LMFDB - Embedded newform 273.2.cd.c.200.2

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			200.2
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	273.200
Dual form			273.2.cd.c.86.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-1.33195 - 1.10721i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.151613 + 0.565826i) q^{5} +(-1.41421 + 1.00000i) q^{6} +(-1.15539 - 2.38014i) q^{7} +(2.12132 - 2.12132i) q^{8} +(0.548188 + 2.94949i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-1.33195 - 1.10721i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.151613 + 0.565826i) q^{5} +(-1.41421 + 1.00000i) q^{6} +(-1.15539 - 2.38014i) q^{7} +(2.12132 - 2.12132i) q^{8} +(0.548188 + 2.94949i) q^{9} +(0.507306 + 0.292893i) q^{10} +(-1.50851 - 5.62983i) q^{11} +(-0.599900 - 1.62484i) 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} +(2.99087 + 0.233875i) q^{18} +(-6.43003 - 1.72292i) q^{19} +(-0.414214 + 0.414214i) q^{20} +(-1.09638 + 4.44949i) q^{21} -5.82843 q^{22} +(3.29289 + 5.70346i) q^{23} +(-5.17423 + 0.476756i) 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} +(-0.351414 - 0.951812i) q^{30} +(0.214413 + 0.800199i) q^{31} +(4.82963 - 1.29410i) q^{32} +(-4.22412 + 9.16889i) 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} +(-5.98552 + 1.78144i) q^{39} +(0.878680 + 1.52192i) q^{40} +(4.00000 + 4.00000i) q^{41} +(4.01411 + 2.21063i) q^{42} -6.00000i q^{43} +(1.50851 - 5.62983i) q^{44} +(-1.75201 - 0.137001i) 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} +(2.97091 - 1.09687i) q^{51} +(3.23205 - 1.59808i) q^{52} +(7.49706 + 4.32843i) q^{53} +(-3.72474 - 3.62302i) q^{54} +3.41421 q^{55} +(-7.50000 - 2.59808i) q^{56} +(6.65685 + 9.41421i) q^{57} +(-0.965926 - 0.258819i) q^{58} +(2.45497 + 9.16208i) q^{59} +(1.01033 - 0.0930924i) q^{60} +(0.500000 + 0.866025i) q^{61} +0.828427 q^{62} +(6.38682 - 4.71259i) q^{63} -7.00000i q^{64} +(1.39425 + 1.58649i) q^{65} +(7.76318 + 6.45327i) 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} +(7.41970 + 5.09393i) q^{72} +(12.3913 - 3.32024i) q^{73} +(-3.46410 - 2.00000i) q^{74} +(-2.79365 - 7.56666i) 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} +(0.565826 - 0.151613i) q^{80} +(-8.39898 + 3.23375i) q^{81} +(4.89898 - 2.82843i) q^{82} +(3.07107 + 3.07107i) q^{83} +(-3.17423 + 3.30518i) q^{84} +(-0.757359 - 0.757359i) q^{85} +(-5.79555 - 1.55291i) q^{86} +(-1.10721 + 1.33195i) 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} +(0.600398 - 1.30323i) q^{93} +(-0.328427 + 0.568852i) q^{94} +(1.94975 - 3.37706i) q^{95} +(-7.86566 - 3.62372i) q^{96} +(-7.00000 + 7.00000i) q^{97} +(4.19187 + 5.60609i) 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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

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

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	$-0.801640\pi$
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i	0.995047	−	0.0994033i	$-0.0316934\pi$
$3$	−1.33195	−	1.10721i	−0.769002	−	0.639246i
$3$	−1.33195	−	1.10721i	−0.769002	−	0.639246i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−0.151613	+	0.565826i	−0.0678033	+	0.253045i	−0.991505	−	0.130067i	$-0.958481\pi$
$5$	−0.151613	+	0.565826i	−0.0678033	+	0.253045i	0.923702	+	0.383112i	$0.125148\pi$
$6$	−1.41421	+	1.00000i	−0.577350	+	0.408248i
$7$	−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
$9$	0.548188	+	2.94949i	0.182729	+	0.983163i
$10$	0.507306	+	0.292893i	0.160424	+	0.0926210i
$11$	−1.50851	−	5.62983i	−0.454832	−	1.69746i	−0.688580	−	0.725160i	$-0.741766\pi$
$11$	−1.50851	−	5.62983i	−0.454832	−	1.69746i	0.233748	−	0.972297i	$-0.424901\pi$
$12$	−0.599900	−	1.62484i	−0.173176	−	0.469052i
$13$	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	$0.237837\pi$
$18$	2.99087	+	0.233875i	0.704955	+	0.0551249i
$19$	−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
$21$	−1.09638	+	4.44949i	−0.239249	+	0.970958i
$22$	−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	$0.592429\pi$
$24$	−5.17423	+	0.476756i	−1.05619	+	0.0973174i
$25$	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	$-0.970403\pi$
$29$		−	1.00000i		−	0.185695i	0.995680	−	0.0928477i	$-0.0295970\pi$
$30$	−0.351414	−	0.951812i	−0.0641590	−	0.173776i
$31$	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
$33$	−4.22412	+	9.16889i	−0.735325	+	1.59610i
$34$	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
$39$	−5.98552	+	1.78144i	−0.958451	+	0.285259i
$40$	0.878680	+	1.52192i	0.138931	+	0.240636i
$41$	4.00000	+	4.00000i	0.624695	+	0.624695i	0.946728	−	0.322033i	$-0.104366\pi$
$41$	4.00000	+	4.00000i	0.624695	+	0.624695i	−0.322033	+	0.946728i	$0.604366\pi$
$42$	4.01411	+	2.21063i	0.619391	+	0.341108i
$43$		−	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
$45$	−1.75201	−	0.137001i	−0.261174	−	0.0204229i
$46$	6.36138	−	1.70453i	0.937934	−	0.251319i
$47$	−0.634472	−	0.170006i	−0.0925473	−	0.0247980i	0.212248	−	0.977216i	$-0.431921\pi$
$47$	−0.634472	−	0.170006i	−0.0925473	−	0.0247980i	−0.304796	+	0.952418i	$0.598588\pi$
$48$	−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
$51$	2.97091	−	1.09687i	0.416011	−	0.153593i
$52$	3.23205	−	1.59808i	0.448205	−	0.221613i
$53$	7.49706	+	4.32843i	1.02980	+	0.594555i	0.916927	−	0.399054i	$-0.130662\pi$
$53$	7.49706	+	4.32843i	1.02980	+	0.594555i	0.112872	+	0.993609i	$0.463995\pi$
$54$	−3.72474	−	3.62302i	−0.506874	−	0.493031i
$55$	3.41421			0.460372
$56$	−7.50000	−	2.59808i	−1.00223	−	0.347183i
$57$	6.65685	+	9.41421i	0.881722	+	1.24694i
$58$	−0.965926	−	0.258819i	−0.126832	−	0.0339846i
$59$	2.45497	+	9.16208i	0.319610	+	1.19280i	0.919620	+	0.392809i	$0.128497\pi$
$59$	2.45497	+	9.16208i	0.319610	+	1.19280i	−0.600010	+	0.799992i	$0.704837\pi$
$60$	1.01033	−	0.0930924i	0.130433	−	0.0120182i
$61$	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
$63$	6.38682	−	4.71259i	0.804664	−	0.593730i
$64$		−	7.00000i		−	0.875000i
$65$	1.39425	+	1.58649i	0.172936	+	0.196780i
