LMFDB - Embedded newform 135.2.q.a.32.14

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			32.14
Character	$\chi$	$=$	135.32
Dual form			135.2.q.a.38.14

$q$-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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{4}\right)$

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	−0.558923	−	0.829219i	$-0.688785\pi$
$2$	0.191628	−	2.19031i	0.135501	−	1.54878i	0.694425	−	0.719566i	$-0.255659\pi$
$3$	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	−0.819222	−	0.573476i	$-0.805595\pi$
$7$	−0.000371431	0	0.000530458i	−0.000140388	0	0.000200494i	0.819082	+	0.573677i	$0.194483\pi$
$8$	−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	−0.718520	−	0.695506i	$-0.755180\pi$
$11$	0.925209	−	2.54199i	0.278961	−	0.766439i	0.997481	−	0.0709326i	$-0.0225975\pi$
$12$	−1.17261	−	4.76685i	−0.338502	−	1.37607i
$13$	−3.16625	+	0.277011i	−0.878159	+	0.0768289i	−0.517313	−	0.855797i	$-0.673068\pi$
$13$	−3.16625	+	0.277011i	−0.878159	+	0.0768289i	−0.360846	+	0.932625i	$0.617512\pi$
$14$	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	0.756921	+	0.653507i	$0.226703\pi$
$17$	1.76536	+	6.58840i	0.428162	+	1.59792i	−0.328759	+	0.944414i	$0.606630\pi$
$18$	4.46807	+	4.85222i	1.05313	+	1.14368i
$19$	−1.52337	+	0.879517i	−0.349485	+	0.201775i	−0.664458	−	0.747325i	$-0.731338\pi$
$19$	−1.52337	+	0.879517i	−0.349485	+	0.201775i	0.314974	+	0.949100i	$0.398004\pi$
$20$	−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	−0.921806	−	0.387652i	$-0.873286\pi$
$23$	−4.18584	+	2.93096i	−0.872808	+	0.611147i	0.0489979	+	0.998799i	$0.484397\pi$
$24$	−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	−0.138458	−	0.990368i	$-0.544215\pi$
$29$	4.37718	−	3.67289i	0.812822	−	0.682038i	0.951279	+	0.308330i	$0.0997701\pi$
$30$	6.21636	−	5.81977i	1.13495	−	1.06254i
$31$	−0.944975	+	5.35922i	−0.169723	+	0.962544i	0.774338	+	0.632772i	$0.218083\pi$
$31$	−0.944975	+	5.35922i	−0.169723	+	0.962544i	−0.944061	+	0.329772i	$0.893028\pi$
$32$	−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	−0.237930	−	0.971282i	$-0.576469\pi$
$37$	0.253391	−	0.0678960i	0.0416573	−	0.0111620i	0.279587	+	0.960120i	$0.409802\pi$
$38$	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	0.287537	−	0.957770i	$-0.407164\pi$
$41$	7.56097	−	9.01082i	1.18083	−	1.40725i	0.893289	−	0.449483i	$-0.148392\pi$
$42$	−0.000687195		0.00236841i	−0.000106037		0.000365454i
$43$	−7.88368	+	3.67622i	−1.20225	+	0.560618i	−0.917405	−	0.397955i	$-0.869720\pi$
$43$	−7.88368	+	3.67622i	−1.20225	+	0.560618i	−0.284845	+	0.958574i	$0.591942\pi$
$44$	−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	0.530770	−	0.847516i	$-0.321903\pi$
$47$	−0.576559	−	0.403711i	−0.0840997	−	0.0588873i	−0.614870	+	0.788628i	$0.710792\pi$
$48$	−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	0.193036	−	0.981192i	$-0.438167\pi$
$53$	−5.73786	−	5.73786i	−0.788156	−	0.788156i	−0.981192	+	0.193036i	$0.938167\pi$
$54$	−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	−0.200862	−	0.979620i	$-0.564374\pi$
$59$	2.11198	−	0.768697i	0.274956	−	0.100076i	0.475818	+	0.879544i	$0.342152\pi$
$60$	−6.77498	−	8.63650i	−0.874647	−	1.11497i
$61$	−1.14333	−	6.48417i	−0.146389	−	0.830213i	−0.966241	−	0.257638i	$-0.917056\pi$
$61$	−1.14333	−	6.48417i	−0.146389	−	0.830213i	0.819852	−	0.572575i	$-0.194055\pi$
$62$	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	0.997896	+	0.0648313i	$0.0206509\pi$
$67$	0.216242	+	2.47165i	0.0264181	+	0.301960i	−0.971478	+	0.237129i	$0.923794\pi$
$68$	−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	−0.269314	−	0.963052i	$-0.586797\pi$
$71$	−10.4316	−	6.02267i	−1.23800	−	0.714759i	−0.968685	+	0.248294i	$0.920130\pi$
$72$	−2.96772	−	4.63341i	−0.349749	−	0.546052i
$73$	1.40104	+	0.375408i	0.163979	+	0.0439381i	0.339875	−	0.940471i	$-0.389615\pi$
$73$	1.40104	+	0.375408i	0.163979	+	0.0439381i	−0.175895	+	0.984409i	$0.556282\pi$
