LMFDB - Embedded newform 592.2.bc.d.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(33,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("592.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.bc (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 24x^{10} + 264x^{8} - 1687x^{6} + 6600x^{4} - 15000x^{2} + 15625 $ x^12 - 24x^10 + 264x^8 - 1687x^6 + 6600x^4 - 15000*x^2 + 15625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.2
Root			$2.20976 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	592.49
Dual form			592.2.bc.d.145.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.41262 + 2.02443i) q^{3} +(-1.43969 + 0.524005i) q^{5} +(-4.53424 + 1.65033i) q^{7} +(1.20148 + 6.81391i) q^{9} +O(q^{10})$	\(q+(2.41262 + 2.02443i) q^{3} +(-1.43969 + 0.524005i) q^{5} +(-4.53424 + 1.65033i) q^{7} +(1.20148 + 6.81391i) q^{9} +(-0.546896 - 0.947252i) q^{11} +(0.307284 - 1.74269i) q^{13} +(-4.53424 - 1.65033i) q^{15} +(0.511542 + 2.90110i) q^{17} +(0.632167 + 0.530451i) q^{19} +(-14.2804 - 5.19762i) q^{21} +(-0.121620 + 0.210653i) q^{23} +(-2.03209 + 1.70513i) q^{25} +(-6.17139 + 10.6892i) q^{27} +(2.78587 + 4.82526i) q^{29} +5.73495 q^{31} +(0.598191 - 3.39251i) q^{33} +(5.66313 - 4.75193i) q^{35} +(5.84038 + 1.69999i) q^{37} +(4.26932 - 3.58238i) q^{39} +(0.505653 - 2.86770i) q^{41} -4.37987 q^{43} +(-5.30028 - 9.18036i) q^{45} +(1.13249 - 1.96153i) q^{47} +(12.4734 - 10.4664i) q^{49} +(-4.63890 + 8.03481i) q^{51} +(-5.77859 - 2.10324i) q^{53} +(1.28373 + 1.07717i) q^{55} +(0.451318 + 2.55955i) q^{57} +(8.29301 + 3.01841i) q^{59} +(-2.04075 + 11.5737i) q^{61} +(-16.6930 - 28.9131i) q^{63} +(0.470787 + 2.66996i) q^{65} +(8.44220 - 3.07271i) q^{67} +(-0.719875 + 0.262013i) q^{69} +(0.933535 + 0.783329i) q^{71} +8.79418 q^{73} -8.35455 q^{75} +(4.04303 + 3.39251i) q^{77} +(2.02379 - 0.736599i) q^{79} +(-17.0233 + 6.19599i) q^{81} +(-0.884528 - 5.01641i) q^{83} +(-2.25665 - 3.90864i) q^{85} +(-3.04716 + 17.2813i) q^{87} +(-8.43486 - 3.07004i) q^{89} +(1.48272 + 8.40891i) q^{91} +(13.8362 + 11.6100i) q^{93} +(-1.18809 - 0.432428i) q^{95} +(-2.17954 + 3.77507i) q^{97} +(5.79741 - 4.86460i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 6 * q^5 - 6 * q^7 - 3 * q^9	$ 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9} - 3 q^{11} - 6 q^{13} - 6 q^{15} - 3 q^{17} + 3 q^{19} - 33 q^{21} + 21 q^{23} - 6 q^{25} - 3 q^{27} + 6 q^{29} - 42 q^{31} + 57 q^{33} + 9 q^{35} - 3 q^{37} + 24 q^{39} - 21 q^{41} - 36 q^{43} - 6 q^{45} - 9 q^{47} - 12 q^{49} - 6 q^{53} - 36 q^{57} + 6 q^{59} - 18 q^{61} - 36 q^{63} + 3 q^{65} + 27 q^{67} - 12 q^{69} + 18 q^{71} + 54 q^{73} + 6 q^{75} + 51 q^{77} + 12 q^{79} - 36 q^{81} + 6 q^{83} + 3 q^{85} - 39 q^{87} - 15 q^{89} + 51 q^{91} + 45 q^{93} + 15 q^{95} - 42 q^{97} + 33 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 - 6 * q^5 - 6 * q^7 - 3 * q^9 - 3 * q^11 - 6 * q^13 - 6 * q^15 - 3 * q^17 + 3 * q^19 - 33 * q^21 + 21 * q^23 - 6 * q^25 - 3 * q^27 + 6 * q^29 - 42 * q^31 + 57 * q^33 + 9 * q^35 - 3 * q^37 + 24 * q^39 - 21 * q^41 - 36 * q^43 - 6 * q^45 - 9 * q^47 - 12 * q^49 - 6 * q^53 - 36 * q^57 + 6 * q^59 - 18 * q^61 - 36 * q^63 + 3 * q^65 + 27 * q^67 - 12 * q^69 + 18 * q^71 + 54 * q^73 + 6 * q^75 + 51 * q^77 + 12 * q^79 - 36 * q^81 + 6 * q^83 + 3 * q^85 - 39 * q^87 - 15 * q^89 + 51 * q^91 + 45 * q^93 + 15 * q^95 - 42 * q^97 + 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.41262	+	2.02443i	1.39293	+	1.16880i	0.964139	+	0.265397i	$0.0855031\pi$
$3$	2.41262	+	2.02443i	1.39293	+	1.16880i	0.428786	+	0.903406i	$0.358941\pi$
$4$		0			0
$5$	−1.43969	+	0.524005i	−0.643850	+	0.234342i	−0.643248	−	0.765658i	$-0.722414\pi$
$5$	−1.43969	+	0.524005i	−0.643850	+	0.234342i	−0.000601695		1.00000i	$0.500192\pi$
$6$		0			0
$7$	−4.53424	+	1.65033i	−1.71378	+	0.623765i	−0.997272	−	0.0738128i	$-0.976483\pi$
$7$	−4.53424	+	1.65033i	−1.71378	+	0.623765i	−0.716509	+	0.697578i	$0.754261\pi$
$8$		0			0
$9$	1.20148	+	6.81391i	0.400492	+	2.27130i
$10$		0			0
$11$	−0.546896	−	0.947252i	−0.164895	−	0.285607i	0.771723	−	0.635959i	$-0.219395\pi$
$11$	−0.546896	−	0.947252i	−0.164895	−	0.285607i	−0.936618	+	0.350352i	$0.886062\pi$
$12$		0			0
$13$	0.307284	−	1.74269i	0.0852253	−	0.483337i	−0.912082	−	0.410007i	$-0.865526\pi$
$13$	0.307284	−	1.74269i	0.0852253	−	0.483337i	0.997308	−	0.0733298i	$-0.0233626\pi$
$14$		0			0
$15$	−4.53424	−	1.65033i	−1.17074	−	0.426113i
$16$		0			0
$17$	0.511542	+	2.90110i	0.124067	+	0.703619i	0.981858	+	0.189620i	$0.0607255\pi$
$17$	0.511542	+	2.90110i	0.124067	+	0.703619i	−0.857791	+	0.513999i	$0.828163\pi$
$18$		0			0
$19$	0.632167	+	0.530451i	0.145029	+	0.121694i	0.712416	−	0.701758i	$-0.247601\pi$
$19$	0.632167	+	0.530451i	0.145029	+	0.121694i	−0.567387	+	0.823451i	$0.692046\pi$
$20$		0			0
$21$	−14.2804	−	5.19762i	−3.11623	−	1.13421i
$22$		0			0
$23$	−0.121620	+	0.210653i	−0.0253596	+	0.0439241i	−0.878427	−	0.477877i	$-0.841406\pi$
$23$	−0.121620	+	0.210653i	−0.0253596	+	0.0439241i	0.853067	+	0.521801i	$0.174740\pi$
$24$		0			0
$25$	−2.03209	+	1.70513i	−0.406418	+	0.341025i
$26$		0			0
$27$	−6.17139	+	10.6892i	−1.18768	+	2.05713i
$28$		0			0
$29$	2.78587	+	4.82526i	0.517322	+	0.896028i	0.999798	+	0.0201189i	$0.00640447\pi$
$29$	2.78587	+	4.82526i	0.517322	+	0.896028i	−0.482475	+	0.875910i	$0.660262\pi$
$30$		0			0
$31$	5.73495			1.03003			0.515013	−	0.857182i	$-0.327787\pi$
$31$	5.73495			1.03003			0.515013	+	0.857182i	$0.327787\pi$
$32$		0			0
$33$	0.598191	−	3.39251i	0.104132	−	0.590560i
$34$		0			0
$35$	5.66313	−	4.75193i	0.957243	−	0.803223i
$36$		0			0
$37$	5.84038	+	1.69999i	0.960152	+	0.279477i
$37$	5.84038	+	1.69999i	0.960152	+	0.279477i
$38$		0			0
$39$	4.26932	−	3.58238i	0.683638	−	0.573640i
$40$		0			0
$41$	0.505653	−	2.86770i	0.0789697	−	0.447859i	−0.919526	−	0.393029i	$-0.871427\pi$
$41$	0.505653	−	2.86770i	0.0789697	−	0.447859i	0.998496	−	0.0548301i	$-0.0174617\pi$
$42$		0			0
$43$	−4.37987			−0.667924			−0.333962	−	0.942587i	$-0.608386\pi$
$43$	−4.37987			−0.667924			−0.333962	+	0.942587i	$0.608386\pi$
$44$		0			0
$45$	−5.30028	−	9.18036i	−0.790119	−	1.36853i
$46$		0			0
$47$	1.13249	−	1.96153i	0.165191	−	0.286119i	−0.771532	−	0.636190i	$-0.780509\pi$
$47$	1.13249	−	1.96153i	0.165191	−	0.286119i	0.936723	+	0.350071i	$0.113843\pi$
$48$		0			0
$49$	12.4734	−	10.4664i	1.78192	−	1.49521i
$50$		0			0
$51$	−4.63890	+	8.03481i	−0.649576	+	1.12510i
$52$		0			0
$53$	−5.77859	−	2.10324i	−0.793751	−	0.288902i	−0.0868564	−	0.996221i	$-0.527682\pi$
$53$	−5.77859	−	2.10324i	−0.793751	−	0.288902i	−0.706894	+	0.707319i	$0.749904\pi$
$54$		0			0
$55$	1.28373	+	1.07717i	0.173098	+	0.145246i
$56$		0			0
$57$	0.451318	+	2.55955i	0.0597785	+	0.339021i
$58$		0			0
$59$	8.29301	+	3.01841i	1.07966	+	0.392963i	0.819780	−	0.572678i	$-0.194096\pi$
$59$	8.29301	+	3.01841i	1.07966	+	0.392963i	0.259878	+	0.965642i	$0.416318\pi$
$60$		0			0
$61$	−2.04075	+	11.5737i	−0.261292	+	1.48186i	0.518098	+	0.855321i	$0.326640\pi$
