LMFDB - Embedded newform 273.2.cd.c.242.1

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			242.1
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	273.242
Dual form			273.2.cd.c.44.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(1.62484 + 0.599900i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.565826 + 0.151613i) q^{5} +(-1.41421 - 1.00000i) q^{6} +(-2.38014 + 1.15539i) q^{7} +(2.12132 + 2.12132i) q^{8} +(2.28024 + 1.94949i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(1.62484 + 0.599900i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.565826 + 0.151613i) q^{5} +(-1.41421 - 1.00000i) q^{6} +(-2.38014 + 1.15539i) q^{7} +(2.12132 + 2.12132i) q^{8} +(2.28024 + 1.94949i) q^{9} +(-0.507306 - 0.292893i) q^{10} +(5.62983 - 1.50851i) q^{11} +(-1.10721 - 1.33195i) q^{12} +(2.00000 + 3.00000i) q^{13} +(2.59808 - 0.500000i) q^{14} +(0.828427 + 0.585786i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.914214 + 1.58346i) q^{17} +(-1.69798 - 2.47323i) q^{18} +(1.72292 - 6.43003i) q^{19} +(-0.414214 - 0.414214i) q^{20} +(-4.56048 + 0.449490i) q^{21} -5.82843 q^{22} +(3.29289 + 5.70346i) q^{23} +(2.17423 + 4.71940i) q^{24} +(-4.03295 - 2.32843i) q^{25} +(-1.15539 - 3.41542i) q^{26} +(2.53553 + 4.53553i) q^{27} +(2.63896 + 0.189469i) q^{28} +1.00000i q^{29} +(-0.648586 - 0.780239i) q^{30} +(-0.800199 + 0.214413i) q^{31} +(-1.29410 - 4.82963i) q^{32} +(10.0525 + 0.926246i) q^{33} +(1.29289 - 1.29289i) q^{34} +(-1.52192 + 0.292893i) q^{35} +(-1.00000 - 2.82843i) q^{36} +(-3.86370 - 1.03528i) q^{37} +(-3.32843 + 5.76500i) q^{38} +(1.44999 + 6.07433i) q^{39} +(0.878680 + 1.52192i) q^{40} +(4.00000 - 4.00000i) q^{41} +(4.52142 + 0.746165i) q^{42} +6.00000i q^{43} +(-5.62983 - 1.50851i) q^{44} +(0.994652 + 1.44879i) q^{45} +(-1.70453 - 6.36138i) q^{46} +(0.170006 - 0.634472i) 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} +(-0.232051 - 3.59808i) q^{52} +(-7.49706 - 4.32843i) q^{53} +(-1.27526 - 5.03723i) q^{54} +3.41421 q^{55} +(-7.50000 - 2.59808i) q^{56} +(6.65685 - 9.41421i) q^{57} +(0.258819 - 0.965926i) q^{58} +(-9.16208 + 2.45497i) q^{59} +(-0.424546 - 0.921519i) q^{60} +(0.500000 + 0.866025i) q^{61} +0.828427 q^{62} +(-7.67972 - 2.00548i) q^{63} +7.00000i q^{64} +(0.676814 + 2.00070i) q^{65} +(-9.47029 - 3.49648i) q^{66} +(-13.0258 + 3.49025i) q^{67} +(1.58346 - 0.914214i) q^{68} +(1.92893 + 11.2426i) q^{69} +(1.54587 + 0.110988i) q^{70} +(0.464466 - 0.464466i) q^{71} +(0.701625 + 8.97261i) q^{72} +(-3.32024 - 12.3913i) 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} +(0.171573 - 6.24264i) q^{78} +(-0.707107 - 1.22474i) q^{79} +(-0.151613 - 0.565826i) q^{80} +(1.39898 + 8.89060i) q^{81} +(-4.89898 + 2.82843i) q^{82} +(3.07107 - 3.07107i) q^{83} +(4.17423 + 1.89097i) q^{84} +(-0.757359 + 0.757359i) q^{85} +(1.55291 - 5.79555i) q^{86} +(-0.599900 + 1.62484i) q^{87} +(15.1427 + 8.74264i) q^{88} +(3.23143 - 12.0599i) q^{89} +(-0.585786 - 1.65685i) q^{90} +(-8.22646 - 4.82963i) q^{91} -6.58579i q^{92} +(-1.42883 - 0.131652i) q^{93} +(-0.328427 + 0.568852i) q^{94} +(1.94975 - 3.37706i) q^{95} +(0.794593 - 8.62372i) q^{96} +(-7.00000 - 7.00000i) q^{97} +(-5.60609 + 4.19187i) q^{98} +(15.7782 + 7.53553i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 4 q^{5}+O(q^{10}) $ 8 * q + 4 * q^3 - 4 * q^5	$ 8 q + 4 q^{3} - 4 q^{5} + 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} - 24 q^{22} + 32 q^{23} - 12 q^{24} - 8 q^{27} - 4 q^{30} - 8 q^{31} + 12 q^{33} + 16 q^{34} - 8 q^{36} - 4 q^{38} - 4 q^{39} + 24 q^{40} + 32 q^{41} + 20 q^{42} - 8 q^{44} - 20 q^{45} - 4 q^{46} - 16 q^{47} - 8 q^{48} + 32 q^{50} - 12 q^{51} + 12 q^{52} - 20 q^{54} + 16 q^{55} - 60 q^{56} + 8 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} + 24 q^{78} - 4 q^{80} - 28 q^{81} - 32 q^{83} + 4 q^{84} - 40 q^{85} - 4 q^{87} - 24 q^{89} - 16 q^{90} + 8 q^{93} + 20 q^{94} - 24 q^{95} - 56 q^{97} + 64 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 4 * q^5 + 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 - 24 * q^22 + 32 * q^23 - 12 * q^24 - 8 * q^27 - 4 * q^30 - 8 * q^31 + 12 * q^33 + 16 * q^34 - 8 * q^36 - 4 * q^38 - 4 * q^39 + 24 * q^40 + 32 * q^41 + 20 * q^42 - 8 * q^44 - 20 * q^45 - 4 * q^46 - 16 * q^47 - 8 * q^48 + 32 * q^50 - 12 * q^51 + 12 * q^52 - 20 * q^54 + 16 * q^55 - 60 * q^56 + 8 * 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 + 24 * q^78 - 4 * q^80 - 28 * q^81 - 32 * q^83 + 4 * q^84 - 40 * q^85 - 4 * q^87 - 24 * q^89 - 16 * q^90 + 8 * q^93 + 20 * q^94 - 24 * q^95 - 56 * q^97 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i	−0.0994033	−	0.995047i	$-0.531693\pi$
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i	−0.583609	+	0.812035i	$0.698360\pi$
$3$	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
$5$	0.565826	+	0.151613i	0.253045	+	0.0678033i	0.383112	−	0.923702i	$-0.374852\pi$
$5$	0.565826	+	0.151613i	0.253045	+	0.0678033i	−0.130067	+	0.991505i	$0.541519\pi$
$6$	−1.41421	−	1.00000i	−0.577350	−	0.408248i
$7$	−2.38014	+	1.15539i	−0.899608	+	0.436698i
$7$	−2.38014	+	1.15539i	−0.899608	+	0.436698i
$8$	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
$11$	5.62983	−	1.50851i	1.69746	−	0.454832i	0.725160	−	0.688580i	$-0.241766\pi$
$11$	5.62983	−	1.50851i	1.69746	−	0.454832i	0.972297	+	0.233748i	$0.0750991\pi$
$12$	−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
$15$	0.828427	+	0.585786i	0.213899	+	0.151249i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.914214	+	1.58346i	−0.221729	+	0.384047i	−0.955333	−	0.295531i	$-0.904503\pi$
$17$	−0.914214	+	1.58346i	−0.221729	+	0.384047i	0.733604	+	0.679577i	$0.237837\pi$
$18$	−1.69798	−	2.47323i	−0.400217	−	0.582946i
$19$	1.72292	−	6.43003i	0.395265	−	1.47515i	−0.426063	−	0.904693i	$-0.640100\pi$
$19$	1.72292	−	6.43003i	0.395265	−	1.47515i	0.821328	−	0.570456i	$-0.193233\pi$
$20$	−0.414214	−	0.414214i	−0.0926210	−	0.0926210i
$21$	−4.56048	+	0.449490i	−0.995178	+	0.0980867i
$22$	−5.82843			−1.24262
$23$	3.29289	+	5.70346i	0.686616	+	1.18925i	0.972926	+	0.231116i	$0.0742378\pi$
$23$	3.29289	+	5.70346i	0.686616	+	1.18925i	−0.286310	+	0.958137i	$0.592429\pi$
$24$	2.17423	+	4.71940i	0.443814	+	0.963343i
$25$	−4.03295	−	2.32843i	−0.806591	−	0.465685i
$26$	−1.15539	−	3.41542i	−0.226592	−	0.669818i
$27$	2.53553	+	4.53553i	0.487964	+	0.872864i
$28$	2.63896	+	0.189469i	0.498716	+	0.0358062i
$29$			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
$31$	−0.800199	+	0.214413i	−0.143720	+	0.0385097i	−0.329962	−	0.943994i	$-0.607036\pi$
$31$	−0.800199	+	0.214413i	−0.143720	+	0.0385097i	0.186242	+	0.982504i	$0.440369\pi$
$32$	−1.29410	−	4.82963i	−0.228766	−	0.853766i
$33$	10.0525	+	0.926246i	1.74992	+	0.161239i
$34$	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
$37$	−3.86370	−	1.03528i	−0.635189	−	0.170198i	−0.0731657	−	0.997320i	$-0.523310\pi$
$37$	−3.86370	−	1.03528i	−0.635189	−	0.170198i	−0.562023	+	0.827121i	$0.689977\pi$
$38$	−3.32843	+	5.76500i	−0.539942	+	0.935207i
$39$	1.44999	+	6.07433i	0.232184	+	0.972672i
$40$	0.878680	+	1.52192i	0.138931	+	0.240636i
$41$	4.00000	−	4.00000i	0.624695	−	0.624695i	−0.322033	−	0.946728i	$-0.604366\pi$
$41$	4.00000	−	4.00000i	0.624695	−	0.624695i	0.946728	+	0.322033i	$0.104366\pi$
$42$	4.52142	+	0.746165i	0.697670	+	0.115136i
$43$			6.00000i			0.914991i	0.889212	+	0.457496i	$0.151253\pi$
$43$			6.00000i			0.914991i	−0.889212	+	0.457496i	$0.848747\pi$
$44$	−5.62983	−	1.50851i	−0.848729	−	0.227416i
$45$	0.994652	+	1.44879i	0.148274	+	0.215972i
$46$	−1.70453	−	6.36138i	−0.251319	−	0.937934i
$47$	0.170006	−	0.634472i	0.0247980	−	0.0925473i	−0.952418	−	0.304796i	$-0.901412\pi$
$47$	0.170006	−	0.634472i	0.0247980	−	0.0925473i	0.977216	+	0.212248i	$0.0680785\pi$
$48$	−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
$52$	−0.232051	−	3.59808i	−0.0321797	−	0.498963i
$53$	−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	$0.869338\pi$
$54$	−1.27526	−	5.03723i	−0.173540	−	0.685481i
$55$	3.41421			0.460372
$56$	−7.50000	−	2.59808i	−1.00223	−	0.347183i
$57$	6.65685	−	9.41421i	0.881722	−	1.24694i
$58$	0.258819	−	0.965926i	0.0339846	−	0.126832i
