LMFDB - Embedded newform 740.2.i.a.121.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(121,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.121"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,0,-7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 24x^{12} + 204x^{10} + 727x^{8} + 1008x^{6} + 426x^{4} + 64x^{2} + 3 $ x^14 + 24x^12 + 204x^10 + 727x^8 + 1008x^6 + 426x^4 + 64x^2 + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.4
Root			$0.300390i$ of defining polynomial
Character	$\chi$	$=$	740.121
Dual form			740.2.i.a.581.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.117270 - 0.203117i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(1.58956 + 2.75319i) q^{7} +(1.47250 - 2.55044i) q^{9} -0.358097 q^{11} +(1.27583 + 2.20981i) q^{13} +(-0.117270 + 0.203117i) q^{15} +(1.54539 - 2.67670i) q^{17} +(1.01569 + 1.75923i) q^{19} +(0.372813 - 0.645732i) q^{21} -3.34172 q^{23} +(-0.500000 + 0.866025i) q^{25} -1.39433 q^{27} +7.38568 q^{29} +9.08508 q^{31} +(0.0419939 + 0.0727356i) q^{33} +(1.58956 - 2.75319i) q^{35} +(5.87847 + 1.56320i) q^{37} +(0.299233 - 0.518287i) q^{39} +(-2.89049 - 5.00648i) q^{41} -2.22829 q^{43} -2.94499 q^{45} +9.00068 q^{47} +(-1.55338 + 2.69054i) q^{49} -0.724910 q^{51} +(0.203682 - 0.352787i) q^{53} +(0.179048 + 0.310121i) q^{55} +(0.238219 - 0.412607i) q^{57} +(-0.0726432 + 0.125822i) q^{59} +(-4.28240 - 7.41733i) q^{61} +9.36246 q^{63} +(1.27583 - 2.20981i) q^{65} +(7.24066 + 12.5412i) q^{67} +(0.391883 + 0.678761i) q^{69} +(-4.28335 - 7.41898i) q^{71} +2.69982 q^{73} +0.234539 q^{75} +(-0.569216 - 0.985910i) q^{77} +(-2.64213 - 4.57631i) q^{79} +(-4.25397 - 7.36810i) q^{81} +(-2.53863 + 4.39704i) q^{83} -3.09078 q^{85} +(-0.866116 - 1.50016i) q^{87} +(-7.56983 + 13.1113i) q^{89} +(-4.05602 + 7.02524i) q^{91} +(-1.06540 - 1.84533i) q^{93} +(1.01569 - 1.75923i) q^{95} -11.9914 q^{97} +(-0.527296 + 0.913304i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 7 q^{5} + 4 q^{7} - 13 q^{9} + 14 q^{11} + 4 q^{13} + q^{17} + 4 q^{19} - 3 q^{21} + 12 q^{23} - 7 q^{25} - 6 q^{27} - 4 q^{29} - 24 q^{31} + 13 q^{33} + 4 q^{35} + 10 q^{37} + 21 q^{39} + 5 q^{41}+ \cdots - 58 q^{99}+O(q^{100}) $ 14 * q - 7 * q^5 + 4 * q^7 - 13 * q^9 + 14 * q^11 + 4 * q^13 + q^17 + 4 * q^19 - 3 * q^21 + 12 * q^23 - 7 * q^25 - 6 * q^27 - 4 * q^29 - 24 * q^31 + 13 * q^33 + 4 * q^35 + 10 * q^37 + 21 * q^39 + 5 * q^41 - 6 * q^43 + 26 * q^45 - 16 * q^47 - 11 * q^49 + 26 * q^51 + 14 * q^53 - 7 * q^55 + 24 * q^57 - 16 * q^59 + 12 * q^61 - 98 * q^63 + 4 * q^65 + 21 * q^69 - 9 * q^71 - 40 * q^73 + 3 * q^77 + 3 * q^79 - 43 * q^81 + 5 * q^83 - 2 * q^85 + 31 * q^87 + 20 * q^89 - 2 * q^91 + 37 * q^93 + 4 * q^95 - 58 * q^97 - 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	−0.117270	−	0.203117i	−0.0677056	−	0.117270i	0.830185	−	0.557487i	$-0.188235\pi$
$3$	−0.117270	−	0.203117i	−0.0677056	−	0.117270i	−0.897891	+	0.440218i	$0.854901\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	1.58956	+	2.75319i	0.600796	+	1.04061i	0.992701	+	0.120604i	$0.0384830\pi$
$7$	1.58956	+	2.75319i	0.600796	+	1.04061i	−0.391905	+	0.920006i	$0.628184\pi$
$8$		0			0
$9$	1.47250	−	2.55044i	0.490832	−	0.850146i
$10$		0			0
$11$	−0.358097			−0.107970			−0.0539852	−	0.998542i	$-0.517192\pi$
$11$	−0.358097			−0.107970			−0.0539852	+	0.998542i	$0.517192\pi$
$12$		0			0
$13$	1.27583	+	2.20981i	0.353853	+	0.612891i	0.986921	−	0.161205i	$-0.0515380\pi$
$13$	1.27583	+	2.20981i	0.353853	+	0.612891i	−0.633068	+	0.774096i	$0.718205\pi$
$14$		0			0
$15$	−0.117270	+	0.203117i	−0.0302789	+	0.0524446i
$16$		0			0
$17$	1.54539	−	2.67670i	0.374812	−	0.649194i	−0.615487	−	0.788147i	$-0.711040\pi$
$17$	1.54539	−	2.67670i	0.374812	−	0.649194i	0.990299	+	0.138953i	$0.0443738\pi$
$18$		0			0
$19$	1.01569	+	1.75923i	0.233015	+	0.403594i	0.958694	−	0.284440i	$-0.0918075\pi$
$19$	1.01569	+	1.75923i	0.233015	+	0.403594i	−0.725679	+	0.688034i	$0.758474\pi$
$20$		0			0
$21$	0.372813	−	0.645732i	0.0813546	−	0.140910i
$22$		0			0
$23$	−3.34172			−0.696798			−0.348399	−	0.937346i	$-0.613275\pi$
$23$	−3.34172			−0.696798			−0.348399	+	0.937346i	$0.613275\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−1.39433			−0.268340
$28$		0			0
$29$	7.38568			1.37149			0.685743	−	0.727844i	$-0.259477\pi$
$29$	7.38568			1.37149			0.685743	+	0.727844i	$0.259477\pi$
$30$		0			0
$31$	9.08508			1.63173			0.815865	−	0.578243i	$-0.196261\pi$
$31$	9.08508			1.63173			0.815865	+	0.578243i	$0.196261\pi$
$32$		0			0
$33$	0.0419939	+	0.0727356i	0.00731020	+	0.0126616i
$34$		0			0
$35$	1.58956	−	2.75319i	0.268684	−	0.465375i
$36$		0			0
$37$	5.87847	+	1.56320i	0.966414	+	0.256989i
$37$	5.87847	+	1.56320i	0.966414	+	0.256989i
$38$		0			0
$39$	0.299233	−	0.518287i	0.0479157	−	0.0829924i
$40$		0			0
$41$	−2.89049	−	5.00648i	−0.451419	−	0.781881i	0.547055	−	0.837096i	$-0.315749\pi$
$41$	−2.89049	−	5.00648i	−0.451419	−	0.781881i	−0.998474	+	0.0552157i	$0.982415\pi$
$42$		0			0
$43$	−2.22829			−0.339811			−0.169906	−	0.985460i	$-0.554346\pi$
$43$	−2.22829			−0.339811			−0.169906	+	0.985460i	$0.554346\pi$
$44$		0			0
$45$	−2.94499			−0.439013
$46$		0			0
$47$	9.00068			1.31288			0.656442	−	0.754376i	$-0.272061\pi$
$47$	9.00068			1.31288			0.656442	+	0.754376i	$0.272061\pi$
$48$		0			0
$49$	−1.55338	+	2.69054i	−0.221912	+	0.384363i
$50$		0			0
$51$	−0.724910			−0.101508
$52$		0			0
$53$	0.203682	−	0.352787i	0.0279779	−	0.0484591i	−0.851697	−	0.524034i	$-0.824427\pi$
$53$	0.203682	−	0.352787i	0.0279779	−	0.0484591i	0.879675	+	0.475575i	$0.157760\pi$
$54$		0			0
$55$	0.179048	+	0.310121i	0.0241429	+	0.0418167i
$56$		0			0
$57$	0.238219	−	0.412607i	0.0315529	−	0.0546512i
$58$		0			0
$59$	−0.0726432	+	0.125822i	−0.00945733	+	0.0163806i	−0.870715	−	0.491787i	$-0.836344\pi$
$59$	−0.0726432	+	0.125822i	−0.00945733	+	0.0163806i	0.861258	+	0.508168i	$0.169677\pi$
$60$		0			0
$61$	−4.28240	−	7.41733i	−0.548305	−	0.949692i	−0.998391	−	0.0567065i	$-0.981940\pi$
$61$	−4.28240	−	7.41733i	−0.548305	−	0.949692i	0.450086	−	0.892985i	$-0.351393\pi$
$62$		0			0
$63$	9.36246			1.17956
$64$		0			0
$65$	1.27583	−	2.20981i	0.158248	−	0.274093i
$66$		0			0
$67$	7.24066	+	12.5412i	0.884588	+	1.53215i	0.846186	+	0.532888i	$0.178893\pi$
$67$	7.24066	+	12.5412i	0.884588	+	1.53215i	0.0384021	+	0.999262i	$0.487773\pi$
$68$		0			0
$69$	0.391883	+	0.678761i	0.0471771	+	0.0817132i
$70$		0			0
