LMFDB - Embedded newform 1134.2.k.d.647.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(647,1134)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1134.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 796 x^{12} - 2228 x^{11} + 5254 x^{10} - 10232 x^{9} + \cdots + 225 $ x^16 - 8x^15 + 52x^14 - 224x^13 + 796x^12 - 2228x^11 + 5254x^10 - 10232x^9 + 16903x^8 - 23292x^7 + 26994x^6 - 25716x^5 + 19962x^4 - 12096x^3 + 5454x^2 - 1620*x + 225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			647.5
Root			$0.500000 + 1.42873i$ of defining polynomial
Character	$\chi$	$=$	1134.647
Dual form			1134.2.k.d.971.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.894533 - 1.54938i) q^{5} +(2.54252 + 0.731847i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.894533 - 1.54938i) q^{5} +(2.54252 + 0.731847i) q^{7} -1.00000i q^{8} +(-1.54938 - 0.894533i) q^{10} +(4.52838 + 2.61446i) q^{11} +5.03863i q^{13} +(2.56781 - 0.637461i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.13182 - 1.96037i) q^{17} +(-3.45534 + 1.99494i) q^{19} -1.78907 q^{20} +5.22892 q^{22} +(6.84102 - 3.94966i) q^{23} +(0.899620 - 1.55819i) q^{25} +(2.51931 + 4.36358i) q^{26} +(1.90506 - 1.83596i) q^{28} -3.38604i q^{29} +(6.73522 + 3.88858i) q^{31} +(-0.866025 - 0.500000i) q^{32} -2.26364i q^{34} +(-1.14046 - 4.59398i) q^{35} +(-3.74728 - 6.49047i) q^{37} +(-1.99494 + 3.45534i) q^{38} +(-1.54938 + 0.894533i) q^{40} -9.03171 q^{41} -8.81060 q^{43} +(4.52838 - 2.61446i) q^{44} +(3.94966 - 6.84102i) q^{46} +(2.07085 + 3.58682i) q^{47} +(5.92880 + 3.72147i) q^{49} -1.79924i q^{50} +(4.36358 + 2.51931i) q^{52} +(-1.93277 - 1.11588i) q^{53} -9.35489i q^{55} +(0.731847 - 2.54252i) q^{56} +(-1.69302 - 2.93240i) q^{58} +(5.43025 - 9.40546i) q^{59} +(3.65589 - 2.11073i) q^{61} +7.77717 q^{62} -1.00000 q^{64} +(7.80674 - 4.50722i) q^{65} +(-0.705066 + 1.22121i) q^{67} +(-1.13182 - 1.96037i) q^{68} +(-3.28466 - 3.40827i) q^{70} -2.11331i q^{71} +(-4.06851 - 2.34896i) q^{73} +(-6.49047 - 3.74728i) q^{74} +3.98988i q^{76} +(9.60011 + 9.96140i) q^{77} +(3.53115 + 6.11613i) q^{79} +(-0.894533 + 1.54938i) q^{80} +(-7.82169 + 4.51585i) q^{82} +3.52907 q^{83} -4.04979 q^{85} +(-7.63021 + 4.40530i) q^{86} +(2.61446 - 4.52838i) q^{88} +(-2.97335 - 5.15000i) q^{89} +(-3.68750 + 12.8108i) q^{91} -7.89932i q^{92} +(3.58682 + 2.07085i) q^{94} +(6.18183 + 3.56908i) q^{95} +19.3006i q^{97} +(6.99523 + 0.258485i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 + 8 * q^7	$ 16 q + 8 q^{4} + 8 q^{7} + 12 q^{11} + 12 q^{14} - 8 q^{16} + 12 q^{23} - 8 q^{25} + 4 q^{28} + 12 q^{31} + 60 q^{35} + 4 q^{37} - 12 q^{38} - 48 q^{41} - 32 q^{43} + 12 q^{44} + 4 q^{49} - 12 q^{52} + 12 q^{56} - 12 q^{58} - 24 q^{59} - 12 q^{61} - 48 q^{62} - 16 q^{64} + 48 q^{65} - 4 q^{67} - 24 q^{70} + 36 q^{73} + 36 q^{74} + 84 q^{77} + 8 q^{79} - 72 q^{83} + 24 q^{85} + 24 q^{86} + 24 q^{89} - 12 q^{91} - 36 q^{94} + 12 q^{95} + 36 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 + 8 * q^7 + 12 * q^11 + 12 * q^14 - 8 * q^16 + 12 * q^23 - 8 * q^25 + 4 * q^28 + 12 * q^31 + 60 * q^35 + 4 * q^37 - 12 * q^38 - 48 * q^41 - 32 * q^43 + 12 * q^44 + 4 * q^49 - 12 * q^52 + 12 * q^56 - 12 * q^58 - 24 * q^59 - 12 * q^61 - 48 * q^62 - 16 * q^64 + 48 * q^65 - 4 * q^67 - 24 * q^70 + 36 * q^73 + 36 * q^74 + 84 * q^77 + 8 * q^79 - 72 * q^83 + 24 * q^85 + 24 * q^86 + 24 * q^89 - 12 * q^91 - 36 * q^94 + 12 * q^95 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.894533	−	1.54938i	−0.400048	−	0.692903i	0.593684	−	0.804699i	$-0.297673\pi$
$5$	−0.894533	−	1.54938i	−0.400048	−	0.692903i	−0.993731	+	0.111796i	$0.964340\pi$
$6$		0			0
$7$	2.54252	+	0.731847i	0.960982	+	0.276612i
$7$	2.54252	+	0.731847i	0.960982	+	0.276612i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−1.54938	−	0.894533i	−0.489956	−	0.282876i
$11$	4.52838	+	2.61446i	1.36536	+	0.788290i	0.990331	−	0.138724i	$-0.0443001\pi$
$11$	4.52838	+	2.61446i	1.36536	+	0.788290i	0.375027	+	0.927014i	$0.377633\pi$
$12$		0			0
$13$			5.03863i			1.39746i	0.715383	+	0.698732i	$0.246252\pi$
$13$			5.03863i			1.39746i	−0.715383	+	0.698732i	$0.753748\pi$
$14$	2.56781	−	0.637461i	0.686276	−	0.170369i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.13182	−	1.96037i	0.274506	−	0.475458i	−0.695504	−	0.718522i	$-0.744819\pi$
$17$	1.13182	−	1.96037i	0.274506	−	0.475458i	0.970010	+	0.243063i	$0.0781523\pi$
$18$		0			0
$19$	−3.45534	+	1.99494i	−0.792709	+	0.457671i	−0.840915	−	0.541167i	$-0.817983\pi$
$19$	−3.45534	+	1.99494i	−0.792709	+	0.457671i	0.0482065	+	0.998837i	$0.484649\pi$
$20$	−1.78907			−0.400048
$21$		0			0
$22$	5.22892			1.11481
$23$	6.84102	−	3.94966i	1.42645	−	0.823561i	0.429612	−	0.903014i	$-0.358650\pi$
$23$	6.84102	−	3.94966i	1.42645	−	0.823561i	0.996839	+	0.0794524i	$0.0253172\pi$
$24$		0			0
$25$	0.899620	−	1.55819i	0.179924	−	0.311637i
$26$	2.51931	+	4.36358i	0.494078	+	0.855769i
$27$		0			0
$28$	1.90506	−	1.83596i	0.360022	−	0.346964i
$29$		−	3.38604i		−	0.628772i	−0.949295	−	0.314386i	$-0.898201\pi$
$29$		−	3.38604i		−	0.628772i	0.949295	−	0.314386i	$-0.101799\pi$
$30$		0			0
$31$	6.73522	+	3.88858i	1.20968	+	0.698410i	0.962690	−	0.270607i	$-0.0872245\pi$
$31$	6.73522	+	3.88858i	1.20968	+	0.698410i	0.246992	+	0.969017i	$0.420558\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$		−	2.26364i		−	0.388210i
$35$	−1.14046	−	4.59398i	−0.192773	−	0.776525i
$36$		0			0
$37$	−3.74728	−	6.49047i	−0.616049	−	1.06703i	−0.990200	−	0.139660i	$-0.955399\pi$
$37$	−3.74728	−	6.49047i	−0.616049	−	1.06703i	0.374151	−	0.927368i	$-0.377934\pi$
$38$	−1.99494	+	3.45534i	−0.323622	+	0.560530i
$39$		0			0
$40$	−1.54938	+	0.894533i	−0.244978	+	0.141438i
$41$	−9.03171			−1.41052			−0.705258	−	0.708951i	$-0.749169\pi$
$41$	−9.03171			−1.41052			−0.705258	+	0.708951i	$0.749169\pi$
$42$		0			0
$43$	−8.81060			−1.34360			−0.671802	−	0.740731i	$-0.734479\pi$
$43$	−8.81060			−1.34360			−0.671802	+	0.740731i	$0.734479\pi$
$44$	4.52838	−	2.61446i	0.682679	−	0.394145i
$45$		0			0
$46$	3.94966	−	6.84102i	0.582346	−	1.00865i
$47$	2.07085	+	3.58682i	0.302064	+	0.523191i	0.976603	−	0.215048i	$-0.0689909\pi$
$47$	2.07085	+	3.58682i	0.302064	+	0.523191i	−0.674539	+	0.738239i	$0.735658\pi$
$48$		0			0
$49$	5.92880	+	3.72147i	0.846972	+	0.531638i
$50$		−	1.79924i		−	0.254451i
$51$		0			0
$52$	4.36358	+	2.51931i	0.605120	+	0.349366i
$53$	−1.93277	−	1.11588i	−0.265486	−	0.153278i	0.361349	−	0.932431i	$-0.382316\pi$
$53$	−1.93277	−	1.11588i	−0.265486	−	0.153278i	−0.626834	+	0.779152i	$0.715650\pi$
$54$		0			0
$55$		−	9.35489i		−	1.26141i
$56$	0.731847	−	2.54252i	0.0977971	−	0.339758i
$57$		0			0
$58$	−1.69302	−	2.93240i	−0.222304	−	0.385042i
$59$	5.43025	−	9.40546i	0.706958	−	1.22449i	−0.259023	−	0.965871i	$-0.583400\pi$
$59$	5.43025	−	9.40546i	0.706958	−	1.22449i	0.965980	−	0.258616i	$-0.0832663\pi$
$60$		0			0
$61$	3.65589	−	2.11073i	0.468089	−	0.270251i	−0.247350	−	0.968926i	$-0.579560\pi$
$61$	3.65589	−	2.11073i	0.468089	−	0.270251i	0.715440	+	0.698675i	$0.246226\pi$
$62$	7.77717			0.987701
$63$		0			0
$64$	−1.00000			−0.125000
$65$	7.80674	−	4.50722i	0.968307	−	0.559052i
$66$		0			0
$67$	−0.705066	+	1.22121i	−0.0861376	+	0.149195i	−0.905875	−	0.423544i	$-0.860786\pi$
$67$	−0.705066	+	1.22121i	−0.0861376	+	0.149195i	0.819738	+	0.572739i	$0.194119\pi$
