LMFDB - Embedded newform 882.2.m.b.587.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(293,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("882.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.m (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:	$7.04280545828$
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} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			587.6
Root			$-1.70672 + 0.295146i$ of defining polynomial
Character	$\chi$	$=$	882.587
Dual form			882.2.m.b.293.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.991125 + 1.42045i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.483662 + 0.837727i) q^{5} +(-1.56856 + 0.734581i) q^{6} +1.00000i q^{8} +(-1.03534 - 2.81568i) q^{9} +0.967324i q^{10} +(-4.82689 - 2.78681i) q^{11} +(-1.72571 - 0.148116i) q^{12} +(-3.76893 + 2.17600i) q^{13} +(-1.66932 - 0.143276i) q^{15} +(-0.500000 + 0.866025i) q^{16} -3.94535 q^{17} +(0.511208 - 2.95612i) q^{18} +4.46634i q^{19} +(-0.483662 + 0.837727i) q^{20} +(-2.78681 - 4.82689i) q^{22} +(-2.29786 + 1.32667i) q^{23} +(-1.42045 - 0.991125i) q^{24} +(2.03214 - 3.51977i) q^{25} -4.35199 q^{26} +(5.02568 + 1.32004i) q^{27} +(4.61157 + 2.66249i) q^{29} +(-1.37403 - 0.958739i) q^{30} +(-5.34038 + 3.08327i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(8.74256 - 4.09427i) q^{33} +(-3.41677 - 1.97267i) q^{34} +(1.92078 - 2.30447i) q^{36} -0.487217 q^{37} +(-2.23317 + 3.86796i) q^{38} +(0.644598 - 7.51026i) q^{39} +(-0.837727 + 0.483662i) q^{40} +(0.0818856 + 0.141830i) q^{41} +(-4.35045 + 7.53520i) q^{43} -5.57361i q^{44} +(1.85802 - 2.22917i) q^{45} -2.65334 q^{46} +(4.74500 - 8.21859i) q^{47} +(-0.734581 - 1.56856i) q^{48} +(3.51977 - 2.03214i) q^{50} +(3.91033 - 5.60416i) q^{51} +(-3.76893 - 2.17600i) q^{52} +2.01518i q^{53} +(3.69235 + 3.65603i) q^{54} -5.39149i q^{55} +(-6.34420 - 4.42670i) q^{57} +(2.66249 + 4.61157i) q^{58} +(-0.836931 - 1.44961i) q^{59} +(-0.710578 - 1.51731i) q^{60} +(-4.47927 - 2.58611i) q^{61} -6.16655 q^{62} -1.00000 q^{64} +(-3.64578 - 2.10489i) q^{65} +(9.61842 + 0.825539i) q^{66} +(2.72126 + 4.71336i) q^{67} +(-1.97267 - 3.41677i) q^{68} +(0.393002 - 4.57889i) q^{69} -3.64006i q^{71} +(2.81568 - 1.03534i) q^{72} +2.48801i q^{73} +(-0.421942 - 0.243608i) q^{74} +(2.98555 + 6.37509i) q^{75} +(-3.86796 + 2.23317i) q^{76} +(4.31337 - 6.18177i) q^{78} +(-2.30121 + 3.98581i) q^{79} -0.967324 q^{80} +(-6.85613 + 5.83039i) q^{81} +0.163771i q^{82} +(-4.20979 + 7.29158i) q^{83} +(-1.90821 - 3.30512i) q^{85} +(-7.53520 + 4.35045i) q^{86} +(-8.35257 + 3.91163i) q^{87} +(2.78681 - 4.82689i) q^{88} +4.11622 q^{89} +(2.72368 - 1.00151i) q^{90} +(-2.29786 - 1.32667i) q^{92} +(0.913362 - 10.6416i) q^{93} +(8.21859 - 4.74500i) q^{94} +(-3.74157 + 2.16020i) q^{95} +(0.148116 - 1.72571i) q^{96} +(10.2669 + 5.92762i) q^{97} +(-2.84928 + 16.4763i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 6 q^{9} - 12 q^{11} + 6 q^{13} - 18 q^{15} - 8 q^{16} + 36 q^{17} + 6 q^{23} - 6 q^{24} - 8 q^{25} - 24 q^{26} + 36 q^{27} + 6 q^{29} + 18 q^{30} + 6 q^{31} + 18 q^{33} + 4 q^{37} + 42 q^{39}+ \cdots + 18 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 6 * q^9 - 12 * q^11 + 6 * q^13 - 18 * q^15 - 8 * q^16 + 36 * q^17 + 6 * q^23 - 6 * q^24 - 8 * q^25 - 24 * q^26 + 36 * q^27 + 6 * q^29 + 18 * q^30 + 6 * q^31 + 18 * q^33 + 4 * q^37 + 42 * q^39 - 6 * q^41 - 2 * q^43 + 42 * q^45 - 12 * q^46 + 18 * q^47 - 12 * q^50 - 6 * q^51 + 6 * q^52 + 6 * q^57 + 6 * q^58 - 30 * q^59 - 12 * q^60 - 60 * q^61 + 36 * q^62 - 16 * q^64 - 42 * q^65 + 24 * q^66 + 14 * q^67 + 18 * q^68 - 42 * q^69 - 12 * q^72 - 18 * q^74 - 30 * q^75 - 16 * q^79 - 18 * q^81 - 12 * q^85 - 24 * q^86 - 24 * q^87 + 48 * q^89 + 18 * q^90 + 6 * q^92 + 12 * q^93 + 66 * q^95 - 6 * q^96 + 6 * q^97 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.991125	+	1.42045i	−0.572226	+	0.820096i
$3$	−0.991125	+	1.42045i	−0.572226	+	0.820096i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.483662	+	0.837727i	0.216300	+	0.374643i	0.953674	−	0.300842i	$-0.0972677\pi$
$5$	0.483662	+	0.837727i	0.216300	+	0.374643i	−0.737374	+	0.675485i	$0.763934\pi$
$6$	−1.56856	+	0.734581i	−0.640363	+	0.299892i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−1.03534	−	2.81568i	−0.345114	−	0.938561i
$10$			0.967324i			0.305895i
$11$	−4.82689	−	2.78681i	−1.45536	−	0.840254i	−0.456584	−	0.889680i	$-0.650927\pi$
$11$	−4.82689	−	2.78681i	−1.45536	−	0.840254i	−0.998778	+	0.0494264i	$0.984261\pi$
$12$	−1.72571	−	0.148116i	−0.498168	−	0.0427573i
$13$	−3.76893	+	2.17600i	−1.04531	+	0.603512i	−0.921334	−	0.388772i	$-0.872899\pi$
$13$	−3.76893	+	2.17600i	−1.04531	+	0.603512i	−0.123980	+	0.992285i	$0.539566\pi$
$14$		0			0
$15$	−1.66932	−	0.143276i	−0.431016	−	0.0369937i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.94535			−0.956887			−0.478443	−	0.878118i	$-0.658799\pi$
$17$	−3.94535			−0.956887			−0.478443	+	0.878118i	$0.658799\pi$
$18$	0.511208	−	2.95612i	0.120493	−	0.696765i
$19$			4.46634i			1.02465i	0.858792	+	0.512324i	$0.171215\pi$
$19$			4.46634i			1.02465i	−0.858792	+	0.512324i	$0.828785\pi$
$20$	−0.483662	+	0.837727i	−0.108150	+	0.187322i
$21$		0			0
$22$	−2.78681	−	4.82689i	−0.594149	−	1.02910i
$23$	−2.29786	+	1.32667i	−0.479137	+	0.276630i	−0.720057	−	0.693915i	$-0.755884\pi$
$23$	−2.29786	+	1.32667i	−0.479137	+	0.276630i	0.240920	+	0.970545i	$0.422551\pi$
$24$	−1.42045	−	0.991125i	−0.289948	−	0.202313i
$25$	2.03214	−	3.51977i	0.406428	−	0.703955i
$26$	−4.35199			−0.853496
$27$	5.02568	+	1.32004i	0.967193	+	0.254042i
$28$		0			0
$29$	4.61157	+	2.66249i	0.856347	+	0.494412i	0.862787	−	0.505567i	$-0.168717\pi$
$29$	4.61157	+	2.66249i	0.856347	+	0.494412i	−0.00644015	+	0.999979i	$0.502050\pi$
$30$	−1.37403	−	0.958739i	−0.250863	−	0.175041i
$31$	−5.34038	+	3.08327i	−0.959161	+	0.553772i	−0.895915	−	0.444226i	$-0.853479\pi$
$31$	−5.34038	+	3.08327i	−0.959161	+	0.553772i	−0.0632466	+	0.997998i	$0.520145\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	8.74256	−	4.09427i	1.52189	−	0.712721i
$34$	−3.41677	−	1.97267i	−0.585971	−	0.338311i
$35$		0			0
$36$	1.92078	−	2.30447i	0.320130	−	0.384079i
$37$	−0.487217			−0.0800980			−0.0400490	−	0.999198i	$-0.512751\pi$
$37$	−0.487217			−0.0800980			−0.0400490	+	0.999198i	$0.512751\pi$
$38$	−2.23317	+	3.86796i	−0.362268	+	0.627466i
$39$	0.644598	−	7.51026i	0.103218	−	1.20260i
$40$	−0.837727	+	0.483662i	−0.132456	+	0.0764737i
$41$	0.0818856	+	0.141830i	0.0127884	+	0.0221501i	0.872349	−	0.488884i	$-0.162596\pi$
$41$	0.0818856	+	0.141830i	0.0127884	+	0.0221501i	−0.859560	+	0.511034i	$0.829263\pi$
$42$		0			0
$43$	−4.35045	+	7.53520i	−0.663437	+	1.14911i	0.316270	+	0.948669i	$0.397570\pi$
$43$	−4.35045	+	7.53520i	−0.663437	+	1.14911i	−0.979707	+	0.200437i	$0.935764\pi$
$44$		−	5.57361i		−	0.840254i
$45$	1.85802	−	2.22917i	0.276977	−	0.332306i
$46$	−2.65334			−0.391214
$47$	4.74500	−	8.21859i	0.692130	−	1.19880i	−0.279009	−	0.960289i	$-0.590006\pi$
$47$	4.74500	−	8.21859i	0.692130	−	1.19880i	0.971139	−	0.238516i	$-0.0766609\pi$
$48$	−0.734581	−	1.56856i	−0.106028	−	0.226403i
$49$		0			0
$50$	3.51977	−	2.03214i	0.497771	−	0.287388i
$51$	3.91033	−	5.60416i	0.547556	−	0.784739i
$52$	−3.76893	−	2.17600i	−0.522657	−	0.301756i
$53$			2.01518i			0.276807i	0.990376	+	0.138403i	$0.0441970\pi$
$53$			2.01518i			0.276807i	−0.990376	+	0.138403i	$0.955803\pi$
$54$	3.69235	+	3.65603i	0.502465	+	0.497523i
$55$		−	5.39149i		−	0.726988i
$56$		0			0
$57$	−6.34420	−	4.42670i	−0.840310	−	0.586331i
$58$	2.66249	+	4.61157i	0.349602	+	0.605529i
$59$	−0.836931	−	1.44961i	−0.108959	−	0.188723i	0.806390	−	0.591384i	$-0.201418\pi$
$59$	−0.836931	−	1.44961i	−0.108959	−	0.188723i	−0.915349	+	0.402662i	$0.868085\pi$
$60$	−0.710578	−	1.51731i	−0.0917352	−	0.195884i
$61$	−4.47927	−	2.58611i	−0.573512	−	0.331117i	0.185039	−	0.982731i	$-0.440759\pi$
$61$	−4.47927	−	2.58611i	−0.573512	−	0.331117i	−0.758551	+	0.651614i	$0.774092\pi$
$62$	−6.16655			−0.783152
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−3.64578	−	2.10489i	−0.452203	−	0.261080i
$66$	9.61842	+	0.825539i	1.18395	+	0.101617i
$67$	2.72126	+	4.71336i	0.332455	+	0.575828i	0.982993	−	0.183645i	$-0.0587898\pi$
$67$	2.72126	+	4.71336i	0.332455	+	0.575828i	−0.650538	+	0.759474i	$0.725456\pi$
$68$	−1.97267	−	3.41677i	−0.239222	−	0.414344i
$69$	0.393002	−	4.57889i	0.0473118	−	0.551234i
$70$		0			0
$71$		−	3.64006i		−	0.431996i	−0.976394	−	0.215998i	$-0.930700\pi$