$66$	7.76318	+	6.45327i	0.955581	+	0.794343i
$67$	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	0.734130	−	0.679008i	$-0.237590\pi$
$71$	0.464466	+	0.464466i	0.0551220	+	0.0551220i	−0.679008	+	0.734130i	$0.737590\pi$
$72$	7.41970	+	5.09393i	0.874419	+	0.600325i
$73$	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
$75$	−2.79365	−	7.56666i	−0.322583	−	0.873723i
$76$	−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	$0.858683\pi$
$80$	0.565826	−	0.151613i	0.0632613	−	0.0169508i
$81$	−8.39898	+	3.23375i	−0.933220	+	0.359306i
$82$	4.89898	−	2.82843i	0.541002	−	0.312348i
$83$	3.07107	+	3.07107i	0.337093	+	0.337093i	0.855272	−	0.518179i	$-0.173390\pi$
$83$	3.07107	+	3.07107i	0.337093	+	0.337093i	−0.518179	+	0.855272i	$0.673390\pi$
$84$	−3.17423	+	3.30518i	−0.346337	+	0.360625i
$85$	−0.757359	−	0.757359i	−0.0821472	−	0.0821472i
$86$	−5.79555	−	1.55291i	−0.624951	−	0.167455i
$87$	−1.10721	+	1.33195i	−0.118705	+	0.142800i
$88$	−15.1427	−	8.74264i	−1.61422	−	0.931969i
$89$	−12.0599	−	3.23143i	−1.27834	−	0.342531i	−0.445121	−	0.895470i	$-0.646839\pi$
$89$	−12.0599	−	3.23143i	−1.27834	−	0.342531i	−0.833221	+	0.552940i	$0.813506\pi$
$90$	−0.585786	+	1.65685i	−0.0617473	+	0.174648i
$91$	−9.45121	−	1.29410i	−0.990756	−	0.135658i
$92$			6.58579i			0.686616i
$93$	0.600398	−	1.30323i	0.0622584	−	0.135138i
$94$	−0.328427	+	0.568852i	−0.0338747	+	0.0586727i
$95$	1.94975	−	3.37706i	0.200040	−	0.346479i
$96$	−7.86566	−	3.62372i	−0.802786	−	0.369845i
$97$	−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
$99$	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	$0.102895\pi$
$102$	−0.290571	−	3.15357i	−0.0287708	−	0.312250i
$103$	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
$105$	−2.35141	−	1.29496i	−0.229474	−	0.126375i
$106$	6.12132	−	6.12132i	0.594555	−	0.594555i
$107$	−5.91359	+	3.41421i	−0.571688	+	0.330064i	−0.757823	−	0.652460i	$-0.773737\pi$
$107$	−5.91359	+	3.41421i	−0.571688	+	0.330064i	0.186135	+	0.982524i	$0.440404\pi$
$108$	4.46360	−	2.66012i	0.429510	−	0.255970i
$109$	−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
$111$	−5.65685	+	4.00000i	−0.536925	+	0.379663i
$112$	−1.48356	+	2.19067i	−0.140184	+	0.206999i
$113$		−	9.00000i		−	0.846649i	−0.905978	−	0.423324i	$-0.860863\pi$
$113$		−	9.00000i		−	0.846649i	0.905978	−	0.423324i	$-0.139137\pi$
$114$	10.8164	−	3.99345i	1.01304	−	0.374021i
$115$	−3.72641	+	0.998489i	−0.347490	+	0.0931096i
$116$	0.500000	−	0.866025i	0.0464238	−	0.0804084i
$117$	9.94485	+	4.25442i	0.919401	+	0.393321i
$118$	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
$123$	−0.898979	−	9.75663i	−0.0810583	−	0.879726i
$124$	−0.214413	+	0.800199i	−0.0192548	+	0.0718600i
$125$	−4.00000	+	4.00000i	−0.357771	+	0.357771i
$126$	−2.89898	−	7.38891i	−0.258262	−	0.658256i
$127$			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
$129$	−6.64324	+	7.99171i	−0.584905	+	0.703631i
$130$	1.89329	−	0.936131i	0.166053	−	0.0821042i
$131$	11.1097	−	6.41421i	0.970663	−	0.560412i	0.0712246	−	0.997460i	$-0.477309\pi$
$131$	11.1097	−	6.41421i	0.970663	−	0.560412i	0.899438	+	0.437048i	$0.143976\pi$
$132$	−8.24264	+	5.82843i	−0.717430	+	0.507299i
$133$	3.32843	+	17.2950i	0.288611	+	1.49967i
$134$	13.4853			1.16495
$135$	2.18191	+	2.12232i	0.187788	+	0.182660i
$136$	1.41970	+	5.29837i	0.121738	+	0.454332i
$137$	−2.95422	−	11.0253i	−0.252396	−	0.941954i	−0.969521	−	0.245009i	$-0.921209\pi$
$137$	−2.95422	−	11.0253i	−0.252396	−	0.941954i	0.717125	−	0.696944i	$-0.245458\pi$
$138$	−10.3603	−	4.77301i	−0.881928	−	0.406306i
$139$	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
$143$	−19.9065	−	6.73413i	−1.66467	−	0.563136i
$144$	2.28024	−	1.94949i	0.190020	−	0.162457i
$145$	0.565826	+	0.151613i	0.0469893	+	0.0125907i
$146$		−	12.8284i		−	1.06169i
$147$	11.8572	−	2.53139i	0.977961	−	0.208785i
$148$	2.82843	−	2.82843i	0.232495	−	0.232495i
$149$	−3.74907	+	13.9917i	−0.307136	+	1.14625i	0.623956	+	0.781460i	$0.285524\pi$
$149$	−3.74907	+	13.9917i	−0.307136	+	1.14625i	−0.931091	+	0.364786i	$0.881142\pi$
$150$	−8.03189	+	0.740061i	−0.655801	+	0.0604257i
$151$	−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
$156$	−6.07433	−	1.44999i	−0.486336	−	0.116092i
$157$	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
$159$	−5.19325	−	14.0660i	−0.411852	−	1.11551i
$160$			2.92893i			0.231552i
$161$	9.77044	−	14.4273i	0.770018	−	1.13703i
$162$	0.949747	+	8.94975i	0.0746192	+	0.703159i
$163$	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
$165$	−4.54757	−	3.78024i	−0.354028	−	0.294291i
$166$	3.76127	−	2.17157i	0.291932	−	0.168547i
$167$	15.5355	−	15.5355i	1.20218	−	1.20218i	0.228672	−	0.973503i	$-0.426562\pi$
$167$	15.5355	−	15.5355i	1.20218	−	1.20218i	0.973503	−	0.228672i	$-0.0734384\pi$
$168$	7.11303	+	11.7646i	0.548782	+	0.907655i
$169$	−5.00000	−	12.0000i	−0.384615	−	0.923077i
$170$	−0.927572	+	0.535534i	−0.0711415	+	0.0410736i
$171$	1.55687	−	19.9098i	0.119057	−	1.52254i
$172$	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
$175$	0.882328	−	12.2892i	0.0666977	−	0.928980i
$176$	−4.12132	+	4.12132i	−0.310656	+	0.310656i
$177$	6.87441	−	14.9216i	0.516712	−	1.12158i
$178$	−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	$0.148638\pi$
$180$	−1.44879	−	0.994652i	−0.107986	−	0.0741370i
$181$			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
$186$	−1.10342	−	0.917240i	−0.0809070	−	0.0672553i
$187$	10.2937	+	2.75820i	0.752752	+	0.201699i
$188$	−0.464466	−	0.464466i	−0.0338747	−	0.0338747i
$189$	−13.7247	−	0.794593i	−0.998328	−	0.0577981i
$190$	−2.75736	−	2.75736i	−0.200040	−	0.200040i
$191$	14.6969	−	8.48528i	1.06343	−	0.613973i	0.137053	−	0.990564i	$-0.456237\pi$
$191$	14.6969	−	8.48528i	1.06343	−	0.613973i	0.926380	+	0.376590i	$0.122904\pi$
$192$	−7.75044	+	9.32366i	−0.559340	+	0.672877i
$193$	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
$195$	−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	0.506188	−	0.862423i	$-0.331054\pi$
$197$	−5.00000	−	5.00000i	−0.356235	−	0.356235i	−0.862423	+	0.506188i	$0.831054\pi$
