LMFDB - Embedded newform 729.2.e.q.568.2

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			568.2
Root			$0.342020 + 0.939693i$ of defining polynomial
Character	$\chi$	$=$	729.568
Dual form			729.2.e.q.163.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20805 + 0.439693i) q^{2} +(-0.266044 - 0.223238i) q^{4} +(-0.0775297 + 0.439693i) q^{5} +(-2.70574 + 2.27038i) q^{7} +(-1.50881 - 2.61334i) q^{8} +O(q^{10})$	\(q+(1.20805 + 0.439693i) q^{2} +(-0.266044 - 0.223238i) q^{4} +(-0.0775297 + 0.439693i) q^{5} +(-2.70574 + 2.27038i) q^{7} +(-1.50881 - 2.61334i) q^{8} +(-0.286989 + 0.497079i) q^{10} +(0.482753 + 2.73783i) q^{11} +(-3.09240 + 1.12554i) q^{13} +(-4.26692 + 1.55303i) q^{14} +(-0.553033 - 3.13641i) q^{16} +(-3.51968 + 6.09627i) q^{17} +(2.59240 + 4.49016i) q^{19} +(0.118782 - 0.0996702i) q^{20} +(-0.620615 + 3.51968i) q^{22} +(-5.57445 - 4.67752i) q^{23} +(4.51114 + 1.64192i) q^{25} -4.23065 q^{26} +1.22668 q^{28} +(3.40090 + 1.23783i) q^{29} +(-1.48293 - 1.24432i) q^{31} +(-0.337044 + 1.91147i) q^{32} +(-6.93242 + 5.81699i) q^{34} +(-0.788496 - 1.36571i) q^{35} +(1.61334 - 2.79439i) q^{37} +(1.15744 + 6.56418i) q^{38} +(1.26604 - 0.460802i) q^{40} +(-4.56769 + 1.66250i) q^{41} +(-1.00000 - 5.67128i) q^{43} +(0.482753 - 0.836152i) q^{44} +(-4.67752 - 8.10170i) q^{46} +(-2.31164 + 1.93969i) q^{47} +(0.950837 - 5.39246i) q^{49} +(4.72773 + 3.96703i) q^{50} +(1.07398 + 0.390896i) q^{52} -8.77141 q^{53} -1.24123 q^{55} +(10.0157 + 3.64543i) q^{56} +(3.56418 + 2.99070i) q^{58} +(-0.514654 + 2.91875i) q^{59} +(6.04189 - 5.06975i) q^{61} +(-1.24432 - 2.15523i) q^{62} +(-4.43242 + 7.67717i) q^{64} +(-0.255139 - 1.44697i) q^{65} +(8.86959 - 3.22826i) q^{67} +(2.29731 - 0.836152i) q^{68} +(-0.352044 - 1.99654i) q^{70} +(2.65366 - 4.59627i) q^{71} +(0.777189 + 1.34613i) q^{73} +(3.17766 - 2.66637i) q^{74} +(0.312681 - 1.77330i) q^{76} +(-7.52211 - 6.31180i) q^{77} +(11.1839 + 4.07061i) q^{79} +1.42193 q^{80} -6.24897 q^{82} +(-15.2768 - 5.56031i) q^{83} +(-2.40760 - 2.02022i) q^{85} +(1.28558 - 7.29086i) q^{86} +(6.42649 - 5.39246i) q^{88} +(9.21291 + 15.9572i) q^{89} +(5.81180 - 10.0663i) q^{91} +(0.438852 + 2.48886i) q^{92} +(-3.64543 + 1.32683i) q^{94} +(-2.17528 + 0.791737i) q^{95} +(1.75624 + 9.96016i) q^{97} +(3.51968 - 6.09627i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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	$-0.238700\pi$
$2$	1.20805	+	0.439693i	0.854217	+	0.310910i	0.122459	+	0.992474i	$0.460922\pi$
$3$		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	$-0.976276\pi$
$5$	−0.0775297	+	0.439693i	−0.0346723	+	0.196637i	0.962552	+	0.271099i	$0.0873870\pi$
$6$		0			0
$7$	−2.70574	+	2.27038i	−1.02267	+	0.858124i	−0.989961	−	0.141341i	$-0.954859\pi$
$7$	−2.70574	+	2.27038i	−1.02267	+	0.858124i	−0.0327115	+	0.999465i	$0.510414\pi$
$8$	−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	0.966920	+	0.255081i	$0.0821023\pi$
$11$	0.482753	+	2.73783i	0.145555	+	0.825486i	−0.821364	+	0.570404i	$0.806787\pi$
$12$		0			0
$13$	−3.09240	+	1.12554i	−0.857676	+	0.312169i	−0.733166	−	0.680050i	$-0.761958\pi$
$13$	−3.09240	+	1.12554i	−0.857676	+	0.312169i	−0.124510	+	0.992218i	$0.539736\pi$
$14$	−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	0.0242455	+	0.999706i	$0.492282\pi$
$17$	−3.51968	+	6.09627i	−0.853648	+	1.47856i	−0.877894	+	0.478856i	$0.841052\pi$
$18$		0			0
$19$	2.59240	+	4.49016i	0.594736	+	1.03011i	0.993584	+	0.113097i	$0.0360769\pi$
$19$	2.59240	+	4.49016i	0.594736	+	1.03011i	−0.398848	+	0.917017i	$0.630590\pi$
$20$	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	$-0.551929\pi$
$23$	−5.57445	−	4.67752i	−1.16235	−	0.975330i	−0.999935	+	0.0113920i	$0.996374\pi$
$24$		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	$-0.279804\pi$
$29$	3.40090	+	1.23783i	0.631531	+	0.229859i	−0.00636650	+	0.999980i	$0.502027\pi$
$30$		0			0
$31$	−1.48293	−	1.24432i	−0.266341	−	0.223487i	0.499830	−	0.866124i	$-0.333396\pi$
$31$	−1.48293	−	1.24432i	−0.266341	−	0.223487i	−0.766171	+	0.642637i	$0.777840\pi$
$32$	−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	−0.702393	−	0.711790i	$-0.747885\pi$
$37$	1.61334	−	2.79439i	0.265232	−	0.459395i	0.967624	+	0.252395i	$0.0812183\pi$
$38$	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	$-0.735038\pi$
$41$	−4.56769	+	1.66250i	−0.713354	+	0.259639i	−0.0402521	+	0.999190i	$0.512816\pi$
$42$		0			0
$43$	−1.00000	−	5.67128i	−0.152499	−	0.864862i	−0.961037	−	0.276419i	$-0.910852\pi$
$43$	−1.00000	−	5.67128i	−0.152499	−	0.864862i	0.808539	−	0.588443i	$-0.200259\pi$
$44$	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	$-0.792855\pi$
