i	0.244362	−	0.0654766i
$501$	−34.5626	+	15.9231i	−1.54414	+	0.711390i
$502$	−0.517638	+	1.93185i	−0.0231033	+	0.0862228i
$503$		−	13.0711i		−	0.582810i	−0.956600	−	0.291405i	$-0.905877\pi$
$503$		−	13.0711i		−	0.582810i	0.956600	−	0.291405i	$-0.0941227\pi$
$504$	12.0369	+	20.5454i	0.536165	+	0.915165i
$505$	1.65685	+	1.65685i	0.0737290	+	0.0737290i
$506$	19.1924	+	33.2422i	0.853206	+	1.47780i
$507$	−0.925417	−	22.4976i	−0.0410992	−	0.999155i
$508$	−8.07107	+	13.9795i	−0.358096	+	0.620240i
$509$	−6.91770	+	25.8172i	−0.306621	+	1.14433i	0.624919	+	0.780689i	$0.285132\pi$
$509$	−6.91770	+	25.8172i	−0.306621	+	1.14433i	−0.931541	+	0.363637i	$0.881535\pi$
$510$	1.82843	−	0.313708i	0.0809641	−	0.0138912i
$511$	−22.2195	−	25.6569i	−0.982932	−	1.13499i
$512$	7.77817	+	7.77817i	0.343750	+	0.343750i
$513$	−8.48919	−	33.5321i	−0.374807	−	1.48048i
$514$	18.1869	−	4.87316i	0.802188	−	0.214946i
$515$	−0.983251	−	3.66954i	−0.0433272	−	0.161699i
$516$	7.99171	−	6.64324i	0.351815	−	0.292452i
$517$			3.82843i			0.168374i
$518$	0.757875	−	10.5558i	0.0332991	−	0.463797i
$519$	4.53553	+	26.4350i	0.199088	+	1.16037i
$520$	6.32311	+	0.407797i	0.277287	+	0.0178831i
$521$	4.72490	+	2.72792i	0.207002	+	0.119512i	0.599917	−	0.800062i	$-0.295200\pi$
$521$	4.72490	+	2.72792i	0.207002	+	0.119512i	−0.392916	+	0.919575i	$0.628534\pi$
$522$	−1.69798	−	2.47323i	−0.0743184	−	0.108250i
$523$	−4.75736	−	8.23999i	−0.208025	−	0.360310i	0.743067	−	0.669217i	$-0.233370\pi$
$523$	−4.75736	−	8.23999i	−0.208025	−	0.360310i	−0.951092	+	0.308907i	$0.900037\pi$
$524$	−12.8284			−0.560412
$525$	8.80597	−	19.4388i	0.384324	−	0.848379i
$526$	−14.4853	+	14.4853i	−0.631588	+	0.631588i
$527$	1.46311	+	0.392038i	0.0637339	+	0.0170774i
$528$	9.16889	−	4.22412i	0.399025	−	0.183831i
$529$	−10.1863	+	17.6432i	−0.442882	+	0.767095i
$530$	−2.53553	−	4.39167i	−0.110137	−	0.190762i
$531$	12.2635	−	25.6777i	0.532189	−	1.11432i
$532$	−5.76500	+	16.6421i	−0.249945	+	0.721528i
$533$	−20.0000	+	4.00000i	−0.866296	+	0.173259i
$534$	−16.6298	+	13.8238i	−0.719641	+	0.598214i
$535$	−1.03528	−	3.86370i	−0.0447589	−	0.167042i
$536$	−35.0358	−	20.2279i	−1.51332	−	0.873713i
$537$	−2.01753	+	1.67711i	−0.0870629	+	0.0723725i
$538$	4.94975	−	4.94975i	0.213399	−	0.213399i
$539$	−37.4961	−	16.0811i	−1.61507	−	0.692661i
$540$	2.92893	+	0.828427i	0.126041	+	0.0356498i
$541$	−8.93622	+	33.3504i	−0.384198	+	1.43385i	0.455229	+	0.890375i	$0.349558\pi$
$541$	−8.93622	+	33.3504i	−0.384198	+	1.43385i	−0.839427	+	0.543473i	$0.817109\pi$
$542$	−3.61269	−	2.08579i	−0.155178	−	0.0895922i
$543$	−5.48437	+	14.8545i	−0.235357	+	0.637470i
$544$	−2.36616	+	8.83062i	−0.101448	+	0.378610i
$545$	−4.34315			−0.186040
$546$	11.2813	−	12.0719i	0.482797	−	0.516631i
$547$	15.0711			0.644392			0.322196	−	0.946673i	$-0.395579\pi$
$547$	15.0711			0.644392			0.322196	+	0.946673i	$0.395579\pi$
$548$	−2.95422	+	11.0253i	−0.126198	+	0.470977i
$549$	−0.548188	+	2.94949i	−0.0233961	+	0.125881i
$550$	−23.5058	−	13.5711i	−1.00229	−	0.578672i
$551$	1.72292	−	6.43003i	0.0733989	−	0.273928i
$552$	27.9411	+	19.7574i	1.18925	+	0.840929i
$553$	−2.09808	+	3.09808i	−0.0892193	+	0.131744i
$554$	−2.70711	+	2.70711i	−0.115014	+	0.115014i
$555$	−2.59435	−	3.12096i	−0.110124	−	0.132477i
$556$	2.53653	+	1.46447i	0.107573	+	0.0621072i
$557$	−8.47061	−	31.6127i	−0.358911	−	1.33948i	−0.875490	−	0.483236i	$-0.839461\pi$
$557$	−8.47061	−	31.6127i	−0.358911	−	1.33948i	0.516579	−	0.856239i	$-0.327205\pi$
$558$	−1.88901	−	1.61501i	−0.0799682	−	0.0683688i
$559$	−18.0000	−	12.0000i	−0.761319	−	0.507546i
$560$	1.01461	+	1.17157i	0.0428752	+	0.0495080i
$561$	15.0711	+	10.6569i	0.636301	+	0.449933i
$562$	5.70711	+	9.88500i	0.240740	+	0.416974i
$563$	1.75736	−	3.04384i	0.0740639	−	0.128282i	−0.826615	−	0.562768i	$-0.809736\pi$
$563$	1.75736	−	3.04384i	0.0740639	−	0.128282i	0.900679	+	0.434486i	$0.143070\pi$
$564$	0.476052	+	1.03332i	0.0200454	+	0.0435106i
$565$	5.09244	+	1.36451i	0.214240	+	0.0574055i
$566$	12.5858	−	12.5858i	0.529020	−	0.529020i
$567$	19.5445	−	13.6019i	0.820792	−	0.571227i
$568$	1.97056			0.0826830
$569$	−21.7426	−	37.6594i	−0.911499	−	1.57876i	−0.811948	−	0.583730i	$-0.801593\pi$
$569$	−21.7426	−	37.6594i	−0.911499	−	1.57876i	−0.0995511	−	0.995032i	$-0.531741\pi$
$570$	−2.82614	−	6.13442i	−0.118374	−	0.256943i
$571$	−12.1604	−	7.02082i	−0.508897	−	0.293812i	0.223483	−	0.974708i	$-0.428257\pi$
$571$	−12.1604	−	7.02082i	−0.508897	−	0.293812i	−0.732380	+	0.680896i	$0.761591\pi$
$572$	13.8725	+	15.7852i	0.580037	+	0.660012i
$573$	−28.9706	+	4.97056i	−1.21026	+	0.207648i
$574$	−12.3923	−	8.39230i	−0.517245	−	0.350288i
$575$		−	30.6690i		−	1.27899i