$198$	−3.19507	−	17.1909i	−0.227064	−	1.22170i
$199$	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
$201$	9.77339	−	21.2141i	0.689362	−	1.49633i
$202$	−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
$207$	−15.0172	+	12.8389i	−1.04377	+	0.892367i
$208$	−3.59808	−	0.232051i	−0.249482	−	0.0160898i
$209$			38.7990i			2.68378i
$210$	−1.85942	+	1.93613i	−0.128312	+	0.133606i
$211$	−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
$213$	−0.104386	−	1.13291i	−0.00715244	−	0.0776254i
$214$	1.76733	+	6.59575i	0.120812	+	0.450876i
$215$	3.39496	+	0.909676i	0.231534	+	0.0620394i
$216$	−4.24264	−	15.0000i	−0.288675	−	1.02062i
$217$	1.65685	−	1.43488i	0.112475	−	0.0974059i
$218$	−7.41421			−0.502154
$219$	−20.1808	−	9.29734i	−1.36369	−	0.628256i
$220$	2.95680	+	1.70711i	0.199347	+	0.115093i
$221$	2.92197	+	5.90957i	0.196553	+	0.397521i
$222$	2.39960	+	6.49938i	0.161051	+	0.436210i
$223$	−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	−0.0613041	−	0.998119i	$-0.519526\pi$
$227$	5.79555	−	1.55291i	0.384664	−	0.103071i	0.445969	+	0.895049i	$0.352859\pi$
$228$	1.05790	+	11.4814i	0.0700610	+	0.760373i
$229$	−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
$231$	26.7038	−	0.539680i	1.75698	−	0.0355084i
$232$	−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	$0.847342\pi$
$234$	6.68336	−	8.50486i	0.436905	−	0.555980i
$235$	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	0.547816	−	0.836599i	$-0.315459\pi$
$239$	−4.46447	−	4.46447i	−0.288782	−	0.288782i	−0.836599	+	0.547816i	$0.815459\pi$
$240$	−0.921519	−	0.424546i	−0.0594838	−	0.0274043i
$241$	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
$243$	14.7675	+	4.99221i	0.947333	+	0.320250i
$244$			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
$249$	−0.690207	−	7.49082i	−0.0437401	−	0.474711i
$250$	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	$0.520105\pi$
$252$	7.88745	−	0.887810i	0.496862	−	0.0559268i
$253$	27.1421	−	27.1421i	1.70641	−	1.70641i
$254$	15.5921	+	4.17789i	0.978336	+	0.262144i
$255$	0.170213	+	1.84732i	0.0106591	+	0.115684i
$256$	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
$261$	2.94949	−	0.548188i	0.182569	−	0.0339320i
$262$	−3.32024	−	12.3913i	−0.205125	−	0.765538i
$263$	−17.7408	−	10.2426i	−1.09394	−	0.631588i	−0.159320	−	0.987227i	$-0.550930\pi$
$263$	−17.7408	−	10.2426i	−1.09394	−	0.631588i	−0.934623	+	0.355639i	$0.884263\pi$
$264$	10.4894	+	28.4109i	0.645580	+	1.74857i
$265$	−3.58579	+	3.58579i	−0.220273	+	0.220273i
$266$	17.5672	+	1.26127i	1.07711	+	0.0773331i
$267$	12.4853	+	17.6569i	0.764087	+	1.08058i
$268$	−3.49025	+	13.0258i	−0.213201	+	0.795676i
$269$	6.06218	+	3.50000i	0.369618	+	0.213399i	0.673291	−	0.739377i	$-0.264880\pi$
$269$	6.06218	+	3.50000i	0.369618	+	0.213399i	−0.303674	+	0.952776i	$0.598213\pi$
$270$	2.61472	−	1.55826i	0.159127	−	0.0948328i
$271$	−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
$273$	11.1557	+	12.1881i	0.675175	+	0.737658i
$274$	−11.4142			−0.689558
$275$	7.02490	−	26.2173i	0.423618	−	1.58096i
$276$	7.29182	−	8.77195i	0.438916	−	0.528009i
$277$	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
$279$	−2.24264	+	1.07107i	−0.134263	+	0.0641232i
$280$	2.60715	−	3.84980i	0.155807	−	0.230069i
$281$	−8.07107	+	8.07107i	−0.481480	+	0.481480i	−0.905604	−	0.424124i	$-0.860582\pi$
$281$	−8.07107	+	8.07107i	−0.481480	+	0.481480i	0.424124	+	0.905604i	$0.360582\pi$
$282$	1.06729	−	0.394047i	0.0635560	−	0.0234652i
$283$	−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
$285$	−6.33607	+	2.33931i	−0.375317	+	0.138569i
$286$	−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
$291$	17.0741	−	1.57321i	1.00090	−	0.0922234i
$292$	12.3913	+	3.32024i	0.725147	+	0.194302i
$293$	−9.14214	+	9.14214i	−0.534089	+	0.534089i	−0.921787	−	0.387697i	$-0.873271\pi$
$293$	−9.14214	+	9.14214i	−0.534089	+	0.534089i	0.387697	+	0.921787i	$0.373271\pi$
$294$	0.623724	−	12.1083i	0.0363763	−	0.706170i
$295$	−5.55635			−0.323503
$296$	−6.00000	−	10.3923i	−0.348743	−	0.604040i
$297$	−29.3592	−	7.43273i	−1.70359	−	0.431291i
$298$	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
$303$	−6.49938	+	2.39960i	−0.373379	+	0.137854i
$304$	1.72292	+	6.43003i	0.0988163	+	0.368787i
$305$	−0.565826	+	0.151613i	−0.0323991	+	0.00868132i
$306$	−3.10463	+	4.52212i	−0.177480	+	0.258513i
$307$	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	−0.891161	−	0.453688i	$-0.850108\pi$
$311$	−0.928932	+	1.60896i	−0.0526749	+	0.0912356i	0.838486	+	0.544924i	$0.183441\pi$
$312$	−8.91820	+	16.4762i	−0.504894	+	0.932782i
$313$	−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
$315$	1.69818	+	4.32832i	0.0956818	+	0.243873i
$316$		−	1.41421i		−	0.0795557i
$317$	−4.38153	+	16.3521i	−0.246091	+	0.918425i	0.726741	+	0.686912i	$0.241034\pi$
$317$	−4.38153	+	16.3521i	−0.246091	+	0.918425i	−0.972832	+	0.231513i	$0.925632\pi$
$318$	−14.9309	+	1.37574i	−0.837281	+	0.0771474i
$319$	−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
$324$	−8.89060	−	1.39898i	−0.493922	−	0.0777211i
$325$	15.0512	−	7.44201i	0.834890	−	0.412808i
$326$	−1.88064	−	1.08579i	−0.104159	−	0.0601361i
$327$	−5.37341	+	11.6635i	−0.297150	+	0.644995i
$328$	16.9706			0.937043
$329$	0.328427	+	1.70656i	0.0181068	+	0.0940856i
$330$	−4.82843	+	3.41421i	−0.265796	+	0.187946i
$331$	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
$333$	11.9635	+	0.935500i	0.655595	+	0.0512651i
$334$	−10.9853	−	19.0271i	−0.601088	−	1.04111i
$335$	−7.89949			−0.431596
$336$	4.40156	−	1.27526i	0.240125	−	0.0695709i
$337$		−	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
$339$	−9.96486	+	11.9876i	−0.541217	+	0.651075i
$340$	−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
$345$	6.06893	+	2.79597i	0.326740	+	0.150530i
$346$	−14.9576	+	4.00789i	−0.804127	+	0.215465i
$347$	−4.05845	−	2.34315i	−0.217869	−	0.125787i	0.387094	−	0.922040i	$-0.373479\pi$
$347$	−4.05845	−	2.34315i	−0.217869	−	0.125787i	−0.604963	+	0.796254i	$0.706812\pi$
