LMFDB - Embedded newform 845.2.o.f.258.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(258,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 7]))

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

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

chi := DirichletCharacter("845.258");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.o (of order $12$, degree $4$, 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			258.2
Root			$0.274809i$ of defining polynomial
Character	$\chi$	$=$	845.258
Dual form			845.2.o.f.357.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.137404 + 0.237991i) q^{2} +(0.611610 - 2.28256i) q^{3} +(0.962240 - 1.66665i) q^{4} +(-1.69883 - 1.45395i) q^{5} +(0.627267 - 0.168076i) q^{6} +(-0.334376 - 0.193052i) q^{7} +1.07848 q^{8} +(-2.23793 - 1.29207i) q^{9} +(0.112600 - 0.604086i) q^{10} +(-4.21249 - 1.12873i) q^{11} +(-3.21571 - 3.21571i) q^{12} -0.106105i q^{14} +(-4.35775 + 2.98844i) q^{15} +(-1.77629 - 3.07663i) q^{16} +(-1.90527 + 0.510514i) q^{17} -0.710144i q^{18} +(1.29673 + 4.83947i) q^{19} +(-4.05791 + 1.43231i) q^{20} +(-0.645159 + 0.645159i) q^{21} +(-0.310185 - 1.15763i) q^{22} +(-0.322241 - 0.0863441i) q^{23} +(0.659609 - 2.46170i) q^{24} +(0.772064 + 4.94003i) q^{25} +(0.694880 - 0.694880i) q^{27} +(-0.643499 + 0.371524i) q^{28} +(7.07031 - 4.08205i) q^{29} +(-1.30999 - 0.626482i) q^{30} +(2.54187 + 2.54187i) q^{31} +(1.56662 - 2.71347i) q^{32} +(-5.15280 + 8.92491i) q^{33} +(-0.383290 - 0.383290i) q^{34} +(0.287361 + 0.814128i) q^{35} +(-4.30685 + 2.48656i) q^{36} +(4.17859 - 2.41251i) q^{37} +(-0.973575 + 0.973575i) q^{38} +(-1.83216 - 1.56806i) q^{40} +(1.20515 - 4.49768i) q^{41} +(-0.242190 - 0.0648946i) q^{42} +(1.76471 + 6.58600i) q^{43} +(-5.93462 + 5.93462i) q^{44} +(1.92327 + 5.44885i) q^{45} +(-0.0237281 - 0.0885545i) q^{46} -9.83310i q^{47} +(-8.10898 + 2.17280i) q^{48} +(-3.42546 - 5.93307i) q^{49} +(-1.06960 + 0.862526i) q^{50} +4.66112i q^{51} +(-7.17155 - 7.17155i) q^{53} +(0.260855 + 0.0698958i) q^{54} +(5.51519 + 8.04227i) q^{55} +(-0.360618 - 0.208203i) q^{56} +11.8395 q^{57} +(1.94298 + 1.12178i) q^{58} +(2.34451 - 0.628209i) q^{59} +(0.787474 + 10.1384i) q^{60} +(-5.32338 + 9.22037i) q^{61} +(-0.255679 + 0.954209i) q^{62} +(0.498873 + 0.864073i) q^{63} -6.24413 q^{64} -2.83207 q^{66} +(-3.18796 - 5.52170i) q^{67} +(-0.982475 + 3.66665i) q^{68} +(-0.394171 + 0.682724i) q^{69} +(-0.154271 + 0.180254i) q^{70} +(-4.20542 + 1.12684i) q^{71} +(-2.41357 - 1.39347i) q^{72} -6.08593 q^{73} +(1.14831 + 0.662979i) q^{74} +(11.7481 + 1.25909i) q^{75} +(9.31346 + 2.49554i) q^{76} +(1.19065 + 1.19065i) q^{77} +3.34944i q^{79} +(-1.45564 + 7.80932i) q^{80} +(-5.03732 - 8.72489i) q^{81} +(1.23600 - 0.331185i) q^{82} -5.18834i q^{83} +(0.454456 + 1.69605i) q^{84} +(3.97899 + 1.90288i) q^{85} +(-1.32493 + 1.32493i) q^{86} +(-4.99324 - 18.6350i) q^{87} +(-4.54309 - 1.21732i) q^{88} +(-1.29374 + 4.82829i) q^{89} +(-1.03251 + 1.20642i) q^{90} +(-0.453978 + 0.453978i) q^{92} +(7.35661 - 4.24734i) q^{93} +(2.34019 - 1.35111i) q^{94} +(4.83341 - 10.1068i) q^{95} +(-5.23549 - 5.23549i) q^{96} +(7.37402 - 12.7722i) q^{97} +(0.941346 - 1.63046i) q^{98} +(7.96886 + 7.96886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} - 2 q^{3} - 6 q^{4} + 6 q^{5} - 4 q^{6} - 6 q^{7} - 12 q^{8} + 12 q^{9} + 2 q^{10} - 8 q^{11} + 24 q^{12} - 12 q^{15} - 2 q^{16} - 4 q^{17} + 16 q^{19} - 8 q^{20} - 4 q^{21} + 16 q^{22} + 10 q^{23}+ \cdots + 60 q^{99}+O(q^{100}) $ 20 * q + 4 * q^2 - 2 * q^3 - 6 * q^4 + 6 * q^5 - 4 * q^6 - 6 * q^7 - 12 * q^8 + 12 * q^9 + 2 * q^10 - 8 * q^11 + 24 * q^12 - 12 * q^15 - 2 * q^16 - 4 * q^17 + 16 * q^19 - 8 * q^20 - 4 * q^21 + 16 * q^22 + 10 * q^23 - 28 * q^24 - 18 * q^25 + 4 * q^27 + 6 * q^28 + 26 * q^30 + 6 * q^32 + 18 * q^33 + 2 * q^34 + 40 * q^35 - 36 * q^36 + 42 * q^37 + 8 * q^38 - 16 * q^40 - 28 * q^41 + 40 * q^42 - 10 * q^43 - 36 * q^44 + 32 * q^45 + 8 * q^46 - 56 * q^48 - 18 * q^49 - 8 * q^50 - 10 * q^53 + 12 * q^54 - 10 * q^55 + 12 * q^57 - 90 * q^58 + 8 * q^59 + 92 * q^60 - 16 * q^61 + 44 * q^62 + 32 * q^63 - 20 * q^64 - 32 * q^66 + 58 * q^67 + 22 * q^68 + 16 * q^69 - 32 * q^70 - 56 * q^71 - 66 * q^72 - 72 * q^73 + 18 * q^74 + 38 * q^75 - 80 * q^76 + 28 * q^77 - 68 * q^80 - 14 * q^81 - 56 * q^82 + 32 * q^84 - 6 * q^85 - 60 * q^86 - 34 * q^87 - 82 * q^88 - 6 * q^89 - 46 * q^90 - 8 * q^92 + 48 * q^93 - 48 * q^94 + 26 * q^95 - 56 * q^96 + 22 * q^97 - 4 * q^98 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.137404	+	0.237991i	0.0971595	+	0.168285i	0.910508	−	0.413492i	$-0.135691\pi$
$2$	0.137404	+	0.237991i	0.0971595	+	0.168285i	−0.813348	+	0.581777i	$0.802358\pi$
$3$	0.611610	−	2.28256i	0.353113	−	1.31784i	−0.529729	−	0.848167i	$-0.677707\pi$
$3$	0.611610	−	2.28256i	0.353113	−	1.31784i	0.882842	−	0.469669i	$-0.155627\pi$
$4$	0.962240	−	1.66665i	0.481120	−	0.833324i
$5$	−1.69883	−	1.45395i	−0.759741	−	0.650226i
$5$	−1.69883	−	1.45395i	−0.759741	−	0.650226i
$6$	0.627267	−	0.168076i	0.256081	−	0.0686166i
$7$	−0.334376	−	0.193052i	−0.126382	−	0.0729667i	0.435476	−	0.900200i	$-0.356580\pi$
$7$	−0.334376	−	0.193052i	−0.126382	−	0.0729667i	−0.561858	+	0.827234i	$0.689913\pi$
$8$	1.07848			0.381301
$9$	−2.23793	−	1.29207i	−0.745977	−	0.430690i
$10$	0.112600	−	0.604086i	0.0356073	−	0.191029i
$11$	−4.21249	−	1.12873i	−1.27011	−	0.340326i	−0.440039	−	0.897979i	$-0.645035\pi$
$11$	−4.21249	−	1.12873i	−1.27011	−	0.340326i	−0.830074	+	0.557653i	$0.811702\pi$
$12$	−3.21571	−	3.21571i	−0.928295	−	0.928295i
$13$		0			0
$13$		0			0
$14$		−	0.106105i		−	0.0283576i
$15$	−4.35775	+	2.98844i	−1.12517	+	0.771611i
$16$	−1.77629	−	3.07663i	−0.444073	−	0.769157i
$17$	−1.90527	+	0.510514i	−0.462095	+	0.123818i	−0.482353	−	0.875977i	$-0.660218\pi$
$17$	−1.90527	+	0.510514i	−0.462095	+	0.123818i	0.0202583	+	0.999795i	$0.493551\pi$
$18$		−	0.710144i		−	0.167383i
$19$	1.29673	+	4.83947i	0.297491	+	1.11025i	0.939219	+	0.343318i	$0.111551\pi$
$19$	1.29673	+	4.83947i	0.297491	+	1.11025i	−0.641728	+	0.766932i	$0.721782\pi$
$20$	−4.05791	+	1.43231i	−0.907376	+	0.320274i
$21$	−0.645159	+	0.645159i	−0.140785	+	0.140785i
$22$	−0.310185	−	1.15763i	−0.0661318	−	0.246807i
$23$	−0.322241	−	0.0863441i	−0.0671918	−	0.0180040i	0.225067	−	0.974343i	$-0.427740\pi$
$23$	−0.322241	−	0.0863441i	−0.0671918	−	0.0180040i	−0.292258	+	0.956339i	$0.594407\pi$
$24$	0.659609	−	2.46170i	0.134642	−	0.502492i
$25$	0.772064	+	4.94003i	0.154413	+	0.988006i
$26$		0			0
$27$	0.694880	−	0.694880i	0.133730	−	0.133730i
$28$	−0.643499	+	0.371524i	−0.121610	+	0.0702115i
$29$	7.07031	−	4.08205i	1.31292	−	0.758017i	0.330345	−	0.943860i	$-0.392835\pi$
$29$	7.07031	−	4.08205i	1.31292	−	0.758017i	0.982579	+	0.185843i	$0.0595016\pi$
$30$	−1.30999	−	0.626482i	−0.239171	−	0.114379i
$31$	2.54187	+	2.54187i	0.456534	+	0.456534i	0.897516	−	0.440982i	$-0.145370\pi$
$31$	2.54187	+	2.54187i	0.456534	+	0.456534i	−0.440982	+	0.897516i	$0.645370\pi$
$32$	1.56662	−	2.71347i	0.276942	−	0.479678i
$33$	−5.15280	+	8.92491i	−0.896987	+	1.55363i
$34$	−0.383290	−	0.383290i	−0.0657336	−	0.0657336i
$35$	0.287361	+	0.814128i	0.0485728	+	0.137613i
$36$	−4.30685	+	2.48656i	−0.717809	+	0.414427i
$37$	4.17859	−	2.41251i	0.686956	−	0.396614i	−0.115514	−	0.993306i	$-0.536852\pi$
$37$	4.17859	−	2.41251i	0.686956	−	0.396614i	0.802471	+	0.596691i	$0.203518\pi$
$38$	−0.973575	+	0.973575i	−0.157935	+	0.157935i
$39$		0			0
$40$	−1.83216	−	1.56806i	−0.289690	−	0.247931i
$41$	1.20515	−	4.49768i	0.188213	−	0.702419i	−0.805707	−	0.592314i	$-0.798214\pi$
$41$	1.20515	−	4.49768i	0.188213	−	0.702419i	0.993920	−	0.110105i	$-0.0351188\pi$
$42$	−0.242190	−	0.0648946i	−0.0373707	−	0.0100135i
$43$	1.76471	+	6.58600i	0.269116	+	1.00436i	0.959682	+	0.281087i	$0.0906948\pi$
$43$	1.76471	+	6.58600i	0.269116	+	1.00436i	−0.690566	+	0.723269i	$0.742638\pi$
$44$	−5.93462	+	5.93462i	−0.894678	+	0.894678i
$45$	1.92327	+	5.44885i	0.286704	+	0.812267i
$46$	−0.0237281	−	0.0885545i	−0.00349852	−	0.0130566i
$47$		−	9.83310i		−	1.43430i	−0.696917	−	0.717152i	$-0.745445\pi$
$47$		−	9.83310i		−	1.43430i	0.696917	−	0.717152i	$-0.254555\pi$
$48$	−8.10898	+	2.17280i	−1.17043	+	0.313616i
$49$	−3.42546	−	5.93307i	−0.489352	−	0.847582i
$50$	−1.06960	+	0.862526i	−0.151264	+	0.121980i
$51$			4.66112i			0.652687i
$52$		0			0
$53$	−7.17155	−	7.17155i	−0.985088	−	0.985088i	0.0148021	−	0.999890i	$-0.495288\pi$
$53$	−7.17155	−	7.17155i	−0.985088	−	0.985088i	−0.999890	+	0.0148021i	$0.995288\pi$
$54$	0.260855	+	0.0698958i	0.0354978	+	0.00951161i
$55$	5.51519	+	8.04227i	0.743668	+	1.08442i
$56$	−0.360618	−	0.208203i	−0.0481896	−	0.0278223i
$57$	11.8395			1.56818
$58$	1.94298	+	1.12178i	0.255126	+	0.147297i
$59$	2.34451	−	0.628209i	0.305229	−	0.0817858i	−0.102954	−	0.994686i	$-0.532829\pi$
$59$	2.34451	−	0.628209i	0.305229	−	0.0817858i	0.408183	+	0.912900i	$0.366163\pi$
$60$	0.787474	+	10.1384i	0.101662	+	1.30887i
$61$	−5.32338	+	9.22037i	−0.681589	+	1.18055i	0.292906	+	0.956141i	$0.405378\pi$
$61$	−5.32338	+	9.22037i	−0.681589	+	1.18055i	−0.974496	+	0.224406i	$0.927956\pi$
$62$	−0.255679	+	0.954209i	−0.0324713	+	0.121185i
$63$	0.498873	+	0.864073i	0.0628521	+	0.108863i
$64$	−6.24413			−0.780516
