LMFDB - Embedded newform 925.2.y.b.393.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(193,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.193"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.y (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [68] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			393.11
Character	$\chi$	$=$	925.393
Dual form			925.2.y.b.732.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.336728 + 0.194410i) q^{2} +(2.95460 + 0.791682i) q^{3} +(-0.924410 - 1.60112i) q^{4} +(0.840985 + 0.840985i) q^{6} +(3.04240 + 0.815208i) q^{7} -1.49650i q^{8} +(5.50482 + 3.17821i) q^{9} +5.40976i q^{11} +(-1.46368 - 5.46252i) q^{12} +(-0.424546 + 0.245112i) q^{13} +(0.865975 + 0.865975i) q^{14} +(-1.55789 + 2.69834i) q^{16} +(0.959776 - 1.66238i) q^{17} +(1.23575 + 2.14038i) q^{18} +(-3.33608 - 0.893901i) q^{19} +(8.34368 + 4.81723i) q^{21} +(-1.05171 + 1.82162i) q^{22} -2.76865i q^{23} +(1.18475 - 4.42155i) q^{24} -0.190608 q^{26} +(7.25964 + 7.25964i) q^{27} +(-1.50717 - 5.62484i) q^{28} +(-5.54567 - 5.54567i) q^{29} +(1.40152 - 1.40152i) q^{31} +(-3.64118 + 2.10223i) q^{32} +(-4.28281 + 15.9837i) q^{33} +(0.646366 - 0.373180i) q^{34} -11.7519i q^{36} +(5.62947 - 2.30414i) q^{37} +(-0.949569 - 0.949569i) q^{38} +(-1.44841 + 0.388101i) q^{39} +(-1.77472 + 1.02463i) q^{41} +(1.87303 + 3.24419i) q^{42} -4.07381i q^{43} +(8.66170 - 5.00084i) q^{44} +(0.538252 - 0.932280i) q^{46} +(-1.75880 + 1.75880i) q^{47} +(-6.73915 + 6.73915i) q^{48} +(2.52944 + 1.46037i) q^{49} +(4.15183 - 4.15183i) q^{51} +(0.784908 + 0.453167i) q^{52} +(9.91602 - 2.65699i) q^{53} +(1.03318 + 3.85587i) q^{54} +(1.21996 - 4.55294i) q^{56} +(-9.14910 - 5.28224i) q^{57} +(-0.789248 - 2.94551i) q^{58} +(3.54546 + 13.2318i) q^{59} +(1.33066 + 0.356550i) q^{61} +(0.744399 - 0.199461i) q^{62} +(14.1569 + 14.1569i) q^{63} +4.59676 q^{64} +(-4.54953 + 4.54953i) q^{66} +(1.99697 - 7.45279i) q^{67} -3.54890 q^{68} +(2.19189 - 8.18024i) q^{69} +(-4.08391 - 7.07355i) q^{71} +(4.75618 - 8.23794i) q^{72} +(0.148203 - 0.148203i) q^{73} +(2.34355 + 0.318555i) q^{74} +(1.65266 + 6.16781i) q^{76} +(-4.41008 + 16.4586i) q^{77} +(-0.563171 - 0.150901i) q^{78} +(-14.2072 - 3.80679i) q^{79} +(6.16738 + 10.6822i) q^{81} -0.796795 q^{82} +(-15.5054 + 4.15466i) q^{83} -17.8124i q^{84} +(0.791990 - 1.37177i) q^{86} +(-11.9948 - 20.7756i) q^{87} +8.09569 q^{88} +(-2.74139 + 0.734553i) q^{89} +(-1.49145 + 0.399634i) q^{91} +(-4.43295 + 2.55936i) q^{92} +(5.25048 - 3.03137i) q^{93} +(-0.934165 + 0.250309i) q^{94} +(-12.4225 + 3.32860i) q^{96} -2.02493 q^{97} +(0.567822 + 0.983497i) q^{98} +(-17.1933 + 29.7797i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.336728	+	0.194410i	0.238102	+	0.137469i	0.614304	−	0.789069i	$-0.289437\pi$
$2$	0.336728	+	0.194410i	0.238102	+	0.137469i	−0.376202	+	0.926538i	$0.622770\pi$
$3$	2.95460	+	0.791682i	1.70584	+	0.457078i	0.974398	−	0.224828i	$-0.0721820\pi$
$3$	2.95460	+	0.791682i	1.70584	+	0.457078i	0.731440	+	0.681906i	$0.238849\pi$
$4$	−0.924410	−	1.60112i	−0.462205	−	0.800562i
$5$		0			0
$5$		0			0
$6$	0.840985	+	0.840985i	0.343330	+	0.343330i
$7$	3.04240	+	0.815208i	1.14992	+	0.308120i	0.782932	−	0.622107i	$-0.213723\pi$
$7$	3.04240	+	0.815208i	1.14992	+	0.308120i	0.366986	+	0.930227i	$0.380390\pi$
$8$		−	1.49650i		−	0.529092i
$9$	5.50482	+	3.17821i	1.83494	+	1.05940i
$10$		0			0
$11$			5.40976i			1.63110i	0.578683	+	0.815552i	$0.303567\pi$
$11$			5.40976i			1.63110i	−0.578683	+	0.815552i	$0.696433\pi$
$12$	−1.46368	−	5.46252i	−0.422527	−	1.57689i
$13$	−0.424546	+	0.245112i	−0.117748	+	0.0679817i	−0.557717	−	0.830031i	$-0.688323\pi$
$13$	−0.424546	+	0.245112i	−0.117748	+	0.0679817i	0.439969	+	0.898013i	$0.354989\pi$
$14$	0.865975	+	0.865975i	0.231442	+	0.231442i
$15$		0			0
$16$	−1.55789	+	2.69834i	−0.389471	+	0.674584i
$17$	0.959776	−	1.66238i	0.232780	−	0.403186i	−0.725845	−	0.687858i	$-0.758551\pi$
$17$	0.959776	−	1.66238i	0.232780	−	0.403186i	0.958625	+	0.284672i	$0.0918845\pi$
$18$	1.23575	+	2.14038i	0.291269	+	0.504493i
$19$	−3.33608	−	0.893901i	−0.765350	−	0.205075i	−0.145034	−	0.989427i	$-0.546329\pi$
$19$	−3.33608	−	0.893901i	−0.765350	−	0.205075i	−0.620316	+	0.784352i	$0.712996\pi$
$20$		0			0
$21$	8.34368	+	4.81723i	1.82074	+	1.05120i
$22$	−1.05171	+	1.82162i	−0.224226	+	0.388370i
$23$		−	2.76865i		−	0.577303i	−0.957434	−	0.288651i	$-0.906793\pi$
$23$		−	2.76865i		−	0.577303i	0.957434	−	0.288651i	$-0.0932068\pi$
$24$	1.18475	−	4.42155i	0.241836	−	0.902545i
$25$		0			0
$26$	−0.190608			−0.0373814
$27$	7.25964	+	7.25964i	1.39712	+	1.39712i
$28$	−1.50717	−	5.62484i	−0.284829	−	1.06300i
$29$	−5.54567	−	5.54567i	−1.02981	−	1.02981i	−0.999542	−	0.0302632i	$-0.990365\pi$
$29$	−5.54567	−	5.54567i	−1.02981	−	1.02981i	−0.0302632	−	0.999542i	$-0.509635\pi$
$30$		0			0
$31$	1.40152	−	1.40152i	0.251720	−	0.251720i	−0.569955	−	0.821676i	$-0.693040\pi$
$31$	1.40152	−	1.40152i	0.251720	−	0.251720i	0.821676	+	0.569955i	$0.193040\pi$
$32$	−3.64118	+	2.10223i	−0.643675	+	0.371626i
$33$	−4.28281	+	15.9837i	−0.745542	+	2.78240i
$34$	0.646366	−	0.373180i	0.110851	−	0.0639998i
$35$		0			0
$36$		−	11.7519i		−	1.95864i
$37$	5.62947	−	2.30414i	0.925479	−	0.378799i
$37$	5.62947	−	2.30414i	0.925479	−	0.378799i
$38$	−0.949569	−	0.949569i	−0.154040	−	0.154040i
$39$	−1.44841	+	0.388101i	−0.231932	+	0.0621459i
$40$		0			0
$41$	−1.77472	+	1.02463i	−0.277164	+	0.160021i	−0.632139	−	0.774855i	$-0.717823\pi$
$41$	−1.77472	+	1.02463i	−0.277164	+	0.160021i	0.354975	+	0.934876i	$0.384489\pi$
$42$	1.87303	+	3.24419i	0.289015	+	0.500589i
$43$		−	4.07381i		−	0.621251i	−0.950532	−	0.310625i	$-0.899462\pi$
$43$		−	4.07381i		−	0.621251i	0.950532	−	0.310625i	$-0.100538\pi$
$44$	8.66170	−	5.00084i	1.30580	−	0.753904i
$45$		0			0
$46$	0.538252	−	0.932280i	0.0793609	−	0.137457i
$47$	−1.75880	+	1.75880i	−0.256547	+	0.256547i	−0.823648	−	0.567101i	$-0.808065\pi$
$47$	−1.75880	+	1.75880i	−0.256547	+	0.256547i	0.567101	+	0.823648i	$0.308065\pi$
$48$	−6.73915	+	6.73915i	−0.972713	+	0.972713i
$49$	2.52944	+	1.46037i	0.361349	+	0.208625i
$50$		0			0
$51$	4.15183	−	4.15183i	0.581372	−	0.581372i
$52$	0.784908	+	0.453167i	0.108847	+	0.0628430i
$53$	9.91602	−	2.65699i	1.36207	−	0.364965i	0.497494	−	0.867468i	$-0.334254\pi$
$53$	9.91602	−	2.65699i	1.36207	−	0.364965i	0.864576	+	0.502502i	$0.167587\pi$
$54$	1.03318	+	3.85587i	0.140598	+	0.524717i
$55$		0			0
$56$	1.21996	−	4.55294i	0.163024	−	0.608412i
$57$	−9.14910	−	5.28224i	−1.21183	−	0.699649i
$58$	−0.789248	−	2.94551i	−0.103633	−	0.386765i
$59$	3.54546	+	13.2318i	0.461579	+	1.72264i	0.667989	+	0.744171i	$0.267155\pi$
$59$	3.54546	+	13.2318i	0.461579	+	1.72264i	−0.206410	+	0.978466i	$0.566178\pi$
$60$		0			0
$61$	1.33066	+	0.356550i	0.170374	+	0.0456516i	0.342998	−	0.939336i	$-0.388558\pi$
$61$	1.33066	+	0.356550i	0.170374	+	0.0456516i	−0.172624	+	0.984988i	$0.555224\pi$
$62$	0.744399	−	0.199461i	0.0945388	−	0.0253316i
$63$	14.1569	+	14.1569i	1.78361	+	1.78361i
$64$	4.59676			0.574595
$65$		0			0
$66$	−4.54953	+	4.54953i	−0.560008	+	0.560008i
$67$	1.99697	−	7.45279i	0.243969	−	0.910503i	−0.729931	−	0.683521i	$-0.760448\pi$
$67$	1.99697	−	7.45279i	0.243969	−	0.910503i	0.973899	−	0.226982i	$-0.0728857\pi$
$68$	−3.54890			−0.430368
$69$	2.19189	−	8.18024i	0.263872	−	0.984785i
$70$		0			0
$71$	−4.08391	−	7.07355i	−0.484671	−	0.839476i	0.515173	−	0.857086i	$-0.327728\pi$
$71$	−4.08391	−	7.07355i	−0.484671	−	0.839476i	−0.999845	+	0.0176103i	$0.994394\pi$
$72$	4.75618	−	8.23794i	0.560521	−	0.970851i
$73$	0.148203	−	0.148203i	0.0173459	−	0.0173459i	−0.698381	−	0.715727i	$-0.746096\pi$
$73$	0.148203	−	0.148203i	0.0173459	−	0.0173459i	0.715727	+	0.698381i	$0.246096\pi$
$74$	2.34355	+	0.318555i	0.272432	+	0.0370313i
$75$		0			0
$76$	1.65266	+	6.16781i	0.189573	+	0.707497i
$77$	−4.41008	+	16.4586i	−0.502575	+	1.87564i
$78$	−0.563171	−	0.150901i	−0.0637666	−	0.0170862i
$79$	−14.2072	−	3.80679i	−1.59843	−	0.428298i	−0.653862	−	0.756614i	$-0.726852\pi$