$348$	−1.62484	+	0.599900i	−0.0871008	+	0.0321580i
$349$	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
$351$	−8.53553	−	16.6777i	−0.455593	−	0.890188i
$352$	−14.5711	−	25.2378i	−0.776641	−	1.34518i
$353$	6.92721	−	1.85614i	0.368698	−	0.0987923i	−0.0697126	−	0.997567i	$-0.522208\pi$
$353$	6.92721	−	1.85614i	0.368698	−	0.0987923i	0.438411	+	0.898775i	$0.355542\pi$
$354$	−12.6339	−	10.5022i	−0.671486	−	0.558184i
$355$	−0.333226	+	0.192388i	−0.0176858	+	0.0102109i
$356$	−8.82843	−	8.82843i	−0.467906	−	0.467906i
$357$	−6.04329	−	5.80386i	−0.319845	−	0.307173i
$358$	−1.07107	−	1.07107i	−0.0566077	−	0.0566077i
$359$	−21.7191	−	5.81962i	−1.14629	−	0.307148i	−0.364813	−	0.931081i	$-0.618867\pi$
$359$	−21.7191	−	5.81962i	−1.14629	−	0.307148i	−0.781478	+	0.623933i	$0.785534\pi$
$360$	−4.00720	+	3.42595i	−0.211198	+	0.180564i
$361$	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
$366$	−1.57313	−	0.724745i	−0.0822289	−	0.0378830i
$367$	−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
$369$	−9.60521	+	13.9907i	−0.500027	+	0.728327i
$370$	1.65685	−	1.65685i	0.0861358	−	0.0861358i
$371$	1.64020	−	22.8451i	0.0851551	−	1.18606i
$372$	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
$375$	9.75663	−	0.898979i	0.503830	−	0.0464231i
$376$	−1.70656	+	0.985281i	−0.0880090	+	0.0508120i
$377$	−3.00000	−	2.00000i	−0.154508	−	0.103005i
$378$	−4.31974	+	13.0514i	−0.222184	+	0.671293i
$379$	−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
$381$	17.8727	−	21.5005i	0.915645	−	1.10151i
$382$	−4.39230	−	16.3923i	−0.224730	−	0.838703i
$383$	−1.85614	+	6.92721i	−0.0948443	+	0.353964i	−0.996996	−	0.0774556i	$-0.975320\pi$
$383$	−1.85614	+	6.92721i	−0.0948443	+	0.353964i	0.902151	+	0.431419i	$0.141987\pi$
$384$	−3.00000	−	4.24264i	−0.153093	−	0.216506i
$385$	−3.94476	−	8.12630i	−0.201044	−	0.414155i
$386$		−	2.82843i		−	0.143963i
$387$	17.6969	−	3.28913i	0.899586	−	0.167196i
$388$	−9.56218	+	2.56218i	−0.485446	+	0.130075i
$389$	−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	$0.242784\pi$
$390$	−3.55826	−	0.849383i	−0.180180	−	0.0430102i
$391$	−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
$396$	17.4321	+	1.36312i	0.875994	+	0.0684995i
$397$	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
$399$	14.7158	−	26.7214i	0.736714	−	1.33774i
$400$		−	4.65685i		−	0.232843i
$401$	−11.8255	−	3.16863i	−0.590536	−	0.158234i	−0.0488381	−	0.998807i	$-0.515552\pi$
$401$	−11.8255	−	3.16863i	−0.590536	−	0.158234i	−0.541698	+	0.840573i	$0.682218\pi$
$402$	−17.9617	−	14.9310i	−0.895850	−	0.744690i
$403$	2.82942	+	0.957160i	0.140944	+	0.0476795i
$404$	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
$408$	3.97543	−	8.62907i	0.196813	−	0.427203i
$409$	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
$411$	−8.27239	+	17.9561i	−0.408047	+	0.885707i
$412$	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
$416$	5.77697	−	17.0771i	0.283239	−	0.837273i
$417$	−3.90119	−	3.24293i	−0.191042	−	0.158807i
$418$	37.4769	+	10.0419i	1.83306	+	0.491166i
$419$			16.9289i			0.827032i	0.910497	+	0.413516i	$0.135700\pi$
$419$			16.9289i			0.827032i	−0.910497	+	0.413516i	$0.864300\pi$
$420$	−1.38891	−	2.29717i	−0.0677716	−	0.112091i
$421$	−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
$423$	0.153622	−	1.96457i	0.00746935	−	0.0955204i
$424$	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
$429$	19.0584	+	31.0101i	0.920149	+	1.49718i
$430$	1.75736	−	3.04384i	0.0847474	−	0.146787i
$431$	−14.6546	+	3.92669i	−0.705888	+	0.189142i	−0.593866	−	0.804564i	$-0.702399\pi$
$431$	−14.6546	+	3.92669i	−0.705888	+	0.189142i	−0.112022	+	0.993706i	$0.535733\pi$
$432$	−5.19565	+	0.0719302i	−0.249976	+	0.00346074i
$433$		−	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
$435$	−0.585786	−	0.828427i	−0.0280863	−	0.0397200i
$436$	1.91894	−	7.16158i	0.0919005	−	0.342977i
$437$	−11.3468	−	42.3468i	−0.542790	−	2.02572i
$438$	−14.2037	+	17.0868i	−0.678680	+	0.816441i
$439$	−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
$441$	−18.5959	−	9.75663i	−0.885520	−	0.464601i
$442$	6.46447	−	1.29289i	0.307483	−	0.0614967i
$443$	−4.56575	+	2.63604i	−0.216925	+	0.125242i	−0.604526	−	0.796586i	$-0.706637\pi$
$443$	−4.56575	+	2.63604i	−0.216925	+	0.125242i	0.387600	+	0.921828i	$0.373304\pi$
$444$	−6.89898	+	0.635674i	−0.327411	+	0.0301678i
$445$	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
$448$	−16.6610	+	8.08776i	−0.787157	+	0.382111i
$449$	−2.00000	+	2.00000i	−0.0943858	+	0.0943858i	−0.752723	−	0.658337i	$-0.771260\pi$
$449$	−2.00000	+	2.00000i	−0.0943858	+	0.0943858i	0.658337	+	0.752723i	$0.271260\pi$
$450$	11.5175	+	7.90723i	0.542939	+	0.372750i
$451$	16.4853	−	28.5533i	0.776262	−	1.34452i
$452$	4.50000	−	7.79423i	0.211662	−	0.366610i
$453$	31.1927	+	14.3706i	1.46556	+	0.675187i
$454$		−	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
$459$	4.86384	+	8.16137i	0.227024	+	0.380940i
$460$	−3.72641	−	0.998489i	−0.173745	−	0.0465548i
$461$	−28.0711	−	28.0711i	−1.30740	−	1.30740i	−0.923285	−	0.384115i	$-0.874507\pi$
$461$	−28.0711	−	28.0711i	−1.30740	−	1.30740i	−0.384115	−	0.923285i	$-0.625493\pi$
$462$	6.39015	−	25.9335i	0.297297	−	1.20654i
$463$	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
$465$	0.646371	+	0.537307i	0.0299747	+	0.0249170i
$466$	−1.29738	+	0.347632i	−0.0600999	+	0.0161037i
$467$	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
$471$	−2.97091	+	1.09687i	−0.136892	+	0.0505413i
$472$	24.6435	+	14.2279i	1.13431	+	0.654893i
$473$	−33.7790	+	9.05105i	−1.55316	+	0.416168i
$474$	2.22474	+	1.02494i	0.102186	+	0.0470772i
$475$	−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	$0.151923\pi$
$479$	7.63135	+	28.4806i	0.348685	+	1.30131i	−0.539562	+	0.841946i	$0.681410\pi$
$480$	3.24293	−	3.90119i	0.148019	−	0.178064i
$481$	−9.52056	−	10.8332i	−0.434100	−	0.493953i
$482$		−	22.2426i		−	1.01312i
$483$	−28.9877	+	8.39856i	−1.31899	+	0.382148i
$484$	−22.9706			−1.04412
$485$	−2.89949	−	5.02207i	−0.131659	−	0.228041i
