LMFDB - Embedded newform 726.2.b.f.725.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [726,2,Mod(725,726)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("726.725"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(726, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,8,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.3588489216.5
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 10x^{6} - 8x^{5} + 8x^{4} + 4x^{3} + 16x^{2} + 32x + 22 $ x^8 - 4x^7 + 10x^6 - 8x^5 + 8x^4 + 4x^3 + 16x^2 + 32*x + 22
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			725.5
Root			$1.25299 - 1.71348i$ of defining polynomial
Character	$\chi$	$=$	726.725
Dual form			726.2.b.f.725.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(1.25299 - 1.19584i) q^{3} +1.00000 q^{4} -0.197913i q^{5} +(1.25299 - 1.19584i) q^{6} -3.42695i q^{7} +1.00000 q^{8} +(0.139946 - 2.99673i) q^{9} -0.197913i q^{10} +(1.25299 - 1.19584i) q^{12} -1.66994i q^{13} -3.42695i q^{14} +(-0.236672 - 0.247982i) q^{15} +1.00000 q^{16} -7.62036 q^{17} +(0.139946 - 2.99673i) q^{18} +5.55672i q^{19} -0.197913i q^{20} +(-4.09808 - 4.29392i) q^{21} +6.63432i q^{23} +(1.25299 - 1.19584i) q^{24} +4.96083 q^{25} -1.66994i q^{26} +(-3.40826 - 3.92222i) q^{27} -3.42695i q^{28} -0.102447 q^{29} +(-0.236672 - 0.247982i) q^{30} +5.60842 q^{31} +1.00000 q^{32} -7.62036 q^{34} -0.678239 q^{35} +(0.139946 - 2.99673i) q^{36} +7.34047 q^{37} +5.55672i q^{38} +(-1.99698 - 2.09241i) q^{39} -0.197913i q^{40} +9.53662 q^{41} +(-4.09808 - 4.29392i) q^{42} -1.95492i q^{43} +(-0.593093 - 0.0276971i) q^{45} +6.63432i q^{46} -7.98932i q^{47} +(1.25299 - 1.19584i) q^{48} -4.74399 q^{49} +4.96083 q^{50} +(-9.54820 + 9.11271i) q^{51} -1.66994i q^{52} +7.54638i q^{53} +(-3.40826 - 3.92222i) q^{54} -3.42695i q^{56} +(6.64493 + 6.96248i) q^{57} -0.102447 q^{58} -6.53418i q^{59} +(-0.236672 - 0.247982i) q^{60} +8.42607i q^{61} +5.60842 q^{62} +(-10.2697 - 0.479587i) q^{63} +1.00000 q^{64} -0.330504 q^{65} -4.42223 q^{67} -7.62036 q^{68} +(7.93356 + 8.31270i) q^{69} -0.678239 q^{70} +8.48528i q^{71} +(0.139946 - 2.99673i) q^{72} +0.919646i q^{73} +7.34047 q^{74} +(6.21585 - 5.93235i) q^{75} +5.55672i q^{76} +(-1.99698 - 2.09241i) q^{78} -4.27050i q^{79} -0.197913i q^{80} +(-8.96083 - 0.838761i) q^{81} +9.53662 q^{82} +1.23802 q^{83} +(-4.09808 - 4.29392i) q^{84} +1.50817i q^{85} -1.95492i q^{86} +(-0.128365 + 0.122510i) q^{87} +2.04888i q^{89} +(-0.593093 - 0.0276971i) q^{90} -5.72281 q^{91} +6.63432i q^{92} +(7.02727 - 6.70676i) q^{93} -7.98932i q^{94} +1.09975 q^{95} +(1.25299 - 1.19584i) q^{96} +1.55978 q^{97} -4.74399 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 4 q^{6} + 8 q^{8} - 4 q^{9} + 4 q^{12} - 8 q^{15} + 8 q^{16} - 16 q^{17} - 4 q^{18} - 12 q^{21} + 4 q^{24} - 40 q^{25} + 16 q^{27} + 8 q^{29} - 8 q^{30} + 24 q^{31} + 8 q^{32}+ \cdots - 8 q^{97}+O(q^{100}) $ 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 4 * q^6 + 8 * q^8 - 4 * q^9 + 4 * q^12 - 8 * q^15 + 8 * q^16 - 16 * q^17 - 4 * q^18 - 12 * q^21 + 4 * q^24 - 40 * q^25 + 16 * q^27 + 8 * q^29 - 8 * q^30 + 24 * q^31 + 8 * q^32 - 16 * q^34 - 4 * q^36 + 24 * q^37 + 28 * q^39 - 12 * q^42 - 16 * q^45 + 4 * q^48 - 40 * q^50 - 28 * q^51 + 16 * q^54 + 16 * q^57 + 8 * q^58 - 8 * q^60 + 24 * q^62 - 12 * q^63 + 8 * q^64 - 32 * q^65 + 8 * q^67 - 16 * q^68 + 40 * q^69 - 4 * q^72 + 24 * q^74 - 12 * q^75 + 28 * q^78 + 8 * q^81 - 16 * q^83 - 12 * q^84 + 32 * q^87 - 16 * q^90 + 8 * q^91 + 64 * q^95 + 4 * q^96 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.25299	−	1.19584i	0.723412	−	0.690417i
$3$	1.25299	−	1.19584i	0.723412	−	0.690417i
$4$	1.00000			0.500000
$5$		−	0.197913i		−	0.0885095i	−0.999020	−	0.0442547i	$-0.985909\pi$
$5$		−	0.197913i		−	0.0885095i	0.999020	−	0.0442547i	$-0.0140913\pi$
$6$	1.25299	−	1.19584i	0.511529	−	0.488199i
$7$		−	3.42695i		−	1.29527i	−0.761953	−	0.647633i	$-0.775759\pi$
$7$		−	3.42695i		−	1.29527i	0.761953	−	0.647633i	$-0.224241\pi$
$8$	1.00000			0.353553
$9$	0.139946	−	2.99673i	0.0466486	−	0.998911i
$10$		−	0.197913i		−	0.0625857i
$11$		0			0
$11$		0			0
$12$	1.25299	−	1.19584i	0.361706	−	0.345209i
$13$		−	1.66994i		−	0.463158i	−0.972816	−	0.231579i	$-0.925611\pi$
$13$		−	1.66994i		−	0.463158i	0.972816	−	0.231579i	$-0.0743893\pi$
$14$		−	3.42695i		−	0.915891i
$15$	−0.236672	−	0.247982i	−0.0611085	−	0.0640288i
$16$	1.00000			0.250000
$17$	−7.62036			−1.84821			−0.924105	−	0.382140i	$-0.875187\pi$
$17$	−7.62036			−1.84821			−0.924105	+	0.382140i	$0.875187\pi$
$18$	0.139946	−	2.99673i	0.0329855	−	0.706337i
$19$			5.55672i			1.27480i	0.770534	+	0.637399i	$0.219990\pi$
$19$			5.55672i			1.27480i	−0.770534	+	0.637399i	$0.780010\pi$
$20$		−	0.197913i		−	0.0442547i
$21$	−4.09808	−	4.29392i	−0.894274	−	0.937010i
$22$		0			0
$23$			6.63432i			1.38335i	0.722209	+	0.691675i	$0.243127\pi$
$23$			6.63432i			1.38335i	−0.722209	+	0.691675i	$0.756873\pi$
$24$	1.25299	−	1.19584i	0.255765	−	0.244099i
$25$	4.96083			0.992166
$26$		−	1.66994i		−	0.327503i
$27$	−3.40826	−	3.92222i	−0.655919	−	0.754831i
$28$		−	3.42695i		−	0.647633i
$29$	−0.102447			−0.0190240			−0.00951200	−	0.999955i	$-0.503028\pi$
$29$	−0.102447			−0.0190240			−0.00951200	+	0.999955i	$0.503028\pi$
$30$	−0.236672	−	0.247982i	−0.0432102	−	0.0452752i
$31$	5.60842			1.00730			0.503651	−	0.863907i	$-0.331990\pi$
$31$	5.60842			1.00730			0.503651	+	0.863907i	$0.331990\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−7.62036			−1.30688
$35$	−0.678239			−0.114643
$36$	0.139946	−	2.99673i	0.0233243	−	0.499456i
$37$	7.34047			1.20677			0.603383	−	0.797452i	$-0.293819\pi$
$37$	7.34047			1.20677			0.603383	+	0.797452i	$0.293819\pi$
$38$			5.55672i			0.901418i
$39$	−1.99698	−	2.09241i	−0.319773	−	0.335054i
$40$		−	0.197913i		−	0.0312928i
$41$	9.53662			1.48937			0.744685	−	0.667416i	$-0.232600\pi$
$41$	9.53662			1.48937			0.744685	+	0.667416i	$0.232600\pi$
$42$	−4.09808	−	4.29392i	−0.632347	−	0.662566i
$43$		−	1.95492i		−	0.298123i	−0.988828	−	0.149061i	$-0.952375\pi$
$43$		−	1.95492i		−	0.298123i	0.988828	−	0.149061i	$-0.0476252\pi$
$44$		0			0
$45$	−0.593093	−	0.0276971i	−0.0884131	−	0.00412884i
$46$			6.63432i			0.978176i
$47$		−	7.98932i		−	1.16536i	−0.812701	−	0.582681i	$-0.802004\pi$
$47$		−	7.98932i		−	1.16536i	0.812701	−	0.582681i	$-0.197996\pi$
$48$	1.25299	−	1.19584i	0.180853	−	0.172604i
$49$	−4.74399			−0.677713
$50$	4.96083			0.701567
$51$	−9.54820	+	9.11271i	−1.33702	+	1.27604i
$52$		−	1.66994i		−	0.231579i
$53$			7.54638i			1.03658i	0.855206	+	0.518288i	$0.173430\pi$
$53$			7.54638i			1.03658i	−0.855206	+	0.518288i	$0.826570\pi$
$54$	−3.40826	−	3.92222i	−0.463805	−	0.533746i
$55$		0			0
$56$		−	3.42695i		−	0.457946i
$57$	6.64493	+	6.96248i	0.880142	+	0.922204i
$58$	−0.102447			−0.0134520
$59$		−	6.53418i		−	0.850677i	−0.905034	−	0.425339i	$-0.860155\pi$
$59$		−	6.53418i		−	0.850677i	0.905034	−	0.425339i	$-0.139845\pi$
$60$	−0.236672	−	0.247982i	−0.0305542	−	0.0320144i
$61$			8.42607i			1.07885i	0.842034	+	0.539424i	$0.181358\pi$
$61$			8.42607i			1.07885i	−0.842034	+	0.539424i	$0.818642\pi$
$62$	5.60842			0.712270
$63$	−10.2697	−	0.479587i	−1.29386	−	0.0604223i
$64$	1.00000			0.125000
$65$	−0.330504			−0.0409939
$66$		0			0
$67$	−4.42223			−0.540262			−0.270131	−	0.962824i	$-0.587067\pi$