$47$	−2.31164	+	1.93969i	−0.337187	+	0.282933i	0.458434	+	0.888729i	$0.348411\pi$
$48$		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	$-0.705798\pi$
$53$	−8.77141			−1.20485			−0.602423	+	0.798177i	$0.705798\pi$
$54$		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	0.932805	+	0.360380i	$0.117353\pi$
$59$	−0.514654	+	2.91875i	−0.0670022	+	0.379989i	−0.999808	+	0.0196084i	$0.993758\pi$
$60$		0			0
$61$	6.04189	−	5.06975i	0.773585	−	0.649115i	−0.168040	−	0.985780i	$-0.553744\pi$
$61$	6.04189	−	5.06975i	0.773585	−	0.649115i	0.941624	+	0.336666i	$0.109299\pi$
$62$	−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	0.262349	−	0.964973i	$-0.415503\pi$
$67$	8.86959	−	3.22826i	1.08359	−	0.394395i	0.821244	+	0.570578i	$0.193281\pi$
$68$	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	$-0.731352\pi$
$71$	2.65366	−	4.59627i	0.314931	−	0.545476i	0.979423	+	0.201819i	$0.0646853\pi$
$72$		0			0
$73$	0.777189	+	1.34613i	0.0909631	+	0.157553i	0.907917	−	0.419151i	$-0.137672\pi$
$73$	0.777189	+	1.34613i	0.0909631	+	0.157553i	−0.816954	+	0.576703i	$0.804339\pi$
$74$	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	0.883194	−	0.469007i	$-0.155388\pi$
$79$	11.1839	+	4.07061i	1.25829	+	0.457980i	0.375094	+	0.926987i	$0.377610\pi$
$80$	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	$-0.739751\pi$
$83$	−15.2768	−	5.56031i	−1.67685	−	0.610323i	−0.992873	+	0.119181i	$0.961973\pi$
$84$		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	0.674665	+	0.738125i	$0.264288\pi$
$89$	9.21291	+	15.9572i	0.976567	+	1.69146i	0.301902	+	0.953339i	$0.402378\pi$
$90$		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	0.934242	+	0.356640i	$0.116078\pi$
$97$	1.75624	+	9.96016i	0.178320	+	1.01130i	−0.755922	+	0.654661i	$0.772811\pi$
$98$	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	$-0.689211\pi$
$101$	1.59397	−	1.33750i	0.158606	−	0.133086i	0.718637	+	0.695386i	$0.244766\pi$
$102$		0			0
$103$	−0.251497	+	1.42631i	−0.0247807	+	0.140538i	−0.994688	−	0.102936i	$-0.967176\pi$
$103$	−0.251497	+	1.42631i	−0.0247807	+	0.140538i	0.969907	+	0.243475i	$0.0782873\pi$
$104$	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	$-0.465532\pi$
$107$	2.23583			0.216146			0.108073	+	0.994143i	$0.465532\pi$
$108$		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	$-0.969746\pi$
$113$	−0.293144	+	1.66250i	−0.0275767	+	0.156395i	0.967910	+	0.251297i	$0.0808572\pi$
$114$		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	0.919199	−	0.393793i	$-0.128837\pi$
$127$	1.33615	+	2.31428i	0.118564	+	0.205359i	−0.800635	+	0.599153i	$0.795504\pi$
$128$	−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	$-0.237065\pi$
$131$	2.23675	+	1.87686i	0.195426	+	0.163982i	−0.539824	+	0.841778i	$0.681509\pi$
$132$		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	$-0.452641\pi$
$137$	−4.37636	−	1.59286i	−0.373897	−	0.136087i	−0.522132	+	0.852865i	$0.674863\pi$
$138$		0			0
$139$	−6.13041	−	5.14403i	−0.519975	−	0.436311i	0.344648	−	0.938732i	$-0.387998\pi$
$139$	−6.13041	−	5.14403i	−0.519975	−	0.436311i	−0.864623	+	0.502421i	$0.832443\pi$
$140$	−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	$-0.300644\pi$
$149$	18.9928	−	6.91282i	1.55595	−	0.566320i	0.969804	+	0.243884i	$0.0784217\pi$
$150$		0			0
$151$	1.16385	+	6.60051i	0.0947126	+	0.537142i	0.994835	+	0.101505i	$0.0323657\pi$
$151$	1.16385	+	6.60051i	0.0947126	+	0.537142i	−0.900122	+	0.435637i	$0.856523\pi$
$152$	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	−0.925419	−	0.378945i	$-0.876287\pi$
$157$	0.924678	−	5.24411i	0.0737973	−	0.418525i	0.999216	−	0.0395801i	$-0.0126020\pi$
$158$	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	−0.859861	−	0.510528i	$-0.829450\pi$
$167$	1.58634	−	8.99660i	0.122755	−	0.696178i	0.982616	−	0.185650i	$-0.0594389\pi$
$168$		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	0.998292	+	0.0584296i	$0.0186093\pi$
$173$	1.05471	+	5.98158i	0.0801884	+	0.454771i	−0.918103	+	0.396342i	$0.870280\pi$
$174$		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	$-0.958864\pi$
$179$	−5.14057	+	8.90373i	−0.384224	+	0.665496i	0.607437	+	0.794368i	$0.292198\pi$
$180$		0			0
$181$	11.5706	+	20.0408i	0.860034	+	1.48962i	0.871895	+	0.489693i	$0.162891\pi$
$181$	11.5706	+	20.0408i	0.860034	+	1.48962i	−0.0118609	+	0.999930i	$0.503776\pi$
$182$	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	$-0.566980\pi$
$191$	−13.7856	−	5.01754i	−0.997490	−	0.363057i	−0.788616	+	0.614886i	$0.789202\pi$
$192$		0			0
$193$	17.9572	+	15.0679i	1.29259	+	1.08461i	0.991375	+	0.131055i	$0.0418366\pi$