$486$	8.64420	−	12.9722i	0.392109	−	0.588431i
$487$	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
$489$	−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	$0.433339\pi$
$492$	4.09978	−	8.89898i	0.184832	−	0.401197i
$493$	1.58346	+	0.914214i	0.0713156	+	0.0411741i
$494$	10.6382	+	21.5153i	0.478633	+	0.968019i
$495$	1.87163	+	10.0702i	0.0841236	+	0.452621i
$496$	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
$501$	−37.8936	+	3.49153i	−1.69296	+	0.155990i
$502$	−0.517638	+	1.93185i	−0.0231033	+	0.0862228i
$503$			13.0711i			0.582810i	0.956600	+	0.291405i	$0.0941227\pi$
$503$			13.0711i			0.582810i	−0.956600	+	0.291405i	$0.905877\pi$
$504$	3.55159	−	23.5454i	0.158200	−	1.04880i
$505$	1.65685	+	1.65685i	0.0737290	+	0.0737290i
$506$	−19.1924	−	33.2422i	−0.853206	−	1.47780i
$507$	−6.62672	+	21.5194i	−0.294303	+	0.955712i
$508$	−8.07107	+	13.9795i	−0.358096	+	0.620240i
$509$	6.91770	−	25.8172i	0.306621	−	1.14433i	−0.624919	−	0.780689i	$-0.714868\pi$
$509$	6.91770	−	25.8172i	0.306621	−	1.14433i	0.931541	−	0.363637i	$-0.118465\pi$
$510$	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
$513$	−24.1179	+	24.7951i	−1.06483	+	1.09473i
$514$	18.1869	−	4.87316i	0.802188	−	0.214946i
$515$	0.983251	+	3.66954i	0.0433272	+	0.161699i
$516$	−9.74907	+	3.59940i	−0.429179	+	0.158455i
$517$			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	0.392916	−	0.919575i	$-0.371466\pi$
$521$	−4.72490	−	2.72792i	−0.207002	−	0.119512i	−0.599917	+	0.800062i	$0.704800\pi$
$522$	0.233875	−	2.99087i	0.0102364	−	0.130907i
$523$	−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
$525$	−14.7819	+	15.3918i	−0.645137	+	0.671751i
$526$	−14.4853	+	14.4853i	−0.631588	+	0.631588i
$527$	−1.46311	−	0.392038i	−0.0637339	−	0.0170774i
$528$	10.0525	−	0.926246i	0.437481	−	0.0403097i
$529$	−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
$534$	20.2866	−	7.48993i	0.877889	−	0.324121i
$535$	−1.03528	−	3.86370i	−0.0447589	−	0.167042i
$536$	35.0358	+	20.2279i	1.51332	+	0.873713i
$537$	−2.46118	+	0.908680i	−0.106208	+	0.0392125i
$538$	4.94975	−	4.94975i	0.213399	−	0.213399i
$539$	37.4961	+	16.0811i	1.61507	+	0.692661i
$540$	0.828427	+	2.92893i	0.0356498	+	0.126041i
$541$	−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
$543$	10.1222	−	12.1769i	0.434386	−	0.522560i
$544$	−2.36616	+	8.83062i	−0.101448	+	0.378610i
$545$	4.34315			0.186040
$546$	14.6601	−	7.62108i	0.627395	−	0.326152i
$547$	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
$549$	−2.28024	+	1.94949i	−0.0973182	+	0.0832022i
$550$	−23.5058	−	13.5711i	−1.00229	−	0.578672i
$551$	−1.72292	+	6.43003i	−0.0733989	+	0.273928i
$552$	−19.7574	−	27.9411i	−0.840929	−	1.18925i
$553$	−2.09808	+	3.09808i	−0.0892193	+	0.131744i
$554$	2.70711	−	2.70711i	0.115014	−	0.115014i
$555$	−1.40565	−	3.80725i	−0.0596667	−	0.161609i
$556$	2.53653	+	1.46447i	0.107573	+	0.0621072i
$557$	8.47061	+	31.6127i	0.358911	+	1.33948i	0.875490	+	0.483236i	$0.160539\pi$
$557$	8.47061	+	31.6127i	0.358911	+	1.33948i	−0.516579	+	0.856239i	$0.672795\pi$
$558$	0.454134	+	2.44344i	0.0192250	+	0.103439i
$559$	−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	$0.190264\pi$
$564$	0.104386	+	1.13291i	0.00439546	+	0.0477039i
$565$	5.09244	+	1.36451i	0.214240	+	0.0574055i
$566$	−12.5858	+	12.5858i	−0.529020	+	0.529020i
$567$	17.4009	+	16.2545i	0.730770	+	0.682624i
$568$	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	$0.468259\pi$
$570$	0.619702	+	6.72563i	0.0259565	+	0.281706i
$571$	−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
$576$	20.6464	−	3.83732i	0.860268	−	0.159888i
$577$	−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
$579$	−4.44949	−	2.04989i	−0.184914	−	0.0851904i
$580$	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
$585$	−3.91502	+	4.98203i	−0.161866	+	0.205982i
$586$	6.46447	+	11.1968i	0.267045	+	0.462535i
$587$	23.5355	+	23.5355i	0.971415	+	0.971415i	0.999603	−	0.0281872i	$-0.00897346\pi$
$587$	23.5355	+	23.5355i	0.971415	+	0.971415i	−0.0281872	+	0.999603i	$0.508973\pi$
$588$	11.5343	+	3.73633i	0.475666	+	0.154084i
$589$		−	5.51472i		−	0.227230i
$590$	−1.43809	+	5.36702i	−0.0592052	+	0.220957i
$591$	1.12372	+	12.1958i	0.0462238	+	0.501668i
$592$	−3.86370	+	1.03528i	−0.158797	+	0.0425496i
$593$	32.2188	+	8.63300i	1.32307	+	0.354515i	0.850126	−	0.526579i	$-0.176526\pi$
$593$	32.2188	+	8.63300i	1.32307	+	0.354515i	0.472941	+	0.881094i	$0.343192\pi$
$594$	−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
$597$	−9.04114	−	24.4881i	−0.370029	−	1.00223i
$598$	7.60918	−	22.4932i	0.311163	−	0.919815i
$599$	−21.7122	−	12.5355i	−0.887136	−	0.512188i	−0.0141312	−	0.999900i	$-0.504498\pi$
$599$	−21.7122	−	12.5355i	−0.887136	−	0.512188i	−0.873005	+	0.487712i	$0.837832\pi$
$600$	−21.9775	−	10.1251i	−0.897229	−	0.413355i
$601$	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
$604$	−19.1528	−	5.13197i	−0.779316	−	0.208817i
$605$	−3.48263	−	12.9973i	−0.141589	−	0.528417i
$606$	0.635674	+	6.89898i	0.0258225	+	0.280252i
$607$	−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
$609$	4.44949	+	1.09638i	0.180302	+	0.0444274i
$610$			0.585786i			0.0237178i
$611$	−1.77896	+	1.56340i	−0.0719692	+	0.0632486i
$612$	−3.56450	−	4.16925i	−0.144086	−	0.168532i
$613$	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	0.550298	−	0.834968i	$-0.314514\pi$
$617$	−7.07107	−	7.07107i	−0.284670	−	0.284670i	−0.834968	+	0.550298i	$0.814514\pi$
$618$	−4.70017	+	10.2022i	−0.189069	+	0.410393i
$619$	−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
$621$	34.2175	−	0.473717i	1.37310	−	0.0190096i
$622$	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
$626$	−22.8508	+	6.12284i	−0.913300	+	0.244718i
$627$	42.9585	−	51.6784i	1.71560	−	2.06383i
$628$	1.58346	−	0.914214i	0.0631871	−	0.0364811i
$629$	5.17157	+	5.17157i	0.206204	+	0.206204i
$630$	4.62036	−	0.520067i	0.184079	−	0.0207200i
$631$	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
$633$	20.0739	+	16.6868i	0.797867	+	0.663240i
