LMFDB - Embedded newform 459.2.y.a.116.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,2,Mod(44,459)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([40, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("459.44"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	459.y (of order $48$, degree $16$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	no (minimal twist has level 153)
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			116.10
Character	$\chi$	$=$	459.116
Dual form			459.2.y.a.368.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.999782 + 0.131624i) q^{2} +(-0.949612 - 0.254448i) q^{4} +(-1.57233 + 3.18837i) q^{5} +(-0.0400335 + 0.0197423i) q^{7} +(-2.77921 - 1.15119i) q^{8} +(-1.99165 + 2.98072i) q^{10} +(-5.72491 - 1.94335i) q^{11} +(0.940868 - 3.51137i) q^{13} +(-0.0426233 + 0.0144687i) q^{14} +(-0.924284 - 0.533636i) q^{16} +(-3.77050 + 1.66834i) q^{17} +(-2.46918 + 1.02277i) q^{19} +(2.30438 - 2.62764i) q^{20} +(-5.46788 - 2.69646i) q^{22} +(4.75485 + 5.42187i) q^{23} +(-4.64968 - 6.05958i) q^{25} +(1.40284 - 3.38676i) q^{26} +(0.0430397 - 0.00856112i) q^{28} +(-0.00257534 - 0.0392922i) q^{29} +(1.33921 + 3.94517i) q^{31} +(3.91928 + 3.00737i) q^{32} +(-3.98927 + 1.17169i) q^{34} -0.158683i q^{35} +(-1.01343 + 5.09486i) q^{37} +(-2.60326 + 0.697541i) q^{38} +(8.04025 - 7.05111i) q^{40} +(-4.78533 - 0.313647i) q^{41} +(-0.651975 + 0.500278i) q^{43} +(4.94197 + 3.30212i) q^{44} +(4.04017 + 6.04654i) q^{46} +(0.435110 + 1.62385i) q^{47} +(-4.26012 + 5.55189i) q^{49} +(-3.85108 - 6.67026i) q^{50} +(-1.78692 + 3.09503i) q^{52} +(1.17550 + 2.83792i) q^{53} +(15.1976 - 15.1976i) q^{55} +(0.133989 - 0.00878208i) q^{56} +(0.00259700 - 0.0396226i) q^{58} +(-1.31603 - 9.99628i) q^{59} +(0.0408012 + 0.0827367i) q^{61} +(0.819636 + 4.12059i) q^{62} +(5.03194 + 5.03194i) q^{64} +(9.71618 + 8.52086i) q^{65} +(5.04699 - 2.91388i) q^{67} +(4.00501 - 0.624883i) q^{68} +(0.0208865 - 0.158648i) q^{70} +(5.65982 + 1.12581i) q^{71} +(-6.75916 + 4.51633i) q^{73} +(-1.68381 + 4.96035i) q^{74} +(2.60500 - 0.342955i) q^{76} +(0.267554 - 0.0352242i) q^{77} +(1.72936 - 5.09453i) q^{79} +(3.15471 - 2.10791i) q^{80} +(-4.74300 - 0.943442i) q^{82} +(0.760640 - 5.77763i) q^{83} +(0.609173 - 14.6449i) q^{85} +(-0.717681 + 0.414353i) q^{86} +(13.6736 + 11.9914i) q^{88} +(-12.7569 - 12.7569i) q^{89} +(0.0316563 + 0.159147i) q^{91} +(-3.13568 - 6.35853i) q^{92} +(0.221278 + 1.68077i) q^{94} +(0.621403 - 9.48077i) q^{95} +(-3.62426 + 0.237547i) q^{97} +(-4.98995 + 4.98995i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 24 q^{2} - 8 q^{4} + 24 q^{5} - 8 q^{7} - 32 q^{10} + 24 q^{11} - 8 q^{13} + 24 q^{14} - 32 q^{19} + 24 q^{20} - 8 q^{22} + 24 q^{23} - 8 q^{25} - 32 q^{28} + 24 q^{29} - 8 q^{31} + 24 q^{32} - 56 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) $ 256 * q + 24 * q^2 - 8 * q^4 + 24 * q^5 - 8 * q^7 - 32 * q^10 + 24 * q^11 - 8 * q^13 + 24 * q^14 - 32 * q^19 + 24 * q^20 - 8 * q^22 + 24 * q^23 - 8 * q^25 - 32 * q^28 + 24 * q^29 - 8 * q^31 + 24 * q^32 - 56 * q^34 - 32 * q^37 - 8 * q^40 + 24 * q^41 + 16 * q^43 - 32 * q^46 - 96 * q^47 - 8 * q^49 - 16 * q^52 - 32 * q^55 - 216 * q^56 - 8 * q^58 + 24 * q^59 - 8 * q^61 - 96 * q^64 - 24 * q^65 + 24 * q^68 + 8 * q^70 - 32 * q^73 + 24 * q^74 - 8 * q^76 + 24 * q^77 - 8 * q^79 + 160 * q^82 + 24 * q^83 - 8 * q^85 - 192 * q^86 - 8 * q^88 - 128 * q^91 + 24 * q^92 - 8 * q^94 - 216 * q^95 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{16}\right)$

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 $

$2$	0.999782	+	0.131624i	0.706953	+	0.0930721i	0.475425	−	0.879756i	$-0.342294\pi$
$2$	0.999782	+	0.131624i	0.706953	+	0.0930721i	0.231528	+	0.972828i	$0.425628\pi$
$3$		0			0
$3$		0			0
$4$	−0.949612	−	0.254448i	−0.474806	−	0.127224i
$5$	−1.57233	+	3.18837i	−0.703167	+	1.42588i	0.192563	+	0.981285i	$0.438320\pi$
$5$	−1.57233	+	3.18837i	−0.703167	+	1.42588i	−0.895730	+	0.444598i	$0.853347\pi$
$6$		0			0
$7$	−0.0400335	+	0.0197423i	−0.0151312	+	0.00746190i	−0.449839	−	0.893110i	$-0.648518\pi$
$7$	−0.0400335	+	0.0197423i	−0.0151312	+	0.00746190i	0.434707	+	0.900572i	$0.356852\pi$
$8$	−2.77921	−	1.15119i	−0.982600	−	0.407006i
$9$		0			0
$10$	−1.99165	+	2.98072i	−0.629816	+	0.942586i
$11$	−5.72491	−	1.94335i	−1.72613	−	0.585941i	−0.730807	−	0.682584i	$-0.760856\pi$
$11$	−5.72491	−	1.94335i	−1.72613	−	0.585941i	−0.995319	+	0.0966431i	$0.969189\pi$
$12$		0			0
$13$	0.940868	−	3.51137i	0.260950	−	0.973878i	−0.703733	−	0.710464i	$-0.748485\pi$
$13$	0.940868	−	3.51137i	0.260950	−	0.973878i	0.964683	−	0.263414i	$-0.0848484\pi$
$14$	−0.0426233	+	0.0144687i	−0.0113916	+	0.00386691i
$15$		0			0
$16$	−0.924284	−	0.533636i	−0.231071	−	0.133409i
$17$	−3.77050	+	1.66834i	−0.914479	+	0.404632i
$17$	−3.77050	+	1.66834i	−0.914479	+	0.404632i
$18$		0			0
$19$	−2.46918	+	1.02277i	−0.566468	+	0.234639i	−0.647490	−	0.762074i	$-0.724181\pi$
$19$	−2.46918	+	1.02277i	−0.566468	+	0.234639i	0.0810227	+	0.996712i	$0.474181\pi$
$20$	2.30438	−	2.62764i	0.515275	−	0.587558i
$21$		0			0
$22$	−5.46788	−	2.69646i	−1.16575	−	0.574887i
$23$	4.75485	+	5.42187i	0.991455	+	1.13054i	0.991443	+	0.130537i	$0.0416702\pi$
$23$	4.75485	+	5.42187i	0.991455	+	1.13054i	1.10977e−5		1.00000i	$0.499996\pi$
$24$		0			0
$25$	−4.64968	−	6.05958i	−0.929935	−	1.21192i
$26$	1.40284	−	3.38676i	0.275120	−	0.664198i
$27$		0			0
$28$	0.0430397	−	0.00856112i	0.00813373	−	0.00161790i
$29$	−0.00257534	−	0.0392922i	−0.000478230	−	0.00729637i	0.997613	−	0.0690509i	$-0.0219971\pi$
$29$	−0.00257534	−	0.0392922i	−0.000478230	−	0.00729637i	−0.998091	+	0.0617545i	$0.980330\pi$
$30$		0			0
$31$	1.33921	+	3.94517i	0.240529	+	0.708574i	0.998420	+	0.0561934i	$0.0178963\pi$
$31$	1.33921	+	3.94517i	0.240529	+	0.708574i	−0.757891	+	0.652381i	$0.773770\pi$
$32$	3.91928	+	3.00737i	0.692838	+	0.531633i
$33$		0			0
$34$	−3.98927	+	1.17169i	−0.684154	+	0.200943i
$35$		−	0.158683i		−	0.0268223i
$36$		0			0
$37$	−1.01343	+	5.09486i	−0.166607	+	0.837589i	0.803574	+	0.595205i	$0.202929\pi$
$37$	−1.01343	+	5.09486i	−0.166607	+	0.837589i	−0.970180	+	0.242384i	$0.922071\pi$
$38$	−2.60326	+	0.697541i	−0.422304	+	0.113156i
$39$		0			0
$40$	8.04025	−	7.05111i	1.27127	−	1.11488i
$41$	−4.78533	−	0.313647i	−0.747343	−	0.0489834i	−0.313027	−	0.949744i	$-0.601343\pi$
$41$	−4.78533	−	0.313647i	−0.747343	−	0.0489834i	−0.434316	+	0.900761i	$0.643010\pi$
$42$		0			0
$43$	−0.651975	+	0.500278i	−0.0994252	+	0.0762916i	−0.657278	−	0.753648i	$-0.728292\pi$
$43$	−0.651975	+	0.500278i	−0.0994252	+	0.0762916i	0.557853	+	0.829940i	$0.311625\pi$
$44$	4.94197	+	3.30212i	0.745030	+	0.497813i
$45$		0			0
$46$	4.04017	+	6.04654i	0.595690	+	0.891513i
$47$	0.435110	+	1.62385i	0.0634673	+	0.236863i	0.990372	−	0.138435i	$-0.0442071\pi$
$47$	0.435110	+	1.62385i	0.0634673	+	0.236863i	−0.926904	+	0.375298i	$0.877540\pi$
$48$		0			0
$49$	−4.26012	+	5.55189i	−0.608588	+	0.793128i
$50$	−3.85108	−	6.67026i	−0.544625	−	0.943318i
$51$		0			0
$52$	−1.78692	+	3.09503i	−0.247801	+	0.429204i
$53$	1.17550	+	2.83792i	0.161468	+	0.389818i	0.983820	−	0.179161i	$-0.0573385\pi$
$53$	1.17550	+	2.83792i	0.161468	+	0.389818i	−0.822352	+	0.568979i	$0.807338\pi$
$54$		0			0
$55$	15.1976	−	15.1976i	2.04924	−	2.04924i
$56$	0.133989	−	0.00878208i	0.0179050	−	0.00117355i
$57$		0			0
$58$	0.00259700	−	0.0396226i	0.000341003	−	0.00520270i
$59$	−1.31603	−	9.99628i	−0.171333	−	1.30140i	−0.833697	−	0.552222i	$-0.813780\pi$
$59$	−1.31603	−	9.99628i	−0.171333	−	1.30140i	0.662364	−	0.749182i	$-0.269553\pi$
$60$		0			0
$61$	0.0408012	+	0.0827367i	0.00522406	+	0.0105933i	0.899469	−	0.436984i	$-0.143953\pi$
$61$	0.0408012	+	0.0827367i	0.00522406	+	0.0105933i	−0.894245	+	0.447578i	$0.852287\pi$
$62$	0.819636	+	4.12059i	0.104094	+	0.523315i
$63$		0			0
$64$	5.03194	+	5.03194i	0.628992	+	0.628992i
$65$	9.71618	+	8.52086i	1.20514	+	1.05688i
$66$		0			0
$67$	5.04699	−	2.91388i	0.616588	−	0.355987i	−0.158951	−	0.987286i	$-0.550811\pi$