$193$	17.9572	+	15.0679i	1.29259	+	1.08461i	0.301215	+	0.953556i	$0.402608\pi$
$194$	−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	$-0.0624468\pi$
$197$	4.51384	+	7.81820i	0.321598	+	0.557024i	−0.659220	+	0.751950i	$0.729113\pi$
$198$		0			0
$199$	−1.30200	+	2.25514i	−0.0922966	+	0.159862i	−0.908477	−	0.417935i	$-0.862754\pi$
$199$	−1.30200	+	2.25514i	−0.0922966	+	0.159862i	0.816181	+	0.577797i	$0.196087\pi$
$200$	−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	0.716168	+	0.697928i	$0.245894\pi$
$211$	−2.84002	+	16.1066i	−0.195515	+	1.10882i	−0.911683	+	0.410894i	$0.865217\pi$
$212$	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	−0.542868	−	0.839818i	$-0.682662\pi$
$223$	2.83615	−	2.37981i	0.189923	−	0.159364i	0.732791	+	0.680454i	$0.238217\pi$
$224$	−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	−0.983203	−	0.182513i	$-0.941577\pi$
$227$	−1.83386	−	10.4003i	−0.121717	−	0.690294i	0.861486	−	0.507781i	$-0.169534\pi$
$228$		0			0
$229$	−12.7096	+	4.62592i	−0.839875	+	0.305689i	−0.725905	−	0.687795i	$-0.758579\pi$
$229$	−12.7096	+	4.62592i	−0.839875	+	0.305689i	−0.113969	+	0.993484i	$0.536357\pi$
$230$	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	$-0.969910\pi$
$233$	−6.35035	+	10.9991i	−0.416025	+	0.720576i	0.579510	+	0.814965i	$0.303244\pi$
$234$		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	$-0.338384\pi$
$239$	−4.48254	−	3.76130i	−0.289951	−	0.243298i	−0.776147	+	0.630552i	$0.782829\pi$
$240$		0			0
$241$	8.02481	+	2.92079i	0.516924	+	0.188145i	0.587290	−	0.809376i	$-0.300195\pi$
$241$	8.02481	+	2.92079i	0.516924	+	0.188145i	−0.0703666	+	0.997521i	$0.522417\pi$
$242$	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	$-0.0982529\pi$
$251$	3.37895	+	5.85251i	0.213277	+	0.369407i	−0.739461	+	0.673199i	$0.764920\pi$
$252$		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	$-0.647756\pi$
$257$	−3.46085	+	1.25965i	−0.215882	+	0.0785747i	0.231815	+	0.972760i	$0.425534\pi$
$258$		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	$-0.686445\pi$
$263$	2.78677	−	2.33837i	0.171839	−	0.144190i	0.724651	+	0.689116i	$0.242001\pi$
$264$		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	$-0.569315\pi$
$269$	−7.08672			−0.432085			−0.216042	+	0.976384i	$0.569315\pi$
$270$		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	−0.903839	−	0.427872i	$-0.859263\pi$
$277$	−10.6420	+	8.92972i	−0.639417	+	0.536535i	0.264422	+	0.964407i	$0.414819\pi$
$278$	−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	0.854455	+	0.519526i	$0.173891\pi$
$281$	3.84240	+	21.7913i	0.229218	+	1.29996i	−0.625236	+	0.780435i	$0.714997\pi$
$282$		0			0
$283$	22.3011	−	8.11695i	1.32566	−	0.482502i	0.420395	−	0.907341i	$-0.361891\pi$
$283$	22.3011	−	8.11695i	1.32566	−	0.482502i	0.905269	+	0.424839i	$0.139669\pi$
$284$	−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	$-0.0948805\pi$
$293$	14.2531	+	11.9598i	0.832674	+	0.698697i	−0.123229	+	0.992378i	$0.539325\pi$
$294$		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	0.401912	+	0.915678i	$0.368346\pi$
$307$	−10.3735	+	17.9674i	−0.592044	+	1.02545i	−0.993957	+	0.109773i	$0.964988\pi$
$308$	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	$-0.807269\pi$
$311$	−19.1561	+	6.97225i	−1.08624	+	0.395360i	−0.264015	+	0.964519i	$0.585047\pi$
$312$		0			0
$313$	−5.18180	−	29.3874i	−0.292893	−	1.66108i	−0.675646	−	0.737226i	$-0.736135\pi$
$313$	−5.18180	−	29.3874i	−0.292893	−	1.66108i	0.382753	−	0.923851i	$-0.374976\pi$
$314$	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	$-0.683541\pi$
$317$	3.30671	−	2.77466i	0.185724	−	0.155841i	0.730909	+	0.682475i	$0.239096\pi$
$318$		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	−0.702167	−	0.712012i	$-0.747784\pi$
$331$	−2.23601	+	1.87624i	−0.122902	+	0.103127i	0.579265	+	0.815139i	$0.303340\pi$
$332$	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	−0.684069	−	0.729417i	$-0.739791\pi$
$337$	−13.5706	+	4.93929i	−0.739236	+	0.269060i	−0.0551671	+	0.998477i	$0.517569\pi$
$338$	−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	$-0.290204\pi$
$347$	−1.11386	−	0.934640i	−0.0597952	−	0.0501741i	−0.672195	+	0.740374i	$0.734649\pi$
$348$		0			0
$349$	25.9183	+	9.43350i	1.38738	+	0.504964i	0.924406	−	0.381410i	$-0.124561\pi$
$349$	25.9183	+	9.43350i	1.38738	+	0.504964i	0.462971	+	0.886374i	$0.346784\pi$
$350$	−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	$-0.479318\pi$
$353$	−9.89695	−	3.60220i	−0.526762	−	0.191726i	−0.591692	+	0.806164i	$0.701540\pi$
$354$		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	$-0.293522\pi$
$359$	−7.35273	−	12.7353i	−0.388062	−	0.672143i	−0.992189	+	0.124745i	$0.960189\pi$
