LMFDB - Embedded newform 495.2.ba.a.379.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(64,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 6]))

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

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

chi := DirichletCharacter("495.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.ba (of order $10$, degree $4$, 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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
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} - 7x^{14} + 25x^{12} - 57x^{10} + 194x^{8} - 303x^{6} + 235x^{4} - 33x^{2} + 121 $ x^16 - 7x^14 + 25x^12 - 57x^10 + 194x^8 - 303x^6 + 235x^4 - 33*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			379.4
Root			$0.972539 - 1.33858i$ of defining polynomial
Character	$\chi$	$=$	495.379
Dual form			495.2.ba.a.64.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.57360 - 0.511294i) q^{2} +(0.596764 - 0.433574i) q^{4} +(-1.09069 + 1.95203i) q^{5} +(1.31845 + 1.81468i) q^{7} +(-1.22769 + 1.68978i) q^{8} +O(q^{10})$	\(q+(1.57360 - 0.511294i) q^{2} +(0.596764 - 0.433574i) q^{4} +(-1.09069 + 1.95203i) q^{5} +(1.31845 + 1.81468i) q^{7} +(-1.22769 + 1.68978i) q^{8} +(-0.718246 + 3.62937i) q^{10} +(3.27115 - 0.547326i) q^{11} +(-3.51868 + 1.14329i) q^{13} +(3.00254 + 2.18148i) q^{14} +(-1.52381 + 4.68982i) q^{16} +(2.11573 + 0.687441i) q^{17} +(4.27714 + 3.10753i) q^{19} +(0.195466 + 1.63779i) q^{20} +(4.86764 - 2.53379i) q^{22} -3.85415i q^{23} +(-2.62081 - 4.25810i) q^{25} +(-4.95244 + 3.59816i) q^{26} +(1.57360 + 0.511294i) q^{28} +(-0.152450 + 0.110762i) q^{29} +(0.212253 + 0.653249i) q^{31} +3.98166i q^{32} +3.68079 q^{34} +(-4.98032 + 0.594387i) q^{35} +(-1.52422 - 2.09791i) q^{37} +(8.31938 + 2.70313i) q^{38} +(-1.95946 - 4.23950i) q^{40} +(6.40421 + 4.65293i) q^{41} -8.41368i q^{43} +(1.71480 - 1.74491i) q^{44} +(-1.97060 - 6.06490i) q^{46} +(7.06117 - 9.71886i) q^{47} +(0.608337 - 1.87227i) q^{49} +(-6.30124 - 5.36054i) q^{50} +(-1.60412 + 2.20788i) q^{52} +(-12.0371 + 3.91110i) q^{53} +(-2.49941 + 6.98233i) q^{55} -4.68506 q^{56} +(-0.183264 + 0.252241i) q^{58} +(0.278050 - 0.202015i) q^{59} +(0.535643 - 1.64854i) q^{61} +(0.668004 + 0.919429i) q^{62} +(-1.01183 - 3.11409i) q^{64} +(1.60605 - 8.11552i) q^{65} +0.650461i q^{67} +(1.56065 - 0.507084i) q^{68} +(-7.53313 + 3.48174i) q^{70} +(-1.43619 + 4.42013i) q^{71} +(-5.20684 - 7.16660i) q^{73} +(-3.47116 - 2.52195i) q^{74} +3.89979 q^{76} +(5.30606 + 5.21449i) q^{77} +(2.23551 + 6.88019i) q^{79} +(-7.49264 - 8.08965i) q^{80} +(12.4567 + 4.04742i) q^{82} +(3.02593 + 0.983185i) q^{83} +(-3.64950 + 3.38017i) q^{85} +(-4.30186 - 13.2398i) q^{86} +(-3.09111 + 6.19946i) q^{88} +9.92195 q^{89} +(-6.71389 - 4.87793i) q^{91} +(-1.67106 - 2.30002i) q^{92} +(6.14226 - 18.9039i) q^{94} +(-10.7310 + 4.95976i) q^{95} +(-2.15710 + 0.700884i) q^{97} -3.25724i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} + 2 q^{5}+O(q^{10}) $ 16 * q - 4 * q^4 + 2 * q^5	$ 16 q - 4 q^{4} + 2 q^{5} + 6 q^{11} + 12 q^{14} + 16 q^{16} + 6 q^{19} + 8 q^{20} - 16 q^{25} - 40 q^{26} - 2 q^{29} + 8 q^{31} - 16 q^{34} - 22 q^{35} + 12 q^{40} + 52 q^{41} - 4 q^{44} - 62 q^{46} - 10 q^{49} - 28 q^{50} - 8 q^{55} + 20 q^{56} - 2 q^{59} - 40 q^{61} - 8 q^{64} + 40 q^{65} - 34 q^{70} - 36 q^{71} - 48 q^{74} + 56 q^{76} + 38 q^{79} - 34 q^{80} + 58 q^{85} - 22 q^{86} - 24 q^{89} - 20 q^{91} + 14 q^{94} - 48 q^{95}+O(q^{100}) $ 16 * q - 4 * q^4 + 2 * q^5 + 6 * q^11 + 12 * q^14 + 16 * q^16 + 6 * q^19 + 8 * q^20 - 16 * q^25 - 40 * q^26 - 2 * q^29 + 8 * q^31 - 16 * q^34 - 22 * q^35 + 12 * q^40 + 52 * q^41 - 4 * q^44 - 62 * q^46 - 10 * q^49 - 28 * q^50 - 8 * q^55 + 20 * q^56 - 2 * q^59 - 40 * q^61 - 8 * q^64 + 40 * q^65 - 34 * q^70 - 36 * q^71 - 48 * q^74 + 56 * q^76 + 38 * q^79 - 34 * q^80 + 58 * q^85 - 22 * q^86 - 24 * q^89 - 20 * q^91 + 14 * q^94 - 48 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$-1$

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 $

$2$	1.57360	−	0.511294i	1.11270	−	0.361539i	0.305725	−	0.952120i	$-0.401101\pi$
$2$	1.57360	−	0.511294i	1.11270	−	0.361539i	0.806979	+	0.590581i	$0.201101\pi$
$3$		0			0
$3$		0			0
$4$	0.596764	−	0.433574i	0.298382	−	0.216787i
$5$	−1.09069	+	1.95203i	−0.487770	+	0.872972i
$5$	−1.09069	+	1.95203i	−0.487770	+	0.872972i
$6$		0			0
$7$	1.31845	+	1.81468i	0.498326	+	0.685886i	0.981896	−	0.189419i	$-0.0606604\pi$
$7$	1.31845	+	1.81468i	0.498326	+	0.685886i	−0.483571	+	0.875305i	$0.660660\pi$
$8$	−1.22769	+	1.68978i	−0.434055	+	0.597426i
$9$		0			0
$10$	−0.718246	+	3.62937i	−0.227129	+	1.14771i
$11$	3.27115	−	0.547326i	0.986289	−	0.165025i
$11$	3.27115	−	0.547326i	0.986289	−	0.165025i
$12$		0			0
$13$	−3.51868	+	1.14329i	−0.975906	+	0.317091i	−0.753198	−	0.657794i	$-0.771490\pi$
$13$	−3.51868	+	1.14329i	−0.975906	+	0.317091i	−0.222708	+	0.974885i	$0.571490\pi$
$14$	3.00254	+	2.18148i	0.802464	+	0.583024i
$15$		0			0
$16$	−1.52381	+	4.68982i	−0.380954	+	1.17245i
$17$	2.11573	+	0.687441i	0.513139	+	0.166729i	0.554129	−	0.832431i	$-0.313051\pi$
$17$	2.11573	+	0.687441i	0.513139	+	0.166729i	−0.0409903	+	0.999160i	$0.513051\pi$
$18$		0			0
$19$	4.27714	+	3.10753i	0.981244	+	0.712916i	0.957986	−	0.286814i	$-0.0925961\pi$
$19$	4.27714	+	3.10753i	0.981244	+	0.712916i	0.0232580	+	0.999729i	$0.492596\pi$
$20$	0.195466	+	1.63779i	0.0437074	+	0.366221i
$21$		0			0
$22$	4.86764	−	2.53379i	1.03778	−	0.540206i
$23$		−	3.85415i		−	0.803647i	−0.915717	−	0.401823i	$-0.868377\pi$
$23$		−	3.85415i		−	0.803647i	0.915717	−	0.401823i	$-0.131623\pi$
$24$		0			0
$25$	−2.62081	−	4.25810i	−0.524161	−	0.851619i
$26$	−4.95244	+	3.59816i	−0.971253	+	0.705657i
$27$		0			0
$28$	1.57360	+	0.511294i	0.297383	+	0.0966255i
$29$	−0.152450	+	0.110762i	−0.0283093	+	0.0205679i	−0.601850	−	0.798609i	$-0.705569\pi$
$29$	−0.152450	+	0.110762i	−0.0283093	+	0.0205679i	0.573541	+	0.819177i	$0.305569\pi$
$30$		0			0
$31$	0.212253	+	0.653249i	0.0381218	+	0.117327i	0.968306	−	0.249765i	$-0.0803534\pi$
$31$	0.212253	+	0.653249i	0.0381218	+	0.117327i	−0.930185	+	0.367092i	$0.880353\pi$
$32$			3.98166i			0.703866i
$33$		0			0
$34$	3.68079			0.631251
$35$	−4.98032	+	0.594387i	−0.841828	+	0.100470i
$36$		0			0
$37$	−1.52422	−	2.09791i	−0.250580	−	0.344894i	0.665134	−	0.746724i	$-0.268374\pi$
$37$	−1.52422	−	2.09791i	−0.250580	−	0.344894i	−0.915714	+	0.401830i	$0.868374\pi$
$38$	8.31938	+	2.70313i	1.34958	+	0.438506i
$39$		0			0
$40$	−1.95946	−	4.23950i	−0.309817	−	0.670324i
$41$	6.40421	+	4.65293i	1.00017	+	0.726666i	0.962124	−	0.272611i	$-0.0878870\pi$
$41$	6.40421	+	4.65293i	1.00017	+	0.726666i	0.0380448	+	0.999276i	$0.487887\pi$
$42$		0			0
$43$		−	8.41368i		−	1.28307i	−0.767092	−	0.641537i	$-0.778297\pi$
$43$		−	8.41368i		−	1.28307i	0.767092	−	0.641537i	$-0.221703\pi$
$44$	1.71480	−	1.74491i	0.258515	−	0.263055i
$45$		0			0
$46$	−1.97060	−	6.06490i	−0.290550	−	0.894220i
$47$	7.06117	−	9.71886i	1.02998	−	1.41764i	0.125012	−	0.992155i	$-0.460103\pi$
$47$	7.06117	−	9.71886i	1.02998	−	1.41764i	0.904965	−	0.425486i	$-0.139897\pi$
$48$		0			0
$49$	0.608337	−	1.87227i	0.0869053	−	0.267467i
$50$	−6.30124	−	5.36054i	−0.891130	−	0.758095i
$51$		0			0
$52$	−1.60412	+	2.20788i	−0.222451	+	0.306178i
$53$	−12.0371	+	3.91110i	−1.65343	+	0.537231i	−0.979479	−	0.201549i	$-0.935403\pi$
$53$	−12.0371	+	3.91110i	−1.65343	+	0.537231i	−0.673947	+	0.738779i	$0.735403\pi$
$54$		0			0
$55$	−2.49941	+	6.98233i	−0.337020	+	0.941498i
$56$	−4.68506			−0.626067
$57$		0			0
$58$	−0.183264	+	0.252241i	−0.0240638	+	0.0331209i
$59$	0.278050	−	0.202015i	0.0361990	−	0.0263001i	−0.569539	−	0.821965i	$-0.692878\pi$
$59$	0.278050	−	0.202015i	0.0361990	−	0.0263001i	0.605738	+	0.795664i	$0.292878\pi$
$60$		0			0
$61$	0.535643	−	1.64854i	0.0685821	−	0.211074i	−0.910892	−	0.412645i	$-0.864605\pi$
$61$	0.535643	−	1.64854i	0.0685821	−	0.211074i	0.979474	+	0.201572i	$0.0646049\pi$