$67$	−4.42223			−0.540262			−0.270131	+	0.962824i	$0.587067\pi$
$68$	−7.62036			−0.924105
$69$	7.93356	+	8.31270i	0.955089	+	1.00073i
$70$	−0.678239			−0.0810651
$71$			8.48528i			1.00702i	0.863990	+	0.503509i	$0.167958\pi$
$71$			8.48528i			1.00702i	−0.863990	+	0.503509i	$0.832042\pi$
$72$	0.139946	−	2.99673i	0.0164928	−	0.353168i
$73$			0.919646i			0.107636i	0.998551	+	0.0538182i	$0.0171392\pi$
$73$			0.919646i			0.107636i	−0.998551	+	0.0538182i	$0.982861\pi$
$74$	7.34047			0.853312
$75$	6.21585	−	5.93235i	0.717744	−	0.685008i
$76$			5.55672i			0.637399i
$77$		0			0
$78$	−1.99698	−	2.09241i	−0.226113	−	0.236919i
$79$		−	4.27050i		−	0.480468i	−0.970715	−	0.240234i	$-0.922776\pi$
$79$		−	4.27050i		−	0.480468i	0.970715	−	0.240234i	$-0.0772242\pi$
$80$		−	0.197913i		−	0.0221274i
$81$	−8.96083	−	0.838761i	−0.995648	−	0.0931956i
$82$	9.53662			1.05314
$83$	1.23802			0.135891			0.0679453	−	0.997689i	$-0.478356\pi$
$83$	1.23802			0.135891			0.0679453	+	0.997689i	$0.478356\pi$
$84$	−4.09808	−	4.29392i	−0.447137	−	0.468505i
$85$			1.50817i			0.163584i
$86$		−	1.95492i		−	0.210805i
$87$	−0.128365	+	0.122510i	−0.0137622	+	0.0131345i
$88$		0			0
$89$			2.04888i			0.217181i	0.994087	+	0.108590i	$0.0346337\pi$
$89$			2.04888i			0.217181i	−0.994087	+	0.108590i	$0.965366\pi$
$90$	−0.593093	−	0.0276971i	−0.0625175	−	0.00291953i
$91$	−5.72281			−0.599913
$92$			6.63432i			0.691675i
$93$	7.02727	−	6.70676i	0.728694	−	0.695458i
$94$		−	7.98932i		−	0.824035i
$95$	1.09975			0.112832
$96$	1.25299	−	1.19584i	0.127882	−	0.122050i
$97$	1.55978			0.158372			0.0791860	−	0.996860i	$-0.474768\pi$
$97$	1.55978			0.158372			0.0791860	+	0.996860i	$0.474768\pi$
$98$	−4.74399			−0.479216
$99$		0			0
$100$	4.96083			0.496083
$101$	−8.75594			−0.871248			−0.435624	−	0.900129i	$-0.643472\pi$
$101$	−8.75594			−0.871248			−0.435624	+	0.900129i	$0.643472\pi$
$102$	−9.54820	+	9.11271i	−0.945413	+	0.902293i
$103$	−8.55978			−0.843420			−0.421710	−	0.906731i	$-0.638570\pi$
$103$	−8.55978			−0.843420			−0.421710	+	0.906731i	$0.638570\pi$
$104$		−	1.66994i		−	0.163751i
$105$	−0.849824	+	0.811063i	−0.0829343	+	0.0791517i
$106$			7.54638i			0.732969i
$107$	−10.8253			−1.04652			−0.523258	−	0.852174i	$-0.675284\pi$
$107$	−10.8253			−1.04652			−0.523258	+	0.852174i	$0.675284\pi$
$108$	−3.40826	−	3.92222i	−0.327960	−	0.377416i
$109$			6.84912i			0.656027i	0.944673	+	0.328013i	$0.106379\pi$
$109$			6.84912i			0.656027i	−0.944673	+	0.328013i	$0.893621\pi$
$110$		0			0
$111$	9.19750	−	8.77801i	0.872988	−	0.833172i
$112$		−	3.42695i		−	0.323816i
$113$			10.6236i			0.999389i	0.866202	+	0.499694i	$0.166554\pi$
$113$			10.6236i			0.999389i	−0.866202	+	0.499694i	$0.833446\pi$
$114$	6.64493	+	6.96248i	0.622355	+	0.652096i
$115$	1.31302			0.122440
$116$	−0.102447			−0.00951200
$117$	−5.00437	−	0.233701i	−0.462654	−	0.0216057i
$118$		−	6.53418i		−	0.601520i
$119$			26.1146i			2.39392i
$120$	−0.236672	−	0.247982i	−0.0216051	−	0.0226376i
$121$		0			0
$122$			8.42607i			0.762860i
$123$	11.9492	−	11.4042i	1.07743	−	1.02829i
$124$	5.60842			0.503651
$125$		−	1.97138i		−	0.176326i
$126$	−10.2697	−	0.479587i	−0.914894	−	0.0427250i
$127$			4.46362i			0.396083i	0.980194	+	0.198041i	$0.0634580\pi$
$127$			4.46362i			0.396083i	−0.980194	+	0.198041i	$0.936542\pi$
$128$	1.00000			0.0883883
$129$	−2.33777	−	2.44949i	−0.205829	−	0.215666i
$130$	−0.330504			−0.0289871
$131$	21.3040			1.86134			0.930670	−	0.365861i	$-0.119225\pi$
$131$	21.3040			1.86134			0.930670	+	0.365861i	$0.119225\pi$
$132$		0			0
$133$	19.0426			1.65120
$134$	−4.42223			−0.382023
$135$	−0.776259	+	0.674539i	−0.0668097	+	0.0580551i
$136$	−7.62036			−0.653441
$137$		−	10.3810i		−	0.886908i	−0.896297	−	0.443454i	$-0.853753\pi$
$137$		−	10.3810i		−	0.886908i	0.896297	−	0.443454i	$-0.146247\pi$
$138$	7.93356	+	8.31270i	0.675350	+	0.707624i
$139$		−	4.51762i		−	0.383180i	−0.981475	−	0.191590i	$-0.938636\pi$
$139$		−	4.51762i		−	0.383180i	0.981475	−	0.191590i	$-0.0613643\pi$
$140$	−0.678239			−0.0573216
$141$	−9.55392	−	10.0105i	−0.804586	−	0.843036i
$142$			8.48528i			0.712069i
$143$		0			0
$144$	0.139946	−	2.99673i	0.0116621	−	0.249728i
$145$			0.0202757i			0.00168381i
$146$			0.919646i			0.0761105i
$147$	−5.94416	+	5.67304i	−0.490266	+	0.467905i
$148$	7.34047			0.603383
$149$	3.73007			0.305580			0.152790	−	0.988259i	$-0.451174\pi$
$149$	3.73007			0.305580			0.152790	+	0.988259i	$0.451174\pi$
$150$	6.21585	−	5.93235i	0.507522	−	0.484374i
$151$		−	3.06248i		−	0.249221i	−0.992206	−	0.124611i	$-0.960232\pi$
$151$		−	3.06248i		−	0.249221i	0.992206	−	0.124611i	$-0.0397682\pi$
$152$			5.55672i			0.450709i
$153$	−1.06644	+	22.8362i	−0.0862163	+	1.84620i
$154$		0			0
$155$		−	1.10998i		−	0.0891558i
$156$	−1.99698	−	2.09241i	−0.159886	−	0.167527i
$157$	−16.3671			−1.30623			−0.653117	−	0.757257i	$-0.726539\pi$
$157$	−16.3671			−1.30623			−0.653117	+	0.757257i	$0.726539\pi$
$158$		−	4.27050i		−	0.339742i
$159$	9.02425	+	9.45551i	0.715669	+	0.749871i
$160$		−	0.197913i		−	0.0156464i
$161$	22.7355			1.79181
$162$	−8.96083	−	0.838761i	−0.704029	−	0.0658993i
$163$	−22.6749			−1.77603			−0.888017	−	0.459810i	$-0.847918\pi$
$163$	−22.6749			−1.77603			−0.888017	+	0.459810i	$0.847918\pi$
$164$	9.53662			0.744685
$165$		0			0
$166$	1.23802			0.0960891
$167$	6.06328			0.469191			0.234595	−	0.972093i	$-0.424624\pi$
$167$	6.06328			0.469191			0.234595	+	0.972093i	$0.424624\pi$
$168$	−4.09808	−	4.29392i	−0.316173	−	0.331283i
$169$	10.2113			0.785484
$170$			1.50817i			0.115671i
$171$	16.6520	+	0.777639i	1.27341	+	0.0594675i
$172$		−	1.95492i		−	0.149061i
$173$	3.03917			0.231064			0.115532	−	0.993304i	$-0.463143\pi$
$173$	3.03917			0.231064			0.115532	+	0.993304i	$0.463143\pi$
$174$	−0.128365	+	0.122510i	−0.00973134	+	0.00928749i
$175$		−	17.0005i		−	1.28512i
$176$		0			0
$177$	−7.81381	−	8.18723i	−0.587322	−	0.615390i
$178$			2.04888i			0.153570i
$179$			0.669410i			0.0500340i	0.999687	+	0.0250170i	$0.00796399\pi$
$179$			0.669410i			0.0500340i	−0.999687	+	0.0250170i	$0.992036\pi$
$180$	−0.593093	−	0.0276971i	−0.0442066	−	0.00206442i
$181$	−20.7141			−1.53966			−0.769832	−	0.638246i	$-0.779660\pi$
$181$	−20.7141			−1.53966			−0.769832	+	0.638246i	$0.779660\pi$
$182$	−5.72281			−0.424203
$183$	10.0762	+	10.5577i	0.744855	+	0.780451i
$184$			6.63432i			0.489088i
$185$		−	1.45278i		−	0.106810i
$186$	7.02727	−	6.70676i	0.515264	−	0.491763i
$187$		0			0
$188$		−	7.98932i		−	0.582681i
$189$	−13.4412	+	11.6799i	−0.977707	+	0.849590i
$190$	1.09975			0.0797841
$191$			15.6889i			1.13521i	0.823302	+	0.567603i	$0.192129\pi$
$191$			15.6889i			1.13521i	−0.823302	+	0.567603i	$0.807871\pi$
$192$	1.25299	−	1.19584i	0.0904264	−	0.0863021i
$193$			11.7928i			0.848867i	0.905459	+	0.424434i	$0.139527\pi$
$193$			11.7928i			0.848867i	−0.905459	+	0.424434i	$0.860473\pi$
$194$	1.55978			0.111986
$195$	−0.414116	+	0.395228i	−0.0296555	+	0.0283029i
$196$	−4.74399			−0.338857
$197$	−3.06328			−0.218250			−0.109125	−	0.994028i	$-0.534805\pi$
$197$	−3.06328			−0.218250			−0.109125	+	0.994028i	$0.534805\pi$
$198$		0			0
$199$	−12.0633			−0.855143			−0.427572	−	0.903982i	$-0.640631\pi$
$199$	−12.0633			−0.855143			−0.427572	+	0.903982i	$0.640631\pi$
$200$	4.96083			0.350784