$71$		−	3.64006i		−	0.431996i	0.976394	−	0.215998i	$-0.0693005\pi$
$72$	2.81568	−	1.03534i	0.331831	−	0.122016i
$73$			2.48801i			0.291200i	0.989344	+	0.145600i	$0.0465112\pi$
$73$			2.48801i			0.291200i	−0.989344	+	0.145600i	$0.953489\pi$
$74$	−0.421942	−	0.243608i	−0.0490498	−	0.0283189i
$75$	2.98555	+	6.37509i	0.344741	+	0.736132i
$76$	−3.86796	+	2.23317i	−0.443686	+	0.256162i
$77$		0			0
$78$	4.31337	−	6.18177i	0.488393	−	0.699948i
$79$	−2.30121	+	3.98581i	−0.258906	+	0.448438i	−0.965949	−	0.258732i	$-0.916695\pi$
$79$	−2.30121	+	3.98581i	−0.258906	+	0.448438i	0.707043	+	0.707170i	$0.250029\pi$
$80$	−0.967324			−0.108150
$81$	−6.85613	+	5.83039i	−0.761792	+	0.647821i
$82$			0.163771i			0.0180855i
$83$	−4.20979	+	7.29158i	−0.462085	+	0.800355i	−0.999065	−	0.0432405i	$-0.986232\pi$
$83$	−4.20979	+	7.29158i	−0.462085	+	0.800355i	0.536980	+	0.843595i	$0.319565\pi$
$84$		0			0
$85$	−1.90821	−	3.30512i	−0.206975	−	0.358491i
$86$	−7.53520	+	4.35045i	−0.812541	+	0.469121i
$87$	−8.35257	+	3.91163i	−0.895490	+	0.419371i
$88$	2.78681	−	4.82689i	0.297075	−	0.514548i
$89$	4.11622			0.436318			0.218159	−	0.975913i	$-0.429995\pi$
$89$	4.11622			0.436318			0.218159	+	0.975913i	$0.429995\pi$
$90$	2.72368	−	1.00151i	0.287101	−	0.105569i
$91$		0			0
$92$	−2.29786	−	1.32667i	−0.239569	−	0.138315i
$93$	0.913362	−	10.6416i	0.0947112	−	1.10349i
$94$	8.21859	−	4.74500i	0.847683	−	0.489410i
$95$	−3.74157	+	2.16020i	−0.383877	+	0.221632i
$96$	0.148116	−	1.72571i	0.0151170	−	0.176129i
$97$	10.2669	+	5.92762i	1.04245	+	0.601859i	0.920526	−	0.390681i	$-0.127760\pi$
$97$	10.2669	+	5.92762i	1.04245	+	0.601859i	0.121924	+	0.992539i	$0.461094\pi$
$98$		0			0
$99$	−2.84928	+	16.4763i	−0.286363	+	1.65593i
$100$	4.06428			0.406428
$101$	2.65813	−	4.60402i	0.264494	−	0.458117i	−0.702937	−	0.711252i	$-0.748128\pi$
$101$	2.65813	−	4.60402i	0.264494	−	0.458117i	0.967431	+	0.253135i	$0.0814618\pi$
$102$	6.18852	−	2.89818i	0.612755	−	0.286962i
$103$	−7.74616	+	4.47225i	−0.763252	+	0.440664i	−0.830462	−	0.557075i	$-0.811924\pi$
$103$	−7.74616	+	4.47225i	−0.763252	+	0.440664i	0.0672102	+	0.997739i	$0.478590\pi$
$104$	−2.17600	−	3.76893i	−0.213374	−	0.369574i
$105$		0			0
$106$	−1.00759	+	1.74520i	−0.0978659	+	0.169509i
$107$			19.1563i			1.85191i	0.377639	+	0.925953i	$0.376736\pi$
$107$			19.1563i			1.85191i	−0.377639	+	0.925953i	$0.623264\pi$
$108$	1.36965	+	5.01239i	0.131795	+	0.482317i
$109$	19.2434			1.84318			0.921590	−	0.388164i	$-0.126891\pi$
$109$	19.2434			1.84318			0.921590	+	0.388164i	$0.126891\pi$
$110$	2.69574	−	4.66917i	0.257029	−	0.445188i
$111$	0.482893	−	0.692066i	0.0458342	−	0.0656880i
$112$		0			0
$113$	7.31199	−	4.22158i	0.687854	−	0.397133i	−0.114953	−	0.993371i	$-0.536672\pi$
$113$	7.31199	−	4.22158i	0.687854	−	0.397133i	0.802808	+	0.596238i	$0.203339\pi$
$114$	−3.28089	−	7.00573i	−0.307283	−	0.656147i
$115$	−2.22278	−	1.28332i	−0.207275	−	0.119670i
$116$			5.32498i			0.494412i
$117$	10.0290	+	8.35922i	0.927186	+	0.772810i
$118$		−	1.67386i		−	0.154091i
$119$		0			0
$120$	0.143276	−	1.66932i	0.0130792	−	0.152387i
$121$	10.0326	+	17.3769i	0.912053	+	1.57972i
$122$	−2.58611	−	4.47927i	−0.234135	−	0.405534i
$123$	−0.282621	−	0.0242571i	−0.0254831	−	0.00218719i
$124$	−5.34038	−	3.08327i	−0.479581	−	0.276886i
$125$	8.76810			0.784243
$126$		0			0
$127$	3.31883			0.294498			0.147249	−	0.989099i	$-0.452958\pi$
$127$	3.31883			0.294498			0.147249	+	0.989099i	$0.452958\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−6.39151	−	13.6479i	−0.562741	−	1.20163i
$130$	−2.10489	−	3.64578i	−0.184611	−	0.319756i
$131$	−9.37335	−	16.2351i	−0.818954	−	1.41847i	−0.906454	−	0.422305i	$-0.861221\pi$
$131$	−9.37335	−	16.2351i	−0.818954	−	1.41847i	0.0875000	−	0.996165i	$-0.472112\pi$
$132$	7.91702	+	5.52415i	0.689089	+	0.480815i
$133$		0			0
$134$			5.44252i			0.470162i
$135$	1.32490	+	4.84861i	0.114029	+	0.417302i
$136$		−	3.94535i		−	0.338311i
$137$	−14.6656	−	8.46717i	−1.25296	−	0.723399i	−0.281267	−	0.959630i	$-0.590755\pi$
$137$	−14.6656	−	8.46717i	−1.25296	−	0.723399i	−0.971697	+	0.236230i	$0.924088\pi$
$138$	2.62979	−	3.76893i	0.223863	−	0.320833i
$139$	−10.5033	+	6.06406i	−0.890875	+	0.514347i	−0.874229	−	0.485514i	$-0.838632\pi$
$139$	−10.5033	+	6.06406i	−0.890875	+	0.514347i	−0.0166466	+	0.999861i	$0.505299\pi$
$140$		0			0
$141$	6.97118	+	14.8857i	0.587079	+	1.25360i
$142$	1.82003	−	3.15239i	0.152734	−	0.264543i
$143$	24.2563			2.02841
$144$	2.95612	+	0.511208i	0.246344	+	0.0426007i
$145$			5.15098i			0.427766i
$146$	−1.24401	+	2.15468i	−0.102955	+	0.178323i
$147$		0			0
$148$	−0.243608	−	0.421942i	−0.0200245	−	0.0346834i
$149$	7.56951	−	4.37026i	0.620118	−	0.358025i	−0.156797	−	0.987631i	$-0.550117\pi$
$149$	7.56951	−	4.37026i	0.620118	−	0.358025i	0.776915	+	0.629606i	$0.216783\pi$
$150$	−0.601984	+	7.01376i	−0.0491518	+	0.572671i
$151$	−11.0471	+	19.1341i	−0.898997	+	1.55711i	−0.0702195	+	0.997532i	$0.522370\pi$
$151$	−11.0471	+	19.1341i	−0.898997	+	1.55711i	−0.828778	+	0.559578i	$0.810963\pi$
$152$	−4.46634			−0.362268
$153$	4.08478	+	11.1088i	0.330235	+	0.898096i
$154$		0			0
$155$	−5.16588	−	2.98252i	−0.414934	−	0.239562i
$156$	6.82637	−	3.19689i	0.546547	−	0.255956i
$157$	1.23372	−	0.712287i	0.0984614	−	0.0568467i	−0.449961	−	0.893048i	$-0.648562\pi$
$157$	1.23372	−	0.712287i	0.0984614	−	0.0568467i	0.548422	+	0.836202i	$0.315229\pi$
$158$	−3.98581	+	2.30121i	−0.317094	+	0.183074i
$159$	−2.86246	−	1.99730i	−0.227008	−	0.158396i
$160$	−0.837727	−	0.483662i	−0.0662282	−	0.0382368i
$161$		0			0
$162$	−8.85278	+	1.62120i	−0.695540	+	0.127374i
$163$	7.44296			0.582977			0.291489	−	0.956574i	$-0.405849\pi$
$163$	7.44296			0.582977			0.291489	+	0.956574i	$0.405849\pi$
$164$	−0.0818856	+	0.141830i	−0.00639419	+	0.0110751i
$165$	7.65833	+	5.34364i	0.596200	+	0.416002i
$166$	−7.29158	+	4.20979i	−0.565936	+	0.326743i
$167$	−3.24855	−	5.62665i	−0.251380	−	0.435404i	0.712526	−	0.701646i	$-0.247551\pi$
$167$	−3.24855	−	5.62665i	−0.251380	−	0.435404i	−0.963906	+	0.266242i	$0.914218\pi$
$168$		0			0
$169$	2.96991	−	5.14404i	0.228455	−	0.395695i
$170$		−	3.81643i		−	0.292707i
$171$	12.5758	−	4.62419i	0.961695	−	0.353621i
$172$	−8.70089			−0.663437
$173$	−5.90938	+	10.2354i	−0.449282	+	0.778179i	−0.998339	−	0.0576053i	$-0.981654\pi$
$173$	−5.90938	+	10.2354i	−0.449282	+	0.778179i	0.549057	+	0.835785i	$0.314987\pi$
$174$	−9.18936	−	0.788713i	−0.696643	−	0.0597922i
$175$		0			0
$176$	4.82689	−	2.78681i	0.363841	−	0.210063i
$177$	2.88859	+	0.247925i	0.217120	+	0.0186352i
$178$	3.56475	+	2.05811i	0.267189	+	0.154262i
$179$			2.43370i			0.181903i	0.995855	+	0.0909515i	$0.0289908\pi$
$179$			2.43370i			0.181903i	−0.995855	+	0.0909515i	$0.971009\pi$
$180$	2.85953	+	0.494504i	0.213137	+	0.0368581i
$181$		−	11.5342i		−	0.857327i	−0.903464	−	0.428663i	$-0.858985\pi$
$181$		−	11.5342i		−	0.857327i	0.903464	−	0.428663i	$-0.141015\pi$
$182$		0			0
$183$	8.11294	−	3.79941i	0.599726	−	0.280861i
$184$	−1.32667	−	2.29786i	−0.0978035	−	0.169401i
$185$	−0.235648	−	0.408155i	−0.0173252	−	0.0300081i
$186$	6.11182	−	8.75925i	0.448140	−	0.642260i
$187$	19.0438	+	10.9949i	1.39262	+	0.804028i
$188$	9.49001			0.692130
$189$		0			0
$190$	−4.32040			−0.313435
$191$	−19.1122	−	11.0345i	−1.38291	−	0.798425i	−0.390409	−	0.920641i	$-0.627666\pi$
$191$	−19.1122	−	11.0345i	−1.38291	−	0.798425i	−0.992503	+	0.122216i	$0.961000\pi$
$192$	0.991125	−	1.42045i	0.0715283	−	0.102512i
$193$	9.96979	+	17.2682i	0.717641	+	1.24299i	0.961932	+	0.273289i	$0.0881116\pi$
$193$	9.96979	+	17.2682i	0.717641	+	1.24299i	−0.244291	+	0.969702i	$0.578555\pi$
$194$	5.92762	+	10.2669i	0.425578	+	0.737123i
$195$	6.60331	−	3.09243i	0.472873	−	0.221453i
$196$		0			0
$197$			4.62560i			0.329560i	0.986330	+	0.164780i	$0.0526914\pi$
$197$			4.62560i			0.329560i	−0.986330	+	0.164780i	$0.947309\pi$
$198$	−10.7057	+	12.8442i	−0.760820	+	0.912801i
$199$			20.9028i			1.48176i	0.671635	+	0.740882i	$0.265592\pi$
$199$			20.9028i			1.48176i	−0.671635	+	0.740882i	$0.734408\pi$
$200$	3.51977	+	2.03214i	0.248886	+	0.143694i
$201$	−9.39219	−	0.806122i	−0.662474	−	0.0568595i
$202$	4.60402	−	2.65813i	0.323938	−	0.187025i
$203$		0			0
$204$	6.80851	+	0.584367i	0.476691	+	0.0409139i
$205$	−0.0792099	+	0.137196i	−0.00553226	+	0.00958215i
$206$	−8.94450			−0.623193
$207$	6.11456	+	5.09649i	0.424991	+	0.354231i
$208$		−	4.35199i		−	0.301756i
$209$	12.4468	−	21.5585i	0.860965	−	1.49123i
$210$		0			0
$211$	−3.34310	−	5.79042i	−0.230148	−	0.398629i	0.727703	−	0.685892i	$-0.240588\pi$
