LMFDB - Embedded newform 136.2.k.d.89.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [136,2,Mod(81,136)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(136, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("136.81"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	136.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,4,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$1.08596546749$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			89.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	136.89
Dual form			136.2.k.d.81.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.00000 - 2.00000i) q^{3} +(-1.00000 + 1.00000i) q^{5} +(2.00000 + 2.00000i) q^{7} -5.00000i q^{9} +(-2.00000 - 2.00000i) q^{11} -4.00000 q^{13} +4.00000i q^{15} +(-1.00000 - 4.00000i) q^{17} +8.00000i q^{19} +8.00000 q^{21} +(2.00000 + 2.00000i) q^{23} +3.00000i q^{25} +(-4.00000 - 4.00000i) q^{27} +(-3.00000 + 3.00000i) q^{29} +(6.00000 - 6.00000i) q^{31} -8.00000 q^{33} -4.00000 q^{35} +(-5.00000 + 5.00000i) q^{37} +(-8.00000 + 8.00000i) q^{39} +(1.00000 + 1.00000i) q^{41} -8.00000i q^{43} +(5.00000 + 5.00000i) q^{45} +1.00000i q^{49} +(-10.0000 - 6.00000i) q^{51} -12.0000i q^{53} +4.00000 q^{55} +(16.0000 + 16.0000i) q^{57} -8.00000i q^{59} +(-1.00000 - 1.00000i) q^{61} +(10.0000 - 10.0000i) q^{63} +(4.00000 - 4.00000i) q^{65} +12.0000 q^{67} +8.00000 q^{69} +(-6.00000 + 6.00000i) q^{71} +(-3.00000 + 3.00000i) q^{73} +(6.00000 + 6.00000i) q^{75} -8.00000i q^{77} +(-2.00000 - 2.00000i) q^{79} -1.00000 q^{81} +(5.00000 + 3.00000i) q^{85} +12.0000i q^{87} -8.00000 q^{89} +(-8.00000 - 8.00000i) q^{91} -24.0000i q^{93} +(-8.00000 - 8.00000i) q^{95} +(3.00000 - 3.00000i) q^{97} +(-10.0000 + 10.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{3} - 2 q^{5} + 4 q^{7} - 4 q^{11} - 8 q^{13} - 2 q^{17} + 16 q^{21} + 4 q^{23} - 8 q^{27} - 6 q^{29} + 12 q^{31} - 16 q^{33} - 8 q^{35} - 10 q^{37} - 16 q^{39} + 2 q^{41} + 10 q^{45} - 20 q^{51}+ \cdots - 20 q^{99}+O(q^{100}) $ 2 * q + 4 * q^3 - 2 * q^5 + 4 * q^7 - 4 * q^11 - 8 * q^13 - 2 * q^17 + 16 * q^21 + 4 * q^23 - 8 * q^27 - 6 * q^29 + 12 * q^31 - 16 * q^33 - 8 * q^35 - 10 * q^37 - 16 * q^39 + 2 * q^41 + 10 * q^45 - 20 * q^51 + 8 * q^55 + 32 * q^57 - 2 * q^61 + 20 * q^63 + 8 * q^65 + 24 * q^67 + 16 * q^69 - 12 * q^71 - 6 * q^73 + 12 * q^75 - 4 * q^79 - 2 * q^81 + 10 * q^85 - 16 * q^89 - 16 * q^91 - 16 * q^95 + 6 * q^97 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.00000	−	2.00000i	1.15470	−	1.15470i	0.169102	−	0.985599i	$-0.445913\pi$
$3$	2.00000	−	2.00000i	1.15470	−	1.15470i	0.985599	−	0.169102i	$-0.0540867\pi$
$4$		0			0
$5$	−1.00000	+	1.00000i	−0.447214	+	0.447214i	−0.894427	−	0.447214i	$-0.852416\pi$
$5$	−1.00000	+	1.00000i	−0.447214	+	0.447214i	0.447214	+	0.894427i	$0.352416\pi$
$6$		0			0
$7$	2.00000	+	2.00000i	0.755929	+	0.755929i	0.975579	−	0.219650i	$-0.0704915\pi$
$7$	2.00000	+	2.00000i	0.755929	+	0.755929i	−0.219650	+	0.975579i	$0.570491\pi$
$8$		0			0
$9$		−	5.00000i		−	1.66667i
$10$		0			0
$11$	−2.00000	−	2.00000i	−0.603023	−	0.603023i	0.338091	−	0.941113i	$-0.390219\pi$
$11$	−2.00000	−	2.00000i	−0.603023	−	0.603023i	−0.941113	+	0.338091i	$0.890219\pi$
$12$		0			0
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$		0			0
$15$			4.00000i			1.03280i
$16$		0			0
$17$	−1.00000	−	4.00000i	−0.242536	−	0.970143i
$17$	−1.00000	−	4.00000i	−0.242536	−	0.970143i
$18$		0			0
$19$			8.00000i			1.83533i	0.397360	+	0.917663i	$0.369927\pi$
$19$			8.00000i			1.83533i	−0.397360	+	0.917663i	$0.630073\pi$
$20$		0			0
$21$	8.00000			1.74574
$22$		0			0
$23$	2.00000	+	2.00000i	0.417029	+	0.417029i	0.884178	−	0.467150i	$-0.154719\pi$
$23$	2.00000	+	2.00000i	0.417029	+	0.417029i	−0.467150	+	0.884178i	$0.654719\pi$
$24$		0			0
$25$			3.00000i			0.600000i
$26$		0			0
$27$	−4.00000	−	4.00000i	−0.769800	−	0.769800i
$28$		0			0
$29$	−3.00000	+	3.00000i	−0.557086	+	0.557086i	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−3.00000	+	3.00000i	−0.557086	+	0.557086i	0.371391	+	0.928477i	$0.378881\pi$
$30$		0			0
$31$	6.00000	−	6.00000i	1.07763	−	1.07763i	0.0809104	−	0.996721i	$-0.474217\pi$
$31$	6.00000	−	6.00000i	1.07763	−	1.07763i	0.996721	−	0.0809104i	$-0.0257828\pi$
$32$		0			0
$33$	−8.00000			−1.39262
$34$		0			0
$35$	−4.00000			−0.676123
$36$		0			0
$37$	−5.00000	+	5.00000i	−0.821995	+	0.821995i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$	−5.00000	+	5.00000i	−0.821995	+	0.821995i	0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$	−8.00000	+	8.00000i	−1.28103	+	1.28103i
$40$		0			0
$41$	1.00000	+	1.00000i	0.156174	+	0.156174i	0.780869	−	0.624695i	$-0.214777\pi$
$41$	1.00000	+	1.00000i	0.156174	+	0.156174i	−0.624695	+	0.780869i	$0.714777\pi$
$42$		0			0
$43$		−	8.00000i		−	1.21999i	−0.792406	−	0.609994i	$-0.791172\pi$
$43$		−	8.00000i		−	1.21999i	0.792406	−	0.609994i	$-0.208828\pi$
$44$		0			0
$45$	5.00000	+	5.00000i	0.745356	+	0.745356i
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	−10.0000	−	6.00000i	−1.40028	−	0.840168i
$52$		0			0
$53$		−	12.0000i		−	1.64833i	−0.566352	−	0.824163i	$-0.691646\pi$
$53$		−	12.0000i		−	1.64833i	0.566352	−	0.824163i	$-0.308354\pi$
$54$		0			0
$55$	4.00000			0.539360
$56$		0			0
$57$	16.0000	+	16.0000i	2.11925	+	2.11925i
$58$		0			0
$59$		−	8.00000i		−	1.04151i	−0.853706	−	0.520756i	$-0.825650\pi$
$59$		−	8.00000i		−	1.04151i	0.853706	−	0.520756i	$-0.174350\pi$
$60$		0			0
$61$	−1.00000	−	1.00000i	−0.128037	−	0.128037i	0.640184	−	0.768221i	$-0.278858\pi$
$61$	−1.00000	−	1.00000i	−0.128037	−	0.128037i	−0.768221	+	0.640184i	$0.778858\pi$
$62$		0			0
$63$	10.0000	−	10.0000i	1.25988	−	1.25988i
$64$		0			0
$65$	4.00000	−	4.00000i	0.496139	−	0.496139i
$66$		0			0
$67$	12.0000			1.46603			0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000			1.46603			0.733017	+	0.680211i	$0.238112\pi$
$68$		0			0
$69$	8.00000			0.963087
$70$		0			0
$71$	−6.00000	+	6.00000i	−0.712069	+	0.712069i	−0.966968	−	0.254899i	$-0.917958\pi$
