LMFDB - Embedded newform 882.2.m.b.293.6

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			293.6
Root			$-1.70672 - 0.295146i$ of defining polynomial
Character	$\chi$	$=$	882.293
Dual form			882.2.m.b.587.6

$q$-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 $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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	−0.737374	−	0.675485i	$-0.763934\pi$
$5$	0.483662	−	0.837727i	0.216300	−	0.374643i	0.953674	+	0.300842i	$0.0972677\pi$
$6$	−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	−0.998778	−	0.0494264i	$-0.984261\pi$
$11$	−4.82689	+	2.78681i	−1.45536	+	0.840254i	−0.456584	+	0.889680i	$0.650927\pi$
$12$	−1.72571	+	0.148116i	−0.498168	+	0.0427573i
$13$	−3.76893	−	2.17600i	−1.04531	−	0.603512i	−0.123980	−	0.992285i	$-0.539566\pi$
$13$	−3.76893	−	2.17600i	−1.04531	−	0.603512i	−0.921334	+	0.388772i	$0.872899\pi$
$14$		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	$-0.828785\pi$
$19$		−	4.46634i		−	1.02465i	0.858792	−	0.512324i	$-0.171215\pi$
$20$	−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	0.240920	−	0.970545i	$-0.422551\pi$
$23$	−2.29786	−	1.32667i	−0.479137	−	0.276630i	−0.720057	+	0.693915i	$0.755884\pi$
$24$	−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	−0.00644015	−	0.999979i	$-0.502050\pi$
$29$	4.61157	−	2.66249i	0.856347	−	0.494412i	0.862787	+	0.505567i	$0.168717\pi$
$30$	−1.37403	+	0.958739i	−0.250863	+	0.175041i
$31$	−5.34038	−	3.08327i	−0.959161	−	0.553772i	−0.0632466	−	0.997998i	$-0.520145\pi$
$31$	−5.34038	−	3.08327i	−0.959161	−	0.553772i	−0.895915	+	0.444226i	$0.853479\pi$
$32$	−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	−0.859560	−	0.511034i	$-0.829263\pi$
$41$	0.0818856	−	0.141830i	0.0127884	−	0.0221501i	0.872349	+	0.488884i	$0.162596\pi$
$42$		0			0
$43$	−4.35045	−	7.53520i	−0.663437	−	1.14911i	−0.979707	−	0.200437i	$-0.935764\pi$
$43$	−4.35045	−	7.53520i	−0.663437	−	1.14911i	0.316270	−	0.948669i	$-0.397570\pi$
$44$			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	0.971139	+	0.238516i	$0.0766609\pi$
$47$	4.74500	+	8.21859i	0.692130	+	1.19880i	−0.279009	+	0.960289i	$0.590006\pi$
$48$	−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	$-0.955803\pi$
$53$		−	2.01518i		−	0.276807i	0.990376	−	0.138403i	$-0.0441970\pi$
$54$	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	−0.915349	−	0.402662i	$-0.868085\pi$
$59$	−0.836931	+	1.44961i	−0.108959	+	0.188723i	0.806390	+	0.591384i	$0.201418\pi$
$60$	−0.710578	+	1.51731i	−0.0917352	+	0.195884i
$61$	−4.47927	+	2.58611i	−0.573512	+	0.331117i	−0.758551	−	0.651614i	$-0.774092\pi$
$61$	−4.47927	+	2.58611i	−0.573512	+	0.331117i	0.185039	+	0.982731i	$0.440759\pi$
$62$	−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	−0.650538	−	0.759474i	$-0.725456\pi$
$67$	2.72126	−	4.71336i	0.332455	−	0.575828i	0.982993	+	0.183645i	$0.0587898\pi$
$68$	−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	$0.0693005\pi$
$71$			3.64006i			0.431996i	−0.976394	+	0.215998i	$0.930700\pi$
$72$	2.81568	+	1.03534i	0.331831	+	0.122016i
$73$		−	2.48801i		−	0.291200i	−0.989344	−	0.145600i	$-0.953489\pi$
$73$		−	2.48801i		−	0.291200i	0.989344	−	0.145600i	$-0.0465112\pi$
$74$	−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	0.707043	−	0.707170i	$-0.250029\pi$
$79$	−2.30121	−	3.98581i	−0.258906	−	0.448438i	−0.965949	+	0.258732i	$0.916695\pi$
$80$	−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	0.536980	−	0.843595i	$-0.319565\pi$
