LMFDB - Embedded newform 729.2.e.q.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			163.1
Root			$-0.342020 + 0.939693i$ of defining polynomial
Character	$\chi$	$=$	729.163
Dual form			729.2.e.q.568.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20805 + 0.439693i) q^{2} +(-0.266044 + 0.223238i) q^{4} +(0.0775297 + 0.439693i) q^{5} +(-2.70574 - 2.27038i) q^{7} +(1.50881 - 2.61334i) q^{8} +O(q^{10})$	\(q+(-1.20805 + 0.439693i) q^{2} +(-0.266044 + 0.223238i) q^{4} +(0.0775297 + 0.439693i) q^{5} +(-2.70574 - 2.27038i) q^{7} +(1.50881 - 2.61334i) q^{8} +(-0.286989 - 0.497079i) q^{10} +(-0.482753 + 2.73783i) q^{11} +(-3.09240 - 1.12554i) q^{13} +(4.26692 + 1.55303i) q^{14} +(-0.553033 + 3.13641i) q^{16} +(3.51968 + 6.09627i) q^{17} +(2.59240 - 4.49016i) q^{19} +(-0.118782 - 0.0996702i) q^{20} +(-0.620615 - 3.51968i) q^{22} +(5.57445 - 4.67752i) q^{23} +(4.51114 - 1.64192i) q^{25} +4.23065 q^{26} +1.22668 q^{28} +(-3.40090 + 1.23783i) q^{29} +(-1.48293 + 1.24432i) q^{31} +(0.337044 + 1.91147i) q^{32} +(-6.93242 - 5.81699i) q^{34} +(0.788496 - 1.36571i) q^{35} +(1.61334 + 2.79439i) q^{37} +(-1.15744 + 6.56418i) q^{38} +(1.26604 + 0.460802i) q^{40} +(4.56769 + 1.66250i) q^{41} +(-1.00000 + 5.67128i) q^{43} +(-0.482753 - 0.836152i) q^{44} +(-4.67752 + 8.10170i) q^{46} +(2.31164 + 1.93969i) q^{47} +(0.950837 + 5.39246i) q^{49} +(-4.72773 + 3.96703i) q^{50} +(1.07398 - 0.390896i) q^{52} +8.77141 q^{53} -1.24123 q^{55} +(-10.0157 + 3.64543i) q^{56} +(3.56418 - 2.99070i) q^{58} +(0.514654 + 2.91875i) q^{59} +(6.04189 + 5.06975i) q^{61} +(1.24432 - 2.15523i) q^{62} +(-4.43242 - 7.67717i) q^{64} +(0.255139 - 1.44697i) q^{65} +(8.86959 + 3.22826i) q^{67} +(-2.29731 - 0.836152i) q^{68} +(-0.352044 + 1.99654i) q^{70} +(-2.65366 - 4.59627i) q^{71} +(0.777189 - 1.34613i) q^{73} +(-3.17766 - 2.66637i) q^{74} +(0.312681 + 1.77330i) q^{76} +(7.52211 - 6.31180i) q^{77} +(11.1839 - 4.07061i) q^{79} -1.42193 q^{80} -6.24897 q^{82} +(15.2768 - 5.56031i) q^{83} +(-2.40760 + 2.02022i) q^{85} +(-1.28558 - 7.29086i) q^{86} +(6.42649 + 5.39246i) q^{88} +(-9.21291 + 15.9572i) q^{89} +(5.81180 + 10.0663i) q^{91} +(-0.438852 + 2.48886i) q^{92} +(-3.64543 - 1.32683i) q^{94} +(2.17528 + 0.791737i) q^{95} +(1.75624 - 9.96016i) q^{97} +(-3.51968 - 6.09627i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} - 12 q^{7}+O(q^{10}) $ 12 * q + 6 * q^4 - 12 * q^7	$ 12 q + 6 q^{4} - 12 q^{7} + 12 q^{10} - 30 q^{13} + 18 q^{16} + 24 q^{19} - 30 q^{22} + 42 q^{25} - 12 q^{28} + 24 q^{31} - 36 q^{34} + 6 q^{37} + 6 q^{40} - 12 q^{43} - 6 q^{46} - 12 q^{49} - 18 q^{52} - 60 q^{55} + 6 q^{58} + 60 q^{61} - 6 q^{64} + 78 q^{67} - 66 q^{70} - 12 q^{73} + 48 q^{76} + 6 q^{79} - 24 q^{82} - 36 q^{85} - 24 q^{88} - 12 q^{94} + 6 q^{97}+O(q^{100}) $ 12 * q + 6 * q^4 - 12 * q^7 + 12 * q^10 - 30 * q^13 + 18 * q^16 + 24 * q^19 - 30 * q^22 + 42 * q^25 - 12 * q^28 + 24 * q^31 - 36 * q^34 + 6 * q^37 + 6 * q^40 - 12 * q^43 - 6 * q^46 - 12 * q^49 - 18 * q^52 - 60 * q^55 + 6 * q^58 + 60 * q^61 - 6 * q^64 + 78 * q^67 - 66 * q^70 - 12 * q^73 + 48 * q^76 + 6 * q^79 - 24 * q^82 - 36 * q^85 - 24 * q^88 - 12 * q^94 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	−1.20805	+	0.439693i	−0.854217	+	0.310910i	−0.731759	−	0.681564i	$-0.761300\pi$
$2$	−1.20805	+	0.439693i	−0.854217	+	0.310910i	−0.122459	+	0.992474i	$0.539078\pi$
$3$		0			0
$3$		0			0
$4$	−0.266044	+	0.223238i	−0.133022	+	0.111619i
$5$	0.0775297	+	0.439693i	0.0346723	+	0.196637i	0.997224	−	0.0744624i	$-0.0237241\pi$
$5$	0.0775297	+	0.439693i	0.0346723	+	0.196637i	−0.962552	+	0.271099i	$0.912613\pi$
$6$		0			0
$7$	−2.70574	−	2.27038i	−1.02267	−	0.858124i	−0.0327115	−	0.999465i	$-0.510414\pi$
$7$	−2.70574	−	2.27038i	−1.02267	−	0.858124i	−0.989961	+	0.141341i	$0.954859\pi$
$8$	1.50881	−	2.61334i	0.533446	−	0.923956i
$9$		0			0
$10$	−0.286989	−	0.497079i	−0.0907539	−	0.157190i
$11$	−0.482753	+	2.73783i	−0.145555	+	0.825486i	0.821364	+	0.570404i	$0.193213\pi$
$11$	−0.482753	+	2.73783i	−0.145555	+	0.825486i	−0.966920	+	0.255081i	$0.917898\pi$
$12$		0			0
$13$	−3.09240	−	1.12554i	−0.857676	−	0.312169i	−0.124510	−	0.992218i	$-0.539736\pi$
$13$	−3.09240	−	1.12554i	−0.857676	−	0.312169i	−0.733166	+	0.680050i	$0.761958\pi$
$14$	4.26692	+	1.55303i	1.14038	+	0.415066i
$15$		0			0
$16$	−0.553033	+	3.13641i	−0.138258	+	0.784102i
$17$	3.51968	+	6.09627i	0.853648	+	1.47856i	0.877894	+	0.478856i	$0.158948\pi$
$17$	3.51968	+	6.09627i	0.853648	+	1.47856i	−0.0242455	+	0.999706i	$0.507718\pi$
$18$		0			0
$19$	2.59240	−	4.49016i	0.594736	−	1.03011i	−0.398848	−	0.917017i	$-0.630590\pi$
$19$	2.59240	−	4.49016i	0.594736	−	1.03011i	0.993584	−	0.113097i	$-0.0360769\pi$
$20$	−0.118782	−	0.0996702i	−0.0265605	−	0.0222869i
$21$		0			0
$22$	−0.620615	−	3.51968i	−0.132316	−	0.750399i
$23$	5.57445	−	4.67752i	1.16235	−	0.975330i	0.162418	−	0.986722i	$-0.448071\pi$
$23$	5.57445	−	4.67752i	1.16235	−	0.975330i	0.999935	+	0.0113920i	$0.00362627\pi$
$24$		0			0
$25$	4.51114	−	1.64192i	0.902229	−	0.328384i
$26$	4.23065			0.829698
$27$		0			0
$28$	1.22668			0.231821
$29$	−3.40090	+	1.23783i	−0.631531	+	0.229859i	−0.637898	−	0.770121i	$-0.720196\pi$
$29$	−3.40090	+	1.23783i	−0.631531	+	0.229859i	0.00636650	+	0.999980i	$0.497973\pi$
$30$		0			0
$31$	−1.48293	+	1.24432i	−0.266341	+	0.223487i	−0.766171	−	0.642637i	$-0.777840\pi$
$31$	−1.48293	+	1.24432i	−0.266341	+	0.223487i	0.499830	+	0.866124i	$0.333396\pi$
$32$	0.337044	+	1.91147i	0.0595816	+	0.337904i
$33$		0			0
$34$	−6.93242	−	5.81699i	−1.18890	−	0.997606i
$35$	0.788496	−	1.36571i	0.133280	−	0.230848i
$36$		0			0
$37$	1.61334	+	2.79439i	0.265232	+	0.459395i	0.967624	−	0.252395i	$-0.0812183\pi$
$37$	1.61334	+	2.79439i	0.265232	+	0.459395i	−0.702393	+	0.711790i	$0.747885\pi$
$38$	−1.15744	+	6.56418i	−0.187762	+	1.06485i
$39$		0			0
$40$	1.26604	+	0.460802i	0.200179	+	0.0728593i
$41$	4.56769	+	1.66250i	0.713354	+	0.259639i	0.673102	−	0.739550i	$-0.264962\pi$
$41$	4.56769	+	1.66250i	0.713354	+	0.259639i	0.0402521	+	0.999190i	$0.487184\pi$
$42$		0			0
$43$	−1.00000	+	5.67128i	−0.152499	+	0.864862i	0.808539	+	0.588443i	$0.200259\pi$
$43$	−1.00000	+	5.67128i	−0.152499	+	0.864862i	−0.961037	+	0.276419i	$0.910852\pi$