$71$	−6.00000	+	6.00000i	−0.712069	+	0.712069i	0.254899	+	0.966968i	$0.417958\pi$
$72$		0			0
$73$	−3.00000	+	3.00000i	−0.351123	+	0.351123i	−0.860527	−	0.509404i	$-0.829866\pi$
$73$	−3.00000	+	3.00000i	−0.351123	+	0.351123i	0.509404	+	0.860527i	$0.329866\pi$
$74$		0			0
$75$	6.00000	+	6.00000i	0.692820	+	0.692820i
$76$		0			0
$77$		−	8.00000i		−	0.911685i
$78$		0			0
$79$	−2.00000	−	2.00000i	−0.225018	−	0.225018i	0.585590	−	0.810607i	$-0.300863\pi$
$79$	−2.00000	−	2.00000i	−0.225018	−	0.225018i	−0.810607	+	0.585590i	$0.800863\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$		0			0
$85$	5.00000	+	3.00000i	0.542326	+	0.325396i
$86$		0			0
$87$			12.0000i			1.28654i
$88$		0			0
$89$	−8.00000			−0.847998			−0.423999	−	0.905663i	$-0.639374\pi$
$89$	−8.00000			−0.847998			−0.423999	+	0.905663i	$0.639374\pi$
$90$		0			0
$91$	−8.00000	−	8.00000i	−0.838628	−	0.838628i
$92$		0			0
$93$		−	24.0000i		−	2.48868i
$94$		0			0
$95$	−8.00000	−	8.00000i	−0.820783	−	0.820783i
$96$		0			0
$97$	3.00000	−	3.00000i	0.304604	−	0.304604i	−0.538208	−	0.842812i	$-0.680899\pi$
$97$	3.00000	−	3.00000i	0.304604	−	0.304604i	0.842812	+	0.538208i	$0.180899\pi$
$98$		0			0
$99$	−10.0000	+	10.0000i	−1.00504	+	1.00504i
$100$		0			0
$101$	−12.0000			−1.19404			−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000			−1.19404			−0.597022	+	0.802225i	$0.703650\pi$
$102$		0			0
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$		0			0
$105$	−8.00000	+	8.00000i	−0.780720	+	0.780720i
$106$		0			0
$107$	2.00000	−	2.00000i	0.193347	−	0.193347i	−0.603793	−	0.797141i	$-0.706345\pi$
$107$	2.00000	−	2.00000i	0.193347	−	0.193347i	0.797141	+	0.603793i	$0.206345\pi$
$108$		0			0
$109$	3.00000	+	3.00000i	0.287348	+	0.287348i	0.836031	−	0.548683i	$-0.184871\pi$
$109$	3.00000	+	3.00000i	0.287348	+	0.287348i	−0.548683	+	0.836031i	$0.684871\pi$
$110$		0			0
$111$			20.0000i			1.89832i
$112$		0			0
$113$	7.00000	+	7.00000i	0.658505	+	0.658505i	0.955026	−	0.296522i	$-0.0958267\pi$
$113$	7.00000	+	7.00000i	0.658505	+	0.658505i	−0.296522	+	0.955026i	$0.595827\pi$
$114$		0			0
$115$	−4.00000			−0.373002
$116$		0			0
$117$			20.0000i			1.84900i
$118$		0			0
$119$	6.00000	−	10.0000i	0.550019	−	0.916698i
$120$		0			0
$121$		−	3.00000i		−	0.272727i
$122$		0			0
$123$	4.00000			0.360668
$124$		0			0
$125$	−8.00000	−	8.00000i	−0.715542	−	0.715542i
$126$		0			0
$127$			4.00000i			0.354943i	0.984126	+	0.177471i	$0.0567917\pi$
$127$			4.00000i			0.354943i	−0.984126	+	0.177471i	$0.943208\pi$
$128$		0			0
$129$	−16.0000	−	16.0000i	−1.40872	−	1.40872i
$130$		0			0
$131$	−2.00000	+	2.00000i	−0.174741	+	0.174741i	−0.789059	−	0.614318i	$-0.789431\pi$
$131$	−2.00000	+	2.00000i	−0.174741	+	0.174741i	0.614318	+	0.789059i	$0.289431\pi$
$132$		0			0
$133$	−16.0000	+	16.0000i	−1.38738	+	1.38738i
$134$		0			0
$135$	8.00000			0.688530
$136$		0			0
$137$	16.0000			1.36697			0.683486	−	0.729964i	$-0.260463\pi$
$137$	16.0000			1.36697			0.683486	+	0.729964i	$0.260463\pi$
$138$		0			0
$139$	−2.00000	+	2.00000i	−0.169638	+	0.169638i	−0.786820	−	0.617182i	$-0.788274\pi$
$139$	−2.00000	+	2.00000i	−0.169638	+	0.169638i	0.617182	+	0.786820i	$0.288274\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	8.00000	+	8.00000i	0.668994	+	0.668994i
$144$		0			0
$145$		−	6.00000i		−	0.498273i
$146$		0			0
$147$	2.00000	+	2.00000i	0.164957	+	0.164957i
$148$		0			0
$149$	22.0000			1.80231			0.901155	−	0.433497i	$-0.142720\pi$
$149$	22.0000			1.80231			0.901155	+	0.433497i	$0.142720\pi$
$150$		0			0
$151$		−	12.0000i		−	0.976546i	−0.872691	−	0.488273i	$-0.837627\pi$
$151$		−	12.0000i		−	0.976546i	0.872691	−	0.488273i	$-0.162373\pi$
$152$		0			0
$153$	−20.0000	+	5.00000i	−1.61690	+	0.404226i
$154$		0			0
$155$			12.0000i			0.963863i
$156$		0			0
$157$	−2.00000			−0.159617			−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000			−0.159617			−0.0798087	+	0.996810i	$0.525431\pi$
$158$		0			0
$159$	−24.0000	−	24.0000i	−1.90332	−	1.90332i
$160$		0			0
$161$			8.00000i			0.630488i
$162$		0			0
$163$	6.00000	+	6.00000i	0.469956	+	0.469956i	0.901900	−	0.431944i	$-0.142172\pi$
$163$	6.00000	+	6.00000i	0.469956	+	0.469956i	−0.431944	+	0.901900i	$0.642172\pi$
$164$		0			0
$165$	8.00000	−	8.00000i	0.622799	−	0.622799i
$166$		0			0
$167$	−10.0000	+	10.0000i	−0.773823	+	0.773823i	−0.978773	−	0.204949i	$-0.934297\pi$
$167$	−10.0000	+	10.0000i	−0.773823	+	0.773823i	0.204949	+	0.978773i	$0.434297\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$	40.0000			3.05888
$172$		0			0
$173$	−11.0000	+	11.0000i	−0.836315	+	0.836315i	−0.988372	−	0.152057i	$-0.951410\pi$
$173$	−11.0000	+	11.0000i	−0.836315	+	0.836315i	0.152057	+	0.988372i	$0.451410\pi$
$174$		0			0
$175$	−6.00000	+	6.00000i	−0.453557	+	0.453557i
$176$		0			0
$177$	−16.0000	−	16.0000i	−1.20263	−	1.20263i
$178$		0			0
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$		0			0
$181$	−5.00000	−	5.00000i	−0.371647	−	0.371647i	0.496430	−	0.868077i	$-0.334644\pi$
$181$	−5.00000	−	5.00000i	−0.371647	−	0.371647i	−0.868077	+	0.496430i	$0.834644\pi$
$182$		0			0
$183$	−4.00000			−0.295689
$184$		0			0
$185$		−	10.0000i		−	0.735215i
$186$		0			0
$187$	−6.00000	+	10.0000i	−0.438763	+	0.731272i
$188$		0			0
$189$		−	16.0000i		−	1.16383i
$190$		0			0
$191$	−8.00000			−0.578860			−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$		0			0
$193$	−3.00000	−	3.00000i	−0.215945	−	0.215945i	0.590842	−	0.806787i	$-0.298796\pi$
$193$	−3.00000	−	3.00000i	−0.215945	−	0.215945i	−0.806787	+	0.590842i	$0.798796\pi$
$194$		0			0
$195$		−	16.0000i		−	1.14578i
$196$		0			0
$197$	13.0000	+	13.0000i	0.926212	+	0.926212i	0.997459	−	0.0712470i	$-0.0226979\pi$
$197$	13.0000	+	13.0000i	0.926212	+	0.926212i	−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	6.00000	−	6.00000i	0.425329	−	0.425329i	−0.461705	−	0.887034i	$-0.652762\pi$
$199$	6.00000	−	6.00000i	0.425329	−	0.425329i	0.887034	+	0.461705i	$0.152762\pi$
$200$		0			0
$201$	24.0000	−	24.0000i	1.69283	−	1.69283i
$202$		0			0
$203$	−12.0000			−0.842235