$61$	−2.04075	+	11.5737i	−0.261292	+	1.48186i	−0.779390	+	0.626539i	$0.784471\pi$
$62$		0			0
$63$	−16.6930	−	28.9131i	−2.10312	−	3.64270i
$64$		0			0
$65$	0.470787	+	2.66996i	0.0583939	+	0.331168i
$66$		0			0
$67$	8.44220	−	3.07271i	1.03138	−	0.375391i	0.229773	−	0.973244i	$-0.426202\pi$
$67$	8.44220	−	3.07271i	1.03138	−	0.375391i	0.801606	+	0.597853i	$0.203979\pi$
$68$		0			0
$69$	−0.719875	+	0.262013i	−0.0866627	+	0.0315427i
$70$		0			0
$71$	0.933535	+	0.783329i	0.110790	+	0.0929640i	0.696500	−	0.717557i	$-0.254740\pi$
$71$	0.933535	+	0.783329i	0.110790	+	0.0929640i	−0.585710	+	0.810521i	$0.699184\pi$
$72$		0			0
$73$	8.79418			1.02928			0.514640	−	0.857406i	$-0.327925\pi$
$73$	8.79418			1.02928			0.514640	+	0.857406i	$0.327925\pi$
$74$		0			0
$75$	−8.35455			−0.964701
$76$		0			0
$77$	4.04303	+	3.39251i	0.460746	+	0.386612i
$78$		0			0
$79$	2.02379	−	0.736599i	0.227694	−	0.0828739i	−0.225654	−	0.974208i	$-0.572452\pi$
$79$	2.02379	−	0.736599i	0.227694	−	0.0828739i	0.453348	+	0.891334i	$0.350230\pi$
$80$		0			0
$81$	−17.0233	+	6.19599i	−1.89148	+	0.688443i
$82$		0			0
$83$	−0.884528	−	5.01641i	−0.0970895	−	0.550622i	−0.994087	−	0.108586i	$-0.965368\pi$
$83$	−0.884528	−	5.01641i	−0.0970895	−	0.550622i	0.896997	−	0.442036i	$-0.145744\pi$
$84$		0			0
$85$	−2.25665	−	3.90864i	−0.244768	−	0.423951i
$86$		0			0
$87$	−3.04716	+	17.2813i	−0.326690	+	1.85275i
$88$		0			0
$89$	−8.43486	−	3.07004i	−0.894093	−	0.325423i	−0.146210	−	0.989254i	$-0.546708\pi$
$89$	−8.43486	−	3.07004i	−0.894093	−	0.325423i	−0.747883	+	0.663830i	$0.768930\pi$
$90$		0			0
$91$	1.48272	+	8.40891i	0.155431	+	0.881494i
$92$		0			0
$93$	13.8362	+	11.6100i	1.43475	+	1.20390i
$94$		0			0
$95$	−1.18809	−	0.432428i	−0.121895	−	0.0443661i
$96$		0			0
$97$	−2.17954	+	3.77507i	−0.221298	+	0.383300i	−0.955203	−	0.295953i	$-0.904363\pi$
$97$	−2.17954	+	3.77507i	−0.221298	+	0.383300i	0.733904	+	0.679253i	$0.237696\pi$
$98$		0			0
$99$	5.79741	−	4.86460i	0.582661	−	0.488911i
$100$		0			0
$101$	2.19444	−	3.80089i	0.218355	−	0.378203i	−0.735950	−	0.677036i	$-0.763264\pi$
$101$	2.19444	−	3.80089i	0.218355	−	0.378203i	0.954305	+	0.298833i	$0.0965975\pi$
$102$		0			0
$103$	6.32262	+	10.9511i	0.622987	+	1.07904i	0.988927	+	0.148406i	$0.0474142\pi$
$103$	6.32262	+	10.9511i	0.622987	+	1.07904i	−0.365940	+	0.930638i	$0.619252\pi$
$104$		0			0
$105$	23.2829			2.27218
$106$		0			0
$107$	−3.27495	+	18.5731i	−0.316601	+	1.79553i	0.246497	+	0.969144i	$0.420721\pi$
$107$	−3.27495	+	18.5731i	−0.316601	+	1.79553i	−0.563098	+	0.826390i	$0.690391\pi$
$108$		0			0
$109$	−6.44574	+	5.40862i	−0.617390	+	0.518052i	−0.896982	−	0.442067i	$-0.854245\pi$
$109$	−6.44574	+	5.40862i	−0.617390	+	0.518052i	0.279592	+	0.960119i	$0.409801\pi$
$110$		0			0
$111$	10.6491	+	15.9249i	1.01077	+	1.51152i
$112$		0			0
$113$	−4.89090	+	4.10395i	−0.460097	+	0.386067i	−0.843167	−	0.537652i	$-0.819311\pi$
$113$	−4.89090	+	4.10395i	−0.460097	+	0.386067i	0.383070	+	0.923719i	$0.374867\pi$
$114$		0			0
$115$	0.0647129	−	0.367005i	0.00603451	−	0.0342234i
$116$		0			0
$117$	12.2438			1.13194
$118$		0			0
$119$	−7.10721	−	12.3100i	−0.651517	−	1.12846i
$120$		0			0
$121$	4.90181	−	8.49018i	0.445619	−	0.771835i
$122$		0			0
$123$	7.02539	−	5.89500i	0.633458	−	0.531535i
$124$		0			0
$125$	5.86231	−	10.1538i	0.524341	−	0.908185i
$126$		0			0
$127$	−4.46592	−	1.62546i	−0.396287	−	0.144237i	0.136187	−	0.990683i	$-0.456515\pi$
$127$	−4.46592	−	1.62546i	−0.396287	−	0.144237i	−0.532474	+	0.846447i	$0.678737\pi$
$128$		0			0
$129$	−10.5670	−	8.86673i	−0.930368	−	0.780672i
$130$		0			0
$131$	−3.12341	−	17.7137i	−0.272893	−	1.54765i	−0.745575	−	0.666422i	$-0.767825\pi$
$131$	−3.12341	−	17.7137i	−0.272893	−	1.54765i	0.472682	−	0.881233i	$-0.343286\pi$
$132$		0			0
$133$	−3.74181	−	1.36191i	−0.324456	−	0.118092i
$134$		0			0
$135$	3.28373	−	18.6229i	0.282618	−	1.60281i
$136$		0			0
$137$	−11.0546	−	19.1471i	−0.944456	−	1.63585i	−0.756837	−	0.653603i	$-0.773256\pi$
$137$	−11.0546	−	19.1471i	−0.944456	−	1.63585i	−0.187619	−	0.982242i	$-0.560077\pi$
$138$		0			0
$139$	0.462854	+	2.62497i	0.0392587	+	0.222647i	0.998125	−	0.0612114i	$-0.0194964\pi$
$139$	0.462854	+	2.62497i	0.0392587	+	0.222647i	−0.958866	+	0.283859i	$0.908385\pi$
$140$		0			0
$141$	6.70325	−	2.43978i	0.564516	−	0.205467i
$142$		0			0
$143$	−1.81882	+	0.661998i	−0.152098	+	0.0553590i
$144$		0			0
$145$	−6.53925	−	5.48708i	−0.543055	−	0.455678i
$146$		0			0
$147$	51.2822			4.22968
$148$		0			0
$149$	6.13622			0.502699			0.251349	−	0.967896i	$-0.419126\pi$
$149$	6.13622			0.502699			0.251349	+	0.967896i	$0.419126\pi$
$150$		0			0
$151$	0.334584	+	0.280749i	0.0272281	+	0.0228471i	0.656300	−	0.754500i	$-0.272121\pi$
$151$	0.334584	+	0.280749i	0.0272281	+	0.0228471i	−0.629072	+	0.777347i	$0.716565\pi$
$152$		0			0
$153$	−19.1532	+	6.97120i	−1.54845	+	0.563588i
$154$		0			0
$155$	−8.25656	+	3.00514i	−0.663183	+	0.241379i
$156$		0			0
$157$	1.05255	+	5.96930i	0.0840025	+	0.476402i	0.997567	+	0.0697089i	$0.0222070\pi$
$157$	1.05255	+	5.96930i	0.0840025	+	0.476402i	−0.913565	+	0.406693i	$0.866682\pi$
$158$		0			0
$159$	−9.68369	−	16.7726i	−0.767966	−	1.33016i
$160$		0			0
$161$	0.203810	−	1.15586i	0.0160625	−	0.0910948i
$162$		0			0
$163$	12.9066	+	4.69763i	1.01093	+	0.367947i	0.793788	−	0.608194i	$-0.208106\pi$
$163$	12.9066	+	4.69763i	1.01093	+	0.367947i	0.217137	+	0.976141i	$0.430328\pi$
$164$		0			0
$165$	0.916481	+	5.19762i	0.0713480	+	0.404634i
$166$		0			0
$167$	−18.2471	−	15.3112i	−1.41201	−	1.18481i	−0.955463	−	0.295112i	$-0.904643\pi$
$167$	−18.2471	−	15.3112i	−1.41201	−	1.18481i	−0.456543	−	0.889701i	$-0.650913\pi$
$168$		0			0
$169$	9.27344	+	3.37526i	0.713342	+	0.259635i
$170$		0			0
$171$	−2.85491	+	4.94486i	−0.218321	+	0.378143i
$172$		0			0
$173$	16.4280	−	13.7847i	1.24899	−	1.04803i	0.252229	−	0.967668i	$-0.418836\pi$
$173$	16.4280	−	13.7847i	1.24899	−	1.04803i	0.996766	−	0.0803630i	$-0.0256080\pi$
$174$		0			0
$175$	6.39996	−	11.0851i	0.483791	−	0.837951i
$176$		0			0
$177$	13.8973	+	24.0709i	1.04459	+	1.80928i
$178$		0			0
$179$	−11.5247			−0.861400			−0.430700	−	0.902495i	$-0.641733\pi$
$179$	−11.5247			−0.861400			−0.430700	+	0.902495i	$0.641733\pi$
$180$		0			0
$181$	−3.08553	+	17.4989i	−0.229346	+	1.30068i	0.624855	+	0.780740i	$0.285158\pi$
$181$	−3.08553	+	17.4989i	−0.229346	+	1.30068i	−0.854201	+	0.519943i	$0.825953\pi$
$182$		0			0
$183$	−28.3537	+	23.7915i	−2.09596	+	1.75872i
$184$		0			0
$185$	−9.29916	+	0.612921i	−0.683688	+	0.0450629i
$186$		0			0
$187$	2.46831	−	2.07116i	0.180501	−	0.151458i
$188$		0			0
$189$	10.3419	−	58.6520i	0.752265	−	4.26631i
$190$		0			0
$191$	25.9113			1.87487			0.937437	−	0.348155i	$-0.113192\pi$
$191$	25.9113			1.87487			0.937437	+	0.348155i	$0.113192\pi$
$192$		0			0
$193$	−5.45149	−	9.44225i	−0.392407	−	0.679668i	0.600360	−	0.799730i	$-0.295024\pi$
$193$	−5.45149	−	9.44225i	−0.392407	−	0.679668i	−0.992766	+	0.120062i	$0.961691\pi$
$194$		0			0
$195$	−4.26932	+	7.39467i	−0.305732	+	0.529544i
