LMFDB - Embedded newform 135.2.q.a.38.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			38.14
Character	$\chi$	$=$	135.38
Dual form			135.2.q.a.32.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.191628 + 2.19031i) q^{2} +(0.699511 - 1.58451i) q^{3} +(-2.79113 + 0.492152i) q^{4} +(2.03807 + 0.919920i) q^{5} +(3.60463 + 1.22851i) q^{6} +(-0.000371431 - 0.000530458i) q^{7} +(-0.474704 - 1.77162i) q^{8} +(-2.02137 - 2.21677i) q^{9} +O(q^{10})$	\(q+(0.191628 + 2.19031i) q^{2} +(0.699511 - 1.58451i) q^{3} +(-2.79113 + 0.492152i) q^{4} +(2.03807 + 0.919920i) q^{5} +(3.60463 + 1.22851i) q^{6} +(-0.000371431 - 0.000530458i) q^{7} +(-0.474704 - 1.77162i) q^{8} +(-2.02137 - 2.21677i) q^{9} +(-1.62436 + 4.64030i) q^{10} +(0.925209 + 2.54199i) q^{11} +(-1.17261 + 4.76685i) q^{12} +(-3.16625 - 0.277011i) q^{13} +(0.00109069 - 0.000915200i) q^{14} +(2.88328 - 2.58586i) q^{15} +(-1.53710 + 0.559459i) q^{16} +(1.76536 - 6.58840i) q^{17} +(4.46807 - 4.85222i) q^{18} +(-1.52337 - 0.879517i) q^{19} +(-6.14128 - 1.56458i) q^{20} +(-0.00110034 + 0.000217476i) q^{21} +(-5.39046 + 2.51361i) q^{22} +(-4.18584 - 2.93096i) q^{23} +(-3.13922 - 0.487092i) q^{24} +(3.30749 + 3.74973i) q^{25} -6.98815i q^{26} +(-4.92647 + 1.65223i) q^{27} +(0.00129778 + 0.00129778i) q^{28} +(4.37718 + 3.67289i) q^{29} +(6.21636 + 5.81977i) q^{30} +(-0.944975 - 5.35922i) q^{31} +(-3.07020 - 6.58407i) q^{32} +(4.67501 + 0.312144i) q^{33} +(14.7689 + 2.60416i) q^{34} +(-0.000269024 - 0.00142280i) q^{35} +(6.73289 + 5.19248i) q^{36} +(0.253391 + 0.0678960i) q^{37} +(1.63450 - 3.50519i) q^{38} +(-2.65375 + 4.82319i) q^{39} +(0.662267 - 4.04738i) q^{40} +(7.56097 + 9.01082i) q^{41} +(-0.000687195 - 0.00236841i) q^{42} +(-7.88368 - 3.67622i) q^{43} +(-3.83342 - 6.63969i) q^{44} +(-2.08045 - 6.37744i) q^{45} +(5.61759 - 9.72995i) q^{46} +(-0.576559 + 0.403711i) q^{47} +(-0.188748 + 2.82690i) q^{48} +(2.39414 - 6.57785i) q^{49} +(-7.57928 + 7.96300i) q^{50} +(-9.20452 - 7.40589i) q^{51} +(8.97374 - 0.785101i) q^{52} +(-5.73786 + 5.73786i) q^{53} +(-4.56295 - 10.4739i) q^{54} +(-0.452784 + 6.03188i) q^{55} +(-0.000763450 + 0.000909845i) q^{56} +(-2.45922 + 1.79857i) q^{57} +(-7.20599 + 10.2912i) q^{58} +(2.11198 + 0.768697i) q^{59} +(-6.77498 + 8.63650i) q^{60} +(-1.14333 + 6.48417i) q^{61} +(11.5573 - 3.09676i) q^{62} +(-0.000425105 + 0.00189563i) q^{63} +(10.9996 - 6.35064i) q^{64} +(-6.19822 - 3.47726i) q^{65} +(0.212168 + 10.2996i) q^{66} +(0.216242 - 2.47165i) q^{67} +(-1.68485 + 19.2579i) q^{68} +(-7.57218 + 4.58228i) q^{69} +(0.00306482 - 0.000861895i) q^{70} +(-10.4316 + 6.02267i) q^{71} +(-2.96772 + 4.63341i) q^{72} +(1.40104 - 0.375408i) q^{73} +(-0.100157 + 0.568017i) q^{74} +(8.25513 - 2.61779i) q^{75} +(4.68478 + 1.70512i) q^{76} +(0.00100477 - 0.00143496i) q^{77} +(-11.0728 - 4.88829i) q^{78} +(-3.36157 + 4.00616i) q^{79} +(-3.64738 - 0.273791i) q^{80} +(-0.828138 + 8.96182i) q^{81} +(-18.2876 + 18.2876i) q^{82} +(15.9554 - 1.39592i) q^{83} +(0.00296416 - 0.00114854i) q^{84} +(9.65872 - 11.8037i) q^{85} +(6.54134 - 17.9722i) q^{86} +(8.88163 - 4.36647i) q^{87} +(4.06424 - 2.84581i) q^{88} +(-2.99426 + 5.18621i) q^{89} +(13.5699 - 5.77892i) q^{90} +(0.00102910 + 0.00178245i) q^{91} +(13.1257 + 6.12062i) q^{92} +(-9.15278 - 2.25151i) q^{93} +(-0.994737 - 1.18548i) q^{94} +(-2.29565 - 3.19390i) q^{95} +(-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} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{3}{4}\right)$

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	$0.255659\pi$
$2$	0.191628	+	2.19031i	0.135501	+	1.54878i	−0.558923	+	0.829219i	$0.688785\pi$
$3$	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
$5$	2.03807	+	0.919920i	0.911455	+	0.411401i
$5$	2.03807	+	0.919920i	0.911455	+	0.411401i
$6$	3.60463	+	1.22851i	1.47158	+	0.501538i
$7$	−0.000371431	0	0.000530458i	−0.000140388	0	0.000200494i	0.819082	−	0.573677i	$-0.194483\pi$
$7$	−0.000371431	0	0.000530458i	−0.000140388	0	0.000200494i	−0.819222	+	0.573476i	$0.805595\pi$
$8$	−0.474704	−	1.77162i	−0.167833	−	0.626362i
$9$	−2.02137	−	2.21677i	−0.673790	−	0.738923i
$10$	−1.62436	+	4.64030i	−0.513668	+	1.46739i
$11$	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	−0.360846	−	0.932625i	$-0.617512\pi$
$13$	−3.16625	−	0.277011i	−0.878159	−	0.0768289i	−0.517313	+	0.855797i	$0.673068\pi$
$14$	0.00109069		0.000915200i	0.000291500		0.000244597i
$15$	2.88328	−	2.58586i	0.744460	−	0.667667i
$16$	−1.53710	+	0.559459i	−0.384275	+	0.139865i
$17$	1.76536	−	6.58840i	0.428162	−	1.59792i	−0.328759	−	0.944414i	$-0.606630\pi$
$17$	1.76536	−	6.58840i	0.428162	−	1.59792i	0.756921	−	0.653507i	$-0.226703\pi$
$18$	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	$0.731338\pi$
$20$	−6.14128	−	1.56458i	−1.37323	−	0.349850i
$21$	−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	0.0489979	−	0.998799i	$-0.484397\pi$
$23$	−4.18584	−	2.93096i	−0.872808	−	0.611147i	−0.921806	+	0.387652i	$0.873286\pi$
$24$	−3.13922	−	0.487092i	−0.640790	−	0.0994273i
$25$	3.30749	+	3.74973i	0.661499	+	0.749946i
$26$		−	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	$0.544215\pi$
$30$	6.21636	+	5.81977i	1.13495	+	1.06254i
$31$	−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
$35$	−0.000269024	−	0.00142280i	−4.54734e−5	−	0.000240497i
$36$	6.73289	+	5.19248i	1.12215	+	0.865413i
$37$	0.253391	+	0.0678960i	0.0416573	+	0.0111620i	0.279587	−	0.960120i	$-0.409802\pi$
$37$	0.253391	+	0.0678960i	0.0416573	+	0.0111620i	−0.237930	+	0.971282i	$0.576469\pi$
$38$	1.63450	−	3.50519i	0.265151	−	0.568617i
$39$	−2.65375	+	4.82319i	−0.424940	+	0.772328i
$40$	0.662267	−	4.04738i	0.104714	−	0.639947i
$41$	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	−0.284845	−	0.958574i	$-0.591942\pi$
$43$	−7.88368	−	3.67622i	−1.20225	−	0.560618i	−0.917405	+	0.397955i	$0.869720\pi$
$44$	−3.83342	−	6.63969i	−0.577910	−	1.00097i
$45$	−2.08045	−	6.37744i	−0.310135	−	0.950693i
$46$	5.61759	−	9.72995i	0.828268	−	1.43460i
$47$	−0.576559	+	0.403711i	−0.0840997	+	0.0588873i	−0.614870	−	0.788628i	$-0.710792\pi$
