LMFDB - Embedded newform 840.2.z.d.811.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(811,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 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("840.811"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.z (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,2,0,-2,28] 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:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			811.19
Character	$\chi$	$=$	840.811
Dual form			840.2.z.d.811.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.818985 - 1.15294i) q^{2} +1.00000i q^{3} +(-0.658528 - 1.88848i) q^{4} +1.00000 q^{5} +(1.15294 + 0.818985i) q^{6} +(-0.864047 - 2.50068i) q^{7} +(-2.71662 - 0.787391i) q^{8} -1.00000 q^{9} +(0.818985 - 1.15294i) q^{10} -5.95444 q^{11} +(1.88848 - 0.658528i) q^{12} -3.87212 q^{13} +(-3.59077 - 1.05183i) q^{14} +1.00000i q^{15} +(-3.13268 + 2.48723i) q^{16} +2.66013i q^{17} +(-0.818985 + 1.15294i) q^{18} -6.21337i q^{19} +(-0.658528 - 1.88848i) q^{20} +(2.50068 - 0.864047i) q^{21} +(-4.87660 + 6.86510i) q^{22} -4.60261i q^{23} +(0.787391 - 2.71662i) q^{24} +1.00000 q^{25} +(-3.17121 + 4.46431i) q^{26} -1.00000i q^{27} +(-4.15348 + 3.27850i) q^{28} +0.579589i q^{29} +(1.15294 + 0.818985i) q^{30} +5.65561 q^{31} +(0.302000 + 5.64879i) q^{32} -5.95444i q^{33} +(3.06696 + 2.17860i) q^{34} +(-0.864047 - 2.50068i) q^{35} +(0.658528 + 1.88848i) q^{36} -2.21144i q^{37} +(-7.16362 - 5.08865i) q^{38} -3.87212i q^{39} +(-2.71662 - 0.787391i) q^{40} +5.75803i q^{41} +(1.05183 - 3.59077i) q^{42} +5.16410 q^{43} +(3.92117 + 11.2448i) q^{44} -1.00000 q^{45} +(-5.30653 - 3.76947i) q^{46} +5.39666 q^{47} +(-2.48723 - 3.13268i) q^{48} +(-5.50685 + 4.32142i) q^{49} +(0.818985 - 1.15294i) q^{50} -2.66013 q^{51} +(2.54990 + 7.31241i) q^{52} -10.3132i q^{53} +(-1.15294 - 0.818985i) q^{54} -5.95444 q^{55} +(0.378268 + 7.47375i) q^{56} +6.21337 q^{57} +(0.668230 + 0.474675i) q^{58} -10.7610i q^{59} +(1.88848 - 0.658528i) q^{60} -10.9463 q^{61} +(4.63185 - 6.52056i) q^{62} +(0.864047 + 2.50068i) q^{63} +(6.76003 + 4.27808i) q^{64} -3.87212 q^{65} +(-6.86510 - 4.87660i) q^{66} -10.0435 q^{67} +(5.02358 - 1.75177i) q^{68} +4.60261 q^{69} +(-3.59077 - 1.05183i) q^{70} -0.496099i q^{71} +(2.71662 + 0.787391i) q^{72} +2.04057i q^{73} +(-2.54965 - 1.81114i) q^{74} +1.00000i q^{75} +(-11.7338 + 4.09168i) q^{76} +(5.14492 + 14.8902i) q^{77} +(-4.46431 - 3.17121i) q^{78} -10.6941i q^{79} +(-3.13268 + 2.48723i) q^{80} +1.00000 q^{81} +(6.63865 + 4.71574i) q^{82} +11.3326i q^{83} +(-3.27850 - 4.15348i) q^{84} +2.66013i q^{85} +(4.22932 - 5.95388i) q^{86} -0.579589 q^{87} +(16.1759 + 4.68848i) q^{88} +10.8922i q^{89} +(-0.818985 + 1.15294i) q^{90} +(3.34569 + 9.68295i) q^{91} +(-8.69193 + 3.03095i) q^{92} +5.65561i q^{93} +(4.41978 - 6.22201i) q^{94} -6.21337i q^{95} +(-5.64879 + 0.302000i) q^{96} -16.2633i q^{97} +(0.472300 + 9.88822i) q^{98} +5.95444 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} - 2 q^{4} + 28 q^{5} + 4 q^{6} + 4 q^{7} - 10 q^{8} - 28 q^{9} + 2 q^{10} - 8 q^{12} - 8 q^{13} + 2 q^{14} + 6 q^{16} - 2 q^{18} - 2 q^{20} - 4 q^{24} + 28 q^{25} + 16 q^{26} + 10 q^{28}+ \cdots - 30 q^{98}+O(q^{100}) $ 28 * q + 2 * q^2 - 2 * q^4 + 28 * q^5 + 4 * q^6 + 4 * q^7 - 10 * q^8 - 28 * q^9 + 2 * q^10 - 8 * q^12 - 8 * q^13 + 2 * q^14 + 6 * q^16 - 2 * q^18 - 2 * q^20 - 4 * q^24 + 28 * q^25 + 16 * q^26 + 10 * q^28 + 4 * q^30 + 24 * q^31 + 2 * q^32 + 8 * q^34 + 4 * q^35 + 2 * q^36 + 36 * q^38 - 10 * q^40 + 24 * q^43 - 4 * q^44 - 28 * q^45 - 44 * q^46 - 24 * q^47 + 16 * q^48 + 28 * q^49 + 2 * q^50 + 16 * q^52 - 4 * q^54 - 22 * q^56 + 8 * q^57 - 12 * q^58 - 8 * q^60 - 16 * q^61 - 28 * q^62 - 4 * q^63 + 22 * q^64 - 8 * q^65 - 20 * q^66 - 8 * q^67 - 12 * q^68 - 24 * q^69 + 2 * q^70 + 10 * q^72 - 8 * q^74 - 16 * q^76 + 16 * q^77 + 20 * q^78 + 6 * q^80 + 28 * q^81 + 24 * q^82 - 12 * q^84 - 4 * q^86 + 16 * q^87 + 40 * q^88 - 2 * q^90 + 48 * q^91 + 40 * q^92 + 52 * q^94 - 16 * q^96 - 30 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.818985	−	1.15294i	0.579110	−	0.815250i
$2$	0.818985	−	1.15294i	0.579110	−	0.815250i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−0.658528	−	1.88848i	−0.329264	−	0.944238i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.15294	+	0.818985i	0.470685	+	0.334349i
$7$	−0.864047	−	2.50068i	−0.326579	−	0.945170i
$7$	−0.864047	−	2.50068i	−0.326579	−	0.945170i
$8$	−2.71662	−	0.787391i	−0.960470	−	0.278385i
$9$	−1.00000			−0.333333
$10$	0.818985	−	1.15294i	0.258986	−	0.364591i
$11$	−5.95444			−1.79533			−0.897666	−	0.440676i	$-0.854739\pi$
$11$	−5.95444			−1.79533			−0.897666	+	0.440676i	$0.854739\pi$
$12$	1.88848	−	0.658528i	0.545156	−	0.190101i
$13$	−3.87212			−1.07393			−0.536967	−	0.843603i	$-0.680430\pi$
$13$	−3.87212			−1.07393			−0.536967	+	0.843603i	$0.680430\pi$
$14$	−3.59077	−	1.05183i	−0.959675	−	0.281114i
$15$			1.00000i			0.258199i
$16$	−3.13268	+	2.48723i	−0.783170	+	0.621807i
$17$			2.66013i			0.645175i	0.946540	+	0.322588i	$0.104553\pi$
$17$			2.66013i			0.645175i	−0.946540	+	0.322588i	$0.895447\pi$
$18$	−0.818985	+	1.15294i	−0.193037	+	0.271750i
$19$		−	6.21337i		−	1.42544i	−0.701447	−	0.712722i	$-0.747462\pi$
$19$		−	6.21337i		−	1.42544i	0.701447	−	0.712722i	$-0.252538\pi$
$20$	−0.658528	−	1.88848i	−0.147251	−	0.422276i
$21$	2.50068	−	0.864047i	0.545694	−	0.188551i
$22$	−4.87660	+	6.86510i	−1.03969	+	1.46364i
$23$		−	4.60261i		−	0.959711i	−0.877347	−	0.479856i	$-0.840689\pi$
$23$		−	4.60261i		−	0.959711i	0.877347	−	0.479856i	$-0.159311\pi$
$24$	0.787391	−	2.71662i	0.160726	−	0.554527i
$25$	1.00000			0.200000
$26$	−3.17121	+	4.46431i	−0.621925	+	0.875524i
$27$		−	1.00000i		−	0.192450i
$28$	−4.15348	+	3.27850i	−0.784934	+	0.619579i
$29$			0.579589i			0.107627i	0.998551	+	0.0538135i	$0.0171376\pi$
$29$			0.579589i			0.107627i	−0.998551	+	0.0538135i	$0.982862\pi$
$30$	1.15294	+	0.818985i	0.210497	+	0.149525i
$31$	5.65561			1.01578			0.507888	−	0.861423i	$-0.330426\pi$
$31$	5.65561			1.01578			0.507888	+	0.861423i	$0.330426\pi$
$32$	0.302000	+	5.64879i	0.0533865	+	0.998574i
$33$		−	5.95444i		−	1.03654i
$34$	3.06696	+	2.17860i	0.525979	+	0.373627i
$35$	−0.864047	−	2.50068i	−0.146051	−	0.422693i
$36$	0.658528	+	1.88848i	0.109755	+	0.314746i
$37$		−	2.21144i		−	0.363559i	−0.983339	−	0.181779i	$-0.941814\pi$
$37$		−	2.21144i		−	0.363559i	0.983339	−	0.181779i	$-0.0581857\pi$
$38$	−7.16362	−	5.08865i	−1.16209	−	0.825488i
$39$		−	3.87212i		−	0.620036i
$40$	−2.71662	−	0.787391i	−0.429535	−	0.124498i
$41$			5.75803i			0.899253i	0.893217	+	0.449627i	$0.148443\pi$
$41$			5.75803i			0.899253i	−0.893217	+	0.449627i	$0.851557\pi$
$42$	1.05183	−	3.59077i	0.162301	−	0.554068i
$43$	5.16410			0.787518			0.393759	−	0.919214i	$-0.371175\pi$
$43$	5.16410			0.787518			0.393759	+	0.919214i	$0.371175\pi$
$44$	3.92117	+	11.2448i	0.591138	+	1.69522i
$45$	−1.00000			−0.149071
$46$	−5.30653	−	3.76947i	−0.782404	−	0.555778i
$47$	5.39666			0.787184			0.393592	−	0.919285i	$-0.371232\pi$
$47$	5.39666			0.787184			0.393592	+	0.919285i	$0.371232\pi$
$48$	−2.48723	−	3.13268i	−0.359001	−	0.452164i
$49$	−5.50685	+	4.32142i	−0.786692	+	0.617345i
$50$	0.818985	−	1.15294i	0.115822	−	0.163050i
$51$	−2.66013			−0.372492
$52$	2.54990	+	7.31241i	0.353608	+	1.01405i
$53$		−	10.3132i		−	1.41662i	−0.705899	−	0.708312i	$-0.749457\pi$
$53$		−	10.3132i		−	1.41662i	0.705899	−	0.708312i	$-0.250543\pi$
$54$	−1.15294	−	0.818985i	−0.156895	−	0.111450i
$55$	−5.95444			−0.802897
$56$	0.378268	+	7.47375i	0.0505482	+	0.998722i
$57$	6.21337			0.822980
$58$	0.668230	+	0.474675i	0.0877429	+	0.0623278i
$59$		−	10.7610i		−	1.40097i	−0.713669	−	0.700483i	$-0.752968\pi$
$59$		−	10.7610i		−	1.40097i	0.713669	−	0.700483i	$-0.247032\pi$
$60$	1.88848	−	0.658528i	0.243801	−	0.0850156i
$61$	−10.9463			−1.40153			−0.700763	−	0.713394i	$-0.747157\pi$
$61$	−10.9463			−1.40153			−0.700763	+	0.713394i	$0.747157\pi$
$62$	4.63185	−	6.52056i	0.588246	−	0.828112i
$63$	0.864047	+	2.50068i	0.108860	+	0.315057i
$64$	6.76003	+	4.27808i	0.845004	+	0.534760i
$65$	−3.87212			−0.480278