$360$		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	−0.914342	−	0.404942i	$-0.867292\pi$
$367$	−3.70961	−	21.0382i	−0.193640	−	1.09819i	0.720702	−	0.693245i	$-0.243819\pi$
$368$	−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	−0.696484	−	0.717572i	$-0.745253\pi$
$373$	3.92871	−	22.2808i	0.203421	−	1.15366i	0.899905	−	0.436085i	$-0.143635\pi$
$374$	−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	−0.0870812	+	0.996201i	$0.527754\pi$
$383$	−6.77082	+	38.3992i	−0.345973	+	1.96211i	−0.258891	+	0.965906i	$0.583357\pi$
$384$		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	0.996189	+	0.0872245i	$0.0277997\pi$
$389$	1.77330	+	10.0569i	0.0899101	+	0.509905i	−0.906279	+	0.422681i	$0.861089\pi$
$390$		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	0.880009	−	0.474956i	$-0.157536\pi$
$397$	0.571452	+	0.989783i	0.0286803	+	0.0496758i	−0.851329	+	0.524632i	$0.824203\pi$
$398$	−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	$-0.449321\pi$
$401$	−15.7452	−	13.2118i	−0.786280	−	0.659767i	−0.944822	+	0.327585i	$0.893765\pi$
$402$		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	0.475730	−	0.879592i	$-0.342184\pi$
$409$	−6.22668	−	5.22481i	−0.307890	−	0.258350i	−0.783619	+	0.621242i	$0.786629\pi$
$410$	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	$-0.949558\pi$
$419$	−33.6207	+	12.2369i	−1.64248	+	0.597814i	−0.655010	+	0.755620i	$0.727336\pi$
$420$		0			0
$421$	−2.27807	−	12.9196i	−0.111026	−	0.629661i	−0.988641	−	0.150295i	$-0.951978\pi$
$421$	−2.27807	−	12.9196i	−0.111026	−	0.629661i	0.877615	−	0.479366i	$-0.159133\pi$
$422$	−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	$-0.426645\pi$
$431$	9.48411			0.456833			0.228417	+	0.973563i	$0.426645\pi$
$432$		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	−0.905816	−	0.423672i	$-0.860741\pi$
$439$	−13.5326	+	11.3552i	−0.645874	+	0.541952i	0.259942	+	0.965624i	$0.416297\pi$
$440$	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	−0.990324	−	0.138777i	$-0.955683\pi$
$443$	−2.25606	−	12.7947i	−0.107188	−	0.607896i	0.883135	−	0.469119i	$-0.155428\pi$
$444$		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	$-0.798499\pi$
$449$	2.31428	−	4.00846i	0.109218	−	0.189171i	0.915454	+	0.402424i	$0.131832\pi$
$450$		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	−0.152188	−	0.988352i	$-0.548632\pi$
$457$	−19.3268	−	7.03439i	−0.904070	−	0.329055i	−0.751883	+	0.659297i	$0.770854\pi$
$458$	−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	$-0.103184\pi$
$461$	31.5478	+	11.4825i	1.46933	+	0.534791i	0.521410	+	0.853307i	$0.325406\pi$
$462$		0			0
$463$	10.0590	+	8.44047i	0.467480	+	0.392262i	0.845874	−	0.533382i	$-0.179079\pi$
$463$	10.0590	+	8.44047i	0.467480	+	0.392262i	−0.378395	+	0.925644i	$0.623524\pi$
$464$	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	−0.998495	−	0.0548513i	$-0.982532\pi$
$467$	−11.8154	−	20.4648i	−0.546750	−	0.946999i	0.451745	−	0.892147i	$-0.350802\pi$
$468$		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	$-0.765113\pi$
$479$	−4.50449	+	3.77972i	−0.205815	+	0.172700i	0.534054	+	0.845451i	$0.320668\pi$
$480$		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	0.374557	+	0.927204i	$0.377795\pi$
$491$	−6.52644	+	37.0133i	−0.294534	+	1.67039i	−0.669090	+	0.743181i	$0.733316\pi$
$492$		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	−0.933997	−	0.357281i	$-0.883704\pi$
$499$	−31.7165	+	11.5439i	−1.41982	+	0.516774i	−0.485827	+	0.874055i	$0.661482\pi$
$500$	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	$-0.696358\pi$
$503$	9.35597	−	16.2050i	0.417162	−	0.722546i	0.995653	+	0.0931429i	$0.0296913\pi$
$504$		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	$-0.117533\pi$
$509$	16.6754	+	13.9923i	0.739124	+	0.620198i	−0.193478	+	0.981105i	$0.561977\pi$
$510$		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	$-0.121356\pi$
$521$	3.23822	+	5.60876i	0.141869	+	0.245724i	−0.786332	+	0.617805i	$0.788022\pi$
$522$		0			0
$523$	5.43629	−	9.41593i	0.237712	−	0.411730i	−0.722345	−	0.691533i	$-0.756936\pi$
$523$	5.43629	−	9.41593i	0.237712	−	0.411730i	0.960057	+	0.279803i	$0.0902691\pi$
$524$	−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	0.0242526	−	0.999706i	$-0.492279\pi$
$547$	23.6917	−	19.8797i	1.01298	−	0.849993i	0.988729	+	0.149713i	$0.0478350\pi$
$548$	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	$-0.998148\pi$
$557$	−11.6813	+	20.2327i	−0.494954	+	0.857286i	0.505029	+	0.863102i	$0.331482\pi$
$558$		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	$-0.0265251\pi$
