LMFDB - Embedded newform 882.2.f.m.589.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(295,882)]

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([4, 0]))

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

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

chi := DirichletCharacter("882.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.f (of order $3$, 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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			589.2
Root			$0.500000 - 2.05195i$ of defining polynomial
Character	$\chi$	$=$	882.589
Dual form			882.2.f.m.295.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.933463 + 1.45899i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.230252 + 0.398809i) q^{5} +(0.796790 - 1.53790i) q^{6} +1.00000 q^{8} +(-1.25729 + 2.72382i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.933463 + 1.45899i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.230252 + 0.398809i) q^{5} +(0.796790 - 1.53790i) q^{6} +1.00000 q^{8} +(-1.25729 + 2.72382i) q^{9} +0.460505 q^{10} +(1.82383 + 3.15897i) q^{11} +(-1.73025 + 0.0789082i) q^{12} +(-0.730252 + 1.26483i) q^{13} +(-0.796790 + 0.0363376i) q^{15} +(-0.500000 - 0.866025i) q^{16} -3.73385 q^{17} +(2.98755 - 0.273062i) q^{18} -4.05408 q^{19} +(-0.230252 - 0.398809i) q^{20} +(1.82383 - 3.15897i) q^{22} +(-0.566537 + 0.981271i) q^{23} +(0.933463 + 1.45899i) q^{24} +(2.39397 + 4.14647i) q^{25} +1.46050 q^{26} +(-5.14766 + 0.708209i) q^{27} +(-4.48755 - 7.77266i) q^{29} +(0.429864 + 0.671871i) q^{30} +(-0.257295 + 0.445647i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.90642 + 5.60973i) q^{33} +(1.86693 + 3.23361i) q^{34} +(-1.73025 - 2.45076i) q^{36} +9.10817 q^{37} +(2.02704 + 3.51094i) q^{38} +(-2.52704 + 0.115246i) q^{39} +(-0.230252 + 0.398809i) q^{40} +(0.472958 - 0.819187i) q^{41} +(4.66372 + 8.07779i) q^{43} -3.64766 q^{44} +(-0.796790 - 1.12859i) q^{45} +1.13307 q^{46} +(1.16372 + 2.01561i) q^{47} +(0.796790 - 1.53790i) q^{48} +(2.39397 - 4.14647i) q^{50} +(-3.48541 - 5.44765i) q^{51} +(-0.730252 - 1.26483i) q^{52} -12.4356 q^{53} +(3.18716 + 4.10390i) q^{54} -1.67977 q^{55} +(-3.78434 - 5.91486i) q^{57} +(-4.48755 + 7.77266i) q^{58} +(-6.44805 + 11.1684i) q^{59} +(0.366926 - 0.708209i) q^{60} +(6.04163 + 10.4644i) q^{61} +0.514589 q^{62} +1.00000 q^{64} +(-0.336285 - 0.582462i) q^{65} +(6.31138 - 0.287831i) q^{66} +(1.16012 - 2.00938i) q^{67} +(1.86693 - 3.23361i) q^{68} +(-1.96050 + 0.0894089i) q^{69} +1.67977 q^{71} +(-1.25729 + 2.72382i) q^{72} -13.2412 q^{73} +(-4.55408 - 7.88791i) q^{74} +(-3.81498 + 7.36335i) q^{75} +(2.02704 - 3.51094i) q^{76} +(1.36333 + 2.13086i) q^{78} +(2.50360 + 4.33636i) q^{79} +0.460505 q^{80} +(-5.83842 - 6.84929i) q^{81} -0.945916 q^{82} +(-3.32383 - 5.75705i) q^{83} +(0.859728 - 1.48909i) q^{85} +(4.66372 - 8.07779i) q^{86} +(7.15126 - 13.8028i) q^{87} +(1.82383 + 3.15897i) q^{88} -2.72665 q^{89} +(-0.578990 + 1.25433i) q^{90} +(-0.566537 - 0.981271i) q^{92} +(-0.890369 + 0.0406053i) q^{93} +(1.16372 - 2.01561i) q^{94} +(0.933463 - 1.61680i) q^{95} +(-1.73025 + 0.0789082i) q^{96} +(5.59358 + 9.68836i) q^{97} +(-10.8976 + 0.996040i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 5 q^{5} + 2 q^{6} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 5 * q^5 + 2 * q^6 + 6 * q^8 + 8 * q^9	$ 6 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 5 q^{5} + 2 q^{6} + 6 q^{8} + 8 q^{9} - 10 q^{10} - q^{11} - 4 q^{12} + 2 q^{13} - 2 q^{15} - 3 q^{16} - 8 q^{17} - 4 q^{18} - 6 q^{19} + 5 q^{20} - q^{22} - 7 q^{23} + 2 q^{24} - 2 q^{25} - 4 q^{26} - 7 q^{27} - 5 q^{29} + 7 q^{30} + 14 q^{31} - 3 q^{32} - 23 q^{33} + 4 q^{34} - 4 q^{36} + 18 q^{37} + 3 q^{38} - 6 q^{39} + 5 q^{40} + 12 q^{41} + 18 q^{43} + 2 q^{44} - 2 q^{45} + 14 q^{46} - 3 q^{47} + 2 q^{48} - 2 q^{50} - 52 q^{51} + 2 q^{52} - 18 q^{53} + 8 q^{54} - 14 q^{55} + 2 q^{57} - 5 q^{58} - 4 q^{59} - 5 q^{60} - 4 q^{61} - 28 q^{62} + 6 q^{64} - 12 q^{65} + 4 q^{66} + 5 q^{67} + 4 q^{68} + q^{69} + 14 q^{71} + 8 q^{72} - 50 q^{73} - 9 q^{74} + 19 q^{75} + 3 q^{76} + 9 q^{78} + 7 q^{79} - 10 q^{80} + 8 q^{81} - 24 q^{82} - 8 q^{83} + 14 q^{85} + 18 q^{86} + 11 q^{87} - q^{88} - 18 q^{89} - 29 q^{90} - 7 q^{92} + 3 q^{93} - 3 q^{94} + 2 q^{95} - 4 q^{96} + 28 q^{97} - 41 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 5 * q^5 + 2 * q^6 + 6 * q^8 + 8 * q^9 - 10 * q^10 - q^11 - 4 * q^12 + 2 * q^13 - 2 * q^15 - 3 * q^16 - 8 * q^17 - 4 * q^18 - 6 * q^19 + 5 * q^20 - q^22 - 7 * q^23 + 2 * q^24 - 2 * q^25 - 4 * q^26 - 7 * q^27 - 5 * q^29 + 7 * q^30 + 14 * q^31 - 3 * q^32 - 23 * q^33 + 4 * q^34 - 4 * q^36 + 18 * q^37 + 3 * q^38 - 6 * q^39 + 5 * q^40 + 12 * q^41 + 18 * q^43 + 2 * q^44 - 2 * q^45 + 14 * q^46 - 3 * q^47 + 2 * q^48 - 2 * q^50 - 52 * q^51 + 2 * q^52 - 18 * q^53 + 8 * q^54 - 14 * q^55 + 2 * q^57 - 5 * q^58 - 4 * q^59 - 5 * q^60 - 4 * q^61 - 28 * q^62 + 6 * q^64 - 12 * q^65 + 4 * q^66 + 5 * q^67 + 4 * q^68 + q^69 + 14 * q^71 + 8 * q^72 - 50 * q^73 - 9 * q^74 + 19 * q^75 + 3 * q^76 + 9 * q^78 + 7 * q^79 - 10 * q^80 + 8 * q^81 - 24 * q^82 - 8 * q^83 + 14 * q^85 + 18 * q^86 + 11 * q^87 - q^88 - 18 * q^89 - 29 * q^90 - 7 * q^92 + 3 * q^93 - 3 * q^94 + 2 * q^95 - 4 * q^96 + 28 * q^97 - 41 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.933463	+	1.45899i	0.538935	+	0.842347i
$3$	0.933463	+	1.45899i	0.538935	+	0.842347i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.230252	+	0.398809i	−0.102972	+	0.178353i	−0.912908	−	0.408166i	$-0.866169\pi$
$5$	−0.230252	+	0.398809i	−0.102972	+	0.178353i	0.809936	+	0.586519i	$0.199502\pi$
$6$	0.796790	−	1.53790i	0.325288	−	0.627844i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−1.25729	+	2.72382i	−0.419098	+	0.907941i
$10$	0.460505			0.145624
$11$	1.82383	+	3.15897i	0.549906	+	0.952465i	0.998280	+	0.0586193i	$0.0186698\pi$
$11$	1.82383	+	3.15897i	0.549906	+	0.952465i	−0.448374	+	0.893846i	$0.647997\pi$
$12$	−1.73025	+	0.0789082i	−0.499481	+	0.0227788i
$13$	−0.730252	+	1.26483i	−0.202536	+	0.350802i	−0.949345	−	0.314236i	$-0.898252\pi$
$13$	−0.730252	+	1.26483i	−0.202536	+	0.350802i	0.746809	+	0.665038i	$0.231585\pi$
$14$		0			0
$15$	−0.796790	+	0.0363376i	−0.205730	+	0.00938234i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.73385			−0.905592			−0.452796	−	0.891614i	$-0.649573\pi$
$17$	−3.73385			−0.905592			−0.452796	+	0.891614i	$0.649573\pi$
$18$	2.98755	−	0.273062i	0.704172	−	0.0643614i
$19$	−4.05408			−0.930071			−0.465035	−	0.885292i	$-0.653958\pi$
$19$	−4.05408			−0.930071			−0.465035	+	0.885292i	$0.653958\pi$
$20$	−0.230252	−	0.398809i	−0.0514860	−	0.0891764i
$21$		0			0
$22$	1.82383	−	3.15897i	0.388842	−	0.673495i
$23$	−0.566537	+	0.981271i	−0.118131	+	0.204609i	−0.919027	−	0.394194i	$-0.871024\pi$
$23$	−0.566537	+	0.981271i	−0.118131	+	0.204609i	0.800896	+	0.598804i	$0.204357\pi$
$24$	0.933463	+	1.45899i	0.190542	+	0.297815i
$25$	2.39397	+	4.14647i	0.478794	+	0.829295i
$26$	1.46050			0.286429
$27$	−5.14766	+	0.708209i	−0.990668	+	0.136295i
$28$		0			0
$29$	−4.48755	−	7.77266i	−0.833317	−	1.44335i	−0.895394	−	0.445275i	$-0.853106\pi$
$29$	−4.48755	−	7.77266i	−0.833317	−	1.44335i	0.0620772	−	0.998071i	$-0.480228\pi$
$30$	0.429864	+	0.671871i	0.0784821	+	0.122666i
$31$	−0.257295	+	0.445647i	−0.0462115	+	0.0800406i	−0.888206	−	0.459446i	$-0.848048\pi$
$31$	−0.257295	+	0.445647i	−0.0462115	+	0.0800406i	0.841994	+	0.539486i	$0.181381\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.90642	+	5.60973i	−0.505943	+	0.976529i
$34$	1.86693	+	3.23361i	0.320175	+	0.554560i
$35$		0			0
$36$	−1.73025	−	2.45076i	−0.288375	−	0.408460i
$37$	9.10817			1.49737			0.748687	−	0.662924i	$-0.230685\pi$
$37$	9.10817			1.49737			0.748687	+	0.662924i	$0.230685\pi$
$38$	2.02704	+	3.51094i	0.328830	+	0.569550i
$39$	−2.52704	+	0.115246i	−0.404651	+	0.0184541i
$40$	−0.230252	+	0.398809i	−0.0364061	+	0.0630572i
$41$	0.472958	−	0.819187i	0.0738636	−	0.127936i	−0.826728	−	0.562602i	$-0.809800\pi$
$41$	0.472958	−	0.819187i	0.0738636	−	0.127936i	0.900592	+	0.434666i	$0.143134\pi$
$42$		0			0
$43$	4.66372	+	8.07779i	0.711210	+	1.23185i	0.964403	+	0.264436i	$0.0851858\pi$
$43$	4.66372	+	8.07779i	0.711210	+	1.23185i	−0.253193	+	0.967416i	$0.581481\pi$
$44$	−3.64766			−0.549906
$45$	−0.796790	−	1.12859i	−0.118778	−	0.168240i
$46$	1.13307			0.167063
$47$	1.16372	+	2.01561i	0.169745	+	0.294007i	0.938330	−	0.345740i	$-0.112372\pi$
$47$	1.16372	+	2.01561i	0.169745	+	0.294007i	−0.768585	+	0.639748i	$0.779039\pi$
$48$	0.796790	−	1.53790i	0.115007	−	0.221976i
$49$		0			0
$50$	2.39397	−	4.14647i	0.338558	−	0.586400i
$51$	−3.48541	−	5.44765i	−0.488055	−	0.762823i
$52$	−0.730252	−	1.26483i	−0.101268	−	0.175401i
$53$	−12.4356			−1.70816			−0.854080	−	0.520141i	$-0.825879\pi$
$53$	−12.4356			−1.70816			−0.854080	+	0.520141i	$0.825879\pi$