$47$	−0.576559	+	0.403711i	−0.0840997	+	0.0588873i	0.530770	+	0.847516i	$0.321903\pi$
$48$	−0.188748	+	2.82690i	−0.0272435	+	0.408028i
$49$	2.39414	−	6.57785i	0.342020	−	0.939693i
$50$	−7.57928	+	7.96300i	−1.07187	+	1.12614i
$51$	−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	−0.981192	−	0.193036i	$-0.938167\pi$
$53$	−5.73786	+	5.73786i	−0.788156	+	0.788156i	0.193036	+	0.981192i	$0.438167\pi$
$54$	−4.56295	−	10.4739i	−0.620939	−	1.42532i
$55$	−0.452784	+	6.03188i	−0.0610534	+	0.813339i
$56$	−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	$0.564374\pi$
$60$	−6.77498	+	8.63650i	−0.874647	+	1.11497i
$61$	−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
$65$	−6.19822	−	3.47726i	−0.768794	−	0.431301i
$66$	0.212168	+	10.2996i	0.0261161	+	1.26779i
$67$	0.216242	−	2.47165i	0.0264181	−	0.301960i	−0.971478	−	0.237129i	$-0.923794\pi$
$67$	0.216242	−	2.47165i	0.0264181	−	0.301960i	0.997896	−	0.0648313i	$-0.0206509\pi$
$68$	−1.68485	+	19.2579i	−0.204318	+	2.33536i
$69$	−7.57218	+	4.58228i	−0.911583	+	0.551642i
$70$	0.00306482		0.000861895i	0.000366316		0.000103016i
$71$	−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	−0.175895	−	0.984409i	$-0.556282\pi$
$73$	1.40104	−	0.375408i	0.163979	−	0.0439381i	0.339875	+	0.940471i	$0.389615\pi$
$74$	−0.100157	+	0.568017i	−0.0116430	+	0.0660306i
$75$	8.25513	−	2.61779i	0.953220	−	0.302276i
$76$	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	$0.317273\pi$
$80$	−3.64738	−	0.273791i	−0.407790	−	0.0306108i
$81$	−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	0.834113	−	0.551594i	$-0.185980\pi$
$83$	15.9554	−	1.39592i	1.75134	−	0.153222i	0.917224	+	0.398372i	$0.130425\pi$
$84$	0.00296416	−	0.00114854i	0.000323416	−	0.000125316i
$85$	9.65872	−	11.8037i	1.04764	−	1.28029i
$86$	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	$0.269473\pi$
$90$	13.5699	−	5.77892i	1.43039	−	0.609152i
$91$	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
$95$	−2.29565	−	3.19390i	−0.235529	−	0.327687i
$96$	−12.5802	+	0.259149i	−1.28396	+	0.0264492i
$97$	3.55678	−	7.62753i	0.361136	−	0.774459i	−0.638851	−	0.769331i	$-0.720590\pi$
$97$	3.55678	−	7.62753i	0.361136	−	0.774459i	0.999987	−	0.00512815i	$-0.00163235\pi$
$98$	14.8663	+	3.98342i	1.50173	+	0.402386i
$99$	3.76482	−	7.18927i	0.378378	−	0.722549i
$100$	−11.0771	−	8.83821i	−1.10771	−	0.883821i
$101$	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	0.995798	−	0.0915740i	$-0.0291898\pi$
$103$	2.89813	+	6.21507i	0.285562	+	0.612389i	−0.710237	+	0.703963i	$0.751412\pi$
$104$	1.01227	+	5.74088i	0.0992615	+	0.562940i
$105$	−0.00244263		0.000568991i	−0.000238376		5.55279e-5i
$106$	−13.6672	−	11.4682i	−1.32748	−	1.11389i
$107$	9.67551	+	9.67551i	0.935367	+	0.935367i	0.998034	−	0.0626673i	$-0.0199607\pi$
$107$	9.67551	+	9.67551i	0.935367	+	0.935367i	−0.0626673	+	0.998034i	$0.519961\pi$
$108$	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	$0.942703\pi$
$110$	−13.2985	+	0.164136i	−1.26796	+	0.0156498i
$111$	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	−0.374391	−	0.927271i	$-0.622148\pi$
$113$	1.01289	−	0.472320i	0.0952851	−	0.0444322i	0.469676	+	0.882839i	$0.344371\pi$
$114$	−4.41068	−	5.04180i	−0.413098	−	0.472208i
$115$	−5.83480	−	9.82414i	−0.544098	−	0.916106i
$116$	−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
$120$	−5.94987	−	3.88056i	−0.543146	−	0.354245i
$121$	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
$125$	3.29146	+	10.6849i	0.294397	+	0.955683i
$126$	−0.00423348		0.000567858i	−0.000377148		5.05889e-5i
$127$	2.70398	+	10.0914i	0.239940	+	0.895467i	0.975860	+	0.218398i	$0.0700832\pi$
$127$	2.70398	+	10.0914i	0.239940	+	0.895467i	−0.735920	+	0.677068i	$0.763250\pi$
$128$	7.68398	+	10.9739i	0.679175	+	0.969962i
$129$	−11.3397	+	9.92024i	−0.998409	+	0.873429i
$130$	6.42854	−	14.2424i	0.563820	−	1.24914i
$131$	−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
$135$	−11.5604	−	1.16459i	−0.994964	−	0.100232i
$136$	−12.5102			−1.07274
$137$	0.637262	+	7.28394i	0.0544450	+	0.622309i	0.973577	+	0.228359i	$0.0733361\pi$
$137$	0.637262	+	7.28394i	0.0544450	+	0.622309i	−0.919132	+	0.393950i	$0.871108\pi$
$138$	−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	$0.485763\pi$
$140$	0.00145112	+	0.00383882i	0.000122642	+	0.000324440i
$141$	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
$145$	5.54225	+	11.5123i	0.460259	+	0.956043i
$146$	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	$0.141482\pi$
$150$	7.31569	+	17.5797i	0.597324	+	1.43537i
$151$	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
$155$	3.00413	−	11.7918i	0.241297	−	0.947139i
$156$	5.03323	−	14.7682i	0.402981	−	1.18240i
$157$	−0.293204	+	0.136723i	−0.0234002	+	0.0109117i	−0.434283	−	0.900776i	$-0.642998\pi$
$157$	−0.293204	+	0.136723i	−0.0234002	+	0.0109117i	0.410883	+	0.911688i	$0.365220\pi$
$158$	−9.41892	−	6.59520i	−0.749329	−	0.524686i
$159$	5.07803	+	13.1054i	0.402714	+	1.03933i
$160$	−0.200481	−	16.2432i	−0.0158494	−	1.28413i
$161$			0.00330906i			0.000260790i
$162$	−19.7879	−	0.0965494i	−1.55468	−	0.00758564i
$163$	−3.86594	−	3.86594i	−0.302804	−	0.302804i	0.539306	−	0.842110i	$-0.318687\pi$
$163$	−3.86594	−	3.86594i	−0.302804	−	0.302804i	−0.842110	+	0.539306i	$0.818687\pi$
$164$	−25.5384	−	21.4292i	−1.99421	−	1.67334i
$165$	9.24087	+	4.93681i	0.719401	+	0.384330i
$166$	6.11500	+	34.6799i	0.474616	+	2.69168i
$167$	−7.78235	−	16.6893i	−0.602217	−	1.29146i	−0.937055	−	0.349182i	$-0.886459\pi$
$167$	−7.78235	−	16.6893i	−0.602217	−	1.29146i	0.334838	−	0.942276i	$-0.391318\pi$
$168$	0.000907620		0.00184614i	7.00244e−5		0.000142433i
$169$	−2.85412	−	0.503259i	−0.219548	−	0.0387122i
$170$	27.7046	+	18.8937i	2.12484	+	1.44908i
$171$	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	−0.852639	−	0.522501i	$-0.824999\pi$
$173$	1.25855	−	2.69896i	0.0956855	−	0.205198i	0.948324	+	0.317302i	$0.102777\pi$
$174$	11.2659	+	18.6168i	0.854066	+	1.41134i
$175$	0.000760571	−	0.00314725i	5.74937e−5	−	0.000237910i
$176$	−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	$-0.378547\pi$