$79$	−14.2072	−	3.80679i	−1.59843	−	0.428298i	−0.944568	+	0.328316i	$0.893519\pi$
$80$		0			0
$81$	6.16738	+	10.6822i	0.685265	+	1.18691i
$82$	−0.796795			−0.0879913
$83$	−15.5054	+	4.15466i	−1.70194	+	0.456033i	−0.973427	−	0.228999i	$-0.926455\pi$
$83$	−15.5054	+	4.15466i	−1.70194	+	0.456033i	−0.728513	+	0.685032i	$0.759788\pi$
$84$		−	17.8124i		−	1.94349i
$85$		0			0
$86$	0.791990	−	1.37177i	0.0854025	−	0.147921i
$87$	−11.9948	−	20.7756i	−1.28598	−	2.22738i
$88$	8.09569			0.863004
$89$	−2.74139	+	0.734553i	−0.290587	+	0.0778624i	−0.401168	−	0.916005i	$-0.631395\pi$
$89$	−2.74139	+	0.734553i	−0.290587	+	0.0778624i	0.110581	+	0.993867i	$0.464729\pi$
$90$		0			0
$91$	−1.49145	+	0.399634i	−0.156347	+	0.0418930i
$92$	−4.43295	+	2.55936i	−0.462167	+	0.266832i
$93$	5.25048	−	3.03137i	0.544450	−	0.314338i
$94$	−0.934165	+	0.250309i	−0.0963518	+	0.0258174i
$95$		0			0
$96$	−12.4225	+	3.32860i	−1.26787	+	0.339724i
$97$	−2.02493			−0.205601			−0.102800	−	0.994702i	$-0.532780\pi$
$97$	−2.02493			−0.205601			−0.102800	+	0.994702i	$0.532780\pi$
$98$	0.567822	+	0.983497i	0.0573587	+	0.0993482i
$99$	−17.1933	+	29.7797i	−1.72800	+	2.99298i
$100$		0			0
$101$			0.549156i			0.0546431i	0.999627	+	0.0273215i	$0.00869780\pi$
$101$			0.549156i			0.0546431i	−0.999627	+	0.0273215i	$0.991302\pi$
$102$	2.20519	−	0.590880i	0.218347	−	0.0585058i
$103$	−13.5624			−1.33634			−0.668172	−	0.744007i	$-0.732923\pi$
$103$	−13.5624			−1.33634			−0.668172	+	0.744007i	$0.732923\pi$
$104$	0.366809	+	0.635331i	0.0359685	+	0.0622994i
$105$		0			0
$106$	3.85554	+	1.03309i	0.374483	+	0.100343i
$107$	−1.20864	−	0.323853i	−0.116843	−	0.0313080i	0.199924	−	0.979811i	$-0.435931\pi$
$107$	−1.20864	−	0.323853i	−0.116843	−	0.0313080i	−0.316767	+	0.948503i	$0.602597\pi$
$108$	4.91271	−	18.3345i	0.472726	−	1.76424i
$109$	0.0307250	+	0.114667i	0.00294292	+	0.0109831i	0.967382	−	0.253323i	$-0.0815236\pi$
$109$	0.0307250	+	0.114667i	0.00294292	+	0.0109831i	−0.964439	+	0.264306i	$0.914857\pi$
$110$		0			0
$111$	18.4570	−	2.35107i	1.75186	−	0.223154i
$112$	−6.93941	+	6.93941i	−0.655713	+	0.655713i
$113$	−3.25248	+	5.63347i	−0.305968	+	0.529952i	−0.977476	−	0.211045i	$-0.932313\pi$
$113$	−3.25248	+	5.63347i	−0.305968	+	0.529952i	0.671508	+	0.740997i	$0.265647\pi$
$114$	−2.05384	−	3.55735i	−0.192359	−	0.333176i
$115$		0			0
$116$	−3.75284	+	14.0058i	−0.348442	+	1.30040i
$117$	−3.11606			−0.288080
$118$	−1.37854	+	5.14479i	−0.126905	+	0.473617i
$119$	4.27520	−	4.27520i	0.391907	−	0.391907i
$120$		0			0
$121$	−18.2655			−1.66050
$122$	0.378755	+	0.378755i	0.0342908	+	0.0342908i
$123$	−6.05476	+	1.62237i	−0.545939	+	0.146284i
$124$	−3.53958	−	0.948429i	−0.317864	−	0.0851714i
$125$		0			0
$126$	2.01479	+	7.51928i	0.179491	+	0.669871i
$127$	1.05728	+	3.94583i	0.0938185	+	0.350135i	0.996838	−	0.0794648i	$-0.0253211\pi$
$127$	1.05728	+	3.94583i	0.0938185	+	0.350135i	−0.903019	+	0.429600i	$0.858654\pi$
$128$	8.83021	+	5.09812i	0.780487	+	0.450615i
$129$	3.22517	−	12.0365i	0.283960	−	1.05975i
$130$		0			0
$131$	−2.83341	−	10.5744i	−0.247556	−	0.923893i	−0.972081	−	0.234645i	$-0.924607\pi$
$131$	−2.83341	−	10.5744i	−0.247556	−	0.923893i	0.724525	−	0.689249i	$-0.242059\pi$
$132$	29.5509	−	7.91815i	2.57208	−	0.689186i
$133$	−9.42098	−	5.43920i	−0.816902	−	0.471639i
$134$	2.12133	−	2.12133i	0.183255	−	0.183255i
$135$		0			0
$136$	−2.48775	−	1.43630i	−0.213323	−	0.123162i
$137$	−3.16424	+	3.16424i	−0.270339	+	0.270339i	−0.829237	−	0.558897i	$-0.811225\pi$
$137$	−3.16424	+	3.16424i	−0.270339	+	0.270339i	0.558897	+	0.829237i	$0.311225\pi$
$138$	2.32839	−	2.32839i	0.198206	−	0.198206i
$139$	10.0902	−	17.4767i	0.855839	−	1.48236i	−0.0200261	−	0.999799i	$-0.506375\pi$
$139$	10.0902	−	17.4767i	0.855839	−	1.48236i	0.875865	−	0.482557i	$-0.160292\pi$
$140$		0			0
$141$	−6.58896	+	3.80414i	−0.554891	+	0.320366i
$142$		−	3.17581i		−	0.266508i
$143$	−1.32600	−	2.29669i	−0.110885	−	0.192059i
$144$	−17.1517	+	9.90257i	−1.42931	+	0.825214i
$145$		0			0
$146$	0.0787164	−	0.0210920i	0.00651461	−	0.00174559i
$147$	6.31733	+	6.31733i	0.521045	+	0.521045i
$148$	−8.89316	−	6.88351i	−0.731013	−	0.565821i
$149$			17.4033i			1.42573i	0.701301	+	0.712866i	$0.252603\pi$
$149$			17.4033i			1.42573i	−0.701301	+	0.712866i	$0.747397\pi$
$150$		0			0
$151$	14.5658	−	8.40956i	1.18535	−	0.684360i	0.228102	−	0.973637i	$-0.426748\pi$
$151$	14.5658	−	8.40956i	1.18535	−	0.684360i	0.957245	+	0.289277i	$0.0934148\pi$
$152$	−1.33772	+	4.99244i	−0.108503	+	0.404940i
$153$	10.5668	−	6.10073i	0.854273	−	0.493215i
$154$	−4.68472	+	4.68472i	−0.377505	+	0.377505i
$155$		0			0
$156$	1.96032	+	1.96032i	0.156952	+	0.156952i
$157$	−1.40627	−	5.24826i	−0.112232	−	0.418857i	0.886833	−	0.462091i	$-0.152901\pi$
$157$	−1.40627	−	5.24826i	−0.112232	−	0.418857i	−0.999065	+	0.0432340i	$0.986234\pi$
$158$	−4.04386	−	4.04386i	−0.321713	−	0.321713i
$159$	31.4013			2.49029
$160$		0			0
$161$	2.25702	−	8.42332i	0.177878	−	0.663851i
$162$			4.79600i			0.376809i
$163$	11.0643	−	19.1640i	0.866624	−	1.50104i	0.00119876	−	0.999999i	$-0.499618\pi$
$163$	11.0643	−	19.1640i	0.866624	−	1.50104i	0.865425	−	0.501038i	$-0.167048\pi$
$164$	3.28113	+	1.89436i	0.256213	+	0.147925i
$165$		0			0
$166$	−6.02881	−	1.61541i	−0.467926	−	0.125380i
$167$	2.83580	+	4.91176i	0.219441	+	0.380083i	0.954637	−	0.297771i	$-0.0962433\pi$
$167$	2.83580	+	4.91176i	0.219441	+	0.380083i	−0.735196	+	0.677854i	$0.762910\pi$
$168$	7.20896	−	12.4863i	0.556183	−	0.963338i
$169$	−6.37984	+	11.0502i	−0.490757	+	0.850016i
$170$		0			0
$171$	−15.5235	−	15.5235i	−1.18711	−	1.18711i
$172$	−6.52268	+	3.76587i	−0.497350	+	0.287145i
$173$	1.22092	+	4.55655i	0.0928252	+	0.346428i	0.996681	−	0.0814094i	$-0.0259421\pi$
$173$	1.22092	+	4.55655i	0.0928252	+	0.346428i	−0.903856	+	0.427838i	$0.859275\pi$
$174$		−	9.32765i		−	0.707127i
$175$		0			0
$176$	−14.5974	−	8.42779i	−1.10032	−	0.635268i
$177$			41.9016i			3.14952i
$178$	−1.06591	−	0.285609i	−0.0798930	−	0.0214073i
$179$	5.34956	+	5.34956i	0.399845	+	0.399845i	0.878178	−	0.478333i	$-0.158759\pi$
$179$	5.34956	+	5.34956i	0.399845	+	0.399845i	−0.478333	+	0.878178i	$0.658759\pi$
$180$		0			0
$181$	5.52605	+	9.57140i	0.410748	+	0.711436i	0.994972	−	0.100156i	$-0.0319343\pi$
$181$	5.52605	+	9.57140i	0.410748	+	0.711436i	−0.584224	+	0.811593i	$0.698601\pi$
$182$	−0.579907	−	0.155386i	−0.0429855	−	0.0115179i
$183$	3.64930	+	2.10693i	0.269764	+	0.155748i
$184$	−4.14327			−0.305446
$185$		0			0
$186$	2.35731			0.172846
$187$	8.99308	+	5.19216i	0.657639	+	0.379688i
$188$	4.44191	+	1.19021i	0.323960	+	0.0868047i
$189$	16.1686	+	28.0048i	1.17609	+	2.03705i
$190$		0			0
$191$	9.74810	+	9.74810i	0.705348	+	0.705348i	0.965553	−	0.260205i	$-0.0837902\pi$
$191$	9.74810	+	9.74810i	0.705348	+	0.705348i	−0.260205	+	0.965553i	$0.583790\pi$
$192$	13.5816	+	3.63918i	0.980167	+	0.262635i
$193$			16.2149i			1.16717i	0.812052	+	0.583586i	$0.198351\pi$
$193$			16.2149i			1.16717i	−0.812052	+	0.583586i	$0.801649\pi$
$194$	−0.681851	−	0.393667i	−0.0489540	−	0.0282636i
$195$		0			0
$196$		−	5.39994i		−	0.385710i
$197$	−3.48937	−	13.0225i	−0.248607	−	0.927815i	−0.971536	−	0.236893i	$-0.923871\pi$
$197$	−3.48937	−	13.0225i	−0.248607	−	0.927815i	0.722928	−	0.690923i	$-0.242796\pi$
$198$	−11.5790	+	6.68511i	−0.822880	+	0.475090i
$199$	−11.8257	−	11.8257i	−0.838302	−	0.838302i	0.150333	−	0.988635i	$-0.451965\pi$
$199$	−11.8257	−	11.8257i	−0.838302	−	0.838302i	−0.988635	+	0.150333i	$0.951965\pi$
$200$		0			0
$201$	11.8005	−	20.4390i	0.832342	−	1.44166i
$202$	−0.106761	+	0.184916i	−0.00751170	+	0.0130107i
$203$	−12.3513	−	21.3930i	−0.866889	−	1.50149i
$204$	−10.4856	−	2.80960i	−0.734138	−	0.196712i
$205$		0			0
$206$	−4.56684	−	2.63667i	−0.318187	−	0.183705i
$207$	8.79933	−	15.2409i	0.611596	−	1.05931i
$208$		−	1.52742i		−	0.105908i
$209$	4.83579	−	18.0474i	0.334499	−	1.24837i
$210$		0			0
$211$	−10.9455			−0.753516			−0.376758	−	0.926312i	$-0.622961\pi$