$71$	−4.28335	−	7.41898i	−0.508340	−	0.880470i	−0.999953	−	0.00965693i	$-0.996926\pi$
$71$	−4.28335	−	7.41898i	−0.508340	−	0.880470i	0.491614	−	0.870813i	$-0.336407\pi$
$72$		0			0
$73$	2.69982			0.315990			0.157995	−	0.987440i	$-0.449497\pi$
$73$	2.69982			0.315990			0.157995	+	0.987440i	$0.449497\pi$
$74$		0			0
$75$	0.234539			0.0270823
$76$		0			0
$77$	−0.569216	−	0.985910i	−0.0648681	−	0.112355i
$78$		0			0
$79$	−2.64213	−	4.57631i	−0.297263	−	0.514875i	0.678246	−	0.734835i	$-0.262741\pi$
$79$	−2.64213	−	4.57631i	−0.297263	−	0.514875i	−0.975509	+	0.219960i	$0.929407\pi$
$80$		0			0
$81$	−4.25397	−	7.36810i	−0.472664	−	0.818678i
$82$		0			0
$83$	−2.53863	+	4.39704i	−0.278651	+	0.482638i	−0.971050	−	0.238877i	$-0.923221\pi$
$83$	−2.53863	+	4.39704i	−0.278651	+	0.482638i	0.692399	+	0.721515i	$0.256554\pi$
$84$		0			0
$85$	−3.09078			−0.335242
$86$		0			0
$87$	−0.866116	−	1.50016i	−0.0928573	−	0.160834i
$88$		0			0
$89$	−7.56983	+	13.1113i	−0.802400	+	1.38980i	0.115632	+	0.993292i	$0.463111\pi$
$89$	−7.56983	+	13.1113i	−0.802400	+	1.38980i	−0.918032	+	0.396506i	$0.870223\pi$
$90$		0			0
$91$	−4.05602	+	7.02524i	−0.425187	+	0.736445i
$92$		0			0
$93$	−1.06540	−	1.84533i	−0.110477	−	0.191352i
$94$		0			0
$95$	1.01569	−	1.75923i	0.104208	−	0.180493i
$96$		0			0
$97$	−11.9914			−1.21755			−0.608773	−	0.793344i	$-0.708338\pi$
$97$	−11.9914			−1.21755			−0.608773	+	0.793344i	$0.708338\pi$
$98$		0			0
$99$	−0.527296	+	0.913304i	−0.0529953	+	0.0917905i
$100$		0			0
$101$	−10.2361			−1.01853			−0.509265	−	0.860609i	$-0.670083\pi$
$101$	−10.2361			−1.01853			−0.509265	+	0.860609i	$0.670083\pi$
$102$		0			0
$103$	4.67427			0.460570			0.230285	−	0.973123i	$-0.426034\pi$
$103$	4.67427			0.460570			0.230285	+	0.973123i	$0.426034\pi$
$104$		0			0
$105$	−0.745627			−0.0727657
$106$		0			0
$107$	5.20934	+	9.02284i	0.503606	+	0.872271i	0.999991	+	0.00416847i	$0.00132687\pi$
$107$	5.20934	+	9.02284i	0.503606	+	0.872271i	−0.496386	+	0.868102i	$0.665340\pi$
$108$		0			0
$109$	−7.61208	+	13.1845i	−0.729105	+	1.26285i	0.228156	+	0.973624i	$0.426730\pi$
$109$	−7.61208	+	13.1845i	−0.729105	+	1.26285i	−0.957262	+	0.289223i	$0.906603\pi$
$110$		0			0
$111$	−0.371853	−	1.37733i	−0.0352947	−	0.130731i
$112$		0			0
$113$	10.5831	−	18.3305i	0.995574	−	1.72438i	0.416395	−	0.909184i	$-0.363293\pi$
$113$	10.5831	−	18.3305i	0.995574	−	1.72438i	0.579179	−	0.815201i	$-0.303373\pi$
$114$		0			0
$115$	1.67086	+	2.89402i	0.155809	+	0.269869i
$116$		0			0
$117$	7.51464			0.694729
$118$		0			0
$119$	9.82595			0.900743
$120$		0			0
$121$	−10.8718			−0.988342
$122$		0			0
$123$	−0.677934	+	1.17422i	−0.0611272	+	0.105875i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−7.28172	+	12.6123i	−0.646148	+	1.11916i	0.337887	+	0.941187i	$0.390288\pi$
$127$	−7.28172	+	12.6123i	−0.646148	+	1.11916i	−0.984035	+	0.177975i	$0.943045\pi$
$128$		0			0
$129$	0.261311	+	0.452604i	0.0230072	+	0.0398496i
$130$		0			0
$131$	−1.65473	+	2.86608i	−0.144575	+	0.250411i	−0.929214	−	0.369542i	$-0.879515\pi$
$131$	−1.65473	+	2.86608i	−0.144575	+	0.250411i	0.784639	+	0.619952i	$0.212848\pi$
$132$		0			0
$133$	−3.22899	+	5.59278i	−0.279989	+	0.484955i
$134$		0			0
$135$	0.697167	+	1.20753i	0.0600026	+	0.103927i
$136$		0			0
$137$	−12.9133			−1.10326			−0.551629	−	0.834090i	$-0.685994\pi$
$137$	−12.9133			−1.10326			−0.551629	+	0.834090i	$0.685994\pi$
$138$		0			0
$139$	1.89258	−	3.27805i	0.160527	−	0.278041i	−0.774531	−	0.632536i	$-0.782014\pi$
$139$	1.89258	−	3.27805i	0.160527	−	0.278041i	0.935058	+	0.354495i	$0.115347\pi$
$140$		0			0
$141$	−1.05551	−	1.82819i	−0.0888897	−	0.153961i
$142$		0			0
$143$	−0.456872	−	0.791326i	−0.0382056	−	0.0661740i
$144$		0			0
$145$	−3.69284	−	6.39619i	−0.306674	−	0.531174i
$146$		0			0
$147$	0.728659			0.0600988
$148$		0			0
$149$	1.02661			0.0841030			0.0420515	−	0.999115i	$-0.486611\pi$
$149$	1.02661			0.0841030			0.0420515	+	0.999115i	$0.486611\pi$
$150$		0			0
$151$	−6.96022	−	12.0555i	−0.566415	−	0.981059i	−0.996917	−	0.0784693i	$-0.974997\pi$
$151$	−6.96022	−	12.0555i	−0.566415	−	0.981059i	0.430502	−	0.902590i	$-0.358337\pi$
$152$		0			0
$153$	−4.55116	−	7.88285i	−0.367940	−	0.637290i
$154$		0			0
$155$	−4.54254	−	7.86791i	−0.364866	−	0.631966i
$156$		0			0
$157$	1.70126	−	2.94667i	0.135776	−	0.235170i	−0.790118	−	0.612955i	$-0.789981\pi$
$157$	1.70126	−	2.94667i	0.135776	−	0.235170i	0.925893	+	0.377785i	$0.123314\pi$
$158$		0			0
$159$	−0.0955428			−0.00757704
$160$		0			0
$161$	−5.31186	−	9.20041i	−0.418633	−	0.725094i
$162$		0			0
$163$	−5.70641	+	9.88379i	−0.446960	+	0.774158i	−0.998186	−	0.0601979i	$-0.980827\pi$
$163$	−5.70641	+	9.88379i	−0.446960	+	0.774158i	0.551226	+	0.834356i	$0.314160\pi$
$164$		0			0
$165$	0.0419939	−	0.0727356i	0.00326922	−	0.00566246i
$166$		0			0
$167$	−0.0241496	−	0.0418284i	−0.00186875	−	0.00323678i	0.865090	−	0.501618i	$-0.167262\pi$
$167$	−0.0241496	−	0.0418284i	−0.00186875	−	0.00323678i	−0.866958	+	0.498381i	$0.833928\pi$
$168$		0			0
$169$	3.24449	−	5.61963i	0.249576	−	0.432279i
$170$		0			0
$171$	5.98239			0.457485
$172$		0			0
$173$	−6.05578	+	10.4889i	−0.460412	+	0.797457i	−0.998981	−	0.0451241i	$-0.985632\pi$
$173$	−6.05578	+	10.4889i	−0.460412	+	0.797457i	0.538569	+	0.842581i	$0.318965\pi$
$174$		0			0
$175$	−3.17911			−0.240318
$176$		0			0
$177$	0.0340753			0.00256126
$178$		0			0
$179$	1.60239			0.119768			0.0598841	−	0.998205i	$-0.480927\pi$
$179$	1.60239			0.119768			0.0598841	+	0.998205i	$0.480927\pi$
$180$		0			0
$181$	−7.90842	−	13.6978i	−0.587828	−	1.01815i	−0.994516	−	0.104581i	$-0.966650\pi$
$181$	−7.90842	−	13.6978i	−0.587828	−	1.01815i	0.406688	−	0.913567i	$-0.366683\pi$
$182$		0			0
$183$	−1.00439	+	1.73965i	−0.0742466	+	0.128599i
$184$		0			0
$185$	−1.58546	−	5.87250i	−0.116565	−	0.431755i
$186$		0			0
$187$	−0.553400	+	0.958517i	−0.0404686	+	0.0700937i
$188$		0			0
$189$	−2.21637	−	3.83887i	−0.161217	−	0.279237i
$190$		0			0
$191$	−14.5252			−1.05101			−0.525505	−	0.850791i	$-0.676123\pi$
$191$	−14.5252			−1.05101			−0.525505	+	0.850791i	$0.676123\pi$
$192$		0			0
$193$	5.16326			0.371660			0.185830	−	0.982582i	$-0.440503\pi$
$193$	5.16326			0.371660			0.185830	+	0.982582i	$0.440503\pi$
$194$		0			0
$195$	−0.598466			−0.0428571
$196$		0			0
$197$	3.00915	−	5.21200i	0.214393	−	0.371340i	−0.738691	−	0.674044i	$-0.764556\pi$
$197$	3.00915	−	5.21200i	0.214393	−	0.371340i	0.953085	+	0.302704i	$0.0978893\pi$
$198$		0			0
$199$	3.32727			0.235864			0.117932	−	0.993022i	$-0.462374\pi$