$204$		0			0
$205$	−2.00000			−0.139686
$206$		0			0
$207$	10.0000	−	10.0000i	0.695048	−	0.695048i
$208$		0			0
$209$	16.0000	−	16.0000i	1.10674	−	1.10674i
$210$		0			0
$211$	6.00000	+	6.00000i	0.413057	+	0.413057i	0.882802	−	0.469745i	$-0.155654\pi$
$211$	6.00000	+	6.00000i	0.413057	+	0.413057i	−0.469745	+	0.882802i	$0.655654\pi$
$212$		0			0
$213$			24.0000i			1.64445i
$214$		0			0
$215$	8.00000	+	8.00000i	0.545595	+	0.545595i
$216$		0			0
$217$	24.0000			1.62923
$218$		0			0
$219$			12.0000i			0.810885i
$220$		0			0
$221$	4.00000	+	16.0000i	0.269069	+	1.07628i
$222$		0			0
$223$		−	4.00000i		−	0.267860i	−0.990991	−	0.133930i	$-0.957240\pi$
$223$		−	4.00000i		−	0.267860i	0.990991	−	0.133930i	$-0.0427597\pi$
$224$		0			0
$225$	15.0000			1.00000
$226$		0			0
$227$	14.0000	+	14.0000i	0.929213	+	0.929213i	0.997655	−	0.0684424i	$-0.0218029\pi$
$227$	14.0000	+	14.0000i	0.929213	+	0.929213i	−0.0684424	+	0.997655i	$0.521803\pi$
$228$		0			0
$229$		−	18.0000i		−	1.18947i	−0.803921	−	0.594737i	$-0.797256\pi$
$229$		−	18.0000i		−	1.18947i	0.803921	−	0.594737i	$-0.202744\pi$
$230$		0			0
$231$	−16.0000	−	16.0000i	−1.05272	−	1.05272i
$232$		0			0
$233$	−5.00000	+	5.00000i	−0.327561	+	0.327561i	−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−5.00000	+	5.00000i	−0.327561	+	0.327561i	0.524097	+	0.851658i	$0.324403\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−8.00000			−0.519656
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	−19.0000	+	19.0000i	−1.22390	+	1.22390i	−0.257663	+	0.966235i	$0.582952\pi$
$241$	−19.0000	+	19.0000i	−1.22390	+	1.22390i	−0.966235	+	0.257663i	$0.917048\pi$
$242$		0			0
$243$	10.0000	−	10.0000i	0.641500	−	0.641500i
$244$		0			0
$245$	−1.00000	−	1.00000i	−0.0638877	−	0.0638877i
$246$		0			0
$247$		−	32.0000i		−	2.03611i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−4.00000			−0.252478			−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000			−0.252478			−0.126239	+	0.992000i	$0.540291\pi$
$252$		0			0
$253$		−	8.00000i		−	0.502956i
$254$		0			0
$255$	16.0000	−	4.00000i	1.00196	−	0.250490i
$256$		0			0
$257$			22.0000i			1.37232i	0.727450	+	0.686161i	$0.240706\pi$
$257$			22.0000i			1.37232i	−0.727450	+	0.686161i	$0.759294\pi$
$258$		0			0
$259$	−20.0000			−1.24274
$260$		0			0
$261$	15.0000	+	15.0000i	0.928477	+	0.928477i
$262$		0			0
$263$		−	4.00000i		−	0.246651i	−0.992366	−	0.123325i	$-0.960644\pi$
$263$		−	4.00000i		−	0.246651i	0.992366	−	0.123325i	$-0.0393559\pi$
$264$		0			0
$265$	12.0000	+	12.0000i	0.737154	+	0.737154i
$266$		0			0
$267$	−16.0000	+	16.0000i	−0.979184	+	0.979184i
$268$		0			0
$269$	−5.00000	+	5.00000i	−0.304855	+	0.304855i	−0.842910	−	0.538055i	$-0.819159\pi$
$269$	−5.00000	+	5.00000i	−0.304855	+	0.304855i	0.538055	+	0.842910i	$0.319159\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$		0			0
$273$	−32.0000			−1.93673
$274$		0			0
$275$	6.00000	−	6.00000i	0.361814	−	0.361814i
$276$		0			0
$277$	−15.0000	+	15.0000i	−0.901263	+	0.901263i	−0.995545	−	0.0942828i	$-0.969944\pi$
$277$	−15.0000	+	15.0000i	−0.901263	+	0.901263i	0.0942828	+	0.995545i	$0.469944\pi$
$278$		0			0
$279$	−30.0000	−	30.0000i	−1.79605	−	1.79605i
$280$		0			0
$281$			16.0000i			0.954480i	0.878773	+	0.477240i	$0.158363\pi$
$281$			16.0000i			0.954480i	−0.878773	+	0.477240i	$0.841637\pi$
$282$		0			0
$283$	−10.0000	−	10.0000i	−0.594438	−	0.594438i	0.344389	−	0.938827i	$-0.388086\pi$
$283$	−10.0000	−	10.0000i	−0.594438	−	0.594438i	−0.938827	+	0.344389i	$0.888086\pi$
$284$		0			0
$285$	−32.0000			−1.89552
$286$		0			0
$287$			4.00000i			0.236113i
$288$		0			0
$289$	−15.0000	+	8.00000i	−0.882353	+	0.470588i
$290$		0			0
$291$		−	12.0000i		−	0.703452i
$292$		0			0
$293$	26.0000			1.51894			0.759468	−	0.650545i	$-0.225459\pi$
$293$	26.0000			1.51894			0.759468	+	0.650545i	$0.225459\pi$
$294$		0			0
$295$	8.00000	+	8.00000i	0.465778	+	0.465778i
$296$		0			0
$297$			16.0000i			0.928414i
$298$		0			0
$299$	−8.00000	−	8.00000i	−0.462652	−	0.462652i
$300$		0			0
$301$	16.0000	−	16.0000i	0.922225	−	0.922225i
$302$		0			0
$303$	−24.0000	+	24.0000i	−1.37876	+	1.37876i
$304$		0			0
$305$	2.00000			0.114520
$306$		0			0
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$		0			0
$309$	16.0000	−	16.0000i	0.910208	−	0.910208i
$310$		0			0
$311$	−18.0000	+	18.0000i	−1.02069	+	1.02069i	−0.0209049	+	0.999781i	$0.506655\pi$
$311$	−18.0000	+	18.0000i	−1.02069	+	1.02069i	−0.999781	+	0.0209049i	$0.993345\pi$
$312$		0			0
$313$	9.00000	+	9.00000i	0.508710	+	0.508710i	0.914130	−	0.405420i	$-0.132875\pi$
$313$	9.00000	+	9.00000i	0.508710	+	0.508710i	−0.405420	+	0.914130i	$0.632875\pi$
$314$		0			0
$315$			20.0000i			1.12687i
$316$		0			0
$317$	−15.0000	−	15.0000i	−0.842484	−	0.842484i	0.146697	−	0.989181i	$-0.453136\pi$
$317$	−15.0000	−	15.0000i	−0.842484	−	0.842484i	−0.989181	+	0.146697i	$0.953136\pi$
$318$		0			0
$319$	12.0000			0.671871
$320$		0			0
$321$		−	8.00000i		−	0.446516i
$322$		0			0
$323$	32.0000	−	8.00000i	1.78053	−	0.445132i
$324$		0			0
$325$		−	12.0000i		−	0.665640i
$326$		0			0
$327$	12.0000			0.663602
$328$		0			0
$329$		0			0
$330$		0			0
$331$			32.0000i			1.75888i	0.476011	+	0.879440i	$0.342082\pi$
$331$			32.0000i			1.75888i	−0.476011	+	0.879440i	$0.657918\pi$
$332$		0			0
$333$	25.0000	+	25.0000i	1.36999	+	1.36999i
$334$		0			0
$335$	−12.0000	+	12.0000i	−0.655630	+	0.655630i
$336$		0			0
$337$	25.0000	−	25.0000i	1.36184	−	1.36184i	0.490261	−	0.871576i	$-0.336901\pi$
$337$	25.0000	−	25.0000i	1.36184	−	1.36184i	0.871576	−	0.490261i	$-0.163099\pi$
$338$		0			0
$339$	28.0000			1.52075
$340$		0			0
$341$	−24.0000			−1.29967
$342$		0			0
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$		0			0
$345$	−8.00000	+	8.00000i	−0.430706	+	0.430706i
$346$		0			0
$347$	18.0000	+	18.0000i	0.966291	+	0.966291i	0.999450	−	0.0331594i	$-0.0105569\pi$
$347$	18.0000	+	18.0000i	0.966291	+	0.966291i	−0.0331594	+	0.999450i	$0.510557\pi$
$348$		0			0
$349$		−	20.0000i		−	1.07058i	−0.844670	−	0.535288i	$-0.820203\pi$