$211$	−10.9455			−0.753516			−0.376758	+	0.926312i	$0.622961\pi$
$212$	−13.4206	−	13.4206i	−0.921733	−	0.921733i
$213$	−6.46633	−	24.1327i	−0.443065	−	1.65354i
$214$	−0.344021	−	0.344021i	−0.0235168	−	0.0235168i
$215$		0			0
$216$	10.8640	−	10.8640i	0.739204	−	0.739204i
$217$	5.40651	−	3.12145i	0.367018	−	0.211898i
$218$	−0.0119465	+	0.0445849i	−0.000809119	+	0.00301967i
$219$	0.555212	−	0.320552i	0.0375177	−	0.0216609i
$220$		0			0
$221$			0.941008i			0.0632991i
$222$	6.67205	+	2.79655i	0.447798	+	0.187692i
$223$	16.5949	+	16.5949i	1.11128	+	1.11128i	0.992978	+	0.118301i	$0.0377448\pi$
$223$	16.5949	+	16.5949i	1.11128	+	1.11128i	0.118301	+	0.992978i	$0.462255\pi$
$224$	−12.7917	+	3.42752i	−0.854679	+	0.229010i
$225$		0			0
$226$	−2.19040	+	1.26463i	−0.145703	+	0.0841219i
$227$	1.45267	+	2.51610i	0.0964172	+	0.166999i	0.910199	−	0.414171i	$-0.135928\pi$
$227$	1.45267	+	2.51610i	0.0964172	+	0.166999i	−0.813782	+	0.581170i	$0.802595\pi$
$228$			19.5318i			1.29352i
$229$	0.474824	−	0.274140i	0.0313773	−	0.0181157i	−0.484229	−	0.874941i	$-0.660900\pi$
$229$	0.474824	−	0.274140i	0.0313773	−	0.0181157i	0.515607	+	0.856825i	$0.327567\pi$
$230$		0			0
$231$	−26.0600	+	45.1373i	−1.71462	+	2.96982i
$232$	−8.29908	+	8.29908i	−0.544861	+	0.544861i
$233$	3.42406	−	3.42406i	0.224318	−	0.224318i	−0.585996	−	0.810314i	$-0.699297\pi$
$233$	3.42406	−	3.42406i	0.224318	−	0.224318i	0.810314	+	0.585996i	$0.199297\pi$
$234$	−1.04926	−	0.605793i	−0.0685926	−	0.0396019i
$235$		0			0
$236$	17.9083	−	17.9083i	1.16573	−	1.16573i
$237$	−38.9627	−	22.4951i	−2.53090	−	1.46121i
$238$	2.27072	−	0.608438i	0.147189	−	0.0394392i
$239$	1.69865	+	6.33944i	0.109876	+	0.410064i	0.998853	−	0.0478891i	$-0.0152494\pi$
$239$	1.69865	+	6.33944i	0.109876	+	0.410064i	−0.888976	+	0.457953i	$0.848583\pi$
$240$		0			0
$241$	−5.22983	+	19.5180i	−0.336883	+	1.25726i	0.564930	+	0.825139i	$0.308903\pi$
$241$	−5.22983	+	19.5180i	−0.336883	+	1.25726i	−0.901813	+	0.432126i	$0.857764\pi$
$242$	−6.15051	−	3.55100i	−0.395370	−	0.228267i
$243$	1.79357	+	6.69370i	0.115058	+	0.429401i
$244$	−0.659197	−	2.46016i	−0.0422008	−	0.157495i
$245$		0			0
$246$	−2.35421	−	0.630809i	−0.150099	−	0.0402189i
$247$	1.63542	−	0.438211i	0.104060	−	0.0278827i
$248$	−2.09737	−	2.09737i	−0.133183	−	0.133183i
$249$	−49.1014			−3.11168
$250$		0			0
$251$	−8.09134	+	8.09134i	−0.510721	+	0.510721i	−0.914747	−	0.404027i	$-0.867610\pi$
$251$	−8.09134	+	8.09134i	−0.510721	+	0.510721i	0.404027	+	0.914747i	$0.367610\pi$
$252$	9.58021	−	35.7538i	0.603497	−	2.25228i
$253$	14.9777			0.941641
$254$	−0.411092	+	1.53422i	−0.0257942	+	0.0962652i
$255$		0			0
$256$	−2.61451	−	4.52847i	−0.163407	−	0.283029i
$257$	1.20066	−	2.07961i	0.0748953	−	0.129722i	−0.826145	−	0.563457i	$-0.809471\pi$
$257$	1.20066	−	2.07961i	0.0748953	−	0.129722i	0.901041	+	0.433734i	$0.142804\pi$
$258$	3.42602	−	3.42602i	0.213294	−	0.213294i
$259$	19.0054	−	2.42094i	1.18094	−	0.150430i
$260$		0			0
$261$	−12.9026	−	48.1532i	−0.798651	−	2.98061i
$262$	1.10169	−	4.11155i	0.0680624	−	0.254013i
$263$	0.649790	+	0.174111i	0.0400678	+	0.0107361i	0.278797	−	0.960350i	$-0.410064\pi$
$263$	0.649790	+	0.174111i	0.0400678	+	0.0107361i	−0.238729	+	0.971086i	$0.576731\pi$
$264$	23.9195	+	6.40922i	1.47214	+	0.394460i
$265$		0			0
$266$	−2.11487	−	3.66306i	−0.129671	−	0.224597i
$267$	−8.68123			−0.531283
$268$	−13.7789	+	3.69203i	−0.841678	+	0.225527i
$269$			11.1924i			0.682413i	0.939988	+	0.341207i	$0.110836\pi$
$269$			11.1924i			0.682413i	−0.939988	+	0.341207i	$0.889164\pi$
$270$		0			0
$271$	0.729450	−	1.26345i	0.0443110	−	0.0767488i	−0.843019	−	0.537883i	$-0.819224\pi$
$271$	0.729450	−	1.26345i	0.0443110	−	0.0767488i	0.887330	+	0.461134i	$0.152557\pi$
$272$	2.99044	+	5.17960i	0.181322	+	0.314059i
$273$	−4.72303			−0.285851
$274$	−1.68065	+	0.450328i	−0.101532	+	0.0272053i
$275$		0			0
$276$	−15.1238	+	4.05240i	−0.910344	+	0.243926i
$277$	6.57388	−	3.79543i	0.394986	−	0.228045i	−0.289332	−	0.957229i	$-0.593433\pi$
$277$	6.57388	−	3.79543i	0.394986	−	0.228045i	0.684318	+	0.729183i	$0.260100\pi$
$278$	6.79529	−	3.92326i	0.407555	−	0.235302i
$279$	12.1694	−	3.26079i	0.728564	−	0.195218i
$280$		0			0
$281$	18.0851	−	4.84588i	1.07886	−	0.289081i	0.324734	−	0.945805i	$-0.394725\pi$
$281$	18.0851	−	4.84588i	1.07886	−	0.289081i	0.754131	+	0.656724i	$0.228059\pi$
$282$	−2.95825			−0.176161
$283$	−12.5540	−	21.7442i	−0.746259	−	1.29256i	−0.949604	−	0.313451i	$-0.898515\pi$
$283$	−12.5540	−	21.7442i	−0.746259	−	1.29256i	0.203345	−	0.979107i	$-0.434819\pi$
$284$	−7.55042	+	13.0777i	−0.448035	+	0.776019i
$285$		0			0
$286$		−	1.03115i		−	0.0609729i
$287$	−6.23469	+	1.67058i	−0.368022	+	0.0986112i
$288$	−26.7253			−1.57481
$289$	6.65766	+	11.5314i	0.391627	+	0.678318i
$290$		0			0
$291$	−5.98286	−	1.60310i	−0.350721	−	0.0939755i
$292$	−0.374293	−	0.100291i	−0.0219038	−	0.00586911i
$293$	0.383198	−	1.43011i	0.0223867	−	0.0835482i	−0.953829	−	0.300351i	$-0.902896\pi$
$293$	0.383198	−	1.43011i	0.0223867	−	0.0835482i	0.976215	+	0.216803i	$0.0695629\pi$
$294$	0.899070	+	3.35537i	0.0524348	+	0.195689i
$295$		0			0
$296$	−3.44814	−	8.42448i	−0.200419	−	0.489663i
$297$	−39.2729	+	39.2729i	−2.27885	+	2.27885i
$298$	−3.38337	+	5.86016i	−0.195993	+	0.339470i
$299$	0.678627	+	1.17542i	0.0392460	+	0.0679761i
$300$		0			0
$301$	3.32101	−	12.3942i	0.191420	−	0.714388i
$302$	6.53961			0.376312
$303$	−0.434757	+	1.62254i	−0.0249761	+	0.0932123i
$304$	7.60928	−	7.60928i	0.436422	−	0.436422i
$305$		0			0
$306$	4.74417			0.271206
$307$	−13.9807	−	13.9807i	−0.797920	−	0.797920i	0.184847	−	0.982767i	$-0.440821\pi$
$307$	−13.9807	−	13.9807i	−0.797920	−	0.797920i	−0.982767	+	0.184847i	$0.940821\pi$
$308$	30.4291	−	8.15344i	1.73386	−	0.464585i
$309$	−40.0715	−	10.7371i	−2.27959	−	0.610813i
$310$		0			0
$311$	−0.610669	−	2.27905i	−0.0346278	−	0.129233i	0.946448	−	0.322856i	$-0.104643\pi$
$311$	−0.610669	−	2.27905i	−0.0346278	−	0.129233i	−0.981076	+	0.193623i	$0.937976\pi$
$312$	0.580792	+	2.16754i	0.0328809	+	0.122713i
$313$	7.07463	+	4.08454i	0.399882	+	0.230872i	0.686433	−	0.727193i	$-0.259176\pi$
$313$	7.07463	+	4.08454i	0.399882	+	0.230872i	−0.286551	+	0.958065i	$0.592509\pi$
$314$	0.546784	−	2.04063i	0.0308568	−	0.115159i
$315$		0			0
$316$	7.03807	+	26.2665i	0.395923	+	1.47760i
$317$	−21.7621	+	5.83113i	−1.22228	+	0.327509i	−0.811569	−	0.584256i	$-0.801386\pi$
$317$	−21.7621	+	5.83113i	−1.22228	+	0.327509i	−0.410711	+	0.911765i	$0.634720\pi$
$318$	10.5737	+	6.10473i	0.592944	+	0.342336i
$319$	30.0008	−	30.0008i	1.67972	−	1.67972i
$320$		0			0
$321$	−3.31464	−	1.91371i	−0.185005	−	0.106813i
$322$	2.39758	−	2.39758i	0.133612	−	0.133612i
$323$	−4.68789	+	4.68789i	−0.260841	+	0.260841i
$324$	11.4024	−	19.7495i	0.633465	−	1.09719i
$325$		0			0
$326$	7.45132	−	4.30202i	0.412691	−	0.238267i
$327$			0.363120i			0.0200806i
$328$	1.53336	+	2.65586i	0.0846657	+	0.146645i
$329$	−6.78476	+	3.91718i	−0.374056	+	0.215961i
$330$		0			0
$331$	−11.8707	+	3.18073i	−0.652470	+	0.174829i	−0.569845	−	0.821752i	$-0.692997\pi$
$331$	−11.8707	+	3.18073i	−0.652470	+	0.174829i	−0.0826246	+	0.996581i	$0.526330\pi$
$332$	20.9855	+	20.9855i	1.15173	+	1.15173i
$333$	38.3122	+	5.20773i	2.09950	+	0.285382i
$334$			2.20523i			0.120665i
$335$		0			0
$336$	−25.9970	+	15.0094i	−1.41825	+	0.818828i
$337$	−3.67654	+	13.7210i	−0.200274	+	0.747433i	0.790564	+	0.612379i	$0.209787\pi$
$337$	−3.67654	+	13.7210i	−0.200274	+	0.747433i	−0.990838	+	0.135054i	$0.956879\pi$
$338$	−4.29654	+	2.48061i	−0.233701	+	0.134927i
$339$	−14.0697	+	14.0697i	−0.764161	+	0.764161i
$340$		0			0
$341$	7.58188	+	7.58188i	0.410582	+	0.410582i
$342$	−2.20927	−	8.24513i	−0.119464	−	0.445845i
$343$	−9.08527	−	9.08527i	−0.490558	−	0.490558i
$344$	−6.09645			−0.328699
$345$		0			0
$346$	−0.474720	+	1.77168i	−0.0255211	+	0.0952460i
$347$		−	2.31008i		−	0.124011i	−0.998076	−	0.0620057i	$-0.980250\pi$
$347$		−	2.31008i		−	0.124011i	0.998076	−	0.0620057i	$-0.0197497\pi$
