LMFDB - Embedded newform 714.2.m.d.463.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [714,2,Mod(421,714)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(714, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("714.421"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 714 = 2 \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	714.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,-12,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.70131870432$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 38x^{10} + 509x^{8} + 2748x^{6} + 4804x^{4} + 2496x^{2} + 256 $ x^12 + 38x^10 + 509x^8 + 2748x^6 + 4804x^4 + 2496*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			463.1
Root			$3.38067i$ of defining polynomial
Character	$\chi$	$=$	714.463
Dual form			714.2.m.d.421.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.39049 + 2.39049i) q^{5} +(0.707107 + 0.707107i) q^{6} +(0.707107 + 0.707107i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(2.39049 + 2.39049i) q^{10} +(1.39049 + 1.39049i) q^{11} +(0.707107 - 0.707107i) q^{12} -1.28498 q^{13} +(0.707107 - 0.707107i) q^{14} -3.38067i q^{15} +1.00000 q^{16} +(-3.78907 - 1.62572i) q^{17} -1.00000 q^{18} -8.42622i q^{19} +(2.39049 - 2.39049i) q^{20} -1.00000 q^{21} +(1.39049 - 1.39049i) q^{22} +(-2.44833 - 2.44833i) q^{23} +(-0.707107 - 0.707107i) q^{24} -6.42892i q^{25} +1.28498i q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.707107 - 0.707107i) q^{28} +(-2.63153 + 2.63153i) q^{29} -3.38067 q^{30} +(-4.74744 + 4.74744i) q^{31} -1.00000i q^{32} -1.96645 q^{33} +(-1.62572 + 3.78907i) q^{34} -3.38067 q^{35} +1.00000i q^{36} +(-1.22714 + 1.22714i) q^{37} -8.42622 q^{38} +(0.908617 - 0.908617i) q^{39} +(-2.39049 - 2.39049i) q^{40} +(1.33266 + 1.33266i) q^{41} +1.00000i q^{42} -12.0495i q^{43} +(-1.39049 - 1.39049i) q^{44} +(2.39049 + 2.39049i) q^{45} +(-2.44833 + 2.44833i) q^{46} -5.10769 q^{47} +(-0.707107 + 0.707107i) q^{48} +1.00000i q^{49} -6.42892 q^{50} +(3.82883 - 1.52972i) q^{51} +1.28498 q^{52} -13.8832i q^{53} +(0.707107 - 0.707107i) q^{54} -6.64793 q^{55} +(-0.707107 + 0.707107i) q^{56} +(5.95823 + 5.95823i) q^{57} +(2.63153 + 2.63153i) q^{58} +12.5311i q^{59} +3.38067i q^{60} +(-7.70568 - 7.70568i) q^{61} +(4.74744 + 4.74744i) q^{62} +(0.707107 - 0.707107i) q^{63} -1.00000 q^{64} +(3.07173 - 3.07173i) q^{65} +1.96645i q^{66} +15.9824 q^{67} +(3.78907 + 1.62572i) q^{68} +3.46246 q^{69} +3.38067i q^{70} +(-5.22932 + 5.22932i) q^{71} +1.00000 q^{72} +(-2.40439 + 2.40439i) q^{73} +(1.22714 + 1.22714i) q^{74} +(4.54593 + 4.54593i) q^{75} +8.42622i q^{76} +1.96645i q^{77} +(-0.908617 - 0.908617i) q^{78} +(-9.16596 - 9.16596i) q^{79} +(-2.39049 + 2.39049i) q^{80} -1.00000 q^{81} +(1.33266 - 1.33266i) q^{82} +7.05798i q^{83} +1.00000 q^{84} +(12.9440 - 5.17148i) q^{85} -12.0495 q^{86} -3.72154i q^{87} +(-1.39049 + 1.39049i) q^{88} +0.0821301 q^{89} +(2.39049 - 2.39049i) q^{90} +(-0.908617 - 0.908617i) q^{91} +(2.44833 + 2.44833i) q^{92} -6.71390i q^{93} +5.10769i q^{94} +(20.1428 + 20.1428i) q^{95} +(0.707107 + 0.707107i) q^{96} +(2.30951 - 2.30951i) q^{97} +1.00000 q^{98} +(1.39049 - 1.39049i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} - 4 q^{5} + 4 q^{10} - 8 q^{11} + 12 q^{13} + 12 q^{16} - 12 q^{17} - 12 q^{18} + 4 q^{20} - 12 q^{21} - 8 q^{22} + 8 q^{23} + 12 q^{29} - 4 q^{30} + 12 q^{31} - 4 q^{33} + 4 q^{34} - 4 q^{35}+ \cdots - 8 q^{99}+O(q^{100}) $ 12 * q - 12 * q^4 - 4 * q^5 + 4 * q^10 - 8 * q^11 + 12 * q^13 + 12 * q^16 - 12 * q^17 - 12 * q^18 + 4 * q^20 - 12 * q^21 - 8 * q^22 + 8 * q^23 + 12 * q^29 - 4 * q^30 + 12 * q^31 - 4 * q^33 + 4 * q^34 - 4 * q^35 - 24 * q^38 + 4 * q^39 - 4 * q^40 + 4 * q^41 + 8 * q^44 + 4 * q^45 + 8 * q^46 + 8 * q^47 - 16 * q^50 - 8 * q^51 - 12 * q^52 - 68 * q^55 + 8 * q^57 - 12 * q^58 + 40 * q^61 - 12 * q^62 - 12 * q^64 + 20 * q^65 - 12 * q^67 + 12 * q^68 + 24 * q^71 + 12 * q^72 - 16 * q^75 - 4 * q^78 - 8 * q^79 - 4 * q^80 - 12 * q^81 + 4 * q^82 + 12 * q^84 - 12 * q^85 + 20 * q^86 + 8 * q^88 - 44 * q^89 + 4 * q^90 - 4 * q^91 - 8 * q^92 + 92 * q^95 - 32 * q^97 + 12 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/714\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$547$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$	−2.39049	+	2.39049i	−1.06906	+	1.06906i	−0.0716299	+	0.997431i	$0.522820\pi$
$5$	−2.39049	+	2.39049i	−1.06906	+	1.06906i	−0.997431	+	0.0716299i	$0.977180\pi$
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$			1.00000i			0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	2.39049	+	2.39049i	0.755940	+	0.755940i
$11$	1.39049	+	1.39049i	0.419250	+	0.419250i	0.884945	−	0.465695i	$-0.154196\pi$
$11$	1.39049	+	1.39049i	0.419250	+	0.419250i	−0.465695	+	0.884945i	$0.654196\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−1.28498			−0.356389			−0.178194	−	0.983995i	$-0.557026\pi$
$13$	−1.28498			−0.356389			−0.178194	+	0.983995i	$0.557026\pi$
$14$	0.707107	−	0.707107i	0.188982	−	0.188982i
$15$		−	3.38067i		−	0.872885i
$16$	1.00000			0.250000
$17$	−3.78907	−	1.62572i	−0.918984	−	0.394294i
$17$	−3.78907	−	1.62572i	−0.918984	−	0.394294i
$18$	−1.00000			−0.235702
$19$		−	8.42622i		−	1.93311i	−0.256466	−	0.966553i	$-0.582558\pi$
$19$		−	8.42622i		−	1.93311i	0.256466	−	0.966553i	$-0.417442\pi$
$20$	2.39049	−	2.39049i	0.534531	−	0.534531i
$21$	−1.00000			−0.218218
$22$	1.39049	−	1.39049i	0.296454	−	0.296454i
$23$	−2.44833	−	2.44833i	−0.510512	−	0.510512i	0.404171	−	0.914683i	$-0.367560\pi$
$23$	−2.44833	−	2.44833i	−0.510512	−	0.510512i	−0.914683	+	0.404171i	$0.867560\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$		−	6.42892i		−	1.28578i
$26$			1.28498i			0.252005i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−0.707107	−	0.707107i	−0.133631	−	0.133631i
$29$	−2.63153	+	2.63153i	−0.488663	+	0.488663i	−0.907884	−	0.419221i	$-0.862303\pi$
$29$	−2.63153	+	2.63153i	−0.488663	+	0.488663i	0.419221	+	0.907884i	$0.362303\pi$
$30$	−3.38067			−0.617223
$31$	−4.74744	+	4.74744i	−0.852666	+	0.852666i	−0.990461	−	0.137795i	$-0.955998\pi$
$31$	−4.74744	+	4.74744i	−0.852666	+	0.852666i	0.137795	+	0.990461i	$0.455998\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.96645			−0.342316
$34$	−1.62572	+	3.78907i	−0.278808	+	0.649820i
$35$	−3.38067			−0.571437
$36$			1.00000i			0.166667i
$37$	−1.22714	+	1.22714i	−0.201741	+	0.201741i	−0.800745	−	0.599005i	$-0.795563\pi$
$37$	−1.22714	+	1.22714i	−0.201741	+	0.201741i	0.599005	+	0.800745i	$0.295563\pi$
$38$	−8.42622			−1.36691
$39$	0.908617	−	0.908617i	0.145495	−	0.145495i
$40$	−2.39049	−	2.39049i	−0.377970	−	0.377970i
$41$	1.33266	+	1.33266i	0.208126	+	0.208126i	0.803470	−	0.595345i	$-0.202984\pi$
$41$	1.33266	+	1.33266i	0.208126	+	0.208126i	−0.595345	+	0.803470i	$0.702984\pi$
$42$			1.00000i			0.154303i
$43$		−	12.0495i		−	1.83754i	−0.394799	−	0.918768i	$-0.629186\pi$
$43$		−	12.0495i		−	1.83754i	0.394799	−	0.918768i	$-0.370814\pi$
$44$	−1.39049	−	1.39049i	−0.209625	−	0.209625i
$45$	2.39049	+	2.39049i	0.356354	+	0.356354i
$46$	−2.44833	+	2.44833i	−0.360987	+	0.360987i
$47$	−5.10769			−0.745033			−0.372517	−	0.928025i	$-0.621505\pi$
$47$	−5.10769			−0.745033			−0.372517	+	0.928025i	$0.621505\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$			1.00000i			0.142857i
$50$	−6.42892			−0.909186
$51$	3.82883	−	1.52972i	0.536144	−	0.214204i
$52$	1.28498			0.178194
$53$		−	13.8832i		−	1.90700i	−0.301387	−	0.953502i	$-0.597449\pi$
$53$		−	13.8832i		−	1.90700i	0.301387	−	0.953502i	$-0.402551\pi$
$54$	0.707107	−	0.707107i	0.0962250	−	0.0962250i
$55$	−6.64793			−0.896407
$56$	−0.707107	+	0.707107i	−0.0944911	+	0.0944911i
$57$	5.95823	+	5.95823i	0.789187	+	0.789187i
$58$	2.63153	+	2.63153i	0.345537	+	0.345537i
$59$			12.5311i			1.63141i	0.578465	+	0.815707i	$0.303652\pi$
$59$			12.5311i			1.63141i	−0.578465	+	0.815707i	$0.696348\pi$
$60$			3.38067i			0.436442i
$61$	−7.70568	−	7.70568i	−0.986611	−	0.986611i	0.0133008	−	0.999912i	$-0.495766\pi$
$61$	−7.70568	−	7.70568i	−0.986611	−	0.986611i	−0.999912	+	0.0133008i	$0.995766\pi$
$62$	4.74744	+	4.74744i	0.602926	+	0.602926i