$68$	−1.13182	−	1.96037i	−0.137253	−	0.237729i
$69$		0			0
$70$	−3.28466	−	3.40827i	−0.392592	−	0.407367i
$71$		−	2.11331i		−	0.250804i	−0.992106	−	0.125402i	$-0.959978\pi$
$71$		−	2.11331i		−	0.250804i	0.992106	−	0.125402i	$-0.0400221\pi$
$72$		0			0
$73$	−4.06851	−	2.34896i	−0.476184	−	0.274925i	0.242641	−	0.970116i	$-0.421986\pi$
$73$	−4.06851	−	2.34896i	−0.476184	−	0.274925i	−0.718825	+	0.695191i	$0.755320\pi$
$74$	−6.49047	−	3.74728i	−0.754502	−	0.435612i
$75$		0			0
$76$			3.98988i			0.457671i
$77$	9.60011	+	9.96140i	1.09403	+	1.13521i
$78$		0			0
$79$	3.53115	+	6.11613i	0.397285	+	0.688119i	0.993390	−	0.114788i	$-0.0366190\pi$
$79$	3.53115	+	6.11613i	0.397285	+	0.688119i	−0.596105	+	0.802907i	$0.703286\pi$
$80$	−0.894533	+	1.54938i	−0.100012	+	0.173226i
$81$		0			0
$82$	−7.82169	+	4.51585i	−0.863761	+	0.498693i
$83$	3.52907			0.387365			0.193683	−	0.981064i	$-0.437957\pi$
$83$	3.52907			0.387365			0.193683	+	0.981064i	$0.437957\pi$
$84$		0			0
$85$	−4.04979			−0.439262
$86$	−7.63021	+	4.40530i	−0.822786	+	0.475036i
$87$		0			0
$88$	2.61446	−	4.52838i	0.278703	−	0.482727i
$89$	−2.97335	−	5.15000i	−0.315175	−	0.545899i	0.664300	−	0.747466i	$-0.268730\pi$
$89$	−2.97335	−	5.15000i	−0.315175	−	0.545899i	−0.979475	+	0.201567i	$0.935396\pi$
$90$		0			0
$91$	−3.68750	+	12.8108i	−0.386555	+	1.34294i
$92$		−	7.89932i		−	0.823561i
$93$		0			0
$94$	3.58682	+	2.07085i	0.369952	+	0.213592i
$95$	6.18183	+	3.56908i	0.634242	+	0.366180i
$96$		0			0
$97$			19.3006i			1.95968i	0.199777	+	0.979841i	$0.435978\pi$
$97$			19.3006i			1.95968i	−0.199777	+	0.979841i	$0.564022\pi$
$98$	6.99523	+	0.258485i	0.706625	+	0.0261109i
$99$		0			0
$100$	−0.899620	−	1.55819i	−0.0899620	−	0.155819i
$101$	−0.511479	+	0.885907i	−0.0508940	+	0.0881510i	−0.890350	−	0.455277i	$-0.849540\pi$
$101$	−0.511479	+	0.885907i	−0.0508940	+	0.0881510i	0.839456	+	0.543428i	$0.182874\pi$
$102$		0			0
$103$	−8.66075	+	5.00029i	−0.853369	+	0.492693i	−0.861786	−	0.507272i	$-0.830654\pi$
$103$	−8.66075	+	5.00029i	−0.853369	+	0.492693i	0.00841718	+	0.999965i	$0.497321\pi$
$104$	5.03863			0.494078
$105$		0			0
$106$	−2.23177			−0.216768
$107$	0.265236	−	0.153134i	0.0256414	−	0.0148040i	−0.487125	−	0.873333i	$-0.661954\pi$
$107$	0.265236	−	0.153134i	0.0256414	−	0.0148040i	0.512766	+	0.858528i	$0.328621\pi$
$108$		0			0
$109$	−1.55347	+	2.69068i	−0.148795	+	0.257721i	−0.930782	−	0.365574i	$-0.880873\pi$
$109$	−1.55347	+	2.69068i	−0.148795	+	0.257721i	0.781987	+	0.623294i	$0.214206\pi$
$110$	−4.67745	−	8.10158i	−0.445977	−	0.772455i
$111$		0			0
$112$	−0.637461	−	2.56781i	−0.0602344	−	0.242635i
$113$		−	2.49935i		−	0.235119i	−0.993066	−	0.117560i	$-0.962493\pi$
$113$		−	2.49935i		−	0.235119i	0.993066	−	0.117560i	$-0.0375071\pi$
$114$		0			0
$115$	−12.2390	−	7.06621i	−1.14130	−	0.658927i
$116$	−2.93240	−	1.69302i	−0.272266	−	0.157193i
$117$		0			0
$118$		−	10.8605i		−	0.999789i
$119$	4.31235	−	4.15595i	0.395313	−	0.380975i
$120$		0			0
$121$	8.17082	+	14.1523i	0.742802	+	1.28657i
$122$	2.11073	−	3.65589i	0.191097	−	0.330989i
$123$		0			0
$124$	6.73522	−	3.88858i	0.604841	−	0.349205i
$125$	−12.1643			−1.08801
$126$		0			0
$127$	5.26929			0.467574			0.233787	−	0.972288i	$-0.424888\pi$
$127$	5.26929			0.467574			0.233787	+	0.972288i	$0.424888\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	4.50722	−	7.80674i	0.395310	−	0.684696i
$131$	4.16632	+	7.21628i	0.364013	+	0.630489i	0.988617	−	0.150452i	$-0.0480730\pi$
$131$	4.16632	+	7.21628i	0.364013	+	0.630489i	−0.624604	+	0.780941i	$0.714740\pi$
$132$		0			0
$133$	−10.2453	+	2.54339i	−0.888376	+	0.220540i
$134$			1.41013i			0.121817i
$135$		0			0
$136$	−1.96037	−	1.13182i	−0.168100	−	0.0970526i
$137$	11.8291	+	6.82952i	1.01063	+	0.583485i	0.911375	−	0.411577i	$-0.135022\pi$
$137$	11.8291	+	6.82952i	1.01063	+	0.583485i	0.0992512	+	0.995062i	$0.468355\pi$
$138$		0			0
$139$		−	6.36383i		−	0.539773i	−0.962892	−	0.269887i	$-0.913014\pi$
$139$		−	6.36383i		−	0.539773i	0.962892	−	0.269887i	$-0.0869863\pi$
$140$	−4.54874	−	1.30932i	−0.384438	−	0.110658i
$141$		0			0
$142$	−1.05666	−	1.83018i	−0.0886727	−	0.153586i
$143$	−13.1733	+	22.8168i	−1.10161	+	1.90804i
$144$		0			0
$145$	−5.24625	+	3.02892i	−0.435677	+	0.251539i
$146$	−4.69792			−0.388802
$147$		0			0
$148$	−7.49455			−0.616049
$149$	−14.9759	+	8.64636i	−1.22688	+	0.708337i	−0.966375	−	0.257137i	$-0.917221\pi$
$149$	−14.9759	+	8.64636i	−1.22688	+	0.708337i	−0.260501	+	0.965474i	$0.583888\pi$
$150$		0			0
$151$	8.12261	−	14.0688i	0.661009	−	1.14490i	−0.319342	−	0.947639i	$-0.603462\pi$
$151$	8.12261	−	14.0688i	0.661009	−	1.14490i	0.980351	−	0.197261i	$-0.0632047\pi$
$152$	1.99494	+	3.45534i	0.161811	+	0.280265i
$153$		0			0
$154$	13.2946	+	3.82677i	1.07131	+	0.308370i
$155$		−	13.9139i		−	1.11759i
$156$		0			0
$157$	−17.0877	−	9.86561i	−1.36375	−	0.787361i	−0.373629	−	0.927578i	$-0.621887\pi$
$157$	−17.0877	−	9.86561i	−1.36375	−	0.787361i	−0.990121	+	0.140217i	$0.955220\pi$
$158$	6.11613	+	3.53115i	0.486573	+	0.280923i
$159$		0			0
$160$			1.78907i			0.141438i
$161$	20.2840	−	5.03551i	1.59860	−	0.396854i
$162$		0			0
$163$	6.61394	+	11.4557i	0.518043	+	0.897277i	0.999780	+	0.0209616i	$0.00667277\pi$
$163$	6.61394	+	11.4557i	0.518043	+	0.897277i	−0.481737	+	0.876316i	$0.659994\pi$
$164$	−4.51585	+	7.82169i	−0.352629	+	0.610771i
$165$		0			0
$166$	3.05626	−	1.76453i	0.237212	−	0.136954i
$167$	−13.8250			−1.06981			−0.534905	−	0.844912i	$-0.679653\pi$
$167$	−13.8250			−1.06981			−0.534905	+	0.844912i	$0.679653\pi$
$168$		0			0
$169$	−12.3878			−0.952906
$170$	−3.50723	+	2.02490i	−0.268992	+	0.155303i
$171$		0			0
$172$	−4.40530	+	7.63021i	−0.335901	+	0.581798i
$173$	4.99869	+	8.65798i	0.380043	+	0.658254i	0.991068	−	0.133357i	$-0.0425758\pi$
$173$	4.99869	+	8.65798i	0.380043	+	0.658254i	−0.611025	+	0.791611i	$0.709242\pi$
$174$		0			0
$175$	3.42765	−	3.30334i	0.259106	−	0.249709i
$176$		−	5.22892i		−	0.394145i
$177$		0			0
$178$	−5.15000	−	2.97335i	−0.386009	−	0.222862i
$179$	−13.0876	−	7.55610i	−0.978209	−	0.564769i	−0.0764804	−	0.997071i	$-0.524368\pi$
$179$	−13.0876	−	7.55610i	−0.978209	−	0.564769i	−0.901729	+	0.432302i	$0.857702\pi$
$180$		0			0
$181$			16.6235i			1.23562i	0.786329	+	0.617808i	$0.211979\pi$
$181$			16.6235i			1.23562i	−0.786329	+	0.617808i	$0.788021\pi$
$182$	3.21193	+	12.9382i	0.238084	+	0.959046i
$183$		0			0
$184$	−3.94966	−	6.84102i	−0.291173	−	0.504326i
$185$	−6.70413	+	11.6119i	−0.492897	+	0.853723i
$186$		0			0
$187$	10.2506	−	5.91819i	0.749598	−	0.432781i
$188$	4.14170			0.302064
$189$		0			0
$190$	7.13816			0.517857
$191$	−17.3858	+	10.0377i	−1.25799	+	0.726302i	−0.972684	−	0.232134i	$-0.925429\pi$
$191$	−17.3858	+	10.0377i	−1.25799	+	0.726302i	−0.285308	+	0.958436i	$0.592096\pi$
$192$		0			0
$193$	2.34219	−	4.05680i	0.168595	−	0.292015i	−0.769331	−	0.638850i	$-0.779410\pi$
$193$	2.34219	−	4.05680i	0.168595	−	0.292015i	0.937926	+	0.346835i	$0.112744\pi$
$194$	9.65032	+	16.7148i	0.692852	+	1.20006i
$195$		0			0
$196$	6.18729	−	3.27376i	0.441949	−	0.233840i
$197$		−	12.0673i		−	0.859760i	−0.902886	−	0.429880i	$-0.858556\pi$
$197$		−	12.0673i		−	0.859760i	0.902886	−	0.429880i	$-0.141444\pi$
$198$		0			0
$199$	−19.9506	−	11.5185i	−1.41426	−	0.816524i	−0.418475	−	0.908228i	$-0.637435\pi$
