LMFDB - Embedded newform 882.2.e.p.655.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(373,882)]

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([2, 2]))

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

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

chi := DirichletCharacter("882.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.e (of order $3$, degree $2$, not 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			655.2
Root			$0.500000 - 2.05195i$ of defining polynomial
Character	$\chi$	$=$	882.655
Dual form			882.2.e.p.373.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(0.796790 + 1.53790i) q^{3} +1.00000 q^{4} +(-0.230252 + 0.398809i) q^{5} +(0.796790 + 1.53790i) q^{6} +1.00000 q^{8} +(-1.73025 + 2.45076i) q^{9} +(-0.230252 + 0.398809i) q^{10} +(1.82383 + 3.15897i) q^{11} +(0.796790 + 1.53790i) q^{12} +(-0.730252 - 1.26483i) q^{13} +(-0.796790 - 0.0363376i) q^{15} +1.00000 q^{16} +(1.86693 - 3.23361i) q^{17} +(-1.73025 + 2.45076i) q^{18} +(2.02704 + 3.51094i) q^{19} +(-0.230252 + 0.398809i) q^{20} +(1.82383 + 3.15897i) q^{22} +(-0.566537 + 0.981271i) q^{23} +(0.796790 + 1.53790i) q^{24} +(2.39397 + 4.14647i) q^{25} +(-0.730252 - 1.26483i) q^{26} +(-5.14766 - 0.708209i) q^{27} +(-4.48755 + 7.77266i) q^{29} +(-0.796790 - 0.0363376i) q^{30} +0.514589 q^{31} +1.00000 q^{32} +(-3.40496 + 5.32190i) q^{33} +(1.86693 - 3.23361i) q^{34} +(-1.73025 + 2.45076i) q^{36} +(-4.55408 - 7.88791i) q^{37} +(2.02704 + 3.51094i) q^{38} +(1.36333 - 2.13086i) q^{39} +(-0.230252 + 0.398809i) q^{40} +(0.472958 + 0.819187i) q^{41} +(4.66372 - 8.07779i) q^{43} +(1.82383 + 3.15897i) q^{44} +(-0.578990 - 1.25433i) q^{45} +(-0.566537 + 0.981271i) q^{46} -2.32743 q^{47} +(0.796790 + 1.53790i) q^{48} +(2.39397 + 4.14647i) q^{50} +(6.46050 + 0.294632i) q^{51} +(-0.730252 - 1.26483i) q^{52} +(6.21780 - 10.7695i) q^{53} +(-5.14766 - 0.708209i) q^{54} -1.67977 q^{55} +(-3.78434 + 5.91486i) q^{57} +(-4.48755 + 7.77266i) q^{58} +12.8961 q^{59} +(-0.796790 - 0.0363376i) q^{60} -12.0833 q^{61} +0.514589 q^{62} +1.00000 q^{64} +0.672570 q^{65} +(-3.40496 + 5.32190i) q^{66} -2.32023 q^{67} +(1.86693 - 3.23361i) q^{68} +(-1.96050 - 0.0894089i) q^{69} +1.67977 q^{71} +(-1.73025 + 2.45076i) q^{72} +(6.62062 - 11.4673i) q^{73} +(-4.55408 - 7.88791i) q^{74} +(-4.46936 + 6.98554i) q^{75} +(2.02704 + 3.51094i) q^{76} +(1.36333 - 2.13086i) q^{78} -5.00720 q^{79} +(-0.230252 + 0.398809i) q^{80} +(-3.01245 - 8.48087i) q^{81} +(0.472958 + 0.819187i) q^{82} +(-3.32383 + 5.75705i) q^{83} +(0.859728 + 1.48909i) q^{85} +(4.66372 - 8.07779i) q^{86} +(-15.5292 - 0.708209i) q^{87} +(1.82383 + 3.15897i) q^{88} +(1.36333 + 2.36135i) q^{89} +(-0.578990 - 1.25433i) q^{90} +(-0.566537 + 0.981271i) q^{92} +(0.410019 + 0.791385i) q^{93} -2.32743 q^{94} -1.86693 q^{95} +(0.796790 + 1.53790i) q^{96} +(5.59358 - 9.68836i) q^{97} +(-10.8976 - 0.996040i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} + 5 q^{5} + 2 q^{6} + 6 q^{8} - 4 q^{9} + 5 q^{10} - q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{15} + 6 q^{16} + 4 q^{17} - 4 q^{18} + 3 q^{19} + 5 q^{20} - q^{22} - 7 q^{23}+ \cdots - 41 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 + 5 * q^5 + 2 * q^6 + 6 * q^8 - 4 * q^9 + 5 * q^10 - q^11 + 2 * q^12 + 2 * q^13 - 2 * q^15 + 6 * q^16 + 4 * q^17 - 4 * q^18 + 3 * q^19 + 5 * q^20 - q^22 - 7 * q^23 + 2 * q^24 - 2 * q^25 + 2 * q^26 - 7 * q^27 - 5 * q^29 - 2 * q^30 - 28 * q^31 + 6 * q^32 + 19 * q^33 + 4 * q^34 - 4 * q^36 - 9 * q^37 + 3 * q^38 + 9 * q^39 + 5 * q^40 + 12 * q^41 + 18 * q^43 - q^44 - 29 * q^45 - 7 * q^46 + 6 * q^47 + 2 * q^48 - 2 * q^50 + 26 * q^51 + 2 * q^52 + 9 * q^53 - 7 * q^54 - 14 * q^55 + 2 * q^57 - 5 * q^58 + 8 * q^59 - 2 * q^60 + 8 * q^61 - 28 * q^62 + 6 * q^64 + 24 * q^65 + 19 * q^66 - 10 * q^67 + 4 * q^68 + q^69 + 14 * q^71 - 4 * q^72 + 25 * q^73 - 9 * q^74 - 44 * q^75 + 3 * q^76 + 9 * q^78 - 14 * q^79 + 5 * q^80 - 40 * q^81 + 12 * q^82 - 8 * q^83 + 14 * q^85 + 18 * q^86 - 31 * q^87 - q^88 + 9 * q^89 - 29 * q^90 - 7 * q^92 + 6 * q^94 - 4 * q^95 + 2 * q^96 + 28 * q^97 - 41 * q^99

Character values

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

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.796790	+	1.53790i	0.460027	+	0.887905i
$3$	0.796790	+	1.53790i	0.460027	+	0.887905i
$4$	1.00000			0.500000
$5$	−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
$9$	−1.73025	+	2.45076i	−0.576751	+	0.816920i
$10$	−0.230252	+	0.398809i	−0.0728122	+	0.126114i
$11$	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	$0.647997\pi$
$12$	0.796790	+	1.53790i	0.230013	+	0.443953i
$13$	−0.730252	−	1.26483i	−0.202536	−	0.350802i	0.746809	−	0.665038i	$-0.231585\pi$
$13$	−0.730252	−	1.26483i	−0.202536	−	0.350802i	−0.949345	+	0.314236i	$0.898252\pi$
$14$		0			0
$15$	−0.796790	−	0.0363376i	−0.205730	−	0.00938234i
$16$	1.00000			0.250000
$17$	1.86693	−	3.23361i	0.452796	−	0.784266i	−0.545763	−	0.837940i	$-0.683760\pi$
$17$	1.86693	−	3.23361i	0.452796	−	0.784266i	0.998558	+	0.0536743i	$0.0170933\pi$
$18$	−1.73025	+	2.45076i	−0.407824	+	0.577650i
$19$	2.02704	+	3.51094i	0.465035	+	0.805465i	0.999203	−	0.0399136i	$-0.0127083\pi$
$19$	2.02704	+	3.51094i	0.465035	+	0.805465i	−0.534168	+	0.845378i	$0.679375\pi$
$20$	−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	$0.204357\pi$
$24$	0.796790	+	1.53790i	0.162644	+	0.313922i
$25$	2.39397	+	4.14647i	0.478794	+	0.829295i
$26$	−0.730252	−	1.26483i	−0.143214	−	0.248054i
$27$	−5.14766	−	0.708209i	−0.990668	−	0.136295i
$28$		0			0
$29$	−4.48755	+	7.77266i	−0.833317	+	1.44335i	0.0620772	+	0.998071i	$0.480228\pi$
$29$	−4.48755	+	7.77266i	−0.833317	+	1.44335i	−0.895394	+	0.445275i	$0.853106\pi$
$30$	−0.796790	−	0.0363376i	−0.145473	−	0.00663431i
$31$	0.514589			0.0924229			0.0462115	−	0.998932i	$-0.485285\pi$
$31$	0.514589			0.0924229			0.0462115	+	0.998932i	$0.485285\pi$
$32$	1.00000			0.176777
$33$	−3.40496	+	5.32190i	−0.592727	+	0.926424i
$34$	1.86693	−	3.23361i	0.320175	−	0.554560i
$35$		0			0
$36$	−1.73025	+	2.45076i	−0.288375	+	0.408460i
$37$	−4.55408	−	7.88791i	−0.748687	−	1.29676i	−0.948452	−	0.316920i	$-0.897351\pi$
$37$	−4.55408	−	7.88791i	−0.748687	−	1.29676i	0.199765	−	0.979844i	$-0.435982\pi$
$38$	2.02704	+	3.51094i	0.328830	+	0.569550i
$39$	1.36333	−	2.13086i	0.218307	−	0.341211i
$40$	−0.230252	+	0.398809i	−0.0364061	+	0.0630572i
$41$	0.472958	+	0.819187i	0.0738636	+	0.127936i	0.900592	−	0.434666i	$-0.143134\pi$
$41$	0.472958	+	0.819187i	0.0738636	+	0.127936i	−0.826728	+	0.562602i	$0.809800\pi$
$42$		0			0
$43$	4.66372	−	8.07779i	0.711210	−	1.23185i	−0.253193	−	0.967416i	$-0.581481\pi$
$43$	4.66372	−	8.07779i	0.711210	−	1.23185i	0.964403	−	0.264436i	$-0.0851858\pi$
$44$	1.82383	+	3.15897i	0.274953	+	0.476233i
$45$	−0.578990	−	1.25433i	−0.0863108	−	0.186985i
$46$	−0.566537	+	0.981271i	−0.0835314	+	0.144681i
$47$	−2.32743			−0.339491			−0.169745	−	0.985488i	$-0.554295\pi$
$47$	−2.32743			−0.339491			−0.169745	+	0.985488i	$0.554295\pi$
$48$	0.796790	+	1.53790i	0.115007	+	0.221976i
$49$		0			0
$50$	2.39397	+	4.14647i	0.338558	+	0.586400i
$51$	6.46050	+	0.294632i	0.904652	+	0.0412567i