$67$	5.04699	−	2.91388i	0.616588	−	0.355987i	0.775539	+	0.631299i	$0.217478\pi$
$68$	4.00501	−	0.624883i	0.485679	−	0.0757782i
$69$		0			0
$70$	0.0208865	−	0.158648i	0.00249641	−	0.0189621i
$71$	5.65982	+	1.12581i	0.671697	+	0.133609i	0.519144	−	0.854687i	$-0.326251\pi$
$71$	5.65982	+	1.12581i	0.671697	+	0.133609i	0.152552	+	0.988295i	$0.451251\pi$
$72$		0			0
$73$	−6.75916	+	4.51633i	−0.791100	+	0.528596i	−0.884227	−	0.467058i	$-0.845314\pi$
$73$	−6.75916	+	4.51633i	−0.791100	+	0.528596i	0.0931267	+	0.995654i	$0.470314\pi$
$74$	−1.68381	+	4.96035i	−0.195739	+	0.576629i
$75$		0			0
$76$	2.60500	−	0.342955i	0.298814	−	0.0393396i
$77$	0.267554	−	0.0352242i	0.0304906	−	0.00401417i
$78$		0			0
$79$	1.72936	−	5.09453i	0.194568	−	0.573179i	−0.805236	−	0.592954i	$-0.797962\pi$
$79$	1.72936	−	5.09453i	0.194568	−	0.573179i	0.999804	+	0.0197748i	$0.00629493\pi$
$80$	3.15471	−	2.10791i	0.352707	−	0.235671i
$81$		0			0
$82$	−4.74300	−	0.943442i	−0.523777	−	0.104186i
$83$	0.760640	−	5.77763i	0.0834911	−	0.634178i	−0.897625	−	0.440759i	$-0.854709\pi$
$83$	0.760640	−	5.77763i	0.0834911	−	0.634178i	0.981116	−	0.193418i	$-0.0619575\pi$
$84$		0			0
$85$	0.609173	−	14.6449i	0.0660740	−	1.58846i
$86$	−0.717681	+	0.414353i	−0.0773895	+	0.0446809i
$87$		0			0
$88$	13.6736	+	11.9914i	1.45761	+	1.27829i
$89$	−12.7569	−	12.7569i	−1.35223	−	1.35223i	−0.883161	−	0.469070i	$-0.844589\pi$
$89$	−12.7569	−	12.7569i	−1.35223	−	1.35223i	−0.469070	−	0.883161i	$-0.655411\pi$
$90$		0			0
$91$	0.0316563	+	0.159147i	0.00331848	+	0.0166832i
$92$	−3.13568	−	6.35853i	−0.326917	−	0.662923i
$93$		0			0
$94$	0.221278	+	1.68077i	0.0228230	+	0.173358i
$95$	0.621403	−	9.48077i	0.0637546	−	0.972707i
$96$		0			0
$97$	−3.62426	+	0.237547i	−0.367988	+	0.0241192i	−0.248276	−	0.968689i	$-0.579864\pi$
$97$	−3.62426	+	0.237547i	−0.367988	+	0.0241192i	−0.119712	+	0.992809i	$0.538197\pi$
$98$	−4.98995	+	4.98995i	−0.504061	+	0.504061i
$99$		0			0
$100$	2.87354	+	6.93735i	0.287354	+	0.693735i
$101$	−2.53423	+	4.38941i	−0.252165	+	0.436763i	−0.964122	−	0.265461i	$-0.914476\pi$
$101$	−2.53423	+	4.38941i	−0.252165	+	0.436763i	0.711956	+	0.702224i	$0.247809\pi$
$102$		0			0
$103$	−0.363059	−	0.628837i	−0.0357733	−	0.0619611i	0.847584	−	0.530661i	$-0.178056\pi$
$103$	−0.363059	−	0.628837i	−0.0357733	−	0.0619611i	−0.883358	+	0.468699i	$0.844723\pi$
$104$	−6.65711	+	8.67571i	−0.652783	+	0.850724i
$105$		0			0
$106$	0.801710	+	2.99202i	0.0778690	+	0.290611i
$107$	−1.35228	−	2.02383i	−0.130730	−	0.195651i	0.760330	−	0.649537i	$-0.225037\pi$
$107$	−1.35228	−	2.02383i	−0.130730	−	0.195651i	−0.891060	+	0.453886i	$0.850037\pi$
$108$		0			0
$109$	−7.52425	−	5.02754i	−0.720692	−	0.481551i	0.140339	−	0.990104i	$-0.455181\pi$
$109$	−7.52425	−	5.02754i	−0.720692	−	0.481551i	−0.861031	+	0.508552i	$0.830181\pi$
$110$	17.1946	−	13.1939i	1.63944	−	1.25799i
$111$		0			0
$112$	0.0475375	+	0.00311577i	0.00449187	+	0.000294413i
$113$	0.126876	−	0.111267i	0.0119355	−	0.0104671i	−0.653357	−	0.757050i	$-0.726640\pi$
$113$	0.126876	−	0.111267i	0.0119355	−	0.0104671i	0.665293	+	0.746583i	$0.268307\pi$
$114$		0			0
$115$	−24.7631	+	6.63526i	−2.30917	+	0.618741i
$116$	−0.00755223	+	0.0379676i	−0.000701207	+	0.00352520i
$117$		0			0
$118$		−	10.1673i		−	0.935978i
$119$	0.118009	−	0.141228i	0.0108179	−	0.0129463i
$120$		0			0
$121$	20.2711	+	15.5546i	1.84283	+	1.41405i
$122$	0.0299022	+	0.0880891i	0.00270722	+	0.00797521i
$123$		0			0
$124$	−0.267886	−	4.08714i	−0.0240568	−	0.367036i
$125$	9.19761	−	1.82952i	0.822659	−	0.163637i
$126$		0			0
$127$	−5.60153	+	13.5233i	−0.497055	+	1.20000i	0.454007	+	0.890998i	$0.349994\pi$
$127$	−5.60153	+	13.5233i	−0.497055	+	1.20000i	−0.951062	+	0.309000i	$0.900006\pi$
$128$	−1.64622	−	2.14540i	−0.145507	−	0.189628i
$129$		0			0
$130$	8.59252	+	9.79789i	0.753614	+	0.859332i
$131$	14.9561	+	7.37552i	1.30672	+	0.644402i	0.956354	−	0.292211i	$-0.0943910\pi$
$131$	14.9561	+	7.37552i	1.30672	+	0.644402i	0.350365	+	0.936613i	$0.386058\pi$
$132$		0			0
$133$	0.0786579	−	0.0896921i	0.00682050	−	0.00777729i
$134$	5.42943	−	2.24894i	0.469031	−	0.194279i
$135$		0			0
$136$	12.3996	−	0.296129i	1.06325	−	0.0253929i
$137$	7.73940	+	4.46834i	0.661221	+	0.381756i	0.792742	−	0.609557i	$-0.208653\pi$
$137$	7.73940	+	4.46834i	0.661221	+	0.381756i	−0.131521	+	0.991313i	$0.541986\pi$
$138$		0			0
$139$	−10.3891	+	3.52663i	−0.881194	+	0.299125i	−0.725122	−	0.688621i	$-0.758217\pi$
$139$	−10.3891	+	3.52663i	−0.881194	+	0.299125i	−0.156072	+	0.987746i	$0.549883\pi$
$140$	−0.0403765	+	0.150687i	−0.00341244	+	0.0127354i
$141$		0			0
$142$	5.51040	+	1.87053i	0.462422	+	0.156971i
$143$	−12.2102	+	18.2738i	−1.02107	+	1.52813i
$144$		0			0
$145$	0.129327	+	0.0535691i	0.0107400	+	0.00444867i
$146$	−7.35214	+	3.62568i	−0.608468	+	0.300063i
$147$		0			0
$148$	2.25874	−	4.58027i	0.185667	−	0.376496i
$149$	−9.01133	−	2.41458i	−0.738237	−	0.197810i	−0.129942	−	0.991522i	$-0.541479\pi$
$149$	−9.01133	−	2.41458i	−0.738237	−	0.197810i	−0.608294	+	0.793712i	$0.708146\pi$
$150$		0			0
$151$	8.85413	+	1.16567i	0.720539	+	0.0948607i	0.481873	−	0.876241i	$-0.339957\pi$
$151$	8.85413	+	1.16567i	0.720539	+	0.0948607i	0.238666	+	0.971102i	$0.423290\pi$
$152$	8.03975			0.652110
$153$		0			0
$154$	0.272132			0.0219291
$155$	−14.6844	−	1.93323i	−1.17948	−	0.155281i
$156$		0			0
$157$	−9.89256	−	2.65070i	−0.789512	−	0.211549i	−0.158538	−	0.987353i	$-0.550678\pi$
$157$	−9.89256	−	2.65070i	−0.789512	−	0.211549i	−0.630974	+	0.775804i	$0.717345\pi$
$158$	2.39954	−	4.86579i	0.190897	−	0.387102i
$159$		0			0
$160$	−15.7510	+	7.76754i	−1.24523	+	0.614078i
$161$	−0.297393	−	0.123184i	−0.0234379	−	0.00970829i
$162$		0			0
$163$	1.34058	−	2.00633i	0.105003	−	0.157148i	−0.775247	−	0.631658i	$-0.782375\pi$
$163$	1.34058	−	2.00633i	0.105003	−	0.157148i	0.880250	+	0.474510i	$0.157375\pi$
$164$	4.46440	+	1.51546i	0.348611	+	0.118337i
$165$		0			0
$166$	1.52095	−	5.67626i	0.118048	−	0.440563i
$167$	10.3361	−	3.50863i	0.799832	−	0.271506i	0.108549	−	0.994091i	$-0.465379\pi$
$167$	10.3361	−	3.50863i	0.799832	−	0.271506i	0.691282	+	0.722585i	$0.257046\pi$
$168$		0			0
$169$	−0.186131	−	0.107463i	−0.0143178	−	0.00826638i
$170$	2.53666	−	14.5615i	0.194553	−	1.11682i
$171$		0			0
$172$	0.746417	−	0.309176i	0.0569138	−	0.0235745i
$173$	−0.692519	+	0.789666i	−0.0526512	+	0.0600372i	−0.777566	−	0.628801i	$-0.783546\pi$
$173$	−0.692519	+	0.789666i	−0.0526512	+	0.0600372i	0.724915	+	0.688839i	$0.241879\pi$
$174$		0			0
$175$	0.305773	+	0.150790i	0.0231143	+	0.0113987i
$176$	4.25441	+	4.85122i	0.320688	+	0.365675i
$177$		0			0
$178$	−11.0750	−	14.4333i	−0.830109	−	1.08182i
$179$	3.32973	−	8.03868i	0.248876	−	0.600839i	−0.749233	−	0.662306i	$-0.769578\pi$
$179$	3.32973	−	8.03868i	0.248876	−	0.600839i	0.998109	+	0.0614667i	$0.0195778\pi$
$180$		0			0
$181$	−11.3744	+	2.26251i	−0.845453	+	0.168171i	−0.598766	−	0.800924i	$-0.704342\pi$
$181$	−11.3744	+	2.26251i	−0.845453	+	0.168171i	−0.246687	+	0.969095i	$0.579342\pi$
$182$	0.0107019	+	0.163279i	0.000793276	+	0.0121031i
$183$		0			0
$184$	−6.97315	−	20.5422i	−0.514067	−	1.51439i
$185$	−14.6508	−	11.2420i	−1.07715	−	0.826527i
$186$		0			0
$187$	24.8279	−	2.22373i	1.81560	−	0.162616i
$188$		−	1.65274i		−	0.120539i
$189$		0			0
$190$	1.86916	−	9.39691i	0.135603	−	0.681724i
$191$	−20.7138	+	5.55024i	−1.49880	+	0.401602i	−0.912697	−	0.408637i	$-0.866004\pi$
$191$	−20.7138	+	5.55024i	−1.49880	+	0.401602i	−0.586100	+	0.810238i	$0.699338\pi$
$192$		0			0
$193$	−0.399786	+	0.350603i	−0.0287772	+	0.0252369i	−0.673614	−	0.739084i	$-0.735259\pi$
$193$	−0.399786	+	0.350603i	−0.0287772	+	0.0252369i	0.644836	+	0.764321i	$0.276925\pi$
$194$	−3.65474	−	0.239544i	−0.262395	−	0.0171983i
$195$		0			0
$196$	5.45813	−	4.18817i	0.389866	−	0.299155i
$197$	6.66381	+	4.45262i	0.474777	+	0.317236i	0.769834	−	0.638244i	$-0.220339\pi$
$197$	6.66381	+	4.45262i	0.474777	+	0.317236i	−0.295057	+	0.955480i	$0.595339\pi$
$198$		0			0