$201$	−5.54099	+	5.28827i	−0.390832	+	0.373006i
$202$	−8.75594			−0.616065
$203$			0.351082i			0.0246411i
$204$	−9.54820	+	9.11271i	−0.668508	+	0.638018i
$205$		−	1.88742i		−	0.131823i
$206$	−8.55978			−0.596388
$207$	19.8813	+	0.928444i	1.38184	+	0.0645313i
$208$		−	1.66994i		−	0.115790i
$209$		0			0
$210$	−0.849824	+	0.811063i	−0.0586434	+	0.0559687i
$211$		−	17.1623i		−	1.18150i	−0.806854	−	0.590751i	$-0.798832\pi$
$211$		−	17.1623i		−	1.18150i	0.806854	−	0.590751i	$-0.201168\pi$
$212$			7.54638i			0.518288i
$213$	10.1470	+	10.6319i	0.695262	+	0.728488i
$214$	−10.8253			−0.739999
$215$	−0.386905			−0.0263867
$216$	−3.40826	−	3.92222i	−0.231902	−	0.266873i
$217$		−	19.2198i		−	1.30472i
$218$			6.84912i			0.463881i
$219$	1.09975	+	1.15230i	0.0743140	+	0.0778655i
$220$		0			0
$221$			12.7256i			0.856014i
$222$	9.19750	−	8.77801i	0.617296	−	0.589141i
$223$	−25.9621			−1.73855			−0.869274	−	0.494331i	$-0.835413\pi$
$223$	−25.9621			−1.73855			−0.869274	+	0.494331i	$0.835413\pi$
$224$		−	3.42695i		−	0.228973i
$225$	0.694247	−	14.8663i	0.0462832	−	0.991086i
$226$			10.6236i			0.706675i
$227$	−6.80507			−0.451668			−0.225834	−	0.974166i	$-0.572511\pi$
$227$	−6.80507			−0.451668			−0.225834	+	0.974166i	$0.572511\pi$
$228$	6.64493	+	6.96248i	0.440071	+	0.461102i
$229$	−5.56248			−0.367579			−0.183790	−	0.982966i	$-0.558837\pi$
$229$	−5.56248			−0.367579			−0.183790	+	0.982966i	$0.558837\pi$
$230$	1.31302			0.0865779
$231$		0			0
$232$	−0.102447			−0.00672600
$233$	−18.1509			−1.18911			−0.594554	−	0.804056i	$-0.702671\pi$
$233$	−18.1509			−1.18911			−0.594554	+	0.804056i	$0.702671\pi$
$234$	−5.00437	−	0.233701i	−0.327146	−	0.0152775i
$235$	−1.58119			−0.103146
$236$		−	6.53418i		−	0.425339i
$237$	−5.10682	−	5.35087i	−0.331724	−	0.347576i
$238$			26.1146i			1.69276i
$239$	7.16303			0.463338			0.231669	−	0.972795i	$-0.425581\pi$
$239$	7.16303			0.463338			0.231669	+	0.972795i	$0.425581\pi$
$240$	−0.236672	−	0.247982i	−0.0152771	−	0.0160072i
$241$		−	8.92445i		−	0.574875i	−0.957799	−	0.287437i	$-0.907197\pi$
$241$		−	8.92445i		−	0.574875i	0.957799	−	0.287437i	$-0.0928033\pi$
$242$		0			0
$243$	−12.2308	+	9.66474i	−0.784607	+	0.619993i
$244$			8.42607i			0.539424i
$245$			0.938899i			0.0599841i
$246$	11.9492	−	11.4042i	0.761856	−	0.727108i
$247$	9.27939			0.590434
$248$	5.60842			0.356135
$249$	1.55122	−	1.48047i	0.0983048	−	0.0938212i
$250$		−	1.97138i		−	0.124681i
$251$		−	25.8964i		−	1.63457i	−0.576236	−	0.817284i	$-0.695479\pi$
$251$		−	25.8964i		−	1.63457i	0.576236	−	0.817284i	$-0.304521\pi$
$252$	−10.2697	−	0.479587i	−0.646928	−	0.0302112i
$253$		0			0
$254$			4.46362i			0.280073i
$255$	1.80353	+	1.88972i	0.112941	+	0.118339i
$256$	1.00000			0.0625000
$257$			14.6153i			0.911680i	0.890062	+	0.455840i	$0.150661\pi$
$257$			14.6153i			0.911680i	−0.890062	+	0.455840i	$0.849339\pi$
$258$	−2.33777	−	2.44949i	−0.145543	−	0.152499i
$259$		−	25.1554i		−	1.56308i
$260$	−0.330504			−0.0204970
$261$	−0.0143371	+	0.307008i	−0.000887443	+	0.0190033i
$262$	21.3040			1.31617
$263$	−9.22928			−0.569102			−0.284551	−	0.958661i	$-0.591844\pi$
$263$	−9.22928			−0.569102			−0.284551	+	0.958661i	$0.591844\pi$
$264$		0			0
$265$	1.49353			0.0917467
$266$	19.0426			1.16758
$267$	2.45013	+	2.56722i	0.149945	+	0.157111i
$268$	−4.42223			−0.270131
$269$			20.7596i			1.26574i	0.774260	+	0.632868i	$0.218122\pi$
$269$			20.7596i			1.26574i	−0.774260	+	0.632868i	$0.781878\pi$
$270$	−0.776259	+	0.674539i	−0.0472416	+	0.0410511i
$271$		−	12.2210i		−	0.742372i	−0.928558	−	0.371186i	$-0.878951\pi$
$271$		−	12.2210i		−	0.742372i	0.928558	−	0.371186i	$-0.121049\pi$
$272$	−7.62036			−0.462052
$273$	−7.17060	+	6.84355i	−0.433984	+	0.414190i
$274$		−	10.3810i		−	0.627139i
$275$		0			0
$276$	7.93356	+	8.31270i	0.477544	+	0.500366i
$277$			28.6802i			1.72322i	0.507568	+	0.861612i	$0.330545\pi$
$277$			28.6802i			1.72322i	−0.507568	+	0.861612i	$0.669455\pi$
$278$		−	4.51762i		−	0.270949i
$279$	0.784874	−	16.8069i	0.0469892	−	1.00621i
$280$	−0.678239			−0.0405325
$281$	4.28863			0.255838			0.127919	−	0.991785i	$-0.459170\pi$
$281$	4.28863			0.255838			0.127919	+	0.991785i	$0.459170\pi$
$282$	−9.55392	−	10.0105i	−0.568928	−	0.596117i
$283$		−	1.51575i		−	0.0901020i	−0.998985	−	0.0450510i	$-0.985655\pi$
$283$		−	1.51575i		−	0.0901020i	0.998985	−	0.0450510i	$-0.0143450\pi$
$284$			8.48528i			0.503509i
$285$	1.37797	−	1.31512i	0.0816238	−	0.0779009i
$286$		0			0
$287$		−	32.6815i		−	1.92913i
$288$	0.139946	−	2.99673i	0.00824638	−	0.176584i
$289$	41.0699			2.41588
$290$			0.0202757i			0.00119063i
$291$	1.95439	−	1.86525i	0.114568	−	0.109343i
$292$			0.919646i			0.0538182i
$293$	−12.3823			−0.723384			−0.361692	−	0.932298i	$-0.617801\pi$
$293$	−12.3823			−0.723384			−0.361692	+	0.932298i	$0.617801\pi$
$294$	−5.94416	+	5.67304i	−0.346670	+	0.330859i
$295$	−1.29320			−0.0752930
$296$	7.34047			0.426656
$297$		0			0
$298$	3.73007			0.216077
$299$	11.0789			0.640710
$300$	6.21585	−	5.93235i	0.358872	−	0.342504i
$301$	−6.69942			−0.386148
$302$		−	3.06248i		−	0.176226i
$303$	−10.9711	+	10.4707i	−0.630271	+	0.601525i
$304$			5.55672i			0.318700i
$305$	1.66763			0.0954882
$306$	−1.06644	+	22.8362i	−0.0609642	+	1.30546i
$307$			4.80739i			0.274372i	0.990545	+	0.137186i	$0.0438058\pi$
$307$			4.80739i			0.274372i	−0.990545	+	0.137186i	$0.956194\pi$
$308$		0			0
$309$	−10.7253	+	10.2361i	−0.610140	+	0.582312i
$310$		−	1.10998i		−	0.0630426i
$311$		−	13.1417i		−	0.745195i	−0.927993	−	0.372598i	$-0.878467\pi$
$311$		−	13.1417i		−	0.745195i	0.927993	−	0.372598i	$-0.121533\pi$
$312$	−1.99698	−	2.09241i	−0.113057	−	0.118460i
$313$	4.47284			0.252820			0.126410	−	0.991978i	$-0.459654\pi$
$313$	4.47284			0.252820			0.126410	+	0.991978i	$0.459654\pi$
$314$	−16.3671			−0.923646
$315$	−0.0949167	+	2.03250i	−0.00534795	+	0.114518i
$316$		−	4.27050i		−	0.240234i
$317$		−	32.5486i		−	1.82811i	−0.405586	−	0.914057i	$-0.632932\pi$
$317$		−	32.5486i		−	1.82811i	0.405586	−	0.914057i	$-0.367068\pi$
$318$	9.02425	+	9.45551i	0.506055	+	0.530239i
$319$		0			0
$320$		−	0.197913i		−	0.0110637i
$321$	−13.5639	+	12.9452i	−0.757062	+	0.722533i
$322$	22.7355			1.26700
$323$		−	42.3442i		−	2.35609i
$324$	−8.96083	−	0.838761i	−0.497824	−	0.0465978i
$325$		−	8.28430i		−	0.459530i
$326$	−22.6749			−1.25585
$327$	8.19043	+	8.58185i	0.452932	+	0.474577i
$328$	9.53662			0.526572
$329$	−27.3790			−1.50945
$330$		0			0
$331$	0.533922			0.0293470			0.0146735	−	0.999892i	$-0.495329\pi$
$331$	0.533922			0.0293470			0.0146735	+	0.999892i	$0.495329\pi$
$332$	1.23802			0.0679453
$333$	1.02727	−	21.9974i	0.0562939	−	1.20545i
$334$	6.06328			0.331768
$335$			0.875218i			0.0478183i
$336$	−4.09808	−	4.29392i	−0.223568	−	0.234253i
$337$		−	18.4416i		−	1.00458i	−0.864699	−	0.502290i	$-0.832491\pi$
$337$		−	18.4416i		−	1.00458i	0.864699	−	0.502290i	$-0.167509\pi$
$338$	10.2113			0.555421
$339$	12.7042	+	13.3113i	0.689995	+	0.722969i
$340$			1.50817i			0.0817920i
$341$		0			0
$342$	16.6520	+	0.777639i	0.900437	+	0.0420499i
$343$		−	7.73122i		−	0.417447i
$344$		−	1.95492i		−	0.105402i
$345$	1.64519	−	1.57016i	0.0885742	−	0.0845344i
$346$	3.03917			0.163387
$347$	22.7472			1.22113			0.610567	−	0.791965i	$-0.290942\pi$
$347$	22.7472			1.22113			0.610567	+	0.791965i	$0.290942\pi$
