LMFDB - Embedded newform 675.2.ba.b.443.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(32,675)] 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("675.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([10, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [192] 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			443.3
Character	$\chi$	$=$	675.443
Dual form			675.2.ba.b.32.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.191628 - 2.19031i) q^{2} +(-0.699511 + 1.58451i) q^{3} +(-2.79113 + 0.492152i) q^{4} +(3.60463 + 1.22851i) q^{6} +(0.000371431 + 0.000530458i) q^{7} +(0.474704 + 1.77162i) q^{8} +(-2.02137 - 2.21677i) q^{9} +(0.925209 + 2.54199i) q^{11} +(1.17261 - 4.76685i) q^{12} +(3.16625 + 0.277011i) q^{13} +(0.00109069 - 0.000915200i) q^{14} +(-1.53710 + 0.559459i) q^{16} +(-1.76536 + 6.58840i) q^{17} +(-4.46807 + 4.85222i) q^{18} +(-1.52337 - 0.879517i) q^{19} +(-0.00110034 + 0.000217476i) q^{21} +(5.39046 - 2.51361i) q^{22} +(4.18584 + 2.93096i) q^{23} +(-3.13922 - 0.487092i) q^{24} -6.98815i q^{26} +(4.92647 - 1.65223i) q^{27} +(-0.00129778 - 0.00129778i) q^{28} +(4.37718 + 3.67289i) q^{29} +(-0.944975 - 5.35922i) q^{31} +(3.07020 + 6.58407i) q^{32} +(-4.67501 - 0.312144i) q^{33} +(14.7689 + 2.60416i) q^{34} +(6.73289 + 5.19248i) q^{36} +(-0.253391 - 0.0678960i) q^{37} +(-1.63450 + 3.50519i) q^{38} +(-2.65375 + 4.82319i) q^{39} +(7.56097 + 9.01082i) q^{41} +(0.000687195 + 0.00236841i) q^{42} +(7.88368 + 3.67622i) q^{43} +(-3.83342 - 6.63969i) q^{44} +(5.61759 - 9.72995i) q^{46} +(0.576559 - 0.403711i) q^{47} +(0.188748 - 2.82690i) q^{48} +(2.39414 - 6.57785i) q^{49} +(-9.20452 - 7.40589i) q^{51} +(-8.97374 + 0.785101i) q^{52} +(5.73786 - 5.73786i) q^{53} +(-4.56295 - 10.4739i) q^{54} +(-0.000763450 + 0.000909845i) q^{56} +(2.45922 - 1.79857i) q^{57} +(7.20599 - 10.2912i) q^{58} +(2.11198 + 0.768697i) q^{59} +(-1.14333 + 6.48417i) q^{61} +(-11.5573 + 3.09676i) q^{62} +(0.000425105 - 0.00189563i) q^{63} +(10.9996 - 6.35064i) q^{64} +(0.212168 + 10.2996i) q^{66} +(-0.216242 + 2.47165i) q^{67} +(1.68485 - 19.2579i) q^{68} +(-7.57218 + 4.58228i) q^{69} +(-10.4316 + 6.02267i) q^{71} +(2.96772 - 4.63341i) q^{72} +(-1.40104 + 0.375408i) q^{73} +(-0.100157 + 0.568017i) q^{74} +(4.68478 + 1.70512i) q^{76} +(-0.00100477 + 0.00143496i) q^{77} +(11.0728 + 4.88829i) q^{78} +(-3.36157 + 4.00616i) q^{79} +(-0.828138 + 8.96182i) q^{81} +(18.2876 - 18.2876i) q^{82} +(-15.9554 + 1.39592i) q^{83} +(0.00296416 - 0.00114854i) q^{84} +(6.54134 - 17.9722i) q^{86} +(-8.88163 + 4.36647i) q^{87} +(-4.06424 + 2.84581i) q^{88} +(-2.99426 + 5.18621i) q^{89} +(0.00102910 + 0.00178245i) q^{91} +(-13.1257 - 6.12062i) q^{92} +(9.15278 + 2.25151i) q^{93} +(-0.994737 - 1.18548i) q^{94} +(-12.5802 + 0.259149i) q^{96} +(-3.55678 + 7.62753i) q^{97} +(-14.8663 - 3.98342i) q^{98} +(3.76482 - 7.18927i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.191628	−	2.19031i	−0.135501	−	1.54878i	−0.694425	−	0.719566i	$-0.744341\pi$
$2$	−0.191628	−	2.19031i	−0.135501	−	1.54878i	0.558923	−	0.829219i	$-0.311215\pi$
$3$	−0.699511	+	1.58451i	−0.403863	+	0.914820i
$3$	−0.699511	+	1.58451i	−0.403863	+	0.914820i
$4$	−2.79113	+	0.492152i	−1.39557	+	0.246076i
$5$		0			0
$5$		0			0
$6$	3.60463	+	1.22851i	1.47158	+	0.501538i
$7$	0.000371431	0	0.000530458i	0.000140388	0	0.000200494i	0.819222	−	0.573476i	$-0.194405\pi$
$7$	0.000371431	0	0.000530458i	0.000140388	0	0.000200494i	−0.819082	+	0.573677i	$0.805517\pi$
$8$	0.474704	+	1.77162i	0.167833	+	0.626362i
$9$	−2.02137	−	2.21677i	−0.673790	−	0.738923i
$10$		0			0
$11$	0.925209	+	2.54199i	0.278961	+	0.766439i	0.997481	+	0.0709326i	$0.0225975\pi$
$11$	0.925209	+	2.54199i	0.278961	+	0.766439i	−0.718520	+	0.695506i	$0.755180\pi$
$12$	1.17261	−	4.76685i	0.338502	−	1.37607i
$13$	3.16625	+	0.277011i	0.878159	+	0.0768289i	0.517313	−	0.855797i	$-0.326932\pi$
$13$	3.16625	+	0.277011i	0.878159	+	0.0768289i	0.360846	+	0.932625i	$0.382488\pi$
$14$	0.00109069		0.000915200i	0.000291500		0.000244597i
$15$		0			0
$16$	−1.53710	+	0.559459i	−0.384275	+	0.139865i
$17$	−1.76536	+	6.58840i	−0.428162	+	1.59792i	0.328759	+	0.944414i	$0.393370\pi$
$17$	−1.76536	+	6.58840i	−0.428162	+	1.59792i	−0.756921	+	0.653507i	$0.773297\pi$
$18$	−4.46807	+	4.85222i	−1.05313	+	1.14368i
$19$	−1.52337	−	0.879517i	−0.349485	−	0.201775i	0.314974	−	0.949100i	$-0.398004\pi$
$19$	−1.52337	−	0.879517i	−0.349485	−	0.201775i	−0.664458	+	0.747325i	$0.731338\pi$
$20$		0			0
$21$	−0.00110034		0.000217476i	−0.000240113		4.74571e-5i
$22$	5.39046	−	2.51361i	1.14925	−	0.535904i
$23$	4.18584	+	2.93096i	0.872808	+	0.611147i	0.921806	−	0.387652i	$-0.126714\pi$
$23$	4.18584	+	2.93096i	0.872808	+	0.611147i	−0.0489979	+	0.998799i	$0.515603\pi$
$24$	−3.13922	−	0.487092i	−0.640790	−	0.0994273i
$25$		0			0
$26$		−	6.98815i		−	1.37049i
$27$	4.92647	−	1.65223i	0.948100	−	0.317972i
$28$	−0.00129778	−	0.00129778i	−0.000245257	−	0.000245257i
$29$	4.37718	+	3.67289i	0.812822	+	0.682038i	0.951279	−	0.308330i	$-0.0997701\pi$
$29$	4.37718	+	3.67289i	0.812822	+	0.682038i	−0.138458	+	0.990368i	$0.544215\pi$
$30$		0			0
$31$	−0.944975	−	5.35922i	−0.169723	−	0.962544i	−0.944061	−	0.329772i	$-0.893028\pi$
$31$	−0.944975	−	5.35922i	−0.169723	−	0.962544i	0.774338	−	0.632772i	$-0.218083\pi$
$32$	3.07020	+	6.58407i	0.542740	+	1.16391i
$33$	−4.67501	−	0.312144i	−0.813815	−	0.0543373i
$34$	14.7689	+	2.60416i	2.53285	+	0.446610i
$35$		0			0
$36$	6.73289	+	5.19248i	1.12215	+	0.865413i
$37$	−0.253391	−	0.0678960i	−0.0416573	−	0.0111620i	0.237930	−	0.971282i	$-0.423531\pi$
$37$	−0.253391	−	0.0678960i	−0.0416573	−	0.0111620i	−0.279587	+	0.960120i	$0.590198\pi$
$38$	−1.63450	+	3.50519i	−0.265151	+	0.568617i
$39$	−2.65375	+	4.82319i	−0.424940	+	0.772328i
$40$		0			0
$41$	7.56097	+	9.01082i	1.18083	+	1.40725i	0.893289	+	0.449483i	$0.148392\pi$
$41$	7.56097	+	9.01082i	1.18083	+	1.40725i	0.287537	+	0.957770i	$0.407164\pi$
$42$	0.000687195		0.00236841i	0.000106037		0.000365454i
$43$	7.88368	+	3.67622i	1.20225	+	0.560618i	0.917405	−	0.397955i	$-0.130280\pi$
$43$	7.88368	+	3.67622i	1.20225	+	0.560618i	0.284845	+	0.958574i	$0.408058\pi$
$44$	−3.83342	−	6.63969i	−0.577910	−	1.00097i
$45$		0			0
$46$	5.61759	−	9.72995i	0.828268	−	1.43460i
$47$	0.576559	−	0.403711i	0.0840997	−	0.0588873i	−0.530770	−	0.847516i	$-0.678097\pi$
$47$	0.576559	−	0.403711i	0.0840997	−	0.0588873i	0.614870	+	0.788628i	$0.289208\pi$
$48$	0.188748	−	2.82690i	0.0272435	−	0.408028i
$49$	2.39414	−	6.57785i	0.342020	−	0.939693i
$50$		0			0
$51$	−9.20452	−	7.40589i	−1.28889	−	1.03703i
$52$	−8.97374	+	0.785101i	−1.24443	+	0.108874i
$53$	5.73786	−	5.73786i	0.788156	−	0.788156i	−0.193036	−	0.981192i	$-0.561833\pi$
$53$	5.73786	−	5.73786i	0.788156	−	0.788156i	0.981192	+	0.193036i	$0.0618333\pi$
$54$	−4.56295	−	10.4739i	−0.620939	−	1.42532i
$55$		0			0
$56$	−0.000763450	0	0.000909845i	−0.000102020	0	0.000121583i
$57$	2.45922	−	1.79857i	0.325732	−	0.238226i
$58$	7.20599	−	10.2912i	0.946193	−	1.35130i
$59$	2.11198	+	0.768697i	0.274956	+	0.100076i	0.475818	−	0.879544i	$-0.342152\pi$
$59$	2.11198	+	0.768697i	0.274956	+	0.100076i	−0.200862	+	0.979620i	$0.564374\pi$
$60$		0			0
$61$	−1.14333	+	6.48417i	−0.146389	+	0.830213i	0.819852	+	0.572575i	$0.194055\pi$
$61$	−1.14333	+	6.48417i	−0.146389	+	0.830213i	−0.966241	+	0.257638i	$0.917056\pi$
$62$	−11.5573	+	3.09676i	−1.46778	+	0.393290i
$63$	0.000425105	−	0.00189563i	5.35582e−5	−	0.000238827i
$64$	10.9996	−	6.35064i	1.37495	−	0.793830i
$65$		0			0
$66$	0.212168	+	10.2996i	0.0261161	+	1.26779i
$67$	−0.216242	+	2.47165i	−0.0264181	+	0.301960i	0.971478	+	0.237129i	$0.0762065\pi$
$67$	−0.216242	+	2.47165i	−0.0264181	+	0.301960i	−0.997896	+	0.0648313i	$0.979349\pi$
$68$	1.68485	−	19.2579i	0.204318	−	2.33536i
$69$	−7.57218	+	4.58228i	−0.911583	+	0.551642i
$70$		0			0
$71$	−10.4316	+	6.02267i	−1.23800	+	0.714759i	−0.968685	−	0.248294i	$-0.920130\pi$
$71$	−10.4316	+	6.02267i	−1.23800	+	0.714759i	−0.269314	+	0.963052i	$0.586797\pi$
$72$	2.96772	−	4.63341i	0.349749	−	0.546052i
$73$	−1.40104	+	0.375408i	−0.163979	+	0.0439381i	−0.339875	−	0.940471i	$-0.610385\pi$
$73$	−1.40104	+	0.375408i	−0.163979	+	0.0439381i	0.175895	+	0.984409i	$0.443718\pi$
$74$	−0.100157	+	0.568017i	−0.0116430	+	0.0660306i
$75$		0			0
$76$	4.68478	+	1.70512i	0.537381	+	0.195591i
$77$	−0.00100477	+	0.00143496i	−0.000114504	+	0.000163529i
$78$	11.0728	+	4.88829i	1.25375	+	0.553490i