$74$	−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	0.543041	−	0.839706i	$-0.317273\pi$
$79$	−3.36157	−	4.00616i	−0.378206	−	0.450729i	−0.921247	+	0.388978i	$0.872828\pi$
$80$	−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	0.917224	−	0.398372i	$-0.130425\pi$
$83$	15.9554	+	1.39592i	1.75134	+	0.153222i	0.834113	+	0.551594i	$0.185980\pi$
$84$	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	0.662552	−	0.749016i	$-0.269473\pi$
$89$	−2.99426	−	5.18621i	−0.317391	−	0.549737i	−0.979943	+	0.199279i	$0.936140\pi$
$90$	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	0.999987	+	0.00512815i	$0.00163235\pi$
$97$	3.55678	+	7.62753i	0.361136	+	0.774459i	−0.638851	+	0.769331i	$0.720590\pi$
$98$	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	0.421496	−	0.906830i	$-0.361505\pi$
$101$	11.3335	−	1.99841i	1.12773	−	0.198849i	0.706231	+	0.707981i	$0.250394\pi$
$102$	14.4574	+	21.5799i	1.43149	+	2.13673i
$103$	2.89813	−	6.21507i	0.285562	−	0.612389i	−0.710237	−	0.703963i	$-0.751412\pi$
$103$	2.89813	−	6.21507i	0.285562	−	0.612389i	0.995798	+	0.0915740i	$0.0291898\pi$
$104$	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	−0.0626673	−	0.998034i	$-0.519961\pi$
$107$	9.67551	−	9.67551i	0.935367	−	0.935367i	0.998034	+	0.0626673i	$0.0199607\pi$
$108$	12.9373	+	7.03617i	1.24489	+	0.677056i
$109$		−	3.73835i		−	0.358069i	−0.983843	−	0.179034i	$-0.942703\pi$
$109$		−	3.73835i		−	0.358069i	0.983843	−	0.179034i	$-0.0572974\pi$
$110$	−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	0.469676	−	0.882839i	$-0.344371\pi$
$113$	1.01289	+	0.472320i	0.0952851	+	0.0444322i	−0.374391	+	0.927271i	$0.622148\pi$
$114$	−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	−0.735920	−	0.677068i	$-0.763250\pi$
$127$	2.70398	−	10.0914i	0.239940	−	0.895467i	0.975860	−	0.218398i	$-0.0700832\pi$
$128$	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	−0.492341	−	0.870402i	$-0.663859\pi$
$131$	−14.3376	−	2.52811i	−1.25269	−	0.220882i	−0.760345	+	0.649520i	$0.774970\pi$
$132$	−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	−0.919132	−	0.393950i	$-0.871108\pi$
$137$	0.637262	−	7.28394i	0.0544450	−	0.622309i	0.973577	−	0.228359i	$-0.0733361\pi$
$138$	−11.4877	+	15.7074i	−0.977896	+	1.33710i
$139$	−3.00586	−	0.530014i	−0.254953	−	0.0449552i	0.0447106	−	0.999000i	$-0.485763\pi$
$139$	−3.00586	−	0.530014i	−0.254953	−	0.0449552i	−0.299664	+	0.954045i	$0.596875\pi$
$140$	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	0.902834	−	0.429988i	$-0.141482\pi$
$149$	7.76525	+	6.51582i	0.636154	+	0.533797i	−0.266680	+	0.963785i	$0.585927\pi$
$150$	7.31569	−	17.5797i	0.597324	−	1.43537i
$151$	17.4779	+	6.36142i	1.42233	+	0.517685i	0.934722	−	0.355379i	$-0.115648\pi$
$151$	17.4779	+	6.36142i	1.42233	+	0.517685i	0.487605	+	0.873064i	$0.337870\pi$
$152$	−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	0.410883	−	0.911688i	$-0.365220\pi$
$157$	−0.293204	−	0.136723i	−0.0234002	−	0.0109117i	−0.434283	+	0.900776i	$0.642998\pi$
$158$	−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	−0.842110	−	0.539306i	$-0.818687\pi$
$163$	−3.86594	+	3.86594i	−0.302804	+	0.302804i	0.539306	+	0.842110i	$0.318687\pi$
$164$	−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	0.334838	+	0.942276i	$0.391318\pi$
$167$	−7.78235	+	16.6893i	−0.602217	+	1.29146i	−0.937055	+	0.349182i	$0.886459\pi$
$168$	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	0.948324	−	0.317302i	$-0.102777\pi$
$173$	1.25855	+	2.69896i	0.0956855	+	0.205198i	−0.852639	+	0.522501i	$0.824999\pi$
$174$	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	0.372365	+	0.928087i	$0.378547\pi$
$179$	−8.26245	+	14.3110i	−0.617564	+	1.06965i	−0.989929	+	0.141566i	$0.954786\pi$
$180$	8.94547	−	16.7764i	0.666756	−	1.25044i
$181$	4.81540	+	8.34051i	0.357926	+	0.619945i	0.987614	−	0.156902i	$-0.0501508\pi$
$181$	4.81540	+	8.34051i	0.357926	+	0.619945i	−0.629688	+	0.776848i	$0.716817\pi$