$44$	−0.482753	−	0.836152i	−0.0727777	−	0.126055i
$45$		0			0
$46$	−4.67752	+	8.10170i	−0.689662	+	1.19453i
$47$	2.31164	+	1.93969i	0.337187	+	0.282933i	0.795621	−	0.605795i	$-0.207145\pi$
$47$	2.31164	+	1.93969i	0.337187	+	0.282933i	−0.458434	+	0.888729i	$0.651589\pi$
$48$		0			0
$49$	0.950837	+	5.39246i	0.135834	+	0.770352i
$50$	−4.72773	+	3.96703i	−0.668602	+	0.561023i
$51$		0			0
$52$	1.07398	−	0.390896i	0.148934	−	0.0542075i
$53$	8.77141			1.20485			0.602423	−	0.798177i	$-0.294202\pi$
$53$	8.77141			1.20485			0.602423	+	0.798177i	$0.294202\pi$
$54$		0			0
$55$	−1.24123			−0.167367
$56$	−10.0157	+	3.64543i	−1.33841	+	0.487141i
$57$		0			0
$58$	3.56418	−	2.99070i	0.467999	−	0.392698i
$59$	0.514654	+	2.91875i	0.0670022	+	0.379989i	0.999808	+	0.0196084i	$0.00624194\pi$
$59$	0.514654	+	2.91875i	0.0670022	+	0.379989i	−0.932805	+	0.360380i	$0.882647\pi$
$60$		0			0
$61$	6.04189	+	5.06975i	0.773585	+	0.649115i	0.941624	−	0.336666i	$-0.109299\pi$
$61$	6.04189	+	5.06975i	0.773585	+	0.649115i	−0.168040	+	0.985780i	$0.553744\pi$
$62$	1.24432	−	2.15523i	0.158029	−	0.273714i
$63$		0			0
$64$	−4.43242	−	7.67717i	−0.554052	−	0.959647i
$65$	0.255139	−	1.44697i	0.0316461	−	0.179474i
$66$		0			0
$67$	8.86959	+	3.22826i	1.08359	+	0.394395i	0.821244	−	0.570578i	$-0.193281\pi$
$67$	8.86959	+	3.22826i	1.08359	+	0.394395i	0.262349	+	0.964973i	$0.415503\pi$
$68$	−2.29731	−	0.836152i	−0.278590	−	0.101398i
$69$		0			0
$70$	−0.352044	+	1.99654i	−0.0420773	+	0.238632i
$71$	−2.65366	−	4.59627i	−0.314931	−	0.545476i	0.664492	−	0.747296i	$-0.268648\pi$
$71$	−2.65366	−	4.59627i	−0.314931	−	0.545476i	−0.979423	+	0.201819i	$0.935315\pi$
$72$		0			0
$73$	0.777189	−	1.34613i	0.0909631	−	0.157553i	−0.816954	−	0.576703i	$-0.804339\pi$
$73$	0.777189	−	1.34613i	0.0909631	−	0.157553i	0.907917	+	0.419151i	$0.137672\pi$
$74$	−3.17766	−	2.66637i	−0.369396	−	0.309960i
$75$		0			0
$76$	0.312681	+	1.77330i	0.0358670	+	0.203412i
$77$	7.52211	−	6.31180i	0.857225	−	0.719297i
$78$		0			0
$79$	11.1839	−	4.07061i	1.25829	−	0.457980i	0.375094	−	0.926987i	$-0.377610\pi$
$79$	11.1839	−	4.07061i	1.25829	−	0.457980i	0.883194	+	0.469007i	$0.155388\pi$
$80$	−1.42193			−0.158977
$81$		0			0
$82$	−6.24897			−0.690083
$83$	15.2768	−	5.56031i	1.67685	−	0.610323i	0.683976	−	0.729504i	$-0.260249\pi$
$83$	15.2768	−	5.56031i	1.67685	−	0.610323i	0.992873	+	0.119181i	$0.0380270\pi$
$84$		0			0
$85$	−2.40760	+	2.02022i	−0.261141	+	0.219124i
$86$	−1.28558	−	7.29086i	−0.138627	−	0.786194i
$87$		0			0
$88$	6.42649	+	5.39246i	0.685066	+	0.574839i
$89$	−9.21291	+	15.9572i	−0.976567	+	1.69146i	−0.301902	+	0.953339i	$0.597622\pi$
$89$	−9.21291	+	15.9572i	−0.976567	+	1.69146i	−0.674665	+	0.738125i	$0.735712\pi$
$90$		0			0
$91$	5.81180	+	10.0663i	0.609243	+	1.05524i
$92$	−0.438852	+	2.48886i	−0.0457535	+	0.259481i
$93$		0			0
$94$	−3.64543	−	1.32683i	−0.375997	−	0.136852i
$95$	2.17528	+	0.791737i	0.223179	+	0.0812305i
$96$		0			0
$97$	1.75624	−	9.96016i	0.178320	−	1.01130i	−0.755922	−	0.654661i	$-0.772811\pi$
$97$	1.75624	−	9.96016i	0.178320	−	1.01130i	0.934242	−	0.356640i	$-0.116078\pi$
$98$	−3.51968	−	6.09627i	−0.355541	−	0.615816i
$99$		0			0
$100$	−0.833626	+	1.44388i	−0.0833626	+	0.144388i
$101$	−1.59397	−	1.33750i	−0.158606	−	0.133086i	0.560031	−	0.828472i	$-0.310789\pi$
$101$	−1.59397	−	1.33750i	−0.158606	−	0.133086i	−0.718637	+	0.695386i	$0.755234\pi$
$102$		0			0
$103$	−0.251497	−	1.42631i	−0.0247807	−	0.140538i	0.969907	−	0.243475i	$-0.0782873\pi$
$103$	−0.251497	−	1.42631i	−0.0247807	−	0.140538i	−0.994688	+	0.102936i	$0.967176\pi$
$104$	−7.60727	+	6.38326i	−0.745954	+	0.625930i
$105$		0			0
$106$	−10.5963	+	3.85673i	−1.02920	+	0.374598i
$107$	−2.23583			−0.216146			−0.108073	−	0.994143i	$-0.534468\pi$
$107$	−2.23583			−0.216146			−0.108073	+	0.994143i	$0.534468\pi$
$108$		0			0
$109$	−11.5030			−1.10179			−0.550893	−	0.834576i	$-0.685713\pi$
$109$	−11.5030			−1.10179			−0.550893	+	0.834576i	$0.685713\pi$
$110$	1.49946	−	0.545759i	0.142968	−	0.0520361i
$111$		0			0
$112$	8.61721	−	7.23070i	0.814250	−	0.683237i
$113$	0.293144	+	1.66250i	0.0275767	+	0.156395i	0.995487	−	0.0949023i	$-0.0302539\pi$
$113$	0.293144	+	1.66250i	0.0275767	+	0.156395i	−0.967910	+	0.251297i	$0.919143\pi$
$114$		0			0
$115$	2.48886	+	2.08840i	0.232087	+	0.194744i
$116$	0.628461	−	1.08853i	0.0583511	−	0.101067i
$117$		0			0
$118$	−1.90508	−	3.29969i	−0.175377	−	0.303761i
$119$	4.31753	−	24.4859i	0.395787	−	2.24462i
$120$		0			0
$121$	3.07398	+	1.11884i	0.279453	+	0.101712i
$122$	−9.52801	−	3.46791i	−0.862625	−	0.313970i
$123$		0			0
$124$	0.116744	−	0.662090i	0.0104840	−	0.0594575i
$125$	2.18788	+	3.78952i	0.195690	+	0.338945i
$126$		0			0
$127$	1.33615	−	2.31428i	0.118564	−	0.205359i	−0.800635	−	0.599153i	$-0.795504\pi$
$127$	1.33615	−	2.31428i	0.118564	−	0.205359i	0.919199	+	0.393793i	$0.128837\pi$
$128$	5.75643	+	4.83022i	0.508802	+	0.426935i
$129$		0			0
$130$	0.328001	+	1.86018i	0.0287676	+	0.163149i
$131$	−2.23675	+	1.87686i	−0.195426	+	0.163982i	−0.735250	−	0.677796i	$-0.762935\pi$
$131$	−2.23675	+	1.87686i	−0.195426	+	0.163982i	0.539824	+	0.841778i	$0.318491\pi$
$132$		0			0
$133$	−17.2087	+	6.26347i	−1.49219	+	0.543111i
$134$	−12.1343			−1.04824
$135$		0			0
$136$	21.2422			1.82150
$137$	4.37636	−	1.59286i	0.373897	−	0.136087i	−0.148235	−	0.988952i	$-0.547359\pi$
$137$	4.37636	−	1.59286i	0.373897	−	0.136087i	0.522132	+	0.852865i	$0.325137\pi$
$138$		0			0
$139$	−6.13041	+	5.14403i	−0.519975	+	0.436311i	−0.864623	−	0.502421i	$-0.832443\pi$
$139$	−6.13041	+	5.14403i	−0.519975	+	0.436311i	0.344648	+	0.938732i	$0.387998\pi$
$140$	0.0951042	+	0.539363i	0.00803777	+	0.0455845i
$141$		0			0
$142$	5.22668	+	4.38571i	0.438613	+	0.368040i
$143$	4.57440	−	7.92309i	0.382530	−	0.662562i
$144$		0			0
$145$	−0.807934	−	1.39938i	−0.0670952	−	0.116212i
$146$	−0.346996	+	1.96791i	−0.0287176	+	0.162865i
$147$		0			0
$148$	−1.05303	−	0.383273i	−0.0865588	−	0.0315048i
$149$	−18.9928	−	6.91282i	−1.55595	−	0.566320i	−0.586147	−	0.810204i	$-0.699356\pi$
$149$	−18.9928	−	6.91282i	−1.55595	−	0.566320i	−0.969804	+	0.243884i	$0.921578\pi$
$150$		0			0