$79$	−3.36157	+	4.00616i	−0.378206	+	0.450729i	−0.921247	−	0.388978i	$-0.872828\pi$
$79$	−3.36157	+	4.00616i	−0.378206	+	0.450729i	0.543041	+	0.839706i	$0.317273\pi$
$80$		0			0
$81$	−0.828138	+	8.96182i	−0.0920153	+	0.995758i
$82$	18.2876	−	18.2876i	2.01953	−	2.01953i
$83$	−15.9554	+	1.39592i	−1.75134	+	0.153222i	−0.917224	−	0.398372i	$-0.869575\pi$
$83$	−15.9554	+	1.39592i	−1.75134	+	0.153222i	−0.834113	+	0.551594i	$0.814020\pi$
$84$	0.00296416	−	0.00114854i	0.000323416	−	0.000125316i
$85$		0			0
$86$	6.54134	−	17.9722i	0.705371	−	1.93799i
$87$	−8.88163	+	4.36647i	−0.952211	+	0.468135i
$88$	−4.06424	+	2.84581i	−0.433249	+	0.303364i
$89$	−2.99426	+	5.18621i	−0.317391	+	0.549737i	−0.979943	−	0.199279i	$-0.936140\pi$
$89$	−2.99426	+	5.18621i	−0.317391	+	0.549737i	0.662552	+	0.749016i	$0.269473\pi$
$90$		0			0
$91$	0.00102910	+	0.00178245i	0.000107879	+	0.000186852i
$92$	−13.1257	−	6.12062i	−1.36845	−	0.638118i
$93$	9.15278	+	2.25151i	0.949099	+	0.233470i
$94$	−0.994737	−	1.18548i	−0.102599	−	0.122273i
$95$		0			0
$96$	−12.5802	+	0.259149i	−1.28396	+	0.0264492i
$97$	−3.55678	+	7.62753i	−0.361136	+	0.774459i	0.638851	+	0.769331i	$0.279410\pi$
$97$	−3.55678	+	7.62753i	−0.361136	+	0.774459i	−0.999987	+	0.00512815i	$0.998368\pi$
$98$	−14.8663	−	3.98342i	−1.50173	−	0.402386i
$99$	3.76482	−	7.18927i	0.378378	−	0.722549i
$100$		0			0
$101$	11.3335	+	1.99841i	1.12773	+	0.198849i	0.706231	−	0.707981i	$-0.250394\pi$
$101$	11.3335	+	1.99841i	1.12773	+	0.198849i	0.421496	+	0.906830i	$0.361505\pi$
$102$	−14.4574	+	21.5799i	−1.43149	+	2.13673i
$103$	−2.89813	−	6.21507i	−0.285562	−	0.612389i	0.710237	−	0.703963i	$-0.248588\pi$
$103$	−2.89813	−	6.21507i	−0.285562	−	0.612389i	−0.995798	+	0.0915740i	$0.970810\pi$
$104$	1.01227	+	5.74088i	0.0992615	+	0.562940i
$105$		0			0
$106$	−13.6672	−	11.4682i	−1.32748	−	1.11389i
$107$	−9.67551	−	9.67551i	−0.935367	−	0.935367i	0.0626673	−	0.998034i	$-0.480039\pi$
$107$	−9.67551	−	9.67551i	−0.935367	−	0.935367i	−0.998034	+	0.0626673i	$0.980039\pi$
$108$	−12.9373	+	7.03617i	−1.24489	+	0.677056i
$109$			3.73835i			0.358069i	0.983843	+	0.179034i	$0.0572974\pi$
$109$			3.73835i			0.358069i	−0.983843	+	0.179034i	$0.942703\pi$
$110$		0			0
$111$	0.284832	−	0.354008i	0.0270351	−	0.0336010i
$112$	−0.000867696	0	0.000607567i	−8.19895e−5	0	5.74097e-5i
$113$	−1.01289	+	0.472320i	−0.0952851	+	0.0444322i	−0.469676	−	0.882839i	$-0.655629\pi$
$113$	−1.01289	+	0.472320i	−0.0952851	+	0.0444322i	0.374391	+	0.927271i	$0.377852\pi$
$114$	−4.41068	−	5.04180i	−0.413098	−	0.472208i
$115$		0			0
$116$	−14.0249	−	8.09728i	−1.30218	−	0.751814i
$117$	−5.78608	−	7.57878i	−0.534923	−	0.700658i
$118$	1.27897	−	4.77320i	0.117739	−	0.439408i
$119$	−0.00415058	+	0.00151069i	−0.000380483	+	0.000138484i
$120$		0			0
$121$	2.82079	−	2.36692i	0.256435	−	0.215175i
$122$	14.4215	+	1.26171i	1.30566	+	0.114230i
$123$	−19.5667	+	5.67730i	−1.76427	+	0.511905i
$124$	5.27510	+	14.4932i	0.473718	+	1.30153i
$125$		0			0
$126$	−0.00423348		0.000567858i	−0.000377148		5.05889e-5i
$127$	−2.70398	−	10.0914i	−0.239940	−	0.895467i	−0.975860	−	0.218398i	$-0.929917\pi$
$127$	−2.70398	−	10.0914i	−0.239940	−	0.895467i	0.735920	−	0.677068i	$-0.236750\pi$
$128$	−7.68398	−	10.9739i	−0.679175	−	0.969962i
$129$	−11.3397	+	9.92024i	−0.998409	+	0.873429i
$130$		0			0
$131$	−14.3376	+	2.52811i	−1.25269	+	0.220882i	−0.760345	−	0.649520i	$-0.774970\pi$
$131$	−14.3376	+	2.52811i	−1.25269	+	0.220882i	−0.492341	+	0.870402i	$0.663859\pi$
$132$	13.2022	−	1.42958i	1.14910	−	0.124429i
$133$	−9.92788e−5	−	0.00113476i	−8.60857e−6	−	9.83964e-5i
$134$	5.45513			0.471251
$135$		0			0
$136$	−12.5102			−1.07274
$137$	−0.637262	−	7.28394i	−0.0544450	−	0.622309i	−0.973577	−	0.228359i	$-0.926664\pi$
$137$	−0.637262	−	7.28394i	−0.0544450	−	0.622309i	0.919132	−	0.393950i	$-0.128892\pi$
$138$	11.4877	+	15.7074i	0.977896	+	1.33710i
$139$	−3.00586	+	0.530014i	−0.254953	+	0.0449552i	−0.299664	−	0.954045i	$-0.596875\pi$
$139$	−3.00586	+	0.530014i	−0.254953	+	0.0449552i	0.0447106	+	0.999000i	$0.485763\pi$
$140$		0			0
$141$	0.236376	+	1.19597i	0.0199065	+	0.100718i
$142$	15.1905	+	21.6943i	1.27476	+	1.82054i
$143$	2.22528	+	8.30486i	0.186087	+	0.694487i
$144$	4.34724	+	2.27652i	0.362270	+	0.189710i
$145$		0			0
$146$	1.09074	+	2.99678i	0.0902701	+	0.248015i
$147$	8.74796	+	8.39483i	0.721520	+	0.692394i
$148$	0.740664	+	0.0647997i	0.0608822	+	0.00532650i
$149$	7.76525	−	6.51582i	0.636154	−	0.533797i	−0.266680	−	0.963785i	$-0.585927\pi$
$149$	7.76525	−	6.51582i	0.636154	−	0.533797i	0.902834	+	0.429988i	$0.141482\pi$
$150$		0			0
$151$	17.4779	−	6.36142i	1.42233	−	0.517685i	0.487605	−	0.873064i	$-0.337870\pi$
$151$	17.4779	−	6.36142i	1.42233	−	0.517685i	0.934722	+	0.355379i	$0.115648\pi$
$152$	0.835020	−	3.11634i	0.0677291	−	0.252768i
$153$	18.1734	−	9.40419i	1.46923	−	0.760284i
$154$	0.00333555	+	0.00192578i	0.000268786	+	0.000155184i
$155$		0			0
$156$	5.03323	−	14.7682i	0.402981	−	1.18240i
$157$	0.293204	−	0.136723i	0.0234002	−	0.0109117i	−0.410883	−	0.911688i	$-0.634780\pi$
$157$	0.293204	−	0.136723i	0.0234002	−	0.0109117i	0.434283	+	0.900776i	$0.357002\pi$
$158$	9.41892	+	6.59520i	0.749329	+	0.524686i
$159$	5.07803	+	13.1054i	0.402714	+	1.03933i
$160$		0			0
$161$			0.00330906i			0.000260790i
$162$	19.7879	+	0.0965494i	1.55468	+	0.00758564i
$163$	3.86594	+	3.86594i	0.302804	+	0.302804i	0.842110	−	0.539306i	$-0.181313\pi$
$163$	3.86594	+	3.86594i	0.302804	+	0.302804i	−0.539306	+	0.842110i	$0.681313\pi$
$164$	−25.5384	−	21.4292i	−1.99421	−	1.67334i
$165$		0			0
$166$	6.11500	+	34.6799i	0.474616	+	2.69168i
$167$	7.78235	+	16.6893i	0.602217	+	1.29146i	0.937055	+	0.349182i	$0.113541\pi$
$167$	7.78235	+	16.6893i	0.602217	+	1.29146i	−0.334838	+	0.942276i	$0.608682\pi$
$168$	−0.000907620	−	0.00184614i	−7.00244e−5	−	0.000142433i
$169$	−2.85412	−	0.503259i	−0.219548	−	0.0387122i
$170$		0			0
$171$	1.12960	+	5.15478i	0.0863828	+	0.394196i
$172$	−23.8136	−	6.38085i	−1.81577	−	0.486535i
$173$	−1.25855	+	2.69896i	−0.0956855	+	0.205198i	−0.948324	−	0.317302i	$-0.897223\pi$
$173$	−1.25855	+	2.69896i	−0.0956855	+	0.205198i	0.852639	+	0.522501i	$0.175001\pi$
$174$	11.2659	+	18.6168i	0.854066	+	1.41134i
$175$		0			0
$176$	−2.84428	−	3.38968i	−0.214395	−	0.255506i
$177$	−2.69536	+	2.80875i	−0.202596	+	0.211118i
$178$	11.9332	+	5.56454i	0.894431	+	0.417080i
$179$	−8.26245	−	14.3110i	−0.617564	−	1.06965i	−0.989929	−	0.141566i	$-0.954786\pi$
$179$	−8.26245	−	14.3110i	−0.617564	−	1.06965i	0.372365	−	0.928087i	$-0.378547\pi$
$180$		0			0
$181$	4.81540	−	8.34051i	0.357926	−	0.619945i	−0.629688	−	0.776848i	$-0.716817\pi$
$181$	4.81540	−	8.34051i	0.357926	−	0.619945i	0.987614	+	0.156902i	$0.0501508\pi$
$182$	0.00370692	−	0.00259561i	0.000274775	−	0.000192400i
$183$	−9.47449	−	6.34738i	−0.700374	−	0.469212i
$184$	−3.20550	+	8.80705i	−0.236313	+	0.649264i
$185$		0			0
$186$	3.17758	−	20.4789i	0.232992	−	1.50159i
$187$	−18.3810	+	1.60813i	−1.34415	+	0.117598i
$188$	−1.41056	+	1.41056i	−0.102876	+	0.102876i
$189$	0.00270628	+	0.00199960i	0.000196853	+	0.000145449i
$190$		0			0
$191$	0.797244	−	0.950119i	0.0576866	−	0.0687482i	−0.736430	−	0.676514i	$-0.763490\pi$
$191$	0.797244	−	0.950119i	0.0576866	−	0.0687482i	0.794116	+	0.607766i	$0.207934\pi$
$192$	2.36831	+	21.8714i	0.170918	+	1.57843i
$193$	−10.1567	+	14.5052i	−0.731093	+	1.04411i	0.265698	+	0.964056i	$0.414398\pi$
$193$	−10.1567	+	14.5052i	−0.731093	+	1.04411i	−0.996791	+	0.0800524i	$0.974491\pi$
$194$	17.3883	+	6.32881i	1.24840	+	0.454382i
$195$		0			0
$196$	−3.44506	+	19.5379i	−0.246076	+	1.39557i
$197$	16.4067	−	4.39615i	1.16893	−	0.313213i	0.378401	−	0.925642i	$-0.376474\pi$
$197$	16.4067	−	4.39615i	1.16893	−	0.313213i	0.790526	+	0.612429i	$0.209807\pi$
$198$	−16.4682	−	6.86847i	−1.17034	−	0.488121i
$199$	−9.13371	+	5.27335i	−0.647472	+	0.373818i	−0.787487	−	0.616331i	$-0.788618\pi$
$199$	−9.13371	+	5.27335i	−0.647472	+	0.373818i	0.140015	+	0.990149i	$0.455285\pi$
$200$		0			0
$201$	−3.76510	−	2.07159i	−0.265570	−	0.146118i
$202$	2.20532	−	25.2069i	0.155166	−	1.77355i
$203$	−0.000322495		0.00368613i	−2.26347e−5		0.000258716i
$204$	29.3358	+	16.1408i	2.05392	+	1.13008i
$205$		0			0
$206$	−13.0576	+	7.53880i	−0.909765	+	0.525253i
$207$	−1.96387	−	15.2036i	−0.136498	−	1.05672i
$208$	−5.02181	+	1.34559i	−0.348200	+	0.0932999i
$209$	0.826290	−	4.68612i	0.0571557	−	0.324146i
$210$		0			0
$211$	0.169003	+	0.0615119i	0.0116346	+	0.00423465i	0.347831	−	0.937557i	$-0.386918\pi$