$180$	8.94547	+	16.7764i	0.666756	+	1.25044i
$181$	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
$185$	0.453971	+	0.371477i	0.0333766	+	0.0273115i
$186$	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
$190$	6.55572	−	5.64023i	0.475602	−	0.409185i
$191$	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	$-0.585602\pi$
$193$	10.1567	−	14.5052i	0.731093	−	1.04411i	0.996791	−	0.0800524i	$-0.0255088\pi$
$194$	17.3883	+	6.32881i	1.24840	+	0.454382i
$195$	−9.84549	+	7.38878i	−0.705050	+	0.529121i
$196$	−3.44506	+	19.5379i	−0.246076	+	1.39557i
$197$	−16.4067	+	4.39615i	−1.16893	+	0.313213i	−0.790526	−	0.612429i	$-0.790193\pi$
$197$	−16.4067	+	4.39615i	−1.16893	+	0.313213i	−0.378401	+	0.925642i	$0.623526\pi$
$198$	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	$0.455285\pi$
$200$	5.07302	−	7.63963i	0.358717	−	0.540204i
$201$	−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
$205$	7.12059	+	25.3202i	0.497324	+	1.76844i
$206$	−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
$210$	0.000778193	−	0.00545916i	5.37004e−5	−	0.000376718i
$211$	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
$215$	−12.6857	−	14.7448i	−0.865157	−	1.00558i
$216$	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
$220$	−1.70482	−	17.0586i	−0.114939	−	1.15009i
$221$	−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	−0.956870	−	0.290516i	$-0.906173\pi$
$223$	−15.0996	+	10.5728i	−1.01114	+	0.708010i	−0.0542728	+	0.998526i	$0.517284\pi$
$224$	−0.00235221	+	0.00407414i	−0.000157163	+	0.000272215i
$225$	1.62663	−	14.9115i	0.108442	−	0.994103i
$226$	1.22863	+	2.12804i	0.0817271	+	0.141555i
$227$	−14.1883	−	6.61613i	−0.941713	−	0.439128i	−0.109750	−	0.993959i	$-0.535005\pi$
$227$	−14.1883	−	6.61613i	−0.941713	−	0.439128i	−0.831963	+	0.554831i	$0.812783\pi$
$228$	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	$0.852830\pi$
$230$	20.3998	−	14.6626i	1.34513	−	0.966825i
$231$	−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	0.330457	−	0.943821i	$-0.392797\pi$
$233$	2.20921	+	0.591957i	0.144730	+	0.0387804i	−0.185726	+	0.982601i	$0.559464\pi$
$234$	−15.4911	+	14.1256i	−1.01269	+	0.923421i
$235$	−1.54645	+	0.292404i	−0.100879	+	0.0190744i
$236$	−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	$-0.135648\pi$
$240$	−2.98521	+	5.58781i	−0.192694	+	0.360691i
$241$	−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
$245$	10.9305	−	11.2037i	0.698326	−	0.715780i
$246$	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
$250$	−22.7725	+	9.25685i	−1.44026	+	0.585454i
$251$	−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
$255$	−11.9467	−	23.5612i	−0.748129	−	1.47546i
$256$	−3.10423	+	2.60476i	−0.194015	+	0.162798i
$257$	−12.0332	−	1.05277i	−0.750612	−	0.0656701i	−0.294572	−	0.955629i	$-0.595177\pi$
$257$	−12.0332	−	1.05277i	−0.750612	−	0.0656701i	−0.456040	+	0.889959i	$0.650733\pi$
$258$	−23.9014	−	22.9366i	−1.48804	−	1.42797i
$259$	−5.81013e−5	0	0.000159632i	−3.61024e−6	0	9.91906e-6i
$260$	19.0114	+	6.65503i	1.17904	+	0.412728i
$261$	−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	0.638629	−	0.769515i	$-0.279502\pi$
$263$	−4.91225	−	7.01542i	−0.302902	−	0.432589i	−0.941531	+	0.336926i	$0.890613\pi$
$264$	−1.66625	−	8.43052i	−0.102550	−	0.518863i
$265$	−16.9726	+	6.41581i	−1.04262	+	0.394120i
$266$	−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	$0.322703\pi$
$270$	0.335520	−	25.5441i	0.0204191	−	1.55457i
$271$	−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
$275$	−6.47166	+	11.8769i	−0.390256	+	0.716204i
$276$	18.8798	−	16.5164i	1.13643	−	0.994172i
$277$	11.4745	+	16.3872i	0.689433	+	0.984613i	0.999426	+	0.0338740i	$0.0107845\pi$
$277$	11.4745	+	16.3872i	0.689433	+	0.984613i	−0.309993	+	0.950739i	$0.600327\pi$
$278$	−1.73690	−	6.48220i	−0.104172	−	0.388776i
$279$	−9.97002	+	12.9278i	−0.596889	+	0.773964i
$280$	−0.00239295	+	0.00115202i	−0.000143006	+	6.88462e-5i
$281$	−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	0.522916	−	0.852384i	$-0.324844\pi$
$283$	14.9700	+	1.30970i	0.889873	+	0.0778538i	0.366957	+	0.930238i	$0.380400\pi$
$284$	26.1518	−	21.9440i	1.55182	−	1.30213i
$285$	−6.66661	+	1.40333i	−0.394896	+	0.0831258i
$286$	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
$290$	−24.1534	+	14.3453i	−1.41834	+	0.842387i
$291$	−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	0.971144	−	0.238495i	$-0.0766542\pi$
$293$	18.4726	+	12.9347i	1.07918	+	0.755651i	0.108038	+	0.994147i	$0.465543\pi$
$294$	16.7109	−	20.7695i	0.974602	−	1.21130i
$295$	3.59723	+	3.50951i	0.209439	+	0.204332i
$296$		−	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
$300$	−21.7528	+	11.3694i	−1.25590	+	0.656411i
$301$	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
$305$	−8.29512	+	12.1634i	−0.474977	+	0.696477i
$306$	−24.0806	−	38.0033i	−1.37660	−	2.17250i
$307$	4.88220	+	1.30818i	0.278642	+	0.0746619i	0.395434	−	0.918495i	$-0.370594\pi$
$307$	4.88220	+	1.30818i	0.278642	+	0.0746619i	−0.116792	+	0.993156i	$0.537261\pi$
$308$	−0.00209822	+	0.00449965i	−0.000119557	+	0.000256392i
$309$	11.8751	−	0.244625i	0.675553	−	0.0139162i
$310$	26.4034	+	4.32034i	1.49961	+	0.245379i
$311$	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	−0.423734	−	0.905787i	$-0.639281\pi$
$313$	−24.5912	−	11.4671i	−1.38998	−	0.648157i	−0.966244	+	0.257629i	$0.917059\pi$
$314$	−0.355652	−	0.616007i	−0.0200706	−	0.0347633i
$315$	−0.00261022	+	0.00347237i	−0.000147069	+	0.000195646i
$316$	7.41094	−	12.8361i	0.416898	−	0.722089i
$317$	0.204479	−	0.143177i	0.0114847	−	0.00804165i	−0.567820	−	0.823153i	$-0.692213\pi$
$317$	0.204479	−	0.143177i	0.0114847	−	0.00804165i	0.579305	+	0.815111i	$0.303324\pi$
$318$	−27.7319	+	13.6338i	−1.55513	+	0.764547i
$319$	−5.28664	+	14.5249i	−0.295995	+	0.813240i
$320$	28.2602	−	2.82429i	1.57979	−	0.157883i
$321$	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
$325$	−9.43362	−	12.7888i	−0.523283	−	0.709394i
$326$	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
$330$	−9.04235	+	21.1864i	−0.497765	+	1.16627i
$331$	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