$349$		−	20.0000i		−	1.07058i	0.844670	−	0.535288i	$-0.179797\pi$
$350$		0			0
$351$	16.0000	+	16.0000i	0.854017	+	0.854017i
$352$		0			0
$353$	−2.00000			−0.106449			−0.0532246	−	0.998583i	$-0.516950\pi$
$353$	−2.00000			−0.106449			−0.0532246	+	0.998583i	$0.516950\pi$
$354$		0			0
$355$		−	12.0000i		−	0.636894i
$356$		0			0
$357$	−8.00000	−	32.0000i	−0.423405	−	1.69362i
$358$		0			0
$359$			4.00000i			0.211112i	0.994413	+	0.105556i	$0.0336622\pi$
$359$			4.00000i			0.211112i	−0.994413	+	0.105556i	$0.966338\pi$
$360$		0			0
$361$	−45.0000			−2.36842
$362$		0			0
$363$	−6.00000	−	6.00000i	−0.314918	−	0.314918i
$364$		0			0
$365$		−	6.00000i		−	0.314054i
$366$		0			0
$367$	10.0000	+	10.0000i	0.521996	+	0.521996i	0.918174	−	0.396178i	$-0.129664\pi$
$367$	10.0000	+	10.0000i	0.521996	+	0.521996i	−0.396178	+	0.918174i	$0.629664\pi$
$368$		0			0
$369$	5.00000	−	5.00000i	0.260290	−	0.260290i
$370$		0			0
$371$	24.0000	−	24.0000i	1.24602	−	1.24602i
$372$		0			0
$373$	12.0000			0.621336			0.310668	−	0.950518i	$-0.399447\pi$
$373$	12.0000			0.621336			0.310668	+	0.950518i	$0.399447\pi$
$374$		0			0
$375$	−32.0000			−1.65247
$376$		0			0
$377$	12.0000	−	12.0000i	0.618031	−	0.618031i
$378$		0			0
$379$	−2.00000	+	2.00000i	−0.102733	+	0.102733i	−0.756605	−	0.653872i	$-0.773143\pi$
$379$	−2.00000	+	2.00000i	−0.102733	+	0.102733i	0.653872	+	0.756605i	$0.273143\pi$
$380$		0			0
$381$	8.00000	+	8.00000i	0.409852	+	0.409852i
$382$		0			0
$383$		−	36.0000i		−	1.83951i	−0.392488	−	0.919757i	$-0.628386\pi$
$383$		−	36.0000i		−	1.83951i	0.392488	−	0.919757i	$-0.371614\pi$
$384$		0			0
$385$	8.00000	+	8.00000i	0.407718	+	0.407718i
$386$		0			0
$387$	−40.0000			−2.03331
$388$		0			0
$389$		−	2.00000i		−	0.101404i	−0.998714	−	0.0507020i	$-0.983854\pi$
$389$		−	2.00000i		−	0.101404i	0.998714	−	0.0507020i	$-0.0161459\pi$
$390$		0			0
$391$	6.00000	−	10.0000i	0.303433	−	0.505722i
$392$		0			0
$393$			8.00000i			0.403547i
$394$		0			0
$395$	4.00000			0.201262
$396$		0			0
$397$	−9.00000	−	9.00000i	−0.451697	−	0.451697i	0.444220	−	0.895918i	$-0.353481\pi$
$397$	−9.00000	−	9.00000i	−0.451697	−	0.451697i	−0.895918	+	0.444220i	$0.853481\pi$
$398$		0			0
$399$			64.0000i			3.20401i
$400$		0			0
$401$	−11.0000	−	11.0000i	−0.549314	−	0.549314i	0.376929	−	0.926242i	$-0.376980\pi$
$401$	−11.0000	−	11.0000i	−0.549314	−	0.549314i	−0.926242	+	0.376929i	$0.876980\pi$
$402$		0			0
$403$	−24.0000	+	24.0000i	−1.19553	+	1.19553i
$404$		0			0
$405$	1.00000	−	1.00000i	0.0496904	−	0.0496904i
$406$		0			0
$407$	20.0000			0.991363
$408$		0			0
$409$	−10.0000			−0.494468			−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000			−0.494468			−0.247234	+	0.968956i	$0.579522\pi$
$410$		0			0
$411$	32.0000	−	32.0000i	1.57844	−	1.57844i
$412$		0			0
$413$	16.0000	−	16.0000i	0.787309	−	0.787309i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			8.00000i			0.391762i
$418$		0			0
$419$	−6.00000	−	6.00000i	−0.293119	−	0.293119i	0.545192	−	0.838311i	$-0.316457\pi$
$419$	−6.00000	−	6.00000i	−0.293119	−	0.293119i	−0.838311	+	0.545192i	$0.816457\pi$
$420$		0			0
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	12.0000	−	3.00000i	0.582086	−	0.145521i
$426$		0			0
$427$		−	4.00000i		−	0.193574i
$428$		0			0
$429$	32.0000			1.54497
$430$		0			0
$431$	6.00000	+	6.00000i	0.289010	+	0.289010i	0.836689	−	0.547679i	$-0.184488\pi$
$431$	6.00000	+	6.00000i	0.289010	+	0.289010i	−0.547679	+	0.836689i	$0.684488\pi$
$432$		0			0
$433$		−	10.0000i		−	0.480569i	−0.970702	−	0.240285i	$-0.922759\pi$
$433$		−	10.0000i		−	0.480569i	0.970702	−	0.240285i	$-0.0772408\pi$
$434$		0			0
$435$	−12.0000	−	12.0000i	−0.575356	−	0.575356i
$436$		0			0
$437$	−16.0000	+	16.0000i	−0.765384	+	0.765384i
$438$		0			0
$439$	18.0000	−	18.0000i	0.859093	−	0.859093i	−0.132138	−	0.991231i	$-0.542184\pi$
$439$	18.0000	−	18.0000i	0.859093	−	0.859093i	0.991231	+	0.132138i	$0.0421843\pi$
$440$		0			0
$441$	5.00000			0.238095
$442$		0			0
$443$	12.0000			0.570137			0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000			0.570137			0.285069	+	0.958507i	$0.407984\pi$
$444$		0			0
$445$	8.00000	−	8.00000i	0.379236	−	0.379236i
$446$		0			0
$447$	44.0000	−	44.0000i	2.08113	−	2.08113i
$448$		0			0
$449$	−13.0000	−	13.0000i	−0.613508	−	0.613508i	0.330350	−	0.943858i	$-0.392833\pi$
$449$	−13.0000	−	13.0000i	−0.613508	−	0.613508i	−0.943858	+	0.330350i	$0.892833\pi$
$450$		0			0
$451$		−	4.00000i		−	0.188353i
$452$		0			0
$453$	−24.0000	−	24.0000i	−1.12762	−	1.12762i
$454$		0			0
$455$	16.0000			0.750092
$456$		0			0
$457$			14.0000i			0.654892i	0.944870	+	0.327446i	$0.106188\pi$
$457$			14.0000i			0.654892i	−0.944870	+	0.327446i	$0.893812\pi$
$458$		0			0
$459$	−12.0000	+	20.0000i	−0.560112	+	0.933520i
$460$		0			0
$461$			20.0000i			0.931493i	0.884918	+	0.465746i	$0.154214\pi$
$461$			20.0000i			0.931493i	−0.884918	+	0.465746i	$0.845786\pi$
$462$		0			0
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$		0			0
$465$	24.0000	+	24.0000i	1.11297	+	1.11297i
$466$		0			0
$467$			8.00000i			0.370196i	0.982720	+	0.185098i	$0.0592602\pi$
$467$			8.00000i			0.370196i	−0.982720	+	0.185098i	$0.940740\pi$
$468$		0			0
$469$	24.0000	+	24.0000i	1.10822	+	1.10822i
$470$		0			0
$471$	−4.00000	+	4.00000i	−0.184310	+	0.184310i
$472$		0			0
$473$	−16.0000	+	16.0000i	−0.735681	+	0.735681i
$474$		0			0
$475$	−24.0000			−1.10120
$476$		0			0
$477$	−60.0000			−2.74721
$478$		0			0
$479$	−22.0000	+	22.0000i	−1.00521	+	1.00521i	−0.00521928	+	0.999986i	$0.501661\pi$
$479$	−22.0000	+	22.0000i	−1.00521	+	1.00521i	−0.999986	+	0.00521928i	$0.998339\pi$
$480$		0			0
$481$	20.0000	−	20.0000i	0.911922	−	0.911922i
$482$		0			0
$483$	16.0000	+	16.0000i	0.728025	+	0.728025i
$484$		0			0
$485$			6.00000i			0.272446i
$486$		0			0
$487$	14.0000	+	14.0000i	0.634401	+	0.634401i	0.949169	−	0.314768i	$-0.101927\pi$
$487$	14.0000	+	14.0000i	0.634401	+	0.634401i	−0.314768	+	0.949169i	$0.601927\pi$
$488$		0			0
$489$	24.0000			1.08532
$490$		0			0