$211$	0.169003	+	0.0615119i	0.0116346	+	0.00423465i	−0.336196	+	0.941792i	$0.609141\pi$
$212$	−13.1912	+	18.8390i	−0.905978	+	1.29387i
$213$	−2.24600	−	20.7419i	−0.153894	−	1.42121i
$214$	−19.3383	+	23.0465i	−1.32194	+	1.57543i
$215$		0			0
$216$	5.26574	+	7.94351i	0.358288	+	0.540488i
$217$	0.00249185	−	0.00249185i	0.000169158	−	0.000169158i
$218$	8.18815	−	0.716371i	0.554572	−	0.0485187i
$219$	0.385205	−	2.48257i	0.0260297	−	0.167757i
$220$		0			0
$221$	−7.41460	+	20.3715i	−0.498760	+	1.37033i
$222$	−0.829970	−	0.556034i	−0.0557039	−	0.0373185i
$223$	15.0996	−	10.5728i	1.01114	−	0.708010i	0.0542728	−	0.998526i	$-0.482716\pi$
$223$	15.0996	−	10.5728i	1.01114	−	0.708010i	0.956870	+	0.290516i	$0.0938271\pi$
$224$	−0.00235221	+	0.00407414i	−0.000157163	+	0.000272215i
$225$		0			0
$226$	1.22863	+	2.12804i	0.0817271	+	0.141555i
$227$	14.1883	+	6.61613i	0.941713	+	0.439128i	0.831963	−	0.554831i	$-0.187217\pi$
$227$	14.1883	+	6.61613i	0.941713	+	0.439128i	0.109750	+	0.993959i	$0.464995\pi$
$228$	−5.97884	+	6.23034i	−0.395958	+	0.412615i
$229$	−4.54463	−	5.41608i	−0.300318	−	0.357904i	0.594690	−	0.803955i	$-0.297275\pi$
$229$	−4.54463	−	5.41608i	−0.300318	−	0.357904i	−0.895008	+	0.446050i	$0.852830\pi$
$230$		0			0
$231$	−0.00157086	−	0.00259584i	−0.000103355	−	0.000170794i
$232$	−4.42910	+	9.49823i	−0.290785	+	0.623590i
$233$	−2.20921	−	0.591957i	−0.144730	−	0.0387804i	0.185726	−	0.982601i	$-0.440536\pi$
$233$	−2.20921	−	0.591957i	−0.144730	−	0.0387804i	−0.330457	+	0.943821i	$0.607203\pi$
$234$	−15.4911	+	14.1256i	−1.01269	+	0.923421i
$235$		0			0
$236$	−6.27313	−	1.10612i	−0.408346	−	0.0720024i
$237$	−3.99637	−	8.12881i	−0.259592	−	0.528023i
$238$	0.00410424	+	0.00880157i	0.000266038	+	0.000570521i
$239$	−1.33675	−	7.58107i	−0.0864670	−	0.490379i	−0.997030	−	0.0770092i	$-0.975463\pi$
$239$	−1.33675	−	7.58107i	−0.0864670	−	0.490379i	0.910563	−	0.413369i	$-0.135648\pi$
$240$		0			0
$241$	−7.35154	−	6.16868i	−0.473555	−	0.397359i	0.374535	−	0.927213i	$-0.377802\pi$
$241$	−7.35154	−	6.16868i	−0.473555	−	0.397359i	−0.848089	+	0.529853i	$0.822247\pi$
$242$	−5.72484	−	5.72484i	−0.368007	−	0.368007i
$243$	−13.6208	−	7.58109i	−0.873777	−	0.486327i
$244$		−	18.6609i		−	1.19464i
$245$		0			0
$246$	16.1846	+	41.7694i	1.03189	+	2.66312i
$247$	−4.57972	−	3.20676i	−0.291401	−	0.204041i
$248$	9.04592	−	4.21818i	0.574416	−	0.267855i
$249$	8.94915	−	26.2581i	0.567129	−	1.66404i
$250$		0			0
$251$	−4.10987	−	2.37283i	−0.259413	−	0.149772i	0.364654	−	0.931143i	$-0.381187\pi$
$251$	−4.10987	−	2.37283i	−0.259413	−	0.149772i	−0.624067	+	0.781371i	$0.714521\pi$
$252$	−0.000253588		0.00550016i	−1.59745e−5		0.000346478i
$253$	−3.57769	+	13.3521i	−0.224927	+	0.839440i
$254$	−21.5852	+	7.85635i	−1.35437	+	0.492951i
$255$		0			0
$256$	−3.10423	+	2.60476i	−0.194015	+	0.162798i
$257$	12.0332	+	1.05277i	0.750612	+	0.0656701i	0.456040	−	0.889959i	$-0.349267\pi$
$257$	12.0332	+	1.05277i	0.750612	+	0.0656701i	0.294572	+	0.955629i	$0.404823\pi$
$258$	23.9014	+	22.9366i	1.48804	+	1.42797i
$259$	−5.81013e−5	0	0.000159632i	−3.61024e−6	0	9.91906e-6i
$260$		0			0
$261$	−0.705942	−	17.1275i	−0.0436967	−	1.06016i
$262$	8.28485	+	30.9195i	0.511840	+	1.91021i
$263$	4.91225	+	7.01542i	0.302902	+	0.432589i	0.941531	−	0.336926i	$-0.109387\pi$
$263$	4.91225	+	7.01542i	0.302902	+	0.432589i	−0.638629	+	0.769515i	$0.720498\pi$
$264$	−1.66625	−	8.43052i	−0.102550	−	0.518863i
$265$		0			0
$266$	−0.00246646		0.000434903i	−0.000151228		2.66656e-5i
$267$	−6.12310	−	8.37225i	−0.374728	−	0.512374i
$268$	−0.612870	−	7.00513i	−0.0374370	−	0.427907i
$269$	17.3406			1.05728			0.528638	−	0.848847i	$-0.322703\pi$
$269$	17.3406			1.05728			0.528638	+	0.848847i	$0.322703\pi$
$270$		0			0
$271$	−11.8573			−0.720278			−0.360139	−	0.932899i	$-0.617271\pi$
$271$	−11.8573			−0.720278			−0.360139	+	0.932899i	$0.617271\pi$
$272$	−0.972407	−	11.1147i	−0.0589609	−	0.673926i
$273$	−0.00354418		0.000383777i	−0.000214504		2.32272e-5i
$274$	−15.8320	+	2.79161i	−0.956446	+	0.168647i
$275$		0			0
$276$	18.8798	−	16.5164i	1.13643	−	0.994172i
$277$	−11.4745	−	16.3872i	−0.689433	−	0.984613i	−0.999426	−	0.0338740i	$-0.989216\pi$
$277$	−11.4745	−	16.3872i	−0.689433	−	0.984613i	0.309993	−	0.950739i	$-0.399673\pi$
$278$	1.73690	+	6.48220i	0.104172	+	0.388776i
$279$	−9.97002	+	12.9278i	−0.596889	+	0.773964i
$280$		0			0
$281$	−2.66069	−	7.31019i	−0.158724	−	0.436089i	0.834683	−	0.550730i	$-0.185651\pi$
$281$	−2.66069	−	7.31019i	−0.158724	−	0.436089i	−0.993407	+	0.114641i	$0.963428\pi$
$282$	2.57424	−	0.746917i	0.153294	−	0.0444783i
$283$	−14.9700	−	1.30970i	−0.889873	−	0.0778538i	−0.366957	−	0.930238i	$-0.619600\pi$
$283$	−14.9700	−	1.30970i	−0.889873	−	0.0778538i	−0.522916	+	0.852384i	$0.675156\pi$
$284$	26.1518	−	21.9440i	1.55182	−	1.30213i
$285$		0			0
$286$	17.7638	−	6.46550i	1.05040	−	0.382313i
$287$	−0.00197148	+	0.00735767i	−0.000116373	+	0.000434310i
$288$	8.38936	−	20.1148i	0.494348	−	1.18527i
$289$	−25.5680	−	14.7617i	−1.50400	−	0.868336i
$290$		0			0
$291$	−9.59793	−	10.9713i	−0.562641	−	0.643150i
$292$	3.72573	−	1.73734i	0.218032	−	0.101670i
$293$	−18.4726	−	12.9347i	−1.07918	−	0.755651i	−0.108038	−	0.994147i	$-0.534457\pi$
$293$	−18.4726	−	12.9347i	−1.07918	−	0.755651i	−0.971144	+	0.238495i	$0.923346\pi$
$294$	16.7109	−	20.7695i	0.974602	−	1.21130i
$295$		0			0
$296$		−	0.481143i		−	0.0279659i
$297$	8.75797	+	10.9944i	0.508189	+	0.637959i
$298$	−15.7597	−	15.7597i	−0.912936	−	0.912936i
$299$	12.4415	+	10.4396i	0.719510	+	0.603740i
$300$		0			0
$301$	0.000978160		0.00554742i	5.63802e−5		0.000319748i
$302$	−17.2827	−	37.0629i	−0.994510	−	2.13273i
$303$	−11.0944	+	16.5602i	−0.637358	+	0.951360i
$304$	2.83362	+	0.499644i	0.162519	+	0.0286566i
$305$		0			0
$306$	−24.0806	−	38.0033i	−1.37660	−	2.17250i
$307$	−4.88220	−	1.30818i	−0.278642	−	0.0746619i	0.116792	−	0.993156i	$-0.462739\pi$
$307$	−4.88220	−	1.30818i	−0.278642	−	0.0746619i	−0.395434	+	0.918495i	$0.629406\pi$
$308$	0.00209822	−	0.00449965i	0.000119557	−	0.000256392i
$309$	11.8751	−	0.244625i	0.675553	−	0.0139162i
$310$		0			0
$311$	12.6744	+	15.1048i	0.718699	+	0.856512i	0.994504	−	0.104702i	$-0.0333888\pi$
$311$	12.6744	+	15.1048i	0.718699	+	0.856512i	−0.275805	+	0.961214i	$0.588944\pi$
$312$	−9.80460	−	2.41185i	−0.555076	−	0.136544i
$313$	24.5912	+	11.4671i	1.38998	+	0.648157i	0.966244	−	0.257629i	$-0.0829413\pi$
$313$	24.5912	+	11.4671i	1.38998	+	0.648157i	0.423734	+	0.905787i	$0.360719\pi$
$314$	−0.355652	−	0.616007i	−0.0200706	−	0.0347633i
$315$		0			0
$316$	7.41094	−	12.8361i	0.416898	−	0.722089i
$317$	−0.204479	+	0.143177i	−0.0114847	+	0.00804165i	−0.579305	−	0.815111i	$-0.696676\pi$
$317$	−0.204479	+	0.143177i	−0.0114847	+	0.00804165i	0.567820	+	0.823153i	$0.307787\pi$
$318$	27.7319	−	13.6338i	1.55513	−	0.764547i
$319$	−5.28664	+	14.5249i	−0.295995	+	0.813240i
$320$		0			0
$321$	22.0991	−	8.56286i	1.23345	−	0.477932i
$322$	0.00724787		0.000634107i	0.000403908		3.53374e-5i
$323$	8.48389	−	8.48389i	0.472056	−	0.472056i
$324$	−2.09913	−	25.4212i	−0.116619	−	1.41229i
$325$		0			0
$326$	7.72680	−	9.20844i	0.427948	−	0.510009i
$327$	−5.92347	−	2.61502i	−0.327569	−	0.144611i
$328$	−12.3745	+	17.6726i	−0.683268	+	0.975808i
$329$	0.000428303	0	0.000155890i	2.36131e−5	0	8.59448e-6i
$330$		0			0
$331$	0.820786	−	4.65491i	0.0451145	−	0.255857i	−0.953906	−	0.300105i	$-0.902978\pi$
$331$	0.820786	−	4.65491i	0.0451145	−	0.255857i	0.999021	+	0.0442484i	$0.0140893\pi$
$332$	43.8467	−	11.7487i	2.40640	−	0.644794i
$333$	0.361687	+	0.698953i	0.0198203	+	0.0383024i
$334$	35.0635	−	20.2439i	1.91859	−	1.10770i
$335$		0			0
$336$	0.00156966		0.000949876i	8.56320e−5		5.18200e-5i
$337$	−0.943046	+	10.7791i	−0.0513710	+	0.587173i	0.926266	+	0.376872i	$0.123000\pi$
$337$	−0.943046	+	10.7791i	−0.0513710	+	0.587173i	−0.977637	+	0.210302i	$0.932555\pi$
$338$	−0.555366	+	6.34786i	−0.0302079	+	0.345278i
$339$	−0.0398674	−	1.93534i	−0.00216530	−	0.105113i
$340$		0			0
$341$	12.7488	−	7.36051i	0.690385	−	0.398594i
$342$	11.0741	−	3.46198i	0.598820	−	0.187202i
$343$	0.00875706	−	0.00234645i	0.000472837	−	0.000126696i
$344$	−2.77045	+	15.7120i	−0.149373	+	0.847134i
$345$		0			0
$346$	6.15274	+	2.23942i	0.330774	+	0.120392i
$347$	−13.7981	+	19.7058i	−0.740723	+	1.05786i	0.255132	+	0.966906i	$0.417881\pi$
$347$	−13.7981	+	19.7058i	−0.740723	+	1.05786i	−0.995855	+	0.0909561i	$0.971008\pi$
$348$	22.6408	−	16.5585i	1.21368	−	0.887630i
