LMFDB - Embedded newform 729.2.e.t.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:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 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			$1.37340i$ of defining polynomial
Character	$\chi$	$=$	729.568
Dual form			729.2.e.t.163.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.54193 + 0.925187i) q^{2} +(4.07335 + 3.41794i) q^{4} +(0.290407 - 1.64698i) q^{5} +(0.383475 - 0.321774i) q^{7} +(4.48686 + 7.77147i) q^{8} +O(q^{10})$	\(q+(2.54193 + 0.925187i) q^{2} +(4.07335 + 3.41794i) q^{4} +(0.290407 - 1.64698i) q^{5} +(0.383475 - 0.321774i) q^{7} +(4.48686 + 7.77147i) q^{8} +(2.26195 - 3.91782i) q^{10} +(0.333008 + 1.88858i) q^{11} +(-2.92473 + 1.06452i) q^{13} +(1.27247 - 0.463140i) q^{14} +(2.36851 + 13.4325i) q^{16} +(1.33234 - 2.30767i) q^{17} +(-2.89832 - 5.02003i) q^{19} +(6.81220 - 5.71612i) q^{20} +(-0.900809 + 5.10874i) q^{22} +(3.55894 + 2.98631i) q^{23} +(2.07026 + 0.753515i) q^{25} -8.41934 q^{26} +2.66183 q^{28} +(-2.45736 - 0.894407i) q^{29} +(-3.53499 - 2.96621i) q^{31} +(-3.29045 + 18.6611i) q^{32} +(5.52173 - 4.63328i) q^{34} +(-0.418591 - 0.725020i) q^{35} +(2.42934 - 4.20773i) q^{37} +(-2.72285 - 15.4421i) q^{38} +(14.1024 - 5.13287i) q^{40} +(-10.8517 + 3.94970i) q^{41} +(-1.56359 - 8.86754i) q^{43} +(-5.09861 + 8.83106i) q^{44} +(6.28369 + 10.8837i) q^{46} +(-5.23380 + 4.39168i) q^{47} +(-1.17202 + 6.64687i) q^{49} +(4.56532 + 3.83076i) q^{50} +(-15.5519 - 5.66043i) q^{52} +5.43322 q^{53} +3.20716 q^{55} +(4.22125 + 1.53641i) q^{56} +(-5.41895 - 4.54704i) q^{58} +(0.380517 - 2.15802i) q^{59} +(5.24000 - 4.39688i) q^{61} +(-6.24140 - 10.8104i) q^{62} +(-11.9893 + 20.7661i) q^{64} +(0.903872 + 5.12611i) q^{65} +(-11.7307 + 4.26964i) q^{67} +(13.3146 - 4.84610i) q^{68} +(-0.393249 - 2.23022i) q^{70} +(-1.41784 + 2.45578i) q^{71} +(-4.96749 - 8.60394i) q^{73} +(10.0681 - 8.44817i) q^{74} +(5.35234 - 30.3546i) q^{76} +(0.735397 + 0.617071i) q^{77} +(-4.99091 - 1.81654i) q^{79} +22.8109 q^{80} -31.2385 q^{82} +(-2.56362 - 0.933082i) q^{83} +(-3.41377 - 2.86449i) q^{85} +(4.22960 - 23.9873i) q^{86} +(-13.1829 + 11.0618i) q^{88} +(5.60945 + 9.71585i) q^{89} +(-0.779029 + 1.34932i) q^{91} +(4.28977 + 24.3285i) q^{92} +(-17.3671 + 6.32110i) q^{94} +(-9.10957 + 3.31561i) q^{95} +(-1.19629 - 6.78448i) q^{97} +(-9.12879 + 15.8115i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8	$ 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8} - 6 q^{10} - 15 q^{11} - 3 q^{13} - 21 q^{14} + 9 q^{16} - 9 q^{17} - 12 q^{19} - 3 q^{20} + 33 q^{22} + 15 q^{23} - 12 q^{25} - 48 q^{26} + 6 q^{28} - 6 q^{29} - 12 q^{31} - 27 q^{32} + 27 q^{34} + 30 q^{35} - 3 q^{37} - 39 q^{38} + 24 q^{40} - 39 q^{41} + 24 q^{43} - 33 q^{44} + 3 q^{46} - 42 q^{47} - 30 q^{49} - 15 q^{50} - 45 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} - 30 q^{58} + 15 q^{59} - 3 