$199$	−19.9506	−	11.5185i	−1.41426	−	0.816524i	−0.995786	+	0.0917037i	$0.970769\pi$
$200$	−1.55819	−	0.899620i	−0.110180	−	0.0636127i
$201$		0			0
$202$			1.02296i			0.0719750i
$203$	2.47806	−	8.60907i	0.173926	−	0.604238i
$204$		0			0
$205$	8.07917	+	13.9935i	0.564273	+	0.977350i
$206$	−5.00029	+	8.66075i	−0.348386	+	0.603423i
$207$		0			0
$208$	4.36358	−	2.51931i	0.302560	−	0.174683i
$209$	−20.8628			−1.44311
$210$		0			0
$211$	−22.4011			−1.54215			−0.771076	−	0.636743i	$-0.780281\pi$
$211$	−22.4011			−1.54215			−0.771076	+	0.636743i	$0.780281\pi$
$212$	−1.93277	+	1.11588i	−0.132743	+	0.0766392i
$213$		0			0
$214$	0.153134	−	0.265236i	0.0104680	−	0.0181312i
$215$	7.88138	+	13.6509i	0.537506	+	0.930987i
$216$		0			0
$217$	14.2786	+	14.8159i	0.969294	+	1.00577i
$218$			3.10693i			0.210428i
$219$		0			0
$220$	−8.10158	−	4.67745i	−0.546208	−	0.315353i
$221$	9.87755	+	5.70281i	0.664436	+	0.383612i
$222$		0			0
$223$			9.99069i			0.669026i	0.942391	+	0.334513i	$0.108572\pi$
$223$			9.99069i			0.669026i	−0.942391	+	0.334513i	$0.891428\pi$
$224$	−1.83596	−	1.90506i	−0.122670	−	0.127287i
$225$		0			0
$226$	−1.24968	−	2.16450i	−0.0831272	−	0.143981i
$227$	−1.59918	+	2.76985i	−0.106141	+	0.183842i	−0.914204	−	0.405255i	$-0.867183\pi$
$227$	−1.59918	+	2.76985i	−0.106141	+	0.183842i	0.808063	+	0.589096i	$0.200516\pi$
$228$		0			0
$229$	14.6832	−	8.47736i	0.970294	−	0.560200i	0.0709683	−	0.997479i	$-0.477391\pi$
$229$	14.6832	−	8.47736i	0.970294	−	0.560200i	0.899326	+	0.437279i	$0.144058\pi$
$230$	−14.1324			−0.931864
$231$		0			0
$232$	−3.38604			−0.222304
$233$	7.24714	−	4.18414i	0.474776	−	0.274112i	−0.243461	−	0.969911i	$-0.578283\pi$
$233$	7.24714	−	4.18414i	0.474776	−	0.274112i	0.718237	+	0.695799i	$0.244949\pi$
$234$		0			0
$235$	3.70489	−	6.41705i	0.241680	−	0.418602i
$236$	−5.43025	−	9.40546i	−0.353479	−	0.612243i
$237$		0			0
$238$	1.65663	−	5.75533i	0.107384	−	0.373063i
$239$		−	13.6753i		−	0.884581i	−0.896872	−	0.442290i	$-0.854166\pi$
$239$		−	13.6753i		−	0.884581i	0.896872	−	0.442290i	$-0.145834\pi$
$240$		0			0
$241$	22.5782	+	13.0355i	1.45439	+	0.839692i	0.998726	−	0.0504597i	$-0.0160687\pi$
$241$	22.5782	+	13.0355i	1.45439	+	0.839692i	0.455664	+	0.890152i	$0.349402\pi$
$242$	14.1523	+	8.17082i	0.909742	+	0.525240i
$243$		0			0
$244$		−	4.22146i		−	0.270251i
$245$	0.462447	−	12.5149i	0.0295446	−	0.799549i
$246$		0			0
$247$	−10.0518	−	17.4102i	−0.639578	−	1.10778i
$248$	3.88858	−	6.73522i	0.246925	−	0.427687i
$249$		0			0
$250$	−10.5346	+	6.08215i	−0.666266	+	0.384669i
$251$	−15.2554			−0.962913			−0.481456	−	0.876470i	$-0.659892\pi$
$251$	−15.2554			−0.962913			−0.481456	+	0.876470i	$0.659892\pi$
$252$		0			0
$253$	41.3050			2.59682
$254$	4.56334	−	2.63465i	0.286330	−	0.165312i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.5586	−	20.0200i	−0.721004	−	1.24882i	−0.960598	−	0.277943i	$-0.910347\pi$
$257$	−11.5586	−	20.0200i	−0.721004	−	1.24882i	0.239593	−	0.970873i	$-0.422986\pi$
$258$		0			0
$259$	−4.77749	−	19.2446i	−0.296859	−	1.19580i
$260$		−	9.01444i		−	0.559052i
$261$		0			0
$262$	7.21628	+	4.16632i	0.445823	+	0.257396i
$263$	−13.8951	−	8.02232i	−0.856806	−	0.494677i	0.00613517	−	0.999981i	$-0.498047\pi$
$263$	−13.8951	−	8.02232i	−0.856806	−	0.494677i	−0.862942	+	0.505304i	$0.831380\pi$
$264$		0			0
$265$			3.99278i			0.245274i
$266$	−7.60095	+	7.32527i	−0.466044	+	0.449141i
$267$		0			0
$268$	0.705066	+	1.22121i	0.0430688	+	0.0745973i
$269$	−2.80639	+	4.86081i	−0.171109	+	0.296369i	−0.938808	−	0.344442i	$-0.888068\pi$
$269$	−2.80639	+	4.86081i	−0.171109	+	0.296369i	0.767699	+	0.640811i	$0.221402\pi$
$270$		0			0
$271$	−4.94080	+	2.85257i	−0.300132	+	0.173281i	−0.642502	−	0.766284i	$-0.722104\pi$
$271$	−4.94080	+	2.85257i	−0.300132	+	0.173281i	0.342370	+	0.939565i	$0.388770\pi$
$272$	−2.26364			−0.137253
$273$		0			0
$274$	13.6590			0.825173
$275$	8.14764	−	4.70404i	0.491321	−	0.283664i
$276$		0			0
$277$	3.40114	−	5.89094i	0.204355	−	0.353953i	−0.745572	−	0.666425i	$-0.767824\pi$
$277$	3.40114	−	5.89094i	0.204355	−	0.353953i	0.949927	+	0.312472i	$0.101157\pi$
$278$	−3.18192	−	5.51124i	−0.190839	−	0.330542i
$279$		0			0
$280$	−4.59398	+	1.14046i	−0.274543	+	0.0681556i
$281$			29.5436i			1.76243i	0.472720	+	0.881213i	$0.343272\pi$
$281$			29.5436i			1.76243i	−0.472720	+	0.881213i	$0.656728\pi$
$282$		0			0
$283$	−8.27866	−	4.77969i	−0.492115	−	0.284123i	0.233336	−	0.972396i	$-0.425036\pi$
$283$	−8.27866	−	4.77969i	−0.492115	−	0.284123i	−0.725452	+	0.688273i	$0.758369\pi$
$284$	−1.83018	−	1.05666i	−0.108601	−	0.0627011i
$285$		0			0
$286$			26.3466i			1.55791i
$287$	−22.9633	−	6.60983i	−1.35548	−	0.390166i
$288$		0			0
$289$	5.93798	+	10.2849i	0.349293	+	0.604993i
$290$	−3.02892	+	5.24625i	−0.177865	+	0.308070i
$291$		0			0
$292$	−4.06851	+	2.34896i	−0.238092	+	0.137462i
$293$	−24.9693			−1.45872			−0.729360	−	0.684130i	$-0.760182\pi$
$293$	−24.9693			−1.45872			−0.729360	+	0.684130i	$0.760182\pi$
$294$		0			0
$295$	−19.4301			−1.13127
$296$	−6.49047	+	3.74728i	−0.377251	+	0.217806i
$297$		0			0
$298$	−8.64636	+	14.9759i	−0.500870	+	0.867532i
$299$	19.9009	+	34.4693i	1.15090	+	1.99341i
$300$		0			0
$301$	−22.4011	−	6.44801i	−1.29118	−	0.371657i
$302$		−	16.2452i		−	0.934808i
$303$		0			0
$304$	3.45534	+	1.99494i	0.198177	+	0.114418i
$305$	−6.54064	−	3.77624i	−0.374516	−	0.216227i
$306$		0			0
$307$		−	29.7991i		−	1.70072i	−0.526199	−	0.850362i	$-0.676383\pi$
$307$		−	29.7991i		−	1.70072i	0.526199	−	0.850362i	$-0.323617\pi$
$308$	13.4269	−	3.33324i	0.765067	−	0.189929i
$309$		0			0
$310$	−6.95694	−	12.0498i	−0.395127	−	0.684381i
$311$	−6.16702	+	10.6816i	−0.349700	+	0.605697i	−0.986196	−	0.165582i	$-0.947050\pi$
$311$	−6.16702	+	10.6816i	−0.349700	+	0.605697i	0.636496	+	0.771280i	$0.280383\pi$
$312$		0			0
$313$	20.5823	−	11.8832i	1.16338	−	0.671678i	0.211268	−	0.977428i	$-0.432241\pi$
$313$	20.5823	−	11.8832i	1.16338	−	0.671678i	0.952112	+	0.305750i	$0.0989073\pi$
$314$	−19.7312			−1.11350
$315$		0			0
$316$	7.06230			0.397285
$317$	−13.5850	+	7.84330i	−0.763009	+	0.440524i	−0.830375	−	0.557205i	$-0.811874\pi$
$317$	−13.5850	+	7.84330i	−0.763009	+	0.440524i	0.0673660	+	0.997728i	$0.478540\pi$
$318$		0			0
$319$	8.85267	−	15.3333i	0.495654	−	0.858498i
$320$	0.894533	+	1.54938i	0.0500059	+	0.0866128i
$321$		0			0
$322$	15.0487	−	14.5029i	0.838629	−	0.808213i
$323$			9.03163i			0.502534i
$324$		0			0
$325$	7.85113	+	4.53285i	0.435502	+	0.251437i
$326$	11.4557	+	6.61394i	0.634471	+	0.366312i
$327$		0			0
$328$			9.03171i			0.498693i
$329$	2.64017	+	10.6351i	0.145557	+	0.586331i
$330$		0			0
$331$	0.228762	+	0.396228i	0.0125739	+	0.0217787i	0.872244	−	0.489071i	$-0.162664\pi$
$331$	0.228762	+	0.396228i	0.0125739	+	0.0217787i	−0.859670	+	0.510850i	$0.829331\pi$
$332$	1.76453	−	3.05626i	0.0968413	−	0.167734i
$333$		0			0
$334$	−11.9728	+	6.91250i	−0.655123	+	0.378235i
$335$	2.52282			0.137836
$336$		0			0
$337$	24.8429			1.35328			0.676640	−	0.736314i	$-0.263435\pi$
$337$	24.8429			1.35328			0.676640	+	0.736314i	$0.263435\pi$
$338$	−10.7281	+	6.19389i	−0.583533	+	0.336903i
$339$		0			0
$340$	−2.02490	+	3.50723i	−0.109815	+	0.190206i
$341$	20.3331	+	35.2180i	1.10110	+	1.90716i
$342$		0			0
$343$	12.3505	+	13.8009i	0.666867	+	0.745177i
$344$			8.81060i			0.475036i
$345$		0			0
$346$	8.65798	+	4.99869i	0.465456	+	0.268731i