$151$	1.16385	−	6.60051i	0.0947126	−	0.537142i	−0.900122	−	0.435637i	$-0.856523\pi$
$151$	1.16385	−	6.60051i	0.0947126	−	0.537142i	0.994835	−	0.101505i	$-0.0323657\pi$
$152$	−7.82288	−	13.5496i	−0.634520	−	1.09902i
$153$		0			0
$154$	−6.31180	+	10.9324i	−0.508620	+	0.880955i
$155$	−0.662090	−	0.555560i	−0.0531804	−	0.0446236i
$156$		0			0
$157$	0.924678	+	5.24411i	0.0737973	+	0.418525i	0.999216	+	0.0395801i	$0.0126020\pi$
$157$	0.924678	+	5.24411i	0.0737973	+	0.418525i	−0.925419	+	0.378945i	$0.876287\pi$
$158$	−11.7209	+	9.83497i	−0.932462	+	0.782428i
$159$		0			0
$160$	−0.814330	+	0.296392i	−0.0643784	+	0.0234318i
$161$	−25.7028			−2.02566
$162$		0			0
$163$	3.81521			0.298830			0.149415	−	0.988775i	$-0.452261\pi$
$163$	3.81521			0.298830			0.149415	+	0.988775i	$0.452261\pi$
$164$	−1.58634	+	0.577382i	−0.123873	+	0.0450859i
$165$		0			0
$166$	−16.0103	+	13.4342i	−1.24264	+	1.04270i
$167$	−1.58634	−	8.99660i	−0.122755	−	0.696178i	−0.982616	−	0.185650i	$-0.940561\pi$
$167$	−1.58634	−	8.99660i	−0.122755	−	0.696178i	0.859861	−	0.510528i	$-0.170550\pi$
$168$		0			0
$169$	−1.66250	−	1.39501i	−0.127885	−	0.107308i
$170$	2.02022	−	3.49912i	0.154944	−	0.268370i
$171$		0			0
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	−1.05471	+	5.98158i	−0.0801884	+	0.454771i	0.918103	+	0.396342i	$0.129720\pi$
$173$	−1.05471	+	5.98158i	−0.0801884	+	0.454771i	−0.998292	+	0.0584296i	$0.981391\pi$
$174$		0			0
$175$	−15.9338	−	5.79942i	−1.20448	−	0.438395i
$176$	−8.31996	−	3.02822i	−0.627141	−	0.228261i
$177$		0			0
$178$	4.11334	−	23.3279i	0.308308	−	1.74850i
$179$	5.14057	+	8.90373i	0.384224	+	0.665496i	0.991661	−	0.128872i	$-0.0411355\pi$
$179$	5.14057	+	8.90373i	0.384224	+	0.665496i	−0.607437	+	0.794368i	$0.707802\pi$
$180$		0			0
$181$	11.5706	−	20.0408i	0.860034	−	1.48962i	−0.0118609	−	0.999930i	$-0.503776\pi$
$181$	11.5706	−	20.0408i	0.860034	−	1.48962i	0.871895	−	0.489693i	$-0.162891\pi$
$182$	−11.4470	−	9.60519i	−0.848510	−	0.711984i
$183$		0			0
$184$	−3.81315	−	21.6254i	−0.281109	−	1.59425i
$185$	−1.10359	+	0.926022i	−0.0811376	+	0.0680825i
$186$		0			0
$187$	−18.3897	+	6.69329i	−1.34478	+	0.489462i
$188$	−1.04801			−0.0764340
$189$		0			0
$190$	−2.97596			−0.215899
$191$	13.7856	−	5.01754i	0.997490	−	0.363057i	0.208874	−	0.977943i	$-0.433020\pi$
$191$	13.7856	−	5.01754i	0.997490	−	0.363057i	0.788616	+	0.614886i	$0.210798\pi$
$192$		0			0
$193$	17.9572	−	15.0679i	1.29259	−	1.08461i	0.301215	−	0.953556i	$-0.402608\pi$
$193$	17.9572	−	15.0679i	1.29259	−	1.08461i	0.991375	−	0.131055i	$-0.0418366\pi$
$194$	2.25778	+	12.8045i	0.162099	+	0.919312i
$195$		0			0
$196$	−1.45677	−	1.22237i	−0.104055	−	0.0873123i
$197$	−4.51384	+	7.81820i	−0.321598	+	0.557024i	−0.980818	−	0.194926i	$-0.937553\pi$
$197$	−4.51384	+	7.81820i	−0.321598	+	0.557024i	0.659220	+	0.751950i	$0.270887\pi$
$198$		0			0
$199$	−1.30200	−	2.25514i	−0.0922966	−	0.159862i	0.816181	−	0.577797i	$-0.196087\pi$
$199$	−1.30200	−	2.25514i	−0.0922966	−	0.159862i	−0.908477	+	0.417935i	$0.862754\pi$
$200$	2.51557	−	14.2665i	0.177878	−	1.00879i
$201$		0			0
$202$	2.51367	+	0.914901i	0.176861	+	0.0643722i
$203$	12.0123	+	4.37211i	0.843097	+	0.306862i
$204$		0			0
$205$	−0.376859	+	2.13727i	−0.0263210	+	0.149274i
$206$	0.930956	+	1.61246i	0.0648628	+	0.112346i
$207$		0			0
$208$	5.24035	−	9.07656i	0.363353	−	0.629346i
$209$	11.0418	+	9.26517i	0.763777	+	0.640885i
$210$		0			0
$211$	−2.84002	−	16.1066i	−0.195515	−	1.10882i	−0.911683	−	0.410894i	$-0.865217\pi$
$211$	−2.84002	−	16.1066i	−0.195515	−	1.10882i	0.716168	−	0.697928i	$-0.245894\pi$
$212$	−2.33359	+	1.95811i	−0.160271	+	0.134484i
$213$		0			0
$214$	2.70099	−	0.983080i	0.184636	−	0.0672019i
$215$	−2.57115			−0.175351
$216$		0			0
$217$	6.83750			0.464159
$218$	13.8961	−	5.05778i	0.941165	−	0.342556i
$219$		0			0
$220$	0.330222	−	0.277089i	0.0222636	−	0.0186814i
$221$	−4.02266	−	22.8136i	−0.270593	−	1.53461i
$222$		0			0
$223$	2.83615	+	2.37981i	0.189923	+	0.159364i	0.732791	−	0.680454i	$-0.238217\pi$
$223$	2.83615	+	2.37981i	0.189923	+	0.159364i	−0.542868	+	0.839818i	$0.682662\pi$
$224$	3.42782	−	5.93717i	0.229031	−	0.396694i
$225$		0			0
$226$	−1.08512	−	1.87949i	−0.0721813	−	0.125022i
$227$	1.83386	−	10.4003i	0.121717	−	0.690294i	−0.861486	−	0.507781i	$-0.830466\pi$
$227$	1.83386	−	10.4003i	0.121717	−	0.690294i	0.983203	−	0.182513i	$-0.0584231\pi$
$228$		0			0
$229$	−12.7096	−	4.62592i	−0.839875	−	0.305689i	−0.113969	−	0.993484i	$-0.536357\pi$
$229$	−12.7096	−	4.62592i	−0.839875	−	0.305689i	−0.725905	+	0.687795i	$0.758579\pi$
$230$	−3.92490	−	1.42855i	−0.258801	−	0.0941957i
$231$		0			0
$232$	−1.89646	+	10.7554i	−0.124509	+	0.706124i
$233$	6.35035	+	10.9991i	0.416025	+	0.720576i	0.995535	−	0.0943883i	$-0.0300895\pi$
$233$	6.35035	+	10.9991i	0.416025	+	0.720576i	−0.579510	+	0.814965i	$0.696756\pi$
$234$		0			0
$235$	−0.673648	+	1.16679i	−0.0439440	+	0.0761132i
$236$	−0.788496	−	0.661626i	−0.0513267	−	0.0430682i
$237$		0			0
$238$	5.55051	+	31.4785i	0.359786	+	2.04045i
$239$	4.48254	−	3.76130i	0.289951	−	0.243298i	−0.486196	−	0.873850i	$-0.661616\pi$
$239$	4.48254	−	3.76130i	0.289951	−	0.243298i	0.776147	+	0.630552i	$0.217171\pi$
$240$		0			0
$241$	8.02481	−	2.92079i	0.516924	−	0.188145i	−0.0703666	−	0.997521i	$-0.522417\pi$
$241$	8.02481	−	2.92079i	0.516924	−	0.188145i	0.587290	+	0.809376i	$0.300195\pi$
$242$	−4.20545			−0.270337
$243$		0			0
$244$	−2.73917			−0.175357
$245$	−2.29731	+	0.836152i	−0.146770	+	0.0534198i
$246$		0			0
$247$	−13.0706	+	10.9675i	−0.831661	+	0.697846i
$248$	1.01438	+	5.75284i	0.0644133	+	0.365306i
$249$		0			0
$250$	−4.30928	−	3.61591i	−0.272543	−	0.228690i
$251$	−3.37895	+	5.85251i	−0.213277	+	0.369407i	−0.952738	−	0.303792i	$-0.901747\pi$
$251$	−3.37895	+	5.85251i	−0.213277	+	0.369407i	0.739461	+	0.673199i	$0.235080\pi$
$252$		0			0
$253$	10.1152	+	17.5200i	0.635934	+	1.10147i
$254$	−0.596559	+	3.38326i	−0.0374315	+	0.212284i
$255$		0			0
$256$	7.58260	+	2.75984i	0.473912	+	0.172490i
$257$	3.46085	+	1.25965i	0.215882	+	0.0785747i	0.447697	−	0.894185i	$-0.352244\pi$
$257$	3.46085	+	1.25965i	0.215882	+	0.0785747i	−0.231815	+	0.972760i	$0.574466\pi$
$258$		0			0