$199$	1.66134	+	2.48637i	0.117769	+	0.176254i	0.885671	−	0.464314i	$-0.153699\pi$
$199$	1.66134	+	2.48637i	0.117769	+	0.176254i	−0.767902	+	0.640568i	$0.778699\pi$
$200$	5.94673	+	22.1935i	0.420497	+	1.56932i
$201$		0			0
$202$	−3.11143	+	4.05489i	−0.218919	+	0.285301i
$203$	0.000878819		0.00152216i	6.16810e−5		0.000106835i
$204$		0			0
$205$	8.52414	−	14.7642i	0.595352	−	1.03118i
$206$	−0.280210	−	0.676487i	−0.0195232	−	0.0471331i
$207$		0			0
$208$	−2.74342	+	2.74342i	−0.190222	+	0.190222i
$209$	16.1234	−	1.05678i	1.11528	−	0.0730992i
$210$		0			0
$211$	−0.791339	+	12.0735i	−0.0544780	+	0.831174i	0.879960	+	0.475048i	$0.157569\pi$
$211$	−0.791339	+	12.0735i	−0.0544780	+	0.831174i	−0.934438	+	0.356126i	$0.884097\pi$
$212$	−0.394171	−	2.99402i	−0.0270718	−	0.205630i
$213$		0			0
$214$	−1.08560	−	2.20139i	−0.0742103	−	0.150484i
$215$	−0.569951	−	2.86534i	−0.0388703	−	0.195414i
$216$		0			0
$217$	−0.131500	−	0.131500i	−0.00892680	−	0.00892680i
$218$	−6.86086	−	6.01682i	−0.464676	−	0.407510i
$219$		0			0
$220$	−18.2988	+	10.5648i	−1.23370	+	0.712279i
$221$	2.31062	+	14.8093i	0.155429	+	0.996180i
$222$		0			0
$223$	1.02008	−	7.74830i	0.0683098	−	0.518865i	−0.922745	−	0.385411i	$-0.874060\pi$
$223$	1.02008	−	7.74830i	0.0683098	−	0.518865i	0.991055	−	0.133454i	$-0.0426069\pi$
$224$	−0.216275	−	0.0430198i	−0.0144505	−	0.00287438i
$225$		0			0
$226$	0.141494	−	0.0945431i	0.00941203	−	0.00628892i
$227$	1.90304	−	5.60618i	0.126309	−	0.372095i	−0.865319	−	0.501222i	$-0.832884\pi$
$227$	1.90304	−	5.60618i	0.126309	−	0.372095i	0.991628	+	0.129127i	$0.0412174\pi$
$228$		0			0
$229$	−13.7620	+	1.81181i	−0.909422	+	0.119728i	−0.570700	−	0.821159i	$-0.693328\pi$
$229$	−13.7620	+	1.81181i	−0.909422	+	0.119728i	−0.338722	+	0.940886i	$0.609995\pi$
$230$	−25.6311	+	3.37439i	−1.69006	+	0.222501i
$231$		0			0
$232$	−0.0380752	+	0.112166i	−0.00249976	+	0.00736405i
$233$	−12.5770	+	8.40367i	−0.823946	+	0.550543i	−0.894553	−	0.446961i	$-0.852506\pi$
$233$	−12.5770	+	8.40367i	−0.823946	+	0.550543i	0.0706075	+	0.997504i	$0.477506\pi$
$234$		0			0
$235$	−5.86158	−	1.16594i	−0.382367	−	0.0760576i
$236$	−1.29381	+	9.82745i	−0.0842197	+	0.639712i
$237$		0			0
$238$	0.136572	−	0.125664i	0.00885267	−	0.00814561i
$239$	4.27091	−	2.46581i	0.276262	−	0.159500i	−0.355468	−	0.934689i	$-0.615678\pi$
$239$	4.27091	−	2.46581i	0.276262	−	0.159500i	0.631730	+	0.775188i	$0.282345\pi$
$240$		0			0
$241$	11.2735	+	9.88659i	0.726189	+	0.636851i	0.940453	−	0.339925i	$-0.110402\pi$
$241$	11.2735	+	9.88659i	0.726189	+	0.636851i	−0.214263	+	0.976776i	$0.568735\pi$
$242$	18.2194	+	18.2194i	1.17119	+	1.17119i
$243$		0			0
$244$	−0.0176932	−	0.0889495i	−0.00113269	−	0.00569441i
$245$	−11.0032	−	22.3122i	−0.702967	−	1.42548i
$246$		0			0
$247$	1.26814	+	9.63247i	0.0806897	+	0.612899i
$248$	0.819696	−	12.5061i	0.0520508	−	0.794141i
$249$		0			0
$250$	9.43641	−	0.618495i	0.596811	−	0.0391171i
$251$	−2.57518	+	2.57518i	−0.162544	+	0.162544i	−0.783693	−	0.621149i	$-0.786666\pi$
$251$	−2.57518	+	2.57518i	−0.162544	+	0.162544i	0.621149	+	0.783693i	$0.286666\pi$
$252$		0			0
$253$	−16.6845	−	40.2800i	−1.04895	−	2.53238i
$254$	−7.38030	+	12.7830i	−0.463081	+	0.802080i
$255$		0			0
$256$	−8.47971	−	14.6873i	−0.529982	−	0.917956i
$257$	−11.5866	+	15.0999i	−0.722751	+	0.941907i	−0.999821	−	0.0189424i	$-0.993970\pi$
$257$	−11.5866	+	15.0999i	−0.722751	+	0.941907i	0.277070	+	0.960850i	$0.410637\pi$
$258$		0			0
$259$	−0.0600132	−	0.223972i	−0.00372904	−	0.0139170i
$260$	−7.05849	−	10.5638i	−0.437749	−	0.655138i
$261$		0			0
$262$	13.9820	+	9.34249i	0.863812	+	0.577181i
$263$	−9.93307	+	7.62191i	−0.612499	+	0.469987i	−0.867826	−	0.496867i	$-0.834484\pi$
$263$	−9.93307	+	7.62191i	−0.612499	+	0.469987i	0.255327	+	0.966855i	$0.417817\pi$
$264$		0			0
$265$	−10.8966	−	0.714201i	−0.669373	−	0.0438730i
$266$	0.0904464	−	0.0793193i	0.00554562	−	0.00486338i
$267$		0			0
$268$	−5.53412	+	1.48286i	−0.338050	+	0.0905802i
$269$	−3.23153	+	16.2460i	−0.197030	+	0.990536i	0.748036	+	0.663658i	$0.230997\pi$
$269$	−3.23153	+	16.2460i	−0.197030	+	0.990536i	−0.945066	+	0.326879i	$0.894003\pi$
$270$		0			0
$271$			21.3512i			1.29699i	0.761218	+	0.648496i	$0.224602\pi$
$271$			21.3512i			1.29699i	−0.761218	+	0.648496i	$0.775398\pi$
$272$	4.37530	+	0.470049i	0.265291	+	0.0285009i
$273$		0			0
$274$	7.14957	+	5.48606i	0.431921	+	0.331425i
$275$	14.8431	+	43.7265i	0.895075	+	2.63681i
$276$		0			0
$277$	−2.06864	−	31.5613i	−0.124292	−	1.89633i	−0.373116	−	0.927785i	$-0.621711\pi$
$277$	−2.06864	−	31.5613i	−0.124292	−	1.89633i	0.248824	−	0.968549i	$-0.419956\pi$
$278$	−10.8510	+	2.15841i	−0.650803	+	0.129453i
$279$		0			0
$280$	−0.182674	+	0.441014i	−0.0109168	+	0.0263556i
$281$	−1.63529	−	2.13116i	−0.0975535	−	0.127134i	0.742026	−	0.670371i	$-0.233865\pi$
$281$	−1.63529	−	2.13116i	−0.0975535	−	0.127134i	−0.839579	+	0.543237i	$0.817198\pi$
$282$		0			0
$283$	2.36408	+	2.69572i	0.140530	+	0.160244i	0.817823	−	0.575469i	$-0.195181\pi$
$283$	2.36408	+	2.69572i	0.140530	+	0.160244i	−0.677293	+	0.735713i	$0.736847\pi$
$284$	−5.08817	−	2.50921i	−0.301927	−	0.148894i
$285$		0			0
$286$	−14.6128	+	16.6627i	−0.864073	+	0.985286i
$287$	0.197765	−	0.0819171i	0.0116737	−	0.00483541i
$288$		0			0
$289$	11.4333	−	12.5810i	0.672545	−	0.740056i
$290$	0.122248	+	0.0705800i	0.00717866	+	0.00414460i
$291$		0			0
$292$	7.56775	−	2.56890i	0.442869	−	0.150334i
$293$	2.78802	−	10.4050i	0.162878	−	0.607868i	−0.835423	−	0.549607i	$-0.814778\pi$
$293$	2.78802	−	10.4050i	0.162878	−	0.607868i	0.998301	−	0.0582617i	$-0.0185558\pi$
$294$		0			0
$295$	33.9411	+	11.5214i	1.97613	+	0.670804i
$296$	8.68167	−	12.9930i	0.504612	−	0.755205i
$297$		0			0
$298$	−8.69155	−	3.60016i	−0.503488	−	0.208551i
$299$	23.5118	−	11.5948i	1.35972	−	0.670542i
$300$		0			0
$301$	0.0162242	−	0.0328993i	0.000935145	−	0.00189629i
$302$	8.69877	+	2.33083i	0.500558	+	0.134124i
$303$		0			0
$304$	2.82800	+	0.372314i	0.162197	+	0.0213537i
$305$	−0.327948			−0.0187783
$306$		0			0
$307$	1.09298			0.0623795			0.0311897	−	0.999513i	$-0.490070\pi$
$307$	1.09298			0.0623795			0.0311897	+	0.999513i	$0.490070\pi$
$308$	−0.263036	−	0.0346293i	−0.0149878	−	0.00197319i
$309$		0			0
$310$	−14.4267	−	3.86562i	−0.819381	−	0.219552i
$311$	14.6585	−	29.7246i	0.831209	−	1.68553i	0.108797	−	0.994064i	$-0.465300\pi$
$311$	14.6585	−	29.7246i	0.831209	−	1.68553i	0.722413	−	0.691462i	$-0.243033\pi$
$312$		0			0
$313$	−3.69317	+	1.82127i	−0.208750	+	0.102944i	−0.543659	−	0.839306i	$-0.682961\pi$
$313$	−3.69317	+	1.82127i	−0.208750	+	0.102944i	0.334908	+	0.942251i	$0.391295\pi$
$314$	−9.54151	−	3.95222i	−0.538459	−	0.223037i
$315$		0			0
$316$	−2.93851	+	4.39779i	−0.165304	+	0.247395i
$317$	−19.5630	−	6.64074i	−1.09877	−	0.372981i	−0.287574	−	0.957759i	$-0.592849\pi$
$317$	−19.5630	−	6.64074i	−1.09877	−	0.372981i	−0.811194	+	0.584777i	$0.801182\pi$
$318$		0			0
$319$	−0.0616147	+	0.229949i	−0.00344976	+	0.0128747i
$320$	−23.9555	+	8.13181i	−1.33916	+	0.454582i
$321$		0			0
$322$	−0.281115	−	0.162302i	−0.0156659	−	0.00904471i
$323$	7.60369	−	7.97576i	0.423081	−	0.443783i
$324$		0			0
$325$	−25.6521	+	10.6255i	−1.42292	+	0.589394i
$326$	1.60437	−	1.82944i	0.0888580	−	0.101323i
$327$		0			0
$328$	12.9384	+	6.38050i	0.714402	+	0.352304i
$329$	−0.0494776	−	0.0564184i	−0.00272779	−	0.00311045i
$330$		0			0
$331$	−8.78625	−	11.4505i	−0.482936	−	0.629375i	0.486805	−	0.873511i	$-0.338162\pi$
$331$	−8.78625	−	11.4505i	−0.482936	−	0.629375i	−0.969741	+	0.244136i	$0.921496\pi$
$332$	−2.19242	+	5.29297i	−0.120325	+	0.290489i
$333$		0			0
$334$	10.7957	−	2.14739i	0.590713	−	0.117500i
$335$	1.35500	+	20.6733i	0.0740314	+	1.12950i
$336$		0			0
$337$	8.74316	+	25.7565i	0.476270	+	1.40305i	0.874171	+	0.485618i	$0.161405\pi$
$337$	8.74316	+	25.7565i	0.476270	+	1.40305i	−0.397901	+	0.917428i	$0.630261\pi$
$338$	−0.171946	−	0.131939i	−0.00935263	−	0.00717653i
$339$		0			0
$340$	−4.30485	+	13.7520i	−0.233463	+	0.745806i