$348$	−0.128365	+	0.122510i	−0.00688109	+	0.00656725i
$349$			31.5774i			1.69030i	0.534531	+	0.845149i	$0.320488\pi$
$349$			31.5774i			1.69030i	−0.534531	+	0.845149i	$0.679512\pi$
$350$		−	17.0005i		−	0.908716i
$351$	−6.54987	+	5.69159i	−0.349606	+	0.303795i
$352$		0			0
$353$		−	1.52435i		−	0.0811331i	−0.999177	−	0.0405665i	$-0.987084\pi$
$353$		−	1.52435i		−	0.0811331i	0.999177	−	0.0405665i	$-0.0129163\pi$
$354$	−7.81381	−	8.18723i	−0.415299	−	0.435146i
$355$	1.67935			0.0891306
$356$			2.04888i			0.108590i
$357$	31.2288	+	32.7212i	1.65280	+	1.73179i
$358$			0.669410i			0.0353794i
$359$	3.16600			0.167095			0.0835476	−	0.996504i	$-0.473375\pi$
$359$	3.16600			0.167095			0.0835476	+	0.996504i	$0.473375\pi$
$360$	−0.593093	−	0.0276971i	−0.0312588	−	0.00145977i
$361$	−11.8771			−0.625110
$362$	−20.7141			−1.08871
$363$		0			0
$364$	−5.72281			−0.299957
$365$	0.182010			0.00952685
$366$	10.0762	+	10.5577i	0.526692	+	0.551862i
$367$	8.99273			0.469417			0.234708	−	0.972066i	$-0.424586\pi$
$367$	8.99273			0.469417			0.234708	+	0.972066i	$0.424586\pi$
$368$			6.63432i			0.345838i
$369$	1.33461	−	28.5787i	0.0694770	−	1.48775i
$370$		−	1.45278i		−	0.0755262i
$371$	25.8611			1.34264
$372$	7.02727	−	6.70676i	0.364347	−	0.347729i
$373$		−	2.25776i		−	0.116902i	−0.998290	−	0.0584511i	$-0.981384\pi$
$373$		−	2.25776i		−	0.116902i	0.998290	−	0.0584511i	$-0.0186162\pi$
$374$		0			0
$375$	−2.35745	−	2.47011i	−0.121738	−	0.127556i
$376$		−	7.98932i		−	0.412018i
$377$			0.171081i			0.00881113i
$378$	−13.4412	+	11.6799i	−0.691343	+	0.600751i
$379$	5.62763			0.289072			0.144536	−	0.989500i	$-0.453831\pi$
$379$	5.62763			0.289072			0.144536	+	0.989500i	$0.453831\pi$
$380$	1.09975			0.0564159
$381$	5.33777	+	5.59286i	0.273462	+	0.286531i
$382$			15.6889i			0.802712i
$383$			4.50977i			0.230438i	0.993340	+	0.115219i	$0.0367570\pi$
$383$			4.50977i			0.230438i	−0.993340	+	0.115219i	$0.963243\pi$
$384$	1.25299	−	1.19584i	0.0639412	−	0.0610248i
$385$		0			0
$386$			11.7928i			0.600240i
$387$	−5.85838	−	0.273583i	−0.297798	−	0.0139070i
$388$	1.55978			0.0791860
$389$			26.6308i			1.35024i	0.737709	+	0.675119i	$0.235908\pi$
$389$			26.6308i			1.35024i	−0.737709	+	0.675119i	$0.764092\pi$
$390$	−0.414116	+	0.395228i	−0.0209696	+	0.0200132i
$391$		−	50.5559i		−	2.55672i
$392$	−4.74399			−0.239608
$393$	26.6936	−	25.4761i	1.34651	−	1.28510i
$394$	−3.06328			−0.154326
$395$	−0.845188			−0.0425260
$396$		0			0
$397$	15.3405			0.769916			0.384958	−	0.922934i	$-0.374216\pi$
$397$	15.3405			0.769916			0.384958	+	0.922934i	$0.374216\pi$
$398$	−12.0633			−0.604677
$399$	23.8601	−	22.7718i	1.19450	−	1.14002i
$400$	4.96083			0.248042
$401$		−	4.80782i		−	0.240091i	−0.992768	−	0.120045i	$-0.961696\pi$
$401$		−	4.80782i		−	0.240091i	0.992768	−	0.120045i	$-0.0383040\pi$
$402$	−5.54099	+	5.28827i	−0.276360	+	0.263755i
$403$		−	9.36573i		−	0.466540i
$404$	−8.75594			−0.435624
$405$	−0.166002	+	1.77347i	−0.00824870	+	0.0881243i
$406$			0.351082i			0.0174239i
$407$		0			0
$408$	−9.54820	+	9.11271i	−0.472706	+	0.451147i
$409$		−	25.5532i		−	1.26353i	−0.775161	−	0.631763i	$-0.782331\pi$
$409$		−	25.5532i		−	1.26353i	0.775161	−	0.631763i	$-0.217669\pi$
$410$		−	1.88742i		−	0.0932132i
$411$	−12.4140	−	13.0072i	−0.612336	−	0.641599i
$412$	−8.55978			−0.421710
$413$	−22.3923			−1.10185
$414$	19.8813	+	0.928444i	0.977112	+	0.0456306i
$415$		−	0.245021i		−	0.0120276i
$416$		−	1.66994i		−	0.0818756i
$417$	−5.40234	−	5.66051i	−0.264554	−	0.277197i
$418$		0			0
$419$			0.820215i			0.0400701i	0.999799	+	0.0200351i	$0.00637779\pi$
$419$			0.820215i			0.0400701i	−0.999799	+	0.0200351i	$0.993622\pi$
$420$	−0.849824	+	0.811063i	−0.0414671	+	0.0395758i
$421$	11.5211			0.561505			0.280752	−	0.959780i	$-0.409416\pi$
$421$	11.5211			0.561505			0.280752	+	0.959780i	$0.409416\pi$
$422$		−	17.1623i		−	0.835447i
$423$	−23.9419	−	1.11807i	−1.16409	−	0.0543625i
$424$			7.54638i			0.366485i
$425$	−37.8033			−1.83373
$426$	10.1470	+	10.6319i	0.491625	+	0.515119i
$427$	28.8757			1.39739
$428$	−10.8253			−0.523258
$429$		0			0
$430$	−0.386905			−0.0186582
$431$	24.8280			1.19592			0.597960	−	0.801526i	$-0.295978\pi$
$431$	24.8280			1.19592			0.597960	+	0.801526i	$0.295978\pi$
$432$	−3.40826	−	3.92222i	−0.163980	−	0.188708i
$433$	16.9217			0.813203			0.406602	−	0.913606i	$-0.366714\pi$
$433$	16.9217			0.813203			0.406602	+	0.913606i	$0.366714\pi$
$434$		−	19.2198i		−	0.922579i
$435$	0.0242464	+	0.0254052i	0.00116253	+	0.00121808i
$436$			6.84912i			0.328013i
$437$	−36.8650			−1.76349
$438$	1.09975	+	1.15230i	0.0525480	+	0.0550592i
$439$		−	0.597501i		−	0.0285172i	−0.999898	−	0.0142586i	$-0.995461\pi$
$439$		−	0.597501i		−	0.0285172i	0.999898	−	0.0142586i	$-0.00453880\pi$
$440$		0			0
$441$	−0.663902	+	14.2165i	−0.0316144	+	0.676976i
$442$			12.7256i			0.605293i
$443$		−	8.28500i		−	0.393632i	−0.980440	−	0.196816i	$-0.936940\pi$
$443$		−	8.28500i		−	0.393632i	0.980440	−	0.196816i	$-0.0630602\pi$
$444$	9.19750	−	8.77801i	0.436494	−	0.416586i
$445$	0.405500			0.0192226
$446$	−25.9621			−1.22934
$447$	4.67373	−	4.46056i	0.221060	−	0.210977i
$448$		−	3.42695i		−	0.161908i
$449$		−	17.7377i		−	0.837096i	−0.908195	−	0.418548i	$-0.862539\pi$
$449$		−	17.7377i		−	0.837096i	0.908195	−	0.418548i	$-0.137461\pi$
$450$	0.694247	−	14.8663i	0.0327271	−	0.700804i
$451$		0			0
$452$			10.6236i			0.499694i
$453$	−3.66223	−	3.83725i	−0.172067	−	0.180290i
$454$	−6.80507			−0.319378
$455$			1.13262i			0.0530980i
$456$	6.64493	+	6.96248i	0.311177	+	0.326048i
$457$			41.0955i			1.92237i	0.275911	+	0.961183i	$0.411021\pi$
$457$			41.0955i			1.92237i	−0.275911	+	0.961183i	$0.588979\pi$
$458$	−5.56248			−0.259918
$459$	25.9721	+	29.8887i	1.21228	+	1.39509i
$460$	1.31302			0.0612198
$461$	12.1741			0.567004			0.283502	−	0.958972i	$-0.408504\pi$
$461$	12.1741			0.567004			0.283502	+	0.958972i	$0.408504\pi$
$462$		0			0
$463$	−32.5767			−1.51397			−0.756985	−	0.653433i	$-0.773328\pi$
$463$	−32.5767			−1.51397			−0.756985	+	0.653433i	$0.773328\pi$
$464$	−0.102447			−0.00475600
$465$	−1.32736	−	1.39079i	−0.0615547	−	0.0644963i
$466$	−18.1509			−0.840826
$467$		−	27.0064i		−	1.24971i	−0.780742	−	0.624853i	$-0.785159\pi$
$467$		−	27.0064i		−	1.24971i	0.780742	−	0.624853i	$-0.214841\pi$
$468$	−5.00437	−	0.233701i	−0.231327	−	0.0108028i
$469$			15.1548i			0.699782i
$470$	−1.58119			−0.0729349
$471$	−20.5077	+	19.5723i	−0.944944	+	0.901846i
$472$		−	6.53418i		−	0.300760i
$473$		0			0
$474$	−5.10682	−	5.35087i	−0.234564	−	0.245774i
$475$			27.5659i			1.26481i
$476$			26.1146i			1.19696i
$477$	22.6145	+	1.05608i	1.03545	+	0.0483548i
$478$	7.16303			0.327629
$479$	10.7388			0.490669			0.245335	−	0.969438i	$-0.421102\pi$
$479$	10.7388			0.490669			0.245335	+	0.969438i	$0.421102\pi$
$480$	−0.236672	−	0.247982i	−0.0108026	−	0.0113188i
$481$		−	12.2582i		−	0.558924i
$482$		−	8.92445i		−	0.406498i
$483$	28.4872	−	27.1879i	1.29621	−	1.23709i
$484$		0			0
$485$		−	0.308702i		−	0.0140174i
$486$	−12.2308	+	9.66474i	−0.554801	+	0.438402i
$487$	−19.5744			−0.887002			−0.443501	−	0.896274i	$-0.646264\pi$
$487$	−19.5744			−0.887002			−0.443501	+	0.896274i	$0.646264\pi$
$488$			8.42607i			0.381430i
$489$	−28.4113	+	27.1155i	−1.28480	+	1.22620i
$490$			0.938899i			0.0424151i