$65$		0			0
$66$	−2.83207			−0.348603
$67$	−3.18796	−	5.52170i	−0.389471	−	0.674583i	0.602908	−	0.797811i	$-0.294009\pi$
$67$	−3.18796	−	5.52170i	−0.389471	−	0.674583i	−0.992378	+	0.123228i	$0.960675\pi$
$68$	−0.982475	+	3.66665i	−0.119143	+	0.444646i
$69$	−0.394171	+	0.682724i	−0.0474526	+	0.0821903i
$70$	−0.154271	+	0.180254i	−0.0184389	+	0.0215445i
$71$	−4.20542	+	1.12684i	−0.499091	+	0.133731i	−0.499578	−	0.866269i	$-0.666512\pi$
$71$	−4.20542	+	1.12684i	−0.499091	+	0.133731i	0.000486883		1.00000i	$0.499845\pi$
$72$	−2.41357	−	1.39347i	−0.284442	−	0.164222i
$73$	−6.08593			−0.712304			−0.356152	−	0.934428i	$-0.615912\pi$
$73$	−6.08593			−0.712304			−0.356152	+	0.934428i	$0.615912\pi$
$74$	1.14831	+	0.662979i	0.133489	+	0.0770697i
$75$	11.7481	+	1.25909i	1.35656	+	0.145387i
$76$	9.31346	+	2.49554i	1.06833	+	0.286258i
$77$	1.19065	+	1.19065i	0.135687	+	0.135687i
$78$		0			0
$79$			3.34944i			0.376842i	0.982088	+	0.188421i	$0.0603369\pi$
$79$			3.34944i			0.376842i	−0.982088	+	0.188421i	$0.939663\pi$
$80$	−1.45564	+	7.80932i	−0.162745	+	0.873108i
$81$	−5.03732	−	8.72489i	−0.559702	−	0.969433i
$82$	1.23600	−	0.331185i	0.136493	−	0.0365733i
$83$		−	5.18834i		−	0.569494i	−0.958603	−	0.284747i	$-0.908090\pi$
$83$		−	5.18834i		−	0.569494i	0.958603	−	0.284747i	$-0.0919096\pi$
$84$	0.454456	+	1.69605i	0.0495852	+	0.185054i
$85$	3.97899	+	1.90288i	0.431582	+	0.206396i
$86$	−1.32493	+	1.32493i	−0.142871	+	0.142871i
$87$	−4.99324	−	18.6350i	−0.535332	−	1.99788i
$88$	−4.54309	−	1.21732i	−0.484295	−	0.129766i
$89$	−1.29374	+	4.82829i	−0.137136	+	0.511798i	0.862844	+	0.505470i	$0.168681\pi$
$89$	−1.29374	+	4.82829i	−0.137136	+	0.511798i	−0.999980	+	0.00632782i	$0.997986\pi$
$90$	−1.03251	+	1.20642i	−0.108836	+	0.127167i
$91$		0			0
$92$	−0.453978	+	0.453978i	−0.0473305	+	0.0473305i
$93$	7.35661	−	4.24734i	0.762845	−	0.440429i
$94$	2.34019	−	1.35111i	0.241372	−	0.139356i
$95$	4.83341	−	10.1068i	0.495898	−	1.03694i
$96$	−5.23549	−	5.23549i	−0.534345	−	0.534345i
$97$	7.37402	−	12.7722i	0.748718	−	1.29682i	−0.199719	−	0.979853i	$-0.564003\pi$
$97$	7.37402	−	12.7722i	0.748718	−	1.29682i	0.948437	−	0.316965i	$-0.102664\pi$
$98$	0.941346	−	1.63046i	0.0950903	−	0.164701i
$99$	7.96886	+	7.96886i	0.800900	+	0.800900i
$100$	8.97621	+	3.46674i	0.897621	+	0.346674i
$101$	−4.57218	+	2.63975i	−0.454949	+	0.262665i	−0.709918	−	0.704284i	$-0.751268\pi$
$101$	−4.57218	+	2.63975i	−0.454949	+	0.262665i	0.254969	+	0.966949i	$0.417935\pi$
$102$	−1.10930	+	0.640458i	−0.109838	+	0.0634147i
$103$	1.21001	−	1.21001i	0.119226	−	0.119226i	−0.644976	−	0.764203i	$-0.723133\pi$
$103$	1.21001	−	1.21001i	0.119226	−	0.119226i	0.764203	+	0.644976i	$0.223133\pi$
$104$		0			0
$105$	2.03405	−	0.157989i	0.198503	−	0.0154181i
$106$	0.721364	−	2.69217i	0.0700651	−	0.261487i
$107$	−3.91480	−	1.04897i	−0.378458	−	0.101408i	0.0645749	−	0.997913i	$-0.479431\pi$
$107$	−3.91480	−	1.04897i	−0.378458	−	0.101408i	−0.443033	+	0.896505i	$0.646098\pi$
$108$	−0.489479	−	1.82676i	−0.0471002	−	0.175780i
$109$	−5.02898	+	5.02898i	−0.481689	+	0.481689i	−0.905671	−	0.423982i	$-0.860632\pi$
$109$	−5.02898	+	5.02898i	−0.481689	+	0.481689i	0.423982	+	0.905671i	$0.360632\pi$
$110$	−1.15618	+	2.41761i	−0.110237	+	0.230510i
$111$	−2.95103	−	11.0134i	−0.280099	−	1.04535i
$112$			1.37167i			0.129610i
$113$	3.83891	−	1.02863i	0.361134	−	0.0967655i	−0.0736896	−	0.997281i	$-0.523477\pi$
$113$	3.83891	−	1.02863i	0.361134	−	0.0967655i	0.434824	+	0.900516i	$0.356811\pi$
$114$	1.62679	+	2.81769i	0.152363	+	0.263901i
$115$	0.421893	+	0.615206i	0.0393417	+	0.0573682i
$116$		−	15.7116i		−	1.45879i
$117$		0			0
$118$	0.471653	+	0.471653i	0.0434192	+	0.0434192i
$119$	0.735630	+	0.197111i	0.0674351	+	0.0180692i
$120$	−4.69975	+	3.22297i	−0.429026	+	0.294216i
$121$	6.94473	+	4.00954i	0.631339	+	0.364504i
$122$	−2.92582			−0.264892
$123$	−9.52914	−	5.50165i	−0.859213	−	0.496067i
$124$	6.68231	−	1.79052i	0.600089	−	0.160793i
$125$	5.87095	−	9.51483i	0.525113	−	0.851032i
$126$	−0.137095	+	0.237455i	−0.0122134	+	0.0211542i
$127$	2.95156	−	11.0154i	0.261908	−	0.977455i	−0.702207	−	0.711972i	$-0.747802\pi$
$127$	2.95156	−	11.0154i	0.261908	−	0.977455i	0.964116	−	0.265483i	$-0.0855313\pi$
$128$	−3.99121	−	6.91298i	−0.352777	−	0.611027i
$129$	16.1123			1.41860
$130$		0			0
$131$	20.8627			1.82279			0.911393	−	0.411536i	$-0.135008\pi$
$131$	20.8627			1.82279			0.911393	+	0.411536i	$0.135008\pi$
$132$	9.91645	+	17.1758i	0.863117	+	1.49496i
$133$	0.500673	−	1.86854i	0.0434138	−	0.162023i
$134$	0.876078	−	1.51741i	0.0756816	−	0.131084i
$135$	−2.19080	+	0.170165i	−0.188554	+	0.0146454i
$136$	−2.05479	+	0.550580i	−0.176197	+	0.0472119i
$137$	0.211266	+	0.121975i	0.0180497	+	0.0104210i	0.508998	−	0.860768i	$-0.330016\pi$
$137$	0.211266	+	0.121975i	0.0180497	+	0.0104210i	−0.490948	+	0.871189i	$0.663349\pi$
$138$	−0.216643			−0.0184419
$139$	10.1187	+	5.84202i	0.858255	+	0.495514i	0.863428	−	0.504473i	$-0.168313\pi$
$139$	10.1187	+	5.84202i	0.858255	+	0.495514i	−0.00517263	+	0.999987i	$0.501647\pi$
$140$	1.63337	+	0.304457i	0.138045	+	0.0257313i
$141$	−22.4446	−	6.01402i	−1.89018	−	0.506472i
$142$	−0.846020	−	0.846020i	−0.0709965	−	0.0709965i
$143$		0			0
$144$			9.18038i			0.765032i
$145$	−17.9464	−	3.34516i	−1.49036	−	0.277800i
$146$	−0.836233	−	1.44840i	−0.0692071	−	0.119870i
$147$	−15.6376	+	4.19009i	−1.28977	+	0.345593i
$148$		−	9.28566i		−	0.763277i
$149$	0.655457	+	2.44620i	0.0536971	+	0.200400i	0.987563	−	0.157223i	$-0.0502540\pi$
$149$	0.655457	+	2.44620i	0.0536971	+	0.200400i	−0.933866	+	0.357623i	$0.883587\pi$
$150$	1.31459	+	2.96895i	0.107336	+	0.242414i
$151$	−2.58498	+	2.58498i	−0.210362	+	0.210362i	−0.804421	−	0.594059i	$-0.797525\pi$
$151$	−2.58498	+	2.58498i	−0.210362	+	0.210362i	0.594059	+	0.804421i	$0.297525\pi$
$152$	1.39850	+	5.21928i	0.113433	+	0.423339i
$153$	4.92348	+	1.31924i	0.398039	+	0.106654i
$154$	−0.119764	+	0.446964i	−0.00965083	+	0.0360174i
$155$	−0.622463	−	8.01398i	−0.0499974	−	0.643698i
$156$		0			0
$157$	−2.21767	+	2.21767i	−0.176990	+	0.176990i	−0.790042	−	0.613053i	$-0.789941\pi$
$157$	−2.21767	+	2.21767i	−0.176990	+	0.176990i	0.613053	+	0.790042i	$0.289941\pi$
$158$	−0.797137	+	0.460228i	−0.0634169	+	0.0366137i
$159$	−20.7557	+	11.9833i	−1.64603	+	0.950337i
$160$	−6.60667	+	2.33194i	−0.522303	+	0.184356i
$161$	0.0910805	+	0.0910805i	0.00717815	+	0.00717815i
$162$	1.38430	−	2.39768i	0.108761	−	0.188379i
$163$	7.40642	−	12.8283i	0.580116	−	1.00479i	−0.415349	−	0.909662i	$-0.636341\pi$
$163$	7.40642	−	12.8283i	0.580116	−	1.00479i	0.995465	−	0.0951279i	$-0.0303260\pi$
$164$	−6.33641	−	6.33641i	−0.494790	−	0.494790i
$165$	21.7301	−	7.67002i	1.69169	−	0.597110i
$166$	1.23478	−	0.712900i	0.0958374	−	0.0553318i
$167$	3.00348	−	1.73406i	0.232417	−	0.134186i	−0.379270	−	0.925286i	$-0.623825\pi$
$167$	3.00348	−	1.73406i	0.232417	−	0.134186i	0.611686	+	0.791100i	$0.290491\pi$
$168$	−0.695792	+	0.695792i	−0.0536815	+	0.0536815i
$169$		0			0
$170$	0.0938613	+	1.20843i	0.00719883	+	0.0926823i
$171$	3.35094	−	12.5059i	0.256253	−	0.956348i
$172$	12.6746	+	3.39616i	0.966432	+	0.258955i
$173$	1.01194	+	3.77661i	0.0769362	+	0.287130i	0.993665	−	0.112379i	$-0.0358472\pi$
$173$	1.01194	+	3.77661i	0.0769362	+	0.287130i	−0.916729	+	0.399509i	$0.869181\pi$
$174$	3.74888	−	3.74888i	0.284202	−	0.284202i
$175$	0.695523	−	1.80087i	0.0525766	−	0.136133i
$176$	4.00992	+	14.9652i	0.302259	+	1.12805i
$177$		−	5.73569i		−	0.431121i
$178$	−1.32686	+	0.355530i	−0.0994521	+	0.0266481i
$179$	3.24880	+	5.62708i	0.242827	+	0.420588i	0.961518	−	0.274741i	$-0.0885921\pi$
$179$	3.24880	+	5.62708i	0.242827	+	0.420588i	−0.718692	+	0.695329i	$0.755259\pi$
$180$	10.9320	+	2.03769i	0.814820	+	0.151881i
$181$			11.9845i			0.890802i	0.895331	+	0.445401i	$0.146939\pi$
$181$			11.9845i			0.890802i	−0.895331	+	0.445401i	$0.853061\pi$
$182$		0			0
$183$	17.7902	+	17.7902i	1.31509	+	1.31509i
$184$	−0.347530	−	0.0931205i	−0.0256203	−	0.00686493i
$185$	−10.6064	−	1.97701i	−0.779798	−	0.145352i
$186$	2.02166	+	1.16721i	0.148235	+	0.0855837i
$187$	8.60214			0.629051
$188$	−16.3883	−	9.46180i	−1.19524	−	0.690073i
$189$	−0.366499	+	0.0982030i	−0.0266588	+	0.00714322i
$190$	3.06947	−	0.238412i	0.222683	−	0.0172963i
$191$	2.59646	−	4.49719i	0.187873	−	0.325405i	−0.756668	−	0.653799i	$-0.773174\pi$
$191$	2.59646	−	4.49719i	0.187873	−	0.325405i	0.944541	+	0.328394i	$0.106507\pi$
$192$	−3.81897	+	14.2526i	−0.275610	+	1.02859i
$193$	3.33706	+	5.77996i	0.240207	+	0.416051i	0.960773	−	0.277335i	$-0.0894513\pi$
$193$	3.33706	+	5.77996i	0.240207	+	0.416051i	−0.720566	+	0.693386i	$0.756118\pi$
$194$	4.05289			0.290980
$195$		0			0
$196$	−13.1845			−0.941748
$197$	9.79857	+	16.9716i	0.698119	+	1.20918i	0.969118	+	0.246598i	$0.0793127\pi$
$197$	9.79857	+	16.9716i	0.698119	+	1.20918i	−0.270999	+	0.962580i	$0.587354\pi$
$198$	−0.801563	+	2.99147i	−0.0569646	+	0.212595i
$199$	7.35302	−	12.7358i	0.521242	−	0.902817i	−0.478453	−	0.878113i	$-0.658802\pi$
$199$	7.35302	−	12.7358i	0.521242	−	0.902817i	0.999695	−	0.0247042i	$-0.00786439\pi$
$200$	0.832657	+	5.32773i	0.0588777	+	0.376727i
$201$	−14.5534	+	3.89957i	−1.02652	+	0.275054i