$349$	−0.752338	+	0.896601i	−0.0402717	+	0.0479940i	−0.785804	−	0.618475i	$-0.787751\pi$
$349$	−0.752338	+	0.896601i	−0.0402717	+	0.0479940i	0.745533	+	0.666469i	$0.232195\pi$
$350$		0			0
$351$	16.0561	−	3.86669i	0.857012	−	0.206388i
$352$	−13.8961	+	13.8961i	−0.740662	+	0.740662i
$353$	20.1919	−	1.76656i	1.07470	−	0.0940245i	0.463963	−	0.885855i	$-0.346427\pi$
$353$	20.1919	−	1.76656i	1.07470	−	0.0940245i	0.610741	+	0.791830i	$0.290871\pi$
$354$	6.66854	+	5.36546i	0.354429	+	0.285171i
$355$		0			0
$356$	5.80497	−	15.9490i	0.307663	−	0.845296i
$357$	0.000509670	−	0.00763339i	2.69746e−5	−	0.000404002i
$358$	−29.7622	+	20.8397i	−1.57298	+	1.10141i
$359$	13.1082	−	22.7040i	0.691823	−	1.19827i	−0.279418	−	0.960170i	$-0.590141\pi$
$359$	13.1082	−	22.7040i	0.691823	−	1.19827i	0.971240	−	0.238102i	$-0.0765253\pi$
$360$		0			0
$361$	−7.95290	−	13.7748i	−0.418574	−	0.724991i
$362$	−19.1911	−	8.94895i	−1.00866	−	0.470347i
$363$	1.77725	+	6.12527i	0.0932814	+	0.321493i
$364$	−0.00374959	−	0.00446858i	−0.000196532	−	0.000234217i
$365$		0			0
$366$	−12.0872	+	21.9684i	−0.631807	+	1.14831i
$367$	8.86817	−	19.0178i	0.462914	−	0.992723i	−0.526843	−	0.849963i	$-0.676624\pi$
$367$	8.86817	−	19.0178i	0.462914	−	0.992723i	0.989757	−	0.142761i	$-0.0455979\pi$
$368$	−8.07380	−	2.16337i	−0.420876	−	0.112773i
$369$	4.69139	−	34.9751i	0.244224	−	1.82073i
$370$		0			0
$371$	0.00517492		0.000912477i	0.000268668		4.73735e-5i
$372$	−26.6547	−	1.77970i	−1.38198	−	0.0922730i
$373$	0.710169	+	1.52296i	0.0367712	+	0.0788560i	0.923835	−	0.382790i	$-0.125037\pi$
$373$	0.710169	+	1.52296i	0.0367712	+	0.0788560i	−0.887064	+	0.461646i	$0.847259\pi$
$374$	7.04459	+	39.9519i	0.364267	+	2.06586i
$375$		0			0
$376$	0.988917	+	0.829800i	0.0509995	+	0.0427937i
$377$	12.8418	+	12.8418i	0.661386	+	0.661386i
$378$	0.00386115	−	0.00631078i	0.000198596	−	0.000324592i
$379$			11.6637i			0.599126i	0.954077	+	0.299563i	$0.0968408\pi$
$379$			11.6637i			0.599126i	−0.954077	+	0.299563i	$0.903159\pi$
$380$		0			0
$381$	17.8814	+	2.77455i	0.916093	+	0.142144i
$382$	−2.23383	−	1.56415i	−0.114293	−	0.0800286i
$383$	−9.54105	+	4.44907i	−0.487525	+	0.227337i	−0.650808	−	0.759243i	$-0.725570\pi$
$383$	−9.54105	+	4.44907i	−0.487525	+	0.227337i	0.163283	+	0.986579i	$0.447792\pi$
$384$	22.7633	−	4.49904i	1.16163	−	0.229591i
$385$		0			0
$386$	33.7173	+	19.4667i	1.71616	+	0.990828i
$387$	−7.78649	−	24.9073i	−0.395809	−	1.26611i
$388$	6.17353	−	23.0399i	0.313414	−	1.16968i
$389$	−36.8621	+	13.4167i	−1.86898	+	0.680254i	−0.898557	+	0.438858i	$0.855383\pi$
$389$	−36.8621	+	13.4167i	−1.86898	+	0.680254i	−0.970427	+	0.241396i	$0.922395\pi$
$390$		0			0
$391$	−26.6998	+	22.4038i	−1.35027	+	1.13301i
$392$	12.7900	+	1.11898i	0.645990	+	0.0565168i
$393$	6.02351	−	24.4866i	0.303846	−	1.23519i
$394$	−12.7729	−	35.0933i	−0.643491	−	1.76798i
$395$		0			0
$396$	−6.96989	+	21.9191i	−0.350250	+	1.10147i
$397$	−2.69699	−	10.0653i	−0.135358	−	0.505162i	−0.999996	−	0.00276748i	$-0.999119\pi$
$397$	−2.69699	−	10.0653i	−0.135358	−	0.505162i	0.864638	−	0.502395i	$-0.167548\pi$
$398$	13.3006	+	18.9952i	0.666697	+	0.952141i
$399$	0.00186749		0.000636470i	9.34916e−5		3.18634e-5i
$400$		0			0
$401$	26.3401	−	4.64448i	1.31536	−	0.231934i	0.528433	−	0.848975i	$-0.322780\pi$
$401$	26.3401	−	4.64448i	1.31536	−	0.231934i	0.786931	+	0.617041i	$0.211669\pi$
$402$	−3.81592	+	8.64373i	−0.190321	+	0.431110i
$403$	−1.50746	−	17.2304i	−0.0750921	−	0.858306i
$404$	−32.6169			−1.62275
$405$		0			0
$406$	0.00813559			0.000403762
$407$	−0.0618489	−	0.706936i	−0.00306574	−	0.0350415i
$408$	8.75099	−	19.8225i	0.433239	−	0.981361i
$409$	33.6400	−	5.93165i	1.66339	−	0.293301i	0.738705	−	0.674028i	$-0.235438\pi$
$409$	33.6400	−	5.93165i	1.66339	−	0.293301i	0.924687	+	0.380727i	$0.124326\pi$
$410$		0			0
$411$	11.9873	+	4.08545i	0.591289	+	0.201520i
$412$	11.1478	+	15.9208i	0.549214	+	0.784359i
$413$	0.000376692		0.00140583i	1.85358e−5		6.91766e-5i
$414$	−32.9243	+	7.21491i	−1.61814	+	0.354594i
$415$		0			0
$416$	7.89716	+	21.6973i	0.387190	+	1.06380i
$417$	1.26282	−	5.13357i	0.0618403	−	0.251392i
$418$	−10.4224	−	0.911843i	−0.509777	−	0.0445997i
$419$	−12.2431	+	10.2731i	−0.598112	+	0.501876i	−0.890838	−	0.454321i	$-0.849882\pi$
$419$	−12.2431	+	10.2731i	−0.598112	+	0.501876i	0.292726	+	0.956196i	$0.405438\pi$
$420$		0			0
$421$	29.9345	−	10.8953i	1.45892	−	0.531002i	0.513850	−	0.857880i	$-0.328219\pi$
$421$	29.9345	−	10.8953i	1.45892	−	0.531002i	0.945067	+	0.326878i	$0.105997\pi$
$422$	0.102345	−	0.381956i	0.00498206	−	0.0185933i
$423$	−2.06037	−	0.462050i	−0.100179	−	0.0224656i
$424$	12.8891	+	7.44152i	0.625950	+	0.361392i
$425$		0			0
$426$	−45.0008	+	8.89416i	−2.18030	+	0.430924i
$427$	−0.00386425	+	0.00180193i	−0.000187004	+	8.72015e-5i
$428$	31.7675	+	22.2438i	1.53554	+	1.07520i
$429$	−14.7158	−	2.28335i	−0.710484	−	0.110241i
$430$		0			0
$431$		−	5.93676i		−	0.285963i	−0.989725	−	0.142982i	$-0.954331\pi$
$431$		−	5.93676i		−	0.285963i	0.989725	−	0.142982i	$-0.0456690\pi$
$432$	−6.64813	+	5.29580i	−0.319858	+	0.254794i
$433$	7.73933	+	7.73933i	0.371929	+	0.371929i	0.868179	−	0.496251i	$-0.165290\pi$
$433$	7.73933	+	7.73933i	0.371929	+	0.371929i	−0.496251	+	0.868179i	$0.665290\pi$
$434$	−0.00593543	−	0.00498042i	−0.000284910	−	0.000239068i
$435$		0			0
$436$	−1.83984	−	10.4342i	−0.0881122	−	0.499709i
$437$	−3.79875	−	8.14644i	−0.181719	−	0.389697i
$438$	−5.51142	−	0.367990i	−0.263346	−	0.0175832i
$439$	28.6483	+	5.05146i	1.36731	+	0.241093i	0.808642	−	0.588300i	$-0.200203\pi$
$439$	28.6483	+	5.05146i	1.36731	+	0.241093i	0.558665	+	0.829394i	$0.311314\pi$
$440$		0			0
$441$	−19.4210	+	7.98900i	−0.924810	+	0.380428i
$442$	46.0407	+	12.3366i	2.18993	+	0.586791i
$443$	11.4725	−	24.6030i	0.545077	−	1.16892i	−0.420137	−	0.907461i	$-0.638018\pi$
$443$	11.4725	−	24.6030i	0.545077	−	1.16892i	0.965214	−	0.261461i	$-0.0842043\pi$
$444$	−0.620778	+	1.12826i	−0.0294608	+	0.0535450i
$445$		0			0
$446$	−26.0513	−	31.0468i	−1.23357	−	1.47011i
$447$	4.89253	+	16.8620i	0.231409	+	0.797547i
$448$	0.00745435	+	0.00347602i	0.000352185	+	0.000164227i
$449$	1.73698	+	3.00854i	0.0819733	+	0.141982i	0.904097	−	0.427326i	$-0.140544\pi$
$449$	1.73698	+	3.00854i	0.0819733	+	0.141982i	−0.822124	+	0.569308i	$0.807211\pi$
$450$		0			0
$451$	−15.9099	+	27.5568i	−0.749169	+	1.29760i
$452$	2.59467	−	1.81681i	0.122043	−	0.0854554i
$453$	−2.14620	+	32.1438i	−0.100837	+	1.51025i
$454$	11.7725	−	32.3447i	0.552511	−	1.51801i
$455$		0			0
$456$	4.35378	+	3.50301i	0.203884	+	0.164044i
$457$	23.5029	−	2.05624i	1.09942	−	0.0961868i	0.477025	−	0.878890i	$-0.341715\pi$
$457$	23.5029	−	2.05624i	1.09942	−	0.0961868i	0.622395	+	0.782703i	$0.286160\pi$
$458$	−10.9920	+	10.9920i	−0.513624	+	0.513624i
$459$	2.18858	+	35.3743i	0.102154	+	1.65113i
$460$		0			0
$461$	5.14645	−	6.13330i	0.239694	−	0.285656i	−0.632765	−	0.774344i	$-0.718080\pi$
$461$	5.14645	−	6.13330i	0.239694	−	0.285656i	0.872459	+	0.488688i	$0.162524\pi$
$462$	−0.00538467	+	0.00393812i	−0.000250518	+	0.000183218i
$463$	1.35473	−	1.93475i	0.0629594	−	0.0899154i	−0.786438	−	0.617670i	$-0.788077\pi$
$463$	1.35473	−	1.93475i	0.0629594	−	0.0899154i	0.849397	+	0.527754i	$0.176966\pi$
$464$	−8.78299	−	3.19675i	−0.407740	−	0.148405i
$465$		0			0
$466$	−0.873225	+	4.95230i	−0.0404514	+	0.229411i
$467$	−19.8687	+	5.32380i	−0.919414	+	0.246356i	−0.687335	−	0.726341i	$-0.741220\pi$
$467$	−19.8687	+	5.32380i	−0.919414	+	0.246356i	−0.232079	+	0.972697i	$0.574553\pi$
$468$	19.8796	+	18.3057i	0.918936	+	0.846183i
$469$	−0.00139143		0.000803341i	−6.42501e−5		3.70948e-5i
$470$		0			0
$471$	0.0115405	+	0.560224i	0.000531757	+	0.0258138i
$472$	−0.359274	+	4.10653i	−0.0165369	+	0.189018i
$473$	−2.05087	+	23.4415i	−0.0942989	+	1.07784i
$474$	−17.0388	+	10.3110i	−0.782619	+	0.473600i
$475$		0			0
$476$	0.0108413	−	0.00625924i	0.000496911	−	0.000286892i
$477$	−24.3179	−	1.12119i	−1.11344	−	0.0513356i
$478$	−16.3488	+	4.38064i	−0.747775	+	0.200366i
$479$	−3.74161	+	21.2197i	−0.170958	+	0.969553i	0.771748	+	0.635929i	$0.219383\pi$
$479$	−3.74161	+	21.2197i	−0.170958	+	0.969553i	−0.942706	+	0.333624i	$0.891728\pi$
$480$		0			0
$481$	−0.783491	−	0.285167i	−0.0357241	−	0.0130025i
$482$	−12.1026	+	17.2843i	−0.551257	+	0.787277i
$483$	−0.00524325	−	0.00231472i	−0.000238576	−	0.000105324i
$484$	−6.70831	+	7.99465i	−0.304923	+	0.363393i
$485$		0			0
$486$	−13.9948	+	31.2866i	−0.634818	+	1.41919i