$83$	−4.20979	−	7.29158i	−0.462085	−	0.800355i	−0.999065	+	0.0432405i	$0.986232\pi$
$84$		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	0.121924	−	0.992539i	$-0.461094\pi$
$97$	10.2669	−	5.92762i	1.04245	−	0.601859i	0.920526	+	0.390681i	$0.127760\pi$
$98$		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	0.967431	−	0.253135i	$-0.0814618\pi$
$101$	2.65813	+	4.60402i	0.264494	+	0.458117i	−0.702937	+	0.711252i	$0.748128\pi$
$102$	6.18852	+	2.89818i	0.612755	+	0.286962i
$103$	−7.74616	−	4.47225i	−0.763252	−	0.440664i	0.0672102	−	0.997739i	$-0.478590\pi$
$103$	−7.74616	−	4.47225i	−0.763252	−	0.440664i	−0.830462	+	0.557075i	$0.811924\pi$
$104$	−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	$-0.623264\pi$
$107$		−	19.1563i		−	1.85191i	0.377639	−	0.925953i	$-0.376736\pi$
$108$	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	0.802808	−	0.596238i	$-0.203339\pi$
$113$	7.31199	+	4.22158i	0.687854	+	0.397133i	−0.114953	+	0.993371i	$0.536672\pi$
$114$	−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	0.0875000	+	0.996165i	$0.472112\pi$
$131$	−9.37335	+	16.2351i	−0.818954	+	1.41847i	−0.906454	+	0.422305i	$0.861221\pi$
$132$	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	−0.971697	−	0.236230i	$-0.924088\pi$
$137$	−14.6656	+	8.46717i	−1.25296	+	0.723399i	−0.281267	+	0.959630i	$0.590755\pi$
$138$	2.62979	+	3.76893i	0.223863	+	0.320833i
$139$	−10.5033	−	6.06406i	−0.890875	−	0.514347i	−0.0166466	−	0.999861i	$-0.505299\pi$
$139$	−10.5033	−	6.06406i	−0.890875	−	0.514347i	−0.874229	+	0.485514i	$0.838632\pi$
$140$		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	0.776915	−	0.629606i	$-0.216783\pi$
$149$	7.56951	+	4.37026i	0.620118	+	0.358025i	−0.156797	+	0.987631i	$0.550117\pi$
$150$	−0.601984	−	7.01376i	−0.0491518	−	0.572671i
$151$	−11.0471	−	19.1341i	−0.898997	−	1.55711i	−0.828778	−	0.559578i	$-0.810963\pi$
$151$	−11.0471	−	19.1341i	−0.898997	−	1.55711i	−0.0702195	−	0.997532i	$-0.522370\pi$
$152$	−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	0.548422	−	0.836202i	$-0.315229\pi$
$157$	1.23372	+	0.712287i	0.0984614	+	0.0568467i	−0.449961	+	0.893048i	$0.648562\pi$
$158$	−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	−0.963906	−	0.266242i	$-0.914218\pi$
$167$	−3.24855	+	5.62665i	−0.251380	+	0.435404i	0.712526	+	0.701646i	$0.247551\pi$
$168$		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	0.549057	−	0.835785i	$-0.314987\pi$
$173$	−5.90938	−	10.2354i	−0.449282	−	0.778179i	−0.998339	+	0.0576053i	$0.981654\pi$
$174$	−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	$-0.971009\pi$
$179$		−	2.43370i		−	0.181903i	0.995855	−	0.0909515i	$-0.0289908\pi$
$180$	2.85953	−	0.494504i	0.213137	−	0.0368581i
$181$			11.5342i			0.857327i	0.903464	+	0.428663i	$0.141015\pi$
$181$			11.5342i			0.857327i	−0.903464	+	0.428663i	$0.858985\pi$
$182$		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	−0.992503	−	0.122216i	$-0.961000\pi$
$191$	−19.1122	+	11.0345i	−1.38291	+	0.798425i	−0.390409	+	0.920641i	$0.627666\pi$
$192$	0.991125	+	1.42045i	0.0715283	+	0.102512i
$193$	9.96979	−	17.2682i	0.717641	−	1.24299i	−0.244291	−	0.969702i	$-0.578555\pi$
$193$	9.96979	−	17.2682i	0.717641	−	1.24299i	0.961932	−	0.273289i	$-0.0881116\pi$
$194$	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	$-0.947309\pi$
$197$		−	4.62560i		−	0.329560i	0.986330	−	0.164780i	$-0.0526914\pi$
$198$	−10.7057	−	12.8442i	−0.760820	−	0.912801i
$199$		−	20.9028i		−	1.48176i	−0.671635	−	0.740882i	$-0.734408\pi$