$348$	−22.1763	+	38.4104i	−1.18877	+	2.05901i
$349$	12.0330	+	6.94728i	0.644114	+	0.371879i	0.786197	−	0.617975i	$-0.212047\pi$
$349$	12.0330	+	6.94728i	0.644114	+	0.371879i	−0.142084	+	0.989855i	$0.545380\pi$
$350$		0			0
$351$	−4.86147	−	1.30263i	−0.259486	−	0.0695291i
$352$	−11.3726	−	19.6979i	−0.606161	−	1.04990i
$353$	−10.2684	+	17.7853i	−0.546529	+	0.946617i	0.451979	+	0.892028i	$0.350718\pi$
$353$	−10.2684	+	17.7853i	−0.546529	+	0.946617i	−0.998509	+	0.0545884i	$0.982615\pi$
$354$	−8.14608	+	14.1094i	−0.432959	+	0.749908i
$355$		0			0
$356$	3.71028	+	3.71028i	0.196644	+	0.196644i
$357$	16.0161	−	9.24691i	0.847663	−	0.489398i
$358$	0.761338	+	2.84135i	0.0402380	+	0.150170i
$359$			27.9245i			1.47380i	0.676001	+	0.736900i	$0.263711\pi$
$359$			27.9245i			1.47380i	−0.676001	+	0.736900i	$0.736289\pi$
$360$		0			0
$361$	−6.12409	−	3.53575i	−0.322321	−	0.186092i
$362$			4.29727i			0.225860i
$363$	−53.9673	−	14.4605i	−2.83255	−	0.758979i
$364$	2.01858	+	2.01858i	0.105802	+	0.105802i
$365$		0			0
$366$	0.819214	+	1.41892i	0.0428210	+	0.0741682i
$367$	17.9431	+	4.80784i	0.936622	+	0.250967i	0.694676	−	0.719322i	$-0.255548\pi$
$367$	17.9431	+	4.80784i	0.936622	+	0.250967i	0.241946	+	0.970290i	$0.422214\pi$
$368$	7.47074	+	4.31323i	0.389439	+	0.224843i
$369$	−13.0260			−0.678106
$370$		0			0
$371$	32.3345			1.67872
$372$	−9.70720	−	5.60445i	−0.503295	−	0.290577i
$373$	2.56767	+	0.688006i	0.132949	+	0.0356236i	0.324680	−	0.945824i	$-0.394743\pi$
$373$	2.56767	+	0.688006i	0.132949	+	0.0356236i	−0.191731	+	0.981448i	$0.561410\pi$
$374$	2.01881	+	3.49669i	0.104390	+	0.180809i
$375$		0			0
$376$	2.63204	+	2.63204i	0.135737	+	0.135737i
$377$	3.71370	+	0.995082i	0.191265	+	0.0512494i
$378$			12.5733i			0.646703i
$379$	−19.2622	−	11.1210i	−0.989433	−	0.571249i	−0.0843279	−	0.996438i	$-0.526874\pi$
$379$	−19.2622	−	11.1210i	−0.989433	−	0.571249i	−0.905105	+	0.425189i	$0.860208\pi$
$380$		0			0
$381$			12.4954i			0.640157i
$382$	1.38733	+	5.17758i	0.0709820	+	0.264908i
$383$	8.12659	−	4.69189i	0.415249	−	0.239744i	−0.277793	−	0.960641i	$-0.589603\pi$
$383$	8.12659	−	4.69189i	0.415249	−	0.239744i	0.693043	+	0.720897i	$0.256270\pi$
$384$	22.0536	+	22.0536i	1.12542	+	1.12542i
$385$		0			0
$386$	−3.15233	+	5.45999i	−0.160449	+	0.277906i
$387$	12.9474	−	22.4256i	0.658155	−	1.13996i
$388$	1.87187	+	3.24217i	0.0950296	+	0.164596i
$389$	0.958452	+	0.256816i	0.0485954	+	0.0130211i	0.283035	−	0.959110i	$-0.408659\pi$
$389$	0.958452	+	0.256816i	0.0485954	+	0.0130211i	−0.234439	+	0.972131i	$0.575325\pi$
$390$		0			0
$391$	−4.60254	−	2.65728i	−0.232761	−	0.134384i
$392$	2.18545	−	3.78530i	0.110382	−	0.191187i
$393$		−	33.4864i		−	1.68917i
$394$	1.35674	−	5.06341i	0.0683514	−	0.255091i
$395$		0			0
$396$	63.5748			3.19475
$397$	−8.65853	−	8.65853i	−0.434559	−	0.434559i	0.455617	−	0.890176i	$-0.349419\pi$
$397$	−8.65853	−	8.65853i	−0.434559	−	0.434559i	−0.890176	+	0.455617i	$0.849419\pi$
$398$	−1.68301	−	6.28108i	−0.0843616	−	0.314842i
$399$	−23.5291	−	23.5291i	−1.17793	−	1.17793i
$400$		0			0
$401$	−12.6663	+	12.6663i	−0.632526	+	0.632526i	−0.948701	−	0.316175i	$-0.897601\pi$
$401$	−12.6663	+	12.6663i	−0.632526	+	0.632526i	0.316175	+	0.948701i	$0.397601\pi$
$402$	7.94710	−	4.58826i	0.396365	−	0.228842i
$403$	−0.251480	+	0.938537i	−0.0125271	+	0.0467519i
$404$	0.879267	−	0.507645i	0.0437452	−	0.0252563i
$405$		0			0
$406$		−	9.60483i		−	0.476680i
$407$	12.4649	+	30.4541i	0.617861	+	1.50955i
$408$	−6.21320	−	6.21320i	−0.307599	−	0.307599i
$409$	−0.410151	+	0.109900i	−0.0202807	+	0.00543419i	−0.268945	−	0.963156i	$-0.586675\pi$
$409$	−0.410151	+	0.109900i	−0.0202807	+	0.00543419i	0.248664	+	0.968590i	$0.420008\pi$
$410$		0			0
$411$	−11.8541	+	6.84399i	−0.584721	+	0.337589i
$412$	12.5372	+	21.7151i	0.617664	+	1.06983i
$413$			43.1467i			2.12311i
$414$	5.92596	−	3.42135i	0.291245	−	0.168150i
$415$		0			0
$416$	1.03056	−	1.78499i	0.0505275	−	0.0875162i
$417$	43.6485	−	43.6485i	2.13747	−	2.13747i
$418$	5.13694	−	5.13694i	0.251256	−	0.251256i
$419$	−18.0063	−	10.3959i	−0.879664	−	0.507874i	−0.00911645	−	0.999958i	$-0.502902\pi$
$419$	−18.0063	−	10.3959i	−0.879664	−	0.507874i	−0.870548	+	0.492084i	$0.836235\pi$
$420$		0			0
$421$	15.3463	−	15.3463i	0.747934	−	0.747934i	−0.226157	−	0.974091i	$-0.572616\pi$
$421$	15.3463	−	15.3463i	0.747934	−	0.747934i	0.974091	+	0.226157i	$0.0726161\pi$
$422$	−3.68564	−	2.12790i	−0.179414	−	0.103585i
$423$	−15.2717	+	4.09204i	−0.742536	+	0.198962i
$424$	−3.97617	−	14.8393i	−0.193100	−	0.720659i
$425$		0			0
$426$	2.51423	−	9.38325i	0.121815	−	0.454620i
$427$	3.75775	+	2.16954i	0.181850	+	0.104991i
$428$	0.598745	+	2.23455i	0.0289414	+	0.108011i
$429$	−2.09953	−	7.83557i	−0.101366	−	0.378305i
$430$		0			0
$431$	31.0889	+	8.33025i	1.49750	+	0.401254i	0.912262	−	0.409608i	$-0.134334\pi$
$431$	31.0889	+	8.33025i	1.49750	+	0.401254i	0.585238	+	0.810862i	$0.301001\pi$
$432$	−30.8987	+	8.27927i	−1.48661	+	0.398337i
$433$	7.64871	+	7.64871i	0.367573	+	0.367573i	0.866592	−	0.499018i	$-0.166306\pi$
$433$	7.64871	+	7.64871i	0.367573	+	0.367573i	−0.499018	+	0.866592i	$0.666306\pi$
$434$	2.42736			0.116517
$435$		0			0
$436$	0.155194	−	0.155194i	0.00743245	−	0.00743245i
$437$	−2.47489	+	9.23643i	−0.118390	+	0.441838i
$438$	0.249273			0.0119107
$439$	1.06390	−	3.97053i	0.0507772	−	0.189503i	−0.935879	−	0.352322i	$-0.885392\pi$
$439$	1.06390	−	3.97053i	0.0507772	−	0.189503i	0.986656	+	0.162819i	$0.0520588\pi$
$440$		0			0
$441$	9.28274	+	16.0782i	0.442035	+	0.765628i
$442$	−0.182941	+	0.316864i	−0.00870163	+	0.0150717i
$443$	2.43232	−	2.43232i	0.115563	−	0.115563i	−0.646960	−	0.762524i	$-0.723960\pi$
$443$	2.43232	−	2.43232i	0.115563	−	0.115563i	0.762524	+	0.646960i	$0.223960\pi$
$444$	−20.8262	−	27.3786i	−0.988366	−	1.29933i
$445$		0			0
$446$	2.36176	+	8.81419i	0.111832	+	0.417364i
$447$	−13.7779	+	51.4197i	−0.651670	+	2.43207i
$448$	13.9852	+	3.74732i	0.660738	+	0.177044i
$449$	33.1099	+	8.87177i	1.56255	+	0.418684i	0.933470	−	0.358655i	$-0.116764\pi$
$449$	33.1099	+	8.87177i	1.56255	+	0.418684i	0.629082	+	0.777339i	$0.283431\pi$
$450$		0			0
$451$	−5.54302	−	9.60080i	−0.261011	−	0.452084i
$452$	12.0265			0.565679
$453$	49.6938	−	13.3154i	2.33482	−	0.625612i
$454$			1.12965i			0.0530173i
$455$		0			0
$456$	−7.90485	+	13.6916i	−0.370178	+	0.641168i
$457$	−6.06294	−	10.5013i	−0.283612	−	0.491231i	0.688659	−	0.725085i	$-0.258200\pi$
$457$	−6.06294	−	10.5013i	−0.283612	−	0.491231i	−0.972272	+	0.233854i	$0.924866\pi$
$458$	0.213182			0.00996134
$459$	19.0359	−	5.10066i	0.888521	−	0.238078i
$460$		0			0
$461$	24.6374	−	6.60156i	1.14748	−	0.307465i	0.365523	−	0.930802i	$-0.380890\pi$
$461$	24.6374	−	6.60156i	1.14748	−	0.307465i	0.781953	+	0.623337i	$0.214224\pi$
$462$	−17.5503	+	10.1327i	−0.816513	+	0.471414i
$463$	−4.84319	+	2.79622i	−0.225082	+	0.129951i	−0.608301	−	0.793706i	$-0.708149\pi$
$463$	−4.84319	+	2.79622i	−0.225082	+	0.129951i	0.383219	+	0.923658i	$0.374815\pi$
$464$	23.6036	−	6.32457i	1.09577	−	0.293611i
$465$		0			0
$466$	1.81865	−	0.487305i	0.0842472	−	0.0225740i
$467$	41.2557			1.90909			0.954544	−	0.298069i	$-0.0963427\pi$
$467$	41.2557			1.90909			0.954544	+	0.298069i	$0.0963427\pi$
$468$	2.88052	+	4.98920i	0.133152	+	0.230626i
$469$	12.1511	−	21.0464i	0.561088	−	0.971832i
$470$		0			0
$471$		−	16.6198i		−	0.765801i
$472$	19.8014	−	5.30576i	0.911432	−	0.244218i
$473$	22.0384			1.01333
$474$	−8.74654	−	15.1494i	−0.401742	−	0.695837i
$475$		0			0
$476$	−10.7972	−	2.89309i	−0.494888	−	0.132605i
$477$	63.0303	+	16.8889i	2.88596	+	0.773291i
$478$	−0.660467	+	2.46490i	−0.0302091	+	0.112742i
$479$	−0.353440	−	1.31906i	−0.0161491	−	0.0602693i	0.957381	−	0.288828i	$-0.0932655\pi$
$479$	−0.353440	−	1.31906i	−0.0161491	−	0.0602693i	−0.973530	+	0.228558i	$0.926599\pi$
$480$		0			0
$481$	−1.82519	+	2.35806i	−0.0832217	+	0.107518i
$482$	−5.55552	+	5.55552i	−0.253047	+	0.253047i
$483$	13.3372	−	23.1007i	0.606863	−	1.05112i