$196$		0			0
$197$	−4.93573	+	4.14157i	−0.351656	+	0.295075i	−0.801455	−	0.598055i	$-0.795940\pi$
$197$	−4.93573	+	4.14157i	−0.351656	+	0.295075i	0.449798	+	0.893130i	$0.351496\pi$
$198$		0			0
$199$	9.42779	−	16.3294i	0.668318	−	1.15756i	−0.310056	−	0.950718i	$-0.600348\pi$
$199$	9.42779	−	16.3294i	0.668318	−	1.15756i	0.978374	−	0.206843i	$-0.0663189\pi$
$200$		0			0
$201$	26.5883	+	9.67734i	1.87539	+	0.682587i
$202$		0			0
$203$	−20.5950	−	17.2813i	−1.44549	−	1.21291i
$204$		0			0
$205$	0.774705	+	4.39357i	0.0541077	+	0.306860i
$206$		0			0
$207$	−1.58149	−	0.575617i	−0.109921	−	0.0400081i
$208$		0			0
$209$	0.156741	−	0.888923i	0.0108420	−	0.0614881i
$210$		0			0
$211$	−0.707251	−	1.22499i	−0.0486891	−	0.0843321i	0.840654	−	0.541573i	$-0.182171\pi$
$211$	−0.707251	−	1.22499i	−0.0486891	−	0.0843321i	−0.889343	+	0.457241i	$0.848838\pi$
$212$		0			0
$213$	0.666471	+	3.77975i	0.0456659	+	0.258984i
$214$		0			0
$215$	6.30567	−	2.29507i	0.430043	−	0.156523i
$216$		0			0
$217$	−26.0036	+	9.46454i	−1.76524	+	0.642495i
$218$		0			0
$219$	21.2170	+	17.8032i	1.43371	+	1.20303i
$220$		0			0
$221$	5.21291			0.350659
$222$		0			0
$223$	12.1750			0.815302			0.407651	−	0.913138i	$-0.366348\pi$
$223$	12.1750			0.815302			0.407651	+	0.913138i	$0.366348\pi$
$224$		0			0
$225$	−14.0601	−	11.7978i	−0.937339	−	0.786520i
$226$		0			0
$227$	−20.0154	+	7.28501i	−1.32847	+	0.483523i	−0.906162	−	0.422930i	$-0.861002\pi$
$227$	−20.0154	+	7.28501i	−1.32847	+	0.483523i	−0.422306	+	0.906453i	$0.638779\pi$
$228$		0			0
$229$	2.67775	−	0.974622i	0.176951	−	0.0644048i	−0.252025	−	0.967721i	$-0.581097\pi$
$229$	2.67775	−	0.974622i	0.176951	−	0.0644048i	0.428976	+	0.903316i	$0.358874\pi$
$230$		0			0
$231$	2.88641	+	16.3696i	0.189912	+	1.07704i
$232$		0			0
$233$	−11.7583	−	20.3659i	−0.770310	−	1.33422i	−0.937393	−	0.348273i	$-0.886768\pi$
$233$	−11.7583	−	20.3659i	−0.770310	−	1.33422i	0.167083	−	0.985943i	$-0.446565\pi$
$234$		0			0
$235$	−0.602587	+	3.41744i	−0.0393084	+	0.222929i
$236$		0			0
$237$	6.37382	+	2.31988i	0.414024	+	0.150692i
$238$		0			0
$239$	−1.39581	−	7.91601i	−0.0902872	−	0.512044i	−0.996090	−	0.0883447i	$-0.971842\pi$
$239$	−1.39581	−	7.91601i	−0.0902872	−	0.512044i	0.905803	−	0.423700i	$-0.139269\pi$
$240$		0			0
$241$	14.1349	+	11.8606i	0.910511	+	0.764010i	0.972216	−	0.234085i	$-0.0752093\pi$
$241$	14.1349	+	11.8606i	0.910511	+	0.764010i	−0.0617048	+	0.998094i	$0.519654\pi$
$242$		0			0
$243$	−18.8189	−	6.84951i	−1.20723	−	0.439397i
$244$		0			0
$245$	−12.4734	+	21.6046i	−0.796898	+	1.38027i
$246$		0			0
$247$	1.11867	−	0.938675i	0.0711792	−	0.0597265i
$248$		0			0
$249$	8.02132	−	13.8933i	0.508330	−	0.880454i
$250$		0			0
$251$	11.6472	+	20.1736i	0.735167	+	1.27335i	0.954650	+	0.297731i	$0.0962297\pi$
$251$	11.6472	+	20.1736i	0.735167	+	1.27335i	−0.219483	+	0.975616i	$0.570437\pi$
$252$		0			0
$253$	0.266055			0.0167267
$254$		0			0
$255$	2.46831	−	13.9985i	0.154571	−	0.876618i
$256$		0			0
$257$	−3.26092	+	2.73624i	−0.203411	+	0.170682i	−0.738803	−	0.673922i	$-0.764608\pi$
$257$	−3.26092	+	2.73624i	−0.203411	+	0.170682i	0.535392	+	0.844604i	$0.320164\pi$
$258$		0			0
$259$	−29.2872	+	1.93036i	−1.81982	+	0.119947i
$260$		0			0
$261$	−29.5317	+	24.7801i	−1.82797	+	1.53385i
$262$		0			0
$263$	1.19565	−	6.78086i	0.0737269	−	0.418126i	−0.925498	−	0.378753i	$-0.876353\pi$
$263$	1.19565	−	6.78086i	0.0737269	−	0.418126i	0.999225	−	0.0393727i	$-0.0125359\pi$
$264$		0			0
$265$	9.42150			0.578758
$266$		0			0
$267$	−14.1350	−	24.4826i	−0.865050	−	1.49831i
$268$		0			0
$269$	−4.83783	+	8.37936i	−0.294968	+	0.510899i	−0.974977	−	0.222304i	$-0.928642\pi$
$269$	−4.83783	+	8.37936i	−0.294968	+	0.510899i	0.680010	+	0.733203i	$0.261976\pi$
$270$		0			0
$271$	−5.87002	+	4.92553i	−0.356578	+	0.299205i	−0.803425	−	0.595406i	$-0.796991\pi$
$271$	−5.87002	+	4.92553i	−0.356578	+	0.299205i	0.446847	+	0.894610i	$0.352547\pi$
$272$		0			0
$273$	−13.4460	+	23.2891i	−0.813789	+	1.40952i
$274$		0			0
$275$	2.72652	+	0.992374i	0.164416	+	0.0598424i
$276$		0			0
$277$	3.07917	+	2.58373i	0.185009	+	0.155241i	0.730589	−	0.682818i	$-0.239246\pi$
$277$	3.07917	+	2.58373i	0.185009	+	0.155241i	−0.545579	+	0.838059i	$0.683690\pi$
$278$		0			0
$279$	6.89040	+	39.0774i	0.412518	+	2.33950i
$280$		0			0
$281$	6.57717	+	2.39389i	0.392361	+	0.142808i	0.530664	−	0.847582i	$-0.321943\pi$
$281$	6.57717	+	2.39389i	0.392361	+	0.142808i	−0.138303	+	0.990390i	$0.544165\pi$
$282$		0			0
$283$	0.816946	−	4.63313i	0.0485624	−	0.275411i	−0.950851	−	0.309648i	$-0.899789\pi$
$283$	0.816946	−	4.63313i	0.0485624	−	0.275411i	0.999414	+	0.0342367i	$0.0109000\pi$
$284$		0			0
$285$	−1.99098	−	3.44847i	−0.117935	−	0.204270i
$286$		0			0
$287$	2.43989	+	13.8373i	0.144022	+	0.816791i
$288$		0			0
$289$	7.82009	−	2.84628i	0.460005	−	0.167428i
$290$		0			0
$291$	−12.9007	+	4.69549i	−0.756255	+	0.275254i
$292$		0			0
$293$	−10.9016	−	9.14751i	−0.636877	−	0.534403i	0.266180	−	0.963923i	$-0.414238\pi$
$293$	−10.9016	−	9.14751i	−0.636877	−	0.534403i	−0.903057	+	0.429520i	$0.858683\pi$
$294$		0			0
$295$	−13.5210			−0.787226
$296$		0			0
$297$	13.5004			0.783374
$298$		0			0
$299$	0.329731	+	0.276678i	0.0190689	+	0.0160007i
$300$		0			0
$301$	19.8594	−	7.22822i	1.14468	−	0.416628i
$302$		0			0
$303$	12.9890	−	4.72760i	0.746197	−	0.271594i
$304$		0			0
$305$	−3.12662	−	17.7319i	−0.179030	−	1.01533i
$306$		0			0
$307$	0.401308	+	0.695086i	0.0229039	+	0.0396707i	0.877250	−	0.480034i	$-0.159376\pi$
$307$	0.401308	+	0.695086i	0.0229039	+	0.0396707i	−0.854346	+	0.519704i	$0.826042\pi$
$308$		0			0
$309$	−6.91563	+	39.2205i	−0.393417	+	2.23118i
$310$		0			0
$311$	−2.32051	−	0.844598i	−0.131584	−	0.0478928i	0.275389	−	0.961333i	$-0.411193\pi$
$311$	−2.32051	−	0.844598i	−0.131584	−	0.0478928i	−0.406973	+	0.913440i	$0.633416\pi$
$312$		0			0
$313$	−3.09856	−	17.5728i	−0.175141	−	0.993273i	−0.937981	−	0.346686i	$-0.887307\pi$
$313$	−3.09856	−	17.5728i	−0.175141	−	0.993273i	0.762840	−	0.646587i	$-0.223804\pi$
$314$		0			0
$315$	39.1833	+	32.8787i	2.20773	+	1.85251i
$316$		0			0
$317$	−3.32609	−	1.21060i	−0.186812	−	0.0679940i	0.246920	−	0.969036i	$-0.420581\pi$
$317$	−3.32609	−	1.21060i	−0.186812	−	0.0679940i	−0.433732	+	0.901042i	$0.642804\pi$
$318$		0			0
$319$	3.04716	−	5.27783i	0.170608	−	0.295502i
$320$		0			0
$321$	−45.5012	+	38.1800i	−2.53963	+	2.13100i
$322$		0			0
$323$	−1.21551	+	2.10533i	−0.0676328	+	0.117143i
$324$		0			0
$325$	2.34708	+	4.06527i	0.130193	+	0.225501i
$326$		0			0
$327$	−26.5005			−1.46548
$328$		0			0
$329$	−1.89782	+	10.7630i	−0.104630	+	0.593386i
$330$		0			0
$331$	−2.93110	+	2.45948i	−0.161108	+	0.135185i	−0.719778	−	0.694205i	$-0.755756\pi$
$331$	−2.93110	+	2.45948i	−0.161108	+	0.135185i	0.558670	+	0.829390i	$0.311312\pi$
$332$		0			0
$333$	−4.56653	+	41.8383i	−0.250244	+	2.29273i
$334$		0			0
$335$	−10.5441	+	8.84751i	−0.576083	+	0.483391i
$336$		0			0
$337$	−3.71542	+	21.0712i	−0.202392	+	1.14782i	0.699100	+	0.715024i	$0.253584\pi$