$52$	−0.730252	−	1.26483i	−0.101268	−	0.175401i
$53$	6.21780	−	10.7695i	0.854080	−	1.47931i	−0.0234151	−	0.999726i	$-0.507454\pi$
$53$	6.21780	−	10.7695i	0.854080	−	1.47931i	0.877495	−	0.479585i	$-0.159213\pi$
$54$	−5.14766	−	0.708209i	−0.700508	−	0.0963750i
$55$	−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
$59$	12.8961			1.67893			0.839465	−	0.543414i	$-0.182869\pi$
$59$	12.8961			1.67893			0.839465	+	0.543414i	$0.182869\pi$
$60$	−0.796790	−	0.0363376i	−0.102865	−	0.00469117i
$61$	−12.0833			−1.54710			−0.773552	−	0.633733i	$-0.781522\pi$
$61$	−12.0833			−1.54710			−0.773552	+	0.633733i	$0.781522\pi$
$62$	0.514589			0.0653529
$63$		0			0
$64$	1.00000			0.125000
$65$	0.672570			0.0834220
$66$	−3.40496	+	5.32190i	−0.419121	+	0.655080i
$67$	−2.32023			−0.283462			−0.141731	−	0.989905i	$-0.545267\pi$
$67$	−2.32023			−0.283462			−0.141731	+	0.989905i	$0.545267\pi$
$68$	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	$0.468219\pi$
$72$	−1.73025	+	2.45076i	−0.203912	+	0.288825i
$73$	6.62062	−	11.4673i	0.774885	−	1.34214i	−0.159974	−	0.987121i	$-0.551141\pi$
$73$	6.62062	−	11.4673i	0.774885	−	1.34214i	0.934859	−	0.355019i	$-0.115526\pi$
$74$	−4.55408	−	7.88791i	−0.529402	−	0.916950i
$75$	−4.46936	+	6.98554i	−0.516077	+	0.806621i
$76$	2.02704	+	3.51094i	0.232518	+	0.402732i
$77$		0			0
$78$	1.36333	−	2.13086i	0.154366	−	0.241272i
$79$	−5.00720			−0.563354			−0.281677	−	0.959509i	$-0.590891\pi$
$79$	−5.00720			−0.563354			−0.281677	+	0.959509i	$0.590891\pi$
$80$	−0.230252	+	0.398809i	−0.0257430	+	0.0445882i
$81$	−3.01245	−	8.48087i	−0.334717	−	0.942319i
$82$	0.472958	+	0.819187i	0.0522295	+	0.0904641i
$83$	−3.32383	+	5.75705i	−0.364838	+	0.631918i	−0.988750	−	0.149577i	$-0.952209\pi$
$83$	−3.32383	+	5.75705i	−0.364838	+	0.631918i	0.623912	+	0.781494i	$0.285542\pi$
$84$		0			0
$85$	0.859728	+	1.48909i	0.0932506	+	0.161515i
$86$	4.66372	−	8.07779i	0.502901	−	0.871051i
$87$	−15.5292	−	0.708209i	−1.66490	−	0.0759280i
$88$	1.82383	+	3.15897i	0.194421	+	0.336747i
$89$	1.36333	+	2.36135i	0.144512	+	0.250303i	0.929191	−	0.369600i	$-0.120505\pi$
$89$	1.36333	+	2.36135i	0.144512	+	0.250303i	−0.784679	+	0.619903i	$0.787172\pi$
$90$	−0.578990	−	1.25433i	−0.0610309	−	0.132218i
$91$		0			0
$92$	−0.566537	+	0.981271i	−0.0590656	+	0.102305i
$93$	0.410019	+	0.791385i	0.0425170	+	0.0820628i
$94$	−2.32743			−0.240056
$95$	−1.86693			−0.191543
$96$	0.796790	+	1.53790i	0.0813220	+	0.156961i
$97$	5.59358	−	9.68836i	0.567942	−	0.983704i	−0.428827	−	0.903386i	$-0.641073\pi$
$97$	5.59358	−	9.68836i	0.567942	−	0.983704i	0.996769	−	0.0803178i	$-0.0255935\pi$
$98$		0			0
$99$	−10.8976	−	0.996040i	−1.09525	−	0.100106i
$100$	2.39397	+	4.14647i	0.239397	+	0.414647i
$101$	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	$0.593407\pi$
$102$	6.46050	+	0.294632i	0.639685	+	0.0291729i
$103$	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
$107$	−3.89037	−	6.73832i	−0.376096	−	0.651418i	0.614394	−	0.788999i	$-0.289400\pi$
$107$	−3.89037	−	6.73832i	−0.376096	−	0.651418i	−0.990490	+	0.137581i	$0.956067\pi$
$108$	−5.14766	−	0.708209i	−0.495334	−	0.0681474i
$109$	−3.75729	+	6.50783i	−0.359884	+	0.623337i	−0.987941	−	0.154830i	$-0.950517\pi$
$109$	−3.75729	+	6.50783i	−0.359884	+	0.623337i	0.628058	+	0.778167i	$0.283850\pi$
$110$	−1.67977			−0.160159
$111$	8.50214	−	13.2887i	0.806987	−	1.26131i
$112$		0			0
$113$	3.03064	+	5.24922i	0.285099	+	0.493805i	0.972633	−	0.232346i	$-0.0746403\pi$
$113$	3.03064	+	5.24922i	0.285099	+	0.493805i	−0.687534	+	0.726152i	$0.741307\pi$
$114$	−3.78434	+	5.91486i	−0.354436	+	0.553978i
$115$	−0.260893	−	0.451880i	−0.0243284	−	0.0421380i
$116$	−4.48755	+	7.77266i	−0.416658	+	0.721673i
$117$	4.36333	+	0.398809i	0.403390	+	0.0368699i
$118$	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
$122$	−12.0833			−1.09397
$123$	−0.882977	+	1.38008i	−0.0796154	+	0.124438i
$124$	0.514589			0.0462115
$125$	−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	$0.372172\pi$
$128$	1.00000			0.0883883
$129$	16.1388	+	0.736011i	1.42094	+	0.0648022i
$130$	0.672570			0.0589883
$131$	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
$135$	1.46770	−	1.88987i	0.126320	−	0.162654i
$136$	1.86693	−	3.23361i	0.160088	−	0.277280i
$137$	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	$0.773057\pi$
$138$	−1.96050	−	0.0894089i	−0.166889	−	0.00761099i
$139$	1.01245	+	1.75362i	0.0858751	+	0.148740i	0.905764	−	0.423783i	$-0.139298\pi$
$139$	1.01245	+	1.75362i	0.0858751	+	0.148740i	−0.819889	+	0.572523i	$0.805965\pi$
$140$		0			0
$141$	−1.85447	−	3.57935i	−0.156175	−	0.301435i
$142$	1.67977			0.140963
$143$	2.66372	−	4.61369i	0.222751	−	0.385816i
$144$	−1.73025	+	2.45076i	−0.144188	+	0.204230i
$145$	−2.06654	−	3.57935i	−0.171617	−	0.297249i
$146$	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	$0.0442062\pi$
$150$	−4.46936	+	6.98554i	−0.364922	+	0.570367i
$151$	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	$0.831988\pi$
$152$	2.02704	+	3.51094i	0.164415	+	0.284775i
$153$	4.69455	+	10.1703i	0.379532	+	0.822224i
$154$		0			0
$155$	−0.118485	+	0.205223i	−0.00951698	+	0.0164839i
$156$	1.36333	−	2.13086i	0.109154	−	0.170605i
$157$	−20.9823			−1.67457			−0.837285	−	0.546767i	$-0.815858\pi$
$157$	−20.9823			−1.67457			−0.837285	+	0.546767i	$0.815858\pi$
$158$	−5.00720			−0.398351
$159$	21.5167	+	0.981271i	1.70639	+	0.0778199i
$160$	−0.230252	+	0.398809i	−0.0182031	+	0.0315286i
$161$		0			0
$162$	−3.01245	−	8.48087i	−0.236681	−	0.666320i
$163$	−11.5182	−	19.9501i	−0.902174	−	1.56261i	−0.824666	−	0.565620i	$-0.808637\pi$
$163$	−11.5182	−	19.9501i	−0.902174	−	1.56261i	−0.0775078	−	0.996992i	$-0.524696\pi$
$164$	0.472958	+	0.819187i	0.0369318	+	0.0639678i
$165$	−1.33842	−	2.58331i	−0.104196	−	0.201110i
$166$	−3.32383	+	5.75705i	−0.257979	+	0.446833i
$167$	5.31498	+	9.20581i	0.411285	+	0.712367i	0.995031	−	0.0995698i	$-0.0317467\pi$
$167$	5.31498	+	9.20581i	0.411285	+	0.712367i	−0.583745	+	0.811937i	$0.698413\pi$
$168$		0			0
$169$	5.43346	−	9.41103i	0.417959	−	0.723926i
$170$	0.859728	+	1.48909i	0.0659382	+	0.114208i
$171$	−12.1118	−	1.10702i	−0.926210	−	0.0846558i
$172$	4.66372	−	8.07779i	0.355605	−	0.615926i
$173$	−2.93872			−0.223427			−0.111713	−	0.993740i	$-0.535634\pi$
$173$	−2.93872			−0.223427			−0.111713	+	0.993740i	$0.535634\pi$
$174$	−15.5292	−	0.708209i	−1.17726	−	0.0536892i
$175$		0			0
$176$	1.82383	+	3.15897i	0.137476	+	0.238116i
$177$	10.2755	+	19.8329i	0.772353	+	1.49073i
$178$	1.36333	+	2.36135i	0.102186	+	0.176991i
$179$	−4.58113	+	7.93474i	−0.342409	+	0.593071i	−0.984880	−	0.173240i	$-0.944576\pi$
$179$	−4.58113	+	7.93474i	−0.342409	+	0.593071i	0.642470	+	0.766311i	$0.277910\pi$
$180$	−0.578990	−	1.25433i	−0.0431554	−	0.0934925i
$181$	−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
$185$	4.19436			0.308375
$186$	0.410019	+	0.791385i	0.0300641	+	0.0580272i
$187$	13.6198			0.995981
$188$	−2.32743			−0.169745
$189$		0			0
$190$	−1.86693			−0.135441
$191$	2.48968			0.180147			0.0900736	−	0.995935i	$-0.471290\pi$
$191$	2.48968			0.180147			0.0900736	+	0.995935i	$0.471290\pi$
$192$	0.796790	+	1.53790i	0.0575033	+	0.110988i