$335$	2.71444	−	4.83849i	0.148306	−	0.264355i
$336$	0.00156966		0.000949876i	8.56320e−5		5.18200e-5i
$337$	0.943046	−	10.7791i	0.0513710	−	0.587173i	−0.926266	−	0.376872i	$-0.877000\pi$
$337$	0.943046	−	10.7791i	0.0513710	−	0.587173i	0.977637	−	0.210302i	$-0.0674446\pi$
$338$	0.555366	−	6.34786i	0.0302079	−	0.345278i
$339$	−0.0398674	−	1.93534i	−0.00216530	−	0.105113i
$340$	−21.1496	+	37.6991i	−1.14700	+	2.04452i
$341$	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
$345$	−19.6480	+	2.37323i	−1.05781	+	0.127771i
$346$	6.15274	+	2.23942i	0.330774	+	0.120392i
$347$	13.7981	−	19.7058i	0.740723	−	1.05786i	−0.255132	−	0.966906i	$-0.582119\pi$
$347$	13.7981	−	19.7058i	0.740723	−	1.05786i	0.995855	−	0.0909561i	$-0.0289923\pi$
$348$	−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	$0.232195\pi$
$350$	0.00703921	+	0.00106279i	0.000376262	+	5.68084e-5i
$351$	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	−0.610741	−	0.791830i	$-0.709129\pi$
$353$	−20.1919	+	1.76656i	−1.07470	+	0.0940245i	−0.463963	+	0.885855i	$0.653573\pi$
$354$	6.66854	+	5.36546i	0.354429	+	0.285171i
$355$	−26.8007	+	2.67843i	−1.42243	+	0.142157i
$356$	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	$-0.0765253\pi$
$360$	−10.3108	+	6.71316i	−0.543427	+	0.353815i
$361$	−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
$365$	3.20077	+	0.523737i	0.167536	+	0.0274136i
$366$	−12.0872	+	21.9684i	−0.631807	+	1.14831i
$367$	−8.86817	+	19.0178i	−0.462914	+	0.992723i	0.526843	+	0.849963i	$0.323376\pi$
$367$	−8.86817	+	19.0178i	−0.462914	+	0.992723i	−0.989757	+	0.142761i	$0.954402\pi$
$368$	8.07380	+	2.16337i	0.420876	+	0.112773i
$369$	4.69139	−	34.9751i	0.244224	−	1.82073i
$370$	−0.726657	+	1.06552i	−0.0377771	+	0.0553940i
$371$	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	0.887064	−	0.461646i	$-0.152741\pi$
$373$	−0.710169	−	1.52296i	−0.0367712	−	0.0788560i	−0.923835	+	0.382790i	$0.874963\pi$
$374$	7.04459	+	39.9519i	0.364267	+	2.06586i
$375$	19.2327	+	2.25881i	0.993174	+	0.116644i
$376$	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	$0.903159\pi$
$380$	7.97935	+	7.78478i	0.409332	+	0.399351i
$381$	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	−0.163283	−	0.986579i	$-0.552208\pi$
$383$	9.54105	−	4.44907i	0.487525	−	0.227337i	0.650808	+	0.759243i	$0.274430\pi$
$384$	22.7633	−	4.49904i	1.16163	−	0.229591i
$385$	0.00336784	−	0.00200024i	0.000171641	−	0.000101942i
$386$	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	$0.922395\pi$
$390$	−18.0704	−	20.1488i	−0.915030	−	1.02027i
$391$	−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
$395$	−10.5365	+	5.07248i	−0.530148	+	0.255224i
$396$	−6.96989	+	21.9191i	−0.350250	+	1.10147i
$397$	2.69699	+	10.0653i	0.135358	+	0.505162i	0.999996	+	0.00276748i	$0.000880917\pi$
$397$	2.69699	+	10.0653i	0.135358	+	0.505162i	−0.864638	+	0.502395i	$0.832452\pi$
$398$	−13.3006	−	18.9952i	−0.666697	−	0.952141i
$399$	0.00186749		0.000636470i	9.34916e−5		3.18634e-5i
$400$	−7.18177	−	3.91331i	−0.359088	−	0.195665i
$401$	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
$405$	−9.93196	+	17.5030i	−0.493523	+	0.869733i
$406$	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	$0.124326\pi$
$410$	−54.0947	+	20.4484i	−2.67154	+	1.00987i
$411$	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
$415$	33.8025	+	11.8327i	1.65930	+	0.580847i
$416$	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	$0.405438\pi$
$420$	0.00709774		0.000385984i	0.000346334		1.88341e-5i
$421$	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
$425$	30.5436	−	15.1715i	1.48158	−	0.735924i
$426$	−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
$430$	29.8647	−	30.6111i	1.44020	−	1.47620i
$431$		−	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	0.496251	−	0.868179i	$-0.334710\pi$
$433$	−7.73933	−	7.73933i	−0.371929	−	0.371929i	−0.868179	+	0.496251i	$0.834710\pi$
$434$	−0.00593543	−	0.00498042i	−0.000284910	−	0.000239068i
$435$	22.1182	−	0.728809i	1.06049	−	0.0349437i
$436$	−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	$0.311314\pi$
$440$	10.9011	−	2.06120i	0.519691	−	0.0982637i
$441$	−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	$0.361982\pi$
$443$	−11.4725	+	24.6030i	−0.545077	+	1.16892i	−0.965214	+	0.261461i	$0.915796\pi$
$444$	−0.620778	+	1.12826i	−0.0294608	+	0.0535450i
$445$	−10.8734	+	7.81540i	−0.515449	+	0.370485i
$446$	−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	$0.807211\pi$
$450$	32.9726	+	0.705363i	1.55435	+	0.0332512i
$451$	−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
$455$	0.000457667		0.00457946i	2.14557e−5		0.000214688i
$456$	4.35378	+	3.50301i	0.203884	+	0.164044i
$457$	−23.5029	+	2.05624i	−1.09942	+	0.0961868i	−0.622395	−	0.782703i	$-0.713840\pi$
$457$	−23.5029	+	2.05624i	−1.09942	+	0.0961868i	−0.477025	+	0.878890i	$0.658285\pi$
$458$	10.9920	−	10.9920i	0.513624	−	0.513624i
$459$	2.18858	+	35.3743i	0.102154	+	1.65113i
$460$	21.1207	+	24.5489i	0.984757	+	1.14460i
$461$	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	−0.849397	−	0.527754i	$-0.823034\pi$
$463$	−1.35473	+	1.93475i	−0.0629594	+	0.0899154i	0.786438	+	0.617670i	$0.211923\pi$
$464$	−8.78299	−	3.19675i	−0.407740	−	0.148405i
$465$	−16.5828	−	13.0086i	−0.769011	−	0.603258i
$466$	−0.873225	+	4.95230i	−0.0404514	+	0.229411i
$467$	19.8687	−	5.32380i	0.919414	−	0.246356i	0.232079	−	0.972697i	$-0.425447\pi$
$467$	19.8687	−	5.32380i	0.919414	−	0.246356i	0.687335	+	0.726341i	$0.258780\pi$
$468$	−19.8796	−	18.3057i	−0.918936	−	0.846183i
$469$	−0.00139143		0.000803341i	−6.42501e−5		3.70948e-5i
$470$	−0.936800	−	3.33118i	−0.0432114	−	0.153656i
$471$	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
$475$	−1.74058	−	8.62122i	−0.0798632	−	0.395569i
$476$	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	$0.891728\pi$
$480$	−25.8778	−	11.0446i	−1.18115	−	0.504115i
$481$	−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
$485$	14.2657	−	12.2735i	0.647772	−	0.557312i
$486$	−13.9948	+	31.2866i	−0.634818	+	1.41919i