$59$	−9.16208	+	2.45497i	−1.19280	+	0.319610i	−0.799992	−	0.600010i	$-0.795163\pi$
$59$	−9.16208	+	2.45497i	−1.19280	+	0.319610i	−0.392809	+	0.919620i	$0.628497\pi$
$60$	−0.424546	−	0.921519i	−0.0548086	−	0.118968i
$61$	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
$63$	−7.67972	−	2.00548i	−0.967553	−	0.252667i
$64$			7.00000i			0.875000i
$65$	0.676814	+	2.00070i	0.0839485	+	0.248157i
$66$	−9.47029	−	3.49648i	−1.16571	−	0.430386i
$67$	−13.0258	+	3.49025i	−1.59135	+	0.426402i	−0.942417	−	0.334441i	$-0.891452\pi$
$67$	−13.0258	+	3.49025i	−1.59135	+	0.426402i	−0.648936	+	0.760843i	$0.724786\pi$
$68$	1.58346	−	0.914214i	0.192023	−	0.110865i
$69$	1.92893	+	11.2426i	0.232216	+	1.35345i
$70$	1.54587	+	0.110988i	0.184766	+	0.0132656i
$71$	0.464466	−	0.464466i	0.0551220	−	0.0551220i	−0.679008	−	0.734130i	$-0.737590\pi$
$71$	0.464466	−	0.464466i	0.0551220	−	0.0551220i	0.734130	+	0.679008i	$0.237590\pi$
$72$	0.701625	+	8.97261i	0.0826873	+	1.05743i
$73$	−3.32024	−	12.3913i	−0.388605	−	1.45029i	−0.832405	−	0.554167i	$-0.813037\pi$
$73$	−3.32024	−	12.3913i	−0.388605	−	1.45029i	0.443800	−	0.896126i	$-0.353630\pi$
$74$	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
$78$	0.171573	−	6.24264i	0.0194268	−	0.706840i
$79$	−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	$0.858683\pi$
$80$	−0.151613	−	0.565826i	−0.0169508	−	0.0632613i
$81$	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	$-0.673390\pi$
$83$	3.07107	−	3.07107i	0.337093	−	0.337093i	0.855272	+	0.518179i	$0.173390\pi$
$84$	4.17423	+	1.89097i	0.455446	+	0.206322i
$85$	−0.757359	+	0.757359i	−0.0821472	+	0.0821472i
$86$	1.55291	−	5.79555i	0.167455	−	0.624951i
$87$	−0.599900	+	1.62484i	−0.0643161	+	0.174202i
$88$	15.1427	+	8.74264i	1.61422	+	0.931969i
$89$	3.23143	−	12.0599i	0.342531	−	1.27834i	−0.552940	−	0.833221i	$-0.686494\pi$
$89$	3.23143	−	12.0599i	0.342531	−	1.27834i	0.895470	−	0.445121i	$-0.146839\pi$
$90$	−0.585786	−	1.65685i	−0.0617473	−	0.174648i
$91$	−8.22646	−	4.82963i	−0.862368	−	0.506283i
$92$		−	6.58579i		−	0.686616i
$93$	−1.42883	−	0.131652i	−0.148162	−	0.0136517i
$94$	−0.328427	+	0.568852i	−0.0338747	+	0.0586727i
$95$	1.94975	−	3.37706i	0.200040	−	0.346479i
$96$	0.794593	−	8.62372i	0.0810978	−	0.880155i
$97$	−7.00000	−	7.00000i	−0.710742	−	0.710742i	0.255948	−	0.966691i	$-0.417612\pi$
$97$	−7.00000	−	7.00000i	−0.710742	−	0.710742i	−0.966691	+	0.255948i	$0.917612\pi$
$98$	−5.60609	+	4.19187i	−0.566300	+	0.423443i
$99$	15.7782	+	7.53553i	1.58577	+	0.757350i
$100$	2.32843	+	4.03295i	0.232843	+	0.403295i
$101$	2.00000	−	3.46410i	0.199007	−	0.344691i	−0.749199	−	0.662344i	$-0.769562\pi$
$101$	2.00000	−	3.46410i	0.199007	−	0.344691i	0.948207	+	0.317653i	$0.102895\pi$
$102$	2.87636	−	1.32514i	0.284802	−	0.131209i
$103$	−5.61642	+	3.24264i	−0.553402	+	0.319507i	−0.750493	−	0.660878i	$-0.770184\pi$
$103$	−5.61642	+	3.24264i	−0.553402	+	0.319507i	0.197091	+	0.980385i	$0.436851\pi$
$104$	−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
$109$	7.16158	−	1.91894i	0.685955	−	0.183801i	0.101024	−	0.994884i	$-0.467788\pi$
$109$	7.16158	−	1.91894i	0.685955	−	0.183801i	0.584931	+	0.811083i	$0.301122\pi$
$110$	−3.29788	−	0.883663i	−0.314440	−	0.0842540i
$111$	−5.65685	−	4.00000i	−0.536925	−	0.379663i
$112$	2.19067	+	1.48356i	0.206999	+	0.140184i
$113$			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
$115$	0.998489	+	3.72641i	0.0931096	+	0.347490i
$116$	0.500000	−	0.866025i	0.0464238	−	0.0804084i
$117$	−1.28799	+	10.7397i	−0.119075	+	0.992885i
$118$	9.48528			0.873191
$119$	0.346430	−	4.82514i	0.0317572	−	0.442320i
$120$	0.514719	+	3.00000i	0.0469872	+	0.273861i
$121$	19.8931	−	11.4853i	1.80846	−	1.04412i
$122$	−0.258819	−	0.965926i	−0.0234324	−	0.0874508i
$123$	8.89898	−	4.09978i	0.802394	−	0.369664i
$124$	0.800199	+	0.214413i	0.0718600	+	0.0192548i
$125$	−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	$-0.745884\pi$
$127$		−	16.1421i		−	1.43238i	0.697904	−	0.716191i	$-0.254116\pi$
$128$	−0.776457	+	2.89778i	−0.0686298	+	0.256130i
$129$	−3.59940	+	9.74907i	−0.316910	+	0.858357i
$130$	−0.135932	−	2.10770i	−0.0119220	−	0.184858i
$131$	−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	$0.522691\pi$
$132$	−8.24264	−	5.82843i	−0.717430	−	0.507299i
$133$	3.32843	+	17.2950i	0.288611	+	1.49967i
$134$	13.4853			1.16495
$135$	0.747027	+	2.95074i	0.0642939	+	0.253960i
$136$	−5.29837	+	1.41970i	−0.454332	+	0.121738i
$137$	11.0253	−	2.95422i	0.941954	−	0.252396i	0.245009	−	0.969521i	$-0.421209\pi$
$137$	11.0253	−	2.95422i	0.941954	−	0.252396i	0.696944	+	0.717125i	$0.254542\pi$
$138$	1.04660	−	11.3588i	0.0890929	−	0.966925i
$139$	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
$141$	0.656854	−	0.928932i	0.0553171	−	0.0782302i
$142$	−0.568852	+	0.328427i	−0.0477370	+	0.0275610i
$143$	15.7852	+	13.8725i	1.32002	+	1.16007i
$144$	0.548188	−	2.94949i	0.0456823	−	0.245791i
$145$	−0.151613	+	0.565826i	−0.0125907	+	0.0469893i
$146$			12.8284i			1.06169i
$147$	10.3352	−	6.33900i	0.852436	−	0.522832i
$148$	2.82843	+	2.82843i	0.232495	+	0.232495i
$149$	13.9917	+	3.74907i	1.14625	+	0.307136i	0.781460	−	0.623956i	$-0.214476\pi$
$149$	13.9917	+	3.74907i	1.14625	+	0.307136i	0.364786	+	0.931091i	$0.381142\pi$
$150$	3.37503	+	7.32585i	0.275570	+	0.598153i
$151$	5.13197	+	19.1528i	0.417634	+	1.55863i	0.779500	+	0.626402i	$0.215473\pi$
$151$	5.13197	+	19.1528i	0.417634	+	1.55863i	−0.361866	+	0.932230i	$0.617860\pi$
$152$	17.2950	−	9.98528i	1.40281	−	0.809913i
$153$	−5.17157	+	1.82843i	−0.418097	+	0.147820i
$154$	13.8725	−	6.73413i	1.11788	−	0.542652i
$155$	−0.485281			−0.0389787
$156$	1.78144	−	5.98552i	0.142629	−	0.479225i
$157$	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	$0.143421\pi$
$158$	0.366025	+	1.36603i	0.0291194	+	0.108675i
$159$	−9.58492	−	11.5305i	−0.760134	−	0.914429i
$160$		−	2.92893i		−	0.231552i
$161$	−14.4273	−	9.77044i	−1.13703	−	0.770018i
$162$	0.949747	−	8.94975i	0.0746192	−	0.703159i
$163$	−2.09758	−	0.562044i	−0.164295	−	0.0440227i	0.175734	−	0.984438i	$-0.443770\pi$
$163$	−2.09758	−	0.562044i	−0.164295	−	0.0440227i	−0.340029	+	0.940415i	$0.610437\pi$
$164$	−5.46410	+	1.46410i	−0.426675	+	0.114327i
$165$	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	0.973503	+	0.228672i	$0.0734384\pi$
$167$	15.5355	+	15.5355i	1.20218	+	1.20218i	0.228672	+	0.973503i	$0.426562\pi$
$168$	−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
$171$	16.4639	−	11.3032i	1.25903	−	0.864376i
$172$	3.00000	−	5.19615i	0.228748	−	0.396203i
$173$	−7.74264	−	13.4106i	−0.588662	−	1.01959i	−0.994408	−	0.105607i	$-0.966322\pi$
$173$	−7.74264	−	13.4106i	−0.588662	−	1.01959i	0.405746	−	0.913986i	$-0.367012\pi$
$174$	1.00000	−	1.41421i	0.0758098	−	0.107211i
$175$	12.2892	+	0.882328i	0.928980	+	0.0666977i
$176$	−4.12132	−	4.12132i	−0.310656	−	0.310656i
$177$	−16.3597	−	1.50739i	−1.22967	−	0.113302i
$178$	−6.24264	+	10.8126i	−0.467906	+	0.810436i
$179$	0.757359	−	1.31178i	0.0566077	−	0.0980474i	−0.836333	−	0.548222i	$-0.815305\pi$
$179$	0.757359	−	1.31178i	0.0566077	−	0.0980474i	0.892941	+	0.450175i	$0.148638\pi$
$180$	−0.137001	−	1.75201i	−0.0102114	−	0.130587i
$181$		−	9.14214i		−	0.679530i	−0.940510	−	0.339765i	$-0.889653\pi$
$181$		−	9.14214i		−	0.679530i	0.940510	−	0.339765i	$-0.110347\pi$
$182$	6.69615	+	6.79423i	0.496352	+	0.503622i
$183$	0.292893	+	1.70711i	0.0216513	+	0.126193i
$184$	−5.11358	+	19.0841i	−0.376978	+	1.40690i
$185$	−2.02922	−	1.17157i	−0.149191	−	0.0861358i
$186$	1.34607	+	0.496974i	0.0986983	+	0.0364399i
$187$	−2.75820	+	10.2937i	−0.201699	+	0.752752i
$188$	−0.464466	+	0.464466i	−0.0338747	+	0.0338747i
$189$	−11.2753	−	7.86566i	−0.820154	−	0.572143i
$190$	−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
$193$	−0.732051	−	2.73205i	−0.0526942	−	0.196657i	0.934561	−	0.355803i	$-0.115793\pi$
$193$	−0.732051	−	2.73205i	−0.0526942	−	0.196657i	−0.987255	+	0.159146i	$0.949126\pi$
$194$	4.94975	+	8.57321i	0.355371	+	0.615521i
$195$	−0.100505	+	3.65685i	−0.00719732	+	0.261873i
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$	−5.00000	+	5.00000i	−0.356235	+	0.356235i	−0.862423	−	0.506188i	$-0.831054\pi$