$199$	3.32727			0.235864			0.117932	+	0.993022i	$0.462374\pi$
$200$		0			0
$201$	1.69822	−	2.94140i	0.119783	−	0.207470i
$202$		0			0
$203$	11.7400	+	20.3342i	0.823984	+	1.42718i
$204$		0			0
$205$	−2.89049	+	5.00648i	−0.201881	+	0.349668i
$206$		0			0
$207$	−4.92067	+	8.52286i	−0.342011	+	0.592380i
$208$		0			0
$209$	−0.363715	−	0.629973i	−0.0251587	−	0.0435762i
$210$		0			0
$211$	−26.2788			−1.80911			−0.904553	−	0.426361i	$-0.859795\pi$
$211$	−26.2788			−1.80911			−0.904553	+	0.426361i	$0.859795\pi$
$212$		0			0
$213$	−1.00461	+	1.74004i	−0.0688349	+	0.119226i
$214$		0			0
$215$	1.11415	+	1.92976i	0.0759842	+	0.131608i
$216$		0			0
$217$	14.4413	+	25.0130i	0.980337	+	1.69799i
$218$		0			0
$219$	−0.316607	−	0.548379i	−0.0213943	−	0.0370560i
$220$		0			0
$221$	7.88665			0.530514
$222$		0			0
$223$	−21.3598			−1.43036			−0.715181	−	0.698940i	$-0.753656\pi$
$223$	−21.3598			−1.43036			−0.715181	+	0.698940i	$0.753656\pi$
$224$		0			0
$225$	1.47250	+	2.55044i	0.0981664	+	0.170029i
$226$		0			0
$227$	4.03577	+	6.99016i	0.267863	+	0.463953i	0.968310	−	0.249752i	$-0.0803491\pi$
$227$	4.03577	+	6.99016i	0.267863	+	0.463953i	−0.700446	+	0.713705i	$0.747016\pi$
$228$		0			0
$229$	−4.88902	−	8.46804i	−0.323076	−	0.559584i	0.658045	−	0.752978i	$-0.271384\pi$
$229$	−4.88902	−	8.46804i	−0.323076	−	0.559584i	−0.981121	+	0.193395i	$0.938050\pi$
$230$		0			0
$231$	−0.133503	+	0.231235i	−0.00878388	+	0.0152141i
$232$		0			0
$233$	−17.0421			−1.11647			−0.558233	−	0.829684i	$-0.688520\pi$
$233$	−17.0421			−1.11647			−0.558233	+	0.829684i	$0.688520\pi$
$234$		0			0
$235$	−4.50034	−	7.79482i	−0.293570	−	0.508478i
$236$		0			0
$237$	−0.619684	+	1.07332i	−0.0402528	+	0.0697199i
$238$		0			0
$239$	−5.95003	+	10.3058i	−0.384876	+	0.666624i	−0.991752	−	0.128172i	$-0.959089\pi$
$239$	−5.95003	+	10.3058i	−0.384876	+	0.666624i	0.606876	+	0.794796i	$0.292422\pi$
$240$		0			0
$241$	13.3763	+	23.1684i	0.861643	+	1.49241i	0.870342	+	0.492447i	$0.163897\pi$
$241$	13.3763	+	23.1684i	0.861643	+	1.49241i	−0.00869951	+	0.999962i	$0.502769\pi$
$242$		0			0
$243$	−3.08922	+	5.35069i	−0.198174	+	0.343247i
$244$		0			0
$245$	3.10677			0.198484
$246$		0			0
$247$	−2.59170	+	4.48896i	−0.164906	+	0.285626i
$248$		0			0
$249$	1.19082			0.0754650
$250$		0			0
$251$	15.5729			0.982952			0.491476	−	0.870891i	$-0.336458\pi$
$251$	15.5729			0.982952			0.491476	+	0.870891i	$0.336458\pi$
$252$		0			0
$253$	1.19666			0.0752335
$254$		0			0
$255$	0.362455	+	0.627790i	0.0226978	+	0.0393137i
$256$		0			0
$257$	8.82199	−	15.2801i	0.550301	−	0.953148i	−0.447952	−	0.894058i	$-0.647846\pi$
$257$	8.82199	−	15.2801i	0.550301	−	0.953148i	0.998253	−	0.0590909i	$-0.0188202\pi$
$258$		0			0
$259$	5.04036	+	18.6694i	0.313193	+	1.16006i
$260$		0			0
$261$	10.8754	−	18.8367i	0.673169	−	1.16596i
$262$		0			0
$263$	−6.21900	−	10.7716i	−0.383480	−	0.664206i	0.608077	−	0.793878i	$-0.291941\pi$
$263$	−6.21900	−	10.7716i	−0.383480	−	0.664206i	−0.991557	+	0.129671i	$0.958608\pi$
$264$		0			0
$265$	−0.407364			−0.0250242
$266$		0			0
$267$	3.55084			0.217308
$268$		0			0
$269$	0.200438			0.0122209			0.00611047	−	0.999981i	$-0.498055\pi$
$269$	0.200438			0.0122209			0.00611047	+	0.999981i	$0.498055\pi$
$270$		0			0
$271$	5.73770	−	9.93798i	0.348540	−	0.603690i	−0.637450	−	0.770492i	$-0.720011\pi$
$271$	5.73770	−	9.93798i	0.348540	−	0.603690i	0.985990	+	0.166802i	$0.0533441\pi$
$272$		0			0
$273$	1.90259			0.115150
$274$		0			0
$275$	0.179048	−	0.310121i	0.0107970	−	0.0187010i
$276$		0			0
$277$	4.34516	+	7.52604i	0.261075	+	0.452196i	0.966528	−	0.256561i	$-0.0825896\pi$
$277$	4.34516	+	7.52604i	0.261075	+	0.452196i	−0.705453	+	0.708757i	$0.749256\pi$
$278$		0			0
$279$	13.3777	−	23.1709i	0.800905	−	1.38721i
$280$		0			0
$281$	−1.78860	+	3.09795i	−0.106699	+	0.184808i	−0.914431	−	0.404742i	$-0.867361\pi$
$281$	−1.78860	+	3.09795i	−0.106699	+	0.184808i	0.807732	+	0.589550i	$0.200695\pi$
$282$		0			0
$283$	−0.250526	−	0.433924i	−0.0148922	−	0.0257941i	0.858483	−	0.512842i	$-0.171407\pi$
$283$	−0.250526	−	0.433924i	−0.0148922	−	0.0257941i	−0.873375	+	0.487048i	$0.838074\pi$
$284$		0			0
$285$	−0.476438			−0.0282217
$286$		0			0
$287$	9.18921	−	15.9162i	0.542422	−	0.939502i
$288$		0			0
$289$	3.72353	+	6.44935i	0.219031	+	0.379373i
$290$		0			0
$291$	1.40623	+	2.43567i	0.0824348	+	0.142781i
$292$		0			0
$293$	−6.11349	−	10.5889i	−0.357154	−	0.618609i	0.630330	−	0.776327i	$-0.282919\pi$
$293$	−6.11349	−	10.5889i	−0.357154	−	0.618609i	−0.987484	+	0.157719i	$0.949586\pi$
$294$		0			0
$295$	0.145286			0.00845890
$296$		0			0
$297$	0.499307			0.0289727
$298$		0			0
$299$	−4.26349	−	7.38458i	−0.246564	−	0.427061i
$300$		0			0
$301$	−3.54200	−	6.13492i	−0.204157	−	0.353611i
$302$		0			0
$303$	1.20038	+	2.07913i	0.0689603	+	0.119443i
$304$		0			0
$305$	−4.28240	+	7.41733i	−0.245209	+	0.424715i
$306$		0			0
$307$	−0.390030			−0.0222602			−0.0111301	−	0.999938i	$-0.503543\pi$
$307$	−0.390030			−0.0222602			−0.0111301	+	0.999938i	$0.503543\pi$
$308$		0			0
$309$	−0.548150	−	0.949424i	−0.0311832	−	0.0540108i
$310$		0			0
$311$	12.9130	−	22.3660i	0.732230	−	1.26826i	−0.223698	−	0.974658i	$-0.571813\pi$
$311$	12.9130	−	22.3660i	0.732230	−	1.26826i	0.955928	−	0.293601i	$-0.0948536\pi$
$312$		0			0
$313$	6.57799	−	11.3934i	0.371810	−	0.643994i	−0.618034	−	0.786151i	$-0.712071\pi$
$313$	6.57799	−	11.3934i	0.371810	−	0.643994i	0.989844	+	0.142157i	$0.0454039\pi$
$314$		0			0
$315$	−4.68123	−	8.10813i	−0.263758	−	0.456841i
$316$		0			0
$317$	−1.27662	+	2.21117i	−0.0717022	+	0.124192i	−0.899647	−	0.436617i	$-0.856176\pi$
$317$	−1.27662	+	2.21117i	−0.0717022	+	0.124192i	0.827945	+	0.560809i	$0.189510\pi$
$318$		0			0
$319$	−2.64479			−0.148080
$320$		0			0
$321$	1.22179	−	2.11621i	0.0681939	−	0.118115i
$322$		0			0
$323$	6.27855			0.349348
$324$		0			0
$325$	−2.55167			−0.141541
$326$		0			0
$327$	3.57066			0.197458
$328$		0			0
$329$	14.3071	+	24.7806i	0.788776	+	1.36620i
$330$		0			0
$331$	−11.0258	+	19.0972i	−0.606032	+	1.04968i	0.385855	+	0.922559i	$0.373906\pi$
$331$	−11.0258	+	19.0972i	−0.606032	+	1.04968i	−0.991887	+	0.127119i	$0.959427\pi$
$332$		0			0
$333$	12.6429	−	12.6909i	0.692825	−	0.695455i
$334$		0			0
$335$	7.24066	−	12.5412i	0.395600	−	0.685199i
$336$		0			0
$337$	1.51760	+	2.62856i	0.0826691	+	0.143187i	0.904396	−	0.426695i	$-0.140322\pi$
$337$	1.51760	+	2.62856i	0.0826691	+	0.143187i	−0.821727	+	0.569882i	$0.806989\pi$