$484$	16.8848	+	29.2454i	0.767492	+	1.32933i
$485$		0			0
$486$	−0.697376	+	2.60264i	−0.0316336	+	0.118058i
$487$	30.4648			1.38049			0.690246	−	0.723575i	$-0.257502\pi$
$487$	30.4648			1.38049			0.690246	+	0.723575i	$0.257502\pi$
$488$	0.533576	−	1.99133i	0.0241539	−	0.0901435i
$489$	47.8624	−	47.8624i	2.16441	−	2.16441i
$490$		0			0
$491$	14.1300			0.637678			0.318839	−	0.947809i	$-0.396707\pi$
$491$	14.1300			0.637678			0.318839	+	0.947809i	$0.396707\pi$
$492$	8.19469	+	8.19469i	0.369445	+	0.369445i
$493$	−14.5416	+	3.89641i	−0.654921	+	0.175486i
$494$	0.635885	+	0.170385i	0.0286098	+	0.00766598i
$495$		0			0
$496$	1.59836	+	5.96518i	0.0717687	+	0.267844i
$497$	−6.65848	−	24.8498i	−0.298674	−	1.11467i
$498$	−16.5338	−	9.54580i	−0.740898	−	0.427758i
$499$	−2.26583	+	8.45621i	−0.101433	+	0.378552i	−0.997916	−	0.0645254i	$-0.979447\pi$
$499$	−2.26583	+	8.45621i	−0.101433	+	0.378552i	0.896483	+	0.443077i	$0.146113\pi$
$500$		0			0
$501$	4.49011	+	16.7573i	0.200603	+	0.748662i
$502$	−4.29761	+	1.15154i	−0.191812	+	0.0513958i
$503$	2.86527	+	1.65426i	0.127756	+	0.0737599i	0.562516	−	0.826786i	$-0.309833\pi$
$503$	2.86527	+	1.65426i	0.127756	+	0.0737599i	−0.434760	+	0.900546i	$0.643167\pi$
$504$	21.1858	−	21.1858i	0.943691	−	0.943691i
$505$		0			0
$506$	5.04341	+	2.91181i	0.224207	+	0.129446i
$507$	−27.5981	+	27.5981i	−1.22568	+	1.22568i
$508$	5.34040	−	5.34040i	0.236942	−	0.236942i
$509$	4.62265	−	8.00666i	0.204895	−	0.354889i	−0.745204	−	0.666836i	$-0.767648\pi$
$509$	4.62265	−	8.00666i	0.204895	−	0.354889i	0.950099	+	0.311948i	$0.100981\pi$
$510$		0			0
$511$	0.571710	−	0.330077i	0.0252910	−	0.0146017i
$512$		−	22.4256i		−	0.991083i
$513$	−17.7294	−	30.7082i	−0.782771	−	1.35580i
$514$	0.808593	−	0.466841i	0.0356655	−	0.0205915i
$515$		0			0
$516$	−22.2533	+	5.96275i	−0.979646	+	0.262495i
$517$	−9.51469	−	9.51469i	−0.418456	−	0.418456i
$518$	6.87031	+	2.87965i	0.301864	+	0.126525i
$519$			14.4294i			0.633379i
$520$		0			0
$521$	21.6531	−	12.5014i	0.948641	−	0.547698i	0.0559823	−	0.998432i	$-0.482171\pi$
$521$	21.6531	−	12.5014i	0.948641	−	0.547698i	0.892658	+	0.450734i	$0.148838\pi$
$522$	5.01679	−	18.7229i	0.219579	−	0.819479i
$523$	−18.5479	+	10.7087i	−0.811044	+	0.468257i	−0.847318	−	0.531085i	$-0.821784\pi$
$523$	−18.5479	+	10.7087i	−0.811044	+	0.468257i	0.0362741	+	0.999342i	$0.488451\pi$
$524$	−14.3118	+	14.3118i	−0.625212	+	0.625212i
$525$		0			0
$526$	0.184954	+	0.184954i	0.00806436	+	0.00806436i
$527$	−0.984714	−	3.67500i	−0.0428948	−	0.160086i
$528$	−36.4572	−	36.4572i	−1.58660	−	1.58660i
$529$	15.3346			0.666722
$530$		0			0
$531$	−22.5364	+	84.1069i	−0.977996	+	3.64993i
$532$			20.1122i			0.871975i
$533$	0.502299	−	0.870007i	0.0217570	−	0.0376842i
$534$	−2.92321	−	1.68772i	−0.126500	−	0.0730347i
$535$		0			0
$536$	−11.1531	−	2.98846i	−0.481739	−	0.129082i
$537$	11.5706	+	20.0410i	0.499310	+	0.864831i
$538$	−2.17592	+	3.76880i	−0.0938104	+	0.162484i
$539$	−7.90028	+	13.6837i	−0.340289	+	0.589398i
$540$		0			0
$541$	−14.4487	−	14.4487i	−0.621199	−	0.621199i	0.324639	−	0.945838i	$-0.394757\pi$
$541$	−14.4487	−	14.4487i	−0.621199	−	0.621199i	−0.945838	+	0.324639i	$0.894757\pi$
$542$	0.491252	−	0.283625i	0.0211011	−	0.0121827i
$543$	8.74975	+	32.6545i	0.375488	+	1.40134i
$544$			8.07069i			0.346028i
$545$		0			0
$546$	−1.59038	−	0.918204i	−0.0680618	−	0.0392955i
$547$		−	44.9717i		−	1.92285i	−0.275065	−	0.961426i	$-0.588699\pi$
$547$		−	44.9717i		−	1.92285i	0.275065	−	0.961426i	$-0.411301\pi$
$548$	7.99140	+	2.14129i	0.341376	+	0.0914713i
$549$	6.19187	+	6.19187i	0.264263	+	0.264263i
$550$		0			0
$551$	13.5435	+	23.4581i	0.576974	+	0.999348i
$552$	−12.2417	−	3.28015i	−0.521041	−	0.139613i
$553$	−40.1205	−	23.1636i	−1.70610	−	0.985015i
$554$	2.95148			0.125396
$555$		0			0
$556$	−37.3099			−1.58229
$557$	−8.38521	−	4.84121i	−0.355293	−	0.205128i	0.311721	−	0.950174i	$-0.399095\pi$
$557$	−8.38521	−	4.84121i	−0.355293	−	0.205128i	−0.667014	+	0.745045i	$0.732428\pi$
$558$	4.73171	+	1.26786i	0.200309	+	0.0536727i
$559$	0.998539	+	1.72952i	0.0422337	+	0.0731509i
$560$		0			0
$561$	22.4604	+	22.4604i	0.948279	+	0.948279i
$562$	7.03183	+	1.88417i	0.296620	+	0.0794790i
$563$		−	1.67768i		−	0.0707056i	−0.999375	−	0.0353528i	$-0.988745\pi$
$563$		−	1.67768i		−	0.0707056i	0.999375	−	0.0353528i	$-0.0112555\pi$
$564$	12.1818	+	7.03316i	0.512946	+	0.296150i
$565$		0			0
$566$		−	9.76250i		−	0.410349i
$567$	10.0554	+	37.5273i	0.422287	+	1.57600i
$568$	−10.5855	+	6.11156i	−0.444159	+	0.256436i
$569$	21.0954	+	21.0954i	0.884366	+	0.884366i	0.993975	−	0.109609i	$-0.0349598\pi$
$569$	21.0954	+	21.0954i	0.884366	+	0.884366i	−0.109609	+	0.993975i	$0.534960\pi$
$570$		0			0
$571$	−19.7886	+	34.2748i	−0.828126	+	1.43436i	0.0713808	+	0.997449i	$0.477259\pi$
$571$	−19.7886	+	34.2748i	−0.828126	+	1.43436i	−0.899507	+	0.436907i	$0.856074\pi$
$572$	−2.45153	+	4.24617i	−0.102503	+	0.177541i
$573$	21.0843	+	36.5191i	0.880811	+	1.52561i
$574$	−2.42417	−	0.649554i	−0.101183	−	0.0271119i
$575$		0			0
$576$	25.3043	+	14.6095i	1.05435	+	0.608728i
$577$	11.1596	−	19.3289i	0.464578	−	0.804673i	−0.534604	−	0.845103i	$-0.679539\pi$
$577$	11.1596	−	19.3289i	0.464578	−	0.804673i	0.999182	+	0.0404293i	$0.0128725\pi$
$578$			5.17726i			0.215346i
$579$	−12.8370	+	47.9084i	−0.533488	+	1.99101i
$580$		0			0
$581$	−50.5605			−2.09760
$582$	−1.70294	−	1.70294i	−0.0705890	−	0.0705890i
$583$	14.3737	+	53.6433i	0.595297	+	2.22168i
$584$	−0.221786	−	0.221786i	−0.00917756	−	0.00917756i
$585$		0			0
$586$	0.407062	−	0.407062i	0.0168156	−	0.0168156i
$587$	−20.5950	+	11.8905i	−0.850047	+	0.490775i	−0.860667	−	0.509169i	$-0.829953\pi$
$587$	−20.5950	+	11.8905i	−0.850047	+	0.490775i	0.0106195	+	0.999944i	$0.496620\pi$
$588$	4.27503	−	15.9546i	0.176299	−	0.657958i
$589$	−5.92840	+	3.42276i	−0.244276	+	0.141033i
$590$		0			0
$591$		−	41.2388i		−	1.69634i
$592$	−2.55271	+	18.7798i	−0.104916	+	0.771845i
$593$	24.4760	+	24.4760i	1.00511	+	1.00511i	0.999987	+	0.00511997i	$0.00162974\pi$
$593$	24.4760	+	24.4760i	1.00511	+	1.00511i	0.00511997	+	0.999987i	$0.498370\pi$
$594$	−20.8593	+	5.58924i	−0.855869	+	0.229329i
$595$		0			0
$596$	27.8648	−	16.0877i	1.14139	−	0.658980i
$597$	−25.5780	−	44.3024i	−1.04684	−	1.81318i
$598$			0.527727i			0.0215804i
$599$	−0.950077	+	0.548527i	−0.0388191	+	0.0224122i	−0.519284	−	0.854602i	$-0.673801\pi$
$599$	−0.950077	+	0.548527i	−0.0388191	+	0.0224122i	0.480465	+	0.877014i	$0.340468\pi$
$600$		0			0
$601$	13.0027	−	22.5213i	0.530390	−	0.918663i	−0.468981	−	0.883208i	$-0.655379\pi$
$601$	13.0027	−	22.5213i	0.530390	−	0.918663i	0.999371	−	0.0354548i	$-0.0112880\pi$
$602$	3.52782	−	3.52782i	0.143783	−	0.143783i
$603$	34.6795	−	34.6795i	1.41226	−	1.41226i
$604$	−26.9295	−	15.5478i	−1.09575	−	0.632629i
$605$		0			0
$606$	−0.461832	+	0.461832i	−0.0187606	+	0.0187606i
$607$	−28.7465	−	16.5968i	−1.16679	−	0.673644i	−0.213865	−	0.976863i	$-0.568605\pi$
$607$	−28.7465	−	16.5968i	−1.16679	−	0.673644i	−0.952921	+	0.303219i	$0.901939\pi$
$608$	14.0264	−	3.75838i	0.568848	−	0.152422i
$609$	−19.5565	−	72.9860i	−0.792471	−	2.95754i
$610$		0			0
$611$	0.315589	−	1.17779i	0.0127674	−	0.0476484i
$612$	−19.5361	−	11.2791i	−0.789698	−	0.455933i
$613$	10.8981	+	40.6721i	0.440169	+	1.64273i	0.728386	+	0.685167i	$0.240271\pi$
$613$	10.8981	+	40.6721i	0.440169	+	1.64273i	−0.288217	+	0.957565i	$0.593062\pi$
$614$	−1.98970	−	7.42567i	−0.0802979	−	0.299676i
$615$		0			0
$616$	24.6303	+	6.59967i	0.992384	+	0.265908i
$617$	−19.9307	+	5.34041i	−0.802379	+	0.214997i	−0.636628	−	0.771171i	$-0.719671\pi$
$617$	−19.9307	+	5.34041i	−0.802379	+	0.214997i	−0.165751	+	0.986168i	$0.553005\pi$
$618$	−11.4058	−	11.4058i	−0.458807	−	0.458807i
$619$	−19.2166			−0.772379			−0.386189	−	0.922419i	$-0.626209\pi$
$619$	−19.2166			−0.772379			−0.386189	+	0.922419i	$0.626209\pi$
$620$		0			0
$621$	20.0994	−	20.0994i	0.806560	−	0.806560i
$622$	0.237440	−	0.886138i	0.00952048	−	0.0355309i
$623$	−8.93921			−0.358142