$66$	−6.86510	−	4.87660i	−0.845035	−	0.600268i
$67$	−10.0435			−1.22700			−0.613502	−	0.789693i	$-0.710240\pi$
$67$	−10.0435			−1.22700			−0.613502	+	0.789693i	$0.710240\pi$
$68$	5.02358	−	1.75177i	0.609199	−	0.212433i
$69$	4.60261			0.554090
$70$	−3.59077	−	1.05183i	−0.429179	−	0.125718i
$71$		−	0.496099i		−	0.0588761i	−0.999567	−	0.0294381i	$-0.990628\pi$
$71$		−	0.496099i		−	0.0588761i	0.999567	−	0.0294381i	$-0.00937178\pi$
$72$	2.71662	+	0.787391i	0.320157	+	0.0927950i
$73$			2.04057i			0.238831i	0.992844	+	0.119415i	$0.0381020\pi$
$73$			2.04057i			0.238831i	−0.992844	+	0.119415i	$0.961898\pi$
$74$	−2.54965	−	1.81114i	−0.296391	−	0.210540i
$75$			1.00000i			0.115470i
$76$	−11.7338	+	4.09168i	−1.34596	+	0.469347i
$77$	5.14492	+	14.8902i	0.586318	+	1.69689i
$78$	−4.46431	−	3.17121i	−0.505484	−	0.359069i
$79$		−	10.6941i		−	1.20318i	−0.798805	−	0.601590i	$-0.794534\pi$
$79$		−	10.6941i		−	1.20318i	0.798805	−	0.601590i	$-0.205466\pi$
$80$	−3.13268	+	2.48723i	−0.350244	+	0.278081i
$81$	1.00000			0.111111
$82$	6.63865	+	4.71574i	0.733116	+	0.520766i
$83$			11.3326i			1.24392i	0.783051	+	0.621958i	$0.213662\pi$
$83$			11.3326i			1.24392i	−0.783051	+	0.621958i	$0.786338\pi$
$84$	−3.27850	−	4.15348i	−0.357714	−	0.453182i
$85$			2.66013i			0.288531i
$86$	4.22932	−	5.95388i	0.456059	−	0.642023i
$87$	−0.579589			−0.0621385
$88$	16.1759	+	4.68848i	1.72436	+	0.499793i
$89$			10.8922i			1.15457i	0.816541	+	0.577287i	$0.195889\pi$
$89$			10.8922i			1.15457i	−0.816541	+	0.577287i	$0.804111\pi$
$90$	−0.818985	+	1.15294i	−0.0863286	+	0.121530i
$91$	3.34569	+	9.68295i	0.350724	+	1.01505i
$92$	−8.69193	+	3.03095i	−0.906196	+	0.315998i
$93$			5.65561i			0.586459i
$94$	4.41978	−	6.22201i	0.455866	−	0.641751i
$95$		−	6.21337i		−	0.637478i
$96$	−5.64879	+	0.302000i	−0.576527	+	0.0308227i
$97$		−	16.2633i		−	1.65129i	−0.564189	−	0.825645i	$-0.690811\pi$
$97$		−	16.2633i		−	1.65129i	0.564189	−	0.825645i	$-0.309189\pi$
$98$	0.472300	+	9.88822i	0.0477095	+	0.998861i
$99$	5.95444			0.598444
$100$	−0.658528	−	1.88848i	−0.0658528	−	0.188848i
$101$	−0.355906			−0.0354140			−0.0177070	−	0.999843i	$-0.505637\pi$
$101$	−0.355906			−0.0354140			−0.0177070	+	0.999843i	$0.505637\pi$
$102$	−2.17860	+	3.06696i	−0.215714	+	0.303674i
$103$	0.542418			0.0534460			0.0267230	−	0.999643i	$-0.491493\pi$
$103$	0.542418			0.0534460			0.0267230	+	0.999643i	$0.491493\pi$
$104$	10.5191	+	3.04888i	1.03148	+	0.298967i
$105$	2.50068	−	0.864047i	0.244042	−	0.0843223i
$106$	−11.8905	−	8.44634i	−1.15490	−	0.820381i
$107$	13.2688			1.28275			0.641373	−	0.767230i	$-0.278365\pi$
$107$	13.2688			1.28275			0.641373	+	0.767230i	$0.278365\pi$
$108$	−1.88848	+	0.658528i	−0.181719	+	0.0633669i
$109$		−	5.40596i		−	0.517797i	−0.965904	−	0.258899i	$-0.916640\pi$
$109$		−	5.40596i		−	0.517797i	0.965904	−	0.258899i	$-0.0833596\pi$
$110$	−4.87660	+	6.86510i	−0.464965	+	0.654561i
$111$	2.21144			0.209901
$112$	8.92656	+	5.68477i	0.843480	+	0.537160i
$113$	2.78366			0.261865			0.130932	−	0.991391i	$-0.458203\pi$
$113$	2.78366			0.261865			0.130932	+	0.991391i	$0.458203\pi$
$114$	5.08865	−	7.16362i	0.476596	−	0.670934i
$115$		−	4.60261i		−	0.429196i
$116$	1.09454	−	0.381676i	0.101625	−	0.0354377i
$117$	3.87212			0.357978
$118$	−12.4068	−	8.81311i	−1.14214	−	0.811313i
$119$	6.65213	−	2.29847i	0.609800	−	0.210701i
$120$	0.787391	−	2.71662i	0.0718787	−	0.247992i
$121$	24.4554			2.22322
$122$	−8.96482	+	12.6204i	−0.811637	+	1.14259i
$123$	−5.75803			−0.519184
$124$	−3.72438	−	10.6805i	−0.334459	−	0.959135i
$125$	1.00000			0.0894427
$126$	3.59077	+	1.05183i	0.319892	+	0.0937045i
$127$		−	13.3363i		−	1.18340i	−0.806157	−	0.591701i	$-0.798457\pi$
$127$		−	13.3363i		−	1.18340i	0.806157	−	0.591701i	$-0.201543\pi$
$128$	10.4687	−	4.29020i	0.925313	−	0.379204i
$129$			5.16410i			0.454673i
$130$	−3.17121	+	4.46431i	−0.278133	+	0.391546i
$131$			7.81808i			0.683069i	0.939869	+	0.341534i	$0.110947\pi$
$131$			7.81808i			0.683069i	−0.939869	+	0.341534i	$0.889053\pi$
$132$	−11.2448	+	3.92117i	−0.978736	+	0.341294i
$133$	−15.5377	+	5.36864i	−1.34729	+	0.465520i
$134$	−8.22544	+	11.5795i	−0.710570	+	1.00031i
$135$		−	1.00000i		−	0.0860663i
$136$	2.09456	−	7.22654i	0.179607	−	0.619671i
$137$	14.6304			1.24996			0.624978	−	0.780643i	$-0.285108\pi$
$137$	14.6304			1.24996			0.624978	+	0.780643i	$0.285108\pi$
$138$	3.76947	−	5.30653i	0.320879	−	0.451721i
$139$			11.6895i			0.991493i	0.868467	+	0.495746i	$0.165105\pi$
$139$			11.6895i			0.991493i	−0.868467	+	0.495746i	$0.834895\pi$
$140$	−4.15348	+	3.27850i	−0.351033	+	0.277084i
$141$			5.39666i			0.454481i
$142$	−0.571971	−	0.406298i	−0.0479988	−	0.0340957i
$143$	23.0563			1.92807
$144$	3.13268	−	2.48723i	0.261057	−	0.207269i
$145$			0.579589i			0.0481323i
$146$	2.35265	+	1.67119i	0.194707	+	0.138309i
$147$	−4.32142	−	5.50685i	−0.356425	−	0.454197i
$148$	−4.17625	+	1.45630i	−0.343286	+	0.119707i
$149$			5.32066i			0.435885i	0.975962	+	0.217943i	$0.0699345\pi$
$149$			5.32066i			0.435885i	−0.975962	+	0.217943i	$0.930065\pi$
$150$	1.15294	+	0.818985i	0.0941369	+	0.0668698i
$151$		−	19.6499i		−	1.59908i	−0.600611	−	0.799542i	$-0.705076\pi$
$151$		−	19.6499i		−	1.59908i	0.600611	−	0.799542i	$-0.294924\pi$
$152$	−4.89235	+	16.8793i	−0.396822	+	1.36910i
$153$		−	2.66013i		−	0.215058i
$154$	21.3811	+	6.26307i	1.72293	+	0.504692i
$155$	5.65561			0.454269
$156$	−7.31241	+	2.54990i	−0.585461	+	0.204155i
$157$	17.2576			1.37731			0.688655	−	0.725090i	$-0.258202\pi$
$157$	17.2576			1.37731			0.688655	+	0.725090i	$0.258202\pi$
$158$	−12.3296	−	8.75830i	−0.980892	−	0.696773i
$159$	10.3132			0.817889
$160$	0.302000	+	5.64879i	0.0238752	+	0.446576i
$161$	−11.5097	+	3.97688i	−0.907090	+	0.313422i
$162$	0.818985	−	1.15294i	0.0643455	−	0.0905833i
$163$	1.54126			0.120721			0.0603604	−	0.998177i	$-0.480775\pi$
$163$	1.54126			0.120721			0.0603604	+	0.998177i	$0.480775\pi$
$164$	10.8739	−	3.79183i	0.849109	−	0.296092i
$165$		−	5.95444i		−	0.463553i
$166$	13.0658	+	9.28124i	1.01410	+	0.720364i
$167$	14.2666			1.10398			0.551992	−	0.833849i	$-0.313868\pi$
$167$	14.2666			1.10398			0.551992	+	0.833849i	$0.313868\pi$
$168$	−7.47375	+	0.378268i	−0.576612	+	0.0291840i
$169$	1.99333			0.153333
$170$	3.06696	+	2.17860i	0.235225	+	0.167091i
$171$			6.21337i			0.475148i
$172$	−3.40070	−	9.75227i	−0.259301	−	0.743604i
$173$	−15.8094			−1.20196			−0.600982	−	0.799262i	$-0.705224\pi$
$173$	−15.8094			−1.20196			−0.600982	+	0.799262i	$0.705224\pi$
$174$	−0.474675	+	0.668230i	−0.0359850	+	0.0506584i
$175$	−0.864047	−	2.50068i	−0.0653158	−	0.189034i
$176$	18.6534	−	14.8101i	1.40605	−	1.11635i
$177$	10.7610			0.808848
$178$	12.5581	+	8.92057i	0.941266	+	0.668625i
$179$	−25.0087			−1.86924			−0.934619	−	0.355650i	$-0.884259\pi$
$179$	−25.0087			−1.86924			−0.934619	+	0.355650i	$0.884259\pi$
$180$	0.658528	+	1.88848i	0.0490838	+	0.140759i
$181$	−7.61578			−0.566077			−0.283038	−	0.959109i	$-0.591342\pi$
$181$	−7.61578			−0.566077			−0.283038	+	0.959109i	$0.591342\pi$
$182$	13.9039	+	4.07282i	1.03063	+	0.301897i
$183$		−	10.9463i		−	0.809171i
$184$	−3.62406	+	12.5035i	−0.267169	+	0.921774i
$185$		−	2.21144i		−	0.162588i
$186$	6.52056	+	4.63185i	0.478111	+	0.339624i
$187$		−	15.8396i		−	1.15830i
$188$	−3.55385	−	10.1915i	−0.259191	−	0.743289i
$189$	−2.50068	+	0.864047i	−0.181898	+	0.0628502i
$190$	−7.16362	−	5.08865i	−0.519704	−	0.369170i
$191$			2.89329i			0.209351i	0.994506	+	0.104675i	$0.0333804\pi$
$191$			2.89329i			0.209351i	−0.994506	+	0.104675i	$0.966620\pi$
$192$	−4.27808	+	6.76003i	−0.308744	+	0.487863i
$193$	4.72265			0.339943			0.169972	−	0.985449i	$-0.445632\pi$
$193$	4.72265			0.339943			0.169972	+	0.985449i	$0.445632\pi$
$194$	−18.7506	−	13.3194i	−1.34621	−	0.956278i
$195$		−	3.87212i		−	0.277288i
$196$	11.7873	+	7.55377i	0.841950	+	0.539555i
$197$			6.98065i			0.497351i	0.968587	+	0.248675i	$0.0799952\pi$
$197$			6.98065i			0.497351i	−0.968587	+	0.248675i	$0.920005\pi$
$198$	4.87660	−	6.86510i	0.346565	−	0.487881i
$199$	−26.9627			−1.91133			−0.955666	−	0.294452i	$-0.904863\pi$
$199$	−26.9627			−1.91133			−0.955666	+	0.294452i	$0.904863\pi$