$338$		0			0
$339$	−4.96430			−0.269624
$340$		0			0
$341$	−3.25334			−0.176178
$342$		0			0
$343$	12.3770			0.668297
$344$		0			0
$345$	0.391883	−	0.678761i	0.0210983	−	0.0365432i
$346$		0			0
$347$	23.8075			1.27805			0.639027	−	0.769184i	$-0.279337\pi$
$347$	23.8075			1.27805			0.639027	+	0.769184i	$0.279337\pi$
$348$		0			0
$349$	−2.07920	+	3.60127i	−0.111297	+	0.192772i	−0.916293	−	0.400508i	$-0.868834\pi$
$349$	−2.07920	+	3.60127i	−0.111297	+	0.192772i	0.804997	+	0.593279i	$0.202167\pi$
$350$		0			0
$351$	−1.77894	−	3.08121i	−0.0949527	−	0.164463i
$352$		0			0
$353$	2.55747	−	4.42966i	0.136120	−	0.235767i	−0.789905	−	0.613230i	$-0.789870\pi$
$353$	2.55747	−	4.42966i	0.136120	−	0.235767i	0.926025	+	0.377463i	$0.123203\pi$
$354$		0			0
$355$	−4.28335	+	7.41898i	−0.227336	+	0.393758i
$356$		0			0
$357$	−1.15229	−	1.99582i	−0.0609854	−	0.105630i
$358$		0			0
$359$	27.3507			1.44352			0.721758	−	0.692145i	$-0.243334\pi$
$359$	27.3507			1.44352			0.721758	+	0.692145i	$0.243334\pi$
$360$		0			0
$361$	7.43675	−	12.8808i	0.391408	−	0.677938i
$362$		0			0
$363$	1.27493	+	2.20824i	0.0669164	+	0.115903i
$364$		0			0
$365$	−1.34991	−	2.33811i	−0.0706575	−	0.122382i
$366$		0			0
$367$	−3.32960	−	5.76704i	−0.173804	−	0.301037i	0.765943	−	0.642909i	$-0.222272\pi$
$367$	−3.32960	−	5.76704i	−0.173804	−	0.301037i	−0.939747	+	0.341872i	$0.888939\pi$
$368$		0			0
$369$	−17.0249			−0.886283
$370$		0			0
$371$	1.29506			0.0672360
$372$		0			0
$373$	3.95814	+	6.85571i	0.204945	+	0.354975i	0.950115	−	0.311899i	$-0.100965\pi$
$373$	3.95814	+	6.85571i	0.204945	+	0.354975i	−0.745170	+	0.666874i	$0.767632\pi$
$374$		0			0
$375$	−0.117270	−	0.203117i	−0.00605578	−	0.0104889i
$376$		0			0
$377$	9.42290	+	16.3209i	0.485304	+	0.840572i
$378$		0			0
$379$	5.63238	−	9.75556i	0.289316	−	0.501110i	−0.684331	−	0.729172i	$-0.739906\pi$
$379$	5.63238	−	9.75556i	0.289316	−	0.501110i	0.973647	+	0.228062i	$0.0732389\pi$
$380$		0			0
$381$	3.41570			0.174991
$382$		0			0
$383$	4.23049	+	7.32742i	0.216168	+	0.374413i	0.953633	−	0.300971i	$-0.0973109\pi$
$383$	4.23049	+	7.32742i	0.216168	+	0.374413i	−0.737465	+	0.675385i	$0.763978\pi$
$384$		0			0
$385$	−0.569216	+	0.985910i	−0.0290099	+	0.0502466i
$386$		0			0
$387$	−3.28115	+	5.68312i	−0.166790	+	0.288889i
$388$		0			0
$389$	5.56052	+	9.63110i	0.281929	+	0.488316i	0.971860	−	0.235560i	$-0.0756923\pi$
$389$	5.56052	+	9.63110i	0.281929	+	0.488316i	−0.689931	+	0.723876i	$0.742359\pi$
$390$		0			0
$391$	−5.16427	+	8.94478i	−0.261168	+	0.452357i
$392$		0			0
$393$	0.776200			0.0391541
$394$		0			0
$395$	−2.64213	+	4.57631i	−0.132940	+	0.230259i
$396$		0			0
$397$	−22.5615			−1.13233			−0.566165	−	0.824292i	$-0.691574\pi$
$397$	−22.5615			−1.13233			−0.566165	+	0.824292i	$0.691574\pi$
$398$		0			0
$399$	1.51465			0.0758274
$400$		0			0
$401$	−6.88260			−0.343701			−0.171850	−	0.985123i	$-0.554975\pi$
$401$	−6.88260			−0.343701			−0.171850	+	0.985123i	$0.554975\pi$
$402$		0			0
$403$	11.5911	+	20.0763i	0.577392	+	1.00007i
$404$		0			0
$405$	−4.25397	+	7.36810i	−0.211382	+	0.366124i
$406$		0			0
$407$	−2.10506	−	0.559778i	−0.104344	−	0.0277472i
$408$		0			0
$409$	−6.56614	+	11.3729i	−0.324675	+	0.562353i	−0.981446	−	0.191736i	$-0.938588\pi$
$409$	−6.56614	+	11.3729i	−0.324675	+	0.562353i	0.656772	+	0.754089i	$0.271921\pi$
$410$		0			0
$411$	1.51434	+	2.62291i	0.0746968	+	0.129379i
$412$		0			0
$413$	−0.461882			−0.0227277
$414$		0			0
$415$	5.07726			0.249233
$416$		0			0
$417$	−0.887770			−0.0434743
$418$		0			0
$419$	8.03510	−	13.9172i	0.392540	−	0.679899i	−0.600244	−	0.799817i	$-0.704930\pi$
$419$	8.03510	−	13.9172i	0.392540	−	0.679899i	0.992784	+	0.119918i	$0.0382631\pi$
$420$		0			0
$421$	19.4118			0.946071			0.473036	−	0.881043i	$-0.343158\pi$
$421$	19.4118			0.946071			0.473036	+	0.881043i	$0.343158\pi$
$422$		0			0
$423$	13.2535	−	22.9557i	0.644405	−	1.11614i
$424$		0			0
$425$	1.54539	+	2.67670i	0.0749625	+	0.129839i
$426$		0			0
$427$	13.6142	−	23.5805i	0.658839	−	1.14114i
$428$		0			0
$429$	−0.107155	+	0.185597i	−0.00517347	+	0.00896071i
$430$		0			0
$431$	13.1905	+	22.8467i	0.635366	+	1.10049i	0.986437	+	0.164138i	$0.0524841\pi$
$431$	13.1905	+	22.8467i	0.635366	+	1.10049i	−0.351071	+	0.936349i	$0.614183\pi$
$432$		0			0
$433$	25.7940			1.23958			0.619790	−	0.784768i	$-0.287218\pi$
$433$	25.7940			1.23958			0.619790	+	0.784768i	$0.287218\pi$
$434$		0			0
$435$	−0.866116	+	1.50016i	−0.0415271	+	0.0719270i
$436$		0			0
$437$	−3.39415	−	5.87885i	−0.162364	−	0.281223i
$438$		0			0
$439$	4.21259	+	7.29642i	0.201056	+	0.348239i	0.948869	−	0.315670i	$-0.102229\pi$
$439$	4.21259	+	7.29642i	0.201056	+	0.348239i	−0.747813	+	0.663910i	$0.768896\pi$
$440$		0			0
$441$	4.57470	+	7.92362i	0.217843	+	0.377315i
$442$		0			0
$443$	−24.0523			−1.14276			−0.571379	−	0.820686i	$-0.693592\pi$
$443$	−24.0523			−1.14276			−0.571379	+	0.820686i	$0.693592\pi$
$444$		0			0
$445$	15.1397			0.717689
$446$		0			0
$447$	−0.120390	−	0.208521i	−0.00569424	−	0.00986272i
$448$		0			0
$449$	−2.29380	−	3.97297i	−0.108251	−	0.187496i	0.806811	−	0.590810i	$-0.201192\pi$
$449$	−2.29380	−	3.97297i	−0.108251	−	0.187496i	−0.915062	+	0.403314i	$0.867858\pi$
$450$		0			0
$451$	1.03508	+	1.79281i	0.0487399	+	0.0844199i
$452$		0			0
$453$	−1.63244	+	2.82748i	−0.0766989	+	0.132846i
$454$		0			0
$455$	8.11205			0.380299
$456$		0			0
$457$	9.00292	+	15.5935i	0.421139	+	0.729434i	0.996051	−	0.0887812i	$-0.0282972\pi$
$457$	9.00292	+	15.5935i	0.421139	+	0.729434i	−0.574912	+	0.818215i	$0.694964\pi$
$458$		0			0
$459$	−2.15479	+	3.73221i	−0.100577	+	0.174204i
$460$		0			0
$461$	11.6529	−	20.1834i	0.542728	−	0.940032i	−0.456018	−	0.889970i	$-0.650725\pi$
$461$	11.6529	−	20.1834i	0.542728	−	0.940032i	0.998746	−	0.0500619i	$-0.0159419\pi$
$462$		0			0
$463$	1.74309	+	3.01913i	0.0810085	+	0.140311i	0.903683	−	0.428201i	$-0.140853\pi$
$463$	1.74309	+	3.01913i	0.0810085	+	0.140311i	−0.822675	+	0.568512i	$0.807519\pi$
$464$		0			0
$465$	−1.06540	+	1.84533i	−0.0494069	+	0.0855753i
$466$		0			0
$467$	−34.5016			−1.59655			−0.798273	−	0.602296i	$-0.794253\pi$
$467$	−34.5016			−1.59655			−0.798273	+	0.602296i	$0.794253\pi$
$468$		0			0
$469$	−23.0189	+	39.8699i	−1.06291	+	1.84102i
$470$		0			0
$471$	−0.798026			−0.0367711
$472$		0			0
$473$	0.797945			0.0366895
$474$		0			0
$475$	−2.03138			−0.0932060
$476$		0			0
$477$	−0.599841	−	1.03896i	−0.0274649	−	0.0475705i