$491$		−	24.0000i		−	1.08310i	−0.840667	−	0.541552i	$-0.817837\pi$
$491$		−	24.0000i		−	1.08310i	0.840667	−	0.541552i	$-0.182163\pi$
$492$		0			0
$493$	15.0000	+	9.00000i	0.675566	+	0.405340i
$494$		0			0
$495$		−	20.0000i		−	0.898933i
$496$		0			0
$497$	−24.0000			−1.07655
$498$		0			0
$499$	6.00000	+	6.00000i	0.268597	+	0.268597i	0.828535	−	0.559938i	$-0.189175\pi$
$499$	6.00000	+	6.00000i	0.268597	+	0.268597i	−0.559938	+	0.828535i	$0.689175\pi$
$500$		0			0
$501$			40.0000i			1.78707i
$502$		0			0
$503$	14.0000	+	14.0000i	0.624229	+	0.624229i	0.946610	−	0.322381i	$-0.104483\pi$
$503$	14.0000	+	14.0000i	0.624229	+	0.624229i	−0.322381	+	0.946610i	$0.604483\pi$
$504$		0			0
$505$	12.0000	−	12.0000i	0.533993	−	0.533993i
$506$		0			0
$507$	6.00000	−	6.00000i	0.266469	−	0.266469i
$508$		0			0
$509$	−30.0000			−1.32973			−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000			−1.32973			−0.664863	+	0.746965i	$0.731510\pi$
$510$		0			0
$511$	−12.0000			−0.530849
$512$		0			0
$513$	32.0000	−	32.0000i	1.41283	−	1.41283i
$514$		0			0
$515$	−8.00000	+	8.00000i	−0.352522	+	0.352522i
$516$		0			0
$517$		0			0
$518$		0			0
$519$			44.0000i			1.93139i
$520$		0			0
$521$	−31.0000	−	31.0000i	−1.35813	−	1.35813i	−0.876216	−	0.481919i	$-0.839940\pi$
$521$	−31.0000	−	31.0000i	−1.35813	−	1.35813i	−0.481919	−	0.876216i	$-0.660060\pi$
$522$		0			0
$523$	−36.0000			−1.57417			−0.787085	−	0.616844i	$-0.788411\pi$
$523$	−36.0000			−1.57417			−0.787085	+	0.616844i	$0.788411\pi$
$524$		0			0
$525$			24.0000i			1.04745i
$526$		0			0
$527$	−30.0000	−	18.0000i	−1.30682	−	0.784092i
$528$		0			0
$529$		−	15.0000i		−	0.652174i
$530$		0			0
$531$	−40.0000			−1.73585
$532$		0			0
$533$	−4.00000	−	4.00000i	−0.173259	−	0.173259i
$534$		0			0
$535$			4.00000i			0.172935i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	2.00000	−	2.00000i	0.0861461	−	0.0861461i
$540$		0			0
$541$	7.00000	−	7.00000i	0.300954	−	0.300954i	−0.540433	−	0.841387i	$-0.681740\pi$
$541$	7.00000	−	7.00000i	0.300954	−	0.300954i	0.841387	+	0.540433i	$0.181740\pi$
$542$		0			0
$543$	−20.0000			−0.858282
$544$		0			0
$545$	−6.00000			−0.257012
$546$		0			0
$547$	−2.00000	+	2.00000i	−0.0855138	+	0.0855138i	−0.748570	−	0.663056i	$-0.769259\pi$
$547$	−2.00000	+	2.00000i	−0.0855138	+	0.0855138i	0.663056	+	0.748570i	$0.269259\pi$
$548$		0			0
$549$	−5.00000	+	5.00000i	−0.213395	+	0.213395i
$550$		0			0
$551$	−24.0000	−	24.0000i	−1.02243	−	1.02243i
$552$		0			0
$553$		−	8.00000i		−	0.340195i
$554$		0			0
$555$	−20.0000	−	20.0000i	−0.848953	−	0.848953i
$556$		0			0
$557$	20.0000			0.847427			0.423714	−	0.905796i	$-0.360726\pi$
$557$	20.0000			0.847427			0.423714	+	0.905796i	$0.360726\pi$
$558$		0			0
$559$			32.0000i			1.35346i
$560$		0			0
$561$	8.00000	+	32.0000i	0.337760	+	1.35104i
$562$		0			0
$563$		−	24.0000i		−	1.01148i	−0.862686	−	0.505740i	$-0.831220\pi$
$563$		−	24.0000i		−	1.01148i	0.862686	−	0.505740i	$-0.168780\pi$
$564$		0			0
$565$	−14.0000			−0.588984
$566$		0			0
$567$	−2.00000	−	2.00000i	−0.0839921	−	0.0839921i
$568$		0			0
$569$			24.0000i			1.00613i	0.864248	+	0.503066i	$0.167795\pi$
$569$			24.0000i			1.00613i	−0.864248	+	0.503066i	$0.832205\pi$
$570$		0			0
$571$	30.0000	+	30.0000i	1.25546	+	1.25546i	0.953237	+	0.302224i	$0.0977291\pi$
$571$	30.0000	+	30.0000i	1.25546	+	1.25546i	0.302224	+	0.953237i	$0.402271\pi$
$572$		0			0
$573$	−16.0000	+	16.0000i	−0.668410	+	0.668410i
$574$		0			0
$575$	−6.00000	+	6.00000i	−0.250217	+	0.250217i
$576$		0			0
$577$	8.00000			0.333044			0.166522	−	0.986038i	$-0.446746\pi$
$577$	8.00000			0.333044			0.166522	+	0.986038i	$0.446746\pi$
$578$		0			0
$579$	−12.0000			−0.498703
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−24.0000	+	24.0000i	−0.993978	+	0.993978i
$584$		0			0
$585$	−20.0000	−	20.0000i	−0.826898	−	0.826898i
$586$		0			0
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$		0			0
$589$	48.0000	+	48.0000i	1.97781	+	1.97781i
$590$		0			0
$591$	52.0000			2.13899
$592$		0			0
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$		0			0
$595$	4.00000	+	16.0000i	0.163984	+	0.655936i
$596$		0			0
$597$		−	24.0000i		−	0.982255i
$598$		0			0
$599$	32.0000			1.30748			0.653742	−	0.756717i	$-0.273198\pi$
$599$	32.0000			1.30748			0.653742	+	0.756717i	$0.273198\pi$
$600$		0			0
$601$	−27.0000	−	27.0000i	−1.10135	−	1.10135i	−0.994248	−	0.107105i	$-0.965842\pi$
$601$	−27.0000	−	27.0000i	−1.10135	−	1.10135i	−0.107105	−	0.994248i	$-0.534158\pi$
$602$		0			0
$603$		−	60.0000i		−	2.44339i
$604$		0			0
$605$	3.00000	+	3.00000i	0.121967	+	0.121967i
$606$		0			0
$607$	14.0000	−	14.0000i	0.568242	−	0.568242i	−0.363393	−	0.931636i	$-0.618382\pi$
$607$	14.0000	−	14.0000i	0.568242	−	0.568242i	0.931636	+	0.363393i	$0.118382\pi$
$608$		0			0
$609$	−24.0000	+	24.0000i	−0.972529	+	0.972529i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	38.0000			1.53481			0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000			1.53481			0.767403	+	0.641165i	$0.221549\pi$
$614$		0			0
$615$	−4.00000	+	4.00000i	−0.161296	+	0.161296i
$616$		0			0
$617$	3.00000	−	3.00000i	0.120775	−	0.120775i	−0.644136	−	0.764911i	$-0.722783\pi$
$617$	3.00000	−	3.00000i	0.120775	−	0.120775i	0.764911	+	0.644136i	$0.222783\pi$
$618$		0			0
$619$	−14.0000	−	14.0000i	−0.562708	−	0.562708i	0.367368	−	0.930076i	$-0.380259\pi$
$619$	−14.0000	−	14.0000i	−0.562708	−	0.562708i	−0.930076	+	0.367368i	$0.880259\pi$
$620$		0			0
$621$		−	16.0000i		−	0.642058i
$622$		0			0
$623$	−16.0000	−	16.0000i	−0.641026	−	0.641026i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$		−	64.0000i		−	2.55591i
$628$		0			0
$629$	25.0000	+	15.0000i	0.996815	+	0.598089i
$630$		0			0
$631$			28.0000i			1.11466i	0.830290	+	0.557331i	$0.188175\pi$
$631$			28.0000i			1.11466i	−0.830290	+	0.557331i	$0.811825\pi$
$632$		0			0
$633$	24.0000			0.953914
$634$		0			0
$635$	−4.00000	−	4.00000i	−0.158735	−	0.158735i
$636$		0			0
$637$		−	4.00000i		−	0.158486i
$638$		0			0
$639$	30.0000	+	30.0000i	1.18678	+	1.18678i
$640$		0			0