$199$		−	20.9028i		−	1.48176i	0.671635	−	0.740882i	$-0.265592\pi$
$200$	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	−0.957852	−	0.287263i	$-0.907254\pi$
$211$	−3.34310	+	5.79042i	−0.230148	+	0.398629i	0.727703	+	0.685892i	$0.240588\pi$
$212$	−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	−0.243605	−	0.969875i	$-0.578330\pi$
$223$	7.08622	−	4.09123i	0.474528	−	0.273969i	0.718133	+	0.695905i	$0.244997\pi$
$224$		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	0.632214	−	0.774794i	$-0.282147\pi$
$227$	−5.34688	−	9.26106i	−0.354885	−	0.614678i	−0.987098	+	0.160116i	$0.948813\pi$
$228$	0.661535	+	7.70759i	0.0438112	+	0.510447i
$229$	−25.2942	−	14.6036i	−1.67149	−	0.965034i	−0.966806	−	0.255510i	$-0.917757\pi$
$229$	−25.2942	−	14.6036i	−1.67149	−	0.965034i	−0.704682	−	0.709524i	$-0.748910\pi$
$230$	−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	$-0.932352\pi$
$233$		−	6.43935i		−	0.421856i	0.977502	−	0.210928i	$-0.0676485\pi$
$234$	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	0.364510	−	0.931200i	$-0.381237\pi$
$239$	−4.01452	−	2.31778i	−0.259678	−	0.149925i	−0.624187	+	0.781275i	$0.714570\pi$
$240$	0.958739	+	1.37403i	0.0618863	+	0.0886935i
$241$	−9.08846	+	5.24722i	−0.585439	+	0.338003i	−0.763292	−	0.646054i	$-0.776418\pi$
$241$	−9.08846	+	5.24722i	−0.585439	+	0.338003i	0.177853	+	0.984057i	$0.443085\pi$
$242$		−	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	−0.914562	−	0.404445i	$-0.867465\pi$
$257$	−1.71568	+	2.97164i	−0.107021	+	0.185366i	0.807541	+	0.589811i	$0.200798\pi$
$258$	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	−0.399044	−	0.916932i	$-0.630658\pi$
$263$	3.17080	−	1.83066i	0.195520	−	0.112883i	0.594564	+	0.804048i	$0.297325\pi$
$264$	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	$0.206311\pi$
$271$			19.8766i			1.20742i	−0.797206	+	0.603708i	$0.793689\pi$
$272$	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	0.956108	−	0.293015i	$-0.0946585\pi$
$277$	3.73302	+	6.46579i	0.224296	+	0.388491i	−0.731812	+	0.681506i	$0.761325\pi$
$278$	−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	−0.948845	−	0.315741i	$-0.897747\pi$
$281$	−19.2746	+	11.1282i	−1.14983	+	0.663854i	−0.200983	+	0.979595i	$0.564414\pi$
$282$	−1.40562	−	16.3770i	−0.0837034	−	0.975234i
$283$	14.0125	+	8.09012i	0.832957	+	0.480908i	0.854864	−	0.518852i	$-0.173641\pi$
$283$	14.0125	+	8.09012i	0.832957	+	0.480908i	−0.0219073	+	0.999760i	$0.506974\pi$
$284$	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	−0.965985	−	0.258597i	$-0.916740\pi$
$293$	−4.43406	+	7.68002i	−0.259041	+	0.448672i	0.706944	+	0.707269i	$0.250073\pi$
$294$		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	$-0.717972\pi$
$307$		−	27.1427i		−	1.54912i	0.632501	−	0.774559i	$-0.282028\pi$
$308$		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	−0.999711	−	0.0240499i	$-0.992344\pi$
$311$	−8.44774	+	14.6319i	−0.479028	+	0.829700i	0.520683	+	0.853750i	$0.325677\pi$
$312$	7.51026	−	0.644598i	0.425185	−	0.0364932i
$313$	3.70433	−	2.13870i	0.209381	−	0.120886i	−0.391643	−	0.920117i	$-0.628093\pi$
$313$	3.70433	−	2.13870i	0.209381	−	0.120886i	0.601024	+	0.799231i	$0.294760\pi$
$314$	1.42457			0.0803934
$315$		0			0
$316$	−4.60242			−0.258906
$317$	5.74123	−	3.31470i	0.322460	−	0.186172i	−0.330029	−	0.943971i	$-0.607058\pi$
$317$	5.74123	−	3.31470i	0.322460	−	0.186172i	0.652488	+	0.757799i	$0.273725\pi$
$318$	−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	0.876251	−	0.481856i	$-0.160037\pi$