$63$	0.707107	−	0.707107i	0.0890871	−	0.0890871i
$64$	−1.00000			−0.125000
$65$	3.07173	−	3.07173i	0.381002	−	0.381002i
$66$			1.96645i			0.242054i
$67$	15.9824			1.95257			0.976283	−	0.216500i	$-0.0694642\pi$
$67$	15.9824			1.95257			0.976283	+	0.216500i	$0.0694642\pi$
$68$	3.78907	+	1.62572i	0.459492	+	0.197147i
$69$	3.46246			0.416832
$70$			3.38067i			0.404067i
$71$	−5.22932	+	5.22932i	−0.620606	+	0.620606i	−0.945686	−	0.325080i	$-0.894609\pi$
$71$	−5.22932	+	5.22932i	−0.620606	+	0.620606i	0.325080	+	0.945686i	$0.394609\pi$
$72$	1.00000			0.117851
$73$	−2.40439	+	2.40439i	−0.281412	+	0.281412i	−0.833672	−	0.552260i	$-0.813766\pi$
$73$	−2.40439	+	2.40439i	−0.281412	+	0.281412i	0.552260	+	0.833672i	$0.313766\pi$
$74$	1.22714	+	1.22714i	0.142652	+	0.142652i
$75$	4.54593	+	4.54593i	0.524919	+	0.524919i
$76$			8.42622i			0.966553i
$77$			1.96645i			0.224098i
$78$	−0.908617	−	0.908617i	−0.102881	−	0.102881i
$79$	−9.16596	−	9.16596i	−1.03125	−	1.03125i	−0.999496	−	0.0317556i	$-0.989890\pi$
$79$	−9.16596	−	9.16596i	−1.03125	−	1.03125i	−0.0317556	−	0.999496i	$-0.510110\pi$
$80$	−2.39049	+	2.39049i	−0.267265	+	0.267265i
$81$	−1.00000			−0.111111
$82$	1.33266	−	1.33266i	0.147167	−	0.147167i
$83$			7.05798i			0.774714i	0.921930	+	0.387357i	$0.126612\pi$
$83$			7.05798i			0.774714i	−0.921930	+	0.387357i	$0.873388\pi$
$84$	1.00000			0.109109
$85$	12.9440	−	5.17148i	1.40398	−	0.560926i
$86$	−12.0495			−1.29933
$87$		−	3.72154i		−	0.398991i
$88$	−1.39049	+	1.39049i	−0.148227	+	0.148227i
$89$	0.0821301			0.00870577			0.00435288	−	0.999991i	$-0.498614\pi$
$89$	0.0821301			0.00870577			0.00435288	+	0.999991i	$0.498614\pi$
$90$	2.39049	−	2.39049i	0.251980	−	0.251980i
$91$	−0.908617	−	0.908617i	−0.0952489	−	0.0952489i
$92$	2.44833	+	2.44833i	0.255256	+	0.255256i
$93$		−	6.71390i		−	0.696199i
$94$			5.10769i			0.526818i
$95$	20.1428	+	20.1428i	2.06661	+	2.06661i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	2.30951	−	2.30951i	0.234495	−	0.234495i	−0.580071	−	0.814566i	$-0.696975\pi$
$97$	2.30951	−	2.30951i	0.234495	−	0.234495i	0.814566	+	0.580071i	$0.196975\pi$
$98$	1.00000			0.101015
$99$	1.39049	−	1.39049i	0.139750	−	0.139750i
$100$			6.42892i			0.642892i
$101$	4.17200			0.415130			0.207565	−	0.978221i	$-0.433446\pi$
$101$	4.17200			0.415130			0.207565	+	0.978221i	$0.433446\pi$
$102$	−1.52972	−	3.82883i	−0.151465	−	0.379111i
$103$	−14.8586			−1.46406			−0.732030	−	0.681273i	$-0.761427\pi$
$103$	−14.8586			−1.46406			−0.732030	+	0.681273i	$0.761427\pi$
$104$		−	1.28498i		−	0.126003i
$105$	2.39049	−	2.39049i	0.233288	−	0.233288i
$106$	−13.8832			−1.34846
$107$	0.434436	−	0.434436i	0.0419985	−	0.0419985i	−0.685796	−	0.727794i	$-0.740546\pi$
$107$	0.434436	−	0.434436i	0.0419985	−	0.0419985i	0.727794	+	0.685796i	$0.240546\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	4.96966	+	4.96966i	0.476008	+	0.476008i	0.903852	−	0.427845i	$-0.140727\pi$
$109$	4.96966	+	4.96966i	0.476008	+	0.476008i	−0.427845	+	0.903852i	$0.640727\pi$
$110$			6.64793i			0.633855i
$111$		−	1.73544i		−	0.164721i
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	−2.49227	−	2.49227i	−0.234453	−	0.234453i	0.580095	−	0.814549i	$-0.303015\pi$
$113$	−2.49227	−	2.49227i	−0.234453	−	0.234453i	−0.814549	+	0.580095i	$0.803015\pi$
$114$	5.95823	−	5.95823i	0.558040	−	0.558040i
$115$	11.7054			1.09154
$116$	2.63153	−	2.63153i	0.244331	−	0.244331i
$117$			1.28498i			0.118796i
$118$	12.5311			1.15358
$119$	−1.52972	−	3.82883i	−0.140229	−	0.350988i
$120$	3.38067			0.308611
$121$		−	7.13306i		−	0.648460i
$122$	−7.70568	+	7.70568i	−0.697639	+	0.697639i
$123$	−1.88466			−0.169934
$124$	4.74744	−	4.74744i	0.426333	−	0.426333i
$125$	3.41582	+	3.41582i	0.305520	+	0.305520i
$126$	−0.707107	−	0.707107i	−0.0629941	−	0.0629941i
$127$			10.1157i			0.897621i	0.893627	+	0.448811i	$0.148152\pi$
$127$			10.1157i			0.897621i	−0.893627	+	0.448811i	$0.851848\pi$
$128$			1.00000i			0.0883883i
$129$	8.52030	+	8.52030i	0.750171	+	0.750171i
$130$	−3.07173	−	3.07173i	−0.269409	−	0.269409i
$131$	−6.65114	+	6.65114i	−0.581113	+	0.581113i	−0.935209	−	0.354096i	$-0.884789\pi$
$131$	−6.65114	+	6.65114i	−0.581113	+	0.581113i	0.354096	+	0.935209i	$0.384789\pi$
$132$	1.96645			0.171158
$133$	5.95823	−	5.95823i	0.516644	−	0.516644i
$134$		−	15.9824i		−	1.38067i
$135$	−3.38067			−0.290962
$136$	1.62572	−	3.78907i	0.139404	−	0.324910i
$137$	−12.5049			−1.06837			−0.534184	−	0.845368i	$-0.679381\pi$
$137$	−12.5049			−1.06837			−0.534184	+	0.845368i	$0.679381\pi$
$138$		−	3.46246i		−	0.294744i
$139$	6.51482	−	6.51482i	0.552580	−	0.552580i	−0.374605	−	0.927185i	$-0.622222\pi$
$139$	6.51482	−	6.51482i	0.552580	−	0.552580i	0.927185	+	0.374605i	$0.122222\pi$
$140$	3.38067			0.285719
$141$	3.61168	−	3.61168i	0.304159	−	0.304159i
$142$	5.22932	+	5.22932i	0.438835	+	0.438835i
$143$	−1.78675	−	1.78675i	−0.149416	−	0.149416i
$144$		−	1.00000i		−	0.0833333i
$145$		−	12.5813i		−	1.04482i
$146$	2.40439	+	2.40439i	0.198989	+	0.198989i
$147$	−0.707107	−	0.707107i	−0.0583212	−	0.0583212i
$148$	1.22714	−	1.22714i	0.100870	−	0.100870i
$149$	−4.64339			−0.380401			−0.190201	−	0.981745i	$-0.560914\pi$
$149$	−4.64339			−0.380401			−0.190201	+	0.981745i	$0.560914\pi$
$150$	4.54593	−	4.54593i	0.371174	−	0.371174i
$151$			13.5227i			1.10046i	0.835013	+	0.550230i	$0.185460\pi$
$151$			13.5227i			1.10046i	−0.835013	+	0.550230i	$0.814540\pi$
$152$	8.42622			0.683456
$153$	−1.62572	+	3.78907i	−0.131431	+	0.306328i
$154$	1.96645			0.158461
$155$		−	22.6975i		−	1.82310i
$156$	−0.908617	+	0.908617i	−0.0727476	+	0.0727476i
$157$	3.96117			0.316136			0.158068	−	0.987428i	$-0.449473\pi$
$157$	3.96117			0.316136			0.158068	+	0.987428i	$0.449473\pi$
$158$	−9.16596	+	9.16596i	−0.729205	+	0.729205i
$159$	9.81690	+	9.81690i	0.778531	+	0.778531i
$160$	2.39049	+	2.39049i	0.188985	+	0.188985i
$161$		−	3.46246i		−	0.272880i
$162$			1.00000i			0.0785674i
$163$	6.08099	+	6.08099i	0.476300	+	0.476300i	0.903946	−	0.427647i	$-0.140657\pi$
$163$	6.08099	+	6.08099i	0.476300	+	0.476300i	−0.427647	+	0.903946i	$0.640657\pi$
$164$	−1.33266	−	1.33266i	−0.104063	−	0.104063i
$165$	4.70080	−	4.70080i	0.365957	−	0.365957i
$166$	7.05798			0.547806
$167$	−12.2454	+	12.2454i	−0.947577	+	0.947577i	−0.998693	−	0.0511160i	$-0.983722\pi$
$167$	−12.2454	+	12.2454i	−0.947577	+	0.947577i	0.0511160	+	0.998693i	$0.483722\pi$
$168$		−	1.00000i		−	0.0771517i
$169$	−11.3488			−0.872987
$170$	−5.17148	−	12.9440i	−0.396634	−	0.992760i
$171$	−8.42622			−0.644369
$172$			12.0495i			0.918768i
$173$	8.45952	−	8.45952i	0.643166	−	0.643166i	−0.308167	−	0.951332i	$-0.599715\pi$
$173$	8.45952	−	8.45952i	0.643166	−	0.643166i	0.951332	+	0.308167i	$0.0997154\pi$
$174$	−3.72154			−0.282130
$175$	4.54593	−	4.54593i	0.343640	−	0.343640i
$176$	1.39049	+	1.39049i	0.104812	+	0.104812i
$177$	−8.86085	−	8.86085i	−0.666022	−	0.666022i
$178$		−	0.0821301i		−	0.00615591i
$179$			17.0913i			1.27746i	0.769431	+	0.638730i	$0.220540\pi$
$179$			17.0913i			1.27746i	−0.769431	+	0.638730i	$0.779460\pi$
$180$	−2.39049	−	2.39049i	−0.178177	−	0.178177i
$181$	8.35361	+	8.35361i	0.620919	+	0.620919i	0.945766	−	0.324848i	$-0.105313\pi$
$181$	8.35361	+	8.35361i	0.620919	+	0.620919i	−0.324848	+	0.945766i	$0.605313\pi$
$182$	−0.908617	+	0.908617i	−0.0673512	+	0.0673512i
$183$	10.8975			0.805564
$184$	2.44833	−	2.44833i	0.180493	−	0.180493i
$185$		−	5.86694i		−	0.431346i
$186$	−6.71390			−0.492287
$187$	−3.00813	−	7.52922i	−0.219976	−	0.550591i
$188$	5.10769			0.372517
$189$			1.00000i			0.0727393i
$190$	20.1428	−	20.1428i	1.46131	−	1.46131i
$191$	1.31277			0.0949886			0.0474943	−	0.998872i	$-0.484876\pi$
$191$	1.31277			0.0949886			0.0474943	+	0.998872i	$0.484876\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	3.84808	+	3.84808i	0.276991	+	0.276991i	0.831907	−	0.554916i	$-0.187250\pi$
$193$	3.84808	+	3.84808i	0.276991	+	0.276991i	−0.554916	+	0.831907i	$0.687250\pi$
$194$	−2.30951	−	2.30951i	−0.165813	−	0.165813i
$195$			4.34409i			0.311086i
$196$		−	1.00000i		−	0.0714286i
$197$	−9.16814	−	9.16814i	−0.653203	−	0.653203i	0.300560	−	0.953763i	$-0.402826\pi$