$341$		−	25.1883i		−	1.36402i
$342$		0			0
$343$	0.121897	−	0.612820i	0.00658184	−	0.0330891i
$344$	2.38789	−	0.639833i	0.128746	−	0.0344975i
$345$		0			0
$346$	−0.796307	+	0.698342i	−0.0428097	+	0.0375431i
$347$	32.4168	+	2.12471i	1.74023	+	0.114060i	0.902131	−	0.431463i	$-0.142002\pi$
$347$	32.4168	+	2.12471i	1.74023	+	0.114060i	0.838096	+	0.545523i	$0.183669\pi$
$348$		0			0
$349$	−21.9139	+	16.8152i	−1.17303	+	0.900095i	−0.996450	−	0.0841918i	$-0.973169\pi$
$349$	−21.9139	+	16.8152i	−1.17303	+	0.900095i	−0.176577	+	0.984287i	$0.556502\pi$
$350$	0.285859	+	0.191005i	0.0152798	+	0.0102096i
$351$		0			0
$352$	−16.5932	−	24.8335i	−0.884420	−	1.32363i
$353$	−6.83386	−	25.5043i	−0.363729	−	1.35746i	−0.869135	−	0.494575i	$-0.835324\pi$
$353$	−6.83386	−	25.5043i	−0.363729	−	1.35746i	0.505406	−	0.862882i	$-0.331343\pi$
$354$		0			0
$355$	−12.4886	+	16.2754i	−0.662826	+	0.863811i
$356$	8.86816	+	15.3601i	0.470011	+	0.814084i
$357$		0			0
$358$	4.38709	−	7.59866i	0.231865	−	0.401602i
$359$	−3.39378	−	8.19330i	−0.179117	−	0.432426i	0.808665	−	0.588269i	$-0.200190\pi$
$359$	−3.39378	−	8.19330i	−0.179117	−	0.432426i	−0.987782	+	0.155843i	$0.950190\pi$
$360$		0			0
$361$	−8.38425	+	8.38425i	−0.441276	+	0.441276i
$362$	−11.6697	+	0.764874i	−0.613347	+	0.0402009i
$363$		0			0
$364$	0.0104334	−	0.159183i	0.000546859	−	0.00834345i
$365$	−3.77209	−	28.6519i	−0.197440	−	1.49971i
$366$		0			0
$367$	16.4128	+	33.2819i	0.856742	+	1.73730i	0.651590	+	0.758571i	$0.274102\pi$
$367$	16.4128	+	33.2819i	0.856742	+	1.73730i	0.205152	+	0.978730i	$0.434231\pi$
$368$	−1.50153	−	7.54870i	−0.0782727	−	0.393503i
$369$		0			0
$370$	−13.1679	−	13.1679i	−0.684568	−	0.684568i
$371$	−0.103087	−	0.0904045i	−0.00535199	−	0.00469357i
$372$		0			0
$373$	12.4589	−	7.19313i	0.645096	−	0.372446i	−0.141479	−	0.989941i	$-0.545186\pi$
$373$	12.4589	−	7.19313i	0.645096	−	0.372446i	0.786575	+	0.617495i	$0.211852\pi$
$374$	25.1152	+	1.04470i	1.29868	+	0.0540200i
$375$		0			0
$376$	0.660095	−	5.01392i	0.0340418	−	0.258573i
$377$	−0.140392	−	0.0279258i	−0.00723057	−	0.00143825i
$378$		0			0
$379$	13.9109	−	9.29500i	0.714557	−	0.477452i	−0.144387	−	0.989521i	$-0.546121\pi$
$379$	13.9109	−	9.29500i	0.714557	−	0.477452i	0.858944	+	0.512069i	$0.171121\pi$
$380$	−3.00245	+	8.84494i	−0.154023	+	0.453736i
$381$		0			0
$382$	−21.4398	+	2.82261i	−1.09696	+	0.144417i
$383$	−36.2651	+	4.77439i	−1.85306	+	0.243960i	−0.972983	−	0.230876i	$-0.925841\pi$
$383$	−36.2651	+	4.77439i	−1.85306	+	0.243960i	−0.880075	+	0.474835i	$0.842508\pi$
$384$		0			0
$385$	−0.308376	+	0.908446i	−0.0157163	+	0.0462987i
$386$	−0.445846	+	0.297905i	−0.0226930	+	0.0151630i
$387$		0			0
$388$	3.50209	+	0.696608i	0.177791	+	0.0353649i
$389$	2.30488	−	17.5073i	0.116862	−	0.887655i	−0.828124	−	0.560545i	$-0.810592\pi$
$389$	2.30488	−	17.5073i	0.116862	−	0.887655i	0.944986	−	0.327110i	$-0.106075\pi$
$390$		0			0
$391$	−26.9737	−	12.5104i	−1.36412	−	0.632679i
$392$	18.2310	−	10.5257i	0.920806	−	0.531628i
$393$		0			0
$394$	6.07629	+	5.32877i	0.306119	+	0.268459i
$395$	13.5241	+	13.5241i	0.680472	+	0.680472i
$396$		0			0
$397$	−3.93979	−	19.8067i	−0.197732	−	0.994068i	−0.944382	−	0.328850i	$-0.893339\pi$
$397$	−3.93979	−	19.8067i	−0.197732	−	0.994068i	0.746650	−	0.665217i	$-0.231661\pi$
$398$	1.33371	+	2.70450i	0.0668530	+	0.135564i
$399$		0			0
$400$	1.06402	+	8.08200i	0.0532008	+	0.404100i
$401$	−0.917905	+	14.0045i	−0.0458380	+	0.699352i	0.911666	+	0.410932i	$0.134797\pi$
$401$	−0.917905	+	14.0045i	−0.0458380	+	0.699352i	−0.957504	+	0.288420i	$0.906870\pi$
$402$		0			0
$403$	15.1130	−	0.990556i	0.752831	−	0.0493431i
$404$	3.52341	−	3.52341i	0.175296	−	0.175296i
$405$		0			0
$406$	0.000678275		0.00163750i	3.36622e−5		8.12678e-5i
$407$	15.7029	−	27.1982i	0.778362	−	1.34816i
$408$		0			0
$409$	2.43755	+	4.22196i	0.120529	+	0.208762i	0.919976	−	0.391974i	$-0.128208\pi$
$409$	2.43755	+	4.22196i	0.120529	+	0.208762i	−0.799447	+	0.600736i	$0.794874\pi$
$410$	10.4656	−	13.6390i	0.516860	−	0.673584i
$411$		0			0
$412$	0.184759	+	0.689531i	0.00910243	+	0.0339707i
$413$	0.250035	+	0.374204i	0.0123034	+	0.0184134i
$414$		0			0
$415$	17.2253	+	11.5096i	0.845555	+	0.564982i
$416$	14.2475	−	10.9325i	0.698541	−	0.536010i
$417$		0			0
$418$	16.2590	+	1.06567i	0.795253	+	0.0521236i
$419$	−20.0238	+	17.5604i	−0.978226	+	0.857881i	−0.989859	−	0.142051i	$-0.954630\pi$
$419$	−20.0238	+	17.5604i	−0.978226	+	0.857881i	0.0116336	+	0.999932i	$0.496297\pi$
$420$		0			0
$421$	32.1037	−	8.60215i	1.56464	−	0.419243i	0.630509	−	0.776182i	$-0.282846\pi$
$421$	32.1037	−	8.60215i	1.56464	−	0.419243i	0.934128	+	0.356939i	$0.116180\pi$
$422$	−2.38033	+	11.9667i	−0.115872	+	0.582530i
$423$		0			0
$424$		−	9.24039i		−	0.448753i
$425$	27.6410	+	15.0904i	1.34079	+	0.731990i
$426$		0			0
$427$	−0.00326683	−	0.00250673i	−0.000158093	−	0.000121309i
$428$	0.769184	+	2.26594i	0.0371799	+	0.109529i
$429$		0			0
$430$	−0.192680	−	2.93973i	−0.00929187	−	0.141767i
$431$	19.7216	−	3.92286i	0.949955	−	0.188958i	0.304291	−	0.952579i	$-0.401581\pi$
$431$	19.7216	−	3.92286i	0.949955	−	0.188958i	0.645664	+	0.763622i	$0.276581\pi$
$432$		0			0
$433$	1.73656	−	4.19243i	0.0834538	−	0.201475i	−0.876644	−	0.481139i	$-0.840223\pi$
$433$	1.73656	−	4.19243i	0.0834538	−	0.201475i	0.960098	+	0.279664i	$0.0902231\pi$
$434$	−0.114163	−	0.148780i	−0.00547999	−	0.00714166i
$435$		0			0
$436$	5.86587	+	6.68874i	0.280924	+	0.320333i
$437$	−17.2859	−	8.52444i	−0.826895	−	0.407779i
$438$		0			0
$439$	1.17259	−	1.33709i	0.0559648	−	0.0638157i	−0.723180	−	0.690660i	$-0.757320\pi$
$439$	1.17259	−	1.33709i	0.0559648	−	0.0638157i	0.779145	+	0.626844i	$0.215654\pi$
$440$	−59.7325	+	24.7420i	−2.84763	+	1.17953i
$441$		0			0
$442$	0.360864	+	15.1102i	0.0171646	+	0.718718i
$443$	26.7176	+	15.4254i	1.26939	+	0.732883i	0.974873	−	0.222763i	$-0.0715077\pi$
$443$	26.7176	+	15.4254i	1.26939	+	0.732883i	0.294518	+	0.955646i	$0.404841\pi$
$444$		0			0
$445$	60.7319	−	20.6157i	2.87897	−	0.977278i
$446$	2.03972	−	7.61235i	0.0965837	−	0.360455i
$447$		0			0
$448$	−0.300788	−	0.102104i	−0.0142109	−	0.00482395i
$449$	−19.7458	+	29.5517i	−0.931861	+	1.39463i	−0.0130574	+	0.999915i	$0.504156\pi$
$449$	−19.7458	+	29.5517i	−0.931861	+	1.39463i	−0.918804	+	0.394714i	$0.870844\pi$
$450$		0			0
$451$	26.7861	+	11.0952i	1.26131	+	0.522450i
$452$	−0.148795	+	0.0733774i	−0.00699872	+	0.00345138i
$453$		0			0
$454$	2.64053	−	5.35447i	0.123926	−	0.251298i
$455$	−0.557194	−	0.149300i	−0.0261217	−	0.00699928i
$456$		0			0
$457$	−6.03354	−	0.794331i	−0.282237	−	0.0371572i	−0.0119214	−	0.999929i	$-0.503795\pi$
$457$	−6.03354	−	0.794331i	−0.282237	−	0.0371572i	−0.270316	+	0.962772i	$0.587128\pi$
$458$	−13.9975			−0.654061
$459$		0			0
$460$	25.2037			1.17513
$461$	38.1625	+	5.02418i	1.77740	+	0.233999i	0.946564	−	0.322515i	$-0.104528\pi$
$461$	38.1625	+	5.02418i	1.77740	+	0.233999i	0.830838	+	0.556514i	$0.187861\pi$
$462$		0			0
$463$	18.8431	+	5.04899i	0.875712	+	0.234646i	0.668556	−	0.743662i	$-0.266913\pi$
$463$	18.8431	+	5.04899i	0.875712	+	0.234646i	0.207156	+	0.978308i	$0.433579\pi$
$464$	−0.0185874	+	0.0376914i	−0.000862896	+	0.00174978i
$465$		0			0
$466$	−13.6804	+	6.74641i	−0.633731	+	0.312522i
$467$	−1.38122	−	0.572119i	−0.0639152	−	0.0264745i	0.350497	−	0.936564i	$-0.386013\pi$
$467$	−1.38122	−	0.572119i	−0.0639152	−	0.0264745i	−0.414412	+	0.910089i	$0.636013\pi$
$468$		0			0
$469$	−0.144522	+	0.216292i	−0.00667340	+	0.00998744i
$470$	−5.70684	−	1.93721i	−0.263237	−	0.0893568i
$471$		0			0
$472$	−7.85004	+	29.2968i	−0.361328	+	1.34849i
$473$	4.70471	−	1.59703i	0.216323	−	0.0734317i
$474$		0			0
$475$	17.6784	+	10.2066i	0.811140	+	0.468312i
$476$	−0.147998	+	0.104085i	−0.00678348	+	0.00477071i
$477$		0			0
$478$	4.59454	−	1.90312i	0.210149	−	0.0870467i
$479$	−1.82949	+	2.08614i	−0.0835917	+	0.0953181i	−0.792124	−	0.610361i	$-0.791024\pi$
$479$	−1.82949	+	2.08614i	−0.0835917	+	0.0953181i	0.708532	+	0.705679i	$0.249358\pi$