$491$	−0.0551780			−0.00249015			−0.00124507	−	0.999999i	$-0.500396\pi$
$491$	−0.0551780			−0.00249015			−0.00124507	+	0.999999i	$0.500396\pi$
$492$	11.9492	−	11.4042i	0.538714	−	0.514143i
$493$	0.780686			0.0351603
$494$	9.27939			0.417500
$495$		0			0
$496$	5.60842			0.251825
$497$	29.0786			1.30436
$498$	1.55122	−	1.48047i	0.0695120	−	0.0663416i
$499$	10.0239			0.448731			0.224365	−	0.974505i	$-0.427969\pi$
$499$	10.0239			0.448731			0.224365	+	0.974505i	$0.427969\pi$
$500$		−	1.97138i		−	0.0881628i
$501$	7.59720	−	7.25069i	0.339418	−	0.323937i
$502$		−	25.8964i		−	1.15581i
$503$	−40.0976			−1.78786			−0.893932	−	0.448202i	$-0.852065\pi$
$503$	−40.0976			−1.78786			−0.893932	+	0.448202i	$0.852065\pi$
$504$	−10.2697	−	0.479587i	−0.457447	−	0.0213625i
$505$			1.73292i			0.0771137i
$506$		0			0
$507$	12.7946	−	12.2110i	0.568228	−	0.542312i
$508$			4.46362i			0.198041i
$509$		−	19.4803i		−	0.863449i	−0.902006	−	0.431724i	$-0.857905\pi$
$509$		−	19.4803i		−	0.863449i	0.902006	−	0.431724i	$-0.142095\pi$
$510$	1.80353	+	1.88972i	0.0798615	+	0.0836780i
$511$	3.15158			0.139418
$512$	1.00000			0.0441942
$513$	21.7946	−	18.9387i	0.962257	−	0.836165i
$514$			14.6153i			0.644655i
$515$			1.69409i			0.0746507i
$516$	−2.33777	−	2.44949i	−0.102915	−	0.107833i
$517$		0			0
$518$		−	25.1554i		−	1.10527i
$519$	3.80804	−	3.63435i	0.167154	−	0.159530i
$520$	−0.330504			−0.0144935
$521$		−	37.3546i		−	1.63654i	−0.574837	−	0.818268i	$-0.694934\pi$
$521$		−	37.3546i		−	1.63654i	0.574837	−	0.818268i	$-0.305066\pi$
$522$	−0.0143371	+	0.307008i	−0.000627517	+	0.0134374i
$523$			17.8602i			0.780974i	0.920608	+	0.390487i	$0.127693\pi$
$523$			17.8602i			0.780974i	−0.920608	+	0.390487i	$0.872307\pi$
$524$	21.3040			0.930670
$525$	−20.3299	−	21.3014i	−0.887268	−	0.929670i
$526$	−9.22928			−0.402416
$527$	−42.7382			−1.86170
$528$		0			0
$529$	−21.0141			−0.913658
$530$	1.49353			0.0648747
$531$	−19.5812	−	0.914430i	−0.849751	−	0.0396829i
$532$	19.0426			0.825601
$533$		−	15.9256i		−	0.689814i
$534$	2.45013	+	2.56722i	0.106027	+	0.111094i
$535$			2.14246i			0.0926267i
$536$	−4.42223			−0.191011
$537$	0.800505	+	0.838761i	0.0345443	+	0.0361952i
$538$			20.7596i			0.895011i
$539$		0			0
$540$	−0.776259	+	0.674539i	−0.0334049	+	0.0290275i
$541$			19.5264i			0.839507i	0.907638	+	0.419753i	$0.137883\pi$
$541$			19.5264i			0.839507i	−0.907638	+	0.419753i	$0.862117\pi$
$542$		−	12.2210i		−	0.524937i
$543$	−25.9544	+	24.7707i	−1.11381	+	1.06301i
$544$	−7.62036			−0.326720
$545$	1.35553			0.0580646
$546$	−7.17060	+	6.84355i	−0.306873	+	0.292877i
$547$		−	25.3055i		−	1.08199i	−0.841027	−	0.540993i	$-0.818049\pi$
$547$		−	25.3055i		−	1.08199i	0.841027	−	0.540993i	$-0.181951\pi$
$548$		−	10.3810i		−	0.443454i
$549$	25.2507	+	1.17919i	1.07767	+	0.0503267i
$550$		0			0
$551$		−	0.569271i		−	0.0242518i
$552$	7.93356	+	8.31270i	0.337675	+	0.353812i
$553$	−14.6348			−0.622334
$554$			28.6802i			1.21850i
$555$	−1.73728	−	1.82031i	−0.0737436	−	0.0772677i
$556$		−	4.51762i		−	0.191590i
$557$	5.82378			0.246761			0.123381	−	0.992359i	$-0.460626\pi$
$557$	5.82378			0.246761			0.123381	+	0.992359i	$0.460626\pi$
$558$	0.784874	−	16.8069i	0.0332264	−	0.711494i
$559$	−3.26461			−0.138078
$560$	−0.678239			−0.0286608
$561$		0			0
$562$	4.28863			0.180905
$563$	15.3272			0.645963			0.322981	−	0.946405i	$-0.395315\pi$
$563$	15.3272			0.645963			0.322981	+	0.946405i	$0.395315\pi$
$564$	−9.55392	−	10.0105i	−0.402293	−	0.421518i
$565$	2.10256			0.0884554
$566$		−	1.51575i		−	0.0637117i
$567$	−2.87439	+	30.7083i	−0.120713	+	1.28963i
$568$			8.48528i			0.356034i
$569$	18.2765			0.766193			0.383096	−	0.923708i	$-0.374858\pi$
$569$	18.2765			0.766193			0.383096	+	0.923708i	$0.374858\pi$
$570$	1.37797	−	1.31512i	0.0577167	−	0.0550843i
$571$			3.71463i			0.155452i	0.996975	+	0.0777262i	$0.0247660\pi$
$571$			3.71463i			0.155452i	−0.996975	+	0.0777262i	$0.975234\pi$
$572$		0			0
$573$	18.7613	+	19.6579i	0.783766	+	0.821222i
$574$		−	32.6815i		−	1.36410i
$575$			32.9117i			1.37251i
$576$	0.139946	−	2.99673i	0.00583107	−	0.124864i
$577$	−16.1516			−0.672399			−0.336200	−	0.941791i	$-0.609142\pi$
$577$	−16.1516			−0.672399			−0.336200	+	0.941791i	$0.609142\pi$
$578$	41.0699			1.70828
$579$	14.1023	+	14.7763i	0.586072	+	0.614080i
$580$			0.0202757i			0.000841903i
$581$		−	4.24264i		−	0.176014i
$582$	1.95439	−	1.86525i	0.0810119	−	0.0773170i
$583$		0			0
$584$			0.919646i			0.0380552i
$585$	−0.0462526	+	0.990431i	−0.00191231	+	0.0409493i
$586$	−12.3823			−0.511510
$587$			25.1733i			1.03901i	0.854466	+	0.519507i	$0.173885\pi$
$587$			25.1733i			1.03901i	−0.854466	+	0.519507i	$0.826115\pi$
$588$	−5.94416	+	5.67304i	−0.245133	+	0.233952i
$589$			31.1644i			1.28411i
$590$	−1.29320			−0.0532402
$591$	−3.83824	+	3.66318i	−0.157884	+	0.150683i
$592$	7.34047			0.301691
$593$	27.7761			1.14063			0.570314	−	0.821427i	$-0.306821\pi$
$593$	27.7761			1.14063			0.570314	+	0.821427i	$0.306821\pi$
$594$		0			0
$595$	5.16843			0.211885
$596$	3.73007			0.152790
$597$	−15.1151	+	14.4257i	−0.618620	+	0.590405i
$598$	11.0789			0.453051
$599$		−	7.27097i		−	0.297084i	−0.988906	−	0.148542i	$-0.952542\pi$
$599$		−	7.27097i		−	0.297084i	0.988906	−	0.148542i	$-0.0474580\pi$
$600$	6.21585	−	5.93235i	0.253761	−	0.242187i
$601$			10.3617i			0.422664i	0.977414	+	0.211332i	$0.0677801\pi$
$601$			10.3617i			0.422664i	−0.977414	+	0.211332i	$0.932220\pi$
$602$	−6.69942			−0.273048
$603$	−0.618873	+	13.2523i	−0.0252024	+	0.539673i
$604$		−	3.06248i		−	0.124611i
$605$		0			0
$606$	−10.9711	+	10.4707i	−0.445669	+	0.425342i
$607$		−	25.9022i		−	1.05134i	−0.850690	−	0.525668i	$-0.823815\pi$
$607$		−	25.9022i		−	1.05134i	0.850690	−	0.525668i	$-0.176185\pi$
$608$			5.55672i			0.225355i
$609$	0.419837	+	0.439901i	0.0170127	+	0.0178257i
$610$	1.66763			0.0675204
$611$	−13.3417			−0.539747
$612$	−1.06644	+	22.8362i	−0.0431082	+	0.923098i
$613$			45.7223i			1.84671i	0.383952	+	0.923353i	$0.374563\pi$
$613$			45.7223i			1.84671i	−0.383952	+	0.923353i	$0.625437\pi$
$614$			4.80739i			0.194010i
$615$	−2.25705	−	2.36491i	−0.0910131	−	0.0953626i
$616$		0			0
$617$		−	29.7020i		−	1.19576i	−0.801586	−	0.597880i	$-0.796010\pi$
$617$		−	29.7020i		−	1.19576i	0.801586	−	0.597880i	$-0.203990\pi$
$618$	−10.7253	+	10.2361i	−0.431434	+	0.411757i
$619$	−11.7945			−0.474059			−0.237030	−	0.971502i	$-0.576174\pi$
$619$	−11.7945			−0.474059			−0.237030	+	0.971502i	$0.576174\pi$
$620$		−	1.10998i		−	0.0445779i
$621$	26.0212	−	22.6115i	1.04420	−	0.907366i
$622$		−	13.1417i		−	0.526933i
$623$	7.02141			0.281307
$624$	−1.99698	−	2.09241i	−0.0799431	−	0.0837636i
$625$	24.4140			0.976560
$626$	4.47284			0.178771
$627$		0			0
$628$	−16.3671			−0.653117
$629$	−55.9370			−2.23036
$630$	−0.0949167	+	2.03250i	−0.00378157	+	0.0809768i
$631$	−2.63587			−0.104932			−0.0524662	−	0.998623i	$-0.516708\pi$
$631$	−2.63587			−0.104932			−0.0524662	+	0.998623i	$0.516708\pi$
$632$		−	4.27050i		−	0.169871i
$633$	−20.5233	−	21.5041i	−0.815728	−	0.854712i
$634$		−	32.5486i		−	1.29267i
$635$	0.883410			0.0350571
$636$	9.02425	+	9.45551i	0.357835	+	0.374935i
$637$			7.92219i			0.313889i
$638$		0			0
$639$	25.4281	+	1.18748i	1.00592	+	0.0469760i
$640$		−	0.197913i		−	0.00782321i