$197$	−9.16814	−	9.16814i	−0.653203	−	0.653203i	−0.953763	+	0.300560i	$0.902826\pi$
$198$	−1.39049	−	1.39049i	−0.0988181	−	0.0988181i
$199$	−1.71232	+	1.71232i	−0.121383	+	0.121383i	−0.765189	−	0.643806i	$-0.777354\pi$
$199$	−1.71232	+	1.71232i	−0.121383	+	0.121383i	0.643806	+	0.765189i	$0.277354\pi$
$200$	6.42892			0.454593
$201$	−11.3013	+	11.3013i	−0.797131	+	0.797131i
$202$		−	4.17200i		−	0.293541i
$203$	−3.72154			−0.261201
$204$	−3.82883	+	1.52972i	−0.268072	+	0.107102i
$205$	−6.37141			−0.444999
$206$			14.8586i			1.03525i
$207$	−2.44833	+	2.44833i	−0.170171	+	0.170171i
$208$	−1.28498			−0.0890972
$209$	11.7166	−	11.7166i	0.810454	−	0.810454i
$210$	−2.39049	−	2.39049i	−0.164960	−	0.164960i
$211$	12.7938	+	12.7938i	0.880759	+	0.880759i	0.993612	−	0.112853i	$-0.0359990\pi$
$211$	12.7938	+	12.7938i	0.880759	+	0.880759i	−0.112853	+	0.993612i	$0.535999\pi$
$212$			13.8832i			0.953502i
$213$		−	7.39537i		−	0.506723i
$214$	−0.434436	−	0.434436i	−0.0296974	−	0.0296974i
$215$	28.8043	+	28.8043i	1.96444	+	1.96444i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	−6.71390			−0.455769
$218$	4.96966	−	4.96966i	0.336588	−	0.336588i
$219$		−	3.40032i		−	0.229772i
$220$	6.64793			0.448203
$221$	4.86887	+	2.08901i	0.327516	+	0.140522i
$222$	−1.73544			−0.116475
$223$			9.43942i			0.632110i	0.948741	+	0.316055i	$0.102358\pi$
$223$			9.43942i			0.632110i	−0.948741	+	0.316055i	$0.897642\pi$
$224$	0.707107	−	0.707107i	0.0472456	−	0.0472456i
$225$	−6.42892			−0.428595
$226$	−2.49227	+	2.49227i	−0.165784	+	0.165784i
$227$	−19.0383	−	19.0383i	−1.26362	−	1.26362i	−0.949326	−	0.314292i	$-0.898233\pi$
$227$	−19.0383	−	19.0383i	−1.26362	−	1.26362i	−0.314292	−	0.949326i	$-0.601767\pi$
$228$	−5.95823	−	5.95823i	−0.394594	−	0.394594i
$229$			20.6547i			1.36490i	0.730931	+	0.682452i	$0.239086\pi$
$229$			20.6547i			1.36490i	−0.730931	+	0.682452i	$0.760914\pi$
$230$		−	11.7054i		−	0.771834i
$231$	−1.39049	−	1.39049i	−0.0914878	−	0.0914878i
$232$	−2.63153	−	2.63153i	−0.172768	−	0.172768i
$233$	11.4172	−	11.4172i	0.747966	−	0.747966i	−0.226131	−	0.974097i	$-0.572608\pi$
$233$	11.4172	−	11.4172i	0.747966	−	0.747966i	0.974097	+	0.226131i	$0.0726078\pi$
$234$	1.28498			0.0840017
$235$	12.2099	−	12.2099i	0.796486	−	0.796486i
$236$		−	12.5311i		−	0.815707i
$237$	12.9626			0.842013
$238$	−3.82883	+	1.52972i	−0.248186	+	0.0991571i
$239$	−14.5531			−0.941359			−0.470679	−	0.882304i	$-0.655991\pi$
$239$	−14.5531			−0.941359			−0.470679	+	0.882304i	$0.655991\pi$
$240$		−	3.38067i		−	0.218221i
$241$	5.63110	−	5.63110i	0.362731	−	0.362731i	−0.502087	−	0.864817i	$-0.667434\pi$
$241$	5.63110	−	5.63110i	0.362731	−	0.362731i	0.864817	+	0.502087i	$0.167434\pi$
$242$	−7.13306			−0.458530
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	7.70568	+	7.70568i	0.493305	+	0.493305i
$245$	−2.39049	−	2.39049i	−0.152723	−	0.152723i
$246$			1.88466i			0.120162i
$247$			10.8275i			0.688938i
$248$	−4.74744	−	4.74744i	−0.301463	−	0.301463i
$249$	−4.99075	−	4.99075i	−0.316276	−	0.316276i
$250$	3.41582	−	3.41582i	0.216035	−	0.216035i
$251$	−4.23248			−0.267152			−0.133576	−	0.991039i	$-0.542646\pi$
$251$	−4.23248			−0.267152			−0.133576	+	0.991039i	$0.542646\pi$
$252$	−0.707107	+	0.707107i	−0.0445435	+	0.0445435i
$253$		−	6.80878i		−	0.428064i
$254$	10.1157			0.634714
$255$	−5.49601	+	12.8096i	−0.344173	+	0.802167i
$256$	1.00000			0.0625000
$257$		−	2.93720i		−	0.183218i	−0.995795	−	0.0916088i	$-0.970799\pi$
$257$		−	2.93720i		−	0.183218i	0.995795	−	0.0916088i	$-0.0292009\pi$
$258$	8.52030	−	8.52030i	0.530451	−	0.530451i
$259$	−1.73544			−0.107835
$260$	−3.07173	+	3.07173i	−0.190501	+	0.190501i
$261$	2.63153	+	2.63153i	0.162888	+	0.162888i
$262$	6.65114	+	6.65114i	0.410909	+	0.410909i
$263$			5.34017i			0.329289i	0.986353	+	0.164644i	$0.0526477\pi$
$263$			5.34017i			0.329289i	−0.986353	+	0.164644i	$0.947352\pi$
$264$		−	1.96645i		−	0.121027i
$265$	33.1877	+	33.1877i	2.03870	+	2.03870i
$266$	−5.95823	−	5.95823i	−0.365323	−	0.365323i
$267$	−0.0580747	+	0.0580747i	−0.00355411	+	0.00355411i
$268$	−15.9824			−0.976283
$269$	18.3598	−	18.3598i	1.11942	−	1.11942i	0.127592	−	0.991827i	$-0.459275\pi$
$269$	18.3598	−	18.3598i	1.11942	−	1.11942i	0.991827	−	0.127592i	$-0.0407247\pi$
$270$			3.38067i			0.205741i
$271$	−22.7631			−1.38276			−0.691381	−	0.722490i	$-0.742998\pi$
$271$	−22.7631			−1.38276			−0.691381	+	0.722490i	$0.742998\pi$
$272$	−3.78907	−	1.62572i	−0.229746	−	0.0985735i
$273$	1.28498			0.0777704
$274$			12.5049i			0.755451i
$275$	8.93937	−	8.93937i	0.539064	−	0.539064i
$276$	−3.46246			−0.208416
$277$	0.737840	−	0.737840i	0.0443325	−	0.0443325i	−0.684593	−	0.728926i	$-0.740020\pi$
$277$	0.737840	−	0.737840i	0.0443325	−	0.0443325i	0.728926	+	0.684593i	$0.240020\pi$
$278$	−6.51482	−	6.51482i	−0.390733	−	0.390733i
$279$	4.74744	+	4.74744i	0.284222	+	0.284222i
$280$		−	3.38067i		−	0.202034i
$281$			5.01320i			0.299063i	0.988757	+	0.149531i	$0.0477765\pi$
$281$			5.01320i			0.299063i	−0.988757	+	0.149531i	$0.952224\pi$
$282$	−3.61168	−	3.61168i	−0.215073	−	0.215073i
$283$	−23.5506	−	23.5506i	−1.39994	−	1.39994i	−0.800185	−	0.599753i	$-0.795265\pi$
$283$	−23.5506	−	23.5506i	−1.39994	−	1.39994i	−0.599753	−	0.800185i	$-0.704735\pi$
$284$	5.22932	−	5.22932i	0.310303	−	0.310303i
$285$	−28.4862			−1.68738
$286$	−1.78675	+	1.78675i	−0.105653	+	0.105653i
$287$			1.88466i			0.111248i
$288$	−1.00000			−0.0589256
$289$	11.7141	+	12.3199i	0.689064	+	0.724700i
$290$	−12.5813			−0.738800
$291$			3.26614i			0.191464i
$292$	2.40439	−	2.40439i	0.140706	−	0.140706i
$293$	−1.91153			−0.111673			−0.0558363	−	0.998440i	$-0.517782\pi$
$293$	−1.91153			−0.111673			−0.0558363	+	0.998440i	$0.517782\pi$
$294$	−0.707107	+	0.707107i	−0.0412393	+	0.0412393i
$295$	−29.9556	−	29.9556i	−1.74408	−	1.74408i
$296$	−1.22714	−	1.22714i	−0.0713261	−	0.0713261i
$297$			1.96645i			0.114105i
$298$			4.64339i			0.268984i
$299$	3.14605	+	3.14605i	0.181941	+	0.181941i
$300$	−4.54593	−	4.54593i	−0.262459	−	0.262459i
$301$	8.52030	−	8.52030i	0.491102	−	0.491102i
$302$	13.5227			0.778142
$303$	−2.95005	+	2.95005i	−0.169476	+	0.169476i
$304$		−	8.42622i		−	0.483277i
$305$	36.8407			2.10949
$306$	3.78907	+	1.62572i	0.216607	+	0.0929360i
$307$	−4.52564			−0.258292			−0.129146	−	0.991626i	$-0.541224\pi$
$307$	−4.52564			−0.258292			−0.129146	+	0.991626i	$0.541224\pi$
$308$		−	1.96645i		−	0.112049i
$309$	10.5066	−	10.5066i	0.597700	−	0.597700i
$310$	−22.6975			−1.28913
$311$	−19.0542	+	19.0542i	−1.08046	+	1.08046i	−0.0839966	+	0.996466i	$0.526769\pi$
$311$	−19.0542	+	19.0542i	−1.08046	+	1.08046i	−0.996466	+	0.0839966i	$0.973231\pi$
$312$	0.908617	+	0.908617i	0.0514403	+	0.0514403i
$313$	−12.6439	−	12.6439i	−0.714676	−	0.714676i	0.252834	−	0.967510i	$-0.418637\pi$
$313$	−12.6439	−	12.6439i	−0.714676	−	0.714676i	−0.967510	+	0.252834i	$0.918637\pi$
$314$		−	3.96117i		−	0.223542i
$315$			3.38067i			0.190479i
$316$	9.16596	+	9.16596i	0.515626	+	0.515626i
$317$	0.765710	+	0.765710i	0.0430066	+	0.0430066i	0.728283	−	0.685276i	$-0.240319\pi$
$317$	0.765710	+	0.765710i	0.0430066	+	0.0430066i	−0.685276	+	0.728283i	$0.740319\pi$
$318$	9.81690	−	9.81690i	0.550505	−	0.550505i
$319$	−7.31825			−0.409743
$320$	2.39049	−	2.39049i	0.133633	−	0.133633i
$321$			0.614386i			0.0342917i
$322$	−3.46246			−0.192956
$323$	−13.6986	+	31.9275i	−0.762213	+	1.77649i
$324$	1.00000			0.0555556
$325$			8.26102i			0.458239i
$326$	6.08099	−	6.08099i	0.336795	−	0.336795i
$327$	−7.02817			−0.388659
$328$	−1.33266	+	1.33266i	−0.0735836	+	0.0735836i
$329$	−3.61168	−	3.61168i	−0.199119	−	0.199119i
$330$	−4.70080	−	4.70080i	−0.258770	−	0.258770i
$331$			25.7000i			1.41260i	0.707914	+	0.706299i	$0.249636\pi$
$331$			25.7000i			1.41260i	−0.707914	+	0.706299i	$0.750364\pi$
$332$		−	7.05798i		−	0.387357i
$333$	1.22714	+	1.22714i	0.0672469	+	0.0672469i
$334$	12.2454	+	12.2454i	0.670038	+	0.670038i
$335$	−38.2059	+	38.2059i	−2.08741	+	2.08741i
$336$	−1.00000			−0.0545545
$337$	−24.0901	+	24.0901i	−1.31227	+	1.31227i	−0.392536	+	0.919737i	$0.628402\pi$
$337$	−24.0901	+	24.0901i	−1.31227	+	1.31227i	−0.919737	+	0.392536i	$0.871598\pi$
$338$			11.3488i			0.617295i