$576$	13.6464	−	15.9617i	0.568601	−	0.665070i
$577$	−2.53617	−	9.46510i	−0.105582	−	0.394037i	0.892829	−	0.450397i	$-0.148717\pi$
$577$	−2.53617	−	9.46510i	−0.105582	−	0.394037i	−0.998411	+	0.0563594i	$0.982051\pi$
$578$	−13.1915	+	3.53465i	−0.548694	+	0.147022i
$579$	4.87832	+	0.449490i	0.202736	+	0.0186802i
$580$	0.414214	+	0.414214i	0.0171993	+	0.0171993i
$581$	−3.76127	+	10.8579i	−0.156044	+	0.450460i
$582$	−2.89949	−	16.8995i	−0.120188	−	0.700507i
$583$	13.0589	−	48.7366i	0.540846	−	2.01846i
$584$	−19.2426	+	33.3292i	−0.796266	+	1.37917i
$585$	−0.0863838	−	6.33566i	−0.00357153	−	0.261947i
$586$	6.46447	+	11.1968i	0.267045	+	0.462535i
$587$	−23.5355	−	23.5355i	−0.971415	−	0.971415i	0.0281872	−	0.999603i	$-0.491027\pi$
$587$	−23.5355	−	23.5355i	−0.971415	−	0.971415i	−0.999603	+	0.0281872i	$0.991027\pi$
$588$	−12.1201	+	0.322117i	−0.499824	+	0.0132839i
$589$		−	5.51472i		−	0.227230i
$590$	1.43809	−	5.36702i	0.0592052	−	0.220957i
$591$	5.12472	+	11.1237i	0.210803	+	0.457569i
$592$	−3.86370	+	1.03528i	−0.158797	+	0.0425496i
$593$	−32.2188	−	8.63300i	−1.32307	−	0.354515i	−0.472941	−	0.881094i	$-0.656808\pi$
$593$	−32.2188	−	8.63300i	−1.32307	−	0.354515i	−0.850126	+	0.526579i	$0.823474\pi$
$594$	−14.7782	−	26.4350i	−0.606356	−	1.08464i
$595$	−0.927572	+	2.67767i	−0.0380267	+	0.109774i
$596$	10.2426	−	10.2426i	0.419555	−	0.419555i
$597$	16.6868	+	20.0739i	0.682945	+	0.821571i
$598$	7.60918	−	22.4932i	0.311163	−	0.919815i
$599$	21.7122	+	12.5355i	0.887136	+	0.512188i	0.873005	−	0.487712i	$-0.162168\pi$
$599$	21.7122	+	12.5355i	0.887136	+	0.512188i	0.0141312	+	0.999900i	$0.495502\pi$
$600$	−24.0957	−	2.22018i	−0.983701	−	0.0906386i
$601$	45.2843			1.84718			0.923592	−	0.383377i	$-0.125239\pi$
$601$	45.2843			1.84718			0.923592	+	0.383377i	$0.125239\pi$
$602$	−3.00000	−	15.5885i	−0.122271	−	0.635338i
$603$	−17.4350	+	36.5061i	−0.710009	+	1.48664i
$604$	−19.1528	−	5.13197i	−0.779316	−	0.208817i
$605$	3.48263	+	12.9973i	0.141589	+	0.528417i
$606$	−2.89898	−	6.29253i	−0.117763	−	0.255617i
$607$	−11.4853	−	19.8931i	−0.466173	−	0.807436i	0.533080	−	0.846065i	$-0.321034\pi$
$607$	−11.4853	−	19.8931i	−0.466173	−	0.807436i	−0.999254	+	0.0386289i	$0.987701\pi$
$608$	33.2843			1.34986
$609$	4.56048	−	0.449490i	0.184800	−	0.0182142i
$610$			0.585786i			0.0237178i
$611$	1.77896	−	1.56340i	0.0719692	−	0.0632486i
$612$	5.39293	+	1.00232i	0.217996	+	0.0405165i
$613$	1.58970	+	5.93285i	0.0642074	+	0.239625i	0.990570	−	0.137008i	$-0.0437485\pi$
$613$	1.58970	+	5.93285i	0.0642074	+	0.239625i	−0.926363	+	0.376633i	$0.877082\pi$
$614$	−4.33013	+	2.50000i	−0.174750	+	0.100892i
$615$	−5.65685	+	0.970563i	−0.228106	+	0.0391369i
$616$	−3.31291	+	46.1429i	−0.133481	+	1.85915i
$617$	7.07107	+	7.07107i	0.284670	+	0.284670i	0.834968	−	0.550298i	$-0.185486\pi$
$617$	7.07107	+	7.07107i	0.284670	+	0.284670i	−0.550298	+	0.834968i	$0.685486\pi$
$618$	−1.03063	+	11.1855i	−0.0414581	+	0.449945i
$619$	−21.7191	+	5.81962i	−0.872965	+	0.233910i	−0.667369	−	0.744727i	$-0.732580\pi$
$619$	−21.7191	+	5.81962i	−0.872965	+	0.233910i	−0.205595	+	0.978637i	$0.565913\pi$
$620$	0.420266	+	0.242641i	0.0168783	+	0.00974468i
$621$	17.5190	−	29.3963i	0.703013	−	1.17963i
$622$	1.31371	+	1.31371i	0.0526749	+	0.0526749i
$623$	−6.24264	−	32.4377i	−0.250106	−	1.29959i
$624$	−5.70711	−	2.53553i	−0.228467	−	0.101503i
$625$	9.98528	+	17.2950i	0.399411	+	0.691801i
$626$	22.8508	−	6.12284i	0.913300	−	0.244718i
$627$	23.2755	−	63.0423i	0.929535	−	2.51767i
$628$	1.58346	−	0.914214i	0.0631871	−	0.0364811i
$629$	−5.17157	−	5.17157i	−0.206204	−	0.206204i
$630$	3.26673	−	3.30857i	0.130150	−	0.131817i
$631$	13.0711	+	13.0711i	0.520351	+	0.520351i	0.917677	−	0.397326i	$-0.130062\pi$
$631$	13.0711	+	13.0711i	0.520351	+	0.520351i	−0.397326	+	0.917677i	$0.630062\pi$
$632$	4.09808	+	1.09808i	0.163013	+	0.0436791i
$633$	−24.4881	−	9.04114i	−0.973316	−	0.359353i
$634$	14.6609	+	8.46447i	0.582258	+	0.336167i
$635$	9.13364	+	2.44735i	0.362458	+	0.0971202i
$636$	−2.53553	−	14.7782i	−0.100540	−	0.585993i
$637$	7.83975	+	23.9904i	0.310622	+	0.950534i
$638$		−	5.82843i		−	0.230750i
$639$	−0.153622	−	1.96457i	−0.00607718	−	0.0777170i
$640$	−0.878680	+	1.52192i	−0.0347329	+	0.0601591i
$641$	12.1421	−	21.0308i	0.479586	−	0.830666i	−0.520140	−	0.854081i	$-0.674120\pi$
$641$	12.1421	−	21.0308i	0.479586	−	0.830666i	0.999726	+	0.0234143i	$0.00745369\pi$
$642$	−1.08516	+	11.7773i	−0.0428280	+	0.464813i
$643$	7.67767	−	7.67767i	0.302778	−	0.302778i	−0.539322	−	0.842100i	$-0.681319\pi$
$643$	7.67767	−	7.67767i	0.302778	−	0.302778i	0.842100	+	0.539322i	$0.181319\pi$
$644$	−15.6751	+	7.60918i	−0.617685	+	0.299844i
$645$	−4.97056	−	3.51472i	−0.195716	−	0.138392i