$202$	−1.25647	−	0.725425i	−0.0884052	−	0.0510408i
$203$	−3.15219			−0.221240
$204$	7.76844	+	4.48511i	0.543900	+	0.314021i
$205$	−8.58674	+	5.88858i	−0.599724	+	0.411276i
$206$	0.454234	+	0.121712i	0.0316480	+	0.00848005i
$207$	0.609590	+	0.609590i	0.0423694	+	0.0423694i
$208$		0			0
$209$		−	21.8499i		−	1.51139i
$210$	0.317087	+	0.462377i	0.0218811	+	0.0319070i
$211$	10.7072	+	18.5453i	0.737111	+	1.27671i	0.953791	+	0.300471i	$0.0971440\pi$
$211$	10.7072	+	18.5453i	0.737111	+	1.27671i	−0.216679	+	0.976243i	$0.569523\pi$
$212$	−18.8532	+	5.05170i	−1.29484	+	0.346952i
$213$			10.2883i			0.704943i
$214$	−0.288265	−	1.07582i	−0.0197054	−	0.0735416i
$215$	6.57776	−	13.7543i	0.448599	−	0.938037i
$216$	0.749414	−	0.749414i	0.0509912	−	0.0509912i
$217$	−0.359227	−	1.34065i	−0.0243859	−	0.0910095i
$218$	−1.88786	−	0.505850i	−0.127862	−	0.0342605i
$219$	−3.72221	+	13.8915i	−0.251524	+	0.938700i
$220$	18.7106	−	1.45329i	1.26147	−	0.0979809i
$221$		0			0
$222$	2.21561	−	2.21561i	0.148702	−	0.148702i
$223$	23.6733	−	13.6678i	1.58528	−	0.915264i	0.591214	−	0.806515i	$-0.298649\pi$
$223$	23.6733	−	13.6678i	1.58528	−	0.915264i	0.994069	−	0.108749i	$-0.0346846\pi$
$224$	−1.04768	+	0.604878i	−0.0700010	+	0.0404151i
$225$	4.65504	−	12.0530i	0.310336	−	0.803534i
$226$	0.772287	+	0.772287i	0.0513718	+	0.0513718i
$227$	3.46369	−	5.99928i	0.229893	−	0.398186i	−0.727883	−	0.685701i	$-0.759496\pi$
$227$	3.46369	−	5.99928i	0.229893	−	0.398186i	0.957776	+	0.287515i	$0.0928290\pi$
$228$	11.3924	−	19.7322i	0.754481	−	1.30680i
$229$	4.56825	+	4.56825i	0.301879	+	0.301879i	0.841749	−	0.539870i	$-0.181527\pi$
$229$	4.56825	+	4.56825i	0.301879	+	0.301879i	−0.539870	+	0.841749i	$0.681527\pi$
$230$	−0.0884436	+	0.184939i	−0.00583180	+	0.0121945i
$231$	3.44594	−	1.98951i	0.226726	−	0.130900i
$232$	7.62520	−	4.40241i	0.500619	−	0.289032i
$233$	−5.49074	+	5.49074i	−0.359711	+	0.359711i	−0.863706	−	0.503996i	$-0.831863\pi$
$233$	−5.49074	+	5.49074i	−0.359711	+	0.359711i	0.503996	+	0.863706i	$0.331863\pi$
$234$		0			0
$235$	−14.2968	+	16.7048i	−0.932622	+	1.08970i
$236$	1.20898	−	4.51196i	0.0786976	−	0.293703i
$237$	7.64529	+	2.04855i	0.496615	+	0.133068i
$238$	0.0541679	+	0.202157i	0.00351119	+	0.0131039i
$239$	8.33949	−	8.33949i	0.539437	−	0.539437i	−0.383927	−	0.923363i	$-0.625429\pi$
$239$	8.33949	−	8.33949i	0.539437	−	0.539437i	0.923363	+	0.383927i	$0.125429\pi$
$240$	16.9349	+	8.09883i	1.09315	+	0.522777i
$241$	−0.377680	−	1.40952i	−0.0243285	−	0.0907952i	0.952694	−	0.303931i	$-0.0982991\pi$
$241$	−0.377680	−	1.40952i	−0.0243285	−	0.0907952i	−0.977023	+	0.213135i	$0.931632\pi$
$242$			2.20371i			0.141660i
$243$	−20.1483	+	5.39872i	−1.29251	+	0.346328i
$244$	10.2447	+	17.7444i	0.655853	+	1.13597i
$245$	−2.80710	+	15.0597i	−0.179339	+	0.962132i
$246$		−	3.02380i		−	0.192791i
$247$		0			0
$248$	2.74136	+	2.74136i	0.174077	+	0.174077i
$249$	−11.8427	−	3.17324i	−0.750500	−	0.201096i
$250$	3.07114	+	0.0898555i	0.194236	+	0.00568296i
$251$	11.2668	+	6.50488i	0.711153	+	0.410585i	0.811488	−	0.584369i	$-0.198658\pi$
$251$	11.2668	+	6.50488i	0.711153	+	0.410585i	−0.100335	+	0.994954i	$0.531991\pi$
$252$	1.92014			0.120958
$253$	1.25997	+	0.727447i	0.0792139	+	0.0457342i
$254$	3.02712	−	0.811113i	0.189938	−	0.0508938i
$255$	6.77703	−	7.91846i	0.424394	−	0.495873i
$256$	−5.14731	+	8.91540i	−0.321707	+	0.557212i
$257$	7.62518	−	28.4576i	0.475646	−	1.77513i	−0.143276	−	0.989683i	$-0.545764\pi$
$257$	7.62518	−	28.4576i	0.475646	−	1.77513i	0.618922	−	0.785452i	$-0.287570\pi$
$258$	2.21389	+	3.83458i	0.137831	+	0.238730i
$259$	−1.86296			−0.115759
$260$		0			0
$261$	−21.0972			−1.30588
$262$	2.86663	+	4.96515i	0.177101	+	0.306748i
$263$	−1.30768	+	4.88034i	−0.0806351	+	0.300934i	−0.994452	−	0.105192i	$-0.966454\pi$
$263$	−1.30768	+	4.88034i	−0.0806351	+	0.300934i	0.913817	+	0.406127i	$0.133121\pi$
$264$	−5.55719	+	9.62534i	−0.342022	+	0.592399i
$265$	1.75619	+	22.6103i	0.107882	+	1.38894i
$266$	0.513490	−	0.137589i	0.0314841	−	0.00843614i
$267$	10.2296	+	5.90606i	0.626041	+	0.361445i
$268$	−12.2703			−0.749529
$269$	7.49111	+	4.32499i	0.456741	+	0.263699i	0.710673	−	0.703523i	$-0.248391\pi$
$269$	7.49111	+	4.32499i	0.456741	+	0.263699i	−0.253932	+	0.967222i	$0.581724\pi$
$270$	−0.341524	−	0.498011i	−0.0207845	−	0.0303080i
$271$	22.2448	+	5.96047i	1.35127	+	0.362073i	0.860605	−	0.509273i	$-0.170086\pi$
$271$	22.2448	+	5.96047i	1.35127	+	0.362073i	0.490669	+	0.871346i	$0.336752\pi$
$272$	4.95497	+	4.95497i	0.300439	+	0.300439i
$273$		0			0
$274$			0.0670394i			0.00405000i
$275$	2.32366	−	21.6813i	0.140122	−	1.30743i
$276$	0.758574	+	1.31389i	0.0456608	+	0.0790868i
$277$	20.9037	−	5.60114i	1.25598	−	0.336540i	0.431338	−	0.902190i	$-0.358042\pi$
$277$	20.9037	−	5.60114i	1.25598	−	0.336540i	0.824645	+	0.565650i	$0.191375\pi$
$278$			3.21087i			0.192575i
$279$	−2.40426	−	8.97282i	−0.143939	−	0.537189i
$280$	0.309913	+	0.878021i	0.0185208	+	0.0524718i
$281$	−8.17717	+	8.17717i	−0.487809	+	0.487809i	−0.907614	−	0.419805i	$-0.862098\pi$
$281$	−8.17717	+	8.17717i	−0.487809	+	0.487809i	0.419805	+	0.907614i	$0.362098\pi$
$282$	−1.65270	−	6.16797i	−0.0984171	−	0.367298i
$283$	4.34603	+	1.16452i	0.258345	+	0.0692233i	0.385667	−	0.922638i	$-0.373971\pi$
$283$	4.34603	+	1.16452i	0.258345	+	0.0692233i	−0.127322	+	0.991861i	$0.540638\pi$
$284$	−2.16858	+	8.09325i	−0.128681	+	0.480246i
$285$	−20.1133	−	17.2140i	−1.19141	−	1.01967i
$286$		0			0
$287$	−1.27126	+	1.27126i	−0.0750400	+	0.0750400i
$288$	−7.01198	+	4.04837i	−0.413185	+	0.238552i
$289$	−11.3530	+	6.55467i	−0.667825	+	0.385569i
$290$	−1.66979	−	4.73072i	−0.0980534	−	0.277797i
$291$	−24.6432	−	24.6432i	−1.44461	−	1.44461i
$292$	−5.85613	+	10.1431i	−0.342704	+	0.593580i
$293$	−6.55274	+	11.3497i	−0.382815	+	0.663056i	−0.991463	−	0.130385i	$-0.958379\pi$
$293$	−6.55274	+	11.3497i	−0.382815	+	0.663056i	0.608648	+	0.793440i	$0.291712\pi$
$294$	−3.14588	−	3.14588i	−0.183472	−	0.183472i
$295$	−4.89631	−	2.34157i	−0.285074	−	0.136332i
$296$	4.50653	−	2.60185i	0.261937	−	0.151229i
$297$	−3.71150	+	2.14284i	−0.215363	+	0.124340i
$298$	−0.492111	+	0.492111i	−0.0285072	+	0.0285072i
$299$		0			0
$300$	13.4030	−	18.3684i	0.773821	−	1.06050i
$301$	0.681363	−	2.54288i	0.0392731	−	0.146569i
$302$	−0.970388	−	0.260015i	−0.0558396	−	0.0149622i
$303$	3.22899	+	12.0508i	0.185501	+	0.692298i
$304$	12.5859	−	12.5859i	0.721849	−	0.721849i
$305$	22.4495	−	7.92394i	1.28545	−	0.453723i
$306$	0.362539	+	1.35301i	0.0207250	+	0.0773466i
$307$			7.75447i			0.442571i	0.975209	+	0.221285i	$0.0710252\pi$
$307$			7.75447i			0.442571i	−0.975209	+	0.221285i	$0.928975\pi$
$308$	3.13008	−	0.838703i	0.178353	−	0.0477896i
$309$	−2.02187	−	3.50198i	−0.115020	−	0.199221i
$310$	1.82173	−	1.24930i	0.103467	−	0.0709552i
$311$			11.6030i			0.657947i	0.944339	+	0.328974i	$0.106703\pi$
$311$			11.6030i			0.657947i	−0.944339	+	0.328974i	$0.893297\pi$
$312$		0			0
$313$	−10.1565	−	10.1565i	−0.574078	−	0.574078i	0.359188	−	0.933265i	$-0.383054\pi$
$313$	−10.1565	−	10.1565i	−0.574078	−	0.574078i	−0.933265	+	0.359188i	$0.883054\pi$
$314$	−0.832505	−	0.223069i	−0.0469810	−	0.0125885i
$315$	0.408817	−	2.19325i	0.0230342	−	0.123576i
$316$	5.58234	+	3.22297i	0.314031	+	0.181306i
$317$	−21.7686			−1.22265			−0.611323	−	0.791381i	$-0.709362\pi$
$317$	−21.7686			−1.22265			−0.611323	+	0.791381i	$0.709362\pi$
$318$	−5.70384	−	3.29311i	−0.319855	−	0.184669i
$319$	−34.3911	+	9.21508i	−1.92553	+	0.515945i
$320$	10.6077	+	9.07864i	0.592990	+	0.507512i
$321$	−4.78866	+	8.29420i	−0.267277	+	0.462937i
$322$	−0.00916151	+	0.0341912i	−0.000510551	+	0.00190540i
$323$	−4.94124	−	8.55848i	−0.274938	−	0.476206i
$324$	−19.3884			−1.07714
$325$		0			0
$326$	4.07070			0.225455
$327$	8.40318	+	14.5547i	0.464697	+	0.804878i
$328$	1.29973	−	4.85066i	0.0717656	−	0.267833i
$329$	−1.89830	+	3.28795i	−0.104657	+	0.181270i
$330$	4.81121	+	4.11768i	0.264848	+	0.226671i
$331$	−18.9511	+	5.07792i	−1.04164	+	0.279108i	−0.738795	−	0.673931i	$-0.764605\pi$
$331$	−18.9511	+	5.07792i	−1.04164	+	0.279108i	−0.302850	+	0.953038i	$0.597938\pi$
$332$	−8.64714	−	4.99243i	−0.474573	−	0.273995i
$333$	−12.4685			−0.683272
$334$	0.825383	+	0.476535i	0.0451630	+	0.0260748i
$335$	−2.61247	+	14.0156i	−0.142734	+	0.765753i
$336$	3.13091	+	0.838924i	0.170805	+	0.0457671i
$337$	9.35946	+	9.35946i	0.509842	+	0.509842i	0.914478	−	0.404636i	$-0.132602\pi$
$337$	9.35946	+	9.35946i	0.509842	+	0.509842i	−0.404636	+	0.914478i	$0.632602\pi$
$338$		0			0
$339$		−	9.39165i		−	0.510084i
$340$	7.00018	−	4.80055i	0.379638	−	0.260346i
$341$	−7.83852	−	13.5767i	−0.424480	−	0.735220i
$342$	3.43672	−	0.920867i	0.185837	−	0.0497948i
$343$			5.34789i			0.288759i
$344$	1.90321	+	7.10288i	0.102614	+	0.382962i
$345$	1.66228	−	0.586730i	0.0894940	−	0.0315885i
$346$	−0.759754	+	0.759754i	−0.0408446	+	0.0408446i
$347$	−7.15698	−	26.7102i	−0.384207	−	1.43388i	−0.839414	−	0.543493i	$-0.817101\pi$
$347$	−7.15698	−	26.7102i	−0.384207	−	1.43388i	0.455207	−	0.890386i	$-0.349565\pi$
$348$	−35.8627	−	9.60939i	−1.92244	−	0.515118i
$349$	7.63958	−	28.5113i	0.408938	−	1.52618i	−0.387739	−	0.921769i	$-0.626744\pi$
$349$	7.63958	−	28.5113i	0.408938	−	1.52618i	0.796676	−	0.604406i	$-0.206590\pi$