$487$	−2.20133	+	2.20133i	−0.0997518	+	0.0997518i	−0.755221	−	0.655470i	$-0.772471\pi$
$487$	−2.20133	+	2.20133i	−0.0997518	+	0.0997518i	0.655470	+	0.755221i	$0.272471\pi$
$488$	−12.0302	+	1.05251i	−0.544583	+	0.0476449i
$489$	−8.82991	+	3.42137i	−0.399302	+	0.154720i
$490$		0			0
$491$	−2.81965	+	7.74693i	−0.127249	+	0.349614i	−0.986915	−	0.161243i	$-0.948450\pi$
$491$	−2.81965	+	7.74693i	−0.127249	+	0.349614i	0.859666	+	0.510857i	$0.170672\pi$
$492$	51.8193	−	25.4759i	2.33619	−	1.14854i
$493$	−31.9257	+	22.3546i	−1.43786	+	1.00680i
$494$	−6.14620	+	10.6455i	−0.276530	+	0.478965i
$495$		0			0
$496$	4.45078	+	7.70898i	0.199846	+	0.346144i
$497$	−0.00706937	−	0.00329650i	−0.000317105	−	0.000147868i
$498$	−59.2283	−	14.5697i	−2.65408	−	0.652882i
$499$	−16.9583	−	20.2101i	−0.759156	−	0.904727i	0.238638	−	0.971109i	$-0.423299\pi$
$499$	−16.9583	−	20.2101i	−0.759156	−	0.904727i	−0.997794	+	0.0663815i	$0.978855\pi$
$500$		0			0
$501$	−31.8883	+	0.656890i	−1.42466	+	0.0293477i
$502$	−4.40968	+	9.45659i	−0.196814	+	0.422068i
$503$	−7.51109	−	2.01259i	−0.334903	−	0.0897370i	0.0874487	−	0.996169i	$-0.472129\pi$
$503$	−7.51109	−	2.01259i	−0.334903	−	0.0897370i	−0.422352	+	0.906432i	$0.638795\pi$
$504$	0.00356013		0.000146738i	0.000158581		6.53622e-6i
$505$		0			0
$506$	29.9309	+	5.27762i	1.33059	+	0.234619i
$507$	2.79391	−	4.17036i	0.124082	−	0.185212i
$508$	12.5137	+	26.8357i	0.555204	+	1.19064i
$509$	5.25087	+	29.7791i	0.232741	+	1.31994i	0.847320	+	0.531082i	$0.178215\pi$
$509$	5.25087	+	29.7791i	0.232741	+	1.31994i	−0.614580	+	0.788855i	$0.710674\pi$
$510$		0			0
$511$	−0.000719528	0	0.000603755i	−3.18300e−5	0	2.67086e-5i
$512$	−12.6456	−	12.6456i	−0.558861	−	0.558861i
$513$	−8.95800	−	1.81596i	−0.395505	−	0.0801765i
$514$		−	26.5583i		−	1.17144i
$515$		0			0
$516$	26.7684	−	33.2696i	1.17842	−	1.46461i
$517$	1.55967	+	1.09209i	0.0685940	+	0.0480300i
$518$	−0.000338510	0	0.000157850i	−1.48733e−5	0	6.93553e-6i
$519$	−3.39618	−	3.88214i	−0.149076	−	0.170407i
$520$		0			0
$521$	2.44020	+	1.40885i	0.106907	+	0.0617227i	0.552500	−	0.833513i	$-0.313674\pi$
$521$	2.44020	+	1.40885i	0.106907	+	0.0617227i	−0.445593	+	0.895236i	$0.647007\pi$
$522$	−37.3792	+	4.82833i	−1.63604	+	0.211330i
$523$	3.41584	−	12.7481i	0.149364	−	0.557436i	−0.850158	−	0.526528i	$-0.823494\pi$
$523$	3.41584	−	12.7481i	0.149364	−	0.557436i	0.999522	−	0.0309077i	$-0.00983981\pi$
$524$	38.7741	−	14.1126i	1.69385	−	0.616512i
$525$		0			0
$526$	14.4246	−	12.1037i	0.628944	−	0.527747i
$527$	36.9769	+	3.23506i	1.61074	+	0.140921i
$528$	7.36059	−	2.13568i	0.320329	−	0.0929435i
$529$	1.06428	+	2.92409i	0.0462731	+	0.127134i
$530$		0			0
$531$	−2.56506	−	6.23559i	−0.111314	−	0.270602i
$532$	0.000835576		0.00311841i	3.62268e−5		0.000135200i
$533$	21.4438	+	30.6249i	0.928834	+	1.32651i
$534$	−17.1645	+	15.0159i	−0.742780	+	0.649800i
$535$		0			0
$536$	−4.48148	+	0.790206i	−0.193570	+	0.0341317i
$537$	28.4556	−	3.08127i	1.22795	−	0.132967i
$538$	−3.32294	−	37.9814i	−0.143262	−	1.63749i
$539$	18.9359			0.815627
$540$		0			0
$541$	−11.4416			−0.491911			−0.245956	−	0.969281i	$-0.579102\pi$
$541$	−11.4416			−0.491911			−0.245956	+	0.969281i	$0.579102\pi$
$542$	2.27218	+	25.9711i	0.0975985	+	1.11556i
$543$	9.84723	+	13.4643i	0.422585	+	0.577810i
$544$	−48.7984	+	8.60448i	−2.09222	+	0.368914i
$545$		0			0
$546$	0.00151975	+	0.00768933i	6.50395e−5	+	0.000329073i
$547$	18.3834	+	26.2542i	0.786018	+	1.12255i	0.989650	+	0.143503i	$0.0458367\pi$
$547$	18.3834	+	26.2542i	0.786018	+	1.12255i	−0.203632	+	0.979048i	$0.565274\pi$
$548$	5.36349	+	20.0168i	0.229117	+	0.855076i
$549$	16.6850	−	10.5724i	0.712099	−	0.451219i
$550$		0			0
$551$	−3.43769	−	9.44496i	−0.146450	−	0.402369i
$552$	−11.7126	−	11.2398i	−0.498522	−	0.478398i
$553$	−0.00337369		0.000295160i	−0.000143464		1.25515e-5i
$554$	−33.6943	+	28.2729i	−1.43153	+	1.20120i
$555$		0			0
$556$	8.12889	−	2.95868i	0.344742	−	0.125476i
$557$	7.68893	−	28.6955i	0.325791	−	1.21587i	−0.587724	−	0.809061i	$-0.699976\pi$
$557$	7.68893	−	28.6955i	0.325791	−	1.21587i	0.913515	−	0.406806i	$-0.133357\pi$
$558$	30.2263	+	19.3601i	1.27958	+	0.819580i
$559$	23.9433	+	13.8237i	1.01269	+	0.584679i
$560$		0			0
$561$	10.3096	−	30.2498i	0.435271	−	1.27715i
$562$	−15.5017	+	7.22858i	−0.653902	+	0.304919i
$563$	−4.91264	−	3.43987i	−0.207043	−	0.144973i	0.465456	−	0.885071i	$-0.345890\pi$
$563$	−4.91264	−	3.43987i	−0.207043	−	0.144973i	−0.672499	+	0.740098i	$0.734779\pi$
$564$	−1.24835	−	3.22176i	−0.0525652	−	0.135661i
$565$		0			0
$566$			33.0399i			1.38877i
$567$	−0.00506147	+	0.00288940i	−0.000212562	+	0.000121344i
$568$	−15.6218	−	15.6218i	−0.655475	−	0.655475i
$569$	8.00903	+	6.72037i	0.335756	+	0.281733i	0.795040	−	0.606557i	$-0.207450\pi$
$569$	8.00903	+	6.72037i	0.335756	+	0.281733i	−0.459284	+	0.888289i	$0.651894\pi$
$570$		0			0
$571$	−1.98699	−	11.2688i	−0.0831531	−	0.471584i	−0.997740	−	0.0671948i	$-0.978595\pi$
$571$	−1.98699	−	11.2688i	−0.0831531	−	0.471584i	0.914587	−	0.404390i	$-0.132516\pi$
$572$	−10.2983	−	22.0848i	−0.430594	−	0.923411i
$573$	0.947795	+	1.92786i	0.0395947	+	0.0805376i
$574$	0.0164934	+	0.00290823i	0.000688421	+	0.000121387i
$575$		0			0
$576$	−36.3122	−	11.5467i	−1.51301	−	0.481111i
$577$	44.1170	+	11.8211i	1.83662	+	0.492120i	0.998569	−	0.0534774i	$-0.0170305\pi$
$577$	44.1170	+	11.8211i	1.83662	+	0.492120i	0.838047	+	0.545597i	$0.183697\pi$
$578$	−27.4332	+	58.8308i	−1.14107	+	2.44704i
$579$	−15.8790	−	26.2399i	−0.659910	−	1.09049i
$580$		0			0
$581$	−0.00666682	−	0.00794521i	−0.000276586	−	0.000329623i
$582$	−22.1914	+	23.1249i	−0.919862	+	0.958557i
$583$	19.8943	+	9.27687i	0.823938	+	0.384209i
$584$	−1.33016	−	2.30390i	−0.0550424	−	0.0953362i
$585$		0			0
$586$	−24.7911	+	42.9394i	−1.02411	+	1.77381i
$587$	−22.7446	+	15.9259i	−0.938770	+	0.657334i	−0.939457	−	0.342666i	$-0.888670\pi$
$587$	−22.7446	+	15.9259i	−0.938770	+	0.657334i	0.000687603		1.00000i	$0.499781\pi$
$588$	−28.5483	−	19.1257i	−1.17731	−	0.788732i
$589$	−3.27398	+	8.99519i	−0.134902	+	0.370640i
$590$		0			0
$591$	−4.51088	+	29.0718i	−0.185553	+	1.19585i
$592$	0.427473	−	0.0373990i	0.0175690	−	0.00153709i
$593$	12.5526	−	12.5526i	0.515474	−	0.515474i	−0.400725	−	0.916199i	$-0.631242\pi$
$593$	12.5526	−	12.5526i	0.515474	−	0.515474i	0.916199	+	0.400725i	$0.131242\pi$
$594$	22.4029	−	21.2895i	0.919201	−	0.873519i
$595$		0			0
$596$	−18.4671	+	22.0082i	−0.756441	+	0.901491i
$597$	−1.96657	−	18.1613i	−0.0804862	−	0.743291i
$598$	20.4820	−	29.2513i	0.837570	−	1.19617i
$599$	−9.47392	−	3.44823i	−0.387094	−	0.140891i	0.141140	−	0.989990i	$-0.454923\pi$
$599$	−9.47392	−	3.44823i	−0.387094	−	0.140891i	−0.528234	+	0.849099i	$0.677146\pi$
$600$		0			0
$601$	−0.977209	+	5.54203i	−0.0398612	+	0.226064i	−0.998230	−	0.0594686i	$-0.981059\pi$
$601$	−0.977209	+	5.54203i	−0.0398612	+	0.226064i	0.958369	+	0.285533i	$0.0921705\pi$
$602$	0.0119631	−	0.00320552i	0.000487581	−	0.000130647i
$603$	5.91619	−	4.51676i	0.240926	−	0.183937i
$604$	−45.6522	+	26.3573i	−1.85756	+	1.07246i
$605$		0			0
$606$	38.3980	+	21.1269i	1.55981	+	0.858220i
$607$	−1.06222	+	12.1412i	−0.0431140	+	0.492796i	0.943685	+	0.330846i	$0.107334\pi$
$607$	−1.06222	+	12.1412i	−0.0431140	+	0.492796i	−0.986799	+	0.161950i	$0.948222\pi$
$608$	1.11375	−	12.7303i	0.0451686	−	0.516280i
$609$	−0.00561514	−	0.00308949i	−0.000227537	−	0.000125192i
$610$		0			0
$611$	1.93736	−	1.11853i	0.0783771	−	0.0452511i
$612$	−46.0960	+	35.1924i	−1.86332	+	1.42257i
$613$	21.2470	−	5.69311i	0.858157	−	0.229942i	0.197197	−	0.980364i	$-0.436816\pi$
$613$	21.2470	−	5.69311i	0.858157	−	0.229942i	0.660960	+	0.750422i	$0.270149\pi$
$614$	−1.92976	+	10.9442i	−0.0778789	+	0.441673i
$615$		0			0
$616$	−0.00301917	−	0.00109889i	−0.000121646	−	4.42754e-5i
$617$	4.11472	−	5.87642i	0.165652	−	0.236576i	−0.727740	−	0.685853i	$-0.759429\pi$
$617$	4.11472	−	5.87642i	0.165652	−	0.236576i	0.893393	+	0.449277i	$0.148318\pi$
$618$	−2.81141	−	25.9634i	−0.113091	−	1.04440i
$619$	0.611202	−	0.728403i	0.0245663	−	0.0292770i	−0.753621	−	0.657309i	$-0.771695\pi$
$619$	0.611202	−	0.728403i	0.0245663	−	0.0292770i	0.778188	+	0.628032i	$0.216139\pi$
$620$		0			0
$621$	25.4640	+	7.52330i	1.02184	+	0.301900i
$622$	30.6554	−	30.6554i	1.22917	−	1.22917i
$623$	−0.00386323		0.000337988i	−0.000154777		1.35412e-5i
$624$	1.38071	−	8.89839i	0.0552725	−	0.356221i
$625$		0			0
$626$	20.4041	−	56.0599i	0.815513	−	2.24060i
$627$	6.84723	+	4.58726i	0.273452	+	0.183198i