$193$	4.48968			0.323174			0.161587	−	0.986858i	$-0.448339\pi$
$193$	4.48968			0.323174			0.161587	+	0.986858i	$0.448339\pi$
$194$	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	$0.350131\pi$
$198$	−10.8976	−	0.996040i	−0.774456	−	0.0707855i
$199$	1.47296	−	2.55124i	0.104415	−	0.180852i	−0.809084	−	0.587693i	$-0.800036\pi$
$199$	1.47296	−	2.55124i	0.104415	−	0.180852i	0.913499	+	0.406841i	$0.133370\pi$
$200$	2.39397	+	4.14647i	0.169279	+	0.293200i
$201$	−1.84874	−	3.56828i	−0.130400	−	0.251687i
$202$	6.87792	+	11.9129i	0.483928	+	0.838189i
$203$		0			0
$204$	6.46050	+	0.294632i	0.452326	+	0.0206283i
$205$	−0.435599			−0.0304235
$206$	5.58113	−	9.66679i	0.388855	−	0.673517i
$207$	−1.42461	−	3.08629i	−0.0990171	−	0.214512i
$208$	−0.730252	−	1.26483i	−0.0506339	−	0.0877005i
$209$	−7.39397	+	12.8067i	−0.511451	+	0.885860i
$210$		0			0
$211$	−0.608168	−	1.05338i	−0.0418680	−	0.0725176i	0.844332	−	0.535820i	$-0.179998\pi$
$211$	−0.608168	−	1.05338i	−0.0418680	−	0.0725176i	−0.886200	+	0.463303i	$0.846664\pi$
$212$	6.21780	−	10.7695i	0.427040	−	0.739655i
$213$	1.33842	+	2.58331i	0.0917071	+	0.177005i
$214$	−3.89037	−	6.73832i	−0.265940	−	0.460622i
$215$	2.14766	+	3.71986i	0.146469	+	0.253693i
$216$	−5.14766	−	0.708209i	−0.350254	−	0.0481875i
$217$		0			0
$218$	−3.75729	+	6.50783i	−0.254476	+	0.440766i
$219$	22.9107	+	1.04484i	1.54816	+	0.0706040i
$220$	−1.67977			−0.113250
$221$	−5.45331			−0.366829
$222$	8.50214	−	13.2887i	0.570626	−	0.891880i
$223$	0.445916	−	0.772349i	0.0298607	−	0.0517203i	−0.850709	−	0.525637i	$-0.823827\pi$
$223$	0.445916	−	0.772349i	0.0298607	−	0.0517203i	0.880570	+	0.473917i	$0.157160\pi$
$224$		0			0
$225$	−14.3042	−	1.30740i	−0.953612	−	0.0871603i
$226$	3.03064	+	5.24922i	0.201595	+	0.349173i
$227$	−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	$0.994966\pi$
$228$	−3.78434	+	5.91486i	−0.250624	+	0.391721i
$229$	−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
$233$	7.21420	+	12.4954i	0.472618	+	0.818598i	0.999509	−	0.0313345i	$-0.00997571\pi$
$233$	7.21420	+	12.4954i	0.472618	+	0.818598i	−0.526891	+	0.849933i	$0.676642\pi$
$234$	4.36333	+	0.398809i	0.285240	+	0.0260710i
$235$	0.535897	−	0.928200i	0.0349580	−	0.0605491i
$236$	12.8961			0.839465
$237$	−3.98968	−	7.70055i	−0.259158	−	0.500205i
$238$		0			0
$239$	−9.15486	−	15.8567i	−0.592179	−	1.02568i	−0.993938	−	0.109938i	$-0.964935\pi$
$239$	−9.15486	−	15.8567i	−0.592179	−	1.02568i	0.401760	−	0.915745i	$-0.368399\pi$
$240$	−0.796790	−	0.0363376i	−0.0514326	−	0.00234558i
$241$	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	$0.832376\pi$
$242$	−1.15272	+	1.99658i	−0.0741000	+	0.128345i
$243$	10.6424	−	11.3903i	0.682711	−	0.730689i
$244$	−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
$248$	0.514589			0.0326764
$249$	−11.5021	−	0.524555i	−0.728918	−	0.0332424i
$250$	−4.50739			−0.285072
$251$	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
$254$	8.80992			0.552783
$255$	−1.60505	+	2.50867i	−0.100512	+	0.157099i
$256$	1.00000			0.0625000
$257$	−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
$261$	−11.2843	−	24.4466i	−0.698483	−	1.51320i
$262$	10.5687	−	18.3055i	0.652935	−	1.13092i
$263$	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	$0.782426\pi$
$264$	−3.40496	+	5.32190i	−0.209561	+	0.327540i
$265$	2.86333	+	4.95943i	0.175893	+	0.304655i
$266$		0			0
$267$	−2.54523	+	3.97816i	−0.155766	+	0.243459i
$268$	−2.32023			−0.141731
$269$	−8.42840	+	14.5984i	−0.513889	+	0.890081i	0.485981	+	0.873969i	$0.338462\pi$
$269$	−8.42840	+	14.5984i	−0.513889	+	0.890081i	−0.999870	+	0.0161123i	$0.994871\pi$
$270$	1.46770	−	1.88987i	0.0893215	−	0.115014i
$271$	−12.5562	−	21.7480i	−0.762736	−	1.32110i	−0.941435	−	0.337194i	$-0.890522\pi$
$271$	−12.5562	−	21.7480i	−0.762736	−	1.32110i	0.178699	−	0.983904i	$-0.442811\pi$
$272$	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
$276$	−1.96050	−	0.0894089i	−0.118009	−	0.00538178i
$277$	−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	$0.865726\pi$
$278$	1.01245	+	1.75362i	0.0607229	+	0.105175i
$279$	−0.890369	+	1.26113i	−0.0533050	+	0.0755022i
$280$		0			0
$281$	−10.1388	+	17.5609i	−0.604831	+	1.04760i	0.387248	+	0.921976i	$0.373426\pi$
$281$	−10.1388	+	17.5609i	−0.604831	+	1.04760i	−0.992078	+	0.125622i	$0.959907\pi$
$282$	−1.85447	−	3.57935i	−0.110432	−	0.213147i
$283$	−17.3494			−1.03132			−0.515658	−	0.856795i	$-0.672452\pi$
$283$	−17.3494			−1.03132			−0.515658	+	0.856795i	$0.672452\pi$
$284$	1.67977			0.0996758
$285$	−1.48755	−	2.87114i	−0.0881147	−	0.170072i
$286$	2.66372	−	4.61369i	0.157509	−	0.272813i
$287$		0			0
$288$	−1.73025	+	2.45076i	−0.101956	+	0.144412i
$289$	1.52918	+	2.64861i	0.0899517	+	0.155801i
$290$	−2.06654	−	3.57935i	−0.121351	−	0.210187i
$291$	19.3566	+	0.882759i	1.13470	+	0.0517483i
$292$	6.62062	−	11.4673i	0.387443	−	0.671070i
$293$	4.93560	+	8.54871i	0.288341	+	0.499421i	0.973414	−	0.229054i	$-0.0735631\pi$
$293$	4.93560	+	8.54871i	0.288341	+	0.499421i	−0.685073	+	0.728474i	$0.740230\pi$
$294$		0			0
$295$	−2.96936	+	5.14308i	−0.172883	+	0.299442i
$296$	−4.55408	−	7.88791i	−0.264701	−	0.458475i
$297$	−7.15126	−	17.5530i	−0.414958	−	1.01853i
$298$	4.58113	−	7.93474i	0.265378	−	0.459647i
$299$	1.65486			0.0957031
$300$	−4.46936	+	6.98554i	−0.258039	+	0.403310i
$301$		0			0
$302$	0.0519482	+	0.0899768i	0.00298928	+	0.00517759i
$303$	−12.8406	+	20.0696i	−0.737671	+	1.15297i
$304$	2.02704	+	3.51094i	0.116259	+	0.201366i
$305$	2.78220	−	4.81891i	0.159308	−	0.275930i
$306$	4.69455	+	10.1703i	0.268370	+	0.581400i
$307$	−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
$311$	−15.4107			−0.873860			−0.436930	−	0.899495i	$-0.643934\pi$
$311$	−15.4107			−0.873860			−0.436930	+	0.899495i	$0.643934\pi$
$312$	1.36333	−	2.13086i	0.0771832	−	0.120636i
$313$	−8.49688			−0.480272			−0.240136	−	0.970739i	$-0.577192\pi$
$313$	−8.49688			−0.480272			−0.240136	+	0.970739i	$0.577192\pi$
$314$	−20.9823			−1.18410
$315$		0			0
$316$	−5.00720			−0.281677
$317$	−14.1052			−0.792229			−0.396115	−	0.918201i	$-0.629642\pi$
$317$	−14.1052			−0.792229			−0.396115	+	0.918201i	$0.629642\pi$
$318$	21.5167	+	0.981271i	1.20660	+	0.0550270i
$319$	−32.7381			−1.83298
$320$	−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
$324$	−3.01245	−	8.48087i	−0.167359	−	0.471159i
$325$	3.49640	−	6.05594i	0.193945	−	0.335923i
$326$	−11.5182	−	19.9501i	−0.637933	−	1.10493i
$327$	−13.0021	−	0.592963i	−0.719020	−	0.0327909i
$328$	0.472958	+	0.819187i	0.0261147	+	0.0452320i
$329$		0			0
$330$	−1.33842	−	2.58331i	−0.0736776	−	0.142206i
$331$	27.5438			1.51394			0.756971	−	0.653448i	$-0.226678\pi$
$331$	27.5438			1.51394			0.756971	+	0.653448i	$0.226678\pi$
$332$	−3.32383	+	5.75705i	−0.182419	+	0.315959i
$333$	27.2111	+	2.48710i	1.49116	+	0.136292i
$334$	5.31498	+	9.20581i	0.290823	+	0.503720i
$335$	0.534239	−	0.925330i	0.0291886	−	0.0505562i
$336$		0			0
$337$	0.748440	+	1.29634i	0.0407701	+	0.0706159i	0.885690	−	0.464276i	$-0.153686\pi$
$337$	0.748440	+	1.29634i	0.0407701	+	0.0706159i	−0.844920	+	0.534892i	$0.820352\pi$
$338$	5.43346	−	9.41103i	0.295541	−	0.511893i
$339$	−5.65798	+	8.84334i	−0.307299	+	0.480304i