$350$	0.524160	−	0.0819196i	0.0280175	−	0.00437878i
$351$		0			0
$352$	−9.66215	+	9.66215i	−0.514994	+	0.514994i
$353$	−13.5408	+	7.81777i	−0.720702	+	0.416098i	−0.815011	−	0.579445i	$-0.803269\pi$
$353$	−13.5408	+	7.81777i	−0.720702	+	0.416098i	0.0943088	+	0.995543i	$0.469936\pi$
$354$	1.36504	−	0.788109i	0.0725513	−	0.0418875i
$355$	8.78267	+	4.20015i	0.466136	+	0.222921i
$356$	6.80218	+	6.80218i	0.360515	+	0.360515i
$357$	0.899837	−	1.55856i	0.0476244	−	0.0824879i
$358$	−0.892798	+	1.54637i	−0.0471858	+	0.0817282i
$359$	14.0592	+	14.0592i	0.742017	+	0.742017i	0.972966	−	0.230949i	$-0.0741830\pi$
$359$	14.0592	+	14.0592i	0.742017	+	0.742017i	−0.230949	+	0.972966i	$0.574183\pi$
$360$	2.07421	+	5.87648i	0.109320	+	0.309718i
$361$	−5.28447	+	3.05099i	−0.278130	+	0.160578i
$362$	−2.85221	+	1.64672i	−0.149909	+	0.0865499i
$363$	13.3995	−	13.3995i	0.703290	−	0.703290i
$364$		0			0
$365$	10.3390	+	8.84863i	0.541167	+	0.463159i
$366$	−1.78946	+	6.67836i	−0.0935367	+	0.349084i
$367$	21.2746	+	5.70052i	1.11053	+	0.297565i	0.767045	−	0.641594i	$-0.221727\pi$
$367$	21.2746	+	5.70052i	1.11053	+	0.297565i	0.343483	+	0.939159i	$0.388393\pi$
$368$	0.306745	+	1.14479i	0.0159902	+	0.0596761i
$369$	−8.50836	+	8.50836i	−0.442928	+	0.442928i
$370$	−0.986854	−	2.79588i	−0.0513041	−	0.145351i
$371$	1.01351	+	3.78247i	0.0526188	+	0.196376i
$372$		−	16.3479i		−	0.847597i
$373$	1.12584	−	0.301668i	0.0582937	−	0.0156198i	−0.229554	−	0.973296i	$-0.573727\pi$
$373$	1.12584	−	0.301668i	0.0582937	−	0.0156198i	0.287848	+	0.957676i	$0.407060\pi$
$374$	1.18197	+	2.04723i	0.0611183	+	0.105860i
$375$	−18.1274	−	19.2201i	−0.936096	−	0.992524i
$376$		−	10.6048i		−	0.546901i
$377$		0			0
$378$	−0.0737299	−	0.0737299i	−0.00379226	−	0.00379226i
$379$	−25.4765	−	6.82640i	−1.30864	−	0.350649i	−0.463928	−	0.885873i	$-0.653560\pi$
$379$	−25.4765	−	6.82640i	−1.30864	−	0.350649i	−0.844710	+	0.535224i	$0.820227\pi$
$380$	−12.1936	−	17.7808i	−0.625520	−	0.912136i
$381$	−23.3380	−	13.4742i	−1.19564	−	0.690304i
$382$	1.42706			0.0730146
$383$	28.4058	+	16.4001i	1.45147	+	0.838004i	0.998565	−	0.0535563i	$-0.0170557\pi$
$383$	28.4058	+	16.4001i	1.45147	+	0.838004i	0.452901	+	0.891561i	$0.350389\pi$
$384$	−18.2204	+	4.88213i	−0.929804	+	0.249140i
$385$	−0.291570	−	3.75386i	−0.0148598	−	0.191314i
$386$	−0.917054	+	1.58838i	−0.0466768	+	0.0808466i
$387$	4.56027	−	17.0192i	0.231812	−	0.865132i
$388$	−14.1912	−	24.5798i	−0.720447	−	1.24785i
$389$	−9.36826			−0.474989			−0.237495	−	0.971389i	$-0.576326\pi$
$389$	−9.36826			−0.474989			−0.237495	+	0.971389i	$0.576326\pi$
$390$		0			0
$391$	0.658034			0.0332782
$392$	−3.69430	−	6.39871i	−0.186590	−	0.323184i
$393$	12.7599	−	47.6205i	0.643650	−	2.40213i
$394$	−2.69273	+	4.66395i	−0.135658	+	0.234966i
$395$	4.86992	−	5.69014i	0.245032	−	0.286302i
$396$	20.9492	−	5.61333i	1.05274	−	0.282080i
$397$	10.0909	+	5.82600i	0.506449	+	0.292399i	0.731373	−	0.681978i	$-0.238880\pi$
$397$	10.0909	+	5.82600i	0.506449	+	0.292399i	−0.224924	+	0.974376i	$0.572213\pi$
$398$	4.04135			0.202574
$399$	−3.95883	−	2.28563i	−0.198189	−	0.114425i
$400$	13.8272	−	11.1503i	0.691362	−	0.557515i
$401$	−19.9142	−	5.33600i	−0.994469	−	0.266467i	−0.275342	−	0.961346i	$-0.588791\pi$
$401$	−19.9142	−	5.33600i	−0.994469	−	0.266467i	−0.719126	+	0.694879i	$0.755458\pi$
$402$	−2.92776	−	2.92776i	−0.146024	−	0.146024i
$403$		0			0
$404$			10.1603i			0.505493i
$405$	−4.12799	+	22.1461i	−0.205121	+	1.10045i
$406$	−0.433124	−	0.750193i	−0.0214956	−	0.0372314i
$407$	−20.3253	+	5.44616i	−1.00749	+	0.269956i
$408$			5.02693i			0.248870i
$409$	−1.17965	−	4.40250i	−0.0583297	−	0.217689i	0.930609	−	0.366015i	$-0.119278\pi$
$409$	−1.17965	−	4.40250i	−0.0583297	−	0.217689i	−0.988939	+	0.148326i	$0.952612\pi$
$410$	−2.58129	−	1.23445i	−0.127481	−	0.0609653i
$411$	0.407627	−	0.407627i	0.0201067	−	0.0201067i
$412$	−0.852344	−	3.18099i	−0.0419920	−	0.156716i
$413$	−0.905223	−	0.242554i	−0.0445431	−	0.0119353i
$414$	−0.0613168	+	0.228837i	−0.00301355	+	0.0112467i
$415$	−7.54358	+	8.81412i	−0.370300	+	0.432668i
$416$		0			0
$417$	19.5234	−	19.5234i	0.956067	−	0.956067i
$418$	5.20008	−	3.00227i	0.254344	−	0.146846i
$419$	0.564687	−	0.326022i	0.0275868	−	0.0159272i	−0.486143	−	0.873879i	$-0.661597\pi$
$419$	0.564687	−	0.326022i	0.0275868	−	0.0159272i	0.513730	+	0.857952i	$0.328263\pi$
$420$	1.69393	−	3.54206i	0.0826553	−	0.172835i
$421$	5.58095	+	5.58095i	0.271999	+	0.271999i	0.829904	−	0.557906i	$-0.188395\pi$
$421$	5.58095	+	5.58095i	0.271999	+	0.271999i	−0.557906	+	0.829904i	$0.688395\pi$
$422$	−2.94242	+	5.09642i	−0.143235	+	0.248090i
$423$	−12.7051	+	22.0058i	−0.617741	+	1.06996i
$424$	−7.73438	−	7.73438i	−0.375615	−	0.375615i
$425$	−3.99295	−	9.01792i	−0.193686	−	0.437434i
$426$	−2.44853	+	1.41366i	−0.118631	+	0.0684919i
$427$	3.56002	−	2.05538i	0.172281	−	0.0994667i
$428$	−5.51524	+	5.51524i	−0.266589	+	0.266589i
$429$		0			0
$430$	4.17722	−	0.324454i	0.201443	−	0.0156466i
$431$	−9.25295	+	34.5325i	−0.445699	+	1.66337i	0.268385	+	0.963312i	$0.413510\pi$
$431$	−9.25295	+	34.5325i	−0.445699	+	1.66337i	−0.714084	+	0.700060i	$0.753157\pi$
$432$	−3.37220	−	0.903577i	−0.162245	−	0.0434734i
$433$	−6.82761	−	25.4810i	−0.328114	−	1.22454i	−0.911144	−	0.412087i	$-0.864800\pi$
$433$	−6.82761	−	25.4810i	−0.328114	−	1.22454i	0.583031	−	0.812450i	$-0.301867\pi$
$434$	0.269705	−	0.269705i	0.0129462	−	0.0129462i
$435$	−18.6117	+	38.9177i	−0.892363	+	1.86596i
$436$	3.54246	+	13.2206i	0.169653	+	0.633154i
$437$		−	1.67144i		−	0.0799558i
$438$	−3.81750	+	1.02290i	−0.182407	+	0.0488759i
$439$	0.864675	+	1.49766i	0.0412687	+	0.0714794i	0.885922	−	0.463834i	$-0.153527\pi$
$439$	0.864675	+	1.49766i	0.0412687	+	0.0714794i	−0.844653	+	0.535314i	$0.820193\pi$
$440$	5.94803	+	8.67343i	0.283561	+	0.413490i
$441$			17.7038i			0.843036i
$442$		0			0
$443$	2.86737	+	2.86737i	0.136233	+	0.136233i	0.771935	−	0.635702i	$-0.219289\pi$
$443$	2.86737	+	2.86737i	0.136233	+	0.136233i	−0.635702	+	0.771935i	$0.719289\pi$
$444$	−21.1951	−	5.67920i	−1.00587	−	0.269523i
$445$	9.21793	−	6.32143i	0.436972	−	0.299665i
$446$	6.50564	+	3.75603i	0.308051	+	0.177853i
$447$	5.98448			0.283056
$448$	2.08788	+	1.20544i	0.0986432	+	0.0569517i
$449$	19.5003	−	5.22508i	0.920274	−	0.246587i	0.232571	−	0.972579i	$-0.425286\pi$
$449$	19.5003	−	5.22508i	0.920274	−	0.246587i	0.687702	+	0.725993i	$0.258619\pi$
$450$	3.50813	−	0.548277i	0.165375	−	0.0258460i
$451$	−10.1534	+	17.5861i	−0.478103	+	0.828098i
$452$	1.97958	−	7.38790i	0.0931117	−	0.347497i
$453$	4.31936	+	7.48135i	0.202941	+	0.351505i
$454$	1.90370			0.0893452
$455$		0			0
$456$	12.7686			0.597946
$457$	−7.39079	−	12.8012i	−0.345727	−	0.598816i	0.639759	−	0.768576i	$-0.279034\pi$
$457$	−7.39079	−	12.8012i	−0.345727	−	0.598816i	−0.985486	+	0.169759i	$0.945701\pi$
$458$	−0.459507	+	1.71490i	−0.0214713	+	0.0801321i
$459$	−0.969184	+	1.67868i	−0.0452377	+	0.0783539i
$460$	1.43129	−	0.111172i	0.0667344	−	0.00518341i
$461$	−5.86696	+	1.57205i	−0.273252	+	0.0732175i	−0.392843	−	0.919606i	$-0.628508\pi$
$461$	−5.86696	+	1.57205i	−0.273252	+	0.0732175i	0.119591	+	0.992823i	$0.461842\pi$
$462$	0.946973	+	0.546735i	0.0440572	+	0.0254364i
$463$	36.0148			1.67375			0.836874	−	0.547396i	$-0.184381\pi$
$463$	36.0148			1.67375			0.836874	+	0.547396i	$0.184381\pi$
$464$	−25.1179	−	14.5018i	−1.16607	−	0.673230i
$465$	−18.6731	−	3.48062i	−0.865943	−	0.161410i
$466$	−2.06120	−	0.552297i	−0.0954833	−	0.0255847i
$467$	−7.68952	−	7.68952i	−0.355829	−	0.355829i	0.506444	−	0.862273i	$-0.330960\pi$
$467$	−7.68952	−	7.68952i	−0.355829	−	0.355829i	−0.862273	+	0.506444i	$0.830960\pi$
$468$		0			0
$469$			2.46176i			0.113674i
$470$	−5.94004	−	1.10721i	−0.273993	−	0.0510717i
$471$	3.70562	+	6.41832i	0.170746	+	0.295741i
$472$	2.52851	−	0.677511i	0.116384	−	0.0311850i
$473$		−	29.7353i		−	1.36723i
$474$	0.562959	+	2.10099i	0.0258576	+	0.0965018i
$475$	−22.9060	+	10.1423i	−1.05100	+	0.465360i
$476$	1.03637	−	1.03637i	0.0475019	−	0.0475019i
$477$	6.78329	+	25.3156i	0.310586	+	1.15912i
$478$	3.13061	+	0.838843i	0.143191	+	0.0383678i
$479$	2.37697	−	8.87096i	0.108606	−	0.405324i	−0.890123	−	0.455720i	$-0.849382\pi$
$479$	2.37697	−	8.87096i	0.108606	−	0.405324i	0.998729	+	0.0503960i	$0.0160484\pi$
$480$	1.28208	+	16.5064i	0.0585189	+	0.753408i
$481$		0			0
$482$	0.283559	−	0.283559i	0.0129157	−	0.0129157i
$483$	0.263602	−	0.152191i	0.0119943	−	0.00692492i
$484$	13.3650	−	7.71629i	0.607500	−	0.350740i
$485$	−31.0973	+	10.9763i	−1.41206	+	0.498410i
$486$	−4.05331	−	4.05331i	−0.183862	−	0.183862i
$487$	12.8657	−	22.2840i	0.582998	−	1.00978i	−0.412123	−	0.911128i	$-0.635213\pi$
$487$	12.8657	−	22.2840i	0.582998	−	1.00978i	0.995122	−	0.0986549i	$-0.0314540\pi$
$488$	−5.74117	+	9.94399i	−0.259890	+	0.450143i
$489$	−24.7515	−	24.7515i	−1.11930	−	1.11930i
$490$	−3.96980	+	1.40121i	−0.179337	+	0.0633001i
$491$	−11.4291	+	6.59859i	−0.515788	+	0.297790i	−0.735210	−	0.677840i	$-0.762916\pi$
$491$	−11.4291	+	6.59859i	−0.515788	+	0.297790i	0.219422	+	0.975630i	$0.429583\pi$
$492$	−18.3386	+	10.5878i	−0.826769	+	0.477336i
$493$	−11.3869	+	11.3869i	−0.512839	+	0.512839i
$494$		0			0
$495$	−1.95144	−	25.1241i	−0.0877108	−	1.12924i