$62$	0.668004	+	0.919429i	0.0848366	+	0.116768i
$63$		0			0
$64$	−1.01183	−	3.11409i	−0.126479	−	0.389261i
$65$	1.60605	−	8.11552i	0.199206	−	1.00661i
$66$		0			0
$67$			0.650461i			0.0794664i	0.999210	+	0.0397332i	$0.0126508\pi$
$67$			0.650461i			0.0794664i	−0.999210	+	0.0397332i	$0.987349\pi$
$68$	1.56065	−	0.507084i	0.189256	−	0.0614930i
$69$		0			0
$70$	−7.53313	+	3.48174i	−0.900381	+	0.416147i
$71$	−1.43619	+	4.42013i	−0.170444	+	0.524573i	−0.999396	−	0.0347464i	$-0.988938\pi$
$71$	−1.43619	+	4.42013i	−0.170444	+	0.524573i	0.828952	+	0.559320i	$0.188938\pi$
$72$		0			0
$73$	−5.20684	−	7.16660i	−0.609415	−	0.838787i	0.387115	−	0.922032i	$-0.373472\pi$
$73$	−5.20684	−	7.16660i	−0.609415	−	0.838787i	−0.996529	+	0.0832444i	$0.973472\pi$
$74$	−3.47116	−	2.52195i	−0.403515	−	0.293171i
$75$		0			0
$76$	3.89979			0.447336
$77$	5.30606	+	5.21449i	0.604682	+	0.594246i
$78$		0			0
$79$	2.23551	+	6.88019i	0.251514	+	0.774082i	0.994496	+	0.104770i	$0.0334108\pi$
$79$	2.23551	+	6.88019i	0.251514	+	0.774082i	−0.742982	+	0.669311i	$0.766589\pi$
$80$	−7.49264	−	8.08965i	−0.837703	−	0.904450i
$81$		0			0
$82$	12.4567	+	4.04742i	1.37561	+	0.446963i
$83$	3.02593	+	0.983185i	0.332139	+	0.107919i	0.470339	−	0.882486i	$-0.344132\pi$
$83$	3.02593	+	0.983185i	0.332139	+	0.107919i	−0.138200	+	0.990404i	$0.544132\pi$
$84$		0			0
$85$	−3.64950	+	3.38017i	−0.395844	+	0.366631i
$86$	−4.30186	−	13.2398i	−0.463882	−	1.42768i
$87$		0			0
$88$	−3.09111	+	6.19946i	−0.329514	+	0.660865i
$89$	9.92195			1.05172			0.525862	−	0.850570i	$-0.323743\pi$
$89$	9.92195			1.05172			0.525862	+	0.850570i	$0.323743\pi$
$90$		0			0
$91$	−6.71389	−	4.87793i	−0.703807	−	0.511346i
$92$	−1.67106	−	2.30002i	−0.174220	−	0.239793i
$93$		0			0
$94$	6.14226	−	18.9039i	0.633526	−	1.94979i
$95$	−10.7310	+	4.95976i	−1.10098	+	0.508860i
$96$		0			0
$97$	−2.15710	+	0.700884i	−0.219020	+	0.0711640i	−0.416472	−	0.909149i	$-0.636734\pi$
$97$	−2.15710	+	0.700884i	−0.219020	+	0.0711640i	0.197451	+	0.980313i	$0.436734\pi$
$98$		−	3.25724i		−	0.329031i
$99$		0			0
$100$	−3.41020	−	1.40476i	−0.341020	−	0.140476i
$101$	−3.05830	−	9.41247i	−0.304312	−	0.936576i	−0.979933	−	0.199327i	$-0.936124\pi$
$101$	−3.05830	−	9.41247i	−0.304312	−	0.936576i	0.675621	−	0.737249i	$-0.263876\pi$
$102$		0			0
$103$	6.01958	+	8.28525i	0.593127	+	0.816370i	0.995057	−	0.0993007i	$-0.0316606\pi$
$103$	6.01958	+	8.28525i	0.593127	+	0.816370i	−0.401930	+	0.915670i	$0.631661\pi$
$104$	2.38796	−	7.34938i	0.234159	−	0.720666i
$105$		0			0
$106$	−16.9419	+	12.3090i	−1.64554	+	1.19556i
$107$	−5.90536	+	8.12803i	−0.570893	+	0.785767i	−0.992660	−	0.120937i	$-0.961410\pi$
$107$	−5.90536	+	8.12803i	−0.570893	+	0.785767i	0.421767	+	0.906704i	$0.361410\pi$
$108$		0			0
$109$	8.80173			0.843053			0.421527	−	0.906816i	$-0.361494\pi$
$109$	8.80173			0.843053			0.421527	+	0.906816i	$0.361494\pi$
$110$	−0.363043	+	12.2653i	−0.0346148	+	1.16945i
$111$		0			0
$112$	−10.5196	+	3.41803i	−0.994010	+	0.322973i
$113$	0.135985	−	0.187168i	0.0127924	−	0.0176073i	−0.802573	−	0.596554i	$-0.796536\pi$
$113$	0.135985	−	0.187168i	0.0127924	−	0.0176073i	0.815365	+	0.578947i	$0.196536\pi$
$114$		0			0
$115$	7.52341	+	4.20367i	0.701561	+	0.391995i
$116$	−0.0429534	+	0.132197i	−0.00398812	+	0.0122742i
$117$		0			0
$118$	0.334250	−	0.460056i	0.0307702	−	0.0423516i
$119$	1.54198	+	4.74573i	0.141353	+	0.435040i
$120$		0			0
$121$	10.4009	−	3.58078i	0.945533	−	0.325525i
$122$		−	2.86801i		−	0.259658i
$123$		0			0
$124$	0.409897	+	0.297808i	0.0368098	+	0.0267439i
$125$	11.1704	−	0.471632i	0.999110	−	0.0421840i
$126$		0			0
$127$	−2.31140	−	0.751018i	−0.205103	−	0.0666421i	0.204664	−	0.978832i	$-0.434390\pi$
$127$	−2.31140	−	0.751018i	−0.205103	−	0.0666421i	−0.409767	+	0.912190i	$0.634390\pi$
$128$	−7.86516	−	10.8255i	−0.695188	−	0.956844i
$129$		0			0
$130$	−1.62214	−	13.5917i	−0.142271	−	1.19207i
$131$	−1.58846			−0.138785			−0.0693924	−	0.997589i	$-0.522106\pi$
$131$	−1.58846			−0.138785			−0.0693924	+	0.997589i	$0.522106\pi$
$132$		0			0
$133$			11.8588i			1.02829i
$134$	0.332577	+	1.02357i	0.0287302	+	0.0884226i
$135$		0			0
$136$	−3.75909	+	2.73114i	−0.322339	+	0.234193i
$137$	17.7866	+	5.77920i	1.51961	+	0.493750i	0.945664	−	0.325145i	$-0.105413\pi$
$137$	17.7866	+	5.77920i	1.51961	+	0.493750i	0.573943	+	0.818895i	$0.305413\pi$
$138$		0			0
$139$	9.40675	−	6.83441i	0.797870	−	0.579687i	−0.112418	−	0.993661i	$-0.535860\pi$
$139$	9.40675	−	6.83441i	0.797870	−	0.579687i	0.910289	+	0.413974i	$0.135860\pi$
$140$	−2.71436	+	2.51405i	−0.229406	+	0.212476i
$141$		0			0
$142$			7.68984i			0.645317i
$143$	−10.8844	+	5.66573i	−0.910197	+	0.473792i
$144$		0			0
$145$	−0.0499340	−	0.418393i	−0.00414679	−	0.0347457i
$146$	−11.8577	−	8.61514i	−0.981352	−	0.712994i
$147$		0			0
$148$	−1.81920	−	0.591094i	−0.149537	−	0.0485876i
$149$	1.82800	−	5.62600i	0.149755	−	0.460900i	−0.847836	−	0.530258i	$-0.822095\pi$
$149$	1.82800	−	5.62600i	0.149755	−	0.460900i	0.997592	+	0.0693580i	$0.0220951\pi$
$150$		0			0
$151$	−10.3375	−	7.51064i	−0.841254	−	0.611207i	0.0814664	−	0.996676i	$-0.474040\pi$
$151$	−10.3375	−	7.51064i	−0.841254	−	0.611207i	−0.922721	+	0.385469i	$0.874040\pi$
$152$	−10.5020	+	3.41232i	−0.851828	+	0.276776i
$153$		0			0
$154$	11.0158	+	5.49257i	0.887675	+	0.442604i
$155$	−1.50666	−	0.298166i	−0.121018	−	0.0239492i
$156$		0			0
$157$	8.43394	−	11.6083i	0.673102	−	0.926445i	−0.326724	−	0.945120i	$-0.605945\pi$
$157$	8.43394	−	11.6083i	0.673102	−	0.926445i	0.999826	+	0.0186749i	$0.00594475\pi$
$158$	7.03560	+	9.68367i	0.559722	+	0.770391i
$159$		0			0
$160$	−7.77231	−	4.34275i	−0.614455	−	0.343324i
$161$	6.99407	−	5.08149i	0.551210	−	0.400478i
$162$		0			0
$163$	−3.44963	+	1.12085i	−0.270196	+	0.0877921i	−0.440982	−	0.897516i	$-0.645370\pi$
$163$	−3.44963	+	1.12085i	−0.270196	+	0.0877921i	0.170785	+	0.985308i	$0.445370\pi$
$164$	5.83919			0.455964
$165$		0			0
$166$	5.26430			0.408589
$167$	−3.63370	+	1.18066i	−0.281184	+	0.0913623i	−0.446214	−	0.894926i	$-0.647228\pi$
$167$	−3.63370	+	1.18066i	−0.281184	+	0.0913623i	0.165030	+	0.986289i	$0.447228\pi$
$168$		0			0
$169$	0.556767	−	0.404515i	0.0428282	−	0.0311165i
$170$	−4.01459	+	7.18500i	−0.307905	+	0.551065i
$171$		0			0
$172$	−3.64795	−	5.02098i	−0.278154	−	0.382846i
$173$	1.23855	−	1.70472i	0.0941651	−	0.129607i	−0.759335	−	0.650700i	$-0.774476\pi$
$173$	1.23855	−	1.70472i	0.0941651	−	0.129607i	0.853500	+	0.521093i	$0.174476\pi$
$174$		0			0
$175$	4.27171	−	10.3700i	0.322911	−	0.783899i
$176$	−2.41777	+	16.1751i	−0.182246	+	1.21925i
$177$		0			0
$178$	15.6132	−	5.07303i	1.17026	−	0.380240i
$179$	−4.06448	−	2.95302i	−0.303793	−	0.220719i	0.425435	−	0.904989i	$-0.360121\pi$
$179$	−4.06448	−	2.95302i	−0.303793	−	0.220719i	−0.729229	+	0.684270i	$0.760121\pi$
$180$		0			0
$181$	−4.83538	+	14.8818i	−0.359411	+	1.10615i	0.593997	+	0.804467i	$0.297549\pi$
$181$	−4.83538	+	14.8818i	−0.359411	+	1.10615i	−0.953408	+	0.301685i	$0.902451\pi$
$182$	−13.0590	−	4.24314i	−0.968000	−	0.314522i
$183$		0			0
$184$	6.51265	+	4.73172i	0.480119	+	0.348827i
$185$	5.75762	−	0.687156i	0.423309	−	0.0505207i
$186$		0			0
$187$	7.29712	+	1.09073i	0.533618	+	0.0797622i
$188$		−	8.86140i		−	0.646284i
$189$		0			0
$190$	−14.3504	+	13.2914i	−1.04109	+	0.964257i
$191$	2.52078	−	1.83145i	0.182397	−	0.132519i	−0.492840	−	0.870120i	$-0.664041\pi$
$191$	2.52078	−	1.83145i	0.182397	−	0.132519i	0.675237	+	0.737601i	$0.264041\pi$
$192$		0			0
$193$	9.16474	+	2.97780i	0.659692	+	0.214347i	0.619683	−	0.784852i	$-0.287261\pi$
$193$	9.16474	+	2.97780i	0.659692	+	0.214347i	0.0400095	+	0.999199i	$0.487261\pi$
$194$	−3.03606	+	2.20582i	−0.217976	+	0.158369i
$195$		0			0
$196$	−0.448734	−	1.38106i	−0.0320524	−	0.0986472i
$197$		−	14.3974i		−	1.02577i	−0.858457	−	0.512885i	$-0.828577\pi$
$197$		−	14.3974i		−	1.02577i	0.858457	−	0.512885i	$-0.171423\pi$
$198$		0			0
$199$	−14.7978			−1.04899			−0.524493	−	0.851415i	$-0.675745\pi$