$337$	−3.71542	+	21.0712i	−0.202392	+	1.14782i	−0.901492	+	0.432797i	$0.857527\pi$
$338$		0			0
$339$	−20.1080			−1.09212
$340$		0			0
$341$	−3.13642	−	5.43244i	−0.169847	−	0.294183i
$342$		0			0
$343$	−22.3961	+	38.7912i	−1.20927	+	2.09453i
$344$		0			0
$345$	0.899102	−	0.754436i	0.0484060	−	0.0406175i
$346$		0			0
$347$	−12.8181	+	22.2016i	−0.688113	+	1.19185i	0.284334	+	0.958725i	$0.408227\pi$
$347$	−12.8181	+	22.2016i	−0.688113	+	1.19185i	−0.972448	+	0.233122i	$0.925106\pi$
$348$		0			0
$349$	−14.5983	−	5.31334i	−0.781428	−	0.284417i	−0.0796600	−	0.996822i	$-0.525383\pi$
$349$	−14.5983	−	5.31334i	−0.781428	−	0.284417i	−0.701768	+	0.712406i	$0.747606\pi$
$350$		0			0
$351$	16.7316	+	14.0395i	0.893065	+	0.749371i
$352$		0			0
$353$	−0.235520	−	1.33570i	−0.0125355	−	0.0710923i	0.977898	−	0.209081i	$-0.0670473\pi$
$353$	−0.235520	−	1.33570i	−0.0125355	−	0.0710923i	−0.990434	+	0.137989i	$0.955936\pi$
$354$		0			0
$355$	−1.75447	−	0.638576i	−0.0931177	−	0.0338921i
$356$		0			0
$357$	7.77381	−	44.0875i	0.411434	−	2.33336i
$358$		0			0
$359$	−11.1573	−	19.3251i	−0.588862	−	1.01994i	−0.994382	−	0.105853i	$-0.966243\pi$
$359$	−11.1573	−	19.3251i	−0.588862	−	1.01994i	0.405519	−	0.914086i	$-0.367091\pi$
$360$		0			0
$361$	−3.18106	−	18.0407i	−0.167424	−	0.949509i
$362$		0			0
$363$	29.0139	−	10.5602i	1.52284	−	0.554267i
$364$		0			0
$365$	−12.6609	+	4.60819i	−0.662702	+	0.241204i
$366$		0			0
$367$	−5.53730	−	4.64635i	−0.289045	−	0.242538i	0.486722	−	0.873557i	$-0.338192\pi$
$367$	−5.53730	−	4.64635i	−0.289045	−	0.242538i	−0.775767	+	0.631019i	$0.782637\pi$
$368$		0			0
$369$	20.1478			1.04885
$370$		0			0
$371$	29.6725			1.54052
$372$		0			0
$373$	−8.98788	−	7.54173i	−0.465375	−	0.390496i	0.379729	−	0.925098i	$-0.376017\pi$
$373$	−8.98788	−	7.54173i	−0.465375	−	0.390496i	−0.845104	+	0.534602i	$0.820462\pi$
$374$		0			0
$375$	34.6992	−	12.6295i	1.79186	−	0.652183i
$376$		0			0
$377$	9.26501	−	3.37219i	0.477172	−	0.173677i
$378$		0			0
$379$	0.480627	+	2.72577i	0.0246881	+	0.140013i	0.994660	−	0.103202i	$-0.0329089\pi$
$379$	0.480627	+	2.72577i	0.0246881	+	0.140013i	−0.969972	+	0.243216i	$0.921798\pi$
$380$		0			0
$381$	−7.48394	−	12.9626i	−0.383414	−	0.664092i
$382$		0			0
$383$	−3.38122	+	19.1758i	−0.172772	+	0.979840i	0.767912	+	0.640556i	$0.221296\pi$
$383$	−3.38122	+	19.1758i	−0.172772	+	0.979840i	−0.940684	+	0.339284i	$0.889815\pi$
$384$		0			0
$385$	−7.59842	−	2.76560i	−0.387251	−	0.140948i
$386$		0			0
$387$	−5.26231	−	29.8440i	−0.267498	−	1.51706i
$388$		0			0
$389$	−1.79849	−	1.50911i	−0.0911870	−	0.0765150i	0.596055	−	0.802944i	$-0.296734\pi$
$389$	−1.79849	−	1.50911i	−0.0911870	−	0.0765150i	−0.687242	+	0.726429i	$0.741179\pi$
$390$		0			0
$391$	−0.673338	−	0.245075i	−0.0340522	−	0.0123940i
$392$		0			0
$393$	28.3245	−	49.0595i	1.42878	−	2.47473i
$394$		0			0
$395$	−2.52765	+	2.12095i	−0.127180	+	0.106717i
$396$		0			0
$397$	−1.13774	+	1.97062i	−0.0571015	+	0.0989026i	−0.893163	−	0.449733i	$-0.851519\pi$
$397$	−1.13774	+	1.97062i	−0.0571015	+	0.0989026i	0.836062	+	0.548635i	$0.184853\pi$
$398$		0			0
$399$	−6.27048	−	10.8608i	−0.313917	−	0.543720i
$400$		0			0
$401$	17.5482			0.876316			0.438158	−	0.898898i	$-0.355631\pi$
$401$	17.5482			0.876316			0.438158	+	0.898898i	$0.355631\pi$
$402$		0			0
$403$	1.76226	−	9.99426i	0.0877843	−	0.497850i
$404$		0			0
$405$	21.2616	−	17.8406i	1.05650	−	0.886508i
$406$		0			0
$407$	−1.58376	−	6.46203i	−0.0785040	−	0.320311i
$408$		0			0
$409$	17.3730	−	14.5777i	0.859041	−	0.720821i	−0.102720	−	0.994710i	$-0.532755\pi$
$409$	17.3730	−	14.5777i	0.859041	−	0.720821i	0.961761	+	0.273889i	$0.0883102\pi$
$410$		0			0
$411$	12.0914	−	68.5738i	0.596425	−	3.38249i
$412$		0			0
$413$	−42.5838			−2.09541
$414$		0			0
$415$	3.90207	+	6.75859i	0.191545	+	0.331766i
$416$		0			0
$417$	−4.19738	+	7.27007i	−0.205547	+	0.356017i
$418$		0			0
$419$	−14.4180	+	12.0981i	−0.704365	+	0.591032i	−0.923012	−	0.384772i	$-0.874280\pi$
$419$	−14.4180	+	12.0981i	−0.704365	+	0.591032i	0.218647	+	0.975804i	$0.429836\pi$
$420$		0			0
$421$	8.96330	−	15.5249i	0.436844	−	0.756637i	−0.560600	−	0.828087i	$-0.689429\pi$
$421$	8.96330	−	15.5249i	0.436844	−	0.756637i	0.997444	+	0.0714502i	$0.0227627\pi$
$422$		0			0
$423$	14.7264	+	5.35997i	0.716021	+	0.260610i
$424$		0			0
$425$	−5.98623	−	5.02304i	−0.290375	−	0.243653i
$426$		0			0
$427$	−9.84712	−	55.8458i	−0.476536	−	2.70257i
$428$		0			0
$429$	−5.72829	−	2.08493i	−0.276564	−	0.100661i
$430$		0			0
$431$	−2.12908	+	12.0746i	−0.102554	+	0.581613i	0.889615	+	0.456711i	$0.150973\pi$
$431$	−2.12908	+	12.0746i	−0.102554	+	0.581613i	−0.992169	+	0.124902i	$0.960138\pi$
$432$		0			0
$433$	−10.5573	−	18.2858i	−0.507351	−	0.878758i	−0.999964	−	0.00850909i	$-0.997291\pi$
$433$	−10.5573	−	18.2858i	−0.507351	−	0.878758i	0.492613	−	0.870249i	$-0.336042\pi$
$434$		0			0
$435$	−4.66852	−	26.4765i	−0.223838	−	1.26945i
$436$		0			0
$437$	−0.188625	+	0.0686540i	−0.00902318	+	0.00328417i
$438$		0			0
$439$	−22.6396	+	8.24015i	−1.08053	+	0.393281i	−0.820105	−	0.572213i	$-0.806085\pi$
$439$	−22.6396	+	8.24015i	−1.08053	+	0.393281i	−0.260425	+	0.965494i	$0.583863\pi$
$440$		0			0
$441$	86.3040	+	72.4176i	4.10971	+	3.44846i
$442$		0			0
$443$	−19.2348			−0.913871			−0.456936	−	0.889500i	$-0.651053\pi$
$443$	−19.2348			−0.913871			−0.456936	+	0.889500i	$0.651053\pi$
$444$		0			0
$445$	13.7523			0.651923
$446$		0			0
$447$	14.8043	+	12.4223i	0.700222	+	0.587556i
$448$		0			0
$449$	6.19008	−	2.25301i	0.292128	−	0.106326i	−0.191799	−	0.981434i	$-0.561432\pi$
$449$	6.19008	−	2.25301i	0.292128	−	0.106326i	0.483927	+	0.875108i	$0.339210\pi$
$450$		0			0
$451$	−2.99297	+	1.08935i	−0.140934	+	0.0512956i
$452$		0			0
$453$	0.238867	+	1.35468i	0.0112229	+	0.0636485i
$454$		0			0
$455$	−6.54097	−	11.3293i	−0.306646	−	0.531126i
$456$		0			0
$457$	−5.03427	+	28.5507i	−0.235493	+	1.33555i	0.606080	+	0.795404i	$0.292741\pi$
$457$	−5.03427	+	28.5507i	−0.235493	+	1.33555i	−0.841573	+	0.540144i	$0.818370\pi$
$458$		0			0
$459$	−34.1672	−	12.4358i	−1.59479	−	0.580455i
$460$		0			0
$461$	6.22553	+	35.3067i	0.289952	+	1.64440i	0.687041	+	0.726618i	$0.258909\pi$
$461$	6.22553	+	35.3067i	0.289952	+	1.64440i	−0.397089	+	0.917780i	$0.629980\pi$
$462$		0			0
$463$	14.2350	+	11.9446i	0.661556	+	0.555111i	0.910553	−	0.413393i	$-0.135656\pi$
$463$	14.2350	+	11.9446i	0.661556	+	0.555111i	−0.248997	+	0.968504i	$0.580101\pi$
$464$		0			0
$465$	−26.0036	−	9.46454i	−1.20589	−	0.438908i
$466$		0			0
$467$	−0.823127	+	1.42570i	−0.0380898	+	0.0659734i	−0.884442	−	0.466650i	$-0.845461\pi$
$467$	−0.823127	+	1.42570i	−0.0380898	+	0.0659734i	0.846352	+	0.532624i	$0.178794\pi$
$468$		0			0
$469$	−33.2080	+	27.8648i	−1.53340	+	1.28668i
$470$		0			0
$471$	−9.54501	+	16.5324i	−0.439811	+	0.761775i
$472$		0			0
$473$	2.39533	+	4.14884i	0.110138	+	0.190764i
$474$		0			0
$475$	−2.18911			−0.100443
$476$		0			0
$477$	7.38842	−	41.9018i	0.338292	−	1.91855i
$478$		0			0