$211$	−3.34310	−	5.79042i	−0.230148	−	0.398629i	−0.957852	+	0.287263i	$0.907254\pi$
$212$	−1.74520	+	1.00759i	−0.119861	+	0.0692017i
$213$	5.17052	+	3.60776i	0.354278	+	0.247200i
$214$	−9.57813	+	16.5898i	−0.654747	+	1.13406i
$215$	−8.41658			−0.574006
$216$	−1.32004	+	5.02568i	−0.0898176	+	0.341954i
$217$		0			0
$218$	16.6652	+	9.62168i	1.12871	+	0.651663i
$219$	−3.53409	−	2.46593i	−0.238812	−	0.166632i
$220$	4.66917	−	2.69574i	0.314795	−	0.181747i
$221$	14.8697	−	8.58505i	1.00025	−	0.577493i
$222$	0.764231	−	0.357900i	0.0512918	−	0.0240207i
$223$	7.08622	+	4.09123i	0.474528	+	0.273969i	0.718133	−	0.695905i	$-0.244997\pi$
$223$	7.08622	+	4.09123i	0.474528	+	0.273969i	−0.243605	+	0.969875i	$0.578330\pi$
$224$		0			0
$225$	−12.0145	−	2.07770i	−0.800968	−	0.138513i
$226$	8.44316			0.561631
$227$	−5.34688	+	9.26106i	−0.354885	+	0.614678i	−0.987098	−	0.160116i	$-0.948813\pi$
$227$	−5.34688	+	9.26106i	−0.354885	+	0.614678i	0.632214	+	0.774794i	$0.282147\pi$
$228$	0.661535	−	7.70759i	0.0438112	−	0.510447i
$229$	−25.2942	+	14.6036i	−1.67149	+	0.965034i	−0.704682	+	0.709524i	$0.748910\pi$
$229$	−25.2942	+	14.6036i	−1.67149	+	0.965034i	−0.966806	+	0.255510i	$0.917757\pi$
$230$	−1.28332	−	2.22278i	−0.0846197	−	0.146566i
$231$		0			0
$232$	−2.66249	+	4.61157i	−0.174801	+	0.302764i
$233$			6.43935i			0.421856i	0.977502	+	0.210928i	$0.0676485\pi$
$233$			6.43935i			0.421856i	−0.977502	+	0.210928i	$0.932352\pi$
$234$	4.50580	+	12.2538i	0.294553	+	0.801057i
$235$	9.17991			0.598832
$236$	0.836931	−	1.44961i	0.0544796	−	0.0943614i
$237$	−3.38085	−	7.21918i	−0.219610	−	0.468936i
$238$		0			0
$239$	−4.01452	+	2.31778i	−0.259678	+	0.149925i	−0.624187	−	0.781275i	$-0.714570\pi$
$239$	−4.01452	+	2.31778i	−0.259678	+	0.149925i	0.364510	+	0.931200i	$0.381237\pi$
$240$	0.958739	−	1.37403i	0.0618863	−	0.0886935i
$241$	−9.08846	−	5.24722i	−0.585439	−	0.338003i	0.177853	−	0.984057i	$-0.443085\pi$
$241$	−9.08846	−	5.24722i	−0.585439	−	0.338003i	−0.763292	+	0.646054i	$0.776418\pi$
$242$			20.0652i			1.28984i
$243$	−1.48648	−	15.5174i	−0.0953578	−	0.995443i
$244$		−	5.17221i		−	0.331117i
$245$		0			0
$246$	−0.232628	−	0.162318i	−0.0148318	−	0.0103490i
$247$	−9.71873	−	16.8333i	−0.618388	−	1.07108i
$248$	−3.08327	−	5.34038i	−0.195788	−	0.339115i
$249$	−6.18487	−	13.2067i	−0.391950	−	0.836938i
$250$	7.59340	+	4.38405i	0.480249	+	0.277272i
$251$	7.85271			0.495659			0.247829	−	0.968804i	$-0.420283\pi$
$251$	7.85271			0.495659			0.247829	+	0.968804i	$0.420283\pi$
$252$		0			0
$253$	14.7887			0.929758
$254$	2.87419	+	1.65941i	0.180343	+	0.104121i
$255$	6.58603	+	0.565273i	0.412433	+	0.0353987i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.71568	−	2.97164i	−0.107021	−	0.185366i	0.807541	−	0.589811i	$-0.200798\pi$
$257$	−1.71568	−	2.97164i	−0.107021	−	0.185366i	−0.914562	+	0.404445i	$0.867465\pi$
$258$	1.28874	−	15.0152i	0.0802334	−	0.934805i
$259$		0			0
$260$		−	4.20979i		−	0.261080i
$261$	2.72217	−	15.7413i	0.168498	−	0.974363i
$262$		−	18.7467i		−	1.15818i
$263$	3.17080	+	1.83066i	0.195520	+	0.112883i	0.594564	−	0.804048i	$-0.297325\pi$
$263$	3.17080	+	1.83066i	0.195520	+	0.112883i	−0.399044	+	0.916932i	$0.630658\pi$
$264$	4.09427	+	8.74256i	0.251985	+	0.538068i
$265$	−1.68817	+	0.974668i	−0.103704	+	0.0598734i
$266$		0			0
$267$	−4.07969	+	5.84687i	−0.249673	+	0.357823i
$268$	−2.72126	+	4.71336i	−0.166227	+	0.287914i
$269$	12.6861			0.773483			0.386741	−	0.922188i	$-0.373601\pi$
$269$	12.6861			0.773483			0.386741	+	0.922188i	$0.373601\pi$
$270$	−1.27691	+	4.86146i	−0.0777102	+	0.295859i
$271$		−	19.8766i		−	1.20742i	−0.797206	−	0.603708i	$-0.793689\pi$
$271$		−	19.8766i		−	1.20742i	0.797206	−	0.603708i	$-0.206311\pi$
$272$	1.97267	−	3.41677i	0.119611	−	0.207172i
$273$		0			0
$274$	−8.46717	−	14.6656i	−0.511520	−	0.885979i
$275$	−19.6179	+	11.3264i	−1.18300	+	0.683006i
$276$	4.16194	−	1.94910i	0.250519	−	0.117322i
$277$	3.73302	−	6.46579i	0.224296	−	0.388491i	−0.731812	−	0.681506i	$-0.761325\pi$
$277$	3.73302	−	6.46579i	0.224296	−	0.388491i	0.956108	+	0.293015i	$0.0946585\pi$
$278$	−12.1281			−0.727397
$279$	14.2106	+	11.8446i	0.850769	+	0.709117i
$280$		0			0
$281$	−19.2746	−	11.1282i	−1.14983	−	0.663854i	−0.200983	−	0.979595i	$-0.564414\pi$
$281$	−19.2746	−	11.1282i	−1.14983	−	0.663854i	−0.948845	+	0.315741i	$0.897747\pi$
$282$	−1.40562	+	16.3770i	−0.0837034	+	0.975234i
$283$	14.0125	−	8.09012i	0.832957	−	0.480908i	−0.0219073	−	0.999760i	$-0.506974\pi$
$283$	14.0125	−	8.09012i	0.832957	−	0.480908i	0.854864	+	0.518852i	$0.173641\pi$
$284$	3.15239	−	1.82003i	0.187060	−	0.107999i
$285$	0.639918	−	7.45573i	0.0379055	−	0.441640i
$286$	21.0066	+	12.1282i	1.24215	+	0.717153i
$287$		0			0
$288$	2.30447	+	1.92078i	0.135792	+	0.113183i
$289$	−1.43425			−0.0843675
$290$	−2.57549	+	4.46088i	−0.151238	+	0.261952i
$291$	−18.5957	+	8.70864i	−1.09010	+	0.510509i
$292$	−2.15468	+	1.24401i	−0.126093	+	0.0727999i
$293$	−4.43406	−	7.68002i	−0.259041	−	0.448672i	0.706944	−	0.707269i	$-0.250073\pi$
$293$	−4.43406	−	7.68002i	−0.259041	−	0.448672i	−0.965985	+	0.258597i	$0.916740\pi$
$294$		0			0
$295$	0.809584	−	1.40224i	0.0471358	−	0.0816416i
$296$		−	0.487217i		−	0.0283189i
$297$	−20.5797	−	20.3773i	−1.19416	−	1.18241i
$298$	8.74051			0.506324
$299$	5.77366	−	10.0003i	0.333899	−	0.578331i
$300$	−4.02821	+	5.77310i	−0.232569	+	0.333310i
$301$		0			0
$302$	−19.1341	+	11.0471i	−1.10104	+	0.635687i
$303$	3.90523	+	8.33889i	0.224349	+	0.479057i
$304$	−3.86796	−	2.23317i	−0.221843	−	0.128081i
$305$		−	5.00321i		−	0.286483i
$306$	−2.01689	+	11.6629i	−0.115298	+	0.666725i
$307$			27.1427i			1.54912i	0.632501	+	0.774559i	$0.282028\pi$
$307$			27.1427i			1.54912i	−0.632501	+	0.774559i	$0.717972\pi$
$308$		0			0
$309$	1.32482	−	15.4356i	0.0753664	−	0.878099i
$310$	−2.98252	−	5.16588i	−0.169396	−	0.293402i
$311$	−8.44774	−	14.6319i	−0.479028	−	0.829700i	0.520683	−	0.853750i	$-0.325677\pi$
$311$	−8.44774	−	14.6319i	−0.479028	−	0.829700i	−0.999711	+	0.0240499i	$0.992344\pi$
$312$	7.51026	+	0.644598i	0.425185	+	0.0364932i
$313$	3.70433	+	2.13870i	0.209381	+	0.120886i	0.601024	−	0.799231i	$-0.294760\pi$
$313$	3.70433	+	2.13870i	0.209381	+	0.120886i	−0.391643	+	0.920117i	$0.628093\pi$
$314$	1.42457			0.0803934
$315$		0			0
$316$	−4.60242			−0.258906
$317$	5.74123	+	3.31470i	0.322460	+	0.186172i	0.652488	−	0.757799i	$-0.273725\pi$
$317$	5.74123	+	3.31470i	0.322460	+	0.186172i	−0.330029	+	0.943971i	$0.607058\pi$
$318$	−1.48032	−	3.16094i	−0.0830120	−	0.177257i
$319$	−14.8397	−	25.7031i	−0.830864	−	1.43910i
$320$	−0.483662	−	0.837727i	−0.0270375	−	0.0468304i
$321$	−27.2105	−	18.9862i	−1.51874	−	1.05971i
$322$		0			0
$323$		−	17.6212i		−	0.980472i
$324$	−8.47733	−	3.02239i	−0.470963	−	0.167910i
$325$			17.6877i			0.981138i
$326$	6.44579	+	3.72148i	0.356999	+	0.206114i
$327$	−19.0726	+	27.3342i	−1.05472	+	1.51158i
$328$	−0.141830	+	0.0818856i	−0.00783125	+	0.00452137i
$329$		0			0
$330$	3.96049	+	8.45689i	0.218018	+	0.465537i
$331$	0.378896	−	0.656267i	0.0208260	−	0.0360717i	−0.855425	−	0.517927i	$-0.826704\pi$
$331$	0.378896	−	0.656267i	0.0208260	−	0.0360717i	0.876251	+	0.481856i	$0.160037\pi$
$332$	−8.41959			−0.462085
$333$	0.504436	+	1.37185i	0.0276429	+	0.0751768i
$334$		−	6.49710i		−	0.355506i
$335$	−2.63234	+	4.55935i	−0.143820	+	0.249104i
$336$		0			0
$337$	1.01088	+	1.75089i	0.0550660	+	0.0953772i	0.892244	−	0.451553i	$-0.149130\pi$
$337$	1.01088	+	1.75089i	0.0550660	+	0.0953772i	−0.837178	+	0.546930i	$0.815796\pi$
$338$	5.14404	−	2.96991i	0.279799	−	0.161542i
$339$	−1.25056	+	14.5704i	−0.0679213	+	0.791356i
$340$	1.90821	−	3.30512i	0.103487	−	0.179245i
$341$	34.3699			1.86124
$342$	13.2030	+	2.28323i	0.713939	+	0.123463i
$343$		0			0
$344$	−7.53520	−	4.35045i	−0.406271	−	0.234560i
$345$	4.02594	−	1.88541i	0.216749	−	0.101507i
$346$	−10.2354	+	5.90938i	−0.550256	+	0.317690i
$347$	−18.1572	+	10.4831i	−0.974730	+	0.562761i	−0.900675	−	0.434494i	$-0.856927\pi$
$347$	−18.1572	+	10.4831i	−0.974730	+	0.562761i	−0.0740550	+	0.997254i	$0.523594\pi$
$348$	−7.56386	−	5.27772i	−0.405465	−	0.282916i
$349$	−5.36406	−	3.09694i	−0.287132	−	0.165776i	0.349516	−	0.936930i	$-0.386346\pi$
$349$	−5.36406	−	3.09694i	−0.287132	−	0.165776i	−0.636648	+	0.771155i	$0.719679\pi$
$350$		0			0
$351$	−21.8139	+	5.96071i	−1.16434	+	0.318159i
$352$	5.57361			0.297075
$353$	9.41889	−	16.3140i	0.501317	−	0.868306i	−0.498682	−	0.866785i	$-0.666182\pi$
$353$	9.41889	−	16.3140i	0.501317	−	0.868306i	0.999999	−	0.00152110i	$-0.000484180\pi$