$480$		0			0
$481$	16.9364	+	8.35211i	0.772233	+	0.380823i
$482$	9.96972	+	11.3683i	0.454108	+	0.517811i
$483$		0			0
$484$	−15.2919	−	19.9288i	−0.695086	−	0.905854i
$485$	4.94115	−	11.9290i	0.224366	−	0.541667i
$486$		0			0
$487$	−20.5857	+	4.09475i	−0.932828	+	0.185551i	−0.638033	−	0.770009i	$-0.720252\pi$
$487$	−20.5857	+	4.09475i	−0.932828	+	0.185551i	−0.294795	+	0.955560i	$0.595252\pi$
$488$	−0.0181498	−	0.276913i	−0.000821603	−	0.0125352i
$489$		0			0
$490$	−8.06396	−	23.7557i	−0.364293	−	1.07317i
$491$	18.9495	+	14.5405i	0.855180	+	0.656202i	0.940367	−	0.340163i	$-0.110482\pi$
$491$	18.9495	+	14.5405i	0.855180	+	0.656202i	−0.0851870	+	0.996365i	$0.527149\pi$
$492$		0			0
$493$	0.0752631	+	0.143854i	0.00338968	+	0.00647888i
$494$			9.79728i			0.440801i
$495$		0			0
$496$	0.867479	−	4.36111i	0.0389509	−	0.195820i
$497$	−0.248808	+	0.0666679i	−0.0111606	+	0.00299047i
$498$		0			0
$499$	−1.64660	+	1.44403i	−0.0737120	+	0.0646437i	−0.695409	−	0.718614i	$-0.744777\pi$
$499$	−1.64660	+	1.44403i	−0.0737120	+	0.0646437i	0.621697	+	0.783258i	$0.286443\pi$
$500$	−9.19968	−	0.602979i	−0.411422	−	0.0269660i
$501$		0			0
$502$	−2.91357	+	2.23566i	−0.130039	+	0.0997825i
$503$	13.6455	+	9.11766i	0.608425	+	0.406536i	0.821262	−	0.570551i	$-0.193270\pi$
$503$	13.6455	+	9.11766i	0.608425	+	0.406536i	−0.212837	+	0.977088i	$0.568270\pi$
$504$		0			0
$505$	−10.0104	−	14.9817i	−0.445458	−	0.666675i
$506$	−11.3791	−	42.4673i	−0.505862	−	1.88790i
$507$		0			0
$508$	8.76025	−	11.4166i	0.388673	−	0.506529i
$509$	−2.71304	−	4.69913i	−0.120254	−	0.208285i	0.799614	−	0.600514i	$-0.205037\pi$
$509$	−2.71304	−	4.69913i	−0.120254	−	0.208285i	−0.919868	+	0.392229i	$0.871704\pi$
$510$		0			0
$511$	0.181430	−	0.314246i	0.00802598	−	0.0139014i
$512$	−4.47495	−	10.8035i	−0.197767	−	0.477451i
$513$		0			0
$514$	−13.5716	+	13.5716i	−0.598616	+	0.598616i
$515$	2.57581	−	0.168828i	0.113504	−	0.00743944i
$516$		0			0
$517$	0.664741	−	10.1420i	0.0292353	−	0.446044i
$518$	−0.0305200	−	0.231823i	−0.00134097	−	0.0101857i
$519$		0			0
$520$	−17.1942	−	34.8664i	−0.754016	−	1.52899i
$521$	5.58058	+	28.0555i	0.244490	+	1.22913i	0.886606	+	0.462525i	$0.153057\pi$
$521$	5.58058	+	28.0555i	0.244490	+	1.22913i	−0.642116	+	0.766607i	$0.721943\pi$
$522$		0			0
$523$	6.31889	+	6.31889i	0.276306	+	0.276306i	0.831632	−	0.555326i	$-0.187407\pi$
$523$	6.31889	+	6.31889i	0.276306	+	0.276306i	−0.555326	+	0.831632i	$0.687407\pi$
$524$	−12.3258	−	10.8094i	−0.538454	−	0.472212i
$525$		0			0
$526$	−10.9341	+	6.31282i	−0.476751	+	0.275252i
$527$	−11.6314	−	12.6410i	−0.506670	−	0.550651i
$528$		0			0
$529$	−3.78594	+	28.7571i	−0.164606	+	1.25031i
$530$	−10.8002	−	2.14830i	−0.469132	−	0.0933161i
$531$		0			0
$532$	−0.0975164	+	0.0651584i	−0.00422787	+	0.00282498i
$533$	−5.60369	+	16.5079i	−0.242723	+	0.715038i
$534$		0			0
$535$	8.57897	−	1.12944i	0.370901	−	0.0488301i
$536$	−17.3811	+	2.28826i	−0.750748	+	0.0988379i
$537$		0			0
$538$	−5.36919	+	15.8171i	−0.231482	+	0.681924i
$539$	35.1780	−	23.5052i	1.51523	−	1.01244i
$540$		0			0
$541$	24.1708	+	4.80786i	1.03918	+	0.206706i	0.685055	−	0.728491i	$-0.259778\pi$
$541$	24.1708	+	4.80786i	1.03918	+	0.206706i	0.354127	+	0.935197i	$0.384778\pi$
$542$	−2.81033	+	21.3465i	−0.120714	+	0.916912i
$543$		0			0
$544$	−19.7950	−	4.80058i	−0.848702	−	0.205823i
$545$	27.8603	−	16.0851i	1.19340	−	0.689011i
$546$		0			0
$547$	−30.8714	−	27.0735i	−1.31997	−	1.15758i	−0.975799	−	0.218671i	$-0.929828\pi$
$547$	−30.8714	−	27.0735i	−1.31997	−	1.15758i	−0.344168	−	0.938908i	$-0.611839\pi$
$548$	−6.21246	−	6.21246i	−0.265383	−	0.265383i
$549$		0			0
$550$	9.08446	+	45.6707i	0.387363	+	1.94740i
$551$	0.0465457	+	0.0943853i	0.00198291	+	0.00402095i
$552$		0			0
$553$	0.0313456	+	0.238093i	0.00133295	+	0.0101248i
$554$	2.08603	−	31.8267i	0.0886270	−	1.35219i
$555$		0			0
$556$	10.7630	−	0.705443i	0.456452	−	0.0299174i
$557$	4.89600	−	4.89600i	0.207450	−	0.207450i	−0.595733	−	0.803183i	$-0.703138\pi$
$557$	4.89600	−	4.89600i	0.207450	−	0.207450i	0.803183	+	0.595733i	$0.203138\pi$
$558$		0			0
$559$	1.14324	+	2.76002i	0.0483537	+	0.116736i
$560$	−0.0846789	+	0.146668i	−0.00357834	+	0.00619786i
$561$		0			0
$562$	−1.35443	−	2.34594i	−0.0571331	−	0.0989574i
$563$	−16.1053	+	20.9888i	−0.678757	+	0.884573i	−0.998007	−	0.0630974i	$-0.979902\pi$
$563$	−16.1053	+	20.9888i	−0.678757	+	0.884573i	0.319251	+	0.947670i	$0.396569\pi$
$564$		0			0
$565$	0.155270	+	0.579477i	0.00653227	+	0.0243788i
$566$	2.00875	+	3.00630i	0.0844339	+	0.126364i
$567$		0			0
$568$	−14.4338	−	9.64436i	−0.605629	−	0.404668i
$569$	−8.41736	+	6.45887i	−0.352874	+	0.270770i	−0.769953	−	0.638100i	$-0.779720\pi$
$569$	−8.41736	+	6.45887i	−0.352874	+	0.270770i	0.417079	+	0.908870i	$0.363054\pi$
$570$		0			0
$571$	−31.1973	−	2.04478i	−1.30557	−	0.0855713i	−0.603316	−	0.797502i	$-0.706154\pi$
$571$	−31.1973	−	2.04478i	−1.30557	−	0.0855713i	−0.702250	+	0.711931i	$0.747821\pi$
$572$	16.2447	−	14.2462i	0.679224	−	0.595664i
$573$		0			0
$574$	0.208505	−	0.0558686i	0.00870281	−	0.00233191i
$575$	10.7457	−	54.0223i	0.448127	−	2.25289i
$576$		0			0
$577$		−	2.52465i		−	0.105103i	−0.998618	−	0.0525513i	$-0.983265\pi$
$577$		−	2.52465i		−	0.105103i	0.998618	−	0.0525513i	$-0.0167353\pi$
$578$	13.0867	−	11.0733i	0.544336	−	0.460589i
$579$		0			0
$580$	−0.109180	−	0.0837769i	−0.00453346	−	0.00347865i
$581$	0.0836129	+	0.246316i	0.00346885	+	0.0102189i
$582$		0			0
$583$	−1.21460	−	18.5312i	−0.0503036	−	0.767485i
$584$	23.9843	−	4.77077i	0.992476	−	0.197416i
$585$		0			0
$586$	4.15696	−	10.0358i	0.171723	−	0.414575i
$587$	13.5376	+	17.6425i	0.558756	+	0.728184i	0.984251	−	0.176776i	$-0.0565669\pi$
$587$	13.5376	+	17.6425i	0.558756	+	0.728184i	−0.425496	+	0.904961i	$0.639900\pi$
$588$		0			0
$589$	−7.34172	−	8.37163i	−0.302510	−	0.344947i
$590$	32.4172	+	15.9864i	1.33459	+	0.658149i
$591$		0			0
$592$	3.65549	−	4.16829i	0.150240	−	0.171316i
$593$	33.8563	−	14.0237i	1.39031	−	0.575885i	0.443092	−	0.896476i	$-0.353881\pi$
$593$	33.8563	−	14.0237i	1.39031	−	0.575885i	0.947218	+	0.320591i	$0.103881\pi$
$594$		0			0
$595$	0.264737	+	0.598314i	0.0108532	+	0.0245285i
$596$	7.94288	+	4.58582i	0.325353	+	0.187843i
$597$		0			0
$598$	25.0329	−	8.49751i	1.02367	−	0.347489i
$599$	4.68679	−	17.4913i	0.191497	−	0.714677i	−0.801649	−	0.597795i	$-0.796044\pi$
$599$	4.68679	−	17.4913i	0.191497	−	0.714677i	0.993146	−	0.116882i	$-0.0372898\pi$
$600$		0			0
$601$	−23.5054	−	7.97899i	−0.958803	−	0.325470i	−0.202200	−	0.979344i	$-0.564809\pi$
$601$	−23.5054	−	7.97899i	−0.958803	−	0.325470i	−0.756603	+	0.653874i	$0.773143\pi$
$602$	0.0205510	−	0.0307567i	0.000837595	−	0.00125355i
$603$		0			0
$604$	−8.11138	−	3.35985i	−0.330048	−	0.136710i
$605$	−81.4668	+	40.1750i	−3.31210	+	1.63334i
$606$		0			0
$607$	10.4101	−	21.1095i	0.422531	−	0.856808i	−0.576675	−	0.816974i	$-0.695650\pi$
$607$	10.4101	−	21.1095i	0.422531	−	0.856808i	0.999206	−	0.0398349i	$-0.0126832\pi$
$608$	−12.7532	−	3.41722i	−0.517212	−	0.138586i
$609$		0			0
$610$	−0.327877	−	0.0431658i	−0.0132753	−	0.00174773i
$611$	6.11132			0.247238
$612$		0			0
$613$	−17.8940			−0.722732			−0.361366	−	0.932424i	$-0.617689\pi$
$613$	−17.8940			−0.722732			−0.361366	+	0.932424i	$0.617689\pi$
$614$	1.09274	+	0.143862i	0.0440993	+	0.00580579i
$615$		0			0
$616$	−0.784140	−	0.210110i	−0.0315939	−	0.00846556i
$617$	−12.7713	+	25.8976i	−0.514153	+	1.04260i	0.472737	+	0.881203i	$0.343266\pi$
$617$	−12.7713	+	25.8976i	−0.514153	+	1.04260i	−0.986890	+	0.161395i	$0.948401\pi$
$618$		0			0
$619$	−16.0085	+	7.89453i	−0.643437	+	0.317308i	−0.734572	−	0.678531i	$-0.762617\pi$
$619$	−16.0085	+	7.89453i	−0.643437	+	0.317308i	0.0911354	+	0.995839i	$0.470950\pi$
$620$	13.4525	+	5.57222i	0.540267	+	0.223786i
$621$		0			0
$622$	18.5678	−	27.7887i	0.744501	−	1.11422i
$623$	0.762555	+	0.258853i	0.0305511	+	0.0103707i
$624$		0			0
$625$	1.25571	−	4.68638i	0.0502284	−	0.187455i
$626$	−3.93209	+	1.33476i	−0.157158	+	0.0533479i