$479$	26.1002	−	21.9007i	1.19255	−	1.00067i	0.192737	−	0.981250i	$-0.438264\pi$
$479$	26.1002	−	21.9007i	1.19255	−	1.00067i	0.999811	−	0.0194166i	$-0.00618087\pi$
$480$		0			0
$481$	4.75723	−	9.65562i	0.216911	−	0.440258i
$482$		0			0
$483$	2.83168	−	2.37606i	0.128846	−	0.108114i
$484$		0			0
$485$	1.15971	−	6.57703i	0.0526596	−	0.298647i
$486$		0			0
$487$	31.0898			1.40881			0.704407	−	0.709796i	$-0.251213\pi$
$487$	31.0898			1.40881			0.704407	+	0.709796i	$0.251213\pi$
$488$		0			0
$489$	21.6288	+	37.4621i	0.978086	+	1.69409i
$490$		0			0
$491$	17.5270	−	30.3576i	0.790981	−	1.37002i	−0.134379	−	0.990930i	$-0.542904\pi$
$491$	17.5270	−	30.3576i	0.790981	−	1.37002i	0.925360	−	0.379089i	$-0.123763\pi$
$492$		0			0
$493$	−12.5735	+	10.5504i	−0.566280	+	0.475165i
$494$		0			0
$495$	−5.79741	+	10.0414i	−0.260574	+	0.451328i
$496$		0			0
$497$	−5.52562	−	2.01116i	−0.247858	−	0.0902129i
$498$		0			0
$499$	26.9427	+	22.6076i	1.20612	+	1.01205i	0.999434	+	0.0336472i	$0.0107122\pi$
$499$	26.9427	+	22.6076i	1.20612	+	1.01205i	0.206686	+	0.978407i	$0.433732\pi$
$500$		0			0
$501$	−13.0270	−	73.8800i	−0.582005	−	3.30071i
$502$		0			0
$503$	4.35300	+	1.58436i	0.194091	+	0.0706432i	0.437237	−	0.899346i	$-0.355957\pi$
$503$	4.35300	+	1.58436i	0.194091	+	0.0706432i	−0.243146	+	0.969990i	$0.578179\pi$
$504$		0			0
$505$	−1.16764	+	6.62201i	−0.0519593	+	0.294676i
$506$		0			0
$507$	15.5403	+	26.9166i	0.690169	+	1.19541i
$508$		0			0
$509$	−4.14162	−	23.4883i	−0.183574	−	1.04110i	−0.927774	−	0.373144i	$-0.878280\pi$
$509$	−4.14162	−	23.4883i	−0.183574	−	1.04110i	0.744199	−	0.667958i	$-0.232831\pi$
$510$		0			0
$511$	−39.8749	+	14.5133i	−1.76396	+	0.642029i
$512$		0			0
$513$	−9.57142	+	3.48371i	−0.422589	+	0.153810i
$514$		0			0
$515$	−14.8411	−	12.4531i	−0.653976	−	0.548751i
$516$		0			0
$517$	−2.47742			−0.108957
$518$		0			0
$519$	67.5405			2.96470
$520$		0			0
$521$	14.8610	+	12.4698i	0.651071	+	0.546313i	0.907396	−	0.420278i	$-0.138067\pi$
$521$	14.8610	+	12.4698i	0.651071	+	0.546313i	−0.256325	+	0.966591i	$0.582512\pi$
$522$		0			0
$523$	1.82296	−	0.663503i	0.0797125	−	0.0290130i	−0.301856	−	0.953353i	$-0.597606\pi$
$523$	1.82296	−	0.663503i	0.0797125	−	0.0290130i	0.381569	+	0.924341i	$0.375384\pi$
$524$		0			0
$525$	37.8815	−	13.7878i	1.65329	−	0.601747i
$526$		0			0
$527$	2.93366	+	16.6376i	0.127792	+	0.724747i
$528$		0			0
$529$	11.4704	+	19.8673i	0.498714	+	0.863798i
$530$		0			0
$531$	−10.6033	+	60.1344i	−0.460145	+	2.60961i
$532$		0			0
$533$	−4.84214	−	1.76240i	−0.209737	−	0.0763379i
$534$		0			0
$535$	−5.01751	−	28.4557i	−0.216926	−	1.23025i
$536$		0			0
$537$	−27.8048	−	23.3310i	−1.19987	−	1.00681i
$538$		0			0
$539$	−16.7360	−	6.09141i	−0.720872	−	0.262376i
$540$		0			0
$541$	2.15605	−	3.73439i	0.0926958	−	0.160554i	−0.815949	−	0.578124i	$-0.803785\pi$
$541$	2.15605	−	3.73439i	0.0926958	−	0.160554i	0.908645	+	0.417570i	$0.137118\pi$
$542$		0			0
$543$	−42.8694	+	35.9717i	−1.83970	+	1.54370i
$544$		0			0
$545$	6.44574	−	11.1644i	0.276105	−	0.478228i
$546$		0			0
$547$	8.75830	+	15.1698i	0.374478	+	0.648615i	0.990249	−	0.139311i	$-0.0444887\pi$
$547$	8.75830	+	15.1698i	0.374478	+	0.648615i	−0.615771	+	0.787925i	$0.711155\pi$
$548$		0			0
$549$	−81.3141			−3.47040
$550$		0			0
$551$	−0.798433	+	4.52814i	−0.0340144	+	0.192905i
$552$		0			0
$553$	−7.96071	+	6.67983i	−0.338524	+	0.284055i
$554$		0			0
$555$	−23.6761	−	17.3467i	−1.00500	−	0.736327i
$556$		0			0
$557$	17.4740	−	14.6624i	0.740398	−	0.621268i	−0.192546	−	0.981288i	$-0.561675\pi$
$557$	17.4740	−	14.6624i	0.740398	−	0.621268i	0.932945	+	0.360020i	$0.117230\pi$
$558$		0			0
$559$	−1.34586	+	7.63278i	−0.0569240	+	0.322832i
$560$		0			0
$561$	10.1480			0.428448
$562$		0			0
$563$	−13.2921	−	23.0226i	−0.560195	−	0.970287i	−0.997479	−	0.0709631i	$-0.977393\pi$
$563$	−13.2921	−	23.0226i	−0.560195	−	0.970287i	0.437284	−	0.899324i	$-0.355941\pi$
$564$		0			0
$565$	4.89090	−	8.47128i	0.205762	−	0.356389i
$566$		0			0
$567$	66.9625	−	56.1882i	2.81216	−	2.35968i
$568$		0			0
$569$	6.98492	−	12.0982i	0.292823	−	0.507184i	−0.681653	−	0.731676i	$-0.738739\pi$
$569$	6.98492	−	12.0982i	0.292823	−	0.507184i	0.974476	+	0.224491i	$0.0720720\pi$
$570$		0			0
$571$	20.6390	+	7.51199i	0.863717	+	0.314367i	0.735620	−	0.677395i	$-0.236891\pi$
$571$	20.6390	+	7.51199i	0.863717	+	0.314367i	0.128097	+	0.991762i	$0.459113\pi$
$572$		0			0
$573$	62.5140	+	52.4555i	2.61156	+	2.19136i
$574$		0			0
$575$	−0.112046	−	0.635443i	−0.00467263	−	0.0264998i
$576$		0			0
$577$	−29.6115	−	10.7777i	−1.23274	−	0.448682i	−0.358207	−	0.933642i	$-0.616612\pi$
$577$	−29.6115	−	10.7777i	−1.23274	−	0.448682i	−0.874536	+	0.484961i	$0.838834\pi$
$578$		0			0
$579$	5.96279	−	33.8167i	0.247805	−	1.40537i
$580$		0			0
$581$	12.2894	+	21.2858i	0.509849	+	0.883085i
$582$		0			0
$583$	1.16800	+	6.62403i	0.0483734	+	0.274339i
$584$		0			0
$585$	−17.6273	+	6.41580i	−0.728797	+	0.265261i
$586$		0			0
$587$	−39.3494	+	14.3220i	−1.62412	+	0.591133i	−0.984162	−	0.177273i	$-0.943273\pi$
$587$	−39.3494	+	14.3220i	−1.62412	+	0.591133i	−0.639963	+	0.768406i	$0.721050\pi$
$588$		0			0
$589$	3.62544	+	3.04211i	0.149384	+	0.125348i
$590$		0			0
$591$	−20.2923			−0.834715
$592$		0			0
$593$	−30.7471			−1.26263			−0.631316	−	0.775525i	$-0.717485\pi$
$593$	−30.7471			−1.26263			−0.631316	+	0.775525i	$0.717485\pi$
$594$		0			0
$595$	16.6827	+	13.9985i	0.683925	+	0.573881i
$596$		0			0
$597$	55.8033	−	20.3108i	2.28388	−	0.831264i
$598$		0			0
$599$	28.2700	−	10.2894i	1.15508	−	0.420415i	0.307742	−	0.951470i	$-0.400427\pi$
$599$	28.2700	−	10.2894i	1.15508	−	0.420415i	0.847337	+	0.531055i	$0.178204\pi$
$600$		0			0
$601$	5.27054	+	29.8907i	0.214990	+	1.21927i	0.880924	+	0.473257i	$0.156922\pi$
$601$	5.27054	+	29.8907i	0.214990	+	1.21927i	−0.665935	+	0.746010i	$0.731967\pi$
$602$		0			0
$603$	31.0803	+	53.8326i	1.26569	+	2.19223i
$604$		0			0
$605$	−2.60820	+	14.7918i	−0.106038	+	0.601373i
$606$		0			0
$607$	−1.08095	−	0.393434i	−0.0438744	−	0.0159690i	0.319990	−	0.947421i	$-0.396321\pi$
$607$	−1.08095	−	0.393434i	−0.0438744	−	0.0159690i	−0.363864	+	0.931452i	$0.618543\pi$
$608$		0			0
$609$	−14.7033	−	83.3863i	−0.595806	−	3.37898i
$610$		0			0
$611$	−3.07036	−	2.57634i	−0.124213	−	0.104227i
$612$		0			0
$613$	14.5282	+	5.28784i	0.586789	+	0.213574i	0.618317	−	0.785929i	$-0.287815\pi$
$613$	14.5282	+	5.28784i	0.586789	+	0.213574i	−0.0315273	+	0.999503i	$0.510037\pi$
$614$		0			0
$615$	−7.02539	+	12.1683i	−0.283291	+	0.490675i
$616$		0			0
$617$	16.0733	−	13.4871i	0.647086	−	0.542970i	−0.259099	−	0.965851i	$-0.583426\pi$
$617$	16.0733	−	13.4871i	0.647086	−	0.542970i	0.906185	+	0.422881i	$0.138981\pi$
$618$		0			0
$619$	15.4275	−	26.7212i	0.620084	−	1.07402i	−0.369386	−	0.929276i	$-0.620432\pi$
$619$	15.4275	−	26.7212i	0.620084	−	1.07402i	0.989470	−	0.144741i	$-0.0462349\pi$
$620$		0			0
$621$	−1.50113	−	2.60004i	−0.0602384	−	0.104336i
$622$		0			0
$623$	43.3122			1.73527
$624$		0			0
$625$	−0.816085	+	4.62825i	−0.0326434	+	0.185130i
$626$		0			0