$200$	−2.71662	−	0.787391i	−0.192094	−	0.0556770i
$201$		−	10.0435i		−	0.708411i
$202$	−0.291482	+	0.410337i	−0.0205086	+	0.0288712i
$203$	1.44937	−	0.500792i	0.101726	−	0.0351487i
$204$	1.75177	+	5.02358i	0.122648	+	0.351721i
$205$			5.75803i			0.402158i
$206$	0.444232	−	0.625373i	0.0309511	−	0.0435718i
$207$			4.60261i			0.319904i
$208$	12.1301	−	9.63085i	0.841073	−	0.667779i
$209$			36.9971i			2.55915i
$210$	1.05183	−	3.59077i	0.0725832	−	0.247787i
$211$	−12.3556			−0.850591			−0.425296	−	0.905054i	$-0.639830\pi$
$211$	−12.3556			−0.850591			−0.425296	+	0.905054i	$0.639830\pi$
$212$	−19.4762	+	6.79152i	−1.33763	+	0.466444i
$213$	0.496099			0.0339922
$214$	10.8670	−	15.2981i	0.742850	−	1.04576i
$215$	5.16410			0.352189
$216$	−0.787391	+	2.71662i	−0.0535752	+	0.184842i
$217$	−4.88671	−	14.1429i	−0.331731	−	0.960082i
$218$	−6.23274	−	4.42740i	−0.422134	−	0.299862i
$219$	−2.04057			−0.137889
$220$	3.92117	+	11.2448i	0.264365	+	0.758126i
$221$		−	10.3003i		−	0.692875i
$222$	1.81114	−	2.54965i	0.121556	−	0.171121i
$223$	−21.6991			−1.45308			−0.726539	−	0.687125i	$-0.758872\pi$
$223$	−21.6991			−1.45308			−0.726539	+	0.687125i	$0.758872\pi$
$224$	13.8649	−	5.63602i	0.926387	−	0.376573i
$225$	−1.00000			−0.0666667
$226$	2.27978	−	3.20939i	0.151649	−	0.213485i
$227$		−	2.80461i		−	0.186148i	−0.995659	−	0.0930741i	$-0.970331\pi$
$227$		−	2.80461i		−	0.186148i	0.995659	−	0.0930741i	$-0.0296694\pi$
$228$	−4.09168	−	11.7338i	−0.270978	−	0.777089i
$229$	27.1243			1.79242			0.896211	−	0.443629i	$-0.146309\pi$
$229$	27.1243			1.79242			0.896211	+	0.443629i	$0.146309\pi$
$230$	−5.30653	−	3.76947i	−0.349902	−	0.248552i
$231$	−14.8902	+	5.14492i	−0.979702	+	0.338511i
$232$	0.456363	−	1.57452i	0.0299617	−	0.103372i
$233$	15.4554			1.01252			0.506260	−	0.862381i	$-0.331028\pi$
$233$	15.4554			1.01252			0.506260	+	0.862381i	$0.331028\pi$
$234$	3.17121	−	4.46431i	0.207308	−	0.291841i
$235$	5.39666			0.352039
$236$	−20.3219	+	7.08644i	−1.32285	+	0.461288i
$237$	10.6941			0.694656
$238$	2.79800	−	9.55191i	0.181367	−	0.619158i
$239$			13.4730i			0.871498i	0.900068	+	0.435749i	$0.143516\pi$
$239$			13.4730i			0.871498i	−0.900068	+	0.435749i	$0.856484\pi$
$240$	−2.48723	−	3.13268i	−0.160550	−	0.202214i
$241$			0.816750i			0.0526115i	0.999654	+	0.0263057i	$0.00837434\pi$
$241$			0.816750i			0.0526115i	−0.999654	+	0.0263057i	$0.991626\pi$
$242$	20.0286	−	28.1955i	1.28749	−	1.81248i
$243$			1.00000i			0.0641500i
$244$	7.20842	+	20.6718i	0.461472	+	1.32337i
$245$	−5.50685	+	4.32142i	−0.351819	+	0.276085i
$246$	−4.71574	+	6.63865i	−0.300665	+	0.423265i
$247$			24.0589i			1.53083i
$248$	−15.3641	−	4.45318i	−0.975623	−	0.282777i
$249$	−11.3326			−0.718175
$250$	0.818985	−	1.15294i	0.0517971	−	0.0729181i
$251$		−	20.6191i		−	1.30147i	−0.759306	−	0.650733i	$-0.774462\pi$
$251$		−	20.6191i		−	1.30147i	0.759306	−	0.650733i	$-0.225538\pi$
$252$	4.15348	−	3.27850i	0.261645	−	0.206526i
$253$			27.4060i			1.72300i
$254$	−15.3759	−	10.9222i	−0.964768	−	0.685320i
$255$	−2.66013			−0.166583
$256$	3.62739	−	15.5834i	0.226712	−	0.973962i
$257$		−	14.6010i		−	0.910785i	−0.890291	−	0.455393i	$-0.849499\pi$
$257$		−	14.6010i		−	0.910785i	0.890291	−	0.455393i	$-0.150501\pi$
$258$	5.95388	+	4.22932i	0.370672	+	0.263306i
$259$	−5.53012	+	1.91079i	−0.343625	+	0.118731i
$260$	2.54990	+	7.31241i	0.158138	+	0.453496i
$261$		−	0.579589i		−	0.0358757i
$262$	9.01375	+	6.40289i	0.556872	+	0.395572i
$263$		−	13.6585i		−	0.842219i	−0.907010	−	0.421109i	$-0.861641\pi$
$263$		−	13.6585i		−	0.842219i	0.907010	−	0.421109i	$-0.138359\pi$
$264$	−4.68848	+	16.1759i	−0.288556	+	0.995561i
$265$		−	10.3132i		−	0.633534i
$266$	−6.53541	+	22.3108i	−0.400712	+	1.36796i
$267$	−10.8922			−0.666594
$268$	6.61390	+	18.9668i	0.404008	+	1.15858i
$269$	−18.0418			−1.10003			−0.550013	−	0.835156i	$-0.685377\pi$
$269$	−18.0418			−1.10003			−0.550013	+	0.835156i	$0.685377\pi$
$270$	−1.15294	−	0.818985i	−0.0701655	−	0.0498418i
$271$	−27.9012			−1.69488			−0.847438	−	0.530894i	$-0.821856\pi$
$271$	−27.9012			−1.69488			−0.847438	+	0.530894i	$0.821856\pi$
$272$	−6.61634	−	8.33332i	−0.401174	−	0.505282i
$273$	−9.68295	+	3.34569i	−0.586039	+	0.202491i
$274$	11.9820	−	16.8679i	0.723861	−	1.01903i
$275$	−5.95444			−0.359066
$276$	−3.03095	−	8.69193i	−0.182442	−	0.523192i
$277$		−	4.22886i		−	0.254088i	−0.991897	−	0.127044i	$-0.959451\pi$
$277$		−	4.22886i		−	0.254088i	0.991897	−	0.127044i	$-0.0405489\pi$
$278$	13.4773	+	9.57354i	0.808314	+	0.574183i
$279$	−5.65561			−0.338592
$280$	0.378268	+	7.47375i	0.0226059	+	0.446642i
$281$	−1.40338			−0.0837185			−0.0418592	−	0.999124i	$-0.513328\pi$
$281$	−1.40338			−0.0837185			−0.0418592	+	0.999124i	$0.513328\pi$
$282$	6.22201	+	4.41978i	0.370515	+	0.263194i
$283$			0.0994881i			0.00591395i	0.999996	+	0.00295698i	$0.000941236\pi$
$283$			0.0994881i			0.00591395i	−0.999996	+	0.00295698i	$0.999059\pi$
$284$	−0.936871	+	0.326695i	−0.0555931	+	0.0193858i
$285$	6.21337			0.368048
$286$	18.8828	−	26.5825i	1.11656	−	1.57186i
$287$	14.3990	−	4.97521i	0.849947	−	0.293677i
$288$	−0.302000	−	5.64879i	−0.0177955	−	0.332858i
$289$	9.92373			0.583749
$290$	0.668230	+	0.474675i	0.0392398	+	0.0278739i
$291$	16.2633			0.953373
$292$	3.85357	−	1.34377i	0.225513	−	0.0786383i
$293$	28.3618			1.65691			0.828456	−	0.560055i	$-0.189220\pi$
$293$	28.3618			1.65691			0.828456	+	0.560055i	$0.189220\pi$
$294$	−9.88822	+	0.472300i	−0.576693	+	0.0275451i
$295$		−	10.7610i		−	0.626531i
$296$	−1.74127	+	6.00764i	−0.101209	+	0.349187i
$297$			5.95444i			0.345512i
$298$	6.13438	+	4.35754i	0.355355	+	0.252425i
$299$			17.8219i			1.03067i
$300$	1.88848	−	0.658528i	0.109031	−	0.0380201i
$301$	−4.46202	−	12.9138i	−0.257187	−	0.744338i
$302$	−22.6551	−	16.0929i	−1.30365	−	0.926044i
$303$		−	0.355906i		−	0.0204463i
$304$	15.4541	+	19.4645i	0.886351	+	1.11637i
$305$	−10.9463			−0.626781
$306$	−3.06696	−	2.17860i	−0.175326	−	0.124542i
$307$		−	18.9155i		−	1.07956i	−0.841805	−	0.539781i	$-0.818507\pi$
$307$		−	18.9155i		−	1.07956i	0.841805	−	0.539781i	$-0.181493\pi$
$308$	24.7317	−	19.5217i	1.40922	−	1.11235i
$309$			0.542418i			0.0308571i
$310$	4.63185	−	6.52056i	0.263072	−	0.370343i
$311$	−8.04529			−0.456207			−0.228103	−	0.973637i	$-0.573252\pi$
$311$	−8.04529			−0.456207			−0.228103	+	0.973637i	$0.573252\pi$
$312$	−3.04888	+	10.5191i	−0.172609	+	0.595525i
$313$		−	13.7262i		−	0.775850i	−0.921691	−	0.387925i	$-0.873192\pi$
$313$		−	13.7262i		−	0.775850i	0.921691	−	0.387925i	$-0.126808\pi$
$314$	14.1337	−	19.8970i	0.797613	−	1.12285i
$315$	0.864047	+	2.50068i	0.0486835	+	0.140898i
$316$	−20.1955	+	7.04236i	−1.13609	+	0.396164i
$317$		−	3.73683i		−	0.209881i	−0.994478	−	0.104941i	$-0.966535\pi$
$317$		−	3.73683i		−	0.209881i	0.994478	−	0.104941i	$-0.0334652\pi$
$318$	8.44634	−	11.8905i	0.473647	−	0.666784i
$319$		−	3.45113i		−	0.193226i
$320$	6.76003	+	4.27808i	0.377897	+	0.239152i
$321$			13.2688i			0.740593i
$322$	−4.84117	+	16.5269i	−0.269788	+	0.921011i
$323$	16.5283			0.919661
$324$	−0.658528	−	1.88848i	−0.0365849	−	0.104915i
$325$	−3.87212			−0.214787
$326$	1.26227	−	1.77698i	0.0699106	−	0.0984177i
$327$	5.40596			0.298951
$328$	4.53382	−	15.6424i	0.250339	−	0.863706i
$329$	−4.66297	−	13.4953i	−0.257078	−	0.744023i
$330$	−6.86510	−	4.87660i	−0.377911	−	0.268448i
$331$	−10.4741			−0.575708			−0.287854	−	0.957674i	$-0.592942\pi$
$331$	−10.4741			−0.575708			−0.287854	+	0.957674i	$0.592942\pi$
$332$	21.4014	−	7.46284i	1.17455	−	0.409577i
$333$			2.21144i			0.121186i
$334$	11.6841	−	16.4485i	0.639328	−	0.900023i
$335$	−10.0435			−0.548733
$336$	−5.68477	+	8.92656i	−0.310129	+	0.486984i
$337$	6.62370			0.360816			0.180408	−	0.983592i	$-0.442258\pi$
$337$	6.62370			0.360816			0.180408	+	0.983592i	$0.442258\pi$
$338$	1.63250	−	2.29818i	0.0887965	−	0.125004i
$339$			2.78366i			0.151188i
$340$	5.02358	−	1.75177i	0.272442	−	0.0950029i
$341$	−33.6760			−1.82366
$342$	7.16362	+	5.08865i	0.387364	+	0.275163i
$343$	15.5647	+	10.0370i	0.840413	+	0.541946i
$344$	−14.0289	−	4.06617i	−0.756387	−	0.219233i
$345$	4.60261			0.247796