$627$		0			0
$628$	8.71963	+	5.03428i	0.347951	+	0.200890i
$629$	−4.67883	−	20.9009i	−0.186557	−	0.833373i
$630$		0			0
$631$	−25.8159	+	10.6933i	−1.02772	+	0.425694i	−0.831888	−	0.554944i	$-0.812740\pi$
$631$	−25.8159	+	10.6933i	−1.02772	+	0.425694i	−0.195829	+	0.980638i	$0.562740\pi$
$632$	−10.6710	+	12.1680i	−0.424470	+	0.484015i
$633$		0			0
$634$	−18.6847	−	9.21425i	−0.742063	−	0.365945i
$635$	−34.3098	−	39.1228i	−1.36154	−	1.55254i
$636$		0			0
$637$	15.4865	+	20.1824i	0.613598	+	0.799657i
$638$	−0.0918680	+	0.221789i	−0.00363709	+	0.00878071i
$639$		0			0
$640$	9.42874	−	1.87549i	0.372704	−	0.0741354i
$641$	2.75382	+	42.0152i	0.108769	+	1.65950i	0.608675	+	0.793420i	$0.291701\pi$
$641$	2.75382	+	42.0152i	0.108769	+	1.65950i	−0.499905	+	0.866080i	$0.666632\pi$
$642$		0			0
$643$	7.44695	+	21.9380i	0.293679	+	0.865151i	0.989191	+	0.146636i	$0.0468445\pi$
$643$	7.44695	+	21.9380i	0.293679	+	0.865151i	−0.695511	+	0.718515i	$0.744822\pi$
$644$	0.251064	+	0.192648i	0.00989332	+	0.00759141i
$645$		0			0
$646$	8.65183	−	6.97320i	0.340402	−	0.274357i
$647$			19.0689i			0.749678i	0.927090	+	0.374839i	$0.122302\pi$
$647$			19.0689i			0.749678i	−0.927090	+	0.374839i	$0.877698\pi$
$648$		0			0
$649$	−11.8920	+	59.7853i	−0.466803	+	2.34678i
$650$	−27.0451	+	7.24671i	−1.06080	+	0.284239i
$651$		0			0
$652$	−1.78354	+	1.56412i	−0.0698488	+	0.0612558i
$653$	−30.9295	−	2.02723i	−1.21036	−	0.0793315i	−0.553180	−	0.833062i	$-0.686586\pi$
$653$	−30.9295	−	2.02723i	−1.21036	−	0.0793315i	−0.657184	+	0.753730i	$0.728253\pi$
$654$		0			0
$655$	−47.0318	+	36.0888i	−1.83768	+	1.41010i
$656$	4.25563	+	2.84352i	0.166154	+	0.111021i
$657$		0			0
$658$	−0.0420408	−	0.0629185i	−0.00163892	−	0.00245282i
$659$	5.39159	+	20.1217i	0.210026	+	0.783829i	0.987858	+	0.155357i	$0.0496528\pi$
$659$	5.39159	+	20.1217i	0.210026	+	0.783829i	−0.777832	+	0.628472i	$0.783681\pi$
$660$		0			0
$661$	−11.3554	+	14.7986i	−0.441673	+	0.575600i	−0.960148	−	0.279493i	$-0.909834\pi$
$661$	−11.3554	+	14.7986i	−0.441673	+	0.575600i	0.518474	+	0.855093i	$0.326500\pi$
$662$	−7.27718	−	12.6045i	−0.282836	−	0.489886i
$663$		0			0
$664$	−8.76512	+	15.1816i	−0.340152	+	0.589161i
$665$	0.162296	+	0.391816i	0.00629355	+	0.0151940i
$666$		0			0
$667$	0.200792	−	0.200792i	0.00777468	−	0.00777468i
$668$	−10.7081	+	0.701843i	−0.414307	+	0.0271551i
$669$		0			0
$670$	−1.36639	+	20.8471i	−0.0527883	+	0.805394i
$671$	−0.0727974	−	0.552951i	−0.00281031	−	0.0213464i
$672$		0			0
$673$	−14.9298	−	30.2746i	−0.575500	−	1.16700i	−0.968859	−	0.247614i	$-0.920354\pi$
$673$	−14.9298	−	30.2746i	−0.575500	−	1.16700i	0.393359	−	0.919385i	$-0.371313\pi$
$674$	5.35108	+	26.9017i	0.206116	+	1.03621i
$675$		0			0
$676$	0.149409	+	0.149409i	0.00574649	+	0.00574649i
$677$	−33.4580	−	29.3419i	−1.28590	−	1.12770i	−0.984722	−	0.174132i	$-0.944288\pi$
$677$	−33.4580	−	29.3419i	−1.28590	−	1.12770i	−0.301174	−	0.953569i	$-0.597379\pi$
$678$		0			0
$679$	0.140402	−	0.0810611i	0.00538813	−	0.00311084i
$680$	−18.5521	+	40.0001i	−0.711439	+	1.53393i
$681$		0			0
$682$	3.31538	−	25.1828i	0.126953	−	0.964300i
$683$	−30.5882	−	6.08436i	−1.17042	−	0.232812i	−0.428655	−	0.903468i	$-0.641013\pi$
$683$	−30.5882	−	6.08436i	−1.17042	−	0.232812i	−0.741768	+	0.670656i	$0.766013\pi$
$684$		0			0
$685$	−26.4156	+	17.6504i	−1.00929	+	0.674385i
$686$	0.202532	−	0.596641i	0.00773273	−	0.0227799i
$687$		0			0
$688$	0.869576	−	0.114482i	0.0331523	−	0.00436458i
$689$	11.0710	−	1.45752i	0.421770	−	0.0555271i
$690$		0			0
$691$	−0.539407	+	1.58904i	−0.0205200	+	0.0604500i	−0.956708	−	0.291051i	$-0.905995\pi$
$691$	−0.539407	+	1.58904i	−0.0205200	+	0.0604500i	0.936188	+	0.351501i	$0.114329\pi$
$692$	0.858553	−	0.573667i	0.0326373	−	0.0218075i
$693$		0			0
$694$	32.1301	+	6.39107i	1.21964	+	0.242602i
$695$	5.09092	−	38.6694i	0.193110	−	1.46681i
$696$		0			0
$697$	18.5663	−	6.80096i	0.703250	−	0.257605i
$698$	−24.1224	+	13.9271i	−0.913048	+	0.527149i
$699$		0			0
$700$	−0.251997	−	0.220996i	−0.00952460	−	0.00835285i
$701$	31.7515	+	31.7515i	1.19924	+	1.19924i	0.974395	+	0.224844i	$0.0721874\pi$
$701$	31.7515	+	31.7515i	1.19924	+	1.19924i	0.224844	+	0.974395i	$0.427813\pi$
$702$		0			0
$703$	−2.70851	−	13.6166i	−0.102153	−	0.513560i
$704$	−19.0286	−	38.5862i	−0.717167	−	1.45427i
$705$		0			0
$706$	−3.47539	−	26.3982i	−0.130798	−	0.993511i
$707$	0.0147968	−	0.225755i	0.000556490	−	0.00849039i
$708$		0			0
$709$	29.9533	−	1.96325i	1.12492	−	0.0737312i	0.508438	−	0.861099i	$-0.330223\pi$
$709$	29.9533	−	1.96325i	1.12492	−	0.0737312i	0.616484	+	0.787368i	$0.288557\pi$
$710$	−14.6281	+	14.6281i	−0.548983	+	0.548983i
$711$		0			0
$712$	20.7686	+	50.1398i	0.778335	+	1.87907i
$713$	−15.0225	+	26.0197i	−0.562596	+	0.974445i
$714$		0			0
$715$	−39.0653	−	67.6631i	−1.46096	−	2.53046i
$716$	−5.20738	+	6.78639i	−0.194609	+	0.253619i
$717$		0			0
$718$	−2.31460	−	8.63821i	−0.0863802	−	0.322375i
$719$	8.11589	+	12.1463i	0.302672	+	0.452980i	0.951363	−	0.308071i	$-0.0996835\pi$
$719$	8.11589	+	12.1463i	0.302672	+	0.452980i	−0.648692	+	0.761051i	$0.724684\pi$
$720$		0			0
$721$	0.0269492	+	0.0180069i	0.00100364	+	0.000670612i
$722$	−9.48599	+	7.27886i	−0.353032	+	0.270891i
$723$		0			0
$724$	11.3770	+	0.745685i	0.422821	+	0.0277132i
$725$	−0.226119	+	0.198301i	−0.00839786	+	0.00736473i
$726$		0			0
$727$	−11.3208	+	3.03341i	−0.419867	+	0.112503i	−0.462566	−	0.886585i	$-0.653071\pi$
$727$	−11.3208	+	3.03341i	−0.419867	+	0.112503i	0.0426988	+	0.999088i	$0.486404\pi$
$728$	0.0952285	−	0.478746i	0.00352940	−	0.0177435i
$729$		0			0
$730$		−	29.1421i		−	1.07860i
$731$	1.62363	−	2.97401i	0.0600522	−	0.109998i
$732$		0			0
$733$	−21.5440	−	16.5313i	−0.795746	−	0.610597i	0.128799	−	0.991671i	$-0.458888\pi$
$733$	−21.5440	−	16.5313i	−0.795746	−	0.610597i	−0.924545	+	0.381074i	$0.875554\pi$
$734$	12.0286	+	35.4350i	0.443982	+	1.30793i
$735$		0			0
$736$	2.33003	+	35.5494i	0.0858861	+	1.31037i
$737$	−34.5563	+	6.87367i	−1.27290	+	0.253195i
$738$		0			0
$739$	15.1973	−	36.6896i	0.559044	−	1.34965i	−0.351481	−	0.936195i	$-0.614322\pi$
$739$	15.1973	−	36.6896i	0.559044	−	1.34965i	0.910524	−	0.413455i	$-0.135678\pi$
$740$	11.0521	+	14.4034i	0.406284	+	0.529480i
$741$		0			0
$742$	−0.0911647	−	0.103953i	−0.00334676	−	0.00381625i
$743$	7.47802	+	3.68775i	0.274342	+	0.135290i	0.574256	−	0.818676i	$-0.305291\pi$
$743$	7.47802	+	3.68775i	0.274342	+	0.135290i	−0.299914	+	0.953966i	$0.596958\pi$
$744$		0			0
$745$	21.8673	−	24.9349i	0.801158	−	0.913545i
$746$	13.4029	−	5.55168i	0.490717	−	0.203262i
$747$		0			0
$748$	−24.1427	−	4.20573i	−0.882745	−	0.153777i
$749$	0.0940918	+	0.0543239i	0.00343804	+	0.00198495i
$750$		0			0
$751$	−25.8590	+	8.77796i	−0.943609	+	0.320312i	−0.750504	−	0.660866i	$-0.770189\pi$
$751$	−25.8590	+	8.77796i	−0.943609	+	0.320312i	−0.193105	+	0.981178i	$0.561856\pi$
$752$	0.464380	−	1.73309i	0.0169342	−	0.0631993i
$753$		0			0
$754$	−0.136686	−	0.0463986i	−0.00497781	−	0.00168974i
$755$	−17.6382	+	26.3974i	−0.641920	+	0.960700i
$756$		0			0
$757$	19.8952	+	8.24087i	0.723104	+	0.299520i	0.713715	−	0.700436i	$-0.247011\pi$
$757$	19.8952	+	8.24087i	0.723104	+	0.299520i	0.00938948	+	0.999956i	$0.497011\pi$
$758$	15.1314	−	7.46196i	0.549596	−	0.271031i
$759$		0			0
$760$	−12.6411	+	25.6337i	−0.458543	+	0.929833i
$761$	13.0970	+	3.50934i	0.474767	+	0.127213i	0.488265	−	0.872695i	$-0.337630\pi$
$761$	13.0970	+	3.50934i	0.474767	+	0.127213i	−0.0134978	+	0.999909i	$0.504297\pi$
$762$		0			0
$763$	0.400477	+	0.0527238i	0.0144982	+	0.00190873i
$764$	21.0823			0.762731
$765$		0			0
$766$	−36.8856			−1.33273
$767$	−36.3388	−	4.78409i	−1.31212	−	0.172744i
$768$		0			0
$769$	23.0034	+	6.16375i	0.829525	+	0.222271i	0.648507	−	0.761209i	$-0.275394\pi$
$769$	23.0034	+	6.16375i	0.829525	+	0.222271i	0.181019	+	0.983480i	$0.442061\pi$
$770$	−0.427882	+	0.867659i	−0.0154198	+	0.0312683i
$771$		0			0
$772$	0.468851	−	0.231212i	0.0168743	−	0.00832150i