$182$	−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	0.794116	−	0.607766i	$-0.207934\pi$
$191$	0.797244	+	0.950119i	0.0576866	+	0.0687482i	−0.736430	+	0.676514i	$0.763490\pi$
$192$	−2.36831	+	21.8714i	−0.170918	+	1.57843i
$193$	10.1567	+	14.5052i	0.731093	+	1.04411i	0.996791	+	0.0800524i	$0.0255088\pi$
$193$	10.1567	+	14.5052i	0.731093	+	1.04411i	−0.265698	+	0.964056i	$0.585602\pi$
$194$	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	−0.378401	−	0.925642i	$-0.623526\pi$
$197$	−16.4067	−	4.39615i	−1.16893	−	0.313213i	−0.790526	+	0.612429i	$0.790193\pi$
$198$	16.4682	−	6.86847i	1.17034	−	0.488121i
$199$	−9.13371	−	5.27335i	−0.647472	−	0.373818i	0.140015	−	0.990149i	$-0.455285\pi$
$199$	−9.13371	−	5.27335i	−0.647472	−	0.373818i	−0.787487	+	0.616331i	$0.788618\pi$
$200$	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	−0.336196	−	0.941792i	$-0.609141\pi$
$211$	0.169003	−	0.0615119i	0.0116346	−	0.00423465i	0.347831	+	0.937557i	$0.386918\pi$
$212$	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	−0.0542728	−	0.998526i	$-0.517284\pi$
$223$	−15.0996	−	10.5728i	−1.01114	−	0.708010i	−0.956870	+	0.290516i	$0.906173\pi$
$224$	−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	−0.831963	−	0.554831i	$-0.812783\pi$
$227$	−14.1883	+	6.61613i	−0.941713	+	0.439128i	−0.109750	+	0.993959i	$0.535005\pi$
$228$	5.97884	+	6.23034i	0.395958	+	0.412615i
$229$	−4.54463	+	5.41608i	−0.300318	+	0.357904i	−0.895008	−	0.446050i	$-0.852830\pi$
$229$	−4.54463	+	5.41608i	−0.300318	+	0.357904i	0.594690	+	0.803955i	$0.297275\pi$
$230$	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	−0.185726	−	0.982601i	$-0.559464\pi$
$233$	2.20921	−	0.591957i	0.144730	−	0.0387804i	0.330457	+	0.943821i	$0.392797\pi$
$234$	−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	0.910563	+	0.413369i	$0.135648\pi$
$239$	−1.33675	+	7.58107i	−0.0864670	+	0.490379i	−0.997030	+	0.0770092i	$0.975463\pi$
$240$	−2.98521	−	5.58781i	−0.192694	−	0.360691i
$241$	−7.35154	+	6.16868i	−0.473555	+	0.397359i	−0.848089	−	0.529853i	$-0.822247\pi$
$241$	−7.35154	+	6.16868i	−0.473555	+	0.397359i	0.374535	+	0.927213i	$0.377802\pi$
$242$	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	−0.624067	−	0.781371i	$-0.714521\pi$
$251$	−4.10987	+	2.37283i	−0.259413	+	0.149772i	0.364654	+	0.931143i	$0.381187\pi$
$252$	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	−0.456040	−	0.889959i	$-0.650733\pi$
$257$	−12.0332	+	1.05277i	−0.750612	+	0.0656701i	−0.294572	+	0.955629i	$0.595177\pi$
$258$	−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	−0.941531	−	0.336926i	$-0.890613\pi$
$263$	−4.91225	+	7.01542i	−0.302902	+	0.432589i	0.638629	+	0.769515i	$0.279502\pi$
$264$	−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	−0.309993	−	0.950739i	$-0.600327\pi$
$277$	11.4745	−	16.3872i	0.689433	−	0.984613i	0.999426	−	0.0338740i	$-0.0107845\pi$
$278$	−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	−0.993407	−	0.114641i	$-0.963428\pi$
$281$	−2.66069	+	7.31019i	−0.158724	+	0.436089i	0.834683	+	0.550730i	$0.185651\pi$
$282$	−2.57424	−	0.746917i	−0.153294	−	0.0444783i
$283$	14.9700	−	1.30970i	0.889873	−	0.0778538i	0.366957	−	0.930238i	$-0.380400\pi$
$283$	14.9700	−	1.30970i	0.889873	−	0.0778538i	0.522916	+	0.852384i	$0.324844\pi$
$284$	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	0.108038	−	0.994147i	$-0.465543\pi$
$293$	18.4726	−	12.9347i	1.07918	−	0.755651i	0.971144	+	0.238495i	$0.0766542\pi$
$294$	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	−0.116792	−	0.993156i	$-0.537261\pi$
$307$	4.88220	−	1.30818i	0.278642	−	0.0746619i	0.395434	+	0.918495i	$0.370594\pi$
$308$	−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	−0.275805	−	0.961214i	$-0.588944\pi$
$311$	12.6744	−	15.1048i	0.718699	−	0.856512i	0.994504	+	0.104702i	$0.0333888\pi$
$312$	9.80460	−	2.41185i	0.555076	−	0.136544i
$313$	−24.5912	+	11.4671i	−1.38998	+	0.648157i	−0.966244	−	0.257629i	$-0.917059\pi$