$199$	−14.7978			−1.04899			−0.524493	+	0.851415i	$0.675745\pi$
$200$	10.4128	+	0.799064i	0.736294	+	0.0565023i
$201$		0			0
$202$	−9.62508	−	13.2478i	−0.677218	−	0.932111i
$203$	−0.401995	−	0.130616i	−0.0282145	−	0.00916745i
$204$		0			0
$205$	−16.0676	+	7.42629i	−1.12221	+	0.518675i
$206$	13.7086	+	9.95989i	0.955125	+	0.693939i
$207$		0			0
$208$		−	18.2441i		−	1.26500i
$209$	15.6920	+	7.82420i	1.08544	+	0.541211i
$210$		0			0
$211$	−2.09250	−	6.44005i	−0.144054	−	0.443352i	0.852834	−	0.522181i	$-0.174882\pi$
$211$	−2.09250	−	6.44005i	−0.144054	−	0.443352i	−0.996888	+	0.0788298i	$0.974882\pi$
$212$	−5.48756	+	7.55299i	−0.376888	+	0.518741i
$213$		0			0
$214$	−5.13687	+	15.8097i	−0.351149	+	1.08073i
$215$	16.4237	+	9.17669i	1.12009	+	0.625845i
$216$		0			0
$217$	−0.905596	+	1.24645i	−0.0614759	+	0.0846143i
$218$	13.8504	−	4.50027i	0.938069	−	0.304797i
$219$		0			0
$220$	1.53580	+	5.25048i	0.103544	+	0.353987i
$221$	−8.23051			−0.553644
$222$		0			0
$223$	−5.12388	+	7.05242i	−0.343121	+	0.472265i	−0.945350	−	0.326058i	$-0.894279\pi$
$223$	−5.12388	+	7.05242i	−0.343121	+	0.472265i	0.602229	+	0.798323i	$0.294279\pi$
$224$	−7.22547	+	5.24961i	−0.482772	+	0.350754i
$225$		0			0
$226$	0.118289	−	0.364056i	0.00786846	−	0.0242166i
$227$	−2.23795	−	3.08028i	−0.148538	−	0.204445i	0.728264	−	0.685297i	$-0.240328\pi$
$227$	−2.23795	−	3.08028i	−0.148538	−	0.204445i	−0.876802	+	0.480852i	$0.840328\pi$
$228$		0			0
$229$	0.838570	+	2.58085i	0.0554142	+	0.170547i	0.974933	−	0.222499i	$-0.0714213\pi$
$229$	0.838570	+	2.58085i	0.0554142	+	0.170547i	−0.919519	+	0.393046i	$0.871421\pi$
$230$	13.9881	+	2.76823i	0.922351	+	0.182532i
$231$		0			0
$232$		−	0.393588i		−	0.0258403i
$233$	−9.99634	+	3.24801i	−0.654882	+	0.212784i	−0.617566	−	0.786519i	$-0.711881\pi$
$233$	−9.99634	+	3.24801i	−0.654882	+	0.212784i	−0.0373166	+	0.999303i	$0.511881\pi$
$234$		0			0
$235$	11.2699	+	24.3838i	0.735170	+	1.59062i
$236$	0.0783415	−	0.241110i	0.00509959	−	0.0156949i
$237$		0			0
$238$	4.85293	+	6.67948i	0.314569	+	0.432966i
$239$	−16.2124	−	11.7790i	−1.04869	−	0.761919i	−0.0767288	−	0.997052i	$-0.524448\pi$
$239$	−16.2124	−	11.7790i	−1.04869	−	0.761919i	−0.971963	+	0.235133i	$0.924448\pi$
$240$		0			0
$241$	28.4450			1.83230			0.916152	−	0.400832i	$-0.131279\pi$
$241$	28.4450			1.83230			0.916152	+	0.400832i	$0.131279\pi$
$242$	14.5360	−	10.9526i	0.934408	−	0.704060i
$243$		0			0
$244$	−0.395112	−	1.21603i	−0.0252944	−	0.0778483i
$245$	2.99121	+	3.22955i	0.191101	+	0.206328i
$246$		0			0
$247$	−18.6027	−	6.04438i	−1.18366	−	0.384595i
$248$	−1.36443	−	0.443329i	−0.0866411	−	0.0281514i
$249$		0			0
$250$	17.3366	−	6.45351i	1.09646	−	0.408156i
$251$	7.36604	+	22.6703i	0.464940	+	1.43094i	0.859058	+	0.511879i	$0.171050\pi$
$251$	7.36604	+	22.6703i	0.464940	+	1.43094i	−0.394117	+	0.919060i	$0.628950\pi$
$252$		0			0
$253$	−2.10948	−	12.6075i	−0.132622	−	0.792628i
$254$	−4.02120			−0.252313
$255$		0			0
$256$	−12.6136	−	9.16432i	−0.788350	−	0.572770i
$257$	−14.5044	−	19.9636i	−0.904758	−	1.24529i	−0.968925	−	0.247354i	$-0.920439\pi$
$257$	−14.5044	−	19.9636i	−0.904758	−	1.24529i	0.0641671	−	0.997939i	$-0.479561\pi$
$258$		0			0
$259$	1.79744	−	5.53196i	0.111688	−	0.343739i
$260$	−2.56025	−	5.53939i	−0.158780	−	0.343538i
$261$		0			0
$262$	−2.49961	+	0.812172i	−0.154426	+	0.0501761i
$263$		−	5.44098i		−	0.335505i	−0.985829	−	0.167753i	$-0.946349\pi$
$263$		−	5.44098i		−	0.335505i	0.985829	−	0.167753i	$-0.0536510\pi$
$264$		0			0
$265$	5.49416	−	27.7625i	0.337504	−	1.70544i
$266$	6.06332	+	18.6610i	0.371766	+	1.14418i
$267$		0			0
$268$	0.282023	+	0.388171i	0.0172273	+	0.0237113i
$269$	−2.07213	+	6.37738i	−0.126340	+	0.388835i	−0.994143	−	0.108074i	$-0.965532\pi$
$269$	−2.07213	+	6.37738i	−0.126340	+	0.388835i	0.867803	+	0.496909i	$0.165532\pi$
$270$		0			0
$271$	4.09349	−	2.97409i	0.248662	−	0.180663i	−0.456472	−	0.889738i	$-0.650887\pi$
$271$	4.09349	−	2.97409i	0.248662	−	0.180663i	0.705134	+	0.709075i	$0.250887\pi$
$272$	−6.44795	+	8.87484i	−0.390964	+	0.538116i
$273$		0			0
$274$	30.9438			1.86938
$275$	−10.9036	−	12.4944i	−0.657513	−	0.753443i
$276$		0			0
$277$	−10.1703	+	3.30453i	−0.611074	+	0.198550i	−0.598173	−	0.801367i	$-0.704107\pi$
$277$	−10.1703	+	3.30453i	−0.611074	+	0.198550i	−0.0129009	+	0.999917i	$0.504107\pi$
$278$	11.3081	−	15.5642i	0.678214	−	0.933481i
$279$		0			0
$280$	5.10993	−	9.14535i	0.305377	−	0.546539i
$281$	4.23963	−	13.0482i	0.252915	−	0.778392i	−0.741319	−	0.671153i	$-0.765799\pi$
$281$	4.23963	−	13.0482i	0.252915	−	0.778392i	0.994233	−	0.107238i	$-0.0342008\pi$
$282$		0			0
$283$	−12.9132	+	17.7735i	−0.767611	+	1.05653i	0.228932	+	0.973442i	$0.426477\pi$
$283$	−12.9132	+	17.7735i	−0.767611	+	1.05653i	−0.996543	+	0.0830832i	$0.973523\pi$
$284$	1.05939	+	3.26047i	0.0628633	+	0.193473i
$285$		0			0
$286$	−14.2308	+	14.4807i	−0.841485	+	0.856263i
$287$			17.7563i			1.04812i
$288$		0			0
$289$	−9.74956	−	7.08347i	−0.573504	−	0.416675i
$290$	−0.292498	−	0.632853i	−0.0171761	−	0.0371624i
$291$		0			0
$292$	−6.21450	−	2.01922i	−0.363676	−	0.118166i
$293$	8.25135	+	11.3570i	0.482049	+	0.663483i	0.978897	−	0.204354i	$-0.0655094\pi$
$293$	8.25135	+	11.3570i	0.482049	+	0.663483i	−0.496848	+	0.867837i	$0.665509\pi$
$294$		0			0
$295$	0.0910732	+	0.763095i	0.00530249	+	0.0444291i
$296$	5.41627			0.314815
$297$		0			0
$298$		−	9.78772i		−	0.566988i
$299$	4.40641	+	13.5615i	0.254829	+	0.784283i
$300$		0			0
$301$	15.2682	−	11.0930i	0.880043	−	0.639389i
$302$	−20.1073	−	6.53324i	−1.15704	−	0.375946i
$303$		0			0
$304$	−21.0913	+	15.3237i	−1.20967	+	0.878877i
$305$	2.63377	+	2.84363i	0.150809	+	0.162826i
$306$		0			0
$307$			6.86951i			0.392064i	0.980598	+	0.196032i	$0.0628056\pi$
$307$			6.86951i			0.392064i	−0.980598	+	0.196032i	$0.937194\pi$
$308$	5.42733	+	0.811246i	0.309251	+	0.0462251i
$309$		0			0
$310$	−2.52333	+	0.301152i	−0.143316	+	0.0171043i
$311$	−4.45087	−	3.23374i	−0.252385	−	0.183369i	0.454398	−	0.890799i	$-0.349854\pi$
$311$	−4.45087	−	3.23374i	−0.252385	−	0.183369i	−0.706783	+	0.707430i	$0.749854\pi$
$312$		0			0
$313$	13.5354	+	4.39793i	0.765068	+	0.248586i	0.665452	−	0.746440i	$-0.268239\pi$
$313$	13.5354	+	4.39793i	0.765068	+	0.248586i	0.0996156	+	0.995026i	$0.468239\pi$
$314$	7.33639	−	22.5791i	0.414016	−	1.27421i
$315$		0			0
$316$	4.31714	+	3.13659i	0.242858	+	0.176447i
$317$	−17.7718	+	5.77442i	−0.998166	+	0.324324i	−0.762132	−	0.647421i	$-0.775847\pi$
$317$	−17.7718	+	5.77442i	−0.998166	+	0.324324i	−0.236033	+	0.971745i	$0.575847\pi$
$318$		0			0
$319$	−0.438065	+	0.445758i	−0.0245269	+	0.0249577i
$320$	7.18237	+	1.42138i	0.401506	+	0.0794575i
$321$		0			0
$322$	8.40774	−	11.5723i	0.468545	−	0.644897i
$323$	6.91303	+	9.51497i	0.384651	+	0.529427i
$324$		0			0
$325$	14.0900	+	11.9865i	0.781573	+	0.664893i
$326$	−4.85526	+	3.52755i	−0.268908	+	0.195373i
$327$		0			0
$328$	−15.7248	+	5.10930i	−0.868257	+	0.282114i
$329$	26.9464			1.48560
$330$		0			0
$331$	0.468249			0.0257373			0.0128686	−	0.999917i	$-0.495904\pi$
$331$	0.468249			0.0257373			0.0128686	+	0.999917i	$0.495904\pi$
$332$	2.23205	−	0.725237i	0.122500	−	0.0398025i
$333$		0			0
$334$	−5.11433	+	3.71578i	−0.279844	+	0.203318i
$335$	−1.26972	−	0.709449i	−0.0693720	−	0.0387613i
$336$		0			0
$337$	20.0360	+	27.5771i	1.09143	+	1.50222i	0.846282	+	0.532735i	$0.178836\pi$
$337$	20.0360	+	27.5771i	1.09143	+	1.50222i	0.245146	+	0.969486i	$0.421164\pi$
$338$	0.669303	−	0.921216i	0.0364053	−	0.0501075i
$339$		0			0
$340$	−0.712333	+	3.59949i	−0.0386317	+	0.195210i
$341$	1.05185	+	2.02070i	0.0569611	+	0.109427i
$342$		0			0
$343$	19.1327	−	6.21658i	1.03307	−	0.335664i
$344$	14.2172	+	10.3294i	0.766542	+	0.556925i
$345$		0			0
$346$	1.07737	−	3.31580i	0.0579198	−	0.178259i
$347$	3.41707	+	1.11027i	0.183438	+	0.0596026i	0.399296	−	0.916822i	$-0.369255\pi$
$347$	3.41707	+	1.11027i	0.183438	+	0.0596026i	−0.215858	+	0.976425i	$0.569255\pi$
$348$		0			0