$634$	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
$639$	−1.11532	+	1.62455i	−0.0441215	+	0.0642663i
$640$	−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	$0.325880\pi$
$642$	4.94887	−	10.7420i	0.195316	−	0.423954i
$643$	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
$645$	−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	$0.855459\pi$
$648$	−10.9571	+	24.6767i	−0.430436	+	0.969394i
$649$	47.8776	−	27.6421i	1.87936	−	1.08505i
$650$	−3.29289	−	16.4645i	−0.129158	−	0.645789i
$651$	−3.79555	+	0.0767078i	−0.148760	+	0.00300642i
$652$	1.53553	−	1.53553i	0.0601361	−	0.0601361i
$653$	27.5387	−	15.8995i	1.07767	−	0.622195i	0.147406	−	0.989076i	$-0.452908\pi$
$653$	27.5387	−	15.8995i	1.07767	−	0.622195i	0.930268	+	0.366881i	$0.119574\pi$
$654$	9.87537	+	8.20906i	0.386158	+	0.321000i
$655$	1.94495	+	7.25866i	0.0759956	+	0.283619i
$656$	1.46410	−	5.46410i	0.0571636	−	0.213337i
$657$	16.5858	+	34.7279i	0.647073	+	1.35487i
$658$	1.73341	+	0.124453i	0.0675754	+	0.00485170i
$659$			21.0711i			0.820812i	0.911903	+	0.410406i	$0.134613\pi$
$659$			21.0711i			0.820812i	−0.911903	+	0.410406i	$0.865387\pi$
$660$	−2.04819	−	5.54757i	−0.0797256	−	0.215939i
$661$	−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
$663$	2.65120	−	11.1065i	0.102964	−	0.431340i
$664$	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
$669$	8.62372	−	0.794593i	0.333412	−	0.0307207i
$670$	−2.04454	+	7.63033i	−0.0789875	+	0.294785i
$671$	4.12132	−	4.12132i	0.159102	−	0.159102i
$672$	0.462972	+	22.9082i	0.0178595	+	0.883703i
$673$			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
$675$	20.7864	−	12.3878i	0.800067	−	0.476806i
$676$	1.66987	−	12.8923i	0.0642259	−	0.495858i
$677$	−22.4912	+	12.9853i	−0.864406	+	0.499065i	−0.865485	−	0.500935i	$-0.832990\pi$
$677$	−22.4912	+	12.9853i	−0.864406	+	0.499065i	0.00107942	+	0.999999i	$0.499656\pi$
$678$	9.00000	+	12.7279i	0.345643	+	0.488813i
$679$	24.7487	+	8.57321i	0.949769	+	0.329010i
$680$	−3.21320			−0.123221
$681$	−9.43879	−	4.34847i	−0.361695	−	0.166634i
$682$	−1.24969	−	4.66390i	−0.0478531	−	0.178590i
$683$	−13.0145	−	48.5709i	−0.497987	−	1.85851i	−0.512613	−	0.858620i	$-0.671322\pi$
$683$	−13.0145	−	48.5709i	−0.497987	−	1.85851i	0.0146258	−	0.999893i	$-0.495344\pi$
$684$	11.3032	−	16.4639i	0.432188	−	0.629515i
$685$	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
$689$	27.9794	−	13.8343i	1.06593	−	0.527045i
$690$	4.27145	−	5.13849i	0.162611	−	0.195619i
$691$	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
$693$	−36.1656	−	28.8477i	−1.37382	−	1.09584i
$694$	−3.31371	+	3.31371i	−0.125787	+	0.125787i
$695$	−0.444063	+	1.65727i	−0.0168443	+	0.0628637i
$696$	0.476756	+	5.17423i	0.0180714	+	0.196129i
$697$	−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	$-0.259706\pi$
$701$	36.2843			1.37044			0.685219	+	0.728337i	$0.259706\pi$
$702$	−18.3186	+	3.92819i	−0.691389	+	0.148260i
$703$	−13.3137	+	23.0600i	−0.502136	+	0.869725i
$704$	−39.4088	+	10.5596i	−1.48527	+	0.397978i
$705$	−0.625202	+	0.230827i	−0.0235465	+	0.00869347i
$706$		−	7.17157i		−	0.269906i
$707$	−10.5558	−	0.757875i	−0.396993	−	0.0285028i
$708$	13.4142	−	9.48528i	0.504137	−	0.356479i
$709$	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
$711$	3.22474	−	2.75699i	0.120937	−	0.103395i
$712$	−32.4377	+	18.7279i	−1.21565	+	0.701859i
$713$	−3.85786	+	3.85786i	−0.144478	+	0.144478i
$714$	−7.17021	+	4.33522i	−0.268338	+	0.162241i
$715$	6.82843	−	10.2426i	0.255369	−	0.383053i
$716$	1.31178	−	0.757359i	0.0490237	−	0.0283038i
$717$	1.00337	+	10.8895i	0.0374714	+	0.406677i
$718$	−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
$721$	−14.2071	−	9.62133i	−0.529101	−	0.358317i
$722$	17.8995	−	17.8995i	0.666150	−	0.666150i
$723$	−34.9906	−	16.1202i	−1.30131	−	0.599518i
$724$	−4.57107	+	7.91732i	−0.169882	+	0.294245i
$725$	2.32843	−	4.03295i	0.0864756	−	0.149780i
$726$	16.6478	−	36.1357i	0.617858	−	1.34112i
$727$			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
$732$	1.10721	−	1.33195i	0.0409235	−	0.0492303i
$733$	−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
$735$	−0.365369	+	7.09288i	−0.0134768	+	0.261625i
$736$	23.2843	+	23.2843i	0.858270	+	0.858270i
$737$	68.0678	−	39.2990i	2.50731	−	1.44760i
$738$	11.0280	+	12.8990i	0.405946	+	0.474818i
$739$	−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
$741$	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	0.617540	−	0.786540i	$-0.288129\pi$
$743$	−4.60660	−	4.60660i	−0.169000	−	0.169000i	−0.786540	+	0.617540i	$0.788129\pi$
$744$	−1.49092	−	4.03820i	−0.0546598	−	0.148047i
$745$	−7.34847	−	4.24264i	−0.269227	−	0.155438i
$746$	−22.0221	+	5.90081i	−0.806288	+	0.216044i
$747$	−7.37456	+	10.7416i	−0.269821	+	0.393015i
$748$	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
$753$	2.66390	+	2.21441i	0.0970780	+	0.0806977i
$754$	−2.70831	+	2.38014i	−0.0986308	+	0.0866796i
$755$		−	11.6152i		−	0.422721i
$756$	−11.4887	−	7.55051i	−0.417839	−	0.274609i
$757$	−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
$759$	−66.2039	+	6.10006i	−2.40305	+	0.221418i
$760$	−3.02779	−	11.2999i	−0.109830	−	0.409889i
$761$	−24.3139	−	6.51488i	−0.881377	−	0.236164i	−0.210376	−	0.977621i	$-0.567469\pi$
$761$	−24.3139	−	6.51488i	−0.881377	−	0.236164i	−0.671001	+	0.741456i	$0.734135\pi$
$762$	−16.1421	−	22.8284i	−0.584768	−	0.826987i
$763$	−14.8284	+	12.8418i	−0.536825	+	0.464904i
$764$	16.9706			0.613973
$765$	1.81865	−	2.64900i	0.0657534	−	0.0957748i
$766$	6.21076	+	3.58579i	0.224404	+	0.129560i
$767$	32.3962	+	10.9592i	1.16976	+	0.395715i
$768$	−27.6224	+	10.1983i	−0.996736	+	0.368000i
$769$	−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	−0.888433	−	0.459007i	$-0.848205\pi$
$773$	−39.7118	+	10.6407i	−1.42833	+	0.382721i	−0.539902	+	0.841728i	$0.681539\pi$
$774$	1.40325	−	17.9452i	0.0504388	−	0.645028i
$775$	−0.998489	+	3.72641i	−0.0358668	+	0.133857i
$776$			29.6985i			1.06611i
$777$	16.0565	+	8.84252i	0.576022	+	0.317224i
$778$	6.60660	+	6.60660i	0.236858	+	0.236858i