$563$	25.8063	+	21.6540i	1.08761	+	0.912609i	0.0910754	+	0.995844i	$0.470970\pi$
$564$		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	$-0.165532\pi$
$569$	28.9386	+	10.5328i	1.21317	+	0.441558i	0.345368	+	0.938467i	$0.387754\pi$
$570$		0			0
$571$	−22.8858	−	19.2035i	−0.957740	−	0.803639i	0.0228438	−	0.999739i	$-0.492728\pi$
$571$	−22.8858	−	19.2035i	−0.957740	−	0.803639i	−0.980584	+	0.196100i	$0.937172\pi$
$572$	−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	−0.911713	−	0.410828i	$-0.865240\pi$
$577$	−2.40373	+	4.16339i	−0.100069	+	0.173324i	0.811644	+	0.584152i	$0.198573\pi$
$578$	−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	$-0.669844\pi$
$587$	6.08056	−	5.10220i	0.250972	−	0.210590i	0.759591	+	0.650402i	$0.225399\pi$
$588$		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	$-0.232533\pi$
$593$	36.2753			1.48965			0.744824	+	0.667261i	$0.232533\pi$
$594$		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	−0.595936	−	0.803032i	$-0.703219\pi$
$599$	5.84240	−	33.1339i	0.238714	−	1.35381i	0.834650	−	0.550781i	$-0.185670\pi$
$600$		0			0
$601$	−2.28106	+	1.91404i	−0.0930463	+	0.0780752i	−0.688124	−	0.725593i	$-0.741566\pi$
$601$	−2.28106	+	1.91404i	−0.0930463	+	0.0780752i	0.595078	+	0.803668i	$0.297121\pi$
$602$	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	−0.0258885	−	0.999665i	$-0.508242\pi$
$607$	14.7049	−	5.35213i	0.596852	−	0.217236i	0.622740	+	0.782429i	$0.286019\pi$
$608$	−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	0.876597	−	0.481225i	$-0.159808\pi$
$613$	0.533433	+	0.923933i	0.0215452	+	0.0373173i	−0.855052	+	0.518543i	$0.826475\pi$
$614$	−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	$-0.362519\pi$
$617$	−10.0122	−	8.40121i	−0.403075	−	0.338220i	−0.821681	+	0.569948i	$0.806963\pi$
$618$		0			0
$619$	−19.2802	−	7.01741i	−0.774936	−	0.282054i	−0.0758765	−	0.997117i	$-0.524175\pi$
$619$	−19.2802	−	7.01741i	−0.774936	−	0.282054i	−0.699059	+	0.715064i	$0.746398\pi$
$620$	−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	−0.744955	−	0.667115i	$-0.767529\pi$
$631$	5.15611	−	8.93064i	0.205261	−	0.355523i	0.950216	+	0.311592i	$0.100862\pi$
$632$	−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	$-0.700164\pi$
$641$	2.68588	−	2.25372i	0.106086	−	0.0890165i	0.694288	+	0.719698i	$0.255720\pi$
$642$		0			0
$643$	5.47889	−	31.0723i	0.216066	−	1.22537i	−0.662980	−	0.748637i	$-0.730708\pi$
$643$	5.47889	−	31.0723i	0.216066	−	1.22537i	0.879046	−	0.476736i	$-0.158180\pi$
$644$	−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	$-0.519072\pi$
$647$	−3.04628			−0.119762			−0.0598808	+	0.998206i	$0.519072\pi$
$648$		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	0.682357	+	0.731019i	$0.260955\pi$
$653$	−5.33749	+	30.2704i	−0.208872	+	1.18457i	−0.891229	+	0.453553i	$0.850156\pi$
$654$		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	−0.863699	−	0.504009i	$-0.831858\pi$
$659$	−5.76233	−	32.6798i	−0.224469	−	1.27302i	0.639230	−	0.769016i	$-0.279253\pi$
$660$		0			0
$661$	14.0086	−	5.09872i	0.544872	−	0.198317i	−0.0548946	−	0.998492i	$-0.517482\pi$
$661$	14.0086	−	5.09872i	0.544872	−	0.198317i	0.599767	+	0.800175i	$0.295260\pi$
$662$	−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	0.214226	−	0.976784i	$-0.431277\pi$
$673$	−6.47343	−	2.35614i	−0.249532	−	0.0908224i	−0.463758	+	0.885962i	$0.653499\pi$
$674$	−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	$-0.307323\pi$
$677$	12.3938	+	4.51098i	0.476333	+	0.173371i	−0.0926859	+	0.995695i	$0.529545\pi$
$678$		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	$-0.146080\pi$
$683$	1.68907	+	2.92556i	0.0646305	+	0.111943i	−0.831900	+	0.554926i	$0.812746\pi$
$684$		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	0.959080	+	0.283135i	$0.0913745\pi$
$691$	4.06599	+	23.0594i	0.154678	+	0.877220i	−0.804403	+	0.594085i	$0.797514\pi$
$692$	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	$-0.170926\pi$
$701$	45.5001			1.71852			0.859258	+	0.511543i	$0.170926\pi$
$702$		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	0.112868	−	0.993610i	$-0.463996\pi$
$709$	29.5822	−	24.8224i	1.11098	−	0.932225i	0.998114	+	0.0613851i	$0.0195518\pi$
$710$	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	0.119652	−	0.992816i	$-0.461822\pi$
$719$	24.6591	−	42.7108i	0.919630	−	1.59285i	0.799978	−	0.600030i	$-0.204845\pi$
$720$		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	0.836658	−	0.547726i	$-0.184506\pi$
$727$	30.3469	+	11.0454i	1.12550	+	0.409650i	0.288846	+	0.957376i	$0.406729\pi$
$728$	−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	0.998432	−	0.0559830i	$-0.0178293\pi$