$354$	2.37763	+	1.65901i	0.126370	+	0.0881752i
$355$	3.04938	−	1.76056i	0.161844	−	0.0934409i
$356$	2.05811	+	3.56475i	0.109080	+	0.188931i
$357$		0			0
$358$	−1.21685	+	2.10764i	−0.0643124	+	0.111392i
$359$		−	27.7977i		−	1.46711i	−0.679633	−	0.733553i	$-0.737861\pi$
$359$		−	27.7977i		−	1.46711i	0.679633	−	0.733553i	$-0.262139\pi$
$360$	2.22917	+	1.85802i	0.117488	+	0.0979261i
$361$	−0.948177			−0.0499041
$362$	5.76708	−	9.98887i	0.303111	−	0.525003i
$363$	−34.6266	−	2.97196i	−1.81742	−	0.155988i
$364$		0			0
$365$	−2.08428	+	1.20336i	−0.109096	+	0.0629866i
$366$	8.92572	+	0.766086i	0.466555	+	0.0400439i
$367$	18.8390	+	10.8767i	0.983388	+	0.567759i	0.903291	−	0.429028i	$-0.141144\pi$
$367$	18.8390	+	10.8767i	0.983388	+	0.567759i	0.0800968	+	0.996787i	$0.474477\pi$
$368$		−	2.65334i		−	0.138315i
$369$	0.314569	−	0.377406i	0.0163758	−	0.0196470i
$370$		−	0.471297i		−	0.0245016i
$371$		0			0
$372$	9.67262	−	4.52983i	0.501502	−	0.234861i
$373$	−5.86560	−	10.1595i	−0.303709	−	0.526040i	0.673264	−	0.739402i	$-0.264892\pi$
$373$	−5.86560	−	10.1595i	−0.303709	−	0.526040i	−0.976973	+	0.213362i	$0.931558\pi$
$374$	10.9949	+	19.0438i	0.568533	+	0.984729i
$375$	−8.69028	+	12.4546i	−0.448764	+	0.643154i
$376$	8.21859	+	4.74500i	0.423841	+	0.244705i
$377$	−23.1743			−1.19354
$378$		0			0
$379$	34.8881			1.79208			0.896041	−	0.443971i	$-0.146431\pi$
$379$	34.8881			1.79208			0.896041	+	0.443971i	$0.146431\pi$
$380$	−3.74157	−	2.16020i	−0.191939	−	0.110816i
$381$	−3.28937	+	4.71422i	−0.168520	+	0.241517i
$382$	−11.0345	−	19.1122i	−0.564572	−	0.977867i
$383$	5.92412	+	10.2609i	0.302708	+	0.524306i	0.976748	−	0.214389i	$-0.0687759\pi$
$383$	5.92412	+	10.2609i	0.302708	+	0.524306i	−0.674040	+	0.738695i	$0.735443\pi$
$384$	1.56856	−	0.734581i	0.0800454	−	0.0374864i
$385$		0			0
$386$			19.9396i			1.01490i
$387$	25.7209	+	4.44797i	1.30747	+	0.226103i
$388$			11.8552i			0.601859i
$389$	5.50224	+	3.17672i	0.278975	+	0.161066i	0.632959	−	0.774185i	$-0.281840\pi$
$389$	5.50224	+	3.17672i	0.278975	+	0.161066i	−0.353984	+	0.935251i	$0.615173\pi$
$390$	7.26485	+	0.623535i	0.367870	+	0.0315739i
$391$	9.06586	−	5.23418i	0.458480	−	0.264704i
$392$		0			0
$393$	32.3513	+	2.77668i	1.63191	+	0.140065i
$394$	−2.31280	+	4.00588i	−0.116517	+	0.201814i
$395$	−4.45203			−0.224006
$396$	−15.6935	+	5.77060i	−0.788629	+	0.289983i
$397$		−	8.57535i		−	0.430385i	−0.976572	−	0.215192i	$-0.930962\pi$
$397$		−	8.57535i		−	0.430385i	0.976572	−	0.215192i	$-0.0690378\pi$
$398$	−10.4514	+	18.1024i	−0.523883	+	0.907391i
$399$		0			0
$400$	2.03214	+	3.51977i	0.101607	+	0.175989i
$401$	20.0216	−	11.5595i	0.999833	−	0.577254i	0.0916343	−	0.995793i	$-0.470791\pi$
$401$	20.0216	−	11.5595i	0.999833	−	0.577254i	0.908199	+	0.418539i	$0.137458\pi$
$402$	−7.73081	−	5.39422i	−0.385578	−	0.269039i
$403$	13.4184	−	23.2413i	0.668417	−	1.15773i
$404$	5.31626			0.264494
$405$	−8.20033	−	2.92363i	−0.407478	−	0.145276i
$406$		0			0
$407$	2.35174	+	1.35778i	0.116572	+	0.0673026i
$408$	5.60416	+	3.91033i	0.277447	+	0.193590i
$409$	−1.35091	+	0.779947i	−0.0667981	+	0.0385659i	−0.533027	−	0.846098i	$-0.678946\pi$
$409$	−1.35091	+	0.779947i	−0.0667981	+	0.0385659i	0.466229	+	0.884664i	$0.345612\pi$
$410$	−0.137196	+	0.0792099i	−0.00677561	+	0.00391190i
$411$	26.5626	−	12.4396i	1.31024	−	0.613603i
$412$	−7.74616	−	4.47225i	−0.381626	−	0.220332i
$413$		0			0
$414$	2.74712	+	7.47097i	0.135014	+	0.367178i
$415$	−8.14447			−0.399796
$416$	2.17600	−	3.76893i	0.106687	−	0.184787i
$417$	1.79637	−	20.9296i	0.0879684	−	1.02493i
$418$	21.5585	−	12.4468i	1.05446	−	0.608794i
$419$	3.40822	+	5.90321i	0.166502	+	0.288391i	0.937188	−	0.348825i	$-0.113419\pi$
$419$	3.40822	+	5.90321i	0.166502	+	0.288391i	−0.770685	+	0.637216i	$0.780086\pi$
$420$		0			0
$421$	−6.75727	+	11.7039i	−0.329329	+	0.570415i	−0.982379	−	0.186900i	$-0.940156\pi$
$421$	−6.75727	+	11.7039i	−0.329329	+	0.570415i	0.653050	+	0.757315i	$0.273489\pi$
$422$		−	6.68620i		−	0.325479i
$423$	−28.0536	−	4.85137i	−1.36401	−	0.235882i
$424$	−2.01518			−0.0978659
$425$	−8.01750	+	13.8867i	−0.388906	+	0.673605i
$426$	2.67392	+	5.70967i	0.129552	+	0.276634i
$427$		0			0
$428$	−16.5898	+	9.57813i	−0.801899	+	0.462976i
$429$	−24.0410	+	34.4548i	−1.16071	+	1.66349i
$430$	−7.28898	−	4.20829i	−0.351506	−	0.202942i
$431$		−	14.1598i		−	0.682054i	−0.940053	−	0.341027i	$-0.889225\pi$
$431$		−	14.1598i		−	0.682054i	0.940053	−	0.341027i	$-0.110775\pi$
$432$	−3.65603	+	3.69235i	−0.175901	+	0.177648i
$433$		−	23.4830i		−	1.12852i	−0.825597	−	0.564260i	$-0.809161\pi$
$433$		−	23.4830i		−	1.12852i	0.825597	−	0.564260i	$-0.190839\pi$
$434$		0			0
$435$	−7.31670	−	5.10527i	−0.350809	−	0.244779i
$436$	9.62168	+	16.6652i	0.460795	+	0.798121i
$437$	−5.92536	−	10.2630i	−0.283449	−	0.490947i
$438$	−1.82765	−	3.90260i	−0.0873283	−	0.186474i
$439$	3.66398	+	2.11540i	0.174872	+	0.100963i	0.584881	−	0.811119i	$-0.301141\pi$
$439$	3.66398	+	2.11540i	0.174872	+	0.100963i	−0.410009	+	0.912081i	$0.634474\pi$
$440$	5.39149			0.257029
$441$		0			0
$442$	17.1701			0.816699
$443$	25.8161	+	14.9049i	1.22656	+	0.708154i	0.966308	−	0.257388i	$-0.0828618\pi$
$443$	25.8161	+	14.9049i	1.22656	+	0.708154i	0.260250	+	0.965541i	$0.416195\pi$
$444$	0.840793	+	0.0721645i	0.0399023	+	0.00342477i
$445$	1.99086	+	3.44827i	0.0943757	+	0.163464i
$446$	4.09123	+	7.08622i	0.193725	+	0.335542i
$447$	−1.29461	+	15.0836i	−0.0612328	+	0.713428i
$448$		0			0
$449$		−	8.41716i		−	0.397230i	−0.980078	−	0.198615i	$-0.936356\pi$
$449$		−	8.41716i		−	0.397230i	0.980078	−	0.198615i	$-0.0636444\pi$
$450$	−9.36604	−	7.80660i	−0.441519	−	0.368007i
$451$		−	0.912797i		−	0.0429819i
$452$	7.31199	+	4.22158i	0.343927	+	0.198566i
$453$	−16.2299	−	34.6560i	−0.762549	−	1.62828i
$454$	−9.26106	+	5.34688i	−0.434643	+	0.250941i
$455$		0			0
$456$	4.42670	−	6.34420i	0.207299	−	0.297094i
$457$	1.94109	−	3.36207i	0.0908006	−	0.157271i	−0.817048	−	0.576570i	$-0.804391\pi$
$457$	1.94109	−	3.36207i	0.0908006	−	0.157271i	0.907848	+	0.419299i	$0.137724\pi$
$458$	−29.2072			−1.36476
$459$	−19.8281	−	5.20803i	−0.925494	−	0.243090i
$460$		−	2.56664i		−	0.119670i
$461$	−17.0423	+	29.5181i	−0.793739	+	1.37480i	0.129898	+	0.991527i	$0.458535\pi$
$461$	−17.0423	+	29.5181i	−0.793739	+	1.37480i	−0.923637	+	0.383269i	$0.874798\pi$
$462$		0			0
$463$	−6.10962	−	10.5822i	−0.283938	−	0.491796i	0.688413	−	0.725319i	$-0.258308\pi$
$463$	−6.10962	−	10.5822i	−0.283938	−	0.491796i	−0.972351	+	0.233523i	$0.924974\pi$
$464$	−4.61157	+	2.66249i	−0.214087	+	0.123603i
$465$	9.35655	−	4.38181i	0.433900	−	0.203202i
$466$	−3.21967	+	5.57664i	−0.149148	+	0.258333i
$467$	−30.8115			−1.42579			−0.712893	−	0.701273i	$-0.752615\pi$
$467$	−30.8115			−1.42579			−0.712893	+	0.701273i	$0.752615\pi$
$468$	−2.22477	+	12.8650i	−0.102840	+	0.594686i
$469$		0			0
$470$	7.95004	+	4.58996i	0.366708	+	0.211719i
$471$	−0.211002	+	2.45840i	−0.00972244	+	0.113277i
$472$	1.44961	−	0.836931i	0.0667236	−	0.0385229i
$473$	41.9983	−	24.2477i	1.93108	−	1.11491i
$474$	0.681690	−	7.94242i	0.0313110	−	0.364807i
$475$	15.7205	+	9.07623i	0.721306	+	0.416446i
$476$		0			0
$477$	5.67412	−	2.08640i	0.259800	−	0.0955299i
$478$	−4.63557			−0.212026
$479$	−20.8747	+	36.1560i	−0.953788	+	1.65201i	−0.216670	+	0.976245i	$0.569519\pi$
$479$	−20.8747	+	36.1560i	−0.953788	+	1.65201i	−0.737118	+	0.675764i	$0.763814\pi$
$480$	1.51731	−	0.710578i	0.0692554	−	0.0324333i
$481$	1.83629	−	1.06018i	0.0837276	−	0.0483401i
$482$	−5.24722	−	9.08846i	−0.239004	−	0.413968i
$483$		0			0
$484$	−10.0326	+	17.3769i	−0.456026	+	0.789861i
$485$			11.4679i			0.520729i
$486$	6.47138	−	14.1817i	0.293548	−	0.643296i
$487$	−21.1663			−0.959137			−0.479568	−	0.877504i	$-0.659207\pi$
$487$	−21.1663			−0.959137			−0.479568	+	0.877504i	$0.659207\pi$
$488$	2.58611	−	4.47927i	0.117068	−	0.202767i
$489$	−7.37690	+	10.5723i	−0.333595	+	0.478097i
$490$		0			0
$491$	32.3428	−	18.6731i	1.45961	−	0.842707i	0.460619	−	0.887598i	$-0.347628\pi$
$491$	32.3428	−	18.6731i	1.45961	−	0.842707i	0.998992	+	0.0448915i	$0.0142942\pi$
$492$	−0.120303	−	0.256885i	−0.00542369	−	0.0115813i
$493$	−18.1942	−	10.5044i	−0.819427	−	0.473097i
$494$		−	19.4375i		−	0.874533i
$495$	−15.1807	+	5.58204i	−0.682323	+	0.250894i
$496$		−	6.16655i		−	0.276886i
$497$		0			0
$498$	1.24707	−	14.5297i	0.0558827	−	0.651093i
$499$	−13.7099	−	23.7462i	−0.613738	−	1.06303i	−0.990605	−	0.136758i	$-0.956332\pi$