$331$	0.378896	+	0.656267i	0.0208260	+	0.0360717i	−0.855425	+	0.517927i	$0.826704\pi$
$332$	−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	−0.837178	−	0.546930i	$-0.815796\pi$
$337$	1.01088	−	1.75089i	0.0550660	−	0.0953772i	0.892244	+	0.451553i	$0.149130\pi$
$338$	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	−0.0740550	−	0.997254i	$-0.523594\pi$
$347$	−18.1572	−	10.4831i	−0.974730	−	0.562761i	−0.900675	+	0.434494i	$0.856927\pi$
$348$	−7.56386	+	5.27772i	−0.405465	+	0.282916i
$349$	−5.36406	+	3.09694i	−0.287132	+	0.165776i	−0.636648	−	0.771155i	$-0.719679\pi$
$349$	−5.36406	+	3.09694i	−0.287132	+	0.165776i	0.349516	+	0.936930i	$0.386346\pi$
$350$		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	0.999999	+	0.00152110i	$0.000484180\pi$
$353$	9.41889	+	16.3140i	0.501317	+	0.868306i	−0.498682	+	0.866785i	$0.666182\pi$
$354$	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	$0.262139\pi$
$359$			27.7977i			1.46711i	−0.679633	+	0.733553i	$0.737861\pi$
$360$	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	0.0800968	−	0.996787i	$-0.474477\pi$
$367$	18.8390	−	10.8767i	0.983388	−	0.567759i	0.903291	+	0.429028i	$0.141144\pi$
$368$			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	−0.976973	−	0.213362i	$-0.931558\pi$
$373$	−5.86560	+	10.1595i	−0.303709	+	0.526040i	0.673264	+	0.739402i	$0.264892\pi$
$374$	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	−0.674040	−	0.738695i	$-0.735443\pi$
$383$	5.92412	−	10.2609i	0.302708	−	0.524306i	0.976748	+	0.214389i	$0.0687759\pi$
$384$	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	−0.353984	−	0.935251i	$-0.615173\pi$
$389$	5.50224	−	3.17672i	0.278975	−	0.161066i	0.632959	+	0.774185i	$0.281840\pi$
$390$	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	$0.0690378\pi$
$397$			8.57535i			0.430385i	−0.976572	+	0.215192i	$0.930962\pi$
$398$	−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	0.908199	−	0.418539i	$-0.137458\pi$
$401$	20.0216	+	11.5595i	0.999833	+	0.577254i	0.0916343	+	0.995793i	$0.470791\pi$
$402$	−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	0.466229	−	0.884664i	$-0.345612\pi$
$409$	−1.35091	−	0.779947i	−0.0667981	−	0.0385659i	−0.533027	+	0.846098i	$0.678946\pi$
$410$	−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	−0.770685	−	0.637216i	$-0.780086\pi$
$419$	3.40822	−	5.90321i	0.166502	−	0.288391i	0.937188	+	0.348825i	$0.113419\pi$
$420$		0			0
$421$	−6.75727	−	11.7039i	−0.329329	−	0.570415i	0.653050	−	0.757315i	$-0.273489\pi$
$421$	−6.75727	−	11.7039i	−0.329329	−	0.570415i	−0.982379	+	0.186900i	$0.940156\pi$
$422$			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	$0.110775\pi$
$431$			14.1598i			0.682054i	−0.940053	+	0.341027i	$0.889225\pi$
$432$	−3.65603	−	3.69235i	−0.175901	−	0.177648i
$433$			23.4830i			1.12852i	0.825597	+	0.564260i	$0.190839\pi$
$433$			23.4830i			1.12852i	−0.825597	+	0.564260i	$0.809161\pi$
$434$		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	−0.410009	−	0.912081i	$-0.634474\pi$
$439$	3.66398	−	2.11540i	0.174872	−	0.100963i	0.584881	+	0.811119i	$0.301141\pi$
$440$	5.39149			0.257029
$441$		0			0
$442$	17.1701			0.816699
$443$	25.8161	−	14.9049i	1.22656	−	0.708154i	0.260250	−	0.965541i	$-0.416195\pi$
$443$	25.8161	−	14.9049i	1.22656	−	0.708154i	0.966308	+	0.257388i	$0.0828618\pi$
$444$	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	$0.0636444\pi$
$449$			8.41716i			0.397230i	−0.980078	+	0.198615i	$0.936356\pi$