$641$			30.5879i			1.20815i	0.796928	+	0.604075i	$0.206457\pi$
$641$			30.5879i			1.20815i	−0.796928	+	0.604075i	$0.793543\pi$
$642$	−13.5639	+	12.9452i	−0.535324	+	0.510908i
$643$	−1.76615			−0.0696503			−0.0348252	−	0.999393i	$-0.511087\pi$
$643$	−1.76615			−0.0696503			−0.0348252	+	0.999393i	$0.511087\pi$
$644$	22.7355			0.895903
$645$	−0.484786	+	0.462675i	−0.0190884	+	0.0182178i
$646$		−	42.3442i		−	1.66601i
$647$		−	35.2961i		−	1.38763i	−0.720151	−	0.693817i	$-0.755928\pi$
$647$		−	35.2961i		−	1.38763i	0.720151	−	0.693817i	$-0.244072\pi$
$648$	−8.96083	−	0.838761i	−0.352015	−	0.0329496i
$649$		0			0
$650$		−	8.28430i		−	0.324937i
$651$	−22.9837	−	24.0821i	−0.900803	−	0.943852i
$652$	−22.6749			−0.888017
$653$			40.0032i			1.56545i	0.622371	+	0.782723i	$0.286170\pi$
$653$			40.0032i			1.56545i	−0.622371	+	0.782723i	$0.713830\pi$
$654$	8.19043	+	8.58185i	0.320271	+	0.335577i
$655$		−	4.21634i		−	0.164746i
$656$	9.53662			0.372343
$657$	2.75594	+	0.128701i	0.107519	+	0.00502109i
$658$	−27.3790			−1.06734
$659$	15.3212			0.596830			0.298415	−	0.954436i	$-0.403542\pi$
$659$	15.3212			0.596830			0.298415	+	0.954436i	$0.403542\pi$
$660$		0			0
$661$	10.0745			0.391853			0.195926	−	0.980619i	$-0.437229\pi$
$661$	10.0745			0.391853			0.195926	+	0.980619i	$0.437229\pi$
$662$	0.533922			0.0207515
$663$	15.2177	+	15.9449i	0.591006	+	0.619250i
$664$	1.23802			0.0480446
$665$		−	3.76878i		−	0.146147i
$666$	1.02727	−	21.9974i	0.0398058	−	0.852383i
$667$		−	0.679668i		−	0.0263169i
$668$	6.06328			0.234595
$669$	−32.5301	+	31.0464i	−1.25769	+	1.20032i
$670$			0.875218i			0.0338126i
$671$		0			0
$672$	−4.09808	−	4.29392i	−0.158087	−	0.165642i
$673$		−	21.4133i		−	0.825421i	−0.910862	−	0.412711i	$-0.864582\pi$
$673$		−	21.4133i		−	0.825421i	0.910862	−	0.412711i	$-0.135418\pi$
$674$		−	18.4416i		−	0.710345i
$675$	−16.9078	−	19.4575i	−0.650781	−	0.748918i
$676$	10.2113			0.392742
$677$	42.8376			1.64638			0.823191	−	0.567765i	$-0.192192\pi$
$677$	42.8376			1.64638			0.823191	+	0.567765i	$0.192192\pi$
$678$	12.7042	+	13.3113i	0.487900	+	0.511217i
$679$		−	5.34530i		−	0.205134i
$680$			1.50817i			0.0578357i
$681$	−8.52666	+	8.13776i	−0.326742	+	0.311840i
$682$		0			0
$683$			2.89356i			0.110719i	0.998466	+	0.0553595i	$0.0176305\pi$
$683$			2.89356i			0.110719i	−0.998466	+	0.0553595i	$0.982369\pi$
$684$	16.6520	+	0.777639i	0.636705	+	0.0297338i
$685$	−2.05454			−0.0784998
$686$		−	7.73122i		−	0.295180i
$687$	−6.96971	+	6.65183i	−0.265911	+	0.253783i
$688$		−	1.95492i		−	0.0745307i
$689$	12.6020			0.480099
$690$	1.64519	−	1.57016i	0.0626314	−	0.0597749i
$691$	−30.5073			−1.16055			−0.580276	−	0.814420i	$-0.697055\pi$
$691$	−30.5073			−1.16055			−0.580276	+	0.814420i	$0.697055\pi$
$692$	3.03917			0.115532
$693$		0			0
$694$	22.7472			0.863472
$695$	−0.894097			−0.0339150
$696$	−0.128365	+	0.122510i	−0.00486567	+	0.00464375i
$697$	−72.6725			−2.75267
$698$			31.5774i			1.19522i
$699$	−22.7429	+	21.7056i	−0.860214	+	0.820980i
$700$		−	17.0005i		−	0.642559i
$701$	−32.1166			−1.21303			−0.606513	−	0.795073i	$-0.707432\pi$
$701$	−32.1166			−1.21303			−0.606513	+	0.795073i	$0.707432\pi$
$702$	−6.54987	+	5.69159i	−0.247209	+	0.214815i
$703$			40.7889i			1.53838i
$704$		0			0
$705$	−1.98121	+	1.89085i	−0.0746167	+	0.0712134i
$706$		−	1.52435i		−	0.0573697i
$707$			30.0062i			1.12850i
$708$	−7.81381	−	8.18723i	−0.293661	−	0.307695i
$709$	23.5254			0.883515			0.441758	−	0.897134i	$-0.354355\pi$
$709$	23.5254			0.883515			0.441758	+	0.897134i	$0.354355\pi$
$710$	1.67935			0.0630249
$711$	−12.7975	−	0.597638i	−0.479945	−	0.0224132i
$712$			2.04888i			0.0767850i
$713$			37.2080i			1.39345i
$714$	31.2288	+	32.7212i	1.16871	+	1.22456i
$715$		0			0
$716$			0.669410i			0.0250170i
$717$	8.97517	−	8.56581i	0.335184	−	0.319896i
$718$	3.16600			0.118154
$719$		−	18.1927i		−	0.678472i	−0.940701	−	0.339236i	$-0.889831\pi$
$719$		−	18.1927i		−	0.678472i	0.940701	−	0.339236i	$-0.110169\pi$
$720$	−0.593093	−	0.0276971i	−0.0221033	−	0.00103221i
$721$			29.3340i			1.09245i
$722$	−11.8771			−0.442020
$723$	−10.6722	−	11.1822i	−0.396903	−	0.415871i
$724$	−20.7141			−0.769832
$725$	−0.508224			−0.0188750
$726$		0			0
$727$	35.7165			1.32465			0.662326	−	0.749216i	$-0.269570\pi$
$727$	35.7165			1.32465			0.662326	+	0.749216i	$0.269570\pi$
$728$	−5.72281			−0.212101
$729$	−3.76757	+	26.7358i	−0.139540	+	0.990216i
$730$	0.182010			0.00673650
$731$			14.8972i			0.550993i
$732$	10.0762	+	10.5577i	0.372427	+	0.390225i
$733$			39.8789i			1.47296i	0.676458	+	0.736481i	$0.263514\pi$
$733$			39.8789i			1.47296i	−0.676458	+	0.736481i	$0.736486\pi$
$734$	8.99273			0.331928
$735$	1.12277	+	1.17643i	0.0414140	+	0.0433932i
$736$			6.63432i			0.244544i
$737$		0			0
$738$	1.33461	−	28.5787i	0.0491277	−	1.05200i
$739$			23.5502i			0.866308i	0.901320	+	0.433154i	$0.142599\pi$
$739$			23.5502i			0.866308i	−0.901320	+	0.433154i	$0.857401\pi$
$740$		−	1.45278i		−	0.0534051i
$741$	11.6269	−	11.0966i	0.427126	−	0.407645i
$742$	25.8611			0.949390
$743$	−27.7107			−1.01661			−0.508304	−	0.861178i	$-0.669727\pi$
$743$	−27.7107			−1.01661			−0.508304	+	0.861178i	$0.669727\pi$
$744$	7.02727	−	6.70676i	0.257632	−	0.245882i
$745$		−	0.738231i		−	0.0270467i
$746$		−	2.25776i		−	0.0826624i
$747$	0.173256	−	3.71002i	0.00633910	−	0.135743i
$748$		0			0
$749$			37.0976i			1.35552i
$750$	−2.35745	−	2.47011i	−0.0860819	−	0.0901957i
$751$	28.2921			1.03239			0.516196	−	0.856471i	$-0.327348\pi$
$751$	28.2921			1.03239			0.516196	+	0.856471i	$0.327348\pi$
$752$		−	7.98932i		−	0.291340i
$753$	−30.9679	−	32.4478i	−1.12853	−	1.18246i
$754$			0.171081i			0.00623041i
$755$	−0.606106			−0.0220584
$756$	−13.4412	+	11.6799i	−0.488853	+	0.424795i
$757$	38.3101			1.39241			0.696203	−	0.717845i	$-0.254872\pi$
$757$	38.3101			1.39241			0.696203	+	0.717845i	$0.254872\pi$
$758$	5.62763			0.204405
$759$		0			0
$760$	1.09975			0.0398920
$761$	21.2534			0.770435			0.385217	−	0.922826i	$-0.374126\pi$
$761$	21.2534			0.770435			0.385217	+	0.922826i	$0.374126\pi$
$762$	5.33777	+	5.59286i	0.193367	+	0.202608i
$763$	23.4716			0.849729
$764$			15.6889i			0.567603i
$765$	4.51958	+	0.211062i	0.163406	+	0.00763096i
$766$			4.50977i			0.162944i
$767$	−10.9117			−0.393998
$768$	1.25299	−	1.19584i	0.0452132	−	0.0431511i
$769$			42.1983i			1.52171i	0.648921	+	0.760855i	$0.275220\pi$
$769$			42.1983i			1.52171i	−0.648921	+	0.760855i	$0.724780\pi$
$770$		0			0
$771$	17.4776	+	18.3128i	0.629440	+	0.659520i
$772$			11.7928i			0.424434i
$773$			12.6236i			0.454039i	0.973890	+	0.227020i	$0.0728981\pi$
$773$			12.6236i			0.454039i	−0.973890	+	0.227020i	$0.927102\pi$
$774$	−5.85838	−	0.273583i	−0.210575	−	0.00983374i
$775$	27.8224			0.999411
$776$	1.55978			0.0559930
$777$	−30.0818	−	31.5194i	−1.07918	−	1.13075i
$778$			26.6308i			0.954762i
$779$			52.9923i			1.89865i
$780$	−0.414116	+	0.395228i	−0.0148277	+	0.0141514i
$781$		0			0
$782$		−	50.5559i		−	1.80787i
$783$	0.349167	+	0.401821i	0.0124782	+	0.0143599i
$784$	−4.74399			−0.169428
$785$			3.23926i			0.115614i
$786$	26.6936	−	25.4761i	0.952129	−	0.908703i
$787$		−	12.3366i		−	0.439753i	−0.975528	−	0.219877i	$-0.929435\pi$
$787$		−	12.3366i		−	0.439753i	0.975528	−	0.219877i	$-0.0705654\pi$
$788$	−3.06328			−0.109125