$346$	−12.9476	+	18.2272i	−0.696069	+	0.979901i
$347$	8.44117			0.453146			0.226573	−	0.973994i	$-0.427248\pi$
$347$	8.44117			0.453146			0.226573	+	0.973994i	$0.427248\pi$
$348$	0.381676	+	1.09454i	0.0204600	+	0.0586735i
$349$	−15.7699			−0.844144			−0.422072	−	0.906562i	$-0.638697\pi$
$349$	−15.7699			−0.844144			−0.422072	+	0.906562i	$0.638697\pi$
$350$	−3.59077	−	1.05183i	−0.191935	−	0.0562227i
$351$			3.87212i			0.206679i
$352$	−1.79824	−	33.6354i	−0.0958466	−	1.79277i
$353$			14.0292i			0.746698i	0.927691	+	0.373349i	$0.121791\pi$
$353$			14.0292i			0.746698i	−0.927691	+	0.373349i	$0.878209\pi$
$354$	8.81311	−	12.4068i	0.468412	−	0.659413i
$355$		−	0.496099i		−	0.0263302i
$356$	20.5697	−	7.17284i	1.09019	−	0.380160i
$357$	2.29847	+	6.65213i	0.121648	+	0.352068i
$358$	−20.4817	+	28.8335i	−1.08249	+	1.52390i
$359$			27.5646i			1.45480i	0.686213	+	0.727401i	$0.259272\pi$
$359$			27.5646i			1.45480i	−0.686213	+	0.727401i	$0.740728\pi$
$360$	2.71662	+	0.787391i	0.143178	+	0.0414992i
$361$	−19.6059			−1.03189
$362$	−6.23721	+	8.78052i	−0.327820	+	0.461494i
$363$			24.4554i			1.28358i
$364$	16.0828	−	12.6948i	0.842967	−	0.665386i
$365$			2.04057i			0.106808i
$366$	−12.6204	−	8.96482i	−0.659677	−	0.468599i
$367$	2.31358			0.120768			0.0603839	−	0.998175i	$-0.480768\pi$
$367$	2.31358			0.120768			0.0603839	+	0.998175i	$0.480768\pi$
$368$	11.4478	+	14.4185i	0.596755	+	0.751618i
$369$		−	5.75803i		−	0.299751i
$370$	−2.54965	−	1.81114i	−0.132550	−	0.0941565i
$371$	−25.7900	+	8.91108i	−1.33895	+	0.462640i
$372$	10.6805	−	3.72438i	0.553757	−	0.193100i
$373$			1.92416i			0.0996291i	0.998758	+	0.0498145i	$0.0158630\pi$
$373$			1.92416i			0.0996291i	−0.998758	+	0.0498145i	$0.984137\pi$
$374$	−18.2620	−	12.9724i	−0.944307	−	0.670785i
$375$			1.00000i			0.0516398i
$376$	−14.6607	−	4.24928i	−0.756066	−	0.219140i
$377$		−	2.24424i		−	0.115584i
$378$	−1.05183	+	3.59077i	−0.0541003	+	0.184689i
$379$	29.2829			1.50416			0.752082	−	0.659070i	$-0.229050\pi$
$379$	29.2829			1.50416			0.752082	+	0.659070i	$0.229050\pi$
$380$	−11.7338	+	4.09168i	−0.601931	+	0.209899i
$381$	13.3363			0.683238
$382$	3.33578	+	2.36956i	0.170673	+	0.121237i
$383$	1.37050			0.0700293			0.0350146	−	0.999387i	$-0.488852\pi$
$383$	1.37050			0.0700293			0.0350146	+	0.999387i	$0.488852\pi$
$384$	4.29020	+	10.4687i	0.218934	+	0.534230i
$385$	5.14492	+	14.8902i	0.262209	+	0.758874i
$386$	3.86777	−	5.44491i	0.196865	−	0.277139i
$387$	−5.16410			−0.262506
$388$	−30.7129	+	10.7099i	−1.55921	+	0.543711i
$389$			17.9104i			0.908094i	0.890978	+	0.454047i	$0.150020\pi$
$389$			17.9104i			0.908094i	−0.890978	+	0.454047i	$0.849980\pi$
$390$	−4.46431	−	3.17121i	−0.226059	−	0.160580i
$391$	12.2435			0.619182
$392$	18.3626	−	7.40360i	0.927454	−	0.373938i
$393$	−7.81808			−0.394370
$394$	8.04825	+	5.71704i	0.405465	+	0.288021i
$395$		−	10.6941i		−	0.538078i
$396$	−3.92117	−	11.2448i	−0.197046	−	0.565074i
$397$	7.24462			0.363597			0.181799	−	0.983336i	$-0.441808\pi$
$397$	7.24462			0.363597			0.181799	+	0.983336i	$0.441808\pi$
$398$	−22.0820	+	31.0863i	−1.10687	+	1.55821i
$399$	−5.36864	−	15.5377i	−0.268768	−	0.777856i
$400$	−3.13268	+	2.48723i	−0.156634	+	0.124361i
$401$	19.6062			0.979089			0.489545	−	0.871978i	$-0.337163\pi$
$401$	19.6062			0.979089			0.489545	+	0.871978i	$0.337163\pi$
$402$	−11.5795	−	8.22544i	−0.577532	−	0.410248i
$403$	−21.8992			−1.09088
$404$	0.234374	+	0.672120i	0.0116605	+	0.0334392i
$405$	1.00000			0.0496904
$406$	0.609630	−	2.08117i	0.0302554	−	0.103287i
$407$			13.1679i			0.652709i
$408$	7.22654	+	2.09456i	0.357767	+	0.103696i
$409$			10.0037i			0.494652i	0.968932	+	0.247326i	$0.0795518\pi$
$409$			10.0037i			0.494652i	−0.968932	+	0.247326i	$0.920448\pi$
$410$	6.63865	+	4.71574i	0.327859	+	0.232894i
$411$			14.6304i			0.721662i
$412$	−0.357197	−	1.02434i	−0.0175978	−	0.0504657i
$413$	−26.9099	+	9.29803i	−1.32415	+	0.457526i
$414$	5.30653	+	3.76947i	0.260801	+	0.185259i
$415$			11.3326i			0.556296i
$416$	−1.16938	−	21.8728i	−0.0573336	−	1.07240i
$417$	−11.6895			−0.572439
$418$	42.6554	+	30.3001i	2.08634	+	1.48203i
$419$		−	16.1466i		−	0.788811i	−0.918937	−	0.394405i	$-0.870951\pi$
$419$		−	16.1466i		−	0.788811i	0.918937	−	0.394405i	$-0.129049\pi$
$420$	−3.27850	−	4.15348i	−0.159975	−	0.202669i
$421$			15.7233i			0.766309i	0.923684	+	0.383155i	$0.125162\pi$
$421$			15.7233i			0.766309i	−0.923684	+	0.383155i	$0.874838\pi$
$422$	−10.1190	+	14.2452i	−0.492586	+	0.693444i
$423$	−5.39666			−0.262395
$424$	−8.12051	+	28.0170i	−0.394367	+	1.36063i
$425$			2.66013i			0.129035i
$426$	0.406298	−	0.571971i	0.0196852	−	0.0277121i
$427$	9.45809	+	27.3732i	0.457709	+	1.32468i
$428$	−8.73789	−	25.0578i	−0.422362	−	1.21122i
$429$			23.0563i			1.11317i
$430$	4.22932	−	5.95388i	0.203956	−	0.287122i
$431$			26.5802i			1.28032i	0.768240	+	0.640162i	$0.221133\pi$
$431$			26.5802i			1.28032i	−0.768240	+	0.640162i	$0.778867\pi$
$432$	2.48723	+	3.13268i	0.119667	+	0.150721i
$433$		−	14.6714i		−	0.705062i	−0.935800	−	0.352531i	$-0.885321\pi$
$433$		−	14.6714i		−	0.705062i	0.935800	−	0.352531i	$-0.114679\pi$
$434$	−20.3080	−	5.94874i	−0.974815	−	0.285549i
$435$	−0.579589			−0.0277892
$436$	−10.2090	+	3.55998i	−0.488924	+	0.170492i
$437$	−28.5977			−1.36801
$438$	−1.67119	+	2.35265i	−0.0798528	+	0.112414i
$439$	1.65415			0.0789484			0.0394742	−	0.999221i	$-0.487432\pi$
$439$	1.65415			0.0789484			0.0394742	+	0.999221i	$0.487432\pi$
$440$	16.1759	+	4.68848i	0.771158	+	0.223514i
$441$	5.50685	−	4.32142i	0.262231	−	0.205782i
$442$	−11.8756	−	8.43581i	−0.564866	−	0.401251i
$443$	−30.7651			−1.46169			−0.730846	−	0.682542i	$-0.760874\pi$
$443$	−30.7651			−1.46169			−0.730846	+	0.682542i	$0.760874\pi$
$444$	−1.45630	−	4.17625i	−0.0691128	−	0.198196i
$445$			10.8922i			0.516341i
$446$	−17.7712	+	25.0177i	−0.841492	+	1.18462i
$447$	−5.32066			−0.251658
$448$	4.85715	−	20.6012i	0.229479	−	0.973314i
$449$	−16.0095			−0.755536			−0.377768	−	0.925900i	$-0.623308\pi$
$449$	−16.0095			−0.755536			−0.377768	+	0.925900i	$0.623308\pi$
$450$	−0.818985	+	1.15294i	−0.0386073	+	0.0543500i
$451$		−	34.2859i		−	1.61446i
$452$	−1.83312	−	5.25688i	−0.0862227	−	0.247263i
$453$	19.6499			0.923231
$454$	−3.23353	−	2.29693i	−0.151757	−	0.107800i
$455$	3.34569	+	9.68295i	0.156849	+	0.453944i
$456$	−16.8793	−	4.89235i	−0.790448	−	0.229105i
$457$	−22.1590			−1.03655			−0.518277	−	0.855213i	$-0.673426\pi$
$457$	−22.1590			−1.03655			−0.518277	+	0.855213i	$0.673426\pi$
$458$	22.2144	−	31.2726i	1.03801	−	1.46127i
$459$	2.66013			0.124164
$460$	−8.69193	+	3.03095i	−0.405263	+	0.141319i
$461$	−5.74707			−0.267668			−0.133834	−	0.991004i	$-0.542729\pi$
$461$	−5.74707			−0.267668			−0.133834	+	0.991004i	$0.542729\pi$
$462$	−6.26307	+	21.3811i	−0.291384	+	0.994737i
$463$			9.66858i			0.449337i	0.974435	+	0.224669i	$0.0721299\pi$
$463$			9.66858i			0.449337i	−0.974435	+	0.224669i	$0.927870\pi$
$464$	−1.44157	−	1.81567i	−0.0669232	−	0.0842903i
$465$			5.65561i			0.262272i
$466$	12.6578	−	17.8192i	0.586360	−	0.825457i
$467$		−	29.3178i		−	1.35667i	−0.734754	−	0.678333i	$-0.762703\pi$
$467$		−	29.3178i		−	1.35667i	0.734754	−	0.678333i	$-0.237297\pi$
$468$	−2.54990	−	7.31241i	−0.117869	−	0.338016i
$469$	8.67802	+	25.1155i	0.400714	+	1.15973i
$470$	4.41978	−	6.22201i	0.203869	−	0.287000i
$471$			17.2576i			0.795190i
$472$	−8.47314	+	29.2336i	−0.390008	+	1.34559i
$473$	−30.7493			−1.41386
$474$	8.75830	−	12.3296i	0.402282	−	0.566318i
$475$		−	6.21337i		−	0.285089i
$476$	−8.72123	−	11.0488i	−0.399737	−	0.506420i
$477$			10.3132i			0.472208i
$478$	15.5336	+	11.0342i	0.710488	+	0.504693i
$479$	−10.9088			−0.498435			−0.249218	−	0.968447i	$-0.580173\pi$
$479$	−10.9088			−0.498435			−0.249218	+	0.968447i	$0.580173\pi$
$480$	−5.64879	+	0.302000i	−0.257831	+	0.0137843i
$481$			8.56297i			0.390438i
$482$	0.941661	+	0.668905i	0.0428915	+	0.0304678i
$483$	−3.97688	−	11.5097i	−0.180954	−	0.523709i
$484$	−16.1046	−	46.1834i	−0.732026	−	2.09925i
$485$		−	16.2633i		−	0.738480i
$486$	1.15294	+	0.818985i	0.0522983	+	0.0371499i
$487$		−	10.3951i		−	0.471049i	−0.971868	−	0.235525i	$-0.924319\pi$