$646$	−6.08579	−	10.5409i	−0.239442	−	0.414726i
$647$	21.0919	−	36.5322i	0.829207	−	1.43623i	−0.0694533	−	0.997585i	$-0.522125\pi$
$647$	21.0919	−	36.5322i	0.829207	−	1.43623i	0.898661	−	0.438644i	$-0.144541\pi$
$648$	−21.8275	−	15.8921i	−0.857465	−	0.624302i
$649$	47.8776	−	27.6421i	1.87936	−	1.08505i
$650$	3.29289	+	16.4645i	0.129158	+	0.645789i
$651$	3.55291	−	1.33751i	0.139250	−	0.0524210i
$652$	1.53553	−	1.53553i	0.0601361	−	0.0601361i
$653$	−27.5387	+	15.8995i	−1.07767	+	0.622195i	−0.930268	−	0.366881i	$-0.880426\pi$
$653$	−27.5387	+	15.8995i	−1.07767	+	0.622195i	−0.147406	+	0.989076i	$0.547092\pi$
$654$	12.0469	+	4.44779i	0.471073	+	0.173922i
$655$	1.94495	+	7.25866i	0.0759956	+	0.283619i
$656$	−1.46410	+	5.46410i	−0.0571636	+	0.213337i
$657$	34.7279	+	16.5858i	1.35487	+	0.647073i
$658$	1.73341	+	0.124453i	0.0675754	+	0.00485170i
$659$		−	21.0711i		−	0.820812i	−0.911903	−	0.410406i	$-0.865387\pi$
$659$		−	21.0711i		−	0.820812i	0.911903	−	0.410406i	$-0.134613\pi$
$660$	3.78024	+	4.54757i	0.147146	+	0.177014i
$661$	−22.3252	+	5.98201i	−0.868348	+	0.232673i	−0.665373	−	0.746511i	$-0.731728\pi$
$661$	−22.3252	+	5.98201i	−0.868348	+	0.232673i	−0.202975	+	0.979184i	$0.565061\pi$
$662$	−11.7279	+	20.3134i	−0.455819	+	0.789501i
$663$	−1.20259	−	11.3550i	−0.0467046	−	0.440992i
$664$	13.0294			0.505640
$665$	10.2906	+	0.738832i	0.399053	+	0.0286507i
$666$	4.00000	+	11.3137i	0.154997	+	0.438397i
$667$	5.70346	−	3.29289i	0.220839	−	0.127501i
$668$	−21.2219	+	5.68640i	−0.821101	+	0.220013i
$669$	−7.86566	+	3.62372i	−0.304104	+	0.140101i
$670$	−2.04454	+	7.63033i	−0.0789875	+	0.294785i
$671$	−4.12132	+	4.12132i	−0.159102	+	0.159102i
$672$	8.07256	+	21.4437i	0.311406	+	0.827210i
$673$			9.85786i			0.379993i	0.981785	+	0.189996i	$0.0608476\pi$
$673$			9.85786i			0.379993i	−0.981785	+	0.189996i	$0.939152\pi$
$674$	16.5580	+	4.43671i	0.637792	+	0.170896i
$675$	−0.334968	+	24.1954i	−0.0128929	+	0.931282i
$676$	1.66987	−	12.8923i	0.0642259	−	0.495858i
$677$	22.4912	−	12.9853i	0.864406	−	0.499065i	−0.00107942	−	0.999999i	$-0.500344\pi$
$677$	22.4912	−	12.9853i	0.864406	−	0.499065i	0.865485	+	0.500935i	$0.167010\pi$
$678$	−12.7279	−	9.00000i	−0.488813	−	0.345643i
$679$	24.7487	+	8.57321i	0.949769	+	0.329010i
$680$	3.21320			0.123221
$681$	−10.3485	−	0.953512i	−0.396554	−	0.0365386i
$682$	−1.24969	−	4.66390i	−0.0478531	−	0.178590i
$683$	13.0145	+	48.5709i	0.497987	+	1.85851i	0.512613	+	0.858620i	$0.328678\pi$
$683$	13.0145	+	48.5709i	0.497987	+	1.85851i	−0.0146258	+	0.999893i	$0.504656\pi$
$684$	−1.55687	−	19.9098i	−0.0595285	−	0.761270i
$685$	6.68629			0.255470
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$	−5.51472	+	7.79899i	−0.210400	+	0.297550i
$688$	−5.19615	+	3.00000i	−0.198101	+	0.114374i
$689$	−27.9794	+	13.8343i	−1.06593	+	0.527045i
$690$	2.31433	−	6.26843i	0.0881052	−	0.238635i
$691$	9.82498	+	2.63260i	0.373760	+	0.100149i	0.440809	−	0.897601i	$-0.354692\pi$
$691$	9.82498	+	2.63260i	0.373760	+	0.100149i	−0.0670488	+	0.997750i	$0.521358\pi$
$692$			15.4853i			0.588662i
$693$	46.2608	−	0.294395i	1.75730	−	0.0111832i
$694$	−3.31371	+	3.31371i	−0.125787	+	0.125787i
$695$	0.444063	−	1.65727i	0.0168443	−	0.0628637i
$696$	−2.17423	−	4.71940i	−0.0824142	−	0.178888i
$697$	−9.99071	+	2.67700i	−0.378425	+	0.101399i
$698$	−3.67423	+	2.12132i	−0.139072	+	0.0802932i
$699$	0.393398	+	2.29289i	0.0148797	+	0.0867252i
$700$	6.90874	−	10.2016i	0.261126	−	0.385586i
$701$	−36.2843			−1.37044			−0.685219	−	0.728337i	$-0.740294\pi$
$701$	−36.2843			−1.37044			−0.685219	+	0.728337i	$0.740294\pi$
$702$	−6.24870	+	17.6622i	−0.235842	+	0.666617i
$703$	−13.3137	+	23.0600i	−0.502136	+	0.869725i
$704$	39.4088	−	10.5596i	1.48527	−	0.397978i
$705$	0.512503	−	0.426027i	0.0193020	−	0.0160451i
$706$		−	7.17157i		−	0.269906i
$707$	10.5558	+	0.757875i	0.396993	+	0.0285028i
$708$	9.48528	−	13.4142i	0.356479	−	0.504137i
$709$	5.89319	−	21.9937i	0.221324	−	0.825991i	−0.762521	−	0.646964i	$-0.776038\pi$
$709$	5.89319	−	21.9937i	0.221324	−	0.825991i	0.983844	−	0.179027i	$-0.0572949\pi$
$710$	−0.0995874	−	0.371665i	−0.00373745	−	0.0139484i
$711$	0.775255	−	4.17121i	0.0290743	−	0.156433i
$712$	−32.4377	+	18.7279i	−1.21565	+	0.701859i
$713$	3.85786	−	3.85786i	0.144478	−	0.144478i
$714$	5.31507	−	6.47735i	0.198911	−	0.242409i
$715$	6.82843	−	10.2426i	0.255369	−	0.383053i
$716$	−1.31178	+	0.757359i	−0.0490237	+	0.0283038i
$717$	4.57583	+	9.93230i	0.170887	+	0.370928i
$718$	−11.2426	+	19.4728i	−0.419572	+	0.726719i
$719$	11.9706	+	20.7336i	0.446427	+	0.773234i	0.998150	−	0.0607933i	$-0.0193630\pi$
$719$	11.9706	+	20.7336i	0.446427	+	0.773234i	−0.551724	+	0.834027i	$0.686030\pi$