$487$	2.20133	−	2.20133i	0.0997518	−	0.0997518i	−0.655470	−	0.755221i	$-0.727529\pi$
$487$	2.20133	−	2.20133i	0.0997518	−	0.0997518i	0.755221	+	0.655470i	$0.227529\pi$
$488$	12.0302	−	1.05251i	0.544583	−	0.0476449i
$489$	−8.82991	+	3.42137i	−0.399302	+	0.154720i
$490$	26.6342	+	21.7943i	1.20321	+	0.984568i
$491$	−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
$495$	14.2865	−	11.1889i	0.642132	−	0.502905i
$496$	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	$0.978855\pi$
$500$	−14.4455	−	28.2030i	−0.646022	−	1.26127i
$501$	−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	0.422352	−	0.906432i	$-0.361205\pi$
$503$	7.51109	+	2.01259i	0.334903	+	0.0897370i	−0.0874487	+	0.996169i	$0.527871\pi$
$504$	0.00356013		0.000146738i	0.000158581		6.53622e-6i
$505$	21.2602	+	14.4988i	0.946066	+	0.645190i
$506$	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	$0.710674\pi$
$510$	49.3170	−	30.6819i	2.18379	−	1.35862i
$511$	−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
$515$	0.189245	+	15.3328i	0.00833913	+	0.675645i
$516$	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
$520$	−3.21807	+	12.6316i	−0.141122	+	0.553930i
$521$	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	$0.176506\pi$
$523$	−3.41584	+	12.7481i	−0.149364	+	0.557436i	−0.999522	+	0.0309077i	$0.990160\pi$
$524$	38.7741	−	14.1126i	1.69385	−	0.616512i
$525$	−0.00445484	−	0.00340667i	−0.000194425	−	0.000148679i
$526$	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
$530$	−17.3051	−	35.9458i	−0.751683	−	1.56138i
$531$	−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
$535$	10.8187	+	28.6201i	0.467734	+	1.23736i
$536$	−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
$540$	32.8399	−	2.43896i	1.41320	−	0.104956i
$541$	−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
$545$	−3.43898	+	7.61904i	−0.147310	+	0.326364i
$546$	0.00151975	+	0.00768933i	6.50395e−5	+	0.000329073i
$547$	−18.3834	−	26.2542i	−0.786018	−	1.12255i	−0.989650	−	0.143503i	$-0.954163\pi$
$547$	−18.3834	−	26.2542i	−0.786018	−	1.12255i	0.203632	−	0.979048i	$-0.434726\pi$
$548$	−5.36349	−	20.0168i	−0.229117	−	0.855076i
$549$	16.6850	−	10.5724i	0.712099	−	0.451219i
$550$	−27.2543	−	11.8990i	−1.16213	−	0.507376i
$551$	−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
$555$	0.906168	−	0.459472i	0.0384647	−	0.0195035i
$556$	8.12889	−	2.95868i	0.344742	−	0.125476i
$557$	−7.68893	+	28.6955i	−0.325791	+	1.21587i	0.587724	+	0.809061i	$0.300024\pi$
$557$	−7.68893	+	28.6955i	−0.325791	+	1.21587i	−0.913515	+	0.406806i	$0.866643\pi$
$558$	−30.2263	−	19.3601i	−1.27958	−	0.819580i
$559$	23.9433	+	13.8237i	1.01269	+	0.584679i
$560$	0.00120951	+	0.00203648i	5.11113e−5	+	8.60569e-5i
$561$	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	0.672499	−	0.740098i	$-0.265221\pi$
$563$	4.91264	+	3.43987i	0.207043	+	0.144973i	−0.465456	+	0.885071i	$0.654110\pi$
$564$	−1.24835	−	3.22176i	−0.0525652	−	0.135661i
$565$	2.49885	−	0.0308420i	0.105127	−	0.00129753i
$566$			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	$0.651894\pi$
$570$	−4.35123	−	14.3330i	−0.182253	−	0.600345i
$571$	−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
$575$	−2.85434	−	25.3899i	−0.119034	−	1.05883i
$576$	−36.3122	−	11.5467i	−1.51301	−	0.481111i
$577$	−44.1170	−	11.8211i	−1.83662	−	0.492120i	−0.838047	−	0.545597i	$-0.816303\pi$
$577$	−44.1170	−	11.8211i	−1.83662	−	0.492120i	−0.998569	+	0.0534774i	$0.982969\pi$
$578$	27.4332	−	58.8308i	1.14107	−	2.44704i
$579$	−15.8790	−	26.2399i	−0.659910	−	1.09049i
$580$	−21.1349	−	29.4047i	−0.877581	−	1.22096i
$581$	−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
$585$	4.82059	+	20.7688i	0.199307	+	0.858686i
$586$	−24.7911	+	42.9394i	−1.02411	+	1.77381i
$587$	22.7446	−	15.9259i	0.938770	−	0.657334i	−0.000687603	−	1.00000i	$-0.500219\pi$
$587$	22.7446	−	15.9259i	0.938770	−	0.657334i	0.939457	+	0.342666i	$0.111330\pi$
$588$	28.5483	+	19.1257i	1.17731	+	0.788732i
$589$	−3.27398	+	8.99519i	−0.134902	+	0.370640i
$590$	−6.99760	+	8.55157i	−0.288087	+	0.352063i
$591$	−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	−0.916199	−	0.400725i	$-0.868758\pi$
$593$	−12.5526	+	12.5526i	−0.515474	+	0.515474i	0.400725	+	0.916199i	$0.368758\pi$
$594$	22.4029	−	21.2895i	0.919201	−	0.873519i
$595$	−0.00984889		0.000739308i	−0.000403765		3.03087e-5i
$596$	−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	$0.677146\pi$
$600$	−8.55647	−	13.3823i	−0.349317	−	0.546329i
$601$	−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
$605$	7.92636	−	2.22906i	0.322252	−	0.0906243i
$606$	38.3980	+	21.1269i	1.55981	+	0.858220i
$607$	1.06222	−	12.1412i	0.0431140	−	0.492796i	−0.943685	−	0.330846i	$-0.892666\pi$
$607$	1.06222	−	12.1412i	0.0431140	−	0.492796i	0.986799	−	0.161950i	$-0.0517784\pi$
$608$	−1.11375	+	12.7303i	−0.0451686	+	0.516280i
$609$	−0.00561514	−	0.00308949i	−0.000227537	−	0.000125192i
$610$	−28.2313	−	15.8381i	−1.14305	−	0.641264i
$611$	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	−0.660960	−	0.750422i	$-0.729851\pi$
$613$	−21.2470	+	5.69311i	−0.858157	+	0.229942i	−0.197197	+	0.980364i	$0.563184\pi$
$614$	−1.92976	+	10.9442i	−0.0778789	+	0.441673i
$615$	45.1011	+	6.42909i	1.81865	+	0.259246i
$616$	−0.00301917	−	0.00109889i	−0.000121646	−	4.42754e-5i
$617$	−4.11472	+	5.87642i	−0.165652	+	0.236576i	−0.893393	−	0.449277i	$-0.851682\pi$
$617$	−4.11472	+	5.87642i	−0.165652	+	0.236576i	0.727740	+	0.685853i	$0.240571\pi$
$618$	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	$0.216139\pi$
$620$	−2.58156	+	34.3909i	−0.103678	+	1.38117i
$621$	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
$625$	−3.12097	+	24.8044i	−0.124839	+	0.992177i
$626$	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
$630$	−0.00810576	−	0.00505180i	−0.000322941	−	0.000201269i
$631$	−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
$635$	−3.77236	+	23.0545i	−0.149702	+	0.914888i
$636$	−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
$640$	5.56545	+	29.4342i	0.219994	+	1.16349i
$641$	−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	$0.200009\pi$