$628$	−0.751081	+	0.525913i	−0.0299714	+	0.0209862i
$629$	0.894651	−	1.54958i	0.0356721	−	0.0617859i
$630$		0			0
$631$	−19.0880	−	33.0615i	−0.759883	−	1.31616i	−0.942910	−	0.333048i	$-0.891923\pi$
$631$	−19.0880	−	33.0615i	−0.759883	−	1.31616i	0.183027	−	0.983108i	$-0.441411\pi$
$632$	−8.69315	−	4.05368i	−0.345795	−	0.161247i
$633$	−0.215686	+	0.224759i	−0.00857273	+	0.00893335i
$634$	0.352787	+	0.420435i	0.0140110	+	0.0166976i
$635$		0			0
$636$	−20.6233	−	34.0798i	−0.817767	−	1.35135i
$637$	9.40257	−	20.1639i	0.372543	−	0.798922i
$638$	32.8272	+	8.79602i	1.29964	+	0.348238i
$639$	34.4369	+	10.9503i	1.36230	+	0.433189i
$640$		0			0
$641$	−24.5606	−	4.33069i	−0.970084	−	0.171052i	−0.333916	−	0.942603i	$-0.608370\pi$
$641$	−24.5606	−	4.33069i	−0.970084	−	0.171052i	−0.636168	+	0.771551i	$0.719481\pi$
$642$	−22.9901	−	46.7631i	−0.907348	−	1.84559i
$643$	−18.7461	−	40.2010i	−0.739272	−	1.58537i	−0.809000	−	0.587808i	$-0.799991\pi$
$643$	−18.7461	−	40.2010i	−0.739272	−	1.58537i	0.0697279	−	0.997566i	$-0.477787\pi$
$644$	−0.00162856	−	0.00923602i	−6.41742e−5	−	0.000363950i
$645$		0			0
$646$	−20.2081	−	16.9566i	−0.795078	−	0.667149i
$647$	4.55768	+	4.55768i	0.179181	+	0.179181i	0.790999	−	0.611818i	$-0.209561\pi$
$647$	4.55768	+	4.55768i	0.179181	+	0.179181i	−0.611818	+	0.790999i	$0.709561\pi$
$648$	−16.2701	+	2.78707i	−0.639148	+	0.109486i
$649$			6.07983i			0.238654i
$650$		0			0
$651$	0.00220529	+	0.00569145i	8.64323e−5	+	0.000223065i
$652$	−12.6930	−	8.88773i	−0.497096	−	0.348070i
$653$	−6.12762	+	2.85735i	−0.239792	+	0.111817i	−0.538800	−	0.842434i	$-0.681122\pi$
$653$	−6.12762	+	2.85735i	−0.239792	+	0.111817i	0.299008	+	0.954251i	$0.403344\pi$
$654$	−4.59261	+	13.4754i	−0.179585	+	0.526928i
$655$		0			0
$656$	−16.6632	−	9.62047i	−0.650587	−	0.375616i
$657$	3.66421	+	2.34695i	0.142955	+	0.0915631i
$658$	0.000259372	0	0.000967991i	1.01114e−5	0	3.77362e-5i
$659$	29.5176	−	10.7435i	1.14984	−	0.418508i	0.304383	−	0.952550i	$-0.401550\pi$
$659$	29.5176	−	10.7435i	1.14984	−	0.418508i	0.845458	+	0.534042i	$0.179327\pi$
$660$		0			0
$661$	−12.6918	+	10.6497i	−0.493654	+	0.414225i	−0.855334	−	0.518078i	$-0.826648\pi$
$661$	−12.6918	+	10.6497i	−0.493654	+	0.414225i	0.361680	+	0.932302i	$0.382203\pi$
$662$	−10.3530	−	0.905769i	−0.402380	−	0.0352037i
$663$	−27.0923	−	25.9986i	−1.05218	−	1.00970i
$664$	−10.0472	−	27.6043i	−0.389905	−	1.07126i
$665$		0			0
$666$	1.46162	−	0.926147i	0.0566365	−	0.0358875i
$667$	7.55709	+	28.2034i	0.292612	+	1.09204i
$668$	−29.9353	−	42.7520i	−1.15823	−	1.65412i
$669$	6.19049	+	31.3213i	0.239338	+	1.21095i
$670$		0			0
$671$	−17.5405	+	3.09287i	−0.677144	+	0.119399i
$672$	−0.00481014	−	0.00657701i	−0.000185555	−	0.000253714i
$673$	−0.682431	−	7.80022i	−0.0263058	−	0.300676i	−0.997938	−	0.0641806i	$-0.979557\pi$
$673$	−0.682431	−	7.80022i	−0.0263058	−	0.300676i	0.971633	−	0.236496i	$-0.0759989\pi$
$674$	23.7902			0.916366
$675$		0			0
$676$	8.21392			0.315920
$677$	2.64043	+	30.1802i	0.101480	+	1.15992i	0.860709	+	0.509097i	$0.170021\pi$
$677$	2.64043	+	30.1802i	0.101480	+	1.15992i	−0.759229	+	0.650823i	$0.774424\pi$
$678$	−4.23136	+	0.458186i	−0.162504	+	0.0175965i
$679$	−0.00536718		0.000946379i	−0.000205974		3.63187e-5i
$680$		0			0
$681$	−20.4082	+	17.8536i	−0.782045	+	0.684150i
$682$	−18.5648	−	26.5133i	−0.710885	−	1.01525i
$683$	−8.05741	−	30.0707i	−0.308308	−	1.15062i	−0.930060	−	0.367408i	$-0.880245\pi$
$683$	−8.05741	−	30.0707i	−0.308308	−	1.15062i	0.621752	−	0.783214i	$-0.286421\pi$
$684$	−5.68980	−	13.8317i	−0.217555	−	0.528870i
$685$		0			0
$686$	−0.00681755	−	0.0187311i	−0.000260295	−	0.000715155i
$687$	11.7609	−	3.41242i	0.448705	−	0.130192i
$688$	−14.1747	−	1.24013i	−0.540405	−	0.0472793i
$689$	19.7569	−	16.5780i	0.752679	−	0.631573i
$690$		0			0
$691$	6.70424	−	2.44014i	0.255041	−	0.0928274i	−0.211336	−	0.977414i	$-0.567781\pi$
$691$	6.70424	−	2.44014i	0.255041	−	0.0928274i	0.466377	+	0.884586i	$0.345559\pi$
$692$	2.18447	−	8.15256i	0.0830411	−	0.309914i
$693$	0.00521198		0.000673238i	0.000197987		2.55742e-5i
$694$	45.8059	+	26.4461i	1.73877	+	1.00388i
$695$		0			0
$696$	−11.9519	−	13.6621i	−0.453035	−	0.517860i
$697$	−72.7146	+	33.9074i	−2.75426	+	1.28433i
$698$	2.10801	+	1.47604i	0.0797892	+	0.0558690i
$699$	2.48333	−	3.08645i	0.0939283	−	0.116740i
$700$		0			0
$701$		−	18.1226i		−	0.684482i	−0.939612	−	0.342241i	$-0.888814\pi$
$701$		−	18.1226i		−	0.684482i	0.939612	−	0.342241i	$-0.111186\pi$
$702$	−11.5460	−	34.4269i	−0.435777	−	1.29936i
$703$	0.326292	+	0.326292i	0.0123064	+	0.0123064i
$704$	26.3202	+	22.0853i	0.991981	+	0.832371i
$705$		0			0
$706$	−7.73863	−	43.8880i	−0.291247	−	1.65175i
$707$	0.00314955	+	0.00675423i	0.000118451	+	0.000254019i
$708$	6.14079	−	9.16611i	0.230785	−	0.344484i
$709$	20.6080	+	3.63375i	0.773951	+	0.136469i	0.546656	−	0.837357i	$-0.315901\pi$
$709$	20.6080	+	3.63375i	0.773951	+	0.136469i	0.227296	+	0.973826i	$0.427012\pi$
$710$		0			0
$711$	15.6757	−	0.646105i	0.587885	−	0.0242308i
$712$	−10.6094	−	2.84277i	−0.397603	−	0.106537i
$713$	11.7521	−	25.2025i	0.440121	−	0.943842i
$714$	−0.0168172		0.000346429i	−0.000629367		1.29648e-5i
$715$		0			0
$716$	30.1048	+	35.8774i	1.12507	+	1.34080i
$717$	12.9474	+	3.18495i	0.483529	+	0.118944i
$718$	−52.2408	−	24.3603i	−1.94961	−	0.909117i
$719$	−4.36807	−	7.56572i	−0.162902	−	0.282154i	0.773007	−	0.634398i	$-0.218752\pi$
$719$	−4.36807	−	7.56572i	−0.162902	−	0.282154i	−0.935908	+	0.352244i	$0.885419\pi$
$720$		0			0
$721$	0.00222038	−	0.00384581i	8.26912e−5	−	0.000143225i
$722$	−28.6472	+	20.0590i	−1.06614	+	0.746518i
$723$	14.9168	−	7.33357i	0.554763	−	0.272738i
$724$	−9.33561	+	25.6494i	−0.346955	+	0.953252i
$725$		0			0
$726$	13.0757	−	5.06650i	0.485284	−	0.188035i
$727$	−44.6377	+	3.90529i	−1.65552	+	0.144839i	−0.876253	−	0.481851i	$-0.839965\pi$
$727$	−44.6377	+	3.90529i	−1.65552	+	0.144839i	−0.779268	+	0.626690i	$0.784409\pi$
$728$	−0.00266931	+	0.00266931i	−9.89311e−5	+	9.89311e-5i
$729$	21.5403	−	16.2793i	0.797787	−	0.602939i
$730$		0			0
$731$	−38.1379	+	45.4510i	−1.41058	+	1.68106i
$732$	29.5684	+	13.0535i	1.09288	+	0.482471i
$733$	−12.9159	+	18.4458i	−0.477060	+	0.681312i	−0.983489	−	0.180970i	$-0.942076\pi$
$733$	−12.9159	+	18.4458i	−0.477060	+	0.681312i	0.506429	+	0.862282i	$0.330965\pi$
$734$	−43.3544	−	15.7797i	−1.60024	−	0.582440i
$735$		0			0
$736$	−6.44625	+	36.5585i	−0.237612	+	1.34756i
$737$	−6.48298	+	1.73711i	−0.238804	+	0.0639873i
$738$	−77.5054	−	3.57342i	−2.85301	−	0.131540i
$739$	29.3820	−	16.9637i	1.08084	−	0.624020i	0.149714	−	0.988729i	$-0.452165\pi$
$739$	29.3820	−	16.9637i	1.08084	−	0.624020i	0.931122	+	0.364709i	$0.118832\pi$
$740$		0			0
$741$	8.28471	−	5.01347i	0.304347	−	0.184174i
$742$	0.00100695	−	0.0115095i	3.69664e−5	−	0.000422528i
$743$	2.22992	−	25.4881i	0.0818078	−	0.935068i	−0.838764	−	0.544495i	$-0.816721\pi$
$743$	2.22992	−	25.4881i	0.0818078	−	0.935068i	0.920572	−	0.390573i	$-0.127723\pi$
$744$	0.356047	+	17.2840i	0.0130533	+	0.633664i
$745$		0			0
$746$	3.19968	−	1.84733i	0.117148	−	0.0676357i
$747$	35.3463	+	32.5479i	1.29325	+	1.19086i
$748$	50.5122	−	13.5347i	1.84691	−	0.494878i
$749$	0.00153867	−	0.00872624i	5.62218e−5	−	0.000318850i
$750$		0			0
$751$	−18.3171	−	6.66687i	−0.668400	−	0.243278i	−0.0145411	−	0.999894i	$-0.504629\pi$
$751$	−18.3171	−	6.66687i	−0.668400	−	0.243278i	−0.653859	+	0.756617i	$0.726851\pi$
$752$	−0.660369	+	0.943105i	−0.0240812	+	0.0343915i
$753$	6.63468	−	4.85232i	0.241781	−	0.176828i
$754$	25.6667	−	30.5884i	0.934726	−	1.11396i
$755$		0			0
$756$	−0.00853770	−	0.00424924i	−0.000310513	−	0.000154543i
$757$	−37.3446	+	37.3446i	−1.35731	+	1.35731i	−0.480097	+	0.877215i	$0.659399\pi$
$757$	−37.3446	+	37.3446i	−1.35731	+	1.35731i	−0.877215	+	0.480097i	$0.840601\pi$
$758$	25.5472	−	2.23509i	0.927917	−	0.0811822i
$759$	−18.6540	−	15.0088i	−0.677096	−	0.544786i
$760$		0			0
$761$	13.8978	−	38.1838i	0.503793	−	1.38416i	−0.383750	−	0.923437i	$-0.625368\pi$
$761$	13.8978	−	38.1838i	0.503793	−	1.38416i	0.887543	−	0.460724i	$-0.152410\pi$
$762$	2.65055	−	39.6976i	0.0960194	−	1.43809i
$763$	−0.00198304	+	0.00138854i	−7.17908e−5	+	5.02685e-5i
$764$	−1.75761	+	3.04427i	−0.0635881	+	0.110138i
$765$		0			0
$766$	11.5732	+	20.0453i	0.418156	+	0.724267i
$767$	6.47410	+	3.01892i	0.233766	+	0.109007i
$768$	−1.95584	−	6.74076i	−0.0705751	−	0.243236i
$769$	−1.03060	−	1.22823i	−0.0371646	−	0.0442910i	0.747142	−	0.664664i	$-0.231425\pi$