$349$	−5.15433	−	3.74484i	−0.275905	−	0.200457i	0.441224	−	0.897397i	$-0.354544\pi$
$349$	−5.15433	−	3.74484i	−0.275905	−	0.200457i	−0.717129	+	0.696940i	$0.754544\pi$
$350$	1.41985	−	18.5023i	0.0758941	−	0.988992i
$351$		0			0
$352$	2.17927	+	13.0246i	0.116156	+	0.694215i
$353$			12.1971i			0.649186i	0.945854	+	0.324593i	$0.105227\pi$
$353$			12.1971i			0.649186i	−0.945854	+	0.324593i	$0.894773\pi$
$354$		0			0
$355$	−7.06178	−	7.62446i	−0.374800	−	0.404664i
$356$	5.92106	−	4.30190i	0.313815	−	0.228000i
$357$		0			0
$358$	−7.90573	−	2.56873i	−0.417831	−	0.135761i
$359$	−19.5093	+	14.1744i	−1.02966	+	0.748094i	−0.968241	−	0.250018i	$-0.919564\pi$
$359$	−19.5093	+	14.1744i	−1.02966	+	0.748094i	−0.0614222	+	0.998112i	$0.519564\pi$
$360$		0			0
$361$	2.76592	+	8.51262i	0.145575	+	0.448032i
$362$			25.8902i			1.36076i
$363$		0			0
$364$	−6.12155			−0.320856
$365$	19.6684	−	2.34737i	1.02949	−	0.122867i
$366$		0			0
$367$	−11.9849	−	16.4958i	−0.625606	−	0.861073i	0.372140	−	0.928177i	$-0.378624\pi$
$367$	−11.9849	−	16.4958i	−0.625606	−	0.861073i	−0.997746	+	0.0671034i	$0.978624\pi$
$368$	18.0753	+	5.87302i	0.942239	+	0.306152i
$369$		0			0
$370$	8.70886	−	4.02515i	0.452752	−	0.209257i
$371$	−22.9677	−	16.6870i	−1.19242	−	0.866347i
$372$		0			0
$373$			7.51997i			0.389369i	0.980866	+	0.194685i	$0.0623684\pi$
$373$			7.51997i			0.389369i	−0.980866	+	0.194685i	$0.937632\pi$
$374$	12.0404	−	2.01460i	0.622596	−	0.104172i
$375$		0			0
$376$	7.75374	+	23.8636i	0.399869	+	1.23067i
$377$	0.409791	−	0.564029i	0.0211053	−	0.0290490i
$378$		0			0
$379$	−7.16649	+	22.0562i	−0.368118	+	1.13295i	0.579888	+	0.814696i	$0.303096\pi$
$379$	−7.16649	+	22.0562i	−0.368118	+	1.13295i	−0.948006	+	0.318254i	$0.896904\pi$
$380$	−4.25345	+	7.61248i	−0.218197	+	0.390512i
$381$		0			0
$382$	3.03029	−	4.17083i	0.155043	−	0.213398i
$383$	2.32095	−	0.754123i	0.118595	−	0.0385339i	−0.249118	−	0.968473i	$-0.580141\pi$
$383$	2.32095	−	0.754123i	0.118595	−	0.0385339i	0.367713	+	0.929939i	$0.380141\pi$
$384$		0			0
$385$	−15.9661	+	4.67019i	−0.813706	+	0.238015i
$386$	15.9442			0.811537
$387$		0			0
$388$	−0.983393	+	1.35352i	−0.0499242	+	0.0687148i
$389$	−27.4849	+	19.9689i	−1.39354	+	1.01246i	−0.398071	+	0.917355i	$0.630320\pi$
$389$	−27.4849	+	19.9689i	−1.39354	+	1.01246i	−0.995467	+	0.0951096i	$0.969680\pi$
$390$		0			0
$391$	2.64950	−	8.15434i	0.133991	−	0.412383i
$392$	2.41686	+	3.32653i	0.122070	+	0.168015i
$393$		0			0
$394$	−7.36129	−	22.6557i	−0.370856	−	1.14138i
$395$	−15.8685	−	3.14036i	−0.798433	−	0.158009i
$396$		0			0
$397$			27.4961i			1.37999i	0.723814	+	0.689995i	$0.242387\pi$
$397$			27.4961i			1.37999i	−0.723814	+	0.689995i	$0.757613\pi$
$398$	−23.2858	+	7.56601i	−1.16721	+	0.379250i
$399$		0			0
$400$	23.9633	−	5.80256i	1.19817	−	0.290128i
$401$	0.583247	−	1.79505i	0.0291259	−	0.0896404i	−0.935437	−	0.353494i	$-0.884994\pi$
$401$	0.583247	−	1.79505i	0.0291259	−	0.0896404i	0.964563	+	0.263853i	$0.0849935\pi$
$402$		0			0
$403$	−1.49370	−	2.05591i	−0.0744067	−	0.102412i
$404$	−5.90608	−	4.29102i	−0.293839	−	0.213486i
$405$		0			0
$406$	−0.699363			−0.0347088
$407$	−6.13420	−	6.02834i	−0.304061	−	0.298814i
$408$		0			0
$409$	−4.18949	−	12.8939i	−0.207157	−	0.637563i	−0.999618	−	0.0276408i	$-0.991201\pi$
$409$	−4.18949	−	12.8939i	−0.207157	−	0.637563i	0.792461	−	0.609923i	$-0.208799\pi$
$410$	−21.4870	+	19.9013i	−1.06117	+	0.982855i
$411$		0			0
$412$	7.18454	+	2.33440i	0.353957	+	0.115008i
$413$	0.733187	+	0.238227i	0.0360778	+	0.0117224i
$414$		0			0
$415$	−5.21954	+	4.83435i	−0.256217	+	0.237309i
$416$	−4.55219	−	14.0102i	−0.223189	−	0.686906i
$417$		0			0
$418$	28.6934	+	4.28893i	1.40344	+	0.209779i
$419$	−22.1368			−1.08145			−0.540727	−	0.841198i	$-0.681851\pi$
$419$	−22.1368			−1.08145			−0.540727	+	0.841198i	$0.681851\pi$
$420$		0			0
$421$	−14.4835	−	10.5229i	−0.705881	−	0.512853i	0.175961	−	0.984397i	$-0.443697\pi$
$421$	−14.4835	−	10.5229i	−0.705881	−	0.512853i	−0.881842	+	0.471544i	$0.843697\pi$
$422$	−6.58552	−	9.06419i	−0.320578	−	0.441238i
$423$		0			0
$424$	8.16902	−	25.1417i	0.396723	−	1.22099i
$425$	−2.61772	−	10.8106i	−0.126978	−	0.524392i
$426$		0			0
$427$	3.69780	−	1.20149i	0.178949	−	0.0581440i
$428$			7.41093i			0.358221i
$429$		0			0
$430$	30.5364	+	6.04310i	1.47259	+	0.291424i
$431$	−10.3353	−	31.8087i	−0.497833	−	1.53217i	−0.812495	−	0.582968i	$-0.801891\pi$
$431$	−10.3353	−	31.8087i	−0.497833	−	1.53217i	0.314662	−	0.949204i	$-0.398109\pi$
$432$		0			0
$433$	−18.5102	−	25.4771i	−0.889543	−	1.22435i	−0.973685	−	0.227897i	$-0.926815\pi$
$433$	−18.5102	−	25.4771i	−0.889543	−	1.22435i	0.0841428	−	0.996454i	$-0.473185\pi$
$434$	−0.787747	+	2.42443i	−0.0378130	+	0.116377i
$435$		0			0
$436$	5.25255	−	3.81620i	0.251552	−	0.182763i
$437$	11.9769	−	16.4848i	0.572932	−	0.788574i
$438$		0			0
$439$	−35.6208			−1.70009			−0.850045	−	0.526710i	$-0.823425\pi$
$439$	−35.6208			−1.70009			−0.850045	+	0.526710i	$0.823425\pi$
$440$	−8.73007	−	12.7956i	−0.416190	−	0.610006i
$441$		0			0
$442$	−12.9515	+	4.20821i	−0.616041	+	0.200164i
$443$	−13.8056	+	19.0018i	−0.655926	+	0.902805i	−0.999338	−	0.0363802i	$-0.988417\pi$
$443$	−13.8056	+	19.0018i	−0.655926	+	0.902805i	0.343412	+	0.939185i	$0.388417\pi$
$444$		0			0
$445$	−10.8217	+	19.3679i	−0.513000	+	0.918126i
$446$	−4.45709	+	13.7175i	−0.211049	+	0.649543i
$447$		0			0
$448$	4.31705	−	5.94191i	0.203961	−	0.280729i
$449$	−9.70066	−	29.8555i	−0.457802	−	1.40897i	−0.867814	−	0.496890i	$-0.834475\pi$
$449$	−9.70066	−	29.8555i	−0.457802	−	1.40897i	0.410011	−	0.912080i	$-0.365525\pi$
$450$		0			0
$451$	23.4958	+	11.7152i	1.10637	+	0.551649i
$452$		−	0.170655i		−	0.00802692i
$453$		0			0
$454$	−5.09658	−	3.70288i	−0.239194	−	0.173785i
$455$	16.8446	−	7.78540i	0.789687	−	0.364985i
$456$		0			0
$457$	−37.1964	−	12.0859i	−1.73998	−	0.565352i	−0.745145	−	0.666903i	$-0.767620\pi$
$457$	−37.1964	−	12.0859i	−1.73998	−	0.565352i	−0.994830	+	0.101550i	$0.967620\pi$
$458$	2.63915	+	3.63247i	0.123319	+	0.169734i
$459$		0			0
$460$	6.31230	−	0.753355i	0.294312	−	0.0351253i
$461$	8.88399			0.413769			0.206884	−	0.978365i	$-0.433668\pi$
$461$	8.88399			0.413769			0.206884	+	0.978365i	$0.433668\pi$
$462$		0			0
$463$			4.21081i			0.195693i	0.995202	+	0.0978464i	$0.0311954\pi$
$463$			4.21081i			0.195693i	−0.995202	+	0.0978464i	$0.968805\pi$
$464$	−0.287146	−	0.883744i	−0.0133304	−	0.0410268i
$465$		0			0
$466$	−14.0696	+	10.2221i	−0.651760	+	0.473531i
$467$	−6.39912	−	2.07920i	−0.296116	−	0.0962139i	0.157191	−	0.987568i	$-0.449756\pi$
$467$	−6.39912	−	2.07920i	−0.296116	−	0.0962139i	−0.453307	+	0.891354i	$0.649756\pi$
$468$		0			0
$469$	−1.18038	+	0.857597i	−0.0545049	+	0.0396002i
$470$	30.2017	+	32.6081i	1.39310	+	1.50410i
$471$		0			0
$472$			0.717854i			0.0330419i
$473$	−4.60503	−	27.5224i	−0.211740	−	1.26548i
$474$		0			0
$475$	2.02258	−	26.3567i	0.0928025	−	1.20933i
$476$	2.97782	+	2.16352i	0.136488	+	0.0991646i
$477$		0			0
$478$	−31.5343	−	10.2461i	−1.44235	−	0.468647i
$479$	6.43046	−	19.7909i	0.293815	−	0.904270i	−0.689802	−	0.723998i	$-0.742302\pi$
$479$	6.43046	−	19.7909i	0.293815	−	0.904270i	0.983617	−	0.180272i	$-0.0576977\pi$
$480$		0			0
$481$	7.76176	+	5.63925i	0.353906	+	0.257128i
$482$	44.7611	−	14.5437i	2.03881	−	0.662450i
$483$		0			0
$484$	4.65433	−	6.64642i	0.211560	−	0.302110i
$485$	0.984576	−	4.97516i	0.0447073	−	0.225910i
$486$		0			0
$487$	9.27489	−	12.7658i	0.420285	−	0.578473i	−0.545404	−	0.838173i	$-0.683624\pi$
$487$	9.27489	−	12.7658i	0.420285	−	0.578473i	0.965689	+	0.259700i	$0.0836237\pi$
$488$	2.12806	+	2.92902i	0.0963326	+	0.132590i
$489$		0			0
$490$	6.35822	+	3.55263i	0.287235	+	0.160491i
$491$	15.6386	−	11.3621i	0.705759	−	0.512764i	−0.176044	−	0.984382i	$-0.556330\pi$
$491$	15.6386	−	11.3621i	0.705759	−	0.512764i	0.881803	+	0.471618i	$0.156330\pi$
$492$		0			0
$493$	−0.398685	+	0.129541i	−0.0179559	+	0.00583422i
$494$	−32.3637			−1.45611
$495$		0			0
$496$	−3.38705			−0.152083