$487$		−	10.3951i		−	0.471049i	0.971868	−	0.235525i	$-0.0756808\pi$
$488$	29.7368	+	8.61899i	1.34612	+	0.390164i
$489$			1.54126i			0.0696982i
$490$	0.472300	+	9.88822i	0.0213363	+	0.446704i
$491$	27.5158			1.24177			0.620886	−	0.783901i	$-0.286773\pi$
$491$	27.5158			1.24177			0.620886	+	0.783901i	$0.286773\pi$
$492$	3.79183	+	10.8739i	0.170949	+	0.490233i
$493$	−1.54178			−0.0694383
$494$	27.7384	+	19.7039i	1.24801	+	0.886519i
$495$	5.95444			0.267632
$496$	−17.7172	+	14.0668i	−0.795526	+	0.631617i
$497$	−1.24059	+	0.428653i	−0.0556480	+	0.0192277i
$498$	−9.28124	+	13.0658i	−0.415902	+	0.585492i
$499$	−42.4025			−1.89820			−0.949099	−	0.314977i	$-0.898003\pi$
$499$	−42.4025			−1.89820			−0.949099	+	0.314977i	$0.898003\pi$
$500$	−0.658528	−	1.88848i	−0.0294503	−	0.0844552i
$501$			14.2666i			0.637386i
$502$	−23.7725	−	16.8867i	−1.06102	−	0.753692i
$503$	14.1835			0.632409			0.316204	−	0.948691i	$-0.397591\pi$
$503$	14.1835			0.632409			0.316204	+	0.948691i	$0.397591\pi$
$504$	−0.378268	−	7.47375i	−0.0168494	−	0.332907i
$505$	−0.355906			−0.0158376
$506$	31.5974	+	22.4451i	1.40468	+	0.997806i
$507$			1.99333i			0.0885267i
$508$	−25.1852	+	8.78231i	−1.11741	+	0.389652i
$509$	22.8265			1.01177			0.505884	−	0.862601i	$-0.331166\pi$
$509$	22.8265			1.01177			0.505884	+	0.862601i	$0.331166\pi$
$510$	−2.17860	+	3.06696i	−0.0964701	+	0.135807i
$511$	5.10282	−	1.76315i	0.225735	−	0.0779970i
$512$	−14.9959	−	16.9447i	−0.662731	−	0.748857i
$513$	−6.21337			−0.274327
$514$	−16.8340	−	11.9580i	−0.742517	−	0.527445i
$515$	0.542418			0.0239018
$516$	9.75227	−	3.40070i	0.429320	−	0.149708i
$517$	−32.1341			−1.41326
$518$	−2.32606	+	7.94078i	−0.102201	+	0.348898i
$519$		−	15.8094i		−	0.693955i
$520$	10.5191	+	3.04888i	0.461292	+	0.133702i
$521$		−	33.5925i		−	1.47172i	−0.677136	−	0.735858i	$-0.736779\pi$
$521$		−	33.5925i		−	1.47172i	0.677136	−	0.735858i	$-0.263221\pi$
$522$	−0.668230	−	0.474675i	−0.0292476	−	0.0207759i
$523$			42.5343i			1.85990i	0.367691	+	0.929948i	$0.380149\pi$
$523$			42.5343i			1.85990i	−0.367691	+	0.929948i	$0.619851\pi$
$524$	14.7643	−	5.14842i	0.644979	−	0.224910i
$525$	2.50068	−	0.864047i	0.109139	−	0.0377101i
$526$	−15.7474	−	11.1861i	−0.686618	−	0.487737i
$527$			15.0446i			0.655354i
$528$	14.8101	+	18.6534i	0.644525	+	0.811784i
$529$	1.81594			0.0789539
$530$	−11.8905	−	8.44634i	−0.516488	−	0.366886i
$531$			10.7610i			0.466989i
$532$	20.3705	+	25.8071i	0.883175	+	1.11888i
$533$		−	22.2958i		−	0.965738i
$534$	−8.92057	+	12.5581i	−0.386031	+	0.543440i
$535$	13.2688			0.573661
$536$	27.2842	+	7.90813i	1.17850	+	0.341579i
$537$		−	25.0087i		−	1.07921i
$538$	−14.7759	+	20.8010i	−0.637035	+	0.896795i
$539$	32.7902	−	25.7316i	1.41237	−	1.10834i
$540$	−1.88848	+	0.658528i	−0.0812671	+	0.0283385i
$541$		−	26.5075i		−	1.13965i	−0.821767	−	0.569824i	$-0.807011\pi$
$541$		−	26.5075i		−	1.13965i	0.821767	−	0.569824i	$-0.192989\pi$
$542$	−22.8506	+	32.1683i	−0.981519	+	1.38175i
$543$		−	7.61578i		−	0.326825i
$544$	−15.0265	+	0.803358i	−0.644255	+	0.0344437i
$545$		−	5.40596i		−	0.231566i
$546$	−4.07282	+	13.9039i	−0.174300	+	0.595032i
$547$	46.2467			1.97737			0.988684	−	0.150012i	$-0.0479314\pi$
$547$	46.2467			1.97737			0.988684	+	0.150012i	$0.0479314\pi$
$548$	−9.63450	−	27.6291i	−0.411565	−	1.18026i
$549$	10.9463			0.467175
$550$	−4.87660	+	6.86510i	−0.207939	+	0.292729i
$551$	3.60120			0.153416
$552$	−12.5035	−	3.62406i	−0.532186	−	0.154250i
$553$	−26.7426	+	9.24020i	−1.13721	+	0.392933i
$554$	−4.87561	−	3.46337i	−0.207145	−	0.147145i
$555$	2.21144			0.0938704
$556$	22.0754	−	7.69788i	0.936205	−	0.326463i
$557$		−	22.8146i		−	0.966686i	−0.875431	−	0.483343i	$-0.839422\pi$
$557$		−	22.8146i		−	0.966686i	0.875431	−	0.483343i	$-0.160578\pi$
$558$	−4.63185	+	6.52056i	−0.196082	+	0.276037i
$559$	−19.9960			−0.845741
$560$	8.92656	+	5.68477i	0.377216	+	0.240225i
$561$	15.8396			0.668747
$562$	−1.14934	+	1.61801i	−0.0484822	+	0.0682514i
$563$			26.9029i			1.13382i	0.823779	+	0.566911i	$0.191862\pi$
$563$			26.9029i			1.13382i	−0.823779	+	0.566911i	$0.808138\pi$
$564$	10.1915	−	3.55385i	0.429138	−	0.149644i
$565$	2.78366			0.117110
$566$	0.114704	+	0.0814792i	0.00482135	+	0.00342483i
$567$	−0.864047	−	2.50068i	−0.0362866	−	0.105019i
$568$	−0.390624	+	1.34771i	−0.0163902	+	0.0565488i
$569$	−6.63935			−0.278336			−0.139168	−	0.990269i	$-0.544443\pi$
$569$	−6.63935			−0.278336			−0.139168	+	0.990269i	$0.544443\pi$
$570$	5.08865	−	7.16362i	0.213140	−	0.300051i
$571$	−15.3607			−0.642827			−0.321413	−	0.946939i	$-0.604158\pi$
$571$	−15.3607			−0.642827			−0.321413	+	0.946939i	$0.604158\pi$
$572$	−15.1832	−	43.5413i	−0.634843	−	1.82055i
$573$	−2.89329			−0.120869
$574$	6.05647	−	20.6758i	0.252792	−	0.862991i
$575$		−	4.60261i		−	0.191942i
$576$	−6.76003	−	4.27808i	−0.281668	−	0.178253i
$577$		−	9.64106i		−	0.401362i	−0.979657	−	0.200681i	$-0.935684\pi$
$577$		−	9.64106i		−	0.401362i	0.979657	−	0.200681i	$-0.0643155\pi$
$578$	8.12739	−	11.4414i	0.338055	−	0.475901i
$579$			4.72265i			0.196266i
$580$	1.09454	−	0.381676i	0.0454483	−	0.0158482i
$581$	28.3393	−	9.79191i	1.17571	−	0.406237i
$582$	13.3194	−	18.7506i	0.552108	−	0.777237i
$583$			61.4093i			2.54331i
$584$	1.60673	−	5.54345i	0.0664868	−	0.229389i
$585$	3.87212			0.160093
$586$	23.2278	−	32.6993i	0.959533	−	1.35080i
$587$		−	36.4253i		−	1.50343i	−0.659487	−	0.751716i	$-0.729227\pi$
$587$		−	36.4253i		−	1.50343i	0.659487	−	0.751716i	$-0.270773\pi$
$588$	−7.55377	+	11.7873i	−0.311512	+	0.486100i
$589$		−	35.1403i		−	1.44793i
$590$	−12.4068	−	8.81311i	−0.510779	−	0.362830i
$591$	−6.98065			−0.287146
$592$	5.50036	+	6.92774i	0.226063	+	0.284728i
$593$		−	3.22129i		−	0.132282i	−0.997810	−	0.0661412i	$-0.978931\pi$
$593$		−	3.22129i		−	0.132282i	0.997810	−	0.0661412i	$-0.0210688\pi$
$594$	6.86510	+	4.87660i	0.281678	+	0.200089i
$595$	6.65213	−	2.29847i	0.272711	−	0.0942282i
$596$	10.0479	−	3.50380i	0.411579	−	0.143521i
$597$		−	26.9627i		−	1.10351i
$598$	20.5475	+	14.5959i	0.840250	+	0.596869i
$599$		−	37.8832i		−	1.54787i	−0.633267	−	0.773933i	$-0.718286\pi$
$599$		−	37.8832i		−	1.54787i	0.633267	−	0.773933i	$-0.281714\pi$
$600$	0.787391	−	2.71662i	0.0321451	−	0.110905i
$601$		−	16.4056i		−	0.669197i	−0.942361	−	0.334598i	$-0.891399\pi$
$601$		−	16.4056i		−	0.669197i	0.942361	−	0.334598i	$-0.108601\pi$
$602$	−18.5431	−	5.43176i	−0.755761	−	0.221382i
$603$	10.0435			0.409001
$604$	−37.1083	+	12.9400i	−1.50991	+	0.526521i
$605$	24.4554			0.994253
$606$	−0.410337	−	0.291482i	−0.0166688	−	0.0118406i
$607$	−5.05358			−0.205119			−0.102559	−	0.994727i	$-0.532703\pi$
$607$	−5.05358			−0.205119			−0.102559	+	0.994727i	$0.532703\pi$
$608$	35.0980	−	1.87644i	1.42341	−	0.0760995i
$609$	0.500792	+	1.44937i	0.0202931	+	0.0587314i
$610$	−8.96482	+	12.6204i	−0.362975	+	0.510983i
$611$	−20.8965			−0.845383
$612$	−5.02358	+	1.75177i	−0.203066	+	0.0708110i
$613$		−	29.9222i		−	1.20855i	−0.796777	−	0.604273i	$-0.793464\pi$
$613$		−	29.9222i		−	1.20855i	0.796777	−	0.604273i	$-0.206536\pi$
$614$	−21.8083	−	15.4915i	−0.880113	−	0.625185i
$615$	−5.75803			−0.232186
$616$	−2.25238	−	44.5020i	−0.0907509	−	1.79304i
$617$	4.59051			0.184807			0.0924034	−	0.995722i	$-0.470545\pi$
$617$	4.59051			0.184807			0.0924034	+	0.995722i	$0.470545\pi$
$618$	0.625373	+	0.444232i	0.0251562	+	0.0178696i
$619$		−	19.6151i		−	0.788396i	−0.919026	−	0.394198i	$-0.871022\pi$
$619$		−	19.6151i		−	0.788396i	0.919026	−	0.394198i	$-0.128978\pi$
$620$	−3.72438	−	10.6805i	−0.149575	−	0.428938i
$621$	−4.60261			−0.184697
$622$	−6.58897	+	9.27572i	−0.264194	+	0.371922i
$623$	27.2380	−	9.41140i	1.09127	−	0.377060i
$624$	9.63085	+	12.1301i	0.385543	+	0.485594i
$625$	1.00000			0.0400000
$626$	−15.8254	−	11.2415i	−0.632511	−	0.449302i
$627$	−36.9971			−1.47752
$628$	−11.3646	−	32.5906i	−0.453498	−	1.30051i
$629$	5.88271			0.234559
$630$	3.59077	+	1.05183i	0.143060	+	0.0419059i
$631$		−	18.1499i		−	0.722537i	−0.932462	−	0.361268i	$-0.882344\pi$
$631$		−	18.1499i		−	0.722537i	0.932462	−	0.361268i	$-0.117656\pi$
$632$	−8.42044	+	29.0518i	−0.334947	+	1.15562i