$789$	−11.5642	+	11.0367i	−0.411695	+	0.392918i
$790$	−0.845188			−0.0300704
$791$	36.4067			1.29447
$792$		0			0
$793$	14.0710			0.499677
$794$	15.3405			0.544413
$795$	1.87137	−	1.78602i	0.0663707	−	0.0633435i
$796$	−12.0633			−0.427572
$797$		−	8.83217i		−	0.312852i	−0.987690	−	0.156426i	$-0.950003\pi$
$797$		−	8.83217i		−	0.312852i	0.987690	−	0.156426i	$-0.0499972\pi$
$798$	23.8601	−	22.7718i	0.844638	−	0.806115i
$799$			60.8815i			2.15383i
$800$	4.96083			0.175392
$801$	6.13995	+	0.286732i	0.216944	+	0.0101312i
$802$		−	4.80782i		−	0.169770i
$803$		0			0
$804$	−5.54099	+	5.28827i	−0.195416	+	0.186503i
$805$		−	4.49965i		−	0.158592i
$806$		−	9.36573i		−	0.329894i
$807$	24.8251	+	26.0115i	0.873886	+	0.915648i
$808$	−8.75594			−0.308033
$809$	−15.2178			−0.535031			−0.267515	−	0.963554i	$-0.586203\pi$
$809$	−15.2178			−0.535031			−0.267515	+	0.963554i	$0.586203\pi$
$810$	−0.166002	+	1.77347i	−0.00583271	+	0.0623133i
$811$		−	41.7756i		−	1.46694i	−0.679722	−	0.733470i	$-0.737899\pi$
$811$		−	41.7756i		−	1.46694i	0.679722	−	0.733470i	$-0.262101\pi$
$812$			0.351082i			0.0123206i
$813$	−14.6143	−	15.3127i	−0.512547	−	0.537041i
$814$		0			0
$815$			4.48766i			0.157196i
$816$	−9.54820	+	9.11271i	−0.334254	+	0.319009i
$817$	10.8629			0.380046
$818$		−	25.5532i		−	0.893448i
$819$	−0.800883	+	17.1497i	−0.0279851	+	0.599260i
$820$		−	1.88742i		−	0.0659117i
$821$	−19.0675			−0.665459			−0.332729	−	0.943022i	$-0.607970\pi$
$821$	−19.0675			−0.665459			−0.332729	+	0.943022i	$0.607970\pi$
$822$	−12.4140	−	13.0072i	−0.432987	−	0.453679i
$823$	−9.81259			−0.342045			−0.171023	−	0.985267i	$-0.554707\pi$
$823$	−9.81259			−0.342045			−0.171023	+	0.985267i	$0.554707\pi$
$824$	−8.55978			−0.298194
$825$		0			0
$826$	−22.3923			−0.779128
$827$	−41.7340			−1.45123			−0.725617	−	0.688099i	$-0.758445\pi$
$827$	−41.7340			−1.45123			−0.725617	+	0.688099i	$0.758445\pi$
$828$	19.8813	+	0.928444i	0.690922	+	0.0322657i
$829$	−22.9136			−0.795821			−0.397910	−	0.917424i	$-0.630265\pi$
$829$	−22.9136			−0.795821			−0.397910	+	0.917424i	$0.630265\pi$
$830$		−	0.245021i		−	0.00850480i
$831$	34.2968	+	35.9358i	1.18974	+	1.24660i
$832$		−	1.66994i		−	0.0578948i
$833$	36.1509			1.25256
$834$	−5.40234	−	5.66051i	−0.187068	−	0.196008i
$835$		−	1.20000i		−	0.0415278i
$836$		0			0
$837$	−19.1149	−	21.9974i	−0.660709	−	0.760343i
$838$			0.820215i			0.0283339i
$839$			6.08715i			0.210152i	0.994464	+	0.105076i	$0.0335085\pi$
$839$			6.08715i			0.210152i	−0.994464	+	0.105076i	$0.966491\pi$
$840$	−0.849824	+	0.811063i	−0.0293217	+	0.0279843i
$841$	−28.9895			−0.999638
$842$	11.5211			0.397044
$843$	5.37360	−	5.12851i	0.185076	−	0.176635i
$844$		−	17.1623i		−	0.590751i
$845$		−	2.02095i		−	0.0695228i
$846$	−23.9419	−	1.11807i	−0.823138	−	0.0384401i
$847$		0			0
$848$			7.54638i			0.259144i
$849$	−1.81259	−	1.89921i	−0.0622079	−	0.0651808i
$850$	−37.8033			−1.29664
$851$			48.6990i			1.66938i
$852$	10.1470	+	10.6319i	0.347631	+	0.364244i
$853$		−	25.8152i		−	0.883894i	−0.897041	−	0.441947i	$-0.854288\pi$
$853$		−	25.8152i		−	0.883894i	0.897041	−	0.441947i	$-0.145712\pi$
$854$	28.8757			0.988107
$855$	0.153905	−	3.29565i	0.00526344	−	0.112709i
$856$	−10.8253			−0.370000
$857$	−41.7371			−1.42571			−0.712855	−	0.701311i	$-0.752598\pi$
$857$	−41.7371			−1.42571			−0.712855	+	0.701311i	$0.752598\pi$
$858$		0			0
$859$	−22.9322			−0.782435			−0.391218	−	0.920298i	$-0.627946\pi$
$859$	−22.9322			−0.782435			−0.391218	+	0.920298i	$0.627946\pi$
$860$	−0.386905			−0.0131934
$861$	−39.0818	−	40.9495i	−1.33190	−	1.39555i
$862$	24.8280			0.845644
$863$			24.8329i			0.845322i	0.906288	+	0.422661i	$0.138904\pi$
$863$			24.8329i			0.845322i	−0.906288	+	0.422661i	$0.861096\pi$
$864$	−3.40826	−	3.92222i	−0.115951	−	0.133437i
$865$		−	0.601492i		−	0.0204513i
$866$	16.9217			0.575021
$867$	51.4600	−	49.1129i	1.74767	−	1.66796i
$868$		−	19.2198i		−	0.652362i
$869$		0			0
$870$	0.0242464	+	0.0254052i	0.000822031	+	0.000861315i
$871$			7.38487i			0.250227i
$872$			6.84912i			0.231940i
$873$	0.218285	−	4.67426i	0.00738783	−	0.158200i
$874$	−36.8650			−1.24698
$875$	−6.75582			−0.228388
$876$	1.09975	+	1.15230i	0.0371570	+	0.0389327i
$877$		−	2.16903i		−	0.0732431i	−0.999329	−	0.0366215i	$-0.988340\pi$
$877$		−	2.16903i		−	0.0732431i	0.999329	−	0.0366215i	$-0.0116596\pi$
$878$		−	0.597501i		−	0.0201647i
$879$	−15.5149	+	14.8073i	−0.523304	+	0.499437i
$880$		0			0
$881$		−	32.6529i		−	1.10010i	−0.835131	−	0.550052i	$-0.814608\pi$
$881$		−	32.6529i		−	1.10010i	0.835131	−	0.550052i	$-0.185392\pi$
$882$	−0.663902	+	14.2165i	−0.0223547	+	0.478694i
$883$	25.5513			0.859868			0.429934	−	0.902860i	$-0.358537\pi$
$883$	25.5513			0.859868			0.429934	+	0.902860i	$0.358537\pi$
$884$			12.7256i			0.428007i
$885$	−1.62036	+	1.54646i	−0.0544678	+	0.0519836i
$886$		−	8.28500i		−	0.278340i
$887$	−38.7177			−1.30001			−0.650007	−	0.759928i	$-0.725234\pi$
$887$	−38.7177			−1.30001			−0.650007	+	0.759928i	$0.725234\pi$
$888$	9.19750	−	8.77801i	0.308648	−	0.294571i
$889$	15.2966			0.513032
$890$	0.405500			0.0135924
$891$		0			0
$892$	−25.9621			−0.869274
$893$	44.3944			1.48560
$894$	4.67373	−	4.46056i	0.156313	−	0.149184i
$895$	0.132485			0.00442849
$896$		−	3.42695i		−	0.114486i
$897$	13.8817	−	13.2486i	0.463497	−	0.442357i
$898$		−	17.7377i		−	0.591916i
$899$	−0.574568			−0.0191629
$900$	0.694247	−	14.8663i	0.0231416	−	0.495543i
$901$		−	57.5062i		−	1.91581i
$902$		0			0
$903$	−8.39428	+	8.01142i	−0.279344	+	0.266603i
$904$			10.6236i			0.353337i
$905$			4.09959i			0.136275i
$906$	−3.66223	−	3.83725i	−0.121669	−	0.127484i
$907$	24.0024			0.796987			0.398494	−	0.917171i	$-0.369533\pi$
$907$	24.0024			0.796987			0.398494	+	0.917171i	$0.369533\pi$
$908$	−6.80507			−0.225834
$909$	−1.22536	+	26.2392i	−0.0406425	+	0.870300i
$910$			1.13262i			0.0375460i
$911$		−	3.01161i		−	0.0997792i	−0.998755	−	0.0498896i	$-0.984113\pi$
$911$		−	3.01161i		−	0.0997792i	0.998755	−	0.0498896i	$-0.0158869\pi$
$912$	6.64493	+	6.96248i	0.220036	+	0.230551i
$913$		0			0
$914$			41.0955i			1.35932i
$915$	2.08952	−	1.99421i	0.0690773	−	0.0659267i
$916$	−5.56248			−0.183790
$917$		−	73.0078i		−	2.41093i
$918$	25.9721	+	29.8887i	0.857209	+	0.986474i
$919$		−	3.12099i		−	0.102952i	−0.998674	−	0.0514759i	$-0.983607\pi$
$919$		−	3.12099i		−	0.102952i	0.998674	−	0.0514759i	$-0.0163925\pi$
$920$	1.31302			0.0432889
$921$	5.74885	+	6.02359i	0.189431	+	0.198484i
$922$	12.1741			0.400933
$923$	14.1699			0.466409
$924$		0			0
$925$	36.4148			1.19731
$926$	−32.5767			−1.07054
$927$	−1.19791	+	25.6514i	−0.0393444	+	0.842502i
$928$	−0.102447			−0.00336300
$929$		−	15.4296i		−	0.506230i	−0.967436	−	0.253115i	$-0.918545\pi$
$929$		−	15.4296i		−	0.506230i	0.967436	−	0.253115i	$-0.0814551\pi$
$930$	−1.32736	−	1.39079i	−0.0435257	−	0.0456058i
$931$		−	26.3610i		−	0.863948i
$932$	−18.1509			−0.594554
$933$	−15.7153	−	16.4663i	−0.514495	−	0.539083i
$934$		−	27.0064i		−	0.883676i
$935$		0			0
$936$	−5.00437	−	0.233701i	−0.163573	−	0.00763877i
$937$		−	7.77973i		−	0.254153i	−0.991893	−	0.127076i	$-0.959441\pi$
$937$		−	7.77973i		−	0.254153i	0.991893	−	0.127076i	$-0.0405593\pi$
$938$			15.1548i			0.494821i
$939$	5.60441	−	5.34879i	0.182893	−	0.174551i
$940$	−1.58119			−0.0515728