$499$	−13.7099	−	23.7462i	−0.613738	−	1.06303i	0.376867	−	0.926267i	$-0.377001\pi$
$500$	4.38405	+	7.59340i	0.196061	+	0.339587i
$501$	11.2121	+	0.962322i	0.500919	+	0.0429934i
$502$	6.80065	+	3.92635i	0.303528	+	0.175242i
$503$	−11.2791			−0.502909			−0.251454	−	0.967869i	$-0.580909\pi$
$503$	−11.2791			−0.502909			−0.251454	+	0.967869i	$0.580909\pi$
$504$		0			0
$505$	5.14255			0.228840
$506$	12.8074	+	7.39435i	0.569358	+	0.328719i
$507$	4.36328	+	9.31698i	0.193780	+	0.413782i
$508$	1.65941	+	2.87419i	0.0736246	+	0.127522i
$509$	9.31667	+	16.1370i	0.412954	+	0.715258i	0.995211	−	0.0977470i	$-0.0311636\pi$
$509$	9.31667	+	16.1370i	0.412954	+	0.715258i	−0.582257	+	0.813005i	$0.697830\pi$
$510$	5.42104	+	3.78256i	0.240047	+	0.167494i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−5.89576	+	22.4464i	−0.260304	+	0.991033i
$514$		−	3.43136i		−	0.151351i
$515$	−7.49305	−	4.32611i	−0.330183	−	0.190631i
$516$	8.62367	−	12.3592i	0.379636	−	0.544082i
$517$	−45.8072	+	26.4468i	−2.01460	+	1.16313i
$518$		0			0
$519$	−8.68184	−	18.5385i	−0.381091	−	0.813749i
$520$	2.10489	−	3.64578i	0.0923056	−	0.159878i
$521$	15.2851			0.669652			0.334826	−	0.942280i	$-0.391322\pi$
$521$	15.2851			0.669652			0.334826	+	0.942280i	$0.391322\pi$
$522$	10.2281	−	12.2713i	0.447673	−	0.537100i
$523$		−	36.4875i		−	1.59549i	−0.602997	−	0.797743i	$-0.706027\pi$
$523$		−	36.4875i		−	1.59549i	0.602997	−	0.797743i	$-0.293973\pi$
$524$	9.37335	−	16.2351i	0.409477	−	0.709235i
$525$		0			0
$526$	1.83066	+	3.17080i	0.0798207	+	0.138253i
$527$	21.0697	−	12.1646i	0.917809	−	0.529897i
$528$	−0.825539	+	9.61842i	−0.0359270	+	0.418588i
$529$	−7.97989	+	13.8216i	−0.346952	+	0.600938i
$530$	−1.94934			−0.0846737
$531$	−3.21512	+	3.85737i	−0.139524	+	0.167396i
$532$		0			0
$533$	−0.617243	−	0.356365i	−0.0267358	−	0.0154359i
$534$	−6.45655	+	3.02370i	−0.279402	+	0.130848i
$535$	−16.0477	+	9.26516i	−0.693803	+	0.400568i
$536$	−4.71336	+	2.72126i	−0.203586	+	0.117540i
$537$	−3.45694	−	2.41210i	−0.149178	−	0.104090i
$538$	10.9865	+	6.34303i	0.473660	+	0.273467i
$539$		0			0
$540$	−3.53657	+	3.57170i	−0.152190	+	0.153701i
$541$	−5.27293			−0.226701			−0.113351	−	0.993555i	$-0.536158\pi$
$541$	−5.27293			−0.226701			−0.113351	+	0.993555i	$0.536158\pi$
$542$	9.93828	−	17.2136i	0.426886	−	0.739388i
$543$	16.3837	+	11.4318i	0.703090	+	0.490585i
$544$	3.41677	−	1.97267i	0.146493	−	0.0845776i
$545$	9.30729	+	16.1207i	0.398680	+	0.690535i
$546$		0			0
$547$	−9.29831	+	16.1051i	−0.397567	+	0.688606i	−0.993425	−	0.114484i	$-0.963479\pi$
$547$	−9.29831	+	16.1051i	−0.397567	+	0.688606i	0.595858	+	0.803090i	$0.296812\pi$
$548$		−	16.9343i		−	0.723399i
$549$	−2.64408	+	15.2897i	−0.112846	+	0.652549i
$550$	−22.6527			−0.965916
$551$	−11.8916	+	20.5968i	−0.506599	+	0.877455i
$552$	4.57889	+	0.393002i	0.194890	+	0.0167273i
$553$		0			0
$554$	6.46579	−	3.73302i	0.274705	−	0.158601i
$555$	0.813320	+	0.0698064i	0.0345235	+	0.00296312i
$556$	−10.5033	−	6.06406i	−0.445438	−	0.257174i
$557$		−	27.5620i		−	1.16784i	−0.811811	−	0.583920i	$-0.801518\pi$
$557$		−	27.5620i		−	1.16784i	0.811811	−	0.583920i	$-0.198482\pi$
$558$	6.38449	+	17.3630i	0.270277	+	0.735036i
$559$		−	37.8662i		−	1.60157i
$560$		0			0
$561$	−34.4924	+	16.1533i	−1.45627	+	0.681993i
$562$	−11.1282	−	19.2746i	−0.469416	−	0.813052i
$563$	9.42577	+	16.3259i	0.397249	+	0.688055i	0.993385	−	0.114828i	$-0.0366317\pi$
$563$	9.42577	+	16.3259i	0.397249	+	0.688055i	−0.596137	+	0.802883i	$0.703298\pi$
$564$	−9.40579	+	13.4801i	−0.396055	+	0.567613i
$565$	7.07306	+	4.08364i	0.297566	+	0.171800i
$566$	16.1802			0.680106
$567$		0			0
$568$	3.64006			0.152734
$569$	−3.87103	−	2.23494i	−0.162282	−	0.0936936i	0.416659	−	0.909063i	$-0.363201\pi$
$569$	−3.87103	−	2.23494i	−0.162282	−	0.0936936i	−0.578942	+	0.815369i	$0.696534\pi$
$570$	4.28205	−	6.13690i	0.179355	−	0.257046i
$571$	−9.31245	−	16.1296i	−0.389714	−	0.675004i	0.602697	−	0.797970i	$-0.294093\pi$
$571$	−9.31245	−	16.1296i	−0.389714	−	0.675004i	−0.992411	+	0.122966i	$0.960759\pi$
$572$	12.1282	+	21.0066i	0.507104	+	0.878329i
$573$	34.6165	−	16.2114i	1.44612	−	0.677241i
$574$		0			0
$575$			10.7839i			0.449721i
$576$	1.03534	+	2.81568i	0.0431393	+	0.117320i
$577$		−	36.8833i		−	1.53547i	−0.640767	−	0.767735i	$-0.721384\pi$
$577$		−	36.8833i		−	1.53547i	0.640767	−	0.767735i	$-0.278616\pi$
$578$	−1.24210	−	0.717124i	−0.0516644	−	0.0298284i
$579$	−34.4099	−	2.95336i	−1.43003	−	0.122738i
$580$	−4.46088	+	2.57549i	−0.185228	+	0.106941i
$581$		0			0
$582$	−20.4587	−	1.75595i	−0.848039	−	0.0727863i
$583$	5.61593	−	9.72707i	0.232588	−	0.402854i
$584$	−2.48801			−0.102955
$585$	−2.15208	+	12.4446i	−0.0889774	+	0.514523i
$586$		−	8.86813i		−	0.366339i
$587$	13.2295	−	22.9141i	0.546039	−	0.945766i	−0.452502	−	0.891763i	$-0.649469\pi$
$587$	13.2295	−	22.9141i	0.546039	−	0.945766i	0.998541	−	0.0540032i	$-0.0171981\pi$
$588$		0			0
$589$	−13.7709	−	23.8520i	−0.567422	−	0.982803i
$590$	1.40224	−	0.809584i	0.0577293	−	0.0333300i
$591$	−6.57042	−	4.58454i	−0.270271	−	0.188583i
$592$	0.243608	−	0.421942i	0.0100122	−	0.0173417i
$593$	34.6703			1.42374			0.711869	−	0.702312i	$-0.247849\pi$
$593$	34.6703			1.42374			0.711869	+	0.702312i	$0.247849\pi$
$594$	−7.63390	−	27.9371i	−0.313223	−	1.14627i
$595$		0			0
$596$	7.56951	+	4.37026i	0.310059	+	0.179013i
$597$	−29.6914	−	20.7173i	−1.21519	−	0.847904i
$598$	10.0003	−	5.77366i	0.408942	−	0.236103i
$599$	−21.2079	+	12.2444i	−0.866530	+	0.500291i	−0.866193	−	0.499709i	$-0.833440\pi$
$599$	−21.2079	+	12.2444i	−0.866530	+	0.500291i	−0.000336253		1.00000i	$0.500107\pi$
$600$	−6.37509	+	2.98555i	−0.260262	+	0.121884i
$601$	−19.3812	−	11.1898i	−0.790577	−	0.456440i	0.0495885	−	0.998770i	$-0.484209\pi$
$601$	−19.3812	−	11.1898i	−0.790577	−	0.456440i	−0.840166	+	0.542330i	$0.817542\pi$
$602$		0			0
$603$	10.4539	−	12.5421i	0.425715	−	0.510755i
$604$	−22.0941			−0.898997
$605$	−9.70476	+	16.8091i	−0.394554	+	0.683388i
$606$	−0.787421	+	9.17430i	−0.0319868	+	0.372681i
$607$	28.2180	−	16.2917i	1.14533	−	0.661259i	0.197589	−	0.980285i	$-0.436689\pi$
$607$	28.2180	−	16.2917i	1.14533	−	0.661259i	0.947746	+	0.319026i	$0.103356\pi$
$608$	−2.23317	−	3.86796i	−0.0905670	−	0.156867i
$609$		0			0
$610$	2.50160	−	4.33290i	0.101287	−	0.175434i
$611$			41.3004i			1.67084i
$612$	−7.57814	+	9.09195i	−0.306328	+	0.367520i
$613$	−11.7386			−0.474118			−0.237059	−	0.971495i	$-0.576183\pi$
$613$	−11.7386			−0.474118			−0.237059	+	0.971495i	$0.576183\pi$
$614$	−13.5714	+	23.5063i	−0.547696	+	0.948637i
$615$	−0.116372	−	0.248491i	−0.00469258	−	0.0100201i
$616$		0			0
$617$	−38.1947	+	22.0517i	−1.53766	+	0.887770i	−0.538687	+	0.842506i	$0.681080\pi$
$617$	−38.1947	+	22.0517i	−1.53766	+	0.887770i	−0.998975	+	0.0452639i	$0.985587\pi$
$618$	8.86511	−	12.7052i	0.356607	−	0.511078i
$619$	4.28374	+	2.47322i	0.172178	+	0.0994070i	0.583612	−	0.812032i	$-0.301639\pi$
$619$	4.28374	+	2.47322i	0.172178	+	0.0994070i	−0.411434	+	0.911439i	$0.634972\pi$
$620$		−	5.96505i		−	0.239562i
$621$	−13.2996	+	3.63415i	−0.533694	+	0.145833i
$622$		−	16.8955i		−	0.677447i
$623$		0			0
$624$	6.18177	+	4.31337i	0.247469	+	0.172673i
$625$	−5.91991	−	10.2536i	−0.236797	−	0.410144i
$626$	2.13870	+	3.70433i	0.0854795	+	0.148055i
$627$	18.2864	+	39.0472i	0.730288	+	1.55940i
$628$	1.23372	+	0.712287i	0.0492307	+	0.0284233i
$629$	1.92224			0.0766447
$630$		0			0
$631$	−9.08478			−0.361659			−0.180830	−	0.983514i	$-0.557878\pi$
$631$	−9.08478			−0.361659			−0.180830	+	0.983514i	$0.557878\pi$
$632$	−3.98581	−	2.30121i	−0.158547	−	0.0915371i
$633$	11.5384	+	0.990330i	0.458611	+	0.0393621i
$634$	3.31470	+	5.74123i	0.131644	+	0.228013i
$635$	1.60519	+	2.78027i	0.0637001	+	0.110332i
$636$	0.298480	−	3.47761i	0.0118355	−	0.137896i
$637$		0			0
$638$		−	29.6794i		−	1.17502i
$639$	−10.2493	+	3.76871i	−0.405455	+	0.149088i
$640$		−	0.967324i		−	0.0382368i
$641$	12.1954	+	7.04105i	0.481691	+	0.278105i	0.721121	−	0.692809i	$-0.243627\pi$
$641$	12.1954	+	7.04105i	0.481691	+	0.278105i	−0.239430	+	0.970914i	$0.576960\pi$
$642$	−14.0718	−	30.0478i	−0.555371	−	1.18589i
$643$	7.33157	−	4.23288i	0.289129	−	0.166929i	−0.348420	−	0.937339i	$-0.613282\pi$
$643$	7.33157	−	4.23288i	0.289129	−	0.166929i	0.637549	+	0.770410i	$0.279948\pi$
$644$		0			0
$645$	8.34189	−	11.9553i	0.328461	−	0.470740i
$646$	8.81062	−	15.2604i	0.346649	−	0.600414i
$647$	24.3324			0.956607			0.478304	−	0.878195i	$-0.341252\pi$
$647$	24.3324			0.956607			0.478304	+	0.878195i	$0.341252\pi$