$633$		−	12.3556i		−	0.491089i
$634$	−4.30833	−	3.06041i	−0.171106	−	0.121544i
$635$		−	13.3363i		−	0.529234i
$636$	−6.79152	−	19.4762i	−0.269301	−	0.772282i
$637$	21.3232	−	16.7331i	0.844855	−	0.662988i
$638$	−3.97894	−	2.82642i	−0.157528	−	0.111899i
$639$			0.496099i			0.0196254i
$640$	10.4687	−	4.29020i	0.413813	−	0.169585i
$641$	−47.0253			−1.85739			−0.928694	−	0.370847i	$-0.879068\pi$
$641$	−47.0253			−1.85739			−0.928694	+	0.370847i	$0.879068\pi$
$642$	15.2981	+	10.8670i	0.603768	+	0.428885i
$643$			50.0444i			1.97356i	0.162073	+	0.986779i	$0.448182\pi$
$643$			50.0444i			1.97356i	−0.162073	+	0.986779i	$0.551818\pi$
$644$	15.0897	+	19.1169i	0.594617	+	0.753311i
$645$			5.16410i			0.203336i
$646$	13.5364	−	19.0561i	0.532584	−	0.749753i
$647$	−12.3404			−0.485150			−0.242575	−	0.970133i	$-0.577992\pi$
$647$	−12.3404			−0.485150			−0.242575	+	0.970133i	$0.577992\pi$
$648$	−2.71662	−	0.787391i	−0.106719	−	0.0309317i
$649$			64.0759i			2.51520i
$650$	−3.17121	+	4.46431i	−0.124385	+	0.175105i
$651$	14.1429	−	4.88671i	0.554303	−	0.191525i
$652$	−1.01496	−	2.91063i	−0.0397490	−	0.113989i
$653$		−	8.28124i		−	0.324070i	−0.986785	−	0.162035i	$-0.948194\pi$
$653$		−	8.28124i		−	0.324070i	0.986785	−	0.162035i	$-0.0518058\pi$
$654$	4.42740	−	6.23274i	0.173125	−	0.243719i
$655$			7.81808i			0.305478i
$656$	−14.3215	−	18.0381i	−0.559162	−	0.704269i
$657$		−	2.04057i		−	0.0796102i
$658$	−19.3782	−	5.67637i	−0.755440	−	0.221288i
$659$	44.4516			1.73159			0.865795	−	0.500399i	$-0.166813\pi$
$659$	44.4516			1.73159			0.865795	+	0.500399i	$0.166813\pi$
$660$	−11.2448	+	3.92117i	−0.437704	+	0.152631i
$661$	30.2441			1.17636			0.588180	−	0.808730i	$-0.299845\pi$
$661$	30.2441			1.17636			0.588180	+	0.808730i	$0.299845\pi$
$662$	−8.57812	+	12.0760i	−0.333398	+	0.469346i
$663$	10.3003			0.400032
$664$	8.92320	−	30.7864i	0.346287	−	1.19474i
$665$	−15.5377	+	5.36864i	−0.602525	+	0.208187i
$666$	2.54965	+	1.81114i	0.0987970	+	0.0701801i
$667$	2.66763			0.103291
$668$	−9.39497	−	26.9422i	−0.363502	−	1.04242i
$669$		−	21.6991i		−	0.838935i
$670$	−8.22544	+	11.5795i	−0.317776	+	0.447354i
$671$	65.1789			2.51620
$672$	5.63602	+	13.8649i	0.217414	+	0.534850i
$673$	12.7940			0.493173			0.246587	−	0.969121i	$-0.420691\pi$
$673$	12.7940			0.493173			0.246587	+	0.969121i	$0.420691\pi$
$674$	5.42471	−	7.63671i	0.208952	−	0.294155i
$675$		−	1.00000i		−	0.0384900i
$676$	−1.31266	−	3.76435i	−0.0504870	−	0.144783i
$677$	−33.9939			−1.30649			−0.653246	−	0.757145i	$-0.726593\pi$
$677$	−33.9939			−1.30649			−0.653246	+	0.757145i	$0.726593\pi$
$678$	3.20939	+	2.27978i	0.123256	+	0.0875543i
$679$	−40.6695	+	14.0523i	−1.56075	+	0.539277i
$680$	2.09456	−	7.22654i	0.0803227	−	0.277125i
$681$	2.80461			0.107473
$682$	−27.5801	+	38.8263i	−1.05610	+	1.48674i
$683$	26.2962			1.00619			0.503097	−	0.864230i	$-0.332194\pi$
$683$	26.2962			1.00619			0.503097	+	0.864230i	$0.332194\pi$
$684$	11.7338	−	4.09168i	0.448653	−	0.156449i
$685$	14.6304			0.558997
$686$	24.3192	−	9.72496i	0.928513	−	0.371301i
$687$			27.1243i			1.03485i
$688$	−16.1775	+	12.8443i	−0.616760	+	0.489684i
$689$			39.9339i			1.52136i
$690$	3.76947	−	5.30653i	0.143501	−	0.202016i
$691$			21.2358i			0.807846i	0.914793	+	0.403923i	$0.132354\pi$
$691$			21.2358i			0.807846i	−0.914793	+	0.403923i	$0.867646\pi$
$692$	10.4109	+	29.8556i	0.395764	+	1.13494i
$693$	−5.14492	−	14.8902i	−0.195439	−	0.565631i
$694$	6.91319	−	9.73214i	0.262421	−	0.369427i
$695$			11.6895i			0.443409i
$696$	1.57452	+	0.456363i	0.0596821	+	0.0172984i
$697$	−15.3171			−0.580176
$698$	−12.9153	+	18.1817i	−0.488852	+	0.688188i
$699$			15.4554i			0.584579i
$700$	−4.15348	+	3.27850i	−0.156987	+	0.123916i
$701$			5.53950i			0.209224i	0.994513	+	0.104612i	$0.0333601\pi$
$701$			5.53950i			0.209224i	−0.994513	+	0.104612i	$0.966640\pi$
$702$	4.46431	+	3.17121i	0.168495	+	0.119690i
$703$	−13.7405			−0.518232
$704$	−40.2522	−	25.4736i	−1.51706	−	0.960073i
$705$			5.39666i			0.203250i
$706$	16.1748	+	11.4897i	0.608745	+	0.432420i
$707$	0.307519	+	0.890008i	0.0115655	+	0.0334722i
$708$	−7.08644	−	20.3219i	−0.266325	−	0.763745i
$709$		−	34.3240i		−	1.28906i	−0.764577	−	0.644532i	$-0.777052\pi$
$709$		−	34.3240i		−	1.28906i	0.764577	−	0.644532i	$-0.222948\pi$
$710$	−0.571971	−	0.406298i	−0.0214657	−	0.0152481i
$711$			10.6941i			0.401060i
$712$	8.57645	−	29.5900i	0.321416	−	1.10893i
$713$		−	26.0306i		−	0.974853i
$714$	9.55191	+	2.79800i	0.357471	+	0.104713i
$715$	23.0563			0.862258
$716$	16.4689	+	47.2283i	0.615473	+	1.76501i
$717$	−13.4730			−0.503159
$718$	31.7802	+	22.5750i	1.18603	+	0.842490i
$719$	−18.8344			−0.702406			−0.351203	−	0.936299i	$-0.614227\pi$
$719$	−18.8344			−0.702406			−0.351203	+	0.936299i	$0.614227\pi$
$720$	3.13268	−	2.48723i	0.116748	−	0.0926935i
$721$	−0.468674	−	1.35642i	−0.0174543	−	0.0505155i
$722$	−16.0569	+	22.6044i	−0.597577	+	0.841248i
$723$	−0.816750			−0.0303752
$724$	5.01521	+	14.3822i	0.186389	+	0.534511i
$725$			0.579589i			0.0215254i
$726$	28.1955	+	20.0286i	1.04643	+	0.743331i
$727$	25.9405			0.962081			0.481040	−	0.876698i	$-0.340259\pi$
$727$	25.9405			0.962081			0.481040	+	0.876698i	$0.340259\pi$
$728$	−1.46470	−	28.9393i	−0.0542854	−	1.07256i
$729$	−1.00000			−0.0370370
$730$	2.35265	+	1.67119i	0.0870754	+	0.0618537i
$731$			13.7371i			0.508087i
$732$	−20.6718	+	7.20842i	−0.764050	+	0.266431i
$733$	−35.4734			−1.31024			−0.655120	−	0.755525i	$-0.727382\pi$
$733$	−35.4734			−1.31024			−0.655120	+	0.755525i	$0.727382\pi$
$734$	1.89478	−	2.66741i	0.0699378	−	0.0984559i
$735$	−4.32142	−	5.50685i	−0.159398	−	0.203123i
$736$	25.9992	−	1.38999i	0.958343	−	0.0512357i
$737$	59.8032			2.20288
$738$	−6.63865	−	4.71574i	−0.244372	−	0.173589i
$739$	−15.5323			−0.571364			−0.285682	−	0.958324i	$-0.592220\pi$
$739$	−15.5323			−0.571364			−0.285682	+	0.958324i	$0.592220\pi$
$740$	−4.17625	+	1.45630i	−0.153522	+	0.0535345i
$741$	−24.0589			−0.883826
$742$	−10.8477	+	37.0323i	−0.398232	+	1.35950i
$743$			19.8936i			0.729824i	0.931042	+	0.364912i	$0.118901\pi$
$743$			19.8936i			0.729824i	−0.931042	+	0.364912i	$0.881099\pi$
$744$	4.45318	−	15.3641i	0.163261	−	0.563276i
$745$			5.32066i			0.194934i
$746$	2.21843	+	1.57585i	0.0812226	+	0.0576961i
$747$		−	11.3326i		−	0.414639i
$748$	−29.9126	+	10.4308i	−1.09371	+	0.381388i
$749$	−11.4649	−	33.1811i	−0.418918	−	1.21241i
$750$	1.15294	+	0.818985i	0.0420993	+	0.0299051i
$751$			0.113991i			0.00415958i	0.999998	+	0.00207979i	$0.000662018\pi$
$751$			0.113991i			0.00415958i	−0.999998	+	0.00207979i	$0.999338\pi$
$752$	−16.9060	+	13.4227i	−0.616499	+	0.489477i
$753$	20.6191			0.751402
$754$	−2.58747	−	1.83800i	−0.0942300	−	0.0669359i
$755$		−	19.6499i		−	0.715132i
$756$	3.27850	+	4.15348i	0.119238	+	0.151061i
$757$		−	7.67670i		−	0.279014i	−0.990221	−	0.139507i	$-0.955448\pi$
$757$		−	7.67670i		−	0.279014i	0.990221	−	0.139507i	$-0.0445518\pi$
$758$	23.9823	−	33.7614i	0.871076	−	1.22627i
$759$	−27.4060			−0.994775
$760$	−4.89235	+	16.8793i	−0.177464	+	0.612278i
$761$		−	4.87002i		−	0.176538i	−0.996097	−	0.0882690i	$-0.971866\pi$
$761$		−	4.87002i		−	0.176538i	0.996097	−	0.0882690i	$-0.0281335\pi$
$762$	10.9222	−	15.3759i	0.395670	−	0.557009i
$763$	−13.5186	+	4.67101i	−0.489407	+	0.169102i
$764$	5.46390	−	1.90531i	0.197677	−	0.0689317i
$765$		−	2.66013i		−	0.0961770i
$766$	1.12242	−	1.58010i	0.0405546	−	0.0570914i
$767$			41.6680i			1.50454i
$768$	15.5834	+	3.62739i	0.562317	+	0.130892i
$769$			16.1971i			0.584081i	0.956406	+	0.292041i	$0.0943342\pi$
$769$			16.1971i			0.584081i	−0.956406	+	0.292041i	$0.905666\pi$
$770$	21.3811	+	6.26307i	0.770520	+	0.225705i
$771$	14.6010			0.525842
$772$	−3.10999	−	8.91860i	−0.111931	−	0.320987i
$773$	−45.1867			−1.62525			−0.812626	−	0.582786i	$-0.801963\pi$
$773$	−45.1867			−1.62525			−0.812626	+	0.582786i	$0.801963\pi$
$774$	−4.22932	+	5.95388i	−0.152020	+	0.214008i
$775$	5.65561			0.203155
$776$	−12.8056	+	44.1813i	−0.459694	+	1.58601i
$777$	−1.91079	−	5.53012i	−0.0685492	−	0.198392i
$778$	20.6496	+	14.6683i	0.740323	+	0.525886i
$779$	35.7768			1.28184