$941$	−25.8138			−0.841506			−0.420753	−	0.907175i	$-0.638234\pi$
$941$	−25.8138			−0.841506			−0.420753	+	0.907175i	$0.638234\pi$
$942$	−20.5077	+	19.5723i	−0.668176	+	0.637701i
$943$			63.2690i			2.06032i
$944$		−	6.53418i		−	0.212669i
$945$	2.31161	+	2.66020i	0.0751968	+	0.0865363i
$946$		0			0
$947$			58.4123i			1.89814i	0.315058	+	0.949072i	$0.397976\pi$
$947$			58.4123i			1.89814i	−0.315058	+	0.949072i	$0.602024\pi$
$948$	−5.10682	−	5.35087i	−0.165862	−	0.173788i
$949$	1.53576			0.0498527
$950$			27.5659i			0.894357i
$951$	−38.9229	−	40.7830i	−1.26216	−	1.32248i
$952$			26.1146i			0.846379i
$953$	55.6803			1.80366			0.901831	−	0.432089i	$-0.142223\pi$
$953$	55.6803			1.80366			0.901831	+	0.432089i	$0.142223\pi$
$954$	22.6145	+	1.05608i	0.732172	+	0.0341920i
$955$	3.10503			0.100477
$956$	7.16303			0.231669
$957$		0			0
$958$	10.7388			0.346955
$959$	−35.5751			−1.14878
$960$	−0.236672	−	0.247982i	−0.00763856	−	0.00800360i
$961$	0.454359			0.0146567
$962$		−	12.2582i		−	0.395219i
$963$	−1.51495	+	32.4404i	−0.0488185	+	1.04538i
$964$		−	8.92445i		−	0.287437i
$965$	2.33396			0.0751328
$966$	28.4872	−	27.1879i	0.916561	−	0.874757i
$967$		−	45.0742i		−	1.44949i	−0.689018	−	0.724744i	$-0.741958\pi$
$967$		−	45.0742i		−	1.44949i	0.689018	−	0.724744i	$-0.258042\pi$
$968$		0			0
$969$	−50.6368	−	53.0566i	−1.62669	−	1.70443i
$970$		−	0.308702i		−	0.00991181i
$971$		−	45.7887i		−	1.46943i	−0.678376	−	0.734715i	$-0.737316\pi$
$971$		−	45.7887i		−	1.46943i	0.678376	−	0.734715i	$-0.262684\pi$
$972$	−12.2308	+	9.66474i	−0.392303	+	0.309997i
$973$	−15.4817			−0.496319
$974$	−19.5744			−0.627205
$975$	−9.90667	−	10.3801i	−0.317267	−	0.332429i
$976$			8.42607i			0.269712i
$977$			27.2150i			0.870684i	0.900265	+	0.435342i	$0.143372\pi$
$977$			27.2150i			0.870684i	−0.900265	+	0.435342i	$0.856628\pi$
$978$	−28.4113	+	27.1155i	−0.908494	+	0.867058i
$979$		0			0
$980$			0.938899i			0.0299920i
$981$	20.5250	+	0.958505i	0.655312	+	0.0306027i
$982$	−0.0551780			−0.00176080
$983$		−	8.55859i		−	0.272977i	−0.990642	−	0.136488i	$-0.956418\pi$
$983$		−	8.55859i		−	0.272977i	0.990642	−	0.136488i	$-0.0435816\pi$
$984$	11.9492	−	11.4042i	0.380928	−	0.363554i
$985$			0.606263i			0.0193172i
$986$	0.780686			0.0248621
$987$	−34.3055	+	32.7408i	−1.09196	+	1.04215i
$988$	9.27939			0.295217
$989$	12.9696			0.412408
$990$		0			0
$991$	−47.5069			−1.50911			−0.754553	−	0.656239i	$-0.772147\pi$
$991$	−47.5069			−1.50911			−0.754553	+	0.656239i	$0.772147\pi$
$992$	5.60842			0.178067
$993$	0.668996	−	0.638484i	0.0212300	−	0.0202617i
$994$	29.0786			0.922319
$995$			2.38748i			0.0756883i
$996$	1.55122	−	1.48047i	0.0491524	−	0.0469106i
$997$			11.4127i			0.361444i	0.983534	+	0.180722i	$0.0578434\pi$
$997$			11.4127i			0.361444i	−0.983534	+	0.180722i	$0.942157\pi$
$998$	10.0239			0.317301
$999$	−25.0182	−	28.7909i	−0.791541	−	0.910904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.b.f.725.5	yes	8
3.2	odd	2		726.2.b.d.725.6	yes	8
11.2	odd	10		726.2.h.l.161.3		32
11.3	even	5		726.2.h.k.233.6		32
11.4	even	5		726.2.h.k.215.1		32
11.5	even	5		726.2.h.k.239.7		32
11.6	odd	10		726.2.h.l.239.7		32
11.7	odd	10		726.2.h.l.215.1		32
11.8	odd	10		726.2.h.l.233.6		32
11.9	even	5		726.2.h.k.161.3		32
11.10	odd	2		726.2.b.d.725.5	✓	8
33.2	even	10		726.2.h.k.161.7		32
33.5	odd	10		726.2.h.l.239.3		32
33.8	even	10		726.2.h.k.233.1		32
33.14	odd	10		726.2.h.l.233.1		32
33.17	even	10		726.2.h.k.239.3		32
33.20	odd	10		726.2.h.l.161.7		32
33.26	odd	10		726.2.h.l.215.6		32
33.29	even	10		726.2.h.k.215.6		32
33.32	even	2	inner	726.2.b.f.725.6	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
726.2.b.d.725.5	✓	8	11.10	odd	2
726.2.b.d.725.6	yes	8	3.2	odd	2
726.2.b.f.725.5	yes	8	1.1	even	1	trivial
726.2.b.f.725.6	yes	8	33.32	even	2	inner
726.2.h.k.161.3		32	11.9	even	5
726.2.h.k.161.7		32	33.2	even	10
726.2.h.k.215.1		32	11.4	even	5
726.2.h.k.215.6		32	33.29	even	10
726.2.h.k.233.1		32	33.8	even	10
726.2.h.k.233.6		32	11.3	even	5
726.2.h.k.239.3		32	33.17	even	10
726.2.h.k.239.7		32	11.5	even	5
726.2.h.l.161.3		32	11.2	odd	10
726.2.h.l.161.7		32	33.20	odd	10
726.2.h.l.215.1		32	11.7	odd	10
726.2.h.l.215.6		32	33.26	odd	10
726.2.h.l.233.1		32	33.14	odd	10
726.2.h.l.233.6		32	11.8	odd	10
726.2.h.l.239.3		32	33.5	odd	10
726.2.h.l.239.7		32	11.6	odd	10

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:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.25299 - 1.19584i) q^{3} +1.00000 q^{4} -0.197913i q^{5} +(1.25299 - 1.19584i) q^{6} -3.42695i q^{7} +1.00000 q^{8} +(0.139946 - 2.99673i) q^{9} -0.197913i q^{10} +(1.25299 - 1.19584i) q^{12} -1.66994i q^{13} -3.42695i q^{14} +(-0.236672 - 0.247982i) q^{15} +1.00000 q^{16} -7.62036 q^{17} +(0.139946 - 2.99673i) q^{18} +5.55672i q^{19} -0.197913i q^{20} +(-4.09808 - 4.29392i) q^{21} +6.63432i q^{23} +(1.25299 - 1.19584i) q^{24} +4.96083 q^{25} -1.66994i q^{26} +(-3.40826 - 3.92222i) q^{27} -3.42695i q^{28} -0.102447 q^{29} +(-0.236672 - 0.247982i) q^{30} +5.60842 q^{31} +1.00000 q^{32} -7.62036 q^{34} -0.678239 q^{35} +(0.139946 - 2.99673i) q^{36} +7.34047 q^{37} +5.55672i q^{38} +(-1.99698 - 2.09241i) q^{39} -0.197913i q^{40} +9.53662 q^{41} +(-4.09808 - 4.29392i) q^{42} -1.95492i q^{43} +(-0.593093 - 0.0276971i) q^{45} +6.63432i q^{46} -7.98932i q^{47} +(1.25299 - 1.19584i) q^{48} -4.74399 q^{49} +4.96083 q^{50} +(-9.54820 + 9.11271i) q^{51} -1.66994i q^{52} +7.54638i q^{53} +(-3.40826 - 3.92222i) q^{54} -3.42695i q^{56} +(6.64493 + 6.96248i) q^{57} -0.102447 q^{58} -6.53418i q^{59} +(-0.236672 - 0.247982i) q^{60} +8.42607i q^{61} +5.60842 q^{62} +(-10.2697 - 0.479587i) q^{63} +1.00000 q^{64} -0.330504 q^{65} -4.42223 q^{67} -7.62036 q^{68} +(7.93356 + 8.31270i) q^{69} -0.678239 q^{70} +8.48528i q^{71} +(0.139946 - 2.99673i) q^{72} +0.919646i q^{73} +7.34047 q^{74} +(6.21585 - 5.93235i) q^{75} +5.55672i q^{76} +(-1.99698 - 2.09241i) q^{78} -4.27050i q^{79} -0.197913i q^{80} +(-8.96083 - 0.838761i) q^{81} +9.53662 q^{82} +1.23802 q^{83} +(-4.09808 - 4.29392i) q^{84} +1.50817i q^{85} -1.95492i q^{86} +(-0.128365 + 0.122510i) q^{87} +2.04888i q^{89} +(-0.593093 - 0.0276971i) q^{90} -5.72281 q^{91} +6.63432i q^{92} +(7.02727 - 6.70676i) q^{93} -7.98932i q^{94} +1.09975 q^{95} +(1.25299 - 1.19584i) q^{96} +1.55978 q^{97} -4.74399 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 4 q^{6} + 8 q^{8} - 4 q^{9} + 4 q^{12} - 8 q^{15} + 8 q^{16} - 16 q^{17} - 4 q^{18} - 12 q^{21} + 4 q^{24} - 40 q^{25} + 16 q^{27} + 8 q^{29} - 8 q^{30} + 24 q^{31} + 8 q^{32}+ \cdots - 8 q^{97}+O(q^{100}) \) 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 4 * q^6 + 8 * q^8 - 4 * q^9 + 4 * q^12 - 8 * q^15 + 8 * q^16 - 16 * q^17 - 4 * q^18 - 12 * q^21 + 4 * q^24 - 40 * q^25 + 16 * q^27 + 8 * q^29 - 8 * q^30 + 24 * q^31 + 8 * q^32 - 16 * q^34 - 4 * q^36 + 24 * q^37 + 28 * q^39 - 12 * q^42 - 16 * q^45 + 4 * q^48 - 40 * q^50 - 28 * q^51 + 16 * q^54 + 16 * q^57 + 8 * q^58 - 8 * q^60 + 24 * q^62 - 12 * q^63 + 8 * q^64 - 32 * q^65 + 8 * q^67 - 16 * q^68 + 40 * q^69 - 4 * q^72 + 24 * q^74 - 12 * q^75 + 28 * q^78 + 8 * q^81 - 16 * q^83 - 12 * q^84 + 32 * q^87 - 16 * q^90 + 8 * q^91 + 64 * q^95 + 4 * q^96 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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