LMFDB - Embedded newform 135.2.m.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(8,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(12))

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("135.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.m (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.1
Root			$-1.29724 + 0.347596i$ of defining polynomial
Character	$\chi$	$=$	135.17
Dual form			135.2.m.a.8.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29724 - 0.347596i) q^{2} +(-0.170031 - 0.0981673i) q^{4} +(-0.561484 + 2.16443i) q^{5} +(-0.530190 + 1.97869i) q^{7} +(2.08575 + 2.08575i) q^{8} +O(q^{10})$	\(q+(-1.29724 - 0.347596i) q^{2} +(-0.170031 - 0.0981673i) q^{4} +(-0.561484 + 2.16443i) q^{5} +(-0.530190 + 1.97869i) q^{7} +(2.08575 + 2.08575i) q^{8} +(1.48073 - 2.61262i) q^{10} +(0.762281 - 0.440103i) q^{11} +(1.43820 + 5.36743i) q^{13} +(1.37557 - 2.38256i) q^{14} +(-1.78439 - 3.09066i) q^{16} +(-1.13610 + 1.13610i) q^{17} +1.52456i q^{19} +(0.307945 - 0.312899i) q^{20} +(-1.14184 + 0.305956i) q^{22} +(-1.53331 + 0.410850i) q^{23} +(-4.36947 - 2.43058i) q^{25} -7.46278i q^{26} +(0.284392 - 0.284392i) q^{28} +(0.796583 + 1.37972i) q^{29} +(3.49518 - 6.05383i) q^{31} +(-0.286379 - 1.06878i) q^{32} +(1.86870 - 1.07889i) q^{34} +(-3.98504 - 2.25856i) q^{35} +(-4.25746 - 4.25746i) q^{37} +(0.529931 - 1.97773i) q^{38} +(-5.68555 + 3.34333i) q^{40} +(-3.11546 - 1.79871i) q^{41} +(-1.85841 - 0.497959i) q^{43} -0.172815 q^{44} +2.13189 q^{46} +(7.99942 + 2.14344i) q^{47} +(2.42805 + 1.40183i) q^{49} +(4.82341 + 4.67186i) q^{50} +(0.282368 - 1.05381i) q^{52} +(4.65601 + 4.65601i) q^{53} +(0.524562 + 1.89701i) q^{55} +(-5.23290 + 3.02121i) q^{56} +(-0.553777 - 2.06672i) q^{58} +(3.81780 - 6.61262i) q^{59} +(6.64002 + 11.5008i) q^{61} +(-6.63838 + 6.63838i) q^{62} +8.62358i q^{64} +(-12.4249 + 0.0991472i) q^{65} +(3.20857 - 0.859733i) q^{67} +(0.304699 - 0.0816439i) q^{68} +(4.38451 + 4.31509i) q^{70} +5.89798i q^{71} +(1.58900 - 1.58900i) q^{73} +(4.04309 + 7.00284i) q^{74} +(0.149662 - 0.259222i) q^{76} +(0.466676 + 1.74166i) q^{77} +(6.69401 - 3.86479i) q^{79} +(7.69140 - 2.12683i) q^{80} +(3.41628 + 3.41628i) q^{82} +(2.57170 - 9.59770i) q^{83} +(-1.82110 - 3.09690i) q^{85} +(2.23772 + 1.29195i) q^{86} +(2.50787 + 0.671981i) q^{88} -4.62765 q^{89} -11.3830 q^{91} +(0.301043 + 0.0806641i) q^{92} +(-9.63215 - 5.56112i) q^{94} +(-3.29980 - 0.856017i) q^{95} +(-1.02621 + 3.82988i) q^{97} +(-2.66250 - 2.66250i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} + 6 q^{5} - 2 q^{7}+O(q^{10}) $ 16 * q + 6 * q^2 + 6 * q^5 - 2 * q^7	$ 16 q + 6 q^{2} + 6 q^{5} - 2 q^{7} - 8 q^{10} - 2 q^{13} - 8 q^{16} - 18 q^{20} - 10 q^{22} - 18 q^{23} + 4 q^{25} - 16 q^{28} - 4 q^{31} - 30 q^{32} + 4 q^{37} + 30 q^{38} + 6 q^{40} + 24 q^{41} - 2 q^{43} + 32 q^{46} + 12 q^{47} + 54 q^{50} - 14 q^{52} - 16 q^{55} - 36 q^{56} - 6 q^{58} + 8 q^{61} - 66 q^{65} + 4 q^{67} - 42 q^{68} + 18 q^{70} - 8 q^{73} + 24 q^{76} + 6 q^{77} + 32 q^{82} + 66 q^{83} + 22 q^{85} + 48 q^{86} + 18 q^{88} - 40 q^{91} + 60 q^{92} + 36 q^{95} + 28 q^{97}+O(q^{100}) $ 16 * q + 6 * q^2 + 6 * q^5 - 2 * q^7 - 8 * q^10 - 2 * q^13 - 8 * q^16 - 18 * q^20 - 10 * q^22 - 18 * q^23 + 4 * q^25 - 16 * q^28 - 4 * q^31 - 30 * q^32 + 4 * q^37 + 30 * q^38 + 6 * q^40 + 24 * q^41 - 2 * q^43 + 32 * q^46 + 12 * q^47 + 54 * q^50 - 14 * q^52 - 16 * q^55 - 36 * q^56 - 6 * q^58 + 8 * q^61 - 66 * q^65 + 4 * q^67 - 42 * q^68 + 18 * q^70 - 8 * q^73 + 24 * q^76 + 6 * q^77 + 32 * q^82 + 66 * q^83 + 22 * q^85 + 48 * q^86 + 18 * q^88 - 40 * q^91 + 60 * q^92 + 36 * q^95 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.29724	−	0.347596i	−0.917290	−	0.245787i	−0.230863	−	0.972986i	$-0.574155\pi$
$2$	−1.29724	−	0.347596i	−0.917290	−	0.245787i	−0.686427	+	0.727199i	$0.740822\pi$
$3$		0			0
$3$		0			0
$4$	−0.170031	−	0.0981673i	−0.0850154	−	0.0490837i
$5$	−0.561484	+	2.16443i	−0.251103	+	0.967960i
$5$	−0.561484	+	2.16443i	−0.251103	+	0.967960i
$6$		0			0
$7$	−0.530190	+	1.97869i	−0.200393	+	0.747876i	0.790412	+	0.612576i	$0.209867\pi$
$7$	−0.530190	+	1.97869i	−0.200393	+	0.747876i	−0.990805	+	0.135300i	$0.956800\pi$
$8$	2.08575	+	2.08575i	0.737423	+	0.737423i
$9$		0			0
$10$	1.48073	−	2.61262i	0.468247	−	0.826183i
$11$	0.762281	−	0.440103i	0.229836	−	0.132696i	−0.380660	−	0.924715i	$-0.624303\pi$
$11$	0.762281	−	0.440103i	0.229836	−	0.132696i	0.610497	+	0.792019i	$0.290970\pi$
$12$		0			0
$13$	1.43820	+	5.36743i	0.398885	+	1.48866i	0.815062	+	0.579374i	$0.196703\pi$
$13$	1.43820	+	5.36743i	0.398885	+	1.48866i	−0.416177	+	0.909283i	$0.636630\pi$
$14$	1.37557	−	2.38256i	0.367637	−	0.636766i
$15$		0			0
$16$	−1.78439	−	3.09066i	−0.446098	−	0.772664i
$17$	−1.13610	+	1.13610i	−0.275544	+	0.275544i	−0.831327	−	0.555783i	$-0.812418\pi$
$17$	−1.13610	+	1.13610i	−0.275544	+	0.275544i	0.555783	+	0.831327i	$0.312418\pi$
$18$		0			0
$19$			1.52456i			0.349758i	0.984590	+	0.174879i	$0.0559535\pi$
$19$			1.52456i			0.349758i	−0.984590	+	0.174879i	$0.944047\pi$
$20$	0.307945	−	0.312899i	0.0688587	−	0.0699665i
$21$		0			0
$22$	−1.14184	+	0.305956i	−0.243442	+	0.0652300i
$23$	−1.53331	+	0.410850i	−0.319718	+	0.0856682i	−0.415109	−	0.909772i	$-0.636257\pi$
$23$	−1.53331	+	0.410850i	−0.319718	+	0.0856682i	0.0953909	+	0.995440i	$0.469590\pi$
$24$		0			0
$25$	−4.36947	−	2.43058i	−0.873894	−	0.486116i
$26$		−	7.46278i		−	1.46357i
$27$		0			0
$28$	0.284392	−	0.284392i	0.0537450	−	0.0537450i
$29$	0.796583	+	1.37972i	0.147922	+	0.256208i	0.930459	−	0.366396i	$-0.119408\pi$
$29$	0.796583	+	1.37972i	0.147922	+	0.256208i	−0.782537	+	0.622603i	$0.786075\pi$
$30$		0			0
$31$	3.49518	−	6.05383i	0.627752	−	1.08730i	−0.360249	−	0.932856i	$-0.617308\pi$
$31$	3.49518	−	6.05383i	0.627752	−	1.08730i	0.988002	−	0.154443i	$-0.0493583\pi$
$32$	−0.286379	−	1.06878i	−0.0506251	−	0.188936i
$33$		0			0
$34$	1.86870	−	1.07889i	0.320479	−	0.185029i
$35$	−3.98504	−	2.25856i	−0.673595	−	0.381767i
$36$		0			0
$37$	−4.25746	−	4.25746i	−0.699922	−	0.699922i	0.264472	−	0.964393i	$-0.414802\pi$
$37$	−4.25746	−	4.25746i	−0.699922	−	0.699922i	−0.964393	+	0.264472i	$0.914802\pi$
$38$	0.529931	−	1.97773i	0.0859661	−	0.320830i
$39$		0			0
$40$	−5.68555	+	3.34333i	−0.898965	+	0.528627i
$41$	−3.11546	−	1.79871i	−0.486552	−	0.280911i	0.236591	−	0.971609i	$-0.423970\pi$
$41$	−3.11546	−	1.79871i	−0.486552	−	0.280911i	−0.723143	+	0.690698i	$0.757303\pi$
$42$		0			0
$43$	−1.85841	−	0.497959i	−0.283404	−	0.0759380i	0.114317	−	0.993444i	$-0.463532\pi$
$43$	−1.85841	−	0.497959i	−0.283404	−	0.0759380i	−0.397721	+	0.917506i	$0.630199\pi$
$44$	−0.172815			−0.0260528
$45$		0			0
$46$	2.13189			0.314330
$47$	7.99942	+	2.14344i	1.16683	+	0.312652i	0.789693	−	0.613503i	$-0.210240\pi$
$47$	7.99942	+	2.14344i	1.16683	+	0.312652i	0.377142	+	0.926155i	$0.376907\pi$
$48$		0			0
$49$	2.42805	+	1.40183i	0.346864	+	0.200262i
$50$	4.82341	+	4.67186i	0.682134	+	0.660701i
$51$		0			0
$52$	0.282368	−	1.05381i	0.0391574	−	0.146137i
$53$	4.65601	+	4.65601i	0.639552	+	0.639552i	0.950445	−	0.310893i	$-0.100628\pi$
$53$	4.65601	+	4.65601i	0.639552	+	0.639552i	−0.310893	+	0.950445i	$0.600628\pi$
$54$		0			0
$55$	0.524562	+	1.89701i	0.0707319	+	0.255793i
$56$	−5.23290	+	3.02121i	−0.699275	+	0.403727i
$57$		0			0
$58$	−0.553777	−	2.06672i	−0.0727145	−	0.271374i
$59$	3.81780	−	6.61262i	0.497035	−	0.860890i	−0.502959	−	0.864310i	$-0.667755\pi$
$59$	3.81780	−	6.61262i	0.497035	−	0.860890i	0.999994	+	0.00342048i	$0.00108877\pi$
$60$		0			0
$61$	6.64002	+	11.5008i	0.850167	+	1.47253i	0.881057	+	0.473010i	$0.156833\pi$
$61$	6.64002	+	11.5008i	0.850167	+	1.47253i	−0.0308900	+	0.999523i	$0.509834\pi$
$62$	−6.63838	+	6.63838i	−0.843075	+	0.843075i
$63$		0			0
$64$			8.62358i			1.07795i
$65$	−12.4249	+	0.0991472i	−1.54112	+	0.0122977i
$66$		0			0
$67$	3.20857	−	0.859733i	0.391989	−	0.105033i	−0.0574406	−	0.998349i	$-0.518294\pi$