$259$	1.97906	−	11.2238i	0.122973	−	0.697412i
$260$	0.255139	+	0.441914i	0.0158231	+	0.0274064i
$261$		0			0
$262$	1.87686	−	3.25082i	0.115953	−	0.200836i
$263$	−2.78677	−	2.33837i	−0.171839	−	0.144190i	0.552812	−	0.833306i	$-0.313555\pi$
$263$	−2.78677	−	2.33837i	−0.171839	−	0.144190i	−0.724651	+	0.689116i	$0.757999\pi$
$264$		0			0
$265$	0.680045	+	3.85673i	0.0417748	+	0.236917i
$266$	18.0349	−	15.1331i	1.10579	−	0.927870i
$267$		0			0
$268$	−3.08037	+	1.12116i	−0.188164	+	0.0684860i
$269$	7.08672			0.432085			0.216042	−	0.976384i	$-0.430685\pi$
$269$	7.08672			0.432085			0.216042	+	0.976384i	$0.430685\pi$
$270$		0			0
$271$	−19.0000			−1.15417			−0.577084	−	0.816685i	$-0.695809\pi$
$271$	−19.0000			−1.15417			−0.577084	+	0.816685i	$0.695809\pi$
$272$	−21.0669	+	7.66772i	−1.27737	+	0.464924i
$273$		0			0
$274$	−4.58647	+	3.84850i	−0.277079	+	0.232497i
$275$	2.31753	+	13.1434i	0.139752	+	0.792575i
$276$		0			0
$277$	−10.6420	−	8.92972i	−0.639417	−	0.536535i	0.264422	−	0.964407i	$-0.414819\pi$
$277$	−10.6420	−	8.92972i	−0.639417	−	0.536535i	−0.903839	+	0.427872i	$0.859263\pi$
$278$	5.14403	−	8.90972i	0.308518	−	0.534369i
$279$		0			0
$280$	−2.37939	−	4.12122i	−0.142195	−	0.246290i
$281$	−3.84240	+	21.7913i	−0.229218	+	1.29996i	0.625236	+	0.780435i	$0.285003\pi$
$281$	−3.84240	+	21.7913i	−0.229218	+	1.29996i	−0.854455	+	0.519526i	$0.826109\pi$
$282$		0			0
$283$	22.3011	+	8.11695i	1.32566	+	0.482502i	0.905269	−	0.424839i	$-0.139669\pi$
$283$	22.3011	+	8.11695i	1.32566	+	0.482502i	0.420395	+	0.907341i	$0.361891\pi$
$284$	1.73205	+	0.630415i	0.102778	+	0.0374082i
$285$		0			0
$286$	−2.04236	+	11.5828i	−0.120767	+	0.684904i
$287$	−8.58445	−	14.8687i	−0.506724	−	0.877672i
$288$		0			0
$289$	−16.2763	+	28.1914i	−0.957430	+	1.65832i
$290$	1.59132	+	1.33527i	0.0934454	+	0.0784100i
$291$		0			0
$292$	0.0937404	+	0.531628i	0.00548574	+	0.0311112i
$293$	−14.2531	+	11.9598i	−0.832674	+	0.698697i	−0.955903	−	0.293682i	$-0.905119\pi$
$293$	−14.2531	+	11.9598i	−0.832674	+	0.698697i	0.123229	+	0.992378i	$0.460675\pi$
$294$		0			0
$295$	−1.24345	+	0.452579i	−0.0723965	+	0.0263502i
$296$	9.73692			0.565947
$297$		0			0
$298$	25.9837			1.50520
$299$	−22.5031	+	8.19047i	−1.30139	+	0.473667i
$300$		0			0
$301$	15.5817	−	13.0746i	0.898115	−	0.753608i
$302$	1.49621	+	8.48545i	0.0860974	+	0.488283i
$303$		0			0
$304$	12.6493	+	10.6140i	0.725487	+	0.608756i
$305$	−1.76070	+	3.04963i	−0.100818	+	0.174621i
$306$		0			0
$307$	−10.3735	−	17.9674i	−0.592044	−	1.02545i	−0.993957	−	0.109773i	$-0.964988\pi$
$307$	−10.3735	−	17.9674i	−0.592044	−	1.02545i	0.401912	−	0.915678i	$-0.368346\pi$
$308$	−0.592184	+	3.35844i	−0.0337428	+	0.191365i
$309$		0			0
$310$	1.04411	+	0.380025i	0.0593015	+	0.0215840i
$311$	19.1561	+	6.97225i	1.08624	+	0.395360i	0.822228	−	0.569159i	$-0.192731\pi$
$311$	19.1561	+	6.97225i	1.08624	+	0.395360i	0.264015	+	0.964519i	$0.414953\pi$
$312$		0			0
$313$	−5.18180	+	29.3874i	−0.292893	+	1.66108i	0.382753	+	0.923851i	$0.374976\pi$
$313$	−5.18180	+	29.3874i	−0.292893	+	1.66108i	−0.675646	+	0.737226i	$0.736135\pi$
$314$	−3.42285	−	5.92855i	−0.193163	−	0.334567i
$315$		0			0
$316$	−2.06670	+	3.57964i	−0.116261	+	0.201370i
$317$	−3.30671	−	2.77466i	−0.185724	−	0.155841i	0.545186	−	0.838315i	$-0.316459\pi$
$317$	−3.30671	−	2.77466i	−0.185724	−	0.155841i	−0.730909	+	0.682475i	$0.760904\pi$
$318$		0			0
$319$	−1.74716	−	9.90863i	−0.0978221	−	0.554777i
$320$	3.03195	−	2.54411i	0.169491	−	0.142220i
$321$		0			0
$322$	31.0501	−	11.3013i	1.73035	−	0.629797i
$323$	36.4976			2.03078
$324$		0			0
$325$	−15.7983			−0.876332
$326$	−4.60894	+	1.67752i	−0.255266	+	0.0929092i
$327$		0			0
$328$	11.2365	−	9.42853i	0.620431	−	0.520603i
$329$	−1.85083	−	10.4966i	−0.102040	−	0.578696i
$330$		0			0
$331$	−2.23601	−	1.87624i	−0.122902	−	0.103127i	0.579265	−	0.815139i	$-0.303340\pi$
$331$	−2.23601	−	1.87624i	−0.122902	−	0.103127i	−0.702167	+	0.712012i	$0.747784\pi$
$332$	−2.82304	+	4.88965i	−0.154935	+	0.268355i
$333$		0			0
$334$	5.87211	+	10.1708i	0.321308	+	0.556521i
$335$	−0.731788	+	4.15018i	−0.0399819	+	0.226748i
$336$		0			0
$337$	−13.5706	−	4.93929i	−0.739236	−	0.269060i	−0.0551671	−	0.998477i	$-0.517569\pi$
$337$	−13.5706	−	4.93929i	−0.739236	−	0.269060i	−0.684069	+	0.729417i	$0.739791\pi$
$338$	2.62175	+	0.954241i	0.142605	+	0.0519038i
$339$		0			0
$340$	0.189540	−	1.07494i	0.0102793	−	0.0582966i
$341$	−2.69085	−	4.66069i	−0.145718	−	0.252391i
$342$		0			0
$343$	−2.69207	+	4.66280i	−0.145358	+	0.251767i
$344$	13.3122	+	11.1702i	0.717745	+	0.602259i
$345$		0			0
$346$	−1.35591	−	7.68977i	−0.0728944	−	0.413405i
$347$	1.11386	−	0.934640i	0.0597952	−	0.0501741i	−0.612400	−	0.790548i	$-0.709796\pi$
$347$	1.11386	−	0.934640i	0.0597952	−	0.0501741i	0.672195	+	0.740374i	$0.265351\pi$
$348$		0			0
$349$	25.9183	−	9.43350i	1.38738	−	0.504964i	0.462971	−	0.886374i	$-0.346784\pi$
$349$	25.9183	−	9.43350i	1.38738	−	0.504964i	0.924406	+	0.381410i	$0.124561\pi$
$350$	21.7987			1.16519
$351$		0			0
$352$	−5.39599			−0.287607
$353$	9.89695	−	3.60220i	0.526762	−	0.191726i	−0.0649301	−	0.997890i	$-0.520682\pi$
$353$	9.89695	−	3.60220i	0.526762	−	0.191726i	0.591692	+	0.806164i	$0.298460\pi$
$354$		0			0
$355$	1.81521	−	1.52314i	0.0963412	−	0.0808399i
$356$	−1.11121	−	6.30200i	−0.0588942	−	0.334006i
$357$		0			0
$358$	−10.1250	−	8.49584i	−0.535120	−	0.449019i
$359$	7.35273	−	12.7353i	0.388062	−	0.672143i	−0.604127	−	0.796888i	$-0.706478\pi$
$359$	7.35273	−	12.7353i	0.388062	−	0.672143i	0.992189	+	0.124745i	$0.0398112\pi$
$360$		0			0
$361$	−3.94104	−	6.82608i	−0.207423	−	0.359267i
$362$	−5.16598	+	29.2977i	−0.271518	+	1.53985i
$363$		0			0
$364$	−3.79339	−	1.38068i	−0.198827	−	0.0723673i
$365$	0.652139	+	0.237359i	0.0341345	+	0.0124239i
$366$		0			0
$367$	−3.70961	+	21.0382i	−0.193640	+	1.09819i	0.720702	+	0.693245i	$0.243819\pi$
$367$	−3.70961	+	21.0382i	−0.193640	+	1.09819i	−0.914342	+	0.404942i	$0.867292\pi$
$368$	11.5878	+	20.0706i	0.604053	+	1.04625i
$369$		0			0
$370$	0.926022	−	1.60392i	0.0481416	−	0.0833837i
$371$	−23.7331	−	19.9145i	−1.23216	−	1.03391i
$372$		0			0
$373$	3.92871	+	22.2808i	0.203421	+	1.15366i	0.899905	+	0.436085i	$0.143635\pi$