$773$	−34.8872	−	14.4507i	−1.25480	−	0.519757i	−0.346493	−	0.938053i	$-0.612628\pi$
$773$	−34.8872	−	14.4507i	−1.25480	−	0.519757i	−0.908311	+	0.418296i	$0.862628\pi$
$774$		0			0
$775$	17.6792	−	26.4588i	0.635056	−	0.950428i
$776$	10.3460	+	3.51201i	0.371401	+	0.126074i
$777$		0			0
$778$	4.60875	−	17.2001i	0.165232	−	0.616653i
$779$	12.1366	−	4.11982i	0.434839	−	0.147608i
$780$		0			0
$781$	−30.2141	−	17.4441i	−1.08115	−	0.624200i
$782$	−25.3211	−	16.0581i	−0.905481	−	0.574235i
$783$		0			0
$784$	6.90025	−	2.85818i	0.246437	−	0.102078i
$785$	24.0058	−	27.3734i	0.856804	−	0.976997i
$786$		0			0
$787$	−30.8236	−	15.2005i	−1.09874	−	0.541840i	−0.199770	−	0.979843i	$-0.564019\pi$
$787$	−30.8236	−	15.2005i	−1.09874	−	0.541840i	−0.898974	+	0.438003i	$0.855686\pi$
$788$	−5.19508	−	5.92385i	−0.185067	−	0.211029i
$789$		0			0
$790$	11.7411	+	15.3013i	0.417729	+	0.544395i
$791$	−0.00288261	+	0.00695924i	−0.000102494	+	0.000247442i
$792$		0			0
$793$	0.328907	−	0.0654237i	0.0116798	−	0.00232327i
$794$	−1.33190	−	20.3209i	−0.0472675	−	0.721162i
$795$		0			0
$796$	−0.944977	−	2.78381i	−0.0334938	−	0.0986696i
$797$	14.2536	+	10.9372i	0.504888	+	0.387414i	0.829564	−	0.558411i	$-0.188589\pi$
$797$	14.2536	+	10.9372i	0.504888	+	0.387414i	−0.324677	+	0.945825i	$0.605256\pi$
$798$		0			0
$799$	−4.34972	−	5.39682i	−0.153882	−	0.190926i
$800$		−	37.7325i		−	1.33404i
$801$		0			0
$802$	−2.76103	+	13.8807i	−0.0974955	+	0.490143i
$803$	47.4724	−	12.7202i	1.67526	−	0.448886i
$804$		0			0
$805$	0.860358	−	0.754514i	0.0303236	−	0.0265931i
$806$	15.2401	+	0.998886i	0.536808	+	0.0351843i
$807$		0			0
$808$	12.0962	−	9.28174i	0.425543	−	0.326530i
$809$	−33.5595	−	22.4237i	−1.17989	−	0.788377i	−0.198443	−	0.980112i	$-0.563588\pi$
$809$	−33.5595	−	22.4237i	−1.17989	−	0.788377i	−0.981447	+	0.191735i	$0.938588\pi$
$810$		0			0
$811$	27.5220	+	41.1896i	0.966429	+	1.44636i	0.893520	+	0.449024i	$0.148228\pi$
$811$	27.5220	+	41.1896i	0.966429	+	1.44636i	0.0729089	+	0.997339i	$0.476772\pi$
$812$	−0.000447227	−	0.00166907i	−1.56946e−5	−	5.85730e-5i
$813$		0			0
$814$	19.2794	−	25.1254i	0.675742	−	0.880644i
$815$	4.28907	+	7.42889i	0.150240	+	0.260223i
$816$		0			0
$817$	1.09817	−	1.90209i	0.0384202	−	0.0665457i
$818$	1.88131	+	4.54188i	0.0657784	+	0.158803i
$819$		0			0
$820$	−11.8514	+	11.8514i	−0.413867	+	0.413867i
$821$	20.4256	−	1.33876i	0.712858	−	0.0467232i	0.295341	−	0.955392i	$-0.404567\pi$
$821$	20.4256	−	1.33876i	0.712858	−	0.0467232i	0.417518	+	0.908669i	$0.362900\pi$
$822$		0			0
$823$	−0.282792	+	4.31457i	−0.00985750	+	0.150396i	0.990093	+	0.140415i	$0.0448438\pi$
$823$	−0.282792	+	4.31457i	−0.00985750	+	0.150396i	−0.999950	+	0.00998101i	$0.996823\pi$
$824$	0.285109	+	2.16562i	0.00993225	+	0.0754429i
$825$		0			0
$826$	0.200727	+	0.407033i	0.00698417	+	0.0141625i
$827$	−10.3076	−	51.8200i	−0.358432	−	1.80196i	−0.566740	−	0.823896i	$-0.691796\pi$
$827$	−10.3076	−	51.8200i	−0.358432	−	1.80196i	0.208308	−	0.978063i	$-0.433204\pi$
$828$		0			0
$829$	28.8577	+	28.8577i	1.00227	+	1.00227i	0.999997	+	0.00227095i	$0.000722865\pi$
$829$	28.8577	+	28.8577i	1.00227	+	1.00227i	0.00227095	+	0.999997i	$0.499277\pi$
$830$	15.7066	+	13.7743i	0.545183	+	0.478113i
$831$		0			0
$832$	22.4034	−	12.9346i	0.776697	−	0.448426i
$833$	6.80030	−	28.0407i	0.235616	−	0.971553i
$834$		0			0
$835$	−5.06494	+	38.4721i	−0.175280	+	1.33138i
$836$	−15.5799	−	3.09903i	−0.538841	−	0.107182i
$837$		0			0
$838$	−22.3308	+	14.9210i	−0.771404	+	0.515436i
$839$	−10.4629	+	30.8226i	−0.361218	+	1.06411i	0.602712	+	0.797959i	$0.294087\pi$
$839$	−10.4629	+	30.8226i	−0.361218	+	1.06411i	−0.963930	+	0.266155i	$0.914247\pi$
$840$		0			0
$841$	28.7504	−	3.78506i	0.991392	−	0.130519i
$842$	33.2289	−	4.37467i	1.14514	−	0.150761i
$843$		0			0
$844$	3.82354	−	11.2638i	0.131612	−	0.387715i
$845$	0.635291	−	0.424488i	0.0218547	−	0.0146028i
$846$		0			0
$847$	−1.11861	−	0.222505i	−0.0384358	−	0.00764536i
$848$	0.427914	−	3.25033i	0.0146946	−	0.111617i
$849$		0			0
$850$	25.6488	+	18.7253i	0.879745	+	0.642272i
$851$	−32.4423	+	18.7306i	−1.11211	+	0.642076i
$852$		0			0
$853$	−32.9932	−	28.9343i	−1.12967	−	0.990690i	−0.129666	−	0.991558i	$-0.541391\pi$
$853$	−32.9932	−	28.9343i	−1.12967	−	0.990690i	−1.00000		0.000867572i	$0.999724\pi$
$854$	−0.00293617	−	0.00293617i	−0.000100474	−	0.000100474i
$855$		0			0
$856$	1.42847	+	7.18139i	0.0488240	+	0.245455i
$857$	−9.77087	−	19.8134i	−0.333767	−	0.676812i	0.663696	−	0.748002i	$-0.268987\pi$
$857$	−9.77087	−	19.8134i	−0.333767	−	0.676812i	−0.997463	+	0.0711905i	$0.977320\pi$
$858$		0			0
$859$	−1.01473	−	7.70767i	−0.0346223	−	0.262982i	−0.999998	−	0.00211809i	$-0.999326\pi$
$859$	−1.01473	−	7.70767i	−0.0346223	−	0.262982i	0.965375	−	0.260864i	$-0.0840075\pi$
$860$	−0.187846	+	2.86598i	−0.00640551	+	0.0977292i
$861$		0			0
$862$	20.2336	−	1.32618i	0.689160	−	0.0451699i
$863$	0.406686	−	0.406686i	0.0138437	−	0.0138437i	−0.700151	−	0.713995i	$-0.746884\pi$
$863$	0.406686	−	0.406686i	0.0138437	−	0.0138437i	0.713995	+	0.700151i	$0.246884\pi$
$864$		0			0
$865$	−1.42888	−	3.44962i	−0.0485834	−	0.117291i
$866$	2.28801	−	3.96294i	0.0777496	−	0.134666i
$867$		0			0
$868$	0.0914141	+	0.158334i	0.00310280	+	0.00537420i
$869$	−19.8009	+	25.8050i	−0.671698	+	0.875374i
$870$		0			0
$871$	−5.48316	−	20.4634i	−0.185790	−	0.693376i
$872$	15.1238	+	22.6344i	0.512158	+	0.766498i
$873$		0			0
$874$	−16.1601	−	10.7978i	−0.546622	−	0.365241i
$875$	−0.332093	+	0.254824i	−0.0112268	+	0.00861463i
$876$		0			0
$877$	−33.3008	−	2.18265i	−1.12449	−	0.0737028i	−0.508211	−	0.861233i	$-0.669693\pi$
$877$	−33.3008	−	2.18265i	−1.12449	−	0.0737028i	−0.616276	+	0.787530i	$0.711360\pi$
$878$	1.34833	−	1.18245i	0.0455039	−	0.0399059i
$879$		0			0
$880$	−22.1568	+	5.93690i	−0.746907	+	0.200133i
$881$	−4.35402	+	21.8892i	−0.146691	+	0.737465i	0.835487	+	0.549510i	$0.185186\pi$
$881$	−4.35402	+	21.8892i	−0.146691	+	0.737465i	−0.982178	+	0.187954i	$0.939814\pi$
$882$		0			0
$883$		−	11.7962i		−	0.396975i	−0.980103	−	0.198487i	$-0.936397\pi$
$883$		−	11.7962i		−	0.396975i	0.980103	−	0.198487i	$-0.0636029\pi$
$884$	1.57399	−	14.6510i	0.0529392	−	0.492767i
$885$		0			0
$886$	24.6814	+	18.9387i	0.829188	+	0.636258i
$887$	7.08236	+	20.8640i	0.237802	+	0.700543i	0.998666	+	0.0516316i	$0.0164422\pi$
$887$	7.08236	+	20.8640i	0.237802	+	0.700543i	−0.760864	+	0.648912i	$0.775224\pi$
$888$		0			0
$889$	−0.0427325	−	0.651972i	−0.00143320	−	0.0218664i
$890$	63.4322	−	12.6174i	2.12625	−	0.422938i
$891$		0			0
$892$	−2.94022	+	7.09832i	−0.0984459	+	0.237669i
$893$	−2.73518	−	3.56456i	−0.0915294	−	0.119283i
$894$		0			0
$895$	20.3949	+	23.2559i	0.681725	+	0.777359i
$896$	0.108259	+	0.0533876i	0.00361669	+	0.00178355i
$897$		0			0
$898$	−23.6312	+	26.9462i	−0.788583	+	0.899207i
$899$	0.151566	−	0.0627805i	0.00505499	−	0.00209385i
$900$		0			0
$901$	−9.16684	−	8.73921i	−0.305392	−	0.291145i
$902$	25.3198	+	14.6184i	0.843058	+	0.486740i
$903$		0			0
$904$	−0.480705	+	0.163177i	−0.0159880	+	0.00542719i
$905$	10.6706	−	39.8232i	0.354703	−	1.32377i
$906$		0			0
$907$	−39.4579	−	13.3942i	−1.31018	−	0.444746i	−0.422983	−	0.906138i	$-0.639017\pi$
$907$	−39.4579	−	13.3942i	−1.31018	−	0.444746i	−0.887197	+	0.461391i	$0.847350\pi$
$908$	−3.23363	+	4.83947i	−0.107312	+	0.160603i
$909$		0			0
$910$	−0.537421	−	0.222607i	−0.0178153	−	0.00737936i
$911$	3.79090	−	1.86946i	0.125598	−	0.0619381i	−0.378404	−	0.925640i	$-0.623527\pi$
$911$	3.79090	−	1.86946i	0.125598	−	0.0619381i	0.504002	+	0.863702i	$0.331860\pi$
$912$		0			0
$913$	−15.5825	+	31.5983i	−0.515707	+	1.04575i
$914$	−5.92768	−	1.58832i	−0.196070	−	0.0525368i
$915$		0			0
$916$	13.5296	+	1.78121i	0.447031	+	0.0588528i
$917$	−0.744354			−0.0245807
$918$		0			0
$919$	46.8684			1.54604			0.773022	−	0.634379i	$-0.218744\pi$
$919$	46.8684			1.54604			0.773022	+	0.634379i	$0.218744\pi$
$920$	76.4603	+	10.0662i	2.52082	+	0.331873i
$921$		0			0
$922$	37.4928	+	10.0462i	1.23476	+	0.330853i