$67$	3.20857	−	0.859733i	0.391989	−	0.105033i	0.449429	+	0.893316i	$0.351627\pi$
$68$	0.304699	−	0.0816439i	0.0369502	−	0.00990078i
$69$		0			0
$70$	4.38451	+	4.31509i	0.524049	+	0.515752i
$71$			5.89798i			0.699961i	0.936757	+	0.349980i	$0.113812\pi$
$71$			5.89798i			0.699961i	−0.936757	+	0.349980i	$0.886188\pi$
$72$		0			0
$73$	1.58900	−	1.58900i	0.185979	−	0.185979i	−0.607976	−	0.793955i	$-0.708018\pi$
$73$	1.58900	−	1.58900i	0.185979	−	0.185979i	0.793955	+	0.607976i	$0.208018\pi$
$74$	4.04309	+	7.00284i	0.470000	+	0.814063i
$75$		0			0
$76$	0.149662	−	0.259222i	0.0171674	−	0.0297348i
$77$	0.466676	+	1.74166i	0.0531827	+	0.198480i
$78$		0			0
$79$	6.69401	−	3.86479i	0.753135	−	0.434823i	−0.0736905	−	0.997281i	$-0.523478\pi$
$79$	6.69401	−	3.86479i	0.753135	−	0.434823i	0.826826	+	0.562458i	$0.190144\pi$
$80$	7.69140	−	2.12683i	0.859925	−	0.237787i
$81$		0			0
$82$	3.41628	+	3.41628i	0.377265	+	0.377265i
$83$	2.57170	−	9.59770i	0.282280	−	1.05348i	−0.668523	−	0.743691i	$-0.733073\pi$
$83$	2.57170	−	9.59770i	0.282280	−	1.05348i	0.950804	−	0.309794i	$-0.100260\pi$
$84$		0			0
$85$	−1.82110	−	3.09690i	−0.197526	−	0.335906i
$86$	2.23772	+	1.29195i	0.241299	+	0.139314i
$87$		0			0
$88$	2.50787	+	0.671981i	0.267340	+	0.0716334i
$89$	−4.62765			−0.490530			−0.245265	−	0.969456i	$-0.578875\pi$
$89$	−4.62765			−0.490530			−0.245265	+	0.969456i	$0.578875\pi$
$90$		0			0
$91$	−11.3830			−1.19327
$92$	0.301043	+	0.0806641i	0.0313859	+	0.00840982i
$93$		0			0
$94$	−9.63215	−	5.56112i	−0.993480	−	0.573586i
$95$	−3.29980	−	0.856017i	−0.338552	−	0.0878255i
$96$		0			0
$97$	−1.02621	+	3.82988i	−0.104196	+	0.388865i	−0.998253	−	0.0590888i	$-0.981180\pi$
$97$	−1.02621	+	3.82988i	−0.104196	+	0.388865i	0.894057	+	0.447954i	$0.147847\pi$
$98$	−2.66250	−	2.66250i	−0.268953	−	0.268953i
$99$		0			0
$100$	0.504341	+	0.842213i	0.0504341	+	0.0842213i
$101$	2.23195	−	1.28862i	0.222087	−	0.128222i	−0.384829	−	0.922988i	$-0.625740\pi$
$101$	2.23195	−	1.28862i	0.222087	−	0.128222i	0.606916	+	0.794766i	$0.292406\pi$
$102$		0			0
$103$	−3.38106	−	12.6183i	−0.333146	−	1.24332i	−0.905865	−	0.423566i	$-0.860778\pi$
$103$	−3.38106	−	12.6183i	−0.333146	−	1.24332i	0.572719	−	0.819752i	$-0.305889\pi$
$104$	−8.19538	+	14.1948i	−0.803623	+	1.39192i
$105$		0			0
$106$	−4.42157	−	7.65839i	−0.429461	−	0.743848i
$107$	9.23034	−	9.23034i	0.892331	−	0.892331i	−0.102411	−	0.994742i	$-0.532656\pi$
$107$	9.23034	−	9.23034i	0.892331	−	0.892331i	0.994742	+	0.102411i	$0.0326557\pi$
$108$		0			0
$109$		−	8.05480i		−	0.771510i	−0.922601	−	0.385755i	$-0.873941\pi$
$109$		−	8.05480i		−	0.771510i	0.922601	−	0.385755i	$-0.126059\pi$
$110$	−0.0210921	−	2.64322i	−0.00201105	−	0.252021i
$111$		0			0
$112$	7.06153	−	1.89213i	0.667252	−	0.178790i
$113$	−11.5941	+	3.10662i	−1.09068	+	0.292246i	−0.758963	−	0.651134i	$-0.774294\pi$
$113$	−11.5941	+	3.10662i	−1.09068	+	0.292246i	−0.331714	+	0.943380i	$0.607627\pi$
$114$		0			0
$115$	−0.0283234	−	3.54943i	−0.00264117	−	0.330986i
$116$		−	0.312794i		−	0.0290422i
$117$		0			0
$118$	−7.25113	+	7.25113i	−0.667521	+	0.667521i
$119$	−1.64564	−	2.85034i	−0.150856	−	0.261290i
$120$		0			0
$121$	−5.11262	+	8.85532i	−0.464784	+	0.805029i
$122$	−4.61608	−	17.2274i	−0.417920	−	1.55970i
$123$		0			0
$124$	−1.18858	+	0.686224i	−0.106737	+	0.0616248i
$125$	7.71420	−	8.09266i	0.689979	−	0.723830i
$126$		0			0
$127$	1.90230	+	1.90230i	0.168802	+	0.168802i	0.786452	−	0.617651i	$-0.211915\pi$
$127$	1.90230	+	1.90230i	0.168802	+	0.168802i	−0.617651	+	0.786452i	$0.711915\pi$
$128$	2.42476	−	9.04933i	0.214321	−	0.799855i
$129$		0			0
$130$	16.1526	+	4.19023i	1.41668	+	0.367508i
$131$	18.5109	+	10.6873i	1.61731	+	0.933754i	0.987613	+	0.156912i	$0.0501541\pi$
$131$	18.5109	+	10.6873i	1.61731	+	0.933754i	0.629696	+	0.776841i	$0.283179\pi$
$132$		0			0
$133$	−3.01664	−	0.808307i	−0.261576	−	0.0700891i
$134$	−4.46113			−0.385383
$135$		0			0
$136$	−4.73922			−0.406385
$137$	−6.62594	−	1.77541i	−0.566092	−	0.151684i	−0.0355883	−	0.999367i	$-0.511331\pi$
$137$	−6.62594	−	1.77541i	−0.566092	−	0.151684i	−0.530504	+	0.847683i	$0.677997\pi$
$138$		0			0
$139$	1.24863	+	0.720896i	0.105907	+	0.0611456i	0.552018	−	0.833832i	$-0.313858\pi$
$139$	1.24863	+	0.720896i	0.105907	+	0.0611456i	−0.446111	+	0.894978i	$0.647191\pi$
$140$	0.455863	+	0.775226i	0.0385275	+	0.0655186i
$141$		0			0
$142$	2.05011	−	7.65111i	0.172041	−	0.642067i
$143$	3.45853	+	3.45853i	0.289217	+	0.289217i
$144$		0			0
$145$	−3.43357	+	0.949452i	−0.285143	+	0.0788477i
$146$	−2.61366	+	1.50900i	−0.216308	+	0.124885i
$147$		0			0
$148$	0.305956	+	1.14184i	0.0251494	+	0.0938589i
$149$	8.28457	−	14.3493i	0.678699	−	1.17554i	−0.296674	−	0.954979i	$-0.595878\pi$
$149$	8.28457	−	14.3493i	0.678699	−	1.17554i	0.975373	−	0.220562i	$-0.0707891\pi$
$150$		0			0
$151$	0.00283730	+	0.00491435i	0.000230896	+	0.000399924i	0.866141	−	0.499800i	$-0.166593\pi$
$151$	0.00283730	+	0.00491435i	0.000230896	+	0.000399924i	−0.865910	+	0.500200i	$0.833260\pi$
$152$	−3.17985	+	3.17985i	−0.257920	+	0.257920i
$153$		0			0
$154$		−	2.42157i		−	0.195136i
$155$	11.1406	+	10.9642i	0.894832	+	0.880664i
$156$		0			0
$157$	−8.17112	+	2.18944i	−0.652126	+	0.174737i	−0.569690	−	0.821860i	$-0.692937\pi$
$157$	−8.17112	+	2.18944i	−0.652126	+	0.174737i	−0.0824362	+	0.996596i	$0.526270\pi$
$158$	−10.0272	+	2.68677i	−0.797717	+	0.213748i
$159$		0			0
$160$	2.47409	−	0.0197425i	0.195594	−	0.00156078i
$161$		−	3.25179i		−	0.256277i
$162$		0			0
$163$	4.19302	−	4.19302i	0.328422	−	0.328422i	−0.523564	−	0.851986i	$-0.675398\pi$
$163$	4.19302	−	4.19302i	0.328422	−	0.328422i	0.851986	+	0.523564i	$0.175398\pi$
$164$	0.353149	+	0.611672i	0.0275763	+	0.0477635i
$165$		0			0
$166$	−6.67224	+	11.5567i	−0.517866	+	0.896970i
$167$	1.54428	+	5.76334i	0.119500	+	0.445980i	0.999584	−	0.0288375i	$-0.00918054\pi$
$167$	1.54428	+	5.76334i	0.119500	+	0.445980i	−0.880084	+	0.474818i	$0.842514\pi$
$168$		0			0
$169$	−15.4826	+	8.93886i	−1.19097	+	0.687605i
$170$	1.28594	+	4.65044i	0.0986271	+	0.356672i
$171$		0			0
$172$	0.267103	+	0.267103i	0.0203664	+	0.0203664i
$173$	−3.53677	+	13.1994i	−0.268896	+	1.00353i	0.690927	+	0.722925i	$0.257203\pi$
$173$	−3.53677	+	13.1994i	−0.268896	+	1.00353i	−0.959822	+	0.280608i	$0.909464\pi$
$174$		0			0
$175$	7.12602	−	7.35718i	0.538677	−	0.556151i
$176$	−2.72042	−	1.57063i	−0.205059	−	0.118391i
$177$		0			0
$178$	6.00319	+	1.60855i	0.449958	+	0.120566i
$179$	−17.2370			−1.28836			−0.644178	−	0.764875i	$-0.722801\pi$
$179$	−17.2370			−1.28836			−0.644178	+	0.764875i	$0.722801\pi$
$180$		0			0
$181$	14.7708			1.09790			0.548952	−	0.835854i	$-0.315027\pi$
$181$	14.7708			1.09790			0.548952	+	0.835854i	$0.315027\pi$
$182$	14.7666	+	3.95669i	1.09457	+	0.293289i
$183$		0			0
$184$	−4.05503	−	2.34117i	−0.298941	−	0.172594i
$185$	11.6054	−	6.82446i	0.853249	−	0.501744i
$186$		0			0
$187$	−0.366025	+	1.36603i	−0.0267664	+	0.0998937i
$188$	−1.14973	−	1.14973i	−0.0838528	−	0.0838528i
$189$		0			0
$190$	3.98310	+	2.25746i	0.288964	+	0.163773i
$191$	−4.56792	+	2.63729i	−0.330523	+	0.190827i	−0.656073	−	0.754697i	$-0.727784\pi$
$191$	−4.56792	+	2.63729i	−0.330523	+	0.190827i	0.325550	+	0.945525i	$0.394450\pi$
$192$		0			0
$193$	2.40873	+	8.98952i	0.173384	+	0.647080i	0.996821	+	0.0796715i	$0.0253871\pi$
$193$	2.40873	+	8.98952i	0.173384	+	0.647080i	−0.823437	+	0.567408i	$0.807946\pi$
$194$	2.66250	−	4.61158i	0.191156	−	0.331092i
$195$		0			0
$196$	−0.275228	−	0.476709i	−0.0196592	−	0.0340507i
$197$	−9.49539	+	9.49539i	−0.676519	+	0.676519i	−0.959211	−	0.282692i	$-0.908773\pi$
$197$	−9.49539	+	9.49539i	−0.676519	+	0.676519i	0.282692	+	0.959211i	$0.408773\pi$
$198$		0			0
$199$		−	17.6342i		−	1.25005i	−0.780604	−	0.625026i	$-0.785088\pi$
$199$		−	17.6342i		−	1.25005i	0.780604	−	0.625026i	$-0.214912\pi$
$200$	−4.04404	−	14.1832i	−0.285957	−	1.00290i