$641$	−5.00000	+	5.00000i	−0.197488	+	0.197488i	−0.798922	−	0.601434i	$-0.794596\pi$
$641$	−5.00000	+	5.00000i	−0.197488	+	0.197488i	0.601434	+	0.798922i	$0.294596\pi$
$642$		0			0
$643$	−6.00000	+	6.00000i	−0.236617	+	0.236617i	−0.815448	−	0.578831i	$-0.803509\pi$
$643$	−6.00000	+	6.00000i	−0.236617	+	0.236617i	0.578831	+	0.815448i	$0.303509\pi$
$644$		0			0
$645$	32.0000			1.26000
$646$		0			0
$647$	−16.0000			−0.629025			−0.314512	−	0.949253i	$-0.601841\pi$
$647$	−16.0000			−0.629025			−0.314512	+	0.949253i	$0.601841\pi$
$648$		0			0
$649$	−16.0000	+	16.0000i	−0.628055	+	0.628055i
$650$		0			0
$651$	48.0000	−	48.0000i	1.88127	−	1.88127i
$652$		0			0
$653$	5.00000	+	5.00000i	0.195665	+	0.195665i	0.798139	−	0.602474i	$-0.205818\pi$
$653$	5.00000	+	5.00000i	0.195665	+	0.195665i	−0.602474	+	0.798139i	$0.705818\pi$
$654$		0			0
$655$		−	4.00000i		−	0.156293i
$656$		0			0
$657$	15.0000	+	15.0000i	0.585206	+	0.585206i
$658$		0			0
$659$	4.00000			0.155818			0.0779089	−	0.996960i	$-0.475176\pi$
$659$	4.00000			0.155818			0.0779089	+	0.996960i	$0.475176\pi$
$660$		0			0
$661$		−	28.0000i		−	1.08907i	−0.838737	−	0.544537i	$-0.816705\pi$
$661$		−	28.0000i		−	1.08907i	0.838737	−	0.544537i	$-0.183295\pi$
$662$		0			0
$663$	40.0000	+	24.0000i	1.55347	+	0.932083i
$664$		0			0
$665$		−	32.0000i		−	1.24091i
$666$		0			0
$667$	−12.0000			−0.464642
$668$		0			0
$669$	−8.00000	−	8.00000i	−0.309298	−	0.309298i
$670$		0			0
$671$			4.00000i			0.154418i
$672$		0			0
$673$	3.00000	+	3.00000i	0.115642	+	0.115642i	0.762560	−	0.646918i	$-0.223942\pi$
$673$	3.00000	+	3.00000i	0.115642	+	0.115642i	−0.646918	+	0.762560i	$0.723942\pi$
$674$		0			0
$675$	12.0000	−	12.0000i	0.461880	−	0.461880i
$676$		0			0
$677$	13.0000	−	13.0000i	0.499631	−	0.499631i	−0.411692	−	0.911323i	$-0.635062\pi$
$677$	13.0000	−	13.0000i	0.499631	−	0.499631i	0.911323	+	0.411692i	$0.135062\pi$
$678$		0			0
$679$	12.0000			0.460518
$680$		0			0
$681$	56.0000			2.14592
$682$		0			0
$683$	−2.00000	+	2.00000i	−0.0765279	+	0.0765279i	−0.744335	−	0.667807i	$-0.767233\pi$
$683$	−2.00000	+	2.00000i	−0.0765279	+	0.0765279i	0.667807	+	0.744335i	$0.267233\pi$
$684$		0			0
$685$	−16.0000	+	16.0000i	−0.611329	+	0.611329i
$686$		0			0
$687$	−36.0000	−	36.0000i	−1.37349	−	1.37349i
$688$		0			0
$689$			48.0000i			1.82865i
$690$		0			0
$691$	18.0000	+	18.0000i	0.684752	+	0.684752i	0.961067	−	0.276315i	$-0.0891133\pi$
$691$	18.0000	+	18.0000i	0.684752	+	0.684752i	−0.276315	+	0.961067i	$0.589113\pi$
$692$		0			0
$693$	−40.0000			−1.51947
$694$		0			0
$695$		−	4.00000i		−	0.151729i
$696$		0			0
$697$	3.00000	−	5.00000i	0.113633	−	0.189389i
$698$		0			0
$699$			20.0000i			0.756469i
$700$		0			0
$701$	−12.0000			−0.453234			−0.226617	−	0.973984i	$-0.572767\pi$
$701$	−12.0000			−0.453234			−0.226617	+	0.973984i	$0.572767\pi$
$702$		0			0
$703$	−40.0000	−	40.0000i	−1.50863	−	1.50863i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−24.0000	−	24.0000i	−0.902613	−	0.902613i
$708$		0			0
$709$	−15.0000	+	15.0000i	−0.563337	+	0.563337i	−0.930254	−	0.366917i	$-0.880413\pi$
$709$	−15.0000	+	15.0000i	−0.563337	+	0.563337i	0.366917	+	0.930254i	$0.380413\pi$
$710$		0			0
$711$	−10.0000	+	10.0000i	−0.375029	+	0.375029i
$712$		0			0
$713$	24.0000			0.898807
$714$		0			0
$715$	−16.0000			−0.598366
$716$		0			0
$717$		0			0
$718$		0			0
$719$	14.0000	−	14.0000i	0.522112	−	0.522112i	−0.396097	−	0.918209i	$-0.629636\pi$
$719$	14.0000	−	14.0000i	0.522112	−	0.522112i	0.918209	+	0.396097i	$0.129636\pi$
$720$		0			0
$721$	16.0000	+	16.0000i	0.595871	+	0.595871i
$722$		0			0
$723$			76.0000i			2.82647i
$724$		0			0
$725$	−9.00000	−	9.00000i	−0.334252	−	0.334252i
$726$		0			0
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$		0			0
$729$		−	43.0000i		−	1.59259i
$730$		0			0
$731$	−32.0000	+	8.00000i	−1.18356	+	0.295891i
$732$		0			0
$733$			12.0000i			0.443230i	0.975134	+	0.221615i	$0.0711328\pi$
$733$			12.0000i			0.443230i	−0.975134	+	0.221615i	$0.928867\pi$
$734$		0			0
$735$	−4.00000			−0.147542
$736$		0			0
$737$	−24.0000	−	24.0000i	−0.884051	−	0.884051i
$738$		0			0
$739$		−	32.0000i		−	1.17714i	−0.808447	−	0.588570i	$-0.799691\pi$
$739$		−	32.0000i		−	1.17714i	0.808447	−	0.588570i	$-0.200309\pi$
$740$		0			0
$741$	−64.0000	−	64.0000i	−2.35110	−	2.35110i
$742$		0			0
$743$	26.0000	−	26.0000i	0.953847	−	0.953847i	−0.0451335	−	0.998981i	$-0.514371\pi$
$743$	26.0000	−	26.0000i	0.953847	−	0.953847i	0.998981	+	0.0451335i	$0.0143713\pi$
$744$		0			0
$745$	−22.0000	+	22.0000i	−0.806018	+	0.806018i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	8.00000			0.292314
$750$		0			0
$751$	30.0000	−	30.0000i	1.09472	−	1.09472i	0.0996978	−	0.995018i	$-0.468212\pi$
$751$	30.0000	−	30.0000i	1.09472	−	1.09472i	0.995018	−	0.0996978i	$-0.0317876\pi$
$752$		0			0
$753$	−8.00000	+	8.00000i	−0.291536	+	0.291536i
$754$		0			0
$755$	12.0000	+	12.0000i	0.436725	+	0.436725i
$756$		0			0
$757$			14.0000i			0.508839i	0.967094	+	0.254419i	$0.0818843\pi$
$757$			14.0000i			0.508839i	−0.967094	+	0.254419i	$0.918116\pi$
$758$		0			0
$759$	−16.0000	−	16.0000i	−0.580763	−	0.580763i
$760$		0			0
$761$		0			0			−	1.00000i	$-0.5\pi$
$761$		0			0				1.00000i	$0.5\pi$
$762$		0			0
$763$			12.0000i			0.434429i
$764$		0			0
$765$	15.0000	−	25.0000i	0.542326	−	0.903877i
$766$		0			0
$767$			32.0000i			1.15545i
$768$		0			0
$769$	−16.0000			−0.576975			−0.288487	−	0.957484i	$-0.593152\pi$
$769$	−16.0000			−0.576975			−0.288487	+	0.957484i	$0.593152\pi$
$770$		0			0
$771$	44.0000	+	44.0000i	1.58462	+	1.58462i
$772$		0			0
$773$		−	30.0000i		−	1.07903i	−0.841978	−	0.539513i	$-0.818609\pi$
$773$		−	30.0000i		−	1.07903i	0.841978	−	0.539513i	$-0.181391\pi$
$774$		0			0
$775$	18.0000	+	18.0000i	0.646579	+	0.646579i
$776$		0			0
$777$	−40.0000	+	40.0000i	−1.43499	+	1.43499i
$778$		0			0
$779$	−8.00000	+	8.00000i	−0.286630	+	0.286630i
$780$		0			0
$781$	24.0000			0.858788
$782$		0			0
$783$	24.0000			0.857690
$784$		0			0
$785$	2.00000	−	2.00000i	0.0713831	−	0.0713831i