$923$	9.27826	−	18.8145i	0.305398	−	0.619285i
$924$		0			0
$925$	35.5848	−	17.5485i	1.17002	−	0.576990i
$926$	18.1744	+	7.52808i	0.597248	+	0.247388i
$927$		0			0
$928$	0.108073	−	0.161742i	0.00354766	−	0.00530944i
$929$	14.7967	+	5.02279i	0.485463	+	0.164792i	0.553431	−	0.832895i	$-0.313318\pi$
$929$	14.7967	+	5.02279i	0.485463	+	0.164792i	−0.0679681	+	0.997687i	$0.521652\pi$
$930$		0			0
$931$	4.84069	−	18.0657i	0.158647	−	0.592079i
$932$	14.0816	−	4.78004i	0.461257	−	0.156576i
$933$		0			0
$934$	−1.30561	−	0.753796i	−0.0427210	−	0.0246650i
$935$	−31.9476	+	82.6571i	−1.04480	+	2.70317i
$936$		0			0
$937$	39.6097	−	16.4069i	1.29399	−	0.535989i	0.373819	−	0.927502i	$-0.378048\pi$
$937$	39.6097	−	16.4069i	1.29399	−	0.535989i	0.920173	+	0.391512i	$0.128048\pi$
$938$	−0.172960	+	0.197223i	−0.00564733	+	0.00643954i
$939$		0			0
$940$	5.26956	+	2.59866i	0.171874	+	0.0847589i
$941$	16.4572	+	18.7658i	0.536488	+	0.611747i	0.955051	−	0.296440i	$-0.0957996\pi$
$941$	16.4572	+	18.7658i	0.536488	+	0.611747i	−0.418564	+	0.908188i	$0.637466\pi$
$942$		0			0
$943$	−21.0530	−	27.4368i	−0.685579	−	0.893464i
$944$	−4.11798	+	9.94168i	−0.134029	+	0.323574i
$945$		0			0
$946$	4.91389	−	0.977434i	0.159764	−	0.0317791i
$947$	−3.01856	−	46.0544i	−0.0980901	−	1.49657i	−0.709193	−	0.705014i	$-0.750941\pi$
$947$	−3.01856	−	46.0544i	−0.0980901	−	1.49657i	0.611103	−	0.791551i	$-0.290726\pi$
$948$		0			0
$949$	9.49900	+	27.9832i	0.308351	+	0.908372i
$950$	16.3311	+	12.5313i	0.529851	+	0.406569i
$951$		0			0
$952$	−0.490552	+	0.256652i	−0.0158989	+	0.00831812i
$953$		−	27.3799i		−	0.886922i	−0.896294	−	0.443461i	$-0.853751\pi$
$953$		−	27.3799i		−	0.886922i	0.896294	−	0.443461i	$-0.146249\pi$
$954$		0			0
$955$	14.8727	−	74.7701i	0.481269	−	2.41950i
$956$	−4.68313	+	1.25484i	−0.151463	+	0.0405844i
$957$		0			0
$958$	−2.10368	+	1.84488i	−0.0679668	+	0.0596053i
$959$	−0.398050	−	0.0260896i	−0.0128537	−	0.000842477i
$960$		0			0
$961$	10.8230	−	8.30480i	0.349130	−	0.267897i
$962$	15.8334	+	10.5795i	0.510489	+	0.341098i
$963$		0			0
$964$	−8.18982	−	12.2569i	−0.263776	−	0.394769i
$965$	−0.489256	−	1.82593i	−0.0157497	−	0.0587787i
$966$		0			0
$967$	28.5153	−	37.1619i	0.916990	−	1.19504i	−0.0634021	−	0.997988i	$-0.520195\pi$
$967$	28.5153	−	37.1619i	0.916990	−	1.19504i	0.980392	−	0.197057i	$-0.0631383\pi$
$968$	−38.4316	−	66.5654i	−1.23524	−	2.13949i
$969$		0			0
$970$	6.51021	−	11.2760i	0.209030	−	0.362051i
$971$	−12.9063	−	31.1585i	−0.414183	−	0.999925i	−0.984002	−	0.178156i	$-0.942987\pi$
$971$	−12.9063	−	31.1585i	−0.414183	−	0.999925i	0.569820	−	0.821770i	$-0.307013\pi$
$972$		0			0
$973$	0.346289	−	0.346289i	0.0111015	−	0.0111015i
$974$	−21.1202	+	1.38429i	−0.676735	+	0.0443556i
$975$		0			0
$976$	0.00643933	−	0.0982452i	0.000206118	−	0.00314475i
$977$	−0.315025	−	2.39285i	−0.0100785	−	0.0765541i	0.985666	−	0.168706i	$-0.0539588\pi$
$977$	−0.315025	−	2.39285i	−0.0100785	−	0.0765541i	−0.995745	+	0.0921518i	$0.970625\pi$
$978$		0			0
$979$	48.2412	+	97.8234i	1.54179	+	3.12645i
$980$	4.77145	+	23.9877i	0.152418	+	0.766259i
$981$		0			0
$982$	17.0315	+	17.0315i	0.543497	+	0.543497i
$983$	26.6888	+	23.4054i	0.851240	+	0.746517i	0.969141	−	0.246508i	$-0.0792833\pi$
$983$	26.6888	+	23.4054i	0.851240	+	0.746517i	−0.117901	+	0.993025i	$0.537617\pi$
$984$		0			0
$985$	−24.6743	+	14.2457i	−0.786189	+	0.453906i
$986$	0.0563120	+	0.153729i	0.00179334	+	0.00489574i
$987$		0			0
$988$	1.24672	−	9.46978i	0.0396635	−	0.301274i
$989$	−5.81248	−	1.15617i	−0.184826	−	0.0367642i
$990$		0			0
$991$	−6.75372	+	4.51269i	−0.214539	+	0.143350i	−0.658197	−	0.752846i	$-0.728681\pi$
$991$	−6.75372	+	4.51269i	−0.214539	+	0.143350i	0.443658	+	0.896196i	$0.353681\pi$
$992$	−6.61587	+	19.4897i	−0.210054	+	0.618800i
$993$		0			0
$994$	−0.257529	+	0.0339043i	−0.00816832	+	0.00107538i
$995$	−10.5396	+	1.38757i	−0.334129	+	0.0439890i
$996$		0			0
$997$	−16.9384	+	49.8988i	−0.536443	+	1.58031i	0.253632	+	0.967301i	$0.418375\pi$
$997$	−16.9384	+	49.8988i	−0.536443	+	1.58031i	−0.790075	+	0.613010i	$0.789958\pi$
$998$	−1.83631	+	1.22698i	−0.0581274	+	0.0388395i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.y.a.116.10		256
3.2	odd	2		153.2.s.a.65.7	yes	256
9.4	even	3		153.2.s.a.14.7	yes	256
9.5	odd	6	inner	459.2.y.a.422.10		256
17.11	odd	16	inner	459.2.y.a.62.10		256
51.11	even	16		153.2.s.a.11.7	✓	256
153.113	even	48	inner	459.2.y.a.368.10		256
153.130	odd	48		153.2.s.a.113.7	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.7	✓	256	51.11	even	16
153.2.s.a.14.7	yes	256	9.4	even	3
153.2.s.a.65.7	yes	256	3.2	odd	2
153.2.s.a.113.7	yes	256	153.130	odd	48
459.2.y.a.62.10		256	17.11	odd	16	inner
459.2.y.a.116.10		256	1.1	even	1	trivial
459.2.y.a.368.10		256	153.113	even	48	inner
459.2.y.a.422.10		256	9.5	odd	6	inner

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:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.y (of order \(48\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.999782 + 0.131624i) q^{2} +(-0.949612 - 0.254448i) q^{4} +(-1.57233 + 3.18837i) q^{5} +(-0.0400335 + 0.0197423i) q^{7} +(-2.77921 - 1.15119i) q^{8} +(-1.99165 + 2.98072i) q^{10} +(-5.72491 - 1.94335i) q^{11} +(0.940868 - 3.51137i) q^{13} +(-0.0426233 + 0.0144687i) q^{14} +(-0.924284 - 0.533636i) q^{16} +(-3.77050 + 1.66834i) q^{17} +(-2.46918 + 1.02277i) q^{19} +(2.30438 - 2.62764i) q^{20} +(-5.46788 - 2.69646i) q^{22} +(4.75485 + 5.42187i) q^{23} +(-4.64968 - 6.05958i) q^{25} +(1.40284 - 3.38676i) q^{26} +(0.0430397 - 0.00856112i) q^{28} +(-0.00257534 - 0.0392922i) q^{29} +(1.33921 + 3.94517i) q^{31} +(3.91928 + 3.00737i) q^{32} +(-3.98927 + 1.17169i) q^{34} -0.158683i q^{35} +(-1.01343 + 5.09486i) q^{37} +(-2.60326 + 0.697541i) q^{38} +(8.04025 - 7.05111i) q^{40} +(-4.78533 - 0.313647i) q^{41} +(-0.651975 + 0.500278i) q^{43} +(4.94197 + 3.30212i) q^{44} +(4.04017 + 6.04654i) q^{46} +(0.435110 + 1.62385i) q^{47} +(-4.26012 + 5.55189i) q^{49} +(-3.85108 - 6.67026i) q^{50} +(-1.78692 + 3.09503i) q^{52} +(1.17550 + 2.83792i) q^{53} +(15.1976 - 15.1976i) q^{55} +(0.133989 - 0.00878208i) q^{56} +(0.00259700 - 0.0396226i) q^{58} +(-1.31603 - 9.99628i) q^{59} +(0.0408012 + 0.0827367i) q^{61} +(0.819636 + 4.12059i) q^{62} +(5.03194 + 5.03194i) q^{64} +(9.71618 + 8.52086i) q^{65} +(5.04699 - 2.91388i) q^{67} +(4.00501 - 0.624883i) q^{68} +(0.0208865 - 0.158648i) q^{70} +(5.65982 + 1.12581i) q^{71} +(-6.75916 + 4.51633i) q^{73} +(-1.68381 + 4.96035i) q^{74} +(2.60500 - 0.342955i) q^{76} +(0.267554 - 0.0352242i) q^{77} +(1.72936 - 5.09453i) q^{79} +(3.15471 - 2.10791i) q^{80} +(-4.74300 - 0.943442i) q^{82} +(0.760640 - 5.77763i) q^{83} +(0.609173 - 14.6449i) q^{85} +(-0.717681 + 0.414353i) q^{86} +(13.6736 + 11.9914i) q^{88} +(-12.7569 - 12.7569i) q^{89} +(0.0316563 + 0.159147i) q^{91} +(-3.13568 - 6.35853i) q^{92} +(0.221278 + 1.68077i) q^{94} +(0.621403 - 9.48077i) q^{95} +(-3.62426 + 0.237547i) q^{97} +(-4.98995 + 4.98995i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 24 q^{2} - 8 q^{4} + 24 q^{5} - 8 q^{7} - 32 q^{10} + 24 q^{11} - 8 q^{13} + 24 q^{14} - 32 q^{19} + 24 q^{20} - 8 q^{22} + 24 q^{23} - 8 q^{25} - 32 q^{28} + 24 q^{29} - 8 q^{31} + 24 q^{32} - 56 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) \) 256 * q + 24 * q^2 - 8 * q^4 + 24 * q^5 - 8 * q^7 - 32 * q^10 + 24 * q^11 - 8 * q^13 + 24 * q^14 - 32 * q^19 + 24 * q^20 - 8 * q^22 + 24 * q^23 - 8 * q^25 - 32 * q^28 + 24 * q^29 - 8 * q^31 + 24 * q^32 - 56 * q^34 - 32 * q^37 - 8 * q^40 + 24 * q^41 + 16 * q^43 - 32 * q^46 - 96 * q^47 - 8 * q^49 - 16 * q^52 - 32 * q^55 - 216 * q^56 - 8 * q^58 + 24 * q^59 - 8 * q^61 - 96 * q^64 - 24 * q^65 + 24 * q^68 + 8 * q^70 - 32 * q^73 + 24 * q^74 - 8 * q^76 + 24 * q^77 - 8 * q^79 + 160 * q^82 + 24 * q^83 - 8 * q^85 - 192 * q^86 - 8 * q^88 - 128 * q^91 + 24 * q^92 - 8 * q^94 - 216 * q^95 - 8 * q^97

Introduction

L-functions

Modular forms

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