$497$	−9.91469	+	3.22148i	−0.444734	+	0.144503i
$498$		0			0
$499$	−33.5416	+	24.3694i	−1.50153	+	1.09092i	−0.531758	+	0.846896i	$0.678468\pi$
$499$	−33.5416	+	24.3694i	−1.50153	+	1.09092i	−0.969769	+	0.244026i	$0.921532\pi$
$500$	6.46159	−	5.12464i	0.288971	−	0.229181i
$501$		0			0
$502$	23.1824	+	31.9078i	1.03468	+	1.42412i
$503$	19.1978	−	26.4236i	0.855990	−	1.17817i	−0.126521	−	0.991964i	$-0.540381\pi$
$503$	19.1978	−	26.4236i	0.855990	−	1.17817i	0.982511	−	0.186205i	$-0.0596188\pi$
$504$		0			0
$505$	21.7090	+	4.29618i	0.966039	+	0.191178i
$506$	−9.76563	−	18.7606i	−0.434135	−	0.834012i
$507$		0			0
$508$	−1.70498	+	0.553981i	−0.0756462	+	0.0245789i
$509$	−13.4662	−	9.78379i	−0.596881	−	0.433659i	0.247890	−	0.968788i	$-0.420263\pi$
$509$	−13.4662	−	9.78379i	−0.596881	−	0.433659i	−0.844770	+	0.535129i	$0.820263\pi$
$510$		0			0
$511$	6.14019	−	18.8975i	0.271626	−	0.835978i
$512$	0.917749	+	0.298195i	0.0405592	+	0.0131785i
$513$		0			0
$514$	−33.0313	−	23.9987i	−1.45695	−	1.05854i
$515$	−22.7385	+	2.71377i	−1.00198	+	0.119583i
$516$		0			0
$517$	17.7788	−	35.6566i	0.781909	−	1.56818i
$518$		−	9.62412i		−	0.422860i
$519$		0			0
$520$	11.7417	+	12.6772i	0.514906	+	0.555933i
$521$	11.3717	−	8.26206i	0.498205	−	0.361967i	−0.310126	−	0.950696i	$-0.600371\pi$
$521$	11.3717	−	8.26206i	0.498205	−	0.361967i	0.808331	+	0.588728i	$0.200371\pi$
$522$		0			0
$523$	−14.9009	−	4.84159i	−0.651570	−	0.211708i	−0.0354635	−	0.999371i	$-0.511291\pi$
$523$	−14.9009	−	4.84159i	−0.651570	−	0.211708i	−0.616106	+	0.787663i	$0.711291\pi$
$524$	−0.947937	+	0.688717i	−0.0414108	+	0.0300867i
$525$		0			0
$526$	−2.78194	−	8.56194i	−0.121298	−	0.373318i
$527$			1.52801i			0.0665611i
$528$		0			0
$529$	8.14550			0.354152
$530$	−5.54920	−	46.4963i	−0.241042	−	2.01967i
$531$		0			0
$532$	5.14166	+	7.07689i	0.222919	+	0.306822i
$533$	−27.8540	−	9.05031i	−1.20649	−	0.392012i
$534$		0			0
$535$	−9.42523	−	20.3926i	−0.407488	−	0.881647i
$536$	−1.09913	−	0.798567i	−0.0474753	−	0.0344928i
$537$		0			0
$538$			11.0949i			0.478336i
$539$	0.965221	−	6.45743i	0.0415750	−	0.278141i
$540$		0			0
$541$	−12.2489	−	37.6983i	−0.526623	−	1.62078i	−0.761084	−	0.648653i	$-0.775333\pi$
$541$	−12.2489	−	37.6983i	−0.526623	−	1.62078i	0.234461	−	0.972125i	$-0.424667\pi$
$542$	4.92088	−	6.77301i	0.211370	−	0.290926i
$543$		0			0
$544$	−2.73716	+	8.42412i	−0.117355	+	0.361181i
$545$	−9.59993	+	17.1812i	−0.411216	+	0.735962i
$546$		0			0
$547$	24.1970	−	33.3043i	1.03459	−	1.42399i	0.133145	−	0.991097i	$-0.457492\pi$
$547$	24.1970	−	33.3043i	1.03459	−	1.42399i	0.901445	−	0.432895i	$-0.142508\pi$
$548$	13.1201	−	4.26297i	0.560462	−	0.182105i
$549$		0			0
$550$	−23.5463	−	14.0863i	−1.00402	−	0.600642i
$551$	−0.996247			−0.0424415
$552$		0			0
$553$	−9.53798	+	13.1279i	−0.405596	+	0.558255i
$554$	−14.3144	+	10.4000i	−0.608161	+	0.441855i
$555$		0			0
$556$	2.65039	−	8.15705i	0.112401	−	0.345936i
$557$	17.5606	+	24.1702i	0.744069	+	1.02412i	0.998374	+	0.0569987i	$0.0181531\pi$
$557$	17.5606	+	24.1702i	0.744069	+	1.02412i	−0.254306	+	0.967124i	$0.581847\pi$
$558$		0			0
$559$	9.61926	+	29.6050i	0.406851	+	1.25216i
$560$	4.80152	−	24.2625i	0.202901	−	1.02528i
$561$		0			0
$562$		−	22.7004i		−	0.957558i
$563$	−2.05218	+	0.666795i	−0.0864892	+	0.0281021i	−0.351942	−	0.936022i	$-0.614479\pi$
$563$	−2.05218	+	0.666795i	−0.0864892	+	0.0281021i	0.265453	+	0.964124i	$0.414479\pi$
$564$		0			0
$565$	0.217039	+	0.469588i	0.00913090	+	0.0197557i
$566$	−11.2328	+	34.5709i	−0.472148	+	1.45312i
$567$		0			0
$568$	−5.70583	−	7.85341i	−0.239411	−	0.329522i
$569$	−0.580298	−	0.421611i	−0.0243274	−	0.0176749i	0.575555	−	0.817763i	$-0.304786\pi$
$569$	−0.580298	−	0.421611i	−0.0243274	−	0.0176749i	−0.599882	+	0.800088i	$0.704786\pi$
$570$		0			0
$571$	−21.6311			−0.905235			−0.452617	−	0.891705i	$-0.649510\pi$
$571$	−21.6311			−0.905235			−0.452617	+	0.891705i	$0.649510\pi$
$572$	−4.03888	+	8.10029i	−0.168874	+	0.338690i
$573$		0			0
$574$	9.07866	+	27.9413i	0.378936	+	1.16625i
$575$	−16.4114	+	10.1010i	−0.684401	+	0.421240i
$576$		0			0
$577$	22.2810	+	7.23952i	0.927568	+	0.301385i	0.733568	−	0.679616i	$-0.237854\pi$
$577$	22.2810	+	7.23952i	0.927568	+	0.301385i	0.194000	+	0.981001i	$0.437854\pi$
$578$	−18.9637	−	6.16167i	−0.788784	−	0.256291i
$579$		0			0
$580$	−0.211203	−	0.228032i	−0.00876973	−	0.00946850i
$581$	2.20536	+	6.78739i	0.0914936	+	0.281588i
$582$		0			0
$583$	−37.2346	+	19.3820i	−1.54210	+	0.802722i
$584$	18.5023			0.765633
$585$		0			0
$586$	18.7911	+	13.6525i	0.776253	+	0.563981i
$587$	−1.32095	−	1.81814i	−0.0545216	−	0.0750425i	0.780886	−	0.624674i	$-0.214768\pi$
$587$	−1.32095	−	1.81814i	−0.0545216	−	0.0750425i	−0.835407	+	0.549632i	$0.814768\pi$
$588$		0			0
$589$	−1.12215	+	3.45362i	−0.0462374	+	0.142304i
$590$	0.533479	+	1.15424i	0.0219630	+	0.0475194i
$591$		0			0
$592$	12.1615	−	3.95149i	0.499833	−	0.162405i
$593$			25.4034i			1.04319i	0.853193	+	0.521596i	$0.174663\pi$
$593$			25.4034i			1.04319i	−0.853193	+	0.521596i	$0.825337\pi$
$594$		0			0
$595$	−10.9456	−	2.16612i	−0.448726	−	0.0888022i
$596$	−1.34841	−	4.14996i	−0.0552328	−	0.169989i
$597$		0			0
$598$	13.8678	+	19.0875i	0.567098	+	0.780544i
$599$	−5.63194	+	17.3333i	−0.230115	+	0.708220i	0.767617	+	0.640909i	$0.221442\pi$
$599$	−5.63194	+	17.3333i	−0.230115	+	0.708220i	−0.997732	+	0.0673118i	$0.978558\pi$
$600$		0			0
$601$	28.0242	−	20.3608i	1.14313	−	0.830533i	0.155579	−	0.987824i	$-0.450276\pi$
$601$	28.0242	−	20.3608i	1.14313	−	0.830533i	0.987552	+	0.157290i	$0.0502758\pi$
$602$	18.3542	−	25.2625i	0.748063	−	1.02962i
$603$		0			0
$604$	−9.42547			−0.383517
$605$	−4.35432	+	24.2083i	−0.177028	+	0.984206i
$606$		0			0
$607$	−24.2027	+	7.86394i	−0.982358	+	0.319187i	−0.755794	−	0.654809i	$-0.772749\pi$
$607$	−24.2027	+	7.86394i	−0.982358	+	0.319187i	−0.226564	+	0.973996i	$0.572749\pi$
$608$	−12.3731	+	17.0302i	−0.501797	+	0.690664i
$609$		0			0
$610$	5.59844	+	3.12810i	0.226674	+	0.126653i
$611$	−13.7345	+	42.2705i	−0.555639	+	1.71008i
$612$		0			0
$613$	21.7843	−	29.9835i	0.879859	−	1.21102i	−0.0966016	−	0.995323i	$-0.530797\pi$
$613$	21.7843	−	29.9835i	0.879859	−	1.21102i	0.976460	−	0.215698i	$-0.0692027\pi$
$614$	3.51234	+	10.8099i	0.141746	+	0.436251i
$615$		0			0
$616$	−15.3255	+	2.56426i	−0.617483	+	0.103317i
$617$			27.5937i			1.11088i	0.831557	+	0.555439i	$0.187450\pi$
$617$			27.5937i			1.11088i	−0.831557	+	0.555439i	$0.812550\pi$
$618$		0			0
$619$	16.5391	+	12.0164i	0.664764	+	0.482979i	0.868268	−	0.496095i	$-0.165233\pi$
$619$	16.5391	+	12.0164i	0.664764	+	0.482979i	−0.203504	+	0.979074i	$0.565233\pi$
$620$	−1.02840	+	0.475315i	−0.0413014	+	0.0190891i
$621$		0			0
$622$	−8.65728	−	2.81292i	−0.347125	−	0.112788i
$623$	13.0816	+	18.0052i	0.524101	+	0.721364i
$624$		0			0
$625$	−11.2628	+	22.3193i	−0.450510	+	0.892771i
$626$	23.5480			0.941167
$627$		0			0
$628$		−	10.5842i		−	0.422354i
$629$	−1.78265	−	5.48642i	−0.0710787	−	0.218758i
$630$		0			0
$631$	−0.614155	+	0.446210i	−0.0244491	+	0.0177633i	−0.599943	−	0.800043i	$-0.704810\pi$
$631$	−0.614155	+	0.446210i	−0.0244491	+	0.0177633i	0.575494	+	0.817806i	$0.304810\pi$
$632$	−14.3705	−	4.66926i	−0.571627	−	0.185733i
$633$		0			0
$634$	−25.0133	+	18.1733i	−0.993407	+	0.721752i
$635$	3.98701	−	3.69278i	0.158220	−	0.146543i
$636$		0			0
$637$			7.28342i			0.288579i
$638$	−0.461426	+	0.925425i	−0.0182680	+	0.0366379i
$639$		0			0
$640$	29.7100	−	3.54580i	1.17439	−	0.140160i
$641$	−12.0584	−	8.76094i	−0.476278	−	0.346037i	0.323605	−	0.946192i	$-0.395105\pi$
$641$	−12.0584	−	8.76094i	−0.476278	−	0.346037i	−0.799883	+	0.600156i	$0.795105\pi$
$642$		0			0
$643$	−26.2820	−	8.53955i	−1.03646	−	0.336767i	−0.259120	−	0.965845i	$-0.583432\pi$
$643$	−26.2820	−	8.53955i	−1.03646	−	0.336767i	−0.777342	+	0.629078i	$0.783432\pi$
$644$	1.97060	−	6.06490i	0.0776527	−	0.238990i
$645$		0			0
$646$	15.7433	+	11.4382i	0.619411	+	0.450029i