$197$	−5.00000	+	5.00000i	−0.356235	+	0.356235i	0.506188	+	0.862423i	$0.331054\pi$
$198$	−13.2902	−	11.3625i	−0.944494	−	0.807495i
$199$	−13.0519	−	7.53553i	−0.925227	−	0.534180i	−0.0399279	−	0.999203i	$-0.512713\pi$
$199$	−13.0519	−	7.53553i	−0.925227	−	0.534180i	−0.885299	+	0.465023i	$0.846046\pi$
$200$	−3.61585	−	13.4945i	−0.255679	−	0.954207i
$201$	−23.2587	−	2.14306i	−1.64054	−	0.151160i
$202$	−2.82843	+	2.82843i	−0.199007	+	0.199007i
$203$	−1.15539	−	2.38014i	−0.0810928	−	0.167053i
$204$	3.12132	−	0.535534i	0.218536	−	0.0374949i
$205$	2.86976	−	1.65685i	0.200432	−	0.115720i
$206$	6.26430	−	1.67851i	0.436455	−	0.116948i
$207$	−3.61025	+	19.4247i	−0.250930	+	1.35011i
$208$	1.59808	−	3.23205i	0.110807	−	0.224102i
$209$		−	38.7990i		−	2.68378i
$210$	2.44521	+	1.10770i	0.168736	+	0.0764389i
$211$	−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
$213$	1.03332	−	0.476052i	0.0708018	−	0.0326185i
$214$	−6.59575	+	1.76733i	−0.450876	+	0.120812i
$215$	−0.909676	+	3.39496i	−0.0620394	+	0.231534i
$216$	−4.24264	+	15.0000i	−0.288675	+	1.02062i
$217$	1.65685	−	1.43488i	0.112475	−	0.0974059i
$218$	−7.41421			−0.502154
$219$	2.03868	−	22.1258i	0.137761	−	1.49512i
$220$	−2.95680	−	1.70711i	−0.199347	−	0.115093i
$221$	−6.57882	+	0.424288i	−0.442539	+	0.0285407i
$222$	4.42883	+	5.32780i	0.297243	+	0.357579i
$223$	−3.53553	−	3.53553i	−0.236757	−	0.236757i	0.578749	−	0.815506i	$-0.303541\pi$
$223$	−3.53553	−	3.53553i	−0.236757	−	0.236757i	−0.815506	+	0.578749i	$0.803541\pi$
$224$	8.66025	+	10.0000i	0.578638	+	0.668153i
$225$	−4.65685	−	13.1716i	−0.310457	−	0.878105i
$226$	2.32937	−	8.69333i	0.154947	−	0.578272i
$227$	−1.55291	−	5.79555i	−0.103071	−	0.384664i	0.895049	−	0.445969i	$-0.147141\pi$
$227$	−1.55291	−	5.79555i	−0.103071	−	0.384664i	−0.998119	+	0.0613041i	$0.980474\pi$
$228$	−10.4721	+	4.82452i	−0.693533	+	0.319512i
$229$	5.32681	+	1.42731i	0.352005	+	0.0943196i	0.430489	−	0.902596i	$-0.358341\pi$
$229$	5.32681	+	1.42731i	0.352005	+	0.0943196i	−0.0784835	+	0.996915i	$0.525008\pi$
$230$		−	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	0.843189	−	0.537618i	$-0.180676\pi$
$233$	−0.671573	−	1.16320i	−0.0439962	−	0.0762037i	−0.887185	+	0.461414i	$0.847342\pi$
$234$	4.02374	−	10.0404i	0.263040	−	0.656361i
$235$	0.192388	−	0.333226i	0.0125500	−	0.0217373i
$236$	9.16208	+	2.45497i	0.596400	+	0.159805i
$237$	−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	$-0.815459\pi$
$239$	−4.46447	+	4.46447i	−0.288782	+	0.288782i	0.547816	+	0.836599i	$0.315459\pi$
$240$	0.0930924	−	1.01033i	0.00600909	−	0.0652167i
$241$	−5.75682	−	21.4847i	−0.370829	−	1.38395i	−0.859344	−	0.511398i	$-0.829128\pi$
$241$	−5.75682	−	21.4847i	−0.370829	−	1.38395i	0.488515	−	0.872556i	$-0.337539\pi$
$242$	−22.1879	+	5.94522i	−1.42629	+	0.382173i
$243$	−3.06035	+	15.2851i	−0.196322	+	0.980540i
$244$		−	1.00000i		−	0.0640184i
$245$	3.28397	−	2.45554i	0.209805	−	0.156879i
$246$	−9.65685	+	1.65685i	−0.615699	+	0.105637i
$247$	22.7359	−	7.69129i	1.44665	−	0.489385i
$248$	−2.15232	−	1.24264i	−0.136672	−	0.0789078i
$249$	6.83234	−	3.14767i	0.432982	−	0.199476i
$250$	2.82843	+	4.89898i	0.178885	+	0.309839i
$251$	−2.00000			−0.126239			−0.0631194	−	0.998006i	$-0.520105\pi$
$251$	−2.00000			−0.126239			−0.0631194	+	0.998006i	$0.520105\pi$
$252$	5.64809	+	5.57666i	0.355796	+	0.351296i
$253$	27.1421	+	27.1421i	1.70641	+	1.70641i
$254$	−4.17789	+	15.5921i	−0.262144	+	0.978336i
$255$	−1.68493	+	0.776251i	−0.105514	+	0.0486107i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	9.41421	+	16.3059i	0.587243	+	1.01713i	0.994592	+	0.103861i	$0.0331198\pi$
$257$	9.41421	+	16.3059i	0.587243	+	1.01713i	−0.407349	+	0.913272i	$0.633547\pi$
$258$	6.00000	−	8.48528i	0.373544	−	0.528271i
$259$	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
$262$	12.3913	−	3.32024i	0.765538	−	0.205125i
$263$	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
$266$	1.26127	−	17.5672i	0.0773331	−	1.07711i
$267$	12.4853	−	17.6569i	0.764087	−	1.08058i
$268$	13.0258	+	3.49025i	0.795676	+	0.213201i
$269$	−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
$271$	4.02943	+	1.07968i	0.244770	+	0.0655860i	0.379118	−	0.925348i	$-0.376227\pi$
$271$	4.02943	+	1.07968i	0.244770	+	0.0655860i	−0.134348	+	0.990934i	$0.542894\pi$
$272$	1.82843			0.110865
$273$	−10.4694	−	12.7825i	−0.633638	−	0.773629i
$274$	−11.4142			−0.689558
$275$	−26.2173	−	7.02490i	−1.58096	−	0.423618i
$276$	3.95082	−	10.7009i	0.237811	−	0.644117i
$277$	−3.31552	−	1.91421i	−0.199210	−	0.115014i	0.397077	−	0.917785i	$-0.370025\pi$
$277$	−3.31552	−	1.91421i	−0.199210	−	0.115014i	−0.596287	+	0.802771i	$0.703358\pi$
$278$	−2.82913	−	0.758063i	−0.169680	−	0.0454656i
$279$	−2.24264	−	1.07107i	−0.134263	−	0.0641232i
$280$	−3.84980	−	2.60715i	−0.230069	−	0.155807i
$281$	−8.07107	−	8.07107i	−0.481480	−	0.481480i	0.424124	−	0.905604i	$-0.360582\pi$
$281$	−8.07107	−	8.07107i	−0.481480	−	0.481480i	−0.905604	+	0.424124i	$0.860582\pi$
$282$	−0.874898	+	0.727273i	−0.0520994	+	0.0433085i
$283$	15.4144	+	8.89949i	0.916290	+	0.529020i	0.882449	−	0.470407i	$-0.155893\pi$
$283$	15.4144	+	8.89949i	0.916290	+	0.529020i	0.0338402	+	0.999427i	$0.489226\pi$
$284$	−0.634472	+	0.170006i	−0.0376490	+	0.0100880i
$285$	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
$288$	6.46447	−	13.5355i	0.380922	−	0.797589i
$289$	6.82843	+	11.8272i	0.401672	+	0.695717i
$290$	0.292893	−	0.507306i	0.0171993	−	0.0297900i
$291$	−7.17461	−	15.5732i	−0.420583	−	0.912918i
$292$	−3.32024	+	12.3913i	−0.194302	+	0.725147i
$293$	−9.14214	−	9.14214i	−0.534089	−	0.534089i	0.387697	−	0.921787i	$-0.373271\pi$
$293$	−9.14214	−	9.14214i	−0.534089	−	0.534089i	−0.921787	+	0.387697i	$0.873271\pi$
$294$	−11.6237	+	3.44805i	−0.677909	+	0.201094i
$295$	−5.55635			−0.323503
$296$	−6.00000	−	10.3923i	−0.348743	−	0.604040i
$297$	21.1165	+	21.7094i	1.22530	+	1.25971i
$298$	−12.5446	−	7.24264i	−0.726690	−	0.419555i
$299$	−10.5246	+	21.2856i	−0.608653	+	1.23098i
$300$	1.36396	+	7.94975i	0.0787483	+	0.458979i
$301$	−6.93237	−	14.2808i	−0.399575	−	0.823134i
$302$		−	19.8284i		−	1.14100i
$303$	5.32780	−	4.42883i	0.306074	−	0.254429i
$304$	−6.43003	+	1.72292i	−0.368787	+	0.0988163i
$305$	0.151613	+	0.565826i	0.00868132	+	0.0323991i
$306$	5.46859	−	0.427623i	0.312618	−	0.0244456i
$307$	3.53553	−	3.53553i	0.201784	−	0.201784i	−0.598980	−	0.800764i	$-0.704427\pi$
$307$	3.53553	−	3.53553i	0.201784	−	0.201784i	0.800764	+	0.598980i	$0.204427\pi$
$308$	15.1427	−	2.91421i	0.862835	−	0.166053i
$309$	−11.0711	+	1.89949i	−0.629811	+	0.108058i
$310$	0.468746	+	0.125600i	0.0266230	+	0.00713360i
$311$	−0.928932	+	1.60896i	−0.0526749	+	0.0912356i	−0.891161	−	0.453688i	$-0.850108\pi$
$311$	−0.928932	+	1.60896i	−0.0526749	+	0.0912356i	0.838486	+	0.544924i	$0.183441\pi$
$312$	−9.80972	+	15.9615i	−0.555366	+	0.903642i
$313$	−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
$317$	16.3521	+	4.38153i	0.918425	+	0.246091i	0.686912	−	0.726741i	$-0.258966\pi$
$317$	16.3521	+	4.38153i	0.918425	+	0.246091i	0.231513	+	0.972832i	$0.425632\pi$
$318$	6.27401	+	13.6184i	0.351829	+	0.763681i
$319$	1.50851	+	5.62983i	0.0844602	+	0.315210i
$320$	−1.06129	+	3.96078i	−0.0593278	+	0.221415i
$321$	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
$325$	−1.08063	−	16.7557i	−0.0599424	−	0.929440i
$326$	1.88064	+	1.08579i	0.104159	+	0.0601361i
$327$	12.7876	+	1.17826i	0.707157	+	0.0651577i
$328$	16.9706			0.937043
$329$	0.328427	+	1.70656i	0.0181068	+	0.0940856i
$330$	−4.82843	−	3.41421i	−0.265796	−	0.187946i
$331$	−6.07082	+	22.6566i	−0.333682	+	1.24532i	0.571608	+	0.820527i	$0.306320\pi$
$331$	−6.07082	+	22.6566i	−0.333682	+	1.24532i	−0.905291	+	0.424793i	$0.860347\pi$
$332$	−4.19516	+	1.12409i	−0.230239	+	0.0616924i
$333$	−6.79191	−	9.89293i	−0.372194	−	0.542129i
$334$	−10.9853	−	19.0271i	−0.601088	−	1.04111i
$335$	−7.89949			−0.431596
$336$	2.66951	+	3.72474i	0.145634	+	0.203201i
$337$			17.1421i			0.933792i	0.884312	+	0.466896i	$0.154628\pi$
$337$			17.1421i			0.933792i	−0.884312	+	0.466896i	$0.845372\pi$
$338$	7.93546	−	10.2970i	0.431632	−	0.560084i
$339$	−5.39910	+	14.6236i	−0.293239	+	0.794245i
$340$	1.03457	−	0.277213i	0.0561075	−	0.0150340i