$643$	18.7461	+	40.2010i	0.739272	+	1.58537i	−0.0697279	+	0.997566i	$0.522213\pi$
$644$	−0.00162856	−	0.00923602i	−6.41742e−5	−	0.000363950i
$645$	−32.2371	+	9.78653i	−1.26933	+	0.385344i
$646$	−20.2081	−	16.9566i	−0.795078	−	0.667149i
$647$	−4.55768	−	4.55768i	−0.179181	−	0.179181i	0.611818	−	0.790999i	$-0.290439\pi$
$647$	−4.55768	−	4.55768i	−0.179181	−	0.179181i	−0.790999	+	0.611818i	$0.790439\pi$
$648$	16.2701	−	2.78707i	0.639148	−	0.109486i
$649$			6.07983i			0.238654i
$650$	26.2037	−	23.1133i	1.02779	−	0.906577i
$651$	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	−0.299008	−	0.954251i	$-0.596656\pi$
$653$	6.12762	−	2.85735i	0.239792	−	0.111817i	0.538800	+	0.842434i	$0.318878\pi$
$654$	−4.59261	+	13.4754i	−0.179585	+	0.526928i
$655$	−31.5469	−	8.03701i	−1.23264	−	0.314032i
$656$	−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	$0.179327\pi$
$660$	−28.2222	−	9.23138i	−1.09855	−	0.359331i
$661$	−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
$665$	−0.000841553		0.00240406i	−3.26340e−5		9.32254e-5i
$666$	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
$670$	11.1180	+	5.01828i	0.429524	+	0.193873i
$671$	−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	$0.0204434\pi$
$673$	0.682431	+	7.80022i	0.0263058	+	0.300676i	−0.971633	+	0.236496i	$0.924001\pi$
$674$	23.7902			0.916366
$675$	−22.4897	−	13.0082i	−0.865629	−	0.500686i
$676$	8.21392			0.315920
$677$	−2.64043	−	30.1802i	−0.101480	−	1.15992i	−0.860709	−	0.509097i	$-0.829979\pi$
$677$	−2.64043	−	30.1802i	−0.101480	−	1.15992i	0.759229	−	0.650823i	$-0.225576\pi$
$678$	4.23136	−	0.458186i	0.162504	−	0.0175965i
$679$	−0.00536718		0.000946379i	−0.000205974		3.63187e-5i
$680$	−25.4966	−	11.5083i	−0.977751	−	0.441325i
$681$	−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	$0.119755\pi$
$683$	8.05741	+	30.0707i	0.308308	+	1.15062i	−0.621752	+	0.783214i	$0.713579\pi$
$684$	−5.68980	−	13.8317i	−0.217555	−	0.528870i
$685$	−5.40186	+	15.4314i	−0.206394	+	0.589605i
$686$	−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
$690$	−8.96322	−	42.5805i	−0.341224	−	1.62101i
$691$	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
$695$	−6.61373	−	1.68494i	−0.250873	−	0.0639135i
$696$	−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
$700$	−0.000573927		0.00915871i	−2.16924e−5		0.000346167i
$701$		−	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
$705$	−0.618441	+	2.65491i	−0.0232918	+	0.0999898i
$706$	−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	$0.427012\pi$
$710$	−11.0024	−	58.1886i	−0.412911	−	2.18378i
$711$	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
$715$	3.10452	−	18.9730i	0.116102	−	0.709550i
$716$	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	$0.885419\pi$
$720$	6.76577	+	8.63884i	0.252145	+	0.321950i
$721$	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
$725$	0.705142	+	28.5613i	0.0261883	+	1.06074i
$726$	13.0757	−	5.06650i	0.485284	−	0.188035i
$727$	44.6377	−	3.90529i	1.65552	−	0.144839i	0.779268	−	0.626690i	$-0.215591\pi$
$727$	44.6377	−	3.90529i	1.65552	−	0.144839i	0.876253	+	0.481851i	$0.160035\pi$
$728$	0.00266931	−	0.00266931i	9.89311e−5	−	9.89311e-5i
$729$	21.5403	−	16.2793i	0.797787	−	0.602939i
$730$	−0.533792	+	7.11105i	−0.0197565	+	0.263192i
$731$	−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	−0.506429	−	0.862282i	$-0.669035\pi$
$733$	12.9159	−	18.4458i	0.477060	−	0.681312i	0.983489	+	0.180970i	$0.0579237\pi$
$734$	−43.3544	−	15.7797i	−1.60024	−	0.582440i
$735$	−10.1064	−	25.1567i	−0.372781	−	0.927919i
$736$	−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	$0.118832\pi$
$740$	−1.44992	−	0.813418i	−0.0533000	−	0.0299018i
$741$	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	$0.183279\pi$
$743$	−2.22992	+	25.4881i	−0.0818078	+	0.935068i	−0.920572	+	0.390573i	$0.872277\pi$
$744$	0.356047	+	17.2840i	0.0130533	+	0.633664i
$745$	21.8202	−	6.13631i	0.799430	−	0.224817i
$746$	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
$750$	−1.26198	+	42.5585i	−0.0460809	+	1.55402i
$751$	−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
$755$	41.4732	+	3.11319i	1.50936	+	0.113301i
$756$	−0.00853770	−	0.00424924i	−0.000310513	−	0.000154543i
$757$	37.3446	−	37.3446i	1.35731	−	1.35731i	0.480097	−	0.877215i	$-0.340601\pi$
$757$	37.3446	−	37.3446i	1.35731	−	1.35731i	0.877215	−	0.480097i	$-0.159399\pi$
$758$	−25.5472	+	2.23509i	−0.927917	+	0.0811822i
$759$	−18.6540	−	15.0088i	−0.677096	−	0.544786i
$760$	−4.56862	+	5.58318i	−0.165721	+	0.202523i
$761$	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
$765$	−45.6898	+	2.44837i	−1.65192	+	0.0885209i
$766$	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	$0.786981\pi$
$770$	0.00502653	+	0.00699332i	0.000181144	+	0.000252022i
$771$	−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	−0.380108	−	0.924942i	$-0.624113\pi$
$773$	−32.5784	−	8.72934i	−1.17176	−	0.313973i	−0.791654	+	0.610970i	$0.790780\pi$
$774$	−53.0627	+	21.8278i	−1.90730	+	0.784583i
$775$	16.9701	−	21.2690i	0.609585	−	0.764005i
$776$	−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
$780$	23.8437	−	25.4685i	0.853740	−	0.911920i
$781$	−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
$785$	−0.723345	+	0.00892787i	−0.0258173	+	0.000318649i
$786$	−54.7877	−	8.50106i	−1.95421	−	0.303223i
$787$	1.89659	+	1.32801i	0.0676063	+	0.0473384i	0.606891	−	0.794785i	$-0.292416\pi$
$787$	1.89659	+	1.32801i	0.0676063	+	0.0473384i	−0.539285	+	0.842123i	$0.681305\pi$
$788$	43.6296	−	20.3448i	1.55424	−	0.724754i
$789$	−14.5522	+	2.87616i	−0.518072	+	0.102394i
$790$	−13.1294	−	22.1062i	−0.467123	−	0.786502i
$791$	−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
$795$	−1.70655	+	31.3812i	−0.0605251	+	1.11298i
$796$	22.8981	−	19.2138i	0.811602	−	0.681015i
$797$	16.5943	+	1.45181i	0.587801	+	0.0514259i	0.377177	−	0.926141i	$-0.376895\pi$
$797$	16.5943	+	1.45181i	0.587801	+	0.0514259i	0.210624	+	0.977567i	$0.432450\pi$
$798$	−0.00103621	+	0.00421236i	−3.66813e−5	+	0.000149116i
$799$	1.64198	+	4.51129i	0.0580889	+	0.159598i