$647$	23.7560	−	7.71879i	0.933945	−	0.303457i	0.197770	−	0.980248i	$-0.436630\pi$
$647$	23.7560	−	7.71879i	0.933945	−	0.303457i	0.736175	+	0.676791i	$0.236630\pi$
$648$		0			0
$649$	0.798974	−	0.813005i	0.0313625	−	0.0319132i
$650$	28.3007	+	11.6579i	1.11004	+	0.457260i
$651$		0			0
$652$	−1.57264	+	2.16456i	−0.0615895	+	0.0847706i
$653$	−16.3187	−	22.4607i	−0.638599	−	0.878956i	0.359941	−	0.932975i	$-0.382797\pi$
$653$	−16.3187	−	22.4607i	−0.638599	−	0.878956i	−0.998540	+	0.0540191i	$0.982797\pi$
$654$		0			0
$655$	1.73252	−	3.10072i	0.0676950	−	0.121155i
$656$	−31.5802	+	22.9444i	−1.23300	+	0.895827i
$657$		0			0
$658$	42.4029	−	13.7775i	1.65304	−	0.537105i
$659$	−21.5863			−0.840883			−0.420442	−	0.907320i	$-0.638125\pi$
$659$	−21.5863			−0.840883			−0.420442	+	0.907320i	$0.638125\pi$
$660$		0			0
$661$	−16.0174			−0.623003			−0.311502	−	0.950246i	$-0.600832\pi$
$661$	−16.0174			−0.623003			−0.311502	+	0.950246i	$0.600832\pi$
$662$	0.736837	−	0.239413i	0.0286380	−	0.00930504i
$663$		0			0
$664$	−5.37628	+	3.90609i	−0.208640	+	0.151586i
$665$	−23.1486	−	12.9342i	−0.897665	−	0.501567i
$666$		0			0
$667$	0.426892	+	0.587567i	0.0165293	+	0.0227507i
$668$	−1.65656	+	2.28005i	−0.0640941	+	0.0882180i
$669$		0			0
$670$	−2.36076	−	0.467191i	−0.0912042	−	0.0180492i
$671$	0.849880	−	5.68579i	0.0328093	−	0.219498i
$672$		0			0
$673$	29.8127	−	9.68673i	1.14920	−	0.373396i	0.328355	−	0.944554i	$-0.393506\pi$
$673$	29.8127	−	9.68673i	1.14920	−	0.373396i	0.820840	+	0.571158i	$0.193506\pi$
$674$	45.6286	+	33.1511i	1.75755	+	1.27693i
$675$		0			0
$676$	0.156871	−	0.482799i	0.00603350	−	0.0185692i
$677$	29.1654	+	9.47642i	1.12092	+	0.364209i	0.810118	−	0.586267i	$-0.199403\pi$
$677$	29.1654	+	9.47642i	1.12092	+	0.364209i	0.310801	+	0.950475i	$0.399403\pi$
$678$		0			0
$679$	−4.11590	−	2.99038i	−0.157954	−	0.114760i
$680$	−1.23126	−	10.3166i	−0.0472167	−	0.395625i
$681$		0			0
$682$	2.68837	+	2.64198i	0.102943	+	0.101166i
$683$		−	3.27236i		−	0.125213i	−0.998038	−	0.0626066i	$-0.980059\pi$
$683$		−	3.27236i		−	0.125213i	0.998038	−	0.0626066i	$-0.0199414\pi$
$684$		0			0
$685$	−30.6807	+	28.4165i	−1.17225	+	1.08574i
$686$	26.9287	−	19.5648i	1.02814	−	0.746989i
$687$		0			0
$688$	39.4586	+	12.8209i	1.50435	+	0.488792i
$689$	37.8832	−	27.5238i	1.44324	−	1.04857i
$690$		0			0
$691$	−11.2774	−	34.7084i	−0.429014	−	1.32037i	−0.899098	−	0.437748i	$-0.855776\pi$
$691$	−11.2774	−	34.7084i	−0.429014	−	1.32037i	0.470083	−	0.882622i	$-0.344224\pi$
$692$		−	1.55431i		−	0.0590862i
$693$		0			0
$694$	5.94478			0.225661
$695$	3.08111	+	25.8164i	0.116873	+	0.979272i
$696$		0			0
$697$	10.3509	+	14.2468i	0.392070	+	0.539638i
$698$	−10.0256	−	3.25750i	−0.379473	−	0.123298i
$699$		0			0
$700$	−1.94696	−	8.04054i	−0.0735883	−	0.303904i
$701$	37.6684	+	27.3677i	1.42272	+	1.03366i	0.991316	+	0.131502i	$0.0419800\pi$
$701$	37.6684	+	27.3677i	1.42272	+	1.03366i	0.431399	+	0.902161i	$0.358020\pi$
$702$		0			0
$703$		−	13.7096i		−	0.517068i
$704$	−5.01427	−	9.63285i	−0.188982	−	0.363052i
$705$		0			0
$706$	6.23630	+	19.1933i	0.234706	+	0.722351i
$707$	13.0485	−	17.9597i	0.490738	−	0.675443i
$708$		0			0
$709$	11.0000	−	33.8544i	0.413112	−	1.27143i	−0.500817	−	0.865553i	$-0.666967\pi$
$709$	11.0000	−	33.8544i	0.413112	−	1.27143i	0.913929	−	0.405874i	$-0.133033\pi$
$710$	−15.0108	−	8.38721i	−0.563344	−	0.314766i
$711$		0			0
$712$	−12.1811	+	16.7659i	−0.456507	+	0.628327i
$713$	2.51772	−	0.818057i	0.0942894	−	0.0306365i
$714$		0			0
$715$	0.811789	−	27.4261i	0.0303592	−	1.02568i
$716$	−3.70588			−0.138495
$717$		0			0
$718$	−23.4526	+	32.2798i	−0.875245	+	1.20467i
$719$	−17.8722	+	12.9849i	−0.666522	+	0.484256i	−0.868859	−	0.495060i	$-0.835146\pi$
$719$	−17.8722	+	12.9849i	−0.666522	+	0.484256i	0.202337	+	0.979316i	$0.435146\pi$
$720$		0			0
$721$	−7.09862	+	21.8473i	−0.264366	+	0.813636i
$722$	8.70490	+	11.9813i	0.323963	+	0.445896i
$723$		0			0
$724$	3.56677	+	10.9774i	0.132558	+	0.407971i
$725$	0.871176	+	0.358863i	0.0323547	+	0.0133278i
$726$		0			0
$727$			45.5415i			1.68904i	0.535522	+	0.844521i	$0.320115\pi$
$727$			45.5415i			1.68904i	−0.535522	+	0.844521i	$0.679885\pi$
$728$	16.4852	−	5.35637i	0.610982	−	0.198520i
$729$		0			0
$730$	29.7500	−	13.7502i	1.10110	−	0.508916i
$731$	5.78391	−	17.8011i	0.213926	−	0.658396i
$732$		0			0
$733$	6.68835	+	9.20572i	0.247040	+	0.340021i	0.914472	−	0.404650i	$-0.132607\pi$
$733$	6.68835	+	9.20572i	0.247040	+	0.340021i	−0.667432	+	0.744671i	$0.732607\pi$
$734$	−27.2936	−	19.8300i	−1.00743	−	0.731938i
$735$		0			0
$736$	15.3459			0.565659
$737$	0.356014	+	2.12776i	0.0131140	+	0.0783769i
$738$		0			0
$739$	1.34045	+	4.12547i	0.0493091	+	0.151758i	0.972679	−	0.232153i	$-0.0745770\pi$
$739$	1.34045	+	4.12547i	0.0493091	+	0.151758i	−0.923370	+	0.383911i	$0.874577\pi$
$740$	3.13801	−	2.90643i	0.115355	−	0.106842i
$741$		0			0
$742$	−44.6740	−	14.5154i	−1.64003	−	0.532879i
$743$	16.4480	+	5.34429i	0.603420	+	0.196063i	0.594765	−	0.803900i	$-0.297245\pi$
$743$	16.4480	+	5.34429i	0.603420	+	0.196063i	0.00865478	+	0.999963i	$0.497245\pi$
$744$		0			0
$745$	8.98832	+	9.70450i	0.329307	+	0.355545i
$746$	3.84491	+	11.8334i	0.140772	+	0.433253i
$747$		0			0
$748$	4.82757	−	2.51293i	0.176513	−	0.0918819i
$749$	−22.5357			−0.823437
$750$		0			0
$751$	25.4946	+	18.5229i	0.930310	+	0.675910i	0.946069	−	0.323966i	$-0.105016\pi$
$751$	25.4946	+	18.5229i	0.930310	+	0.675910i	−0.0157586	+	0.999876i	$0.505016\pi$
$752$	34.8198	+	47.9253i	1.26975	+	1.74766i
$753$		0			0
$754$	0.356463	−	1.09708i	0.0129816	−	0.0399533i
$755$	25.9359	−	11.9873i	0.943905	−	0.436263i
$756$		0			0
$757$	−8.82332	+	2.86687i	−0.320689	+	0.104198i	−0.464938	−	0.885343i	$-0.653923\pi$
$757$	−8.82332	+	2.86687i	−0.320689	+	0.104198i	0.144249	+	0.989541i	$0.453923\pi$
$758$			38.3718i			1.39373i
$759$		0			0
$760$	4.79350	−	24.2220i	0.173879	−	0.878626i
$761$	1.28492	+	3.95459i	0.0465784	+	0.143354i	0.971641	−	0.236461i	$-0.0759876\pi$
$761$	1.28492	+	3.95459i	0.0465784	+	0.143354i	−0.925062	+	0.379815i	$0.875988\pi$
$762$		0			0
$763$	11.6046	+	15.9724i	0.420115	+	0.578239i
$764$	0.710238	−	2.18589i	0.0256955	−	0.0790827i
$765$		0			0
$766$	3.26667	−	2.37338i	0.118030	−	0.0857536i
$767$	−0.747406	+	1.02872i	−0.0269873	+	0.0371448i
$768$		0			0
$769$	−16.8800			−0.608709			−0.304355	−	0.952559i	$-0.598441\pi$
$769$	−16.8800			−0.608709			−0.304355	+	0.952559i	$0.598441\pi$
$770$	−22.7364	+	15.5124i	−0.819362	+	0.559027i
$771$		0			0
$772$	6.76028	−	2.19655i	0.243308	−	0.0790555i
$773$	−4.98301	+	6.85852i	−0.179226	+	0.246684i	−0.889173	−	0.457572i	$-0.848719\pi$
$773$	−4.98301	+	6.85852i	−0.179226	+	0.246684i	0.709946	+	0.704256i	$0.248719\pi$
$774$		0			0
$775$	2.22532	−	2.61583i	0.0799359	−	0.0939635i
$776$	1.46392	−	4.50548i	0.0525517	−	0.161737i
$777$		0			0
$778$	−33.0402	+	45.4759i	−1.18455	+	1.63039i
$779$	12.9326	+	39.8025i	0.463359	+	1.42607i
$780$		0			0
$781$	−2.27873	+	15.2450i	−0.0815395	+	0.545509i
$782$		−	14.1863i		−	0.507303i
$783$		0			0
$784$	7.85361	+	5.70598i	0.280486	+	0.203785i
$785$	13.4610	+	29.1243i	0.480442	+	1.03949i
$786$		0			0
$787$	50.9924	+	16.5684i	1.81768	+	0.590601i	0.999886	+	0.0150924i	$0.00480424\pi$
$787$	50.9924	+	16.5684i	1.81768	+	0.590601i	0.817796	+	0.575508i	$0.195196\pi$
$788$	−6.24233	−	8.59183i	−0.222374	−	0.306071i
$789$		0			0
$790$	−26.5764	+	3.17182i	−0.945546	+	0.112848i
$791$	0.518940			0.0184514
$792$		0			0
$793$			6.41307i			0.227735i
$794$	14.0586	+	43.2679i	0.498921	+	1.53552i
$795$		0			0
$796$	−8.83077	+	6.41593i	−0.312998	+	0.227407i
$797$	−27.1477	−	8.82082i	−0.961621	−	0.312450i	−0.214192	−	0.976792i	$-0.568712\pi$
$797$	−27.1477	−	8.82082i	−0.961621	−	0.312450i	−0.747429	+	0.664342i	$0.768712\pi$
$798$		0			0
$799$	21.6206	−	15.7083i	0.764883	−	0.555720i
$800$	16.9543	−	10.4352i	0.599425	−	0.368939i
$801$		0			0
$802$		−	3.12290i		−	0.110273i
$803$	−20.9548	−	20.5932i	−0.739480	−	0.726718i
$804$		0			0