$341$	−4.18154	+	2.41421i	−0.226443	+	0.130737i
$342$	−18.8284	+	6.65685i	−1.01812	+	0.359961i
$343$	−3.95164	+	18.0938i	−0.213368	+	0.976972i
$344$	−12.7279	+	12.7279i	−0.686244	+	0.686244i
$345$	−0.613086	+	6.65383i	−0.0330075	+	0.358230i
$346$	4.00789	+	14.9576i	0.215465	+	0.804127i
$347$	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	−0.622240	−	0.782826i	$-0.713777\pi$
$349$	3.00000	−	3.00000i	0.160586	−	0.160586i	0.782826	+	0.622240i	$0.213777\pi$
$350$	−11.6421	−	4.03295i	−0.622298	−	0.215570i
$351$	−8.53553	+	16.6777i	−0.455593	+	0.890188i
$352$	−14.5711	−	25.2378i	−0.776641	−	1.34518i
$353$	−1.85614	−	6.92721i	−0.0987923	−	0.368698i	0.898775	−	0.438411i	$-0.144458\pi$
$353$	−1.85614	−	6.92721i	−0.0987923	−	0.368698i	−0.997567	+	0.0697126i	$0.977792\pi$
$354$	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
$357$	3.45750	−	7.63228i	0.182990	−	0.403943i
$358$	−1.07107	+	1.07107i	−0.0566077	+	0.0566077i
$359$	5.81962	−	21.7191i	0.307148	−	1.14629i	−0.623933	−	0.781478i	$-0.714466\pi$
$359$	5.81962	−	21.7191i	0.307148	−	1.14629i	0.931081	−	0.364813i	$-0.118867\pi$
$360$	−0.963364	+	5.18331i	−0.0507737	+	0.273185i
$361$	−21.9223	−	12.6569i	−1.15381	−	0.666150i
$362$	−2.36616	+	8.83062i	−0.124363	+	0.464127i
$363$	39.2132	−	6.72792i	2.05816	−	0.353124i
$364$	4.70951	+	8.29581i	0.246845	+	0.434819i
$365$		−	7.51472i		−	0.393338i
$366$	0.158919	−	1.72474i	0.00830681	−	0.0901539i
$367$	−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
$369$	16.9189	−	1.32300i	0.880764	−	0.0688725i
$370$	1.65685	+	1.65685i	0.0861358	+	0.0861358i
$371$	22.8451	+	1.64020i	1.18606	+	0.0851551i
$372$	1.17157	+	0.828427i	0.0607432	+	0.0429519i
$373$	−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
$375$	−4.09978	−	8.89898i	−0.211712	−	0.459541i
$376$	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	0.682846	−	0.730562i	$-0.260742\pi$
$379$	−0.928932	−	0.928932i	−0.0477160	−	0.0477160i	−0.730562	+	0.682846i	$0.760742\pi$
$380$	−3.37706	+	1.94975i	−0.173240	+	0.100020i
$381$	9.68367	−	26.2285i	0.496110	−	1.34372i
$382$	16.3923	−	4.39230i	0.838703	−	0.224730i
$383$	6.92721	+	1.85614i	0.353964	+	0.0948443i	0.431419	−	0.902151i	$-0.358013\pi$
$383$	6.92721	+	1.85614i	0.353964	+	0.0948443i	−0.0774556	+	0.996996i	$0.524680\pi$
$384$	−3.00000	+	4.24264i	−0.153093	+	0.216506i
$385$	−8.12630	+	3.94476i	−0.414155	+	0.201044i
$386$			2.82843i			0.143963i
$387$	−11.6969	+	13.6814i	−0.594589	+	0.695466i
$388$	2.56218	+	9.56218i	0.130075	+	0.485446i
$389$	−4.67157	+	8.09140i	−0.236858	+	0.410250i	−0.959811	−	0.280647i	$-0.909451\pi$
$389$	−4.67157	+	8.09140i	−0.236858	+	0.410250i	0.722953	+	0.690897i	$0.242784\pi$
$390$	1.04354	−	3.50624i	0.0528419	−	0.177545i
$391$	−12.0416			−0.608971
$392$	20.8528	−	2.48168i	1.05323	−	0.125344i
$393$	−21.8995	+	3.75736i	−1.10468	+	0.189534i
$394$	6.12372	−	3.53553i	0.308509	−	0.178118i
$395$	−0.214413	−	0.800199i	−0.0107883	−	0.0402624i
$396$	−9.89653	−	14.4151i	−0.497319	−	0.724384i
$397$	−27.1832	−	7.28372i	−1.36429	−	0.365559i	−0.498898	−	0.866661i	$-0.666262\pi$
$397$	−27.1832	−	7.28372i	−1.36429	−	0.365559i	−0.865389	+	0.501101i	$0.832928\pi$
$398$	10.6569	+	10.6569i	0.534180	+	0.534180i
$399$	−4.96711	+	30.0984i	−0.248667	+	1.50681i
$400$			4.65685i			0.232843i
$401$	3.16863	−	11.8255i	0.158234	−	0.590536i	−0.840573	−	0.541698i	$-0.817782\pi$
$401$	3.16863	−	11.8255i	0.158234	−	0.590536i	0.998807	−	0.0488381i	$-0.0155518\pi$
$402$	21.9115	+	8.08983i	1.09285	+	0.403484i
$403$	−2.24364	−	1.97177i	−0.111763	−	0.0982210i
$404$	−3.46410	+	2.00000i	−0.172345	+	0.0995037i
$405$	−0.556349	+	5.24264i	−0.0276452	+	0.260509i
$406$	0.500000	+	2.59808i	0.0248146	+	0.128940i
$407$	−23.3137			−1.15562
$408$	−9.46071	−	0.871713i	−0.468375	−	0.0431562i
$409$	−25.8172	+	6.91770i	−1.27658	+	0.342058i	−0.832547	−	0.553954i	$-0.813118\pi$
$409$	−25.8172	+	6.91770i	−1.27658	+	0.342058i	−0.444030	+	0.896012i	$0.646452\pi$
$410$	−3.20080	+	0.857651i	−0.158076	+	0.0423564i
$411$	19.6866	+	1.81393i	0.971069	+	0.0894746i
$412$	6.48528			0.319507
$413$	18.9706	−	16.4290i	0.933480	−	0.808418i
$414$	8.51472	−	17.8284i	0.418476	−	0.876219i
$415$	2.20330	−	1.27208i	0.108156	−	0.0624439i
$416$	11.9007	−	13.5415i	0.583480	−	0.663929i
$417$	4.75906	+	1.75707i	0.233052	+	0.0860440i
$418$	−10.0419	+	37.4769i	−0.491166	+	1.83306i
$419$		−	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	0.383832	−	0.923403i	$-0.374604\pi$
$421$	−11.0711	−	11.0711i	−0.539571	−	0.539571i	−0.923403	+	0.383832i	$0.874604\pi$
$422$	14.5575	+	3.90068i	0.708650	+	0.189882i
$423$	1.62455	−	1.11532i	0.0789885	−	0.0542289i
$424$	−6.72168	−	25.0856i	−0.326433	−	1.21827i
$425$	7.37396	−	4.25736i	0.357690	−	0.206512i
$426$	−1.12132	+	0.192388i	−0.0543281	+	0.00932124i
$427$	−2.19067	−	1.48356i	−0.106014	−	0.0717947i
$428$	−6.82843			−0.330064
$429$	17.3264	+	32.0101i	0.836525	+	1.54546i
$430$	1.75736	−	3.04384i	0.0847474	−	0.146787i
$431$	3.92669	+	14.6546i	0.189142	+	0.705888i	0.993706	+	0.112022i	$0.0357326\pi$
$431$	3.92669	+	14.6546i	0.189142	+	0.705888i	−0.804564	+	0.593866i	$0.797601\pi$
$432$	2.66012	−	4.46360i	0.127985	−	0.214755i
$433$			5.14214i			0.247115i	0.992337	+	0.123558i	$0.0394304\pi$
$433$			5.14214i			0.247115i	−0.992337	+	0.123558i	$0.960570\pi$
$434$	−1.97177	+	0.957160i	−0.0946481	+	0.0459452i
$435$	−0.585786	+	0.828427i	−0.0280863	+	0.0397200i
$436$	−7.16158	−	1.91894i	−0.342977	−	0.0919005i
$437$	42.3468	−	11.3468i	2.02572	−	0.542790i
$438$	−7.69578	+	20.8442i	−0.367719	+	0.995974i
$439$	27.8359	−	16.0711i	1.32854	−	0.767030i	0.343462	−	0.939167i	$-0.388400\pi$
$439$	27.8359	−	16.0711i	1.32854	−	0.767030i	0.985073	+	0.172136i	$0.0550670\pi$
$440$	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	$0.293363\pi$
$444$	2.89898	+	6.29253i	0.137579	+	0.298630i
$445$	3.65685	−	6.33386i	0.173352	−	0.300254i
$446$	2.50000	+	4.33013i	0.118378	+	0.205037i
$447$	20.4853	+	14.4853i	0.968921	+	0.685130i
$448$	−8.08776	−	16.6610i	−0.382111	−	0.787157i
$449$	−2.00000	−	2.00000i	−0.0943858	−	0.0943858i	0.658337	−	0.752723i	$-0.271260\pi$
$449$	−2.00000	−	2.00000i	−0.0943858	−	0.0943858i	−0.752723	+	0.658337i	$0.771260\pi$
$450$	1.08912	+	13.9280i	0.0513417	+	0.656574i
$451$	16.4853	−	28.5533i	0.776262	−	1.34452i
$452$	4.50000	−	7.79423i	0.211662	−	0.366610i
$453$	−3.15111	+	34.1990i	−0.148052	+	1.60681i
$454$			6.00000i			0.281594i
$455$	−3.92252	−	3.97997i	−0.183890	−	0.186584i
$456$	34.0919	−	5.84924i	1.59650	−	0.273916i
$457$	−1.15010	+	4.29224i	−0.0537995	+	0.200782i	−0.987594	−	0.157026i	$-0.949809\pi$
$457$	−1.15010	+	4.29224i	−0.0537995	+	0.200782i	0.933795	+	0.357809i	$0.116476\pi$
$458$	−4.77589	−	2.75736i	−0.223163	−	0.128843i
$459$	−9.49988	−	0.131519i	−0.443416	−	0.00613879i
$460$	0.998489	−	3.72641i	0.0465548	−	0.173745i
$461$	−28.0711	+	28.0711i	−1.30740	+	1.30740i	−0.384115	+	0.923285i	$0.625493\pi$
$461$	−28.0711	+	28.0711i	−1.30740	+	1.30740i	−0.923285	+	0.384115i	$0.874507\pi$
$462$	26.5804	−	2.61982i	1.23663	−	0.121885i
$463$	4.00000	−	4.00000i	0.185896	−	0.185896i	−0.608023	−	0.793919i	$-0.708037\pi$
$463$	4.00000	−	4.00000i	0.185896	−	0.185896i	0.793919	+	0.608023i	$0.208037\pi$
$464$	0.866025	−	0.500000i	0.0402042	−	0.0232119i
$465$	−0.788507	−	0.291121i	−0.0365661	−	0.0135004i
$466$	0.347632	+	1.29738i	0.0161037	+	0.0600999i
$467$	11.4853	+	19.8931i	0.531475	+	0.920542i	0.999325	+	0.0367344i	$0.0116955\pi$
$467$	11.4853	+	19.8931i	0.531475	+	0.920542i	−0.467850	+	0.883808i	$0.654971\pi$
$468$	6.48528	−	8.65685i	0.299782	−	0.400163i
$469$	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
$473$	9.05105	+	33.7790i	0.416168	+	1.55316i
$474$	−0.224745	+	2.43916i	−0.0103229	+	0.112034i
$475$	−21.9203	+	21.9203i	−1.00577	+	1.00577i
$476$	−2.71259	+	4.00548i	−0.124331	+	0.183591i
$477$	−8.65685	−	24.4853i	−0.396370	−	1.12110i
$478$	5.46783	−	3.15685i	0.250093	−	0.144391i
$479$	−28.4806	+	7.63135i	−1.30131	+	0.348685i	−0.841946	−	0.539562i	$-0.818590\pi$
$479$	−28.4806	+	7.63135i	−1.30131	+	0.348685i	−0.459366	+	0.888247i	$0.651923\pi$
$480$	1.75707	−	4.75906i	0.0801988	−	0.217220i
$481$	−4.62158	−	13.6617i	−0.210726	−	0.622918i