$339$	3.52461			0.191430
$340$	−12.9440	+	5.17148i	−0.701988	+	0.280463i
$341$	−13.2026			−0.714959
$342$			8.42622i			0.455638i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	12.0495			0.649667
$345$	−8.27700	+	8.27700i	−0.445618	+	0.445618i
$346$	−8.45952	−	8.45952i	−0.454787	−	0.454787i
$347$	−5.39049	−	5.39049i	−0.289377	−	0.289377i	0.547457	−	0.836834i	$-0.315596\pi$
$347$	−5.39049	−	5.39049i	−0.289377	−	0.289377i	−0.836834	+	0.547457i	$0.815596\pi$
$348$			3.72154i			0.199496i
$349$		−	25.9178i		−	1.38735i	−0.720289	−	0.693674i	$-0.755991\pi$
$349$		−	25.9178i		−	1.38735i	0.720289	−	0.693674i	$-0.244009\pi$
$350$	−4.54593	−	4.54593i	−0.242990	−	0.242990i
$351$	−0.908617	−	0.908617i	−0.0484984	−	0.0484984i
$352$	1.39049	−	1.39049i	0.0741135	−	0.0741135i
$353$	3.55828			0.189388			0.0946942	−	0.995506i	$-0.469813\pi$
$353$	3.55828			0.189388			0.0946942	+	0.995506i	$0.469813\pi$
$354$	−8.86085	+	8.86085i	−0.470949	+	0.470949i
$355$		−	25.0013i		−	1.32693i
$356$	−0.0821301			−0.00435288
$357$	3.78907	+	1.62572i	0.200539	+	0.0860420i
$358$	17.0913			0.903301
$359$		−	34.2619i		−	1.80827i	−0.427244	−	0.904137i	$-0.640515\pi$
$359$		−	34.2619i		−	1.80827i	0.427244	−	0.904137i	$-0.359485\pi$
$360$	−2.39049	+	2.39049i	−0.125990	+	0.125990i
$361$	−52.0011			−2.73690
$362$	8.35361	−	8.35361i	0.439056	−	0.439056i
$363$	5.04383	+	5.04383i	0.264733	+	0.264733i
$364$	0.908617	+	0.908617i	0.0476245	+	0.0476245i
$365$		−	11.4953i		−	0.601694i
$366$		−	10.8975i		−	0.569620i
$367$	26.7144	+	26.7144i	1.39448	+	1.39448i	0.814957	+	0.579521i	$0.196760\pi$
$367$	26.7144	+	26.7144i	1.39448	+	1.39448i	0.579521	+	0.814957i	$0.303240\pi$
$368$	−2.44833	−	2.44833i	−0.127628	−	0.127628i
$369$	1.33266	−	1.33266i	0.0693753	−	0.0693753i
$370$	−5.86694			−0.305008
$371$	9.81690	−	9.81690i	0.509668	−	0.509668i
$372$			6.71390i			0.348099i
$373$	−22.3260			−1.15600			−0.577999	−	0.816037i	$-0.696166\pi$
$373$	−22.3260			−1.15600			−0.577999	+	0.816037i	$0.696166\pi$
$374$	−7.52922	+	3.00813i	−0.389327	+	0.155547i
$375$	−4.83070			−0.249456
$376$		−	5.10769i		−	0.263409i
$377$	3.38146	−	3.38146i	0.174154	−	0.174154i
$378$	1.00000			0.0514344
$379$	−18.0618	+	18.0618i	−0.927774	+	0.927774i	−0.997562	−	0.0697880i	$-0.977768\pi$
$379$	−18.0618	+	18.0618i	−0.927774	+	0.927774i	0.0697880	+	0.997562i	$0.477768\pi$
$380$	−20.1428	−	20.1428i	−1.03330	−	1.03330i
$381$	−7.15286	−	7.15286i	−0.366452	−	0.366452i
$382$		−	1.31277i		−	0.0671671i
$383$		−	3.61122i		−	0.184525i	−0.995735	−	0.0922623i	$-0.970590\pi$
$383$		−	3.61122i		−	0.184525i	0.995735	−	0.0922623i	$-0.0294098\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	−4.70080	−	4.70080i	−0.239575	−	0.239575i
$386$	3.84808	−	3.84808i	0.195862	−	0.195862i
$387$	−12.0495			−0.612512
$388$	−2.30951	+	2.30951i	−0.117247	+	0.117247i
$389$			2.86642i			0.145333i	0.997356	+	0.0726667i	$0.0231509\pi$
$389$			2.86642i			0.145333i	−0.997356	+	0.0726667i	$0.976849\pi$
$390$	4.34409			0.219971
$391$	5.29660	+	13.2572i	0.267861	+	0.670445i
$392$	−1.00000			−0.0505076
$393$		−	9.40613i		−	0.474477i
$394$	−9.16814	+	9.16814i	−0.461884	+	0.461884i
$395$	43.8223			2.20494
$396$	−1.39049	+	1.39049i	−0.0698749	+	0.0698749i
$397$	7.72306	+	7.72306i	0.387609	+	0.387609i	0.873834	−	0.486225i	$-0.161626\pi$
$397$	7.72306	+	7.72306i	0.387609	+	0.387609i	−0.486225	+	0.873834i	$0.661626\pi$
$398$	1.71232	+	1.71232i	0.0858308	+	0.0858308i
$399$			8.42622i			0.421838i
$400$		−	6.42892i		−	0.321446i
$401$	10.6881	+	10.6881i	0.533740	+	0.533740i	0.921683	−	0.387943i	$-0.126814\pi$
$401$	10.6881	+	10.6881i	0.533740	+	0.533740i	−0.387943	+	0.921683i	$0.626814\pi$
$402$	11.3013	+	11.3013i	0.563657	+	0.563657i
$403$	6.10036	−	6.10036i	0.303881	−	0.303881i
$404$	−4.17200			−0.207565
$405$	2.39049	−	2.39049i	0.118785	−	0.118785i
$406$			3.72154i			0.184697i
$407$	−3.41266			−0.169159
$408$	1.52972	+	3.82883i	0.0757325	+	0.189555i
$409$	6.06041			0.299668			0.149834	−	0.988711i	$-0.452126\pi$
$409$	6.06041			0.299668			0.149834	+	0.988711i	$0.452126\pi$
$410$			6.37141i			0.314661i
$411$	8.84232	−	8.84232i	0.436160	−	0.436160i
$412$	14.8586			0.732030
$413$	−8.86085	+	8.86085i	−0.436014	+	0.436014i
$414$	2.44833	+	2.44833i	0.120329	+	0.120329i
$415$	−16.8721	−	16.8721i	−0.828217	−	0.828217i
$416$			1.28498i			0.0630013i
$417$			9.21335i			0.451180i
$418$	−11.7166	−	11.7166i	−0.573078	−	0.573078i
$419$	16.4842	+	16.4842i	0.805304	+	0.805304i	0.983919	−	0.178615i	$-0.0571617\pi$
$419$	16.4842	+	16.4842i	0.805304	+	0.805304i	−0.178615	+	0.983919i	$0.557162\pi$
$420$	−2.39049	+	2.39049i	−0.116644	+	0.116644i
$421$	−4.62562			−0.225439			−0.112719	−	0.993627i	$-0.535956\pi$
$421$	−4.62562			−0.225439			−0.112719	+	0.993627i	$0.535956\pi$
$422$	12.7938	−	12.7938i	0.622790	−	0.622790i
$423$			5.10769i			0.248344i
$424$	13.8832			0.674228
$425$	−10.4516	+	24.3596i	−0.506977	+	1.18161i
$426$	−7.39537			−0.358307
$427$		−	10.8975i		−	0.527366i
$428$	−0.434436	+	0.434436i	−0.0209993	+	0.0209993i
$429$	2.52685			0.121998
$430$	28.8043	−	28.8043i	1.38907	−	1.38907i
$431$	20.3856	+	20.3856i	0.981940	+	0.981940i	0.999840	−	0.0179002i	$-0.00569812\pi$
$431$	20.3856	+	20.3856i	0.981940	+	0.981940i	−0.0179002	+	0.999840i	$0.505698\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$		−	1.25625i		−	0.0603714i	−0.999544	−	0.0301857i	$-0.990390\pi$
$433$		−	1.25625i		−	0.0603714i	0.999544	−	0.0301857i	$-0.00960987\pi$
$434$			6.71390i			0.322277i
$435$	8.89633	+	8.89633i	0.426546	+	0.426546i
$436$	−4.96966	−	4.96966i	−0.238004	−	0.238004i
$437$	−20.6302	+	20.6302i	−0.986875	+	0.986875i
$438$	−3.40032			−0.162474
$439$	3.35755	−	3.35755i	0.160247	−	0.160247i	−0.622429	−	0.782676i	$-0.713854\pi$
$439$	3.35755	−	3.35755i	0.160247	−	0.160247i	0.782676	+	0.622429i	$0.213854\pi$
$440$		−	6.64793i		−	0.316928i
$441$	1.00000			0.0476190
$442$	2.08901	−	4.86887i	0.0993641	−	0.231589i
$443$	17.6059			0.836484			0.418242	−	0.908336i	$-0.362646\pi$
$443$	17.6059			0.836484			0.418242	+	0.908336i	$0.362646\pi$
$444$			1.73544i			0.0823603i
$445$	−0.196331	+	0.196331i	−0.00930700	+	0.00930700i
$446$	9.43942			0.446969
$447$	3.28337	−	3.28337i	0.155298	−	0.155298i
$448$	−0.707107	−	0.707107i	−0.0334077	−	0.0334077i
$449$	−16.8815	−	16.8815i	−0.796689	−	0.796689i	0.185883	−	0.982572i	$-0.440485\pi$
$449$	−16.8815	−	16.8815i	−0.796689	−	0.796689i	−0.982572	+	0.185883i	$0.940485\pi$
$450$			6.42892i			0.303062i
$451$			3.70610i			0.174513i
$452$	2.49227	+	2.49227i	0.117227	+	0.117227i
$453$	−9.56197	−	9.56197i	−0.449261	−	0.449261i
$454$	−19.0383	+	19.0383i	−0.893513	+	0.893513i
$455$	4.34409			0.203654
$456$	−5.95823	+	5.95823i	−0.279020	+	0.279020i
$457$		−	12.1171i		−	0.566814i	−0.959000	−	0.283407i	$-0.908535\pi$
$457$		−	12.1171i		−	0.566814i	0.959000	−	0.283407i	$-0.0914647\pi$
$458$	20.6547			0.965133
$459$	−1.52972	−	3.82883i	−0.0714013	−	0.178715i
$460$	−11.7054			−0.545769
$461$			11.3954i			0.530735i	0.964147	+	0.265368i	$0.0854933\pi$
$461$			11.3954i			0.530735i	−0.964147	+	0.265368i	$0.914507\pi$
$462$	−1.39049	+	1.39049i	−0.0646916	+	0.0646916i
$463$	0.0322217			0.00149747			0.000748735	−	1.00000i	$-0.499762\pi$
$463$	0.0322217			0.00149747			0.000748735		1.00000i	$0.499762\pi$
$464$	−2.63153	+	2.63153i	−0.122166	+	0.122166i
$465$	16.0495	+	16.0495i	0.744279	+	0.744279i
$466$	−11.4172	−	11.4172i	−0.528892	−	0.528892i
$467$		−	3.55094i		−	0.164318i	−0.996619	−	0.0821589i	$-0.973819\pi$
$467$		−	3.55094i		−	0.164318i	0.996619	−	0.0821589i	$-0.0261815\pi$
$468$		−	1.28498i		−	0.0593982i
$469$	11.3013	+	11.3013i	0.521845	+	0.521845i
$470$	−12.2099	−	12.2099i	−0.563201	−	0.563201i
$471$	−2.80097	+	2.80097i	−0.129062	+	0.129062i
$472$	−12.5311			−0.576792
$473$	16.7548	−	16.7548i	0.770386	−	0.770386i
$474$		−	12.9626i		−	0.595393i
$475$	−54.1714			−2.48556
$476$	1.52972	+	3.82883i	0.0701147	+	0.175494i
$477$	−13.8832			−0.635668
$478$			14.5531i			0.665641i
$479$	11.7195	−	11.7195i	0.535477	−	0.535477i	−0.386720	−	0.922197i	$-0.626392\pi$
$479$	11.7195	−	11.7195i	0.535477	−	0.535477i	0.922197	+	0.386720i	$0.126392\pi$