$779$	−18.8284	−	32.6118i	−0.674598	−	1.16844i
$780$	1.74139	−	3.21718i	0.0623517	−	0.115194i
$781$	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
$786$	−9.29734	+	20.1808i	−0.331625	+	0.719826i
$787$	−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
$789$	12.2891	+	33.2854i	0.437505	+	1.18499i
$790$		−	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
$795$	8.74630	−	0.805887i	0.310199	−	0.0285819i
$796$	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	$0.441696\pi$
$798$	−22.0021	−	21.1304i	−0.778867	−	0.748009i
$799$	0.849242	−	0.849242i	0.0300440	−	0.0300440i
$800$	22.4909	+	6.02641i	0.795173	+	0.213066i
$801$	2.92000	−	37.3419i	0.103173	−	1.31941i
$802$	−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
$807$	−4.19930	−	11.3739i	−0.147822	−	0.400381i
$808$	−3.10583	−	11.5911i	−0.109263	−	0.407774i
$809$	−39.3404	−	22.7132i	−1.38314	−	0.798554i	−0.390606	−	0.920558i	$-0.627735\pi$
$809$	−39.3404	−	22.7132i	−1.38314	−	0.798554i	−0.992530	+	0.122004i	$0.961068\pi$
$810$	−5.20800	−	0.819503i	−0.182990	−	0.0287944i
$811$	−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
$813$	5.89949	−	4.17157i	0.206904	−	0.146303i
$814$	−6.03403	+	22.5193i	−0.211493	+	0.789302i
$815$	1.10165	+	0.636039i	0.0385892	+	0.0222795i
$816$	−2.43538	−	2.02445i	−0.0852552	−	0.0708698i
$817$	−10.3375	+	38.5802i	−0.361664	+	1.34975i
$818$	26.7279			0.934520
$819$	−1.36412	−	28.5856i	−0.0476662	−	0.998863i
$820$	−3.31371			−0.115720
$821$	−7.22092	+	26.9488i	−0.252012	+	0.940521i	0.717717	+	0.696335i	$0.245187\pi$
$821$	−7.22092	+	26.9488i	−0.252012	+	0.940521i	−0.969728	+	0.244186i	$0.921479\pi$
$822$	15.2032	+	12.6379i	0.530272	+	0.440797i
$823$	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
$825$	−38.3848	+	27.1421i	−1.33639	+	0.944968i
$826$	−10.9592	−	22.5763i	−0.381321	−	0.785530i
$827$	−15.6777	+	15.6777i	−0.545166	+	0.545166i	−0.925039	−	0.379873i	$-0.875968\pi$
$827$	−15.6777	+	15.6777i	−0.545166	+	0.545166i	0.379873	+	0.925039i	$0.375968\pi$
$828$	−19.4247	+	3.61025i	−0.675055	+	0.125465i
$829$	−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
$831$	−2.29668	−	6.22060i	−0.0796708	−	0.215790i
$832$	−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
$837$	4.17298	+	1.05646i	0.144239	+	0.0365165i
$838$	16.3521	+	4.38153i	0.564874	+	0.151357i
$839$	−11.3934	+	11.3934i	−0.393344	+	0.393344i	−0.875877	−	0.482534i	$-0.839717\pi$
$839$	−11.3934	+	11.3934i	−0.393344	+	0.393344i	0.482534	+	0.875877i	$0.339717\pi$
$840$	−7.73512	+	2.24108i	−0.266887	+	0.0773247i
$841$	28.0000			0.965517
$842$	7.82843	+	13.5592i	0.269785	+	0.467282i
$843$	19.6866	−	1.81393i	0.678043	−	0.0624751i
$844$	−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
$849$	10.6776	+	28.9206i	0.366455	+	0.992552i
$850$	2.20377	+	8.22459i	0.0755887	+	0.282101i
$851$	25.4455	−	6.81811i	0.872261	−	0.233722i
$852$	0.476052	−	1.03332i	0.0163093	−	0.0354009i
$853$	−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	$-0.501160\pi$
$857$	25.2990	−	43.8191i	0.864197	−	1.49683i	0.867842	−	0.496840i	$-0.165506\pi$
$858$	34.8862	−	10.3830i	1.19099	−	0.354470i
$859$	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
$861$	−22.1835	+	13.4125i	−0.756010	+	0.457095i
$862$			15.1716i			0.516746i
$863$	−12.8369	+	47.9080i	−0.436973	+	1.63081i	0.299327	+	0.954151i	$0.403238\pi$
$863$	−12.8369	+	47.9080i	−0.436973	+	1.63081i	−0.736300	+	0.676656i	$0.763429\pi$
$864$	6.37628	−	25.1862i	0.216925	−	0.856851i
$865$	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
$870$	−0.951812	+	0.351414i	−0.0322694	+	0.0119140i
$871$	46.0578	+	15.5808i	1.56061	+	0.527936i
$872$	−19.2627	−	11.1213i	−0.652317	−	0.376615i
$873$	−24.4837	−	16.8091i	−0.828649	−	0.568902i
$874$	−43.8406			−1.48293
$875$	14.1421	+	4.89898i	0.478091	+	0.165616i
$876$	−12.8284	−	18.1421i	−0.433432	−	0.612966i
$877$	−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
$879$	22.2991	−	2.05465i	0.752130	−	0.0693016i
$880$	−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	$0.510726\pi$
$882$	−14.2372	+	15.4371i	−0.479390	+	0.519793i
$883$		−	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
$885$	7.40079	+	6.15203i	0.248775	+	0.206798i
$886$	1.36451	+	5.09244i	0.0458418	+	0.171084i
$887$	−21.7482	+	12.5563i	−0.730234	+	0.421601i	−0.818508	−	0.574495i	$-0.805198\pi$
$887$	−21.7482	+	12.5563i	−0.730234	+	0.421601i	0.0882736	+	0.996096i	$0.471865\pi$
$888$	−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
$891$	30.8754	+	42.4067i	1.03436	+	1.42068i
$892$	−4.82963	+	1.29410i	−0.161708	+	0.0433295i
$893$	3.78677	+	2.18629i	0.126719	+	0.0731615i
$894$	−8.68973	−	23.5363i	−0.290628	−	0.787173i
$895$	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
$899$	0.800199	−	0.214413i	0.0266881	−	0.00715106i
$900$	−10.6187	+	9.07849i	−0.353958	+	0.302616i
$901$	−13.7078	+	7.91421i	−0.456674	+	0.263661i
$902$	−23.3137	−	23.3137i	−0.776262	−	0.776262i
$903$	26.6969	+	6.57826i	0.888418	+	0.218911i
$904$	−19.0919	−	19.0919i	−0.634987	−	0.634987i
$905$	−5.17286	−	1.38606i	−0.171952	−	0.0460743i
$906$	21.9542	−	26.4105i	0.729378	−	0.877430i
$907$	−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	$-0.665096\pi$
$911$		−	52.4264i		−	1.73696i	0.495720	−	0.868482i	$-0.334904\pi$
$912$	4.82452	−	10.4721i	0.159756	−	0.346766i
$913$	12.6569	−	21.9223i	0.418881	−	0.725523i
$914$	2.22183	−	3.84831i	0.0734915	−	0.127291i
$915$	0.921519	+	0.424546i	0.0304645	+	0.0140350i
$916$	−3.89949	+	3.89949i	−0.128843	+	0.128843i
$917$	−28.1029	−	19.0318i	−0.928038	−	0.628485i
$918$	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
$921$	−0.794593	−	8.62372i	−0.0261827	−	0.284161i
$922$	−34.3799	+	19.8492i	−1.13224	+	0.653700i
$923$	2.32233	−	0.464466i	0.0764404	−	0.0152881i
$924$	23.3960	+	12.8845i	0.769671	+	0.423869i
$925$	13.1716	−	13.1716i	0.433079	−	0.433079i
$926$	4.89898	−	2.82843i	0.160990	−	0.0929479i
$927$	12.6430	+	14.7880i	0.415250	+	0.485701i
$928$	−1.29410	−	4.82963i	−0.0424808	−	0.158540i