$347$	18.9446	+	10.9377i	1.01700	+	0.587165i	0.913233	−	0.407437i	$-0.133577\pi$
$347$	18.9446	+	10.9377i	1.01700	+	0.587165i	0.103766	+	0.994602i	$0.466911\pi$
$348$		0			0
$349$		−	0.272742i		−	0.0145995i	−0.999973	−	0.00729976i	$-0.997676\pi$
$349$		−	0.272742i		−	0.0145995i	0.999973	−	0.00729976i	$-0.00232361\pi$
$350$	1.31677	−	4.57460i	0.0703842	−	0.244523i
$351$		0			0
$352$	−2.61446	−	4.52838i	−0.139351	−	0.241363i
$353$	7.59242	−	13.1504i	0.404103	−	0.699928i	−0.590113	−	0.807321i	$-0.700917\pi$
$353$	7.59242	−	13.1504i	0.404103	−	0.699928i	0.994217	+	0.107393i	$0.0342502\pi$
$354$		0			0
$355$	−3.27432	+	1.89043i	−0.173783	+	0.100334i
$356$	−5.94671			−0.315175
$357$		0			0
$358$	−15.1122			−0.798705
$359$	−19.3894	+	11.1944i	−1.02333	+	0.590820i	−0.915067	−	0.403302i	$-0.867862\pi$
$359$	−19.3894	+	11.1944i	−1.02333	+	0.590820i	−0.108264	+	0.994122i	$0.534529\pi$
$360$		0			0
$361$	−1.54043	+	2.66810i	−0.0810751	+	0.140426i
$362$	8.31176	+	14.3964i	0.436856	+	0.756657i
$363$		0			0
$364$	9.25073	+	9.59888i	0.484870	+	0.503118i
$365$			8.40489i			0.439932i
$366$		0			0
$367$	−1.17856	−	0.680440i	−0.0615202	−	0.0355187i	0.468924	−	0.883238i	$-0.344642\pi$
$367$	−1.17856	−	0.680440i	−0.0615202	−	0.0355187i	−0.530445	+	0.847720i	$0.677975\pi$
$368$	−6.84102	−	3.94966i	−0.356613	−	0.205890i
$369$		0			0
$370$			13.4083i			0.697062i
$371$	−4.09744	−	4.25164i	−0.212728	−	0.220734i
$372$		0			0
$373$	12.8820	+	22.3123i	0.667006	+	1.15529i	0.978737	+	0.205118i	$0.0657578\pi$
$373$	12.8820	+	22.3123i	0.667006	+	1.15529i	−0.311731	+	0.950170i	$0.600909\pi$
$374$	5.91819	−	10.2506i	0.306022	−	0.530046i
$375$		0			0
$376$	3.58682	−	2.07085i	0.184976	−	0.106796i
$377$	17.0610			0.878686
$378$		0			0
$379$	10.5945			0.544201			0.272101	−	0.962269i	$-0.412282\pi$
$379$	10.5945			0.544201			0.272101	+	0.962269i	$0.412282\pi$
$380$	6.18183	−	3.56908i	0.317121	−	0.183090i
$381$		0			0
$382$	−10.0377	+	17.3858i	−0.513573	+	0.889534i
$383$	−5.60081	−	9.70088i	−0.286188	−	0.495692i	0.686709	−	0.726933i	$-0.259055\pi$
$383$	−5.60081	−	9.70088i	−0.286188	−	0.495692i	−0.972897	+	0.231241i	$0.925721\pi$
$384$		0			0
$385$	6.84635	−	23.7850i	0.348922	−	1.21220i
$386$		−	4.68438i		−	0.238429i
$387$		0			0
$388$	16.7148	+	9.65032i	0.848568	+	0.489921i
$389$	−17.1324	−	9.89141i	−0.868648	−	0.501514i	−0.00174936	−	0.999998i	$-0.500557\pi$
$389$	−17.1324	−	9.89141i	−0.868648	−	0.501514i	−0.866899	+	0.498484i	$0.833890\pi$
$390$		0			0
$391$		−	17.8812i		−	0.904290i
$392$	3.72147	−	5.92880i	0.187962	−	0.299450i
$393$		0			0
$394$	−6.03365	−	10.4506i	−0.303971	−	0.526493i
$395$	6.31746	−	10.9422i	0.317866	−	0.550560i
$396$		0			0
$397$	−28.1940	+	16.2778i	−1.41502	+	0.816959i	−0.995855	−	0.0909529i	$-0.971009\pi$
$397$	−28.1940	+	16.2778i	−1.41502	+	0.816959i	−0.419160	+	0.907912i	$0.637675\pi$
$398$	−23.0370			−1.15474
$399$		0			0
$400$	−1.79924			−0.0899620
$401$	25.6068	−	14.7841i	1.27874	−	0.738282i	0.302125	−	0.953268i	$-0.402304\pi$
$401$	25.6068	−	14.7841i	1.27874	−	0.738282i	0.976617	+	0.214987i	$0.0689708\pi$
$402$		0			0
$403$	−19.5931	+	33.9363i	−0.976003	+	1.69049i
$404$	0.511479	+	0.885907i	0.0254470	+	0.0440755i
$405$		0			0
$406$	−2.15847	−	8.69470i	−0.107123	−	0.431511i
$407$		−	39.1884i		−	1.94250i
$408$		0			0
$409$	−4.70610	−	2.71707i	−0.232702	−	0.134350i	0.379116	−	0.925349i	$-0.376228\pi$
$409$	−4.70610	−	2.71707i	−0.232702	−	0.134350i	−0.611818	+	0.790999i	$0.709561\pi$
$410$	13.9935	+	8.07917i	0.691091	+	0.399002i
$411$		0			0
$412$			10.0006i			0.492693i
$413$	20.6899	−	19.9395i	1.01808	−	0.981156i
$414$		0			0
$415$	−3.15687	−	5.46785i	−0.154965	−	0.268406i
$416$	2.51931	−	4.36358i	0.123520	−	0.213942i
$417$		0			0
$418$	−18.0677	+	10.4314i	−0.883720	+	0.510216i
$419$	−4.37591			−0.213777			−0.106888	−	0.994271i	$-0.534089\pi$
$419$	−4.37591			−0.213777			−0.106888	+	0.994271i	$0.534089\pi$
$420$		0			0
$421$	−7.34954			−0.358195			−0.179097	−	0.983831i	$-0.557318\pi$
$421$	−7.34954			−0.358195			−0.179097	+	0.983831i	$0.557318\pi$
$422$	−19.3999	+	11.2005i	−0.944372	+	0.545233i
$423$		0			0
$424$	−1.11588	+	1.93277i	−0.0541921	+	0.0938634i
$425$	−2.03641	−	3.52717i	−0.0987804	−	0.171093i
$426$		0			0
$427$	10.8399	−	2.69102i	0.524580	−	0.130228i
$428$		−	0.306268i		−	0.0148040i
$429$		0			0
$430$	13.6509	+	7.88138i	0.658307	+	0.380074i
$431$	26.3948	+	15.2390i	1.27139	+	0.734038i	0.975250	−	0.221106i	$-0.0709666\pi$
$431$	26.3948	+	15.2390i	1.27139	+	0.734038i	0.296142	+	0.955144i	$0.404300\pi$
$432$		0			0
$433$		−	27.8980i		−	1.34069i	−0.742048	−	0.670347i	$-0.766145\pi$
$433$		−	27.8980i		−	1.34069i	0.742048	−	0.670347i	$-0.233855\pi$
$434$	19.7736	+	5.69169i	0.949163	+	0.273210i
$435$		0			0
$436$	1.55347	+	2.69068i	0.0743975	+	0.128860i
$437$	−15.7587	+	27.2948i	−0.753840	+	1.30569i
$438$		0			0
$439$	7.92025	−	4.57276i	0.378013	−	0.218246i	−0.298941	−	0.954272i	$-0.596633\pi$
$439$	7.92025	−	4.57276i	0.378013	−	0.218246i	0.676953	+	0.736026i	$0.263300\pi$
$440$	−9.35489			−0.445977
$441$		0			0
$442$	11.4056			0.542510
$443$	−18.9603	+	10.9467i	−0.900831	+	0.520095i	−0.877470	−	0.479632i	$-0.840770\pi$
$443$	−18.9603	+	10.9467i	−0.900831	+	0.520095i	−0.0233611	+	0.999727i	$0.507437\pi$
$444$		0			0
$445$	−5.31953	+	9.21369i	−0.252170	+	0.436771i
$446$	4.99534	+	8.65219i	0.236536	+	0.409693i
$447$		0			0
$448$	−2.54252	−	0.731847i	−0.120123	−	0.0345765i
$449$		−	20.8625i		−	0.984564i	−0.870436	−	0.492282i	$-0.836163\pi$
$449$		−	20.8625i		−	0.984564i	0.870436	−	0.492282i	$-0.163837\pi$
$450$		0			0
$451$	−40.8990	−	23.6131i	−1.92586	−	1.11190i
$452$	−2.16450	−	1.24968i	−0.101810	−	0.0587798i
$453$		0			0
$454$			3.19835i			0.150106i
$455$	23.1474	−	5.74636i	1.08517	−	0.269394i
$456$		0			0
$457$	−3.96173	−	6.86192i	−0.185322	−	0.320987i	0.758363	−	0.651832i	$-0.225999\pi$
$457$	−3.96173	−	6.86192i	−0.185322	−	0.320987i	−0.943685	+	0.330845i	$0.892666\pi$
$458$	8.47736	−	14.6832i	0.396121	−	0.686102i
$459$		0			0
$460$	−12.2390	+	7.06621i	−0.570648	+	0.329464i
$461$	9.06227			0.422072			0.211036	−	0.977478i	$-0.432316\pi$
$461$	9.06227			0.422072			0.211036	+	0.977478i	$0.432316\pi$
$462$		0			0
$463$	−0.499886			−0.0232317			−0.0116158	−	0.999933i	$-0.503698\pi$
$463$	−0.499886			−0.0232317			−0.0116158	+	0.999933i	$0.503698\pi$
$464$	−2.93240	+	1.69302i	−0.136133	+	0.0785964i
$465$		0			0
$466$	4.18414	−	7.24714i	0.193826	−	0.335717i
$467$	0.804921	+	1.39416i	0.0372473	+	0.0645142i	0.884048	−	0.467396i	$-0.154808\pi$
$467$	0.804921	+	1.39416i	0.0372473	+	0.0645142i	−0.846801	+	0.531910i	$0.821474\pi$
$468$		0			0
$469$	−2.68638	+	2.58895i	−0.124046	+	0.119547i
$470$		−	7.40977i		−	0.341787i
$471$		0			0
$472$	−9.40546	−	5.43025i	−0.432921	−	0.249947i
$473$	−39.8978	−	23.0350i	−1.83450	−	1.05915i
$474$		0			0
$475$			7.17875i			0.329384i
$476$	−1.44298	−	5.81258i	−0.0661389	−	0.266419i
$477$		0			0
$478$	−6.83764	−	11.8431i	−0.312747	−	0.541693i
$479$	3.26795	−	5.66026i	0.149317	−	0.258624i	−0.781658	−	0.623707i	$-0.785626\pi$
$479$	3.26795	−	5.66026i	0.149317	−	0.258624i	0.930975	+	0.365083i	$0.118959\pi$
$480$		0			0
$481$	32.7031	−	18.8811i	1.49113	−	0.860906i
$482$	26.0711			1.18750
$483$		0			0
$484$	16.3416			0.742802
$485$	29.9040	−	17.2651i	1.35787	−	0.783966i
$486$		0			0