$480$	−3.38067			−0.154306
$481$	1.57685	−	1.57685i	0.0718981	−	0.0718981i
$482$	−5.63110	−	5.63110i	−0.256489	−	0.256489i
$483$	2.44833	+	2.44833i	0.111403	+	0.111403i
$484$			7.13306i			0.324230i
$485$			11.0417i			0.501379i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	−16.2454	−	16.2454i	−0.736149	−	0.736149i	0.235681	−	0.971830i	$-0.424268\pi$
$487$	−16.2454	−	16.2454i	−0.736149	−	0.736149i	−0.971830	+	0.235681i	$0.924268\pi$
$488$	7.70568	−	7.70568i	0.348820	−	0.348820i
$489$	−8.59981			−0.388897
$490$	−2.39049	+	2.39049i	−0.107991	+	0.107991i
$491$		−	5.47202i		−	0.246949i	−0.992348	−	0.123474i	$-0.960596\pi$
$491$		−	5.47202i		−	0.246949i	0.992348	−	0.123474i	$-0.0394037\pi$
$492$	1.88466			0.0849670
$493$	14.2492	−	5.69293i	0.641750	−	0.256396i
$494$	10.8275			0.487153
$495$			6.64793i			0.298802i
$496$	−4.74744	+	4.74744i	−0.213166	+	0.213166i
$497$	−7.39537			−0.331728
$498$	−4.99075	+	4.99075i	−0.223641	+	0.223641i
$499$	−5.70798	−	5.70798i	−0.255524	−	0.255524i	0.567707	−	0.823231i	$-0.307831\pi$
$499$	−5.70798	−	5.70798i	−0.255524	−	0.255524i	−0.823231	+	0.567707i	$0.807831\pi$
$500$	−3.41582	−	3.41582i	−0.152760	−	0.152760i
$501$		−	17.3176i		−	0.773693i
$502$			4.23248i			0.188905i
$503$	−13.7769	−	13.7769i	−0.614281	−	0.614281i	0.329778	−	0.944059i	$-0.393026\pi$
$503$	−13.7769	−	13.7769i	−0.614281	−	0.614281i	−0.944059	+	0.329778i	$0.893026\pi$
$504$	0.707107	+	0.707107i	0.0314970	+	0.0314970i
$505$	−9.97315	+	9.97315i	−0.443799	+	0.443799i
$506$	−6.80878			−0.302687
$507$	8.02483	−	8.02483i	0.356395	−	0.356395i
$508$		−	10.1157i		−	0.448811i
$509$	−1.06167			−0.0470578			−0.0235289	−	0.999723i	$-0.507490\pi$
$509$	−1.06167			−0.0470578			−0.0235289	+	0.999723i	$0.507490\pi$
$510$	12.8096	+	5.49601i	0.567218	+	0.243367i
$511$	−3.40032			−0.150421
$512$		−	1.00000i		−	0.0441942i
$513$	5.95823	−	5.95823i	0.263062	−	0.263062i
$514$	−2.93720			−0.129554
$515$	35.5193	−	35.5193i	1.56517	−	1.56517i
$516$	−8.52030	−	8.52030i	−0.375085	−	0.375085i
$517$	−7.10221	−	7.10221i	−0.312355	−	0.312355i
$518$			1.73544i			0.0762508i
$519$			11.9636i			0.525143i
$520$	3.07173	+	3.07173i	0.134704	+	0.134704i
$521$	−26.6714	−	26.6714i	−1.16850	−	1.16850i	−0.982562	−	0.185935i	$-0.940469\pi$
$521$	−26.6714	−	26.6714i	−1.16850	−	1.16850i	−0.185935	−	0.982562i	$-0.559531\pi$
$522$	2.63153	−	2.63153i	0.115179	−	0.115179i
$523$	23.5170			1.02833			0.514163	−	0.857692i	$-0.328103\pi$
$523$	23.5170			1.02833			0.514163	+	0.857692i	$0.328103\pi$
$524$	6.65114	−	6.65114i	0.290556	−	0.290556i
$525$			6.42892i			0.280581i
$526$	5.34017			0.232842
$527$	25.7064	−	10.2704i	1.11979	−	0.447385i
$528$	−1.96645			−0.0855790
$529$		−	11.0113i		−	0.478754i
$530$	33.1877	−	33.1877i	1.44158	−	1.44158i
$531$	12.5311			0.543805
$532$	−5.95823	+	5.95823i	−0.258322	+	0.258322i
$533$	−1.71243	−	1.71243i	−0.0741737	−	0.0741737i
$534$	0.0580747	+	0.0580747i	0.00251314	+	0.00251314i
$535$			2.07703i			0.0897980i
$536$			15.9824i			0.690336i
$537$	−12.0853	−	12.0853i	−0.521521	−	0.521521i
$538$	−18.3598	−	18.3598i	−0.791548	−	0.791548i
$539$	−1.39049	+	1.39049i	−0.0598928	+	0.0598928i
$540$	3.38067			0.145481
$541$	20.5110	−	20.5110i	0.881837	−	0.881837i	−0.111885	−	0.993721i	$-0.535689\pi$
$541$	20.5110	−	20.5110i	0.881837	−	0.881837i	0.993721	+	0.111885i	$0.0356887\pi$
$542$			22.7631i			0.977761i
$543$	−11.8138			−0.506978
$544$	−1.62572	+	3.78907i	−0.0697020	+	0.162455i
$545$	−23.7599			−1.01776
$546$		−	1.28498i		−	0.0549920i
$547$	10.1454	−	10.1454i	0.433788	−	0.433788i	−0.456127	−	0.889915i	$-0.650764\pi$
$547$	10.1454	−	10.1454i	0.433788	−	0.433788i	0.889915	+	0.456127i	$0.150764\pi$
$548$	12.5049			0.534184
$549$	−7.70568	+	7.70568i	−0.328870	+	0.328870i
$550$	−8.93937	−	8.93937i	−0.381176	−	0.381176i
$551$	22.1738	+	22.1738i	0.944637	+	0.944637i
$552$			3.46246i			0.147372i
$553$		−	12.9626i		−	0.551227i
$554$	−0.737840	−	0.737840i	−0.0313478	−	0.0313478i
$555$	4.14856	+	4.14856i	0.176096	+	0.176096i
$556$	−6.51482	+	6.51482i	−0.276290	+	0.276290i
$557$	−9.60166			−0.406836			−0.203418	−	0.979092i	$-0.565205\pi$
$557$	−9.60166			−0.406836			−0.203418	+	0.979092i	$0.565205\pi$
$558$	4.74744	−	4.74744i	0.200975	−	0.200975i
$559$			15.4834i			0.654877i
$560$	−3.38067			−0.142859
$561$	7.45103	+	3.19690i	0.314583	+	0.134973i
$562$	5.01320			0.211469
$563$		−	41.3596i		−	1.74310i	−0.490308	−	0.871549i	$-0.663116\pi$
$563$		−	41.3596i		−	1.74310i	0.490308	−	0.871549i	$-0.336884\pi$
$564$	−3.61168	+	3.61168i	−0.152079	+	0.152079i
$565$	11.9155			0.501290
$566$	−23.5506	+	23.5506i	−0.989906	+	0.989906i
$567$	−0.707107	−	0.707107i	−0.0296957	−	0.0296957i
$568$	−5.22932	−	5.22932i	−0.219417	−	0.219417i
$569$		−	4.70690i		−	0.197324i	−0.995121	−	0.0986618i	$-0.968544\pi$
$569$		−	4.70690i		−	0.197324i	0.995121	−	0.0986618i	$-0.0314562\pi$
$570$			28.4862i			1.19316i
$571$	−9.94075	−	9.94075i	−0.416007	−	0.416007i	0.467818	−	0.883825i	$-0.345040\pi$
$571$	−9.94075	−	9.94075i	−0.416007	−	0.416007i	−0.883825	+	0.467818i	$0.845040\pi$
$572$	1.78675	+	1.78675i	0.0747079	+	0.0747079i
$573$	−0.928267	+	0.928267i	−0.0387789	+	0.0387789i
$574$	1.88466			0.0786642
$575$	−15.7401	+	15.7401i	−0.656408	+	0.656408i
$576$			1.00000i			0.0416667i
$577$	11.1165			0.462785			0.231393	−	0.972860i	$-0.425672\pi$
$577$	11.1165			0.462785			0.231393	+	0.972860i	$0.425672\pi$
$578$	12.3199	−	11.7141i	0.512441	−	0.487242i
$579$	−5.44200			−0.226162
$580$			12.5813i			0.522410i
$581$	−4.99075	+	4.99075i	−0.207051	+	0.207051i
$582$	3.26614			0.135386
$583$	19.3045	−	19.3045i	0.799511	−	0.799511i
$584$	−2.40439	−	2.40439i	−0.0994943	−	0.0994943i
$585$	−3.07173	−	3.07173i	−0.127001	−	0.127001i
$586$			1.91153i			0.0789644i
$587$		−	9.11270i		−	0.376121i	−0.982157	−	0.188061i	$-0.939780\pi$
$587$		−	9.11270i		−	0.376121i	0.982157	−	0.188061i	$-0.0602202\pi$
$588$	0.707107	+	0.707107i	0.0291606	+	0.0291606i
$589$	40.0030	+	40.0030i	1.64829	+	1.64829i
$590$	−29.9556	+	29.9556i	−1.23325	+	1.23325i
$591$	12.9657			0.533338
$592$	−1.22714	+	1.22714i	−0.0504352	+	0.0504352i
$593$		−	38.4287i		−	1.57808i	−0.614343	−	0.789039i	$-0.710579\pi$
$593$		−	38.4287i		−	1.57808i	0.614343	−	0.789039i	$-0.289421\pi$
$594$	1.96645			0.0806846
$595$	12.8096	+	5.49601i	0.525142	+	0.225314i
$596$	4.64339			0.190201
$597$		−	2.42159i		−	0.0991089i
$598$	3.14605	−	3.14605i	0.128652	−	0.128652i
$599$	30.7270			1.25547			0.627736	−	0.778426i	$-0.283982\pi$
$599$	30.7270			1.25547			0.627736	+	0.778426i	$0.283982\pi$
$600$	−4.54593	+	4.54593i	−0.185587	+	0.185587i
$601$	27.2880	+	27.2880i	1.11310	+	1.11310i	0.992729	+	0.120370i	$0.0384080\pi$
$601$	27.2880	+	27.2880i	1.11310	+	1.11310i	0.120370	+	0.992729i	$0.461592\pi$
$602$	−8.52030	−	8.52030i	−0.347262	−	0.347262i
$603$		−	15.9824i		−	0.650855i
$604$		−	13.5227i		−	0.550230i
$605$	17.0515	+	17.0515i	0.693243	+	0.693243i
$606$	2.95005	+	2.95005i	0.119838	+	0.119838i
$607$	14.2548	−	14.2548i	0.578584	−	0.578584i	−0.355929	−	0.934513i	$-0.615835\pi$
$607$	14.2548	−	14.2548i	0.578584	−	0.578584i	0.934513	+	0.355929i	$0.115835\pi$
$608$	−8.42622			−0.341728
$609$	2.63153	−	2.63153i	0.106635	−	0.106635i
$610$		−	36.8407i		−	1.49164i
$611$	6.56327			0.265522
$612$	1.62572	−	3.78907i	0.0657157	−	0.153164i
$613$	2.29978			0.0928872			0.0464436	−	0.998921i	$-0.485211\pi$
$613$	2.29978			0.0928872			0.0464436	+	0.998921i	$0.485211\pi$
$614$			4.52564i			0.182640i
$615$	4.50527	−	4.50527i	0.181670	−	0.181670i
$616$	−1.96645			−0.0792307
$617$	14.7028	−	14.7028i	0.591914	−	0.591914i	−0.346234	−	0.938148i	$-0.612540\pi$
$617$	14.7028	−	14.7028i	0.591914	−	0.591914i	0.938148	+	0.346234i	$0.112540\pi$
$618$	−10.5066	−	10.5066i	−0.422637	−	0.422637i
$619$	−24.4637	−	24.4637i	−0.983280	−	0.983280i	0.0165830	−	0.999862i	$-0.494721\pi$
$619$	−24.4637	−	24.4637i	−0.983280	−	0.983280i	−0.999862	+	0.0165830i	$0.994721\pi$
$620$			22.6975i			0.911552i
$621$		−	3.46246i		−	0.138944i
$622$	19.0542	+	19.0542i	0.764002	+	0.764002i
$623$	0.0580747	+	0.0580747i	0.00232671	+	0.00232671i
$624$	0.908617	−	0.908617i	0.0363738	−	0.0363738i