$624$	1.20923	−	4.51292i	0.0484081	−	0.180661i
$625$		0			0
$626$	1.58815	+	2.75076i	0.0634752	+	0.109942i
$627$	28.5756	−	49.4945i	1.14120	−	1.97662i
$628$	−7.10315	+	7.10315i	−0.283447	+	0.283447i
$629$	1.57266	−	11.5698i	0.0627062	−	0.461317i
$630$		0			0
$631$	−7.34303	−	27.4045i	−0.292321	−	1.09096i	−0.943322	−	0.331880i	$-0.892317\pi$
$631$	−7.34303	−	27.4045i	−0.292321	−	1.09096i	0.651000	−	0.759077i	$-0.274350\pi$
$632$	−5.69686	+	21.2610i	−0.226609	+	0.845715i
$633$	−32.3394	−	8.66532i	−1.28538	−	0.344416i
$634$	−8.46153	−	2.26726i	−0.336050	−	0.0900444i
$635$		0			0
$636$	−29.0277	−	50.2774i	−1.15102	−	1.99363i
$637$	−1.43182			−0.0567307
$638$	15.9345	−	4.26964i	0.630854	−	0.169037i
$639$		−	51.9181i		−	2.05385i
$640$		0			0
$641$	−5.71476	+	9.89826i	−0.225719	+	0.390958i	−0.956535	−	0.291617i	$-0.905807\pi$
$641$	−5.71476	+	9.89826i	−0.225719	+	0.390958i	0.730816	+	0.682575i	$0.239140\pi$
$642$	−0.744088	−	1.28880i	−0.0293668	−	0.0508648i
$643$	5.49147			0.216562			0.108281	−	0.994120i	$-0.465465\pi$
$643$	5.49147			0.216562			0.108281	+	0.994120i	$0.465465\pi$
$644$	−15.5732	+	4.17283i	−0.613670	+	0.164432i
$645$		0			0
$646$	−2.48992	+	0.667171i	−0.0979645	+	0.0262495i
$647$	19.0310	−	10.9876i	0.748187	−	0.431966i	−0.0768511	−	0.997043i	$-0.524487\pi$
$647$	19.0310	−	10.9876i	0.748187	−	0.431966i	0.825039	+	0.565076i	$0.191153\pi$
$648$	15.9859	−	9.22947i	0.627986	−	0.362568i
$649$	−71.5810	+	19.1801i	−2.80980	+	0.752884i
$650$		0			0
$651$	18.4453	−	4.94239i	0.722927	−	0.193708i
$652$	−40.9118			−1.60223
$653$	16.3919	+	28.3917i	0.641467	+	1.11105i	0.985106	+	0.171951i	$0.0550070\pi$
$653$	16.3919	+	28.3917i	0.641467	+	1.11105i	−0.343639	+	0.939102i	$0.611660\pi$
$654$	−0.0705942	+	0.122273i	−0.00276045	+	0.00478124i
$655$		0			0
$656$		−	6.38505i		−	0.249294i
$657$	1.28685	−	0.344811i	0.0502049	−	0.0134524i
$658$	−3.04615			−0.118751
$659$	1.71645	+	2.97297i	0.0668632	+	0.115810i	0.897519	−	0.440976i	$-0.145368\pi$
$659$	1.71645	+	2.97297i	0.0668632	+	0.115810i	−0.830656	+	0.556786i	$0.812034\pi$
$660$		0			0
$661$	32.2356	+	8.63751i	1.25382	+	0.335960i	0.823811	−	0.566864i	$-0.191844\pi$
$661$	32.2356	+	8.63751i	1.25382	+	0.335960i	0.430009	+	0.902824i	$0.358510\pi$
$662$	−4.61554	−	1.23673i	−0.179388	−	0.0480669i
$663$	−0.744980	+	2.78030i	−0.0289326	+	0.107978i
$664$	6.21744	+	23.2038i	0.241283	+	0.900482i
$665$		0			0
$666$	11.8884	+	9.20186i	0.460665	+	0.356565i
$667$	−15.3540	+	15.3540i	−0.594509	+	0.594509i
$668$	5.24289	−	9.08095i	0.202853	−	0.351352i
$669$	35.8935	+	62.1693i	1.38772	+	2.40360i
$670$		0			0
$671$	−1.92885	+	7.19857i	−0.0744625	+	0.277898i
$672$	−40.5077			−1.56262
$673$	11.5014	−	42.9238i	0.443346	−	1.65459i	−0.276921	−	0.960893i	$-0.589314\pi$
$673$	11.5014	−	42.9238i	0.443346	−	1.65459i	0.720267	−	0.693697i	$-0.244019\pi$
$674$	−3.90550	+	3.90550i	−0.150434	+	0.150434i
$675$		0			0
$676$	23.5903			0.907321
$677$	9.36277	+	9.36277i	0.359841	+	0.359841i	0.863754	−	0.503913i	$-0.168107\pi$
$677$	9.36277	+	9.36277i	0.359841	+	0.359841i	−0.503913	+	0.863754i	$0.668107\pi$
$678$	−7.47295	+	2.00237i	−0.286997	+	0.0769006i
$679$	−6.16065	−	1.65074i	−0.236424	−	0.0633496i
$680$		0			0
$681$	2.30011	+	8.58412i	0.0881404	+	0.328944i
$682$	1.07904	+	4.02702i	0.0413185	+	0.154203i
$683$	−33.7758	−	19.5005i	−1.29240	−	0.746165i	−0.313318	−	0.949648i	$-0.601441\pi$
$683$	−33.7758	−	19.5005i	−1.29240	−	0.746165i	−0.979078	+	0.203483i	$0.934774\pi$
$684$	−10.5050	+	39.2052i	−0.401669	+	1.49905i
$685$		0			0
$686$	−1.29300	−	4.82553i	−0.0493668	−	0.184239i
$687$	1.61995	−	0.434063i	0.0618048	−	0.0165606i
$688$	10.9925	+	6.34654i	0.419086	+	0.241959i
$689$	−3.55854	+	3.55854i	−0.135570	+	0.135570i
$690$		0			0
$691$	8.34887	+	4.82022i	0.317606	+	0.183370i	0.650325	−	0.759656i	$-0.274633\pi$
$691$	8.34887	+	4.82022i	0.317606	+	0.183370i	−0.332719	+	0.943026i	$0.607966\pi$
$692$	6.16698	−	6.16698i	0.234433	−	0.234433i
$693$	−76.5857	+	76.5857i	−2.90925	+	2.90925i
$694$	0.449102	−	0.777867i	0.0170477	−	0.0295274i
$695$		0			0
$696$	−31.0907	+	17.9502i	−1.17849	+	0.680401i
$697$			3.93367i			0.148998i
$698$	2.70124	+	4.67868i	0.102243	+	0.177091i
$699$	12.8275	−	7.40595i	0.485180	−	0.280119i
$700$		0			0
$701$	−10.3952	+	2.78539i	−0.392622	+	0.105203i	−0.449729	−	0.893165i	$-0.648479\pi$
$701$	−10.3952	+	2.78539i	−0.392622	+	0.105203i	0.0571063	+	0.998368i	$0.481813\pi$
$702$	−1.38375	−	1.38375i	−0.0522262	−	0.0522262i
$703$	−20.8401	+	2.65463i	−0.785997	+	0.100121i
$704$			24.8674i			0.937225i
$705$		0			0
$706$	−6.91528	+	3.99254i	−0.260260	+	0.150261i
$707$	−0.447676	+	1.67075i	−0.0168366	+	0.0628351i
$708$	67.0897	−	38.7342i	2.52138	−	1.45572i
$709$	−8.98141	+	8.98141i	−0.337304	+	0.337304i	−0.855352	−	0.518048i	$-0.826659\pi$
$709$	−8.98141	+	8.98141i	−0.337304	+	0.337304i	0.518048	+	0.855352i	$0.326659\pi$
$710$		0			0
$711$	−66.1090	−	66.1090i	−2.47928	−	2.47928i
$712$	1.09926	+	4.10248i	0.0411963	+	0.153747i
$713$	−3.88031	−	3.88031i	−0.145319	−	0.145319i
$714$	7.19076			0.269108
$715$		0			0
$716$	3.62013	−	13.5105i	0.135290	−	0.504911i
$717$			20.0753i			0.749725i
$718$	−5.42881	+	9.40297i	−0.202601	+	0.350916i
$719$	35.4058	+	20.4415i	1.32041	+	0.762340i	0.983794	−	0.179301i	$-0.0573836\pi$
$719$	35.4058	+	20.4415i	1.32041	+	0.762340i	0.336618	+	0.941641i	$0.390717\pi$
$720$		0			0
$721$	−41.2622	−	11.0562i	−1.53669	−	0.411754i
$722$	−1.37477	−	2.38117i	−0.0511636	−	0.0886179i
$723$	−30.9041	+	53.5275i	−1.14934	+	1.99071i
$724$	10.2167	−	17.6958i	0.379699	−	0.657659i
$725$		0			0
$726$	−15.3610	−	15.3610i	−0.570101	−	0.570101i
$727$	−10.5561	+	6.09457i	−0.391505	+	0.226035i	−0.682812	−	0.730594i	$-0.739243\pi$
$727$	−10.5561	+	6.09457i	−0.391505	+	0.226035i	0.291307	+	0.956630i	$0.405910\pi$
$728$	0.598051	+	2.23196i	0.0221652	+	0.0827218i
$729$		−	15.8072i		−	0.585450i
$730$		0			0
$731$	−6.77223	−	3.90995i	−0.250480	−	0.144615i
$732$		−	7.79065i		−	0.287951i
$733$	36.3558	+	9.74150i	1.34283	+	0.359811i	0.857484	−	0.514511i	$-0.172026\pi$
$733$	36.3558	+	9.74150i	1.34283	+	0.359811i	0.485348	+	0.874321i	$0.338693\pi$
$734$	5.10725	+	5.10725i	0.188512	+	0.188512i
$735$		0			0
$736$	5.82034	+	10.0811i	0.214541	+	0.371595i
$737$	40.3178	+	10.8031i	1.48513	+	0.397938i
$738$	−4.38621	−	2.53238i	−0.161459	−	0.0932182i
$739$	−23.6026			−0.868235			−0.434117	−	0.900856i	$-0.642940\pi$
$739$	−23.6026			−0.868235			−0.434117	+	0.900856i	$0.642940\pi$
$740$		0			0
$741$	5.17895			0.190253
$742$	10.8879	+	6.28614i	0.399708	+	0.230771i
$743$	−3.83523	−	1.02765i	−0.140701	−	0.0377007i	0.187781	−	0.982211i	$-0.439870\pi$
$743$	−3.83523	−	1.02765i	−0.140701	−	0.0377007i	−0.328482	+	0.944510i	$0.606537\pi$
$744$	−4.53643	−	7.85733i	−0.166314	−	0.288064i
$745$		0			0
$746$	0.730852	+	0.730852i	0.0267584	+	0.0267584i
$747$	−98.5588	−	26.4087i	−3.60608	−	0.966246i
$748$		−	19.1987i		−	0.701975i
$749$	−3.41314	−	1.97058i	−0.124713	−	0.0720034i
$750$		0			0
$751$			5.02392i			0.183325i	0.995790	+	0.0916627i	$0.0292182\pi$
$751$			5.02392i			0.183325i	−0.995790	+	0.0916627i	$0.970782\pi$
$752$	−2.00583	−	7.48584i	−0.0731449	−	0.272981i
$753$	−30.3124	+	17.5009i	−1.10465	+	0.637768i
$754$	1.05705	+	1.05705i	0.0384955	+	0.0384955i
$755$		0			0
$756$	29.8928	−	51.7759i	1.08719	−	1.88307i
$757$	22.2232	−	38.4917i	0.807715	−	1.39900i	−0.106728	−	0.994288i	$-0.534037\pi$
$757$	22.2232	−	38.4917i	0.807715	−	1.39900i	0.914443	−	0.404715i	$-0.132629\pi$
$758$	−4.32408	−	7.48952i	−0.157058	−	0.272032i
$759$	44.2531	+	11.8576i	1.60629	+	0.430403i
$760$		0			0
$761$	20.2158	+	11.6716i	0.732821	+	0.423095i	0.819453	−	0.573146i	$-0.194277\pi$
$761$	20.2158	+	11.6716i	0.732821	+	0.423095i	−0.0866322	+	0.996240i	$0.527610\pi$
$762$	−2.42922	+	4.20754i	−0.0880014	+	0.152423i
$763$			0.373911i			0.0135365i
$764$	6.59669	−	24.6192i	0.238660	−	0.890690i
$765$		0			0
$766$	3.64860			0.131829
$767$	−4.74848	−	4.74848i	−0.171458	−	0.171458i