$648$	−5.83039	−	6.85613i	−0.229039	−	0.269334i
$649$			9.32946i			0.366213i
$650$	−8.84386	+	15.3180i	−0.346885	+	0.600822i
$651$		0			0
$652$	3.72148	+	6.44579i	0.145744	+	0.252437i
$653$	36.0653	−	20.8223i	1.41134	−	0.814840i	0.415829	−	0.909443i	$-0.363491\pi$
$653$	36.0653	−	20.8223i	1.41134	−	0.814840i	0.995515	+	0.0946029i	$0.0301581\pi$
$654$	−30.1844	+	14.1358i	−1.18030	+	0.552754i
$655$	9.06707	−	15.7046i	0.354280	−	0.613631i
$656$	−0.163771			−0.00639419
$657$	7.00545	−	2.57594i	0.273309	−	0.100497i
$658$		0			0
$659$	−9.09866	−	5.25312i	−0.354434	−	0.204632i	0.312203	−	0.950016i	$-0.398933\pi$
$659$	−9.09866	−	5.25312i	−0.354434	−	0.204632i	−0.666636	+	0.745383i	$0.732267\pi$
$660$	−0.798564	+	9.30413i	−0.0310841	+	0.362163i
$661$	−16.8988	+	9.75655i	−0.657289	+	0.379486i	−0.791243	−	0.611502i	$-0.790566\pi$
$661$	−16.8988	+	9.75655i	−0.657289	+	0.379486i	0.133954	+	0.990987i	$0.457232\pi$
$662$	0.656267	−	0.378896i	0.0255065	−	0.0147262i
$663$	−2.54316	+	29.6306i	−0.0987682	+	1.15076i
$664$	−7.29158	−	4.20979i	−0.282968	−	0.163372i
$665$		0			0
$666$	−0.249069	+	1.44027i	−0.00965124	+	0.0558095i
$667$	−14.1290			−0.547077
$668$	3.24855	−	5.62665i	0.125690	−	0.217702i
$669$	−12.8347	+	6.01068i	−0.496219	+	0.232386i
$670$	−4.55935	+	2.63234i	−0.176143	+	0.101696i
$671$	14.4140	+	24.9657i	0.556445	+	0.963790i
$672$		0			0
$673$	−3.10277	+	5.37415i	−0.119603	+	0.207158i	−0.919610	−	0.392832i	$-0.871495\pi$
$673$	−3.10277	+	5.37415i	−0.119603	+	0.207158i	0.800007	+	0.599990i	$0.204829\pi$
$674$			2.02176i			0.0778751i
$675$	14.8592	−	15.0067i	0.571929	−	0.577610i
$676$	5.93982			0.228455
$677$	−12.3765	+	21.4368i	−0.475669	+	0.823883i	−0.999612	−	0.0278703i	$-0.991127\pi$
$677$	−12.3765	+	21.4368i	−0.475669	+	0.823883i	0.523942	+	0.851754i	$0.324461\pi$
$678$	−8.36823	+	11.9931i	−0.321380	+	0.460591i
$679$		0			0
$680$	3.30512	−	1.90821i	0.126746	−	0.0731767i
$681$	−7.85543	−	16.7738i	−0.301021	−	0.642774i
$682$	29.7652	+	17.1850i	1.13977	+	0.658046i
$683$			21.1448i			0.809083i	0.914520	+	0.404542i	$0.132569\pi$
$683$			21.1448i			0.809083i	−0.914520	+	0.404542i	$0.867431\pi$
$684$	10.2926	+	8.57886i	0.393546	+	0.328021i
$685$		−	16.3810i		−	0.625886i
$686$		0			0
$687$	4.32605	−	50.4031i	0.165049	−	1.92300i
$688$	−4.35045	−	7.53520i	−0.165859	−	0.287277i
$689$	−4.38503	−	7.59509i	−0.167056	−	0.289350i
$690$	4.42927	+	0.380160i	0.168619	+	0.0144724i
$691$	5.58127	+	3.22235i	0.212322	+	0.122584i	0.602390	−	0.798202i	$-0.294215\pi$
$691$	5.58127	+	3.22235i	0.212322	+	0.122584i	−0.390068	+	0.920786i	$0.627549\pi$
$692$	−11.8188			−0.449282
$693$		0			0
$694$	−20.9661			−0.795864
$695$	−10.1601	−	5.86591i	−0.385393	−	0.222507i
$696$	−3.91163	−	8.35257i	−0.148270	−	0.316603i
$697$	−0.323067	−	0.559568i	−0.0122370	−	0.0211952i
$698$	−3.09694	−	5.36406i	−0.117221	−	0.203033i
$699$	−9.14675	−	6.38220i	−0.345962	−	0.241397i
$700$		0			0
$701$			24.5717i			0.928061i	0.885819	+	0.464031i	$0.153597\pi$
$701$			24.5717i			0.928061i	−0.885819	+	0.464031i	$0.846403\pi$
$702$	−21.8717	−	5.74482i	−0.825495	−	0.216824i
$703$		−	2.17608i		−	0.0820723i
$704$	4.82689	+	2.78681i	0.181920	+	0.105032i
$705$	−9.09844	+	13.0396i	−0.342667	+	0.491099i
$706$	16.3140	−	9.41889i	0.613985	−	0.354484i
$707$		0			0
$708$	1.22959	+	2.62556i	0.0462107	+	0.0986745i
$709$	−22.1370	+	38.3424i	−0.831373	+	1.43998i	0.0655765	+	0.997848i	$0.479111\pi$
$709$	−22.1370	+	38.3424i	−0.831373	+	1.43998i	−0.896950	+	0.442133i	$0.854222\pi$
$710$	3.52112			0.132145
$711$	13.6053	+	2.35279i	0.510239	+	0.0882366i
$712$			4.11622i			0.154262i
$713$	8.18098	−	14.1699i	0.306380	−	0.530666i
$714$		0			0
$715$	11.7319	+	20.3202i	0.438747	+	0.759931i
$716$	−2.10764	+	1.21685i	−0.0787663	+	0.0454757i
$717$	0.686600	−	7.99962i	0.0256415	−	0.298751i
$718$	13.8988	−	24.0735i	0.518700	−	0.898415i
$719$	−4.44867			−0.165907			−0.0829537	−	0.996553i	$-0.526435\pi$
$719$	−4.44867			−0.165907			−0.0829537	+	0.996553i	$0.526435\pi$
$720$	1.00151	+	2.72368i	0.0373241	+	0.101505i
$721$		0			0
$722$	−0.821146	−	0.474089i	−0.0305599	−	0.0176438i
$723$	16.4612	−	7.70902i	0.612199	−	0.286702i
$724$	9.98887	−	5.76708i	0.371233	−	0.214332i
$725$	18.7427	−	10.8211i	0.696088	−	0.401886i
$726$	−28.5015	−	19.8871i	−1.05779	−	0.738079i
$727$	30.4270	+	17.5670i	1.12848	+	0.651525i	0.943551	−	0.331227i	$-0.107463\pi$
$727$	30.4270	+	17.5670i	1.12848	+	0.651525i	0.184924	+	0.982753i	$0.440796\pi$
$728$		0			0
$729$	23.5150	+	13.2682i	0.870925	+	0.491416i
$730$	−2.40671			−0.0890765
$731$	17.1640	−	29.7289i	0.634834	−	1.09956i
$732$	7.34686	+	5.12631i	0.271548	+	0.189474i
$733$	5.03789	−	2.90863i	0.186079	−	0.107433i	−0.404067	−	0.914729i	$-0.632404\pi$
$733$	5.03789	−	2.90863i	0.186079	−	0.107433i	0.590145	+	0.807297i	$0.299070\pi$
$734$	10.8767	+	18.8390i	0.401467	+	0.695360i
$735$		0			0
$736$	1.32667	−	2.29786i	0.0489018	−	0.0847003i
$737$		−	30.3345i		−	1.11739i
$738$	0.461128	−	0.169559i	0.0169743	−	0.00624156i
$739$	11.0335			0.405874			0.202937	−	0.979192i	$-0.434951\pi$
$739$	11.0335			0.405874			0.202937	+	0.979192i	$0.434951\pi$
$740$	0.235648	−	0.408155i	0.00866261	−	0.0150041i
$741$	33.5433	+	2.87899i	1.23225	+	0.105762i
$742$		0			0
$743$	−0.543196	+	0.313615i	−0.0199279	+	0.0115054i	−0.509931	−	0.860215i	$-0.670329\pi$
$743$	−0.543196	+	0.313615i	−0.0199279	+	0.0115054i	0.490003	+	0.871721i	$0.336996\pi$
$744$	10.6416	+	0.913362i	0.390142	+	0.0334855i
$745$	7.32216	+	4.22745i	0.268263	+	0.154882i
$746$		−	11.7312i		−	0.429510i
$747$	24.8893	+	4.30416i	0.910653	+	0.157481i
$748$			21.9898i			0.804028i
$749$		0			0
$750$	−13.7533	+	6.44088i	−0.502200	+	0.235188i
$751$	−2.23529	−	3.87163i	−0.0815668	−	0.141278i	0.822356	−	0.568973i	$-0.192659\pi$
$751$	−2.23529	−	3.87163i	−0.0815668	−	0.141278i	−0.903923	+	0.427695i	$0.859326\pi$
$752$	4.74500	+	8.21859i	0.173033	+	0.299701i
$753$	−7.78302	+	11.1544i	−0.283629	+	0.406488i
$754$	−20.0695	−	11.5871i	−0.730889	−	0.421979i
$755$	−21.3722			−0.777813
$756$		0			0
$757$	5.75624			0.209214			0.104607	−	0.994514i	$-0.466642\pi$
$757$	5.75624			0.209214			0.104607	+	0.994514i	$0.466642\pi$
$758$	30.2140	+	17.4441i	1.09742	+	0.633597i
$759$	−14.6575	+	21.0066i	−0.532032	+	0.762491i
$760$	−2.16020	−	3.74157i	−0.0783586	−	0.135721i
$761$	−10.4970	−	18.1813i	−0.380516	−	0.659073i	0.610620	−	0.791924i	$-0.290920\pi$
$761$	−10.4970	−	18.1813i	−0.380516	−	0.659073i	−0.991136	+	0.132851i	$0.957587\pi$
$762$	−5.20579	+	2.43795i	−0.188586	+	0.0883176i
$763$		0			0
$764$		−	22.0689i		−	0.798425i
$765$	−7.33052	+	8.79486i	−0.265036	+	0.317979i
$766$			11.8482i			0.428094i
$767$	6.30868	+	3.64232i	0.227793	+	0.131516i
$768$	1.72571	+	0.148116i	0.0622711	+	0.00534466i
$769$	34.1729	−	19.7298i	1.23231	−	0.711473i	0.264797	−	0.964304i	$-0.414695\pi$
$769$	34.1729	−	19.7298i	1.23231	−	0.711473i	0.967511	+	0.252831i	$0.0813616\pi$
$770$		0			0
$771$	5.92151	+	0.508238i	0.213258	+	0.0183037i
$772$	−9.96979	+	17.2682i	−0.358821	+	0.621496i
$773$	−34.6328			−1.24566			−0.622829	−	0.782358i	$-0.714017\pi$
$773$	−34.6328			−1.24566			−0.622829	+	0.782358i	$0.714017\pi$
$774$	20.0510	+	16.7125i	0.720718	+	0.600719i
$775$			25.0626i			0.900275i
$776$	−5.92762	+	10.2669i	−0.212789	+	0.368562i
$777$		0			0
$778$	3.17672	+	5.50224i	0.113891	+	0.197265i
$779$	−0.633461	+	0.365729i	−0.0226961	+	0.0131036i
$780$	5.97978	+	4.17242i	0.214110	+	0.149397i
$781$	−10.1442	+	17.5702i	−0.362986	+	0.628711i
$782$	10.4684			0.374348
$783$	19.6617	+	19.4683i	0.702651	+	0.695741i
$784$		0			0
$785$	1.19340	+	0.689012i	0.0425944	+	0.0245919i
$786$	26.6287	+	18.5803i	0.949815	+	0.662738i
$787$	30.5793	−	17.6550i	1.09003	−	0.629332i	0.156449	−	0.987686i	$-0.449995\pi$
$787$	30.5793	−	17.6550i	1.09003	−	0.629332i	0.933586	+	0.358355i	$0.116662\pi$
$788$	−4.00588	+	2.31280i	−0.142704	+	0.0823900i
$789$	−5.74302	+	2.68954i	−0.204457	+	0.0957502i
$790$	−3.85557	−	2.22601i	−0.137175	−	0.0791980i
$791$		0			0
$792$	−16.4763	−	2.84928i	−0.585459	−	0.101245i
$793$	22.5094			0.799333
$794$	4.28768	−	7.42647i	0.152164	−	0.263556i
$795$	0.288727	−	3.36398i	0.0102401	−	0.119308i
$796$	−18.1024	+	10.4514i	−0.641622	+	0.370441i
$797$	9.60992	+	16.6449i	0.340401	+	0.589591i	0.984507	−	0.175344i	$-0.0561039\pi$
$797$	9.60992	+	16.6449i	0.340401	+	0.589591i	−0.644106	+	0.764936i	$0.722771\pi$
$798$		0			0
$799$	−18.7207	+	32.4252i	−0.662290	+	1.14712i
$800$			4.06428i			0.143694i
$801$	−4.26169	−	11.5900i	−0.150580	−	0.409511i