$313$	−24.5912	+	11.4671i	−1.38998	+	0.648157i	−0.423734	+	0.905787i	$0.639281\pi$
$314$	−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	0.579305	−	0.815111i	$-0.303324\pi$
$317$	0.204479	+	0.143177i	0.0114847	+	0.00804165i	−0.567820	+	0.823153i	$0.692213\pi$
$318$	−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	0.999021	−	0.0442484i	$-0.0140893\pi$
$331$	0.820786	+	4.65491i	0.0451145	+	0.255857i	−0.953906	+	0.300105i	$0.902978\pi$
$332$	−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	0.977637	+	0.210302i	$0.0674446\pi$
$337$	0.943046	+	10.7791i	0.0513710	+	0.587173i	−0.926266	+	0.376872i	$0.877000\pi$
$338$	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	0.995855	+	0.0909561i	$0.0289923\pi$
$347$	13.7981	+	19.7058i	0.740723	+	1.05786i	−0.255132	+	0.966906i	$0.582119\pi$
$348$	−22.6408	−	16.5585i	−1.21368	−	0.887630i
$349$	−0.752338	−	0.896601i	−0.0402717	−	0.0479940i	0.745533	−	0.666469i	$-0.232195\pi$
$349$	−0.752338	−	0.896601i	−0.0402717	−	0.0479940i	−0.785804	+	0.618475i	$0.787751\pi$
$350$	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	−0.463963	−	0.885855i	$-0.653573\pi$
$353$	−20.1919	−	1.76656i	−1.07470	−	0.0940245i	−0.610741	+	0.791830i	$0.709129\pi$
$354$	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	0.971240	+	0.238102i	$0.0765253\pi$
$359$	13.1082	+	22.7040i	0.691823	+	1.19827i	−0.279418	+	0.960170i	$0.590141\pi$
$360$	−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	−0.989757	−	0.142761i	$-0.954402\pi$
$367$	−8.86817	−	19.0178i	−0.462914	−	0.992723i	0.526843	−	0.849963i	$-0.323376\pi$
$368$	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	−0.923835	−	0.382790i	$-0.874963\pi$
$373$	−0.710169	+	1.52296i	−0.0367712	+	0.0788560i	0.887064	+	0.461646i	$0.152741\pi$
$374$	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	$-0.903159\pi$
$379$		−	11.6637i		−	0.599126i	0.954077	−	0.299563i	$-0.0968408\pi$
$380$	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	0.650808	−	0.759243i	$-0.274430\pi$
$383$	9.54105	+	4.44907i	0.487525	+	0.227337i	−0.163283	+	0.986579i	$0.552208\pi$
$384$	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	−0.970427	−	0.241396i	$-0.922395\pi$
$389$	−36.8621	−	13.4167i	−1.86898	−	0.680254i	−0.898557	−	0.438858i	$-0.855383\pi$
$390$	−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	−0.864638	−	0.502395i	$-0.832452\pi$
$397$	2.69699	−	10.0653i	0.135358	−	0.505162i	0.999996	−	0.00276748i	$-0.000880917\pi$
$398$	−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	0.786931	−	0.617041i	$-0.211669\pi$
$401$	26.3401	+	4.64448i	1.31536	+	0.231934i	0.528433	+	0.848975i	$0.322780\pi$
$402$	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	0.924687	−	0.380727i	$-0.124326\pi$
$409$	33.6400	+	5.93165i	1.66339	+	0.293301i	0.738705	+	0.674028i	$0.235438\pi$
$410$	−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	0.292726	−	0.956196i	$-0.405438\pi$
$419$	−12.2431	−	10.2731i	−0.598112	−	0.501876i	−0.890838	+	0.454321i	$0.849882\pi$
$420$	0.00709774		0.000385984i	0.000346334		1.88341e-5i
$421$	29.9345	+	10.8953i	1.45892	+	0.531002i	0.945067	−	0.326878i	$-0.105997\pi$
$421$	29.9345	+	10.8953i	1.45892	+	0.531002i	0.513850	+	0.857880i	$0.328219\pi$
$422$	−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	$0.0456690\pi$
$431$			5.93676i			0.285963i	−0.989725	+	0.142982i	$0.954331\pi$
$432$	6.64813	+	5.29580i	0.319858	+	0.254794i
$433$	−7.73933	+	7.73933i	−0.371929	+	0.371929i	−0.868179	−	0.496251i	$-0.834710\pi$
$433$	−7.73933	+	7.73933i	−0.371929	+	0.371929i	0.496251	+	0.868179i	$0.334710\pi$
$434$	−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	0.558665	−	0.829394i	$-0.311314\pi$
$439$	28.6483	−	5.05146i	1.36731	−	0.241093i	0.808642	+	0.588300i	$0.200203\pi$
$440$	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	−0.965214	−	0.261461i	$-0.915796\pi$
$443$	−11.4725	−	24.6030i	−0.545077	−	1.16892i	0.420137	−	0.907461i	$-0.361982\pi$