$496$	3.30529	−	12.3355i	0.148412	−	0.553881i
$497$	1.62373	+	0.435076i	0.0728341	+	0.0195158i
$498$	−0.872033	−	3.25447i	−0.0390767	−	0.145836i
$499$	16.7683	−	16.7683i	0.750650	−	0.750650i	−0.223950	−	0.974601i	$-0.571895\pi$
$499$	16.7683	−	16.7683i	0.750650	−	0.750650i	0.974601	+	0.223950i	$0.0718954\pi$
$500$	−10.2086	−	18.9404i	−0.456543	−	0.847039i
$501$	−2.12114	−	7.91620i	−0.0947655	−	0.353670i
$502$			3.57520i			0.159569i
$503$	−7.28214	+	1.95124i	−0.324695	+	0.0870017i	−0.417485	−	0.908684i	$-0.637088\pi$
$503$	−7.28214	+	1.95124i	−0.324695	+	0.0870017i	0.0927898	+	0.995686i	$0.470422\pi$
$504$	0.538025	+	0.931887i	0.0239655	+	0.0415095i
$505$	11.6054	+	2.16322i	0.516435	+	0.0962622i
$506$			0.399817i			0.0177740i
$507$		0			0
$508$	−15.5186	−	15.5186i	−0.688528	−	0.688528i
$509$	29.6074	+	7.93327i	1.31232	+	0.351636i	0.846097	−	0.533030i	$-0.178947\pi$
$509$	29.6074	+	7.93327i	1.31232	+	0.351636i	0.466226	+	0.884666i	$0.345613\pi$
$510$	2.81572	+	0.524843i	0.124682	+	0.0232404i
$511$	2.03499	+	1.17490i	0.0900225	+	0.0519745i
$512$	−18.7939			−0.830581
$513$	4.26392	+	2.46178i	0.188257	+	0.108690i
$514$	7.82039	−	2.09547i	0.344942	−	0.0924271i
$515$	−3.81491	+	0.296312i	−0.168105	+	0.0130571i
$516$	15.5039	−	26.8535i	0.682519	−	1.18216i
$517$	−11.0989	+	41.4218i	−0.488131	+	1.82173i
$518$	−0.255979	−	0.443368i	−0.0112471	−	0.0194805i
$519$	9.23923			0.405557
$520$		0			0
$521$	−7.16076			−0.313719			−0.156859	−	0.987621i	$-0.550137\pi$
$521$	−7.16076			−0.313719			−0.156859	+	0.987621i	$0.550137\pi$
$522$	−2.89884	−	5.02094i	−0.126879	−	0.219761i
$523$	2.78390	−	10.3897i	0.121731	−	0.454308i	−0.877971	−	0.478714i	$-0.841103\pi$
$523$	2.78390	−	10.3897i	0.121731	−	0.454308i	0.999702	+	0.0244065i	$0.00776960\pi$
$524$	20.0750	−	34.7709i	0.876979	−	1.51897i
$525$	−3.68521	−	2.68900i	−0.160836	−	0.117358i
$526$	−1.34116	+	0.359362i	−0.0584773	+	0.0156689i
$527$	−6.14061	−	3.54528i	−0.267489	−	0.154435i
$528$	36.6115			1.59331
$529$	−19.8222	−	11.4444i	−0.861835	−	0.497581i
$530$	−5.13975	+	3.52472i	−0.223257	+	0.153104i
$531$	−6.05854	−	1.62338i	−0.262918	−	0.0704487i
$532$	−2.63243	−	2.63243i	−0.114130	−	0.114130i
$533$		0			0
$534$			3.24607i			0.140471i
$535$	5.12544	+	7.47394i	0.221592	+	0.323127i
$536$	−3.43815	−	5.95505i	−0.148505	−	0.257219i
$537$	14.8311	−	3.97399i	0.640011	−	0.171490i
$538$			2.37709i			0.102484i
$539$	7.73286	+	28.8594i	0.333078	+	1.24306i
$540$	−1.82447	+	3.81504i	−0.0785129	+	0.164173i
$541$	−11.1986	+	11.1986i	−0.481464	+	0.481464i	−0.905599	−	0.424135i	$-0.860578\pi$
$541$	−11.1986	+	11.1986i	−0.481464	+	0.481464i	0.424135	+	0.905599i	$0.360578\pi$
$542$	1.63799	+	6.11306i	0.0703576	+	0.262578i
$543$	27.3554	+	7.32985i	1.17393	+	0.314554i
$544$	−1.59957	+	5.96966i	−0.0685808	+	0.255947i
$545$	15.8553	−	1.23152i	0.679166	−	0.0527523i
$546$		0			0
$547$	−23.6205	+	23.6205i	−1.00994	+	1.00994i	−0.00999077	+	0.999950i	$0.503180\pi$
$547$	−23.6205	+	23.6205i	−1.00994	+	1.00994i	−0.999950	+	0.00999077i	$0.996820\pi$
$548$	0.406578	−	0.234738i	0.0173681	−	0.0100275i
$549$	23.8267	−	13.7564i	1.01690	−	0.587108i
$550$	5.47923	−	2.42609i	0.233635	−	0.103449i
$551$	28.9232	+	28.9232i	1.23217	+	1.23217i
$552$	−0.425106	+	0.736305i	−0.0180937	+	0.0313392i
$553$	0.646616	−	1.11997i	0.0274969	−	0.0476260i
$554$	4.20528	+	4.20528i	0.178665	+	0.178665i
$555$	−10.9996	+	23.0006i	−0.466908	+	0.976320i
$556$	19.4732	−	11.2429i	0.825847	−	0.476803i
$557$	26.9736	−	15.5732i	1.14291	−	0.659859i	0.195759	−	0.980652i	$-0.437283\pi$
$557$	26.9736	−	15.5732i	1.14291	−	0.659859i	0.947149	+	0.320793i	$0.103950\pi$
$558$	1.80510	−	1.80510i	0.0764159	−	0.0764159i
$559$		0			0
$560$	1.99433	−	2.33023i	0.0842759	−	0.0984702i
$561$	5.26115	−	19.6349i	0.222126	−	0.828986i
$562$	−3.06967	−	0.822517i	−0.129486	−	0.0346958i
$563$	5.39509	+	20.1348i	0.227376	+	0.848579i	0.981439	+	0.191776i	$0.0614248\pi$
$563$	5.39509	+	20.1348i	0.227376	+	0.848579i	−0.754063	+	0.656802i	$0.771909\pi$
$564$	−31.6204	+	31.6204i	−1.33146	+	1.33146i
$565$	−8.01724	−	3.83410i	−0.337288	−	0.161302i
$566$	0.320019	+	1.19433i	0.0134514	+	0.0502013i
$567$			3.88985i			0.163359i
$568$	−4.53546	+	1.21527i	−0.190304	+	0.0509918i
$569$	−20.8728	−	36.1527i	−0.875031	−	1.51560i	−0.856729	−	0.515766i	$-0.827507\pi$
$569$	−20.8728	−	36.1527i	−0.875031	−	1.51560i	−0.0183019	−	0.999833i	$-0.505826\pi$
$570$	1.33313	−	7.15206i	0.0558385	−	0.299567i
$571$		−	19.2151i		−	0.804127i	−0.915612	−	0.402064i	$-0.868293\pi$
$571$		−	19.2151i		−	0.804127i	0.915612	−	0.402064i	$-0.131707\pi$
$572$		0			0
$573$	−8.67709	−	8.67709i	−0.362491	−	0.362491i
$574$	−0.477224	−	0.127872i	−0.0199190	−	0.00533727i
$575$	0.177752	−	1.65854i	0.00741278	−	0.0691660i
$576$	13.9739	+	8.06785i	0.582247	+	0.336160i
$577$	21.8168			0.908243			0.454122	−	0.890940i	$-0.349953\pi$
$577$	21.8168			0.908243			0.454122	+	0.890940i	$0.349953\pi$
$578$	−3.11991	−	1.80128i	−0.129771	−	0.0749233i
$579$	15.2341	−	4.08196i	0.633107	−	0.169640i
$580$	−22.8439	+	26.6914i	−0.948542	+	1.10830i
$581$	−1.00162	+	1.73485i	−0.0415541	+	0.0719738i
$582$	2.47879	−	9.25095i	0.102749	−	0.383464i
$583$	22.1153	+	38.3048i	0.915922	+	1.58642i
$584$	−6.56356			−0.271602
$585$		0			0
$586$	−3.60150			−0.148777
$587$	−2.92765	−	5.07084i	−0.120837	−	0.209296i	0.799261	−	0.600984i	$-0.205225\pi$
$587$	−2.92765	−	5.07084i	−0.120837	−	0.209296i	−0.920098	+	0.391688i	$0.871891\pi$
$588$	−8.06375	+	30.0943i	−0.332543	+	1.24107i
$589$	−9.00520	+	15.5975i	−0.371053	+	0.642682i
$590$	−0.115500	−	1.48702i	−0.00475507	−	0.0612197i
$591$	44.7316	−	11.9858i	1.84001	−	0.493030i
$592$	−14.8448	−	8.57065i	−0.610118	−	0.352252i
$593$	−45.6277			−1.87370			−0.936852	−	0.349727i	$-0.886274\pi$
$593$	−45.6277			−1.87370			−0.936852	+	0.349727i	$0.886274\pi$
$594$	−1.01995	−	0.588870i	−0.0418492	−	0.0241616i
$595$	−0.963122	−	1.40443i	−0.0394842	−	0.0575759i
$596$	4.70766	+	1.26141i	0.192833	+	0.0516695i
$597$	−24.5730	−	24.5730i	−1.00571	−	1.00571i
$598$		0			0
$599$			12.7240i			0.519888i	0.965624	+	0.259944i	$0.0837041\pi$
$599$			12.7240i			0.519888i	−0.965624	+	0.259944i	$0.916296\pi$
$600$	12.6701	+	1.35790i	0.517255	+	0.0554362i
$601$	12.3636	+	21.4144i	0.504321	+	0.873510i	0.999988	+	0.00499702i	$0.00159061\pi$
$601$	12.3636	+	21.4144i	0.504321	+	0.873510i	−0.495666	+	0.868513i	$0.665076\pi$
$602$	0.698805	−	0.187244i	0.0284812	−	0.00763151i
$603$			16.4763i			0.670965i
$604$	1.82088	+	6.79561i	0.0740905	+	0.276510i
$605$	−5.96827	−	16.9088i	−0.242644	−	0.687442i
$606$	−2.42430	+	2.42430i	−0.0984804	+	0.0984804i
$607$	1.13924	+	4.25169i	0.0462402	+	0.172571i	0.985184	−	0.171499i	$-0.0548610\pi$
$607$	1.13924	+	4.25169i	0.0462402	+	0.172571i	−0.938944	+	0.344070i	$0.888194\pi$
$608$	15.1632	+	4.06298i	0.614950	+	0.164775i
$609$	−1.92791	+	7.19505i	−0.0781228	+	0.291558i
$610$	4.97048	+	4.25400i	0.201249	+	0.172239i
$611$		0			0
$612$	6.93628	−	6.93628i	0.280382	−	0.280382i
$613$	−1.00509	+	0.580288i	−0.0405951	+	0.0234376i	−0.520160	−	0.854069i	$-0.674128\pi$
$613$	−1.00509	+	0.580288i	−0.0405951	+	0.0234376i	0.479565	+	0.877506i	$0.340794\pi$
$614$	−1.84550	+	1.06550i	−0.0744781	+	0.0430000i
$615$	8.18929	+	23.2013i	0.330224	+	0.935565i
$616$	1.28409	+	1.28409i	0.0517375	+	0.0517375i
$617$	−19.2380	+	33.3212i	−0.774493	+	1.34146i	0.160587	+	0.987022i	$0.448661\pi$
$617$	−19.2380	+	33.3212i	−0.774493	+	1.34146i	−0.935079	+	0.354439i	$0.884672\pi$
$618$	0.555628	−	0.962375i	0.0223506	−	0.0387124i
$619$	24.7229	+	24.7229i	0.993698	+	0.993698i	0.999980	−	0.00628240i	$-0.00199976\pi$
$619$	24.7229	+	24.7229i	0.993698	+	0.993698i	−0.00628240	+	0.999980i	$0.502000\pi$
$620$	−13.9554	−	6.67394i	−0.560464	−	0.268032i
$621$	−0.283917	+	0.163920i	−0.0113932	+	0.00657787i
$622$	−2.76142	+	1.59431i	−0.110723	+	0.0639258i
$623$	1.36470	−	1.36470i	0.0546757	−	0.0546757i
$624$		0			0
$625$	−23.8078	+	7.62804i	−0.952313	+	0.305122i
$626$	1.02161	−	3.81269i	0.0408317	−	0.152386i
$627$	−49.8736	−	13.3636i	−1.99176	−	0.533690i
$628$	1.56215	+	5.83002i	0.0623365	+	0.232643i
$629$	−6.72971	+	6.72971i	−0.268331	+	0.268331i
$630$	0.578148	−	0.204067i	0.0230340	−	0.00813024i
$631$	−1.89090	−	7.05694i	−0.0752756	−	0.280933i	0.918020	−	0.396534i	$-0.129787\pi$
$631$	−1.89090	−	7.05694i	−0.0752756	−	0.280933i	−0.993296	+	0.115601i	$0.963120\pi$
$632$			3.61231i			0.143690i
$633$	48.8794	−	13.0972i	1.94278	−	0.520567i
$634$	−2.99110	−	5.18074i	−0.118792	−	0.205753i
$635$	−21.0300	+	14.4218i	−0.834549	+	0.572313i
$636$			46.1232i			1.82891i
$637$		0			0
$638$	−6.91860	−	6.91860i	−0.273910	−	0.273910i
$639$	10.8674	+	2.91191i	0.429907	+	0.115193i
$640$	−3.27072	+	17.5470i	−0.129287	+	0.693607i
$641$	7.19858	+	4.15610i	0.284327	+	0.164156i	0.635381	−	0.772199i	$-0.280843\pi$
$641$	7.19858	+	4.15610i	0.284327	+	0.164156i	−0.351054	+	0.936355i	$0.614177\pi$
$642$	−2.63193			−0.103874
$643$	9.66101	+	5.57779i	0.380993	+	0.219967i	0.678250	−	0.734831i	$-0.262739\pi$
$643$	9.66101	+	5.57779i	0.380993	+	0.219967i	−0.297257	+	0.954797i	$0.596072\pi$
$644$	0.239440	−	0.0641579i	0.00943528	−	0.00252817i
$645$	−27.3720	−	23.4264i	−1.07777	−	0.922414i