$201$		0			0
$202$	−3.34330	+	0.895835i	−0.235234	+	0.0630307i
$203$	−3.15239	+	0.844680i	−0.221254	+	0.0592849i
$204$		0			0
$205$	5.64245	−	5.73322i	0.394086	−	0.400426i
$206$			17.5443i			1.22237i
$207$		0			0
$208$	14.0226	−	14.0226i	0.972291	−	0.972291i
$209$	0.670964	+	1.16214i	0.0464116	+	0.0803872i
$210$		0			0
$211$	0.0616050	−	0.106703i	0.00424106	−	0.00734574i	−0.863897	−	0.503668i	$-0.831983\pi$
$211$	0.0616050	−	0.106703i	0.00424106	−	0.00734574i	0.868138	+	0.496323i	$0.165317\pi$
$212$	−0.334597	−	1.24873i	−0.0229802	−	0.0857633i
$213$		0			0
$214$	−15.1824	+	8.76558i	−1.03785	+	0.599203i
$215$	2.12126	−	3.74279i	0.144669	−	0.255256i
$216$		0			0
$217$	10.1256	+	10.1256i	0.687368	+	0.687368i
$218$	−2.79981	+	10.4490i	−0.189627	+	0.707698i
$219$		0			0
$220$	0.0970328	−	0.374045i	0.00654195	−	0.0252181i
$221$	−7.73186	−	4.46399i	−0.520101	−	0.300281i
$222$		0			0
$223$	−2.41842	−	0.648014i	−0.161949	−	0.0433942i	0.176933	−	0.984223i	$-0.443382\pi$
$223$	−2.41842	−	0.648014i	−0.161949	−	0.0433942i	−0.338883	+	0.940829i	$0.610049\pi$
$224$	2.26663			0.151445
$225$		0			0
$226$	16.1202			1.07230
$227$	−14.7293	−	3.94671i	−0.977619	−	0.261952i	−0.265577	−	0.964090i	$-0.585563\pi$
$227$	−14.7293	−	3.94671i	−0.977619	−	0.261952i	−0.712042	+	0.702137i	$0.752229\pi$
$228$		0			0
$229$	19.1083	+	11.0322i	1.26271	+	0.729029i	0.973599	−	0.228265i	$-0.0733054\pi$
$229$	19.1083	+	11.0322i	1.26271	+	0.729029i	0.289116	+	0.957294i	$0.406639\pi$
$230$	−1.19702	+	4.61432i	−0.0789294	+	0.304259i
$231$		0			0
$232$	−1.21628	+	4.53922i	−0.0798527	+	0.298014i
$233$	−4.22173	−	4.22173i	−0.276575	−	0.276575i	0.555165	−	0.831740i	$-0.312655\pi$
$233$	−4.22173	−	4.22173i	−0.276575	−	0.276575i	−0.831740	+	0.555165i	$0.812655\pi$
$234$		0			0
$235$	−9.13085	+	16.1106i	−0.595631	+	1.05094i
$236$	−1.29829	+	0.749566i	−0.0845112	+	0.0487926i
$237$		0			0
$238$	1.14404	+	4.26960i	0.0741569	+	0.276757i
$239$	−6.79199	+	11.7641i	−0.439338	+	0.760955i	−0.997639	−	0.0686835i	$-0.978120\pi$
$239$	−6.79199	+	11.7641i	−0.439338	+	0.760955i	0.558301	+	0.829639i	$0.311453\pi$
$240$		0			0
$241$	−2.56728	−	4.44666i	−0.165373	−	0.286434i	0.771415	−	0.636333i	$-0.219549\pi$
$241$	−2.56728	−	4.44666i	−0.165373	−	0.286434i	−0.936788	+	0.349898i	$0.886216\pi$
$242$	9.71038	−	9.71038i	0.624207	−	0.624207i
$243$		0			0
$244$		−	2.60733i		−	0.166917i
$245$	−4.39747	+	4.46822i	−0.280944	+	0.285464i
$246$		0			0
$247$	−8.18298	+	2.19262i	−0.520670	+	0.139513i
$248$	19.9168	−	5.33669i	1.26472	−	0.338880i
$249$		0			0
$250$	−12.8202	+	7.81674i	−0.810819	+	0.494374i
$251$		−	2.60221i		−	0.164250i	−0.996622	−	0.0821251i	$-0.973829\pi$
$251$		−	2.60221i		−	0.164250i	0.996622	−	0.0821251i	$-0.0261707\pi$
$252$		0			0
$253$	−0.987999	+	0.987999i	−0.0621150	+	0.0621150i
$254$	−1.80652	−	3.12898i	−0.113351	−	0.196329i
$255$		0			0
$256$	2.33257	−	4.04013i	0.145786	−	0.252508i
$257$	2.73197	+	10.1958i	0.170415	+	0.635999i	0.997287	+	0.0736085i	$0.0234515\pi$
$257$	2.73197	+	10.1958i	0.170415	+	0.635999i	−0.826872	+	0.562390i	$0.809882\pi$
$258$		0			0
$259$	10.6815	−	6.16695i	0.663714	−	0.383196i
$260$	2.12235	+	1.20286i	0.131623	+	0.0745984i
$261$		0			0
$262$	−20.2984	−	20.2984i	−1.25404	−	1.25404i
$263$	2.17720	−	8.12541i	0.134252	−	0.501034i	−0.865748	−	0.500480i	$-0.833157\pi$
$263$	2.17720	−	8.12541i	0.134252	−	0.501034i	1.00000		0.000554412i	$-0.000176475\pi$
$264$		0			0
$265$	−12.6919	+	7.46331i	−0.779654	+	0.458467i
$266$	3.63236	+	2.09714i	0.222714	+	0.128584i
$267$		0			0
$268$	−0.629953	−	0.168795i	−0.0384805	−	0.0103108i
$269$	26.7708			1.63225			0.816123	−	0.577878i	$-0.196119\pi$
$269$	26.7708			1.63225			0.816123	+	0.577878i	$0.196119\pi$
$270$		0			0
$271$	−18.5850			−1.12896			−0.564480	−	0.825447i	$-0.690923\pi$
$271$	−18.5850			−1.12896			−0.564480	+	0.825447i	$0.690923\pi$
$272$	5.53853	+	1.48405i	0.335823	+	0.0899834i
$273$		0			0
$274$	7.97833	+	4.60629i	0.481989	+	0.278276i
$275$	−4.40047	+	0.0702333i	−0.265358	+	0.00423523i
$276$		0			0
$277$	7.05259	−	26.3206i	0.423749	−	1.58145i	−0.342891	−	0.939375i	$-0.611406\pi$
$277$	7.05259	−	26.3206i	0.423749	−	1.58145i	0.766640	−	0.642078i	$-0.221927\pi$
$278$	−1.36920	−	1.36920i	−0.0821189	−	0.0821189i
$279$		0			0
$280$	−3.60100	−	13.0226i	−0.215201	−	0.778248i
$281$	22.7050	−	13.1087i	1.35447	−	0.782002i	0.365595	−	0.930774i	$-0.380865\pi$
$281$	22.7050	−	13.1087i	1.35447	−	0.782002i	0.988872	+	0.148772i	$0.0475320\pi$
$282$		0			0
$283$	−0.921880	−	3.44050i	−0.0548001	−	0.204517i	0.933098	−	0.359623i	$-0.117095\pi$
$283$	−0.921880	−	3.44050i	−0.0548001	−	0.204517i	−0.987898	+	0.155106i	$0.950428\pi$
$284$	0.578988	−	1.00284i	0.0343566	−	0.0595074i
$285$		0			0
$286$	−3.28439	−	5.68873i	−0.194210	−	0.336382i
$287$	5.21088	−	5.21088i	0.307589	−	0.307589i
$288$		0			0
$289$			14.4186i			0.848151i
$290$	4.78421	−	0.0381765i	0.280938	−	0.00224180i
$291$		0			0
$292$	−0.426168	+	0.114191i	−0.0249396	+	0.00668254i
$293$	−2.87816	+	0.771199i	−0.168144	+	0.0450539i	−0.341909	−	0.939733i	$-0.611073\pi$
$293$	−2.87816	+	0.771199i	−0.168144	+	0.0450539i	0.173765	+	0.984787i	$0.444407\pi$
$294$		0			0
$295$	12.1689	+	11.9762i	0.708500	+	0.697282i
$296$		−	17.7600i		−	1.03228i
$297$		0			0
$298$	−15.7349	+	15.7349i	−0.911496	+	0.911496i
$299$	−4.41042	−	7.63907i	−0.255061	−	0.441779i
$300$		0			0
$301$	1.97062	−	3.41321i	0.113584	−	0.196734i
$302$	−0.00197247	−	0.00736135i	−0.000113503	−	0.000423598i
$303$		0			0
$304$	4.71190	−	2.72042i	0.270246	−	0.156027i
$305$	−28.6210	+	7.91428i	−1.63883	+	0.453170i
$306$		0			0
$307$	21.8017	+	21.8017i	1.24429	+	1.24429i	0.958205	+	0.286081i	$0.0923528\pi$
$307$	21.8017	+	21.8017i	1.24429	+	1.24429i	0.286081	+	0.958205i	$0.407647\pi$
$308$	0.0916247	−	0.341948i	0.00522080	−	0.0194843i
$309$		0			0
$310$	−10.6409	−	18.0956i	−0.604365	−	1.02776i
$311$	−29.3878	−	16.9671i	−1.66643	−	0.962114i	−0.969539	−	0.244939i	$-0.921232\pi$
$311$	−29.3878	−	16.9671i	−1.66643	−	0.962114i	−0.696892	−	0.717176i	$-0.745435\pi$
$312$		0			0
$313$	−22.4027	−	6.00279i	−1.26628	−	0.339298i	−0.437673	−	0.899134i	$-0.644197\pi$
$313$	−22.4027	−	6.00279i	−1.26628	−	0.339298i	−0.828603	+	0.559836i	$0.810864\pi$
$314$	11.3610			0.641137
$315$		0			0
$316$	−1.51758			−0.0853708
$317$	3.86401	+	1.03536i	0.217024	+	0.0581515i	0.365693	−	0.930736i	$-0.380832\pi$
$317$	3.86401	+	1.03536i	0.217024	+	0.0581515i	−0.148669	+	0.988887i	$0.547499\pi$
$318$		0			0
$319$	1.21444	+	0.701157i	0.0679956	+	0.0392573i
$320$	−18.6651	−	4.84200i	−1.04341	−	0.270676i
$321$		0			0
$322$	−1.13031	+	4.21836i	−0.0629896	+	0.235080i
$323$	−1.73205	−	1.73205i	−0.0963739	−	0.0963739i
$324$		0			0
$325$	6.76180	−	26.9485i	0.375077	−	1.49483i
$326$	−6.89684	+	3.98189i	−0.381981	+	0.220537i
$327$		0			0
$328$	−2.74640	−	10.2497i	−0.151645	−	0.565945i
$329$	−8.48242	+	14.6920i	−0.467651	+	0.809995i
$330$		0			0
$331$	−2.98175	−	5.16454i	−0.163892	−	0.283869i	0.772369	−	0.635174i	$-0.219071\pi$
$331$	−2.98175	−	5.16454i	−0.163892	−	0.283869i	−0.936261	+	0.351305i	$0.885738\pi$
$332$	−1.37945	+	1.37945i	−0.0757071	+	0.0757071i
$333$		0			0
$334$		−	8.01324i		−	0.438465i
$335$	0.0592686	+	7.42743i	0.00323819	+	0.405804i
$336$		0			0
$337$	9.56887	−	2.56397i	0.521250	−	0.139668i	0.0114051	−	0.999935i	$-0.496370\pi$
$337$	9.56887	−	2.56397i	0.521250	−	0.139668i	0.509845	+	0.860267i	$0.329703\pi$
$338$	23.1918	−	6.21422i	1.26147	−	0.338009i
$339$		0			0
$340$	0.00562840	+	0.705340i	0.000305243	+	0.0382525i
$341$		−	6.15295i		−	0.333201i
$342$		0			0
$343$	−14.2007	+	14.2007i	−0.766764	+	0.766764i
$344$	−2.83755	−	4.91478i	−0.152990	−	0.264987i
$345$		0			0
$346$	9.17611	−	15.8935i	0.493311	−	0.854440i
$347$	2.74569	+	10.2471i	0.147396	+	0.550091i	0.999637	+	0.0269407i	$0.00857654\pi$
$347$	2.74569	+	10.2471i	0.147396	+	0.550091i	−0.852241	+	0.523150i	$0.824757\pi$