$444$	−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	−0.822124	−	0.569308i	$-0.807211\pi$
$449$	1.73698	−	3.00854i	0.0819733	−	0.141982i	0.904097	+	0.427326i	$0.140544\pi$
$450$	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	−0.477025	−	0.878890i	$-0.658285\pi$
$457$	−23.5029	−	2.05624i	−1.09942	−	0.0961868i	−0.622395	+	0.782703i	$0.713840\pi$
$458$	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	0.872459	−	0.488688i	$-0.162524\pi$
$461$	5.14645	+	6.13330i	0.239694	+	0.285656i	−0.632765	+	0.774344i	$0.718080\pi$
$462$	0.00538467	+	0.00393812i	0.000250518	+	0.000183218i
$463$	−1.35473	−	1.93475i	−0.0629594	−	0.0899154i	0.786438	−	0.617670i	$-0.211923\pi$
$463$	−1.35473	−	1.93475i	−0.0629594	−	0.0899154i	−0.849397	+	0.527754i	$0.823034\pi$
$464$	−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	0.687335	−	0.726341i	$-0.258780\pi$
$467$	19.8687	+	5.32380i	0.919414	+	0.246356i	0.232079	+	0.972697i	$0.425447\pi$
$468$	−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	−0.942706	−	0.333624i	$-0.891728\pi$
$479$	−3.74161	−	21.2197i	−0.170958	−	0.969553i	0.771748	−	0.635929i	$-0.219383\pi$
$480$	−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	0.755221	−	0.655470i	$-0.227529\pi$
$487$	2.20133	+	2.20133i	0.0997518	+	0.0997518i	−0.655470	+	0.755221i	$0.727529\pi$
$488$	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	0.859666	−	0.510857i	$-0.170672\pi$
$491$	−2.81965	−	7.74693i	−0.127249	−	0.349614i	−0.986915	+	0.161243i	$0.948450\pi$
$492$	−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	−0.997794	−	0.0663815i	$-0.978855\pi$
$499$	−16.9583	+	20.2101i	−0.759156	+	0.904727i	0.238638	+	0.971109i	$0.423299\pi$
$500$	−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	−0.0874487	−	0.996169i	$-0.527871\pi$
$503$	7.51109	−	2.01259i	0.334903	−	0.0897370i	0.422352	+	0.906432i	$0.361205\pi$
$504$	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	−0.614580	−	0.788855i	$-0.710674\pi$
$509$	5.25087	−	29.7791i	0.232741	−	1.31994i	0.847320	−	0.531082i	$-0.178215\pi$
$510$	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	−0.445593	−	0.895236i	$-0.647007\pi$
$521$	2.44020	−	1.40885i	0.106907	−	0.0617227i	0.552500	+	0.833513i	$0.313674\pi$
$522$	37.3792	+	4.82833i	1.63604	+	0.211330i
$523$	−3.41584	−	12.7481i	−0.149364	−	0.557436i	−0.999522	−	0.0309077i	$-0.990160\pi$
$523$	−3.41584	−	12.7481i	−0.149364	−	0.557436i	0.850158	−	0.526528i	$-0.176506\pi$
$524$	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	0.203632	+	0.979048i	$0.434726\pi$
$547$	−18.3834	+	26.2542i	−0.786018	+	1.12255i	−0.989650	+	0.143503i	$0.954163\pi$
$548$	−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	−0.913515	−	0.406806i	$-0.866643\pi$
$557$	−7.68893	−	28.6955i	−0.325791	−	1.21587i	0.587724	−	0.809061i	$-0.300024\pi$
$558$	−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	−0.465456	−	0.885071i	$-0.654110\pi$
$563$	4.91264	−	3.43987i	0.207043	−	0.144973i	0.672499	+	0.740098i	$0.265221\pi$
$564$	−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	−0.459284	−	0.888289i	$-0.651894\pi$
$569$	8.00903	−	6.72037i	0.335756	−	0.281733i	0.795040	+	0.606557i	$0.207450\pi$
$570$	−4.35123	+	14.3330i	−0.182253	+	0.600345i
$571$	−1.98699	+	11.2688i	−0.0831531	+	0.471584i	0.914587	+	0.404390i	$0.132516\pi$
$571$	−1.98699	+	11.2688i	−0.0831531	+	0.471584i	−0.997740	+	0.0671948i	$0.978595\pi$
$572$	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	−0.998569	−	0.0534774i	$-0.982969\pi$
$577$	−44.1170	+	11.8211i	−1.83662	+	0.492120i	−0.838047	+	0.545597i	$0.816303\pi$
$578$	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	0.939457	−	0.342666i	$-0.111330\pi$
$587$	22.7446	+	15.9259i	0.938770	+	0.657334i	−0.000687603		1.00000i	$0.500219\pi$
$588$	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	0.400725	−	0.916199i	$-0.368758\pi$
$593$	−12.5526	−	12.5526i	−0.515474	−	0.515474i	−0.916199	+	0.400725i	$0.868758\pi$