$625$	15.8136			0.632544
$626$	−12.6439	+	12.6439i	−0.505352	+	0.505352i
$627$			16.5698i			0.661733i
$628$	−3.96117			−0.158068
$629$	6.64470	−	2.65474i	0.264942	−	0.105851i
$630$	3.38067			0.134689
$631$			23.4333i			0.932867i	0.884556	+	0.466433i	$0.154461\pi$
$631$			23.4333i			0.932867i	−0.884556	+	0.466433i	$0.845539\pi$
$632$	9.16596	−	9.16596i	0.364602	−	0.364602i
$633$	−18.0931			−0.719136
$634$	0.765710	−	0.765710i	0.0304102	−	0.0304102i
$635$	−24.1815	−	24.1815i	−0.959612	−	0.959612i
$636$	−9.81690	−	9.81690i	−0.389266	−	0.389266i
$637$		−	1.28498i		−	0.0509127i
$638$			7.31825i			0.289732i
$639$	5.22932	+	5.22932i	0.206869	+	0.206869i
$640$	−2.39049	−	2.39049i	−0.0944925	−	0.0944925i
$641$	−24.8958	+	24.8958i	−0.983326	+	0.983326i	−0.999863	−	0.0165372i	$-0.994736\pi$
$641$	−24.8958	+	24.8958i	−0.983326	+	0.983326i	0.0165372	+	0.999863i	$0.494736\pi$
$642$	0.614386			0.0242479
$643$	−7.75029	+	7.75029i	−0.305642	+	0.305642i	−0.843216	−	0.537575i	$-0.819341\pi$
$643$	−7.75029	+	7.75029i	−0.305642	+	0.305642i	0.537575	+	0.843216i	$0.319341\pi$
$644$			3.46246i			0.136440i
$645$	−40.7354			−1.60396
$646$	31.9275	+	13.6986i	1.25617	+	0.538966i
$647$	45.2277			1.77809			0.889043	−	0.457824i	$-0.151371\pi$
$647$	45.2277			1.77809			0.889043	+	0.457824i	$0.151371\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−17.4245	+	17.4245i	−0.683970	+	0.683970i
$650$	8.26102			0.324024
$651$	4.74744	−	4.74744i	0.186067	−	0.186067i
$652$	−6.08099	−	6.08099i	−0.238150	−	0.238150i
$653$	−9.20261	−	9.20261i	−0.360126	−	0.360126i	0.503733	−	0.863859i	$-0.331959\pi$
$653$	−9.20261	−	9.20261i	−0.360126	−	0.360126i	−0.863859	+	0.503733i	$0.831959\pi$
$654$			7.02817i			0.274823i
$655$		−	31.7990i		−	1.24249i
$656$	1.33266	+	1.33266i	0.0520315	+	0.0520315i
$657$	2.40439	+	2.40439i	0.0938041	+	0.0938041i
$658$	−3.61168	+	3.61168i	−0.140798	+	0.140798i
$659$	−2.08563			−0.0812448			−0.0406224	−	0.999175i	$-0.512934\pi$
$659$	−2.08563			−0.0812448			−0.0406224	+	0.999175i	$0.512934\pi$
$660$	−4.70080	+	4.70080i	−0.182978	+	0.182978i
$661$		−	27.3092i		−	1.06220i	−0.847308	−	0.531102i	$-0.821778\pi$
$661$		−	27.3092i		−	1.06220i	0.847308	−	0.531102i	$-0.178222\pi$
$662$	25.7000			0.998857
$663$	−4.91997	+	1.96566i	−0.191076	+	0.0763399i
$664$	−7.05798			−0.273903
$665$			28.4862i			1.10465i
$666$	1.22714	−	1.22714i	0.0475507	−	0.0475507i
$667$	12.8857			0.498937
$668$	12.2454	−	12.2454i	0.473788	−	0.473788i
$669$	−6.67468	−	6.67468i	−0.258058	−	0.258058i
$670$	38.2059	+	38.2059i	1.47602	+	1.47602i
$671$		−	21.4294i		−	0.827272i
$672$			1.00000i			0.0385758i
$673$	10.8624	+	10.8624i	0.418715	+	0.418715i	0.884761	−	0.466046i	$-0.154322\pi$
$673$	10.8624	+	10.8624i	0.418715	+	0.418715i	−0.466046	+	0.884761i	$0.654322\pi$
$674$	24.0901	+	24.0901i	0.927917	+	0.927917i
$675$	4.54593	−	4.54593i	0.174973	−	0.174973i
$676$	11.3488			0.436493
$677$	−12.4119	+	12.4119i	−0.477027	+	0.477027i	−0.904180	−	0.427152i	$-0.859517\pi$
$677$	−12.4119	+	12.4119i	−0.477027	+	0.477027i	0.427152	+	0.904180i	$0.359517\pi$
$678$		−	3.52461i		−	0.135362i
$679$	3.26614			0.125343
$680$	5.17148	+	12.9440i	0.198317	+	0.496380i
$681$	26.9243			1.03174
$682$			13.2026i			0.505553i
$683$	5.73473	−	5.73473i	0.219433	−	0.219433i	−0.588826	−	0.808260i	$-0.700410\pi$
$683$	5.73473	−	5.73473i	0.219433	−	0.219433i	0.808260	+	0.588826i	$0.200410\pi$
$684$	8.42622			0.322184
$685$	29.8930	−	29.8930i	1.14215	−	1.14215i
$686$	0.707107	+	0.707107i	0.0269975	+	0.0269975i
$687$	−14.6051	−	14.6051i	−0.557220	−	0.557220i
$688$		−	12.0495i		−	0.459384i
$689$			17.8396i			0.679635i
$690$	8.27700	+	8.27700i	0.315100	+	0.315100i
$691$	11.1292	+	11.1292i	0.423375	+	0.423375i	0.886364	−	0.462989i	$-0.153223\pi$
$691$	11.1292	+	11.1292i	0.423375	+	0.423375i	−0.462989	+	0.886364i	$0.653223\pi$
$692$	−8.45952	+	8.45952i	−0.321583	+	0.321583i
$693$	1.96645			0.0746994
$694$	−5.39049	+	5.39049i	−0.204620	+	0.204620i
$695$			31.1473i			1.18148i
$696$	3.72154			0.141065
$697$	−2.88300	−	7.21605i	−0.109202	−	0.273327i
$698$	−25.9178			−0.981003
$699$			16.1464i			0.610711i
$700$	−4.54593	+	4.54593i	−0.171820	+	0.171820i
$701$	−7.25671			−0.274082			−0.137041	−	0.990565i	$-0.543759\pi$
$701$	−7.25671			−0.274082			−0.137041	+	0.990565i	$0.543759\pi$
$702$	−0.908617	+	0.908617i	−0.0342935	+	0.0342935i
$703$	10.3402	+	10.3402i	0.389986	+	0.389986i
$704$	−1.39049	−	1.39049i	−0.0524062	−	0.0524062i
$705$			17.2674i			0.650328i
$706$		−	3.55828i		−	0.133918i
$707$	2.95005	+	2.95005i	0.110948	+	0.110948i
$708$	8.86085	+	8.86085i	0.333011	+	0.333011i
$709$	−24.5130	+	24.5130i	−0.920604	+	0.920604i	−0.997072	−	0.0764677i	$-0.975636\pi$
$709$	−24.5130	+	24.5130i	−0.920604	+	0.920604i	0.0764677	+	0.997072i	$0.475636\pi$
$710$	−25.0013			−0.938282
$711$	−9.16596	+	9.16596i	−0.343750	+	0.343750i
$712$			0.0821301i			0.00307795i
$713$	23.2466			0.870593
$714$	1.62572	−	3.78907i	0.0608409	−	0.141802i
$715$	8.54245			0.319469
$716$		−	17.0913i		−	0.638730i
$717$	10.2906	−	10.2906i	0.384308	−	0.384308i
$718$	−34.2619			−1.27864
$719$	−6.47064	+	6.47064i	−0.241314	+	0.241314i	−0.817394	−	0.576079i	$-0.804582\pi$
$719$	−6.47064	+	6.47064i	−0.241314	+	0.241314i	0.576079	+	0.817394i	$0.304582\pi$
$720$	2.39049	+	2.39049i	0.0890884	+	0.0890884i
$721$	−10.5066	−	10.5066i	−0.391286	−	0.391286i
$722$			52.0011i			1.93528i
$723$			7.96357i			0.296169i
$724$	−8.35361	−	8.35361i	−0.310459	−	0.310459i
$725$	16.9179	+	16.9179i	0.628314	+	0.628314i
$726$	5.04383	−	5.04383i	0.187194	−	0.187194i
$727$	14.9858			0.555792			0.277896	−	0.960611i	$-0.410363\pi$
$727$	14.9858			0.555792			0.277896	+	0.960611i	$0.410363\pi$
$728$	0.908617	−	0.908617i	0.0336756	−	0.0336756i
$729$			1.00000i			0.0370370i
$730$	−11.4953			−0.425462
$731$	−19.5891	+	45.6565i	−0.724529	+	1.68867i
$732$	−10.8975			−0.402782
$733$			28.3491i			1.04710i	0.851995	+	0.523549i	$0.175392\pi$
$733$			28.3491i			1.04710i	−0.851995	+	0.523549i	$0.824608\pi$
$734$	26.7144	−	26.7144i	0.986045	−	0.986045i
$735$	3.38067			0.124698
$736$	−2.44833	+	2.44833i	−0.0902467	+	0.0902467i
$737$	22.2235	+	22.2235i	0.818612	+	0.818612i
$738$	−1.33266	−	1.33266i	−0.0490557	−	0.0490557i
$739$			39.5670i			1.45550i	0.685845	+	0.727748i	$0.259433\pi$
$739$			39.5670i			1.45550i	−0.685845	+	0.727748i	$0.740567\pi$
$740$			5.86694i			0.215673i
$741$	−7.65620	−	7.65620i	−0.281258	−	0.281258i
$742$	−9.81690	−	9.81690i	−0.360390	−	0.360390i
$743$	31.8319	−	31.8319i	1.16780	−	1.16780i	0.185074	−	0.982725i	$-0.440747\pi$
$743$	31.8319	−	31.8319i	1.16780	−	1.16780i	0.982725	−	0.185074i	$-0.0592526\pi$
$744$	6.71390			0.246143
$745$	11.1000	−	11.1000i	0.406672	−	0.406672i
$746$			22.3260i			0.817415i
$747$	7.05798			0.258238
$748$	3.00813	+	7.52922i	0.109988	+	0.275296i
$749$	0.614386			0.0224492
$750$			4.83070i			0.176392i
$751$	−21.3181	+	21.3181i	−0.777907	+	0.777907i	−0.979475	−	0.201567i	$-0.935396\pi$
$751$	−21.3181	+	21.3181i	−0.777907	+	0.777907i	0.201567	+	0.979475i	$0.435396\pi$
$752$	−5.10769			−0.186258
$753$	2.99281	−	2.99281i	0.109064	−	0.109064i
$754$	−3.38146	−	3.38146i	−0.123145	−	0.123145i
$755$	−32.3259	−	32.3259i	−1.17646	−	1.17646i
$756$		−	1.00000i		−	0.0363696i
$757$			24.7619i			0.899987i	0.893032	+	0.449993i	$0.148574\pi$
$757$			24.7619i			0.899987i	−0.893032	+	0.449993i	$0.851426\pi$
$758$	18.0618	+	18.0618i	0.656035	+	0.656035i
$759$	4.81453	+	4.81453i	0.174756	+	0.174756i
$760$	−20.1428	+	20.1428i	−0.730657	+	0.730657i
$761$	33.7322			1.22279			0.611396	−	0.791325i	$-0.290608\pi$
$761$	33.7322			1.22279			0.611396	+	0.791325i	$0.290608\pi$
$762$	−7.15286	+	7.15286i	−0.259121	+	0.259121i
$763$			7.02817i			0.254437i
$764$	−1.31277			−0.0474943
$765$	−5.17148	−	12.9440i	−0.186975	−	0.467992i
$766$	−3.61122			−0.130479
$767$		−	16.1022i		−	0.581418i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	49.9676			1.80188			0.900939	−	0.433945i	$-0.142879\pi$
$769$	49.9676			1.80188			0.900939	+	0.433945i	$0.142879\pi$
$770$	−4.70080	+	4.70080i	−0.169405	+	0.169405i
$771$	2.07692	+	2.07692i	0.0747983	+	0.0747983i