$348$		0			0
$349$	8.08831	−	4.66979i	0.432957	−	0.249968i	−0.267648	−	0.963517i	$-0.586247\pi$
$349$	8.08831	−	4.66979i	0.432957	−	0.249968i	0.700606	+	0.713549i	$0.252913\pi$
$350$	−11.8015	+	7.06709i	−0.630818	+	0.377752i
$351$		0			0
$352$	−0.688675	−	0.688675i	−0.0367065	−	0.0367065i
$353$	4.96965	−	18.5470i	0.264508	−	0.987156i	−0.698043	−	0.716055i	$-0.745946\pi$
$353$	4.96965	−	18.5470i	0.264508	−	0.987156i	0.962551	−	0.271100i	$-0.0873876\pi$
$354$		0			0
$355$	−12.7657	−	3.31162i	−0.677534	−	0.175762i
$356$	0.786842	+	0.454284i	0.0417026	+	0.0240770i
$357$		0			0
$358$	22.3606	+	5.99152i	1.18180	+	0.316662i
$359$	12.5944			0.664705			0.332352	−	0.943155i	$-0.392158\pi$
$359$	12.5944			0.664705			0.332352	+	0.943155i	$0.392158\pi$
$360$		0			0
$361$	16.6757			0.877669
$362$	−19.1613	−	5.13426i	−1.00710	−	0.269851i
$363$		0			0
$364$	1.93546	+	1.11744i	0.101446	+	0.0585698i
$365$	2.54708	+	4.33148i	0.133320	+	0.226720i
$366$		0			0
$367$	−7.32206	+	27.3263i	−0.382209	+	1.42642i	0.460312	+	0.887757i	$0.347738\pi$
$367$	−7.32206	+	27.3263i	−0.382209	+	1.42642i	−0.842520	+	0.538665i	$0.818929\pi$
$368$	4.00583	+	4.00583i	0.208818	+	0.208818i
$369$		0			0
$370$	−17.4272	+	4.81898i	−0.905999	+	0.250527i
$371$	−11.6814	+	6.74425i	−0.606467	+	0.350144i
$372$		0			0
$373$	0.604851	+	2.25734i	0.0313180	+	0.116880i	0.979815	−	0.199905i	$-0.0640633\pi$
$373$	0.604851	+	2.25734i	0.0313180	+	0.116880i	−0.948497	+	0.316785i	$0.897397\pi$
$374$	0.949649	−	1.64484i	0.0491052	−	0.0850526i
$375$		0			0
$376$	12.2141	+	21.1554i	0.629894	+	1.09101i
$377$	−6.25992	+	6.25992i	−0.322402	+	0.322402i
$378$		0			0
$379$			18.4618i			0.948320i	0.880439	+	0.474160i	$0.157248\pi$
$379$			18.4618i			0.948320i	−0.880439	+	0.474160i	$0.842752\pi$
$380$	0.477035	+	0.469482i	0.0244714	+	0.0240839i
$381$		0			0
$382$	6.84241	−	1.83342i	0.350088	−	0.0938059i
$383$	23.3806	−	6.26481i	1.19469	−	0.320117i	0.393953	−	0.919131i	$-0.371107\pi$
$383$	23.3806	−	6.26481i	1.19469	−	0.320117i	0.800739	+	0.599014i	$0.204441\pi$
$384$		0			0
$385$	−4.03172	+	0.0321719i	−0.205476	+	0.00163963i
$386$		−	12.4989i		−	0.636176i
$387$		0			0
$388$	0.550457	−	0.550457i	0.0279452	−	0.0279452i
$389$	13.5444	+	23.4596i	0.686729	+	1.18945i	0.972890	+	0.231268i	$0.0742876\pi$
$389$	13.5444	+	23.4596i	0.686729	+	1.18945i	−0.286161	+	0.958182i	$0.592379\pi$
$390$		0			0
$391$	1.27523	−	2.20876i	0.0644911	−	0.111702i
$392$	2.14042	+	7.98815i	0.108108	+	0.403463i
$393$		0			0
$394$	15.6184	−	9.01729i	0.786844	−	0.454284i
$395$	4.60647	+	16.6587i	0.231776	+	0.838190i
$396$		0			0
$397$	−18.2252	−	18.2252i	−0.914698	−	0.914698i	0.0819389	−	0.996637i	$-0.473889\pi$
$397$	−18.2252	−	18.2252i	−0.914698	−	0.914698i	−0.996637	+	0.0819389i	$0.973889\pi$
$398$	−6.12955	+	22.8758i	−0.307247	+	1.14666i
$399$		0			0
$400$	0.284760	+	17.8416i	0.0142380	+	0.892082i
$401$	11.1294	+	6.42558i	0.555777	+	0.320878i	0.751449	−	0.659791i	$-0.229355\pi$
$401$	11.1294	+	6.42558i	0.555777	+	0.320878i	−0.195672	+	0.980669i	$0.562689\pi$
$402$		0			0
$403$	37.5202	+	10.0535i	1.86902	+	0.500801i
$404$	−0.506000			−0.0251745
$405$		0			0
$406$	4.38302			0.217526
$407$	−5.11910	−	1.37166i	−0.253744	−	0.0679906i
$408$		0			0
$409$	−22.2450	−	12.8431i	−1.09994	−	0.635053i	−0.163737	−	0.986504i	$-0.552355\pi$
$409$	−22.2450	−	12.8431i	−1.09994	−	0.635053i	−0.936206	+	0.351451i	$0.885688\pi$
$410$	−9.31248	+	5.47610i	−0.459911	+	0.270445i
$411$		0			0
$412$	−0.663820	+	2.47741i	−0.0327041	+	0.122053i
$413$	11.0602	+	11.0602i	0.544237	+	0.544237i
$414$		0			0
$415$	19.3295	+	10.9552i	0.948850	+	0.537770i
$416$	5.32474	−	3.07424i	0.261067	−	0.150727i
$417$		0			0
$418$	−0.466448	−	1.74081i	−0.0228147	−	0.0851457i
$419$	6.13243	−	10.6217i	0.299589	−	0.518903i	−0.676453	−	0.736486i	$-0.736484\pi$
$419$	6.13243	−	10.6217i	0.299589	−	0.518903i	0.976042	+	0.217583i	$0.0698172\pi$
$420$		0			0
$421$	−7.24056	−	12.5410i	−0.352883	−	0.611212i	0.633870	−	0.773439i	$-0.281465\pi$
$421$	−7.24056	−	12.5410i	−0.352883	−	0.611212i	−0.986753	+	0.162228i	$0.948132\pi$
$422$	−0.117006	+	0.117006i	−0.00569577	+	0.00569577i
$423$		0			0
$424$			19.4225i			0.943240i
$425$	7.72552	−	2.20277i	0.374743	−	0.106850i
$426$		0			0
$427$	−26.2771	+	7.04094i	−1.27164	+	0.340735i
$428$	−2.47556	+	0.663324i	−0.119661	+	0.0320630i
$429$		0			0
$430$	−4.05277	+	4.11797i	−0.195442	+	0.198586i
$431$			35.9660i			1.73242i	0.499678	+	0.866211i	$0.333452\pi$
$431$			35.9660i			1.73242i	−0.499678	+	0.866211i	$0.666548\pi$
$432$		0			0
$433$	−0.331545	+	0.331545i	−0.0159331	+	0.0159331i	−0.715028	−	0.699095i	$-0.753586\pi$
$433$	−0.331545	+	0.331545i	−0.0159331	+	0.0159331i	0.699095	+	0.715028i	$0.253586\pi$
$434$	−9.61573	−	16.6549i	−0.461570	−	0.799462i
$435$		0			0
$436$	−0.790718	+	1.36956i	−0.0378685	+	0.0655902i
$437$	−0.626366	−	2.33763i	−0.0299632	−	0.111824i
$438$		0			0
$439$	1.28953	−	0.744511i	0.0615459	−	0.0355336i	−0.468911	−	0.883245i	$-0.655354\pi$
$439$	1.28953	−	0.744511i	0.0615459	−	0.0355336i	0.530457	+	0.847712i	$0.322020\pi$
$440$	−2.86258	+	5.05078i	−0.136468	+	0.240787i
$441$		0			0
$442$	8.47845	+	8.47845i	0.403279	+	0.403279i
$443$	−8.29218	+	30.9468i	−0.393973	+	1.47033i	0.429548	+	0.903044i	$0.358673\pi$
$443$	−8.29218	+	30.9468i	−0.393973	+	1.47033i	−0.823522	+	0.567285i	$0.807994\pi$
$444$		0			0
$445$	2.59835	−	10.0162i	0.123174	−	0.474813i
$446$	2.91203	+	1.68126i	0.137889	+	0.0796101i
$447$		0			0
$448$	−17.0634	−	4.57213i	−0.806172	−	0.216013i
$449$	−21.8283			−1.03014			−0.515071	−	0.857147i	$-0.672234\pi$
$449$	−21.8283			−1.03014			−0.515071	+	0.857147i	$0.672234\pi$
$450$		0			0
$451$	−3.16647			−0.149103
$452$	2.27631	+	0.609937i	0.107069	+	0.0286890i
$453$		0			0
$454$	17.7357	+	10.2397i	0.832376	+	0.480572i
$455$	6.39139	−	24.6377i	0.299633	−	1.15503i
$456$		0			0
$457$	−0.235886	+	0.880339i	−0.0110343	+	0.0411805i	−0.971223	−	0.238170i	$-0.923452\pi$
$457$	−0.235886	+	0.880339i	−0.0110343	+	0.0411805i	0.960189	+	0.279351i	$0.0901191\pi$
$458$	−20.9534	−	20.9534i	−0.979090	−	0.979090i
$459$		0			0
$460$	−0.343622	+	0.606293i	−0.0160215	+	0.0282685i
$461$	18.7320	−	10.8149i	0.872434	−	0.503700i	0.00427761	−	0.999991i	$-0.498638\pi$
$461$	18.7320	−	10.8149i	0.872434	−	0.503700i	0.868156	+	0.496291i	$0.165305\pi$
$462$		0			0
$463$	4.85644	+	18.1245i	0.225698	+	0.842316i	0.982124	+	0.188236i	$0.0602771\pi$
$463$	4.85644	+	18.1245i	0.225698	+	0.842316i	−0.756426	+	0.654079i	$0.773056\pi$
$464$	2.84283	−	4.92393i	0.131975	−	0.228588i
$465$		0			0
$466$	4.00916	+	6.94407i	0.185721	+	0.321678i
$467$	16.8295	−	16.8295i	0.778777	−	0.778777i	−0.200846	−	0.979623i	$-0.564369\pi$
$467$	16.8295	−	16.8295i	0.778777	−	0.778777i	0.979623	+	0.200846i	$0.0643691\pi$
$468$		0			0
$469$			6.80460i			0.314207i
$470$	17.4449	−	17.7256i	0.804675	−	0.817620i
$471$		0			0
$472$	21.7552	−	5.82929i	1.00136	−	0.268315i
$473$	−1.63578	+	0.438306i	−0.0752133	+	0.0201533i
$474$		0			0
$475$	3.70557	−	6.66153i	0.170023	−	0.305652i
$476$			0.646194i			0.0296182i
$477$		0			0
$478$	12.9000	−	12.9000i	0.590033	−	0.590033i
$479$	−8.91724	−	15.4451i	−0.407439	−	0.705705i	0.587163	−	0.809469i	$-0.300245\pi$
$479$	−8.91724	−	15.4451i	−0.407439	−	0.705705i	−0.994602	+	0.103764i	$0.966911\pi$
$480$		0			0
$481$	16.7285	−	28.9747i	0.762756	−	1.32113i
$482$	1.78475	+	6.66078i	0.0812931	+	0.303390i
$483$		0			0
$484$	1.73861	−	1.00378i	0.0790275	−	0.0456265i
$485$	−7.71328	−	4.37158i	−0.350242	−	0.198503i
$486$		0			0
$487$	−21.8232	−	21.8232i	−0.988904	−	0.988904i	0.0110354	−	0.999939i	$-0.496487\pi$
$487$	−21.8232	−	21.8232i	−0.988904	−	0.988904i	−0.999939	+	0.0110354i	$0.996487\pi$
$488$	−10.1385	+	37.8372i	−0.458946	+	1.71281i
$489$		0			0
$490$	7.25773	−	4.26783i	0.327871	−	0.192801i
$491$	−35.1670	−	20.3037i	−1.58707	−	0.916292i	−0.993787	−	0.111295i	$-0.964500\pi$