$373$	3.92871	+	22.2808i	0.203421	+	1.15366i	−0.696484	+	0.717572i	$0.745253\pi$
$374$	19.2725	−	16.1716i	0.996560	−	0.836213i
$375$		0			0
$376$	8.55690	−	3.11446i	0.441289	−	0.160616i
$377$	11.9101			0.613404
$378$		0			0
$379$	−17.0743			−0.877047			−0.438523	−	0.898720i	$-0.644498\pi$
$379$	−17.0743			−0.877047			−0.438523	+	0.898720i	$0.644498\pi$
$380$	−0.755466	+	0.274967i	−0.0387546	+	0.0141055i
$381$		0			0
$382$	−14.4474	+	12.1228i	−0.739195	+	0.620258i
$383$	6.77082	+	38.3992i	0.345973	+	1.96211i	0.258891	+	0.965906i	$0.416643\pi$
$383$	6.77082	+	38.3992i	0.345973	+	1.96211i	0.0870812	+	0.996201i	$0.472246\pi$
$384$		0			0
$385$	3.35844	+	2.81807i	0.171162	+	0.143622i
$386$	−15.0679	+	26.0984i	−0.766936	+	1.32837i
$387$		0			0
$388$	1.75624	+	3.04190i	0.0891598	+	0.154429i
$389$	−1.77330	+	10.0569i	−0.0899101	+	0.509905i	0.906279	+	0.422681i	$0.138911\pi$
$389$	−1.77330	+	10.0569i	−0.0899101	+	0.509905i	−0.996189	+	0.0872245i	$0.972200\pi$
$390$		0			0
$391$	48.1357	+	17.5200i	2.43433	+	0.886022i
$392$	15.5270	+	5.65136i	0.784231	+	0.285437i
$393$		0			0
$394$	2.01532	−	11.4294i	0.101530	−	0.575807i
$395$	2.65690	+	4.60189i	0.133683	+	0.231546i
$396$		0			0
$397$	0.571452	−	0.989783i	0.0286803	−	0.0496758i	−0.851329	−	0.524632i	$-0.824203\pi$
$397$	0.571452	−	0.989783i	0.0286803	−	0.0496758i	0.880009	+	0.474956i	$0.157536\pi$
$398$	2.56445	+	2.15183i	0.128544	+	0.107861i
$399$		0			0
$400$	2.65493	+	15.0568i	0.132746	+	0.752841i
$401$	15.7452	−	13.2118i	0.786280	−	0.659767i	−0.158542	−	0.987352i	$-0.550679\pi$
$401$	15.7452	−	13.2118i	0.786280	−	0.659767i	0.944822	+	0.327585i	$0.106235\pi$
$402$		0			0
$403$	5.98633	−	2.17885i	0.298200	−	0.108536i
$404$	0.722645			0.0359530
$405$		0			0
$406$	−16.4338			−0.815594
$407$	−8.42939	+	3.06805i	−0.417830	+	0.152078i
$408$		0			0
$409$	−6.22668	+	5.22481i	−0.307890	+	0.258350i	−0.783619	−	0.621242i	$-0.786629\pi$
$409$	−6.22668	+	5.22481i	−0.307890	+	0.258350i	0.475730	+	0.879592i	$0.342184\pi$
$410$	−0.484481	−	2.74763i	−0.0239268	−	0.135696i
$411$		0			0
$412$	0.385315	+	0.323318i	0.0189831	+	0.0159287i
$413$	5.23416	−	9.06583i	0.257556	−	0.446100i
$414$		0			0
$415$	3.62923	+	6.28602i	0.178152	+	0.308568i
$416$	1.10917	−	6.29039i	0.0543813	−	0.308412i
$417$		0			0
$418$	−17.4128	−	6.33775i	−0.851689	−	0.309989i
$419$	33.6207	+	12.2369i	1.64248	+	0.597814i	0.987470	−	0.157806i	$-0.0504420\pi$
$419$	33.6207	+	12.2369i	1.64248	+	0.597814i	0.655010	+	0.755620i	$0.272664\pi$
$420$		0			0
$421$	−2.27807	+	12.9196i	−0.111026	+	0.629661i	0.877615	+	0.479366i	$0.159133\pi$
$421$	−2.27807	+	12.9196i	−0.111026	+	0.629661i	−0.988641	+	0.150295i	$0.951978\pi$
$422$	10.5128	+	18.2087i	0.511756	+	0.886387i
$423$		0			0
$424$	13.2344	−	22.9227i	0.642720	−	1.11322i
$425$	25.8874	+	21.7221i	1.25572	+	1.05368i
$426$		0			0
$427$	−4.83750	−	27.4348i	−0.234103	−	1.32766i
$428$	0.594831	−	0.499123i	0.0287523	−	0.0241260i
$429$		0			0
$430$	3.10607	−	1.13052i	0.149788	−	0.0545183i
$431$	−9.48411			−0.456833			−0.228417	−	0.973563i	$-0.573355\pi$
$431$	−9.48411			−0.456833			−0.228417	+	0.973563i	$0.573355\pi$
$432$		0			0
$433$	17.6628			0.848820			0.424410	−	0.905470i	$-0.360481\pi$
$433$	17.6628			0.848820			0.424410	+	0.905470i	$0.360481\pi$
$434$	−8.26001	+	3.00640i	−0.396493	+	0.144312i
$435$		0			0
$436$	3.06031	−	2.56790i	0.146562	−	0.122980i
$437$	−6.55163	−	37.1562i	−0.313407	−	1.77742i
$438$		0			0
$439$	−13.5326	−	11.3552i	−0.645874	−	0.541952i	0.259942	−	0.965624i	$-0.416297\pi$
$439$	−13.5326	−	11.3552i	−0.645874	−	0.541952i	−0.905816	+	0.423672i	$0.860741\pi$
$440$	−1.87278	+	3.24376i	−0.0892814	+	0.154640i
$441$		0			0
$442$	14.8905	+	25.7912i	0.708270	+	1.22676i
$443$	2.25606	−	12.7947i	0.107188	−	0.607896i	−0.883135	−	0.469119i	$-0.844572\pi$
$443$	2.25606	−	12.7947i	0.107188	−	0.607896i	0.990324	−	0.138777i	$-0.0443172\pi$
$444$		0			0
$445$	−7.73055	−	2.81369i	−0.366463	−	0.133382i
$446$	−4.47259	−	1.62789i	−0.211783	−	0.0770828i
$447$		0			0
$448$	−5.43717	+	30.8357i	−0.256882	+	1.45685i
$449$	−2.31428	−	4.00846i	−0.109218	−	0.189171i	0.806236	−	0.591594i	$-0.201501\pi$
$449$	−2.31428	−	4.00846i	−0.109218	−	0.189171i	−0.915454	+	0.402424i	$0.868168\pi$
$450$		0			0
$451$	−6.75671	+	11.7030i	−0.318161	+	0.551071i
$452$	−0.449123	−	0.376859i	−0.0211250	−	0.0177260i
$453$		0			0
$454$	2.35756	+	13.3704i	0.110646	+	0.627504i
$455$	−3.97551	+	3.33585i	−0.186375	+	0.156387i
$456$		0			0
$457$	−19.3268	+	7.03439i	−0.904070	+	0.329055i	−0.751883	−	0.659297i	$-0.770854\pi$
$457$	−19.3268	+	7.03439i	−0.904070	+	0.329055i	−0.152188	+	0.988352i	$0.548632\pi$
$458$	17.3878			0.812477
$459$		0			0
$460$	−1.12836			−0.0526098
$461$	−31.5478	+	11.4825i	−1.46933	+	0.534791i	−0.947918	−	0.318515i	$-0.896816\pi$
$461$	−31.5478	+	11.4825i	−1.46933	+	0.534791i	−0.521410	+	0.853307i	$0.674594\pi$
$462$		0			0
$463$	10.0590	−	8.44047i	0.467480	−	0.392262i	−0.378395	−	0.925644i	$-0.623524\pi$
$463$	10.0590	−	8.44047i	0.467480	−	0.392262i	0.845874	+	0.533382i	$0.179079\pi$
$464$	−2.00152	−	11.3512i	−0.0929181	−	0.526965i
$465$		0			0
$466$	−12.5077	−	10.4952i	−0.579410	−	0.486183i
$467$	11.8154	−	20.4648i	0.546750	−	0.946999i	−0.451745	−	0.892147i	$-0.649198\pi$
$467$	11.8154	−	20.4648i	0.546750	−	0.946999i	0.998495	−	0.0548513i	$-0.0174685\pi$
$468$		0			0
$469$	−16.6694	−	28.8722i	−0.769720	−	1.33319i
$470$	0.300767	−	1.70574i	0.0138734	−	0.0786798i
$471$		0			0
$472$	8.40420	+	3.05888i	0.386835	+	0.140796i
$473$	−15.0442	−	5.47565i	−0.691734	−	0.251771i
$474$		0			0
$475$	4.32218	−	24.5123i	0.198315	−	1.12470i
$476$	4.31753	+	7.47818i	0.197894	+	0.342762i
$477$		0			0
$478$	−3.76130	+	6.51476i	−0.172038	+	0.297978i
$479$	4.50449	+	3.77972i	0.205815	+	0.172700i	0.739869	−	0.672751i	$-0.234887\pi$
$479$	4.50449	+	3.77972i	0.205815	+	0.172700i	−0.534054	+	0.845451i	$0.679332\pi$
$480$		0			0
$481$	−1.84389	−	10.4572i	−0.0840743	−	0.476809i
$482$	−8.41009	+	7.05690i	−0.383069	+	0.321433i
$483$		0			0
$484$	−1.06758	+	0.388568i	−0.0485264	+	0.0176622i
$485$	4.51557			0.205041
$486$		0			0
$487$	38.7965			1.75804			0.879020	−	0.476786i	$-0.158198\pi$