$780$	−7.31241	+	2.54990i	−0.261826	+	0.0913011i
$781$			2.95399i			0.105702i
$782$	10.0273	−	14.1160i	0.358574	−	0.504788i
$783$	0.579589			0.0207128
$784$	6.50284	−	27.2344i	0.232244	−	0.972657i
$785$	17.2576			0.615951
$786$	−6.40289	+	9.01375i	−0.228383	+	0.321510i
$787$			12.9184i			0.460492i	0.973132	+	0.230246i	$0.0739531\pi$
$787$			12.9184i			0.460492i	−0.973132	+	0.230246i	$0.926047\pi$
$788$	13.1828	−	4.59695i	0.469617	−	0.163760i
$789$	13.6585			0.486255
$790$	−12.3296	−	8.75830i	−0.438668	−	0.311606i
$791$	−2.40522	−	6.96106i	−0.0855196	−	0.247507i
$792$	−16.1759	−	4.68848i	−0.574787	−	0.166598i
$793$	42.3853			1.50515
$794$	5.93323	−	8.35259i	0.210563	−	0.296422i
$795$	10.3132			0.365771
$796$	17.7557	+	50.9183i	0.629333	+	1.80475i
$797$	24.8008			0.878490			0.439245	−	0.898367i	$-0.355246\pi$
$797$	24.8008			0.878490			0.439245	+	0.898367i	$0.355246\pi$
$798$	−22.3108	−	6.53541i	−0.789793	−	0.231351i
$799$			14.3558i			0.507871i
$800$	0.302000	+	5.64879i	0.0106773	+	0.199715i
$801$		−	10.8922i		−	0.384858i
$802$	16.0572	−	22.6048i	0.567000	−	0.798202i
$803$		−	12.1505i		−	0.428780i
$804$	−18.9668	+	6.61390i	−0.668908	+	0.233254i
$805$	−11.5097	+	3.97688i	−0.405663	+	0.140166i
$806$	−17.9351	+	25.2484i	−0.631737	+	0.889337i
$807$		−	18.0418i		−	0.635100i
$808$	0.966861	+	0.280237i	0.0340140	+	0.00985871i
$809$	1.17852			0.0414346			0.0207173	−	0.999785i	$-0.493405\pi$
$809$	1.17852			0.0414346			0.0207173	+	0.999785i	$0.493405\pi$
$810$	0.818985	−	1.15294i	0.0287762	−	0.0405101i
$811$			36.4343i			1.27938i	0.768633	+	0.639690i	$0.220937\pi$
$811$			36.4343i			1.27938i	−0.768633	+	0.639690i	$0.779063\pi$
$812$	−1.90018	−	2.40731i	−0.0666834	−	0.0844801i
$813$		−	27.9012i		−	0.978537i
$814$	15.1818	+	10.7843i	0.532120	+	0.377990i
$815$	1.54126			0.0539880
$816$	8.33332	−	6.61634i	0.291725	−	0.231618i
$817$		−	32.0864i		−	1.12256i
$818$	11.5337	+	8.19289i	0.403265	+	0.286458i
$819$	−3.34569	−	9.68295i	−0.116908	−	0.338350i
$820$	10.8739	−	3.79183i	0.379733	−	0.132416i
$821$		−	22.0140i		−	0.768293i	−0.923272	−	0.384147i	$-0.874496\pi$
$821$		−	22.0140i		−	0.768293i	0.923272	−	0.384147i	$-0.125504\pi$
$822$	16.8679	+	11.9820i	0.588335	+	0.417921i
$823$		−	29.5887i		−	1.03140i	−0.856771	−	0.515698i	$-0.827533\pi$
$823$		−	29.5887i		−	1.03140i	0.856771	−	0.515698i	$-0.172467\pi$
$824$	−1.47354	−	0.427095i	−0.0513332	−	0.0148786i
$825$		−	5.95444i		−	0.207307i
$826$	−11.3188	+	38.6404i	−0.393830	+	1.34447i
$827$	43.2966			1.50557			0.752786	−	0.658265i	$-0.228710\pi$
$827$	43.2966			1.50557			0.752786	+	0.658265i	$0.228710\pi$
$828$	8.69193	−	3.03095i	0.302065	−	0.105333i
$829$	52.6765			1.82953			0.914766	−	0.403985i	$-0.132375\pi$
$829$	52.6765			1.82953			0.914766	+	0.403985i	$0.132375\pi$
$830$	13.0658	+	9.28124i	0.453520	+	0.322156i
$831$	4.22886			0.146698
$832$	−26.1757	−	16.5653i	−0.907478	−	0.574297i
$833$	−11.4955	−	14.6489i	−0.398296	−	0.507554i
$834$	−9.57354	+	13.4773i	−0.331505	+	0.466680i
$835$	14.2666			0.493717
$836$	69.8682	−	24.3636i	2.41644	−	0.842634i
$837$		−	5.65561i		−	0.195486i
$838$	−18.6160	−	13.2238i	−0.643078	−	0.456808i
$839$	−30.8293			−1.06435			−0.532173	−	0.846635i	$-0.678625\pi$
$839$	−30.8293			−1.06435			−0.532173	+	0.846635i	$0.678625\pi$
$840$	−7.47375	+	0.378268i	−0.257869	+	0.0130515i
$841$	28.6641			0.988416
$842$	18.1280	+	12.8772i	0.624733	+	0.443777i
$843$		−	1.40338i		−	0.0483349i
$844$	8.13648	+	23.3332i	0.280069	+	0.803161i
$845$	1.99333			0.0685725
$846$	−4.41978	+	6.22201i	−0.151955	+	0.213917i
$847$	−21.1306	−	61.1552i	−0.726056	−	2.10132i
$848$	25.6513	+	32.3079i	0.880868	+	1.10946i
$849$	−0.0994881			−0.00341442
$850$	3.06696	+	2.17860i	0.105196	+	0.0747254i
$851$	−10.1784			−0.348911
$852$	−0.326695	−	0.936871i	−0.0111924	−	0.0320967i
$853$	29.9493			1.02544			0.512722	−	0.858555i	$-0.328637\pi$
$853$	29.9493			1.02544			0.512722	+	0.858555i	$0.328637\pi$
$854$	39.3056	+	11.5136i	1.34501	+	0.393988i
$855$			6.21337i			0.212493i
$856$	−36.0463	−	10.4478i	−1.23204	−	0.357097i
$857$			50.9319i			1.73980i	0.493229	+	0.869899i	$0.335816\pi$
$857$			50.9319i			1.73980i	−0.493229	+	0.869899i	$0.664184\pi$
$858$	26.5825	+	18.8828i	0.907511	+	0.644648i
$859$			7.15532i			0.244136i	0.992522	+	0.122068i	$0.0389527\pi$
$859$			7.15532i			0.244136i	−0.992522	+	0.122068i	$0.961047\pi$
$860$	−3.40070	−	9.75227i	−0.115963	−	0.332550i
$861$	4.97521	+	14.3990i	0.169555	+	0.490717i
$862$	30.6453	+	21.7688i	1.04378	+	0.741448i
$863$		−	10.0924i		−	0.343548i	−0.985136	−	0.171774i	$-0.945050\pi$
$863$		−	10.0924i		−	0.343548i	0.985136	−	0.171774i	$-0.0549498\pi$
$864$	5.64879	−	0.302000i	0.192176	−	0.0102742i
$865$	−15.8094			−0.537535
$866$	−16.9152	−	12.0156i	−0.574801	−	0.408308i
$867$			9.92373i			0.337028i
$868$	−23.4905	+	18.5419i	−0.797318	+	0.629354i
$869$			63.6774i			2.16011i
$870$	−0.474675	+	0.668230i	−0.0160930	+	0.0226551i
$871$	38.8895			1.31772
$872$	−4.25661	+	14.6859i	−0.144147	+	0.497329i
$873$			16.2633i			0.550430i
$874$	−23.4211	+	32.9714i	−0.792231	+	1.11527i
$875$	−0.864047	−	2.50068i	−0.0292101	−	0.0845386i
$876$	1.34377	+	3.85357i	0.0454018	+	0.130200i
$877$			32.0740i			1.08306i	0.840681	+	0.541531i	$0.182155\pi$
$877$			32.0740i			1.08306i	−0.840681	+	0.541531i	$0.817845\pi$
$878$	1.35473	−	1.90713i	0.0457198	−	0.0643627i
$879$			28.3618i			0.956618i
$880$	18.6534	−	14.8101i	0.628805	−	0.499247i
$881$			21.1025i			0.710963i	0.934683	+	0.355481i	$0.115683\pi$
$881$			21.1025i			0.710963i	−0.934683	+	0.355481i	$0.884317\pi$
$882$	−0.472300	−	9.88822i	−0.0159032	−	0.332954i
$883$	−34.2127			−1.15135			−0.575674	−	0.817680i	$-0.695260\pi$
$883$	−34.2127			−1.15135			−0.575674	+	0.817680i	$0.695260\pi$
$884$	−19.4519	+	6.78306i	−0.654239	+	0.228139i
$885$	10.7610			0.361728
$886$	−25.1961	+	35.4702i	−0.846480	+	1.19164i
$887$	5.07770			0.170492			0.0852462	−	0.996360i	$-0.472832\pi$
$887$	5.07770			0.170492			0.0852462	+	0.996360i	$0.472832\pi$
$888$	−6.00764	−	1.74127i	−0.201603	−	0.0584332i
$889$	−33.3498	+	11.5232i	−1.11852	+	0.386474i
$890$	12.5581	+	8.92057i	0.420947	+	0.299018i
$891$	−5.95444			−0.199481
$892$	14.2895	+	40.9782i	0.478446	+	1.37205i
$893$		−	33.5314i		−	1.12209i
$894$	−4.35754	+	6.13438i	−0.145738	+	0.205164i
$895$	−25.0087			−0.835949
$896$	−19.7739	−	22.4720i	−0.660600	−	0.750738i
$897$	−17.8219			−0.595055
$898$	−13.1116	+	18.4580i	−0.437538	+	0.615950i
$899$			3.27793i			0.109325i
$900$	0.658528	+	1.88848i	0.0219509	+	0.0629492i
$901$	27.4344			0.913971
$902$	−39.5295	−	28.0796i	−1.31619	−	0.934949i
$903$	12.9138	−	4.46202i	0.429744	−	0.148487i
$904$	−7.56215	−	2.19183i	−0.251513	−	0.0728992i
$905$	−7.61578			−0.253157
$906$	16.0929	−	22.6551i	0.534652	−	0.752664i
$907$	4.81567			0.159902			0.0799509	−	0.996799i	$-0.474524\pi$
$907$	4.81567			0.159902			0.0799509	+	0.996799i	$0.474524\pi$
$908$	−5.29643	+	1.84691i	−0.175768	+	0.0612919i
$909$	0.355906			0.0118047
$910$	13.9039	+	4.07282i	0.460910	+	0.135013i
$911$		−	54.1431i		−	1.79384i	−0.442191	−	0.896921i	$-0.645799\pi$
$911$		−	54.1431i		−	1.79384i	0.442191	−	0.896921i	$-0.354201\pi$
$912$	−19.4645	+	15.4541i	−0.644534	+	0.511735i
$913$		−	67.4794i		−	2.23324i
$914$	−18.1479	+	25.5479i	−0.600279	+	0.845051i
$915$		−	10.9463i		−	0.361872i
$916$	−17.8621	−	51.2235i	−0.590180	−	1.69247i
$917$	19.5505	−	6.75519i	0.645616	−	0.223076i
$918$	2.17860	−	3.06696i	0.0719046	−	0.101225i
$919$		−	16.6473i		−	0.549144i	−0.961566	−	0.274572i	$-0.911464\pi$
$919$		−	16.6473i		−	0.549144i	0.961566	−	0.274572i	$-0.0885362\pi$
$920$	−3.62406	+	12.5035i	−0.119482	+	0.412230i
$921$	18.9155			0.623286
$922$	−4.70676	+	6.62601i	−0.155009	+	0.218216i
$923$			1.92096i			0.0632291i
$924$	19.5217	+	24.7317i	0.642215	+	0.813612i
$925$		−	2.21144i		−	0.0727117i
$926$	11.1473	+	7.91842i	0.366322	+	0.260215i
$927$	−0.542418			−0.0178153
$928$	−3.27398	+	0.175036i	−0.107474	+	0.00574583i
$929$			6.95181i			0.228081i	0.993476	+	0.114041i	$0.0363794\pi$
$929$			6.95181i			0.228081i	−0.993476	+	0.114041i	$0.963621\pi$
$930$	6.52056	+	4.63185i	0.213818	+	0.151885i