$491$	−35.1670	−	20.3037i	−1.58707	−	0.916292i	−0.593278	−	0.804998i	$-0.702166\pi$
$492$		0			0
$493$	−2.47249	−	0.662503i	−0.111356	−	0.0298376i
$494$	11.3775			0.511896
$495$		0			0
$496$	−24.9471			−1.12016
$497$	−11.6703	−	3.12705i	−0.523484	−	0.140267i
$498$		0			0
$499$	−37.3397	−	21.5581i	−1.67156	−	0.965073i	−0.966768	−	0.255655i	$-0.917709\pi$
$499$	−37.3397	−	21.5581i	−1.67156	−	0.965073i	−0.704788	−	0.709418i	$-0.748958\pi$
$500$	−2.10609	+	0.618720i	−0.0941870	+	0.0276700i
$501$		0			0
$502$	−0.904518	+	3.37571i	−0.0403706	+	0.150665i
$503$	−28.0936	−	28.0936i	−1.25263	−	1.25263i	−0.954537	−	0.298093i	$-0.903649\pi$
$503$	−28.0936	−	28.0936i	−1.25263	−	1.25263i	−0.298093	−	0.954537i	$-0.596351\pi$
$504$		0			0
$505$	1.53591	+	5.55443i	0.0683471	+	0.247169i
$506$	1.62510	−	0.938252i	0.0722445	−	0.0417104i
$507$		0			0
$508$	−0.136706	−	0.510193i	−0.00606534	−	0.0226361i
$509$	7.39188	−	12.8031i	0.327639	−	0.567488i	−0.654404	−	0.756145i	$-0.727080\pi$
$509$	7.39188	−	12.8031i	0.327639	−	0.567488i	0.982043	+	0.188658i	$0.0604136\pi$
$510$		0			0
$511$	2.30168	+	3.98663i	0.101820	+	0.176358i
$512$	−17.6794	+	17.6794i	−0.781325	+	0.781325i
$513$		0			0
$514$		−	14.1761i		−	0.625282i
$515$	29.2098	−	0.233085i	1.28714	−	0.0102710i
$516$		0			0
$517$	7.04114	−	1.88667i	0.309669	−	0.0829755i
$518$	−16.0001	+	4.28721i	−0.703003	+	0.188369i
$519$		0			0
$520$	−26.1220	−	25.7084i	−1.14553	−	1.12739i
$521$		−	28.4812i		−	1.24778i	−0.781511	−	0.623892i	$-0.785551\pi$
$521$		−	28.4812i		−	1.24778i	0.781511	−	0.623892i	$-0.214449\pi$
$522$		0			0
$523$	15.4076	−	15.4076i	0.673726	−	0.673726i	−0.284847	−	0.958573i	$-0.591943\pi$
$523$	15.4076	−	15.4076i	0.673726	−	0.673726i	0.958573	+	0.284847i	$0.0919428\pi$
$524$	−2.09829	−	3.63434i	−0.0916641	−	0.158767i
$525$		0			0
$526$	−5.64872	+	9.78386i	−0.246296	+	0.426597i
$527$	2.90687	+	10.8486i	0.126625	+	0.472572i
$528$		0			0
$529$	−17.7363	+	10.2401i	−0.771145	+	0.445221i
$530$	19.0586	−	5.27010i	0.827855	−	0.228918i
$531$		0			0
$532$	0.433573	+	0.433573i	0.0187978	+	0.0187978i
$533$	5.17380	−	19.3089i	0.224102	−	0.836361i
$534$		0			0
$535$	14.7957	+	25.1611i	0.639674	+	1.08781i
$536$	8.48544	+	4.89907i	0.366515	+	0.211608i
$537$		0			0
$538$	−34.7283	−	9.30542i	−1.49724	−	0.401185i
$539$	2.46780			0.106296
$540$		0			0
$541$	−1.11754			−0.0480466			−0.0240233	−	0.999711i	$-0.507648\pi$
$541$	−1.11754			−0.0480466			−0.0240233	+	0.999711i	$0.507648\pi$
$542$	24.1093	+	6.46008i	1.03558	+	0.277484i
$543$		0			0
$544$	1.53959	+	0.888885i	0.0660096	+	0.0381106i
$545$	17.4340	+	4.52264i	0.746791	+	0.193729i
$546$		0			0
$547$	8.33894	−	31.1213i	0.356547	−	1.33065i	−0.521979	−	0.852958i	$-0.674806\pi$
$547$	8.33894	−	31.1213i	0.356547	−	1.33065i	0.878526	−	0.477694i	$-0.158527\pi$
$548$	0.952326	+	0.952326i	0.0406813	+	0.0406813i
$549$		0			0
$550$	5.73290	+	1.43847i	0.244452	+	0.0613367i
$551$	−2.10347	+	1.21444i	−0.0896109	+	0.0517369i
$552$		0			0
$553$	4.09814	+	15.2945i	0.174271	+	0.650387i
$554$	−18.2979	+	31.6928i	−0.777402	+	1.34650i
$555$		0			0
$556$	−0.141537	−	0.245149i	−0.00600250	−	0.0103966i
$557$	30.4033	−	30.4033i	1.28823	−	1.28823i	0.352366	−	0.935862i	$-0.385377\pi$
$557$	30.4033	−	30.4033i	1.28823	−	1.28823i	0.935862	−	0.352366i	$-0.114623\pi$
$558$		0			0
$559$		−	10.6910i		−	0.452182i
$560$	0.130441	+	16.3466i	0.00551212	+	0.690768i
$561$		0			0
$562$	−34.0105	+	9.11308i	−1.43465	+	0.384412i
$563$	−1.12220	+	0.300692i	−0.0472950	+	0.0126727i	−0.282389	−	0.959300i	$-0.591127\pi$
$563$	−1.12220	+	0.300692i	−0.0472950	+	0.0126727i	0.235094	+	0.971973i	$0.424460\pi$
$564$		0			0
$565$	−0.214165	−	26.8388i	−0.00901001	−	1.12912i
$566$			4.78361i			0.201070i
$567$		0			0
$568$	−12.3017	+	12.3017i	−0.516167	+	0.516167i
$569$	−0.145367	−	0.251784i	−0.00609412	−	0.0105553i	0.862962	−	0.505268i	$-0.168606\pi$
$569$	−0.145367	−	0.251784i	−0.00609412	−	0.0105553i	−0.869056	+	0.494713i	$0.835273\pi$
$570$		0			0
$571$	−13.0283	+	22.5656i	−0.545215	+	0.944341i	0.453378	+	0.891318i	$0.350219\pi$
$571$	−13.0283	+	22.5656i	−0.545215	+	0.944341i	−0.998593	+	0.0530223i	$0.983115\pi$
$572$	−0.248542	−	0.927572i	−0.0103921	−	0.0387837i
$573$		0			0
$574$	−8.57106	+	4.94851i	−0.357749	+	0.206547i
$575$	7.69838	+	1.93164i	0.321044	+	0.0805551i
$576$		0			0
$577$	−2.52834	−	2.52834i	−0.105256	−	0.105256i	0.652517	−	0.757774i	$-0.273713\pi$
$577$	−2.52834	−	2.52834i	−0.105256	−	0.105256i	−0.757774	+	0.652517i	$0.773713\pi$
$578$	5.01183	−	18.7044i	0.208465	−	0.778000i
$579$		0			0
$580$	0.677018	+	0.175629i	0.0281116	+	0.00729258i
$581$	17.6274	+	10.1772i	0.731309	+	0.422222i
$582$		0			0
$583$	5.59831	+	1.50006i	0.231858	+	0.0621262i
$584$	6.62852			0.274290
$585$		0			0
$586$	4.00174			0.165310
$587$	−40.0121	−	10.7212i	−1.65147	−	0.442511i	−0.691449	−	0.722425i	$-0.743027\pi$
$587$	−40.0121	−	10.7212i	−1.65147	−	0.442511i	−0.960025	+	0.279914i	$0.909694\pi$
$588$		0			0
$589$	9.22943	+	5.32861i	0.380292	+	0.219562i
$590$	−11.6231	−	19.7659i	−0.478517	−	0.813750i
$591$		0			0
$592$	−5.56137	+	20.7553i	−0.228571	+	0.853038i
$593$	26.6583	+	26.6583i	1.09473	+	1.09473i	0.995017	+	0.0997087i	$0.0317911\pi$
$593$	26.6583	+	26.6583i	1.09473	+	1.09473i	0.0997087	+	0.995017i	$0.468209\pi$
$594$		0			0
$595$	7.09335	−	1.96145i	0.290799	−	0.0804117i
$596$	−2.81726	+	1.62655i	−0.115400	+	0.0666260i
$597$		0			0
$598$	3.06608	+	11.4428i	0.125382	+	0.467930i
$599$	−13.2427	+	22.9370i	−0.541080	+	0.937178i	0.457762	+	0.889075i	$0.348651\pi$
$599$	−13.2427	+	22.9370i	−0.541080	+	0.937178i	−0.998842	+	0.0481037i	$0.984682\pi$
$600$		0			0
$601$	4.26710	+	7.39084i	0.174059	+	0.301479i	0.939835	−	0.341628i	$-0.110978\pi$
$601$	4.26710	+	7.39084i	0.174059	+	0.301479i	−0.765776	+	0.643107i	$0.777645\pi$
$602$	−3.74279	+	3.74279i	−0.152545	+	0.152545i
$603$		0			0
$604$		−	0.00111412i		−	4.53329e-5i
$605$	−16.2960	−	16.0380i	−0.662527	−	0.652037i
$606$		0			0
$607$	44.4113	−	11.9000i	1.80260	−	0.483005i	0.808220	−	0.588881i	$-0.200431\pi$
$607$	44.4113	−	11.9000i	1.80260	−	0.483005i	0.994379	+	0.105876i	$0.0337645\pi$
$608$	1.62942	−	0.436602i	0.0660818	−	0.0177066i
$609$		0			0
$610$	39.8794	−	0.318225i	1.61467	−	0.0128846i
$611$			46.0190i			1.86173i
$612$		0			0
$613$	17.3219	−	17.3219i	0.699625	−	0.699625i	−0.264705	−	0.964330i	$-0.585274\pi$
$613$	17.3219	−	17.3219i	0.699625	−	0.699625i	0.964330	+	0.264705i	$0.0852744\pi$
$614$	−20.7039	−	35.8602i	−0.835542	−	1.44720i
$615$		0			0
$616$	−2.65929	+	4.60603i	−0.107146	+	0.185582i
$617$	−9.74553	−	36.3708i	−0.392340	−	1.46423i	−0.826263	−	0.563284i	$-0.809538\pi$
$617$	−9.74553	−	36.3708i	−0.392340	−	1.46423i	0.433923	−	0.900950i	$-0.357129\pi$
$618$		0			0
$619$	−8.57434	+	4.95040i	−0.344632	+	0.198973i	−0.662318	−	0.749223i	$-0.730427\pi$
$619$	−8.57434	+	4.95040i	−0.344632	+	0.198973i	0.317687	+	0.948196i	$0.397094\pi$
$620$	−0.817915	−	2.95789i	−0.0328483	−	0.118792i
$621$		0			0
$622$	32.2255	+	32.2255i	1.29213	+	1.29213i
$623$	2.45353	−	9.15670i	0.0982986	−	0.366855i
$624$		0			0
$625$	13.1846	+	21.2407i	0.527383	+	0.849628i
$626$	26.9753	+	15.5742i	1.07815	+	0.622469i
$627$		0			0
$628$	1.60427	+	0.429864i	0.0640175	+	0.0171534i
$629$	9.67378			0.385719
$630$		0			0
$631$	−22.0279			−0.876918			−0.438459	−	0.898751i	$-0.644476\pi$
$631$	−22.0279			−0.876918			−0.438459	+	0.898751i	$0.644476\pi$
$632$	22.0230	+	5.90104i	0.876027	+	0.234731i
$633$		0			0
$634$	−4.65268	−	2.68622i	−0.184781	−	0.106684i
$635$	−5.18549	+	3.04927i	−0.205780	+	0.121007i
$636$		0			0
$637$	−4.03223	+	15.0485i	−0.159763	+	0.596242i
$638$	−1.33171	−	1.33171i	−0.0527227	−	0.0527227i
$639$		0			0
$640$	18.2251	+	10.3293i	0.720412	+	0.408300i
$641$	−21.8054	+	12.5894i	−0.861263	+	0.497251i	−0.864435	−	0.502744i	$-0.832324\pi$