$487$	38.7965			1.75804			0.879020	+	0.476786i	$0.158198\pi$
$488$	22.3651	−	8.14022i	1.01242	−	0.368490i
$489$		0			0
$490$	2.40760	−	2.02022i	0.108764	−	0.0912642i
$491$	6.52644	+	37.0133i	0.294534	+	1.67039i	0.669090	+	0.743181i	$0.266684\pi$
$491$	6.52644	+	37.0133i	0.294534	+	1.67039i	−0.374557	+	0.927204i	$0.622205\pi$
$492$		0			0
$493$	−19.5162	−	16.3760i	−0.878965	−	0.737539i
$494$	10.9675	−	18.9963i	0.493452	−	0.854684i
$495$		0			0
$496$	−3.08260	−	5.33921i	−0.138413	−	0.239738i
$497$	−3.25519	+	18.4611i	−0.146015	+	0.828094i
$498$		0			0
$499$	−31.7165	−	11.5439i	−1.41982	−	0.516774i	−0.485827	−	0.874055i	$-0.661482\pi$
$499$	−31.7165	−	11.5439i	−1.41982	−	0.516774i	−0.933997	+	0.357281i	$0.883704\pi$
$500$	−1.42804	−	0.519762i	−0.0638637	−	0.0232445i
$501$		0			0
$502$	1.50862	−	8.55580i	0.0673329	−	0.381864i
$503$	−9.35597	−	16.2050i	−0.417162	−	0.722546i	0.578491	−	0.815689i	$-0.303642\pi$
$503$	−9.35597	−	16.2050i	−0.417162	−	0.722546i	−0.995653	+	0.0931429i	$0.970309\pi$
$504$		0			0
$505$	0.464508	−	0.804551i	0.0206703	−	0.0358020i
$506$	−19.9230	−	16.7173i	−0.885684	−	0.743177i
$507$		0			0
$508$	0.161160	+	0.913982i	0.00715030	+	0.0405514i
$509$	−16.6754	+	13.9923i	−0.739124	+	0.620198i	−0.932602	−	0.360906i	$-0.882467\pi$
$509$	−16.6754	+	13.9923i	−0.739124	+	0.620198i	0.193478	+	0.981105i	$0.438023\pi$
$510$		0			0
$511$	−5.15910	+	1.87776i	−0.228225	+	0.0830672i
$512$	−25.4026			−1.12265
$513$		0			0
$514$	−4.73473			−0.208840
$515$	0.607639	−	0.221162i	0.0267758	−	0.00974558i
$516$		0			0
$517$	−6.42649	+	5.39246i	−0.282637	+	0.237160i
$518$	2.54422	+	14.4290i	0.111787	+	0.633975i
$519$		0			0
$520$	−3.39646	−	2.84997i	−0.148945	−	0.124979i
$521$	−3.23822	+	5.60876i	−0.141869	+	0.245724i	−0.928200	−	0.372081i	$-0.878644\pi$
$521$	−3.23822	+	5.60876i	−0.141869	+	0.245724i	0.786332	+	0.617805i	$0.211978\pi$
$522$		0			0
$523$	5.43629	+	9.41593i	0.237712	+	0.411730i	0.960057	−	0.279803i	$-0.0902691\pi$
$523$	5.43629	+	9.41593i	0.237712	+	0.411730i	−0.722345	+	0.691533i	$0.756936\pi$
$524$	0.176090	−	0.998656i	0.00769253	−	0.0436265i
$525$		0			0
$526$	4.39470	+	1.59954i	0.191618	+	0.0697433i
$527$	−12.8051	−	4.66069i	−0.557801	−	0.203023i
$528$		0			0
$529$	5.20140	−	29.4986i	0.226148	−	1.28255i
$530$	−2.51730	−	4.36009i	−0.109344	−	0.189390i
$531$		0			0
$532$	3.18004	−	5.50800i	0.137872	−	0.238802i
$533$	−12.2539	−	10.2822i	−0.530775	−	0.445373i
$534$		0			0
$535$	−0.173343	−	0.983080i	−0.00749429	−	0.0425022i
$536$	21.8191	−	18.3084i	0.942442	−	0.790802i
$537$		0			0
$538$	−8.56108	+	3.11598i	−0.369094	+	0.134339i
$539$	−15.2226			−0.655686
$540$		0			0
$541$	24.6459			1.05961			0.529805	−	0.848120i	$-0.322265\pi$
$541$	24.6459			1.05961			0.529805	+	0.848120i	$0.322265\pi$
$542$	22.9529	−	8.35416i	0.985910	−	0.358842i
$543$		0			0
$544$	−10.4666	+	8.78249i	−0.448750	+	0.376546i
$545$	−0.891823	−	5.05778i	−0.0382015	−	0.216652i
$546$		0			0
$547$	23.6917	+	19.8797i	1.01298	+	0.849993i	0.988729	−	0.149713i	$-0.0478350\pi$
$547$	23.6917	+	19.8797i	1.01298	+	0.849993i	0.0242526	+	0.999706i	$0.492279\pi$
$548$	−0.808718	+	1.40074i	−0.0345467	+	0.0598367i
$549$		0			0
$550$	−8.57873	−	14.8588i	−0.365798	−	0.633581i
$551$	−3.25844	+	18.4795i	−0.138814	+	0.787254i
$552$		0			0
$553$	−39.5026	−	14.3778i	−1.67982	−	0.611405i
$554$	16.7824	+	6.10829i	0.713015	+	0.259516i
$555$		0			0
$556$	0.482621	−	2.73708i	0.0204677	−	0.116078i
$557$	11.6813	+	20.2327i	0.494954	+	0.857286i	0.999983	−	0.00581674i	$-0.00185154\pi$
$557$	11.6813	+	20.2327i	0.494954	+	0.857286i	−0.505029	+	0.863102i	$0.668518\pi$
$558$		0			0
$559$	9.47565	−	16.4123i	0.400777	−	0.694167i
$560$	3.84737	+	3.22833i	0.162581	+	0.136422i
$561$		0			0
$562$	−4.93969	−	28.0144i	−0.208368	−	1.18172i
$563$	−25.8063	+	21.6540i	−1.08761	+	0.912609i	−0.996530	−	0.0832347i	$-0.973475\pi$
$563$	−25.8063	+	21.6540i	−1.08761	+	0.912609i	−0.0910754	+	0.995844i	$0.529030\pi$
$564$		0			0
$565$	−0.708263	+	0.257787i	−0.0297969	+	0.0108452i
$566$	−30.5097			−1.28242
$567$		0			0
$568$	−16.0155			−0.671995
$569$	−28.9386	+	10.5328i	−1.21317	+	0.441558i	−0.867803	−	0.496909i	$-0.834468\pi$
$569$	−28.9386	+	10.5328i	−1.21317	+	0.441558i	−0.345368	+	0.938467i	$0.612246\pi$
$570$		0			0
$571$	−22.8858	+	19.2035i	−0.957740	+	0.803639i	−0.980584	−	0.196100i	$-0.937172\pi$
$571$	−22.8858	+	19.2035i	−0.957740	+	0.803639i	0.0228438	+	0.999739i	$0.492728\pi$
$572$	0.551740	+	3.12907i	0.0230694	+	0.130833i
$573$		0			0
$574$	16.9081	+	14.1876i	0.705729	+	0.592177i
$575$	17.4670	−	30.2538i	0.728425	−	1.26167i
$576$		0			0
$577$	−2.40373	−	4.16339i	−0.100069	−	0.173324i	0.811644	−	0.584152i	$-0.198573\pi$
$577$	−2.40373	−	4.16339i	−0.100069	−	0.173324i	−0.911713	+	0.410828i	$0.865240\pi$
$578$	7.26698	−	41.2131i	0.302266	−	1.71424i
$579$		0			0
$580$	0.527341	+	0.191936i	0.0218966	+	0.00796973i
$581$	−53.9591	−	19.6395i	−2.23860	−	0.814784i
$582$		0			0
$583$	−4.23442	+	24.0146i	−0.175372	+	0.994583i
$584$	−2.34527	−	4.06212i	−0.0970478	−	0.168092i
$585$		0			0
$586$	11.9598	−	20.7149i	0.494053	−	0.855725i
$587$	−6.08056	−	5.10220i	−0.250972	−	0.210590i	0.508619	−	0.860992i	$-0.330156\pi$
$587$	−6.08056	−	5.10220i	−0.250972	−	0.210590i	−0.759591	+	0.650402i	$0.774601\pi$
$588$		0			0
$589$	1.74288	+	9.88435i	0.0718141	+	0.407278i
$590$	1.30315	−	1.09347i	0.0536498	−	0.0450176i
$591$		0			0
$592$	−9.65657	+	3.51471i	−0.396883	+	0.144454i
$593$	−36.2753			−1.48965			−0.744824	−	0.667261i	$-0.767467\pi$
$593$	−36.2753			−1.48965			−0.744824	+	0.667261i	$0.767467\pi$
$594$		0			0
$595$	11.1010			0.455097
$596$	6.59613	−	2.40080i	0.270188	−	0.0983405i
$597$		0			0
$598$	23.5835	−	19.7889i	0.964402	−	0.809230i
$599$	−5.84240	−	33.1339i	−0.238714	−	1.35381i	−0.834650	−	0.550781i	$-0.814330\pi$
$599$	−5.84240	−	33.1339i	−0.238714	−	1.35381i	0.595936	−	0.803032i	$-0.296781\pi$
$600$		0			0
$601$	−2.28106	−	1.91404i	−0.0930463	−	0.0780752i	0.595078	−	0.803668i	$-0.297121\pi$
$601$	−2.28106	−	1.91404i	−0.0930463	−	0.0780752i	−0.688124	+	0.725593i	$0.741566\pi$
$602$	−13.0746	+	22.6459i	−0.532882	+	0.922978i
$603$		0			0
$604$	1.16385	+	2.01584i	0.0473563	+	0.0820235i