$772$	−3.84808	−	3.84808i	−0.138495	−	0.138495i
$773$		−	8.00672i		−	0.287982i	−0.989579	−	0.143991i	$-0.954006\pi$
$773$		−	8.00672i		−	0.287982i	0.989579	−	0.143991i	$-0.0459936\pi$
$774$			12.0495i			0.433111i
$775$	30.5209	+	30.5209i	1.09634	+	1.09634i
$776$	2.30951	+	2.30951i	0.0829065	+	0.0829065i
$777$	1.22714	−	1.22714i	0.0440234	−	0.0440234i
$778$	2.86642			0.102766
$779$	11.2292	−	11.2292i	0.402329	−	0.402329i
$780$		−	4.34409i		−	0.155543i
$781$	−14.5427			−0.520377
$782$	13.2572	−	5.29660i	0.474076	−	0.189406i
$783$	−3.72154			−0.132997
$784$			1.00000i			0.0357143i
$785$	−9.46916	+	9.46916i	−0.337969	+	0.337969i
$786$	−9.40613			−0.335506
$787$	−2.32638	+	2.32638i	−0.0829263	+	0.0829263i	−0.747353	−	0.664427i	$-0.768676\pi$
$787$	−2.32638	+	2.32638i	−0.0829263	+	0.0829263i	0.664427	+	0.747353i	$0.268676\pi$
$788$	9.16814	+	9.16814i	0.326601	+	0.326601i
$789$	−3.77607	−	3.77607i	−0.134432	−	0.134432i
$790$		−	43.8223i		−	1.55913i
$791$		−	3.52461i		−	0.125321i
$792$	1.39049	+	1.39049i	0.0494090	+	0.0494090i
$793$	9.90163	+	9.90163i	0.351617	+	0.351617i
$794$	7.72306	−	7.72306i	0.274081	−	0.274081i
$795$	−46.9345			−1.66459
$796$	1.71232	−	1.71232i	0.0606916	−	0.0606916i
$797$		−	44.9964i		−	1.59385i	−0.604076	−	0.796927i	$-0.706458\pi$
$797$		−	44.9964i		−	1.59385i	0.604076	−	0.796927i	$-0.293542\pi$
$798$	8.42622			0.298285
$799$	19.3534	+	8.30366i	0.684674	+	0.293762i
$800$	−6.42892			−0.227297
$801$		−	0.0821301i		−	0.00290192i
$802$	10.6881	−	10.6881i	0.377411	−	0.377411i
$803$	−6.68657			−0.235964
$804$	11.3013	−	11.3013i	0.398566	−	0.398566i
$805$	8.27700	+	8.27700i	0.291726	+	0.291726i
$806$	−6.10036	−	6.10036i	−0.214876	−	0.214876i
$807$			25.9647i			0.914001i
$808$			4.17200i			0.146771i
$809$	−12.5241	−	12.5241i	−0.440323	−	0.440323i	0.451797	−	0.892121i	$-0.350783\pi$
$809$	−12.5241	−	12.5241i	−0.440323	−	0.440323i	−0.892121	+	0.451797i	$0.850783\pi$
$810$	−2.39049	−	2.39049i	−0.0839934	−	0.0839934i
$811$	8.21780	−	8.21780i	0.288566	−	0.288566i	−0.547947	−	0.836513i	$-0.684590\pi$
$811$	8.21780	−	8.21780i	0.288566	−	0.288566i	0.836513	+	0.547947i	$0.184590\pi$
$812$	3.72154			0.130601
$813$	16.0960	−	16.0960i	0.564510	−	0.564510i
$814$			3.41266i			0.119614i
$815$	−29.0731			−1.01839
$816$	3.82883	−	1.52972i	0.134036	−	0.0535510i
$817$	−101.532			−3.55215
$818$		−	6.06041i		−	0.211897i
$819$	−0.908617	+	0.908617i	−0.0317496	+	0.0317496i
$820$	6.37141			0.222499
$821$	−7.25602	+	7.25602i	−0.253237	+	0.253237i	−0.822296	−	0.569059i	$-0.807307\pi$
$821$	−7.25602	+	7.25602i	−0.253237	+	0.253237i	0.569059	+	0.822296i	$0.307307\pi$
$822$	−8.84232	−	8.84232i	−0.308411	−	0.308411i
$823$	−15.3675	−	15.3675i	−0.535676	−	0.535676i	0.386580	−	0.922256i	$-0.373656\pi$
$823$	−15.3675	−	15.3675i	−0.535676	−	0.535676i	−0.922256	+	0.386580i	$0.873656\pi$
$824$		−	14.8586i		−	0.517623i
$825$			12.6422i			0.440144i
$826$	8.86085	+	8.86085i	0.308308	+	0.308308i
$827$	4.43809	+	4.43809i	0.154328	+	0.154328i	0.780048	−	0.625720i	$-0.215195\pi$
$827$	4.43809	+	4.43809i	0.154328	+	0.154328i	−0.625720	+	0.780048i	$0.715195\pi$
$828$	2.44833	−	2.44833i	0.0850854	−	0.0850854i
$829$	30.8153			1.07026			0.535130	−	0.844770i	$-0.320263\pi$
$829$	30.8153			1.07026			0.535130	+	0.844770i	$0.320263\pi$
$830$	−16.8721	+	16.8721i	−0.585638	+	0.585638i
$831$			1.04346i			0.0361973i
$832$	1.28498			0.0445486
$833$	1.62572	−	3.78907i	0.0563277	−	0.131283i
$834$	9.21335			0.319032
$835$		−	58.5450i		−	2.02603i
$836$	−11.7166	+	11.7166i	−0.405227	+	0.405227i
$837$	−6.71390			−0.232066
$838$	16.4842	−	16.4842i	0.569436	−	0.569436i
$839$	−21.2935	−	21.2935i	−0.735132	−	0.735132i	0.236500	−	0.971632i	$-0.424000\pi$
$839$	−21.2935	−	21.2935i	−0.735132	−	0.735132i	−0.971632	+	0.236500i	$0.924000\pi$
$840$	2.39049	+	2.39049i	0.0824799	+	0.0824799i
$841$			15.1501i			0.522418i
$842$			4.62562i			0.159409i
$843$	−3.54487	−	3.54487i	−0.122092	−	0.122092i
$844$	−12.7938	−	12.7938i	−0.440379	−	0.440379i
$845$	27.1293	−	27.1293i	0.933276	−	0.933276i
$846$	5.10769			0.175606
$847$	5.04383	−	5.04383i	0.173308	−	0.173308i
$848$		−	13.8832i		−	0.476751i
$849$	33.3056			1.14304
$850$	24.3596	+	10.4516i	0.835528	+	0.358487i
$851$	6.00889			0.205982
$852$			7.39537i			0.253361i
$853$	−26.0721	+	26.0721i	−0.892691	+	0.892691i	−0.994776	−	0.102085i	$-0.967449\pi$
$853$	−26.0721	+	26.0721i	−0.892691	+	0.892691i	0.102085	+	0.994776i	$0.467449\pi$
$854$	−10.8975			−0.372904
$855$	20.1428	−	20.1428i	0.688870	−	0.688870i
$856$	0.434436	+	0.434436i	0.0148487	+	0.0148487i
$857$	−26.1632	−	26.1632i	−0.893717	−	0.893717i	0.101154	−	0.994871i	$-0.467747\pi$
$857$	−26.1632	−	26.1632i	−0.893717	−	0.893717i	−0.994871	+	0.101154i	$0.967747\pi$
$858$		−	2.52685i		−	0.0862653i
$859$		−	8.62270i		−	0.294203i	−0.989121	−	0.147101i	$-0.953006\pi$
$859$		−	8.62270i		−	0.294203i	0.989121	−	0.147101i	$-0.0469943\pi$
$860$	−28.8043	−	28.8043i	−0.982219	−	0.982219i
$861$	−1.33266	−	1.33266i	−0.0454168	−	0.0454168i
$862$	20.3856	−	20.3856i	0.694336	−	0.694336i
$863$	28.7193			0.977615			0.488808	−	0.872392i	$-0.337432\pi$
$863$	28.7193			0.977615			0.488808	+	0.872392i	$0.337432\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$			40.4449i			1.37517i
$866$	−1.25625			−0.0426891
$867$	−16.9946	−	0.428375i	−0.577167	−	0.0145484i
$868$	6.71390			0.227884
$869$		−	25.4904i		−	0.864703i
$870$	8.89633	−	8.89633i	0.301614	−	0.301614i
$871$	−20.5371			−0.695873
$872$	−4.96966	+	4.96966i	−0.168294	+	0.168294i
$873$	−2.30951	−	2.30951i	−0.0781650	−	0.0781650i
$874$	20.6302	+	20.6302i	0.697826	+	0.697826i
$875$			4.83070i			0.163307i
$876$			3.40032i			0.114886i
$877$	−8.88193	−	8.88193i	−0.299921	−	0.299921i	0.541062	−	0.840983i	$-0.318023\pi$
$877$	−8.88193	−	8.88193i	−0.299921	−	0.299921i	−0.840983	+	0.541062i	$0.818023\pi$
$878$	−3.35755	−	3.35755i	−0.113312	−	0.113312i
$879$	1.35165	−	1.35165i	0.0455901	−	0.0455901i
$880$	−6.64793			−0.224102
$881$	19.6927	−	19.6927i	0.663465	−	0.663465i	−0.292730	−	0.956195i	$-0.594564\pi$
$881$	19.6927	−	19.6927i	0.663465	−	0.663465i	0.956195	+	0.292730i	$0.0945638\pi$
$882$		−	1.00000i		−	0.0336718i
$883$	−38.0434			−1.28026			−0.640131	−	0.768266i	$-0.721120\pi$
$883$	−38.0434			−1.28026			−0.640131	+	0.768266i	$0.721120\pi$
$884$	−4.86887	−	2.08901i	−0.163758	−	0.0702610i
$885$	42.3636			1.42404
$886$		−	17.6059i		−	0.591483i
$887$	3.69274	−	3.69274i	0.123990	−	0.123990i	−0.642389	−	0.766379i	$-0.722057\pi$
$887$	3.69274	−	3.69274i	0.123990	−	0.123990i	0.766379	+	0.642389i	$0.222057\pi$
$888$	1.73544			0.0582375
$889$	−7.15286	+	7.15286i	−0.239899	+	0.239899i
$890$	0.196331	+	0.196331i	0.00658104	+	0.00658104i
$891$	−1.39049	−	1.39049i	−0.0465833	−	0.0465833i
$892$		−	9.43942i		−	0.316055i
$893$			43.0385i			1.44023i
$894$	−3.28337	−	3.28337i	−0.109812	−	0.109812i
$895$	−40.8565	−	40.8565i	−1.36568	−	1.36568i
$896$	−0.707107	+	0.707107i	−0.0236228	+	0.0236228i
$897$	−4.44919			−0.148554
$898$	−16.8815	+	16.8815i	−0.563344	+	0.563344i
$899$		−	24.9861i		−	0.833332i
$900$	6.42892			0.214297
$901$	−22.5701	+	52.6044i	−0.751921	+	1.75251i
$902$	3.70610			0.123400
$903$			12.0495i			0.400983i
$904$	2.49227	−	2.49227i	0.0828918	−	0.0828918i
$905$	−39.9385			−1.32760
$906$	−9.56197	+	9.56197i	−0.317675	+	0.317675i
$907$	−8.32303	−	8.32303i	−0.276362	−	0.276362i	0.555293	−	0.831655i	$-0.312606\pi$
$907$	−8.32303	−	8.32303i	−0.276362	−	0.276362i	−0.831655	+	0.555293i	$0.812606\pi$
$908$	19.0383	+	19.0383i	0.631809	+	0.631809i
$909$		−	4.17200i		−	0.138377i
$910$		−	4.34409i		−	0.144005i
$911$	−6.13788	−	6.13788i	−0.203357	−	0.203357i	0.598080	−	0.801437i	$-0.295931\pi$
$911$	−6.13788	−	6.13788i	−0.203357	−	0.203357i	−0.801437	+	0.598080i	$0.795931\pi$
$912$	5.95823	+	5.95823i	0.197297	+	0.197297i
$913$	−9.81408	+	9.81408i	−0.324799	+	0.324799i
$914$	−12.1171			−0.400798
$915$	−26.0503	+	26.0503i	−0.861197	+	0.861197i
$916$		−	20.6547i		−	0.682452i
$917$	−9.40613			−0.310618
$918$	−3.82883	+	1.52972i	−0.126370	+	0.0504883i
$919$	13.8731			0.457631			0.228816	−	0.973470i	$-0.426515\pi$
$919$	13.8731			0.457631			0.228816	+	0.973470i	$0.426515\pi$