$646$	1.35789	−	2.35194i	0.0534257	−	0.0925360i
$647$	−10.8961	+	40.6647i	−0.428369	+	1.59870i	0.328085	+	0.944648i	$0.393597\pi$
$647$	−10.8961	+	40.6647i	−0.428369	+	1.59870i	−0.756454	+	0.654047i	$0.773070\pi$
$648$	−5.43265	−	9.40963i	−0.213415	−	0.369645i
$649$	−10.5853			−0.415509
$650$		0			0
$651$	−3.27983			−0.128547
$652$	−14.2535	−	24.6878i	−0.558211	−	0.966849i
$653$	−11.0577	+	41.2678i	−0.432721	+	1.61494i	0.313742	+	0.949508i	$0.398417\pi$
$653$	−11.0577	+	41.2678i	−0.432721	+	1.61494i	−0.746463	+	0.665427i	$0.768250\pi$
$654$	−2.30926	+	3.99976i	−0.0902994	+	0.156403i
$655$	−35.4423	−	30.3334i	−1.38485	−	1.18522i
$656$	−15.9784	+	4.28140i	−0.623851	+	0.167160i
$657$	13.6199	+	7.86345i	0.531363	+	0.306782i
$658$	−1.04334			−0.0406735
$659$	15.2491	+	8.80408i	0.594021	+	0.342958i	0.766686	−	0.642023i	$-0.221904\pi$
$659$	15.2491	+	8.80408i	0.594021	+	0.342958i	−0.172665	+	0.984981i	$0.555238\pi$
$660$	8.12635	−	43.5968i	0.316318	−	1.69700i
$661$	26.9167	+	7.21232i	1.04694	+	0.280527i	0.740987	−	0.671520i	$-0.234358\pi$
$661$	26.9167	+	7.21232i	1.04694	+	0.280527i	0.305953	+	0.952047i	$0.401025\pi$
$662$	−3.81246	−	3.81246i	−0.148175	−	0.148175i
$663$		0			0
$664$		−	5.59552i		−	0.217148i
$665$	−3.56732	+	2.44638i	−0.138335	+	0.0948665i
$666$	−1.71323	−	2.96740i	−0.0663863	−	0.114985i
$667$	−2.63080	+	0.704922i	−0.101865	+	0.0272947i
$668$		−	6.67434i		−	0.258238i
$669$	−16.7187	−	62.3951i	−0.646383	−	2.41234i
$670$	−3.69455	+	1.30406i	−0.142733	+	0.0503800i
$671$	32.8320	−	32.8320i	1.26747	−	1.26747i
$672$	0.739899	+	2.76134i	0.0285422	+	0.106521i
$673$	−7.05459	−	1.89027i	−0.271934	−	0.0728646i	0.120275	−	0.992741i	$-0.461622\pi$
$673$	−7.05459	−	1.89027i	−0.271934	−	0.0728646i	−0.392209	+	0.919876i	$0.628289\pi$
$674$	−0.941440	+	3.51350i	−0.0362629	+	0.135335i
$675$	3.96922	+	2.89624i	0.152775	+	0.111476i
$676$		0			0
$677$	3.26988	−	3.26988i	0.125672	−	0.125672i	−0.641473	−	0.767145i	$-0.721677\pi$
$677$	3.26988	−	3.26988i	0.125672	−	0.125672i	0.767145	+	0.641473i	$0.221677\pi$
$678$	2.23513	−	1.29045i	0.0858397	−	0.0495595i
$679$	−4.93138	+	2.84713i	−0.189249	+	0.109263i
$680$	4.29126	+	2.05222i	0.164562	+	0.0786991i
$681$	−11.5753	−	11.5753i	−0.443566	−	0.443566i
$682$	2.15409	−	3.73100i	0.0824845	−	0.142867i
$683$	−13.5476	+	23.4651i	−0.518384	+	0.897868i	0.481388	+	0.876508i	$0.340133\pi$
$683$	−13.5476	+	23.4651i	−0.518384	+	0.897868i	−0.999772	+	0.0213600i	$0.993200\pi$
$684$	−17.6185	−	17.6185i	−0.673660	−	0.673660i
$685$	−0.181561	−	0.514385i	−0.00693709	−	0.0196536i
$686$	−1.27275	+	0.734823i	−0.0485939	+	0.0280557i
$687$	13.2213	−	7.63332i	0.504424	−	0.291229i
$688$	17.1280	−	17.1280i	0.653000	−	0.653000i
$689$		0			0
$690$	0.368040	+	0.314988i	0.0140111	+	0.0119914i
$691$	−3.25221	+	12.1374i	−0.123720	+	0.461729i	−0.999791	−	0.0204532i	$-0.993489\pi$
$691$	−3.25221	+	12.1374i	−0.123720	+	0.461729i	0.876071	+	0.482182i	$0.160156\pi$
$692$	7.26800	+	1.94746i	0.276288	+	0.0740311i
$693$	−1.12619	−	4.20299i	−0.0427804	−	0.159658i
$694$	5.37339	−	5.37339i	0.203971	−	0.203971i
$695$	−8.69594	−	24.6367i	−0.329856	−	0.934522i
$696$	−5.38511	−	20.0975i	−0.204122	−	0.761795i
$697$			9.18452i			0.347889i
$698$	7.83515	−	2.09942i	0.296565	−	0.0794643i
$699$	9.17475	+	15.8911i	0.347021	+	0.601058i
$700$	−2.33217	−	2.89207i	−0.0881476	−	0.109310i
$701$		−	39.3955i		−	1.48795i	−0.668208	−	0.743974i	$-0.732938\pi$
$701$		−	39.3955i		−	1.48795i	0.668208	−	0.743974i	$-0.267062\pi$
$702$		0			0
$703$	17.0938	+	17.0938i	0.644705	+	0.644705i
$704$	26.3033	+	7.04795i	0.991343	+	0.265630i
$705$	29.3856	+	42.8501i	1.10672	+	1.61383i
$706$	−3.72112	−	2.14839i	−0.140046	−	0.0808557i
$707$	2.03843			0.0766631
$708$	−9.55939	−	5.51911i	−0.359264	−	0.207421i
$709$	24.7175	−	6.62303i	0.928285	−	0.248733i	0.237162	−	0.971470i	$-0.423783\pi$
$709$	24.7175	−	6.62303i	0.928285	−	0.248733i	0.691123	+	0.722737i	$0.257116\pi$
$710$	0.207176	+	2.66732i	0.00777519	+	0.100103i
$711$	4.32771	−	7.49582i	0.162302	−	0.281115i
$712$	−1.39527	+	5.20722i	−0.0522900	+	0.195149i
$713$	−0.599619	−	1.03857i	−0.0224559	−	0.0388948i
$714$	0.494566			0.0185087
$715$		0			0
$716$	12.5045			0.467315
$717$	−13.9349	−	24.1359i	−0.520407	−	0.901371i
$718$	−1.41417	+	5.27777i	−0.0527765	+	0.196965i
$719$	−4.34268	+	7.52174i	−0.161955	+	0.280514i	−0.935570	−	0.353142i	$-0.885113\pi$
$719$	−4.34268	+	7.52174i	−0.161955	+	0.280514i	0.773615	+	0.633656i	$0.218446\pi$
$720$	13.3478	−	15.5959i	0.497443	−	0.581226i
$721$	−0.638194	+	0.171004i	−0.0237676	+	0.00636851i
$722$	−1.45222	−	0.838438i	−0.0540460	−	0.0312034i
$723$	−3.44830			−0.128244
$724$	19.9740	+	11.5320i	0.742327	+	0.428583i
$725$	25.6242	+	31.7760i	0.951658	+	1.18013i
$726$	5.03011	+	1.34781i	0.186685	+	0.0500220i
$727$	17.4677	+	17.4677i	0.647841	+	0.647841i	0.952471	−	0.304630i	$-0.0985327\pi$
$727$	17.4677	+	17.4677i	0.647841	+	0.647841i	−0.304630	+	0.952471i	$0.598533\pi$
$728$		0			0
$729$			19.0676i			0.706209i
$730$	−0.685277	+	3.67643i	−0.0253632	+	0.136071i
$731$	−6.72450	−	11.6472i	−0.248715	−	0.430786i
$732$	46.7685	−	12.5316i	1.72861	−	0.463180i
$733$			34.2413i			1.26473i	0.774670	+	0.632365i	$0.217916\pi$
$733$			34.2413i			1.26473i	−0.774670	+	0.632365i	$0.782084\pi$
$734$	1.56655	+	5.84646i	0.0578225	+	0.215797i
$735$	32.6579	+	15.6181i	1.20461	+	0.576081i
$736$	−0.739121	+	0.739121i	−0.0272444	+	0.0272444i
$737$	7.19670	+	26.8584i	0.265094	+	0.989344i
$738$	−3.19400	−	0.855830i	−0.117573	−	0.0315035i
$739$	7.31150	−	27.2869i	0.268958	−	1.00376i	−0.690825	−	0.723022i	$-0.742753\pi$
$739$	7.31150	−	27.2869i	0.268958	−	1.00376i	0.959783	−	0.280743i	$-0.0905808\pi$
$740$	−13.5009	+	15.7748i	−0.496302	+	0.579893i
$741$		0			0
$742$	−0.760935	+	0.760935i	−0.0279348	+	0.0279348i
$743$	−27.4329	+	15.8384i	−1.00642	+	0.581055i	−0.910141	−	0.414299i	$-0.864027\pi$
$743$	−27.4329	+	15.8384i	−1.00642	+	0.581055i	−0.0962765	+	0.995355i	$0.530693\pi$
$744$	7.93397	−	4.58068i	0.290873	−	0.167936i
$745$	2.44314	−	5.10868i	0.0895096	−	0.187168i
$746$	0.226489	+	0.226489i	0.00829237	+	0.00829237i
$747$	−6.70370	+	11.6111i	−0.245275	+	0.424830i
$748$	8.27733	−	14.3367i	0.302649	−	0.524203i
$749$	1.10651	+	1.10651i	0.0404309	+	0.0404309i
$750$	2.08344	−	6.95510i	0.0760764	−	0.253964i
$751$	−2.11351	+	1.22024i	−0.0771231	+	0.0445271i	−0.538066	−	0.842903i	$-0.680845\pi$
$751$	−2.11351	+	1.22024i	−0.0771231	+	0.0445271i	0.460943	+	0.887430i	$0.347511\pi$
$752$	−30.2528	+	17.4665i	−1.10321	+	0.636936i
$753$	21.7387	−	21.7387i	0.792201	−	0.792201i
$754$		0			0
$755$	8.14986	−	0.633018i	0.296604	−	0.0230379i
$756$	−0.188990	+	0.705319i	−0.00687349	+	0.0256522i
$757$	−41.2367	−	11.0493i	−1.49877	−	0.401595i	−0.586084	−	0.810250i	$-0.699331\pi$
$757$	−41.2367	−	11.0493i	−1.49877	−	0.401595i	−0.912689	+	0.408655i	$0.865998\pi$
$758$	−1.87595	−	7.00115i	−0.0681377	−	0.254293i
$759$	2.43105	−	2.43105i	0.0882416	−	0.0882416i
$760$	5.21274	−	10.9000i	0.189086	−	0.395385i
$761$	−10.3427	−	38.5996i	−0.374923	−	1.39923i	−0.853457	−	0.521164i	$-0.825498\pi$
$761$	−10.3427	−	38.5996i	−0.374923	−	1.39923i	0.478533	−	0.878069i	$-0.341169\pi$
$762$		−	7.40565i		−	0.268279i
$763$	2.65242	−	0.710715i	0.0960242	−	0.0257296i
$764$	−4.99683	−	8.65476i	−0.180779	−	0.313118i
$765$	−6.44605	−	9.39965i	−0.233057	−	0.339845i
$766$			9.01376i			0.325680i
$767$		0			0
$768$	17.2018	+	17.2018i	0.620716	+	0.620716i
$769$	37.0208	+	9.91969i	1.33500	+	0.357713i	0.854579	−	0.519322i	$-0.173816\pi$
$769$	37.0208	+	9.91969i	1.33500	+	0.357713i	0.480426	+	0.877035i	$0.340482\pi$
$770$	0.853322	−	0.585187i	0.0307516	−	0.0210887i
$771$	−60.2925	−	34.8099i	−2.17138	−	1.25365i
$772$	12.8442			0.462274
$773$	−12.6256	−	7.28940i	−0.454111	−	0.262181i	0.255454	−	0.966821i	$-0.417775\pi$
$773$	−12.6256	−	7.28940i	−0.454111	−	0.262181i	−0.709565	+	0.704640i	$0.751109\pi$
$774$	4.67701	−	1.25320i	0.168112	−	0.0450454i
$775$	−10.5945	+	14.5194i	−0.380564	+	0.521553i
$776$	7.95274	−	13.7745i	0.285487	−	0.494477i
$777$	−1.13940	+	4.25231i	−0.0408759	+	0.152551i
$778$	−1.28724	−	2.22956i	−0.0461497	−	0.0799337i
$779$	23.3291			0.835853
$780$		0			0
$781$	18.9872			0.679414
$782$	0.0904167	+	0.156606i	0.00323329	+	0.00560023i
$783$	2.07649	−	7.74955i	0.0742075	−	0.276946i
$784$	−12.1692	+	21.0777i	−0.434616	+	0.752777i
$785$	6.99184	−	0.543072i	0.249549	−	0.0193831i
$786$	13.0865	−	3.50652i	0.466780	−	0.125073i
$787$	−0.820823	−	0.473902i	−0.0292592	−	0.0168928i	0.485299	−	0.874348i	$-0.338711\pi$
$787$	−0.820823	−	0.473902i	−0.0292592	−	0.0168928i	−0.514558	+	0.857455i	$0.672044\pi$
$788$	37.7143			1.34352
$789$	10.3399	+	5.96972i	0.368109	+	0.212528i
$790$	2.02335	+	0.377148i	0.0719876	+	0.0134183i
$791$	−1.48222	−	0.397158i	−0.0527015	−	0.0141213i
$792$	8.59426	+	8.59426i	0.305384	+	0.305384i
$793$		0			0
$794$			3.20207i			0.113637i
$795$	52.6835	+	9.82008i	1.86849	+	0.348283i
$796$	−14.1507	−	24.5098i	−0.501560	−	0.868727i
$797$	4.51774	−	1.21053i	0.160027	−	0.0428790i	−0.177916	−	0.984046i	$-0.556936\pi$
$797$	4.51774	−	1.21053i	0.160027	−	0.0428790i	0.337943	+	0.941167i	$0.390269\pi$
$798$		−	1.25622i		−	0.0444698i
$799$	5.01994	+	18.7347i	0.177593	+	0.662785i