$450$	−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	0.907848	−	0.419299i	$-0.137724\pi$
$457$	1.94109	+	3.36207i	0.0908006	+	0.157271i	−0.817048	+	0.576570i	$0.804391\pi$
$458$	−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	−0.923637	−	0.383269i	$-0.874798\pi$
$461$	−17.0423	−	29.5181i	−0.793739	−	1.37480i	0.129898	−	0.991527i	$-0.458535\pi$
$462$		0			0
$463$	−6.10962	+	10.5822i	−0.283938	+	0.491796i	−0.972351	−	0.233523i	$-0.924974\pi$
$463$	−6.10962	+	10.5822i	−0.283938	+	0.491796i	0.688413	+	0.725319i	$0.258308\pi$
$464$	−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	−0.737118	−	0.675764i	$-0.763814\pi$
$479$	−20.8747	−	36.1560i	−0.953788	−	1.65201i	−0.216670	−	0.976245i	$-0.569519\pi$
$480$	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	0.998992	−	0.0448915i	$-0.0142942\pi$
$491$	32.3428	+	18.6731i	1.45961	+	0.842707i	0.460619	+	0.887598i	$0.347628\pi$
$492$	−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	0.376867	+	0.926267i	$0.377001\pi$
$499$	−13.7099	+	23.7462i	−0.613738	+	1.06303i	−0.990605	+	0.136758i	$0.956332\pi$
$500$	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	−0.582257	−	0.813005i	$-0.697830\pi$
$509$	9.31667	−	16.1370i	0.412954	−	0.715258i	0.995211	+	0.0977470i	$0.0311636\pi$
$510$	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	$0.293973\pi$
$523$			36.4875i			1.59549i	−0.602997	+	0.797743i	$0.706027\pi$
$524$	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	0.595858	−	0.803090i	$-0.296812\pi$
$547$	−9.29831	−	16.1051i	−0.397567	−	0.688606i	−0.993425	+	0.114484i	$0.963479\pi$
$548$			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	$0.198482\pi$
$557$			27.5620i			1.16784i	−0.811811	+	0.583920i	$0.801518\pi$
$558$	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	−0.596137	−	0.802883i	$-0.703298\pi$
$563$	9.42577	−	16.3259i	0.397249	−	0.688055i	0.993385	+	0.114828i	$0.0366317\pi$
$564$	−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	−0.578942	−	0.815369i	$-0.696534\pi$
$569$	−3.87103	+	2.23494i	−0.162282	+	0.0936936i	0.416659	+	0.909063i	$0.363201\pi$
$570$	4.28205	+	6.13690i	0.179355	+	0.257046i
$571$	−9.31245	+	16.1296i	−0.389714	+	0.675004i	−0.992411	−	0.122966i	$-0.960759\pi$
$571$	−9.31245	+	16.1296i	−0.389714	+	0.675004i	0.602697	+	0.797970i	$0.294093\pi$
$572$	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	$0.278616\pi$
$577$			36.8833i			1.53547i	−0.640767	+	0.767735i	$0.721384\pi$
$578$	−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	0.998541	+	0.0540032i	$0.0171981\pi$
$587$	13.2295	+	22.9141i	0.546039	+	0.945766i	−0.452502	+	0.891763i	$0.649469\pi$
$588$		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	−0.000336253	−	1.00000i	$-0.500107\pi$
$599$	−21.2079	−	12.2444i	−0.866530	−	0.500291i	−0.866193	+	0.499709i	$0.833440\pi$
$600$	−6.37509	−	2.98555i	−0.260262	−	0.121884i
$601$	−19.3812	+	11.1898i	−0.790577	+	0.456440i	−0.840166	−	0.542330i	$-0.817542\pi$
$601$	−19.3812	+	11.1898i	−0.790577	+	0.456440i	0.0495885	+	0.998770i	$0.484209\pi$
$602$		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	0.947746	−	0.319026i	$-0.103356\pi$
$607$	28.2180	+	16.2917i	1.14533	+	0.661259i	0.197589	+	0.980285i	$0.436689\pi$
$608$	−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	−0.998975	−	0.0452639i	$-0.985587\pi$
$617$	−38.1947	−	22.0517i	−1.53766	−	0.887770i	−0.538687	−	0.842506i	$-0.681080\pi$
$618$	8.86511	+	12.7052i	0.356607	+	0.511078i
$619$	4.28374	−	2.47322i	0.172178	−	0.0994070i	−0.411434	−	0.911439i	$-0.634972\pi$