$769$	−1.03060	−	1.22823i	−0.0371646	−	0.0442910i	−0.784307	+	0.620373i	$0.786981\pi$
$770$		0			0
$771$	−10.0855	+	18.3304i	−0.363221	+	0.660153i
$772$	21.2098	−	45.4846i	0.763358	−	1.63703i
$773$	32.5784	+	8.72934i	1.17176	+	0.313973i	0.791654	−	0.610970i	$-0.209220\pi$
$773$	32.5784	+	8.72934i	1.17176	+	0.313973i	0.380108	+	0.924942i	$0.375887\pi$
$774$	−53.0627	+	21.8278i	−1.90730	+	0.784583i
$775$		0			0
$776$	−15.2015	−	2.68044i	−0.545702	−	0.0962220i
$777$	0.000293582	0	1.96020e-5i	1.05322e−5	0	7.03220e-7i
$778$	36.4506	+	78.1685i	1.30682	+	2.80248i
$779$	−3.59298	−	20.3768i	−0.128732	−	0.730074i
$780$		0			0
$781$	−24.9609	−	20.9447i	−0.893172	−	0.749460i
$782$	54.1877	+	54.1877i	1.93775	+	1.93775i
$783$	27.6325	+	10.8623i	0.987506	+	0.388186i
$784$			11.4502i			0.408937i
$785$		0			0
$786$	−54.7877	−	8.50106i	−1.95421	−	0.303223i
$787$	−1.89659	−	1.32801i	−0.0676063	−	0.0473384i	0.539285	−	0.842123i	$-0.318695\pi$
$787$	−1.89659	−	1.32801i	−0.0676063	−	0.0473384i	−0.606891	+	0.794785i	$0.707584\pi$
$788$	−43.6296	+	20.3448i	−1.55424	+	0.724754i
$789$	−14.5522	+	2.87616i	−0.518072	+	0.102394i
$790$		0			0
$791$	−0.000626766	0	0.000361864i	−2.22852e−5	0	1.28664e-5i
$792$	14.5238	+	3.25705i	0.516082	+	0.115734i
$793$	−5.41626	+	20.2138i	−0.192337	+	0.717812i
$794$	−21.5293	+	7.83603i	−0.764047	+	0.278090i
$795$		0			0
$796$	22.8981	−	19.2138i	0.811602	−	0.681015i
$797$	−16.5943	−	1.45181i	−0.587801	−	0.0514259i	−0.210624	−	0.977567i	$-0.567550\pi$
$797$	−16.5943	−	1.45181i	−0.587801	−	0.0514259i	−0.377177	+	0.926141i	$0.623105\pi$
$798$	0.00103621	−	0.00421236i	3.66813e−5	−	0.000149116i
$799$	1.64198	+	4.51129i	0.0580889	+	0.159598i
$800$		0			0
$801$	17.5491	−	3.84565i	0.620068	−	0.135880i
$802$	−15.2204	−	56.8031i	−0.537449	−	2.00579i
$803$	−2.25054	−	3.21410i	−0.0794197	−	0.113423i
$804$	11.5284	+	3.92907i	0.406577	+	0.138568i
$805$		0			0
$806$	−37.4510	+	6.60363i	−1.31916	+	0.232603i
$807$	−12.1300	+	27.4765i	−0.426995	+	0.967217i
$808$	1.83965	+	21.0273i	0.0647188	+	0.739739i
$809$	−38.2899			−1.34620			−0.673100	−	0.739551i	$-0.735038\pi$
$809$	−38.2899			−1.34620			−0.673100	+	0.739551i	$0.735038\pi$
$810$		0			0
$811$	48.1974			1.69244			0.846220	−	0.532833i	$-0.178873\pi$
$811$	48.1974			1.69244			0.846220	+	0.532833i	$0.178873\pi$
$812$	−0.000914012	−	0.0104472i	−3.20755e−5	−	0.000366625i
$813$	8.29429	−	18.7880i	0.290894	−	0.658924i
$814$	−1.53656	+	0.270937i	−0.0538564	+	0.00949633i
$815$		0			0
$816$	18.2916	+	6.23404i	0.640332	+	0.218235i
$817$	−8.77644	−	12.5341i	−0.307049	−	0.438511i
$818$	−19.4385	−	72.5455i	−0.679652	−	2.53649i
$819$	0.00187110	−	0.00588427i	6.53814e−5	−	0.000205613i
$820$		0			0
$821$	5.73809	+	15.7653i	0.200261	+	0.550212i	0.998651	−	0.0519288i	$-0.0165369\pi$
$821$	5.73809	+	15.7653i	0.200261	+	0.550212i	−0.798390	+	0.602141i	$0.794315\pi$
$822$	6.65131	−	27.0388i	0.231991	−	0.943086i
$823$	34.4725	+	3.01595i	1.20164	+	0.105130i	0.670338	−	0.742056i	$-0.266149\pi$
$823$	34.4725	+	3.01595i	1.20164	+	0.105130i	0.531298	+	0.847185i	$0.321705\pi$
$824$	9.63498	−	8.08471i	0.335651	−	0.281644i
$825$		0			0
$826$	0.00300703	−	0.00109447i	0.000104628	−	3.80815e-5i
$827$	−5.23409	+	19.5339i	−0.182007	+	0.679261i	0.813244	+	0.581923i	$0.197699\pi$
$827$	−5.23409	+	19.5339i	−0.182007	+	0.679261i	−0.995251	+	0.0973378i	$0.968967\pi$
$828$	12.9639	+	41.4687i	0.450526	+	1.44114i
$829$	−45.7476	−	26.4124i	−1.58888	−	0.917340i	−0.993492	−	0.113900i	$-0.963666\pi$
$829$	−45.7476	−	26.4124i	−1.58888	−	0.917340i	−0.595387	−	0.803439i	$-0.703001\pi$
$830$		0			0
$831$	33.9923	−	6.71839i	1.17918	−	0.233059i
$832$	36.5867	−	17.0607i	1.26842	−	0.591473i
$833$	39.1110	+	27.3858i	1.35511	+	0.948861i
$834$	−11.4861	−	1.78223i	−0.397732	−	0.0617135i
$835$		0			0
$836$			13.4862i			0.466432i
$837$	−13.5101	−	24.8407i	−0.466976	−	0.858621i
$838$	24.8475	+	24.8475i	0.858342	+	0.858342i
$839$	1.94021	+	1.62803i	0.0669835	+	0.0562059i	0.675665	−	0.737209i	$-0.263857\pi$
$839$	1.94021	+	1.62803i	0.0669835	+	0.0562059i	−0.608681	+	0.793415i	$0.708301\pi$
$840$		0			0
$841$	0.633784	+	3.59437i	0.0218546	+	0.123944i
$842$	−29.6003	−	63.4780i	−1.02009	−	2.18760i
$843$	13.4443	+	0.897656i	0.463046	+	0.0309169i
$844$	−0.501982	−	0.0885129i	−0.0172789	−	0.00304674i
$845$		0			0
$846$	−0.617209	+	4.60140i	−0.0212201	+	0.158199i
$847$	0.00230328		0.000617162i	7.91417e−5		2.12059e-5i
$848$	−5.60957	+	12.0298i	−0.192634	+	0.413104i
$849$	12.5469	−	22.8040i	0.430609	−	0.782631i
$850$		0			0
$851$	−0.861655	−	1.02688i	−0.0295371	−	0.0352010i
$852$	16.4770	+	56.7879i	0.564494	+	1.94552i
$853$	−37.8798	−	17.6637i	−1.29698	−	0.604792i	−0.353257	−	0.935526i	$-0.614926\pi$
$853$	−37.8798	−	17.6637i	−1.29698	−	0.604792i	−0.943724	+	0.330734i	$0.892704\pi$
$854$	0.00468729	+	0.00811862i	0.000160396	+	0.000277813i
$855$		0			0
$856$	12.5483	−	21.7343i	0.428893	−	0.742864i
$857$	21.9778	−	15.3891i	0.750749	−	0.525680i	−0.134434	−	0.990923i	$-0.542922\pi$
$857$	21.9778	−	15.3891i	0.750749	−	0.525680i	0.885183	+	0.465242i	$0.154033\pi$
$858$	−2.18131	+	32.6697i	−0.0744687	+	1.11532i
$859$	−7.80591	+	21.4466i	−0.266334	+	0.731747i	0.732372	+	0.680904i	$0.238413\pi$
$859$	−7.80591	+	21.4466i	−0.266334	+	0.731747i	−0.998707	+	0.0508429i	$0.983809\pi$
$860$		0			0
$861$	−0.0102793	−	0.00827062i	−0.000350316	−	0.000281862i
$862$	−13.0034	+	1.13765i	−0.442896	+	0.0387484i
$863$	−7.93097	+	7.93097i	−0.269973	+	0.269973i	−0.829089	−	0.559116i	$-0.811141\pi$
$863$	−7.93097	+	7.93097i	−0.269973	+	0.269973i	0.559116	+	0.829089i	$0.311141\pi$
$864$	26.0037	+	27.3635i	0.884663	+	0.930927i
$865$		0			0
$866$	15.4685	−	18.4346i	0.525641	−	0.626434i
$867$	41.2753	−	30.1869i	1.40178	−	1.02520i
$868$	−0.00572871	+	0.00818145i	−0.000194445	+	0.000277696i
$869$	−13.2938	−	4.83854i	−0.450961	−	0.164136i
$870$		0			0
$871$	−1.36935	+	7.76596i	−0.0463986	+	0.263139i
$872$	−6.62293	+	1.77461i	−0.224281	+	0.0600959i
$873$	24.0980	−	7.53350i	0.815595	−	0.254970i
$874$	−17.1153	+	9.88153i	−0.578934	+	0.334248i
$875$		0			0
$876$	0.146645	+	7.11876i	0.00495466	+	0.240521i
$877$	−0.0855499	+	0.977840i	−0.00288882	+	0.0330193i	−0.997502	−	0.0706341i	$-0.977498\pi$
$877$	−0.0855499	+	0.977840i	−0.00288882	+	0.0330193i	0.994613	+	0.103653i	$0.0330533\pi$
$878$	5.57448	−	63.7167i	0.188130	−	2.15033i
$879$	33.4170	−	20.2222i	1.12713	−	0.682077i
$880$		0			0
$881$	22.3414	−	12.8988i	0.752701	−	0.434572i	−0.0739682	−	0.997261i	$-0.523566\pi$
$881$	22.3414	−	12.8988i	0.752701	−	0.434572i	0.826669	+	0.562689i	$0.190233\pi$
$882$	21.2200	+	41.0072i	0.714515	+	1.38078i
$883$	−46.3611	+	12.4224i	−1.56018	+	0.418048i	−0.932719	−	0.360604i	$-0.882571\pi$
$883$	−46.3611	+	12.4224i	−1.56018	+	0.418048i	−0.627457	+	0.778652i	$0.715904\pi$
$884$	10.6693	−	60.5085i	0.358847	−	2.03512i
$885$		0			0
$886$	−56.0866	−	20.4139i	−1.88427	−	0.685817i
$887$	3.82768	−	5.46649i	0.128521	−	0.183547i	−0.749734	−	0.661739i	$-0.769819\pi$
$887$	3.82768	−	5.46649i	0.128521	−	0.183547i	0.878255	+	0.478192i	$0.158708\pi$
$888$	0.762379	+	0.336565i	0.0255837	+	0.0112944i
$889$	0.00434872	−	0.00518260i	0.000145851	−	0.000173819i
$890$		0			0
$891$	−23.5470	+	6.18643i	−0.788856	+	0.207253i
$892$	−36.9415	+	36.9415i	−1.23689	+	1.23689i
$893$	−1.23338	+	0.107907i	−0.0412735	+	0.00361097i
$894$	35.9956	−	13.9474i	1.20387	−	0.466471i
$895$		0			0
$896$	0.00296711	−	0.00815206i	9.91241e−5	−	0.000272341i
$897$	−25.2447	+	12.4111i	−0.842897	+	0.414393i
$898$	6.25679	−	4.38105i	0.208792	−	0.146198i
$899$	15.5475	−	26.9291i	0.518538	−	0.898134i
$900$		0			0
$901$	27.6739	+	47.9327i	0.921953	+	1.59687i
$902$	63.4068	+	29.5671i	2.11121	+	0.984476i
$903$	−0.00947420	−	0.00233057i	−0.000315282	−	7.75567e-5i
$904$	−1.31760	−	1.57025i	−0.0438226	−	0.0522258i
$905$		0			0
$906$	70.8162	−	1.45879i	2.35271	−	0.0484652i
$907$	−0.500360	+	1.07303i	−0.0166142	+	0.0356292i	−0.914440	−	0.404722i	$-0.867368\pi$
$907$	−0.500360	+	1.07303i	−0.0166142	+	0.0356292i	0.897826	+	0.440351i	$0.145146\pi$
$908$	−42.8576	−	11.4837i	−1.42228	−	0.381099i
$909$	−18.4792	−	29.1633i	−0.612917	−	0.967286i
$910$		0			0
$911$	−27.0446	−	4.76870i	−0.896028	−	0.157994i	−0.293375	−	0.955997i	$-0.594779\pi$
$911$	−27.0446	−	4.76870i	−0.896028	−	0.157994i	−0.602653	+	0.798003i	$0.705890\pi$
$912$	−2.77384	+	4.14041i	−0.0918511	+	0.137103i
$913$	−18.3105	−	39.2670i	−0.605990	−	1.29955i
$914$	−9.00761	−	51.0847i	−0.297945	−	1.68973i