$805$	2.29086	+	19.1949i	0.0807422	+	0.676532i
$806$	−3.40166	−	2.47145i	−0.119819	−	0.0870532i
$807$		0			0
$808$	19.6596	+	6.38780i	0.691623	+	0.224722i
$809$	11.4170	−	35.1378i	0.401399	−	1.23538i	−0.522466	−	0.852660i	$-0.674988\pi$
$809$	11.4170	−	35.1378i	0.401399	−	1.23538i	0.923865	−	0.382718i	$-0.125012\pi$
$810$		0			0
$811$	31.0475	+	22.5573i	1.09022	+	0.792094i	0.979437	−	0.201750i	$-0.0646629\pi$
$811$	31.0475	+	22.5573i	1.09022	+	0.792094i	0.110787	+	0.993844i	$0.464663\pi$
$812$	−0.296528	+	0.0963477i	−0.0104061	+	0.00338114i
$813$		0			0
$814$	−12.7350	−	6.34982i	−0.446363	−	0.222561i
$815$	1.57453	−	7.95628i	0.0551535	−	0.278696i
$816$		0			0
$817$	26.1458	−	35.9865i	0.914724	−	1.25901i
$818$	−13.1852	−	18.1478i	−0.461008	−	0.634524i
$819$		0			0
$820$	−6.36872	+	11.3982i	−0.222405	+	0.398044i
$821$	−8.29214	+	6.02459i	−0.289398	+	0.210260i	−0.723006	−	0.690842i	$-0.757240\pi$
$821$	−8.29214	+	6.02459i	−0.289398	+	0.210260i	0.433608	+	0.901101i	$0.357240\pi$
$822$		0			0
$823$	23.9948	−	7.79637i	0.836405	−	0.271764i	0.140664	−	0.990057i	$-0.455076\pi$
$823$	23.9948	−	7.79637i	0.836405	−	0.271764i	0.695741	+	0.718293i	$0.255076\pi$
$824$	−21.3904			−0.745170
$825$		0			0
$826$	1.27555			0.0443820
$827$	−17.4505	+	5.67001i	−0.606813	+	0.197165i	−0.596277	−	0.802779i	$-0.703354\pi$
$827$	−17.4505	+	5.67001i	−0.606813	+	0.197165i	−0.0105362	+	0.999944i	$0.503354\pi$
$828$		0			0
$829$	19.7259	−	14.3317i	0.685110	−	0.497761i	−0.189939	−	0.981796i	$-0.560829\pi$
$829$	19.7259	−	14.3317i	0.685110	−	0.497761i	0.875049	+	0.484035i	$0.160829\pi$
$830$	−5.74170	+	10.2761i	−0.199297	+	0.356687i
$831$		0			0
$832$	7.12060	+	9.80066i	0.246862	+	0.339777i
$833$	2.57415	−	3.54301i	0.0891890	−	0.122758i
$834$		0			0
$835$	1.65855	−	8.38081i	0.0573964	−	0.290030i
$836$	12.7568	−	2.13446i	0.441203	−	0.0738217i
$837$		0			0
$838$	−34.8345	+	11.3184i	−1.20334	+	0.390988i
$839$	34.2059	+	24.8520i	1.18092	+	0.857988i	0.992275	−	0.124058i	$-0.0395908\pi$
$839$	34.2059	+	24.8520i	1.18092	+	0.857988i	0.188644	+	0.982046i	$0.439591\pi$
$840$		0			0
$841$	−8.95052	+	27.5469i	−0.308639	+	0.949892i
$842$	−28.1715	−	9.15347i	−0.970853	−	0.315449i
$843$		0			0
$844$	−4.04097	−	2.93594i	−0.139096	−	0.101059i
$845$	0.182365	+	1.52802i	0.00627355	+	0.0525655i
$846$		0			0
$847$	20.2110	+	14.1532i	0.694457	+	0.486311i
$848$		−	62.4117i		−	2.14323i
$849$		0			0
$850$	−9.64665	−	15.6732i	−0.330877	−	0.537585i
$851$	−8.08567	+	5.87458i	−0.277173	+	0.201378i
$852$		0			0
$853$	−14.6353	−	4.75529i	−0.501103	−	0.162818i	0.0475493	−	0.998869i	$-0.484859\pi$
$853$	−14.6353	−	4.75529i	−0.501103	−	0.162818i	−0.548652	+	0.836051i	$0.684859\pi$
$854$	5.20454	−	3.78132i	0.178096	−	0.129394i
$855$		0			0
$856$	−6.48458	−	19.9575i	−0.221638	−	0.682132i
$857$		−	36.1038i		−	1.23328i	−0.787245	−	0.616641i	$-0.788493\pi$
$857$		−	36.1038i		−	1.23328i	0.787245	−	0.616641i	$-0.211507\pi$
$858$		0			0
$859$	−48.3509			−1.64971			−0.824855	−	0.565344i	$-0.808743\pi$
$859$	−48.3509			−1.64971			−0.824855	+	0.565344i	$0.808743\pi$
$860$	13.7799	−	1.64459i	0.469889	−	0.0560799i
$861$		0			0
$862$	−32.5272	−	44.7699i	−1.10788	−	1.52487i
$863$	35.3685	+	11.4919i	1.20396	+	0.391190i	0.841216	−	0.540699i	$-0.181840\pi$
$863$	35.3685	+	11.4919i	1.20396	+	0.391190i	0.362743	+	0.931889i	$0.381840\pi$
$864$		0			0
$865$	1.97678	+	4.27699i	0.0672125	+	0.145422i
$866$	−42.1539	−	30.6266i	−1.43245	−	1.04073i
$867$		0			0
$868$			1.13648i			0.0385745i
$869$	11.0784	+	21.2826i	0.375809	+	0.721962i
$870$		0			0
$871$	−0.743664	−	2.28876i	−0.0251981	−	0.0775517i
$872$	−10.8058	+	14.8730i	−0.365932	+	0.503662i
$873$		0			0
$874$	10.4183	−	32.0642i	0.352403	−	1.08459i
$875$	15.5834	+	19.6489i	0.526816	+	0.664254i
$876$		0			0
$877$	−15.1609	+	20.8672i	−0.511947	+	0.704634i	−0.984246	−	0.176804i	$-0.943424\pi$
$877$	−15.1609	+	20.8672i	−0.511947	+	0.704634i	0.472299	+	0.881438i	$0.343424\pi$
$878$	−56.0530	+	18.2127i	−1.89170	+	0.614649i
$879$		0			0
$880$	−28.9372	−	22.3615i	−0.975474	−	0.753807i
$881$	45.6820			1.53906			0.769532	−	0.638608i	$-0.220489\pi$
$881$	45.6820			1.53906			0.769532	+	0.638608i	$0.220489\pi$
$882$		0			0
$883$	2.91912	−	4.01783i	0.0982364	−	0.135211i	−0.757069	−	0.653335i	$-0.773369\pi$
$883$	2.91912	−	4.01783i	0.0982364	−	0.135211i	0.855306	+	0.518124i	$0.173369\pi$
$884$	−4.91167	+	3.56853i	−0.165197	+	0.120023i
$885$		0			0
$886$	−12.0090	+	36.9600i	−0.403452	+	1.24170i
$887$	17.0006	+	23.3994i	0.570826	+	0.785674i	0.992652	−	0.121002i	$-0.0386109\pi$
$887$	17.0006	+	23.3994i	0.570826	+	0.785674i	−0.421827	+	0.906677i	$0.638611\pi$
$888$		0			0
$889$	−1.68459	−	5.18463i	−0.0564993	−	0.173887i
$890$	−7.12641	+	36.0104i	−0.238878	+	1.20707i
$891$		0			0
$892$			6.43021i			0.215299i
$893$	60.4033	−	19.6262i	2.02132	−	0.656766i
$894$		0			0
$895$	10.1974	−	4.71315i	0.340863	−	0.157543i
$896$	9.27501	−	28.5456i	0.309856	−	0.953640i
$897$		0			0
$898$	−30.5299	−	42.0208i	−1.01880	−	1.40225i
$899$	−0.104713	−	0.0760785i	−0.00349237	−	0.00253736i
$900$		0			0
$901$	−28.1559			−0.938010
$902$	42.9630	+	6.42186i	1.43051	+	0.213824i
$903$		0			0
$904$	0.149323	+	0.459570i	0.00496642	+	0.0152851i
$905$	−23.7757	−	25.6701i	−0.790331	−	0.853303i
$906$		0			0
$907$	−12.6041	−	4.09531i	−0.418511	−	0.135983i	0.0921887	−	0.995742i	$-0.470614\pi$
$907$	−12.6041	−	4.09531i	−0.418511	−	0.135983i	−0.510700	+	0.859759i	$0.670614\pi$
$908$	−2.67106	−	0.867880i	−0.0886422	−	0.0288016i
$909$		0			0
$910$	22.5260	−	20.8636i	0.746731	−	0.691623i
$911$	−4.24361	−	13.0605i	−0.140597	−	0.432713i	0.855822	−	0.517271i	$-0.173052\pi$
$911$	−4.24361	−	13.0605i	−0.140597	−	0.432713i	−0.996419	+	0.0845580i	$0.973052\pi$
$912$		0			0
$913$	10.4364	+	1.55997i	0.345395	+	0.0516276i
$914$	−64.7117			−2.14047
$915$		0			0
$916$	1.61942	+	1.17658i	0.0535071	+	0.0388752i
$917$	−2.09430	−	2.88256i	−0.0691600	−	0.0951906i
$918$		0			0
$919$	−18.3494	+	56.4737i	−0.605292	+	1.86290i	−0.110517	+	0.993874i	$0.535251\pi$
$919$	−18.3494	+	56.4737i	−0.605292	+	1.86290i	−0.494774	+	0.869022i	$0.664749\pi$
$920$	−16.3397	+	7.55204i	−0.538704	+	0.248983i
$921$		0			0
$922$	13.9798	−	4.54233i	0.460402	−	0.149594i
$923$		−	17.1950i		−	0.565981i
$924$		0			0
$925$	−4.93842	+	11.9885i	−0.162374	+	0.394179i
$926$	2.15296	+	6.62613i	0.0707507	+	0.217748i
$927$		0			0
$928$	−0.441016	−	0.607006i	−0.0144770	−	0.0199259i
$929$	6.05305	−	18.6294i	0.198594	−	0.611210i	−0.801322	−	0.598234i	$-0.795869\pi$
$929$	6.05305	−	18.6294i	0.198594	−	0.611210i	0.999916	−	0.0129763i	$-0.00413060\pi$
$930$		0			0
$931$	8.42007	−	6.11754i	0.275957	−	0.200494i
$932$	−4.55720	+	6.27245i	−0.149276	+	0.205461i
$933$		0			0
$934$	−11.1327			−0.364275
$935$	−10.0880	+	13.0545i	−0.329913	+	0.426928i
$936$		0			0
$937$	−38.5608	+	12.5292i	−1.25973	+	0.409310i	−0.861397	−	0.507933i	$-0.830410\pi$
$937$	−38.5608	+	12.5292i	−1.25973	+	0.409310i	−0.398329	+	0.917242i	$0.630410\pi$
$938$	−1.41896	+	1.95304i	−0.0463308	+	0.0637689i
$939$		0			0
$940$	17.2977	+	9.66501i	0.564188	+	0.315238i
$941$	0.126602	−	0.389640i	0.00412709	−	0.0127019i	−0.948972	−	0.315361i	$-0.897874\pi$
$941$	0.126602	−	0.389640i	0.00412709	−	0.0127019i	0.953099	+	0.302659i	$0.0978744\pi$
$942$		0			0
$943$	17.9331	−	24.6828i	0.583982	−	0.803783i
$944$	0.523717	+	1.61184i	0.0170455	+	0.0524608i
$945$		0			0
$946$	−21.3185	−	40.9548i	−0.693125	−	1.33156i
$947$		−	2.45729i		−	0.0798511i	−0.999203	−	0.0399256i	$-0.987288\pi$
$947$		−	2.45729i		−	0.0798511i	0.999203	−	0.0399256i	$-0.0127121\pi$
$948$		0			0
$949$	26.5147	+	19.2640i	0.860703	+	0.625337i
$950$	−10.2933	−	42.5091i	−0.333958	−	1.37918i
$951$		0			0
$952$	−9.91230	−	3.22070i	−0.321260	−	0.104384i
$953$	−35.8704	−	49.3714i	−1.16196	−	1.59930i	−0.703742	−	0.710456i	$-0.748489\pi$
$953$	−35.8704	−	49.3714i	−1.16196	−	1.59930i	−0.458215	−	0.888841i	$-0.651511\pi$
$954$		0			0