$786$		0			0
$787$	−30.0000	+	30.0000i	−1.06938	+	1.06938i	−0.0719783	+	0.997406i	$0.522931\pi$
$787$	−30.0000	+	30.0000i	−1.06938	+	1.06938i	−0.997406	+	0.0719783i	$0.977069\pi$
$788$		0			0
$789$	−8.00000	−	8.00000i	−0.284808	−	0.284808i
$790$		0			0
$791$			28.0000i			0.995565i
$792$		0			0
$793$	4.00000	+	4.00000i	0.142044	+	0.142044i
$794$		0			0
$795$	48.0000			1.70238
$796$		0			0
$797$		−	36.0000i		−	1.27519i	−0.770374	−	0.637593i	$-0.779930\pi$
$797$		−	36.0000i		−	1.27519i	0.770374	−	0.637593i	$-0.220070\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$			40.0000i			1.41333i
$802$		0			0
$803$	12.0000			0.423471
$804$		0			0
$805$	−8.00000	−	8.00000i	−0.281963	−	0.281963i
$806$		0			0
$807$			20.0000i			0.704033i
$808$		0			0
$809$	−1.00000	−	1.00000i	−0.0351581	−	0.0351581i	0.689309	−	0.724467i	$-0.257914\pi$
$809$	−1.00000	−	1.00000i	−0.0351581	−	0.0351581i	−0.724467	+	0.689309i	$0.757914\pi$
$810$		0			0
$811$	−6.00000	+	6.00000i	−0.210688	+	0.210688i	−0.804560	−	0.593871i	$-0.797599\pi$
$811$	−6.00000	+	6.00000i	−0.210688	+	0.210688i	0.593871	+	0.804560i	$0.297599\pi$
$812$		0			0
$813$	−16.0000	+	16.0000i	−0.561144	+	0.561144i
$814$		0			0
$815$	−12.0000			−0.420342
$816$		0			0
$817$	64.0000			2.23908
$818$		0			0
$819$	−40.0000	+	40.0000i	−1.39771	+	1.39771i
$820$		0			0
$821$	29.0000	−	29.0000i	1.01211	−	1.01211i	0.0121812	−	0.999926i	$-0.496123\pi$
$821$	29.0000	−	29.0000i	1.01211	−	1.01211i	0.999926	−	0.0121812i	$-0.00387748\pi$
$822$		0			0
$823$	10.0000	+	10.0000i	0.348578	+	0.348578i	0.859580	−	0.511002i	$-0.170725\pi$
$823$	10.0000	+	10.0000i	0.348578	+	0.348578i	−0.511002	+	0.859580i	$0.670725\pi$
$824$		0			0
$825$		−	24.0000i		−	0.835573i
$826$		0			0
$827$	−14.0000	−	14.0000i	−0.486828	−	0.486828i	0.420476	−	0.907304i	$-0.361863\pi$
$827$	−14.0000	−	14.0000i	−0.486828	−	0.486828i	−0.907304	+	0.420476i	$0.861863\pi$
$828$		0			0
$829$	30.0000			1.04194			0.520972	−	0.853574i	$-0.325570\pi$
$829$	30.0000			1.04194			0.520972	+	0.853574i	$0.325570\pi$
$830$		0			0
$831$			60.0000i			2.08138i
$832$		0			0
$833$	4.00000	−	1.00000i	0.138592	−	0.0346479i
$834$		0			0
$835$		−	20.0000i		−	0.692129i
$836$		0			0
$837$	−48.0000			−1.65912
$838$		0			0
$839$	−14.0000	−	14.0000i	−0.483334	−	0.483334i	0.422861	−	0.906195i	$-0.361026\pi$
$839$	−14.0000	−	14.0000i	−0.483334	−	0.483334i	−0.906195	+	0.422861i	$0.861026\pi$
$840$		0			0
$841$			11.0000i			0.379310i
$842$		0			0
$843$	32.0000	+	32.0000i	1.10214	+	1.10214i
$844$		0			0
$845$	−3.00000	+	3.00000i	−0.103203	+	0.103203i
$846$		0			0
$847$	6.00000	−	6.00000i	0.206162	−	0.206162i
$848$		0			0
$849$	−40.0000			−1.37280
$850$		0			0
$851$	−20.0000			−0.685591
$852$		0			0
$853$	23.0000	−	23.0000i	0.787505	−	0.787505i	−0.193580	−	0.981085i	$-0.562010\pi$
$853$	23.0000	−	23.0000i	0.787505	−	0.787505i	0.981085	+	0.193580i	$0.0620098\pi$
$854$		0			0
$855$	−40.0000	+	40.0000i	−1.36797	+	1.36797i
$856$		0			0
$857$	−15.0000	−	15.0000i	−0.512390	−	0.512390i	0.402868	−	0.915258i	$-0.368013\pi$
$857$	−15.0000	−	15.0000i	−0.512390	−	0.512390i	−0.915258	+	0.402868i	$0.868013\pi$
$858$		0			0
$859$		−	48.0000i		−	1.63774i	−0.573980	−	0.818869i	$-0.694601\pi$
$859$		−	48.0000i		−	1.63774i	0.573980	−	0.818869i	$-0.305399\pi$
$860$		0			0
$861$	8.00000	+	8.00000i	0.272639	+	0.272639i
$862$		0			0
$863$	−16.0000			−0.544646			−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000			−0.544646			−0.272323	+	0.962206i	$0.587792\pi$
$864$		0			0
$865$		−	22.0000i		−	0.748022i
$866$		0			0
$867$	−14.0000	+	46.0000i	−0.475465	+	1.56224i
$868$		0			0
$869$			8.00000i			0.271381i
$870$		0			0
$871$	−48.0000			−1.62642
$872$		0			0
$873$	−15.0000	−	15.0000i	−0.507673	−	0.507673i
$874$		0			0
$875$		−	32.0000i		−	1.08180i
$876$		0			0
$877$	−29.0000	−	29.0000i	−0.979260	−	0.979260i	0.0205288	−	0.999789i	$-0.493465\pi$
$877$	−29.0000	−	29.0000i	−0.979260	−	0.979260i	−0.999789	+	0.0205288i	$0.993465\pi$
$878$		0			0
$879$	52.0000	−	52.0000i	1.75392	−	1.75392i
$880$		0			0
$881$	−23.0000	+	23.0000i	−0.774890	+	0.774890i	−0.978957	−	0.204067i	$-0.934584\pi$
$881$	−23.0000	+	23.0000i	−0.774890	+	0.774890i	0.204067	+	0.978957i	$0.434584\pi$
$882$		0			0
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$		0			0
$885$	32.0000			1.07567
$886$		0			0
$887$	−34.0000	+	34.0000i	−1.14161	+	1.14161i	−0.153452	+	0.988156i	$0.549039\pi$
$887$	−34.0000	+	34.0000i	−1.14161	+	1.14161i	−0.988156	+	0.153452i	$0.950961\pi$
$888$		0			0
$889$	−8.00000	+	8.00000i	−0.268311	+	0.268311i
$890$		0			0
$891$	2.00000	+	2.00000i	0.0670025	+	0.0670025i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−32.0000			−1.06845
$898$		0			0
$899$			36.0000i			1.20067i
$900$		0			0
$901$	−48.0000	+	12.0000i	−1.59911	+	0.399778i
$902$		0			0
$903$		−	64.0000i		−	2.12979i
$904$		0			0
$905$	10.0000			0.332411
$906$		0			0
$907$	14.0000	+	14.0000i	0.464862	+	0.464862i	0.900245	−	0.435383i	$-0.143387\pi$
$907$	14.0000	+	14.0000i	0.464862	+	0.464862i	−0.435383	+	0.900245i	$0.643387\pi$
$908$		0			0
$909$			60.0000i			1.99007i
$910$		0			0
$911$	−34.0000	−	34.0000i	−1.12647	−	1.12647i	−0.990747	−	0.135724i	$-0.956664\pi$
$911$	−34.0000	−	34.0000i	−1.12647	−	1.12647i	−0.135724	−	0.990747i	$-0.543336\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	4.00000	−	4.00000i	0.132236	−	0.132236i
$916$		0			0
$917$	−8.00000			−0.264183
$918$		0			0
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$		0			0
$921$	−24.0000	+	24.0000i	−0.790827	+	0.790827i
$922$		0			0
$923$	24.0000	−	24.0000i	0.789970	−	0.789970i
$924$		0			0
$925$	−15.0000	−	15.0000i	−0.493197	−	0.493197i
$926$		0			0
$927$		−	40.0000i		−	1.31377i
$928$		0			0
$929$	37.0000	+	37.0000i	1.21393	+	1.21393i	0.969723	+	0.244208i	$0.0785279\pi$
$929$	37.0000	+	37.0000i	1.21393	+	1.21393i	0.244208	+	0.969723i	$0.421472\pi$
$930$		0			0
$931$	−8.00000			−0.262189
$932$		0			0
$933$			72.0000i			2.35717i
$934$		0			0
$935$	−4.00000	−	16.0000i	−0.130814	−	0.523256i