$641$	−21.8054	+	12.5894i	−0.861263	+	0.497251i	0.00317173	+	0.999995i	$0.498990\pi$
$642$		0			0
$643$	−8.05166	−	30.0492i	−0.317526	−	1.18502i	−0.921614	−	0.388107i	$-0.873129\pi$
$643$	−8.05166	−	30.0492i	−0.317526	−	1.18502i	0.604088	−	0.796918i	$-0.293538\pi$
$644$	−0.319219	+	0.552904i	−0.0125790	+	0.0217875i
$645$		0			0
$646$	1.64484	+	2.84895i	0.0647154	+	0.112090i
$647$	−7.86580	+	7.86580i	−0.309237	+	0.309237i	−0.844613	−	0.535377i	$-0.820170\pi$
$647$	−7.86580	+	7.86580i	−0.309237	+	0.309237i	0.535377	+	0.844613i	$0.320170\pi$
$648$		0			0
$649$		−	6.72090i		−	0.263818i
$650$	−18.1389	+	32.6084i	−0.711465	+	1.27901i
$651$		0			0
$652$	−1.12456	+	0.301325i	−0.0440411	+	0.0118008i
$653$	−0.279676	+	0.0749391i	−0.0109446	+	0.00293259i	−0.264287	−	0.964444i	$-0.585137\pi$
$653$	−0.279676	+	0.0749391i	−0.0109446	+	0.00293259i	0.253343	+	0.967377i	$0.418470\pi$
$654$		0			0
$655$	−33.5255	+	34.0648i	−1.30995	+	1.33102i
$656$			12.8384i			0.501256i
$657$		0			0
$658$	16.1106	−	16.1106i	0.628058	−	0.628058i
$659$	13.4009	+	23.2111i	0.522026	+	0.904175i	0.999672	+	0.0256228i	$0.00815688\pi$
$659$	13.4009	+	23.2111i	0.522026	+	0.904175i	−0.477646	+	0.878552i	$0.658510\pi$
$660$		0			0
$661$	−12.6438	+	21.8997i	−0.491787	+	0.851800i	−0.999955	−	0.00945786i	$-0.996989\pi$
$661$	−12.6438	+	21.8997i	−0.491787	+	0.851800i	0.508168	+	0.861258i	$0.330323\pi$
$662$	2.07289	+	7.73611i	0.0805650	+	0.300673i
$663$		0			0
$664$	25.3823	−	14.6545i	0.985024	−	0.568704i
$665$	3.44332	−	6.07544i	0.133526	−	0.235596i
$666$		0			0
$667$	−1.78827	−	1.78827i	−0.0692421	−	0.0692421i
$668$	0.303196	−	1.13154i	0.0117310	−	0.0437807i
$669$		0			0
$670$	2.50486	−	9.65579i	0.0967710	−	0.373036i
$671$	10.1231	+	5.84458i	0.390799	+	0.225628i
$672$		0			0
$673$	−23.5227	−	6.30290i	−0.906735	−	0.242959i	−0.224829	−	0.974398i	$-0.572182\pi$
$673$	−23.5227	−	6.30290i	−0.906735	−	0.242959i	−0.681906	+	0.731439i	$0.738849\pi$
$674$	−13.3044			−0.512466
$675$		0			0
$676$	3.51002			0.135001
$677$	0.896681	+	0.240265i	0.0344623	+	0.00923414i	0.276009	−	0.961155i	$-0.410988\pi$
$677$	0.896681	+	0.240265i	0.0344623	+	0.00923414i	−0.241547	+	0.970389i	$0.577655\pi$
$678$		0			0
$679$	−7.03407	−	4.06112i	−0.269943	−	0.155852i
$680$	2.66100	−	10.2577i	0.102045	−	0.393365i
$681$		0			0
$682$	−2.13874	+	7.98188i	−0.0818966	+	0.305642i
$683$	−22.2024	−	22.2024i	−0.849550	−	0.849550i	0.140526	−	0.990077i	$-0.455120\pi$
$683$	−22.2024	−	22.2024i	−0.849550	−	0.849550i	−0.990077	+	0.140526i	$0.955120\pi$
$684$		0			0
$685$	7.56311	−	13.3445i	0.288972	−	0.509866i
$686$	23.3578	−	13.4856i	0.891805	−	0.514884i
$687$		0			0
$688$	1.77711	+	6.63225i	0.0677515	+	0.252852i
$689$	−18.2945	+	31.6871i	−0.696966	+	1.20718i
$690$		0			0
$691$	−4.05877	−	7.02999i	−0.154403	−	0.267433i	0.778439	−	0.627721i	$-0.216012\pi$
$691$	−4.05877	−	7.02999i	−0.154403	−	0.267433i	−0.932841	+	0.360287i	$0.882679\pi$
$692$	1.89711	−	1.89711i	0.0721173	−	0.0721173i
$693$		0			0
$694$		−	14.2473i		−	0.540821i
$695$	−2.26141	+	2.29779i	−0.0857802	+	0.0871602i
$696$		0			0
$697$	5.58297	−	1.49595i	0.211470	−	0.0566633i
$698$	−12.1157	+	3.24640i	−0.458586	+	0.122878i
$699$		0			0
$700$	−1.93388	+	0.551405i	−0.0730937	+	0.0208411i
$701$			19.6359i			0.741637i	0.928705	+	0.370819i	$0.120923\pi$
$701$			19.6359i			0.741637i	−0.928705	+	0.370819i	$0.879077\pi$
$702$		0			0
$703$	6.49076	−	6.49076i	0.244804	−	0.244804i
$704$	3.79526	+	6.57359i	0.143039	+	0.247752i
$705$		0			0
$706$	−12.8937	+	22.3325i	−0.485260	+	0.840496i
$707$	1.36642	+	5.09956i	0.0513896	+	0.191789i
$708$		0			0
$709$	2.68383	−	1.54951i	0.100793	−	0.0581931i	−0.448756	−	0.893654i	$-0.648133\pi$
$709$	2.68383	−	1.54951i	0.100793	−	0.0581931i	0.549549	+	0.835461i	$0.314799\pi$
$710$	15.4092	+	8.73329i	0.578295	+	0.327754i
$711$		0			0
$712$	−9.65210	−	9.65210i	−0.361728	−	0.361728i
$713$	−2.87199	+	10.7184i	−0.107557	+	0.401408i
$714$		0			0
$715$	−9.42765	+	5.54383i	−0.352574	+	0.207327i
$716$	2.93083	+	1.69211i	0.109530	+	0.0632373i
$717$		0			0
$718$	−16.3380	−	4.37774i	−0.609727	−	0.163376i
$719$	−20.3126			−0.757533			−0.378767	−	0.925492i	$-0.623652\pi$
$719$	−20.3126			−0.757533			−0.378767	+	0.925492i	$0.623652\pi$
$720$		0			0
$721$	26.7604			0.996608
$722$	−21.6325	−	5.79640i	−0.805077	−	0.215720i
$723$		0			0
$724$	−2.51149	−	1.45001i	−0.0933388	−	0.0538892i
$725$	−0.127122	−	7.96481i	−0.00472118	−	0.295806i
$726$		0			0
$727$	4.57247	−	17.0647i	0.169584	−	0.632895i	−0.827827	−	0.560983i	$-0.810423\pi$
$727$	4.57247	−	17.0647i	0.169584	−	0.632895i	0.997411	−	0.0719119i	$-0.0229101\pi$
$728$	−23.7421	−	23.7421i	−0.879941	−	0.879941i
$729$		0			0
$730$	−1.79858	−	6.50434i	−0.0665685	−	0.240736i
$731$	2.67706	−	1.54560i	0.0990147	−	0.0571662i
$732$		0			0
$733$	−6.82693	−	25.4785i	−0.252158	−	0.941068i	−0.969649	−	0.244500i	$-0.921376\pi$
$733$	−6.82693	−	25.4785i	−0.252158	−	0.941068i	0.717491	−	0.696568i	$-0.245291\pi$
$734$	18.9970	−	32.9038i	0.701192	−	1.21450i
$735$		0			0
$736$	0.878218	+	1.52112i	0.0323715	+	0.0560692i
$737$	2.06746	−	2.06746i	0.0761558	−	0.0761558i
$738$		0			0
$739$			6.41459i			0.235965i	0.993016	+	0.117982i	$0.0376426\pi$
$739$			6.41459i			0.235965i	−0.993016	+	0.117982i	$0.962357\pi$
$740$	−2.64322	+	0.0210921i	−0.0971667	+	0.000775361i
$741$		0			0
$742$	17.4979	−	4.68854i	0.642368	−	0.172122i
$743$	18.4970	−	4.95625i	0.678588	−	0.181827i	0.0969677	−	0.995288i	$-0.469086\pi$
$743$	18.4970	−	4.95625i	0.678588	−	0.181827i	0.581620	+	0.813460i	$0.302419\pi$
$744$		0			0
$745$	26.4063	+	25.9882i	0.967453	+	0.952135i
$746$		−	3.13856i		−	0.114911i
$747$		0			0
$748$	0.196335	−	0.196335i	0.00717870	−	0.00717870i
$749$	13.3702	+	23.1579i	0.488536	+	0.846170i
$750$		0			0
$751$	−1.96958	+	3.41141i	−0.0718709	+	0.124484i	−0.899721	−	0.436465i	$-0.856230\pi$
$751$	−1.96958	+	3.41141i	−0.0718709	+	0.124484i	0.827850	+	0.560949i	$0.189564\pi$
$752$	−7.64946	−	28.5482i	−0.278947	−	1.04105i
$753$		0			0
$754$	10.2966	−	5.94472i	0.374979	−	0.216494i
$755$	−0.0122298	+	0.00338180i	−0.000445090	+	0.000123076i
$756$		0			0
$757$	17.3710	+	17.3710i	0.631361	+	0.631361i	0.948409	−	0.317049i	$-0.102692\pi$
$757$	17.3710	+	17.3710i	0.631361	+	0.631361i	−0.317049	+	0.948409i	$0.602692\pi$
$758$	6.41725	−	23.9495i	0.233085	−	0.869885i
$759$		0			0
$760$	−5.09711	−	8.66798i	−0.184892	−	0.314421i
$761$	−7.11860	−	4.10993i	−0.258049	−	0.148985i	0.365395	−	0.930853i	$-0.380934\pi$
$761$	−7.11860	−	4.10993i	−0.258049	−	0.148985i	−0.623444	+	0.781868i	$0.714267\pi$
$762$		0			0
$763$	15.9380	+	4.27057i	0.576994	+	0.154605i
$764$	1.03558			0.0374660
$765$		0			0
$766$	−32.5079			−1.17456
$767$	40.9835	+	10.9815i	1.47983	+	0.396519i
$768$		0			0
$769$	1.91615	+	1.10629i	0.0690983	+	0.0398939i	0.534151	−	0.845389i	$-0.320631\pi$
$769$	1.91615	+	1.10629i	0.0690983	+	0.0398939i	−0.465053	+	0.885283i	$0.653965\pi$
$770$	5.24131	+	1.35967i	0.188884	+	0.0489992i
$771$		0			0
$772$	0.472918	−	1.76495i	0.0170207	−	0.0635221i
$773$	8.23173	+	8.23173i	0.296075	+	0.296075i	0.839474	−	0.543400i	$-0.182863\pi$
$773$	8.23173	+	8.23173i	0.296075	+	0.296075i	−0.543400	+	0.839474i	$0.682863\pi$
$774$		0			0
$775$	−29.9864	+	17.9567i	−1.07714	+	0.645024i
$776$	−10.1286	+	5.84773i	−0.363595	+	0.209921i
$777$		0			0
$778$	−9.41596	−	35.1408i	−0.337579	−	1.25986i
$779$	2.74224	−	4.74970i	0.0982511	−	0.170176i
$780$		0			0
$781$	2.59572	+	4.49591i	0.0928820	+	0.160876i
$782$	−2.42204	+	2.42204i	−0.0866119	+	0.0866119i
$783$		0			0
$784$		−	10.0057i		−	0.357346i
$785$	−0.150937	−	18.9151i	−0.00538717	−	0.675109i
$786$		0			0
$787$	33.8541	−	9.07119i	1.20677	−	0.323353i	0.401276	−	0.915957i	$-0.368567\pi$
$787$	33.8541	−	9.07119i	1.20677	−	0.323353i	0.805494	+	0.592604i	$0.201900\pi$
$788$	2.54665	−	0.682372i	0.0907205	−	0.0243085i
$789$		0			0
$790$	−0.185222	−	23.2116i	−0.00658989	−	0.825831i