$340$	0.859728	+	1.48909i	0.0466253	+	0.0807574i
$341$	0.938524	+	1.62557i	0.0508239	+	0.0880296i
$342$	−12.1118	−	1.10702i	−0.654929	−	0.0598607i
$343$		0			0
$344$	4.66372	−	8.07779i	0.251451	−	0.435525i
$345$	0.487068	−	0.761280i	0.0262229	−	0.0409859i
$346$	−2.93872			−0.157986
$347$	−18.2881			−0.981758			−0.490879	−	0.871228i	$-0.663324\pi$
$347$	−18.2881			−0.981758			−0.490879	+	0.871228i	$0.663324\pi$
$348$	−15.5292	−	0.708209i	−0.832451	−	0.0379640i
$349$	3.90136	−	6.75735i	0.208835	−	0.361713i	−0.742513	−	0.669832i	$-0.766366\pi$
$349$	3.90136	−	6.75735i	0.208835	−	0.361713i	0.951348	+	0.308119i	$0.0996995\pi$
$350$		0			0
$351$	2.86333	+	7.02811i	0.152833	+	0.375133i
$352$	1.82383	+	3.15897i	0.0972106	+	0.168374i
$353$	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	$0.579056\pi$
$354$	10.2755	+	19.8329i	0.546136	+	1.05411i
$355$	−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
$359$	−3.13161	−	5.42411i	−0.165280	−	0.286274i	0.771475	−	0.636260i	$-0.219519\pi$
$359$	−3.13161	−	5.42411i	−0.165280	−	0.286274i	−0.936755	+	0.349987i	$0.886186\pi$
$360$	−0.578990	−	1.25433i	−0.0305155	−	0.0661092i
$361$	1.28220	−	2.22084i	0.0674842	−	0.116886i
$362$	−22.4284			−1.17881
$363$	−3.98901	−	0.181919i	−0.209369	−	0.00954827i
$364$		0			0
$365$	3.04883	+	5.28073i	0.159583	+	0.276406i
$366$	−9.62782	−	18.5828i	−0.503254	−	0.971339i
$367$	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	$0.556552\pi$
$368$	−0.566537	+	0.981271i	−0.0295328	+	0.0511523i
$369$	−2.82597	−	0.258294i	−0.147114	−	0.0134462i
$370$	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	$0.319668\pi$
$374$	13.6198			0.704265
$375$	−3.59144	−	6.93190i	−0.185461	−	0.357962i
$376$	−2.32743			−0.120028
$377$	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	$0.695371\pi$
$380$	−1.86693			−0.0957713
$381$	7.01965	+	13.5487i	0.359628	+	0.694123i
$382$	2.48968			0.127383
$383$	−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
$387$	11.7273	+	25.4063i	0.596134	+	1.29147i
$388$	5.59358	−	9.68836i	0.283971	−	0.491852i
$389$	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	$0.633889\pi$
$390$	0.535897	+	1.03434i	0.0271362	+	0.0523760i
$391$	2.11537	+	3.66392i	0.106979	+	0.185292i
$392$		0			0
$393$	36.5729	+	1.66791i	1.84486	+	0.0841350i
$394$	12.7339			0.641522
$395$	1.15292	−	1.99691i	0.0580097	−	0.100476i
$396$	−10.8976	−	0.996040i	−0.547623	−	0.0500529i
$397$	5.13307	+	8.89075i	0.257622	+	0.446214i	0.965604	−	0.260016i	$-0.0837279\pi$
$397$	5.13307	+	8.89075i	0.257622	+	0.446214i	−0.707983	+	0.706230i	$0.750395\pi$
$398$	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	$0.843405\pi$
$402$	−1.84874	−	3.56828i	−0.0922067	−	0.177970i
$403$	−0.375780	−	0.650870i	−0.0187189	−	0.0324221i
$404$	6.87792	+	11.9129i	0.342189	+	0.592689i
$405$	4.07587	+	0.751347i	0.202532	+	0.0373348i
$406$		0			0
$407$	16.6118	−	28.7724i	0.823415	−	1.42620i
$408$	6.46050	+	0.294632i	0.319843	+	0.0145864i
$409$	3.48968			0.172554			0.0862769	−	0.996271i	$-0.472503\pi$
$409$	3.48968			0.172554			0.0862769	+	0.996271i	$0.472503\pi$
$410$	−0.435599			−0.0215127
$411$	−4.11323	+	6.42892i	−0.202891	+	0.317115i
$412$	5.58113	−	9.66679i	0.274962	−	0.476249i
$413$		0			0
$414$	−1.42461	−	3.08629i	−0.0700157	−	0.151683i
$415$	−1.53064	−	2.65115i	−0.0751362	−	0.130140i
$416$	−0.730252	−	1.26483i	−0.0358036	−	0.0620136i
$417$	−1.89017	+	2.95431i	−0.0925622	+	0.144673i
$418$	−7.39397	+	12.8067i	−0.361651	+	0.626398i
$419$	−14.4897	−	25.0969i	−0.707867	−	1.22606i	−0.965647	−	0.259858i	$-0.916324\pi$
$419$	−14.4897	−	25.0969i	−0.707867	−	1.22606i	0.257779	−	0.966204i	$-0.417009\pi$
$420$		0			0
$421$	−1.06128	+	1.83819i	−0.0517237	+	0.0895881i	−0.890728	−	0.454537i	$-0.849805\pi$
$421$	−1.06128	+	1.83819i	−0.0517237	+	0.0895881i	0.839004	+	0.544125i	$0.183138\pi$
$422$	−0.608168	−	1.05338i	−0.0296052	−	0.0512777i
$423$	4.02704	−	5.70397i	0.195801	−	0.277337i
$424$	6.21780	−	10.7695i	0.301963	−	0.523015i
$425$	17.8774			0.867183
$426$	1.33842	+	2.58331i	0.0648467	+	0.125162i
$427$		0			0
$428$	−3.89037	−	6.73832i	−0.188048	−	0.325709i
$429$	9.21780	+	0.420378i	0.445040	+	0.0202960i
$430$	2.14766	+	3.71986i	0.103570	+	0.179388i
$431$	10.9356	−	18.9410i	0.526749	−	0.912356i	−0.472765	−	0.881189i	$-0.656744\pi$
$431$	10.9356	−	18.9410i	0.526749	−	0.912356i	0.999514	−	0.0311679i	$-0.00992265\pi$
$432$	−5.14766	−	0.708209i	−0.247667	−	0.0340737i
$433$	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
$437$	−4.59358			−0.219741
$438$	22.9107	+	1.04484i	1.09472	+	0.0499245i
$439$	−4.86400			−0.232146			−0.116073	−	0.993241i	$-0.537031\pi$
$439$	−4.86400			−0.232146			−0.116073	+	0.993241i	$0.537031\pi$
$440$	−1.67977			−0.0800797
$441$		0			0
$442$	−5.45331			−0.259387
$443$	−11.5395			−0.548258			−0.274129	−	0.961693i	$-0.588390\pi$
$443$	−11.5395			−0.548258			−0.274129	+	0.961693i	$0.588390\pi$
$444$	8.50214	−	13.2887i	0.403494	−	0.630654i
$445$	−1.25564			−0.0595229
$446$	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	$0.714306\pi$
$450$	−14.3042	−	1.30740i	−0.674306	−	0.0616317i
$451$	−1.72519	+	2.98812i	−0.0812361	+	0.140705i
$452$	3.03064	+	5.24922i	0.142549	+	0.246903i
$453$	−0.0969833	+	0.151584i	−0.00455667	+	0.00712201i
$454$	−7.32597	−	12.6889i	−0.343825	−	0.595522i
$455$		0			0
$456$	−3.78434	+	5.91486i	−0.177218	+	0.276989i
$457$	−3.73812			−0.174862			−0.0874310	−	0.996171i	$-0.527866\pi$
$457$	−3.73812			−0.174862			−0.0874310	+	0.996171i	$0.527866\pi$
$458$	−4.78794	+	8.29295i	−0.223726	+	0.387504i
$459$	−11.9004	+	15.3234i	−0.555462	+	0.715233i
$460$	−0.260893	−	0.451880i	−0.0121642	−	0.0210690i
$461$	7.90496	−	13.6918i	0.368171	−	0.637690i	−0.621109	−	0.783724i	$-0.713318\pi$
$461$	7.90496	−	13.6918i	0.368171	−	0.637690i	0.989280	+	0.146034i	$0.0466509\pi$
$462$		0			0
$463$	19.1965	+	33.2493i	0.892137	+	1.54523i	0.837309	+	0.546730i	$0.184128\pi$
$463$	19.1965	+	33.2493i	0.892137	+	1.54523i	0.0548278	+	0.998496i	$0.482539\pi$
$464$	−4.48755	+	7.77266i	−0.208329	+	0.360837i
$465$	−0.410019	−	0.0186989i	−0.0190142	−	0.000867143i
$466$	7.21420	+	12.4954i	0.334191	+	0.578836i
$467$	−3.15652	−	5.46725i	−0.146066	−	0.252994i	0.783704	−	0.621134i	$-0.213328\pi$
$467$	−3.15652	−	5.46725i	−0.146066	−	0.252994i	−0.929770	+	0.368140i	$0.879995\pi$
$468$	4.36333	+	0.398809i	0.201695	+	0.0184349i
$469$		0			0
$470$	0.535897	−	0.928200i	0.0247191	−	0.0428147i
$471$	−16.7185	−	32.2686i	−0.770347	−	1.48686i
$472$	12.8961			0.593591
$473$	34.0233			1.56439
$474$	−3.98968	−	7.70055i	−0.183252	−	0.353698i
$475$	−9.70535	+	16.8102i	−0.445312	+	0.771303i
$476$		0			0
$477$	15.6352	+	33.8724i	0.715887	+	1.55091i
$478$	−9.15486	−	15.8567i	−0.418734	−	0.725268i
$479$	−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	$0.987769\pi$
$480$	−0.796790	−	0.0363376i	−0.0363683	−	0.00165858i
$481$	−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
$485$	2.57587	+	4.46154i	0.116964	+	0.202588i
$486$	10.6424	−	11.3903i	0.482749	−	0.516675i
$487$	6.18190	−	10.7074i	0.280129	−	0.485197i	−0.691287	−	0.722580i	$-0.742956\pi$
$487$	6.18190	−	10.7074i	0.280129	−	0.485197i	0.971416	+	0.237383i	$0.0762895\pi$