$733$	30.2328	+	25.3684i	1.11668	+	0.937002i	0.118243	+	0.992985i	$0.462274\pi$
$734$	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	0.333827	+	0.942634i	$0.391660\pi$
$739$	−17.6545	+	30.5785i	−0.649432	+	1.12485i	−0.983259	+	0.182215i	$0.941673\pi$
$740$	−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	$-0.275447\pi$
$743$	44.5514	−	16.2154i	1.63443	−	0.594884i	0.986053	+	0.166433i	$0.0532251\pi$
$744$		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	−0.999941	−	0.0109084i	$-0.996528\pi$
$751$	−1.55035	+	8.79244i	−0.0565729	+	0.320841i	0.943368	+	0.331749i	$0.107639\pi$
$752$	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	$-0.983130\pi$
$761$	−1.16150	+	6.58718i	−0.0421043	+	0.238785i	0.956492	+	0.291760i	$0.0942408\pi$
$762$		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	0.0484383	−	0.998826i	$-0.484576\pi$
$769$	20.1763	−	7.34359i	0.727577	−	0.264816i	0.679139	+	0.734010i	$0.262353\pi$
$770$	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	$-0.774355\pi$
$773$	5.12208	−	8.87170i	0.184228	−	0.319093i	0.943316	+	0.331895i	$0.107688\pi$
$774$		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
$780$		0			0
$781$	13.8648	+	5.04639i	0.496123	+	0.180574i
$782$	65.8535			2.35492
$783$		0			0
$784$	−17.4388			−0.622815
$785$	2.23411	+	0.813148i	0.0797387	+	0.0290225i
$786$		0			0
$787$	0.725966	+	0.609158i	0.0258779	+	0.0217141i	0.655635	−	0.755078i	$-0.272401\pi$
$787$	0.725966	+	0.609158i	0.0258779	+	0.0217141i	−0.629757	+	0.776792i	$0.716846\pi$
$788$	0.544436	−	3.08765i	0.0193947	−	0.109993i
$789$		0			0
$790$	−5.23308	+	4.39107i	−0.186185	+	0.156227i
$791$	−2.98135	−	5.16385i	−0.106005	−	0.183605i
$792$		0			0
$793$	−12.9777	+	22.4781i	−0.460852	+	0.798219i
$794$	0.255139	+	1.44697i	0.00905455	+	0.0513509i
$795$		0			0
$796$	0.849823	−	0.309310i	0.0301212	−	0.0109632i
$797$	−6.58791	+	2.39780i	−0.233356	+	0.0849346i	−0.456051	−	0.889953i	$-0.650737\pi$
$797$	−6.58791	+	2.39780i	−0.233356	+	0.0849346i	0.222696	+	0.974888i	$0.428514\pi$
$798$		0			0
$799$	−3.68866	−	20.9194i	−0.130496	−	0.740077i
$800$	−4.65895	+	8.06953i	−0.164719	+	0.285301i
$801$		0			0
$802$	−13.2118	−	22.8836i	−0.466526	−	0.808047i
$803$	−3.31028	+	2.77766i	−0.116817	+	0.0980213i
$804$		0			0
$805$	−1.99273	+	11.3013i	−0.0702344	+	0.398319i
$806$	6.27374	+	5.26429i	0.220983	+	0.185427i
$807$		0			0
$808$	−5.90033	−	2.14754i	−0.207573	−	0.0755503i
$809$	−45.1028			−1.58573			−0.792866	−	0.609396i	$-0.791412\pi$
$809$	−45.1028			−1.58573			−0.792866	+	0.609396i	$0.791412\pi$
$810$		0			0
$811$	8.07285			0.283476			0.141738	−	0.989904i	$-0.454731\pi$
$811$	8.07285			0.283476			0.141738	+	0.989904i	$0.454731\pi$
$812$	4.17182	+	1.51842i	0.146402	+	0.0532860i
$813$		0			0
$814$	8.83409	+	7.41268i	0.309635	+	0.259814i
$815$	−0.295792	+	1.67752i	−0.0103611	+	0.0587609i
$816$		0			0
$817$	22.8726	−	19.1924i	0.800210	−	0.671456i
$818$	−5.22481	−	9.04963i	−0.182681	−	0.316413i
$819$		0			0
$820$	−0.376859	+	0.652739i	−0.0131605	+	0.0227946i
$821$	1.08866	+	6.17412i	0.0379946	+	0.215478i	0.997894	−	0.0648668i	$-0.0206623\pi$
$821$	1.08866	+	6.17412i	0.0379946	+	0.215478i	−0.959899	+	0.280345i	$0.909551\pi$
$822$		0			0
$823$	18.5993	−	6.76958i	0.648329	−	0.235973i	0.00313978	−	0.999995i	$-0.499001\pi$
$823$	18.5993	−	6.76958i	0.648329	−	0.235973i	0.645190	+	0.764022i	$0.276778\pi$
$824$	4.10689	−	1.49479i	0.143070	−	0.0520733i
$825$		0			0
$826$	−2.33692	−	13.2534i	−0.0813120	−	0.461143i
$827$	20.9001	−	36.2001i	0.726769	−	1.25880i	−0.231472	−	0.972841i	$-0.574354\pi$
$827$	20.9001	−	36.2001i	0.726769	−	1.25880i	0.958242	−	0.285960i	$-0.0923124\pi$
$828$		0			0
$829$	−16.8640	−	29.2092i	−0.585710	−	1.01448i	−0.994787	−	0.101979i	$-0.967483\pi$
$829$	−16.8640	−	29.2092i	−0.585710	−	1.01448i	0.409077	−	0.912500i	$-0.365851\pi$
$830$	7.14819	−	5.99805i	0.248117	−	0.208195i
$831$		0			0
$832$	5.06583	−	28.7297i	0.175626	−	0.996024i
$833$	29.5273	+	24.7763i	1.02306	+	0.858448i
$834$		0			0
$835$	3.83275	+	1.39501i	0.132638	+	0.0482762i
$836$	5.00594			0.173134
$837$		0			0
$838$	−45.9959			−1.58890
$839$	−27.5206	−	10.0167i	−0.950115	−	0.345814i	−0.179963	−	0.983673i	$-0.557598\pi$
$839$	−27.5206	−	10.0167i	−0.950115	−	0.345814i	−0.770152	+	0.637860i	$0.779820\pi$
$840$		0			0
$841$	−12.1814	−	10.2214i	−0.420048	−	0.352462i
$842$	2.92863	−	16.6091i	0.100927	−	0.572386i
$843$		0			0
$844$	4.35117	−	3.65106i	0.149773	−	0.125675i
$845$	−0.484481	−	0.839145i	−0.0166666	−	0.0288675i
$846$		0			0
$847$	−5.77719	+	10.0064i	−0.198507	+	0.343823i
$848$	4.85088	+	27.5107i	0.166580	+	0.944722i
$849$		0			0