$791$		−	24.5882i		−	0.874256i
$792$		0			0
$793$	−52.1803	+	52.1803i	−1.85298	+	1.85298i
$794$	17.3076	+	29.9776i	0.614223	+	1.06387i
$795$		0			0
$796$	−1.73110	+	2.99835i	−0.0613571	+	0.106274i
$797$	6.77343	+	25.2788i	0.239927	+	0.895421i	0.975866	+	0.218372i	$0.0700747\pi$
$797$	6.77343	+	25.2788i	0.239927	+	0.895421i	−0.735938	+	0.677049i	$0.763259\pi$
$798$		0			0
$799$	−11.5233	+	6.65297i	−0.407664	+	0.235365i
$800$	−1.34643	+	5.36608i	−0.0476036	+	0.189719i
$801$		0			0
$802$	−12.2041	−	12.2041i	−0.430941	−	0.430941i
$803$	0.511942	−	1.91059i	0.0180660	−	0.0674233i
$804$		0			0
$805$	7.03825	+	1.82583i	0.248066	+	0.0643520i
$806$	−45.1784	−	26.0837i	−1.59134	−	0.918761i
$807$		0			0
$808$	7.34301	+	1.96755i	0.258326	+	0.0692183i
$809$	−40.3389			−1.41824			−0.709120	−	0.705088i	$-0.750908\pi$
$809$	−40.3389			−1.41824			−0.709120	+	0.705088i	$0.750908\pi$
$810$		0			0
$811$	−4.50040			−0.158030			−0.0790152	−	0.996873i	$-0.525178\pi$
$811$	−4.50040			−0.158030			−0.0790152	+	0.996873i	$0.525178\pi$
$812$	0.618923	+	0.165840i	0.0217199	+	0.00581984i
$813$		0			0
$814$	6.16394	+	3.55875i	0.216046	+	0.124734i
$815$	6.72116	+	11.4298i	0.235432	+	0.400368i
$816$		0			0
$817$	0.759168	−	2.83326i	0.0265599	−	0.0991231i
$818$	24.3930	+	24.3930i	0.852880	+	0.852880i
$819$		0			0
$820$	−1.52221	+	0.420920i	−0.0531577	+	0.0146992i
$821$	−13.3109	+	7.68503i	−0.464552	+	0.268209i	−0.713956	−	0.700190i	$-0.753099\pi$
$821$	−13.3109	+	7.68503i	−0.464552	+	0.268209i	0.249404	+	0.968399i	$0.419765\pi$
$822$		0			0
$823$	3.77065	+	14.0723i	0.131437	+	0.490528i	0.999987	−	0.00507263i	$-0.00161467\pi$
$823$	3.77065	+	14.0723i	0.131437	+	0.490528i	−0.868551	+	0.495601i	$0.834948\pi$
$824$	19.2665	−	33.3706i	0.671182	−	1.16252i
$825$		0			0
$826$	−10.5033	−	18.1923i	−0.365457	−	0.632989i
$827$	3.31824	−	3.31824i	0.115387	−	0.115387i	−0.647056	−	0.762443i	$-0.724000\pi$
$827$	3.31824	−	3.31824i	0.115387	−	0.115387i	0.762443	+	0.647056i	$0.224000\pi$
$828$		0			0
$829$			33.9539i			1.17927i	0.807671	+	0.589633i	$0.200728\pi$
$829$			33.9539i			1.17927i	−0.807671	+	0.589633i	$0.799272\pi$
$830$	−21.2672	−	20.9304i	−0.738194	−	0.726506i
$831$		0			0
$832$	−46.2865	+	12.4024i	−1.60469	+	0.429977i
$833$	−4.35112	+	1.16588i	−0.150757	+	0.0403953i
$834$		0			0
$835$	−13.3414	+	0.106460i	−0.461698	+	0.00368421i
$836$		−	0.263467i		−	0.00911220i
$837$		0			0
$838$	−11.6473	+	11.6473i	−0.402349	+	0.402349i
$839$	−5.71824	−	9.90428i	−0.197416	−	0.341934i	0.750274	−	0.661127i	$-0.229921\pi$
$839$	−5.71824	−	9.90428i	−0.197416	−	0.341934i	−0.947690	+	0.319193i	$0.896588\pi$
$840$		0			0
$841$	13.2309	−	22.9166i	0.456238	−	0.790228i
$842$	5.03357	+	18.7855i	0.173468	+	0.647392i
$843$		0			0
$844$	−0.0209495	+	0.0120952i	−0.000721111	+	0.000416334i
$845$	−10.6543	−	38.5299i	−0.366519	−	1.32547i
$846$		0			0
$847$	−14.8113	−	14.8113i	−0.508923	−	0.508923i
$848$	6.08198	−	22.6983i	0.208856	−	0.779462i
$849$		0			0
$850$	−10.7876	+	0.172174i	−0.370010	+	0.00590552i
$851$	8.27720	+	4.77884i	0.283739	+	0.163817i
$852$		0			0
$853$	23.0994	+	6.18947i	0.790909	+	0.211923i	0.631589	−	0.775304i	$-0.282403\pi$
$853$	23.0994	+	6.18947i	0.790909	+	0.211923i	0.159320	+	0.987227i	$0.449070\pi$
$854$	36.5353			1.25021
$855$		0			0
$856$	38.5043			1.31605
$857$	14.4874	+	3.88189i	0.494881	+	0.132603i	0.497623	−	0.867393i	$-0.334206\pi$
$857$	14.4874	+	3.88189i	0.494881	+	0.132603i	−0.00274224	+	0.999996i	$0.500873\pi$
$858$		0			0
$859$	37.5983	+	21.7074i	1.28284	+	0.740646i	0.977366	−	0.211555i	$-0.0678529\pi$
$859$	37.5983	+	21.7074i	1.28284	+	0.740646i	0.305471	+	0.952201i	$0.401186\pi$
$860$	−0.728099	+	0.428150i	−0.0248280	+	0.0145998i
$861$		0			0
$862$	12.5016	−	46.6567i	0.425807	−	1.58913i
$863$	2.78648	+	2.78648i	0.0948527	+	0.0948527i	0.752941	−	0.658088i	$-0.228635\pi$
$863$	2.78648	+	2.78648i	0.0948527	+	0.0948527i	−0.658088	+	0.752941i	$0.728635\pi$
$864$		0			0
$865$	−26.5833	−	15.0663i	−0.903859	−	0.512271i
$866$	0.545339	−	0.314852i	0.0185314	−	0.0106991i
$867$		0			0
$868$	−0.727658	−	2.71566i	−0.0246983	−	0.0921754i
$869$	3.40181	−	5.89211i	0.115399	−	0.199876i
$870$		0			0
$871$	9.22911	+	15.9853i	0.312717	+	0.541641i
$872$	16.8003	−	16.8003i	0.568929	−	0.568929i
$873$		0			0
$874$			3.25020i			0.109940i
$875$	11.9229	+	19.5547i	0.403068	+	0.661069i
$876$		0			0
$877$	−41.5598	+	11.1359i	−1.40338	+	0.376033i	−0.879556	−	0.475796i	$-0.842160\pi$
$877$	−41.5598	+	11.1359i	−1.40338	+	0.376033i	−0.523820	+	0.851829i	$0.675493\pi$
$878$	−1.93163	+	0.517577i	−0.0651892	+	0.0174674i
$879$		0			0
$880$	4.92699	−	5.00625i	0.166089	−	0.168761i
$881$		−	47.0487i		−	1.58511i	−0.609801	−	0.792555i	$-0.708751\pi$
$881$		−	47.0487i		−	1.58511i	0.609801	−	0.792555i	$-0.291249\pi$
$882$		0			0
$883$	21.0669	−	21.0669i	0.708957	−	0.708957i	−0.257359	−	0.966316i	$-0.582852\pi$
$883$	21.0669	−	21.0669i	0.708957	−	0.708957i	0.966316	+	0.257359i	$0.0828523\pi$
$884$	0.876436	+	1.51803i	0.0294777	+	0.0510569i
$885$		0			0
$886$	21.5140	−	37.2633i	0.722776	−	1.25188i
$887$	−0.939801	−	3.50739i	−0.0315554	−	0.117766i	0.948352	−	0.317221i	$-0.102750\pi$
$887$	−0.939801	−	3.50739i	−0.0315554	−	0.117766i	−0.979907	+	0.199454i	$0.936083\pi$
$888$		0			0
$889$	−4.77265	+	2.75549i	−0.160069	+	0.0924161i
$890$	−6.85228	+	12.0903i	−0.229689	+	0.405267i
$891$		0			0
$892$	0.347592	+	0.347592i	0.0116382	+	0.0116382i
$893$	−3.26780	+	12.1956i	−0.109353	+	0.408110i
$894$		0			0
$895$	9.67832	−	37.3083i	0.323511	−	1.24708i
$896$	16.6203	+	9.59572i	0.555245	+	0.320571i
$897$		0			0
$898$	28.3167	+	7.58743i	0.944939	+	0.253196i
$899$	11.1368			0.371433
$900$		0			0
$901$	−10.5794			−0.352450
$902$	4.10768	+	1.10065i	0.136771	+	0.0366477i
$903$		0			0
$904$	−30.6619	−	17.7026i	−1.01980	−	0.588781i
$905$	−8.29356	+	31.9703i	−0.275687	+	1.06273i
$906$		0			0
$907$	−2.71600	+	10.1363i	−0.0901833	+	0.336569i	−0.996245	−	0.0865764i	$-0.972407\pi$
$907$	−2.71600	+	10.1363i	−0.0901833	+	0.336569i	0.906062	+	0.423145i	$0.139074\pi$
$908$	2.11700	+	2.11700i	0.0702551	+	0.0702551i
$909$		0			0
$910$	−16.8551	+	29.7395i	−0.558743	+	0.985855i
$911$	−6.77512	+	3.91162i	−0.224470	+	0.129598i	−0.608018	−	0.793923i	$-0.708035\pi$
$911$	−6.77512	+	3.91162i	−0.224470	+	0.129598i	0.383548	+	0.923521i	$0.374702\pi$
$912$		0			0
$913$	−2.26362	−	8.44796i	−0.0749150	−	0.279587i
$914$	0.612004	−	1.06002i	0.0202433	−	0.0350624i
$915$		0			0
$916$	−2.16600	−	3.75163i	−0.0715668	−	0.123957i
$917$	−30.9612	+	30.9612i	−1.02243	+	1.02243i
$918$		0			0
$919$		−	4.61000i		−	0.152070i	−0.997105	−	0.0760349i	$-0.975774\pi$
$919$		−	4.61000i		−	0.152070i	0.997105	−	0.0760349i	$-0.0242260\pi$
$920$	7.34413	−	7.46228i	0.242129	−	0.246024i
$921$		0			0
$922$	−28.0591	+	7.51842i	−0.924078	+	0.247606i
$923$	−31.6570	+	8.48246i	−1.04200	+	0.279204i
$924$		0			0
$925$	8.25475	+	28.9509i	0.271415	+	0.951901i
$926$		−	25.1999i		−	0.828122i
$927$		0			0
$928$	1.24650	−	1.24650i	0.0409182	−	0.0409182i
$929$	−15.7062	−	27.2039i	−0.515302	−	0.892530i	−0.999842	−	0.0177609i	$-0.994346\pi$
$929$	−15.7062	−	27.2039i	−0.515302	−	0.892530i	0.484540	−	0.874769i	$-0.338987\pi$
$930$		0			0
$931$	−2.13718	+	3.70170i	−0.0700433	+	0.121318i
$932$	0.303388	+	1.13226i	0.00993782	+	0.0370884i
$933$		0			0
$934$	−27.6818	+	15.9821i	−0.905778	+	0.522951i
$935$	−2.75114	−	1.55924i	−0.0899720	−	0.0509925i
$936$		0			0
$937$	−21.3617	−	21.3617i	−0.697856	−	0.697856i	0.266092	−	0.963948i	$-0.414268\pi$
$937$	−21.3617	−	21.3617i	−0.697856	−	0.697856i	−0.963948	+	0.266092i	$0.914268\pi$
$938$	2.36525	−	8.82722i	0.0772281	−	0.288219i
$939$		0			0
$940$	3.13406	−	1.84295i	0.102222	−	0.0601105i
$941$	5.77035	+	3.33151i	0.188108	+	0.108604i	0.591096	−	0.806601i	$-0.298695\pi$
$941$	5.77035	+	3.33151i	0.188108	+	0.108604i	−0.402989	+	0.915205i	$0.632029\pi$
$942$		0			0