$920$			11.7054i			0.385917i
$921$	3.20011	−	3.20011i	0.105447	−	0.105447i
$922$	11.3954			0.375287
$923$	6.71956	−	6.71956i	0.221177	−	0.221177i
$924$	1.39049	+	1.39049i	0.0457439	+	0.0457439i
$925$	7.88919	+	7.88919i	0.259395	+	0.259395i
$926$		−	0.0322217i		−	0.00105887i
$927$			14.8586i			0.488020i
$928$	2.63153	+	2.63153i	0.0863842	+	0.0863842i
$929$	−16.6118	−	16.6118i	−0.545016	−	0.545016i	0.379979	−	0.924995i	$-0.375931\pi$
$929$	−16.6118	−	16.6118i	−0.545016	−	0.545016i	−0.924995	+	0.379979i	$0.875931\pi$
$930$	16.0495	−	16.0495i	0.526285	−	0.526285i
$931$	8.42622			0.276158
$932$	−11.4172	+	11.4172i	−0.373983	+	0.373983i
$933$		−	26.9467i		−	0.882194i
$934$	−3.55094			−0.116190
$935$	25.1895	+	10.8077i	0.823784	+	0.353448i
$936$	−1.28498			−0.0420008
$937$		−	38.2951i		−	1.25105i	−0.780206	−	0.625523i	$-0.784886\pi$
$937$		−	38.2951i		−	1.25105i	0.780206	−	0.625523i	$-0.215114\pi$
$938$	11.3013	−	11.3013i	0.369000	−	0.369000i
$939$	17.8812			0.583530
$940$	−12.2099	+	12.2099i	−0.398243	+	0.398243i
$941$	9.30900	+	9.30900i	0.303465	+	0.303465i	0.842368	−	0.538903i	$-0.181161\pi$
$941$	9.30900	+	9.30900i	0.303465	+	0.303465i	−0.538903	+	0.842368i	$0.681161\pi$
$942$	2.80097	+	2.80097i	0.0912606	+	0.0912606i
$943$		−	6.52557i		−	0.212502i
$944$			12.5311i			0.407854i
$945$	−2.39049	−	2.39049i	−0.0777628	−	0.0777628i
$946$	−16.7548	−	16.7548i	−0.544745	−	0.544745i
$947$	−18.1521	+	18.1521i	−0.589864	+	0.589864i	−0.937594	−	0.347731i	$-0.886952\pi$
$947$	−18.1521	+	18.1521i	−0.589864	+	0.589864i	0.347731	+	0.937594i	$0.386952\pi$
$948$	−12.9626			−0.421007
$949$	3.08959	−	3.08959i	0.100292	−	0.100292i
$950$			54.1714i			1.75755i
$951$	−1.08288			−0.0351147
$952$	3.82883	−	1.52972i	0.124093	−	0.0495786i
$953$	−34.0737			−1.10376			−0.551878	−	0.833925i	$-0.686089\pi$
$953$	−34.0737			−1.10376			−0.551878	+	0.833925i	$0.686089\pi$
$954$			13.8832i			0.449485i
$955$	−3.13816	+	3.13816i	−0.101549	+	0.101549i
$956$	14.5531			0.470679
$957$	5.17478	−	5.17478i	0.167277	−	0.167277i
$958$	−11.7195	−	11.7195i	−0.378639	−	0.378639i
$959$	−8.84232	−	8.84232i	−0.285533	−	0.285533i
$960$			3.38067i			0.109111i
$961$		−	14.0764i		−	0.454078i
$962$	−1.57685	−	1.57685i	−0.0508397	−	0.0508397i
$963$	−0.434436	−	0.434436i	−0.0139995	−	0.0139995i
$964$	−5.63110	+	5.63110i	−0.181365	+	0.181365i
$965$	−18.3976			−0.592240
$966$	2.44833	−	2.44833i	0.0787738	−	0.0787738i
$967$			27.9074i			0.897442i	0.893672	+	0.448721i	$0.148120\pi$
$967$			27.9074i			0.897442i	−0.893672	+	0.448721i	$0.851880\pi$
$968$	7.13306			0.229265
$969$	−12.8898	−	32.2626i	−0.414079	−	1.03642i
$970$	11.0417			0.354528
$971$			46.0034i			1.47632i	0.674627	+	0.738159i	$0.264305\pi$
$971$			46.0034i			1.47632i	−0.674627	+	0.738159i	$0.735695\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	9.21335			0.295366
$974$	−16.2454	+	16.2454i	−0.520536	+	0.520536i
$975$	−5.84142	−	5.84142i	−0.187075	−	0.187075i
$976$	−7.70568	−	7.70568i	−0.246653	−	0.246653i
$977$		−	40.2862i		−	1.28887i	−0.764660	−	0.644434i	$-0.777093\pi$
$977$		−	40.2862i		−	1.28887i	0.764660	−	0.644434i	$-0.222907\pi$
$978$			8.59981i			0.274992i
$979$	0.114201	+	0.114201i	0.00364989	+	0.00364989i
$980$	2.39049	+	2.39049i	0.0763615	+	0.0763615i
$981$	4.96966	−	4.96966i	0.158669	−	0.158669i
$982$	−5.47202			−0.174619
$983$	3.48372	−	3.48372i	0.111113	−	0.111113i	−0.649364	−	0.760478i	$-0.724965\pi$
$983$	3.48372	−	3.48372i	0.111113	−	0.111113i	0.760478	+	0.649364i	$0.224965\pi$
$984$		−	1.88466i		−	0.0600808i
$985$	43.8328			1.39663
$986$	−5.69293	−	14.2492i	−0.181300	−	0.453786i
$987$	5.10769			0.162580
$988$		−	10.8275i		−	0.344469i
$989$	−29.5012	+	29.5012i	−0.938084	+	0.938084i
$990$	6.64793			0.211285
$991$	28.7458	−	28.7458i	0.913140	−	0.913140i	−0.0833781	−	0.996518i	$-0.526571\pi$
$991$	28.7458	−	28.7458i	0.913140	−	0.913140i	0.996518	+	0.0833781i	$0.0265709\pi$
$992$	4.74744	+	4.74744i	0.150731	+	0.150731i
$993$	−18.1726	−	18.1726i	−0.576691	−	0.576691i
$994$			7.39537i			0.234567i
$995$		−	8.18658i		−	0.259532i
$996$	4.99075	+	4.99075i	0.158138	+	0.158138i
$997$	−1.45418	−	1.45418i	−0.0460544	−	0.0460544i	0.683705	−	0.729759i	$-0.260368\pi$
$997$	−1.45418	−	1.45418i	−0.0460544	−	0.0460544i	−0.729759	+	0.683705i	$0.760368\pi$
$998$	−5.70798	+	5.70798i	−0.180683	+	0.180683i
$999$	−1.73544			−0.0549069

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.m.d.463.1	yes	12
3.2	odd	2		2142.2.p.g.1891.6		12
17.13	even	4	inner	714.2.m.d.421.1	✓	12
51.47	odd	4		2142.2.p.g.1135.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.m.d.421.1	✓	12	17.13	even	4	inner
714.2.m.d.463.1	yes	12	1.1	even	1	trivial
2142.2.p.g.1135.6		12	51.47	odd	4
2142.2.p.g.1891.6		12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.39049 + 2.39049i) q^{5} +(0.707107 + 0.707107i) q^{6} +(0.707107 + 0.707107i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(2.39049 + 2.39049i) q^{10} +(1.39049 + 1.39049i) q^{11} +(0.707107 - 0.707107i) q^{12} -1.28498 q^{13} +(0.707107 - 0.707107i) q^{14} -3.38067i q^{15} +1.00000 q^{16} +(-3.78907 - 1.62572i) q^{17} -1.00000 q^{18} -8.42622i q^{19} +(2.39049 - 2.39049i) q^{20} -1.00000 q^{21} +(1.39049 - 1.39049i) q^{22} +(-2.44833 - 2.44833i) q^{23} +(-0.707107 - 0.707107i) q^{24} -6.42892i q^{25} +1.28498i q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.707107 - 0.707107i) q^{28} +(-2.63153 + 2.63153i) q^{29} -3.38067 q^{30} +(-4.74744 + 4.74744i) q^{31} -1.00000i q^{32} -1.96645 q^{33} +(-1.62572 + 3.78907i) q^{34} -3.38067 q^{35} +1.00000i q^{36} +(-1.22714 + 1.22714i) q^{37} -8.42622 q^{38} +(0.908617 - 0.908617i) q^{39} +(-2.39049 - 2.39049i) q^{40} +(1.33266 + 1.33266i) q^{41} +1.00000i q^{42} -12.0495i q^{43} +(-1.39049 - 1.39049i) q^{44} +(2.39049 + 2.39049i) q^{45} +(-2.44833 + 2.44833i) q^{46} -5.10769 q^{47} +(-0.707107 + 0.707107i) q^{48} +1.00000i q^{49} -6.42892 q^{50} +(3.82883 - 1.52972i) q^{51} +1.28498 q^{52} -13.8832i q^{53} +(0.707107 - 0.707107i) q^{54} -6.64793 q^{55} +(-0.707107 + 0.707107i) q^{56} +(5.95823 + 5.95823i) q^{57} +(2.63153 + 2.63153i) q^{58} +12.5311i q^{59} +3.38067i q^{60} +(-7.70568 - 7.70568i) q^{61} +(4.74744 + 4.74744i) q^{62} +(0.707107 - 0.707107i) q^{63} -1.00000 q^{64} +(3.07173 - 3.07173i) q^{65} +1.96645i q^{66} +15.9824 q^{67} +(3.78907 + 1.62572i) q^{68} +3.46246 q^{69} +3.38067i q^{70} +(-5.22932 + 5.22932i) q^{71} +1.00000 q^{72} +(-2.40439 + 2.40439i) q^{73} +(1.22714 + 1.22714i) q^{74} +(4.54593 + 4.54593i) q^{75} +8.42622i q^{76} +1.96645i q^{77} +(-0.908617 - 0.908617i) q^{78} +(-9.16596 - 9.16596i) q^{79} +(-2.39049 + 2.39049i) q^{80} -1.00000 q^{81} +(1.33266 - 1.33266i) q^{82} +7.05798i q^{83} +1.00000 q^{84} +(12.9440 - 5.17148i) q^{85} -12.0495 q^{86} -3.72154i q^{87} +(-1.39049 + 1.39049i) q^{88} +0.0821301 q^{89} +(2.39049 - 2.39049i) q^{90} +(-0.908617 - 0.908617i) q^{91} +(2.44833 + 2.44833i) q^{92} -6.71390i q^{93} +5.10769i q^{94} +(20.1428 + 20.1428i) q^{95} +(0.707107 + 0.707107i) q^{96} +(2.30951 - 2.30951i) q^{97} +1.00000 q^{98} +(1.39049 - 1.39049i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} - 4 q^{5} + 4 q^{10} - 8 q^{11} + 12 q^{13} + 12 q^{16} - 12 q^{17} - 12 q^{18} + 4 q^{20} - 12 q^{21} - 8 q^{22} + 8 q^{23} + 12 q^{29} - 4 q^{30} + 12 q^{31} - 4 q^{33} + 4 q^{34} - 4 q^{35}+ \cdots - 8 q^{99}+O(q^{100}) \) 12 * q - 12 * q^4 - 4 * q^5 + 4 * q^10 - 8 * q^11 + 12 * q^13 + 12 * q^16 - 12 * q^17 - 12 * q^18 + 4 * q^20 - 12 * q^21 - 8 * q^22 + 8 * q^23 + 12 * q^29 - 4 * q^30 + 12 * q^31 - 4 * q^33 + 4 * q^34 - 4 * q^35 - 24 * q^38 + 4 * q^39 - 4 * q^40 + 4 * q^41 + 8 * q^44 + 4 * q^45 + 8 * q^46 + 8 * q^47 - 16 * q^50 - 8 * q^51 - 12 * q^52 - 68 * q^55 + 8 * q^57 - 12 * q^58 + 40 * q^61 - 12 * q^62 - 12 * q^64 + 20 * q^65 - 12 * q^67 + 12 * q^68 + 24 * q^71 + 12 * q^72 - 16 * q^75 - 4 * q^78 - 8 * q^79 - 4 * q^80 - 12 * q^81 + 4 * q^82 + 12 * q^84 - 12 * q^85 + 20 * q^86 + 8 * q^88 - 44 * q^89 + 4 * q^90 - 4 * q^91 - 8 * q^92 + 92 * q^95 - 32 * q^97 + 12 * q^98 - 8 * q^99

Introduction

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