$488$	−12.0833			−0.546984
$489$	21.5036	−	33.6098i	0.972426	−	1.51989i
$490$		0			0
$491$	0.207004	+	0.358541i	0.00934194	+	0.0161807i	0.870659	−	0.491888i	$-0.163693\pi$
$491$	0.207004	+	0.358541i	0.00934194	+	0.0161807i	−0.861317	+	0.508069i	$0.830360\pi$
$492$	−0.882977	+	1.38008i	−0.0398077	+	0.0622188i
$493$	16.7558	+	29.0220i	0.754645	+	1.30708i
$494$	2.96050	−	5.12774i	0.133199	−	0.230708i
$495$	2.90642	−	4.11671i	0.130634	−	0.185032i
$496$	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	$0.160083\pi$
$500$	−4.50739			−0.201577
$501$	−9.92267	+	15.5090i	−0.443312	+	0.692890i
$502$	18.2733			0.815579
$503$	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
$506$	−4.13307			−0.183738
$507$	18.8025	+	0.857490i	0.835049	+	0.0380825i
$508$	8.80992			0.390877
$509$	−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
$513$	−7.94805	−	19.5087i	−0.350915	−	0.861330i
$514$	−10.5256	+	18.2308i	−0.464263	+	0.804128i
$515$	2.57014	+	4.45161i	0.113254	+	0.196161i
$516$	16.1388	+	0.736011i	0.710471	+	0.0324011i
$517$	−4.24484	−	7.35228i	−0.186688	−	0.323353i
$518$		0			0
$519$	−2.34154	−	4.51945i	−0.102782	−	0.198382i
$520$	0.672570			0.0294941
$521$	13.4518	−	23.2993i	0.589336	−	1.02076i	−0.404984	−	0.914324i	$-0.632723\pi$
$521$	13.4518	−	23.2993i	0.589336	−	1.02076i	0.994320	−	0.106436i	$-0.0339439\pi$
$522$	−11.2843	−	24.4466i	−0.493902	−	1.07000i
$523$	7.85301	+	13.6018i	0.343388	+	0.594766i	0.985060	−	0.172214i	$-0.0550920\pi$
$523$	7.85301	+	13.6018i	0.343388	+	0.594766i	−0.641671	+	0.766980i	$0.721759\pi$
$524$	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
$528$	−3.40496	+	5.32190i	−0.148182	+	0.231606i
$529$	10.8581	+	18.8067i	0.472090	+	0.817684i
$530$	2.86333	+	4.95943i	0.124375	+	0.215424i
$531$	−22.3135	+	31.6053i	−0.968324	+	1.37155i
$532$		0			0
$533$	0.690757	−	1.19643i	0.0299200	−	0.0518230i
$534$	−2.54523	+	3.97816i	−0.110143	+	0.172152i
$535$	3.58307			0.154910
$536$	−2.32023			−0.100219
$537$	−15.8530	−	0.722977i	−0.684108	−	0.0311988i
$538$	−8.42840	+	14.5984i	−0.363374	+	0.629383i
$539$		0			0
$540$	1.46770	−	1.88987i	0.0631598	−	0.0813269i
$541$	−2.05934	−	3.56688i	−0.0885379	−	0.153352i	0.818355	−	0.574713i	$-0.194886\pi$
$541$	−2.05934	−	3.56688i	−0.0885379	−	0.153352i	−0.906893	+	0.421360i	$0.861553\pi$
$542$	−12.5562	−	21.7480i	−0.539336	−	0.934157i
$543$	−17.8707	−	34.4926i	−0.766906	−	1.48022i
$544$	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	0.492860	+	0.870108i	$0.335951\pi$
$547$	−11.8602	+	20.5425i	−0.507106	+	0.878333i	−0.999966	+	0.00822465i	$0.997382\pi$
$548$	2.20321	+	3.81607i	0.0941165	+	0.163015i
$549$	20.9071	−	29.6132i	0.892293	−	1.26386i
$550$	−8.73239	+	15.1249i	−0.372350	+	0.644930i
$551$	−36.3858			−1.55009
$552$	−1.96050	−	0.0894089i	−0.0834446	−	0.00380550i
$553$		0			0
$554$	−1.69076	−	2.92848i	−0.0718334	−	0.124419i
$555$	3.34202	+	6.45049i	0.141861	+	0.273808i
$556$	1.01245	+	1.75362i	0.0429376	+	0.0743701i
$557$	−21.0313	+	36.4273i	−0.891125	+	1.54347i	−0.0525975	+	0.998616i	$0.516750\pi$
$557$	−21.0313	+	36.4273i	−0.891125	+	1.54347i	−0.838528	+	0.544859i	$0.816583\pi$
$558$	−0.890369	+	1.26113i	−0.0376923	+	0.0533881i
$559$	−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
$563$	−11.8243			−0.498335			−0.249168	−	0.968460i	$-0.580157\pi$
$563$	−11.8243			−0.498335			−0.249168	+	0.968460i	$0.580157\pi$
$564$	−1.85447	−	3.57935i	−0.0780874	−	0.150718i
$565$	−2.79125			−0.117429
$566$	−17.3494			−0.729250
$567$		0			0
$568$	1.67977			0.0704815
$569$	14.2016			0.595360			0.297680	−	0.954666i	$-0.403787\pi$
$569$	14.2016			0.595360			0.297680	+	0.954666i	$0.403787\pi$
$570$	−1.48755	−	2.87114i	−0.0623065	−	0.120259i
$571$	11.9574			0.500401			0.250200	−	0.968194i	$-0.419503\pi$
$571$	11.9574			0.500401			0.250200	+	0.968194i	$0.419503\pi$
$572$	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
$576$	−1.73025	+	2.45076i	−0.0720939	+	0.102115i
$577$	−21.3135	+	36.9161i	−0.887293	+	1.53684i	−0.0442307	+	0.999021i	$0.514084\pi$
$577$	−21.3135	+	36.9161i	−0.887293	+	1.53684i	−0.843062	+	0.537816i	$0.819250\pi$
$578$	1.52918	+	2.64861i	0.0636054	+	0.110168i
$579$	3.57733	+	6.90467i	0.148669	+	0.286948i
$580$	−2.06654	−	3.57935i	−0.0858083	−	0.148624i
$581$		0			0
$582$	19.3566	+	0.882759i	0.802357	+	0.0365915i
$583$	45.3609			1.87866
$584$	6.62062	−	11.4673i	0.273963	−	0.474518i
$585$	−1.16372	+	1.64831i	−0.0481137	+	0.0681491i
$586$	4.93560	+	8.54871i	0.203888	+	0.353144i
$587$	−20.5328	+	35.5638i	−0.847478	+	1.46788i	0.0359730	+	0.999353i	$0.488547\pi$
$587$	−20.5328	+	35.5638i	−0.847478	+	1.46788i	−0.883451	+	0.468523i	$0.844786\pi$
$588$		0			0
$589$	1.04309	+	1.80669i	0.0429799	+	0.0744434i
$590$	−2.96936	+	5.14308i	−0.122247	+	0.211737i
$591$	10.1462	+	19.5833i	0.417359	+	0.805551i
$592$	−4.55408	−	7.88791i	−0.187172	−	0.324191i
$593$	−16.1008	−	27.8874i	−0.661180	−	1.14520i	−0.980306	−	0.197485i	$-0.936723\pi$
$593$	−16.1008	−	27.8874i	−0.661180	−	1.14520i	0.319126	−	0.947712i	$-0.396611\pi$
$594$	−7.15126	−	17.5530i	−0.293420	−	0.720207i
$595$		0			0
$596$	4.58113	−	7.93474i	0.187650	−	0.325020i
$597$	5.09718	+	0.232457i	0.208614	+	0.00951383i
$598$	1.65486			0.0676723
$599$	19.0718			0.779252			0.389626	−	0.920973i	$-0.372604\pi$
$599$	19.0718			0.779252			0.389626	+	0.920973i	$0.372604\pi$
$600$	−4.46936	+	6.98554i	−0.182461	+	0.285184i
$601$	−4.27188	+	7.39912i	−0.174254	+	0.301816i	−0.939903	−	0.341442i	$-0.889085\pi$
$601$	−4.27188	+	7.39912i	−0.174254	+	0.301816i	0.765649	+	0.643259i	$0.222418\pi$
$602$		0			0
$603$	4.01459	−	5.68634i	0.163487	−	0.231565i
$604$	0.0519482	+	0.0899768i	0.00211374	+	0.00366111i
$605$	−0.530835	−	0.919434i	−0.0215815	−	0.0373803i
$606$	−12.8406	+	20.0696i	−0.521612	+	0.815272i
$607$	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
$611$	1.69961	+	2.94381i	0.0687589	+	0.119094i
$612$	4.69455	+	10.1703i	0.189766	+	0.411112i
$613$	11.3296	−	19.6234i	0.457597	−	0.792581i	−0.541237	−	0.840870i	$-0.682044\pi$
$613$	11.3296	−	19.6234i	0.457597	−	0.792581i	0.998833	+	0.0482894i	$0.0153770\pi$
$614$	−7.78794			−0.314295
$615$	−0.347081	−	0.669906i	−0.0139956	−	0.0270132i
$616$		0			0
$617$	−10.1388	−	17.5609i	−0.408173	−	0.706977i	0.586512	−	0.809941i	$-0.300501\pi$
$617$	−10.1388	−	17.5609i	−0.408173	−	0.706977i	−0.994685	+	0.102964i	$0.967167\pi$
$618$	19.3135	+	0.880794i	0.776904	+	0.0354307i
$619$	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	$0.820144\pi$
$620$	−0.118485	+	0.205223i	−0.00475849	+	0.00824194i
$621$	3.61129	−	4.65003i	0.144916	−	0.186599i
$622$	−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
$626$	−8.49688			−0.339604
$627$	−25.5869	−	1.16689i	−1.02184	−	0.0466011i
$628$	−20.9823			−0.837285
$629$	−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	$0.489625\pi$
$632$	−5.00720			−0.199176
$633$	1.13541	−	1.77462i	0.0451283	−	0.0705349i
$634$	−14.1052			−0.560191
$635$	−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
$639$	−2.90642	+	4.11671i	−0.114976	+	0.162854i
$640$	−0.230252	+	0.398809i	−0.00910153	+	0.0157643i
$641$	−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	$0.975928\pi$