$850$	−40.8242	+	14.8588i	−1.40026	+	0.509652i
$851$	−22.0643	+	8.03074i	−0.756354	+	0.275290i
$852$		0			0
$853$	6.52885	+	37.0269i	0.223543	+	1.26778i	0.865450	+	0.500995i	$0.167033\pi$
$853$	6.52885	+	37.0269i	0.223543	+	1.26778i	−0.641907	+	0.766783i	$0.721856\pi$
$854$	−17.9068	+	31.0155i	−0.612758	+	1.06133i
$855$		0			0
$856$	−3.37346	−	5.84300i	−0.115302	−	0.199710i
$857$	22.2229	−	18.6472i	0.759120	−	0.636978i	−0.178777	−	0.983890i	$-0.557214\pi$
$857$	22.2229	−	18.6472i	0.759120	−	0.636978i	0.937898	+	0.346912i	$0.112770\pi$
$858$		0			0
$859$	−4.31820	+	24.4897i	−0.147335	+	0.835579i	0.818127	+	0.575037i	$0.195012\pi$
$859$	−4.31820	+	24.4897i	−0.147335	+	0.835579i	−0.965463	+	0.260542i	$0.916099\pi$
$860$	−0.684040	−	0.573978i	−0.0233256	−	0.0195725i
$861$		0			0
$862$	11.4572	+	4.17009i	0.390235	+	0.142034i
$863$	−42.4018			−1.44337			−0.721687	−	0.692219i	$-0.756633\pi$
$863$	−42.4018			−1.44337			−0.721687	+	0.692219i	$0.756633\pi$
$864$		0			0
$865$	−2.71183			−0.0922050
$866$	21.3375	+	7.76621i	0.725077	+	0.263906i
$867$		0			0
$868$	−1.81908	−	1.52639i	−0.0617435	−	0.0518090i
$869$	−5.74556	+	32.5847i	−0.194905	+	1.10536i
$870$		0			0
$871$	−23.7947	+	19.9661i	−0.806254	+	0.676527i
$872$	17.3559	+	30.0612i	0.587744	+	1.01800i
$873$		0			0
$874$	24.2520	−	42.0056i	0.820335	−	1.42086i
$875$	−2.68383	−	15.2208i	−0.0907300	−	0.514555i
$876$		0			0
$877$	−11.3277	+	4.12294i	−0.382509	+	0.139222i	−0.526116	−	0.850413i	$-0.676352\pi$
$877$	−11.3277	+	4.12294i	−0.382509	+	0.139222i	0.143607	+	0.989635i	$0.454130\pi$
$878$	−21.3407	+	7.76739i	−0.720215	+	0.262137i
$879$		0			0
$880$	0.686441	+	3.89300i	0.0231399	+	0.131233i
$881$	−7.39133	+	12.8022i	−0.249020	+	0.431316i	−0.963254	−	0.268591i	$-0.913442\pi$
$881$	−7.39133	+	12.8022i	−0.249020	+	0.431316i	0.714234	+	0.699907i	$0.246775\pi$
$882$		0			0
$883$	12.9231	+	22.3834i	0.434896	+	0.753263i	0.997287	−	0.0736089i	$-0.0234516\pi$
$883$	12.9231	+	22.3834i	0.434896	+	0.753263i	−0.562391	+	0.826872i	$0.690118\pi$
$884$	−6.16307	+	5.17143i	−0.207286	+	0.173934i
$885$		0			0
$886$	2.90033	−	16.4486i	0.0974385	−	0.552601i
$887$	−35.1277	−	29.4757i	−1.17947	−	0.989696i	−0.999982	−	0.00593588i	$-0.998111\pi$
$887$	−35.1277	−	29.4757i	−1.17947	−	0.989696i	−0.179491	−	0.983760i	$-0.557445\pi$
$888$		0			0
$889$	−8.86959	−	3.22826i	−0.297476	−	0.108273i
$890$	−10.5760			−0.354509
$891$		0			0
$892$	−1.28581			−0.0430520
$893$	−14.7022	−	5.35117i	−0.491991	−	0.179070i
$894$		0			0
$895$	−3.51636	−	2.95058i	−0.117539	−	0.0986269i
$896$	4.60894	−	26.1386i	0.153974	−	0.873230i
$897$		0			0
$898$	4.55825	−	3.82482i	0.152111	−	0.127636i
$899$	−3.50303	−	6.06742i	−0.116832	−	0.202360i
$900$		0			0
$901$	30.8726	−	53.4729i	1.02851	−	1.78144i
$902$	−3.01671	−	17.1086i	−0.100445	−	0.569654i
$903$		0			0
$904$	4.78699	−	1.74232i	0.159213	−	0.0579488i
$905$	−9.70886	+	3.53374i	−0.322734	+	0.117465i
$906$		0			0
$907$	−2.03168	−	11.5222i	−0.0674608	−	0.382589i	−0.999780	−	0.0209538i	$-0.993330\pi$
$907$	−2.03168	−	11.5222i	−0.0674608	−	0.382589i	0.932320	−	0.361635i	$-0.117781\pi$
$908$	−1.83386	+	3.17634i	−0.0608587	+	0.105410i
$909$		0			0
$910$	3.33585	+	5.77786i	0.110582	+	0.191534i
$911$	−21.9665	+	18.4321i	−0.727784	+	0.610683i	−0.929526	−	0.368755i	$-0.879784\pi$
$911$	−21.9665	+	18.4321i	−0.727784	+	0.610683i	0.201743	+	0.979439i	$0.435340\pi$
$912$		0			0
$913$	7.84823	−	44.5095i	0.259739	−	1.47305i
$914$	−20.2547	−	16.9957i	−0.669966	−	0.562168i
$915$		0			0
$916$	4.41400	+	1.60656i	0.145843	+	0.0530824i
$917$	−10.3133			−0.340574
$918$		0			0
$919$	4.33511			0.143002			0.0715011	−	0.997441i	$-0.477221\pi$
$919$	4.33511			0.143002			0.0715011	+	0.997441i	$0.477221\pi$
$920$	−9.21291	−	3.35323i	−0.303741	−	0.110553i
$921$		0			0
$922$	33.0624	+	27.7427i	1.08885	+	0.913656i
$923$	−3.03287	+	17.2003i	−0.0998282	+	0.566154i
$924$		0			0
$925$	11.8662	−	9.95691i	0.390158	−	0.327381i
$926$	8.44047	+	14.6193i	0.277371	+	0.480421i
$927$		0			0
$928$	−3.51233	+	6.08353i	−0.115298	+	0.199702i
$929$	2.23848	+	12.6951i	0.0734422	+	0.416511i	0.999257	+	0.0385346i	$0.0122690\pi$
$929$	2.23848	+	12.6951i	0.0734422	+	0.416511i	−0.925815	+	0.377977i	$0.876620\pi$
$930$		0			0
$931$	26.6780	−	9.70999i	0.874336	−	0.318232i
$932$	4.14489	−	1.50862i	0.135771	−	0.0494164i
$933$		0			0
$934$	−5.27527	−	29.9176i	−0.172612	−	0.978932i
$935$	4.36873	−	7.56687i	0.142873	−	0.247463i
$936$		0			0
$937$	26.6040	+	46.0795i	0.869115	+	1.50535i	0.862902	+	0.505371i	$0.168644\pi$
$937$	26.6040	+	46.0795i	0.869115	+	1.50535i	0.00621270	+	0.999981i	$0.498022\pi$