$627$	2.17772	−	1.82732i	0.0869696	−	0.0729761i
$628$		0			0
$629$	−1.94425	+	17.8131i	−0.0775222	+	0.710255i
$630$		0			0
$631$	−4.47641	+	3.75615i	−0.178203	+	0.149530i	−0.727526	−	0.686080i	$-0.759330\pi$
$631$	−4.47641	+	3.75615i	−0.178203	+	0.149530i	0.549323	+	0.835610i	$0.314886\pi$
$632$		0			0
$633$	0.773585	−	4.38722i	0.0307472	−	0.174376i
$634$		0			0
$635$	7.28131			0.288950
$636$		0			0
$637$	−14.4069	−	24.9535i	−0.570824	−	0.988695i
$638$		0			0
$639$	−4.21591	+	7.30218i	−0.166779	+	0.288870i
$640$		0			0
$641$	22.8599	−	19.1817i	0.902912	−	0.757633i	−0.0678451	−	0.997696i	$-0.521612\pi$
$641$	22.8599	−	19.1817i	0.902912	−	0.757633i	0.970757	+	0.240062i	$0.0771679\pi$
$642$		0			0
$643$	7.18117	−	12.4382i	0.283198	−	0.490513i	−0.688973	−	0.724787i	$-0.741938\pi$
$643$	7.18117	−	12.4382i	0.283198	−	0.490513i	0.972171	+	0.234274i	$0.0752714\pi$
$644$		0			0
$645$	19.8594	+	7.22822i	0.781962	+	0.284611i
$646$		0			0
$647$	−7.11852	−	5.97315i	−0.279858	−	0.234829i	0.492044	−	0.870570i	$-0.336250\pi$
$647$	−7.11852	−	5.97315i	−0.279858	−	0.234829i	−0.771902	+	0.635742i	$0.780694\pi$
$648$		0			0
$649$	−1.67622	−	9.50632i	−0.0657974	−	0.373156i
$650$		0			0
$651$	−81.8971	−	29.8081i	−3.20980	−	1.16827i
$652$		0			0
$653$	−7.38987	+	41.9101i	−0.289188	+	1.64007i	0.400742	+	0.916191i	$0.368752\pi$
$653$	−7.38987	+	41.9101i	−0.289188	+	1.64007i	−0.689930	+	0.723876i	$0.742359\pi$
$654$		0			0
$655$	13.7788	+	23.8656i	0.538383	+	0.932507i
$656$		0			0
$657$	10.5660	+	59.9227i	0.412219	+	2.33781i
$658$		0			0
$659$	10.3196	−	3.75603i	0.401995	−	0.146314i	−0.133107	−	0.991102i	$-0.542495\pi$
$659$	10.3196	−	3.75603i	0.401995	−	0.146314i	0.535102	+	0.844788i	$0.320273\pi$
$660$		0			0
$661$	−31.5074	+	11.4678i	−1.22550	+	0.446044i	−0.872053	−	0.489412i	$-0.837212\pi$
$661$	−31.5074	+	11.4678i	−1.22550	+	0.446044i	−0.353444	+	0.935456i	$0.614989\pi$
$662$		0			0
$663$	12.5768	+	10.5532i	0.488441	+	0.409851i
$664$		0			0
$665$	6.10071			0.236575
$666$		0			0
$667$	−1.35527			−0.0524764
$668$		0			0
$669$	29.3737	+	24.6475i	1.13565	+	0.952927i
$670$		0			0
$671$	12.0793	−	4.39650i	0.466316	−	0.169725i
$672$		0			0
$673$	41.1753	−	14.9866i	1.58719	−	0.577691i	0.610440	−	0.792063i	$-0.290993\pi$
$673$	41.1753	−	14.9866i	1.58719	−	0.577691i	0.976752	+	0.214372i	$0.0687704\pi$
$674$		0			0
$675$	−5.68554	−	32.2443i	−0.218837	−	1.24108i
$676$		0			0
$677$	1.08790	+	1.88429i	0.0418113	+	0.0724192i	0.886174	−	0.463353i	$-0.153354\pi$
$677$	1.08790	+	1.88429i	0.0418113	+	0.0724192i	−0.844362	+	0.535772i	$0.820021\pi$
$678$		0			0
$679$	3.65244	−	20.7140i	0.140168	−	0.794931i
$680$		0			0
$681$	−63.0375	−	22.9438i	−2.41560	−	0.879207i
$682$		0			0
$683$	5.50558	+	31.2237i	0.210665	+	1.19474i	0.888272	+	0.459318i	$0.151906\pi$
$683$	5.50558	+	31.2237i	0.210665	+	1.19474i	−0.677607	+	0.735424i	$0.736983\pi$
$684$		0			0
$685$	25.9484	+	21.7733i	0.991436	+	0.831913i
$686$		0			0
$687$	8.43344	+	3.06952i	0.321756	+	0.117110i
$688$		0			0
$689$	−5.44097	+	9.42403i	−0.207284	+	0.359027i
$690$		0			0
$691$	−19.5271	+	16.3852i	−0.742847	+	0.623323i	−0.933601	−	0.358315i	$-0.883351\pi$
$691$	−19.5271	+	16.3852i	−0.742847	+	0.623323i	0.190754	+	0.981638i	$0.438907\pi$
$692$		0			0
$693$	−18.2586	+	31.6249i	−0.693588	+	1.20133i
$694$		0			0
$695$	−2.04187	−	3.53662i	−0.0774525	−	0.134152i
$696$		0			0
$697$	8.57813			0.324920
$698$		0			0
$699$	12.8611	−	72.9390i	0.486452	−	2.75880i
$700$		0			0
$701$	−13.7802	+	11.5629i	−0.520470	+	0.436726i	−0.864796	−	0.502124i	$-0.832552\pi$
$701$	−13.7802	+	11.5629i	−0.520470	+	0.436726i	0.344325	+	0.938850i	$0.388108\pi$
$702$		0			0
$703$	2.79033	+	4.17272i	0.105239	+	0.157377i
$704$		0			0
$705$	−8.37216	+	7.02508i	−0.315314	+	0.264580i
$706$		0			0
$707$	−3.67742	+	20.8557i	−0.138304	+	0.784359i
$708$		0			0
$709$	27.8902			1.04744			0.523719	−	0.851891i	$-0.324544\pi$
$709$	27.8902			1.04744			0.523719	+	0.851891i	$0.324544\pi$
$710$		0			0
$711$	7.45066	+	12.9049i	0.279421	+	0.483972i
$712$		0			0
$713$	−0.697487	+	1.20808i	−0.0261211	+	0.0452430i
$714$		0			0
$715$	2.27166	−	1.90615i	0.0849551	−	0.0712858i
$716$		0			0
$717$	12.6578	−	21.9240i	0.472716	−	0.818768i
$718$		0			0
$719$	−25.7753	−	9.38145i	−0.961257	−	0.349869i	−0.186731	−	0.982411i	$-0.559789\pi$
$719$	−25.7753	−	9.38145i	−0.961257	−	0.349869i	−0.774526	+	0.632542i	$0.782012\pi$
$720$		0			0
$721$	−46.7412	−	39.2205i	−1.74073	−	1.46065i
$722$		0			0
$723$	10.0912	+	57.2303i	0.375297	+	2.12842i
$724$		0			0
$725$	−13.8888	−	5.05511i	−0.515817	−	0.187742i
$726$		0			0
$727$	−1.76832	+	10.0286i	−0.0655832	+	0.371941i	0.934298	+	0.356494i	$0.116028\pi$
$727$	−1.76832	+	10.0286i	−0.0655832	+	0.371941i	−0.999881	+	0.0154465i	$0.995083\pi$
$728$		0			0
$729$	−4.36265	−	7.55633i	−0.161580	−	0.279864i
$730$		0			0
$731$	−2.24049	−	12.7064i	−0.0828673	−	0.469964i
$732$		0			0
$733$	33.0879	−	12.0430i	1.22213	−	0.444819i	0.351234	−	0.936288i	$-0.385762\pi$
$733$	33.0879	−	12.0430i	1.22213	−	0.444819i	0.870895	+	0.491469i	$0.163540\pi$
$734$		0			0
$735$	−73.8305	+	26.8721i	−2.72328	+	0.991193i
$736$		0			0
$737$	−7.52763	−	6.31643i	−0.277284	−	0.232669i
$738$		0			0
$739$	8.78122			0.323022			0.161511	−	0.986871i	$-0.448363\pi$
$739$	8.78122			0.323022			0.161511	+	0.986871i	$0.448363\pi$
$740$		0			0
$741$	4.59920			0.168956
$742$		0			0
$743$	−11.2952	−	9.47778i	−0.414380	−	0.347706i	0.411640	−	0.911346i	$-0.364956\pi$
$743$	−11.2952	−	9.47778i	−0.414380	−	0.347706i	−0.826020	+	0.563640i	$0.809400\pi$
$744$		0			0
$745$	−8.83427	+	3.21541i	−0.323663	+	0.117804i
$746$		0			0
$747$	33.1186	−	12.0542i	1.21175	−	0.441040i
$748$		0			0
$749$	−15.8024	−	89.6198i	−0.577407	−	3.27464i
$750$		0			0
$751$	−17.4428	−	30.2118i	−0.636496	−	1.10244i	−0.986196	−	0.165582i	$-0.947050\pi$
$751$	−17.4428	−	30.2118i	−0.636496	−	1.10244i	0.349700	−	0.936862i	$-0.386284\pi$
$752$		0			0
$753$	−12.7397	+	72.2502i	−0.464259	+	2.63294i
$754$		0			0
$755$	−0.628812	−	0.228869i	−0.0228848	−	0.00832939i
$756$		0			0
$757$	9.03260	+	51.2264i	0.328296	+	1.86186i	0.485425	+	0.874278i	$0.338665\pi$
$757$	9.03260	+	51.2264i	0.328296	+	1.86186i	−0.157129	+	0.987578i	$0.550224\pi$
$758$		0			0
$759$	0.641889	+	0.538609i	0.0232991	+	0.0195503i
$760$		0			0
$761$	−5.60441	−	2.03984i	−0.203160	−	0.0739441i	0.238436	−	0.971158i	$-0.423365\pi$
$761$	−5.60441	−	2.03984i	−0.203160	−	0.0739441i	−0.441596	+	0.897214i	$0.645587\pi$
$762$		0			0
$763$	20.3005	−	35.1616i	0.734929	−	1.27293i
$764$		0			0
$765$	23.9218	−	20.0728i	0.864894	−	0.725732i
$766$		0			0
$767$	7.80847	−	13.5247i	0.281948	−	0.488348i
$768$		0			0
$769$	−18.5451	−	32.1210i	−0.668753	−	1.15831i	−0.978253	−	0.207415i	$-0.933495\pi$
$769$	−18.5451	−	32.1210i	−0.668753	−	1.15831i	0.309500	−	0.950900i	$-0.399838\pi$
$770$		0			0
$771$	−13.4067			−0.482830
$772$		0			0
$773$	−0.552148	+	3.13139i	−0.0198594	+	0.112628i	−0.993126	−	0.117050i	$-0.962656\pi$