$800$	14.5338	−	33.2892i	0.513848	−	1.17695i
$801$	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
$805$	−0.00304407	+	0.00674411i	−0.000107289	+	0.000237699i
$806$	−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	$0.735038\pi$
$810$	−40.2403	−	18.4000i	−1.41390	−	0.646512i
$811$	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
$815$	−4.32272	−	11.4354i	−0.151418	−	0.400566i
$816$	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
$820$	−32.3359	−	67.1676i	−1.12922	−	2.34560i
$821$	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	−0.531298	−	0.847185i	$-0.678295\pi$
$823$	−34.4725	−	3.01595i	−1.20164	−	0.105130i	−0.670338	+	0.742056i	$0.733851\pi$
$824$	9.63498	−	8.08471i	0.335651	−	0.281644i
$825$	14.2921	+	18.5625i	0.497588	+	0.646262i
$826$	0.00300703	−	0.00109447i	0.000104628	−	3.80815e-5i
$827$	5.23409	−	19.5339i	0.182007	−	0.679261i	−0.813244	−	0.581923i	$-0.802301\pi$
$827$	5.23409	−	19.5339i	0.182007	−	0.679261i	0.995251	−	0.0973378i	$-0.0310327\pi$
$828$	−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	$-0.703001\pi$
$830$	−19.4399	+	76.3055i	−0.674769	+	2.64860i
$831$	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
$835$	−0.508179	−	41.1732i	−0.0175863	−	1.42486i
$836$			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	$0.708301\pi$
$840$	0.000151491		0.00459752i	5.22693e−6		0.000158629i
$841$	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
$845$	−5.35396	−	3.65125i	−0.184182	−	0.125607i
$846$	−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
$850$	39.0832	+	63.9928i	1.34054	+	2.19493i
$851$	−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	0.943724	−	0.330734i	$-0.107296\pi$
$853$	37.8798	+	17.6637i	1.29698	+	0.604792i	0.353257	+	0.935526i	$0.385074\pi$
$854$	0.00468729	+	0.00811862i	0.000160396	+	0.000277813i
$855$	−2.43978	+	11.5450i	−0.0834387	+	0.394830i
$856$	12.5483	−	21.7343i	0.428893	−	0.742864i
$857$	−21.9778	+	15.3891i	−0.750749	+	0.525680i	−0.885183	−	0.465242i	$-0.845967\pi$
$857$	−21.9778	+	15.3891i	−0.750749	+	0.525680i	0.134434	+	0.990923i	$0.457078\pi$
$858$	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	$0.983809\pi$
$860$	42.6641	+	34.9113i	1.45483	+	1.19047i
$861$	−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	−0.559116	−	0.829089i	$-0.688859\pi$
$863$	7.93097	−	7.93097i	0.269973	−	0.269973i	0.829089	+	0.559116i	$0.188859\pi$
$864$	26.0037	+	27.3635i	0.884663	+	0.930927i
$865$	5.04784	−	4.34292i	0.171632	−	0.147664i
$866$	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
$870$	5.83478	+	48.3062i	0.197818	+	1.63773i
$871$	−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
$875$	0.00444532	−	0.00571467i	0.000150279	−	0.000193191i
$876$	0.146645	+	7.11876i	0.00495466	+	0.240521i
$877$	0.0855499	−	0.977840i	0.00288882	−	0.0330193i	−0.994613	−	0.103653i	$-0.966947\pi$
$877$	0.0855499	−	0.977840i	0.00288882	−	0.0330193i	0.997502	+	0.0706341i	$0.0225023\pi$
$878$	−5.57448	+	63.7167i	−0.188130	+	2.15033i
$879$	33.4170	−	20.2222i	1.12713	−	0.682077i
$880$	−2.67861	−	9.52492i	−0.0902961	−	0.321085i
$881$	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	0.627457	−	0.778652i	$-0.284096\pi$
$883$	46.3611	−	12.4224i	1.56018	−	0.418048i	0.932719	+	0.360604i	$0.117429\pi$
$884$	10.6693	−	60.5085i	0.358847	−	2.03512i
$885$	8.07717	−	3.24492i	0.271511	−	0.109077i
$886$	−56.0866	−	20.4139i	−1.88427	−	0.685817i
$887$	−3.82768	+	5.46649i	−0.128521	+	0.183547i	−0.878255	−	0.478192i	$-0.841292\pi$
$887$	−3.82768	+	5.46649i	−0.128521	+	0.183547i	0.749734	+	0.661739i	$0.230181\pi$
$888$	−0.762379	−	0.336565i	−0.0255837	−	0.0112944i
$889$	0.00434872	−	0.00518260i	0.000145851	−	0.000173819i
$890$	−19.2018	−	22.3185i	−0.643646	−	0.748119i
$891$	−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
$895$	−3.67452	−	36.7676i	−0.122826	−	1.22901i
$896$	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
$900$	2.79861	+	42.4206i	0.0932869	+	1.41402i
$901$	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
$905$	17.4867	−	12.5688i	0.581279	−	0.417801i
$906$	70.8162	−	1.45879i	2.35271	−	0.0484652i
$907$	0.500360	−	1.07303i	0.0166142	−	0.0356292i	−0.897826	−	0.440351i	$-0.854854\pi$
$907$	0.500360	−	1.07303i	0.0166142	−	0.0356292i	0.914440	+	0.404722i	$0.132632\pi$
$908$	42.8576	+	11.4837i	1.42228	+	0.381099i
$909$	−18.4792	−	29.1633i	−0.612917	−	0.967286i
$910$	−0.00994274	+	0.00187998i	−0.000329599	+	6.23208e-5i
$911$	−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
$915$	13.4706	+	21.6522i	0.445325	+	0.715800i
$916$	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	$0.886110\pi$
$920$	−14.6348	+	15.0006i	−0.482496	+	0.494556i
$921$	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
$925$	0.583498	+	1.17471i	0.0191853	+	0.0386244i
$926$	−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	$0.224150\pi$
$930$	25.3151	−	38.8144i	0.830115	−	1.27277i
$931$	−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
$935$	38.9411	+	13.6315i	1.27351	+	0.445799i
$936$	10.6800	−	13.8484i	0.349088	−	0.452650i
$937$	−4.43173	−	16.5394i	−0.144778	−	0.540320i	−0.999765	−	0.0216704i	$-0.993102\pi$
$937$	−4.43173	−	16.5394i	−0.144778	−	0.540320i	0.854987	−	0.518650i	$-0.173565\pi$
$938$	−0.00202620	−	0.00289372i	−6.61579e−5	−	9.44832e-5i
$939$	−35.3716	+	30.9438i	−1.15431	+	1.00981i
$940$	4.17244	−	1.57723i	0.136090	−	0.0514435i
$941$	−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
$945$	0.00367614	+	0.00656489i	0.000119585	+	0.000213556i
$946$	51.7372			1.68212
$947$	2.48308	+	28.3818i	0.0806894	+	0.922284i	0.923380	+	0.383886i	$0.125415\pi$
$947$	2.48308	+	28.3818i	0.0806894	+	0.922284i	−0.842691	+	0.538398i	$0.819030\pi$
$948$	−15.1550	−	20.7218i	−0.492211	−	0.673012i
$949$	−4.54003	+	0.800530i	−0.147376	+	0.0259863i
$950$	18.5496	−	5.46447i	0.601829	−	0.177291i
$951$	−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	$0.223188\pi$
$953$	13.1177	+	48.9558i	0.424923	+	1.58583i	−0.339169	+	0.940726i	$0.610146\pi$
$954$	2.20422	+	53.4786i	0.0713644	+	1.73143i
$955$	2.49888	−	1.20301i	0.0808617	−	0.0389285i