$478$		0			0
$479$	19.3254	−	33.4725i	0.882998	−	1.52940i	0.0350064	−	0.999387i	$-0.488855\pi$
$479$	19.3254	−	33.4725i	0.882998	−	1.52940i	0.847991	−	0.530010i	$-0.177812\pi$
$480$		0			0
$481$	4.04557	+	14.9847i	0.184462	+	0.683243i
$482$		0			0
$483$	−1.24584	+	2.15786i	−0.0566877	+	0.0981859i
$484$		0			0
$485$	5.99572	+	10.3849i	0.272252	+	0.471554i
$486$		0			0
$487$	−34.9917			−1.58562			−0.792812	−	0.609467i	$-0.791384\pi$
$487$	−34.9917			−1.58562			−0.792812	+	0.609467i	$0.791384\pi$
$488$		0			0
$489$	2.67675			0.121047
$490$		0			0
$491$	−42.8253			−1.93268			−0.966339	−	0.257271i	$-0.917177\pi$
$491$	−42.8253			−1.93268			−0.966339	+	0.257271i	$0.917177\pi$
$492$		0			0
$493$	11.4138	−	19.7692i	0.514050	−	0.890361i
$494$		0			0
$495$	1.05459			0.0474004
$496$		0			0
$497$	13.6173	−	23.5858i	0.610817	−	1.05797i
$498$		0			0
$499$	−8.71019	−	15.0865i	−0.389922	−	0.675364i	0.602517	−	0.798106i	$-0.294165\pi$
$499$	−8.71019	−	15.0865i	−0.389922	−	0.675364i	−0.992439	+	0.122742i	$0.960831\pi$
$500$		0			0
$501$	−0.00566403	+	0.00981040i	−0.000253050	+	0.000438296i
$502$		0			0
$503$	−4.59691	+	7.96208i	−0.204966	+	0.355012i	−0.950122	−	0.311879i	$-0.899042\pi$
$503$	−4.59691	+	7.96208i	−0.204966	+	0.355012i	0.745156	+	0.666890i	$0.232375\pi$
$504$		0			0
$505$	5.11805	+	8.86473i	0.227750	+	0.394475i
$506$		0			0
$507$	−1.52192			−0.0675909
$508$		0			0
$509$	19.5611	−	33.8808i	0.867030	−	1.50174i	0.00201193	−	0.999998i	$-0.499360\pi$
$509$	19.5611	−	33.8808i	0.867030	−	1.50174i	0.865018	−	0.501741i	$-0.167307\pi$
$510$		0			0
$511$	4.29152	+	7.43313i	0.189846	+	0.328822i
$512$		0			0
$513$	−1.41621	−	2.45295i	−0.0625272	−	0.108300i
$514$		0			0
$515$	−2.33714	−	4.04804i	−0.102987	−	0.178378i
$516$		0			0
$517$	−3.22312			−0.141752
$518$		0			0
$519$	2.84063			0.124690
$520$		0			0
$521$	−10.0744	−	17.4494i	−0.441368	−	0.764471i	0.556424	−	0.830899i	$-0.312173\pi$
$521$	−10.0744	−	17.4494i	−0.441368	−	0.764471i	−0.997791	+	0.0664275i	$0.978840\pi$
$522$		0			0
$523$	0.809076	+	1.40136i	0.0353784	+	0.0612772i	0.883172	−	0.469048i	$-0.155403\pi$
$523$	0.809076	+	1.40136i	0.0353784	+	0.0612772i	−0.847794	+	0.530326i	$0.822070\pi$
$524$		0			0
$525$	0.372813	+	0.645732i	0.0162709	+	0.0281821i
$526$		0			0
$527$	14.0400	−	24.3180i	0.611592	−	1.05931i
$528$		0			0
$529$	−11.8329			−0.514473
$530$		0			0
$531$	0.213933	+	0.370544i	0.00928392	+	0.0160802i
$532$		0			0
$533$	7.37558	−	12.7749i	0.319472	−	0.553341i
$534$		0			0
$535$	5.20934	−	9.02284i	0.225219	−	0.390091i
$536$		0			0
$537$	−0.187911	−	0.325472i	−0.00810898	−	0.0140452i
$538$		0			0
$539$	0.556262	−	0.963475i	0.0239599	−	0.0414998i
$540$		0			0
$541$	22.3334			0.960190			0.480095	−	0.877217i	$-0.340602\pi$
$541$	22.3334			0.960190			0.480095	+	0.877217i	$0.340602\pi$
$542$		0			0
$543$	−1.85483	+	3.21267i	−0.0795985	+	0.137869i
$544$		0			0
$545$	15.2242			0.652132
$546$		0			0
$547$	15.1368			0.647204			0.323602	−	0.946193i	$-0.395106\pi$
$547$	15.1368			0.647204			0.323602	+	0.946193i	$0.395106\pi$
$548$		0			0
$549$	−25.2232			−1.07650
$550$		0			0
$551$	7.50155	+	12.9931i	0.319577	+	0.553524i
$552$		0			0
$553$	8.39964	−	14.5486i	0.357189	−	0.618670i
$554$		0			0
$555$	−1.00688	+	1.01070i	−0.0427396	+	0.0429018i
$556$		0			0
$557$	−14.4817	+	25.0831i	−0.613610	+	1.06280i	0.377016	+	0.926207i	$0.376950\pi$
$557$	−14.4817	+	25.0831i	−0.613610	+	1.06280i	−0.990627	+	0.136598i	$0.956383\pi$
$558$		0			0
$559$	−2.84293	−	4.92410i	−0.120243	−	0.208267i
$560$		0			0
$561$	0.259588			0.0109598
$562$		0			0
$563$	−29.8156			−1.25658			−0.628288	−	0.777981i	$-0.716244\pi$
$563$	−29.8156			−1.25658			−0.628288	+	0.777981i	$0.716244\pi$
$564$		0			0
$565$	−21.1662			−0.890468
$566$		0			0
$567$	13.5239	−	23.4240i	0.567949	−	0.983717i
$568$		0			0
$569$	−14.6512			−0.614211			−0.307106	−	0.951675i	$-0.599361\pi$
$569$	−14.6512			−0.614211			−0.307106	+	0.951675i	$0.599361\pi$
$570$		0			0
$571$	−11.3742	+	19.7008i	−0.475997	+	0.824452i	−0.999622	−	0.0274974i	$-0.991246\pi$
$571$	−11.3742	+	19.7008i	−0.475997	+	0.824452i	0.523624	+	0.851949i	$0.324580\pi$
$572$		0			0
$573$	1.70337	+	2.95032i	0.0711592	+	0.123251i
$574$		0			0
$575$	1.67086	−	2.89402i	0.0696798	−	0.120689i
$576$		0			0
$577$	14.2713	−	24.7186i	0.594121	−	1.02905i	−0.399549	−	0.916712i	$-0.630833\pi$
$577$	14.2713	−	24.7186i	0.594121	−	1.02905i	0.993670	−	0.112336i	$-0.0358333\pi$
$578$		0			0
$579$	−0.605493	−	1.04875i	−0.0251634	−	0.0435844i
$580$		0			0
$581$	−16.1412			−0.669650
$582$		0			0
$583$	−0.0729379	+	0.126332i	−0.00302078	+	0.00523214i
$584$		0			0
$585$	−3.75732	−	6.50787i	−0.155346	−	0.269067i
$586$		0			0
$587$	−3.86625	−	6.69655i	−0.159577	−	0.276396i	0.775139	−	0.631791i	$-0.217680\pi$
$587$	−3.86625	−	6.69655i	−0.159577	−	0.276396i	−0.934716	+	0.355395i	$0.884346\pi$
$588$		0			0
$589$	9.22762	+	15.9827i	0.380218	+	0.658556i
$590$		0			0
$591$	−1.41153			−0.0580625
$592$		0			0
$593$	10.1609			0.417258			0.208629	−	0.977995i	$-0.433100\pi$
$593$	10.1609			0.417258			0.208629	+	0.977995i	$0.433100\pi$
$594$		0			0
$595$	−4.91298	−	8.50952i	−0.201412	−	0.348856i
$596$		0			0
$597$	−0.390187	−	0.675824i	−0.0159693	−	0.0276596i
$598$		0			0
$599$	4.10424	+	7.10875i	0.167695	+	0.290455i	0.937609	−	0.347692i	$-0.113034\pi$
$599$	4.10424	+	7.10875i	0.167695	+	0.290455i	−0.769914	+	0.638147i	$0.779701\pi$
$600$		0			0
$601$	−6.97048	+	12.0732i	−0.284332	+	0.492477i	−0.972447	−	0.233124i	$-0.925105\pi$
$601$	−6.97048	+	12.0732i	−0.284332	+	0.492477i	0.688115	+	0.725602i	$0.258438\pi$
$602$		0			0
$603$	42.6474			1.73674
$604$		0			0
$605$	5.43588	+	9.41523i	0.221000	+	0.382783i
$606$		0			0
$607$	−17.1624	+	29.7261i	−0.696599	+	1.20654i	0.273040	+	0.962003i	$0.411971\pi$
$607$	−17.1624	+	29.7261i	−0.696599	+	1.20654i	−0.969639	+	0.244542i	$0.921362\pi$
$608$		0			0
$609$	2.75348	−	4.76917i	0.111577	−	0.193256i
$610$		0			0
$611$	11.4834	+	19.8898i	0.464568	+	0.804655i
$612$		0			0
$613$	−20.6918	+	35.8392i	−0.835734	+	1.44753i	0.0576980	+	0.998334i	$0.481624\pi$
$613$	−20.6918	+	35.8392i	−0.835734	+	1.44753i	−0.893432	+	0.449199i	$0.851709\pi$
$614$		0			0
$615$	1.35587			0.0546739
$616$		0			0
$617$	−16.8511	+	29.1870i	−0.678401	+	1.17502i	0.297062	+	0.954858i	$0.403993\pi$
$617$	−16.8511	+	29.1870i	−0.678401	+	1.17502i	−0.975462	+	0.220166i	$0.929340\pi$
$618$		0			0