q^{61} - 30 q^{62} - 6 q^{64} - 6 q^{65} - 3 q^{67} + 36 q^{68} - 75 q^{70} - 12 q^{73} + 60 q^{74} + 30 q^{76} + 33 q^{77} + 33 q^{79} + 42 q^{80} - 42 q^{82} - 33 q^{83} - 18 q^{85} - 30 q^{86} - 42 q^{88} - 9 q^{89} - 18 q^{91} + 33 q^{92} - 66 q^{94} + 12 q^{95} + 15 q^{97} + 18 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8 - 6 * q^10 - 15 * q^11 - 3 * q^13 - 21 * q^14 + 9 * q^16 - 9 * q^17 - 12 * q^19 - 3 * q^20 + 33 * q^22 + 15 * q^23 - 12 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 - 12 * q^31 - 27 * q^32 + 27 * q^34 + 30 * q^35 - 3 * q^37 - 39 * q^38 + 24 * q^40 - 39 * q^41 + 24 * q^43 - 33 * q^44 + 3 * q^46 - 42 * q^47 - 30 * q^49 - 15 * q^50 - 45 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 - 30 * q^58 + 15 * q^59 - 3 * q^61 - 30 * q^62 - 6 * q^64 - 6 * q^65 - 3 * q^67 + 36 * q^68 - 75 * q^70 - 12 * q^73 + 60 * q^74 + 30 * q^76 + 33 * q^77 + 33 * q^79 + 42 * q^80 - 42 * q^82 - 33 * q^83 - 18 * q^85 - 30 * q^86 - 42 * q^88 - 9 * q^89 - 18 * q^91 + 33 * q^92 - 66 * q^94 + 12 * q^95 + 15 * q^97 + 18 * q^98

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 $

$2$	2.54193	+	0.925187i	1.79742	+	0.654206i	0.998615	+	0.0526096i	$0.0167539\pi$
$2$	2.54193	+	0.925187i	1.79742	+	0.654206i	0.798800	+	0.601596i	$0.205468\pi$
$3$		0			0
$3$		0			0
$4$	4.07335	+	3.41794i	2.03667	+	1.70897i
$5$	0.290407	−	1.64698i	0.129874	−	0.736551i	−0.848419	−	0.529325i	$-0.822445\pi$
$5$	0.290407	−	1.64698i	0.129874	−	0.736551i	0.978293	−	0.207226i	$-0.0664436\pi$
$6$		0			0
$7$	0.383475	−	0.321774i	0.144940	−	0.121619i	−0.567435	−	0.823418i	$-0.692064\pi$
$7$	0.383475	−	0.321774i	0.144940	−	0.121619i	0.712375	+	0.701799i	$0.247620\pi$
$8$	4.48686	+	7.77147i	1.58634	+	2.74763i
$9$		0			0
$10$	2.26195	−	3.91782i	0.715293	−	1.23892i
$11$	0.333008	+	1.88858i	0.100406	+	0.569429i	0.992956	+	0.118482i	$0.0378027\pi$
$11$	0.333008	+	1.88858i	0.100406	+	0.569429i	−0.892550	+	0.450948i	$0.851086\pi$
$12$		0			0
$13$	−2.92473	+	1.06452i	−0.811175	+	0.295243i	−0.714109	−	0.700034i	$-0.753168\pi$
$13$	−2.92473	+	1.06452i	−0.811175	+	0.295243i	−0.0970658	+	0.995278i	$0.530946\pi$
$14$	1.27247	−	0.463140i	0.340081	−	0.123779i
$15$		0			0
$16$	2.36851	+	13.4325i	0.592129	+	3.35813i
$17$	1.33234	−	2.30767i	0.323139	−	0.559693i	−0.657995	−	0.753022i	$-0.728595\pi$
$17$	1.33234	−	2.30767i	0.323139	−	0.559693i	0.981134	+	0.193329i	$0.0619285\pi$
$18$		0			0
$19$	−2.89832	−	5.02003i	−0.664920	−	1.15167i	−0.979307	−	0.202380i	$-0.935132\pi$
$19$	−2.89832	−	5.02003i	−0.664920	−	1.15167i	0.314387	−	0.949295i	$-0.398201\pi$
$20$	6.81220	−	5.71612i	1.52325	−	1.27816i
$21$		0			0
$22$	−0.900809	+	5.10874i	−0.192053	+	1.08919i
$23$	3.55894	+	2.98631i	0.742091	+	0.622688i	0.933398	−	0.358842i	$-0.116828\pi$
$23$	3.55894	+	2.98631i	0.742091	+	0.622688i	−0.191308	+	0.981530i	$0.561273\pi$
$24$		0			0
$25$	2.07026	+	0.753515i	0.414053	+	0.150703i