$619$	4.28374	−	2.47322i	0.172178	−	0.0994070i	0.583612	+	0.812032i	$0.301639\pi$
$620$			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	−0.239430	−	0.970914i	$-0.576960\pi$
$641$	12.1954	−	7.04105i	0.481691	−	0.278105i	0.721121	+	0.692809i	$0.243627\pi$
$642$	−14.0718	+	30.0478i	−0.555371	+	1.18589i
$643$	7.33157	+	4.23288i	0.289129	+	0.166929i	0.637549	−	0.770410i	$-0.279948\pi$
$643$	7.33157	+	4.23288i	0.289129	+	0.166929i	−0.348420	+	0.937339i	$0.613282\pi$
$644$		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	0.995515	−	0.0946029i	$-0.0301581\pi$
$653$	36.0653	+	20.8223i	1.41134	+	0.814840i	0.415829	+	0.909443i	$0.363491\pi$
$654$	−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	−0.666636	−	0.745383i	$-0.732267\pi$
$659$	−9.09866	+	5.25312i	−0.354434	+	0.204632i	0.312203	+	0.950016i	$0.398933\pi$
$660$	−0.798564	−	9.30413i	−0.0310841	−	0.362163i
$661$	−16.8988	−	9.75655i	−0.657289	−	0.379486i	0.133954	−	0.990987i	$-0.457232\pi$
$661$	−16.8988	−	9.75655i	−0.657289	−	0.379486i	−0.791243	+	0.611502i	$0.790566\pi$
$662$	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	0.800007	−	0.599990i	$-0.204829\pi$
$673$	−3.10277	−	5.37415i	−0.119603	−	0.207158i	−0.919610	+	0.392832i	$0.871495\pi$
$674$		−	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	0.523942	−	0.851754i	$-0.324461\pi$
$677$	−12.3765	−	21.4368i	−0.475669	−	0.823883i	−0.999612	+	0.0278703i	$0.991127\pi$
$678$	−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	$-0.867431\pi$
$683$		−	21.1448i		−	0.809083i	0.914520	−	0.404542i	$-0.132569\pi$
$684$	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	−0.390068	−	0.920786i	$-0.627549\pi$
$691$	5.58127	−	3.22235i	0.212322	−	0.122584i	0.602390	+	0.798202i	$0.294215\pi$
$692$	−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	$-0.846403\pi$
$701$		−	24.5717i		−	0.928061i	0.885819	−	0.464031i	$-0.153597\pi$
$702$	−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	−0.896950	−	0.442133i	$-0.854222\pi$
$709$	−22.1370	−	38.3424i	−0.831373	−	1.43998i	0.0655765	−	0.997848i	$-0.479111\pi$
$710$	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	0.184924	−	0.982753i	$-0.440796\pi$
$727$	30.4270	−	17.5670i	1.12848	−	0.651525i	0.943551	+	0.331227i	$0.107463\pi$
$728$		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	0.590145	−	0.807297i	$-0.299070\pi$
$733$	5.03789	+	2.90863i	0.186079	+	0.107433i	−0.404067	+	0.914729i	$0.632404\pi$
$734$	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	0.490003	−	0.871721i	$-0.336996\pi$
$743$	−0.543196	−	0.313615i	−0.0199279	−	0.0115054i	−0.509931	+	0.860215i	$0.670329\pi$
$744$	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	−0.903923	−	0.427695i	$-0.859326\pi$
$751$	−2.23529	+	3.87163i	−0.0815668	+	0.141278i	0.822356	+	0.568973i	$0.192659\pi$
$752$	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	−0.991136	−	0.132851i	$-0.957587\pi$
$761$	−10.4970	+	18.1813i	−0.380516	+	0.659073i	0.610620	+	0.791924i	$0.290920\pi$
$762$	−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	0.967511	−	0.252831i	$-0.0813616\pi$
$769$	34.1729	+	19.7298i	1.23231	+	0.711473i	0.264797	+	0.964304i	$0.414695\pi$
$770$		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	0.933586	−	0.358355i	$-0.116662\pi$
$787$	30.5793	+	17.6550i	1.09003	+	0.629332i	0.156449	+	0.987686i	$0.449995\pi$
$788$	−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	−0.644106	−	0.764936i	$-0.722771\pi$