$482$			22.2426i			1.01312i
$483$	−17.5808	−	24.5304i	−0.799955	−	1.11617i
$484$	−22.9706			−1.04412
$485$	−2.89949	−	5.02207i	−0.131659	−	0.228041i
$486$	6.91215	−	13.9722i	0.313541	−	0.633792i
$487$	−9.02479	+	2.41818i	−0.408952	+	0.109578i	−0.457429	−	0.889246i	$-0.651230\pi$
$487$	−9.02479	+	2.41818i	−0.408952	+	0.109578i	0.0484774	+	0.998824i	$0.484563\pi$
$488$	−0.776457	+	2.89778i	−0.0351486	+	0.131176i
$489$	−3.07107	−	2.17157i	−0.138878	−	0.0982019i
$490$	−3.80761	+	1.52192i	−0.172010	+	0.0687532i
$491$	9.21320			0.415786			0.207893	−	0.978152i	$-0.433339\pi$
$491$	9.21320			0.415786			0.207893	+	0.978152i	$0.433339\pi$
$492$	−9.75663	−	0.898979i	−0.439863	−	0.0405291i
$493$	−1.58346	−	0.914214i	−0.0713156	−	0.0411741i
$494$	−23.9519	+	1.54473i	−1.07765	+	0.0695006i
$495$	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
$499$	−4.74756	+	17.7181i	−0.212530	+	0.793172i	0.774492	+	0.632584i	$0.218006\pi$
$499$	−4.74756	+	17.7181i	−0.212530	+	0.793172i	−0.987022	+	0.160588i	$0.948661\pi$
$500$	1.46410	+	5.46410i	0.0654766	+	0.244362i
$501$	15.9231	+	34.5626i	0.711390	+	1.54414i
$502$	1.93185	+	0.517638i	0.0862228	+	0.0231033i
$503$		−	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
$507$	−15.3230	+	16.4986i	−0.680520	+	0.732730i
$508$	−8.07107	+	13.9795i	−0.358096	+	0.620240i
$509$	−25.8172	−	6.91770i	−1.14433	−	0.306621i	−0.363637	−	0.931541i	$-0.618465\pi$
$509$	−25.8172	−	6.91770i	−1.14433	−	0.306621i	−0.780689	+	0.624919i	$0.785132\pi$
$510$	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
$513$	33.5321	−	8.48919i	1.48048	−	0.374807i
$514$	−4.87316	−	18.1869i	−0.214946	−	0.802188i
$515$	−3.66954	+	0.983251i	−0.161699	+	0.0433272i
$516$	7.99171	−	6.64324i	0.351815	−	0.292452i
$517$		−	3.82843i		−	0.168374i
$518$	−10.5558	−	0.757875i	−0.463797	−	0.0332991i
$519$	−4.53553	−	26.4350i	−0.199088	−	1.16037i
$520$	−2.80839	+	5.67987i	−0.123156	+	0.249079i
$521$	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	$0.628534\pi$
$522$	2.47323	−	1.69798i	0.108250	−	0.0743184i
$523$	−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
$525$	19.4388	+	8.80597i	0.848379	+	0.384324i
$526$	−14.4853	−	14.4853i	−0.631588	−	0.631588i
$527$	0.392038	−	1.46311i	0.0170774	−	0.0637339i
$528$	−4.22412	−	9.16889i	−0.183831	−	0.399025i
$529$	−10.1863	+	17.6432i	−0.442882	+	0.767095i
$530$	2.53553	+	4.39167i	0.110137	+	0.190762i
$531$	−25.6777	−	12.2635i	−1.11432	−	0.532189i
$532$	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
$535$	3.86370	−	1.03528i	0.167042	−	0.0447589i
$536$	−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
$539$	16.0811	−	37.4961i	0.692661	−	1.61507i
$540$	0.828427	−	2.92893i	0.0356498	−	0.126041i
$541$	33.3504	+	8.93622i	1.43385	+	0.384198i	0.890375	−	0.455229i	$-0.150442\pi$
$541$	33.3504	+	8.93622i	1.43385	+	0.384198i	0.543473	+	0.839427i	$0.317109\pi$
$542$	−3.61269	−	2.08579i	−0.155178	−	0.0895922i
$543$	5.48437	−	14.8545i	0.235357	−	0.637470i
$544$	8.83062	+	2.36616i	0.378610	+	0.101448i
$545$	4.34315			0.186040
$546$	6.80435	+	15.0566i	0.291199	+	0.644363i
$547$	15.0711			0.644392			0.322196	−	0.946673i	$-0.395579\pi$
$547$	15.0711			0.644392			0.322196	+	0.946673i	$0.395579\pi$
$548$	−11.0253	−	2.95422i	−0.470977	−	0.126198i
$549$	−0.548188	+	2.94949i	−0.0233961	+	0.125881i
$550$	23.5058	+	13.5711i	1.00229	+	0.578672i
$551$	6.43003	+	1.72292i	0.273928	+	0.0733989i
$552$	−19.7574	+	27.9411i	−0.840929	+	1.18925i
$553$	3.09808	+	2.09808i	0.131744	+	0.0892193i
$554$	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
$557$	−31.6127	+	8.47061i	−1.33948	+	0.358911i	−0.856239	−	0.516579i	$-0.827205\pi$
$557$	−31.6127	+	8.47061i	−1.33948	+	0.358911i	−0.483236	+	0.875490i	$0.660539\pi$
$558$	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
$561$	−10.6569	+	15.0711i	−0.449933	+	0.636301i
$562$	5.70711	+	9.88500i	0.240740	+	0.416974i
$563$	−1.75736	+	3.04384i	−0.0740639	+	0.128282i	−0.900679	−	0.434486i	$-0.856930\pi$
$563$	−1.75736	+	3.04384i	−0.0740639	+	0.128282i	0.826615	+	0.562768i	$0.190264\pi$
$564$	−1.03332	+	0.476052i	−0.0435106	+	0.0200454i
$565$	−1.36451	+	5.09244i	−0.0574055	+	0.214240i
$566$	−12.5858	−	12.5858i	−0.529020	−	0.529020i
$567$	−13.6019	−	19.5445i	−0.571227	−	0.820792i
$568$	1.97056			0.0826830
$569$	21.7426	+	37.6594i	0.911499	+	1.57876i	0.811948	+	0.583730i	$0.198407\pi$
$569$	21.7426	+	37.6594i	0.911499	+	1.57876i	0.0995511	+	0.995032i	$0.468259\pi$
$570$	−6.13442	+	2.82614i	−0.256943	+	0.118374i
$571$	12.1604	+	7.02082i	0.508897	+	0.293812i	0.732380	−	0.680896i	$-0.238409\pi$
$571$	12.1604	+	7.02082i	0.508897	+	0.293812i	−0.223483	+	0.974708i	$0.571743\pi$
$572$	−6.73413	−	19.9065i	−0.281568	−	0.832333i
$573$	−28.9706	+	4.97056i	−1.21026	+	0.207648i
$574$	8.39230	−	12.3923i	0.350288	−	0.517245i
$575$		−	30.6690i		−	1.27899i
$576$	−13.6464	+	15.9617i	−0.568601	+	0.665070i
$577$	9.46510	−	2.53617i	0.394037	−	0.105582i	−0.0563594	−	0.998411i	$-0.517949\pi$
$577$	9.46510	−	2.53617i	0.394037	−	0.105582i	0.450397	+	0.892829i	$0.351283\pi$
$578$	−3.53465	−	13.1915i	−0.147022	−	0.548694i
$579$	0.449490	−	4.87832i	0.0186802	−	0.202736i
$580$	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
$583$	−48.7366	−	13.0589i	−2.01846	−	0.540846i
$584$	19.2426	−	33.3292i	0.796266	−	1.37917i
$585$	−2.35705	+	5.88153i	−0.0974522	+	0.243171i
$586$	6.46447	+	11.1968i	0.267045	+	0.462535i
$587$	23.5355	−	23.5355i	0.971415	−	0.971415i	−0.0281872	−	0.999603i	$-0.508973\pi$
$587$	23.5355	−	23.5355i	0.971415	−	0.971415i	0.999603	+	0.0281872i	$0.00897346\pi$
$588$	−12.1201	+	0.322117i	−0.499824	+	0.0132839i
$589$			5.51472i			0.227230i
$590$	5.36702	+	1.43809i	0.220957	+	0.0592052i
$591$	−11.1237	+	5.12472i	−0.457569	+	0.210803i
$592$	1.03528	+	3.86370i	0.0425496	+	0.158797i
$593$	−8.63300	+	32.2188i	−0.354515	+	1.32307i	0.526579	+	0.850126i	$0.323474\pi$
$593$	−8.63300	+	32.2188i	−0.354515	+	1.32307i	−0.881094	+	0.472941i	$0.843192\pi$
$594$	−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
$598$	15.6751	−	17.8363i	0.641002	−	0.729382i
$599$	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	$0.495502\pi$
$600$	2.22018	−	24.0957i	0.0906386	−	0.983701i
$601$	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
$603$	−36.5061	−	17.4350i	−1.48664	−	0.710009i
$604$	5.13197	−	19.1528i	0.208817	−	0.779316i
$605$	12.9973	−	3.48263i	0.528417	−	0.141589i
$606$	−6.29253	+	2.89898i	−0.255617	+	0.117763i
$607$	−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
$609$	−0.449490	−	4.56048i	−0.0182142	−	0.184800i
$610$		−	0.585786i		−	0.0237178i
$611$	2.24343	−	0.758926i	0.0907595	−	0.0307029i
$612$	5.39293	+	1.00232i	0.217996	+	0.0405165i
$613$	−5.93285	+	1.58970i	−0.239625	+	0.0642074i	−0.376633	−	0.926363i	$-0.622918\pi$
$613$	−5.93285	+	1.58970i	−0.239625	+	0.0642074i	0.137008	+	0.990570i	$0.456252\pi$
$614$	−4.33013	+	2.50000i	−0.174750	+	0.100892i
$615$	5.65685	−	0.970563i	0.228106	−	0.0391369i
$616$	−46.1429	−	3.31291i	−1.85915	−	0.133481i
$617$	−7.07107	+	7.07107i	−0.284670	+	0.284670i	−0.834968	−	0.550298i	$-0.814514\pi$
$617$	−7.07107	+	7.07107i	−0.284670	+	0.284670i	0.550298	+	0.834968i	$0.314514\pi$
$618$	11.1855	+	1.03063i	0.449945	+	0.0414581i
$619$	5.81962	+	21.7191i	0.233910	+	0.872965i	0.978637	+	0.205595i	$0.0659131\pi$
$619$	5.81962	+	21.7191i	0.233910	+	0.872965i	−0.744727	+	0.667369i	$0.767420\pi$
$620$	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
$624$	4.53553	−	4.29289i	0.181567	−	0.171853i
$625$	9.98528	+	17.2950i	0.399411	+	0.691801i
$626$	6.12284	+	22.8508i	0.244718	+	0.913300i
$627$	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
$630$	3.30857	+	3.26673i	0.131817	+	0.130150i
$631$	13.0711	−	13.0711i	0.520351	−	0.520351i	−0.397326	−	0.917677i	$-0.630062\pi$
$631$	13.0711	−	13.0711i	0.520351	−	0.520351i	0.917677	+	0.397326i	$0.130062\pi$
$632$	1.09808	−	4.09808i	0.0436791	−	0.163013i
$633$	−24.4881	−	9.04114i	−0.973316	−	0.359353i
$634$	−14.6609	−	8.46447i	−0.582258	−	0.336167i
$635$	2.44735	−	9.13364i	0.0971202	−	0.362458i
$636$	2.53553	+	14.7782i	0.100540	+	0.585993i
$637$	25.1603	+	1.99038i	0.996886	+	0.0788618i