$915$		0			0
$916$	15.3502	+	12.8803i	0.507185	+	0.425578i
$917$	−0.00666650	−	0.00666650i	−0.000220147	−	0.000220147i
$918$	77.0614	−	11.5724i	2.54341	−	0.381945i
$919$			21.2332i			0.700419i	0.936671	+	0.350209i	$0.113890\pi$
$919$			21.2332i			0.700419i	−0.936671	+	0.350209i	$0.886110\pi$
$920$		0			0
$921$	5.48799	−	6.82083i	0.180835	−	0.224754i
$922$	−14.4200	−	10.0970i	−0.474899	−	0.332528i
$923$	−34.6972	+	16.1796i	−1.14207	+	0.532557i
$924$	0.00566203	+	0.00647222i	0.000186267	+	0.000212920i
$925$		0			0
$926$	−4.49731	−	2.59652i	−0.147791	−	0.0853270i
$927$	−7.91918	+	18.9874i	−0.260100	+	0.623630i
$928$	−10.7437	+	40.0962i	−0.352680	+	1.31622i
$929$	28.3403	−	10.3150i	0.929816	−	0.338425i	0.167679	−	0.985842i	$-0.446373\pi$
$929$	28.3403	−	10.3150i	0.929816	−	0.338425i	0.762136	+	0.647416i	$0.224150\pi$
$930$		0			0
$931$	−9.43249	+	7.91479i	−0.309137	+	0.259397i
$932$	6.45754	+	0.564962i	0.211524	+	0.0185059i
$933$	−32.7996	+	9.51681i	−1.07381	+	0.311566i
$934$	15.4682	+	42.4985i	0.506135	+	1.39059i
$935$		0			0
$936$	10.6800	−	13.8484i	0.349088	−	0.452650i
$937$	4.43173	+	16.5394i	0.144778	+	0.540320i	0.999765	+	0.0216704i	$0.00689845\pi$
$937$	4.43173	+	16.5394i	0.144778	+	0.540320i	−0.854987	+	0.518650i	$0.826435\pi$
$938$	0.00202620	+	0.00289372i	6.61579e−5	+	9.44832e-5i
$939$	−35.3716	+	30.9438i	−1.15431	+	1.00981i
$940$		0			0
$941$	−21.0459	+	3.71097i	−0.686078	+	0.120974i	−0.505812	−	0.862644i	$-0.668807\pi$
$941$	−21.0459	+	3.71097i	−0.686078	+	0.120974i	−0.180266	+	0.983618i	$0.557696\pi$
$942$	1.22485	−	0.132632i	0.0399079	−	0.00432137i
$943$	5.23871	+	59.8787i	0.170596	+	1.94992i
$944$	−3.67638			−0.119656
$945$		0			0
$946$	51.7372			1.68212
$947$	−2.48308	−	28.3818i	−0.0806894	−	0.922284i	−0.923380	−	0.383886i	$-0.874585\pi$
$947$	−2.48308	−	28.3818i	−0.0806894	−	0.922284i	0.842691	−	0.538398i	$-0.180970\pi$
$948$	15.1550	+	20.7218i	0.492211	+	0.673012i
$949$	−4.54003	+	0.800530i	−0.147376	+	0.0259863i
$950$		0			0
$951$	−0.0838316	−	0.424153i	−0.00271843	−	0.0137541i
$952$	−0.00464666	−	0.00663611i	−0.000150599	−	0.000215078i
$953$	−13.1177	−	48.9558i	−0.424923	−	1.58583i	−0.764091	−	0.645108i	$-0.776812\pi$
$953$	−13.1177	−	48.9558i	−0.424923	−	1.58583i	0.339169	−	0.940726i	$-0.389854\pi$
$954$	2.20422	+	53.4786i	0.0713644	+	1.73143i
$955$		0			0
$956$	7.46208	+	20.5019i	0.241341	+	0.663078i
$957$	−19.3169	−	18.5371i	−0.624426	−	0.599220i
$958$	47.1948	+	4.12901i	1.52479	+	0.133402i
$959$	0.00362713	−	0.00304352i	0.000117126	−	9.82804e-5i
$960$		0			0
$961$	1.30221	−	0.473965i	0.0420067	−	0.0152892i
$962$	−0.474467	+	1.77074i	−0.0152974	+	0.0570908i
$963$	−1.89061	+	41.0062i	−0.0609240	+	1.32141i
$964$	23.5551	+	13.5995i	0.758657	+	0.438011i
$965$		0			0
$966$	−0.00406522	+	0.0119279i	−0.000130796	+	0.000383775i
$967$	48.1057	−	22.4321i	1.54697	−	0.721366i	0.553229	−	0.833029i	$-0.313396\pi$
$967$	48.1057	−	22.4321i	1.54697	−	0.721366i	0.993746	+	0.111663i	$0.0356178\pi$
$968$	5.53233	+	3.87378i	0.177816	+	0.124508i
$969$	7.50827	+	19.3774i	0.241200	+	0.622492i
$970$		0			0
$971$		−	12.4548i		−	0.399695i	−0.979827	−	0.199847i	$-0.935955\pi$
$971$		−	12.4548i		−	0.399695i	0.979827	−	0.199847i	$-0.0640447\pi$
$972$	41.7486	+	14.4563i	1.33909	+	0.463686i
$973$	−0.00139762	−	0.00139762i	−4.48056e−5	−	4.48056e-5i
$974$	5.24344	+	4.39976i	0.168011	+	0.140978i
$975$		0			0
$976$	−1.87021	−	10.6065i	−0.0598639	−	0.339505i
$977$	−7.99244	−	17.1398i	−0.255701	−	0.548352i	0.735991	−	0.676992i	$-0.236717\pi$
$977$	−7.99244	−	17.1398i	−0.255701	−	0.548352i	−0.991691	+	0.128639i	$0.958939\pi$
$978$	9.18592	+	18.6846i	0.293733	+	0.597469i
$979$	−15.9536	−	2.81305i	−0.509879	−	0.0899055i
$980$		0			0
$981$	8.28706	−	7.55658i	0.264586	−	0.241263i
$982$	17.5085	+	4.69139i	0.558719	+	0.149708i
$983$	5.63921	−	12.0933i	0.179863	−	0.385717i	−0.795619	−	0.605798i	$-0.792854\pi$
$983$	5.63921	−	12.0933i	0.179863	−	0.385717i	0.975482	+	0.220080i	$0.0706319\pi$
$984$	−19.3464	−	31.9698i	−0.616742	−	1.01916i
$985$		0			0
$986$	55.0815	+	65.6436i	1.75415	+	2.09052i
$987$	−0.000546612	0	0.000569606i	−1.73989e−5	0	1.81308e-5i
$988$	14.3608	+	6.69656i	0.456878	+	0.213046i
$989$	22.2250	+	38.4948i	0.706713	+	1.22406i
$990$		0			0
$991$	−2.99736	+	5.19158i	−0.0952142	+	0.164916i	−0.909698	−	0.415270i	$-0.863687\pi$
$991$	−2.99736	+	5.19158i	−0.0952142	+	0.164916i	0.814484	+	0.580186i	$0.197020\pi$
$992$	32.3842	−	22.6757i	1.02820	−	0.719953i
$993$	6.80161	+	4.55670i	0.215843	+	0.144603i
$994$	−0.00586569	+	0.0161158i	−0.000186048	+	0.000511163i
$995$		0			0
$996$	−12.0553	+	77.6941i	−0.381987	+	2.46183i
$997$	45.5235	−	3.98279i	1.44174	−	0.126136i	0.660718	−	0.750634i	$-0.270252\pi$
$997$	45.5235	−	3.98279i	1.44174	−	0.126136i	0.781026	+	0.624498i	$0.214696\pi$
$998$	−41.0167	+	41.0167i	−1.29836	+	1.29836i
$999$	−1.36051	+	0.0841734i	−0.0430445	+	0.00266313i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.b.443.3		192
5.2	odd	4	inner	675.2.ba.b.632.14		192
5.3	odd	4		135.2.q.a.92.3	yes	192
5.4	even	2		135.2.q.a.38.14	yes	192
15.8	even	4		405.2.r.a.197.14		192
15.14	odd	2		405.2.r.a.278.3		192
27.5	odd	18	inner	675.2.ba.b.518.14		192
135.32	even	36	inner	675.2.ba.b.32.3		192
135.49	even	18		405.2.r.a.368.14		192
135.59	odd	18		135.2.q.a.113.3	yes	192
135.103	odd	36		405.2.r.a.287.3		192
135.113	even	36		135.2.q.a.32.14	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.14	✓	192	135.113	even	36
135.2.q.a.38.14	yes	192	5.4	even	2
135.2.q.a.92.3	yes	192	5.3	odd	4
135.2.q.a.113.3	yes	192	135.59	odd	18
405.2.r.a.197.14		192	15.8	even	4
405.2.r.a.278.3		192	15.14	odd	2
405.2.r.a.287.3		192	135.103	odd	36
405.2.r.a.368.14		192	135.49	even	18
675.2.ba.b.32.3		192	135.32	even	36	inner
675.2.ba.b.443.3		192	1.1	even	1	trivial
675.2.ba.b.518.14		192	27.5	odd	18	inner
675.2.ba.b.632.14		192	5.2	odd	4	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.191628 - 2.19031i) q^{2} +(-0.699511 + 1.58451i) q^{3} +(-2.79113 + 0.492152i) q^{4} +(3.60463 + 1.22851i) q^{6} +(0.000371431 + 0.000530458i) q^{7} +(0.474704 + 1.77162i) q^{8} +(-2.02137 - 2.21677i) q^{9} +(0.925209 + 2.54199i) q^{11} +(1.17261 - 4.76685i) q^{12} +(3.16625 + 0.277011i) q^{13} +(0.00109069 - 0.000915200i) q^{14} +(-1.53710 + 0.559459i) q^{16} +(-1.76536 + 6.58840i) q^{17} +(-4.46807 + 4.85222i) q^{18} +(-1.52337 - 0.879517i) q^{19} +(-0.00110034 + 0.000217476i) q^{21} +(5.39046 - 2.51361i) q^{22} +(4.18584 + 2.93096i) q^{23} +(-3.13922 - 0.487092i) q^{24} -6.98815i q^{26} +(4.92647 - 1.65223i) q^{27} +(-0.00129778 - 0.00129778i) q^{28} +(4.37718 + 3.67289i) q^{29} +(-0.944975 - 5.35922i) q^{31} +(3.07020 + 6.58407i) q^{32} +(-4.67501 - 0.312144i) q^{33} +(14.7689 + 2.60416i) q^{34} +(6.73289 + 5.19248i) q^{36} +(-0.253391 - 0.0678960i) q^{37} +(-1.63450 + 3.50519i) q^{38} +(-2.65375 + 4.82319i) q^{39} +(7.56097 + 9.01082i) q^{41} +(0.000687195 + 0.00236841i) q^{42} +(7.88368 + 3.67622i) q^{43} +(-3.83342 - 6.63969i) q^{44} +(5.61759 - 9.72995i) q^{46} +(0.576559 - 0.403711i) q^{47} +(0.188748 - 2.82690i) q^{48} +(2.39414 - 6.57785i) q^{49} +(-9.20452 - 7.40589i) q^{51} +(-8.97374 + 0.785101i) q^{52} +(5.73786 - 5.73786i) q^{53} +(-4.56295 - 10.4739i) q^{54} +(-0.000763450 + 0.000909845i) q^{56} +(2.45922 - 1.79857i) q^{57} +(7.20599 - 10.2912i) q^{58} +(2.11198 + 0.768697i) q^{59} +(-1.14333 + 6.48417i) q^{61} +(-11.5573 + 3.09676i) q^{62} +(0.000425105 - 0.00189563i) q^{63} +(10.9996 - 6.35064i) q^{64} +(0.212168 + 10.2996i) q^{66} +(-0.216242 + 2.47165i) q^{67} +(1.68485 - 19.2579i) q^{68} +(-7.57218 + 4.58228i) q^{69} +(-10.4316 + 6.02267i) q^{71} +(2.96772 - 4.63341i) q^{72} +(-1.40104 + 0.375408i) q^{73} +(-0.100157 + 0.568017i) q^{74} +(4.68478 + 1.70512i) q^{76} +(-0.00100477 + 0.00143496i) q^{77} +(11.0728 + 4.88829i) q^{78} +(-3.36157 + 4.00616i) q^{79} +(-0.828138 + 8.96182i) q^{81} +(18.2876 - 18.2876i) q^{82} +(-15.9554 + 1.39592i) q^{83} +(0.00296416 - 0.00114854i) q^{84} +(6.54134 - 17.9722i) q^{86} +(-8.88163 + 4.36647i) q^{87} +(-4.06424 + 2.84581i) q^{88} +(-2.99426 + 5.18621i) q^{89} +(0.00102910 + 0.00178245i) q^{91} +(-13.1257 - 6.12062i) q^{92} +(9.15278 + 2.25151i) q^{93} +(-0.994737 - 1.18548i) q^{94} +(-12.5802 + 0.259149i) q^{96} +(-3.55678 + 7.62753i) q^{97} +(-14.8663 - 3.98342i) q^{98} +(3.76482 - 7.18927i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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