$768$	−4.13973	−	15.4497i	−0.149379	−	0.557492i
$769$	6.34019	+	6.34019i	0.228633	+	0.228633i	0.812121	−	0.583488i	$-0.198313\pi$
$769$	6.34019	+	6.34019i	0.228633	+	0.228633i	−0.583488	+	0.812121i	$0.698313\pi$
$770$		0			0
$771$	5.19387	−	5.19387i	0.187052	−	0.187052i
$772$	25.9620	−	14.9892i	0.934393	−	0.539472i
$773$	6.39564	−	23.8688i	0.230035	−	0.858503i	−0.750289	−	0.661110i	$-0.770086\pi$
$773$	6.39564	−	23.8688i	0.230035	−	0.858503i	0.980324	−	0.197393i	$-0.0632475\pi$
$774$	8.71952	−	5.03422i	0.313417	−	0.180951i
$775$		0			0
$776$			3.03030i			0.108782i
$777$	58.0701	+	7.89338i	2.08325	+	0.283173i
$778$	0.272810	+	0.272810i	0.00978070	+	0.00978070i
$779$	6.83652	−	1.83184i	0.244944	−	0.0656325i
$780$		0			0
$781$	38.2662	−	22.0930i	1.36927	−	0.790550i
$782$	−1.03320	−	1.78956i	−0.0369472	−	0.0639945i
$783$		−	80.5192i		−	2.87752i
$784$	−7.88116	+	4.55019i	−0.281470	+	0.162507i
$785$		0			0
$786$	6.51009	−	11.2758i	0.232207	−	0.402194i
$787$	−3.92787	+	3.92787i	−0.140014	+	0.140014i	−0.773640	−	0.633626i	$-0.781566\pi$
$787$	−3.92787	+	3.92787i	−0.140014	+	0.140014i	0.633626	+	0.773640i	$0.281566\pi$
$788$	−17.6251	+	17.6251i	−0.627866	+	0.627866i
$789$	1.78203	+	1.02886i	0.0634419	+	0.0366282i
$790$		0			0
$791$	−14.4878	+	14.4878i	−0.515127	+	0.515127i
$792$	44.5653	+	25.7298i	1.58356	+	0.914268i
$793$	−0.652322	+	0.174789i	−0.0231646	+	0.00620695i
$794$	−1.23226	−	4.59887i	−0.0437314	−	0.163208i
$795$		0			0
$796$	−8.00263	+	29.8662i	−0.283646	+	1.05858i
$797$	12.5378	+	7.23871i	0.444112	+	0.256408i	0.705340	−	0.708869i	$-0.250794\pi$
$797$	12.5378	+	7.23871i	0.444112	+	0.256408i	−0.261228	+	0.965277i	$0.584128\pi$
$798$	−3.34861	−	12.4972i	−0.118539	−	0.442395i
$799$	1.23574	+	4.61185i	0.0437174	+	0.163155i
$800$		0			0
$801$	−17.4254	−	4.66912i	−0.615696	−	0.164975i
$802$	−6.72756	+	1.80264i	−0.237558	+	0.0636536i
$803$	0.801745	+	0.801745i	0.0282930	+	0.0282930i
$804$	−43.6339			−1.53885
$805$		0			0
$806$	−0.267141	+	0.267141i	−0.00940965	+	0.00940965i
$807$	−8.86084	+	33.0691i	−0.311916	+	1.16409i
$808$	0.821810			0.0289112
$809$	2.46645	−	9.20493i	0.0867159	−	0.323628i	−0.908918	−	0.416976i	$-0.863090\pi$
$809$	2.46645	−	9.20493i	0.0867159	−	0.323628i	0.995634	+	0.0933474i	$0.0297567\pi$
$810$		0			0
$811$	0.620382	+	1.07453i	0.0217846	+	0.0377320i	0.876712	−	0.481015i	$-0.159732\pi$
$811$	0.620382	+	1.07453i	0.0217846	+	0.0377320i	−0.854928	+	0.518747i	$0.826399\pi$
$812$	−22.8352	+	39.5518i	−0.801360	+	1.38800i
$813$	3.15548	−	3.15548i	0.110668	−	0.110668i
$814$	−1.72331	+	12.6780i	−0.0604018	+	0.444365i
$815$		0			0
$816$	4.73496	+	17.6711i	0.165757	+	0.618612i
$817$	−3.64159	+	13.5906i	−0.127403	+	0.475474i
$818$	−0.159475	−	0.0427312i	−0.00557591	−	0.00149406i
$819$	−9.48030	−	2.54024i	−0.331268	−	0.0887631i
$820$		0			0
$821$	−21.0808	−	36.5130i	−0.735724	−	1.27431i	−0.954405	−	0.298515i	$-0.903509\pi$
$821$	−21.0808	−	36.5130i	−0.735724	−	1.27431i	0.218681	−	0.975796i	$-0.429825\pi$
$822$	−5.32215			−0.185631
$823$	21.2999	−	5.70729i	0.742468	−	0.198944i	0.132293	−	0.991211i	$-0.457766\pi$
$823$	21.2999	−	5.70729i	0.742468	−	0.198944i	0.610175	+	0.792267i	$0.291099\pi$
$824$			20.2961i			0.707048i
$825$		0			0
$826$	−8.38815	+	14.5287i	−0.291861	+	0.505518i
$827$	12.7026	+	22.0015i	0.441713	+	0.765069i	0.997817	−	0.0660440i	$-0.0210378\pi$
$827$	12.7026	+	22.0015i	0.441713	+	0.765069i	−0.556104	+	0.831113i	$0.687704\pi$
$828$	−32.5367			−1.13073
$829$	−34.1099	+	9.13971i	−1.18468	+	0.317435i	−0.796783	−	0.604266i	$-0.793467\pi$
$829$	−34.1099	+	9.13971i	−1.18468	+	0.317435i	−0.387901	+	0.921701i	$0.626800\pi$
$830$		0			0
$831$	22.4280	−	6.00955i	0.778017	−	0.208469i
$832$	−1.95154	+	1.12672i	−0.0676573	+	0.0390620i
$833$	4.85539	−	2.80326i	0.168229	−	0.0971273i
$834$	23.1833	−	6.21196i	0.802774	−	0.215103i
$835$		0			0
$836$	−33.3664	+	8.94050i	−1.15400	+	0.309214i
$837$	20.3491			0.703366
$838$	−4.04214	−	7.00119i	−0.139633	−	0.241852i
$839$	−8.80567	+	15.2519i	−0.304005	+	0.526553i	−0.977039	−	0.213059i	$-0.931657\pi$
$839$	−8.80567	+	15.2519i	−0.304005	+	0.526553i	0.673034	+	0.739611i	$0.264991\pi$
$840$		0			0
$841$			32.5089i			1.12100i
$842$	8.15101	−	2.18406i	0.280902	−	0.0752676i
$843$	57.2705			1.97250
$844$	10.1181	+	17.5250i	0.348279	+	0.603236i
$845$		0			0
$846$	−5.93794	−	1.59107i	−0.204151	−	0.0547020i
$847$	−55.5710	−	14.8902i	−1.90944	−	0.511633i
$848$	−8.27857	+	30.8960i	−0.284287	+	1.06097i
$849$	−19.8776	−	74.1842i	−0.682197	−	2.54599i
$850$		0			0
$851$	−6.37936	−	15.5860i	−0.218682	−	0.534281i
$852$	−32.6619	+	32.6619i	−1.11898	+	1.11898i
$853$	5.05228	−	8.75081i	0.172987	−	0.299622i	−0.766476	−	0.642273i	$-0.777992\pi$
$853$	5.05228	−	8.75081i	0.172987	−	0.299622i	0.939463	+	0.342651i	$0.111325\pi$
$854$	0.843558	+	1.46109i	0.0288660	+	0.0499973i
$855$		0			0
$856$	−0.484645	+	1.80872i	−0.0165648	+	0.0618207i
$857$	−13.8427			−0.472858			−0.236429	−	0.971649i	$-0.575977\pi$
$857$	−13.8427			−0.472858			−0.236429	+	0.971649i	$0.575977\pi$
$858$	0.816340	−	3.04662i	0.0278694	−	0.104010i
$859$	−22.7197	+	22.7197i	−0.775187	+	0.775187i	−0.979008	−	0.203821i	$-0.934664\pi$
$859$	−22.7197	+	22.7197i	−0.775187	+	0.775187i	0.203821	+	0.979008i	$0.434664\pi$
$860$		0			0
$861$	−19.7436			−0.672859
$862$	8.84901	+	8.84901i	0.301399	+	0.301399i
$863$	13.2710	−	3.55596i	0.451751	−	0.121046i	−0.0257675	−	0.999668i	$-0.508203\pi$
$863$	13.2710	−	3.55596i	0.451751	−	0.121046i	0.477519	+	0.878622i	$0.341536\pi$
$864$	−41.6951	−	11.1722i	−1.41850	−	0.380085i
$865$		0			0
$866$	1.08855	+	4.06252i	0.0369904	+	0.138050i
$867$	10.5415	+	39.3414i	0.358008	+	1.33611i
$868$	−9.99566	−	5.77099i	−0.339275	−	0.195880i
$869$	20.5939	−	76.8573i	0.698599	−	2.60721i
$870$		0			0
$871$	0.978960	+	3.65353i	0.0331708	+	0.123795i
$872$	0.171599	−	0.0459799i	0.00581109	−	0.00155708i
$873$	−11.1469	−	6.43565i	−0.377265	−	0.217814i
$874$	−2.62902	+	2.62902i	−0.0889279	+	0.0889279i
$875$		0			0
$876$	−1.02649	−	0.592642i	−0.0346817	−	0.0200235i
$877$	22.9132	−	22.9132i	0.773723	−	0.773723i	−0.205032	−	0.978755i	$-0.565730\pi$
$877$	22.9132	−	22.9132i	0.773723	−	0.773723i	0.978755	+	0.205032i	$0.0657300\pi$
$878$	1.13015	−	1.13015i	0.0381409	−	0.0381409i
$879$	2.26439	−	3.92204i	0.0763761	−	0.132287i
$880$		0			0
$881$	−21.1405	+	12.2055i	−0.712240	+	0.411212i	−0.811890	−	0.583810i	$-0.801561\pi$
$881$	−21.1405	+	12.2055i	−0.712240	+	0.411212i	0.0996497	+	0.995023i	$0.468228\pi$
$882$			7.21863i			0.243064i
$883$	−13.6450	−	23.6339i	−0.459192	−	0.795344i	0.539727	−	0.841840i	$-0.318528\pi$
$883$	−13.6450	−	23.6339i	−0.459192	−	0.795344i	−0.998918	+	0.0464967i	$0.985194\pi$
$884$	1.50667	−	0.869877i	0.0506748	−	0.0292571i
$885$		0			0
$886$	1.29190	−	0.346163i	0.0434022	−	0.0116296i
$887$	−26.0700	−	26.0700i	−0.875344	−	0.875344i	0.117705	−	0.993049i	$-0.462446\pi$
$887$	−26.0700	−	26.0700i	−0.875344	−	0.875344i	−0.993049	+	0.117705i	$0.962446\pi$
$888$	−3.51837	−	27.6208i	−0.118069	−	0.926893i
$889$			12.8667i			0.431535i
$890$		0			0
$891$	−57.7882	+	33.3641i	−1.93598	+	1.11774i
$892$	11.2300	−	41.9111i	0.376009	−	1.40329i
$893$	7.43970	−	4.29531i	0.248960	−	0.143737i
$894$	−14.6359	+	14.6359i	−0.489497	+	0.489497i
$895$		0			0
$896$	22.7090	+	22.7090i	0.758654	+	0.758654i
$897$	1.07451	+	4.01014i	0.0358770	+	0.133895i
$898$	9.42426	+	9.42426i	0.314492	+	0.314492i
$899$	−15.5447			−0.518446
$900$		0			0
$901$	5.10023	−	19.0343i	0.169913	−	0.634124i
$902$		−	4.31047i		−	0.143523i
$903$	19.6245	−	33.9906i	0.653062	−	1.13114i
$904$	8.43047	+	4.86733i	0.280393	+	0.161885i
$905$		0			0
$906$	19.3219	+	5.17729i	0.641928	+	0.172004i
$907$	10.4419	+	18.0858i	0.346716	+	0.600530i	0.985664	−	0.168720i	$-0.0539633\pi$
$907$	10.4419	+	18.0858i	0.346716	+	0.600530i	−0.638948	+	0.769250i	$0.720630\pi$
$908$	2.68573	−	4.65182i	0.0891290	−	0.154376i
$909$	−1.74533	+	3.02300i	−0.0578890	+	0.100267i
$910$		0			0