$943$	5.51597	+	1.47800i	0.179625	+	0.0481303i
$944$	−27.2498			−0.886905
$945$		0			0
$946$	2.27436			0.0739458
$947$	−3.23873	−	0.867814i	−0.105245	−	0.0282002i	0.205812	−	0.978591i	$-0.434016\pi$
$947$	−3.23873	−	0.867814i	−0.105245	−	0.0282002i	−0.311057	+	0.950391i	$0.600683\pi$
$948$		0			0
$949$	10.8142	+	6.24356i	0.351043	+	0.202675i
$950$	−7.12255	+	7.35359i	−0.231086	+	0.238582i
$951$		0			0
$952$	2.51269	−	9.37748i	0.0814367	−	0.303926i
$953$	30.7161	+	30.7161i	0.994992	+	0.994992i	0.999988	−	0.00499525i	$-0.00159004\pi$
$953$	30.7161	+	30.7161i	0.994992	+	0.994992i	−0.00499525	+	0.999988i	$0.501590\pi$
$954$		0			0
$955$	−3.14340	−	11.3677i	−0.101718	−	0.367850i
$956$	2.30970	−	1.33350i	0.0747009	−	0.0431286i
$957$		0			0
$958$	6.19919	+	23.1357i	0.200287	+	0.747480i
$959$	7.02601	−	12.1694i	0.226882	−	0.392970i
$960$		0			0
$961$	−8.93253	−	15.4716i	−0.288146	−	0.499084i
$962$	−31.7725	+	31.7725i	−1.02439	+	1.02439i
$963$		0			0
$964$			1.00809i			0.0324684i
$965$	−20.8096	+	0.166054i	−0.669885	+	0.00534548i
$966$		0			0
$967$	5.53906	−	1.48419i	0.178124	−	0.0477282i	−0.168654	−	0.985675i	$-0.553942\pi$
$967$	5.53906	−	1.48419i	0.178124	−	0.0477282i	0.346779	+	0.937947i	$0.387276\pi$
$968$	−29.1336	+	7.80632i	−0.936388	+	0.250904i
$969$		0			0
$970$	8.48647	+	8.35210i	0.272484	+	0.268170i
$971$		−	14.2248i		−	0.456496i	−0.973603	−	0.228248i	$-0.926700\pi$
$971$		−	14.2248i		−	0.456496i	0.973603	−	0.228248i	$-0.0732998\pi$
$972$		0			0
$973$	−2.08844	+	2.08844i	−0.0669524	+	0.0669524i
$974$	20.7244	+	35.8957i	0.664052	+	1.15017i
$975$		0			0
$976$	23.6968	−	41.0440i	0.758516	−	1.31379i
$977$	−8.07944	−	30.1529i	−0.258484	−	0.964676i	−0.966119	−	0.258097i	$-0.916904\pi$
$977$	−8.07944	−	30.1529i	−0.258484	−	0.964676i	0.707635	−	0.706578i	$-0.249762\pi$
$978$		0			0
$979$	−3.52757	+	2.03664i	−0.112742	+	0.0650913i
$980$	1.18634	−	0.328046i	0.0378962	−	0.0104791i
$981$		0			0
$982$	38.5627	+	38.5627i	1.23059	+	1.23059i
$983$	−2.66543	+	9.94750i	−0.0850139	+	0.317276i	−0.995317	−	0.0966666i	$-0.969182\pi$
$983$	−2.66543	+	9.94750i	−0.0850139	+	0.317276i	0.910303	+	0.413943i	$0.135849\pi$
$984$		0			0
$985$	−15.2206	−	25.8836i	−0.484967	−	0.824719i
$986$	2.97715	+	1.71886i	0.0948116	+	0.0547395i
$987$		0			0
$988$	1.60660	+	0.430488i	0.0511128	+	0.0136956i
$989$	3.05411			0.0971150
$990$		0			0
$991$	37.9180			1.20450			0.602252	−	0.798306i	$-0.294270\pi$
$991$	37.9180			1.20450			0.602252	+	0.798306i	$0.294270\pi$
$992$	−7.47116	−	2.00189i	−0.237210	−	0.0635601i
$993$		0			0
$994$	14.0523	+	8.11308i	0.445711	+	0.257331i
$995$	38.1678	+	9.90130i	1.21000	+	0.313892i
$996$		0			0
$997$	−8.06937	+	30.1153i	−0.255559	+	0.953761i	0.712219	+	0.701957i	$0.247690\pi$
$997$	−8.06937	+	30.1153i	−0.255559	+	0.953761i	−0.967778	+	0.251804i	$0.918976\pi$
$998$	40.9452	+	40.9452i	1.29610	+	1.29610i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.m.a.17.1		16
3.2	odd	2		45.2.l.a.32.4	yes	16
5.2	odd	4		675.2.q.a.368.4		16
5.3	odd	4	inner	135.2.m.a.98.1		16
5.4	even	2		675.2.q.a.557.4		16
9.2	odd	6	inner	135.2.m.a.62.1		16
9.4	even	3		405.2.f.a.242.6		16
9.5	odd	6		405.2.f.a.242.3		16
9.7	even	3		45.2.l.a.2.4	✓	16
12.11	even	2		720.2.cu.c.257.4		16
15.2	even	4		225.2.p.b.68.1		16
15.8	even	4		45.2.l.a.23.4	yes	16
15.14	odd	2		225.2.p.b.32.1		16
36.7	odd	6		720.2.cu.c.497.3		16
45.2	even	12		675.2.q.a.143.4		16
45.7	odd	12		225.2.p.b.218.1		16
45.13	odd	12		405.2.f.a.323.3		16
45.23	even	12		405.2.f.a.323.6		16
45.29	odd	6		675.2.q.a.332.4		16
45.34	even	6		225.2.p.b.182.1		16
45.38	even	12	inner	135.2.m.a.8.1		16
45.43	odd	12		45.2.l.a.38.4	yes	16
60.23	odd	4		720.2.cu.c.113.3		16
180.43	even	12		720.2.cu.c.353.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.4	✓	16	9.7	even	3
45.2.l.a.23.4	yes	16	15.8	even	4
45.2.l.a.32.4	yes	16	3.2	odd	2
45.2.l.a.38.4	yes	16	45.43	odd	12
135.2.m.a.8.1		16	45.38	even	12	inner
135.2.m.a.17.1		16	1.1	even	1	trivial
135.2.m.a.62.1		16	9.2	odd	6	inner
135.2.m.a.98.1		16	5.3	odd	4	inner
225.2.p.b.32.1		16	15.14	odd	2
225.2.p.b.68.1		16	15.2	even	4
225.2.p.b.182.1		16	45.34	even	6
225.2.p.b.218.1		16	45.7	odd	12
405.2.f.a.242.3		16	9.5	odd	6
405.2.f.a.242.6		16	9.4	even	3
405.2.f.a.323.3		16	45.13	odd	12
405.2.f.a.323.6		16	45.23	even	12
675.2.q.a.143.4		16	45.2	even	12
675.2.q.a.332.4		16	45.29	odd	6
675.2.q.a.368.4		16	5.2	odd	4
675.2.q.a.557.4		16	5.4	even	2
720.2.cu.c.113.3		16	60.23	odd	4
720.2.cu.c.257.4		16	12.11	even	2
720.2.cu.c.353.4		16	180.43	even	12
720.2.cu.c.497.3		16	36.7	odd	6

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.m (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.29724 - 0.347596i) q^{2} +(-0.170031 - 0.0981673i) q^{4} +(-0.561484 + 2.16443i) q^{5} +(-0.530190 + 1.97869i) q^{7} +(2.08575 + 2.08575i) q^{8} +O(q^{10})\)	\(q+(-1.29724 - 0.347596i) q^{2} +(-0.170031 - 0.0981673i) q^{4} +(-0.561484 + 2.16443i) q^{5} +(-0.530190 + 1.97869i) q^{7} +(2.08575 + 2.08575i) q^{8} +(1.48073 - 2.61262i) q^{10} +(0.762281 - 0.440103i) q^{11} +(1.43820 + 5.36743i) q^{13} +(1.37557 - 2.38256i) q^{14} +(-1.78439 - 3.09066i) q^{16} +(-1.13610 + 1.13610i) q^{17} +1.52456i q^{19} +(0.307945 - 0.312899i) q^{20} +(-1.14184 + 0.305956i) q^{22} +(-1.53331 + 0.410850i) q^{23} +(-4.36947 - 2.43058i) q^{25} -7.46278i q^{26} +(0.284392 - 0.284392i) q^{28} +(0.796583 + 1.37972i) q^{29} +(3.49518 - 6.05383i) q^{31} +(-0.286379 - 1.06878i) q^{32} +(1.86870 - 1.07889i) q^{34} +(-3.98504 - 2.25856i) q^{35} +(-4.25746 - 4.25746i) q^{37} +(0.529931 - 1.97773i) q^{38} +(-5.68555 + 3.34333i) q^{40} +(-3.11546 - 1.79871i) q^{41} +(-1.85841 - 0.497959i) q^{43} -0.172815 q^{44} +2.13189 q^{46} +(7.99942 + 2.14344i) q^{47} +(2.42805 + 1.40183i) q^{49} +(4.82341 + 4.67186i) q^{50} +(0.282368 - 1.05381i) q^{52} +(4.65601 + 4.65601i) q^{53} +(0.524562 + 1.89701i) q^{55} +(-5.23290 + 3.02121i) q^{56} +(-0.553777 - 2.06672i) q^{58} +(3.81780 - 6.61262i) q^{59} +(6.64002 + 11.5008i) q^{61} +(-6.63838 + 6.63838i) q^{62} +8.62358i q^{64} +(-12.4249 + 0.0991472i) q^{65} +(3.20857 - 0.859733i) q^{67} +(0.304699 - 0.0816439i) q^{68} +(4.38451 + 4.31509i) q^{70} +5.89798i q^{71} +(1.58900 - 1.58900i) q^{73} +(4.04309 + 7.00284i) q^{74} +(0.149662 - 0.259222i) q^{76} +(0.466676 + 1.74166i) q^{77} +(6.69401 - 3.86479i) q^{79} +(7.69140 - 2.12683i) q^{80} +(3.41628 + 3.41628i) q^{82} +(2.57170 - 9.59770i) q^{83} +(-1.82110 - 3.09690i) q^{85} +(2.23772 + 1.29195i) q^{86} +(2.50787 + 0.671981i) q^{88} -4.62765 q^{89} -11.3830 q^{91} +(0.301043 + 0.0806641i) q^{92} +(-9.63215 - 5.56112i) q^{94} +(-3.29980 - 0.856017i) q^{95} +(-1.02621 + 3.82988i) q^{97} +(-2.66250 - 2.66250i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 6 q^{5} - 2 q^{7}+O(q^{10}) \) 16 * q + 6 * q^2 + 6 * q^5 - 2 * q^7	\( 16 q + 6 q^{2} + 6 q^{5} - 2 q^{7} - 8 q^{10} - 2 q^{13} - 8 q^{16} - 18 q^{20} - 10 q^{22} - 18 q^{23} + 4 q^{25} - 16 q^{28} - 4 q^{31} - 30 q^{32} + 4 q^{37} + 30 q^{38} + 6 q^{40} + 24 q^{41} - 2 q^{43} + 32 q^{46} + 12 q^{47} + 54 q^{50} - 14 q^{52} - 16 q^{55} - 36 q^{56} - 6 q^{58} + 8 q^{61} - 66 q^{65} + 4 q^{67} - 42 q^{68} + 18 q^{70} - 8 q^{73} + 24 q^{76} + 6 q^{77} + 32 q^{82} + 66 q^{83} + 22 q^{85} + 48 q^{86} + 18 q^{88} - 40 q^{91} + 60 q^{92} + 36 q^{95} + 28 q^{97}+O(q^{100}) \) 16 * q + 6 * q^2 + 6 * q^5 - 2 * q^7 - 8 * q^10 - 2 * q^13 - 8 * q^16 - 18 * q^20 - 10 * q^22 - 18 * q^23 + 4 * q^25 - 16 * q^28 - 4 * q^31 - 30 * q^32 + 4 * q^37 + 30 * q^38 + 6 * q^40 + 24 * q^41 - 2 * q^43 + 32 * q^46 + 12 * q^47 + 54 * q^50 - 14 * q^52 - 16 * q^55 - 36 * q^56 - 6 * q^58 + 8 * q^61 - 66 * q^65 + 4 * q^67 - 42 * q^68 + 18 * q^70 - 8 * q^73 + 24 * q^76 + 6 * q^77 + 32 * q^82 + 66 * q^83 + 22 * q^85 + 48 * q^86 + 18 * q^88 - 40 * q^91 + 60 * q^92 + 36 * q^95 + 28 * q^97

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