$54$	3.18716	+	4.10390i	0.433717	+	0.558470i
$55$	−1.67977			−0.226500
$56$		0			0
$57$	−3.78434	−	5.91486i	−0.501248	−	0.783443i
$58$	−4.48755	+	7.77266i	−0.589244	+	1.02060i
$59$	−6.44805	+	11.1684i	−0.839465	+	1.45400i	0.0508779	+	0.998705i	$0.483798\pi$
$59$	−6.44805	+	11.1684i	−0.839465	+	1.45400i	−0.890343	+	0.455291i	$0.849535\pi$
$60$	0.366926	−	0.708209i	0.0473699	−	0.0914294i
$61$	6.04163	+	10.4644i	0.773552	+	1.33983i	0.935605	+	0.353049i	$0.114855\pi$
$61$	6.04163	+	10.4644i	0.773552	+	1.33983i	−0.162053	+	0.986782i	$0.551812\pi$
$62$	0.514589			0.0653529
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.336285	−	0.582462i	−0.0417110	−	0.0722456i
$66$	6.31138	−	0.287831i	0.776877	−	0.0354295i
$67$	1.16012	−	2.00938i	0.141731	−	0.245485i	−0.786418	−	0.617695i	$-0.788067\pi$
$67$	1.16012	−	2.00938i	0.141731	−	0.245485i	0.928148	+	0.372210i	$0.121400\pi$
$68$	1.86693	−	3.23361i	0.226398	−	0.392133i
$69$	−1.96050	+	0.0894089i	−0.236017	+	0.0107636i
$70$		0			0
$71$	1.67977			0.199352			0.0996758	−	0.995020i	$-0.468219\pi$
$71$	1.67977			0.199352			0.0996758	+	0.995020i	$0.468219\pi$
$72$	−1.25729	+	2.72382i	−0.148174	+	0.321006i
$73$	−13.2412			−1.54977			−0.774885	−	0.632102i	$-0.782192\pi$
$73$	−13.2412			−1.54977			−0.774885	+	0.632102i	$0.782192\pi$
$74$	−4.55408	−	7.88791i	−0.529402	−	0.916950i
$75$	−3.81498	+	7.36335i	−0.440516	+	0.850246i
$76$	2.02704	−	3.51094i	0.232518	−	0.402732i
$77$		0			0
$78$	1.36333	+	2.13086i	0.154366	+	0.241272i
$79$	2.50360	+	4.33636i	0.281677	+	0.487879i	0.971798	−	0.235815i	$-0.0757761\pi$
$79$	2.50360	+	4.33636i	0.281677	+	0.487879i	−0.690121	+	0.723694i	$0.742443\pi$
$80$	0.460505			0.0514860
$81$	−5.83842	−	6.84929i	−0.648713	−	0.761033i
$82$	−0.945916			−0.104459
$83$	−3.32383	−	5.75705i	−0.364838	−	0.631918i	0.623912	−	0.781494i	$-0.285542\pi$
$83$	−3.32383	−	5.75705i	−0.364838	−	0.631918i	−0.988750	+	0.149577i	$0.952209\pi$
$84$		0			0
$85$	0.859728	−	1.48909i	0.0932506	−	0.161515i
$86$	4.66372	−	8.07779i	0.502901	−	0.871051i
$87$	7.15126	−	13.8028i	0.766696	−	1.47981i
$88$	1.82383	+	3.15897i	0.194421	+	0.336747i
$89$	−2.72665			−0.289025			−0.144512	−	0.989503i	$-0.546161\pi$
$89$	−2.72665			−0.289025			−0.144512	+	0.989503i	$0.546161\pi$
$90$	−0.578990	+	1.25433i	−0.0610309	+	0.132218i
$91$		0			0
$92$	−0.566537	−	0.981271i	−0.0590656	−	0.102305i
$93$	−0.890369	+	0.0406053i	−0.0923270	+	0.00421058i
$94$	1.16372	−	2.01561i	0.120028	−	0.207895i
$95$	0.933463	−	1.61680i	0.0957713	−	0.165881i
$96$	−1.73025	+	0.0789082i	−0.176593	+	0.00805354i
$97$	5.59358	+	9.68836i	0.567942	+	0.983704i	0.996769	+	0.0803178i	$0.0255935\pi$
$97$	5.59358	+	9.68836i	0.567942	+	0.983704i	−0.428827	+	0.903386i	$0.641073\pi$
$98$		0			0
$99$	−10.8976	+	0.996040i	−1.09525	+	0.100106i
$100$	−4.78794			−0.478794
$101$	6.87792	+	11.9129i	0.684378	+	1.18538i	0.973632	+	0.228125i	$0.0732596\pi$
$101$	6.87792	+	11.9129i	0.684378	+	1.18538i	−0.289254	+	0.957253i	$0.593407\pi$
$102$	−2.97509	+	5.74228i	−0.294578	+	0.568570i
$103$	5.58113	−	9.66679i	0.549925	−	0.952498i	−0.448354	−	0.893856i	$-0.647990\pi$
$103$	5.58113	−	9.66679i	0.549925	−	0.952498i	0.998279	−	0.0586417i	$-0.0186769\pi$
$104$	−0.730252	+	1.26483i	−0.0716071	+	0.124027i
$105$		0			0
$106$	6.21780	+	10.7695i	0.603926	+	1.04603i
$107$	7.78074			0.752192			0.376096	−	0.926581i	$-0.377266\pi$
$107$	7.78074			0.752192			0.376096	+	0.926581i	$0.377266\pi$
$108$	1.96050	−	4.81211i	0.188650	−	0.463046i
$109$	7.51459			0.719767			0.359884	−	0.932997i	$-0.382816\pi$
$109$	7.51459			0.719767			0.359884	+	0.932997i	$0.382816\pi$
$110$	0.839883	+	1.45472i	0.0800797	+	0.138702i
$111$	8.50214	+	13.2887i	0.806987	+	1.26131i
$112$		0			0
$113$	3.03064	−	5.24922i	0.285099	−	0.493805i	−0.687534	−	0.726152i	$-0.741307\pi$
$113$	3.03064	−	5.24922i	0.285099	−	0.493805i	0.972633	+	0.232346i	$0.0746403\pi$
$114$	−3.23025	+	6.23476i	−0.302541	+	0.583939i
$115$	−0.260893	−	0.451880i	−0.0243284	−	0.0421380i
$116$	8.97509			0.833317
$117$	−2.52704	−	3.57935i	−0.233625	−	0.330911i
$118$	12.8961			1.18718
$119$		0			0
$120$	−0.796790	+	0.0363376i	−0.0727366	+	0.00331716i
$121$	−1.15272	+	1.99658i	−0.104793	+	0.181507i
$122$	6.04163	−	10.4644i	0.546984	−	0.947403i
$123$	1.63667	−	0.0746406i	0.147574	−	0.00673011i
$124$	−0.257295	−	0.445647i	−0.0231057	−	0.0400203i
$125$	−4.50739			−0.403153
$126$		0			0
$127$	8.80992			0.781754			0.390877	−	0.920443i	$-0.372172\pi$
$127$	8.80992			0.781754			0.390877	+	0.920443i	$0.372172\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−7.43200	+	14.3446i	−0.654351	+	1.26297i
$130$	−0.336285	+	0.582462i	−0.0294941	+	0.0510853i
$131$	10.5687	−	18.3055i	0.923389	−	1.59936i	0.129258	−	0.991611i	$-0.458740\pi$
$131$	10.5687	−	18.3055i	0.923389	−	1.59936i	0.794131	−	0.607746i	$-0.207926\pi$
$132$	−3.40496	−	5.32190i	−0.296364	−	0.463212i
$133$		0			0
$134$	−2.32023			−0.200438
$135$	0.902822	−	2.21600i	0.0777025	−	0.190723i
$136$	−3.73385			−0.320175
$137$	2.20321	+	3.81607i	0.188233	+	0.326029i	0.944661	−	0.328048i	$-0.106391\pi$
$137$	2.20321	+	3.81607i	0.188233	+	0.326029i	−0.756428	+	0.654077i	$0.773057\pi$
$138$	1.05768	+	1.65314i	0.0900359	+	0.140725i
$139$	1.01245	−	1.75362i	0.0858751	−	0.148740i	−0.819889	−	0.572523i	$-0.805965\pi$
$139$	1.01245	−	1.75362i	0.0858751	−	0.148740i	0.905764	+	0.423783i	$0.139298\pi$
$140$		0			0
$141$	−1.85447	+	3.57935i	−0.156175	+	0.301435i
$142$	−0.839883	−	1.45472i	−0.0704815	−	0.122077i
$143$	−5.32743			−0.445502
$144$	2.98755	−	0.273062i	0.248962	−	0.0227552i
$145$	4.13307			0.343233
$146$	6.62062	+	11.4673i	0.547927	+	0.949037i
$147$		0			0
$148$	−4.55408	+	7.88791i	−0.374343	+	0.648382i
$149$	4.58113	−	7.93474i	0.375300	−	0.650040i	−0.615071	−	0.788471i	$-0.710873\pi$
$149$	4.58113	−	7.93474i	0.375300	−	0.650040i	0.990372	+	0.138432i	$0.0442062\pi$
$150$	8.28434	−	0.377808i	0.676413	−	0.0308479i
$151$	0.0519482	+	0.0899768i	0.00422748	+	0.00732221i	0.868131	−	0.496334i	$-0.165321\pi$
$151$	0.0519482	+	0.0899768i	0.00422748	+	0.00732221i	−0.863904	+	0.503657i	$0.831988\pi$
$152$	−4.05408			−0.328830
$153$	4.69455	−	10.1703i	0.379532	−	0.822224i
$154$		0			0
$155$	−0.118485	−	0.205223i	−0.00951698	−	0.0164839i
$156$	1.16372	−	2.24611i	0.0931718	−	0.179832i
$157$	10.4911	−	18.1712i	0.837285	−	1.45022i	−0.0548721	−	0.998493i	$-0.517475\pi$
$157$	10.4911	−	18.1712i	0.837285	−	1.45022i	0.892157	−	0.451726i	$-0.149192\pi$
$158$	2.50360	−	4.33636i	0.199176	−	0.344982i
$159$	−11.6082	−	18.1434i	−0.920588	−	1.43886i
$160$	−0.230252	−	0.398809i	−0.0182031	−	0.0315286i
$161$		0			0
$162$	−3.01245	+	8.48087i	−0.236681	+	0.666320i
$163$	23.0364			1.80435			0.902174	−	0.431372i	$-0.141970\pi$
$163$	23.0364			1.80435			0.902174	+	0.431372i	$0.141970\pi$
$164$	0.472958	+	0.819187i	0.0369318	+	0.0639678i
$165$	−1.56800	−	2.45076i	−0.122069	−	0.190791i
$166$	−3.32383	+	5.75705i	−0.257979	+	0.446833i
$167$	5.31498	−	9.20581i	0.411285	−	0.712367i	−0.583745	−	0.811937i	$-0.698413\pi$
$167$	5.31498	−	9.20581i	0.411285	−	0.712367i	0.995031	+	0.0995698i	$0.0317467\pi$
$168$		0			0
$169$	5.43346	+	9.41103i	0.417959	+	0.723926i
$170$	−1.71946			−0.131876
$171$	5.09718	−	11.0426i	0.389791	−	0.844449i
$172$	−9.32743			−0.711210
$173$	1.46936	+	2.54500i	0.111713	+	0.193493i	0.916461	−	0.400124i	$-0.131033\pi$
$173$	1.46936	+	2.54500i	0.111713	+	0.193493i	−0.804748	+	0.593617i	$0.797699\pi$
$174$	−15.5292	+	0.708209i	−1.17726	+	0.0536892i
$175$		0			0
$176$	1.82383	−	3.15897i	0.137476	−	0.238116i
$177$	−22.3135	+	1.01761i	−1.67719	+	0.0764882i
$178$	1.36333	+	2.36135i	0.102186	+	0.176991i
$179$	9.16225			0.684819			0.342409	−	0.939551i	$-0.388757\pi$
$179$	9.16225			0.684819			0.342409	+	0.939551i	$0.388757\pi$
$180$	1.37578	−	0.125747i	0.102545	−	0.00937259i
$181$	−22.4284			−1.66709			−0.833545	−	0.552452i	$-0.813692\pi$
$181$	−22.4284			−1.66709			−0.833545	+	0.552452i	$0.813692\pi$
$182$		0			0
$183$	−9.62782	+	18.5828i	−0.711709	+	1.37368i
$184$	−0.566537	+	0.981271i	−0.0417657	+	0.0723403i
$185$	−2.09718	+	3.63242i	−0.154188	+	0.267061i
$186$	0.480350	+	0.750780i	0.0352210	+	0.0550498i
$187$	−6.80992	−	11.7951i	−0.497990	−	0.862545i
$188$	−2.32743			−0.169745
$189$		0			0
$190$	−1.86693			−0.135441
$191$	−1.24484	−	2.15613i	−0.0900736	−	0.156012i	0.817468	−	0.575974i	$-0.195377\pi$
$191$	−1.24484	−	2.15613i	−0.0900736	−	0.156012i	−0.907542	+	0.419962i	$0.862044\pi$
$192$	0.933463	+	1.45899i	0.0673669	+	0.105293i
$193$	−2.24484	+	3.88818i	−0.161587	+	0.279877i	−0.935438	−	0.353491i	$-0.884995\pi$
$193$	−2.24484	+	3.88818i	−0.161587	+	0.279877i	0.773851	+	0.633368i	$0.218328\pi$
$194$	5.59358	−	9.68836i	0.401596	−	0.695584i
$195$	0.535897	−	1.03434i	0.0383763	−	0.0740708i
$196$		0			0
$197$	12.7339			0.907249			0.453625	−	0.891193i	$-0.350131\pi$