$956$	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
$960$	15.2932	−	46.7542i	0.493585	−	1.50899i
$961$	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
$965$	34.0437	−	20.2194i	1.09591	−	0.650885i
$966$	−0.00406522	+	0.0119279i	−0.000130796	+	0.000383775i
$967$	−48.1057	+	22.4321i	−1.54697	+	0.721366i	−0.993746	−	0.111663i	$-0.964382\pi$
$967$	−48.1057	+	22.4321i	−1.54697	+	0.721366i	−0.553229	+	0.833029i	$0.686604\pi$
$968$	−5.53233	−	3.87378i	−0.177816	−	0.124508i
$969$	7.50827	+	19.3774i	0.241200	+	0.622492i
$970$	29.6166	+	28.8944i	0.950931	+	0.927743i
$971$		−	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
$975$	−26.8629	+	6.00181i	−0.860302	+	0.192212i
$976$	−1.87021	−	10.6065i	−0.0598639	−	0.339505i
$977$	7.99244	+	17.1398i	0.255701	+	0.548352i	0.991691	−	0.128639i	$-0.0410610\pi$
$977$	7.99244	+	17.1398i	0.255701	+	0.548352i	−0.735991	+	0.676992i	$0.763283\pi$
$978$	−9.18592	−	18.6846i	−0.293733	−	0.597469i
$979$	−15.9536	−	2.81305i	−0.509879	−	0.0899055i
$980$	−24.9946	+	36.6506i	−0.798424	+	1.17076i
$981$	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	−0.975482	−	0.220080i	$-0.929368\pi$
$983$	−5.63921	+	12.0933i	−0.179863	+	0.385717i	0.795619	+	0.605798i	$0.207146\pi$
$984$	−19.3464	−	31.9698i	−0.616742	−	1.01916i
$985$	−37.4821	−	6.13314i	−1.19428	−	0.195418i
$986$	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
$990$	27.2450	+	29.1479i	0.865902	+	0.926380i
$991$	−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
$995$	−23.4662	+	2.34519i	−0.743930	+	0.0743476i
$996$	−12.0553	+	77.6941i	−0.381987	+	2.46183i
$997$	−45.5235	+	3.98279i	−1.44174	+	0.126136i	−0.781026	−	0.624498i	$-0.785304\pi$
$997$	−45.5235	+	3.98279i	−1.44174	+	0.126136i	−0.660718	+	0.750634i	$0.729748\pi$
$998$	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	135.2.q.a.38.14	yes	192
3.2	odd	2		405.2.r.a.278.3		192
5.2	odd	4	inner	135.2.q.a.92.3	yes	192
5.3	odd	4		675.2.ba.b.632.14		192
5.4	even	2		675.2.ba.b.443.3		192
15.2	even	4		405.2.r.a.197.14		192
27.5	odd	18	inner	135.2.q.a.113.3	yes	192
27.22	even	9		405.2.r.a.368.14		192
135.22	odd	36		405.2.r.a.287.3		192
135.32	even	36	inner	135.2.q.a.32.14	✓	192
135.59	odd	18		675.2.ba.b.518.14		192
135.113	even	36		675.2.ba.b.32.3		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.14	✓	192	135.32	even	36	inner
135.2.q.a.38.14	yes	192	1.1	even	1	trivial
135.2.q.a.92.3	yes	192	5.2	odd	4	inner
135.2.q.a.113.3	yes	192	27.5	odd	18	inner
405.2.r.a.197.14		192	15.2	even	4
405.2.r.a.278.3		192	3.2	odd	2
405.2.r.a.287.3		192	135.22	odd	36
405.2.r.a.368.14		192	27.22	even	9
675.2.ba.b.32.3		192	135.113	even	36
675.2.ba.b.443.3		192	5.4	even	2
675.2.ba.b.518.14		192	135.59	odd	18
675.2.ba.b.632.14		192	5.3	odd	4

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.191628 + 2.19031i) q^{2} +(0.699511 - 1.58451i) q^{3} +(-2.79113 + 0.492152i) q^{4} +(2.03807 + 0.919920i) q^{5} +(3.60463 + 1.22851i) q^{6} +(-0.000371431 - 0.000530458i) q^{7} +(-0.474704 - 1.77162i) q^{8} +(-2.02137 - 2.21677i) q^{9} +O(q^{10})\)	\(q+(0.191628 + 2.19031i) q^{2} +(0.699511 - 1.58451i) q^{3} +(-2.79113 + 0.492152i) q^{4} +(2.03807 + 0.919920i) q^{5} +(3.60463 + 1.22851i) q^{6} +(-0.000371431 - 0.000530458i) q^{7} +(-0.474704 - 1.77162i) q^{8} +(-2.02137 - 2.21677i) q^{9} +(-1.62436 + 4.64030i) q^{10} +(0.925209 + 2.54199i) q^{11} +(-1.17261 + 4.76685i) q^{12} +(-3.16625 - 0.277011i) q^{13} +(0.00109069 - 0.000915200i) q^{14} +(2.88328 - 2.58586i) q^{15} +(-1.53710 + 0.559459i) q^{16} +(1.76536 - 6.58840i) q^{17} +(4.46807 - 4.85222i) q^{18} +(-1.52337 - 0.879517i) q^{19} +(-6.14128 - 1.56458i) q^{20} +(-0.00110034 + 0.000217476i) q^{21} +(-5.39046 + 2.51361i) q^{22} +(-4.18584 - 2.93096i) q^{23} +(-3.13922 - 0.487092i) q^{24} +(3.30749 + 3.74973i) q^{25} -6.98815i q^{26} +(-4.92647 + 1.65223i) q^{27} +(0.00129778 + 0.00129778i) q^{28} +(4.37718 + 3.67289i) q^{29} +(6.21636 + 5.81977i) q^{30} +(-0.944975 - 5.35922i) q^{31} +(-3.07020 - 6.58407i) q^{32} +(4.67501 + 0.312144i) q^{33} +(14.7689 + 2.60416i) q^{34} +(-0.000269024 - 0.00142280i) q^{35} +(6.73289 + 5.19248i) q^{36} +(0.253391 + 0.0678960i) q^{37} +(1.63450 - 3.50519i) q^{38} +(-2.65375 + 4.82319i) q^{39} +(0.662267 - 4.04738i) q^{40} +(7.56097 + 9.01082i) q^{41} +(-0.000687195 - 0.00236841i) q^{42} +(-7.88368 - 3.67622i) q^{43} +(-3.83342 - 6.63969i) q^{44} +(-2.08045 - 6.37744i) q^{45} +(5.61759 - 9.72995i) q^{46} +(-0.576559 + 0.403711i) q^{47} +(-0.188748 + 2.82690i) q^{48} +(2.39414 - 6.57785i) q^{49} +(-7.57928 + 7.96300i) q^{50} +(-9.20452 - 7.40589i) q^{51} +(8.97374 - 0.785101i) q^{52} +(-5.73786 + 5.73786i) q^{53} +(-4.56295 - 10.4739i) q^{54} +(-0.452784 + 6.03188i) q^{55} +(-0.000763450 + 0.000909845i) q^{56} +(-2.45922 + 1.79857i) q^{57} +(-7.20599 + 10.2912i) q^{58} +(2.11198 + 0.768697i) q^{59} +(-6.77498 + 8.63650i) q^{60} +(-1.14333 + 6.48417i) q^{61} +(11.5573 - 3.09676i) q^{62} +(-0.000425105 + 0.00189563i) q^{63} +(10.9996 - 6.35064i) q^{64} +(-6.19822 - 3.47726i) q^{65} +(0.212168 + 10.2996i) q^{66} +(0.216242 - 2.47165i) q^{67} +(-1.68485 + 19.2579i) q^{68} +(-7.57218 + 4.58228i) q^{69} +(0.00306482 - 0.000861895i) q^{70} +(-10.4316 + 6.02267i) q^{71} +(-2.96772 + 4.63341i) q^{72} +(1.40104 - 0.375408i) q^{73} +(-0.100157 + 0.568017i) q^{74} +(8.25513 - 2.61779i) q^{75} +(4.68478 + 1.70512i) q^{76} +(0.00100477 - 0.00143496i) q^{77} +(-11.0728 - 4.88829i) q^{78} +(-3.36157 + 4.00616i) q^{79} +(-3.64738 - 0.273791i) q^{80} +(-0.828138 + 8.96182i) q^{81} +(-18.2876 + 18.2876i) q^{82} +(15.9554 - 1.39592i) q^{83} +(0.00296416 - 0.00114854i) q^{84} +(9.65872 - 11.8037i) q^{85} +(6.54134 - 17.9722i) q^{86} +(8.88163 - 4.36647i) q^{87} +(4.06424 - 2.84581i) q^{88} +(-2.99426 + 5.18621i) q^{89} +(13.5699 - 5.77892i) q^{90} +(0.00102910 + 0.00178245i) q^{91} +(13.1257 + 6.12062i) q^{92} +(-9.15278 - 2.25151i) q^{93} +(-0.994737 - 1.18548i) q^{94} +(-2.29565 - 3.19390i) q^{95} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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