$642$	7.26303	−	11.3520i	0.286649	−	0.448028i
$643$	14.1819	+	24.5638i	0.559280	+	0.968701i	0.997557	+	0.0698609i	$0.0222555\pi$
$643$	14.1819	+	24.5638i	0.559280	+	0.968701i	−0.438277	+	0.898840i	$0.644411\pi$
$644$		0			0
$645$	−4.00953	+	6.26683i	−0.157875	+	0.246756i
$646$	15.1373			0.595571
$647$	−17.3904	+	30.1210i	−0.683686	+	1.18418i	0.290162	+	0.956978i	$0.406291\pi$
$647$	−17.3904	+	30.1210i	−0.683686	+	1.18418i	−0.973848	+	0.227201i	$0.927042\pi$
$648$	−3.01245	−	8.48087i	−0.118340	−	0.333160i
$649$	23.5203	+	40.7384i	0.923253	+	1.59912i
$650$	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	$0.146732\pi$
$654$	−13.0021	−	0.592963i	−0.508424	−	0.0231867i
$655$	4.86693	+	8.42976i	0.190167	+	0.329378i
$656$	0.472958	+	0.819187i	0.0184659	+	0.0319839i
$657$	16.6481	+	36.0668i	0.649506	+	1.40710i
$658$		0			0
$659$	5.30418	−	9.18711i	0.206622	−	0.357879i	−0.744027	−	0.668150i	$-0.767086\pi$
$659$	5.30418	−	9.18711i	0.206622	−	0.357879i	0.950648	+	0.310271i	$0.100420\pi$
$660$	−1.33842	−	2.58331i	−0.0520980	−	0.100555i
$661$	−10.1301			−0.394017			−0.197009	−	0.980402i	$-0.563123\pi$
$661$	−10.1301			−0.394017			−0.197009	+	0.980402i	$0.563123\pi$
$662$	27.5438			1.07052
$663$	−4.34514	−	8.38662i	−0.168751	−	0.325709i
$664$	−3.32383	+	5.75705i	−0.128990	+	0.223417i
$665$		0			0
$666$	27.2111	+	2.48710i	1.05441	+	0.0963731i
$667$	−5.08472	−	8.80700i	−0.196881	−	0.341008i
$668$	5.31498	+	9.20581i	0.205643	+	0.356184i
$669$	1.54309	+	0.0703729i	0.0596595	+	0.00272077i
$670$	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	−0.833365	−	0.552724i	$-0.813589\pi$
$673$	1.60817	−	2.78543i	0.0619903	−	0.107370i	0.895355	+	0.445353i	$0.146922\pi$
$674$	0.748440	+	1.29634i	0.0288288	+	0.0499330i
$675$	−9.38677	−	23.0401i	−0.361297	−	0.886813i
$676$	5.43346	−	9.41103i	0.208979	−	0.361963i
$677$	29.3638			1.12854			0.564271	−	0.825589i	$-0.309157\pi$
$677$	29.3638			1.12854			0.564271	+	0.825589i	$0.309157\pi$
$678$	−5.65798	+	8.84334i	−0.217293	+	0.339626i
$679$		0			0
$680$	0.859728	+	1.48909i	0.0329691	+	0.0571041i
$681$	13.6770	−	21.3770i	0.524105	−	0.819169i
$682$	0.938524	+	1.62557i	0.0359379	+	0.0622463i
$683$	12.6278	−	21.8720i	0.483190	−	0.836910i	−0.516624	−	0.856213i	$-0.672811\pi$
$683$	12.6278	−	21.8720i	0.483190	−	0.836910i	0.999814	+	0.0193029i	$0.00614468\pi$
$684$	−12.1118	−	1.10702i	−0.463105	−	0.0423279i
$685$	−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
$689$	−18.1623			−0.691927
$690$	0.487068	−	0.761280i	0.0185424	−	0.0289814i
$691$	15.3638			0.584467			0.292233	−	0.956347i	$-0.405602\pi$
$691$	15.3638			0.584467			0.292233	+	0.956347i	$0.405602\pi$
$692$	−2.93872			−0.111713
$693$		0			0
$694$	−18.2881			−0.694208
$695$	−0.932479			−0.0353709
$696$	−15.5292	−	0.708209i	−0.588632	−	0.0268446i
$697$	3.53191			0.133781
$698$	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	$0.581249\pi$
$702$	2.86333	+	7.02811i	0.108069	+	0.265259i
$703$	18.4626	−	31.9782i	0.696332	−	1.20608i
$704$	1.82383	+	3.15897i	0.0687382	+	0.119058i
$705$	1.85447	+	0.0845733i	0.0698435	+	0.00318522i
$706$	13.4626	+	23.3180i	0.506673	+	0.877584i
$707$		0			0
$708$	10.2755	+	19.8329i	0.386176	+	0.745365i
$709$	−1.12588			−0.0422832			−0.0211416	−	0.999776i	$-0.506730\pi$
$709$	−1.12588			−0.0422832			−0.0211416	+	0.999776i	$0.506730\pi$
$710$	−0.386770	+	0.669906i	−0.0145152	+	0.0251411i
$711$	8.66372	−	12.2714i	0.324915	−	0.460215i
$712$	1.36333	+	2.36135i	0.0510928	+	0.0884954i
$713$	−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
$717$	17.0914	−	26.7137i	0.638292	−	0.997640i
$718$	−3.13161	−	5.42411i	−0.116871	−	0.202426i
$719$	−9.13667	−	15.8252i	−0.340740	−	0.590180i	0.643830	−	0.765169i	$-0.277344\pi$
$719$	−9.13667	−	15.8252i	−0.340740	−	0.590180i	−0.984570	+	0.174989i	$0.944011\pi$
$720$	−0.578990	−	1.25433i	−0.0215777	−	0.0467463i
$721$		0			0
$722$	1.28220	−	2.22084i	0.0477186	−	0.0826510i
$723$	−0.0871712	+	0.136247i	−0.00324193	+	0.00506709i
$724$	−22.4284			−0.833545
$725$	−42.9722			−1.59595
$726$	−3.98901	−	0.181919i	−0.148046	−	0.00675165i
$727$	14.8478	−	25.7171i	0.550673	−	0.953793i	−0.447553	−	0.894257i	$-0.647705\pi$
$727$	14.8478	−	25.7171i	0.550673	−	0.953793i	0.998226	−	0.0595359i	$-0.0189621\pi$
$728$		0			0
$729$	25.9969	+	7.29124i	0.962847	+	0.270046i
$730$	3.04883	+	5.28073i	0.112842	+	0.195448i
$731$	−17.4136	−	30.1613i	−0.644066	−	1.11555i
$732$	−9.62782	−	18.5828i	−0.355854	−	0.686840i
$733$	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
$737$	−4.23171	−	7.32955i	−0.155877	−	0.269987i
$738$	−2.82597	−	0.258294i	−0.104025	−	0.00950793i
$739$	−15.1336	+	26.2121i	−0.556697	+	0.964227i	0.441073	+	0.897471i	$0.354598\pi$
$739$	−15.1336	+	26.2121i	−0.556697	+	0.964227i	−0.997769	+	0.0667556i	$0.978735\pi$
$740$	4.19436			0.154188
$741$	10.2448	+	0.467216i	0.376354	+	0.0171636i
$742$		0			0
$743$	−11.8815	−	20.5794i	−0.435890	−	0.754984i	0.561477	−	0.827492i	$-0.310233\pi$
$743$	−11.8815	−	20.5794i	−0.435890	−	0.754984i	−0.997368	+	0.0725076i	$0.976900\pi$
$744$	0.410019	+	0.791385i	0.0150320	+	0.0290136i
$745$	2.10963	+	3.65399i	0.0772909	+	0.133872i
$746$	−8.92986	+	15.4670i	−0.326946	+	0.566286i
$747$	−8.35807	−	18.1071i	−0.305806	−	0.662503i
$748$	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	$0.240911\pi$
$752$	−2.32743			−0.0848727
$753$	14.5600	+	28.1025i	0.530596	+	1.02411i
$754$	13.1082			0.477371
$755$	−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	$0.677232\pi$
$758$	−22.4255			−0.814530
$759$	−3.29319	−	6.35624i	−0.119535	−	0.230717i
$760$	−1.86693			−0.0677205
$761$	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
$765$	−5.13696	−	0.469519i	−0.185727	−	0.0169755i
$766$	−7.07014	+	12.2458i	−0.255454	+	0.442460i
$767$	−9.41741	−	16.3114i	−0.340043	−	0.588972i
$768$	0.796790	+	1.53790i	0.0287517	+	0.0554941i
$769$	−12.5869	−	21.8011i	−0.453894	−	0.786167i	0.544730	−	0.838611i	$-0.316632\pi$
$769$	−12.5869	−	21.8011i	−0.453894	−	0.786167i	−0.998624	+	0.0524443i	$0.983299\pi$
$770$		0			0
$771$	−36.4238	−	1.66111i	−1.31177	−	0.0598234i
$772$	4.48968			0.161587
$773$	0.752039	−	1.30257i	0.0270490	−	0.0468502i	−0.852184	−	0.523242i	$-0.824722\pi$
$773$	0.752039	−	1.30257i	0.0270490	−	0.0468502i	0.879233	+	0.476392i	$0.158056\pi$
$774$	11.7273	+	25.4063i	0.421530	+	0.913209i
$775$	1.23191	+	2.13373i	0.0442515	+	0.0766458i
$776$	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
$780$	0.535897	+	1.03434i	0.0191882	+	0.0370354i
$781$	3.06361	+	5.30633i	0.109625	+	0.189875i
$782$	2.11537	+	3.66392i	0.0756453	+	0.131022i
$783$	28.6050	−	36.8329i	1.02226	−	1.31630i
$784$		0			0
$785$	4.83122	−	8.36792i	0.172434	−	0.298664i
$786$	36.5729	+	1.66791i	1.30451	+	0.0594924i
$787$	14.9531			0.533021			0.266510	−	0.963832i	$-0.414129\pi$
$787$	14.9531			0.533021			0.266510	+	0.963832i	$0.414129\pi$
$788$	12.7339			0.453625
$789$	−4.82150	+	7.53593i	−0.171650	+	0.268286i
$790$	1.15292	−	1.99691i	0.0410190	−	0.0710470i
$791$		0			0
$792$	−10.8976	−	0.996040i	−0.387228	−	0.0353927i
$793$	8.82383	+	15.2833i	0.313343	+	0.542727i
$794$	5.13307	+	8.89075i	0.182166	+	0.315521i
$795$	−5.34562	+	8.35512i	−0.189590	+	0.296326i