$938$	−32.8322	+	27.5495i	−1.07201	+	0.899524i
$939$		0			0
$940$	−0.0812519	+	0.460802i	−0.00265015	+	0.0150297i
$941$	−25.5916	−	21.4739i	−0.834262	−	0.700029i	0.122003	−	0.992530i	$-0.461068\pi$
$941$	−25.5916	−	21.4739i	−0.834262	−	0.700029i	−0.956265	+	0.292501i	$0.905513\pi$
$942$		0			0
$943$	33.2388	+	12.0979i	1.08240	+	0.393962i
$944$	9.43901			0.307214
$945$		0			0
$946$	20.5817			0.669169
$947$	14.5697	+	5.30294i	0.473452	+	0.172322i	0.567715	−	0.823225i	$-0.307827\pi$
$947$	14.5697	+	5.30294i	0.473452	+	0.172322i	−0.0942636	+	0.995547i	$0.530050\pi$
$948$		0			0
$949$	−3.91850	−	3.28801i	−0.127200	−	0.106733i
$950$	−5.55648	+	31.5124i	−0.180276	+	1.02240i
$951$		0			0
$952$	−57.4757	+	48.2278i	−1.86280	+	1.56307i
$953$	−11.2524	−	19.4898i	−0.364502	−	0.631336i	0.624194	−	0.781269i	$-0.285427\pi$
$953$	−11.2524	−	19.4898i	−0.364502	−	0.631336i	−0.988696	+	0.149933i	$0.952094\pi$
$954$		0			0
$955$	3.27497	−	5.67241i	0.105975	−	0.183555i
$956$	0.352891	+	2.00134i	0.0114133	+	0.0647281i
$957$		0			0
$958$	−7.10354	+	2.58548i	−0.229505	+	0.0835330i
$959$	15.4577	−	5.62613i	0.499154	−	0.181677i
$960$		0			0
$961$	−4.73236	−	26.8386i	−0.152657	−	0.865760i
$962$	−6.82548	+	11.8221i	−0.220062	+	0.381159i
$963$		0			0
$964$	−1.48293	−	2.56850i	−0.0477618	−	0.0827259i
$965$	−8.01747	+	6.72745i	−0.258091	+	0.216564i
$966$		0			0
$967$	−7.25995	+	41.1732i	−0.233464	+	1.32404i	0.612359	+	0.790580i	$0.290221\pi$
$967$	−7.25995	+	41.1732i	−0.233464	+	1.32404i	−0.845824	+	0.533463i	$0.820891\pi$
$968$	−7.56196	−	6.34524i	−0.243051	−	0.203944i
$969$		0			0
$970$	−5.45501	−	1.98546i	−0.175150	−	0.0637493i
$971$	35.8662			1.15100			0.575501	−	0.817801i	$-0.304807\pi$
$971$	35.8662			1.15100			0.575501	+	0.817801i	$0.304807\pi$
$972$		0			0
$973$	28.2662			0.906173
$974$	46.8680	+	17.0586i	1.50175	+	0.546591i
$975$		0			0
$976$	−19.2422	−	16.1461i	−0.615927	−	0.516824i
$977$	2.43977	−	13.8366i	0.0780551	−	0.442673i	−0.920585	−	0.390542i	$-0.872288\pi$
$977$	2.43977	−	13.8366i	0.0780551	−	0.442673i	0.998640	−	0.0521307i	$-0.0166012\pi$
$978$		0			0
$979$	−39.2406	+	32.9267i	−1.25413	+	1.05234i
$980$	−0.424525	−	0.735300i	−0.0135610	−	0.0234883i
$981$		0			0
$982$	−24.1587	+	41.8441i	−0.770935	+	1.33530i
$983$	−3.07169	−	17.4204i	−0.0979716	−	0.555624i	−0.993796	−	0.111217i	$-0.964525\pi$
$983$	−3.07169	−	17.4204i	−0.0979716	−	0.555624i	0.895825	−	0.444408i	$-0.146586\pi$
$984$		0			0
$985$	−3.78756	+	1.37856i	−0.120682	+	0.0439246i
$986$	−30.7769	+	11.2019i	−0.980135	+	0.356740i
$987$		0			0
$988$	1.02899	+	5.83569i	0.0327365	+	0.185658i
$989$	−20.9531	+	36.2918i	−0.666269	+	1.15401i
$990$		0			0
$991$	−16.4479	−	28.4886i	−0.522485	−	0.904970i	−0.999658	−	0.0261608i	$-0.991672\pi$
$991$	−16.4479	−	28.4886i	−0.522485	−	0.904970i	0.477173	−	0.878809i	$-0.341662\pi$
$992$	2.87830	−	2.41518i	0.0913862	−	0.0766821i
$993$		0			0
$994$	−4.18479	+	23.7331i	−0.132734	+	0.752769i
$995$	−0.890623	−	0.747321i	−0.0282346	−	0.0236917i
$996$		0			0
$997$	−18.8002	−	6.84273i	−0.595410	−	0.216711i	0.0266973	−	0.999644i	$-0.491501\pi$
$997$	−18.8002	−	6.84273i	−0.595410	−	0.216711i	−0.622107	+	0.782932i	$0.713723\pi$
$998$	−43.3907			−1.37351
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.q.568.2		12
3.2	odd	2	inner	729.2.e.q.568.1		12
9.2	odd	6		729.2.e.r.82.2		12
9.4	even	3		729.2.e.m.325.1		12
9.5	odd	6		729.2.e.m.325.2		12
9.7	even	3		729.2.e.r.82.1		12
27.2	odd	18		729.2.e.m.406.2		12
27.4	even	9		729.2.c.c.244.5		12
27.5	odd	18		729.2.c.c.487.2		12
27.7	even	9	inner	729.2.e.q.163.2		12
27.11	odd	18		729.2.e.r.649.2		12
27.13	even	9		729.2.a.c.1.2	✓	6
27.14	odd	18		729.2.a.c.1.5	yes	6
27.16	even	9		729.2.e.r.649.1		12
27.20	odd	18	inner	729.2.e.q.163.1		12
27.22	even	9		729.2.c.c.487.5		12
27.23	odd	18		729.2.c.c.244.2		12
27.25	even	9		729.2.e.m.406.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.c.1.2	✓	6	27.13	even	9
729.2.a.c.1.5	yes	6	27.14	odd	18
729.2.c.c.244.2		12	27.23	odd	18
729.2.c.c.244.5		12	27.4	even	9
729.2.c.c.487.2		12	27.5	odd	18
729.2.c.c.487.5		12	27.22	even	9
729.2.e.m.325.1		12	9.4	even	3
729.2.e.m.325.2		12	9.5	odd	6
729.2.e.m.406.1		12	27.25	even	9
729.2.e.m.406.2		12	27.2	odd	18
729.2.e.q.163.1		12	27.20	odd	18	inner
729.2.e.q.163.2		12	27.7	even	9	inner
729.2.e.q.568.1		12	3.2	odd	2	inner
729.2.e.q.568.2		12	1.1	even	1	trivial
729.2.e.r.82.1		12	9.7	even	3
729.2.e.r.82.2		12	9.2	odd	6
729.2.e.r.649.1		12	27.16	even	9
729.2.e.r.649.2		12	27.11	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
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

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