$638$		−	5.82843i		−	0.230750i
$639$	1.96457	−	0.153622i	0.0777170	−	0.00607718i
$640$	−0.878680	+	1.52192i	−0.0347329	+	0.0601591i
$641$	−12.1421	+	21.0308i	−0.479586	+	0.830666i	−0.999726	−	0.0234143i	$-0.992546\pi$
$641$	−12.1421	+	21.0308i	−0.479586	+	0.830666i	0.520140	+	0.854081i	$0.325880\pi$
$642$	−11.7773	−	1.08516i	−0.464813	−	0.0428280i
$643$	7.67767	+	7.67767i	0.302778	+	0.302778i	0.842100	−	0.539322i	$-0.181319\pi$
$643$	7.67767	+	7.67767i	0.302778	+	0.302778i	−0.539322	+	0.842100i	$0.681319\pi$
$644$	7.60918	+	15.6751i	0.299844	+	0.617685i
$645$	−3.51472	+	4.97056i	−0.138392	+	0.195716i
$646$	−6.08579	−	10.5409i	−0.239442	−	0.414726i
$647$	−21.0919	+	36.5322i	−0.829207	+	1.43623i	0.0694533	+	0.997585i	$0.477875\pi$
$647$	−21.0919	+	36.5322i	−0.829207	+	1.43623i	−0.898661	+	0.438644i	$0.855459\pi$
$648$	−15.8921	+	21.8275i	−0.624302	+	0.857465i
$649$	−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
$655$	−7.25866	+	1.94495i	−0.283619	+	0.0759956i
$656$	−5.46410	−	1.46410i	−0.213337	−	0.0571636i
$657$	16.5858	−	34.7279i	0.647073	−	1.35487i
$658$	0.124453	−	1.73341i	0.00485170	−	0.0675754i
$659$		−	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
$661$	5.98201	+	22.3252i	0.232673	+	0.868348i	0.979184	+	0.202975i	$0.0650609\pi$
$661$	5.98201	+	22.3252i	0.232673	+	0.868348i	−0.746511	+	0.665373i	$0.768272\pi$
$662$	11.7279	−	20.3134i	0.455819	−	0.789501i
$663$	−10.9441	−	3.25723i	−0.425033	−	0.126501i
$664$	13.0294			0.505640
$665$	−0.738832	+	10.2906i	−0.0286507	+	0.399053i
$666$	4.00000	+	11.3137i	0.154997	+	0.438397i
$667$	−5.70346	+	3.29289i	−0.220839	+	0.127501i
$668$	−5.68640	−	21.2219i	−0.220013	−	0.821101i
$669$	−3.62372	−	7.86566i	−0.140101	−	0.304104i
$670$	7.63033	+	2.04454i	0.294785	+	0.0789875i
$671$	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	$-0.939152\pi$
$673$		−	9.85786i		−	0.379993i	0.981785	−	0.189996i	$-0.0608476\pi$
$674$	4.43671	−	16.5580i	0.170896	−	0.637792i
$675$	0.334968	−	24.1954i	0.0128929	−	0.931282i
$676$	10.3301	−	7.89230i	0.397313	−	0.303550i
$677$	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	$0.167010\pi$
$678$	9.00000	−	12.7279i	0.345643	−	0.488813i
$679$	24.7487	+	8.57321i	0.949769	+	0.329010i
$680$	−3.21320			−0.123221
$681$	0.953512	−	10.3485i	0.0365386	−	0.396554i
$682$	4.66390	−	1.24969i	0.178590	−	0.0478531i
$683$	48.5709	−	13.0145i	1.85851	−	0.497987i	0.858620	−	0.512613i	$-0.171322\pi$
$683$	48.5709	−	13.0145i	1.85851	−	0.497987i	0.999893	+	0.0146258i	$0.00465569\pi$
$684$	−19.9098	+	1.55687i	−0.761270	+	0.0595285i
$685$	6.68629			0.255470
$686$	8.50000	−	16.4545i	0.324532	−	0.628235i
$687$	7.79899	+	5.51472i	0.297550	+	0.210400i
$688$	5.19615	−	3.00000i	0.198101	−	0.114374i
$689$	−2.00883	−	31.1480i	−0.0765303	−	1.18665i
$690$	2.31433	−	6.26843i	0.0881052	−	0.238635i
$691$	−2.63260	+	9.82498i	−0.100149	+	0.373760i	−0.997750	−	0.0670488i	$-0.978642\pi$
$691$	−2.63260	+	9.82498i	−0.100149	+	0.373760i	0.897601	+	0.440809i	$0.145308\pi$
$692$			15.4853i			0.588662i
$693$	−46.2608	+	0.294395i	−1.75730	+	0.0111832i
$694$	−3.31371	−	3.31371i	−0.125787	−	0.125787i
$695$	1.65727	+	0.444063i	0.0628637	+	0.0168443i
$696$	−4.71940	+	2.17423i	−0.178888	+	0.0824142i
$697$	2.67700	+	9.99071i	0.101399	+	0.378425i
$698$	−3.67423	+	2.12132i	−0.139072	+	0.0802932i
$699$	−0.393398	−	2.29289i	−0.0148797	−	0.0867252i
$700$	−10.2016	−	6.90874i	−0.385586	−	0.261126i
$701$	36.2843			1.37044			0.685219	−	0.728337i	$-0.259706\pi$
$701$	36.2843			1.37044			0.685219	+	0.728337i	$0.259706\pi$
$702$	12.5612	−	13.9002i	0.474092	−	0.524630i
$703$	−13.3137	+	23.0600i	−0.502136	+	0.869725i
$704$	10.5596	+	39.4088i	0.397978	+	1.48527i
$705$	0.512503	−	0.426027i	0.0193020	−	0.0160451i
$706$			7.17157i			0.269906i
$707$	−0.757875	+	10.5558i	−0.0285028	+	0.396993i
$708$	13.4142	+	9.48528i	0.504137	+	0.356479i
$709$	−21.9937	−	5.89319i	−0.825991	−	0.221324i	−0.179027	−	0.983844i	$-0.557295\pi$
$709$	−21.9937	−	5.89319i	−0.825991	−	0.221324i	−0.646964	+	0.762521i	$0.723962\pi$
$710$	−0.371665	+	0.0995874i	−0.0139484	+	0.00373745i
$711$	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
$717$	−9.93230	+	4.57583i	−0.370928	+	0.170887i
$718$	−11.2426	+	19.4728i	−0.419572	+	0.726719i
$719$	−11.9706	−	20.7336i	−0.446427	−	0.773234i	0.551724	−	0.834027i	$-0.313970\pi$
$719$	−11.9706	−	20.7336i	−0.446427	−	0.773234i	−0.998150	+	0.0607933i	$0.980637\pi$
$720$	0.757359	−	1.58579i	0.0282251	−	0.0590988i
$721$	9.62133	−	14.2071i	0.358317	−	0.529101i
$722$	17.8995	+	17.8995i	0.666150	+	0.666150i
$723$	3.53477	−	38.3629i	0.131460	−	1.42673i
$724$	−4.57107	+	7.91732i	−0.169882	+	0.294245i
$725$	2.32843	−	4.03295i	0.0864756	−	0.149780i
$726$	−39.6184	−	3.65045i	−1.47038	−	0.135481i
$727$		−	9.07107i		−	0.336427i	−0.985751	−	0.168214i	$-0.946200\pi$
$727$		−	9.07107i		−	0.336427i	0.985751	−	0.168214i	$-0.0537998\pi$
$728$	−7.20577	−	27.6962i	−0.267064	−	1.02649i
$729$	−14.1421	+	23.0000i	−0.523783	+	0.851852i
$730$	−1.94495	+	7.25866i	−0.0719859	+	0.268655i
$731$	−9.50079	−	5.48528i	−0.351399	−	0.202880i
$732$	0.599900	−	1.62484i	0.0221730	−	0.0600560i
$733$	2.38455	−	8.89927i	0.0880755	−	0.328702i	−0.907803	−	0.419396i	$-0.862242\pi$
$733$	2.38455	−	8.89927i	0.0880755	−	0.328702i	0.995879	+	0.0906940i	$0.0289085\pi$
$734$	10.1716	−	10.1716i	0.375440	−	0.375440i
$735$	6.80902	−	2.01982i	0.251154	−	0.0745022i
$736$	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
$739$	0.643238	+	2.40060i	0.0236619	+	0.0883074i	0.976747	−	0.214395i	$-0.0687779\pi$
$739$	0.643238	+	2.40060i	0.0236619	+	0.0883074i	−0.953085	+	0.302702i	$0.902111\pi$
$740$	1.17157	+	2.02922i	0.0430679	+	0.0745957i
$741$	41.5563	+	1.14214i	1.52661	+	0.0419574i
$742$	−21.6421	−	7.49706i	−0.794508	−	0.275226i
$743$	−4.60660	+	4.60660i	−0.169000	+	0.169000i	−0.786540	−	0.617540i	$-0.788129\pi$
$743$	−4.60660	+	4.60660i	−0.169000	+	0.169000i	0.617540	+	0.786540i	$0.288129\pi$
$744$	−2.75172	−	3.31027i	−0.100883	−	0.121361i
$745$	7.34847	+	4.24264i	0.269227	+	0.155438i
$746$	5.90081	+	22.0221i	0.216044	+	0.806288i
$747$	12.9898	−	1.01575i	0.475271	−	0.0371645i
$748$	7.53553	−	7.53553i	0.275526	−	0.275526i
$749$	−10.1304	+	14.9588i	−0.370157	+	0.546584i
$750$	1.65685	+	9.65685i	0.0604998	+	0.352618i
$751$	12.1604	−	7.02082i	0.443740	−	0.256193i	−0.261443	−	0.965219i	$-0.584198\pi$
$751$	12.1604	−	7.02082i	0.443740	−	0.256193i	0.705183	+	0.709026i	$0.250865\pi$
$752$	−0.634472	+	0.170006i	−0.0231368	+	0.00619950i
$753$	−3.24969	−	1.19980i	−0.118425	−	0.0437232i
$754$	3.41542	−	1.15539i	0.124382	−	0.0420770i
$755$			11.6152i			0.422721i
$756$	5.83183	+	12.4495i	0.212101	+	0.452784i
$757$	−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
$759$	27.8192	+	60.3843i	1.00977	+	2.19181i
$760$	11.2999	−	3.02779i	0.409889	−	0.109830i
$761$	6.51488	−	24.3139i	0.236164	−	0.881377i	−0.741456	−	0.671001i	$-0.765865\pi$
$761$	6.51488	−	24.3139i	0.236164	−	0.881377i	0.977621	−	0.210376i	$-0.0674688\pi$
$762$	−16.1421	+	22.8284i	−0.584768	+	0.826987i
$763$	−14.8284	+	12.8418i	−0.536825	+	0.464904i
$764$	16.9706			0.613973
$765$	−3.20342	+	0.250496i	−0.115820	+	0.00905670i
$766$	−6.21076	−	3.58579i	−0.224404	−	0.129560i
$767$	−25.6891	−	22.5763i	−0.927579	−	0.815183i
$768$	22.6432	−	18.8225i	0.817065	−	0.679199i
$769$	−9.21320	−	9.21320i	−0.332237	−	0.332237i	0.521199	−	0.853435i	$-0.325485\pi$
$769$	−9.21320	−	9.21320i	−0.332237	−	0.332237i	−0.853435	+	0.521199i	$0.825485\pi$
$770$	8.87039	−	1.70711i	0.319667	−	0.0615199i
$771$	5.51472	+	32.1421i	0.198608	+	1.15757i
$772$	−0.732051	+	2.73205i	−0.0263471	+	0.0983287i
$773$	10.6407	+	39.7118i	0.382721	+	1.42833i	0.841728	+	0.539902i	$0.181539\pi$
$773$	10.6407	+	39.7118i	0.382721	+	1.42833i	−0.459007	+	0.888433i	$0.651795\pi$
$774$	14.8394	−	10.1879i	0.533391	−	0.366195i
$775$	3.72641	+	0.998489i	0.133857	+	0.0358668i
$776$		−	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
$780$	1.91547	−	3.11668i	0.0685847	−	0.111595i
$781$	1.91421	−	3.31552i	0.0684959	−	0.118638i
$782$	11.6313	+	3.11660i	0.415935	+	0.111450i
$783$	−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