$796$	1.47296	−	2.55124i	0.0522076	−	0.0904262i
$797$	4.56294	+	7.90324i	0.161628	+	0.279947i	0.935453	−	0.353452i	$-0.114992\pi$
$797$	4.56294	+	7.90324i	0.161628	+	0.279947i	−0.773825	+	0.633400i	$0.781659\pi$
$798$		0			0
$799$	−4.34514	+	7.52600i	−0.153720	+	0.266251i
$800$	2.39397	+	4.14647i	0.0846395	+	0.146600i
$801$	−8.14601	−	0.744547i	−0.287825	−	0.0263073i
$802$	−17.0167	+	29.4738i	−0.600881	+	1.04076i
$803$	48.2996			1.70446
$804$	−1.84874	−	3.56828i	−0.0652000	−	0.125843i
$805$		0			0
$806$	−0.375780	−	0.650870i	−0.0132363	−	0.0229259i
$807$	−29.1665	−	1.33014i	−1.02671	−	0.0468232i
$808$	6.87792	+	11.9129i	0.241964	+	0.419094i
$809$	17.7755	−	30.7880i	0.624953	−	1.08245i	−0.363597	−	0.931556i	$-0.618452\pi$
$809$	17.7755	−	30.7880i	0.624953	−	1.08245i	0.988550	−	0.150894i	$-0.0482151\pi$
$810$	4.07587	+	0.751347i	0.143211	+	0.0263997i
$811$	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
$815$	10.6084			0.371595
$816$	6.46050	+	0.294632i	0.226163	+	0.0103142i
$817$	37.8142			1.32295
$818$	3.48968			0.122014
$819$		0			0
$820$	−0.435599			−0.0152118
$821$	21.6228			0.754639			0.377320	−	0.926083i	$-0.376846\pi$
$821$	21.6228			0.754639			0.377320	+	0.926083i	$0.376846\pi$
$822$	−4.11323	+	6.42892i	−0.143465	+	0.224234i
$823$	−1.50700			−0.0525308			−0.0262654	−	0.999655i	$-0.508361\pi$
$823$	−1.50700			−0.0525308			−0.0262654	+	0.999655i	$0.508361\pi$
$824$	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	$0.366757\pi$
$828$	−1.42461	−	3.08629i	−0.0495086	−	0.107256i
$829$	11.0095	−	19.0691i	0.382377	−	0.662296i	−0.609025	−	0.793151i	$-0.708439\pi$
$829$	11.0095	−	19.0691i	0.382377	−	0.662296i	0.991401	+	0.130855i	$0.0417723\pi$
$830$	−1.53064	−	2.65115i	−0.0531293	−	0.0920227i
$831$	3.15652	−	4.93359i	0.109498	−	0.171144i
$832$	−0.730252	−	1.26483i	−0.0253169	−	0.0438502i
$833$		0			0
$834$	−1.89017	+	2.95431i	−0.0654514	+	0.102300i
$835$	−4.89515			−0.169404
$836$	−7.39397	+	12.8067i	−0.255726	+	0.442930i
$837$	−2.64893	−	0.364437i	−0.0915605	−	0.0125968i
$838$	−14.4897	−	25.0969i	−0.500538	−	0.866957i
$839$	1.06507	−	1.84476i	0.0367705	−	0.0636883i	−0.847055	−	0.531506i	$-0.821626\pi$
$839$	1.06507	−	1.84476i	0.0367705	−	0.0636883i	0.883825	+	0.467818i	$0.154960\pi$
$840$		0			0
$841$	−25.7762	−	44.6456i	−0.888833	−	1.53950i
$842$	−1.06128	+	1.83819i	−0.0365742	+	0.0633483i
$843$	−35.0854	−	1.60007i	−1.20841	−	0.0551094i
$844$	−0.608168	−	1.05338i	−0.0209340	−	0.0362588i
$845$	2.50214	+	4.33383i	0.0860761	+	0.149088i
$846$	4.02704	−	5.70397i	0.138453	−	0.196107i
$847$		0			0
$848$	6.21780	−	10.7695i	0.213520	−	0.369828i
$849$	−13.8238	−	26.6816i	−0.474433	−	0.915710i
$850$	17.8774			0.613191
$851$	10.3202			0.353773
$852$	1.33842	+	2.58331i	0.0458535	+	0.0885027i
$853$	3.50146	−	6.06471i	0.119888	−	0.207652i	−0.799835	−	0.600220i	$-0.795080\pi$
$853$	3.50146	−	6.06471i	0.119888	−	0.207652i	0.919723	+	0.392568i	$0.128413\pi$
$854$		0			0
$855$	3.23025	−	4.57539i	0.110472	−	0.156475i
$856$	−3.89037	−	6.73832i	−0.132970	−	0.230311i
$857$	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	$0.773570\pi$
$858$	9.21780	+	0.420378i	0.314690	+	0.0143515i
$859$	−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
$863$	−18.4231	−	31.9098i	−0.627131	−	1.08622i	−0.988125	−	0.153655i	$-0.950896\pi$
$863$	−18.4231	−	31.9098i	−0.627131	−	1.08622i	0.360993	−	0.932568i	$-0.382438\pi$
$864$	−5.14766	−	0.708209i	−0.175127	−	0.0240938i
$865$	0.676647	−	1.17199i	0.0230067	−	0.0398488i
$866$	13.0512			0.443496
$867$	−2.85486	+	4.46211i	−0.0969562	+	0.151541i
$868$		0			0
$869$	−9.13229	−	15.8176i	−0.309792	−	0.536575i
$870$	3.85807	−	6.03011i	0.130801	−	0.204440i
$871$	1.69436	+	2.93471i	0.0574111	+	0.0994389i
$872$	−3.75729	+	6.50783i	−0.127238	+	0.220383i
$873$	14.0656	+	30.4718i	0.476047	+	1.03132i
$874$	−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	$0.110704\pi$
$878$	−4.86400			−0.164152
$879$	−9.21440	+	14.4020i	−0.310794	+	0.485766i
$880$	−1.67977			−0.0566249
$881$	−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	$0.487705\pi$
$884$	−5.45331			−0.183415
$885$	−10.2755	−	0.468614i	−0.345407	−	0.0157523i
$886$	−11.5395			−0.387677
$887$	−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
$891$	21.2966	−	24.9839i	0.713463	−	0.836993i
$892$	0.445916	−	0.772349i	0.0149304	−	0.0258602i
$893$	−4.71780	−	8.17147i	−0.157875	−	0.273448i
$894$	15.8530	+	0.722977i	0.530204	+	0.0241800i
$895$	−2.10963	−	3.65399i	−0.0705172	−	0.122139i
$896$		0			0
$897$	1.31858	+	2.54500i	0.0440260	+	0.0849752i
$898$	−26.4251			−0.881817
$899$	−2.30924	+	3.99973i	−0.0770176	+	0.133398i
$900$	−14.3042	−	1.30740i	−0.476806	−	0.0435802i
$901$	−23.2163	−	40.2119i	−0.773448	−	1.33965i
$902$	−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
$906$	−0.0969833	+	0.151584i	−0.00322206	+	0.00503602i
$907$	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	$0.817835\pi$
$908$	−7.32597	−	12.6889i	−0.243121	−	0.421098i
$909$	−41.0962	−	3.75620i	−1.36307	−	0.124585i
$910$		0			0
$911$	15.3171	−	26.5300i	0.507479	−	0.878979i	−0.492484	−	0.870322i	$-0.663911\pi$
$911$	15.3171	−	26.5300i	0.507479	−	0.878979i	0.999963	−	0.00865719i	$-0.00275570\pi$
$912$	−3.78434	+	5.91486i	−0.125312	+	0.195861i
$913$	−24.2484			−0.802506
$914$	−3.73812			−0.123646
$915$	9.62782	+	0.439077i	0.318286	+	0.0145154i
$916$	−4.78794	+	8.29295i	−0.158198	+	0.274007i
$917$		0			0
$918$	−11.9004	+	15.3234i	−0.392771	+	0.505746i
$919$	13.1857	+	22.8383i	0.434956	+	0.753366i	0.997292	−	0.0735429i	$-0.0234306\pi$
$919$	13.1857	+	22.8383i	0.434956	+	0.753366i	−0.562336	+	0.826909i	$0.690097\pi$
$920$	−0.260893	−	0.451880i	−0.00860139	−	0.0148980i
$921$	−6.20535	−	11.9770i	−0.204473	−	0.394657i
$922$	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
$926$	19.1965	+	33.2493i	0.630836	+	1.09264i
$927$	14.0342	+	30.4040i	0.460945	+	0.998598i
$928$	−4.48755	+	7.77266i	−0.147311	+	0.255150i
$929$	−17.8741			−0.586431			−0.293215	−	0.956046i	$-0.594725\pi$
$929$	−17.8741			−0.586431			−0.293215	+	0.956046i	$0.594725\pi$
$930$	−0.410019	−	0.0186989i	−0.0134451	−	0.000613163i
$931$		0			0
$932$	7.21420	+	12.4954i	0.236309	+	0.409299i
$933$	−12.2791	−	23.7001i	−0.401999	−	0.775905i
$934$	−3.15652	−	5.46725i	−0.103284	−	0.178894i
$935$	−3.13600	+	5.43171i	−0.102558	+	0.177636i
$936$	4.36333	+	0.398809i	0.142620	+	0.0130355i
$937$	−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
$941$	16.2805			0.530731			0.265365	−	0.964148i	$-0.414507\pi$
$941$	16.2805			0.530731			0.265365	+	0.964148i	$0.414507\pi$
$942$	−16.7185	−	32.2686i	−0.544717	−	1.05137i
$943$	−1.07179			−0.0349024
$944$	12.8961			0.419732
$945$		0			0
$946$	34.0233			1.10619
$947$	−28.5903			−0.929059			−0.464529	−	0.885558i	$-0.653776\pi$
$947$	−28.5903			−0.929059			−0.464529	+	0.885558i	$0.653776\pi$
$948$	−3.98968	−	7.70055i	−0.129579	−	0.250102i
$949$	−19.3389			−0.627767
$950$	−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	$0.657707\pi$
$954$	15.6352	+	33.8724i	0.506209	+	1.09666i
$955$	−0.573256	+	0.992908i	−0.0185501	+	0.0321297i
$956$	−9.15486	−	15.8567i	−0.296089	−	0.512842i