$955$	0.825663	+	6.91816i	0.0267178	+	0.223867i
$956$	−14.7820			−0.478085
$957$		0			0
$958$		−	34.4309i		−	1.11241i
$959$	12.9632	+	39.8965i	0.418603	+	1.28833i
$960$		0			0
$961$	24.6978	−	17.9440i	0.796705	−	0.578840i
$962$	15.0972	+	4.90538i	0.486754	+	0.158156i
$963$		0			0
$964$	16.9749	−	12.3330i	0.546726	−	0.397220i
$965$	−15.8086	+	14.6420i	−0.508897	+	0.471341i
$966$		0			0
$967$			17.1997i			0.553106i	0.960999	+	0.276553i	$0.0891921\pi$
$967$			17.1997i			0.553106i	−0.960999	+	0.276553i	$0.910808\pi$
$968$	−6.71837	+	21.9712i	−0.215937	+	0.706182i
$969$		0			0
$970$	−0.994438	−	8.33232i	−0.0319295	−	0.267535i
$971$	22.0125	+	15.9930i	0.706415	+	0.513241i	0.882015	−	0.471221i	$-0.156187\pi$
$971$	22.0125	+	15.9930i	0.706415	+	0.513241i	−0.175600	+	0.984462i	$0.556187\pi$
$972$		0			0
$973$	24.8046	+	8.05950i	0.795198	+	0.258376i
$974$	8.06790	−	24.8304i	0.258512	−	0.795619i
$975$		0			0
$976$	6.91513	+	5.02414i	0.221348	+	0.160819i
$977$	−18.2339	+	5.92454i	−0.583353	+	0.189543i	−0.585802	−	0.810454i	$-0.699220\pi$
$977$	−18.2339	+	5.92454i	−0.583353	+	0.189543i	0.00244904	+	0.999997i	$0.499220\pi$
$978$		0			0
$979$	32.4562	−	5.43055i	1.03730	−	0.173561i
$980$	3.18529	+	0.630365i	0.101750	+	0.0201363i
$981$		0			0
$982$	18.7995	−	25.8753i	0.599916	−	0.825714i
$983$	14.1835	+	19.5219i	0.452384	+	0.622653i	0.972908	−	0.231194i	$-0.0742632\pi$
$983$	14.1835	+	19.5219i	0.452384	+	0.622653i	−0.520524	+	0.853847i	$0.674263\pi$
$984$		0			0
$985$	28.1040	+	15.7030i	0.895469	+	0.500340i
$986$	−0.561138	+	0.407691i	−0.0178703	+	0.0129835i
$987$		0			0
$988$	−13.7221	+	4.45858i	−0.436558	+	0.141846i
$989$	−32.4276			−1.03114
$990$		0			0
$991$	27.7081			0.880177			0.440089	−	0.897954i	$-0.354947\pi$
$991$	27.7081			0.880177			0.440089	+	0.897954i	$0.354947\pi$
$992$	−2.60102	+	0.845122i	−0.0825824	+	0.0268327i
$993$		0			0
$994$	−13.9546	+	10.1386i	−0.442614	+	0.321578i
$995$	16.1397	−	28.8856i	0.511664	−	0.915735i
$996$		0			0
$997$	−19.6856	−	27.0950i	−0.623451	−	0.858106i	0.374148	−	0.927369i	$-0.377935\pi$
$997$	−19.6856	−	27.0950i	−0.623451	−	0.858106i	−0.997598	+	0.0692628i	$0.977935\pi$
$998$	−40.3211	+	55.4972i	−1.27634	+	1.75673i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.ba.a.379.4		16
3.2	odd	2		55.2.j.a.49.1	yes	16
5.4	even	2	inner	495.2.ba.a.379.1		16
11.9	even	5	inner	495.2.ba.a.64.1		16
12.11	even	2		880.2.cd.c.49.1		16
15.2	even	4		275.2.h.d.126.1		16
15.8	even	4		275.2.h.d.126.4		16
15.14	odd	2		55.2.j.a.49.4	yes	16
33.2	even	10		605.2.j.d.9.1		16
33.5	odd	10		605.2.j.h.444.4		16
33.8	even	10		605.2.b.f.364.2		8
33.14	odd	10		605.2.b.g.364.7		8
33.17	even	10		605.2.j.g.444.1		16
33.20	odd	10		55.2.j.a.9.4	yes	16
33.26	odd	10		605.2.j.h.124.1		16
33.29	even	10		605.2.j.g.124.4		16
33.32	even	2		605.2.j.d.269.4		16
55.9	even	10	inner	495.2.ba.a.64.4		16
60.59	even	2		880.2.cd.c.49.4		16
132.119	even	10		880.2.cd.c.449.4		16
165.8	odd	20		3025.2.a.bk.1.2		8
165.14	odd	10		605.2.b.g.364.2		8
165.29	even	10		605.2.j.g.124.1		16
165.47	even	20		3025.2.a.bl.1.2		8
165.53	even	20		275.2.h.d.251.4		16
165.59	odd	10		605.2.j.h.124.4		16
165.74	even	10		605.2.b.f.364.7		8
165.104	odd	10		605.2.j.h.444.1		16
165.107	odd	20		3025.2.a.bk.1.7		8
165.113	even	20		3025.2.a.bl.1.7		8
165.119	odd	10		55.2.j.a.9.1	✓	16
165.134	even	10		605.2.j.d.9.4		16
165.149	even	10		605.2.j.g.444.4		16
165.152	even	20		275.2.h.d.251.1		16
165.164	even	2		605.2.j.d.269.1		16
660.119	even	10		880.2.cd.c.449.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.9.1	✓	16	165.119	odd	10
55.2.j.a.9.4	yes	16	33.20	odd	10
55.2.j.a.49.1	yes	16	3.2	odd	2
55.2.j.a.49.4	yes	16	15.14	odd	2
275.2.h.d.126.1		16	15.2	even	4
275.2.h.d.126.4		16	15.8	even	4
275.2.h.d.251.1		16	165.152	even	20
275.2.h.d.251.4		16	165.53	even	20
495.2.ba.a.64.1		16	11.9	even	5	inner
495.2.ba.a.64.4		16	55.9	even	10	inner
495.2.ba.a.379.1		16	5.4	even	2	inner
495.2.ba.a.379.4		16	1.1	even	1	trivial
605.2.b.f.364.2		8	33.8	even	10
605.2.b.f.364.7		8	165.74	even	10
605.2.b.g.364.2		8	165.14	odd	10
605.2.b.g.364.7		8	33.14	odd	10
605.2.j.d.9.1		16	33.2	even	10
605.2.j.d.9.4		16	165.134	even	10
605.2.j.d.269.1		16	165.164	even	2
605.2.j.d.269.4		16	33.32	even	2
605.2.j.g.124.1		16	165.29	even	10
605.2.j.g.124.4		16	33.29	even	10
605.2.j.g.444.1		16	33.17	even	10
605.2.j.g.444.4		16	165.149	even	10
605.2.j.h.124.1		16	33.26	odd	10
605.2.j.h.124.4		16	165.59	odd	10
605.2.j.h.444.1		16	165.104	odd	10
605.2.j.h.444.4		16	33.5	odd	10
880.2.cd.c.49.1		16	12.11	even	2
880.2.cd.c.49.4		16	60.59	even	2
880.2.cd.c.449.1		16	660.119	even	10
880.2.cd.c.449.4		16	132.119	even	10
3025.2.a.bk.1.2		8	165.8	odd	20
3025.2.a.bk.1.7		8	165.107	odd	20
3025.2.a.bl.1.2		8	165.47	even	20
3025.2.a.bl.1.7		8	165.113	even	20

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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.57360 - 0.511294i) q^{2} +(0.596764 - 0.433574i) q^{4} +(-1.09069 + 1.95203i) q^{5} +(1.31845 + 1.81468i) q^{7} +(-1.22769 + 1.68978i) q^{8} +O(q^{10})\)	\(q+(1.57360 - 0.511294i) q^{2} +(0.596764 - 0.433574i) q^{4} +(-1.09069 + 1.95203i) q^{5} +(1.31845 + 1.81468i) q^{7} +(-1.22769 + 1.68978i) q^{8} +(-0.718246 + 3.62937i) q^{10} +(3.27115 - 0.547326i) q^{11} +(-3.51868 + 1.14329i) q^{13} +(3.00254 + 2.18148i) q^{14} +(-1.52381 + 4.68982i) q^{16} +(2.11573 + 0.687441i) q^{17} +(4.27714 + 3.10753i) q^{19} +(0.195466 + 1.63779i) q^{20} +(4.86764 - 2.53379i) q^{22} -3.85415i q^{23} +(-2.62081 - 4.25810i) q^{25} +(-4.95244 + 3.59816i) q^{26} +(1.57360 + 0.511294i) q^{28} +(-0.152450 + 0.110762i) q^{29} +(0.212253 + 0.653249i) q^{31} +3.98166i q^{32} +3.68079 q^{34} +(-4.98032 + 0.594387i) q^{35} +(-1.52422 - 2.09791i) q^{37} +(8.31938 + 2.70313i) q^{38} +(-1.95946 - 4.23950i) q^{40} +(6.40421 + 4.65293i) q^{41} -8.41368i q^{43} +(1.71480 - 1.74491i) q^{44} +(-1.97060 - 6.06490i) q^{46} +(7.06117 - 9.71886i) q^{47} +(0.608337 - 1.87227i) q^{49} +(-6.30124 - 5.36054i) q^{50} +(-1.60412 + 2.20788i) q^{52} +(-12.0371 + 3.91110i) q^{53} +(-2.49941 + 6.98233i) q^{55} -4.68506 q^{56} +(-0.183264 + 0.252241i) q^{58} +(0.278050 - 0.202015i) q^{59} +(0.535643 - 1.64854i) q^{61} +(0.668004 + 0.919429i) q^{62} +(-1.01183 - 3.11409i) q^{64} +(1.60605 - 8.11552i) q^{65} +0.650461i q^{67} +(1.56065 - 0.507084i) q^{68} +(-7.53313 + 3.48174i) q^{70} +(-1.43619 + 4.42013i) q^{71} +(-5.20684 - 7.16660i) q^{73} +(-3.47116 - 2.52195i) q^{74} +3.89979 q^{76} +(5.30606 + 5.21449i) q^{77} +(2.23551 + 6.88019i) q^{79} +(-7.49264 - 8.08965i) q^{80} +(12.4567 + 4.04742i) q^{82} +(3.02593 + 0.983185i) q^{83} +(-3.64950 + 3.38017i) q^{85} +(-4.30186 - 13.2398i) q^{86} +(-3.09111 + 6.19946i) q^{88} +9.92195 q^{89} +(-6.71389 - 4.87793i) q^{91} +(-1.67106 - 2.30002i) q^{92} +(6.14226 - 18.9039i) q^{94} +(-10.7310 + 4.95976i) q^{95} +(-2.15710 + 0.700884i) q^{97} -3.25724i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} + 2 q^{5}+O(q^{10}) \) 16 * q - 4 * q^4 + 2 * q^5	\( 16 q - 4 q^{4} + 2 q^{5} + 6 q^{11} + 12 q^{14} + 16 q^{16} + 6 q^{19} + 8 q^{20} - 16 q^{25} - 40 q^{26} - 2 q^{29} + 8 q^{31} - 16 q^{34} - 22 q^{35} + 12 q^{40} + 52 q^{41} - 4 q^{44} - 62 q^{46} - 10 q^{49} - 28 q^{50} - 8 q^{55} + 20 q^{56} - 2 q^{59} - 40 q^{61} - 8 q^{64} + 40 q^{65} - 34 q^{70} - 36 q^{71} - 48 q^{74} + 56 q^{76} + 38 q^{79} - 34 q^{80} + 58 q^{85} - 22 q^{86} - 24 q^{89} - 20 q^{91} + 14 q^{94} - 48 q^{95}+O(q^{100}) \) 16 * q - 4 * q^4 + 2 * q^5 + 6 * q^11 + 12 * q^14 + 16 * q^16 + 6 * q^19 + 8 * q^20 - 16 * q^25 - 40 * q^26 - 2 * q^29 + 8 * q^31 - 16 * q^34 - 22 * q^35 + 12 * q^40 + 52 * q^41 - 4 * q^44 - 62 * q^46 - 10 * q^49 - 28 * q^50 - 8 * q^55 + 20 * q^56 - 2 * q^59 - 40 * q^61 - 8 * q^64 + 40 * q^65 - 34 * q^70 - 36 * q^71 - 48 * q^74 + 56 * q^76 + 38 * q^79 - 34 * q^80 + 58 * q^85 - 22 * q^86 - 24 * q^89 - 20 * q^91 + 14 * q^94 - 48 * q^95

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