$619$	−27.3600			−1.09969			−0.549845	−	0.835267i	$-0.685313\pi$
$619$	−27.3600			−1.09969			−0.549845	+	0.835267i	$0.685313\pi$
$620$		0			0
$621$	4.65948			0.186978
$622$		0			0
$623$	−48.1307			−1.92832
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−0.0853055	+	0.147753i	−0.00340677	+	0.00590070i
$628$		0			0
$629$	13.2688	−	13.3191i	0.529060	−	0.531068i
$630$		0			0
$631$	14.6597	−	25.3914i	0.583594	−	1.01081i	−0.411455	−	0.911430i	$-0.634979\pi$
$631$	14.6597	−	25.3914i	0.583594	−	1.01081i	0.995049	−	0.0993848i	$-0.0316875\pi$
$632$		0			0
$633$	3.08170	+	5.33766i	0.122487	+	0.212153i
$634$		0			0
$635$	14.5634			0.577932
$636$		0			0
$637$	−7.92745			−0.314097
$638$		0			0
$639$	−25.2288			−0.998038
$640$		0			0
$641$	−23.5463	+	40.7833i	−0.930021	+	1.61084i	−0.146742	+	0.989175i	$0.546879\pi$
$641$	−23.5463	+	40.7833i	−0.930021	+	1.61084i	−0.783280	+	0.621670i	$0.786455\pi$
$642$		0			0
$643$	1.20532			0.0475331			0.0237666	−	0.999718i	$-0.492434\pi$
$643$	1.20532			0.0475331			0.0237666	+	0.999718i	$0.492434\pi$
$644$		0			0
$645$	0.261311	−	0.452604i	0.0102891	−	0.0178213i
$646$		0			0
$647$	−21.0217	−	36.4107i	−0.826450	−	1.43145i	−0.900806	−	0.434221i	$-0.857024\pi$
$647$	−21.0217	−	36.4107i	−0.826450	−	1.43145i	0.0743563	−	0.997232i	$-0.476310\pi$
$648$		0			0
$649$	0.0260133	−	0.0450563i	0.00102111	−	0.00176862i
$650$		0			0
$651$	3.38704	−	5.86653i	0.132749	−	0.229927i
$652$		0			0
$653$	11.3994	+	19.7444i	0.446093	+	0.772656i	0.998128	−	0.0611650i	$-0.0194816\pi$
$653$	11.3994	+	19.7444i	0.446093	+	0.772656i	−0.552034	+	0.833821i	$0.686148\pi$
$654$		0			0
$655$	3.30947			0.129312
$656$		0			0
$657$	3.97547	−	6.88572i	0.155098	−	0.268638i
$658$		0			0
$659$	−14.7558	−	25.5578i	−0.574805	−	0.995592i	−0.996063	−	0.0886510i	$-0.971744\pi$
$659$	−14.7558	−	25.5578i	−0.574805	−	0.995592i	0.421257	−	0.906941i	$-0.361589\pi$
$660$		0			0
$661$	22.3134	+	38.6480i	0.867892	+	1.50323i	0.864146	+	0.503241i	$0.167859\pi$
$661$	22.3134	+	38.6480i	0.867892	+	1.50323i	0.00374606	+	0.999993i	$0.498808\pi$
$662$		0			0
$663$	−0.924865	−	1.60191i	−0.0359188	−	0.0622131i
$664$		0			0
$665$	6.45798			0.250430
$666$		0			0
$667$	−24.6809			−0.955648
$668$		0			0
$669$	2.50486	+	4.33855i	0.0968435	+	0.167738i
$670$		0			0
$671$	1.53351	+	2.65612i	0.0592006	+	0.102538i
$672$		0			0
$673$	−8.41622	−	14.5773i	−0.324422	−	0.561915i	0.656974	−	0.753914i	$-0.271836\pi$
$673$	−8.41622	−	14.5773i	−0.324422	−	0.561915i	−0.981395	+	0.191999i	$0.938503\pi$
$674$		0			0
$675$	0.697167	−	1.20753i	0.0268340	−	0.0464778i
$676$		0			0
$677$	2.68978			0.103377			0.0516883	−	0.998663i	$-0.483540\pi$
$677$	2.68978			0.103377			0.0516883	+	0.998663i	$0.483540\pi$
$678$		0			0
$679$	−19.0611	−	33.0148i	−0.731498	−	1.26699i
$680$		0			0
$681$	0.946546	−	1.63947i	0.0362717	−	0.0628245i
$682$		0			0
$683$	−19.7109	+	34.1403i	−0.754216	+	1.30634i	0.191547	+	0.981484i	$0.438650\pi$
$683$	−19.7109	+	34.1403i	−0.754216	+	1.30634i	−0.945763	+	0.324858i	$0.894684\pi$
$684$		0			0
$685$	6.45665	+	11.1832i	0.246696	+	0.427290i
$686$		0			0
$687$	−1.14667	+	1.98609i	−0.0437481	+	0.0757739i
$688$		0			0
$689$	1.03946			0.0396002
$690$		0			0
$691$	−4.24105	+	7.34571i	−0.161337	+	0.279444i	−0.935348	−	0.353728i	$-0.884914\pi$
$691$	−4.24105	+	7.34571i	−0.161337	+	0.279444i	0.774011	+	0.633172i	$0.218247\pi$
$692$		0			0
$693$	−3.35267			−0.127357
$694$		0			0
$695$	−3.78517			−0.143580
$696$		0			0
$697$	−17.8678			−0.676790
$698$		0			0
$699$	1.99852	+	3.46154i	0.0755910	+	0.130927i
$700$		0			0
$701$	−11.4372	+	19.8098i	−0.431977	+	0.748206i	−0.997044	−	0.0768391i	$-0.975517\pi$
$701$	−11.4372	+	19.8098i	−0.431977	+	0.748206i	0.565066	+	0.825045i	$0.308851\pi$
$702$		0			0
$703$	3.22067	+	11.9293i	0.121470	+	0.449921i
$704$		0			0
$705$	−1.05551	+	1.82819i	−0.0397527	+	0.0688536i
$706$		0			0
$707$	−16.2709	−	28.1820i	−0.611930	−	1.05989i
$708$		0			0
$709$	−10.0262			−0.376541			−0.188270	−	0.982117i	$-0.560288\pi$
$709$	−10.0262			−0.376541			−0.188270	+	0.982117i	$0.560288\pi$
$710$		0			0
$711$	−15.5621			−0.583625
$712$		0			0
$713$	−30.3598			−1.13699
$714$		0			0
$715$	−0.456872	+	0.791326i	−0.0170861	+	0.0295939i
$716$		0			0
$717$	2.79103			0.104233
$718$		0			0
$719$	−3.40375	+	5.89547i	−0.126938	+	0.219864i	−0.922489	−	0.386023i	$-0.873848\pi$
$719$	−3.40375	+	5.89547i	−0.126938	+	0.219864i	0.795551	+	0.605887i	$0.207182\pi$
$720$		0			0
$721$	7.43002	+	12.8692i	0.276709	+	0.479273i
$722$		0			0
$723$	3.13727	−	5.43390i	0.116676	−	0.202089i
$724$		0			0
$725$	−3.69284	+	6.39619i	−0.137149	+	0.237548i
$726$		0			0
$727$	−2.10490	−	3.64579i	−0.0780663	−	0.135215i	0.824349	−	0.566081i	$-0.191541\pi$
$727$	−2.10490	−	3.64579i	−0.0780663	−	0.135215i	−0.902416	+	0.430867i	$0.858208\pi$
$728$		0			0
$729$	−24.0748			−0.891658
$730$		0			0
$731$	−3.44358	+	5.96446i	−0.127366	+	0.220604i
$732$		0			0
$733$	−16.1380	−	27.9518i	−0.596070	−	1.03242i	−0.993395	−	0.114745i	$-0.963395\pi$
$733$	−16.1380	−	27.9518i	−0.596070	−	1.03242i	0.397325	−	0.917678i	$-0.369938\pi$
$734$		0			0
$735$	−0.364330	−	0.631037i	−0.0134385	−	0.0232762i
$736$		0			0
$737$	−2.59286	−	4.49096i	−0.0955092	−	0.165427i
$738$		0			0
$739$	12.4330			0.457355			0.228678	−	0.973502i	$-0.426560\pi$
$739$	12.4330			0.457355			0.228678	+	0.973502i	$0.426560\pi$
$740$		0			0
$741$	1.21571			0.0446603
$742$		0			0
$743$	−22.6942	−	39.3074i	−0.832568	−	1.44205i	−0.895995	−	0.444064i	$-0.853536\pi$
$743$	−22.6942	−	39.3074i	−0.832568	−	1.44205i	0.0634271	−	0.997986i	$-0.479797\pi$
$744$		0			0
$745$	−0.513304	−	0.889068i	−0.0188060	−	0.0325729i
$746$		0			0
$747$	7.47625	+	12.9492i	0.273542	+	0.473788i
$748$		0			0
$749$	−16.5611	+	28.6846i	−0.605129	+	1.04811i
$750$		0			0
$751$	37.3536			1.36305			0.681526	−	0.731794i	$-0.261317\pi$
$751$	37.3536			1.36305			0.681526	+	0.731794i	$0.261317\pi$
$752$		0			0
$753$	−1.82623	−	3.16312i	−0.0665514	−	0.115270i
$754$		0			0
$755$	−6.96022	+	12.0555i	−0.253308	+	0.438743i
$756$		0			0
$757$	23.8188	−	41.2554i	0.865711	−	1.49945i	−0.000629280	−	1.00000i	$-0.500200\pi$
$757$	23.8188	−	41.2554i	0.865711	−	1.49945i	0.866340	−	0.499455i	$-0.166466\pi$
$758$		0			0
$759$	−0.140332	−	0.243062i	−0.00509373	−	0.00882260i
$760$		0			0
$761$	8.04302	−	13.9309i	0.291559	−	0.504995i	−0.682619	−	0.730774i	$-0.739159\pi$
$761$	8.04302	−	13.9309i	0.291559	−	0.504995i	0.974179	+	0.225779i	$0.0724926\pi$
$762$		0			0