$487$	1.57311	−	2.72470i	0.0712844	−	0.123468i	−0.828180	−	0.560462i	$-0.810624\pi$
$487$	1.57311	−	2.72470i	0.0712844	−	0.123468i	0.899464	+	0.436994i	$0.143957\pi$
$488$	−2.11073	−	3.65589i	−0.0955483	−	0.165495i
$489$		0			0
$490$	−5.85697	−	11.0695i	−0.264591	−	0.500068i
$491$		−	25.6076i		−	1.15566i	−0.816158	−	0.577828i	$-0.803900\pi$
$491$		−	25.6076i		−	1.15566i	0.816158	−	0.577828i	$-0.196100\pi$
$492$		0			0
$493$	−6.63787	−	3.83238i	−0.298955	−	0.172602i
$494$	−17.4102	−	10.0518i	−0.783320	−	0.452250i
$495$		0			0
$496$		−	7.77717i		−	0.349205i
$497$	1.54662	−	5.37314i	0.0693755	−	0.241018i
$498$		0			0
$499$	5.35305	+	9.27176i	0.239635	+	0.415061i	0.960610	−	0.277901i	$-0.0896387\pi$
$499$	5.35305	+	9.27176i	0.239635	+	0.415061i	−0.720974	+	0.692962i	$0.756305\pi$
$500$	−6.08215	+	10.5346i	−0.272002	+	0.471121i
$501$		0			0
$502$	−13.2116	+	7.62770i	−0.589661	+	0.340441i
$503$	22.4205			0.999681			0.499840	−	0.866118i	$-0.333392\pi$
$503$	22.4205			0.999681			0.499840	+	0.866118i	$0.333392\pi$
$504$		0			0
$505$	1.83014			0.0814401
$506$	35.7711	−	20.6525i	1.59022	−	0.918115i
$507$		0			0
$508$	2.63465	−	4.56334i	0.116894	−	0.202466i
$509$	19.5614	+	33.8814i	0.867045	+	1.50177i	0.865002	+	0.501768i	$0.167317\pi$
$509$	19.5614	+	33.8814i	0.867045	+	1.50177i	0.00204257	+	0.999998i	$0.499350\pi$
$510$		0			0
$511$	−8.62520	−	8.94980i	−0.381556	−	0.395916i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−20.0200	−	11.5586i	−0.883046	−	0.509827i
$515$	15.4947	+	8.94585i	0.682776	+	0.394201i
$516$		0			0
$517$			21.6566i			0.952457i
$518$	−13.7597	−	14.2776i	−0.604567	−	0.627320i
$519$		0			0
$520$	−4.50722	−	7.80674i	−0.197655	−	0.342348i
$521$	−0.205750	+	0.356370i	−0.00901408	+	0.0156128i	−0.870497	−	0.492173i	$-0.836203\pi$
$521$	−0.205750	+	0.356370i	−0.00901408	+	0.0156128i	0.861483	+	0.507786i	$0.169536\pi$
$522$		0			0
$523$	2.69723	−	1.55725i	0.117942	−	0.0680936i	−0.439869	−	0.898062i	$-0.644975\pi$
$523$	2.69723	−	1.55725i	0.117942	−	0.0680936i	0.557810	+	0.829969i	$0.311642\pi$
$524$	8.33264			0.364013
$525$		0			0
$526$	−16.0446			−0.699579
$527$	15.2461	−	8.80233i	0.664130	−	0.383436i
$528$		0			0
$529$	19.6997	−	34.1208i	0.856507	−	1.48351i
$530$	1.99639	+	3.45785i	0.0867176	+	0.150199i
$531$		0			0
$532$	−2.91998	+	10.1443i	−0.126597	+	0.439813i
$533$		−	45.5074i		−	1.97115i
$534$		0			0
$535$	−0.474525	−	0.273967i	−0.0205155	−	0.0118446i
$536$	1.22121	+	0.705066i	0.0527483	+	0.0304542i
$537$		0			0
$538$			5.61279i			0.241984i
$539$	17.1182	+	32.3528i	0.737334	+	1.39354i
$540$		0			0
$541$	−0.540066	−	0.935422i	−0.0232193	−	0.0402170i	0.854182	−	0.519974i	$-0.174058\pi$
$541$	−0.540066	−	0.935422i	−0.0232193	−	0.0402170i	−0.877402	+	0.479757i	$0.840725\pi$
$542$	−2.85257	+	4.94080i	−0.122528	+	0.212225i
$543$		0			0
$544$	−1.96037	+	1.13182i	−0.0840500	+	0.0485263i
$545$	5.55851			0.238100
$546$		0			0
$547$	15.9053			0.680060			0.340030	−	0.940415i	$-0.389563\pi$
$547$	15.9053			0.680060			0.340030	+	0.940415i	$0.389563\pi$
$548$	11.8291	−	6.82952i	0.505313	−	0.291743i
$549$		0			0
$550$	4.70404	−	8.14764i	0.200581	−	0.347417i
$551$	6.75494	+	11.6999i	0.287770	+	0.498433i
$552$		0			0
$553$	4.50194	+	18.1346i	0.191442	+	0.771163i
$554$		−	6.80228i		−	0.289001i
$555$		0			0
$556$	−5.51124	−	3.18192i	−0.233729	−	0.134943i
$557$	24.2503	+	14.0009i	1.02752	+	0.593238i	0.916273	−	0.400555i	$-0.131183\pi$
$557$	24.2503	+	14.0009i	1.02752	+	0.593238i	0.111245	+	0.993793i	$0.464516\pi$
$558$		0			0
$559$		−	44.3934i		−	1.87764i
$560$	−3.40827	+	3.28466i	−0.144026	+	0.138802i
$561$		0			0
$562$	14.7718	+	25.5855i	0.623111	+	1.07926i
$563$	−1.23558	+	2.14008i	−0.0520734	+	0.0901938i	−0.890887	−	0.454225i	$-0.849916\pi$
$563$	−1.23558	+	2.14008i	−0.0520734	+	0.0901938i	0.838814	+	0.544419i	$0.183250\pi$
$564$		0			0
$565$	−3.87244	+	2.23575i	−0.162915	+	0.0940589i
$566$	−9.55937			−0.401810
$567$		0			0
$568$	−2.11331			−0.0886727
$569$	−13.1647	+	7.60064i	−0.551892	+	0.318635i	−0.749885	−	0.661568i	$-0.769891\pi$
$569$	−13.1647	+	7.60064i	−0.551892	+	0.318635i	0.197993	+	0.980204i	$0.436558\pi$
$570$		0			0
$571$	0.754880	−	1.30749i	0.0315907	−	0.0547168i	−0.849798	−	0.527109i	$-0.823276\pi$
$571$	0.754880	−	1.30749i	0.0315907	−	0.0547168i	0.881389	+	0.472392i	$0.156609\pi$
$572$	13.1733	+	22.8168i	0.550803	+	0.954019i
$573$		0			0
$574$	−23.1917	+	5.75737i	−0.968003	+	0.240308i
$575$		−	14.2128i		−	0.592714i
$576$		0			0
$577$	−14.5521	−	8.40169i	−0.605814	−	0.349767i	0.165511	−	0.986208i	$-0.447073\pi$
$577$	−14.5521	−	8.40169i	−0.605814	−	0.349767i	−0.771325	+	0.636441i	$0.780406\pi$
$578$	10.2849	+	5.93798i	0.427795	+	0.246987i
$579$		0			0
$580$			6.05785i			0.251539i
$581$	8.97271	+	2.58273i	0.372251	+	0.107150i
$582$		0			0
$583$	−5.83487	−	10.1063i	−0.241655	−	0.418560i
$584$	−2.34896	+	4.06851i	−0.0972006	+	0.168356i
$585$		0			0
$586$	−21.6240	+	12.4846i	−0.893280	+	0.515735i
$587$	−44.4505			−1.83467			−0.917334	−	0.398118i	$-0.869663\pi$
$587$	−44.4505			−1.83467			−0.917334	+	0.398118i	$0.869663\pi$
$588$		0			0
$589$	−31.0300			−1.27857
$590$	−16.8270	+	9.71507i	−0.692757	+	0.399963i
$591$		0			0
$592$	−3.74728	+	6.49047i	−0.154012	+	0.266757i
$593$	−14.2575	−	24.6947i	−0.585485	−	1.01409i	−0.994815	−	0.101703i	$-0.967571\pi$
$593$	−14.2575	−	24.6947i	−0.585485	−	1.01409i	0.409330	−	0.912386i	$-0.365762\pi$
$594$		0			0
$595$	−10.2967	−	2.96383i	−0.422123	−	0.121505i
$596$			17.2927i			0.708337i
$597$		0			0
$598$	34.4693	+	19.9009i	1.40956	+	0.813807i
$599$	18.0679	+	10.4315i	0.738235	+	0.426220i	0.821427	−	0.570313i	$-0.193178\pi$
$599$	18.0679	+	10.4315i	0.738235	+	0.426220i	−0.0831923	+	0.996534i	$0.526512\pi$
$600$		0			0
$601$			35.7447i			1.45806i	0.684483	+	0.729029i	$0.260028\pi$
$601$			35.7447i			1.45806i	−0.684483	+	0.729029i	$0.739972\pi$
$602$	−22.6239	+	5.61642i	−0.922083	+	0.228908i
$603$		0			0
$604$	−8.12261	−	14.0688i	−0.330504	−	0.572450i
$605$	14.6181	−	25.3194i	0.594312	−	1.02938i
$606$		0			0
$607$	4.76417	−	2.75060i	0.193372	−	0.111643i	−0.400188	−	0.916433i	$-0.631055\pi$
$607$	4.76417	−	2.75060i	0.193372	−	0.111643i	0.593560	+	0.804790i	$0.297722\pi$
$608$	3.98988			0.161811
$609$		0			0
$610$	−7.55248			−0.305791
$611$	−18.0726	+	10.4342i	−0.731140	+	0.422124i
$612$		0			0
$613$	−7.13512	+	12.3584i	−0.288185	+	0.499150i	−0.973376	−	0.229212i	$-0.926385\pi$
$613$	−7.13512	+	12.3584i	−0.288185	+	0.499150i	0.685192	+	0.728363i	$0.259718\pi$
$614$	−14.8995	−	25.8068i	−0.601296	−	1.04148i
$615$		0			0
$616$	9.96140	−	9.60011i	0.401356	−	0.386799i
$617$		−	7.84352i		−	0.315768i	−0.987458	−	0.157884i	$-0.949533\pi$
$617$		−	7.84352i		−	0.315768i	0.987458	−	0.157884i	$-0.0504672\pi$
$618$		0			0
$619$	−15.3512	−	8.86301i	−0.617016	−	0.356235i	0.158690	−	0.987328i	$-0.449273\pi$
$619$	−15.3512	−	8.86301i	−0.617016	−	0.356235i	−0.775706	+	0.631094i	$0.782606\pi$
$620$	−12.0498	−	6.95694i	−0.483930	−	0.279397i
$621$		0			0
$622$			12.3340i			0.494550i
$623$	−3.79080	−	15.2700i	−0.151875	−	0.611780i
$624$		0			0
$625$	6.38327	+	11.0561i	0.255331	+	0.442246i
$626$	11.8832	−	20.5823i	0.474948	−	0.822634i
$627$		0			0
$628$	−17.0877	+	9.86561i	−0.681875	+	0.393681i
$629$	−16.9649			−0.676436
$630$		0			0
$631$	−13.3165			−0.530121			−0.265060	−	0.964232i	$-0.585392\pi$