$773$	−0.552148	+	3.13139i	−0.0198594	+	0.112628i	0.973267	+	0.229678i	$0.0737673\pi$
$774$		0			0
$775$	−11.6539	+	9.77880i	−0.418621	+	0.351265i
$776$		0			0
$777$	−74.5667	−	54.6326i	−2.67507	−	1.95993i
$778$		0			0
$779$	1.84083	−	1.54464i	0.0659546	−	0.0553425i
$780$		0			0
$781$	0.231463	−	1.31269i	0.00828240	−	0.0469718i
$782$		0			0
$783$	−68.7706			−2.45766
$784$		0			0
$785$	−4.64329	−	8.04242i	−0.165726	−	0.287046i
$786$		0			0
$787$	−2.62525	+	4.54707i	−0.0935802	+	0.162086i	−0.909015	−	0.416763i	$-0.863164\pi$
$787$	−2.62525	+	4.54707i	−0.0935802	+	0.162086i	0.815435	+	0.578849i	$0.196498\pi$
$788$		0			0
$789$	16.6120	−	13.9391i	0.591403	−	0.496246i
$790$		0			0
$791$	15.4036	−	26.6799i	0.547690	−	0.948627i
$792$		0			0
$793$	19.5423	+	7.11283i	0.693968	+	0.252584i
$794$		0			0
$795$	22.7305	+	19.0731i	0.806167	+	0.676455i
$796$		0			0
$797$	4.62443	+	26.2264i	0.163806	+	0.928988i	0.950287	+	0.311375i	$0.100789\pi$
$797$	4.62443	+	26.2264i	0.163806	+	0.928988i	−0.786482	+	0.617614i	$0.788100\pi$
$798$		0			0
$799$	6.26992	+	2.28206i	0.221814	+	0.0807336i
$800$		0			0
$801$	10.7847	−	61.1630i	0.381058	−	2.16109i
$802$		0			0
$803$	−4.80950	−	8.33030i	−0.169724	−	0.293970i
$804$		0			0
$805$	0.312255	+	1.77089i	0.0110055	+	0.0624155i
$806$		0			0
$807$	−28.6352	+	10.4224i	−1.00801	+	0.366885i
$808$		0			0
$809$	14.5826	−	5.30762i	0.512696	−	0.186606i	−0.0726995	−	0.997354i	$-0.523161\pi$
$809$	14.5826	−	5.30762i	0.512696	−	0.186606i	0.585396	+	0.810748i	$0.300939\pi$
$810$		0			0
$811$	−25.0817	−	21.0460i	−0.880737	−	0.739026i	0.0855938	−	0.996330i	$-0.472721\pi$
$811$	−25.0817	−	21.0460i	−0.880737	−	0.739026i	−0.966330	+	0.257304i	$0.917166\pi$
$812$		0			0
$813$	−24.1335			−0.846399
$814$		0			0
$815$	−21.0432			−0.737110
$816$		0			0
$817$	−2.76881	−	2.32331i	−0.0968684	−	0.0812822i
$818$		0			0
$819$	−55.5161	+	20.2062i	−1.93989	+	0.706063i
$820$		0			0
$821$	11.4303	−	4.16028i	0.398920	−	0.145195i	−0.134767	−	0.990877i	$-0.543028\pi$
$821$	11.4303	−	4.16028i	0.398920	−	0.145195i	0.533686	+	0.845682i	$0.320806\pi$
$822$		0			0
$823$	−3.78732	−	21.4790i	−0.132018	−	0.748709i	−0.976890	−	0.213742i	$-0.931435\pi$
$823$	−3.78732	−	21.4790i	−0.132018	−	0.748709i	0.844873	−	0.534968i	$-0.179676\pi$
$824$		0			0
$825$	4.56907	+	7.91387i	0.159075	+	0.275525i
$826$		0			0
$827$	2.00178	−	11.3526i	0.0696086	−	0.394770i	−0.930020	−	0.367509i	$-0.880211\pi$
$827$	2.00178	−	11.3526i	0.0696086	−	0.394770i	0.999628	−	0.0272604i	$-0.00867834\pi$
$828$		0			0
$829$	9.86084	+	3.58905i	0.342481	+	0.124653i	0.507534	−	0.861632i	$-0.330557\pi$
$829$	9.86084	+	3.58905i	0.342481	+	0.124653i	−0.165053	+	0.986285i	$0.552779\pi$
$830$		0			0
$831$	2.19829	+	12.4671i	0.0762578	+	0.432479i
$832$		0			0
$833$	36.7448	+	30.8326i	1.27313	+	1.06829i
$834$		0			0
$835$	34.2934	+	12.4818i	1.18677	+	0.431950i
$836$		0			0
$837$	−35.3926	+	61.3018i	−1.22335	+	2.11890i
$838$		0			0
$839$	21.1557	−	17.7517i	0.730375	−	0.612857i	−0.199859	−	0.979825i	$-0.564048\pi$
$839$	21.1557	−	17.7517i	0.730375	−	0.612857i	0.930234	+	0.366968i	$0.119604\pi$
$840$		0			0
$841$	−1.02209	+	1.77032i	−0.0352446	+	0.0610455i
$842$		0			0
$843$	11.0219	+	19.0905i	0.379615	+	0.657513i
$844$		0			0
$845$	−15.1196			−0.520129
$846$		0			0
$847$	−8.21439	+	46.5861i	−0.282250	+	1.60072i
$848$		0			0
$849$	11.3504	−	9.52412i	0.389545	−	0.326867i
$850$		0			0
$851$	−1.06842	+	1.02354i	−0.0366249	+	0.0350864i
$852$		0			0
$853$	15.8103	−	13.2664i	0.541334	−	0.454233i	−0.330660	−	0.943750i	$-0.607271\pi$
$853$	15.8103	−	13.2664i	0.541334	−	0.454233i	0.871994	+	0.489517i	$0.162827\pi$
$854$		0			0
$855$	1.51907	−	8.61506i	0.0519510	−	0.294629i
$856$		0			0
$857$	31.3189			1.06983			0.534917	−	0.844905i	$-0.320343\pi$
$857$	31.3189			1.06983			0.534917	+	0.844905i	$0.320343\pi$
$858$		0			0
$859$	22.7736	+	39.4450i	0.777025	+	1.34585i	0.933649	+	0.358189i	$0.116606\pi$
$859$	22.7736	+	39.4450i	0.777025	+	1.34585i	−0.156624	+	0.987658i	$0.550061\pi$
$860$		0			0
$861$	−22.1261	+	38.3235i	−0.754056	+	1.30606i
$862$		0			0
$863$	38.4587	−	32.2707i	1.30915	−	1.09851i	0.320664	−	0.947193i	$-0.396094\pi$
$863$	38.4587	−	32.2707i	1.30915	−	1.09851i	0.988486	−	0.151314i	$-0.0483503\pi$
$864$		0			0
$865$	−16.4280	+	28.4541i	−0.558567	+	0.967467i
$866$		0			0
$867$	24.6290	+	8.96421i	0.836444	+	0.304441i
$868$		0			0
$869$	−1.80455	−	1.51419i	−0.0612151	−	0.0513655i
$870$		0			0
$871$	−2.76064	−	15.6564i	−0.0935407	−	0.530496i
$872$		0			0
$873$	−28.3417	−	10.3155i	−0.959220	−	0.349127i
$874$		0			0
$875$	−9.82398	+	55.7146i	−0.332111	+	1.88350i
$876$		0			0
$877$	−15.8566	−	27.4644i	−0.535439	−	0.927408i	−0.999142	−	0.0414174i	$-0.986813\pi$
$877$	−15.8566	−	27.4644i	−0.535439	−	0.927408i	0.463702	−	0.885991i	$-0.346521\pi$
$878$		0			0
$879$	−7.78288	−	44.1389i	−0.262510	−	1.48877i
$880$		0			0
$881$	−27.9167	+	10.1609i	−0.940538	+	0.342328i	−0.766378	−	0.642390i	$-0.777943\pi$
$881$	−27.9167	+	10.1609i	−0.940538	+	0.342328i	−0.174160	+	0.984717i	$0.555721\pi$
$882$		0			0
$883$	14.6477	−	5.33132i	0.492934	−	0.179413i	−0.0835793	−	0.996501i	$-0.526635\pi$
$883$	14.6477	−	5.33132i	0.492934	−	0.179413i	0.576513	+	0.817088i	$0.304413\pi$
$884$		0			0
$885$	−32.6211	−	27.3724i	−1.09655	−	0.920112i
$886$		0			0
$887$	39.8038			1.33648			0.668240	−	0.743946i	$-0.267048\pi$
$887$	39.8038			1.33648			0.668240	+	0.743946i	$0.267048\pi$
$888$		0			0
$889$	22.9321			0.769118
$890$		0			0
$891$	15.1792	+	12.7368i	0.508521	+	0.426700i
$892$		0			0
$893$	1.75642	−	0.639285i	0.0587764	−	0.0213929i
$894$		0			0
$895$	16.5921	−	6.03903i	0.554612	−	0.201862i
$896$		0			0
$897$	0.235403	+	1.33503i	0.00785986	+	0.0445755i
$898$		0			0
$899$	15.9768	+	27.6726i	0.532856	+	0.922933i
$900$		0			0
$901$	3.14570	−	17.8401i	0.104798	−	0.594341i
$902$		0			0
$903$	62.5461	+	22.7649i	2.08140	+	0.757569i
$904$		0			0
$905$	−4.72730	−	26.8099i	−0.157141	−	0.891190i
$906$		0			0
$907$	−34.4417	−	28.9000i	−1.14362	−	0.959610i	−0.144067	−	0.989568i	$-0.546018\pi$
$907$	−34.4417	−	28.9000i	−1.14362	−	0.959610i	−0.999551	+	0.0299580i	$0.990463\pi$
$908$		0			0
$909$	28.5355	+	10.3861i	0.946463	+	0.344484i
$910$		0			0
$911$	−7.10212	+	12.3012i	−0.235304	+	0.407558i	−0.959361	−	0.282182i	$-0.908942\pi$
$911$	−7.10212	+	12.3012i	−0.235304	+	0.407558i	0.724057	+	0.689740i	$0.242275\pi$
$912$		0			0
$913$	−4.26805	+	3.58132i	−0.141252	+	0.118524i
$914$		0			0
$915$	28.3537	−	49.1100i	0.937343	−	1.62353i
$916$		0			0
$917$	43.3957	+	75.1636i	1.43305	+	2.48212i
$918$		0			0
$919$	−46.2177			−1.52458			−0.762291	−	0.647235i	$-0.775925\pi$
$919$	−46.2177			−1.52458			−0.762291	+	0.647235i	$0.775925\pi$
$920$		0			0
$921$	−0.438948	+	2.48940i	−0.0144638	+	0.0820284i
$922$		0			0
$923$	1.65196	−	1.38616i	0.0543750	−	0.0456261i
$924$		0			0
$925$	−14.7669	+	6.50404i	−0.485532	+	0.213851i
$926$		0			0
$927$	−67.0234	+	56.2393i	−2.20134	+	1.84714i
$928$		0			0
$929$	−9.34083	+	52.9745i	−0.306463	+	1.73804i	0.310076	+	0.950712i	$0.399645\pi$