$26$	−8.41934			−1.65117
$27$		0			0
$28$	2.66183			0.503039
$29$	−2.45736	−	0.894407i	−0.456321	−	0.166087i	0.103625	−	0.994616i	$-0.466956\pi$
$29$	−2.45736	−	0.894407i	−0.456321	−	0.166087i	−0.559946	+	0.828529i	$0.689178\pi$
$30$		0			0
$31$	−3.53499	−	2.96621i	−0.634903	−	0.532747i	0.267545	−	0.963545i	$-0.413788\pi$
$31$	−3.53499	−	2.96621i	−0.634903	−	0.532747i	−0.902448	+	0.430798i	$0.858232\pi$
$32$	−3.29045	+	18.6611i	−0.581674	+	3.29884i
$33$		0			0
$34$	5.52173	−	4.63328i	0.946969	−	0.794602i
$35$	−0.418591	−	0.725020i	−0.0707547	−	0.122551i
$36$		0			0
$37$	2.42934	−	4.20773i	0.399381	−	0.691747i	−0.594269	−	0.804266i	$-0.702559\pi$
$37$	2.42934	−	4.20773i	0.399381	−	0.691747i	0.993650	+	0.112519i	$0.0358919\pi$
$38$	−2.72285	−	15.4421i	−0.441705	−	2.50503i
$39$		0			0
$40$	14.1024	−	5.13287i	2.22979	−	0.811578i
$41$	−10.8517	+	3.94970i	−1.69475	+	0.616840i	−0.995211	−	0.0977502i	$-0.968835\pi$
$41$	−10.8517	+	3.94970i	−1.69475	+	0.616840i	−0.699543	+	0.714590i	$0.746613\pi$
$42$		0			0
$43$	−1.56359	−	8.86754i	−0.238445	−	1.35229i	−0.835236	−	0.549891i	$-0.814669\pi$
$43$	−1.56359	−	8.86754i	−0.238445	−	1.35229i	0.596792	−	0.802396i	$-0.296442\pi$
$44$	−5.09861	+	8.83106i	−0.768645	+	1.33133i
$45$		0			0
$46$	6.28369	+	10.8837i	0.926479	+	1.60471i
$47$	−5.23380	+	4.39168i	−0.763428	+	0.640592i	−0.939017	−	0.343872i	$-0.888262\pi$
$47$	−5.23380	+	4.39168i	−0.763428	+	0.640592i	0.175589	+	0.984464i	$0.443817\pi$
$48$		0			0
$49$	−1.17202	+	6.64687i	−0.167432	+	0.949553i
$50$	4.56532	+	3.83076i	0.645634	+	0.541752i
$51$		0			0
$52$	−15.5519	−	5.66043i	−2.15666	−	0.784960i
$53$	5.43322			0.746309			0.373155	−	0.927769i	$-0.378276\pi$
$53$	5.43322			0.746309			0.373155	+	0.927769i	$0.378276\pi$
$54$		0			0
$55$	3.20716			0.432454
$56$	4.22125	+	1.53641i	0.564089	+	0.205311i
$57$		0			0
$58$	−5.41895	−	4.54704i	−0.711543	−	0.597055i
$59$	0.380517	−	2.15802i	0.0495392	−	0.280950i	−0.949968	−	0.312348i	$-0.898885\pi$
$59$	0.380517	−	2.15802i	0.0495392	−	0.280950i	0.999507	+	0.0313973i	$0.00999570\pi$
$60$		0			0
$61$	5.24000	−	4.39688i	0.670914	−	0.562963i	−0.242422	−	0.970171i	$-0.577942\pi$
$61$	5.24000	−	4.39688i	0.670914	−	0.562963i	0.913336	+	0.407208i	$0.133497\pi$
$62$	−6.24140	−	10.8104i	−0.792659	−	1.37293i
$63$		0			0
$64$	−11.9893	+	20.7661i	−1.49866	+	2.59576i
$65$	0.903872	+	5.12611i	0.112111	+	0.635816i
$66$		0			0
$67$	−11.7307	+	4.26964i	−1.43314	+	0.521620i	−0.937829	−	0.347097i	$-0.887167\pi$
$67$	−11.7307	+	4.26964i	−1.43314	+	0.521620i	−0.495309	+	0.868717i	$0.664945\pi$
$68$	13.3146	−	4.84610i	1.61463	−	0.587677i
$69$		0			0
$70$	−0.393249	−	2.23022i	−0.0470022	−	0.266563i
$71$	−1.41784	+	2.45578i	−0.168267	+	0.291447i	−0.937811	−	0.347147i	$-0.887150\pi$
$71$	−1.41784	+	2.45578i	−0.168267	+	0.291447i	0.769544	+	0.638594i	$0.220484\pi$
$72$		0			0