$594$	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	−0.528234	−	0.849099i	$-0.677146\pi$
$599$	−9.47392	+	3.44823i	−0.387094	+	0.140891i	0.141140	+	0.989990i	$0.454923\pi$
$600$	−8.55647	+	13.3823i	−0.349317	+	0.546329i
$601$	−0.977209	−	5.54203i	−0.0398612	−	0.226064i	0.958369	−	0.285533i	$-0.0921705\pi$
$601$	−0.977209	−	5.54203i	−0.0398612	−	0.226064i	−0.998230	+	0.0594686i	$0.981059\pi$
$602$	−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	0.986799	+	0.161950i	$0.0517784\pi$
$607$	1.06222	+	12.1412i	0.0431140	+	0.492796i	−0.943685	+	0.330846i	$0.892666\pi$
$608$	−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	−0.197197	−	0.980364i	$-0.563184\pi$
$613$	−21.2470	−	5.69311i	−0.858157	−	0.229942i	−0.660960	+	0.750422i	$0.729851\pi$
$614$	−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	0.727740	−	0.685853i	$-0.240571\pi$
$617$	−4.11472	−	5.87642i	−0.165652	−	0.236576i	−0.893393	+	0.449277i	$0.851682\pi$
$618$	2.81141	−	25.9634i	0.113091	−	1.04440i
$619$	0.611202	+	0.728403i	0.0245663	+	0.0292770i	0.778188	−	0.628032i	$-0.216139\pi$
$619$	0.611202	+	0.728403i	0.0245663	+	0.0292770i	−0.753621	+	0.657309i	$0.771695\pi$
$620$	−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	0.183027	+	0.983108i	$0.441411\pi$
$631$	−19.0880	+	33.0615i	−0.759883	+	1.31616i	−0.942910	+	0.333048i	$0.891923\pi$
$632$	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	−0.636168	−	0.771551i	$-0.719481\pi$
$641$	−24.5606	+	4.33069i	−0.970084	+	0.171052i	−0.333916	+	0.942603i	$0.608370\pi$
$642$	22.9901	−	46.7631i	0.907348	−	1.84559i
$643$	18.7461	−	40.2010i	0.739272	−	1.58537i	−0.0697279	−	0.997566i	$-0.522213\pi$
$643$	18.7461	−	40.2010i	0.739272	−	1.58537i	0.809000	−	0.587808i	$-0.200009\pi$
$644$	−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	−0.790999	−	0.611818i	$-0.790439\pi$
$647$	−4.55768	+	4.55768i	−0.179181	+	0.179181i	0.611818	+	0.790999i	$0.290439\pi$
$648$	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	0.538800	−	0.842434i	$-0.318878\pi$
$653$	6.12762	+	2.85735i	0.239792	+	0.111817i	−0.299008	+	0.954251i	$0.596656\pi$
$654$	−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	0.845458	−	0.534042i	$-0.179327\pi$
$659$	29.5176	+	10.7435i	1.14984	+	0.418508i	0.304383	+	0.952550i	$0.401550\pi$
$660$	−28.2222	+	9.23138i	−1.09855	+	0.359331i
$661$	−12.6918	−	10.6497i	−0.493654	−	0.414225i	0.361680	−	0.932302i	$-0.382203\pi$
$661$	−12.6918	−	10.6497i	−0.493654	−	0.414225i	−0.855334	+	0.518078i	$0.826648\pi$
$662$	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	−0.971633	−	0.236496i	$-0.924001\pi$
$673$	0.682431	−	7.80022i	0.0263058	−	0.300676i	0.997938	−	0.0641806i	$-0.0204434\pi$
$674$	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	0.759229	+	0.650823i	$0.225576\pi$
$677$	−2.64043	+	30.1802i	−0.101480	+	1.15992i	−0.860709	+	0.509097i	$0.829979\pi$
$678$	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	−0.621752	−	0.783214i	$-0.713579\pi$
$683$	8.05741	−	30.0707i	0.308308	−	1.15062i	0.930060	−	0.367408i	$-0.119755\pi$
$684$	−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	0.466377	−	0.884586i	$-0.345559\pi$
$691$	6.70424	+	2.44014i	0.255041	+	0.0928274i	−0.211336	+	0.977414i	$0.567781\pi$
$692$	−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	$0.111186\pi$
$701$			18.1226i			0.684482i	−0.939612	+	0.342241i	$0.888814\pi$
$702$	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	0.227296	−	0.973826i	$-0.427012\pi$
$709$	20.6080	−	3.63375i	0.773951	−	0.136469i	0.546656	+	0.837357i	$0.315901\pi$
$710$	−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	−0.935908	−	0.352244i	$-0.885419\pi$
$719$	−4.36807	+	7.56572i	−0.162902	+	0.282154i	0.773007	+	0.634398i	$0.218752\pi$
$720$	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	0.876253	−	0.481851i	$-0.160035\pi$
$727$	44.6377	+	3.90529i	1.65552	+	0.144839i	0.779268	+	0.626690i	$0.215591\pi$