$936$		0			0
$937$		−	16.0000i		−	0.522697i	−0.965244	−	0.261349i	$-0.915833\pi$
$937$		−	16.0000i		−	0.522697i	0.965244	−	0.261349i	$-0.0841672\pi$
$938$		0			0
$939$	36.0000			1.17482
$940$		0			0
$941$	33.0000	+	33.0000i	1.07577	+	1.07577i	0.996884	+	0.0788856i	$0.0251362\pi$
$941$	33.0000	+	33.0000i	1.07577	+	1.07577i	0.0788856	+	0.996884i	$0.474864\pi$
$942$		0			0
$943$			4.00000i			0.130258i
$944$		0			0
$945$	16.0000	+	16.0000i	0.520480	+	0.520480i
$946$		0			0
$947$	18.0000	−	18.0000i	0.584921	−	0.584921i	−0.351330	−	0.936252i	$-0.614271\pi$
$947$	18.0000	−	18.0000i	0.584921	−	0.584921i	0.936252	+	0.351330i	$0.114271\pi$
$948$		0			0
$949$	12.0000	−	12.0000i	0.389536	−	0.389536i
$950$		0			0
$951$	−60.0000			−1.94563
$952$		0			0
$953$	−48.0000			−1.55487			−0.777436	−	0.628962i	$-0.783480\pi$
$953$	−48.0000			−1.55487			−0.777436	+	0.628962i	$0.783480\pi$
$954$		0			0
$955$	8.00000	−	8.00000i	0.258874	−	0.258874i
$956$		0			0
$957$	24.0000	−	24.0000i	0.775810	−	0.775810i
$958$		0			0
$959$	32.0000	+	32.0000i	1.03333	+	1.03333i
$960$		0			0
$961$		−	41.0000i		−	1.32258i
$962$		0			0
$963$	−10.0000	−	10.0000i	−0.322245	−	0.322245i
$964$		0			0
$965$	6.00000			0.193147
$966$		0			0
$967$		−	28.0000i		−	0.900419i	−0.892923	−	0.450210i	$-0.851349\pi$
$967$		−	28.0000i		−	0.900419i	0.892923	−	0.450210i	$-0.148651\pi$
$968$		0			0
$969$	48.0000	−	80.0000i	1.54198	−	2.56997i
$970$		0			0
$971$			24.0000i			0.770197i	0.922876	+	0.385098i	$0.125832\pi$
$971$			24.0000i			0.770197i	−0.922876	+	0.385098i	$0.874168\pi$
$972$		0			0
$973$	−8.00000			−0.256468
$974$		0			0
$975$	−24.0000	−	24.0000i	−0.768615	−	0.768615i
$976$		0			0
$977$		−	8.00000i		−	0.255943i	−0.991778	−	0.127971i	$-0.959153\pi$
$977$		−	8.00000i		−	0.255943i	0.991778	−	0.127971i	$-0.0408466\pi$
$978$		0			0
$979$	16.0000	+	16.0000i	0.511362	+	0.511362i
$980$		0			0
$981$	15.0000	−	15.0000i	0.478913	−	0.478913i
$982$		0			0
$983$	34.0000	−	34.0000i	1.08443	−	1.08443i	0.0883413	−	0.996090i	$-0.471843\pi$
$983$	34.0000	−	34.0000i	1.08443	−	1.08443i	0.996090	−	0.0883413i	$-0.0281566\pi$
$984$		0			0
$985$	−26.0000			−0.828429
$986$		0			0
$987$		0			0
$988$		0			0
$989$	16.0000	−	16.0000i	0.508770	−	0.508770i
$990$		0			0
$991$	6.00000	−	6.00000i	0.190596	−	0.190596i	−0.605357	−	0.795954i	$-0.706970\pi$
$991$	6.00000	−	6.00000i	0.190596	−	0.190596i	0.795954	+	0.605357i	$0.206970\pi$
$992$		0			0
$993$	64.0000	+	64.0000i	2.03098	+	2.03098i
$994$		0			0
$995$			12.0000i			0.380426i
$996$		0			0
$997$	5.00000	+	5.00000i	0.158352	+	0.158352i	0.781836	−	0.623484i	$-0.214283\pi$
$997$	5.00000	+	5.00000i	0.158352	+	0.158352i	−0.623484	+	0.781836i	$0.714283\pi$
$998$		0			0
$999$	40.0000			1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.k.d.89.1	yes	2
3.2	odd	2		1224.2.w.e.361.1		2
4.3	odd	2		272.2.o.a.225.1		2
8.3	odd	2		1088.2.o.q.769.1		2
8.5	even	2		1088.2.o.b.769.1		2
12.11	even	2		2448.2.be.i.1585.1		2
17.2	even	8		2312.2.b.a.577.1		2
17.8	even	8		2312.2.a.k.1.1		2
17.9	even	8		2312.2.a.k.1.2		2
17.13	even	4	inner	136.2.k.d.81.1	✓	2
17.15	even	8		2312.2.b.a.577.2		2
51.47	odd	4		1224.2.w.e.217.1		2
68.43	odd	8		4624.2.a.t.1.1		2
68.47	odd	4		272.2.o.a.81.1		2
68.59	odd	8		4624.2.a.t.1.2		2
136.13	even	4		1088.2.o.b.897.1		2
136.115	odd	4		1088.2.o.q.897.1		2
204.47	even	4		2448.2.be.i.1441.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.k.d.81.1	✓	2	17.13	even	4	inner
136.2.k.d.89.1	yes	2	1.1	even	1	trivial
272.2.o.a.81.1		2	68.47	odd	4
272.2.o.a.225.1		2	4.3	odd	2
1088.2.o.b.769.1		2	8.5	even	2
1088.2.o.b.897.1		2	136.13	even	4
1088.2.o.q.769.1		2	8.3	odd	2
1088.2.o.q.897.1		2	136.115	odd	4
1224.2.w.e.217.1		2	51.47	odd	4
1224.2.w.e.361.1		2	3.2	odd	2
2312.2.a.k.1.1		2	17.8	even	8
2312.2.a.k.1.2		2	17.9	even	8
2312.2.b.a.577.1		2	17.2	even	8
2312.2.b.a.577.2		2	17.15	even	8
2448.2.be.i.1441.1		2	204.47	even	4
2448.2.be.i.1585.1		2	12.11	even	2
4624.2.a.t.1.1		2	68.43	odd	8
4624.2.a.t.1.2		2	68.59	odd	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	136.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 - 2.00000i) q^{3} +(-1.00000 + 1.00000i) q^{5} +(2.00000 + 2.00000i) q^{7} -5.00000i q^{9} +(-2.00000 - 2.00000i) q^{11} -4.00000 q^{13} +4.00000i q^{15} +(-1.00000 - 4.00000i) q^{17} +8.00000i q^{19} +8.00000 q^{21} +(2.00000 + 2.00000i) q^{23} +3.00000i q^{25} +(-4.00000 - 4.00000i) q^{27} +(-3.00000 + 3.00000i) q^{29} +(6.00000 - 6.00000i) q^{31} -8.00000 q^{33} -4.00000 q^{35} +(-5.00000 + 5.00000i) q^{37} +(-8.00000 + 8.00000i) q^{39} +(1.00000 + 1.00000i) q^{41} -8.00000i q^{43} +(5.00000 + 5.00000i) q^{45} +1.00000i q^{49} +(-10.0000 - 6.00000i) q^{51} -12.0000i q^{53} +4.00000 q^{55} +(16.0000 + 16.0000i) q^{57} -8.00000i q^{59} +(-1.00000 - 1.00000i) q^{61} +(10.0000 - 10.0000i) q^{63} +(4.00000 - 4.00000i) q^{65} +12.0000 q^{67} +8.00000 q^{69} +(-6.00000 + 6.00000i) q^{71} +(-3.00000 + 3.00000i) q^{73} +(6.00000 + 6.00000i) q^{75} -8.00000i q^{77} +(-2.00000 - 2.00000i) q^{79} -1.00000 q^{81} +(5.00000 + 3.00000i) q^{85} +12.0000i q^{87} -8.00000 q^{89} +(-8.00000 - 8.00000i) q^{91} -24.0000i q^{93} +(-8.00000 - 8.00000i) q^{95} +(3.00000 - 3.00000i) q^{97} +(-10.0000 + 10.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{3} - 2 q^{5} + 4 q^{7} - 4 q^{11} - 8 q^{13} - 2 q^{17} + 16 q^{21} + 4 q^{23} - 8 q^{27} - 6 q^{29} + 12 q^{31} - 16 q^{33} - 8 q^{35} - 10 q^{37} - 16 q^{39} + 2 q^{41} + 10 q^{45} - 20 q^{51}+ \cdots - 20 q^{99}+O(q^{100}) \) 2 * q + 4 * q^3 - 2 * q^5 + 4 * q^7 - 4 * q^11 - 8 * q^13 - 2 * q^17 + 16 * q^21 + 4 * q^23 - 8 * q^27 - 6 * q^29 + 12 * q^31 - 16 * q^33 - 8 * q^35 - 10 * q^37 - 16 * q^39 + 2 * q^41 + 10 * q^45 - 20 * q^51 + 8 * q^55 + 32 * q^57 - 2 * q^61 + 20 * q^63 + 8 * q^65 + 24 * q^67 + 16 * q^69 - 12 * q^71 - 6 * q^73 + 12 * q^75 - 4 * q^79 - 2 * q^81 + 10 * q^85 - 16 * q^89 - 16 * q^91 - 16 * q^95 + 6 * q^97 - 20 * q^99

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