$720$	−1.58579	−	0.757359i	−0.0590988	−	0.0282251i
$721$	−14.2071	−	9.62133i	−0.529101	−	0.358317i
$722$	−17.8995	+	17.8995i	−0.666150	+	0.666150i
$723$	38.3629	+	3.53477i	1.42673	+	0.131460i
$724$	−4.57107	+	7.91732i	−0.169882	+	0.294245i
$725$	−2.32843	+	4.03295i	−0.0864756	+	0.149780i
$726$	3.65045	−	39.6184i	0.135481	−	1.47038i
$727$			9.07107i			0.336427i	0.985751	+	0.168214i	$0.0537998\pi$
$727$			9.07107i			0.336427i	−0.985751	+	0.168214i	$0.946200\pi$
$728$	22.7942	−	17.3038i	0.844810	−	0.641323i
$729$	−14.1421	+	23.0000i	−0.523783	+	0.851852i
$730$	7.25866	+	1.94495i	0.268655	+	0.0719859i
$731$	−9.50079	−	5.48528i	−0.351399	−	0.202880i
$732$	−0.599900	+	1.62484i	−0.0221730	+	0.0600560i
$733$	−8.89927	−	2.38455i	−0.328702	−	0.0880755i	0.0906940	−	0.995879i	$-0.471091\pi$
$733$	−8.89927	−	2.38455i	−0.328702	−	0.0880755i	−0.419396	+	0.907803i	$0.637758\pi$
$734$	−10.1716	−	10.1716i	−0.375440	−	0.375440i
$735$	2.01982	+	6.80902i	0.0745022	+	0.251154i
$736$	23.2843	+	23.2843i	0.858270	+	0.858270i
$737$	−68.0678	+	39.2990i	−2.50731	+	1.44760i
$738$	16.6848	+	3.10102i	0.614177	+	0.114150i
$739$	−2.40060	+	0.643238i	−0.0883074	+	0.0236619i	−0.302702	−	0.953085i	$-0.597889\pi$
$739$	−2.40060	+	0.643238i	−0.0883074	+	0.0236619i	0.214395	+	0.976747i	$0.431222\pi$
$740$	−1.17157	−	2.02922i	−0.0430679	−	0.0745957i
$741$	−38.7990	+	14.9289i	−1.42532	+	0.548428i
$742$	−21.6421	−	7.49706i	−0.794508	−	0.275226i
$743$	4.60660	+	4.60660i	0.169000	+	0.169000i	0.786540	−	0.617540i	$-0.211871\pi$
$743$	4.60660	+	4.60660i	0.169000	+	0.169000i	−0.617540	+	0.786540i	$0.711871\pi$
$744$	−2.75172	−	3.31027i	−0.100883	−	0.121361i
$745$	−7.34847	−	4.24264i	−0.269227	−	0.155438i
$746$	22.0221	−	5.90081i	0.806288	−	0.216044i
$747$	−1.01575	−	12.9898i	−0.0371645	−	0.475271i
$748$	7.53553	+	7.53553i	0.275526	+	0.275526i
$749$	−14.9588	−	10.1304i	−0.546584	−	0.370157i
$750$	1.65685	+	9.65685i	0.0604998	+	0.352618i
$751$	−12.1604	+	7.02082i	−0.443740	+	0.256193i	−0.705183	−	0.709026i	$-0.749135\pi$
$751$	−12.1604	+	7.02082i	−0.443740	+	0.256193i	0.261443	+	0.965219i	$0.415802\pi$
$752$	−0.170006	−	0.634472i	−0.00619950	−	0.0231368i
$753$	3.24969	+	1.19980i	0.118425	+	0.0437232i
$754$	−2.70831	+	2.38014i	−0.0986308	+	0.0866796i
$755$			11.6152i			0.422721i
$756$	12.4495	−	5.83183i	0.452784	−	0.212101i
$757$	−11.1421			−0.404968			−0.202484	−	0.979286i	$-0.564901\pi$
$757$	−11.1421			−0.404968			−0.202484	+	0.979286i	$0.564901\pi$
$758$	−0.656854	−	1.13770i	−0.0238580	−	0.0413233i
$759$	60.3843	−	27.8192i	2.19181	−	1.00977i
$760$	−3.02779	−	11.2999i	−0.109830	−	0.409889i
$761$	24.3139	+	6.51488i	0.881377	+	0.236164i	0.671001	−	0.741456i	$-0.265865\pi$
$761$	24.3139	+	6.51488i	0.881377	+	0.236164i	0.210376	+	0.977621i	$0.432531\pi$
$762$	−22.8284	−	16.1421i	−0.826987	−	0.584768i
$763$	−14.8284	+	12.8418i	−0.536825	+	0.464904i
$764$	−16.9706			−0.613973
$765$	−0.250496	−	3.20342i	−0.00905670	−	0.115820i
$766$	6.21076	+	3.58579i	0.224404	+	0.129560i
$767$	−32.3962	−	10.9592i	−1.16976	−	0.395715i
$768$	22.6432	−	18.8225i	0.817065	−	0.679199i
$769$	−9.21320	+	9.21320i	−0.332237	+	0.332237i	−0.853435	−	0.521199i	$-0.825485\pi$
$769$	−9.21320	+	9.21320i	−0.332237	+	0.332237i	0.521199	+	0.853435i	$0.325485\pi$
$770$	8.87039	−	1.70711i	0.319667	−	0.0615199i
$771$	−5.51472	−	32.1421i	−0.198608	−	1.15757i
$772$	2.73205	+	0.732051i	0.0983287	+	0.0263471i
$773$	39.7118	−	10.6407i	1.42833	−	0.382721i	0.539902	−	0.841728i	$-0.318461\pi$
$773$	39.7118	−	10.6407i	1.42833	−	0.382721i	0.888433	+	0.459007i	$0.151795\pi$
$774$	10.1879	+	14.8394i	0.366195	+	0.533391i
$775$	−0.998489	+	3.72641i	−0.0358668	+	0.133857i
$776$		−	29.6985i		−	1.06611i
$777$	−18.0857	−	2.98466i	−0.648820	−	0.107074i
$778$	6.60660	+	6.60660i	0.236858	+	0.236858i
$779$	18.8284	+	32.6118i	0.674598	+	1.16844i
$780$	0.569402	−	3.61365i	0.0203879	−	0.129389i
$781$	1.91421	−	3.31552i	0.0684959	−	0.118638i
$782$	3.11660	−	11.6313i	0.111450	−	0.415935i
$783$	−4.53553	+	2.53553i	−0.162087	+	0.0906126i
$784$	6.92820	+	1.00000i	0.247436	+	0.0357143i
$785$	−0.757359	−	0.757359i	−0.0270313	−	0.0270313i
$786$	2.03868	−	22.1258i	0.0727172	−	0.789200i
$787$	−25.9427	+	6.95133i	−0.924758	+	0.247788i	−0.689618	−	0.724174i	$-0.742221\pi$
$787$	−25.9427	+	6.95133i	−0.924758	+	0.247788i	−0.235140	+	0.971962i	$0.575555\pi$
$788$	1.83013	+	6.83013i	0.0651956	+	0.243313i
$789$	22.6814	+	27.2854i	0.807480	+	0.971386i
$790$		−	0.828427i		−	0.0294741i
$791$	21.4213	−	10.3986i	0.761652	−	0.369730i
$792$	−17.4853	−	49.4558i	−0.621312	−	1.75734i
$793$	3.59808	+	0.232051i	0.127771	+	0.00824037i
$794$	24.3718	+	14.0711i	0.864923	+	0.499364i