$800$	14.6142	+	5.64419i	0.516688	+	0.199552i
$801$	9.13379	−	9.13379i	0.322726	−	0.322726i
$802$	−1.46638	−	5.47260i	−0.0517796	−	0.193244i
$803$	25.6369	+	6.86939i	0.904707	+	0.242415i
$804$	−7.50465	+	28.0077i	−0.264668	+	0.987756i
$805$	−0.0223041	−	0.287157i	−0.000786117	−	0.0101210i
$806$		0			0
$807$	14.4537	−	14.4537i	0.508794	−	0.508794i
$808$	−4.93101	+	2.84692i	−0.173472	+	0.100154i
$809$	21.1627	−	12.2183i	0.744040	−	0.429572i	−0.0794964	−	0.996835i	$-0.525331\pi$
$809$	21.1627	−	12.2183i	0.744040	−	0.429572i	0.823536	+	0.567263i	$0.191998\pi$
$810$	−5.83779	+	2.06055i	−0.205119	+	0.0724003i
$811$	9.34795	+	9.34795i	0.328251	+	0.328251i	0.851921	−	0.523670i	$-0.175438\pi$
$811$	9.34795	+	9.34795i	0.328251	+	0.328251i	−0.523670	+	0.851921i	$0.675438\pi$
$812$	−3.03316	+	5.25359i	−0.106443	+	0.184365i
$813$	27.2103	−	47.1295i	0.954305	−	1.65291i
$814$	−4.08893	−	4.08893i	−0.143317	−	0.143317i
$815$	−31.2340	+	11.0246i	−1.09408	+	0.386174i
$816$	14.3405	−	8.27951i	0.502019	−	0.289841i
$817$	−29.5844	+	17.0806i	−1.03503	+	0.597573i
$818$	0.885667	−	0.885667i	0.0309666	−	0.0309666i
$819$		0			0
$820$	1.55168	+	19.9773i	0.0541871	+	0.697638i
$821$	−0.508771	+	1.89876i	−0.0177562	+	0.0662672i	−0.974236	−	0.225533i	$-0.927588\pi$
$821$	−0.508771	+	1.89876i	−0.0177562	+	0.0662672i	0.956479	+	0.291800i	$0.0942543\pi$
$822$	0.153021	+	0.0410019i	0.00533723	+	0.00143011i
$823$	−4.25627	−	15.8846i	−0.148364	−	0.553703i	−0.999583	−	0.0288913i	$-0.990802\pi$
$823$	−4.25627	−	15.8846i	−0.148364	−	0.553703i	0.851218	−	0.524812i	$-0.175864\pi$
$824$	1.30498	−	1.30498i	0.0454610	−	0.0454610i
$825$	−48.0676	−	18.5644i	−1.67350	−	0.646329i
$826$	−0.0666558	−	0.248763i	−0.00231925	−	0.00865557i
$827$			27.3262i			0.950225i	0.879925	+	0.475113i	$0.157593\pi$
$827$			27.3262i			0.950225i	−0.879925	+	0.475113i	$0.842407\pi$
$828$	1.60254	−	0.429400i	0.0556922	−	0.0149227i
$829$	−7.27764	−	12.6052i	−0.252763	−	0.437798i	0.711523	−	0.702663i	$-0.248006\pi$
$829$	−7.27764	−	12.6052i	−0.252763	−	0.437798i	−0.964286	+	0.264865i	$0.914673\pi$
$830$	−3.13420	−	0.584208i	−0.108790	−	0.0202782i
$831$		−	51.1397i		−	1.77402i
$832$		0			0
$833$	9.55534	+	9.55534i	0.331073	+	0.331073i
$834$	7.32901	+	1.96380i	0.253783	+	0.0680009i
$835$	−7.62366	−	1.42103i	−0.263827	−	0.0491768i
$836$	−36.4161	−	21.0248i	−1.25948	−	0.727159i
$837$	3.53259			0.122104
$838$	0.155181	+	0.0895937i	0.00536063	+	0.00309496i
$839$	23.6250	−	6.33030i	0.815625	−	0.218546i	0.173192	−	0.984888i	$-0.444592\pi$
$839$	23.6250	−	6.33030i	0.815625	−	0.218546i	0.642433	+	0.766342i	$0.277925\pi$
$840$	2.19368	−	0.170388i	0.0756892	−	0.00587895i
$841$	18.8262	−	32.6080i	0.649180	−	1.12441i
$842$	−0.561370	+	2.09506i	−0.0193461	+	0.0722006i
$843$	13.6636	+	23.6661i	0.470601	+	0.815104i
$844$	41.2114			1.41856
$845$		0			0
$846$	−6.98292			−0.240078
$847$	−1.54810	−	2.68139i	−0.0531933	−	0.0921335i
$848$	−9.32543	+	34.8030i	−0.320237	+	1.19514i
$849$	5.31615	−	9.20784i	0.182450	−	0.316012i
$850$	1.59754	−	2.18939i	0.0547951	−	0.0750954i
$851$	−1.55482	+	0.416612i	−0.0532985	+	0.0142813i
$852$	17.1470	+	9.89982i	0.587446	+	0.339162i
$853$	−2.94669			−0.100893			−0.0504464	−	0.998727i	$-0.516064\pi$
$853$	−2.94669			−0.100893			−0.0504464	+	0.998727i	$0.516064\pi$
$854$	0.978324	+	0.564835i	0.0334775	+	0.0193283i
$855$	−23.8756	+	16.3733i	−0.816528	+	0.559955i
$856$	−4.22204	−	1.13129i	−0.144306	−	0.0386667i
$857$	13.0632	+	13.0632i	0.446229	+	0.446229i	0.894099	−	0.447870i	$-0.147817\pi$
$857$	13.0632	+	13.0632i	0.446229	+	0.446229i	−0.447870	+	0.894099i	$0.647817\pi$
$858$		0			0
$859$			3.08382i			0.105219i	0.998615	+	0.0526093i	$0.0167538\pi$
$859$			3.08382i			0.105219i	−0.998615	+	0.0526093i	$0.983246\pi$
$860$	−16.5942	−	24.1978i	−0.565859	−	0.825137i
$861$	2.12421	+	3.67923i	0.0723928	+	0.125388i
$862$	−9.48982	+	2.54279i	−0.323225	+	0.0866078i
$863$		−	50.9818i		−	1.73544i	−0.497053	−	0.867720i	$-0.665585\pi$
$863$		−	50.9818i		−	1.73544i	0.497053	−	0.867720i	$-0.334415\pi$
$864$	−0.796920	−	2.97415i	−0.0271118	−	0.101183i
$865$	3.77188	−	7.88713i	0.128248	−	0.268170i
$866$	5.12611	−	5.12611i	0.174192	−	0.174192i
$867$	8.01780	+	29.9228i	0.272299	+	1.01623i
$868$	−2.58006	−	0.691326i	−0.0875730	−	0.0234651i
$869$	3.78062	−	14.1095i	0.128249	−	0.478631i
$870$	−11.8194	+	0.918039i	−0.400715	+	0.0311244i
$871$		0			0
$872$	−5.42366	+	5.42366i	−0.183668	+	0.183668i
$873$	−33.0051	+	19.0555i	−1.11705	+	0.644931i
$874$	0.397788	−	0.229663i	0.0134554	−	0.00776846i
$875$	−3.79996	+	2.04813i	−0.128462	+	0.0692394i
$876$	19.5706	+	19.5706i	0.661228	+	0.661228i
$877$	−13.3844	+	23.1824i	−0.451958	+	0.782814i	−0.998508	−	0.0546128i	$-0.982608\pi$
$877$	−13.3844	+	23.1824i	−0.451958	+	0.782814i	0.546550	+	0.837427i	$0.315941\pi$
$878$	−0.237620	+	0.411570i	−0.00801929	+	0.0138898i
$879$	21.8986	+	21.8986i	0.738621	+	0.738621i
$880$	14.9465	−	31.2536i	0.503846	−	1.05356i
$881$	−27.2630	+	15.7403i	−0.918512	+	0.530303i	−0.883160	−	0.469072i	$-0.844589\pi$
$881$	−27.2630	+	15.7403i	−0.918512	+	0.530303i	−0.0353521	+	0.999375i	$0.511255\pi$
$882$	−4.21334	+	2.43257i	−0.141870	+	0.0819089i
$883$	−27.3576	+	27.3576i	−0.920657	+	0.920657i	−0.997076	−	0.0764191i	$-0.975651\pi$
$883$	−27.3576	+	27.3576i	−0.920657	+	0.920657i	0.0764191	+	0.997076i	$0.475651\pi$
$884$		0			0
$885$	−8.33941	+	9.74398i	−0.280326	+	0.327540i
$886$	−0.288420	+	1.07640i	−0.00968965	+	0.0361623i
$887$	1.32670	+	0.355489i	0.0445463	+	0.0119362i	0.281023	−	0.959701i	$-0.409326\pi$
$887$	1.32670	+	0.355489i	0.0445463	+	0.0119362i	−0.236477	+	0.971637i	$0.575993\pi$
$888$	−3.18263	−	11.8777i	−0.106802	−	0.398591i
$889$	−3.11346	+	3.11346i	−0.104422	+	0.104422i
$890$	2.77103	+	1.32520i	0.0928851	+	0.0444206i
$891$	11.3716	+	42.4393i	0.380962	+	1.42177i
$892$		−	52.6068i		−	1.76141i
$893$	47.5870	−	12.7509i	1.59244	−	0.426692i
$894$	0.822293	+	1.42425i	0.0275016	+	0.0476341i
$895$	2.66233	−	14.2831i	0.0889918	−	0.477430i
$896$			3.08204i			0.102964i
$897$		0			0
$898$	3.92294	+	3.92294i	0.130910	+	0.130910i
$899$	28.3479	+	7.59580i	0.945456	+	0.253334i
$900$	−15.6089	−	19.3562i	−0.520296	−	0.645207i
$901$	17.3249	+	10.0025i	0.577176	+	0.333233i
$902$	−5.58046			−0.185809
$903$	−5.38754	−	3.11050i	−0.179286	−	0.103511i
$904$	4.14019	−	1.10936i	0.137701	−	0.0368968i
$905$	17.4249	−	20.3597i	0.579223	−	0.676779i
$906$	−1.18700	+	2.05594i	−0.0394354	+	0.0683040i
$907$	6.02625	−	22.4903i	0.200098	−	0.746777i	−0.790790	−	0.612088i	$-0.790330\pi$
$907$	6.02625	−	22.4903i	0.200098	−	0.746777i	0.990888	−	0.134689i	$-0.0430036\pi$
$908$	−6.66580	−	11.5455i	−0.221212	−	0.383151i
$909$	13.6430			0.452508
$910$		0			0
$911$	2.89704			0.0959832			0.0479916	−	0.998848i	$-0.484718\pi$
$911$	2.89704			0.0959832			0.0479916	+	0.998848i	$0.484718\pi$
$912$	−21.0304	−	36.4256i	−0.696385	−	1.20617i
$913$	−5.85624	+	21.8558i	−0.193813	+	0.723322i
$914$	2.03105	−	3.51789i	0.0671813	−	0.116361i
$915$	−4.35653	−	56.0886i	−0.144022	−	1.85423i
$916$	12.0094	−	3.21792i	0.396803	−	0.106323i
$917$	−6.97599	−	4.02759i	−0.230368	−	0.133003i
$918$	−0.532680			−0.0175811
$919$	−14.3846	−	8.30494i	−0.474503	−	0.273955i	0.243620	−	0.969871i	$-0.421665\pi$
$919$	−14.3846	−	8.30494i	−0.474503	−	0.273955i	−0.718123	+	0.695916i	$0.754998\pi$
$920$	0.455003	+	0.663488i	0.0150010	+	0.0218745i
$921$	17.7000	+	4.74271i	0.583236	+	0.156278i
$922$	−1.18028	−	1.18028i	−0.0388704	−	0.0388704i
$923$		0			0
$924$		−	7.65756i		−	0.251915i
$925$	15.1440	+	18.7798i	0.497932	+	0.617475i
$926$	4.94858	+	8.57120i	0.162621	+	0.281667i
$927$	−4.27135	+	1.14451i	−0.140290	+	0.0375905i
$928$		−	25.5801i		−	0.839708i
$929$	−11.0843	−	41.3672i	−0.363664	−	1.35721i	−0.869223	−	0.494420i	$-0.835380\pi$
$929$	−11.0843	−	41.3672i	−0.363664	−	1.35721i	0.505559	−	0.862792i	$-0.331286\pi$
$930$	−1.73740	−	4.92228i	−0.0569717	−	0.161408i
$931$	24.2710	−	24.2710i	0.795451	−	0.795451i
$932$	3.86773	+	14.4346i	0.126692	+	0.472820i
$933$	26.4846	+	7.09653i	0.867067	+	0.232330i
$934$	0.773465	−	2.88661i	0.0253086	−	0.0944528i
$935$	−14.6136	−	12.5071i	−0.477916	−	0.409025i
$936$		0			0
$937$	27.9881	−	27.9881i	0.914331	−	0.914331i	−0.0822783	−	0.996609i	$-0.526220\pi$
$937$	27.9881	−	27.9881i	0.914331	−	0.914331i	0.996609	+	0.0822783i	$0.0262196\pi$
$938$	−0.585878	+	0.338257i	−0.0191296	+	0.0110445i
$939$	−29.3945	+	16.9709i	−0.959254	+	0.553826i
$940$	14.0840	+	39.9018i	0.459371	+	1.30145i
$941$	4.15042	+	4.15042i	0.135300	+	0.135300i	0.771513	−	0.636213i	$-0.219500\pi$
$941$	4.15042	+	4.15042i	0.135300	+	0.135300i	−0.636213	+	0.771513i	$0.719500\pi$
$942$	−1.01834	+	1.76381i	−0.0331792	+	0.0574680i
$943$	−0.776696	+	1.34528i	−0.0252927	+	0.0438083i
$944$	−6.09729	−	6.09729i	−0.198450	−	0.198450i
$945$	0.765402	+	0.366040i	0.0248985	+	0.0119073i
$946$	7.07675	−	4.08576i	0.230085	−	0.132840i
$947$	−21.5292	+	12.4299i	−0.699606	+	0.403918i	−0.807201	−	0.590277i	$-0.799018\pi$
$947$	−21.5292	+	12.4299i	−0.699606	+	0.403918i	0.107595	+	0.994195i	$0.465685\pi$
$948$	10.7708	−	10.7708i	0.349820	−	0.349820i
$949$		0			0
$950$	−5.56115	−	4.05783i	−0.180428	−	0.131653i