$197$	12.7339			0.907249			0.453625	+	0.891193i	$0.350131\pi$
$198$	6.31138	+	8.93955i	0.448530	+	0.635306i
$199$	−2.94592			−0.208830			−0.104415	−	0.994534i	$-0.533297\pi$
$199$	−2.94592			−0.208830			−0.104415	+	0.994534i	$0.533297\pi$
$200$	2.39397	+	4.14647i	0.169279	+	0.293200i
$201$	4.01459	−	0.183086i	0.283167	−	0.0129139i
$202$	6.87792	−	11.9129i	0.483928	−	0.838189i
$203$		0			0
$204$	6.46050	−	0.294632i	0.452326	−	0.0206283i
$205$	0.217799	+	0.377240i	0.0152118	+	0.0263476i
$206$	−11.1623			−0.777711
$207$	−1.96050	−	2.77689i	−0.136265	−	0.193007i
$208$	1.46050			0.101268
$209$	−7.39397	−	12.8067i	−0.511451	−	0.885860i
$210$		0			0
$211$	−0.608168	+	1.05338i	−0.0418680	+	0.0725176i	−0.886200	−	0.463303i	$-0.846664\pi$
$211$	−0.608168	+	1.05338i	−0.0418680	+	0.0725176i	0.844332	+	0.535820i	$0.179998\pi$
$212$	6.21780	−	10.7695i	0.427040	−	0.739655i
$213$	1.56800	+	2.45076i	0.107438	+	0.167923i
$214$	−3.89037	−	6.73832i	−0.265940	−	0.460622i
$215$	−4.29533			−0.292939
$216$	−5.14766	+	0.708209i	−0.350254	+	0.0481875i
$217$		0			0
$218$	−3.75729	−	6.50783i	−0.254476	−	0.440766i
$219$	−12.3602	−	19.3188i	−0.835225	−	1.30544i
$220$	0.839883	−	1.45472i	0.0566249	−	0.0980773i
$221$	2.72665	−	4.72270i	0.183415	−	0.317683i
$222$	7.25729	−	14.0074i	0.487078	−	0.940117i
$223$	0.445916	+	0.772349i	0.0298607	+	0.0517203i	0.880570	−	0.473917i	$-0.157160\pi$
$223$	0.445916	+	0.772349i	0.0298607	+	0.0517203i	−0.850709	+	0.525637i	$0.823827\pi$
$224$		0			0
$225$	−14.3042	+	1.30740i	−0.953612	+	0.0871603i
$226$	−6.06128			−0.403190
$227$	−7.32597	−	12.6889i	−0.486242	−	0.842195i	0.513633	−	0.858010i	$-0.328299\pi$
$227$	−7.32597	−	12.6889i	−0.486242	−	0.842195i	−0.999875	+	0.0158147i	$0.994966\pi$
$228$	7.01459	−	0.319901i	0.464553	−	0.0211859i
$229$	−4.78794	+	8.29295i	−0.316396	+	0.548013i	−0.979733	−	0.200307i	$-0.935806\pi$
$229$	−4.78794	+	8.29295i	−0.316396	+	0.548013i	0.663338	+	0.748320i	$0.269139\pi$
$230$	−0.260893	+	0.451880i	−0.0172028	+	0.0297961i
$231$		0			0
$232$	−4.48755	−	7.77266i	−0.294622	−	0.510300i
$233$	−14.4284			−0.945236			−0.472618	−	0.881267i	$-0.656691\pi$
$233$	−14.4284			−0.945236			−0.472618	+	0.881267i	$0.656691\pi$
$234$	−1.83628	+	3.97816i	−0.120042	+	0.260060i
$235$	−1.07179			−0.0699161
$236$	−6.44805	−	11.1684i	−0.419732	−	0.726998i
$237$	−3.98968	+	7.70055i	−0.259158	+	0.500205i
$238$		0			0
$239$	−9.15486	+	15.8567i	−0.592179	+	1.02568i	0.401760	+	0.915745i	$0.368399\pi$
$239$	−9.15486	+	15.8567i	−0.592179	+	1.02568i	−0.993938	+	0.109938i	$0.964935\pi$
$240$	0.429864	+	0.671871i	0.0277476	+	0.0433691i
$241$	0.0466924	+	0.0808735i	0.00300772	+	0.00520952i	0.867525	−	0.497393i	$-0.165709\pi$
$241$	0.0466924	+	0.0808735i	0.00300772	+	0.00520952i	−0.864518	+	0.502602i	$0.832376\pi$
$242$	2.30545			0.148200
$243$	4.54309	−	14.9118i	0.291440	−	0.956589i
$244$	−12.0833			−0.773552
$245$		0			0
$246$	−0.882977	−	1.38008i	−0.0562966	−	0.0879907i
$247$	2.96050	−	5.12774i	0.188372	−	0.326271i
$248$	−0.257295	+	0.445647i	−0.0163382	+	0.0282986i
$249$	5.29679	−	10.2234i	0.335670	−	0.647883i
$250$	2.25370	+	3.90352i	0.142536	+	0.246880i
$251$	18.2733			1.15340			0.576702	−	0.816955i	$-0.304339\pi$
$251$	18.2733			1.15340			0.576702	+	0.816955i	$0.304339\pi$
$252$		0			0
$253$	−4.13307			−0.259844
$254$	−4.40496	−	7.62961i	−0.276392	−	0.478724i
$255$	2.97509	−	0.135679i	0.186308	−	0.00849657i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.5256	+	18.2308i	−0.656568	+	1.13721i	0.324931	+	0.945738i	$0.394659\pi$
$257$	−10.5256	+	18.2308i	−0.656568	+	1.13721i	−0.981498	+	0.191471i	$0.938674\pi$
$258$	16.1388	−	0.736011i	1.00476	−	0.0458221i
$259$		0			0
$260$	0.672570			0.0417110
$261$	26.8135	−	2.45076i	1.65971	−	0.151698i
$262$	−21.1373			−1.30587
$263$	2.58259	+	4.47318i	0.159249	+	0.275828i	0.934598	−	0.355705i	$-0.115759\pi$
$263$	2.58259	+	4.47318i	0.159249	+	0.275828i	−0.775349	+	0.631533i	$0.782426\pi$
$264$	−2.90642	+	5.60973i	−0.178878	+	0.345255i
$265$	2.86333	−	4.95943i	0.175893	−	0.304655i
$266$		0			0
$267$	−2.54523	−	3.97816i	−0.155766	−	0.243459i
$268$	1.16012	+	2.00938i	0.0708654	+	0.122742i
$269$	16.8568			1.02778			0.513889	−	0.857857i	$-0.328204\pi$
$269$	16.8568			1.02778			0.513889	+	0.857857i	$0.328204\pi$
$270$	−2.37052	+	0.326134i	−0.144266	+	0.0198479i
$271$	25.1124			1.52547			0.762736	−	0.646710i	$-0.223856\pi$
$271$	25.1124			1.52547			0.762736	+	0.646710i	$0.223856\pi$
$272$	1.86693	+	3.23361i	0.113199	+	0.196066i
$273$		0			0
$274$	2.20321	−	3.81607i	0.133101	−	0.230537i
$275$	−8.73239	+	15.1249i	−0.526583	+	0.912068i
$276$	0.902822	−	1.74255i	0.0543435	−	0.104889i
$277$	−1.69076	−	2.92848i	−0.101588	−	0.175955i	0.810751	−	0.585391i	$-0.199059\pi$
$277$	−1.69076	−	2.92848i	−0.101588	−	0.175955i	−0.912339	+	0.409436i	$0.865726\pi$
$278$	−2.02491			−0.121446
$279$	−0.890369	−	1.26113i	−0.0533050	−	0.0755022i
$280$		0			0
$281$	−10.1388	−	17.5609i	−0.604831	−	1.04760i	−0.992078	−	0.125622i	$-0.959907\pi$
$281$	−10.1388	−	17.5609i	−0.604831	−	1.04760i	0.387248	−	0.921976i	$-0.373426\pi$
$282$	4.02704	−	0.183653i	0.239807	−	0.0109364i
$283$	8.67471	−	15.0250i	0.515658	−	0.893145i	−0.484177	−	0.874970i	$-0.660881\pi$
$283$	8.67471	−	15.0250i	0.515658	−	0.893145i	0.999835	−	0.0181754i	$-0.00578571\pi$
$284$	−0.839883	+	1.45472i	−0.0498379	+	0.0863218i
$285$	3.23025	−	0.147316i	0.191344	−	0.00872624i
$286$	2.66372	+	4.61369i	0.157509	+	0.272813i
$287$		0			0
$288$	−1.73025	−	2.45076i	−0.101956	−	0.144412i
$289$	−3.05836			−0.179903
$290$	−2.06654	−	3.57935i	−0.121351	−	0.210187i
$291$	−8.91381	+	17.2047i	−0.522537	+	1.00856i
$292$	6.62062	−	11.4673i	0.387443	−	0.671070i
$293$	4.93560	−	8.54871i	0.288341	−	0.499421i	−0.685073	−	0.728474i	$-0.740230\pi$
$293$	4.93560	−	8.54871i	0.288341	−	0.499421i	0.973414	+	0.229054i	$0.0735631\pi$
$294$		0			0
$295$	−2.96936	−	5.14308i	−0.172883	−	0.299442i
$296$	9.10817			0.529402
$297$	−11.6257	−	14.9697i	−0.674591	−	0.868628i
$298$	−9.16225			−0.530755
$299$	−0.827430	−	1.43315i	−0.0478515	−	0.0828813i
$300$	−4.46936	−	6.98554i	−0.258039	−	0.403310i
$301$		0			0
$302$	0.0519482	−	0.0899768i	0.00298928	−	0.00517759i
$303$	−10.9605	+	21.1550i	−0.629665	+	1.21533i
$304$	2.02704	+	3.51094i	0.116259	+	0.201366i
$305$	−5.56440			−0.318617
$306$	−11.1551	+	1.01957i	−0.637692	+	0.0582852i
$307$	−7.78794			−0.444481			−0.222240	−	0.974992i	$-0.571337\pi$
$307$	−7.78794			−0.444481			−0.222240	+	0.974992i	$0.571337\pi$
$308$		0			0
$309$	19.3135	−	0.880794i	1.09871	−	0.0501066i
$310$	−0.118485	+	0.205223i	−0.00672952	+	0.0116559i
$311$	7.70535	−	13.3461i	0.436930	−	0.756785i	−0.560521	−	0.828140i	$-0.689399\pi$
$311$	7.70535	−	13.3461i	0.436930	−	0.756785i	0.997451	+	0.0713552i	$0.0227324\pi$
$312$	−2.52704	+	0.115246i	−0.143066	+	0.00652451i
$313$	4.24844	+	7.35851i	0.240136	+	0.415928i	0.960753	−	0.277406i	$-0.0894746\pi$
$313$	4.24844	+	7.35851i	0.240136	+	0.415928i	−0.720617	+	0.693334i	$0.756141\pi$
$314$	−20.9823			−1.18410
$315$		0			0
$316$	−5.00720			−0.281677
$317$	7.05262	+	12.2155i	0.396115	+	0.686091i	0.993243	−	0.116055i	$-0.0370249\pi$
$317$	7.05262	+	12.2155i	0.396115	+	0.686091i	−0.597128	+	0.802146i	$0.703692\pi$
$318$	−9.90856	+	19.1247i	−0.555644	+	1.07246i
$319$	16.3691	−	28.3520i	0.916491	−	1.58741i
$320$	−0.230252	+	0.398809i	−0.0128715	+	0.0222941i
$321$	7.26303	+	11.3520i	0.405383	+	0.633607i
$322$		0			0
$323$	15.1373			0.842264
$324$	8.85087	−	1.63157i	0.491715	−	0.0906430i
$325$	−6.99280			−0.387891
$326$	−11.5182	−	19.9501i	−0.637933	−	1.10493i
$327$	7.01459	+	10.9637i	0.387908	+	0.606294i
$328$	0.472958	−	0.819187i	0.0261147	−	0.0452320i
$329$		0			0
$330$	−1.33842	+	2.58331i	−0.0736776	+	0.142206i
$331$	−13.7719	−	23.8536i	−0.756971	−	1.31111i	−0.944388	−	0.328832i	$-0.893345\pi$
$331$	−13.7719	−	23.8536i	−0.756971	−	1.31111i	0.187417	−	0.982280i	$-0.439988\pi$
$332$	6.64766			0.364838
$333$	−11.4517	+	24.8090i	−0.627547	+	1.35953i
$334$	−10.6300			−0.581645
$335$	0.534239	+	0.925330i	0.0291886	+	0.0505562i
$336$		0			0
$337$	0.748440	−	1.29634i	0.0407701	−	0.0706159i	−0.844920	−	0.534892i	$-0.820352\pi$
$337$	0.748440	−	1.29634i	0.0407701	−	0.0706159i	0.885690	+	0.464276i	$0.153686\pi$
$338$	5.43346	−	9.41103i	0.295541	−	0.511893i
$339$	10.4875	−	0.478285i	0.569605	−	0.0259769i
$340$	0.859728	+	1.48909i	0.0466253	+	0.0807574i
$341$	−1.87705			−0.101648
$342$	−12.1118	+	1.10702i	−0.654929	+	0.0598607i
$343$		0			0
$344$	4.66372	+	8.07779i	0.251451	+	0.435525i
$345$	0.415754	−	0.802453i	0.0223834	−	0.0432026i
$346$	1.46936	−	2.54500i	0.0789932	−	0.136820i
$347$	9.14406	−	15.8380i	0.490879	−	0.850228i	−0.509066	−	0.860728i	$-0.670009\pi$
$347$	9.14406	−	15.8380i	0.490879	−	0.850228i	0.999945	+	0.0105001i	$0.00334233\pi$
$348$	8.37792	+	13.0946i	0.449103	+	0.701942i