$728$	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	0.983489	−	0.180970i	$-0.0579237\pi$
$733$	12.9159	+	18.4458i	0.477060	+	0.681312i	−0.506429	+	0.862282i	$0.669035\pi$
$734$	−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	0.931122	−	0.364709i	$-0.118832\pi$
$739$	29.3820	+	16.9637i	1.08084	+	0.624020i	0.149714	+	0.988729i	$0.452165\pi$
$740$	−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	−0.920572	−	0.390573i	$-0.872277\pi$
$743$	−2.22992	−	25.4881i	−0.0818078	−	0.935068i	0.838764	−	0.544495i	$-0.183279\pi$
$744$	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	−0.653859	−	0.756617i	$-0.726851\pi$
$751$	−18.3171	+	6.66687i	−0.668400	+	0.243278i	−0.0145411	+	0.999894i	$0.504629\pi$
$752$	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	0.877215	+	0.480097i	$0.159399\pi$
$757$	37.3446	+	37.3446i	1.35731	+	1.35731i	0.480097	+	0.877215i	$0.340601\pi$
$758$	−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	0.887543	+	0.460724i	$0.152410\pi$
$761$	13.8978	+	38.1838i	0.503793	+	1.38416i	−0.383750	+	0.923437i	$0.625368\pi$
$762$	−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	−0.784307	−	0.620373i	$-0.786981\pi$
$769$	−1.03060	+	1.22823i	−0.0371646	+	0.0442910i	0.747142	+	0.664664i	$0.231425\pi$
$770$	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	−0.791654	−	0.610970i	$-0.790780\pi$
$773$	−32.5784	+	8.72934i	−1.17176	+	0.313973i	−0.380108	+	0.924942i	$0.624113\pi$
$774$	−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	−0.539285	−	0.842123i	$-0.681305\pi$
$787$	1.89659	−	1.32801i	0.0676063	−	0.0473384i	0.606891	+	0.794785i	$0.292416\pi$
$788$	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	0.210624	−	0.977567i	$-0.432450\pi$
$797$	16.5943	−	1.45181i	0.587801	−	0.0514259i	0.377177	+	0.926141i	$0.376895\pi$
$798$	−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	−0.798390	−	0.602141i	$-0.794315\pi$
$821$	5.73809	−	15.7653i	0.200261	−	0.550212i	0.998651	+	0.0519288i	$0.0165369\pi$
$822$	−6.65131	−	27.0388i	−0.231991	−	0.943086i
$823$	−34.4725	+	3.01595i	−1.20164	+	0.105130i	−0.670338	−	0.742056i	$-0.733851\pi$
$823$	−34.4725	+	3.01595i	−1.20164	+	0.105130i	−0.531298	+	0.847185i	$0.678295\pi$
$824$	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	0.995251	+	0.0973378i	$0.0310327\pi$
$827$	5.23409	+	19.5339i	0.182007	+	0.679261i	−0.813244	+	0.581923i	$0.802301\pi$
$828$	−12.9639	+	41.4687i	−0.450526	+	1.44114i
$829$	−45.7476	+	26.4124i	−1.58888	+	0.917340i	−0.595387	+	0.803439i	$0.703001\pi$
$829$	−45.7476	+	26.4124i	−1.58888	+	0.917340i	−0.993492	+	0.113900i	$0.963666\pi$
$830$	−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	−0.608681	−	0.793415i	$-0.708301\pi$
$839$	1.94021	−	1.62803i	0.0669835	−	0.0562059i	0.675665	+	0.737209i	$0.263857\pi$
$840$	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	0.353257	−	0.935526i	$-0.385074\pi$
$853$	37.8798	−	17.6637i	1.29698	−	0.604792i	0.943724	+	0.330734i	$0.107296\pi$
$854$	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	0.134434	−	0.990923i	$-0.457078\pi$
$857$	−21.9778	−	15.3891i	−0.750749	−	0.525680i	−0.885183	+	0.465242i	$0.845967\pi$
$858$	2.18131	+	32.6697i	0.0744687	+	1.11532i
$859$	−7.80591	−	21.4466i	−0.266334	−	0.731747i	−0.998707	−	0.0508429i	$-0.983809\pi$
$859$	−7.80591	−	21.4466i	−0.266334	−	0.731747i	0.732372	−	0.680904i	$-0.238413\pi$
$860$	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	0.829089	−	0.559116i	$-0.188859\pi$
$863$	7.93097	+	7.93097i	0.269973	+	0.269973i	−0.559116	+	0.829089i	$0.688859\pi$
$864$	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	0.997502	−	0.0706341i	$-0.0225023\pi$
$877$	0.0855499	+	0.977840i	0.00288882	+	0.0330193i	−0.994613	+	0.103653i	$0.966947\pi$
$878$	−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	0.826669	−	0.562689i	$-0.190233\pi$
$881$	22.3414	+	12.8988i	0.752701	+	0.434572i	−0.0739682	+	0.997261i	$0.523566\pi$