$795$	−7.97746	+	3.67523i	−0.282931	+	0.130347i
$796$	7.53553	+	13.0519i	0.267090	+	0.462613i
$797$	−10.2843			−0.364288			−0.182144	−	0.983272i	$-0.558304\pi$
$797$	−10.2843			−0.364288			−0.182144	+	0.983272i	$0.558304\pi$
$798$	−27.7873	−	12.5879i	−0.983659	−	0.445607i
$799$	0.849242	−	0.849242i	0.0300440	−	0.0300440i
$800$	−22.4909	−	6.02641i	−0.795173	−	0.213066i
$801$	21.1997	+	30.8790i	0.749055	+	1.09106i
$802$	−6.12132	+	10.6024i	−0.216151	+	0.374385i
$803$	37.3848	+	64.7523i	1.31928	+	2.28506i
$804$	−13.4853	+	19.0711i	−0.475589	+	0.672585i
$805$	6.68202	+	7.71573i	0.235510	+	0.271944i
$806$	−1.65685	+	2.48528i	−0.0583602	+	0.0875403i
$807$	−7.75044	−	9.32366i	−0.272829	−	0.328208i
$808$	−3.10583	−	11.5911i	−0.109263	−	0.407774i
$809$	39.3404	+	22.7132i	1.38314	+	0.798554i	0.992530	−	0.122004i	$-0.0389322\pi$
$809$	39.3404	+	22.7132i	1.38314	+	0.798554i	0.390606	+	0.920558i	$0.372265\pi$
$810$	−1.89429	+	4.92001i	−0.0665585	+	0.172871i
$811$	−6.92893	+	6.92893i	−0.243308	+	0.243308i	−0.818217	−	0.574909i	$-0.805037\pi$
$811$	−6.92893	+	6.92893i	−0.243308	+	0.243308i	0.574909	+	0.818217i	$0.305037\pi$
$812$	2.63896	+	0.189469i	0.0926093	+	0.00664905i
$813$	−4.17157	+	5.89949i	−0.146303	+	0.206904i
$814$	−6.03403	+	22.5193i	−0.211493	+	0.789302i
$815$	−1.10165	−	0.636039i	−0.0385892	−	0.0222795i
$816$	−2.97091	−	1.09687i	−0.104003	−	0.0383983i
$817$	−10.3375	+	38.5802i	−0.361664	+	1.34975i
$818$	−26.7279			−0.934520
$819$	−19.0282	−	21.3759i	−0.664899	−	0.746934i
$820$	−3.31371			−0.115720
$821$	7.22092	−	26.9488i	0.252012	−	0.940521i	−0.717717	−	0.696335i	$-0.754813\pi$
$821$	7.22092	−	26.9488i	0.252012	−	0.940521i	0.969728	−	0.244186i	$-0.0785207\pi$
$822$	−18.5463	−	6.84739i	−0.646877	−	0.238830i
$823$	0.420266	+	0.242641i	0.0146496	+	0.00845792i	0.507307	−	0.861765i	$-0.330641\pi$
$823$	0.420266	+	0.242641i	0.0146496	+	0.00845792i	−0.492657	+	0.870223i	$0.663974\pi$
$824$	−5.03554	+	18.7929i	−0.175421	+	0.654682i
$825$	−27.1421	+	38.3848i	−0.944968	+	1.33639i
$826$	−10.9592	−	22.5763i	−0.381321	−	0.785530i
$827$	15.6777	−	15.6777i	0.545166	−	0.545166i	−0.379873	−	0.925039i	$-0.624032\pi$
$827$	15.6777	−	15.6777i	0.545166	−	0.545166i	0.925039	+	0.379873i	$0.124032\pi$
$828$	12.8389	−	15.0172i	0.446183	−	0.521883i
$829$	−35.6301	−	20.5711i	−1.23749	−	0.714463i	−0.268906	−	0.963166i	$-0.586662\pi$
$829$	−35.6301	−	20.5711i	−1.23749	−	0.714463i	−0.968580	+	0.248704i	$0.919995\pi$
$830$	−0.658476	−	2.45747i	−0.0228560	−	0.0852999i
$831$	4.23886	+	5.09928i	0.147044	+	0.176892i
$832$	−21.0000	−	14.0000i	−0.728044	−	0.485363i
$833$	4.75039	+	11.8848i	0.164591	+	0.411783i
$834$	−2.92893	+	4.14214i	−0.101421	+	0.143430i
$835$	6.43503	+	11.1458i	0.222693	+	0.385716i
$836$	19.3995	−	33.6009i	0.670946	−	1.16211i
$837$	−3.08568	+	3.00141i	−0.106657	+	0.103744i
$838$	16.3521	+	4.38153i	0.564874	+	0.151357i
$839$	11.3934	−	11.3934i	0.393344	−	0.393344i	−0.482534	−	0.875877i	$-0.660283\pi$
$839$	11.3934	−	11.3934i	0.393344	−	0.393344i	0.875877	+	0.482534i	$0.160283\pi$
$840$	6.54572	−	4.69129i	0.225849	−	0.161865i
$841$	28.0000			0.965517
$842$	−7.82843	−	13.5592i	−0.269785	−	0.467282i
$843$	17.9561	−	8.27239i	0.618440	−	0.284916i
$844$	−13.0519	−	7.53553i	−0.449266	−	0.259384i
$845$	−7.54798	+	1.00978i	−0.259658	+	0.0347375i
$846$	−1.85786	+	0.656854i	−0.0638747	+	0.0225831i
$847$	50.3209	+	34.0783i	1.72905	+	1.17094i
$848$			8.65685i			0.297278i
$849$	−19.7072	−	23.7074i	−0.676348	−	0.813635i
$850$	2.20377	+	8.22459i	0.0755887	+	0.282101i
$851$	−25.4455	+	6.81811i	−0.872261	+	0.233722i
$852$	0.104386	−	1.13291i	0.00357622	−	0.0388127i
$853$	−3.07107	−	3.07107i	−0.105151	−	0.105151i	0.652574	−	0.757725i	$-0.273689\pi$
$853$	−3.07107	−	3.07107i	−0.105151	−	0.105151i	−0.757725	+	0.652574i	$0.773689\pi$
$854$	1.73205	+	2.00000i	0.0592696	+	0.0684386i
$855$	−11.0294	+	3.89949i	−0.377199	+	0.133360i
$856$	−5.30198	+	19.7873i	−0.181218	+	0.676315i
$857$	−25.2990	+	43.8191i	−0.864197	+	1.49683i	0.00364524	+	0.999993i	$0.498840\pi$
$857$	−25.2990	+	43.8191i	−0.864197	+	1.49683i	−0.867842	+	0.496840i	$0.834494\pi$
$858$	−29.4300	+	21.4179i	−1.00472	+	0.731195i
$859$	9.89949	+	17.1464i	0.337766	+	0.585029i	0.984012	−	0.178101i	$-0.0569953\pi$
$859$	9.89949	+	17.1464i	0.337766	+	0.585029i	−0.646246	+	0.763129i	$0.723662\pi$
$860$	−2.48528	−	2.48528i	−0.0847474	−	0.0847474i
$861$	−16.4440	+	20.0399i	−0.560408	+	0.682957i
$862$			15.1716i			0.516746i
$863$	12.8369	−	47.9080i	0.436973	−	1.63081i	−0.299327	−	0.954151i	$-0.596762\pi$
$863$	12.8369	−	47.9080i	0.436973	−	1.63081i	0.736300	−	0.676656i	$-0.236571\pi$