$929$	−9.34083	+	52.9745i	−0.306463	+	1.73804i	−0.616539	+	0.787325i	$0.711466\pi$
$930$		0			0
$931$	13.4372			0.440387
$932$		0			0
$933$	−3.88869	−	6.73540i	−0.127310	−	0.220507i
$934$		0			0
$935$	−2.46831	+	4.27524i	−0.0807223	+	0.139815i
$936$		0			0
$937$	−30.8185	+	25.8598i	−1.00680	+	0.844803i	−0.987912	−	0.155018i	$-0.950456\pi$
$937$	−30.8185	+	25.8598i	−1.00680	+	0.844803i	−0.0188857	+	0.999822i	$0.506012\pi$
$938$		0			0
$939$	28.0992	−	48.6692i	0.916983	−	1.58826i
$940$		0			0
$941$	1.65197	+	0.601267i	0.0538526	+	0.0196007i	0.368806	−	0.929506i	$-0.379767\pi$
$941$	1.65197	+	0.601267i	0.0538526	+	0.0196007i	−0.314953	+	0.949107i	$0.601989\pi$
$942$		0			0
$943$	0.542591	+	0.455288i	0.0176692	+	0.0148262i
$944$		0			0
$945$	15.8448	+	89.8601i	0.515430	+	2.92315i
$946$		0			0
$947$	47.7122	+	17.3658i	1.55044	+	0.564313i	0.968520	−	0.248935i	$-0.0800804\pi$
$947$	47.7122	+	17.3658i	1.55044	+	0.564313i	0.581917	+	0.813248i	$0.302303\pi$
$948$		0			0
$949$	2.70231	−	15.3256i	0.0877207	−	0.497489i
$950$		0			0
$951$	−5.57382	−	9.65415i	−0.180744	−	0.313057i
$952$		0			0
$953$	4.28306	+	24.2904i	0.138742	+	0.786845i	0.972181	+	0.234233i	$0.0752577\pi$
$953$	4.28306	+	24.2904i	0.138742	+	0.786845i	−0.833439	+	0.552612i	$0.813631\pi$
$954$		0			0
$955$	−37.3043	+	13.5776i	−1.20714	+	0.439362i
$956$		0			0
$957$	18.0362	−	6.56464i	0.583028	−	0.212205i
$958$		0			0
$959$	81.7230	+	68.5738i	2.63897	+	2.21436i
$960$		0			0
$961$	1.88962			0.0609556
$962$		0			0
$963$	−130.491			−4.20500
$964$		0			0
$965$	12.7963	+	10.7373i	0.411926	+	0.345647i
$966$		0			0
$967$	−29.2331	+	10.6400i	−0.940073	+	0.342158i	−0.766194	−	0.642609i	$-0.777852\pi$
$967$	−29.2331	+	10.6400i	−0.940073	+	0.342158i	−0.173878	+	0.984767i	$0.555630\pi$
$968$		0			0
$969$	−7.19464	+	2.61863i	−0.231125	+	0.0841226i
$970$		0			0
$971$	−3.59887	−	20.4102i	−0.115493	−	0.654995i	−0.986505	−	0.163732i	$-0.947647\pi$
$971$	−3.59887	−	20.4102i	−0.115493	−	0.654995i	0.871011	−	0.491263i	$-0.163464\pi$
$972$		0			0
$973$	−6.43076	−	11.1384i	−0.206161	−	0.357081i
$974$		0			0
$975$	−2.56722	+	14.5594i	−0.0822169	+	0.466275i
$976$		0			0
$977$	25.9583	+	9.44805i	0.830480	+	0.302270i	0.722056	−	0.691835i	$-0.243197\pi$
$977$	25.9583	+	9.44805i	0.830480	+	0.302270i	0.108424	+	0.994105i	$0.465420\pi$
$978$		0			0
$979$	1.70489	+	9.66893i	0.0544886	+	0.309020i
$980$		0			0
$981$	−44.5983	−	37.4224i	−1.42391	−	1.19481i
$982$		0			0
$983$	−29.9156	−	10.8884i	−0.954159	−	0.347285i	−0.182417	−	0.983221i	$-0.558392\pi$
$983$	−29.9156	−	10.8884i	−0.954159	−	0.347285i	−0.771742	+	0.635936i	$0.780614\pi$
$984$		0			0
$985$	4.93573	−	8.54894i	0.157265	−	0.272392i
$986$		0			0
$987$	−26.3677	+	22.1251i	−0.839293	+	0.704251i
$988$		0			0
$989$	0.532682	−	0.922632i	0.0169383	−	0.0293380i
$990$		0			0
$991$	0.0451636	+	0.0782257i	0.00143467	+	0.00248492i	0.866742	−	0.498757i	$-0.166210\pi$
$991$	0.0451636	+	0.0782257i	0.00143467	+	0.00248492i	−0.865307	+	0.501242i	$0.832877\pi$
$992$		0			0
$993$	−12.0507			−0.382416
$994$		0			0
$995$	−5.01642	+	28.4495i	−0.159031	+	0.901911i
$996$		0			0
$997$	35.7709	−	30.0153i	1.13288	−	0.950595i	0.133693	−	0.991023i	$-0.457316\pi$
$997$	35.7709	−	30.0153i	1.13288	−	0.950595i	0.999182	+	0.0404277i	$0.0128720\pi$
$998$		0			0
$999$	−54.2147	+	51.9374i	−1.71528	+	1.64323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.bc.d.49.2		12
4.3	odd	2		74.2.f.b.49.1	✓	12
12.11	even	2		666.2.x.g.271.2		12
37.34	even	9	inner	592.2.bc.d.145.2		12
148.71	odd	18		74.2.f.b.71.1	yes	12
148.95	odd	18		2738.2.a.q.1.1		6
148.127	odd	18		2738.2.a.t.1.1		6
444.71	even	18		666.2.x.g.145.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.49.1	✓	12	4.3	odd	2
74.2.f.b.71.1	yes	12	148.71	odd	18
592.2.bc.d.49.2		12	1.1	even	1	trivial
592.2.bc.d.145.2		12	37.34	even	9	inner
666.2.x.g.145.2		12	444.71	even	18
666.2.x.g.271.2		12	12.11	even	2
2738.2.a.q.1.1		6	148.95	odd	18
2738.2.a.t.1.1		6	148.127	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.bc (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.41262 + 2.02443i) q^{3} +(-1.43969 + 0.524005i) q^{5} +(-4.53424 + 1.65033i) q^{7} +(1.20148 + 6.81391i) q^{9} +O(q^{10})\)	\(q+(2.41262 + 2.02443i) q^{3} +(-1.43969 + 0.524005i) q^{5} +(-4.53424 + 1.65033i) q^{7} +(1.20148 + 6.81391i) q^{9} +(-0.546896 - 0.947252i) q^{11} +(0.307284 - 1.74269i) q^{13} +(-4.53424 - 1.65033i) q^{15} +(0.511542 + 2.90110i) q^{17} +(0.632167 + 0.530451i) q^{19} +(-14.2804 - 5.19762i) q^{21} +(-0.121620 + 0.210653i) q^{23} +(-2.03209 + 1.70513i) q^{25} +(-6.17139 + 10.6892i) q^{27} +(2.78587 + 4.82526i) q^{29} +5.73495 q^{31} +(0.598191 - 3.39251i) q^{33} +(5.66313 - 4.75193i) q^{35} +(5.84038 + 1.69999i) q^{37} +(4.26932 - 3.58238i) q^{39} +(0.505653 - 2.86770i) q^{41} -4.37987 q^{43} +(-5.30028 - 9.18036i) q^{45} +(1.13249 - 1.96153i) q^{47} +(12.4734 - 10.4664i) q^{49} +(-4.63890 + 8.03481i) q^{51} +(-5.77859 - 2.10324i) q^{53} +(1.28373 + 1.07717i) q^{55} +(0.451318 + 2.55955i) q^{57} +(8.29301 + 3.01841i) q^{59} +(-2.04075 + 11.5737i) q^{61} +(-16.6930 - 28.9131i) q^{63} +(0.470787 + 2.66996i) q^{65} +(8.44220 - 3.07271i) q^{67} +(-0.719875 + 0.262013i) q^{69} +(0.933535 + 0.783329i) q^{71} +8.79418 q^{73} -8.35455 q^{75} +(4.04303 + 3.39251i) q^{77} +(2.02379 - 0.736599i) q^{79} +(-17.0233 + 6.19599i) q^{81} +(-0.884528 - 5.01641i) q^{83} +(-2.25665 - 3.90864i) q^{85} +(-3.04716 + 17.2813i) q^{87} +(-8.43486 - 3.07004i) q^{89} +(1.48272 + 8.40891i) q^{91} +(13.8362 + 11.6100i) q^{93} +(-1.18809 - 0.432428i) q^{95} +(-2.17954 + 3.77507i) q^{97} +(5.79741 - 4.86460i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 6 * q^5 - 6 * q^7 - 3 * q^9	\( 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9} - 3 q^{11} - 6 q^{13} - 6 q^{15} - 3 q^{17} + 3 q^{19} - 33 q^{21} + 21 q^{23} - 6 q^{25} - 3 q^{27} + 6 q^{29} - 42 q^{31} + 57 q^{33} + 9 q^{35} - 3 q^{37} + 24 q^{39} - 21 q^{41} - 36 q^{43} - 6 q^{45} - 9 q^{47} - 12 q^{49} - 6 q^{53} - 36 q^{57} + 6 q^{59} - 18 q^{61} - 36 q^{63} + 3 q^{65} + 27 q^{67} - 12 q^{69} + 18 q^{71} + 54 q^{73} + 6 q^{75} + 51 q^{77} + 12 q^{79} - 36 q^{81} + 6 q^{83} + 3 q^{85} - 39 q^{87} - 15 q^{89} + 51 q^{91} + 45 q^{93} + 15 q^{95} - 42 q^{97} + 33 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 6 * q^5 - 6 * q^7 - 3 * q^9 - 3 * q^11 - 6 * q^13 - 6 * q^15 - 3 * q^17 + 3 * q^19 - 33 * q^21 + 21 * q^23 - 6 * q^25 - 3 * q^27 + 6 * q^29 - 42 * q^31 + 57 * q^33 + 9 * q^35 - 3 * q^37 + 24 * q^39 - 21 * q^41 - 36 * q^43 - 6 * q^45 - 9 * q^47 - 12 * q^49 - 6 * q^53 - 36 * q^57 + 6 * q^59 - 18 * q^61 - 36 * q^63 + 3 * q^65 + 27 * q^67 - 12 * q^69 + 18 * q^71 + 54 * q^73 + 6 * q^75 + 51 * q^77 + 12 * q^79 - 36 * q^81 + 6 * q^83 + 3 * q^85 - 39 * q^87 - 15 * q^89 + 51 * q^91 + 45 * q^93 + 15 * q^95 - 42 * q^97 + 33 * q^99

Introduction

L-functions

Modular forms

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