$631$	−13.3165			−0.530121			−0.265060	+	0.964232i	$0.585392\pi$
$632$	6.11613	−	3.53115i	0.243287	−	0.140462i
$633$		0			0
$634$	−7.84330	+	13.5850i	−0.311497	+	0.539529i
$635$	−4.71356	−	8.16412i	−0.187052	−	0.323983i
$636$		0			0
$637$	−18.7511	+	29.8730i	−0.742945	+	1.18361i
$638$		−	17.7053i		−	0.700961i
$639$		0			0
$640$	1.54938	+	0.894533i	0.0612445	+	0.0353595i
$641$	−4.68708	−	2.70609i	−0.185128	−	0.106884i	0.404572	−	0.914506i	$-0.367421\pi$
$641$	−4.68708	−	2.70609i	−0.185128	−	0.106884i	−0.589700	+	0.807622i	$0.700754\pi$
$642$		0			0
$643$		−	1.48634i		−	0.0586156i	−0.999570	−	0.0293078i	$-0.990670\pi$
$643$		−	1.48634i		−	0.0586156i	0.999570	−	0.0293078i	$-0.00933030\pi$
$644$	5.78109	−	20.0842i	0.227807	−	0.791427i
$645$		0			0
$646$	4.51582	+	7.82162i	0.177672	+	0.307738i
$647$	−3.15886	+	5.47131i	−0.124188	+	0.215099i	−0.921415	−	0.388580i	$-0.872966\pi$
$647$	−3.15886	+	5.47131i	−0.124188	+	0.215099i	0.797227	+	0.603679i	$0.206299\pi$
$648$		0			0
$649$	49.1804	−	28.3943i	1.93050	−	1.11458i
$650$	9.06570			0.355586
$651$		0			0
$652$	13.2279			0.518043
$653$	−32.9692	+	19.0348i	−1.29019	+	0.744889i	−0.978687	−	0.205358i	$-0.934164\pi$
$653$	−32.9692	+	19.0348i	−1.29019	+	0.744889i	−0.311498	+	0.950247i	$0.600831\pi$
$654$		0			0
$655$	7.45382	−	12.9104i	0.291245	−	0.504451i
$656$	4.51585	+	7.82169i	0.176314	+	0.305386i
$657$		0			0
$658$	7.60400	+	7.89017i	0.296435	+	0.307591i
$659$		−	36.9345i		−	1.43877i	−0.694614	−	0.719383i	$-0.744425\pi$
$659$		−	36.9345i		−	1.43877i	0.694614	−	0.719383i	$-0.255575\pi$
$660$		0			0
$661$	25.8641	+	14.9327i	1.00600	+	0.580813i	0.910018	−	0.414570i	$-0.136068\pi$
$661$	25.8641	+	14.9327i	1.00600	+	0.580813i	0.0959808	+	0.995383i	$0.469401\pi$
$662$	0.396228	+	0.228762i	0.0153998	+	0.00889110i
$663$		0			0
$664$		−	3.52907i		−	0.136954i
$665$	13.1054	+	13.5986i	0.508206	+	0.527331i
$666$		0			0
$667$	−13.3737	−	23.1639i	−0.517832	−	0.896911i
$668$	−6.91250	+	11.9728i	−0.267453	+	0.463242i
$669$		0			0
$670$	2.18483	−	1.26141i	0.0844073	−	0.0487326i
$671$	22.0737			0.852146
$672$		0			0
$673$	−49.0590			−1.89109			−0.945543	−	0.325498i	$-0.894468\pi$
$673$	−49.0590			−1.89109			−0.945543	+	0.325498i	$0.894468\pi$
$674$	21.5146	−	12.4215i	0.828711	−	0.478457i
$675$		0			0
$676$	−6.19389	+	10.7281i	−0.238227	+	0.412620i
$677$	4.27797	+	7.40965i	0.164416	+	0.284776i	0.936448	−	0.350808i	$-0.114093\pi$
$677$	4.27797	+	7.40965i	0.164416	+	0.284776i	−0.772032	+	0.635584i	$0.780760\pi$
$678$		0			0
$679$	−14.1251	+	49.0722i	−0.542072	+	1.88322i
$680$			4.04979i			0.155303i
$681$		0			0
$682$	35.2180	+	20.3331i	1.34857	+	0.778595i
$683$	6.33101	+	3.65521i	0.242249	+	0.139863i	0.616210	−	0.787582i	$-0.288667\pi$
$683$	6.33101	+	3.65521i	0.242249	+	0.139863i	−0.373961	+	0.927445i	$0.622001\pi$
$684$		0			0
$685$		−	24.4369i		−	0.933687i
$686$	17.5963	+	5.77664i	0.671831	+	0.220553i
$687$		0			0
$688$	4.40530	+	7.63021i	0.167951	+	0.290899i
$689$	5.62252	−	9.73849i	0.214201	−	0.371007i
$690$		0			0
$691$	43.9240	−	25.3596i	1.67095	−	0.964723i	0.703842	−	0.710357i	$-0.251466\pi$
$691$	43.9240	−	25.3596i	1.67095	−	0.964723i	0.967108	−	0.254366i	$-0.0818668\pi$
$692$	9.99738			0.380043
$693$		0			0
$694$	21.8753			0.830377
$695$	−9.85998	+	5.69266i	−0.374010	+	0.215935i
$696$		0			0
$697$	−10.2222	+	17.7054i	−0.387195	+	0.670642i
$698$	−0.136371	−	0.236201i	−0.00516171	−	0.00894035i
$699$		0			0
$700$	−1.14695	−	4.62010i	−0.0433505	−	0.174623i
$701$		−	21.6542i		−	0.817866i	−0.912564	−	0.408933i	$-0.865901\pi$
$701$		−	21.6542i		−	0.817866i	0.912564	−	0.408933i	$-0.134099\pi$
$702$		0			0
$703$	25.8962	+	14.9512i	0.976694	+	0.563895i
$704$	−4.52838	−	2.61446i	−0.170670	−	0.0985362i
$705$		0			0
$706$		−	15.1848i		−	0.571489i
$707$	−1.94879	+	1.87811i	−0.0732919	+	0.0706336i
$708$		0			0
$709$	9.31807	+	16.1394i	0.349947	+	0.606127i	0.986240	−	0.165321i	$-0.0528661\pi$
$709$	9.31807	+	16.1394i	0.349947	+	0.606127i	−0.636292	+	0.771448i	$0.719533\pi$
$710$	−1.89043	+	3.27432i	−0.0709466	+	0.122883i
$711$		0			0
$712$	−5.15000	+	2.97335i	−0.193004	+	0.111431i
$713$	61.4344			2.30074
$714$		0			0
$715$	47.1358			1.76278
$716$	−13.0876	+	7.55610i	−0.489105	+	0.282385i
$717$		0			0
$718$	−11.1944	+	19.3894i	−0.417773	+	0.723604i
$719$	−18.1893	−	31.5048i	−0.678347	−	1.17493i	−0.975479	−	0.220095i	$-0.929363\pi$
$719$	−18.1893	−	31.5048i	−0.678347	−	1.17493i	0.297132	−	0.954836i	$-0.403970\pi$
$720$		0			0
$721$	−25.6796	+	6.37498i	−0.956357	+	0.237417i
$722$			3.08085i			0.114658i
$723$		0			0
$724$	14.3964	+	8.31176i	0.535037	+	0.308904i
$725$	−5.27608	−	3.04615i	−0.195949	−	0.113131i
$726$		0			0
$727$		−	49.7512i		−	1.84517i	−0.385793	−	0.922585i	$-0.626072\pi$
$727$		−	49.7512i		−	1.84517i	0.385793	−	0.922585i	$-0.373928\pi$
$728$	12.8108	+	3.68750i	0.474800	+	0.136668i
$729$		0			0
$730$	4.20244	+	7.27884i	0.155539	+	0.269402i
$731$	−9.97199	+	17.2720i	−0.368828	+	0.638828i
$732$		0			0
$733$	9.91333	−	5.72347i	0.366157	−	0.211401i	−0.305621	−	0.952153i	$-0.598864\pi$
$733$	9.91333	−	5.72347i	0.366157	−	0.211401i	0.671778	+	0.740752i	$0.265531\pi$
$734$	−1.36088			−0.0502310
$735$		0			0
$736$	−7.89932			−0.291173
$737$	−6.38562	+	3.68674i	−0.235217	+	0.135803i
$738$		0			0
$739$	−12.4946	+	21.6413i	−0.459622	+	0.796089i	−0.998941	−	0.0460128i	$-0.985348\pi$
$739$	−12.4946	+	21.6413i	−0.459622	+	0.796089i	0.539319	+	0.842102i	$0.318682\pi$
$740$	6.70413	+	11.6119i	0.246449	+	0.426862i
$741$		0			0
$742$	−5.67431	−	1.63331i	−0.208310	−	0.0599607i
$743$		−	18.0985i		−	0.663971i	−0.943285	−	0.331985i	$-0.892282\pi$
$743$		−	18.0985i		−	0.663971i	0.943285	−	0.331985i	$-0.107718\pi$
$744$		0			0
$745$	26.7929	+	15.4689i	0.981617	+	0.566737i
$746$	22.3123	+	12.8820i	0.816912	+	0.471644i
$747$		0			0
$748$		−	11.8364i		−	0.432781i
$749$	0.786439	−	0.195234i	0.0287358	−	0.00713371i
$750$		0			0
$751$	−1.22436	−	2.12066i	−0.0446776	−	0.0773839i	0.842822	−	0.538193i	$-0.180893\pi$
$751$	−1.22436	−	2.12066i	−0.0446776	−	0.0773839i	−0.887499	+	0.460809i	$0.847559\pi$
$752$	2.07085	−	3.58682i	0.0755161	−	0.130798i
$753$		0			0
$754$	14.7753	−	8.53049i	0.538083	−	0.310662i
$755$	−29.0638			−1.05774
$756$		0			0
$757$	−54.5475			−1.98256			−0.991282	−	0.131758i	$-0.957938\pi$
$757$	−54.5475			−1.98256			−0.991282	+	0.131758i	$0.957938\pi$
$758$	9.17508	−	5.29724i	0.333254	−	0.192404i
$759$		0			0
$760$	3.56908	−	6.18183i	0.129464	−	0.224239i
$761$	−0.524034	−	0.907654i	−0.0189962	−	0.0329024i	0.856371	−	0.516361i	$-0.172714\pi$
$761$	−0.524034	−	0.907654i	−0.0189962	−	0.0329024i	−0.875367	+	0.483459i	$0.839380\pi$
$762$		0			0
$763$	−5.91888	+	5.70421i	−0.214278	+	0.206506i
$764$			20.0754i			0.726302i
$765$		0			0
$766$	−9.70088	−	5.60081i	−0.350507	−	0.202365i
$767$	47.3906	+	27.3610i	1.71118	+	0.987948i
$768$		0			0
$769$		−	39.7610i		−	1.43382i	−0.697166	−	0.716910i	$-0.745556\pi$
$769$		−	39.7610i		−	1.43382i	0.697166	−	0.716910i	$-0.254444\pi$
$770$	−5.96338	−	24.0216i	−0.214905	−	0.865678i
$771$		0			0
$772$	−2.34219	−	4.05680i	−0.0842974	−	0.146007i
$773$	16.9933	−	29.4333i	0.611207	−	1.05864i	−0.379830	−	0.925056i	$-0.624018\pi$
$773$	16.9933	−	29.4333i	0.611207	−	1.05864i	0.991037	−	0.133585i	$-0.0426490\pi$
$774$		0			0