$763$	−48.3994			−1.75217
$764$		0			0
$765$	−4.55116	+	7.88285i	−0.164548	+	0.285005i
$766$		0			0
$767$	−0.370723			−0.0133860
$768$		0			0
$769$	17.0986			0.616590			0.308295	−	0.951291i	$-0.400242\pi$
$769$	17.0986			0.616590			0.308295	+	0.951291i	$0.400242\pi$
$770$		0			0
$771$	−4.13820			−0.149034
$772$		0			0
$773$	−2.44379	−	4.23277i	−0.0878971	−	0.152242i	0.818725	−	0.574186i	$-0.194681\pi$
$773$	−2.44379	−	4.23277i	−0.0878971	−	0.152242i	−0.906622	+	0.421944i	$0.861348\pi$
$774$		0			0
$775$	−4.54254	+	7.86791i	−0.163173	+	0.282624i
$776$		0			0
$777$	3.20098	−	3.21313i	0.114835	−	0.115270i
$778$		0			0
$779$	5.87168	−	10.1701i	0.210375	−	0.364380i
$780$		0			0
$781$	1.53385	+	2.65671i	0.0548856	+	0.0950647i
$782$		0			0
$783$	−10.2981			−0.368024
$784$		0			0
$785$	−3.40253			−0.121441
$786$		0			0
$787$	−42.0717			−1.49969			−0.749847	−	0.661611i	$-0.769873\pi$
$787$	−42.0717			−1.49969			−0.749847	+	0.661611i	$0.769873\pi$
$788$		0			0
$789$	−1.45860	+	2.52637i	−0.0519275	+	0.0899410i
$790$		0			0
$791$	67.2897			2.39255
$792$		0			0
$793$	10.9273	−	18.9266i	0.388038	−	0.672102i
$794$		0			0
$795$	0.0477714	+	0.0827425i	0.00169428	+	0.00293457i
$796$		0			0
$797$	9.47508	−	16.4113i	0.335625	−	0.581319i	−0.647980	−	0.761657i	$-0.724386\pi$
$797$	9.47508	−	16.4113i	0.335625	−	0.581319i	0.983605	+	0.180339i	$0.0577193\pi$
$798$		0			0
$799$	13.9096	−	24.0921i	0.492085	−	0.852317i
$800$		0			0
$801$	22.2931	+	38.6128i	0.787687	+	1.36431i
$802$		0			0
$803$	−0.966798			−0.0341176
$804$		0			0
$805$	−5.31186	+	9.20041i	−0.187219	+	0.324272i
$806$		0			0
$807$	−0.0235053	−	0.0407124i	−0.000827427	−	0.00143315i
$808$		0			0
$809$	13.7920	+	23.8885i	0.484902	+	0.839874i	0.999850	−	0.0173473i	$-0.00552208\pi$
$809$	13.7920	+	23.8885i	0.484902	+	0.839874i	−0.514948	+	0.857221i	$0.672189\pi$
$810$		0			0
$811$	−11.7441	−	20.3414i	−0.412391	−	0.714283i	0.582759	−	0.812645i	$-0.301973\pi$
$811$	−11.7441	−	20.3414i	−0.412391	−	0.714283i	−0.995151	+	0.0983622i	$0.968640\pi$
$812$		0			0
$813$	−2.69143			−0.0943926
$814$		0			0
$815$	11.4128			0.399773
$816$		0			0
$817$	−2.26325	−	3.92007i	−0.0791812	−	0.137146i
$818$		0			0
$819$	11.9450	+	20.6893i	0.417391	+	0.722942i
$820$		0			0
$821$	−4.76257	−	8.24901i	−0.166215	−	0.287893i	0.770871	−	0.636991i	$-0.219821\pi$
$821$	−4.76257	−	8.24901i	−0.166215	−	0.287893i	−0.937086	+	0.349098i	$0.886488\pi$
$822$		0			0
$823$	−14.2633	+	24.7048i	−0.497189	+	0.861156i	−0.999995	−	0.00324298i	$-0.998968\pi$
$823$	−14.2633	+	24.7048i	−0.497189	+	0.861156i	0.502806	+	0.864399i	$0.332301\pi$
$824$		0			0
$825$	−0.0839878			−0.00292408
$826$		0			0
$827$	23.4629	+	40.6389i	0.815883	+	1.41315i	0.908692	+	0.417468i	$0.137082\pi$
$827$	23.4629	+	40.6389i	0.815883	+	1.41315i	−0.0928084	+	0.995684i	$0.529584\pi$
$828$		0			0
$829$	13.7057	−	23.7389i	0.476017	−	0.824486i	−0.523606	−	0.851961i	$-0.675413\pi$
$829$	13.7057	−	23.7389i	0.476017	−	0.824486i	0.999622	+	0.0274753i	$0.00874676\pi$
$830$		0			0
$831$	1.01911	−	1.76515i	0.0353526	−	0.0612324i
$832$		0			0
$833$	4.80117	+	8.31588i	0.166351	+	0.288128i
$834$		0			0
$835$	−0.0241496	+	0.0418284i	−0.000835732	+	0.00144753i
$836$		0			0
$837$	−12.6676			−0.437858
$838$		0			0
$839$	7.91955	−	13.7171i	0.273413	−	0.473565i	−0.696320	−	0.717731i	$-0.745181\pi$
$839$	7.91955	−	13.7171i	0.273413	−	0.473565i	0.969734	+	0.244166i	$0.0785140\pi$
$840$		0			0
$841$	25.5483			0.880974
$842$		0			0
$843$	0.838995			0.0288965
$844$		0			0
$845$	−6.48899			−0.223228
$846$		0			0
$847$	−17.2813	−	29.9321i	−0.593792	−	1.02848i
$848$		0			0
$849$	−0.0587581	+	0.101772i	−0.00201657	+	0.00349281i
$850$		0			0
$851$	−19.6442	−	5.22379i	−0.673395	−	0.179069i
$852$		0			0
$853$	13.2989	−	23.0344i	0.455346	−	0.788683i	−0.543362	−	0.839499i	$-0.682849\pi$
$853$	13.2989	−	23.0344i	0.455346	−	0.788683i	0.998708	+	0.0508157i	$0.0161821\pi$
$854$		0			0
$855$	−2.99120	−	5.18090i	−0.102297	−	0.177183i
$856$		0			0
$857$	−39.6514			−1.35447			−0.677233	−	0.735769i	$-0.736821\pi$
$857$	−39.6514			−1.35447			−0.677233	+	0.735769i	$0.736821\pi$
$858$		0			0
$859$	−48.2955			−1.64782			−0.823910	−	0.566720i	$-0.808212\pi$
$859$	−48.2955			−1.64782			−0.823910	+	0.566720i	$0.808212\pi$
$860$		0			0
$861$	−4.31046			−0.146900
$862$		0			0
$863$	23.2704	−	40.3055i	0.792133	−	1.37201i	−0.132511	−	0.991182i	$-0.542304\pi$
$863$	23.2704	−	40.3055i	0.792133	−	1.37201i	0.924644	−	0.380833i	$-0.124363\pi$
$864$		0			0
$865$	12.1116			0.411805
$866$		0			0
$867$	0.873314	−	1.51263i	0.0296593	−	0.0513714i
$868$		0			0
$869$	0.946140	+	1.63876i	0.0320956	+	0.0555912i
$870$		0			0
$871$	−18.4758	+	32.0010i	−0.626028	+	1.08431i
$872$		0			0
$873$	−17.6574	+	30.5834i	−0.597611	+	1.03509i
$874$		0			0
$875$	1.58956	+	2.75319i	0.0537368	+	0.0930749i
$876$		0			0
$877$	54.8189			1.85110			0.925551	−	0.378623i	$-0.123602\pi$
$877$	54.8189			1.85110			0.925551	+	0.378623i	$0.123602\pi$
$878$		0			0
$879$	−1.43385	+	2.48351i	−0.0483627	+	0.0837666i
$880$		0			0
$881$	−15.8771	−	27.4999i	−0.534912	−	0.926495i	−0.999168	−	0.0407937i	$-0.987011\pi$
$881$	−15.8771	−	27.4999i	−0.534912	−	0.926495i	0.464255	−	0.885701i	$-0.346322\pi$
$882$		0			0
$883$	16.1977	+	28.0552i	0.545096	+	0.944133i	0.998601	+	0.0528798i	$0.0168400\pi$
$883$	16.1977	+	28.0552i	0.545096	+	0.944133i	−0.453505	+	0.891254i	$0.649827\pi$
$884$		0			0
$885$	−0.0170377	−	0.0295101i	−0.000572715	−	0.000991971i
$886$		0			0
$887$	−23.0174			−0.772848			−0.386424	−	0.922321i	$-0.626290\pi$
$887$	−23.0174			−0.772848			−0.386424	+	0.922321i	$0.626290\pi$
$888$		0			0
$889$	−46.2988			−1.55281
$890$		0			0
$891$	1.52334	+	2.63849i	0.0510337	+	0.0883929i
$892$		0			0
$893$	9.14189	+	15.8342i	0.305922	+	0.529872i
$894$		0			0
$895$	−0.801194	−	1.38771i	−0.0267810	−	0.0463860i
$896$		0			0
$897$	−0.999955	+	1.73197i	−0.0333875	+	0.0578289i
$898$		0			0
$899$	67.0995			2.23789
$900$		0			0
$901$	−0.629536	−	1.09039i	−0.0209729	−	0.0363261i
$902$		0			0
$903$	−0.830738	+	1.43888i	−0.0276452	+	0.0478829i
$904$		0			0
$905$	−7.90842	+	13.6978i	−0.262885	+	0.455330i
$906$		0			0
$907$	−0.786574	−	1.36239i	−0.0261178	−	0.0452373i	0.852671	−	0.522448i	$-0.174981\pi$
$907$	−0.786574	−	1.36239i	−0.0261178	−	0.0452373i	−0.878789	+	0.477211i	$0.841648\pi$
$908$		0			0
$909$	−15.0726	+	26.1066i	−0.499927	+	0.865900i
$910$		0			0
$911$	49.5928			1.64308			0.821542	−	0.570148i	$-0.193114\pi$