$802$	23.1190			0.816360
$803$	6.93361	−	12.0094i	0.244682	−	0.423801i
$804$	−3.99797	−	8.53693i	−0.140998	−	0.301074i
$805$		0			0
$806$	23.2413	−	13.4184i	0.818640	−	0.472642i
$807$	−12.5735	+	18.0199i	−0.442607	+	0.634330i
$808$	4.60402	+	2.65813i	0.161969	+	0.0935127i
$809$			39.2779i			1.38094i	0.723362	+	0.690469i	$0.242596\pi$
$809$			39.2779i			1.38094i	−0.723362	+	0.690469i	$0.757404\pi$
$810$	−5.63988	−	6.63210i	−0.198165	−	0.233028i
$811$			9.68436i			0.340064i	0.985439	+	0.170032i	$0.0543871\pi$
$811$			9.68436i			0.340064i	−0.985439	+	0.170032i	$0.945613\pi$
$812$		0			0
$813$	28.2336	+	19.7002i	0.990196	+	0.690915i
$814$	1.35778	+	2.35174i	0.0475901	+	0.0824285i
$815$	3.59987	+	6.23517i	0.126098	+	0.218408i
$816$	2.89818	+	6.18852i	0.101456	+	0.216642i
$817$	−33.6547	−	19.4306i	−1.17743	−	0.679790i
$818$	−1.55989			−0.0545404
$819$		0			0
$820$	−0.158420			−0.00553226
$821$	−10.9919	−	6.34620i	−0.383621	−	0.221484i	0.295771	−	0.955259i	$-0.404423\pi$
$821$	−10.9919	−	6.34620i	−0.383621	−	0.221484i	−0.679393	+	0.733775i	$0.737757\pi$
$822$	29.2237	+	2.50824i	1.01929	+	0.0874849i
$823$	−8.73837	−	15.1353i	−0.304600	−	0.527583i	0.672572	−	0.740032i	$-0.265190\pi$
$823$	−8.73837	−	15.1353i	−0.304600	−	0.527583i	−0.977172	+	0.212448i	$0.931856\pi$
$824$	−4.47225	−	7.74616i	−0.155798	−	0.269850i
$825$	3.35523	−	39.0920i	0.116814	−	1.36101i
$826$		0			0
$827$			46.9482i			1.63255i	0.577665	+	0.816274i	$0.303964\pi$
$827$			46.9482i			1.63255i	−0.577665	+	0.816274i	$0.696036\pi$
$828$	−1.35641	+	7.84361i	−0.0471385	+	0.272584i
$829$			2.30706i			0.0801275i	0.999197	+	0.0400637i	$0.0127561\pi$
$829$			2.30706i			0.0801275i	−0.999197	+	0.0400637i	$0.987244\pi$
$830$	−7.05332	−	4.07224i	−0.244824	−	0.141349i
$831$	5.48442	+	11.7110i	0.190252	+	0.406249i
$832$	3.76893	−	2.17600i	0.130664	−	0.0754391i
$833$		0			0
$834$	12.0205	−	17.2274i	0.416236	−	0.596535i
$835$	3.14240	−	5.44280i	0.108747	−	0.188356i
$836$	24.8936			0.860965
$837$	−30.9091	+	8.44601i	−1.06838	+	0.291937i
$838$			6.81644i			0.235470i
$839$	8.51664	−	14.7513i	0.294027	−	0.509270i	−0.680731	−	0.732533i	$-0.738338\pi$
$839$	8.51664	−	14.7513i	0.294027	−	0.509270i	0.974758	+	0.223264i	$0.0716711\pi$
$840$		0			0
$841$	−0.322276	−	0.558199i	−0.0111130	−	0.0192482i
$842$	−11.7039	+	6.75727i	−0.403344	+	0.232871i
$843$	34.9106	−	16.3492i	1.20239	−	0.563095i
$844$	3.34310	−	5.79042i	0.115074	−	0.199314i
$845$	5.74573			0.197659
$846$	−21.8695	−	18.2282i	−0.751888	−	0.626699i
$847$		0			0
$848$	−1.74520	−	1.00759i	−0.0599304	−	0.0346008i
$849$	−2.39655	+	27.9223i	−0.0822493	+	0.958292i
$850$	−13.8867	+	8.01750i	−0.476311	+	0.274998i
$851$	1.11956	−	0.646377i	0.0383779	−	0.0221575i
$852$	−0.539150	+	6.28168i	−0.0184710	+	0.215207i
$853$	2.87158	+	1.65791i	0.0983209	+	0.0567656i	0.548354	−	0.836246i	$-0.315255\pi$
$853$	2.87158	+	1.65791i	0.0983209	+	0.0567656i	−0.450033	+	0.893012i	$0.648588\pi$
$854$		0			0
$855$	9.95624	+	8.29854i	0.340496	+	0.283804i
$856$	−19.1563			−0.654747
$857$	−4.74512	+	8.21879i	−0.162090	+	0.280748i	−0.935618	−	0.353014i	$-0.885157\pi$
$857$	−4.74512	+	8.21879i	−0.162090	+	0.280748i	0.773528	+	0.633762i	$0.218490\pi$
$858$	−38.0476	+	17.8182i	−1.29892	+	0.608304i
$859$	25.5104	−	14.7284i	0.870404	−	0.502528i	0.00292142	−	0.999996i	$-0.499070\pi$
$859$	25.5104	−	14.7284i	0.870404	−	0.502528i	0.867482	+	0.497468i	$0.165737\pi$
$860$	−4.20829	−	7.28898i	−0.143502	−	0.248552i
$861$		0			0
$862$	7.07990	−	12.2628i	0.241143	−	0.417671i
$863$			15.5434i			0.529105i	0.964371	+	0.264553i	$0.0852243\pi$
$863$			15.5434i			0.529105i	−0.964371	+	0.264553i	$0.914776\pi$
$864$	−5.01239	+	1.36965i	−0.170525	+	0.0465965i
$865$	−11.4326			−0.388719
$866$	11.7415	−	20.3369i	0.398992	−	0.691075i
$867$	1.42152	−	2.03727i	0.0482773	−	0.0691895i
$868$		0			0
$869$	22.2154	−	12.8260i	0.753604	−	0.435094i
$870$	−3.78382	−	8.07964i	−0.128283	−	0.273926i
$871$	−20.5125	−	11.8429i	−0.695039	−	0.401281i
$872$			19.2434i			0.651663i
$873$	6.06050	−	35.0456i	0.205117	−	1.18611i
$874$		−	11.8507i		−	0.400857i
$875$		0			0
$876$	0.368514	−	4.29358i	0.0124509	−	0.145067i
$877$	22.7249	+	39.3606i	0.767364	+	1.32911i	0.938988	+	0.343950i	$0.111765\pi$
$877$	22.7249	+	39.3606i	0.767364	+	1.32911i	−0.171624	+	0.985163i	$0.554901\pi$
$878$	2.11540	+	3.66398i	0.0713913	+	0.123653i
$879$	15.3038	+	1.31351i	0.516184	+	0.0443035i
$880$	4.66917	+	2.69574i	0.157398	+	0.0908735i
$881$	15.6912			0.528651			0.264326	−	0.964433i	$-0.414851\pi$
$881$	15.6912			0.528651			0.264326	+	0.964433i	$0.414851\pi$
$882$		0			0
$883$	−10.5344			−0.354510			−0.177255	−	0.984165i	$-0.556722\pi$
$883$	−10.5344			−0.354510			−0.177255	+	0.984165i	$0.556722\pi$
$884$	14.8697	+	8.58505i	0.500124	+	0.288747i
$885$	1.18941	+	2.53977i	0.0399816	+	0.0853733i
$886$	14.9049	+	25.8161i	0.500740	+	0.867307i
$887$	0.0302741	+	0.0524362i	0.00101650	+	0.00176064i	0.866533	−	0.499119i	$-0.166343\pi$
$887$	0.0302741	+	0.0524362i	0.00101650	+	0.00176064i	−0.865517	+	0.500880i	$0.833010\pi$
$888$	0.692066	+	0.482893i	0.0232242	+	0.0162048i
$889$		0			0
$890$			3.98172i			0.133467i
$891$	49.3420	−	9.03594i	1.65302	−	0.302716i
$892$			8.18246i			0.273969i
$893$	36.7070	+	21.1928i	1.22835	+	0.709190i
$894$	−8.66294	+	12.4154i	−0.289732	+	0.415234i
$895$	−2.03877	+	1.17709i	−0.0681487	+	0.0393456i
$896$		0			0
$897$	8.48245	+	18.1127i	0.283221	+	0.604766i
$898$	4.20858	−	7.28948i	0.140442	−	0.243253i
$899$	−32.8368			−1.09517
$900$	−4.20793	−	11.4437i	−0.140264	−	0.381458i
$901$		−	7.95059i		−	0.264873i
$902$	0.456399	−	0.790505i	0.0151964	−	0.0263210i
$903$		0			0
$904$	4.22158	+	7.31199i	0.140408	+	0.243193i
$905$	9.66247	−	5.57863i	0.321192	−	0.185440i
$906$	3.27249	−	38.1280i	0.108721	−	1.26672i
$907$	−12.0490	+	20.8695i	−0.400081	+	0.692961i	−0.993735	−	0.111760i	$-0.964351\pi$
$907$	−12.0490	+	20.8695i	−0.400081	+	0.692961i	0.593654	+	0.804720i	$0.297685\pi$
$908$	−10.6938			−0.354885
$909$	−15.7155	−	2.71772i	−0.521251	−	0.0901410i
$910$		0			0
$911$	22.0494	+	12.7302i	0.730528	+	0.421771i	0.818615	−	0.574342i	$-0.194742\pi$
$911$	22.0494	+	12.7302i	0.730528	+	0.421771i	−0.0880873	+	0.996113i	$0.528075\pi$
$912$	7.00573	−	3.28089i	0.231983	−	0.108641i
$913$	40.6404	−	23.4638i	1.34500	−	0.776537i
$914$	3.36207	−	1.94109i	0.111208	−	0.0642057i
$915$	7.10679	+	4.95880i	0.234943	+	0.163933i
$916$	−25.2942	−	14.6036i	−0.835744	−	0.482517i
$917$		0			0
$918$	−14.5676	−	14.4243i	−0.480802	−	0.476073i
$919$	−22.9067			−0.755623			−0.377812	−	0.925882i	$-0.623323\pi$
$919$	−22.9067			−0.755623			−0.377812	+	0.925882i	$0.623323\pi$
$920$	1.28332	−	2.22278i	0.0423098	−	0.0732828i
$921$	−38.5548	−	26.9019i	−1.27043	−	0.886446i
$922$	−29.5181	+	17.0423i	−0.972128	+	0.561258i
$923$	7.92076	+	13.7192i	0.260715	+	0.451572i
$924$		0			0
$925$	−0.990094	+	1.71489i	−0.0325541	+	0.0563853i
$926$		−	12.2192i		−	0.401549i
$927$	20.6124	+	17.1804i	0.676999	+	0.564279i
$928$	−5.32498			−0.174801
$929$	−14.3986	+	24.9392i	−0.472404	+	0.818228i	−0.999501	−	0.0315768i	$-0.989947\pi$
$929$	−14.3986	+	24.9392i	−0.472404	+	0.818228i	0.527097	+	0.849805i	$0.323280\pi$
$930$	10.2939	+	0.883517i	0.337551	+	0.0289717i
$931$		0			0
$932$	−5.57664	+	3.21967i	−0.182669	+	0.105464i
$933$	29.1566	+	2.50249i	0.954546	+	0.0819277i
$934$	−26.6835	−	15.4057i	−0.873112	−	0.504091i
$935$			21.2713i			0.695646i
$936$	−8.35922	+	10.0290i	−0.273230	+	0.327810i
$937$			53.6825i			1.75373i	0.480736	+	0.876865i	$0.340369\pi$
$937$			53.6825i			1.75373i	−0.480736	+	0.876865i	$0.659631\pi$
$938$		0			0
$939$	−6.70936	+	3.14209i	−0.218952	+	0.102538i
$940$	4.58996	+	7.95004i	0.149708	+	0.259302i
$941$	22.9511	+	39.7524i	0.748184	+	1.29589i	0.948693	+	0.316200i	$0.102407\pi$
$941$	22.9511	+	39.7524i	0.748184	+	1.29589i	−0.200509	+	0.979692i	$0.564260\pi$
$942$	−1.41193	+	2.02353i	−0.0460032	+	0.0659303i
$943$	−0.376324	−	0.217271i	−0.0122548	−	0.00707530i
$944$	1.67386			0.0544796
$945$		0			0
$946$	48.4954			1.57672
$947$	25.0440	+	14.4591i	0.813820	+	0.469859i	0.848281	−	0.529547i	$-0.177638\pi$
$947$	25.0440	+	14.4591i	0.813820	+	0.469859i	−0.0344607	+	0.999406i	$0.510971\pi$
$948$	4.56157	−	6.53749i	0.148153	−	0.212328i
$949$	−5.41390	−	9.37715i	−0.175743	−	0.304395i
$950$	9.07623	+	15.7205i	0.294472	+	0.510040i
$951$	−10.3986	+	4.86984i	−0.337199	+	0.157915i
$952$		0			0
$953$			12.8715i			0.416949i	0.978028	+	0.208475i	$0.0668498\pi$