$929$	6.60370	−	24.6453i	0.216660	−	0.808587i	−0.768915	−	0.639351i	$-0.779203\pi$
$929$	6.60370	−	24.6453i	0.216660	−	0.808587i	0.985576	−	0.169236i	$-0.0541301\pi$
$930$	0.686292	−	0.485281i	0.0225044	−	0.0159130i
$931$	37.3189	−	27.9047i	1.22308	−	0.914539i
$932$		−	1.34315i		−	0.0439962i
$933$	3.01874	−	1.11453i	0.0988291	−	0.0364882i
$934$	22.1879	−	5.94522i	0.726009	−	0.194534i
$935$	−3.12132	+	5.40629i	−0.102078	+	0.176804i
$936$	30.1212	−	12.0712i	0.984542	−	0.394560i
$937$	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	−0.293955	−	0.955819i	$-0.594971\pi$
$941$	−2.16622	+	0.580438i	−0.0706169	+	0.0189217i	0.223338	+	0.974741i	$0.428305\pi$
$942$	0.290571	+	3.15357i	0.00946732	+	0.102749i
$943$	−9.64226	+	35.9854i	−0.313995	+	1.17185i
$944$	6.70711	−	6.70711i	0.218298	−	0.218298i
$945$	2.53045	−	7.64535i	0.0823154	−	0.248703i
$946$			34.9706i			1.13699i
$947$	−25.6113	−	6.86251i	−0.832254	−	0.223002i	−0.182557	−	0.983195i	$-0.558437\pi$
$947$	−25.6113	−	6.86251i	−0.832254	−	0.223002i	−0.649697	+	0.760194i	$0.725104\pi$
$948$	−1.56583	+	1.88366i	−0.0508557	+	0.0611785i
$949$	14.8219	−	43.8144i	0.481139	−	1.42228i
$950$	−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	$0.366499\pi$
$954$	21.4104	+	14.6991i	0.693188	+	0.475902i
$955$	2.57295	+	9.60239i	0.0832588	+	0.310726i
$956$	−1.63411	−	6.09857i	−0.0528508	−	0.197242i
$957$	9.16889	+	4.22412i	0.296388	+	0.136546i
$958$	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
$962$	−12.9282	+	6.39230i	−0.416822	+	0.206096i
$963$	−13.3119	−	15.5704i	−0.428972	−	0.501751i
$964$	21.4847	+	5.75682i	0.691977	+	0.185415i
$965$			1.65685i			0.0533360i
$966$	0.609808	+	30.1737i	0.0196202	+	0.970823i
$967$	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
$969$	−20.9929	+	1.93429i	−0.674388	+	0.0621383i
$970$	−5.60139	+	1.50089i	−0.179850	+	0.0481906i
$971$	17.2335	−	9.94975i	0.553048	−	0.319303i	−0.197302	−	0.980343i	$-0.563218\pi$
$971$	17.2335	−	9.94975i	0.553048	−	0.319303i	0.750351	+	0.661040i	$0.229885\pi$
$972$	10.2929	+	11.7071i	0.330145	+	0.375506i
$973$	−3.38407	−	6.97127i	−0.108488	−	0.223489i
$974$	9.34315			0.299374
$975$	−28.2873	−	6.75238i	−0.905918	−	0.216249i
$976$	0.500000	−	0.866025i	0.0160046	−	0.0277208i
$977$	43.9472	−	11.7756i	1.40600	−	0.376735i	0.525501	−	0.850793i	$-0.323878\pi$
$977$	43.9472	−	11.7756i	1.40600	−	0.376735i	0.880494	+	0.474058i	$0.157211\pi$
$978$	1.30273	+	3.52847i	0.0416566	+	0.112828i
$979$			72.7696i			2.32572i
$980$	−0.484577	−	4.07177i	−0.0154793	−	0.130068i
$981$	20.0711	−	9.58579i	0.640820	−	0.306051i
$982$	2.38455	−	8.89927i	0.0760941	−	0.283987i
$983$	13.7174	+	51.1941i	0.437517	+	1.63284i	0.734969	+	0.678100i	$0.237197\pi$
$983$	13.7174	+	51.1941i	0.437517	+	1.63284i	−0.297452	+	0.954737i	$0.596137\pi$
$984$	−22.6040	−	18.7899i	−0.720588	−	0.599001i
$985$	3.58719	−	2.07107i	0.114298	−	0.0659897i
$986$	1.29289	−	1.29289i	0.0411741	−	0.0411741i
$987$	1.45206	−	2.63669i	0.0462197	−	0.0839267i
$988$	−23.5355	+	4.70711i	−0.748765	+	0.149753i
$989$	34.2208	−	19.7574i	1.08816	−	0.628247i
$990$	10.2115	+	0.798499i	0.324542	+	0.0253780i
$991$	−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
$994$	−1.43895	−	0.974485i	−0.0456408	−	0.0309088i
$995$	−6.24264	+	6.24264i	−0.197905	+	0.197905i
$996$	3.14767	−	6.83234i	0.0997378	−	0.216491i
$997$	−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
$999$	−14.8990	−	14.4921i	−0.471383	−	0.458509i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.33195 - 1.10721i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.151613 + 0.565826i) q^{5} +(-1.41421 + 1.00000i) q^{6} +(-1.15539 - 2.38014i) q^{7} +(2.12132 - 2.12132i) q^{8} +(0.548188 + 2.94949i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.33195 - 1.10721i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.151613 + 0.565826i) q^{5} +(-1.41421 + 1.00000i) q^{6} +(-1.15539 - 2.38014i) q^{7} +(2.12132 - 2.12132i) q^{8} +(0.548188 + 2.94949i) q^{9} +(0.507306 + 0.292893i) q^{10} +(-1.50851 - 5.62983i) q^{11} +(-0.599900 - 1.62484i) 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} +(2.99087 + 0.233875i) q^{18} +(-6.43003 - 1.72292i) q^{19} +(-0.414214 + 0.414214i) q^{20} +(-1.09638 + 4.44949i) q^{21} -5.82843 q^{22} +(3.29289 + 5.70346i) q^{23} +(-5.17423 + 0.476756i) 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} +(-0.351414 - 0.951812i) q^{30} +(0.214413 + 0.800199i) q^{31} +(4.82963 - 1.29410i) q^{32} +(-4.22412 + 9.16889i) 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} +(-5.98552 + 1.78144i) q^{39} +(0.878680 + 1.52192i) q^{40} +(4.00000 + 4.00000i) q^{41} +(4.01411 + 2.21063i) q^{42} -6.00000i q^{43} +(1.50851 - 5.62983i) q^{44} +(-1.75201 - 0.137001i) 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} +(2.97091 - 1.09687i) q^{51} +(3.23205 - 1.59808i) q^{52} +(7.49706 + 4.32843i) q^{53} +(-3.72474 - 3.62302i) q^{54} +3.41421 q^{55} +(-7.50000 - 2.59808i) q^{56} +(6.65685 + 9.41421i) q^{57} +(-0.965926 - 0.258819i) q^{58} +(2.45497 + 9.16208i) q^{59} +(1.01033 - 0.0930924i) q^{60} +(0.500000 + 0.866025i) q^{61} +0.828427 q^{62} +(6.38682 - 4.71259i) q^{63} -7.00000i q^{64} +(1.39425 + 1.58649i) q^{65} +(7.76318 + 6.45327i) 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} +(7.41970 + 5.09393i) q^{72} +(12.3913 - 3.32024i) q^{73} +(-3.46410 - 2.00000i) q^{74} +(-2.79365 - 7.56666i) 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} +(0.565826 - 0.151613i) q^{80} +(-8.39898 + 3.23375i) q^{81} +(4.89898 - 2.82843i) q^{82} +(3.07107 + 3.07107i) q^{83} +(-3.17423 + 3.30518i) q^{84} +(-0.757359 - 0.757359i) q^{85} +(-5.79555 - 1.55291i) q^{86} +(-1.10721 + 1.33195i) 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} +(0.600398 - 1.30323i) q^{93} +(-0.328427 + 0.568852i) q^{94} +(1.94975 - 3.37706i) q^{95} +(-7.86566 - 3.62372i) q^{96} +(-7.00000 + 7.00000i) q^{97} +(4.19187 + 5.60609i) 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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