$349$	3.90136	+	6.75735i	0.208835	+	0.361713i	0.951348	−	0.308119i	$-0.0996995\pi$
$349$	3.90136	+	6.75735i	0.208835	+	0.361713i	−0.742513	+	0.669832i	$0.766366\pi$
$350$		0			0
$351$	2.86333	−	7.02811i	0.152833	−	0.375133i
$352$	−3.64766			−0.194421
$353$	13.4626	+	23.3180i	0.716544	+	1.24109i	0.962361	+	0.271774i	$0.0876105\pi$
$353$	13.4626	+	23.3180i	0.716544	+	1.24109i	−0.245817	+	0.969316i	$0.579056\pi$
$354$	12.0380	+	18.8153i	0.639814	+	1.00002i
$355$	−0.386770	+	0.669906i	−0.0205276	+	0.0355549i
$356$	1.36333	−	2.36135i	0.0722562	−	0.125151i
$357$		0			0
$358$	−4.58113	−	7.93474i	−0.242120	−	0.419364i
$359$	6.26322			0.330560			0.165280	−	0.986247i	$-0.447147\pi$
$359$	6.26322			0.330560			0.165280	+	0.986247i	$0.447147\pi$
$360$	−0.796790	−	1.12859i	−0.0419945	−	0.0594818i
$361$	−2.56440			−0.134968
$362$	11.2142	+	19.4236i	0.589405	+	1.02088i
$363$	−3.98901	+	0.181919i	−0.209369	+	0.00954827i
$364$		0			0
$365$	3.04883	−	5.28073i	0.159583	−	0.276406i
$366$	20.9071	−	0.953469i	1.09283	−	0.0498386i
$367$	14.6367	+	25.3515i	0.764028	+	1.32334i	0.940759	+	0.339076i	$0.110114\pi$
$367$	14.6367	+	25.3515i	0.764028	+	1.32334i	−0.176731	+	0.984259i	$0.556552\pi$
$368$	1.13307			0.0590656
$369$	1.63667	+	2.31821i	0.0852018	+	0.120681i
$370$	4.19436			0.218054
$371$		0			0
$372$	0.410019	−	0.791385i	0.0212585	−	0.0410314i
$373$	−8.92986	+	15.4670i	−0.462371	+	0.800850i	−0.999079	−	0.0429184i	$-0.986334\pi$
$373$	−8.92986	+	15.4670i	−0.462371	+	0.800850i	0.536708	+	0.843768i	$0.319668\pi$
$374$	−6.80992	+	11.7951i	−0.352132	+	0.609911i
$375$	−4.20748	−	6.57623i	−0.217273	−	0.339595i
$376$	1.16372	+	2.01561i	0.0600140	+	0.103947i
$377$	13.1082			0.675105
$378$		0			0
$379$	−22.4255			−1.15192			−0.575960	−	0.817478i	$-0.695371\pi$
$379$	−22.4255			−1.15192			−0.575960	+	0.817478i	$0.695371\pi$
$380$	0.933463	+	1.61680i	0.0478856	+	0.0829403i
$381$	8.22373	+	12.8536i	0.421314	+	0.658508i
$382$	−1.24484	+	2.15613i	−0.0636916	+	0.110317i
$383$	−7.07014	+	12.2458i	−0.361267	+	0.625733i	−0.988170	−	0.153365i	$-0.950989\pi$
$383$	−7.07014	+	12.2458i	−0.361267	+	0.625733i	0.626903	+	0.779098i	$0.284322\pi$
$384$	0.796790	−	1.53790i	0.0406610	−	0.0784805i
$385$		0			0
$386$	4.48968			0.228519
$387$	−27.8661	+	2.54697i	−1.41652	+	0.129470i
$388$	−11.1872			−0.567942
$389$	11.5651	+	20.0313i	0.586373	+	1.01563i	0.994703	+	0.102793i	$0.0327779\pi$
$389$	11.5651	+	20.0313i	0.586373	+	1.01563i	−0.408330	+	0.912834i	$0.633889\pi$
$390$	−1.16372	+	0.0530713i	−0.0589270	+	0.00268737i
$391$	2.11537	−	3.66392i	0.106979	−	0.185292i
$392$		0			0
$393$	36.5729	−	1.66791i	1.84486	−	0.0841350i
$394$	−6.36693	−	11.0278i	−0.320761	−	0.555574i
$395$	−2.30584			−0.116019
$396$	4.58619	−	9.93559i	0.230465	−	0.499282i
$397$	−10.2661			−0.515243			−0.257622	−	0.966246i	$-0.582939\pi$
$397$	−10.2661			−0.515243			−0.257622	+	0.966246i	$0.582939\pi$
$398$	1.47296	+	2.55124i	0.0738327	+	0.127882i
$399$		0			0
$400$	2.39397	−	4.14647i	0.119698	−	0.207324i
$401$	−17.0167	+	29.4738i	−0.849775	+	1.47185i	0.0316345	+	0.999500i	$0.489929\pi$
$401$	−17.0167	+	29.4738i	−0.849775	+	1.47185i	−0.881409	+	0.472353i	$0.843405\pi$
$402$	−2.16585	−	3.38519i	−0.108023	−	0.168838i
$403$	−0.375780	−	0.650870i	−0.0187189	−	0.0324221i
$404$	−13.7558			−0.684378
$405$	4.07587	−	0.751347i	0.202532	−	0.0373348i
$406$		0			0
$407$	16.6118	+	28.7724i	0.823415	+	1.42620i
$408$	−3.48541	−	5.44765i	−0.172554	−	0.269699i
$409$	−1.74484	+	3.02215i	−0.0862769	+	0.149436i	−0.905935	−	0.423418i	$-0.860830\pi$
$409$	−1.74484	+	3.02215i	−0.0862769	+	0.149436i	0.819658	+	0.572854i	$0.194164\pi$
$410$	0.217799	−	0.377240i	0.0107563	−	0.0186305i
$411$	−3.51099	+	6.77662i	−0.173184	+	0.334266i
$412$	5.58113	+	9.66679i	0.274962	+	0.476249i
$413$		0			0
$414$	−1.42461	+	3.08629i	−0.0700157	+	0.151683i
$415$	3.06128			0.150272
$416$	−0.730252	−	1.26483i	−0.0358036	−	0.0620136i
$417$	3.50360	−	0.159782i	0.171572	−	0.00782455i
$418$	−7.39397	+	12.8067i	−0.361651	+	0.626398i
$419$	−14.4897	+	25.0969i	−0.707867	+	1.22606i	0.257779	+	0.966204i	$0.417009\pi$
$419$	−14.4897	+	25.0969i	−0.707867	+	1.22606i	−0.965647	+	0.259858i	$0.916324\pi$
$420$		0			0
$421$	−1.06128	−	1.83819i	−0.0517237	−	0.0895881i	0.839004	−	0.544125i	$-0.183138\pi$
$421$	−1.06128	−	1.83819i	−0.0517237	−	0.0895881i	−0.890728	+	0.454537i	$0.849805\pi$
$422$	1.21634			0.0592104
$423$	−6.95331	+	0.635534i	−0.338081	+	0.0309007i
$424$	−12.4356			−0.603926
$425$	−8.93872	−	15.4823i	−0.433592	−	0.751003i
$426$	1.33842	−	2.58331i	0.0648467	−	0.125162i
$427$		0			0
$428$	−3.89037	+	6.73832i	−0.188048	+	0.325709i
$429$	−4.97296	−	7.77266i	−0.240097	−	0.375268i
$430$	2.14766	+	3.71986i	0.103570	+	0.179388i
$431$	−21.8712			−1.05350			−0.526749	−	0.850021i	$-0.676589\pi$
$431$	−21.8712			−1.05350			−0.526749	+	0.850021i	$0.676589\pi$
$432$	3.18716	+	4.10390i	0.153342	+	0.197449i
$433$	13.0512			0.627199			0.313599	−	0.949555i	$-0.398465\pi$
$433$	13.0512			0.627199			0.313599	+	0.949555i	$0.398465\pi$
$434$		0			0
$435$	3.85807	+	6.03011i	0.184980	+	0.289122i
$436$	−3.75729	+	6.50783i	−0.179942	+	0.311668i
$437$	2.29679	−	3.97816i	0.109870	−	0.190301i
$438$	−10.5505	+	20.3637i	−0.504122	+	0.973013i
$439$	2.43200	+	4.21235i	0.116073	+	0.201044i	0.918208	−	0.396098i	$-0.129636\pi$
$439$	2.43200	+	4.21235i	0.116073	+	0.201044i	−0.802135	+	0.597143i	$0.796303\pi$
$440$	−1.67977			−0.0800797
$441$		0			0
$442$	−5.45331			−0.259387
$443$	5.76975	+	9.99350i	0.274129	+	0.474805i	0.969915	−	0.243444i	$-0.0782771\pi$
$443$	5.76975	+	9.99350i	0.274129	+	0.474805i	−0.695786	+	0.718249i	$0.744944\pi$
$444$	−15.7594	+	0.718710i	−0.747909	+	0.0341084i
$445$	0.627819	−	1.08741i	0.0297615	−	0.0515484i
$446$	0.445916	−	0.772349i	0.0211147	−	0.0365718i
$447$	15.8530	−	0.722977i	0.749822	−	0.0341957i
$448$		0			0
$449$	−26.4251			−1.24708			−0.623538	−	0.781793i	$-0.714306\pi$
$449$	−26.4251			−1.24708			−0.623538	+	0.781793i	$0.714306\pi$
$450$	8.28434	+	11.7341i	0.390527	+	0.553150i
$451$	3.45038			0.162472
$452$	3.03064	+	5.24922i	0.142549	+	0.246903i
$453$	−0.0827835	+	0.159782i	−0.00388951	+	0.00750720i
$454$	−7.32597	+	12.6889i	−0.343825	+	0.595522i
$455$		0			0
$456$	−3.78434	−	5.91486i	−0.177218	−	0.276989i
$457$	1.86906	+	3.23731i	0.0874310	+	0.151435i	0.906425	−	0.422368i	$-0.138801\pi$
$457$	1.86906	+	3.23731i	0.0874310	+	0.151435i	−0.818994	+	0.573803i	$0.805468\pi$
$458$	9.57587			0.447451
$459$	19.2206	−	2.64435i	0.897141	−	0.123428i
$460$	0.521786			0.0243284
$461$	7.90496	+	13.6918i	0.368171	+	0.637690i	0.989280	−	0.146034i	$-0.0466509\pi$
$461$	7.90496	+	13.6918i	0.368171	+	0.637690i	−0.621109	+	0.783724i	$0.713318\pi$
$462$		0			0
$463$	19.1965	−	33.2493i	0.892137	−	1.54523i	0.0548278	−	0.998496i	$-0.482539\pi$
$463$	19.1965	−	33.2493i	0.892137	−	1.54523i	0.837309	−	0.546730i	$-0.184128\pi$
$464$	−4.48755	+	7.77266i	−0.208329	+	0.360837i
$465$	0.188816	−	0.364437i	0.00875613	−	0.0169003i
$466$	7.21420	+	12.4954i	0.334191	+	0.578836i
$467$	6.31304			0.292132			0.146066	−	0.989275i	$-0.453339\pi$
$467$	6.31304			0.292132			0.146066	+	0.989275i	$0.453339\pi$
$468$	4.36333	−	0.398809i	0.201695	−	0.0184349i
$469$		0			0
$470$	0.535897	+	0.928200i	0.0247191	+	0.0428147i
$471$	36.3047	−	1.65568i	1.67283	−	0.0762895i
$472$	−6.44805	+	11.1684i	−0.296796	+	0.514065i
$473$	−17.0117	+	29.4651i	−0.782197	+	1.35481i
$474$	8.66372	−	0.395109i	0.397938	−	0.0181480i
$475$	−9.70535	−	16.8102i	−0.445312	−	0.771303i
$476$		0			0
$477$	15.6352	−	33.8724i	0.715887	−	1.55091i
$478$	18.3097			0.837467
$479$	−10.2068	−	17.6787i	−0.466361	−	0.807761i	0.532901	−	0.846178i	$-0.321102\pi$
$479$	−10.2068	−	17.6787i	−0.466361	−	0.807761i	−0.999262	+	0.0384168i	$0.987769\pi$
$480$	0.366926	−	0.708209i	0.0167478	−	0.0323252i
$481$	−6.65126	+	11.5203i	−0.303271	+	0.525282i
$482$	0.0466924	−	0.0808735i	0.00212678	−	0.00368369i
$483$		0			0
$484$	−1.15272	−	1.99658i	−0.0523966	−	0.0907535i
$485$	−5.15174			−0.233929
$486$	−15.1855	+	3.52144i	−0.688828	+	0.159736i
$487$	−12.3638			−0.560258			−0.280129	−	0.959962i	$-0.590377\pi$
$487$	−12.3638			−0.560258			−0.280129	+	0.959962i	$0.590377\pi$
$488$	6.04163	+	10.4644i	0.273492	+	0.473702i
$489$	21.5036	+	33.6098i	0.972426	+	1.51989i
$490$		0			0
$491$	0.207004	−	0.358541i	0.00934194	−	0.0161807i	−0.861317	−	0.508069i	$-0.830360\pi$
$491$	0.207004	−	0.358541i	0.00934194	−	0.0161807i	0.870659	+	0.491888i	$0.163693\pi$
$492$	−0.753696	+	1.45472i	−0.0339792	+	0.0655839i
$493$	16.7558	+	29.0220i	0.754645	+	1.30708i
$494$	−5.92101			−0.266399
$495$	2.11196	−	4.57539i	0.0949256	−	0.205648i
$496$	0.514589			0.0231057
$497$		0			0
$498$	−11.5021	+	0.524555i	−0.515423	+	0.0235059i
$499$	0.461967	−	0.800151i	0.0206805	−	0.0358197i	−0.855500	−	0.517803i	$-0.826750\pi$
$499$	0.461967	−	0.800151i	0.0206805	−	0.0358197i	0.876180	+	0.481983i	$0.160083\pi$