$882$	−21.2200	+	41.0072i	−0.714515	+	1.38078i
$883$	46.3611	+	12.4224i	1.56018	+	0.418048i	0.932719	−	0.360604i	$-0.117429\pi$
$883$	46.3611	+	12.4224i	1.56018	+	0.418048i	0.627457	+	0.778652i	$0.284096\pi$
$884$	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	0.749734	−	0.661739i	$-0.230181\pi$
$887$	−3.82768	−	5.46649i	−0.128521	−	0.183547i	−0.878255	+	0.478192i	$0.841292\pi$
$888$	−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	0.914440	−	0.404722i	$-0.132632\pi$
$907$	0.500360	+	1.07303i	0.0166142	+	0.0356292i	−0.897826	+	0.440351i	$0.854854\pi$
$908$	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	−0.602653	−	0.798003i	$-0.705890\pi$
$911$	−27.0446	+	4.76870i	−0.896028	+	0.157994i	−0.293375	+	0.955997i	$0.594779\pi$
$912$	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	$-0.886110\pi$
$919$		−	21.2332i		−	0.700419i	0.936671	−	0.350209i	$-0.113890\pi$
$920$	−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	0.762136	−	0.647416i	$-0.224150\pi$
$929$	28.3403	+	10.3150i	0.929816	+	0.338425i	0.167679	+	0.985842i	$0.446373\pi$
$930$	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	0.854987	+	0.518650i	$0.173565\pi$
$937$	−4.43173	+	16.5394i	−0.144778	+	0.540320i	−0.999765	+	0.0216704i	$0.993102\pi$
$938$	−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	−0.180266	−	0.983618i	$-0.557696\pi$
$941$	−21.0459	−	3.71097i	−0.686078	−	0.120974i	−0.505812	+	0.862644i	$0.668807\pi$
$942$	−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	−0.842691	−	0.538398i	$-0.819030\pi$
$947$	2.48308	−	28.3818i	0.0806894	−	0.922284i	0.923380	−	0.383886i	$-0.125415\pi$
$948$	−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	−0.339169	−	0.940726i	$-0.610146\pi$
$953$	13.1177	−	48.9558i	0.424923	−	1.58583i	0.764091	−	0.645108i	$-0.223188\pi$
$954$	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	−0.553229	−	0.833029i	$-0.686604\pi$
$967$	−48.1057	−	22.4321i	−1.54697	−	0.721366i	−0.993746	+	0.111663i	$0.964382\pi$
$968$	−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	$0.0640447\pi$
$971$			12.4548i			0.399695i	−0.979827	+	0.199847i	$0.935955\pi$
$972$	−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	−0.735991	−	0.676992i	$-0.763283\pi$
$977$	7.99244	−	17.1398i	0.255701	−	0.548352i	0.991691	+	0.128639i	$0.0410610\pi$
$978$	−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	0.795619	−	0.605798i	$-0.207146\pi$
$983$	−5.63921	−	12.0933i	−0.179863	−	0.385717i	−0.975482	+	0.220080i	$0.929368\pi$
$984$	−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	0.814484	−	0.580186i	$-0.197020\pi$
$991$	−2.99736	−	5.19158i	−0.0952142	−	0.164916i	−0.909698	+	0.415270i	$0.863687\pi$
$992$	−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	−0.660718	−	0.750634i	$-0.729748\pi$
$997$	−45.5235	−	3.98279i	−1.44174	−	0.126136i	−0.781026	+	0.624498i	$0.785304\pi$
$998$	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.32.14	✓	192
3.2	odd	2		405.2.r.a.287.3		192
5.2	odd	4		675.2.ba.b.518.14		192
5.3	odd	4	inner	135.2.q.a.113.3	yes	192
5.4	even	2		675.2.ba.b.32.3		192
15.8	even	4		405.2.r.a.368.14		192
27.11	odd	18	inner	135.2.q.a.92.3	yes	192
27.16	even	9		405.2.r.a.197.14		192
135.38	even	36	inner	135.2.q.a.38.14	yes	192
135.43	odd	36		405.2.r.a.278.3		192
135.92	even	36		675.2.ba.b.443.3		192
135.119	odd	18		675.2.ba.b.632.14		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.14	✓	192	1.1	even	1	trivial
135.2.q.a.38.14	yes	192	135.38	even	36	inner
135.2.q.a.92.3	yes	192	27.11	odd	18	inner
135.2.q.a.113.3	yes	192	5.3	odd	4	inner
405.2.r.a.197.14		192	27.16	even	9
405.2.r.a.278.3		192	135.43	odd	36
405.2.r.a.287.3		192	3.2	odd	2
405.2.r.a.368.14		192	15.8	even	4
675.2.ba.b.32.3		192	5.4	even	2
675.2.ba.b.443.3		192	135.92	even	36
675.2.ba.b.518.14		192	5.2	odd	4
675.2.ba.b.632.14		192	135.119	odd	18

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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