$864$	−18.1151	−	18.6237i	−0.616288	−	0.633592i
$865$	8.76198	−	2.34777i	0.297916	−	0.0798264i
$866$	4.96692	+	1.33088i	0.168783	+	0.0452252i
$867$	4.00000	+	23.3137i	0.135847	+	0.791775i
$868$	2.15232	−	0.414214i	0.0730544	−	0.0140593i
$869$	5.82843	−	5.82843i	0.197716	−	0.197716i
$870$	−0.780239	+	0.648586i	−0.0264526	+	0.0219891i
$871$	46.0578	+	15.5808i	1.56061	+	0.527936i
$872$	19.2627	+	11.1213i	0.652317	+	0.376615i
$873$	−29.6081	+	2.31524i	−1.00208	+	0.0783592i
$874$	−43.8406			−1.48293
$875$	−14.1421	−	4.89898i	−0.478091	−	0.165616i
$876$	18.1421	+	12.8284i	0.612966	+	0.433432i
$877$	−33.1729	−	8.88866i	−1.12017	−	0.300149i	−0.349218	−	0.937042i	$-0.613553\pi$
$877$	−33.1729	−	8.88866i	−1.12017	−	0.300149i	−0.770952	+	0.636893i	$0.780219\pi$
$878$	−8.31900	−	31.0469i	−0.280753	−	1.04778i
$879$	20.3389	−	9.37018i	0.686015	−	0.316048i
$880$	−1.70711	−	2.95680i	−0.0575466	−	0.0996736i
$881$	2.00000			0.0673817			0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000			0.0673817			0.0336909	+	0.999432i	$0.489274\pi$
$882$	1.37054	−	20.9552i	0.0461484	−	0.705599i
$883$		−	10.1421i		−	0.341310i	−0.985331	−	0.170655i	$-0.945412\pi$
$883$		−	10.1421i		−	0.341310i	0.985331	−	0.170655i	$-0.0545884\pi$
$884$	0.424288	−	6.57882i	0.0142703	−	0.221270i
$885$	−9.02820	−	3.33326i	−0.303480	−	0.112046i
$886$	1.36451	+	5.09244i	0.0458418	+	0.171084i
$887$	21.7482	−	12.5563i	0.730234	−	0.421601i	−0.0882736	−	0.996096i	$-0.528135\pi$
$887$	21.7482	−	12.5563i	0.730234	−	0.421601i	0.818508	+	0.574495i	$0.194802\pi$
$888$	3.51472	+	20.4853i	0.117946	+	0.687441i
$889$	38.4205	−	18.6505i	1.28858	−	0.625519i
$890$	5.17157	+	5.17157i	0.173352	+	0.173352i
$891$	−47.9422	+	21.2876i	−1.60612	+	0.713160i
$892$	−4.82963	+	1.29410i	−0.161708	+	0.0433295i
$893$	−3.78677	−	2.18629i	−0.126719	−	0.0731615i
$894$	16.0382	+	19.2937i	0.536398	+	0.645277i
$895$	0.627417	+	0.627417i	0.0209722	+	0.0209722i
$896$	1.50000	+	7.79423i	0.0501115	+	0.260387i
$897$	−37.5858	−	16.6985i	−1.25495	−	0.557546i
$898$	1.41421	+	2.44949i	0.0471929	+	0.0817405i
$899$	−0.800199	+	0.214413i	−0.0266881	+	0.00715106i
$900$	−2.55283	+	13.7353i	−0.0850944	+	0.457845i
$901$	−13.7078	+	7.91421i	−0.456674	+	0.263661i
$902$	23.3137	+	23.3137i	0.776262	+	0.776262i
$903$	−27.3629	+	2.69694i	−0.910579	+	0.0897485i
$904$	−19.0919	−	19.0919i	−0.634987	−	0.634987i
$905$	5.17286	+	1.38606i	0.171952	+	0.0460743i
$906$	11.8951	−	32.2181i	0.395188	−	1.07038i
$907$	−26.9954	−	15.5858i	−0.896367	−	0.517518i	−0.0203470	−	0.999793i	$-0.506477\pi$
$907$	−26.9954	−	15.5858i	−0.896367	−	0.517518i	−0.876020	+	0.482275i	$0.839810\pi$
$908$	−5.79555	−	1.55291i	−0.192332	−	0.0515353i
$909$	−11.3137	+	4.00000i	−0.375252	+	0.132672i
$910$	−4.41562	−	3.42470i	−0.146376	−	0.113528i
$911$			52.4264i			1.73696i	0.495720	+	0.868482i	$0.334904\pi$
$911$			52.4264i			1.73696i	−0.495720	+	0.868482i	$0.665096\pi$
$912$	−1.05790	+	11.4814i	−0.0350305	+	0.380186i
$913$	12.6569	−	21.9223i	0.418881	−	0.725523i
$914$	−2.22183	+	3.84831i	−0.0734915	+	0.127291i
$915$	1.01033	+	0.0930924i	0.0334006	+	0.00307754i
$916$	−3.89949	+	3.89949i	−0.128843	+	0.128843i
$917$	28.1029	+	19.0318i	0.928038	+	0.628485i
$918$	−2.58579	+	9.14214i	−0.0853437	+	0.301735i
$919$	−2.17157	−	3.76127i	−0.0716336	−	0.124073i	0.827984	−	0.560752i	$-0.189488\pi$
$919$	−2.17157	−	3.76127i	−0.0716336	−	0.124073i	−0.899617	+	0.436679i	$0.856155\pi$
$920$	5.78680	−	10.0230i	0.190785	−	0.330449i
$921$	3.62372	+	7.86566i	0.119406	+	0.259182i
$922$	−34.3799	+	19.8492i	−1.13224	+	0.653700i
$923$	−2.32233	+	0.464466i	−0.0764404	+	0.0152881i
$924$	26.3528	+	4.34897i	0.866942	+	0.143071i
$925$	13.1716	−	13.1716i	0.433079	−	0.433079i
$926$	−4.89898	+	2.82843i	−0.160990	+	0.0929479i
$927$	19.1283	+	3.55515i	0.628255	+	0.116767i
$928$	−1.29410	−	4.82963i	−0.0424808	−	0.158540i
$929$	−6.60370	+	24.6453i	−0.216660	+	0.808587i	0.768915	+	0.639351i	$0.220797\pi$
$929$	−6.60370	+	24.6453i	−0.216660	+	0.808587i	−0.985576	+	0.169236i	$0.945870\pi$
$930$	−0.485281	+	0.686292i	−0.0159130	+	0.0225044i
$931$	37.3189	−	27.9047i	1.22308	−	0.914539i
$932$			1.34315i			0.0439962i
$933$	2.47458	−	2.05704i	0.0810143	−	0.0673444i
$934$	22.1879	−	5.94522i	0.726009	−	0.194534i
$935$	3.12132	−	5.40629i	0.102078	−	0.176804i
$936$	−15.8403	+	28.3211i	−0.517758	+	0.925703i
$937$	21.2843			0.695327			0.347663	−	0.937619i	$-0.386975\pi$
$937$	21.2843			0.695327			0.347663	+	0.937619i	$0.386975\pi$
$938$	15.5808	+	32.0968i	0.508732	+	1.04800i
$939$	−6.92893	−	40.3848i	−0.226117	−	1.31791i
$940$	0.333226	−	0.192388i	0.0108686	−	0.00627501i
$941$	2.16622	−	0.580438i	0.0706169	−	0.0189217i	−0.223338	−	0.974741i	$-0.571695\pi$