$500$	2.25370	−	3.90352i	0.100788	−	0.174571i
$501$	18.3925	−	0.838791i	0.821717	−	0.0374744i
$502$	−9.13667	−	15.8252i	−0.407790	−	0.706312i
$503$	23.8142			1.06182			0.530911	−	0.847428i	$-0.321850\pi$
$503$	23.8142			1.06182			0.530911	+	0.847428i	$0.321850\pi$
$504$		0			0
$505$	−6.33463			−0.281887
$506$	2.06654	+	3.57935i	0.0918688	+	0.159121i
$507$	−8.65865	+	16.7122i	−0.384544	+	0.742215i
$508$	−4.40496	+	7.62961i	−0.195438	+	0.338509i
$509$	−15.3171	+	26.5300i	−0.678919	+	1.17592i	0.296388	+	0.955068i	$0.404218\pi$
$509$	−15.3171	+	26.5300i	−0.678919	+	1.17592i	−0.975307	+	0.220855i	$0.929115\pi$
$510$	−1.60505	−	2.50867i	−0.0710728	−	0.111086i
$511$		0			0
$512$	1.00000			0.0441942
$513$	20.8691	−	2.87114i	0.921392	−	0.126764i
$514$	21.0512			0.928527
$515$	2.57014	+	4.45161i	0.113254	+	0.196161i
$516$	−8.70681	−	13.6086i	−0.383296	−	0.599086i
$517$	−4.24484	+	7.35228i	−0.186688	+	0.323353i
$518$		0			0
$519$	−2.34154	+	4.51945i	−0.102782	+	0.198382i
$520$	−0.336285	−	0.582462i	−0.0147471	−	0.0255427i
$521$	−26.9037			−1.17867			−0.589336	−	0.807888i	$-0.700611\pi$
$521$	−26.9037			−1.17867			−0.589336	+	0.807888i	$0.700611\pi$
$522$	−15.5292	−	21.9958i	−0.679694	−	0.962730i
$523$	−15.7060			−0.686776			−0.343388	−	0.939194i	$-0.611575\pi$
$523$	−15.7060			−0.686776			−0.343388	+	0.939194i	$0.611575\pi$
$524$	10.5687	+	18.3055i	0.461695	+	0.799679i
$525$		0			0
$526$	2.58259	−	4.47318i	0.112606	−	0.195040i
$527$	0.960699	−	1.66398i	0.0418487	−	0.0724841i
$528$	6.31138	−	0.287831i	0.274668	−	0.0125262i
$529$	10.8581	+	18.8067i	0.472090	+	0.817684i
$530$	−5.72665			−0.248750
$531$	−22.3135	−	31.6053i	−0.968324	−	1.37155i
$532$		0			0
$533$	0.690757	+	1.19643i	0.0299200	+	0.0518230i
$534$	−2.17257	+	4.19331i	−0.0940163	+	0.181462i
$535$	−1.79153	+	3.10303i	−0.0774548	+	0.134156i
$536$	1.16012	−	2.00938i	0.0501094	−	0.0867920i
$537$	8.55262	+	13.3676i	0.369073	+	0.576855i
$538$	−8.42840	−	14.5984i	−0.363374	−	0.629383i
$539$		0			0
$540$	1.46770	+	1.88987i	0.0631598	+	0.0813269i
$541$	4.11868			0.177076			0.0885379	−	0.996073i	$-0.471781\pi$
$541$	4.11868			0.177076			0.0885379	+	0.996073i	$0.471781\pi$
$542$	−12.5562	−	21.7480i	−0.539336	−	0.934157i
$543$	−20.9361	−	32.7228i	−0.898453	−	1.40427i
$544$	1.86693	−	3.23361i	0.0800438	−	0.138640i
$545$	−1.73025	+	2.99689i	−0.0741159	+	0.128372i
$546$		0			0
$547$	−11.8602	−	20.5425i	−0.507106	−	0.878333i	−0.999966	−	0.00822465i	$-0.997382\pi$
$547$	−11.8602	−	20.5425i	−0.507106	−	0.878333i	0.492860	−	0.870108i	$-0.335951\pi$
$548$	−4.40642			−0.188233
$549$	−36.0993	+	3.29948i	−1.54068	+	0.140819i
$550$	17.4648			0.744701
$551$	18.1929	+	31.5110i	0.775043	+	1.34241i
$552$	−1.96050	+	0.0894089i	−0.0834446	+	0.00380550i
$553$		0			0
$554$	−1.69076	+	2.92848i	−0.0718334	+	0.124419i
$555$	−7.25729	+	0.330969i	−0.308055	+	0.0140489i
$556$	1.01245	+	1.75362i	0.0429376	+	0.0743701i
$557$	42.0626			1.78225			0.891125	−	0.453757i	$-0.149917\pi$
$557$	42.0626			1.78225			0.891125	+	0.453757i	$0.149917\pi$
$558$	−0.646990	+	1.40165i	−0.0273893	+	0.0593366i
$559$	−13.6228			−0.576181
$560$		0			0
$561$	10.8521	−	20.9459i	0.458178	−	0.884336i
$562$	−10.1388	+	17.5609i	−0.427680	+	0.740763i
$563$	5.91216	−	10.2402i	0.249168	−	0.431571i	−0.714127	−	0.700016i	$-0.753176\pi$
$563$	5.91216	−	10.2402i	0.249168	−	0.431571i	0.963295	+	0.268445i	$0.0865097\pi$
$564$	−2.17257	−	3.39569i	−0.0914817	−	0.142985i
$565$	1.39562	+	2.41729i	0.0587144	+	0.101696i
$566$	−17.3494			−0.729250
$567$		0			0
$568$	1.67977			0.0704815
$569$	−7.10078	−	12.2989i	−0.297680	−	0.515597i	0.677925	−	0.735131i	$-0.262880\pi$
$569$	−7.10078	−	12.2989i	−0.297680	−	0.515597i	−0.975605	+	0.219534i	$0.929546\pi$
$570$	−1.74271	−	2.72382i	−0.0729939	−	0.114088i
$571$	−5.97869	+	10.3554i	−0.250200	+	0.433360i	−0.963581	−	0.267417i	$-0.913830\pi$
$571$	−5.97869	+	10.3554i	−0.250200	+	0.433360i	0.713380	+	0.700777i	$0.247163\pi$
$572$	2.66372	−	4.61369i	0.111376	−	0.192908i
$573$	1.98375	−	3.82888i	0.0828725	−	0.159954i
$574$		0			0
$575$	−5.42509			−0.226242
$576$	−1.25729	+	2.72382i	−0.0523873	+	0.113493i
$577$	42.6270			1.77459			0.887293	−	0.461206i	$-0.152583\pi$
$577$	42.6270			1.77459			0.887293	+	0.461206i	$0.152583\pi$
$578$	1.52918	+	2.64861i	0.0636054	+	0.110168i
$579$	−7.76829	+	0.354273i	−0.322839	+	0.0147231i
$580$	−2.06654	+	3.57935i	−0.0858083	+	0.148624i
$581$		0			0
$582$	19.3566	−	0.882759i	0.802357	−	0.0365915i
$583$	−22.6804	−	39.2837i	−0.939328	−	1.62696i
$584$	−13.2412			−0.547927
$585$	2.00933	−	0.183653i	0.0830757	−	0.00759314i
$586$	−9.87120			−0.407775
$587$	−20.5328	−	35.5638i	−0.847478	−	1.46788i	−0.883451	−	0.468523i	$-0.844786\pi$
$587$	−20.5328	−	35.5638i	−0.847478	−	1.46788i	0.0359730	−	0.999353i	$-0.488547\pi$
$588$		0			0
$589$	1.04309	−	1.80669i	0.0429799	−	0.0744434i
$590$	−2.96936	+	5.14308i	−0.122247	+	0.211737i
$591$	11.8866	+	18.5785i	0.488948	+	0.764219i
$592$	−4.55408	−	7.88791i	−0.187172	−	0.324191i
$593$	32.2016			1.32236			0.661180	−	0.750228i	$-0.270056\pi$
$593$	32.2016			1.32236			0.661180	+	0.750228i	$0.270056\pi$
$594$	−7.15126	+	17.5530i	−0.293420	+	0.720207i
$595$		0			0
$596$	4.58113	+	7.93474i	0.187650	+	0.325020i
$597$	−2.74990	−	4.29806i	−0.112546	−	0.175908i
$598$	−0.827430	+	1.43315i	−0.0338361	+	0.0586059i
$599$	−9.53590	+	16.5167i	−0.389626	+	0.674852i	−0.992399	−	0.123060i	$-0.960729\pi$
$599$	−9.53590	+	16.5167i	−0.389626	+	0.674852i	0.602773	+	0.797913i	$0.294062\pi$
$600$	−3.81498	+	7.36335i	−0.155746	+	0.300607i
$601$	−4.27188	−	7.39912i	−0.174254	−	0.301816i	0.765649	−	0.643259i	$-0.222418\pi$
$601$	−4.27188	−	7.39912i	−0.174254	−	0.301816i	−0.939903	+	0.341442i	$0.889085\pi$
$602$		0			0
$603$	4.01459	+	5.68634i	0.163487	+	0.231565i
$604$	−0.103896			−0.00422748
$605$	−0.530835	−	0.919434i	−0.0215815	−	0.0373803i
$606$	23.8011	−	1.08545i	0.966852	−	0.0440933i
$607$	19.0057	−	32.9189i	0.771419	−	1.33614i	−0.165366	−	0.986232i	$-0.552881\pi$
$607$	19.0057	−	32.9189i	0.771419	−	1.33614i	0.936785	−	0.349905i	$-0.113786\pi$
$608$	2.02704	−	3.51094i	0.0822074	−	0.142387i
$609$		0			0
$610$	2.78220	+	4.81891i	0.112648	+	0.195112i
$611$	−3.39922			−0.137518
$612$	6.46050	+	9.15077i	0.261150	+	0.369898i
$613$	−22.6591			−0.915194			−0.457597	−	0.889160i	$-0.651290\pi$
$613$	−22.6591			−0.915194			−0.457597	+	0.889160i	$0.651290\pi$
$614$	3.89397	+	6.74455i	0.157148	+	0.272188i
$615$	−0.347081	+	0.669906i	−0.0139956	+	0.0270132i
$616$		0			0
$617$	−10.1388	+	17.5609i	−0.408173	+	0.706977i	−0.994685	−	0.102964i	$-0.967167\pi$
$617$	−10.1388	+	17.5609i	−0.408173	+	0.706977i	0.586512	+	0.809941i	$0.300501\pi$
$618$	−10.4195	−	16.2856i	−0.419136	−	0.655103i
$619$	1.03064	+	1.78512i	0.0414249	+	0.0717501i	0.885994	−	0.463696i	$-0.153477\pi$
$619$	1.03064	+	1.78512i	0.0414249	+	0.0717501i	−0.844570	+	0.535446i	$0.820144\pi$
$620$	0.236971			0.00951698
$621$	2.22140	−	5.45248i	0.0891416	−	0.218801i
$622$	−15.4107			−0.617912
$623$		0			0
$624$	1.36333	+	2.13086i	0.0545768	+	0.0853027i
$625$	−10.9320	+	18.9348i	−0.437280	+	0.757391i
$626$	4.24844	−	7.35851i	0.169802	−	0.294105i
$627$	11.7829	−	22.7423i	0.470563	−	0.908241i
$628$	10.4911	+	18.1712i	0.418642	+	0.725110i
$629$	−34.0085			−1.35601
$630$		0			0
$631$	1.63715			0.0651740			0.0325870	−	0.999469i	$-0.489625\pi$
$631$	1.63715			0.0651740			0.0325870	+	0.999469i	$0.489625\pi$
$632$	2.50360	+	4.33636i	0.0995878	+	0.172491i
$633$	−2.10457	+	0.0959790i	−0.0836491	+	0.00381482i
$634$	7.05262	−	12.2155i	0.280095	−	0.485139i
$635$	−2.02850	+	3.51347i	−0.0804988	+	0.139428i
$636$	21.5167	−	0.981271i	0.853194	−	0.0389099i
$637$		0			0
$638$	−32.7381			−1.29611
$639$	−2.11196	+	4.57539i	−0.0835479	+	0.181000i
$640$	0.460505			0.0182031
$641$	−10.9662	−	18.9941i	−0.433140	−	0.750221i	0.564001	−	0.825774i	$-0.309261\pi$
$641$	−10.9662	−	18.9941i	−0.433140	−	0.750221i	−0.997142	+	0.0755526i	$0.975928\pi$
$642$	6.19961	−	11.9660i	0.244679	−	0.472259i
$643$	14.1819	−	24.5638i	0.559280	−	0.968701i	−0.438277	−	0.898840i	$-0.644411\pi$
$643$	14.1819	−	24.5638i	0.559280	−	0.968701i	0.997557	−	0.0698609i	$-0.0222555\pi$
$644$		0			0
$645$	−4.00953	−	6.26683i	−0.157875	−	0.246756i
$646$	−7.56867	−	13.1093i	−0.297785	−	0.515780i
$647$	34.7807			1.36737			0.683686	−	0.729776i	$-0.260376\pi$
$647$	34.7807			1.36737			0.683686	+	0.729776i	$0.260376\pi$
$648$	−5.83842	−	6.84929i	−0.229355	−	0.269066i
$649$	−47.0406			−1.84651
$650$	3.49640	+	6.05594i	0.137140	+	0.237534i
$651$		0			0
$652$	−11.5182	+	19.9501i	−0.451087	+	0.781306i
$653$	1.59931	−	2.77009i	0.0625860	−	0.108402i	−0.833035	−	0.553221i	$-0.813399\pi$
$653$	1.59931	−	2.77009i	0.0625860	−	0.108402i	0.895621	+	0.444819i	$0.146732\pi$
$654$	5.98755	−	11.5567i	0.234132	−	0.451901i
$655$	4.86693	+	8.42976i	0.190167	+	0.329378i