$911$	31.8066	+	31.8066i	1.05380	+	1.05380i	0.998468	+	0.0553319i	$0.0176217\pi$
$911$	31.8066	+	31.8066i	1.05380	+	1.05380i	0.0553319	+	0.998468i	$0.482378\pi$
$912$	28.5065	−	16.4582i	0.943945	−	0.544987i
$913$	−22.4757	−	83.8805i	−0.743838	−	2.77604i
$914$		−	4.71478i		−	0.155951i
$915$		0			0
$916$	−0.877864	−	0.506835i	−0.0290055	−	0.0167463i
$917$		−	34.4815i		−	1.13868i
$918$	7.40154	+	1.98324i	0.244287	+	0.0654566i
$919$	27.1309	+	27.1309i	0.894965	+	0.894965i	0.994985	−	0.100021i	$-0.0318909\pi$
$919$	27.1309	+	27.1309i	0.894965	+	0.894965i	−0.100021	+	0.994985i	$0.531891\pi$
$920$		0			0
$921$	−30.2391	−	52.3756i	−0.996411	−	1.72584i
$922$	9.57949	+	2.56682i	0.315484	+	0.0845336i
$923$	3.46762	+	2.00203i	0.114138	+	0.0658976i
$924$	96.3606			3.17003
$925$		0			0
$926$	−2.17445			−0.0714569
$927$	−74.6586	−	43.1041i	−2.45211	−	1.41573i
$928$	31.8510	+	8.53446i	1.04556	+	0.280157i
$929$	15.3825	+	26.6433i	0.504684	+	0.874138i	0.999985	+	0.00541681i	$0.00172423\pi$
$929$	15.3825	+	26.6433i	0.504684	+	0.874138i	−0.495302	+	0.868721i	$0.664942\pi$
$930$		0			0
$931$	−7.13300	−	7.13300i	−0.233775	−	0.233775i
$932$	−8.64758	−	2.31711i	−0.283261	−	0.0758995i
$933$		−	7.21712i		−	0.236278i
$934$	13.8920	+	8.02052i	0.454559	+	0.262440i
$935$		0			0
$936$			4.66318i			0.152421i
$937$	−0.585214	−	2.18405i	−0.0191181	−	0.0713498i	0.955708	−	0.294317i	$-0.0950923\pi$
$937$	−0.585214	−	2.18405i	−0.0191181	−	0.0713498i	−0.974826	+	0.222968i	$0.928426\pi$
$938$	8.18326	−	4.72460i	0.267193	−	0.154264i
$939$	17.6690	+	17.6690i	0.576607	+	0.576607i
$940$		0			0
$941$	12.9110	−	22.3625i	0.420887	−	0.728998i	−0.575139	−	0.818056i	$-0.695052\pi$
$941$	12.9110	−	22.3625i	0.420887	−	0.728998i	0.996026	+	0.0890574i	$0.0283855\pi$
$942$	3.23106	−	5.59636i	0.105274	−	0.182339i
$943$	2.83685	+	4.91356i	0.0923805	+	0.160008i
$944$	−41.2273	−	11.0468i	−1.34184	−	0.359544i
$945$		0			0
$946$	7.42093	+	4.28448i	0.241275	+	0.139300i
$947$	11.4207	−	19.7812i	0.371122	−	0.642802i	−0.618617	−	0.785693i	$-0.712307\pi$
$947$	11.4207	−	19.7812i	0.371122	−	0.642802i	0.989738	+	0.142891i	$0.0456400\pi$
$948$			83.1787i			2.70152i
$949$	−0.0265927	+	0.0992455i	−0.000863237	+	0.00322164i
$950$		0			0
$951$	−68.9146			−2.23471
$952$	−6.39783	−	6.39783i	−0.207355	−	0.207355i
$953$	−9.03001	−	33.7005i	−0.292511	−	1.09167i	−0.943174	−	0.332299i	$-0.892176\pi$
$953$	−9.03001	−	33.7005i	−0.292511	−	1.09167i	0.650663	−	0.759366i	$-0.274491\pi$
$954$	17.9407	+	17.9407i	0.580851	+	0.580851i
$955$		0			0
$956$	8.57998	−	8.57998i	0.277496	−	0.277496i
$957$	112.391	−	64.8891i	3.63309	−	2.09757i
$958$	0.137425	−	0.512876i	0.00443999	−	0.0165703i
$959$	−12.2064	+	7.04736i	−0.394165	+	0.227571i
$960$		0			0
$961$			27.0715i			0.873274i
$962$	−1.07302	+	0.439189i	−0.0345957	+	0.0141600i
$963$	−5.62404	−	5.62404i	−0.181232	−	0.181232i
$964$	36.0852	−	9.66901i	1.16223	−	0.311418i
$965$		0			0
$966$	8.98200	−	5.18576i	0.288991	−	0.166849i
$967$	30.1956	+	52.3003i	0.971024	+	1.68186i	0.692477	+	0.721440i	$0.256520\pi$
$967$	30.1956	+	52.3003i	0.971024	+	1.68186i	0.278547	+	0.960423i	$0.410147\pi$
$968$			27.3343i			0.878557i
$969$	−17.5622	+	10.1395i	−0.564178	+	0.325728i
$970$		0			0
$971$	−19.6729	+	34.0744i	−0.631333	+	1.09350i	0.355947	+	0.934506i	$0.384159\pi$
$971$	−19.6729	+	34.0744i	−0.631333	+	1.09350i	−0.987279	+	0.158994i	$0.949175\pi$
$972$	9.05945	−	9.05945i	0.290582	−	0.290582i
$973$	44.9455	−	44.9455i	1.44089	−	1.44089i
$974$	10.2583	+	5.92266i	0.328698	+	0.189774i
$975$		0			0
$976$	−3.03511	+	3.03511i	−0.0971517	+	0.0971517i
$977$	34.6209	+	19.9884i	1.10762	+	0.639486i	0.938213	−	0.346060i	$-0.112481\pi$
$977$	34.6209	+	19.9884i	1.10762	+	0.639486i	0.169410	+	0.985546i	$0.445814\pi$
$978$	25.4215	−	6.81167i	0.812890	−	0.217813i
$979$	−3.97375	−	14.8303i	−0.127002	−	0.473977i
$980$		0			0
$981$	−0.195301	+	0.728873i	−0.00623548	+	0.0232711i
$982$	4.75796	+	2.74701i	0.151833	+	0.0876607i
$983$	−9.30200	−	34.7155i	−0.296688	−	1.10725i	−0.939868	−	0.341539i	$-0.889052\pi$
$983$	−9.30200	−	34.7155i	−0.296688	−	1.10725i	0.643180	−	0.765715i	$-0.277615\pi$
$984$	2.42787	+	9.06093i	0.0773976	+	0.288852i
$985$		0			0
$986$	−5.65407	−	1.51500i	−0.180062	−	0.0482475i
$987$	−23.1474	+	6.20233i	−0.736790	+	0.197422i
$988$	−2.21343	−	2.21343i	−0.0704187	−	0.0704187i
$989$	−11.2789			−0.358650
$990$		0			0
$991$	4.65585	−	4.65585i	0.147898	−	0.147898i	−0.629280	−	0.777178i	$-0.716650\pi$
$991$	4.65585	−	4.65585i	0.147898	−	0.147898i	0.777178	+	0.629280i	$0.216650\pi$
$992$	−2.15686	+	8.04950i	−0.0684802	+	0.255572i
$993$	−37.5911			−1.19292
$994$	2.58895	−	9.66209i	0.0821164	−	0.306463i
$995$		0			0
$996$	45.3898	+	78.6175i	1.43823	+	2.49109i
$997$	−11.4324	+	19.8015i	−0.362067	+	0.627119i	−0.988301	−	0.152516i	$-0.951262\pi$
$997$	−11.4324	+	19.8015i	−0.362067	+	0.627119i	0.626234	+	0.779636i	$0.284596\pi$
$998$	−2.40694	+	2.40694i	−0.0761904	+	0.0761904i
$999$	57.5952	+	24.1407i	1.82223	+	0.763777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.y.b.393.11		68
5.2	odd	4		925.2.t.b.282.7		68
5.3	odd	4		185.2.p.a.97.11	✓	68
5.4	even	2		185.2.u.a.23.7	yes	68
37.29	odd	12		925.2.t.b.843.7		68
185.29	odd	12		185.2.p.a.103.11	yes	68
185.103	even	12		185.2.u.a.177.7	yes	68
185.177	even	12	inner	925.2.y.b.732.11		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.11	✓	68	5.3	odd	4
185.2.p.a.103.11	yes	68	185.29	odd	12
185.2.u.a.23.7	yes	68	5.4	even	2
185.2.u.a.177.7	yes	68	185.103	even	12
925.2.t.b.282.7		68	5.2	odd	4
925.2.t.b.843.7		68	37.29	odd	12
925.2.y.b.393.11		68	1.1	even	1	trivial
925.2.y.b.732.11		68	185.177	even	12	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.336728 + 0.194410i) q^{2} +(2.95460 + 0.791682i) q^{3} +(-0.924410 - 1.60112i) q^{4} +(0.840985 + 0.840985i) q^{6} +(3.04240 + 0.815208i) q^{7} -1.49650i q^{8} +(5.50482 + 3.17821i) q^{9} +5.40976i q^{11} +(-1.46368 - 5.46252i) q^{12} +(-0.424546 + 0.245112i) q^{13} +(0.865975 + 0.865975i) q^{14} +(-1.55789 + 2.69834i) q^{16} +(0.959776 - 1.66238i) q^{17} +(1.23575 + 2.14038i) q^{18} +(-3.33608 - 0.893901i) q^{19} +(8.34368 + 4.81723i) q^{21} +(-1.05171 + 1.82162i) q^{22} -2.76865i q^{23} +(1.18475 - 4.42155i) q^{24} -0.190608 q^{26} +(7.25964 + 7.25964i) q^{27} +(-1.50717 - 5.62484i) q^{28} +(-5.54567 - 5.54567i) q^{29} +(1.40152 - 1.40152i) q^{31} +(-3.64118 + 2.10223i) q^{32} +(-4.28281 + 15.9837i) q^{33} +(0.646366 - 0.373180i) q^{34} -11.7519i q^{36} +(5.62947 - 2.30414i) q^{37} +(-0.949569 - 0.949569i) q^{38} +(-1.44841 + 0.388101i) q^{39} +(-1.77472 + 1.02463i) q^{41} +(1.87303 + 3.24419i) q^{42} -4.07381i q^{43} +(8.66170 - 5.00084i) q^{44} +(0.538252 - 0.932280i) q^{46} +(-1.75880 + 1.75880i) q^{47} +(-6.73915 + 6.73915i) q^{48} +(2.52944 + 1.46037i) q^{49} +(4.15183 - 4.15183i) q^{51} +(0.784908 + 0.453167i) q^{52} +(9.91602 - 2.65699i) q^{53} +(1.03318 + 3.85587i) q^{54} +(1.21996 - 4.55294i) q^{56} +(-9.14910 - 5.28224i) q^{57} +(-0.789248 - 2.94551i) q^{58} +(3.54546 + 13.2318i) q^{59} +(1.33066 + 0.356550i) q^{61} +(0.744399 - 0.199461i) q^{62} +(14.1569 + 14.1569i) q^{63} +4.59676 q^{64} +(-4.54953 + 4.54953i) q^{66} +(1.99697 - 7.45279i) q^{67} -3.54890 q^{68} +(2.19189 - 8.18024i) q^{69} +(-4.08391 - 7.07355i) q^{71} +(4.75618 - 8.23794i) q^{72} +(0.148203 - 0.148203i) q^{73} +(2.34355 + 0.318555i) q^{74} +(1.65266 + 6.16781i) q^{76} +(-4.41008 + 16.4586i) q^{77} +(-0.563171 - 0.150901i) q^{78} +(-14.2072 - 3.80679i) q^{79} +(6.16738 + 10.6822i) q^{81} -0.796795 q^{82} +(-15.5054 + 4.15466i) q^{83} -17.8124i q^{84} +(0.791990 - 1.37177i) q^{86} +(-11.9948 - 20.7756i) q^{87} +8.09569 q^{88} +(-2.74139 + 0.734553i) q^{89} +(-1.49145 + 0.399634i) q^{91} +(-4.43295 + 2.55936i) q^{92} +(5.25048 - 3.03137i) q^{93} +(-0.934165 + 0.250309i) q^{94} +(-12.4225 + 3.32860i) q^{96} -2.02493 q^{97} +(0.567822 + 0.983497i) q^{98} +(-17.1933 + 29.7797i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more