$931$	26.8505	+	34.2160i	0.879991	+	1.12139i
$932$	−10.1778	−	29.1872i	−0.333386	−	0.956060i
$933$		−	8.04529i		−	0.263391i
$934$	−33.8016	−	24.0108i	−1.10602	−	0.785659i
$935$		−	15.8396i		−	0.518009i
$936$	−10.5191	−	3.04888i	−0.343827	−	0.0996556i
$937$		−	15.5643i		−	0.508464i	−0.967143	−	0.254232i	$-0.918177\pi$
$937$		−	15.5643i		−	0.508464i	0.967143	−	0.254232i	$-0.0818227\pi$
$938$	36.0638	+	10.5640i	1.17752	+	0.344927i
$939$	13.7262			0.447937
$940$	−3.55385	−	10.1915i	−0.115914	−	0.332409i
$941$	−31.5509			−1.02853			−0.514264	−	0.857632i	$-0.671935\pi$
$941$	−31.5509			−1.02853			−0.514264	+	0.857632i	$0.671935\pi$
$942$	19.8970	+	14.1337i	0.648278	+	0.460502i
$943$	26.5020			0.863024
$944$	26.7651	+	33.7109i	0.871131	+	1.09720i
$945$	−2.50068	+	0.864047i	−0.0813473	+	0.0281074i
$946$	−25.1832	+	35.4520i	−0.818777	+	1.15265i
$947$	−22.1282			−0.719071			−0.359535	−	0.933131i	$-0.617065\pi$
$947$	−22.1282			−0.719071			−0.359535	+	0.933131i	$0.617065\pi$
$948$	−7.04236	−	20.1955i	−0.228725	−	0.655921i
$949$		−	7.90133i		−	0.256488i
$950$	−7.16362	−	5.08865i	−0.232419	−	0.165098i
$951$	3.73683			0.121175
$952$	−19.8811	+	1.00624i	−0.644350	+	0.0326125i
$953$	10.8508			0.351493			0.175747	−	0.984435i	$-0.443766\pi$
$953$	10.8508			0.351493			0.175747	+	0.984435i	$0.443766\pi$
$954$	11.8905	+	8.44634i	0.384968	+	0.273460i
$955$			2.89329i			0.0936245i
$956$	25.4435	−	8.87237i	0.822901	−	0.286953i
$957$	3.45113			0.111559
$958$	−8.93413	+	12.5771i	−0.288649	+	0.406349i
$959$	−12.6413	−	36.5859i	−0.408209	−	1.18142i
$960$	−4.27808	+	6.76003i	−0.138075	+	0.218179i
$961$	0.985880			0.0318026
$962$	9.87256	+	7.01294i	0.318304	+	0.226106i
$963$	−13.2688			−0.427582
$964$	1.54241	−	0.537852i	0.0496777	−	0.0173231i
$965$	4.72265			0.152027
$966$	−16.5269	−	4.84117i	−0.531746	−	0.155762i
$967$			8.51382i			0.273786i	0.990586	+	0.136893i	$0.0437116\pi$
$967$			8.51382i			0.273786i	−0.990586	+	0.136893i	$0.956288\pi$
$968$	−66.4360	−	19.2560i	−2.13533	−	0.618910i
$969$			16.5283i			0.530966i
$970$	−18.7506	−	13.3194i	−0.602045	−	0.427661i
$971$		−	8.02546i		−	0.257549i	−0.991674	−	0.128775i	$-0.958896\pi$
$971$		−	8.02546i		−	0.257549i	0.991674	−	0.128775i	$-0.0411044\pi$
$972$	1.88848	−	0.658528i	0.0605729	−	0.0211223i
$973$	29.2318	−	10.1003i	0.937129	−	0.323801i
$974$	−11.9849	−	8.51347i	−0.384023	−	0.272789i
$975$		−	3.87212i		−	0.124007i
$976$	34.2912	−	27.2259i	1.09763	−	0.871479i
$977$	34.4370			1.10174			0.550868	−	0.834592i	$-0.314297\pi$
$977$	34.4370			1.10174			0.550868	+	0.834592i	$0.314297\pi$
$978$	1.77698	+	1.26227i	0.0568215	+	0.0403629i
$979$		−	64.8572i		−	2.07284i
$980$	11.7873	+	7.55377i	0.376532	+	0.241296i
$981$			5.40596i			0.172599i
$982$	22.5350	−	31.7240i	0.719122	−	1.01235i
$983$	−35.2731			−1.12504			−0.562518	−	0.826785i	$-0.690167\pi$
$983$	−35.2731			−1.12504			−0.562518	+	0.826785i	$0.690167\pi$
$984$	15.6424	+	4.53382i	0.498661	+	0.144533i
$985$			6.98065i			0.222422i
$986$	−1.26269	+	1.77757i	−0.0402124	+	0.0566095i
$987$	13.4953	−	4.66297i	0.429562	−	0.148424i
$988$	45.4347	−	15.8435i	1.44547	−	0.504048i
$989$		−	23.7684i		−	0.755790i
$990$	4.87660	−	6.86510i	0.154988	−	0.218187i
$991$			56.1436i			1.78346i	0.452569	+	0.891729i	$0.350508\pi$
$991$			56.1436i			1.78346i	−0.452569	+	0.891729i	$0.649492\pi$
$992$	1.70799	+	31.9473i	0.0542288	+	1.01433i
$993$		−	10.4741i		−	0.332385i
$994$	−0.521812	+	1.78138i	−0.0165509	+	0.0565019i
$995$	−26.9627			−0.854774
$996$	7.46284	+	21.4014i	0.236469	+	0.678128i
$997$	3.80753			0.120586			0.0602928	−	0.998181i	$-0.480797\pi$
$997$	3.80753			0.120586			0.0602928	+	0.998181i	$0.480797\pi$
$998$	−34.7270	+	48.8875i	−1.09927	+	1.54751i
$999$	−2.21144			−0.0699669

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.z.d.811.19	yes	28
4.3	odd	2		3360.2.z.d.1231.19		28
7.6	odd	2		840.2.z.c.811.19	✓	28
8.3	odd	2		840.2.z.c.811.20	yes	28
8.5	even	2		3360.2.z.c.1231.9		28
28.27	even	2		3360.2.z.c.1231.10		28
56.13	odd	2		3360.2.z.d.1231.20		28
56.27	even	2	inner	840.2.z.d.811.20	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.z.c.811.19	✓	28	7.6	odd	2
840.2.z.c.811.20	yes	28	8.3	odd	2
840.2.z.d.811.19	yes	28	1.1	even	1	trivial
840.2.z.d.811.20	yes	28	56.27	even	2	inner
3360.2.z.c.1231.9		28	8.5	even	2
3360.2.z.c.1231.10		28	28.27	even	2
3360.2.z.d.1231.19		28	4.3	odd	2
3360.2.z.d.1231.20		28	56.13	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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.z (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.818985 - 1.15294i) q^{2} +1.00000i q^{3} +(-0.658528 - 1.88848i) q^{4} +1.00000 q^{5} +(1.15294 + 0.818985i) q^{6} +(-0.864047 - 2.50068i) q^{7} +(-2.71662 - 0.787391i) q^{8} -1.00000 q^{9} +(0.818985 - 1.15294i) q^{10} -5.95444 q^{11} +(1.88848 - 0.658528i) q^{12} -3.87212 q^{13} +(-3.59077 - 1.05183i) q^{14} +1.00000i q^{15} +(-3.13268 + 2.48723i) q^{16} +2.66013i q^{17} +(-0.818985 + 1.15294i) q^{18} -6.21337i q^{19} +(-0.658528 - 1.88848i) q^{20} +(2.50068 - 0.864047i) q^{21} +(-4.87660 + 6.86510i) q^{22} -4.60261i q^{23} +(0.787391 - 2.71662i) q^{24} +1.00000 q^{25} +(-3.17121 + 4.46431i) q^{26} -1.00000i q^{27} +(-4.15348 + 3.27850i) q^{28} +0.579589i q^{29} +(1.15294 + 0.818985i) q^{30} +5.65561 q^{31} +(0.302000 + 5.64879i) q^{32} -5.95444i q^{33} +(3.06696 + 2.17860i) q^{34} +(-0.864047 - 2.50068i) q^{35} +(0.658528 + 1.88848i) q^{36} -2.21144i q^{37} +(-7.16362 - 5.08865i) q^{38} -3.87212i q^{39} +(-2.71662 - 0.787391i) q^{40} +5.75803i q^{41} +(1.05183 - 3.59077i) q^{42} +5.16410 q^{43} +(3.92117 + 11.2448i) q^{44} -1.00000 q^{45} +(-5.30653 - 3.76947i) q^{46} +5.39666 q^{47} +(-2.48723 - 3.13268i) q^{48} +(-5.50685 + 4.32142i) q^{49} +(0.818985 - 1.15294i) q^{50} -2.66013 q^{51} +(2.54990 + 7.31241i) q^{52} -10.3132i q^{53} +(-1.15294 - 0.818985i) q^{54} -5.95444 q^{55} +(0.378268 + 7.47375i) q^{56} +6.21337 q^{57} +(0.668230 + 0.474675i) q^{58} -10.7610i q^{59} +(1.88848 - 0.658528i) q^{60} -10.9463 q^{61} +(4.63185 - 6.52056i) q^{62} +(0.864047 + 2.50068i) q^{63} +(6.76003 + 4.27808i) q^{64} -3.87212 q^{65} +(-6.86510 - 4.87660i) q^{66} -10.0435 q^{67} +(5.02358 - 1.75177i) q^{68} +4.60261 q^{69} +(-3.59077 - 1.05183i) q^{70} -0.496099i q^{71} +(2.71662 + 0.787391i) q^{72} +2.04057i q^{73} +(-2.54965 - 1.81114i) q^{74} +1.00000i q^{75} +(-11.7338 + 4.09168i) q^{76} +(5.14492 + 14.8902i) q^{77} +(-4.46431 - 3.17121i) q^{78} -10.6941i q^{79} +(-3.13268 + 2.48723i) q^{80} +1.00000 q^{81} +(6.63865 + 4.71574i) q^{82} +11.3326i q^{83} +(-3.27850 - 4.15348i) q^{84} +2.66013i q^{85} +(4.22932 - 5.95388i) q^{86} -0.579589 q^{87} +(16.1759 + 4.68848i) q^{88} +10.8922i q^{89} +(-0.818985 + 1.15294i) q^{90} +(3.34569 + 9.68295i) q^{91} +(-8.69193 + 3.03095i) q^{92} +5.65561i q^{93} +(4.41978 - 6.22201i) q^{94} -6.21337i q^{95} +(-5.64879 + 0.302000i) q^{96} -16.2633i q^{97} +(0.472300 + 9.88822i) q^{98} +5.95444 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} - 2 q^{4} + 28 q^{5} + 4 q^{6} + 4 q^{7} - 10 q^{8} - 28 q^{9} + 2 q^{10} - 8 q^{12} - 8 q^{13} + 2 q^{14} + 6 q^{16} - 2 q^{18} - 2 q^{20} - 4 q^{24} + 28 q^{25} + 16 q^{26} + 10 q^{28}+ \cdots - 30 q^{98}+O(q^{100}) \) 28 * q + 2 * q^2 - 2 * q^4 + 28 * q^5 + 4 * q^6 + 4 * q^7 - 10 * q^8 - 28 * q^9 + 2 * q^10 - 8 * q^12 - 8 * q^13 + 2 * q^14 + 6 * q^16 - 2 * q^18 - 2 * q^20 - 4 * q^24 + 28 * q^25 + 16 * q^26 + 10 * q^28 + 4 * q^30 + 24 * q^31 + 2 * q^32 + 8 * q^34 + 4 * q^35 + 2 * q^36 + 36 * q^38 - 10 * q^40 + 24 * q^43 - 4 * q^44 - 28 * q^45 - 44 * q^46 - 24 * q^47 + 16 * q^48 + 28 * q^49 + 2 * q^50 + 16 * q^52 - 4 * q^54 - 22 * q^56 + 8 * q^57 - 12 * q^58 - 8 * q^60 - 16 * q^61 - 28 * q^62 - 4 * q^63 + 22 * q^64 - 8 * q^65 - 20 * q^66 - 8 * q^67 - 12 * q^68 - 24 * q^69 + 2 * q^70 + 10 * q^72 - 8 * q^74 - 16 * q^76 + 16 * q^77 + 20 * q^78 + 6 * q^80 + 28 * q^81 + 24 * q^82 - 12 * q^84 - 4 * q^86 + 16 * q^87 + 40 * q^88 - 2 * q^90 + 48 * q^91 + 40 * q^92 + 52 * q^94 - 16 * q^96 - 30 * q^98

Introduction

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