$656$	−0.945916			−0.0369318
$657$	16.6481	−	36.0668i	0.649506	−	1.40710i
$658$		0			0
$659$	5.30418	+	9.18711i	0.206622	+	0.357879i	0.950648	−	0.310271i	$-0.100420\pi$
$659$	5.30418	+	9.18711i	0.206622	+	0.357879i	−0.744027	+	0.668150i	$0.767086\pi$
$660$	2.90642	−	0.132547i	0.113132	−	0.00515940i
$661$	5.06507	−	8.77297i	0.197009	−	0.341229i	−0.750549	−	0.660815i	$-0.770211\pi$
$661$	5.06507	−	8.77297i	0.197009	−	0.341229i	0.947557	+	0.319586i	$0.103544\pi$
$662$	−13.7719	+	23.8536i	−0.535259	+	0.927097i
$663$	9.43560	−	0.430311i	0.366448	−	0.0167119i
$664$	−3.32383	−	5.75705i	−0.128990	−	0.223417i
$665$		0			0
$666$	27.2111	−	2.48710i	1.05441	−	0.0963731i
$667$	10.1694			0.393763
$668$	5.31498	+	9.20581i	0.205643	+	0.356184i
$669$	−0.710602	+	1.37154i	−0.0274735	+	0.0530270i
$670$	0.534239	−	0.925330i	0.0206395	−	0.0357486i
$671$	−22.0378	+	38.1707i	−0.850761	+	1.47356i
$672$		0			0
$673$	1.60817	+	2.78543i	0.0619903	+	0.107370i	0.895355	−	0.445353i	$-0.146922\pi$
$673$	1.60817	+	2.78543i	0.0619903	+	0.107370i	−0.833365	+	0.552724i	$0.813589\pi$
$674$	−1.49688			−0.0576577
$675$	−15.2599	−	19.6492i	−0.587354	−	0.756299i
$676$	−10.8669			−0.417959
$677$	−14.6819	−	25.4298i	−0.564271	−	0.977347i	−0.997117	−	0.0758786i	$-0.975824\pi$
$677$	−14.6819	−	25.4298i	−0.564271	−	0.977347i	0.432846	−	0.901468i	$-0.357509\pi$
$678$	−5.65798	−	8.84334i	−0.217293	−	0.339626i
$679$		0			0
$680$	0.859728	−	1.48909i	0.0329691	−	0.0571041i
$681$	11.6745	−	22.5332i	0.447368	−	0.863473i
$682$	0.938524	+	1.62557i	0.0359379	+	0.0622463i
$683$	−25.2556			−0.966380			−0.483190	−	0.875515i	$-0.660522\pi$
$683$	−25.2556			−0.966380			−0.483190	+	0.875515i	$0.660522\pi$
$684$	7.01459	+	9.93559i	0.268210	+	0.379897i
$685$	−2.02918			−0.0775309
$686$		0			0
$687$	−16.5687	+	0.755615i	−0.632134	+	0.0288285i
$688$	4.66372	−	8.07779i	0.177802	−	0.307963i
$689$	9.08113	−	15.7290i	0.345963	−	0.599226i
$690$	−0.902822	+	0.0411732i	−0.0343698	+	0.00156744i
$691$	−7.68190	−	13.3054i	−0.292233	−	0.506163i	0.682104	−	0.731255i	$-0.261065\pi$
$691$	−7.68190	−	13.3054i	−0.292233	−	0.506163i	−0.974338	+	0.225092i	$0.927732\pi$
$692$	−2.93872			−0.111713
$693$		0			0
$694$	−18.2881			−0.694208
$695$	0.466240	+	0.807551i	0.0176855	+	0.0306321i
$696$	7.15126	−	13.8028i	0.271068	−	0.523193i
$697$	−1.76595	+	3.05872i	−0.0668903	+	0.115857i
$698$	3.90136	−	6.75735i	0.147669	−	0.255770i
$699$	−13.4684	−	21.0509i	−0.509421	−	0.796217i
$700$		0			0
$701$	−13.3700			−0.504980			−0.252490	−	0.967600i	$-0.581249\pi$
$701$	−13.3700			−0.504980			−0.252490	+	0.967600i	$0.581249\pi$
$702$	−7.51819	+	1.03434i	−0.283756	+	0.0390387i
$703$	−36.9253			−1.39266
$704$	1.82383	+	3.15897i	0.0687382	+	0.119058i
$705$	−1.00048	−	1.56373i	−0.0376802	−	0.0588936i
$706$	13.4626	−	23.3180i	0.506673	−	0.877584i
$707$		0			0
$708$	10.2755	−	19.8329i	0.386176	−	0.745365i
$709$	0.562939	+	0.975038i	0.0211416	+	0.0366183i	0.876403	−	0.481579i	$-0.159937\pi$
$709$	0.562939	+	0.975038i	0.0211416	+	0.0366183i	−0.855261	+	0.518197i	$0.826603\pi$
$710$	0.773541			0.0290305
$711$	−14.9592	+	1.36728i	−0.561015	+	0.0512769i
$712$	−2.72665			−0.102186
$713$	−0.291534	−	0.504951i	−0.0109180	−	0.0189106i
$714$		0			0
$715$	1.22665	−	2.12463i	0.0458743	−	0.0794565i
$716$	−4.58113	+	7.93474i	−0.171205	+	0.296535i
$717$	−31.6804	+	1.44479i	−1.18313	+	0.0539566i
$718$	−3.13161	−	5.42411i	−0.116871	−	0.202426i
$719$	18.2733			0.681481			0.340740	−	0.940157i	$-0.389322\pi$
$719$	18.2733			0.681481			0.340740	+	0.940157i	$0.389322\pi$
$720$	−0.578990	+	1.25433i	−0.0215777	+	0.0467463i
$721$		0			0
$722$	1.28220	+	2.22084i	0.0477186	+	0.0826510i
$723$	−0.0744080	+	0.143616i	−0.00276726	+	0.00534114i
$724$	11.2142	−	19.4236i	0.416772	−	0.721871i
$725$	21.4861	−	37.2150i	0.797973	−	1.38213i
$726$	2.15205	+	3.36362i	0.0798701	+	0.124836i
$727$	14.8478	+	25.7171i	0.550673	+	0.953793i	0.998226	+	0.0595359i	$0.0189621\pi$
$727$	14.8478	+	25.7171i	0.550673	+	0.953793i	−0.447553	+	0.894257i	$0.647705\pi$
$728$		0			0
$729$	25.9969	−	7.29124i	0.962847	−	0.270046i
$730$	−6.09766			−0.225684
$731$	−17.4136	−	30.1613i	−0.644066	−	1.11555i
$732$	−11.2793	−	17.6293i	−0.416894	−	0.651599i
$733$	9.61390	−	16.6518i	0.355098	−	0.615047i	−0.632037	−	0.774938i	$-0.717781\pi$
$733$	9.61390	−	16.6518i	0.355098	−	0.615047i	0.987135	+	0.159891i	$0.0511143\pi$
$734$	14.6367	−	25.3515i	0.540249	−	0.935740i
$735$		0			0
$736$	−0.566537	−	0.981271i	−0.0208828	−	0.0361701i
$737$	8.46343			0.311754
$738$	1.18929	−	2.57651i	0.0437785	−	0.0948425i
$739$	30.2671			1.11339			0.556697	−	0.830716i	$-0.312069\pi$
$739$	30.2671			1.11339			0.556697	+	0.830716i	$0.312069\pi$
$740$	−2.09718	−	3.63242i	−0.0770938	−	0.133530i
$741$	10.2448	−	0.467216i	0.376354	−	0.0171636i
$742$		0			0
$743$	−11.8815	+	20.5794i	−0.435890	+	0.754984i	−0.997368	−	0.0725076i	$-0.976900\pi$
$743$	−11.8815	+	20.5794i	−0.435890	+	0.754984i	0.561477	+	0.827492i	$0.310233\pi$
$744$	−0.890369	+	0.0406053i	−0.0326425	+	0.00148866i
$745$	2.10963	+	3.65399i	0.0772909	+	0.133872i
$746$	17.8597			0.653891
$747$	19.8602	−	1.81523i	0.726647	−	0.0664157i
$748$	13.6198			0.497990
$749$		0			0
$750$	−3.59144	+	6.93190i	−0.131141	+	0.253117i
$751$	−6.33415	+	10.9711i	−0.231136	+	0.400340i	−0.958143	−	0.286291i	$-0.907578\pi$
$751$	−6.33415	+	10.9711i	−0.231136	+	0.400340i	0.727006	+	0.686631i	$0.240911\pi$
$752$	1.16372	−	2.01561i	0.0424363	−	0.0735019i
$753$	17.0575	+	26.6606i	0.621609	+	0.971566i
$754$	−6.55408	−	11.3520i	−0.238686	−	0.413416i
$755$	−0.0478448			−0.00174125
$756$		0			0
$757$	−29.0799			−1.05693			−0.528464	−	0.848955i	$-0.677232\pi$
$757$	−29.0799			−1.05693			−0.528464	+	0.848955i	$0.677232\pi$
$758$	11.2127	+	19.4210i	0.407265	+	0.705404i
$759$	−3.85807	−	6.03011i	−0.140039	−	0.218879i
$760$	0.933463	−	1.61680i	0.0338603	−	0.0586477i
$761$	14.6015	−	25.2905i	0.529302	−	0.916778i	−0.470114	−	0.882606i	$-0.655787\pi$
$761$	14.6015	−	25.2905i	0.529302	−	0.916778i	0.999416	−	0.0341724i	$-0.0108795\pi$
$762$	7.01965	−	13.5487i	0.254295	−	0.490819i
$763$		0			0
$764$	2.48968			0.0900736
$765$	2.97509	+	4.21398i	0.107565	+	0.152357i
$766$	14.1403			0.510909
$767$	−9.41741	−	16.3114i	−0.340043	−	0.588972i
$768$	−1.73025	+	0.0789082i	−0.0624351	+	0.00284736i
$769$	−12.5869	+	21.8011i	−0.453894	+	0.786167i	−0.998624	−	0.0524443i	$-0.983299\pi$
$769$	−12.5869	+	21.8011i	−0.453894	+	0.786167i	0.544730	+	0.838611i	$0.316632\pi$
$770$		0			0
$771$	−36.4238	+	1.66111i	−1.31177	+	0.0598234i
$772$	−2.24484	−	3.88818i	−0.0807936	−	0.139939i
$773$	−1.50408			−0.0540979			−0.0270490	−	0.999634i	$-0.508611\pi$
$773$	−1.50408			−0.0540979			−0.0270490	+	0.999634i	$0.508611\pi$
$774$	16.1388	+	22.8593i	0.580098	+	0.821660i
$775$	−2.46382			−0.0885030
$776$	5.59358	+	9.68836i	0.200798	+	0.347792i
$777$		0			0
$778$	11.5651	−	20.0313i	0.414628	−	0.718157i
$779$	−1.91741	+	3.32105i	−0.0686984	+	0.118989i
$780$	0.627819	+	0.981271i	0.0224795	+	0.0351351i
$781$	3.06361	+	5.30633i	0.109625	+	0.189875i
$782$	−4.23073			−0.151291
$783$	28.6050	+	36.8329i	1.02226	+	1.31630i
$784$		0			0
$785$	4.83122	+	8.36792i	0.172434	+	0.298664i
$786$	−19.7309	−	30.8391i	−0.703779	−	1.10000i
$787$	−7.47656	+	12.9498i	−0.266510	+	0.461610i	−0.967958	−	0.251111i	$-0.919204\pi$
$787$	−7.47656	+	12.9498i	−0.266510	+	0.461610i	0.701448	+	0.712721i	$0.252537\pi$
$788$	−6.36693	+	11.0278i	−0.226812	+	0.392850i
$789$	−4.11556	+	7.94351i	−0.146518	+	0.282796i
$790$	1.15292	+	1.99691i	0.0410190	+	0.0710470i
$791$		0			0
$792$	−10.8976	+	0.996040i	−0.387228	+	0.0353927i
$793$	−17.6477			−0.626687
$794$	5.13307	+	8.89075i	0.182166	+	0.315521i
$795$	9.90856	−	0.451880i	0.351420	−	0.0160265i
$796$	1.47296	−	2.55124i	0.0522076	−	0.0904262i
$797$	4.56294	−	7.90324i	0.161628	−	0.279947i	−0.773825	−	0.633400i	$-0.781659\pi$
$797$	4.56294	−	7.90324i	0.161628	−	0.279947i	0.935453	+	0.353452i	$0.114992\pi$
$798$		0			0
$799$	−4.34514	−	7.52600i	−0.153720	−	0.266251i
$800$	−4.78794			−0.169279
$801$	3.42821	−	7.42692i	0.121130	−	0.262417i
$802$	34.0335			1.20176
$803$	−24.1498	−	41.8287i	−0.852228	−	1.47610i
$804$	−1.84874	+	3.56828i	−0.0652000	+	0.125843i
$805$		0			0
$806$	−0.375780	+	0.650870i	−0.0132363	+	0.0229259i
$807$	15.7352	+	24.5939i	0.553905	+	0.865746i
$808$	6.87792	+	11.9129i	0.241964	+	0.419094i
$809$	−35.5510			−1.24991			−0.624953	−	0.780663i	$-0.714882\pi$
$809$	−35.5510			−1.24991			−0.624953	+	0.780663i	$0.714882\pi$
$810$	−2.68862	−	3.15413i	−0.0944685	−	0.110825i
$811$	13.5070			0.474295			0.237148	−	0.971474i	$-0.423788\pi$
$811$	13.5070			0.474295			0.237148	+	0.971474i	$0.423788\pi$
$812$		0			0
$813$	23.4415	+	36.6388i	0.822130	+	1.28498i
$814$	16.6118	−	28.7724i	0.582242	−	1.00847i
$815$	−5.30418	+	9.18711i	−0.185797	+	0.321810i
$816$	−2.97509	+	5.74228i	−0.104149	+	0.201020i