$775$	12.1183	−	6.99649i	0.435302	−	0.251321i
$776$	19.3006			0.692852
$777$		0			0
$778$	−19.7828			−0.709248
$779$	31.2076	−	18.0177i	1.11813	−	0.645552i
$780$		0			0
$781$	5.52518	−	9.56989i	0.197706	−	0.342438i
$782$	−8.94059	−	15.4856i	−0.319715	−	0.553763i
$783$		0			0
$784$	0.258485	−	6.99523i	0.00923160	−	0.249829i
$785$			35.3005i			1.25993i
$786$		0			0
$787$	−18.0687	−	10.4320i	−0.644080	−	0.371860i	0.142104	−	0.989852i	$-0.454613\pi$
$787$	−18.0687	−	10.4320i	−0.644080	−	0.371860i	−0.786184	+	0.617992i	$0.787946\pi$
$788$	−10.4506	−	6.03365i	−0.372287	−	0.214940i
$789$		0			0
$790$		−	12.6349i		−	0.449531i
$791$	1.82914	−	6.35465i	0.0650368	−	0.225945i
$792$		0			0
$793$	10.6352	+	18.4207i	0.377667	+	0.654138i
$794$	−16.2778	+	28.1940i	−0.577678	+	1.00057i
$795$		0			0
$796$	−19.9506	+	11.5185i	−0.707131	+	0.408262i
$797$	−12.9251			−0.457832			−0.228916	−	0.973446i	$-0.573518\pi$
$797$	−12.9251			−0.457832			−0.228916	+	0.973446i	$0.573518\pi$
$798$		0			0
$799$	9.37529			0.331674
$800$	−1.55819	+	0.899620i	−0.0550902	+	0.0318064i
$801$		0			0
$802$	14.7841	−	25.6068i	0.522044	−	0.904207i
$803$	−12.2825	−	21.2739i	−0.433441	−	0.750741i
$804$		0			0
$805$	−25.9466	−	26.9231i	−0.914497	−	0.948913i
$806$			39.1863i			1.38028i
$807$		0			0
$808$	0.885907	+	0.511479i	0.0311661	+	0.0179938i
$809$	16.3360	+	9.43161i	0.574344	+	0.331598i	0.758883	−	0.651227i	$-0.225746\pi$
$809$	16.3360	+	9.43161i	0.574344	+	0.331598i	−0.184538	+	0.982825i	$0.559079\pi$
$810$		0			0
$811$		−	3.08486i		−	0.108324i	−0.998532	−	0.0541620i	$-0.982751\pi$
$811$		−	3.08486i		−	0.108324i	0.998532	−	0.0541620i	$-0.0172487\pi$
$812$	−6.21664	−	6.45060i	−0.218161	−	0.226372i
$813$		0			0
$814$	−19.5942	−	33.9382i	−0.686777	−	1.18953i
$815$	11.8328	−	20.4950i	0.414484	−	0.717907i
$816$		0			0
$817$	30.4436	−	17.5766i	1.06509	−	0.614928i
$818$	−5.43413			−0.190000
$819$		0			0
$820$	16.1583			0.564273
$821$	−10.3331	+	5.96584i	−0.360629	+	0.208209i	−0.669357	−	0.742941i	$-0.733430\pi$
$821$	−10.3331	+	5.96584i	−0.360629	+	0.208209i	0.308728	+	0.951150i	$0.400097\pi$
$822$		0			0
$823$	9.32060	−	16.1437i	0.324896	−	0.562736i	−0.656596	−	0.754243i	$-0.728004\pi$
$823$	9.32060	−	16.1437i	0.324896	−	0.562736i	0.981491	+	0.191507i	$0.0613375\pi$
$824$	5.00029	+	8.66075i	0.174193	+	0.301711i
$825$		0			0
$826$	7.94821	−	27.6130i	0.276554	−	0.960779i
$827$			40.8001i			1.41876i	0.704826	+	0.709380i	$0.251025\pi$
$827$			40.8001i			1.41876i	−0.704826	+	0.709380i	$0.748975\pi$
$828$		0			0
$829$	20.2452	+	11.6886i	0.703144	+	0.405961i	0.808517	−	0.588472i	$-0.200270\pi$
$829$	20.2452	+	11.6886i	0.703144	+	0.405961i	−0.105373	+	0.994433i	$0.533604\pi$
$830$	−5.46785	−	3.15687i	−0.189792	−	0.109576i
$831$		0			0
$832$		−	5.03863i		−	0.174683i
$833$	14.0058	−	7.41059i	0.485271	−	0.256762i
$834$		0			0
$835$	12.3669	+	21.4201i	0.427975	+	0.741275i
$836$	−10.4314	+	18.0677i	−0.360777	+	0.624884i
$837$		0			0
$838$	−3.78965	+	2.18795i	−0.130911	+	0.0755816i
$839$	−17.3583			−0.599274			−0.299637	−	0.954053i	$-0.596866\pi$
$839$	−17.3583			−0.599274			−0.299637	+	0.954053i	$0.596866\pi$
$840$		0			0
$841$	17.5347			0.604646
$842$	−6.36489	+	3.67477i	−0.219349	+	0.126641i
$843$		0			0
$844$	−11.2005	+	19.3999i	−0.385538	+	0.667772i
$845$	11.0813	+	19.1933i	0.381208	+	0.660271i
$846$		0			0
$847$	10.4172	+	41.9622i	0.357938	+	1.44184i
$848$			2.23177i			0.0766392i
$849$		0			0
$850$	−3.52717	−	2.03641i	−0.120981	−	0.0698483i
$851$	−51.2704	−	29.6010i	−1.75753	−	1.01471i
$852$		0			0
$853$			5.34663i			0.183065i	0.995802	+	0.0915326i	$0.0291766\pi$
$853$			5.34663i			0.183065i	−0.995802	+	0.0915326i	$0.970823\pi$
$854$	8.04213	−	7.75045i	0.275196	−	0.265215i
$855$		0			0
$856$	−0.153134	−	0.265236i	−0.00523402	−	0.00906559i
$857$	−7.28154	+	12.6120i	−0.248733	+	0.430818i	−0.963174	−	0.268877i	$-0.913347\pi$
$857$	−7.28154	+	12.6120i	−0.248733	+	0.430818i	0.714442	+	0.699695i	$0.246681\pi$
$858$		0			0
$859$	9.29046	−	5.36385i	0.316987	−	0.183012i	−0.333062	−	0.942905i	$-0.608082\pi$
$859$	9.29046	−	5.36385i	0.316987	−	0.183012i	0.650049	+	0.759893i	$0.274749\pi$
$860$	15.7628			0.537506
$861$		0			0
$862$	30.4781			1.03809
$863$	25.0062	−	14.4374i	0.851222	−	0.491453i	−0.00984090	−	0.999952i	$-0.503133\pi$
$863$	25.0062	−	14.4374i	0.851222	−	0.491453i	0.861063	+	0.508498i	$0.169799\pi$
$864$		0			0
$865$	8.94299	−	15.4897i	0.304071	−	0.526666i
$866$	−13.9490	−	24.1604i	−0.474007	−	0.821004i
$867$		0			0
$868$	19.9703	−	4.95764i	0.677835	−	0.168273i
$869$			36.9282i			1.25270i
$870$		0			0
$871$	−6.15323	−	3.55257i	−0.208494	−	0.120374i
$872$	2.69068	+	1.55347i	0.0911180	+	0.0526070i
$873$		0			0
$874$			31.5174i			1.06609i
$875$	−30.9279	−	8.90240i	−1.04556	−	0.300956i
$876$		0			0
$877$	−11.9519	−	20.7013i	−0.403588	−	0.699035i	0.590568	−	0.806988i	$-0.298904\pi$
$877$	−11.9519	−	20.7013i	−0.403588	−	0.699035i	−0.994156	+	0.107953i	$0.965570\pi$
$878$	4.57276	−	7.92025i	0.154323	−	0.267295i
$879$		0			0
$880$	−8.10158	+	4.67745i	−0.273104	+	0.157677i
$881$	−23.6586			−0.797078			−0.398539	−	0.917151i	$-0.630483\pi$
$881$	−23.6586			−0.797078			−0.398539	+	0.917151i	$0.630483\pi$
$882$		0			0
$883$	43.8523			1.47575			0.737873	−	0.674940i	$-0.235830\pi$
$883$	43.8523			1.47575			0.737873	+	0.674940i	$0.235830\pi$
$884$	9.87755	−	5.70281i	0.332218	−	0.191806i
$885$		0			0
$886$	−10.9467	+	18.9603i	−0.367763	+	0.636983i
$887$	−14.7804	−	25.6005i	−0.496279	−	0.859580i	0.503712	−	0.863872i	$-0.331967\pi$
$887$	−14.7804	−	25.6005i	−0.496279	−	0.859580i	−0.999991	+	0.00429142i	$0.998634\pi$
$888$		0			0
$889$	13.3973	+	3.85631i	0.449330	+	0.129337i
$890$			10.6391i			0.356622i
$891$		0			0
$892$	8.65219	+	4.99534i	0.289697	+	0.167256i
$893$	−14.3110	−	8.26244i	−0.478898	−	0.276492i
$894$		0			0
$895$			27.0367i			0.903739i
$896$	−2.56781	+	0.637461i	−0.0857845	+	0.0212961i
$897$		0			0
$898$	−10.4313	−	18.0675i	−0.348096	−	0.602920i
$899$	13.1669	−	22.8057i	0.439140	−	0.760614i
$900$		0			0
$901$	−4.37508	+	2.52595i	−0.145755	+	0.0841517i
$902$	−47.2261			−1.57246
$903$		0			0
$904$	−2.49935			−0.0831272
$905$	25.7561	−	14.8703i	0.856162	−	0.494305i
$906$		0			0
$907$	−5.37858	+	9.31597i	−0.178593	+	0.309332i	−0.941399	−	0.337296i	$-0.890488\pi$
$907$	−5.37858	+	9.31597i	−0.178593	+	0.309332i	0.762806	+	0.646627i	$0.223821\pi$
$908$	1.59918	+	2.76985i	0.0530705	+	0.0919208i
$909$		0			0
$910$	17.1730	−	16.5502i	0.569280	−	0.548633i
$911$			53.5414i			1.77391i	0.461860	+	0.886953i	$0.347182\pi$
$911$			53.5414i			1.77391i	−0.461860	+	0.886953i	$0.652818\pi$
$912$		0			0
$913$	15.9809	+	9.22661i	0.528892	+	0.305356i
$914$	−6.86192	−	3.96173i	−0.226972	−	0.131042i
$915$		0			0
$916$		−	16.9547i		−	0.560200i
$917$	5.31174	+	21.3966i	0.175409	+	0.706579i
$918$		0			0
$919$	−0.817192	−	1.41542i	−0.0269567	−	0.0466903i	0.852232	−	0.523163i	$-0.175248\pi$
$919$	−0.817192	−	1.41542i	−0.0269567	−	0.0466903i	−0.879189	+	0.476473i	$0.841915\pi$
$920$	−7.06621	+	12.2390i	−0.232966	+	0.403509i
$921$		0			0
$922$	7.84815	−	4.53113i	0.258465	−	0.149225i
$923$	10.6482			0.350490
$924$		0			0
$925$	−13.4845			−0.443367
$926$	−0.432914	+	0.249943i	−0.0142264	+	0.00821364i
$927$		0			0
$928$	−1.69302	+	2.93240i	−0.0555761	+	0.0962606i