$797$	9.60992	−	16.6449i	0.340401	−	0.589591i	0.984507	+	0.175344i	$0.0561039\pi$
$798$		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	$-0.757404\pi$
$809$		−	39.2779i		−	1.38094i	0.723362	−	0.690469i	$-0.242596\pi$
$810$	−5.63988	+	6.63210i	−0.198165	+	0.233028i
$811$		−	9.68436i		−	0.340064i	−0.985439	−	0.170032i	$-0.945613\pi$
$811$		−	9.68436i		−	0.340064i	0.985439	−	0.170032i	$-0.0543871\pi$
$812$		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	−0.679393	−	0.733775i	$-0.737757\pi$
$821$	−10.9919	+	6.34620i	−0.383621	+	0.221484i	0.295771	+	0.955259i	$0.404423\pi$
$822$	29.2237	−	2.50824i	1.01929	−	0.0874849i
$823$	−8.73837	+	15.1353i	−0.304600	+	0.527583i	−0.977172	−	0.212448i	$-0.931856\pi$
$823$	−8.73837	+	15.1353i	−0.304600	+	0.527583i	0.672572	+	0.740032i	$0.265190\pi$
$824$	−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	$-0.696036\pi$
$827$		−	46.9482i		−	1.63255i	0.577665	−	0.816274i	$-0.303964\pi$
$828$	−1.35641	−	7.84361i	−0.0471385	−	0.272584i
$829$		−	2.30706i		−	0.0801275i	−0.999197	−	0.0400637i	$-0.987244\pi$
$829$		−	2.30706i		−	0.0801275i	0.999197	−	0.0400637i	$-0.0127561\pi$
$830$	−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	0.974758	−	0.223264i	$-0.0716711\pi$
$839$	8.51664	+	14.7513i	0.294027	+	0.509270i	−0.680731	+	0.732533i	$0.738338\pi$
$840$		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	−0.450033	−	0.893012i	$-0.648588\pi$
$853$	2.87158	−	1.65791i	0.0983209	−	0.0567656i	0.548354	+	0.836246i	$0.315255\pi$
$854$		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	0.773528	−	0.633762i	$-0.218490\pi$
$857$	−4.74512	−	8.21879i	−0.162090	−	0.280748i	−0.935618	+	0.353014i	$0.885157\pi$
$858$	−38.0476	−	17.8182i	−1.29892	−	0.608304i
$859$	25.5104	+	14.7284i	0.870404	+	0.502528i	0.867482	−	0.497468i	$-0.165737\pi$
$859$	25.5104	+	14.7284i	0.870404	+	0.502528i	0.00292142	+	0.999996i	$0.499070\pi$
$860$	−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	$-0.914776\pi$
$863$		−	15.5434i		−	0.529105i	0.964371	−	0.264553i	$-0.0852243\pi$
$864$	−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	−0.171624	−	0.985163i	$-0.554901\pi$
$877$	22.7249	−	39.3606i	0.767364	−	1.32911i	0.938988	−	0.343950i	$-0.111765\pi$
$878$	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	−0.865517	−	0.500880i	$-0.833010\pi$
$887$	0.0302741	−	0.0524362i	0.00101650	−	0.00176064i	0.866533	+	0.499119i	$0.166343\pi$
$888$	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	0.593654	−	0.804720i	$-0.297685\pi$
$907$	−12.0490	−	20.8695i	−0.400081	−	0.692961i	−0.993735	+	0.111760i	$0.964351\pi$
$908$	−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	−0.0880873	−	0.996113i	$-0.528075\pi$
$911$	22.0494	−	12.7302i	0.730528	−	0.421771i	0.818615	+	0.574342i	$0.194742\pi$
$912$	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	0.527097	−	0.849805i	$-0.323280\pi$
$929$	−14.3986	−	24.9392i	−0.472404	−	0.818228i	−0.999501	+	0.0315768i	$0.989947\pi$
$930$	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	$-0.659631\pi$
$937$		−	53.6825i		−	1.75373i	0.480736	−	0.876865i	$-0.340369\pi$
$938$		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	−0.200509	−	0.979692i	$-0.564260\pi$
$941$	22.9511	−	39.7524i	0.748184	−	1.29589i	0.948693	−	0.316200i	$-0.102407\pi$
$942$	−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	−0.0344607	−	0.999406i	$-0.510971\pi$
$947$	25.0440	−	14.4591i	0.813820	−	0.469859i	0.848281	+	0.529547i	$0.177638\pi$