$817$	−18.9071	−	32.7480i	−0.661475	−	1.14571i
$818$	3.48968			0.122014
$819$		0			0
$820$	−0.435599			−0.0152118
$821$	−10.8114	−	18.7259i	−0.377320	−	0.653537i	0.613352	−	0.789810i	$-0.289821\pi$
$821$	−10.8114	−	18.7259i	−0.377320	−	0.653537i	−0.990671	+	0.136273i	$0.956488\pi$
$822$	7.62422	−	0.347703i	0.265925	−	0.0121275i
$823$	0.753501	−	1.30510i	0.0262654	−	0.0454930i	−0.852594	−	0.522574i	$-0.824972\pi$
$823$	0.753501	−	1.30510i	0.0262654	−	0.0454930i	0.878859	+	0.477081i	$0.158305\pi$
$824$	5.58113	−	9.66679i	0.194428	−	0.336759i
$825$	−30.2185	+	1.37811i	−1.05207	+	0.0479798i
$826$		0			0
$827$	23.3786			0.812953			0.406477	−	0.913661i	$-0.366757\pi$
$827$	23.3786			0.812953			0.406477	+	0.913661i	$0.366757\pi$
$828$	3.38511	−	0.309400i	0.117641	−	0.0107524i
$829$	−22.0191			−0.764753			−0.382377	−	0.924007i	$-0.624894\pi$
$829$	−22.0191			−0.764753			−0.382377	+	0.924007i	$0.624894\pi$
$830$	−1.53064	−	2.65115i	−0.0531293	−	0.0920227i
$831$	2.69436	−	5.20042i	0.0934662	−	0.180401i
$832$	−0.730252	+	1.26483i	−0.0253169	+	0.0438502i
$833$		0			0
$834$	−1.89017	−	2.95431i	−0.0654514	−	0.102300i
$835$	2.44757	+	4.23932i	0.0847018	+	0.146708i
$836$	14.7879			0.511451
$837$	1.00885	−	2.47626i	0.0348711	−	0.0855921i
$838$	28.9794			1.00108
$839$	1.06507	+	1.84476i	0.0367705	+	0.0636883i	0.883825	−	0.467818i	$-0.154960\pi$
$839$	1.06507	+	1.84476i	0.0367705	+	0.0636883i	−0.847055	+	0.531506i	$0.821626\pi$
$840$		0			0
$841$	−25.7762	+	44.6456i	−0.888833	+	1.53950i
$842$	−1.06128	+	1.83819i	−0.0365742	+	0.0633483i
$843$	16.1570	−	31.1849i	0.556477	−	1.07406i
$844$	−0.608168	−	1.05338i	−0.0209340	−	0.0362588i
$845$	−5.00427			−0.172152
$846$	4.02704	+	5.70397i	0.138453	+	0.196107i
$847$		0			0
$848$	6.21780	+	10.7695i	0.213520	+	0.369828i
$849$	30.0189	−	1.36901i	1.03024	−	0.0469844i
$850$	−8.93872	+	15.4823i	−0.306596	+	0.531039i
$851$	−5.16012	+	8.93758i	−0.176887	+	0.306376i
$852$	−2.90642	+	0.132547i	−0.0995723	+	0.00454100i
$853$	3.50146	+	6.06471i	0.119888	+	0.207652i	0.919723	−	0.392568i	$-0.128413\pi$
$853$	3.50146	+	6.06471i	0.119888	+	0.207652i	−0.799835	+	0.600220i	$0.795080\pi$
$854$		0			0
$855$	3.23025	+	4.57539i	0.110472	+	0.156475i
$856$	7.78074			0.265940
$857$	5.46410	+	9.46410i	0.186650	+	0.323288i	0.944131	−	0.329569i	$-0.106904\pi$
$857$	5.46410	+	9.46410i	0.186650	+	0.323288i	−0.757481	+	0.652857i	$0.773570\pi$
$858$	−4.24484	+	8.19304i	−0.144917	+	0.279706i
$859$	−6.95379	+	12.0443i	−0.237260	+	0.410947i	−0.959927	−	0.280250i	$-0.909583\pi$
$859$	−6.95379	+	12.0443i	−0.237260	+	0.410947i	0.722667	+	0.691196i	$0.242916\pi$
$860$	2.14766	−	3.71986i	0.0732347	−	0.126846i
$861$		0			0
$862$	10.9356	+	18.9410i	0.372468	+	0.645133i
$863$	36.8463			1.25426			0.627131	−	0.778914i	$-0.284229\pi$
$863$	36.8463			1.25426			0.627131	+	0.778914i	$0.284229\pi$
$864$	1.96050	−	4.81211i	0.0666977	−	0.163711i
$865$	−1.35329			−0.0460134
$866$	−6.52558	−	11.3026i	−0.221748	−	0.384079i
$867$	−2.85486	−	4.46211i	−0.0969562	−	0.151541i
$868$		0			0
$869$	−9.13229	+	15.8176i	−0.309792	+	0.536575i
$870$	3.29319	−	6.35624i	0.111650	−	0.215497i
$871$	1.69436	+	2.93471i	0.0574111	+	0.0994389i
$872$	7.51459			0.254476
$873$	−33.4222	+	3.05479i	−1.13117	+	0.103389i
$874$	−4.59358			−0.155380
$875$		0			0
$876$	22.9107	−	1.04484i	0.774081	−	0.0353020i
$877$	5.17977	−	8.97162i	0.174908	−	0.302950i	−0.765221	−	0.643767i	$-0.777370\pi$
$877$	5.17977	−	8.97162i	0.174908	−	0.302950i	0.940130	+	0.340817i	$0.110704\pi$
$878$	2.43200	−	4.21235i	0.0820760	−	0.142160i
$879$	17.0797	−	0.778919i	0.576083	−	0.0262723i
$880$	0.839883	+	1.45472i	0.0283125	+	0.0490386i
$881$	−9.34806			−0.314944			−0.157472	−	0.987523i	$-0.550334\pi$
$881$	−9.34806			−0.314944			−0.157472	+	0.987523i	$0.550334\pi$
$882$		0			0
$883$	2.29494			0.0772308			0.0386154	−	0.999254i	$-0.487705\pi$
$883$	2.29494			0.0772308			0.0386154	+	0.999254i	$0.487705\pi$
$884$	2.72665	+	4.72270i	0.0917073	+	0.158842i
$885$	4.73191	−	9.13314i	0.159061	−	0.307007i
$886$	5.76975	−	9.99350i	0.193838	−	0.335738i
$887$	−13.8363	+	23.9651i	−0.464577	+	0.804671i	−0.999182	−	0.0404309i	$-0.987127\pi$
$887$	−13.8363	+	23.9651i	−0.464577	+	0.804671i	0.534605	+	0.845102i	$0.320460\pi$
$888$	8.50214	+	13.2887i	0.285313	+	0.445940i
$889$		0			0
$890$	−1.25564			−0.0420891
$891$	10.9884	−	30.9354i	0.368126	−	1.03637i
$892$	−0.891832			−0.0298607
$893$	−4.71780	−	8.17147i	−0.157875	−	0.273448i
$894$	−8.55262	−	13.3676i	−0.286042	−	0.447080i
$895$	−2.10963	+	3.65399i	−0.0705172	+	0.122139i
$896$		0			0
$897$	1.31858	−	2.54500i	0.0440260	−	0.0849752i
$898$	13.2125	+	22.8848i	0.440908	+	0.763676i
$899$	4.61849			0.154035
$900$	6.01984	−	13.0415i	0.200661	−	0.434716i
$901$	46.4327			1.54690
$902$	−1.72519	−	2.98812i	−0.0574426	−	0.0994935i
$903$		0			0
$904$	3.03064	−	5.24922i	0.100798	−	0.174587i
$905$	5.16419	−	8.94465i	0.171664	−	0.297330i
$906$	0.179767	−	0.00819828i	0.00597235	−	0.000272369i
$907$	1.46576	+	2.53877i	0.0486698	+	0.0842985i	0.889334	−	0.457258i	$-0.151168\pi$
$907$	1.46576	+	2.53877i	0.0486698	+	0.0842985i	−0.840664	+	0.541557i	$0.817835\pi$
$908$	14.6519			0.486242
$909$	−41.0962	+	3.75620i	−1.36307	+	0.124585i
$910$		0			0
$911$	15.3171	+	26.5300i	0.507479	+	0.878979i	0.999963	+	0.00865719i	$0.00275570\pi$
$911$	15.3171	+	26.5300i	0.507479	+	0.878979i	−0.492484	+	0.870322i	$0.663911\pi$
$912$	−3.23025	+	6.23476i	−0.106964	+	0.206454i
$913$	12.1242	−	20.9998i	0.401253	−	0.694991i
$914$	1.86906	−	3.23731i	0.0618231	−	0.107081i
$915$	−5.19416	−	8.11840i	−0.171714	−	0.268386i
$916$	−4.78794	−	8.29295i	−0.158198	−	0.274007i
$917$		0			0
$918$	−11.9004	−	15.3234i	−0.392771	−	0.505746i
$919$	−26.3714			−0.869912			−0.434956	−	0.900452i	$-0.643236\pi$
$919$	−26.3714			−0.869912			−0.434956	+	0.900452i	$0.643236\pi$
$920$	−0.260893	−	0.451880i	−0.00860139	−	0.0148980i
$921$	−7.26975	−	11.3625i	−0.239546	−	0.374407i
$922$	7.90496	−	13.6918i	0.260336	−	0.450915i
$923$	−1.22665	+	2.12463i	−0.0403758	+	0.0699329i
$924$		0			0
$925$	21.8047	+	37.7668i	0.716933	+	1.24176i
$926$	−38.3930			−1.26167
$927$	19.3135	+	27.3560i	0.634339	+	0.898489i
$928$	8.97509			0.294622
$929$	8.93706	+	15.4794i	0.293215	+	0.507864i	0.974568	−	0.224091i	$-0.0719413\pi$
$929$	8.93706	+	15.4794i	0.293215	+	0.507864i	−0.681353	+	0.731955i	$0.738608\pi$
$930$	−0.410019	+	0.0186989i	−0.0134451	+	0.000613163i
$931$		0			0
$932$	7.21420	−	12.4954i	0.236309	−	0.409299i
$933$	26.6644	−	1.21603i	0.872953	−	0.0398111i
$934$	−3.15652	−	5.46725i	−0.103284	−	0.178894i
$935$	6.27200			0.205116
$936$	−2.52704	−	3.57935i	−0.0825990	−	0.116995i
$937$	−15.9134			−0.519869			−0.259934	−	0.965626i	$-0.583701\pi$
$937$	−15.9134			−0.519869			−0.259934	+	0.965626i	$0.583701\pi$
$938$		0			0
$939$	−6.77023	+	13.0673i	−0.220938	+	0.426436i
$940$	0.535897	−	0.928200i	0.0174790	−	0.0302745i
$941$	−8.14027	+	14.0994i	−0.265365	+	0.459626i	−0.967659	−	0.252261i	$-0.918826\pi$
$941$	−8.14027	+	14.0994i	−0.265365	+	0.459626i	0.702294	+	0.711887i	$0.252159\pi$
$942$	−19.5862	−	30.6129i	−0.638152	−	0.997423i
$943$	0.535897	+	0.928200i	0.0174512	+	0.0302264i
$944$	12.8961			0.419732
$945$		0			0
$946$	34.0233			1.10619
$947$	14.2951	+	24.7599i	0.464529	+	0.804589i	0.999180	−	0.0404846i	$-0.0128902\pi$
$947$	14.2951	+	24.7599i	0.464529	+	0.804589i	−0.534651	+	0.845073i	$0.679557\pi$
$948$	−4.67403	−	7.30544i	−0.151806	−	0.237270i
$949$	9.66945	−	16.7480i	0.313884	−	0.543662i
$950$	−9.70535	+	16.8102i	−0.314883	+	0.545393i
$951$	−11.2389	+	21.6924i	−0.364447	+	0.703424i
$952$		0			0
$953$	−29.3537			−0.950859			−0.475430	−	0.879754i	$-0.657707\pi$
$953$	−29.3537			−0.950859			−0.475430	+	0.879754i	$0.657707\pi$
$954$	−37.1519	+	3.39569i	−1.20284	+	0.109940i
$955$	1.14651			0.0371002
$956$	−9.15486	−	15.8567i	−0.296089	−	0.512842i
$957$	56.6452	−	2.58331i	1.83108	−	0.0835065i
$958$	−10.2068	+	17.6787i	−0.329767	+	0.571173i
$959$		0			0
$960$	−0.796790	+	0.0363376i	−0.0257163	+	0.00117279i
$961$	15.3676	+	26.6175i	0.495729	+	0.858628i
$962$	13.3025			0.428891
$963$	−9.78268	+	21.1934i	−0.315242	+	0.682946i
$964$	−0.0933847			−0.00300772
$965$	−1.03376	−	1.79053i	−0.0332779	−	0.0576391i
$966$		0			0
$967$	−4.69815	+	8.13743i	−0.151082	+	0.261682i	−0.931626	−	0.363419i	$-0.881609\pi$
$967$	−4.69815	+	8.13743i	−0.151082	+	0.261682i	0.780543	+	0.625102i	$0.214943\pi$
$968$	−1.15272	+	1.99658i	−0.0370500	+	0.0641724i
$969$	14.1301	+	22.0852i	0.453926	+	0.709479i
$970$	2.57587	+	4.46154i	0.0827062	+	0.143251i
$971$	15.5467			0.498917			0.249459	−	0.968385i	$-0.419747\pi$
$971$	15.5467			0.498917			0.249459	+	0.968385i	$0.419747\pi$
$972$	10.6424	+	11.3903i	0.341355	+	0.365344i
$973$		0			0
$974$	6.18190	+	10.7074i	0.198081	+	0.343086i
$975$	−6.52752	−	10.2024i	−0.209048	−	0.326739i