$929$	16.0349	+	27.7733i	0.526088	+	0.911211i	0.999538	+	0.0303906i	$0.00967512\pi$
$929$	16.0349	+	27.7733i	0.526088	+	0.911211i	−0.473450	+	0.880821i	$0.656992\pi$
$930$		0			0
$931$	−27.9101	−	1.03132i	−0.914717	−	0.0338003i
$932$		−	8.36828i		−	0.274112i
$933$		0			0
$934$	1.39416	+	0.804921i	0.0456184	+	0.0263378i
$935$	−18.3390	−	10.5880i	−0.599750	−	0.346266i
$936$		0			0
$937$			11.9407i			0.390086i	0.980795	+	0.195043i	$0.0624847\pi$
$937$			11.9407i			0.390086i	−0.980795	+	0.195043i	$0.937515\pi$
$938$	−1.03200	+	3.58529i	−0.0336960	+	0.117064i
$939$		0			0
$940$	−3.70489	−	6.41705i	−0.120840	−	0.209301i
$941$	−23.8800	+	41.3614i	−0.778467	+	1.34834i	0.154359	+	0.988015i	$0.450669\pi$
$941$	−23.8800	+	41.3614i	−0.778467	+	1.34834i	−0.932825	+	0.360329i	$0.882665\pi$
$942$		0			0
$943$	−61.7860	+	35.6722i	−2.01203	+	1.16165i
$944$	−10.8605			−0.353479
$945$		0			0
$946$	−46.0700			−1.49786
$947$	28.8204	−	16.6395i	0.936537	−	0.540710i	0.0476636	−	0.998863i	$-0.484822\pi$
$947$	28.8204	−	16.6395i	0.936537	−	0.540710i	0.888873	+	0.458154i	$0.151489\pi$
$948$		0			0
$949$	11.8355	−	20.4997i	0.384197	−	0.665449i
$950$	3.58937	+	6.21698i	0.116455	+	0.201705i
$951$		0			0
$952$	−4.15595	−	4.31235i	−0.134695	−	0.139764i
$953$		−	3.57700i		−	0.115870i	−0.998320	−	0.0579352i	$-0.981548\pi$
$953$		−	3.57700i		−	0.115870i	0.998320	−	0.0579352i	$-0.0184517\pi$
$954$		0			0
$955$	31.1043	+	17.9581i	1.00651	+	0.581110i
$956$	−11.8431	−	6.83764i	−0.383035	−	0.221145i
$957$		0			0
$958$		−	6.53591i		−	0.211166i
$959$	25.0775	+	26.0213i	0.809794	+	0.840270i
$960$		0			0
$961$	14.7422	+	25.5342i	0.475554	+	0.823683i
$962$	18.8811	−	32.7031i	0.608752	−	1.05439i
$963$		0			0
$964$	22.5782	−	13.0355i	0.727195	−	0.419846i
$965$	−8.38068			−0.269784
$966$		0			0
$967$	−20.1745			−0.648768			−0.324384	−	0.945925i	$-0.605157\pi$
$967$	−20.1745			−0.648768			−0.324384	+	0.945925i	$0.605157\pi$
$968$	14.1523	−	8.17082i	0.454871	−	0.262620i
$969$		0			0
$970$	17.2651	−	29.9040i	0.554348	−	0.960159i
$971$	−3.86876	−	6.70088i	−0.124154	−	0.215042i	0.797248	−	0.603652i	$-0.206288\pi$
$971$	−3.86876	−	6.70088i	−0.124154	−	0.215042i	−0.921402	+	0.388611i	$0.872955\pi$
$972$		0			0
$973$	4.65735	−	16.1802i	0.149308	−	0.518712i
$974$		−	3.14622i		−	0.100811i
$975$		0			0
$976$	−3.65589	−	2.11073i	−0.117022	−	0.0675629i
$977$	−21.0883	−	12.1753i	−0.674674	−	0.389523i	0.123172	−	0.992385i	$-0.460693\pi$
$977$	−21.0883	−	12.1753i	−0.674674	−	0.389523i	−0.797845	+	0.602862i	$0.794027\pi$
$978$		0			0
$979$		−	31.0949i		−	0.993796i
$980$	−10.6070	−	6.65795i	−0.338829	−	0.212681i
$981$		0			0
$982$	−12.8038	−	22.1769i	−0.408586	−	0.707692i
$983$	7.12004	−	12.3323i	0.227094	−	0.393339i	−0.729852	−	0.683606i	$-0.760411\pi$
$983$	7.12004	−	12.3323i	0.227094	−	0.393339i	0.956946	+	0.290267i	$0.0937442\pi$
$984$		0			0
$985$	−18.6968	+	10.7946i	−0.595730	+	0.343945i
$986$	−7.66476			−0.244096
$987$		0			0
$988$	−20.1035			−0.639578
$989$	−60.2735	+	34.7989i	−1.91658	+	1.10654i
$990$		0			0
$991$	−18.4719	+	31.9943i	−0.586779	+	1.01633i	0.407872	+	0.913039i	$0.366271\pi$
$991$	−18.4719	+	31.9943i	−0.586779	+	1.01633i	−0.994651	+	0.103292i	$0.967062\pi$
$992$	−3.88858	−	6.73522i	−0.123463	−	0.213844i
$993$		0			0
$994$	−1.34716	−	5.42659i	−0.0427292	−	0.172121i
$995$			41.2147i			1.30659i
$996$		0			0
$997$	−17.2946	−	9.98502i	−0.547724	−	0.316229i	0.200480	−	0.979698i	$-0.435750\pi$
$997$	−17.2946	−	9.98502i	−0.547724	−	0.316229i	−0.748204	+	0.663469i	$0.769083\pi$
$998$	9.27176	+	5.35305i	0.293492	+	0.169448i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.k.d.647.5	yes	16
3.2	odd	2		1134.2.k.c.647.4	✓	16
7.5	odd	6		1134.2.k.c.971.4	yes	16
9.2	odd	6		1134.2.t.h.1025.5		16
9.4	even	3		1134.2.l.g.269.5		16
9.5	odd	6		1134.2.l.h.269.4		16
9.7	even	3		1134.2.t.g.1025.4		16
21.5	even	6	inner	1134.2.k.d.971.5	yes	16
63.5	even	6		1134.2.t.g.593.4		16
63.40	odd	6		1134.2.t.h.593.5		16
63.47	even	6		1134.2.l.g.215.1		16
63.61	odd	6		1134.2.l.h.215.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.k.c.647.4	✓	16	3.2	odd	2
1134.2.k.c.971.4	yes	16	7.5	odd	6
1134.2.k.d.647.5	yes	16	1.1	even	1	trivial
1134.2.k.d.971.5	yes	16	21.5	even	6	inner
1134.2.l.g.215.1		16	63.47	even	6
1134.2.l.g.269.5		16	9.4	even	3
1134.2.l.h.215.8		16	63.61	odd	6
1134.2.l.h.269.4		16	9.5	odd	6
1134.2.t.g.593.4		16	63.5	even	6
1134.2.t.g.1025.4		16	9.7	even	3
1134.2.t.h.593.5		16	63.40	odd	6
1134.2.t.h.1025.5		16	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.894533 - 1.54938i) q^{5} +(2.54252 + 0.731847i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.894533 - 1.54938i) q^{5} +(2.54252 + 0.731847i) q^{7} -1.00000i q^{8} +(-1.54938 - 0.894533i) q^{10} +(4.52838 + 2.61446i) q^{11} +5.03863i q^{13} +(2.56781 - 0.637461i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.13182 - 1.96037i) q^{17} +(-3.45534 + 1.99494i) q^{19} -1.78907 q^{20} +5.22892 q^{22} +(6.84102 - 3.94966i) q^{23} +(0.899620 - 1.55819i) q^{25} +(2.51931 + 4.36358i) q^{26} +(1.90506 - 1.83596i) q^{28} -3.38604i q^{29} +(6.73522 + 3.88858i) q^{31} +(-0.866025 - 0.500000i) q^{32} -2.26364i q^{34} +(-1.14046 - 4.59398i) q^{35} +(-3.74728 - 6.49047i) q^{37} +(-1.99494 + 3.45534i) q^{38} +(-1.54938 + 0.894533i) q^{40} -9.03171 q^{41} -8.81060 q^{43} +(4.52838 - 2.61446i) q^{44} +(3.94966 - 6.84102i) q^{46} +(2.07085 + 3.58682i) q^{47} +(5.92880 + 3.72147i) q^{49} -1.79924i q^{50} +(4.36358 + 2.51931i) q^{52} +(-1.93277 - 1.11588i) q^{53} -9.35489i q^{55} +(0.731847 - 2.54252i) q^{56} +(-1.69302 - 2.93240i) q^{58} +(5.43025 - 9.40546i) q^{59} +(3.65589 - 2.11073i) q^{61} +7.77717 q^{62} -1.00000 q^{64} +(7.80674 - 4.50722i) q^{65} +(-0.705066 + 1.22121i) q^{67} +(-1.13182 - 1.96037i) q^{68} +(-3.28466 - 3.40827i) q^{70} -2.11331i q^{71} +(-4.06851 - 2.34896i) q^{73} +(-6.49047 - 3.74728i) q^{74} +3.98988i q^{76} +(9.60011 + 9.96140i) q^{77} +(3.53115 + 6.11613i) q^{79} +(-0.894533 + 1.54938i) q^{80} +(-7.82169 + 4.51585i) q^{82} +3.52907 q^{83} -4.04979 q^{85} +(-7.63021 + 4.40530i) q^{86} +(2.61446 - 4.52838i) q^{88} +(-2.97335 - 5.15000i) q^{89} +(-3.68750 + 12.8108i) q^{91} -7.89932i q^{92} +(3.58682 + 2.07085i) q^{94} +(6.18183 + 3.56908i) q^{95} +19.3006i q^{97} +(6.99523 + 0.258485i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 + 8 * q^7	\( 16 q + 8 q^{4} + 8 q^{7} + 12 q^{11} + 12 q^{14} - 8 q^{16} + 12 q^{23} - 8 q^{25} + 4 q^{28} + 12 q^{31} + 60 q^{35} + 4 q^{37} - 12 q^{38} - 48 q^{41} - 32 q^{43} + 12 q^{44} + 4 q^{49} - 12 q^{52} + 12 q^{56} - 12 q^{58} - 24 q^{59} - 12 q^{61} - 48 q^{62} - 16 q^{64} + 48 q^{65} - 4 q^{67} - 24 q^{70} + 36 q^{73} + 36 q^{74} + 84 q^{77} + 8 q^{79} - 72 q^{83} + 24 q^{85} + 24 q^{86} + 24 q^{89} - 12 q^{91} - 36 q^{94} + 12 q^{95} + 36 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 + 8 * q^7 + 12 * q^11 + 12 * q^14 - 8 * q^16 + 12 * q^23 - 8 * q^25 + 4 * q^28 + 12 * q^31 + 60 * q^35 + 4 * q^37 - 12 * q^38 - 48 * q^41 - 32 * q^43 + 12 * q^44 + 4 * q^49 - 12 * q^52 + 12 * q^56 - 12 * q^58 - 24 * q^59 - 12 * q^61 - 48 * q^62 - 16 * q^64 + 48 * q^65 - 4 * q^67 - 24 * q^70 + 36 * q^73 + 36 * q^74 + 84 * q^77 + 8 * q^79 - 72 * q^83 + 24 * q^85 + 24 * q^86 + 24 * q^89 - 12 * q^91 - 36 * q^94 + 12 * q^95 + 36 * q^98

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