$786$	22.1258	+	2.03868i	0.789200	+	0.0727172i
$787$	6.95133	+	25.9427i	0.247788	+	0.924758i	0.971962	+	0.235140i	$0.0755548\pi$
$787$	6.95133	+	25.9427i	0.247788	+	0.924758i	−0.724174	+	0.689618i	$0.757779\pi$
$788$	6.83013	−	1.83013i	0.243313	−	0.0651956i
$789$	22.6814	+	27.2854i	0.807480	+	0.971386i
$790$			0.828427i			0.0294741i
$791$	−10.3986	−	21.4213i	−0.369730	−	0.761652i
$792$	17.4853	+	49.4558i	0.621312	+	1.75734i
$793$	−1.59808	+	3.23205i	−0.0567494	+	0.114773i
$794$	24.3718	+	14.0711i	0.864923	+	0.499364i
$795$	−3.67523	−	7.97746i	−0.130347	−	0.282931i
$796$	7.53553	+	13.0519i	0.267090	+	0.462613i
$797$	10.2843			0.364288			0.182144	−	0.983272i	$-0.441696\pi$
$797$	10.2843			0.364288			0.182144	+	0.983272i	$0.441696\pi$
$798$	12.5879	−	27.7873i	0.445607	−	0.983659i
$799$	0.849242	+	0.849242i	0.0300440	+	0.0300440i
$800$	−6.02641	+	22.4909i	−0.213066	+	0.795173i
$801$	30.8790	−	21.1997i	1.09106	−	0.749055i
$802$	−6.12132	+	10.6024i	−0.216151	+	0.374385i
$803$	−37.3848	−	64.7523i	−1.31928	−	2.28506i
$804$	19.0711	+	13.4853i	0.672585	+	0.475589i
$805$	−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
$808$	11.5911	−	3.10583i	0.407774	−	0.109263i
$809$	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	0.574909	−	0.818217i	$-0.305037\pi$
$811$	−6.92893	−	6.92893i	−0.243308	−	0.243308i	−0.818217	+	0.574909i	$0.805037\pi$
$812$	−0.189469	+	2.63896i	−0.00664905	+	0.0926093i
$813$	5.89949	+	4.17157i	0.206904	+	0.146303i
$814$	22.5193	+	6.03403i	0.789302	+	0.211493i
$815$	−1.10165	−	0.636039i	−0.0385892	−	0.0222795i
$816$	2.97091	+	1.09687i	0.104003	+	0.0383983i
$817$	38.5802	+	10.3375i	1.34975	+	0.361664i
$818$	26.7279			0.934520
$819$	−9.34299	−	27.0501i	−0.326470	−	0.945207i
$820$	−3.31371			−0.115720
$821$	26.9488	+	7.22092i	0.940521	+	0.252012i	0.696335	−	0.717717i	$-0.254813\pi$
$821$	26.9488	+	7.22092i	0.940521	+	0.252012i	0.244186	+	0.969728i	$0.421479\pi$
$822$	−18.5463	−	6.84739i	−0.646877	−	0.238830i
$823$	−0.420266	−	0.242641i	−0.0146496	−	0.00845792i	0.492657	−	0.870223i	$-0.336026\pi$
$823$	−0.420266	−	0.242641i	−0.0146496	−	0.00845792i	−0.507307	+	0.861765i	$0.669359\pi$
$824$	−18.7929	−	5.03554i	−0.654682	−	0.175421i
$825$	−38.3848	−	27.1421i	−1.33639	−	0.944968i
$826$	−22.5763	+	10.9592i	−0.785530	+	0.381321i
$827$	−15.6777	−	15.6777i	−0.545166	−	0.545166i	0.379873	−	0.925039i	$-0.375968\pi$
$827$	−15.6777	−	15.6777i	−0.545166	−	0.545166i	−0.925039	+	0.379873i	$0.875968\pi$
$828$	12.8389	−	15.0172i	0.446183	−	0.521883i
$829$	35.6301	+	20.5711i	1.23749	+	0.714463i	0.968580	−	0.248704i	$-0.0800045\pi$
$829$	35.6301	+	20.5711i	1.23749	+	0.714463i	0.268906	+	0.963166i	$0.413338\pi$
$830$	−2.45747	+	0.658476i	−0.0852999	+	0.0228560i
$831$	−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
$834$	−4.14214	−	2.92893i	−0.143430	−	0.101421i
$835$	6.43503	+	11.1458i	0.222693	+	0.385716i
$836$	−19.3995	+	33.6009i	−0.670946	+	1.16211i
$837$	−3.00141	−	3.08568i	−0.103744	−	0.106657i
$838$	−4.38153	+	16.3521i	−0.151357	+	0.564874i
$839$	−11.3934	−	11.3934i	−0.393344	−	0.393344i	0.482534	−	0.875877i	$-0.339717\pi$
$839$	−11.3934	−	11.3934i	−0.393344	−	0.393344i	−0.875877	+	0.482534i	$0.839717\pi$
$840$	−4.69129	−	6.54572i	−0.161865	−	0.225849i
$841$	28.0000			0.965517
$842$	7.82843	+	13.5592i	0.269785	+	0.467282i
$843$	−8.27239	−	17.9561i	−0.284916	−	0.618440i
$844$	13.0519	+	7.53553i	0.449266	+	0.259384i
$845$	−4.64848	+	6.03185i	−0.159913	+	0.207502i
$846$	−1.85786	+	0.656854i	−0.0638747	+	0.0225831i
$847$	−34.0783	+	50.3209i	−1.17094	+	1.72905i
$848$			8.65685i			0.297278i
$849$	19.7072	+	23.7074i	0.676348	+	0.813635i
$850$	−8.22459	+	2.20377i	−0.282101	+	0.0755887i
$851$	−6.81811	−	25.4455i	−0.233722	−	0.872261i
$852$	−1.13291	−	0.104386i	−0.0388127	−	0.00357622i
$853$	−3.07107	+	3.07107i	−0.105151	+	0.105151i	−0.757725	−	0.652574i	$-0.773689\pi$
$853$	−3.07107	+	3.07107i	−0.105151	+	0.105151i	0.652574	+	0.757725i	$0.273689\pi$
$854$	1.73205	+	2.00000i	0.0592696	+	0.0684386i
$855$	11.0294	−	3.89949i	0.377199	−	0.133360i
$856$	19.7873	+	5.30198i	0.676315	+	0.181218i
$857$	25.2990	−	43.8191i	0.864197	−	1.49683i	−0.00364524	−	0.999993i	$-0.501160\pi$
$857$	25.2990	−	43.8191i	0.864197	−	1.49683i	0.867842	−	0.496840i	$-0.165506\pi$
$858$	−8.45115	−	35.4038i	−0.288517	−	1.20867i
$859$	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
$863$	47.9080	+	12.8369i	1.63081	+	0.436973i	0.954151	−	0.299327i	$-0.0967620\pi$
$863$	47.9080	+	12.8369i	1.63081	+	0.436973i	0.676656	+	0.736300i	$0.263429\pi$
$864$	18.6237	−	18.1151i	0.633592	−	0.616288i
$865$	−2.34777	−	8.76198i	−0.0798264	−	0.297916i
$866$	1.33088	−	4.96692i	0.0452252	−	0.168783i
$867$	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
$871$	−36.5223	−	32.0968i	−1.23751	−	1.08756i
$872$	19.2627	+	11.1213i	0.652317	+	0.376615i
$873$	−2.31524	−	29.6081i	−0.0783592	−	1.00208i
$874$	−43.8406			−1.48293
$875$	14.1421	+	4.89898i	0.478091	+	0.165616i
$876$	−12.8284	+	18.1421i	−0.433432	+	0.612966i
$877$	8.88866	−	33.1729i	0.300149	−	1.12017i	−0.636893	−	0.770952i	$-0.719781\pi$
$877$	8.88866	−	33.1729i	0.300149	−	1.12017i	0.937042	−	0.349218i	$-0.113553\pi$
$878$	−31.0469	+	8.31900i	−1.04778	+	0.280753i
$879$	−9.37018	−	20.3389i	−0.316048	−	0.686015i
$880$	−1.70711	−	2.95680i	−0.0575466	−	0.0996736i
$881$	−2.00000			−0.0673817			−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000			−0.0673817			−0.0336909	+	0.999432i	$0.510726\pi$
$882$	−20.9552	−	1.37054i	−0.705599	−	0.0461484i
$883$			10.1421i			0.341310i	0.985331	+	0.170655i	$0.0545884\pi$
$883$			10.1421i			0.341310i	−0.985331	+	0.170655i	$0.945412\pi$
$884$	5.90957	+	2.92197i	0.198760	+	0.0982763i
$885$	−9.02820	−	3.33326i	−0.303480	−	0.112046i
$886$	−5.09244	+	1.36451i	−0.171084	+	0.0458418i
$887$	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
$889$	18.6505	+	38.4205i	0.625519	+	1.28858i
$890$	−5.17157	+	5.17157i	−0.173352	+	0.173352i
$891$	21.2876	+	47.9422i	0.713160	+	1.60612i
$892$	1.29410	+	4.82963i	0.0433295	+	0.161708i
$893$	−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
$897$	−29.8701	+	28.2721i	−0.997332	+	0.943977i
$898$	1.41421	+	2.44949i	0.0471929	+	0.0817405i
$899$	−0.214413	−	0.800199i	−0.00715106	−	0.0266881i
$900$	−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
$903$	−2.69694	−	27.3629i	−0.0897485	−	0.910579i
$904$	−19.0919	+	19.0919i	−0.634987	+	0.634987i
$905$	1.38606	−	5.17286i	0.0460743	−	0.171952i
$906$	11.8951	−	32.2181i	0.395188	−	1.07038i
$907$	26.9954	+	15.5858i	0.896367	+	0.517518i	0.876020	−	0.482275i	$-0.160190\pi$
$907$	26.9954	+	15.5858i	0.896367	+	0.517518i	0.0203470	+	0.999793i	$0.493523\pi$
$908$	−1.55291	+	5.79555i	−0.0515353	+	0.192332i
$909$	11.3137	−	4.00000i	0.375252	−	0.132672i
$910$	2.75877	+	4.85957i	0.0914523	+	0.161093i
$911$			52.4264i			1.73696i	0.495720	+	0.868482i	$0.334904\pi$
$911$			52.4264i			1.73696i	−0.495720	+	0.868482i	$0.665096\pi$
$912$	−11.4814	−	1.05790i	−0.380186	−	0.0350305i
$913$	12.6569	−	21.9223i	0.418881	−	0.725523i
$914$	2.22183	−	3.84831i	0.0734915	−	0.127291i
$915$	−0.0930924	+	1.01033i	−0.00307754	+	0.0334006i
$916$	−3.89949	−	3.89949i	−0.128843	−	0.128843i
$917$	19.0318	−	28.1029i	0.628485	−	0.928038i
$918$	9.14214	+	2.58579i	0.301735	+	0.0853437i
$919$	−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
$921$	7.86566	−	3.62372i	0.259182	−	0.119406i
$922$	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
$928$	4.82963	−	1.29410i	0.158540	−	0.0424808i
$929$	−24.6453	−	6.60370i	−0.808587	−	0.216660i	−0.169236	−	0.985576i	$-0.554130\pi$
$929$	−24.6453	−	6.60370i	−0.808587	−	0.216660i	−0.639351	+	0.768915i	$0.720797\pi$
$930$	0.686292	+	0.485281i	0.0225044	+	0.0159130i
$931$	−27.9047	−	37.3189i	−0.914539	−	1.22308i
$932$			1.34315i			0.0439962i
$933$	−2.47458	+	2.05704i	−0.0810143	+	0.0673444i
$934$	−5.94522	−	22.1879i	−0.194534	−	0.726009i
$935$	−3.12132	+	5.40629i	−0.102078	+	0.176804i
$936$	−25.5146	+	20.0501i	−0.833970	+	0.655358i
$937$	21.2843			0.695327			0.347663	−	0.937619i	$-0.386975\pi$
$937$	21.2843			0.695327			0.347663	+	0.937619i	$0.386975\pi$
$938$	−32.0968	+	15.5808i	−1.04800	+	0.508732i