$911$	49.5928			1.64308			0.821542	+	0.570148i	$0.193114\pi$
$912$		0			0
$913$	0.909077	−	1.57457i	0.0300860	−	0.0521106i
$914$		0			0
$915$	2.00878			0.0664082
$916$		0			0
$917$	−10.5212			−0.347440
$918$		0			0
$919$	−38.7411			−1.27795			−0.638976	−	0.769227i	$-0.720642\pi$
$919$	−38.7411			−1.27795			−0.638976	+	0.769227i	$0.720642\pi$
$920$		0			0
$921$	0.0457387	+	0.0792217i	0.00150714	+	0.00261044i
$922$		0			0
$923$	10.9297	−	18.9308i	0.359755	−	0.623114i
$924$		0			0
$925$	−4.29301	+	4.30930i	−0.141153	+	0.141689i
$926$		0			0
$927$	6.88285	−	11.9214i	0.226062	−	0.391551i
$928$		0			0
$929$	13.5542	+	23.4766i	0.444699	+	0.770241i	0.998031	−	0.0627198i	$-0.0199774\pi$
$929$	13.5542	+	23.4766i	0.444699	+	0.770241i	−0.553333	+	0.832960i	$0.686644\pi$
$930$		0			0
$931$	−6.31102			−0.206835
$932$		0			0
$933$	−6.05722			−0.198304
$934$		0			0
$935$	1.10680			0.0361962
$936$		0			0
$937$	23.1438	−	40.0862i	0.756074	−	1.30956i	−0.188765	−	0.982022i	$-0.560448\pi$
$937$	23.1438	−	40.0862i	0.756074	−	1.30956i	0.944839	−	0.327536i	$-0.106218\pi$
$938$		0			0
$939$	−3.08560			−0.100695
$940$		0			0
$941$	13.2485	−	22.9471i	0.431889	−	0.748053i	−0.565147	−	0.824990i	$-0.691181\pi$
$941$	13.2485	−	22.9471i	0.431889	−	0.748053i	0.997036	+	0.0769371i	$0.0245141\pi$
$942$		0			0
$943$	9.65923	+	16.7303i	0.314548	+	0.544813i
$944$		0			0
$945$	−2.21637	+	3.83887i	−0.0720986	+	0.124878i
$946$		0			0
$947$	−16.3802	+	28.3714i	−0.532286	+	0.921946i	0.467004	+	0.884255i	$0.345333\pi$
$947$	−16.3802	+	28.3714i	−0.532286	+	0.921946i	−0.999289	+	0.0376903i	$0.988000\pi$
$948$		0			0
$949$	3.44452	+	5.96609i	0.111814	+	0.193668i
$950$		0			0
$951$	0.598835			0.0194186
$952$		0			0
$953$	14.4949	−	25.1060i	0.469537	−	0.813263i	−0.529856	−	0.848088i	$-0.677754\pi$
$953$	14.4949	−	25.1060i	0.469537	−	0.813263i	0.999393	+	0.0348249i	$0.0110873\pi$
$954$		0			0
$955$	7.26262	+	12.5792i	0.235013	+	0.407054i
$956$		0			0
$957$	0.310153	+	0.537201i	0.0100258	+	0.0173653i
$958$		0			0
$959$	−20.5264	−	35.5528i	−0.662833	−	1.14806i
$960$		0			0
$961$	51.5387			1.66254
$962$		0			0
$963$	30.6829			0.988743
$964$		0			0
$965$	−2.58163	−	4.47151i	−0.0831056	−	0.143943i
$966$		0			0
$967$	0.771849	+	1.33688i	0.0248210	+	0.0429912i	0.878169	−	0.478350i	$-0.158765\pi$
$967$	0.771849	+	1.33688i	0.0248210	+	0.0429912i	−0.853348	+	0.521342i	$0.825432\pi$
$968$		0			0
$969$	−0.736283	−	1.27528i	−0.0236528	−	0.0409679i
$970$		0			0
$971$	−17.0876	+	29.5966i	−0.548367	+	0.949799i	0.450020	+	0.893018i	$0.351417\pi$
$971$	−17.0876	+	29.5966i	−0.548367	+	0.949799i	−0.998387	+	0.0567804i	$0.981917\pi$
$972$		0			0
$973$	12.0335			0.385776
$974$		0			0
$975$	0.299233	+	0.518287i	0.00958313	+	0.0165985i
$976$		0			0
$977$	−20.8391	+	36.0944i	−0.666703	+	1.15476i	0.312118	+	0.950043i	$0.398962\pi$
$977$	−20.8391	+	36.0944i	−0.666703	+	1.15476i	−0.978821	+	0.204719i	$0.934372\pi$
$978$		0			0
$979$	2.71073	−	4.69513i	0.0866354	−	0.150057i
$980$		0			0
$981$	22.4175	+	38.8283i	0.715736	+	1.23969i
$982$		0			0
$983$	−13.4185	+	23.2416i	−0.427985	+	0.741292i	−0.996694	−	0.0812468i	$-0.974110\pi$
$983$	−13.4185	+	23.2416i	−0.427985	+	0.741292i	0.568709	+	0.822539i	$0.307443\pi$
$984$		0			0
$985$	−6.01830			−0.191759
$986$		0			0
$987$	3.35558	−	5.81203i	0.106809	−	0.184999i
$988$		0			0
$989$	7.44634			0.236780
$990$		0			0
$991$	−18.0542			−0.573512			−0.286756	−	0.958004i	$-0.592577\pi$
$991$	−18.0542			−0.573512			−0.286756	+	0.958004i	$0.592577\pi$
$992$		0			0
$993$	5.17196			0.164127
$994$		0			0
$995$	−1.66363	−	2.88150i	−0.0527407	−	0.0913496i
$996$		0			0
$997$	15.8037	−	27.3728i	0.500507	−	0.866904i	−0.499492	−	0.866318i	$-0.666480\pi$
$997$	15.8037	−	27.3728i	0.500507	−	0.866904i	1.00000		0.000586063i	$-0.000186550\pi$
$998$		0			0
$999$	−8.19655	−	2.17963i	−0.259327	−	0.0689603i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.i.a.121.4	✓	14
37.26	even	3	inner	740.2.i.a.581.4	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.i.a.121.4	✓	14	1.1	even	1	trivial
740.2.i.a.581.4	yes	14	37.26	even	3	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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.117270 - 0.203117i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(1.58956 + 2.75319i) q^{7} +(1.47250 - 2.55044i) q^{9} -0.358097 q^{11} +(1.27583 + 2.20981i) q^{13} +(-0.117270 + 0.203117i) q^{15} +(1.54539 - 2.67670i) q^{17} +(1.01569 + 1.75923i) q^{19} +(0.372813 - 0.645732i) q^{21} -3.34172 q^{23} +(-0.500000 + 0.866025i) q^{25} -1.39433 q^{27} +7.38568 q^{29} +9.08508 q^{31} +(0.0419939 + 0.0727356i) q^{33} +(1.58956 - 2.75319i) q^{35} +(5.87847 + 1.56320i) q^{37} +(0.299233 - 0.518287i) q^{39} +(-2.89049 - 5.00648i) q^{41} -2.22829 q^{43} -2.94499 q^{45} +9.00068 q^{47} +(-1.55338 + 2.69054i) q^{49} -0.724910 q^{51} +(0.203682 - 0.352787i) q^{53} +(0.179048 + 0.310121i) q^{55} +(0.238219 - 0.412607i) q^{57} +(-0.0726432 + 0.125822i) q^{59} +(-4.28240 - 7.41733i) q^{61} +9.36246 q^{63} +(1.27583 - 2.20981i) q^{65} +(7.24066 + 12.5412i) q^{67} +(0.391883 + 0.678761i) q^{69} +(-4.28335 - 7.41898i) q^{71} +2.69982 q^{73} +0.234539 q^{75} +(-0.569216 - 0.985910i) q^{77} +(-2.64213 - 4.57631i) q^{79} +(-4.25397 - 7.36810i) q^{81} +(-2.53863 + 4.39704i) q^{83} -3.09078 q^{85} +(-0.866116 - 1.50016i) q^{87} +(-7.56983 + 13.1113i) q^{89} +(-4.05602 + 7.02524i) q^{91} +(-1.06540 - 1.84533i) q^{93} +(1.01569 - 1.75923i) q^{95} -11.9914 q^{97} +(-0.527296 + 0.913304i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 7 q^{5} + 4 q^{7} - 13 q^{9} + 14 q^{11} + 4 q^{13} + q^{17} + 4 q^{19} - 3 q^{21} + 12 q^{23} - 7 q^{25} - 6 q^{27} - 4 q^{29} - 24 q^{31} + 13 q^{33} + 4 q^{35} + 10 q^{37} + 21 q^{39} + 5 q^{41}+ \cdots - 58 q^{99}+O(q^{100}) \) 14 * q - 7 * q^5 + 4 * q^7 - 13 * q^9 + 14 * q^11 + 4 * q^13 + q^17 + 4 * q^19 - 3 * q^21 + 12 * q^23 - 7 * q^25 - 6 * q^27 - 4 * q^29 - 24 * q^31 + 13 * q^33 + 4 * q^35 + 10 * q^37 + 21 * q^39 + 5 * q^41 - 6 * q^43 + 26 * q^45 - 16 * q^47 - 11 * q^49 + 26 * q^51 + 14 * q^53 - 7 * q^55 + 24 * q^57 - 16 * q^59 + 12 * q^61 - 98 * q^63 + 4 * q^65 + 21 * q^69 - 9 * q^71 - 40 * q^73 + 3 * q^77 + 3 * q^79 - 43 * q^81 + 5 * q^83 - 2 * q^85 + 31 * q^87 + 20 * q^89 - 2 * q^91 + 37 * q^93 + 4 * q^95 - 58 * q^97 - 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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