$957$	−26.0854	−	50.3479i	−0.843221	−	1.62751i
$958$	−10.2068	−	17.6787i	−0.329767	−	0.571173i
$959$		0			0
$960$	−0.796790	−	0.0363376i	−0.0257163	−	0.00117279i
$961$	−30.7352			−0.991458
$962$	−6.65126	+	11.5203i	−0.214445	+	0.371430i
$963$	23.2453	+	2.12463i	0.749070	+	0.0684651i
$964$	0.0466924	+	0.0808735i	0.00150386	+	0.00260476i
$965$	−1.03376	+	1.79053i	−0.0332779	+	0.0576391i
$966$		0			0
$967$	−4.69815	−	8.13743i	−0.151082	−	0.261682i	0.780543	−	0.625102i	$-0.214943\pi$
$967$	−4.69815	−	8.13743i	−0.151082	−	0.261682i	−0.931626	+	0.363419i	$0.881609\pi$
$968$	−1.15272	+	1.99658i	−0.0370500	+	0.0641724i
$969$	12.0613	+	23.2797i	0.387464	+	0.747851i
$970$	2.57587	+	4.46154i	0.0827062	+	0.143251i
$971$	−7.77335	−	13.4638i	−0.249459	−	0.432075i	0.713917	−	0.700230i	$-0.246919\pi$
$971$	−7.77335	−	13.4638i	−0.249459	−	0.432075i	−0.963376	+	0.268155i	$0.913586\pi$
$972$	10.6424	−	11.3903i	0.341355	−	0.365344i
$973$		0			0
$974$	6.18190	−	10.7074i	0.198081	−	0.343086i
$975$	12.0993	+	0.551790i	0.387488	+	0.0176714i
$976$	−12.0833			−0.386776
$977$	−9.59785			−0.307062			−0.153531	−	0.988144i	$-0.549065\pi$
$977$	−9.59785			−0.307062			−0.153531	+	0.988144i	$0.549065\pi$
$978$	21.5036	−	33.6098i	0.687609	−	1.07472i
$979$	−4.97296	+	8.61342i	−0.158936	+	0.275286i
$980$		0			0
$981$	−9.44805	−	20.4684i	−0.301653	−	0.653506i
$982$	0.207004	+	0.358541i	0.00660575	+	0.0114415i
$983$	−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	$-0.435268\pi$
$984$	−0.882977	+	1.38008i	−0.0281483	+	0.0439953i
$985$	−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
$989$	5.28434	+	9.15274i	0.168032	+	0.291040i
$990$	2.90642	−	4.11671i	0.0923721	−	0.130838i
$991$	10.8260	−	18.7511i	0.343898	−	0.595649i	−0.641255	−	0.767328i	$-0.721586\pi$
$991$	10.8260	−	18.7511i	0.343898	−	0.595649i	0.985153	+	0.171679i	$0.0549192\pi$
$992$	0.514589			0.0163382
$993$	21.9466	+	42.3595i	0.696454	+	1.34424i
$994$		0			0
$995$	0.678304	+	1.17486i	0.0215037	+	0.0372455i
$996$	−11.5021	−	0.524555i	−0.364459	−	0.0166212i
$997$	−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	$-0.527826\pi$
$998$	0.461967	−	0.800151i	0.0146233	−	0.0253283i
$999$	17.8566	+	43.8295i	0.564958	+	1.38670i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.2	✓	6	7.6	odd	2
126.2.e.d.121.2	yes	6	63.40	odd	6
126.2.h.c.67.3	yes	6	63.13	odd	6
126.2.h.c.79.3	yes	6	7.5	odd	6
378.2.e.c.37.1		6	63.5	even	6
378.2.e.c.235.1		6	21.20	even	2
378.2.h.d.289.3		6	21.5	even	6
378.2.h.d.361.3		6	63.41	even	6
882.2.e.p.373.2		6	63.58	even	3	inner
882.2.e.p.655.2		6	1.1	even	1	trivial
882.2.f.l.295.2		6	7.3	odd	6
882.2.f.l.589.2		6	63.31	odd	6
882.2.f.m.295.2		6	7.4	even	3
882.2.f.m.589.2		6	63.4	even	3
882.2.h.o.67.1		6	9.4	even	3
882.2.h.o.79.1		6	7.2	even	3
1008.2.q.h.529.2		6	28.27	even	2
1008.2.q.h.625.2		6	252.103	even	6
1008.2.t.g.193.1		6	252.139	even	6
1008.2.t.g.961.1		6	28.19	even	6
1134.2.g.k.163.3		6	63.61	odd	6
1134.2.g.k.487.3		6	63.34	odd	6
1134.2.g.n.163.1		6	63.47	even	6
1134.2.g.n.487.1		6	63.20	even	6
2646.2.e.o.1549.3		6	63.23	odd	6
2646.2.e.o.2125.3		6	3.2	odd	2
2646.2.f.n.883.3		6	21.11	odd	6
2646.2.f.n.1765.3		6	63.32	odd	6
2646.2.f.o.883.1		6	21.17	even	6
2646.2.f.o.1765.1		6	63.59	even	6
2646.2.h.p.361.1		6	9.5	odd	6
2646.2.h.p.667.1		6	21.2	odd	6
3024.2.q.h.2305.1		6	252.131	odd	6
3024.2.q.h.2881.1		6	84.83	odd	2
3024.2.t.g.289.3		6	84.47	odd	6
3024.2.t.g.1873.3		6	252.167	odd	6
7938.2.a.bu.1.3		3	63.38	even	6
7938.2.a.bx.1.1		3	63.11	odd	6
7938.2.a.by.1.3		3	63.25	even	3
7938.2.a.cb.1.1		3	63.52	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.796790 + 1.53790i) q^{3} +1.00000 q^{4} +(-0.230252 + 0.398809i) q^{5} +(0.796790 + 1.53790i) q^{6} +1.00000 q^{8} +(-1.73025 + 2.45076i) q^{9} +(-0.230252 + 0.398809i) q^{10} +(1.82383 + 3.15897i) q^{11} +(0.796790 + 1.53790i) q^{12} +(-0.730252 - 1.26483i) q^{13} +(-0.796790 - 0.0363376i) q^{15} +1.00000 q^{16} +(1.86693 - 3.23361i) q^{17} +(-1.73025 + 2.45076i) q^{18} +(2.02704 + 3.51094i) q^{19} +(-0.230252 + 0.398809i) q^{20} +(1.82383 + 3.15897i) q^{22} +(-0.566537 + 0.981271i) q^{23} +(0.796790 + 1.53790i) q^{24} +(2.39397 + 4.14647i) q^{25} +(-0.730252 - 1.26483i) q^{26} +(-5.14766 - 0.708209i) q^{27} +(-4.48755 + 7.77266i) q^{29} +(-0.796790 - 0.0363376i) q^{30} +0.514589 q^{31} +1.00000 q^{32} +(-3.40496 + 5.32190i) q^{33} +(1.86693 - 3.23361i) q^{34} +(-1.73025 + 2.45076i) q^{36} +(-4.55408 - 7.88791i) q^{37} +(2.02704 + 3.51094i) q^{38} +(1.36333 - 2.13086i) q^{39} +(-0.230252 + 0.398809i) q^{40} +(0.472958 + 0.819187i) q^{41} +(4.66372 - 8.07779i) q^{43} +(1.82383 + 3.15897i) q^{44} +(-0.578990 - 1.25433i) q^{45} +(-0.566537 + 0.981271i) q^{46} -2.32743 q^{47} +(0.796790 + 1.53790i) q^{48} +(2.39397 + 4.14647i) q^{50} +(6.46050 + 0.294632i) q^{51} +(-0.730252 - 1.26483i) q^{52} +(6.21780 - 10.7695i) q^{53} +(-5.14766 - 0.708209i) q^{54} -1.67977 q^{55} +(-3.78434 + 5.91486i) q^{57} +(-4.48755 + 7.77266i) q^{58} +12.8961 q^{59} +(-0.796790 - 0.0363376i) q^{60} -12.0833 q^{61} +0.514589 q^{62} +1.00000 q^{64} +0.672570 q^{65} +(-3.40496 + 5.32190i) q^{66} -2.32023 q^{67} +(1.86693 - 3.23361i) q^{68} +(-1.96050 - 0.0894089i) q^{69} +1.67977 q^{71} +(-1.73025 + 2.45076i) q^{72} +(6.62062 - 11.4673i) q^{73} +(-4.55408 - 7.88791i) q^{74} +(-4.46936 + 6.98554i) q^{75} +(2.02704 + 3.51094i) q^{76} +(1.36333 - 2.13086i) q^{78} -5.00720 q^{79} +(-0.230252 + 0.398809i) q^{80} +(-3.01245 - 8.48087i) q^{81} +(0.472958 + 0.819187i) q^{82} +(-3.32383 + 5.75705i) q^{83} +(0.859728 + 1.48909i) q^{85} +(4.66372 - 8.07779i) q^{86} +(-15.5292 - 0.708209i) q^{87} +(1.82383 + 3.15897i) q^{88} +(1.36333 + 2.36135i) q^{89} +(-0.578990 - 1.25433i) q^{90} +(-0.566537 + 0.981271i) q^{92} +(0.410019 + 0.791385i) q^{93} -2.32743 q^{94} -1.86693 q^{95} +(0.796790 + 1.53790i) q^{96} +(5.59358 - 9.68836i) q^{97} +(-10.8976 - 0.996040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} + 5 q^{5} + 2 q^{6} + 6 q^{8} - 4 q^{9} + 5 q^{10} - q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{15} + 6 q^{16} + 4 q^{17} - 4 q^{18} + 3 q^{19} + 5 q^{20} - q^{22} - 7 q^{23}+ \cdots - 41 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 + 5 * q^5 + 2 * q^6 + 6 * q^8 - 4 * q^9 + 5 * q^10 - q^11 + 2 * q^12 + 2 * q^13 - 2 * q^15 + 6 * q^16 + 4 * q^17 - 4 * q^18 + 3 * q^19 + 5 * q^20 - q^22 - 7 * q^23 + 2 * q^24 - 2 * q^25 + 2 * q^26 - 7 * q^27 - 5 * q^29 - 2 * q^30 - 28 * q^31 + 6 * q^32 + 19 * q^33 + 4 * q^34 - 4 * q^36 - 9 * q^37 + 3 * q^38 + 9 * q^39 + 5 * q^40 + 12 * q^41 + 18 * q^43 - q^44 - 29 * q^45 - 7 * q^46 + 6 * q^47 + 2 * q^48 - 2 * q^50 + 26 * q^51 + 2 * q^52 + 9 * q^53 - 7 * q^54 - 14 * q^55 + 2 * q^57 - 5 * q^58 + 8 * q^59 - 2 * q^60 + 8 * q^61 - 28 * q^62 + 6 * q^64 + 24 * q^65 + 19 * q^66 - 10 * q^67 + 4 * q^68 + q^69 + 14 * q^71 - 4 * q^72 + 25 * q^73 - 9 * q^74 - 44 * q^75 + 3 * q^76 + 9 * q^78 - 14 * q^79 + 5 * q^80 - 40 * q^81 + 12 * q^82 - 8 * q^83 + 14 * q^85 + 18 * q^86 - 31 * q^87 - q^88 + 9 * q^89 - 29 * q^90 - 7 * q^92 + 6 * q^94 - 4 * q^95 + 2 * q^96 + 28 * q^97 - 41 * q^99

Introduction

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