$939$	−6.92893	−	40.3848i	−0.226117	−	1.31791i
$940$	−0.333226	+	0.192388i	−0.0108686	+	0.00627501i
$941$	0.580438	+	2.16622i	0.0189217	+	0.0706169i	0.974741	−	0.223338i	$-0.0716952\pi$
$941$	0.580438	+	2.16622i	0.0189217	+	0.0706169i	−0.955819	+	0.293955i	$0.905029\pi$
$942$	−2.87636	+	1.32514i	−0.0937168	+	0.0431755i
$943$	35.9854	+	9.64226i	1.17185	+	0.313995i
$944$	6.70711	+	6.70711i	0.218298	+	0.218298i
$945$	−5.18730	−	6.16007i	−0.168743	−	0.200387i
$946$		−	34.9706i		−	1.13699i
$947$	6.86251	−	25.6113i	0.223002	−	0.832254i	−0.760194	−	0.649697i	$-0.774896\pi$
$947$	6.86251	−	25.6113i	0.223002	−	0.832254i	0.983195	−	0.182557i	$-0.0584374\pi$
$948$	−0.848387	+	2.29788i	−0.0275543	+	0.0746316i
$949$	30.5334	−	34.7433i	0.991158	−	1.12782i
$950$	26.8468	−	15.5000i	0.871025	−	0.502886i
$951$	23.9411	+	16.9289i	0.776344	+	0.548958i
$952$	10.9706	−	9.50079i	0.355558	−	0.307922i
$953$	25.1421			0.814434			0.407217	−	0.913332i	$-0.366499\pi$
$953$	25.1421			0.814434			0.407217	+	0.913332i	$0.366499\pi$
$954$	2.02462	+	25.8915i	0.0655496	+	0.838269i
$955$	−9.60239	+	2.57295i	−0.310726	+	0.0832588i
$956$	6.09857	−	1.63411i	0.197242	−	0.0528508i
$957$	−0.926246	+	10.0525i	−0.0299413	+	0.324953i
$958$	29.4853			0.952626
$959$	−22.8284	+	19.7700i	−0.737168	+	0.638407i
$960$	−4.10051	+	5.79899i	−0.132343	+	0.187162i
$961$	−26.2524	+	15.1569i	−0.846853	+	0.488931i
$962$	0.928203	+	14.3923i	0.0299265	+	0.464027i
$963$	20.1404	+	3.74326i	0.649015	+	0.120625i
$964$	−5.75682	+	21.4847i	−0.185415	+	0.691977i
$965$		−	1.65685i		−	0.0533360i
$966$	10.6328	+	28.2448i	0.342106	+	0.908761i
$967$	17.3934	+	17.3934i	0.559334	+	0.559334i	0.929118	−	0.369784i	$-0.120568\pi$
$967$	17.3934	+	17.3934i	0.559334	+	0.559334i	−0.369784	+	0.929118i	$0.620568\pi$
$968$	66.5636	+	17.8357i	2.13943	+	0.573260i
$969$	8.82129	+	19.1475i	0.283381	+	0.615106i
$970$	1.50089	+	5.60139i	0.0481906	+	0.179850i
$971$	−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
$973$	−6.97127	+	3.38407i	−0.223489	+	0.108488i
$974$	9.34315			0.299374
$975$	8.29591	−	27.8737i	0.265682	−	0.892673i
$976$	0.500000	−	0.866025i	0.0160046	−	0.0277208i
$977$	−11.7756	−	43.9472i	−0.376735	−	1.40600i	−0.850793	−	0.525501i	$-0.823878\pi$
$977$	−11.7756	−	43.9472i	−0.376735	−	1.40600i	0.474058	−	0.880494i	$-0.342789\pi$
$978$	2.40438	+	2.89243i	0.0768836	+	0.0924897i
$979$		−	72.7696i		−	2.32572i
$980$	−4.07177	+	0.484577i	−0.130068	+	0.0154793i
$981$	20.0711	+	9.58579i	0.640820	+	0.306051i
$982$	−8.89927	−	2.38455i	−0.283987	−	0.0760941i
$983$	−51.1941	+	13.7174i	−1.63284	+	0.437517i	−0.954737	−	0.297452i	$-0.903863\pi$
$983$	−51.1941	+	13.7174i	−1.63284	+	0.437517i	−0.678100	+	0.734969i	$0.737197\pi$
$984$	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
$990$	−5.79725	−	8.44414i	−0.184249	−	0.268372i
$991$	−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
$993$	−23.4558	+	33.1716i	−0.744349	+	1.05267i
$994$	0.974485	−	1.43895i	0.0309088	−	0.0456408i
$995$	−6.24264	−	6.24264i	−0.197905	−	0.197905i
$996$	−7.49082	−	0.690207i	−0.237356	−	0.0218700i
$997$	−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
$999$	−5.10102	−	20.1489i	−0.161389	−	0.637484i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cd.c.44.1	✓	8	273.44	even	12	inner
273.2.cd.c.86.2	yes	8	7.2	even	3	inner
273.2.cd.c.200.2	yes	8	39.5	even	4	inner
273.2.cd.c.242.1	yes	8	1.1	even	1	trivial
273.2.cd.d.44.2	yes	8	91.44	odd	12
273.2.cd.d.86.1	yes	8	21.2	odd	6
273.2.cd.d.200.1	yes	8	13.5	odd	4
273.2.cd.d.242.2	yes	8	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(1.62484 + 0.599900i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.565826 + 0.151613i) q^{5} +(-1.41421 - 1.00000i) q^{6} +(-2.38014 + 1.15539i) q^{7} +(2.12132 + 2.12132i) q^{8} +(2.28024 + 1.94949i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(1.62484 + 0.599900i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.565826 + 0.151613i) q^{5} +(-1.41421 - 1.00000i) q^{6} +(-2.38014 + 1.15539i) q^{7} +(2.12132 + 2.12132i) q^{8} +(2.28024 + 1.94949i) q^{9} +(-0.507306 - 0.292893i) q^{10} +(5.62983 - 1.50851i) q^{11} +(-1.10721 - 1.33195i) q^{12} +(2.00000 + 3.00000i) q^{13} +(2.59808 - 0.500000i) q^{14} +(0.828427 + 0.585786i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.914214 + 1.58346i) q^{17} +(-1.69798 - 2.47323i) q^{18} +(1.72292 - 6.43003i) q^{19} +(-0.414214 - 0.414214i) q^{20} +(-4.56048 + 0.449490i) q^{21} -5.82843 q^{22} +(3.29289 + 5.70346i) q^{23} +(2.17423 + 4.71940i) q^{24} +(-4.03295 - 2.32843i) q^{25} +(-1.15539 - 3.41542i) q^{26} +(2.53553 + 4.53553i) q^{27} +(2.63896 + 0.189469i) q^{28} +1.00000i q^{29} +(-0.648586 - 0.780239i) q^{30} +(-0.800199 + 0.214413i) q^{31} +(-1.29410 - 4.82963i) q^{32} +(10.0525 + 0.926246i) q^{33} +(1.29289 - 1.29289i) q^{34} +(-1.52192 + 0.292893i) q^{35} +(-1.00000 - 2.82843i) q^{36} +(-3.86370 - 1.03528i) q^{37} +(-3.32843 + 5.76500i) q^{38} +(1.44999 + 6.07433i) q^{39} +(0.878680 + 1.52192i) q^{40} +(4.00000 - 4.00000i) q^{41} +(4.52142 + 0.746165i) q^{42} +6.00000i q^{43} +(-5.62983 - 1.50851i) q^{44} +(0.994652 + 1.44879i) q^{45} +(-1.70453 - 6.36138i) q^{46} +(0.170006 - 0.634472i) 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} +(-0.232051 - 3.59808i) q^{52} +(-7.49706 - 4.32843i) q^{53} +(-1.27526 - 5.03723i) q^{54} +3.41421 q^{55} +(-7.50000 - 2.59808i) q^{56} +(6.65685 - 9.41421i) q^{57} +(0.258819 - 0.965926i) q^{58} +(-9.16208 + 2.45497i) q^{59} +(-0.424546 - 0.921519i) q^{60} +(0.500000 + 0.866025i) q^{61} +0.828427 q^{62} +(-7.67972 - 2.00548i) q^{63} +7.00000i q^{64} +(0.676814 + 2.00070i) q^{65} +(-9.47029 - 3.49648i) q^{66} +(-13.0258 + 3.49025i) q^{67} +(1.58346 - 0.914214i) q^{68} +(1.92893 + 11.2426i) q^{69} +(1.54587 + 0.110988i) q^{70} +(0.464466 - 0.464466i) q^{71} +(0.701625 + 8.97261i) q^{72} +(-3.32024 - 12.3913i) 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} +(0.171573 - 6.24264i) q^{78} +(-0.707107 - 1.22474i) q^{79} +(-0.151613 - 0.565826i) q^{80} +(1.39898 + 8.89060i) q^{81} +(-4.89898 + 2.82843i) q^{82} +(3.07107 - 3.07107i) q^{83} +(4.17423 + 1.89097i) q^{84} +(-0.757359 + 0.757359i) q^{85} +(1.55291 - 5.79555i) q^{86} +(-0.599900 + 1.62484i) q^{87} +(15.1427 + 8.74264i) q^{88} +(3.23143 - 12.0599i) q^{89} +(-0.585786 - 1.65685i) q^{90} +(-8.22646 - 4.82963i) q^{91} -6.58579i q^{92} +(-1.42883 - 0.131652i) q^{93} +(-0.328427 + 0.568852i) q^{94} +(1.94975 - 3.37706i) q^{95} +(0.794593 - 8.62372i) q^{96} +(-7.00000 - 7.00000i) q^{97} +(-5.60609 + 4.19187i) q^{98} +(15.7782 + 7.53553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{5}+O(q^{10}) \) 8 * q + 4 * q^3 - 4 * q^5	\( 8 q + 4 q^{3} - 4 q^{5} + 8 q^{11} - 4 q^{12} + 16 q^{13} - 16 q^{15} - 4 q^{16} + 4 q^{17} + 8 q^{18} - 16 q^{19} + 8 q^{20} - 24 q^{22} + 32 q^{23} - 12 q^{24} - 8 q^{27} - 4 q^{30} - 8 q^{31} + 12 q^{33} + 16 q^{34} - 8 q^{36} - 4 q^{38} - 4 q^{39} + 24 q^{40} + 32 q^{41} + 20 q^{42} - 8 q^{44} - 20 q^{45} - 4 q^{46} - 16 q^{47} - 8 q^{48} + 32 q^{50} - 12 q^{51} + 12 q^{52} - 20 q^{54} + 16 q^{55} - 60 q^{56} + 8 q^{57} - 24 q^{59} + 8 q^{60} + 4 q^{61} - 16 q^{62} - 8 q^{63} - 20 q^{65} - 4 q^{66} - 24 q^{67} + 72 q^{69} - 16 q^{70} + 32 q^{71} + 24 q^{72} + 8 q^{73} - 12 q^{75} - 32 q^{76} - 48 q^{77} + 24 q^{78} - 4 q^{80} - 28 q^{81} - 32 q^{83} + 4 q^{84} - 40 q^{85} - 4 q^{87} - 24 q^{89} - 16 q^{90} + 8 q^{93} + 20 q^{94} - 24 q^{95} - 56 q^{97} + 64 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 4 * q^5 + 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 - 24 * q^22 + 32 * q^23 - 12 * q^24 - 8 * q^27 - 4 * q^30 - 8 * q^31 + 12 * q^33 + 16 * q^34 - 8 * q^36 - 4 * q^38 - 4 * q^39 + 24 * q^40 + 32 * q^41 + 20 * q^42 - 8 * q^44 - 20 * q^45 - 4 * q^46 - 16 * q^47 - 8 * q^48 + 32 * q^50 - 12 * q^51 + 12 * q^52 - 20 * q^54 + 16 * q^55 - 60 * q^56 + 8 * 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 + 24 * q^78 - 4 * q^80 - 28 * q^81 - 32 * q^83 + 4 * q^84 - 40 * q^85 - 4 * q^87 - 24 * q^89 - 16 * q^90 + 8 * q^93 + 20 * q^94 - 24 * q^95 - 56 * q^97 + 64 * q^99

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