$605$	−0.253620	+	1.43835i	−0.0103111	+	0.0584772i
$606$		0			0
$607$	14.7049	+	5.35213i	0.596852	+	0.217236i	0.622740	−	0.782429i	$-0.286019\pi$
$607$	14.7049	+	5.35213i	0.596852	+	0.217236i	−0.0258885	+	0.999665i	$0.508242\pi$
$608$	9.45658	+	3.44191i	0.383515	+	0.139588i
$609$		0			0
$610$	0.786112	−	4.45826i	0.0318287	−	0.180510i
$611$	−4.96529	−	8.60014i	−0.200874	−	0.347924i
$612$		0			0
$613$	0.533433	−	0.923933i	0.0215452	−	0.0373173i	−0.855052	−	0.518543i	$-0.826475\pi$
$613$	0.533433	−	0.923933i	0.0215452	−	0.0373173i	0.876597	+	0.481225i	$0.159808\pi$
$614$	20.4317	+	17.1442i	0.824557	+	0.691886i
$615$		0			0
$616$	−5.14543	−	29.1812i	−0.207315	−	1.17574i
$617$	10.0122	−	8.40121i	0.403075	−	0.338220i	−0.418606	−	0.908168i	$-0.637481\pi$
$617$	10.0122	−	8.40121i	0.403075	−	0.338220i	0.821681	+	0.569948i	$0.193037\pi$
$618$		0			0
$619$	−19.2802	+	7.01741i	−0.774936	+	0.282054i	−0.699059	−	0.715064i	$-0.746398\pi$
$619$	−19.2802	+	7.01741i	−0.774936	+	0.282054i	−0.0758765	+	0.997117i	$0.524175\pi$
$620$	0.300167			0.0120550
$621$		0			0
$622$	−26.2071			−1.05081
$623$	61.1568	−	22.2592i	2.45019	−	0.891798i
$624$		0			0
$625$	16.8910	−	14.1732i	0.675640	−	0.566929i
$626$	−6.66159	−	37.7798i	−0.266251	−	1.50998i
$627$		0			0
$628$	−1.41669	−	1.18874i	−0.0565320	−	0.0474360i
$629$	−11.3569	+	19.6707i	−0.452829	+	0.784323i
$630$		0			0
$631$	5.15611	+	8.93064i	0.205261	+	0.355523i	0.950216	−	0.311592i	$-0.100862\pi$
$631$	5.15611	+	8.93064i	0.205261	+	0.355523i	−0.744955	+	0.667115i	$0.767529\pi$
$632$	6.23654	−	35.3692i	0.248076	−	1.40691i
$633$		0			0
$634$	5.21466	+	1.89798i	0.207101	+	0.0753785i
$635$	1.12116	+	0.408071i	0.0444921	+	0.0161938i
$636$		0			0
$637$	3.12907	−	17.7458i	0.123978	−	0.703116i
$638$	6.46740	+	11.2019i	0.256047	+	0.443486i
$639$		0			0
$640$	−1.67752	+	2.90555i	−0.0663097	+	0.114852i
$641$	−2.68588	−	2.25372i	−0.106086	−	0.0890165i	0.588202	−	0.808714i	$-0.299836\pi$
$641$	−2.68588	−	2.25372i	−0.106086	−	0.0890165i	−0.694288	+	0.719698i	$0.744280\pi$
$642$		0			0
$643$	5.47889	+	31.0723i	0.216066	+	1.22537i	0.879046	+	0.476736i	$0.158180\pi$
$643$	5.47889	+	31.0723i	0.216066	+	1.22537i	−0.662980	+	0.748637i	$0.730708\pi$
$644$	6.83807	−	5.73783i	0.269458	−	0.226102i
$645$		0			0
$646$	−44.0908	+	16.0477i	−1.73473	+	0.631390i
$647$	3.04628			0.119762			0.0598808	−	0.998206i	$-0.480928\pi$
$647$	3.04628			0.119762			0.0598808	+	0.998206i	$0.480928\pi$
$648$		0			0
$649$	−8.23947			−0.323428
$650$	19.0851	−	6.94639i	0.748578	−	0.272460i
$651$		0			0
$652$	−1.01501	+	0.851698i	−0.0397510	+	0.0333551i
$653$	5.33749	+	30.2704i	0.208872	+	1.18457i	0.891229	+	0.453553i	$0.149844\pi$
$653$	5.33749	+	30.2704i	0.208872	+	1.18457i	−0.682357	+	0.731019i	$0.739045\pi$
$654$		0			0
$655$	−0.998656	−	0.837972i	−0.0390207	−	0.0327423i
$656$	−7.74038	+	13.4067i	−0.302211	+	0.523445i
$657$		0			0
$658$	6.85117	+	11.8666i	0.267086	+	0.462607i
$659$	5.76233	−	32.6798i	0.224469	−	1.27302i	−0.639230	−	0.769016i	$-0.720747\pi$
$659$	5.76233	−	32.6798i	0.224469	−	1.27302i	0.863699	−	0.504009i	$-0.168142\pi$
$660$		0			0
$661$	14.0086	+	5.09872i	0.544872	+	0.198317i	0.599767	−	0.800175i	$-0.295260\pi$
$661$	14.0086	+	5.09872i	0.544872	+	0.198317i	−0.0548946	+	0.998492i	$0.517482\pi$
$662$	3.52618	+	1.28342i	0.137049	+	0.0498817i
$663$		0			0
$664$	8.51889	−	48.3130i	0.330597	−	1.87491i
$665$	−4.08819	−	7.08095i	−0.158533	−	0.274587i
$666$		0			0
$667$	−13.1682	+	22.8080i	−0.509874	+	0.883128i
$668$	2.43042	+	2.03936i	0.0940357	+	0.0789053i
$669$		0			0
$670$	−0.940769	−	5.33537i	−0.0363451	−	0.206123i
$671$	−16.7968	+	14.0942i	−0.648434	+	0.544101i
$672$		0			0
$673$	−6.47343	+	2.35614i	−0.249532	+	0.0908224i	−0.463758	−	0.885962i	$-0.653499\pi$
$673$	−6.47343	+	2.35614i	−0.249532	+	0.0908224i	0.214226	+	0.976784i	$0.431277\pi$
$674$	18.5656			0.715122
$675$		0			0
$676$	0.753718			0.0289892
$677$	−12.3938	+	4.51098i	−0.476333	+	0.173371i	−0.569019	−	0.822324i	$-0.692677\pi$
$677$	−12.3938	+	4.51098i	−0.476333	+	0.173371i	0.0926859	+	0.995695i	$0.470455\pi$
$678$		0			0
$679$	−27.3653	+	22.9622i	−1.05018	+	0.881209i
$680$	1.64690	+	9.34002i	0.0631557	+	0.358174i
$681$		0			0
$682$	5.29994	+	4.44718i	0.202945	+	0.170291i
$683$	−1.68907	+	2.92556i	−0.0646305	+	0.111943i	−0.896530	−	0.442983i	$-0.853920\pi$
$683$	−1.68907	+	2.92556i	−0.0646305	+	0.111943i	0.831900	+	0.554926i	$0.187254\pi$
$684$		0			0
$685$	1.03967	+	1.80076i	0.0397237	+	0.0688034i
$686$	1.20194	−	6.81655i	0.0458904	−	0.260257i
$687$		0			0
$688$	−17.2344	−	6.27282i	−0.657056	−	0.239149i
$689$	−27.1247	−	9.87258i	−1.03337	−	0.376115i
$690$		0			0
$691$	4.06599	−	23.0594i	0.154678	−	0.877220i	−0.804403	−	0.594085i	$-0.797514\pi$
$691$	4.06599	−	23.0594i	0.154678	−	0.877220i	0.959080	−	0.283135i	$-0.0913745\pi$
$692$	−1.05471	−	1.82682i	−0.0400942	−	0.0694452i
$693$		0			0
$694$	−0.934640	+	1.61884i	−0.0354785	+	0.0614505i
$695$	−2.73708	−	2.29668i	−0.103823	−	0.0871182i
$696$		0			0
$697$	5.94175	+	33.6974i	0.225060	+	1.27638i
$698$	−27.1627	+	22.7922i	−1.02812	+	0.862698i
$699$		0			0
$700$	5.53374	−	2.01412i	0.209156	−	0.0761264i
$701$	−45.5001			−1.71852			−0.859258	−	0.511543i	$-0.829074\pi$
$701$	−45.5001			−1.71852			−0.859258	+	0.511543i	$0.829074\pi$
$702$		0			0
$703$	16.7297			0.630972
$704$	23.1585	−	8.42902i	0.872820	−	0.317680i
$705$		0			0
$706$	−10.3721	+	8.70323i	−0.390360	+	0.327551i
$707$	1.27622	+	7.23783i	0.0479973	+	0.272206i
$708$		0			0
$709$	29.5822	+	24.8224i	1.11098	+	0.932225i	0.998114	−	0.0613851i	$-0.0195518\pi$
$709$	29.5822	+	24.8224i	1.11098	+	0.932225i	0.112868	+	0.993610i	$0.463996\pi$
$710$	−1.52314	+	2.63816i	−0.0571624	+	0.0990082i
$711$		0			0
$712$	27.8011	+	48.1530i	1.04189	+	1.80461i
$713$	−2.44615	+	13.8728i	−0.0916092	+	0.519541i
$714$		0			0
$715$	3.83837	+	1.39705i	0.143547	+	0.0522468i
$716$	−3.35527	−	1.22122i	−0.125392	−	0.0456391i
$717$		0			0
$718$	−3.28281	+	18.6178i	−0.122514	+	0.694809i
$719$	−24.6591	−	42.7108i	−0.919630	−	1.59285i	−0.799978	−	0.600030i	$-0.795155\pi$
$719$	−24.6591	−	42.7108i	−0.919630	−	1.59285i	−0.119652	−	0.992816i	$-0.538178\pi$