$951$	−13.3139	+	49.6881i	−0.431732	+	1.61125i
$952$	0.793363	+	0.212581i	0.0257130	+	0.00688979i
$953$	−8.46463	−	31.5904i	−0.274196	−	1.02331i	−0.956378	−	0.292131i	$-0.905636\pi$
$953$	−8.46463	−	31.5904i	−0.274196	−	1.02331i	0.682182	−	0.731182i	$-0.261031\pi$
$954$	−5.09284	+	5.09284i	−0.164887	+	0.164887i
$955$	−10.9496	+	3.86486i	−0.354322	+	0.125064i
$956$	−5.87441	−	21.9236i	−0.189992	−	0.709059i
$957$			84.1358i			2.71973i
$958$	2.43782	−	0.653211i	0.0787622	−	0.0211043i
$959$	−0.0470949	−	0.0815707i	−0.00152077	−	0.00263405i
$960$	27.2103	−	18.6602i	0.878209	−	0.602254i
$961$		−	18.0777i		−	0.583153i
$962$		0			0
$963$	7.40571	+	7.40571i	0.238646	+	0.238646i
$964$	−2.71259	−	0.726837i	−0.0873667	−	0.0234098i
$965$	2.73466	−	14.6711i	0.0880318	−	0.472280i
$966$	0.0724402	+	0.0418234i	0.00233072	+	0.00134564i
$967$	−30.0090			−0.965023			−0.482512	−	0.875890i	$-0.660275\pi$
$967$	−30.0090			−0.965023			−0.482512	+	0.875890i	$0.660275\pi$
$968$	7.48976	+	4.32422i	0.240730	+	0.138986i
$969$	−22.5573	+	6.04422i	−0.724646	+	0.194168i
$970$	−6.88518	−	5.89269i	−0.221070	−	0.189203i
$971$	3.13659	−	5.43273i	0.100658	−	0.174345i	−0.811298	−	0.584633i	$-0.801239\pi$
$971$	3.13659	−	5.43273i	0.100658	−	0.174345i	0.911956	+	0.410288i	$0.134572\pi$
$972$	−10.3897	+	38.7750i	−0.333251	+	1.24371i
$973$	−2.25563	−	3.90686i	−0.0723120	−	0.125248i
$974$	7.07119			0.226575
$975$		0			0
$976$	37.8235			1.21070
$977$	−7.78106	−	13.4772i	−0.248938	−	0.431174i	0.714293	−	0.699847i	$-0.246748\pi$
$977$	−7.78106	−	13.4772i	−0.248938	−	0.431174i	−0.963231	+	0.268673i	$0.913415\pi$
$978$	2.48968	−	9.29160i	0.0796111	−	0.297113i
$979$	10.8997	−	18.8788i	0.348356	−	0.603370i
$980$	22.3982	+	19.1695i	0.715484	+	0.612349i
$981$	17.7523	−	4.75672i	0.566788	−	0.151870i
$982$	−3.14082	−	1.81335i	−0.100227	−	0.0578663i
$983$	−53.4558			−1.70498			−0.852488	−	0.522746i	$-0.824907\pi$
$983$	−53.4558			−1.70498			−0.852488	+	0.522746i	$0.824907\pi$
$984$	−10.2770	−	5.93342i	−0.327619	−	0.189151i
$985$	8.02974	−	43.0786i	0.255849	−	1.37260i
$986$	−4.27459	−	1.14537i	−0.136131	−	0.0364761i
$987$	6.34391	+	6.34391i	0.201929	+	0.201929i
$988$		0			0
$989$		−	2.27465i		−	0.0723297i
$990$	5.71117	−	3.91658i	0.181513	−	0.124477i
$991$	11.8198	+	20.4726i	0.375470	+	0.650333i	0.990397	−	0.138251i	$-0.0441480\pi$
$991$	11.8198	+	20.4726i	0.375470	+	0.650333i	−0.614927	+	0.788584i	$0.710815\pi$
$992$	10.8795	−	2.91514i	0.345423	−	0.0925558i
$993$			46.3626i			1.47127i
$994$	0.119563	+	0.446214i	0.00379230	+	0.0141531i
$995$	−31.0088	+	10.9451i	−0.983044	+	0.346983i
$996$	−16.6842	+	16.6842i	−0.528658	+	0.528658i
$997$	13.3882	+	49.9653i	0.424007	+	1.58242i	0.766082	+	0.642743i	$0.222204\pi$
$997$	13.3882	+	49.9653i	0.424007	+	1.58242i	−0.342075	+	0.939673i	$0.611130\pi$
$998$	6.29473	+	1.68667i	0.199256	+	0.0533905i
$999$	1.22721	−	4.58002i	0.0388273	−	0.144906i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.o.f.258.2		20
5.2	odd	4		845.2.t.e.427.4		20
13.2	odd	12		845.2.f.d.408.5		20
13.3	even	3		845.2.k.d.268.6		20
13.4	even	6		65.2.o.a.33.4	yes	20
13.5	odd	4		845.2.t.g.418.2		20
13.6	odd	12		845.2.t.e.188.4		20
13.7	odd	12		845.2.t.f.188.2		20
13.8	odd	4		65.2.t.a.28.4	yes	20
13.9	even	3		845.2.o.g.488.2		20
13.10	even	6		845.2.k.e.268.5		20
13.11	odd	12		845.2.f.e.408.6		20
13.12	even	2		845.2.o.e.258.4		20
39.8	even	4		585.2.dp.a.28.2		20
39.17	odd	6		585.2.cf.a.163.2		20
65.2	even	12		845.2.k.d.577.6		20
65.4	even	6		325.2.s.b.293.2		20
65.7	even	12		845.2.o.e.357.4		20
65.8	even	4		325.2.s.b.132.2		20
65.12	odd	4		845.2.t.f.427.2		20
65.17	odd	12		65.2.t.a.7.4	yes	20
65.22	odd	12		845.2.t.g.657.2		20
65.32	even	12	inner	845.2.o.f.357.2		20
65.34	odd	4		325.2.x.b.93.2		20
65.37	even	12		845.2.k.e.577.5		20
65.42	odd	12		845.2.f.d.437.6		20
65.43	odd	12		325.2.x.b.7.2		20
65.47	even	4		65.2.o.a.2.4	✓	20
65.57	even	4		845.2.o.g.587.2		20
65.62	odd	12		845.2.f.e.437.5		20
195.17	even	12		585.2.dp.a.397.2		20
195.47	odd	4		585.2.cf.a.262.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.4	✓	20	65.47	even	4
65.2.o.a.33.4	yes	20	13.4	even	6
65.2.t.a.7.4	yes	20	65.17	odd	12
65.2.t.a.28.4	yes	20	13.8	odd	4
325.2.s.b.132.2		20	65.8	even	4
325.2.s.b.293.2		20	65.4	even	6
325.2.x.b.7.2		20	65.43	odd	12
325.2.x.b.93.2		20	65.34	odd	4
585.2.cf.a.163.2		20	39.17	odd	6
585.2.cf.a.262.2		20	195.47	odd	4
585.2.dp.a.28.2		20	39.8	even	4
585.2.dp.a.397.2		20	195.17	even	12
845.2.f.d.408.5		20	13.2	odd	12
845.2.f.d.437.6		20	65.42	odd	12
845.2.f.e.408.6		20	13.11	odd	12
845.2.f.e.437.5		20	65.62	odd	12
845.2.k.d.268.6		20	13.3	even	3
845.2.k.d.577.6		20	65.2	even	12
845.2.k.e.268.5		20	13.10	even	6
845.2.k.e.577.5		20	65.37	even	12
845.2.o.e.258.4		20	13.12	even	2
845.2.o.e.357.4		20	65.7	even	12
845.2.o.f.258.2		20	1.1	even	1	trivial
845.2.o.f.357.2		20	65.32	even	12	inner
845.2.o.g.488.2		20	13.9	even	3
845.2.o.g.587.2		20	65.57	even	4
845.2.t.e.188.4		20	13.6	odd	12
845.2.t.e.427.4		20	5.2	odd	4
845.2.t.f.188.2		20	13.7	odd	12
845.2.t.f.427.2		20	65.12	odd	4
845.2.t.g.418.2		20	13.5	odd	4
845.2.t.g.657.2		20	65.22	odd	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.o (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.137404 + 0.237991i) q^{2} +(0.611610 - 2.28256i) q^{3} +(0.962240 - 1.66665i) q^{4} +(-1.69883 - 1.45395i) q^{5} +(0.627267 - 0.168076i) q^{6} +(-0.334376 - 0.193052i) q^{7} +1.07848 q^{8} +(-2.23793 - 1.29207i) q^{9} +(0.112600 - 0.604086i) q^{10} +(-4.21249 - 1.12873i) q^{11} +(-3.21571 - 3.21571i) q^{12} -0.106105i q^{14} +(-4.35775 + 2.98844i) q^{15} +(-1.77629 - 3.07663i) q^{16} +(-1.90527 + 0.510514i) q^{17} -0.710144i q^{18} +(1.29673 + 4.83947i) q^{19} +(-4.05791 + 1.43231i) q^{20} +(-0.645159 + 0.645159i) q^{21} +(-0.310185 - 1.15763i) q^{22} +(-0.322241 - 0.0863441i) q^{23} +(0.659609 - 2.46170i) q^{24} +(0.772064 + 4.94003i) q^{25} +(0.694880 - 0.694880i) q^{27} +(-0.643499 + 0.371524i) q^{28} +(7.07031 - 4.08205i) q^{29} +(-1.30999 - 0.626482i) q^{30} +(2.54187 + 2.54187i) q^{31} +(1.56662 - 2.71347i) q^{32} +(-5.15280 + 8.92491i) q^{33} +(-0.383290 - 0.383290i) q^{34} +(0.287361 + 0.814128i) q^{35} +(-4.30685 + 2.48656i) q^{36} +(4.17859 - 2.41251i) q^{37} +(-0.973575 + 0.973575i) q^{38} +(-1.83216 - 1.56806i) q^{40} +(1.20515 - 4.49768i) q^{41} +(-0.242190 - 0.0648946i) q^{42} +(1.76471 + 6.58600i) q^{43} +(-5.93462 + 5.93462i) q^{44} +(1.92327 + 5.44885i) q^{45} +(-0.0237281 - 0.0885545i) q^{46} -9.83310i q^{47} +(-8.10898 + 2.17280i) q^{48} +(-3.42546 - 5.93307i) q^{49} +(-1.06960 + 0.862526i) q^{50} +4.66112i q^{51} +(-7.17155 - 7.17155i) q^{53} +(0.260855 + 0.0698958i) q^{54} +(5.51519 + 8.04227i) q^{55} +(-0.360618 - 0.208203i) q^{56} +11.8395 q^{57} +(1.94298 + 1.12178i) q^{58} +(2.34451 - 0.628209i) q^{59} +(0.787474 + 10.1384i) q^{60} +(-5.32338 + 9.22037i) q^{61} +(-0.255679 + 0.954209i) q^{62} +(0.498873 + 0.864073i) q^{63} -6.24413 q^{64} -2.83207 q^{66} +(-3.18796 - 5.52170i) q^{67} +(-0.982475 + 3.66665i) q^{68} +(-0.394171 + 0.682724i) q^{69} +(-0.154271 + 0.180254i) q^{70} +(-4.20542 + 1.12684i) q^{71} +(-2.41357 - 1.39347i) q^{72} -6.08593 q^{73} +(1.14831 + 0.662979i) q^{74} +(11.7481 + 1.25909i) q^{75} +(9.31346 + 2.49554i) q^{76} +(1.19065 + 1.19065i) q^{77} +3.34944i q^{79} +(-1.45564 + 7.80932i) q^{80} +(-5.03732 - 8.72489i) q^{81} +(1.23600 - 0.331185i) q^{82} -5.18834i q^{83} +(0.454456 + 1.69605i) q^{84} +(3.97899 + 1.90288i) q^{85} +(-1.32493 + 1.32493i) q^{86} +(-4.99324 - 18.6350i) q^{87} +(-4.54309 - 1.21732i) q^{88} +(-1.29374 + 4.82829i) q^{89} +(-1.03251 + 1.20642i) q^{90} +(-0.453978 + 0.453978i) q^{92} +(7.35661 - 4.24734i) q^{93} +(2.34019 - 1.35111i) q^{94} +(4.83341 - 10.1068i) q^{95} +(-5.23549 - 5.23549i) q^{96} +(7.37402 - 12.7722i) q^{97} +(0.941346 - 1.63046i) q^{98} +(7.96886 + 7.96886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 2 q^{3} - 6 q^{4} + 6 q^{5} - 4 q^{6} - 6 q^{7} - 12 q^{8} + 12 q^{9} + 2 q^{10} - 8 q^{11} + 24 q^{12} - 12 q^{15} - 2 q^{16} - 4 q^{17} + 16 q^{19} - 8 q^{20} - 4 q^{21} + 16 q^{22} + 10 q^{23}+ \cdots + 60 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 - 2 * q^3 - 6 * q^4 + 6 * q^5 - 4 * q^6 - 6 * q^7 - 12 * q^8 + 12 * q^9 + 2 * q^10 - 8 * q^11 + 24 * q^12 - 12 * q^15 - 2 * q^16 - 4 * q^17 + 16 * q^19 - 8 * q^20 - 4 * q^21 + 16 * q^22 + 10 * q^23 - 28 * q^24 - 18 * q^25 + 4 * q^27 + 6 * q^28 + 26 * q^30 + 6 * q^32 + 18 * q^33 + 2 * q^34 + 40 * q^35 - 36 * q^36 + 42 * q^37 + 8 * q^38 - 16 * q^40 - 28 * q^41 + 40 * q^42 - 10 * q^43 - 36 * q^44 + 32 * q^45 + 8 * q^46 - 56 * q^48 - 18 * q^49 - 8 * q^50 - 10 * q^53 + 12 * q^54 - 10 * q^55 + 12 * q^57 - 90 * q^58 + 8 * q^59 + 92 * q^60 - 16 * q^61 + 44 * q^62 + 32 * q^63 - 20 * q^64 - 32 * q^66 + 58 * q^67 + 22 * q^68 + 16 * q^69 - 32 * q^70 - 56 * q^71 - 66 * q^72 - 72 * q^73 + 18 * q^74 + 38 * q^75 - 80 * q^76 + 28 * q^77 - 68 * q^80 - 14 * q^81 - 56 * q^82 + 32 * q^84 - 6 * q^85 - 60 * q^86 - 34 * q^87 - 82 * q^88 - 6 * q^89 - 46 * q^90 - 8 * q^92 + 48 * q^93 - 48 * q^94 + 26 * q^95 - 56 * q^96 + 22 * q^97 - 4 * q^98 + 60 * q^99

Introduction

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