$941$	2.16622	−	0.580438i	0.0706169	−	0.0189217i	0.293955	+	0.955819i	$0.405029\pi$
$942$	1.32514	+	2.87636i	0.0431755	+	0.0937168i
$943$	−9.64226	+	35.9854i	−0.313995	+	1.17185i
$944$	−6.70711	+	6.70711i	−0.218298	+	0.218298i
$945$	−5.18730	−	6.16007i	−0.168743	−	0.200387i
$946$			34.9706i			1.13699i
$947$	25.6113	+	6.86251i	0.832254	+	0.223002i	0.649697	−	0.760194i	$-0.274896\pi$
$947$	25.6113	+	6.86251i	0.832254	+	0.223002i	0.182557	+	0.983195i	$0.441563\pi$
$948$	0.848387	−	2.29788i	0.0275543	−	0.0746316i
$949$	14.8219	−	43.8144i	0.481139	−	1.42228i
$950$	26.8468	−	15.5000i	0.871025	−	0.502886i
$951$	16.9289	−	23.9411i	0.548958	−	0.776344i
$952$	10.9706	−	9.50079i	0.355558	−	0.307922i
$953$	−25.1421			−0.814434			−0.407217	−	0.913332i	$-0.633501\pi$
$953$	−25.1421			−0.814434			−0.407217	+	0.913332i	$0.633501\pi$
$954$	25.8915	−	2.02462i	0.838269	−	0.0655496i
$955$	2.57295	+	9.60239i	0.0832588	+	0.310726i
$956$	1.63411	+	6.09857i	0.0528508	+	0.197242i
$957$	−10.0525	−	0.926246i	−0.324953	−	0.0299413i
$958$	29.4853			0.952626
$959$	22.8284	−	19.7700i	0.737168	−	0.638407i
$960$	−5.79899	−	4.10051i	−0.187162	−	0.132343i
$961$	26.2524	−	15.1569i	0.846853	−	0.488931i
$962$	12.9282	−	6.39230i	0.416822	−	0.206096i
$963$	20.1404	+	3.74326i	0.649015	+	0.120625i
$964$	21.4847	+	5.75682i	0.691977	+	0.185415i
$965$		−	1.65685i		−	0.0533360i
$966$	−10.6328	−	28.2448i	−0.342106	−	0.908761i
$967$	17.3934	−	17.3934i	0.559334	−	0.559334i	−0.369784	−	0.929118i	$-0.620568\pi$
$967$	17.3934	−	17.3934i	0.559334	−	0.559334i	0.929118	+	0.369784i	$0.120568\pi$
$968$	17.8357	−	66.5636i	0.573260	−	2.13943i
$969$	−19.1475	+	8.82129i	−0.615106	+	0.283381i
$970$	−5.60139	+	1.50089i	−0.179850	+	0.0481906i
$971$	−17.2335	+	9.94975i	−0.553048	+	0.319303i	−0.750351	−	0.661040i	$-0.770115\pi$
$971$	−17.2335	+	9.94975i	−0.553048	+	0.319303i	0.197302	+	0.980343i	$0.436782\pi$
$972$	−10.2929	+	11.7071i	−0.330145	+	0.375506i
$973$	−3.38407	−	6.97127i	−0.108488	−	0.223489i
$974$	−9.34315			−0.299374
$975$	28.9203	−	3.06289i	0.926191	−	0.0980910i
$976$	0.500000	−	0.866025i	0.0160046	−	0.0277208i
$977$	−43.9472	+	11.7756i	−1.40600	+	0.376735i	−0.880494	−	0.474058i	$-0.842789\pi$
$977$	−43.9472	+	11.7756i	−1.40600	+	0.376735i	−0.525501	+	0.850793i	$0.676122\pi$
$978$	2.40438	+	2.89243i	0.0768836	+	0.0924897i
$979$			72.7696i			2.32572i
$980$	0.484577	+	4.07177i	0.0154793	+	0.130068i
$981$	9.58579	−	20.0711i	0.306051	−	0.640820i
$982$	2.38455	−	8.89927i	0.0760941	−	0.283987i
$983$	−13.7174	−	51.1941i	−0.437517	−	1.63284i	−0.734969	−	0.678100i	$-0.762803\pi$
$983$	−13.7174	−	51.1941i	−0.437517	−	1.63284i	0.297452	−	0.954737i	$-0.403863\pi$
$984$	27.5745	+	10.1806i	0.879044	+	0.324547i
$985$	3.58719	−	2.07107i	0.114298	−	0.0659897i
$986$	−1.29289	+	1.29289i	−0.0411741	+	0.0411741i
$987$	0.490122	−	2.96991i	0.0156007	−	0.0945334i
$988$	−23.5355	+	4.70711i	−0.748765	+	0.149753i
$989$	−34.2208	+	19.7574i	−1.08816	+	0.628247i
$990$	−8.44414	+	5.79725i	−0.268372	+	0.184249i
$991$	−20.5355	+	35.5686i	−0.652333	+	1.12987i	0.330223	+	0.943903i	$0.392876\pi$
$991$	−20.5355	+	35.5686i	−0.652333	+	1.12987i	−0.982555	+	0.185970i	$0.940457\pi$
$992$	−2.07107	−	3.58719i	−0.0657565	−	0.113894i
$993$	33.1716	+	23.4558i	1.05267	+	0.744349i
$994$	−1.43895	−	0.974485i	−0.0456408	−	0.0309088i
$995$	6.24264	−	6.24264i	0.197905	−	0.197905i
$996$	0.690207	−	7.49082i	0.0218700	−	0.237356i
$997$	−14.0858	+	24.3973i	−0.446101	+	0.772670i	−0.998128	−	0.0611561i	$-0.980521\pi$
$997$	−14.0858	+	24.3973i	−0.446101	+	0.772670i	0.552027	+	0.833826i	$0.313855\pi$
$998$	−9.17157	+	15.8856i	−0.290321	+	0.502851i
$999$	20.1489	−	5.10102i	0.637484	−	0.161389i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cd.d.200.1	yes	8
3.2	odd	2		273.2.cd.c.200.2	yes	8
7.2	even	3	inner	273.2.cd.d.44.2	yes	8
13.8	odd	4		273.2.cd.c.242.1	yes	8
21.2	odd	6		273.2.cd.c.44.1	✓	8
39.8	even	4	inner	273.2.cd.d.242.2	yes	8
91.86	odd	12		273.2.cd.c.86.2	yes	8
273.86	even	12	inner	273.2.cd.d.86.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cd.c.44.1	✓	8	21.2	odd	6
273.2.cd.c.86.2	yes	8	91.86	odd	12
273.2.cd.c.200.2	yes	8	3.2	odd	2
273.2.cd.c.242.1	yes	8	13.8	odd	4
273.2.cd.d.44.2	yes	8	7.2	even	3	inner
273.2.cd.d.86.1	yes	8	273.86	even	12	inner
273.2.cd.d.200.1	yes	8	1.1	even	1	trivial