$720$		0			0
$721$	−2.55778	+	4.43021i	−0.0952567	+	0.164990i
$722$	7.76233	+	6.51337i	0.288884	+	0.242402i
$723$		0			0
$724$	1.39558	+	7.91474i	0.0518664	+	0.294149i
$725$	−13.3095	+	11.1680i	−0.494304	+	0.414770i
$726$		0			0
$727$	30.3469	−	11.0454i	1.12550	−	0.409650i	0.288846	−	0.957376i	$-0.406729\pi$
$727$	30.3469	−	11.0454i	1.12550	−	0.409650i	0.836658	+	0.547726i	$0.184506\pi$
$728$	35.0757			1.29999
$729$		0			0
$730$	−0.892178			−0.0330210
$731$	−38.0933	+	13.8648i	−1.40893	+	0.512810i
$732$		0			0
$733$	30.2328	−	25.3684i	1.11668	−	0.937002i	0.118243	−	0.992985i	$-0.462274\pi$
$733$	30.2328	−	25.3684i	1.11668	−	0.937002i	0.998432	+	0.0559830i	$0.0178293\pi$
$734$	−4.76898	−	27.0462i	−0.176026	−	0.998294i
$735$		0			0
$736$	10.8198	+	9.07888i	0.398823	+	0.334652i
$737$	−13.1202	+	22.7249i	−0.483290	+	0.837083i
$738$		0			0
$739$	−17.6545	−	30.5785i	−0.649432	−	1.12485i	−0.983259	−	0.182215i	$-0.941673\pi$
$739$	−17.6545	−	30.5785i	−0.649432	−	1.12485i	0.333827	−	0.942634i	$-0.391660\pi$
$740$	0.0868809	−	0.492726i	0.00319381	−	0.0181130i
$741$		0			0
$742$	37.4270	+	13.6223i	1.37399	+	0.500090i
$743$	−44.5514	−	16.2154i	−1.63443	−	0.594884i	−0.648379	−	0.761318i	$-0.724553\pi$
$743$	−44.5514	−	16.2154i	−1.63443	−	0.594884i	−0.986053	+	0.166433i	$0.946775\pi$
$744$		0			0
$745$	1.56701	−	8.88695i	0.0574108	−	0.325593i
$746$	−14.5428	−	25.1888i	−0.532449	−	0.922228i
$747$		0			0
$748$	3.39827	−	5.88598i	0.124253	−	0.215213i
$749$	6.04958	+	5.07620i	0.221047	+	0.185480i
$750$		0			0
$751$	−1.55035	−	8.79244i	−0.0565729	−	0.320841i	0.943368	−	0.331749i	$-0.107639\pi$
$751$	−1.55035	−	8.79244i	−0.0565729	−	0.320841i	−0.999941	+	0.0109084i	$0.996528\pi$
$752$	−7.36208	+	6.17752i	−0.268467	+	0.225271i
$753$		0			0
$754$	−14.3880	+	5.23680i	−0.523980	+	0.190713i
$755$	2.99243			0.108906
$756$		0			0
$757$	−3.63816			−0.132231			−0.0661155	−	0.997812i	$-0.521061\pi$
$757$	−3.63816			−0.132231			−0.0661155	+	0.997812i	$0.521061\pi$
$758$	20.6265	−	7.50744i	0.749189	−	0.272682i
$759$		0			0
$760$	5.35117	−	4.49016i	0.194107	−	0.162875i
$761$	1.16150	+	6.58718i	0.0421043	+	0.238785i	0.998596	−	0.0529748i	$-0.0168703\pi$
$761$	1.16150	+	6.58718i	0.0421043	+	0.238785i	−0.956492	+	0.291760i	$0.905759\pi$
$762$		0			0
$763$	31.1241	+	26.1162i	1.12677	+	0.945470i
$764$	−2.54747	+	4.41235i	−0.0921643	+	0.159633i
$765$		0			0
$766$	−25.0633	−	43.4109i	−0.905574	−	1.56850i
$767$	1.69365	−	9.60519i	0.0611543	−	0.346823i
$768$		0			0
$769$	20.1763	+	7.34359i	0.727577	+	0.264816i	0.679139	−	0.734010i	$-0.262353\pi$
$769$	20.1763	+	7.34359i	0.727577	+	0.264816i	0.0484383	+	0.998826i	$0.484576\pi$
$770$	−5.29623	−	1.92767i	−0.190863	−	0.0694684i
$771$		0			0
$772$	−1.41370	+	8.01747i	−0.0508800	+	0.288555i
$773$	−5.12208	−	8.87170i	−0.184228	−	0.319093i	0.759088	−	0.650988i	$-0.225645\pi$
$773$	−5.12208	−	8.87170i	−0.184228	−	0.319093i	−0.943316	+	0.331895i	$0.892312\pi$
$774$		0			0
$775$	−4.64661	+	8.04817i	−0.166911	+	0.289099i
$776$	−23.3794	−	19.6177i	−0.839273	−	0.704234i
$777$		0			0
$778$	−2.27972	−	12.9289i	−0.0817317	−	0.463524i
$779$	19.3062	−	16.1998i	0.691716	−	0.580418i
$780$

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.20805 + 0.439693i) q^{2} +(-0.266044 + 0.223238i) q^{4} +(0.0775297 + 0.439693i) q^{5} +(-2.70574 - 2.27038i) q^{7} +(1.50881 - 2.61334i) q^{8} +O(q^{10})\)	\(q+(-1.20805 + 0.439693i) q^{2} +(-0.266044 + 0.223238i) q^{4} +(0.0775297 + 0.439693i) q^{5} +(-2.70574 - 2.27038i) q^{7} +(1.50881 - 2.61334i) q^{8} +(-0.286989 - 0.497079i) q^{10} +(-0.482753 + 2.73783i) q^{11} +(-3.09240 - 1.12554i) q^{13} +(4.26692 + 1.55303i) q^{14} +(-0.553033 + 3.13641i) q^{16} +(3.51968 + 6.09627i) q^{17} +(2.59240 - 4.49016i) q^{19} +(-0.118782 - 0.0996702i) q^{20} +(-0.620615 - 3.51968i) q^{22} +(5.57445 - 4.67752i) q^{23} +(4.51114 - 1.64192i) q^{25} +4.23065 q^{26} +1.22668 q^{28} +(-3.40090 + 1.23783i) q^{29} +(-1.48293 + 1.24432i) q^{31} +(0.337044 + 1.91147i) q^{32} +(-6.93242 - 5.81699i) q^{34} +(0.788496 - 1.36571i) q^{35} +(1.61334 + 2.79439i) q^{37} +(-1.15744 + 6.56418i) q^{38} +(1.26604 + 0.460802i) q^{40} +(4.56769 + 1.66250i) q^{41} +(-1.00000 + 5.67128i) q^{43} +(-0.482753 - 0.836152i) q^{44} +(-4.67752 + 8.10170i) q^{46} +(2.31164 + 1.93969i) q^{47} +(0.950837 + 5.39246i) q^{49} +(-4.72773 + 3.96703i) q^{50} +(1.07398 - 0.390896i) q^{52} +8.77141 q^{53} -1.24123 q^{55} +(-10.0157 + 3.64543i) q^{56} +(3.56418 - 2.99070i) q^{58} +(0.514654 + 2.91875i) q^{59} +(6.04189 + 5.06975i) q^{61} +(1.24432 - 2.15523i) q^{62} +(-4.43242 - 7.67717i) q^{64} +(0.255139 - 1.44697i) q^{65} +(8.86959 + 3.22826i) q^{67} +(-2.29731 - 0.836152i) q^{68} +(-0.352044 + 1.99654i) q^{70} +(-2.65366 - 4.59627i) q^{71} +(0.777189 - 1.34613i) q^{73} +(-3.17766 - 2.66637i) q^{74} +(0.312681 + 1.77330i) q^{76} +(7.52211 - 6.31180i) q^{77} +(11.1839 - 4.07061i) q^{79} -1.42193 q^{80} -6.24897 q^{82} +(15.2768 - 5.56031i) q^{83} +(-2.40760 + 2.02022i) q^{85} +(-1.28558 - 7.29086i) q^{86} +(6.42649 + 5.39246i) q^{88} +(-9.21291 + 15.9572i) q^{89} +(5.81180 + 10.0663i) q^{91} +(-0.438852 + 2.48886i) q^{92} +(-3.64543 - 1.32683i) q^{94} +(2.17528 + 0.791737i) q^{95} +(1.75624 - 9.96016i) q^{97} +(-3.51968 - 6.09627i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} - 12 q^{7}+O(q^{10}) \) 12 * q + 6 * q^4 - 12 * q^7	\( 12 q + 6 q^{4} - 12 q^{7} + 12 q^{10} - 30 q^{13} + 18 q^{16} + 24 q^{19} - 30 q^{22} + 42 q^{25} - 12 q^{28} + 24 q^{31} - 36 q^{34} + 6 q^{37} + 6 q^{40} - 12 q^{43} - 6 q^{46} - 12 q^{49} - 18 q^{52} - 60 q^{55} + 6 q^{58} + 60 q^{61} - 6 q^{64} + 78 q^{67} - 66 q^{70} - 12 q^{73} + 48 q^{76} + 6 q^{79} - 24 q^{82} - 36 q^{85} - 24 q^{88} - 12 q^{94} + 6 q^{97}+O(q^{100}) \) 12 * q + 6 * q^4 - 12 * q^7 + 12 * q^10 - 30 * q^13 + 18 * q^16 + 24 * q^19 - 30 * q^22 + 42 * q^25 - 12 * q^28 + 24 * q^31 - 36 * q^34 + 6 * q^37 + 6 * q^40 - 12 * q^43 - 6 * q^46 - 12 * q^49 - 18 * q^52 - 60 * q^55 + 6 * q^58 + 60 * q^61 - 6 * q^64 + 78 * q^67 - 66 * q^70 - 12 * q^73 + 48 * q^76 + 6 * q^79 - 24 * q^82 - 36 * q^85 - 24 * q^88 - 12 * q^94 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more