$976$	6.04163	−	10.4644i	0.193388	−	0.334958i
$977$	4.79893	−	8.31198i	0.153531	−	0.265924i	−0.778992	−	0.627034i	$-0.784269\pi$
$977$	4.79893	−	8.31198i	0.153531	−	0.265924i	0.932523	+	0.361110i	$0.117602\pi$
$978$	18.3551	−	35.4276i	0.586933	−	1.13285i
$979$	−4.97296	−	8.61342i	−0.158936	−	0.275286i
$980$		0			0
$981$	−9.44805	+	20.4684i	−0.301653	+	0.653506i
$982$	−0.414007			−0.0132115
$983$	−23.4267	−	40.5763i	−0.747197	−	1.29418i	−0.949161	−	0.314790i	$-0.898066\pi$
$983$	−23.4267	−	40.5763i	−0.747197	−	1.29418i	0.201964	−	0.979393i	$-0.435268\pi$
$984$	1.63667	−	0.0746406i	0.0521752	−	0.00237945i
$985$	−2.93200	+	5.07837i	−0.0934213	+	0.161810i
$986$	16.7558	−	29.0220i	0.533614	−	0.924247i
$987$		0			0
$988$	2.96050	+	5.12774i	0.0941862	+	0.163135i
$989$	−10.5687			−0.336064
$990$	−5.01838	+	0.458681i	−0.159495	+	0.0145778i
$991$	−21.6519			−0.687796			−0.343898	−	0.939007i	$-0.611748\pi$
$991$	−21.6519			−0.687796			−0.343898	+	0.939007i	$0.611748\pi$
$992$	−0.257295	−	0.445647i	−0.00816911	−	0.0141493i
$993$	21.9466	−	42.3595i	0.696454	−	1.34424i
$994$		0			0
$995$	0.678304	−	1.17486i	0.0215037	−	0.0372455i
$996$	6.20535	+	9.69886i	0.196624	+	0.307320i
$997$	−28.6190	−	49.5695i	−0.906372	−	1.56988i	−0.819065	−	0.573700i	$-0.805507\pi$
$997$	−28.6190	−	49.5695i	−0.906372	−	1.56988i	−0.0873064	−	0.996182i	$-0.527826\pi$
$998$	−0.923935			−0.0292466
$999$	−46.8858	+	6.45049i	−1.48340	+	0.204084i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.f.m.589.2		6
3.2	odd	2		2646.2.f.n.1765.3		6
7.2	even	3		882.2.h.o.67.1		6
7.3	odd	6		126.2.e.d.121.2	yes	6
7.4	even	3		882.2.e.p.373.2		6
7.5	odd	6		126.2.h.c.67.3	yes	6
7.6	odd	2		882.2.f.l.589.2		6
9.2	odd	6		2646.2.f.n.883.3		6
9.4	even	3		7938.2.a.by.1.3		3
9.5	odd	6		7938.2.a.bx.1.1		3
9.7	even	3	inner	882.2.f.m.295.2		6
21.2	odd	6		2646.2.h.p.361.1		6
21.5	even	6		378.2.h.d.361.3		6
21.11	odd	6		2646.2.e.o.1549.3		6
21.17	even	6		378.2.e.c.37.1		6
21.20	even	2		2646.2.f.o.1765.1		6
28.3	even	6		1008.2.q.h.625.2		6
28.19	even	6		1008.2.t.g.193.1		6
63.2	odd	6		2646.2.e.o.2125.3		6
63.5	even	6		1134.2.g.n.487.1		6
63.11	odd	6		2646.2.h.p.667.1		6
63.13	odd	6		7938.2.a.cb.1.1		3
63.16	even	3		882.2.e.p.655.2		6
63.20	even	6		2646.2.f.o.883.1		6
63.25	even	3		882.2.h.o.79.1		6
63.31	odd	6		1134.2.g.k.163.3		6
63.34	odd	6		882.2.f.l.295.2		6
63.38	even	6		378.2.h.d.289.3		6
63.40	odd	6		1134.2.g.k.487.3		6
63.41	even	6		7938.2.a.bu.1.3		3
63.47	even	6		378.2.e.c.235.1		6
63.52	odd	6		126.2.h.c.79.3	yes	6
63.59	even	6		1134.2.g.n.163.1		6
63.61	odd	6		126.2.e.d.25.2	✓	6
84.47	odd	6		3024.2.t.g.1873.3		6
84.59	odd	6		3024.2.q.h.2305.1		6
252.47	odd	6		3024.2.q.h.2881.1		6
252.115	even	6		1008.2.t.g.961.1		6
252.187	even	6		1008.2.q.h.529.2		6
252.227	odd	6		3024.2.t.g.289.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.2	✓	6	63.61	odd	6
126.2.e.d.121.2	yes	6	7.3	odd	6
126.2.h.c.67.3	yes	6	7.5	odd	6
126.2.h.c.79.3	yes	6	63.52	odd	6
378.2.e.c.37.1		6	21.17	even	6
378.2.e.c.235.1		6	63.47	even	6
378.2.h.d.289.3		6	63.38	even	6
378.2.h.d.361.3		6	21.5	even	6
882.2.e.p.373.2		6	7.4	even	3
882.2.e.p.655.2		6	63.16	even	3
882.2.f.l.295.2		6	63.34	odd	6
882.2.f.l.589.2		6	7.6	odd	2
882.2.f.m.295.2		6	9.7	even	3	inner
882.2.f.m.589.2		6	1.1	even	1	trivial
882.2.h.o.67.1		6	7.2	even	3
882.2.h.o.79.1		6	63.25	even	3
1008.2.q.h.529.2		6	252.187	even	6
1008.2.q.h.625.2		6	28.3	even	6
1008.2.t.g.193.1		6	28.19	even	6
1008.2.t.g.961.1		6	252.115	even	6
1134.2.g.k.163.3		6	63.31	odd	6
1134.2.g.k.487.3		6	63.40	odd	6
1134.2.g.n.163.1		6	63.59	even	6
1134.2.g.n.487.1		6	63.5	even	6
2646.2.e.o.1549.3		6	21.11	odd	6
2646.2.e.o.2125.3		6	63.2	odd	6
2646.2.f.n.883.3		6	9.2	odd	6
2646.2.f.n.1765.3		6	3.2	odd	2
2646.2.f.o.883.1		6	63.20	even	6
2646.2.f.o.1765.1		6	21.20	even	2
2646.2.h.p.361.1		6	21.2	odd	6
2646.2.h.p.667.1		6	63.11	odd	6
3024.2.q.h.2305.1		6	84.59	odd	6
3024.2.q.h.2881.1		6	252.47	odd	6
3024.2.t.g.289.3		6	252.227	odd	6
3024.2.t.g.1873.3		6	84.47	odd	6
7938.2.a.bu.1.3		3	63.41	even	6
7938.2.a.bx.1.1		3	9.5	odd	6
7938.2.a.by.1.3		3	9.4	even	3
7938.2.a.cb.1.1		3	63.13	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.933463 + 1.45899i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.230252 + 0.398809i) q^{5} +(0.796790 - 1.53790i) q^{6} +1.00000 q^{8} +(-1.25729 + 2.72382i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.933463 + 1.45899i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.230252 + 0.398809i) q^{5} +(0.796790 - 1.53790i) q^{6} +1.00000 q^{8} +(-1.25729 + 2.72382i) q^{9} +0.460505 q^{10} +(1.82383 + 3.15897i) q^{11} +(-1.73025 + 0.0789082i) q^{12} +(-0.730252 + 1.26483i) q^{13} +(-0.796790 + 0.0363376i) q^{15} +(-0.500000 - 0.866025i) q^{16} -3.73385 q^{17} +(2.98755 - 0.273062i) q^{18} -4.05408 q^{19} +(-0.230252 - 0.398809i) q^{20} +(1.82383 - 3.15897i) q^{22} +(-0.566537 + 0.981271i) q^{23} +(0.933463 + 1.45899i) q^{24} +(2.39397 + 4.14647i) q^{25} +1.46050 q^{26} +(-5.14766 + 0.708209i) q^{27} +(-4.48755 - 7.77266i) q^{29} +(0.429864 + 0.671871i) q^{30} +(-0.257295 + 0.445647i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.90642 + 5.60973i) q^{33} +(1.86693 + 3.23361i) q^{34} +(-1.73025 - 2.45076i) q^{36} +9.10817 q^{37} +(2.02704 + 3.51094i) q^{38} +(-2.52704 + 0.115246i) q^{39} +(-0.230252 + 0.398809i) q^{40} +(0.472958 - 0.819187i) q^{41} +(4.66372 + 8.07779i) q^{43} -3.64766 q^{44} +(-0.796790 - 1.12859i) q^{45} +1.13307 q^{46} +(1.16372 + 2.01561i) q^{47} +(0.796790 - 1.53790i) q^{48} +(2.39397 - 4.14647i) q^{50} +(-3.48541 - 5.44765i) q^{51} +(-0.730252 - 1.26483i) q^{52} -12.4356 q^{53} +(3.18716 + 4.10390i) q^{54} -1.67977 q^{55} +(-3.78434 - 5.91486i) q^{57} +(-4.48755 + 7.77266i) q^{58} +(-6.44805 + 11.1684i) q^{59} +(0.366926 - 0.708209i) q^{60} +(6.04163 + 10.4644i) q^{61} +0.514589 q^{62} +1.00000 q^{64} +(-0.336285 - 0.582462i) q^{65} +(6.31138 - 0.287831i) q^{66} +(1.16012 - 2.00938i) q^{67} +(1.86693 - 3.23361i) q^{68} +(-1.96050 + 0.0894089i) q^{69} +1.67977 q^{71} +(-1.25729 + 2.72382i) q^{72} -13.2412 q^{73} +(-4.55408 - 7.88791i) q^{74} +(-3.81498 + 7.36335i) q^{75} +(2.02704 - 3.51094i) q^{76} +(1.36333 + 2.13086i) q^{78} +(2.50360 + 4.33636i) q^{79} +0.460505 q^{80} +(-5.83842 - 6.84929i) q^{81} -0.945916 q^{82} +(-3.32383 - 5.75705i) q^{83} +(0.859728 - 1.48909i) q^{85} +(4.66372 - 8.07779i) q^{86} +(7.15126 - 13.8028i) q^{87} +(1.82383 + 3.15897i) q^{88} -2.72665 q^{89} +(-0.578990 + 1.25433i) q^{90} +(-0.566537 - 0.981271i) q^{92} +(-0.890369 + 0.0406053i) q^{93} +(1.16372 - 2.01561i) q^{94} +(0.933463 - 1.61680i) q^{95} +(-1.73025 + 0.0789082i) q^{96} +(5.59358 + 9.68836i) q^{97} +(-10.8976 + 0.996040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 5 q^{5} + 2 q^{6} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 5 * q^5 + 2 * q^6 + 6 * q^8 + 8 * q^9	\( 6 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 5 q^{5} + 2 q^{6} + 6 q^{8} + 8 q^{9} - 10 q^{10} - q^{11} - 4 q^{12} + 2 q^{13} - 2 q^{15} - 3 q^{16} - 8 q^{17} - 4 q^{18} - 6 q^{19} + 5 q^{20} - q^{22} - 7 q^{23} + 2 q^{24} - 2 q^{25} - 4 q^{26} - 7 q^{27} - 5 q^{29} + 7 q^{30} + 14 q^{31} - 3 q^{32} - 23 q^{33} + 4 q^{34} - 4 q^{36} + 18 q^{37} + 3 q^{38} - 6 q^{39} + 5 q^{40} + 12 q^{41} + 18 q^{43} + 2 q^{44} - 2 q^{45} + 14 q^{46} - 3 q^{47} + 2 q^{48} - 2 q^{50} - 52 q^{51} + 2 q^{52} - 18 q^{53} + 8 q^{54} - 14 q^{55} + 2 q^{57} - 5 q^{58} - 4 q^{59} - 5 q^{60} - 4 q^{61} - 28 q^{62} + 6 q^{64} - 12 q^{65} + 4 q^{66} + 5 q^{67} + 4 q^{68} + q^{69} + 14 q^{71} + 8 q^{72} - 50 q^{73} - 9 q^{74} + 19 q^{75} + 3 q^{76} + 9 q^{78} + 7 q^{79} - 10 q^{80} + 8 q^{81} - 24 q^{82} - 8 q^{83} + 14 q^{85} + 18 q^{86} + 11 q^{87} - q^{88} - 18 q^{89} - 29 q^{90} - 7 q^{92} + 3 q^{93} - 3 q^{94} + 2 q^{95} - 4 q^{96} + 28 q^{97} - 41 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 5 * q^5 + 2 * q^6 + 6 * q^8 + 8 * q^9 - 10 * q^10 - q^11 - 4 * q^12 + 2 * q^13 - 2 * q^15 - 3 * q^16 - 8 * q^17 - 4 * q^18 - 6 * q^19 + 5 * q^20 - q^22 - 7 * q^23 + 2 * q^24 - 2 * q^25 - 4 * q^26 - 7 * q^27 - 5 * q^29 + 7 * q^30 + 14 * q^31 - 3 * q^32 - 23 * q^33 + 4 * q^34 - 4 * q^36 + 18 * q^37 + 3 * q^38 - 6 * q^39 + 5 * q^40 + 12 * q^41 + 18 * q^43 + 2 * q^44 - 2 * q^45 + 14 * q^46 - 3 * q^47 + 2 * q^48 - 2 * q^50 - 52 * q^51 + 2 * q^52 - 18 * q^53 + 8 * q^54 - 14 * q^55 + 2 * q^57 - 5 * q^58 - 4 * q^59 - 5 * q^60 - 4 * q^61 - 28 * q^62 + 6 * q^64 - 12 * q^65 + 4 * q^66 + 5 * q^67 + 4 * q^68 + q^69 + 14 * q^71 + 8 * q^72 - 50 * q^73 - 9 * q^74 + 19 * q^75 + 3 * q^76 + 9 * q^78 + 7 * q^79 - 10 * q^80 + 8 * q^81 - 24 * q^82 - 8 * q^83 + 14 * q^85 + 18 * q^86 + 11 * q^87 - q^88 - 18 * q^89 - 29 * q^90 - 7 * q^92 + 3 * q^93 - 3 * q^94 + 2 * q^95 - 4 * q^96 + 28 * q^97 - 41 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more