273.2.cd.d.242.2	yes	8	39.8	even	4	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(1.62484 + 0.599900i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.151613 - 0.565826i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(-1.15539 - 2.38014i) q^{7} +(-2.12132 + 2.12132i) q^{8} +(2.28024 + 1.94949i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(1.62484 + 0.599900i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.151613 - 0.565826i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(-1.15539 - 2.38014i) q^{7} +(-2.12132 + 2.12132i) q^{8} +(2.28024 + 1.94949i) q^{9} +(0.507306 + 0.292893i) q^{10} +(1.50851 + 5.62983i) q^{11} +(1.10721 + 1.33195i) q^{12} +(2.00000 - 3.00000i) q^{13} +(2.59808 - 0.500000i) q^{14} +(0.585786 - 0.828427i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.914214 - 1.58346i) q^{17} +(-2.47323 + 1.69798i) q^{18} +(-6.43003 - 1.72292i) q^{19} +(0.414214 - 0.414214i) q^{20} +(-0.449490 - 4.56048i) q^{21} -5.82843 q^{22} +(-3.29289 - 5.70346i) q^{23} +(-4.71940 + 2.17423i) q^{24} +(4.03295 + 2.32843i) q^{25} +(2.38014 + 2.70831i) q^{26} +(2.53553 + 4.53553i) q^{27} +(0.189469 - 2.63896i) q^{28} +1.00000i q^{29} +(0.648586 + 0.780239i) q^{30} +(0.214413 + 0.800199i) q^{31} +(-4.82963 + 1.29410i) q^{32} +(-0.926246 + 10.0525i) q^{33} +(1.29289 + 1.29289i) q^{34} +(-1.52192 + 0.292893i) q^{35} +(1.00000 + 2.82843i) q^{36} +(1.03528 - 3.86370i) q^{37} +(3.32843 - 5.76500i) q^{38} +(5.04939 - 3.67473i) q^{39} +(0.878680 + 1.52192i) q^{40} +(-4.00000 - 4.00000i) q^{41} +(4.52142 + 0.746165i) q^{42} -6.00000i q^{43} +(-1.50851 + 5.62983i) q^{44} +(1.44879 - 0.994652i) q^{45} +(6.36138 - 1.70453i) q^{46} +(0.634472 + 0.170006i) q^{47} +(-0.292893 - 1.70711i) q^{48} +(-4.33013 + 5.50000i) q^{49} +(-3.29289 + 3.29289i) q^{50} +(2.43538 - 2.02445i) q^{51} +(3.23205 - 1.59808i) q^{52} +(-7.49706 - 4.32843i) q^{53} +(-5.03723 + 1.27526i) q^{54} +3.41421 q^{55} +(7.50000 + 2.59808i) q^{56} +(-9.41421 - 6.65685i) q^{57} +(-0.965926 - 0.258819i) q^{58} +(-2.45497 - 9.16208i) q^{59} +(0.921519 - 0.424546i) q^{60} +(0.500000 + 0.866025i) q^{61} -0.828427 q^{62} +(2.00548 - 7.67972i) q^{63} -7.00000i q^{64} +(-1.39425 - 1.58649i) q^{65} +(-9.47029 - 3.49648i) q^{66} +(3.49025 + 13.0258i) q^{67} +(1.58346 - 0.914214i) q^{68} +(-1.92893 - 11.2426i) q^{69} +(0.110988 - 1.54587i) q^{70} +(-0.464466 - 0.464466i) q^{71} +(-8.97261 + 0.701625i) q^{72} +(12.3913 - 3.32024i) q^{73} +(3.46410 + 2.00000i) q^{74} +(5.15610 + 6.20270i) q^{75} +(-4.70711 - 4.70711i) q^{76} +(11.6569 - 10.0951i) q^{77} +(2.24264 + 5.82843i) q^{78} +(-0.707107 - 1.22474i) q^{79} +(-0.565826 + 0.151613i) q^{80} +(1.39898 + 8.89060i) q^{81} +(4.89898 - 2.82843i) q^{82} +(-3.07107 - 3.07107i) q^{83} +(1.89097 - 4.17423i) q^{84} +(-0.757359 - 0.757359i) q^{85} +(5.79555 + 1.55291i) q^{86} +(-0.599900 + 1.62484i) q^{87} +(-15.1427 - 8.74264i) q^{88} +(12.0599 + 3.23143i) q^{89} +(0.585786 + 1.65685i) q^{90} +(-9.45121 - 1.29410i) q^{91} -6.58579i q^{92} +(-0.131652 + 1.42883i) q^{93} +(-0.328427 + 0.568852i) q^{94} +(-1.94975 + 3.37706i) q^{95} +(-8.62372 - 0.794593i) q^{96} +(-7.00000 + 7.00000i) q^{97} +(-4.19187 - 5.60609i) q^{98} +(-7.53553 + 15.7782i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{5} - 8 q^{6}+O(q^{10}) \) 8 * q + 4 * q^3 + 4 * q^5 - 8 * q^6	\( 8 q + 4 q^{3} + 4 q^{5} - 8 q^{6} - 8 q^{11} + 4 q^{12} + 16 q^{13} + 16 q^{15} - 4 q^{16} - 4 q^{17} - 8 q^{18} - 16 q^{19} - 8 q^{20} + 16 q^{21} - 24 q^{22} - 32 q^{23} - 8 q^{27} + 4 q^{30} - 8 q^{31} + 16 q^{33} + 16 q^{34} + 8 q^{36} + 4 q^{38} + 20 q^{39} + 24 q^{40} - 32 q^{41} + 20 q^{42} + 8 q^{44} + 12 q^{45} - 4 q^{46} + 16 q^{47} - 8 q^{48} - 32 q^{50} + 12 q^{51} + 12 q^{52} + 16 q^{55} + 60 q^{56} - 64 q^{57} + 24 q^{59} - 8 q^{60} + 4 q^{61} + 16 q^{62} - 8 q^{63} + 20 q^{65} - 4 q^{66} - 24 q^{67} - 72 q^{69} - 16 q^{70} - 32 q^{71} - 24 q^{72} + 8 q^{73} + 12 q^{75} - 32 q^{76} + 48 q^{77} - 16 q^{78} + 4 q^{80} - 28 q^{81} + 32 q^{83} - 40 q^{85} - 4 q^{87} + 24 q^{89} + 16 q^{90} + 16 q^{93} + 20 q^{94} + 24 q^{95} - 20 q^{96} - 56 q^{97} - 32 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^5 - 8 * q^6 - 8 * q^11 + 4 * q^12 + 16 * q^13 + 16 * q^15 - 4 * q^16 - 4 * q^17 - 8 * q^18 - 16 * q^19 - 8 * q^20 + 16 * q^21 - 24 * q^22 - 32 * q^23 - 8 * q^27 + 4 * q^30 - 8 * q^31 + 16 * q^33 + 16 * q^34 + 8 * q^36 + 4 * q^38 + 20 * q^39 + 24 * q^40 - 32 * q^41 + 20 * q^42 + 8 * q^44 + 12 * q^45 - 4 * q^46 + 16 * q^47 - 8 * q^48 - 32 * q^50 + 12 * q^51 + 12 * q^52 + 16 * q^55 + 60 * q^56 - 64 * q^57 + 24 * q^59 - 8 * q^60 + 4 * q^61 + 16 * q^62 - 8 * q^63 + 20 * q^65 - 4 * q^66 - 24 * q^67 - 72 * q^69 - 16 * q^70 - 32 * q^71 - 24 * q^72 + 8 * q^73 + 12 * q^75 - 32 * q^76 + 48 * q^77 - 16 * q^78 + 4 * q^80 - 28 * q^81 + 32 * q^83 - 40 * q^85 - 4 * q^87 + 24 * q^89 + 16 * q^90 + 16 * q^93 + 20 * q^94 + 24 * q^95 - 20 * q^96 - 56 * q^97 - 32 * q^99

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