$953$			12.8715i			0.416949i	−0.978028	+	0.208475i	$0.933150\pi$
$954$	5.95713	+	1.03018i	0.192869	+	0.0333532i
$955$		−	21.3478i		−	0.690798i
$956$	−4.01452	−	2.31778i	−0.129839	−	0.0749624i
$957$	51.2179	+	4.39598i	1.65564	+	0.142102i
$958$	−36.1560	+	20.8747i	−1.16815	+	0.674430i
$959$		0			0
$960$	1.66932	+	0.143276i	0.0538770	+	0.00462421i
$961$	3.51314	−	6.08494i	0.113327	−	0.196288i
$962$	2.12036			0.0683633
$963$	53.9379	−	19.8333i	1.73813	−	0.639119i
$964$		−	10.4944i		−	0.338003i
$965$	−9.64402	+	16.7039i	−0.310452	+	0.537719i
$966$		0			0
$967$	3.11725	+	5.39923i	0.100244	+	0.173627i	0.911785	−	0.410668i	$-0.134704\pi$
$967$	3.11725	+	5.39923i	0.100244	+	0.173627i	−0.811541	+	0.584295i	$0.801371\pi$
$968$	−17.3769	+	10.0326i	−0.558516	+	0.322459i
$969$	25.0301	+	17.4649i	0.804081	+	0.561052i
$970$	−5.73393	+	9.93146i	−0.184105	+	0.318880i
$971$	39.3727			1.26353			0.631764	−	0.775160i	$-0.282331\pi$
$971$	39.3727			1.26353			0.631764	+	0.775160i	$0.282331\pi$
$972$	12.6952	−	9.04604i	0.407200	−	0.290152i
$973$		0			0
$974$	−18.3306	−	10.5832i	−0.587349	−	0.339106i
$975$	−25.1245	−	17.5307i	−0.804628	−	0.561433i
$976$	4.47927	−	2.58611i	0.143378	−	0.0827793i
$977$	−23.2474	+	13.4219i	−0.743751	+	0.429405i	−0.823431	−	0.567416i	$-0.807943\pi$
$977$	−23.2474	+	13.4219i	−0.743751	+	0.429405i	0.0796807	+	0.996820i	$0.474610\pi$
$978$	−11.6747	+	5.46745i	−0.373317	+	0.174830i
$979$	−19.8685	−	11.4711i	−0.635001	−	0.366618i
$980$		0			0
$981$	−19.9235	−	54.1832i	−0.636108	−	1.72994i
$982$	37.3463			1.19177
$983$	5.98457	−	10.3656i	0.190878	−	0.330611i	−0.754663	−	0.656112i	$-0.772200\pi$
$983$	5.98457	−	10.3656i	0.190878	−	0.330611i	0.945541	+	0.325502i	$0.105533\pi$
$984$	0.0242571	−	0.282621i	0.000773287	−	0.00900963i
$985$	−3.87499	+	2.23723i	−0.123467	+	0.0712839i
$986$	−10.5044	−	18.1942i	−0.334530	−	0.579423i
$987$		0			0
$988$	9.71873	−	16.8333i	0.309194	−	0.535540i
$989$		−	23.0865i		−	0.734107i
$990$	−15.9379	−	2.75617i	−0.506540	−	0.0875969i
$991$	10.8084			0.343340			0.171670	−	0.985154i	$-0.445084\pi$
$991$	10.8084			0.343340			0.171670	+	0.985154i	$0.445084\pi$
$992$	3.08327	−	5.34038i	0.0978940	−	0.169557i
$993$	0.556660	+	1.18864i	0.0176651	+	0.0377205i
$994$		0			0
$995$	−17.5109	+	10.1099i	−0.555132	+	0.320506i
$996$	8.34486	−	11.9596i	0.264417	−	0.378954i
$997$	11.6653	+	6.73498i	0.369445	+	0.213299i	0.673216	−	0.739446i	$-0.264912\pi$
$997$	11.6653	+	6.73498i	0.369445	+	0.213299i	−0.303771	+	0.952745i	$0.598246\pi$
$998$		−	27.4197i		−	0.867956i
$999$	−2.44860	−	0.643147i	−0.0774702	−	0.0203483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.m.b.587.6		16
3.2	odd	2		2646.2.m.b.1763.2		16
7.2	even	3		126.2.l.a.101.3	yes	16
7.3	odd	6		126.2.t.a.47.1	yes	16
7.4	even	3		882.2.t.a.803.4		16
7.5	odd	6		882.2.l.b.227.2		16
7.6	odd	2		882.2.m.a.587.7		16
9.4	even	3		2646.2.m.a.881.3		16
9.5	odd	6		882.2.m.a.293.7		16
21.2	odd	6		378.2.l.a.143.6		16
21.5	even	6		2646.2.l.a.521.7		16
21.11	odd	6		2646.2.t.b.1979.7		16
21.17	even	6		378.2.t.a.89.6		16
21.20	even	2		2646.2.m.a.1763.3		16
28.3	even	6		1008.2.df.c.929.7		16
28.23	odd	6		1008.2.ca.c.353.5		16
63.2	odd	6		1134.2.k.b.647.6		16
63.4	even	3		2646.2.l.a.1097.3		16
63.5	even	6		882.2.t.a.815.4		16
63.13	odd	6		2646.2.m.b.881.2		16
63.16	even	3		1134.2.k.a.647.3		16
63.23	odd	6		126.2.t.a.59.1	yes	16
63.31	odd	6		378.2.l.a.341.2		16
63.32	odd	6		882.2.l.b.509.6		16
63.38	even	6		1134.2.k.a.971.3		16
63.40	odd	6		2646.2.t.b.2285.7		16
63.41	even	6	inner	882.2.m.b.293.6		16
63.52	odd	6		1134.2.k.b.971.6		16
63.58	even	3		378.2.t.a.17.6		16
63.59	even	6		126.2.l.a.5.7	✓	16
84.23	even	6		3024.2.ca.c.2033.4		16
84.59	odd	6		3024.2.df.c.1601.4		16
252.23	even	6		1008.2.df.c.689.7		16
252.31	even	6		3024.2.ca.c.2609.4		16
252.59	odd	6		1008.2.ca.c.257.5		16
252.247	odd	6		3024.2.df.c.17.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.7	✓	16	63.59	even	6
126.2.l.a.101.3	yes	16	7.2	even	3
126.2.t.a.47.1	yes	16	7.3	odd	6
126.2.t.a.59.1	yes	16	63.23	odd	6
378.2.l.a.143.6		16	21.2	odd	6
378.2.l.a.341.2		16	63.31	odd	6
378.2.t.a.17.6		16	63.58	even	3
378.2.t.a.89.6		16	21.17	even	6
882.2.l.b.227.2		16	7.5	odd	6
882.2.l.b.509.6		16	63.32	odd	6
882.2.m.a.293.7		16	9.5	odd	6
882.2.m.a.587.7		16	7.6	odd	2
882.2.m.b.293.6		16	63.41	even	6	inner
882.2.m.b.587.6		16	1.1	even	1	trivial
882.2.t.a.803.4		16	7.4	even	3
882.2.t.a.815.4		16	63.5	even	6
1008.2.ca.c.257.5		16	252.59	odd	6
1008.2.ca.c.353.5		16	28.23	odd	6
1008.2.df.c.689.7		16	252.23	even	6
1008.2.df.c.929.7		16	28.3	even	6
1134.2.k.a.647.3		16	63.16	even	3
1134.2.k.a.971.3		16	63.38	even	6
1134.2.k.b.647.6		16	63.2	odd	6
1134.2.k.b.971.6		16	63.52	odd	6
2646.2.l.a.521.7		16	21.5	even	6
2646.2.l.a.1097.3		16	63.4	even	3
2646.2.m.a.881.3		16	9.4	even	3
2646.2.m.a.1763.3		16	21.20	even	2
2646.2.m.b.881.2		16	63.13	odd	6
2646.2.m.b.1763.2		16	3.2	odd	2
2646.2.t.b.1979.7		16	21.11	odd	6
2646.2.t.b.2285.7		16	63.40	odd	6
3024.2.ca.c.2033.4		16	84.23	even	6
3024.2.ca.c.2609.4		16	252.31	even	6
3024.2.df.c.17.4		16	252.247	odd	6
3024.2.df.c.1601.4		16	84.59	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.991125 + 1.42045i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.483662 + 0.837727i) q^{5} +(-1.56856 + 0.734581i) q^{6} +1.00000i q^{8} +(-1.03534 - 2.81568i) q^{9} +0.967324i q^{10} +(-4.82689 - 2.78681i) q^{11} +(-1.72571 - 0.148116i) q^{12} +(-3.76893 + 2.17600i) q^{13} +(-1.66932 - 0.143276i) q^{15} +(-0.500000 + 0.866025i) q^{16} -3.94535 q^{17} +(0.511208 - 2.95612i) q^{18} +4.46634i q^{19} +(-0.483662 + 0.837727i) q^{20} +(-2.78681 - 4.82689i) q^{22} +(-2.29786 + 1.32667i) q^{23} +(-1.42045 - 0.991125i) q^{24} +(2.03214 - 3.51977i) q^{25} -4.35199 q^{26} +(5.02568 + 1.32004i) q^{27} +(4.61157 + 2.66249i) q^{29} +(-1.37403 - 0.958739i) q^{30} +(-5.34038 + 3.08327i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(8.74256 - 4.09427i) q^{33} +(-3.41677 - 1.97267i) q^{34} +(1.92078 - 2.30447i) q^{36} -0.487217 q^{37} +(-2.23317 + 3.86796i) q^{38} +(0.644598 - 7.51026i) q^{39} +(-0.837727 + 0.483662i) q^{40} +(0.0818856 + 0.141830i) q^{41} +(-4.35045 + 7.53520i) q^{43} -5.57361i q^{44} +(1.85802 - 2.22917i) q^{45} -2.65334 q^{46} +(4.74500 - 8.21859i) q^{47} +(-0.734581 - 1.56856i) q^{48} +(3.51977 - 2.03214i) q^{50} +(3.91033 - 5.60416i) q^{51} +(-3.76893 - 2.17600i) q^{52} +2.01518i q^{53} +(3.69235 + 3.65603i) q^{54} -5.39149i q^{55} +(-6.34420 - 4.42670i) q^{57} +(2.66249 + 4.61157i) q^{58} +(-0.836931 - 1.44961i) q^{59} +(-0.710578 - 1.51731i) q^{60} +(-4.47927 - 2.58611i) q^{61} -6.16655 q^{62} -1.00000 q^{64} +(-3.64578 - 2.10489i) q^{65} +(9.61842 + 0.825539i) q^{66} +(2.72126 + 4.71336i) q^{67} +(-1.97267 - 3.41677i) q^{68} +(0.393002 - 4.57889i) q^{69} -3.64006i q^{71} +(2.81568 - 1.03534i) q^{72} +2.48801i q^{73} +(-0.421942 - 0.243608i) q^{74} +(2.98555 + 6.37509i) q^{75} +(-3.86796 + 2.23317i) q^{76} +(4.31337 - 6.18177i) q^{78} +(-2.30121 + 3.98581i) q^{79} -0.967324 q^{80} +(-6.85613 + 5.83039i) q^{81} +0.163771i q^{82} +(-4.20979 + 7.29158i) q^{83} +(-1.90821 - 3.30512i) q^{85} +(-7.53520 + 4.35045i) q^{86} +(-8.35257 + 3.91163i) q^{87} +(2.78681 - 4.82689i) q^{88} +4.11622 q^{89} +(2.72368 - 1.00151i) q^{90} +(-2.29786 - 1.32667i) q^{92} +(0.913362 - 10.6416i) q^{93} +(8.21859 - 4.74500i) q^{94} +(-3.74157 + 2.16020i) q^{95} +(0.148116 - 1.72571i) q^{96} +(10.2669 + 5.92762i) q^{97} +(-2.84928 + 16.4763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 6 q^{9} - 12 q^{11} + 6 q^{13} - 18 q^{15} - 8 q^{16} + 36 q^{17} + 6 q^{23} - 6 q^{24} - 8 q^{25} - 24 q^{26} + 36 q^{27} + 6 q^{29} + 18 q^{30} + 6 q^{31} + 18 q^{33} + 4 q^{37} + 42 q^{39}+ \cdots + 18 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 6 * q^9 - 12 * q^11 + 6 * q^13 - 18 * q^15 - 8 * q^16 + 36 * q^17 + 6 * q^23 - 6 * q^24 - 8 * q^25 - 24 * q^26 + 36 * q^27 + 6 * q^29 + 18 * q^30 + 6 * q^31 + 18 * q^33 + 4 * q^37 + 42 * q^39 - 6 * q^41 - 2 * q^43 + 42 * q^45 - 12 * q^46 + 18 * q^47 - 12 * q^50 - 6 * q^51 + 6 * q^52 + 6 * q^57 + 6 * q^58 - 30 * q^59 - 12 * q^60 - 60 * q^61 + 36 * q^62 - 16 * q^64 - 42 * q^65 + 24 * q^66 + 14 * q^67 + 18 * q^68 - 42 * q^69 - 12 * q^72 - 18 * q^74 - 30 * q^75 - 16 * q^79 - 18 * q^81 - 12 * q^85 - 24 * q^86 - 24 * q^87 + 48 * q^89 + 18 * q^90 + 6 * q^92 + 12 * q^93 + 66 * q^95 - 6 * q^96 + 6 * q^97 + 18 * q^99

Introduction

L-functions

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