$948$	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	$-0.933150\pi$
$953$		−	12.8715i		−	0.416949i	0.978028	−	0.208475i	$-0.0668498\pi$
$954$	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	−0.811541	−	0.584295i	$-0.801371\pi$
$967$	3.11725	−	5.39923i	0.100244	−	0.173627i	0.911785	+	0.410668i	$0.134704\pi$
$968$	−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	0.0796807	−	0.996820i	$-0.474610\pi$
$977$	−23.2474	−	13.4219i	−0.743751	−	0.429405i	−0.823431	+	0.567416i	$0.807943\pi$
$978$	−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	0.945541	−	0.325502i	$-0.105533\pi$
$983$	5.98457	+	10.3656i	0.190878	+	0.330611i	−0.754663	+	0.656112i	$0.772200\pi$
$984$	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	−0.303771	−	0.952745i	$-0.598246\pi$
$997$	11.6653	−	6.73498i	0.369445	−	0.213299i	0.673216	+	0.739446i	$0.264912\pi$
$998$			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.293.6		16
3.2	odd	2		2646.2.m.b.881.2		16
7.2	even	3		882.2.t.a.815.4		16
7.3	odd	6		882.2.l.b.509.6		16
7.4	even	3		126.2.l.a.5.7	✓	16
7.5	odd	6		126.2.t.a.59.1	yes	16
7.6	odd	2		882.2.m.a.293.7		16
9.2	odd	6		882.2.m.a.587.7		16
9.7	even	3		2646.2.m.a.1763.3		16
21.2	odd	6		2646.2.t.b.2285.7		16
21.5	even	6		378.2.t.a.17.6		16
21.11	odd	6		378.2.l.a.341.2		16
21.17	even	6		2646.2.l.a.1097.3		16
21.20	even	2		2646.2.m.a.881.3		16
28.11	odd	6		1008.2.ca.c.257.5		16
28.19	even	6		1008.2.df.c.689.7		16
63.2	odd	6		882.2.l.b.227.2		16
63.4	even	3		1134.2.k.a.971.3		16
63.5	even	6		1134.2.k.a.647.3		16
63.11	odd	6		126.2.t.a.47.1	yes	16
63.16	even	3		2646.2.l.a.521.7		16
63.20	even	6	inner	882.2.m.b.587.6		16
63.25	even	3		378.2.t.a.89.6		16
63.32	odd	6		1134.2.k.b.971.6		16
63.34	odd	6		2646.2.m.b.1763.2		16
63.38	even	6		882.2.t.a.803.4		16
63.40	odd	6		1134.2.k.b.647.6		16
63.47	even	6		126.2.l.a.101.3	yes	16
63.52	odd	6		2646.2.t.b.1979.7		16
63.61	odd	6		378.2.l.a.143.6		16
84.11	even	6		3024.2.ca.c.2609.4		16
84.47	odd	6		3024.2.df.c.17.4		16
252.11	even	6		1008.2.df.c.929.7		16
252.47	odd	6		1008.2.ca.c.353.5		16
252.151	odd	6		3024.2.df.c.1601.4		16
252.187	even	6		3024.2.ca.c.2033.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.7	✓	16	7.4	even	3
126.2.l.a.101.3	yes	16	63.47	even	6
126.2.t.a.47.1	yes	16	63.11	odd	6
126.2.t.a.59.1	yes	16	7.5	odd	6
378.2.l.a.143.6		16	63.61	odd	6
378.2.l.a.341.2		16	21.11	odd	6
378.2.t.a.17.6		16	21.5	even	6
378.2.t.a.89.6		16	63.25	even	3
882.2.l.b.227.2		16	63.2	odd	6
882.2.l.b.509.6		16	7.3	odd	6
882.2.m.a.293.7		16	7.6	odd	2
882.2.m.a.587.7		16	9.2	odd	6
882.2.m.b.293.6		16	1.1	even	1	trivial
882.2.m.b.587.6		16	63.20	even	6	inner
882.2.t.a.803.4		16	63.38	even	6
882.2.t.a.815.4		16	7.2	even	3
1008.2.ca.c.257.5		16	28.11	odd	6
1008.2.ca.c.353.5		16	252.47	odd	6
1008.2.df.c.689.7		16	28.19	even	6
1008.2.df.c.929.7		16	252.11	even	6
1134.2.k.a.647.3		16	63.5	even	6
1134.2.k.a.971.3		16	63.4	even	3
1134.2.k.b.647.6		16	63.40	odd	6
1134.2.k.b.971.6		16	63.32	odd	6
2646.2.l.a.521.7		16	63.16	even	3
2646.2.l.a.1097.3		16	21.17	even	6
2646.2.m.a.881.3		16	21.20	even	2
2646.2.m.a.1763.3		16	9.7	even	3
2646.2.m.b.881.2		16	3.2	odd	2
2646.2.m.b.1763.2		16	63.34	odd	6
2646.2.t.b.1979.7		16	63.52	odd	6
2646.2.t.b.2285.7		16	21.2	odd	6
3024.2.ca.c.2033.4		16	252.187	even	6
3024.2.ca.c.2609.4		16	84.11	even	6
3024.2.df.c.17.4		16	84.47	odd	6
3024.2.df.c.1601.4		16	252.151	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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