$73$	−4.96749	−	8.60394i	−0.581400	−	1.00701i	−0.995314	−	0.0966986i	$-0.969172\pi$
$73$	−4.96749	−	8.60394i	−0.581400	−	1.00701i	0.413913	−	0.910316i	$-0.364162\pi$
$74$	10.0681	−	8.44817i	1.17040	−	0.982080i
$75$		0			0
$76$	5.35234	−	30.3546i	0.613955	−	3.48191i
$77$	0.735397	+	0.617071i	0.0838063	+	0.0703218i
$78$		0			0
$79$	−4.99091	−	1.81654i	−0.561521	−	0.204377i	0.0456370	−	0.998958i	$-0.485468\pi$
$79$	−4.99091	−	1.81654i	−0.561521	−	0.204377i	−0.607158	+	0.794581i	$0.707690\pi$
$80$	22.8109			2.55033
$81$		0			0
$82$	−31.2385			−3.44972
$83$	−2.56362	−	0.933082i	−0.281394	−	0.102419i	0.197468	−	0.980309i	$-0.436728\pi$
$83$	−2.56362	−	0.933082i	−0.281394	−	0.102419i	−0.478862	+	0.877890i	$0.658950\pi$
$84$		0			0
$85$	−3.41377	−	2.86449i	−0.370275	−	0.310698i
$86$	4.22960	−	23.9873i	0.456090	−	2.58661i
$87$		0			0
$88$	−13.1829	+	11.0618i	−1.40530	+	1.17919i
$89$	5.60945	+	9.71585i	0.594600	+	1.02988i	0.993603	+	0.112928i	$0.0360230\pi$
$89$	5.60945	+	9.71585i	0.594600	+	1.02988i	−0.399003	+	0.916950i	$0.630644\pi$
$90$		0			0
$91$	−0.779029	+	1.34932i	−0.0816644	+	0.141447i
$92$	4.28977	+	24.3285i	0.447240	+	2.53642i
$93$		0			0
$94$	−17.3671	+	6.32110i	−1.79128	+	0.651971i
$95$	−9.10957	+	3.31561i	−0.934623	+	0.340175i
$96$		0			0
$97$	−1.19629	−	6.78448i	−0.121465	−	0.688860i	−0.983345	−	0.181748i	$-0.941824\pi$
$97$	−1.19629	−	6.78448i	−0.121465	−	0.688860i	0.861881	−	0.507111i	$-0.169287\pi$
$98$	−9.12879	+	15.8115i	−0.922147	+	1.59721i
$99$		0			0
$100$	5.85743	+	10.1454i	0.585743	+	1.01454i
$101$	−2.85708	+	2.39737i	−0.284290	+	0.238547i	−0.773769	−	0.633467i	$-0.781631\pi$
$101$	−2.85708	+	2.39737i	−0.284290	+	0.238547i	0.489480	+	0.872015i	$0.337187\pi$
$102$		0			0
$103$	1.33376	−	7.56411i	0.131419	−	0.745314i	−0.845868	−	0.533393i	$-0.820917\pi$
$103$	1.33376	−	7.56411i	0.131419	−	0.745314i	0.977287	−	0.211921i	$-0.0679720\pi$
$104$	−21.3957	−	17.9531i	−2.09802	−	1.76045i
$105$		0			0
$106$	13.8108	+	5.02674i	1.34143	+	0.488240i
$107$	10.7658			1.04077			0.520383	−	0.853933i	$-0.325789\pi$
$107$	10.7658			1.04077			0.520383	+	0.853933i	$0.325789\pi$
$108$		0			0
$109$	12.2298			1.17141			0.585703	−	0.810526i	$-0.300819\pi$
$109$	12.2298			1.17141			0.585703	+	0.810526i	$0.300819\pi$
$110$	8.15238	+	2.96722i	0.777299	+	0.282914i
$111$		0			0
$112$	5.23050	+	4.38891i	0.494236	+	0.414713i
$113$	0.337563	−	1.91442i	0.0317553	−	0.180093i	−0.964805	−	0.262967i	$-0.915299\pi$
$113$	0.337563	−	1.91442i	0.0317553	−	0.180093i	0.996560	+	0.0828742i	$0.0264100\pi$
$114$		0			0
$115$	5.95192	−	4.99425i	0.555019	−	0.465717i
$116$	−6.95266	−	12.0424i	−0.645538	−	1.11810i
$117$		0			0
$118$	2.96382	−	5.13349i	0.272842	−	0.472576i
$119$	−0.231631	−	1.31365i	−0.0212336	−	0.120422i
$120$		0			0
$121$	6.88076	−	2.50439i	0.625524	−	0.227672i
$122$	17.3877	−	6.32859i	1.57420	−	0.572963i
$123$		0			0
$124$	−4.26091	−	24.1648i	−0.382641	−	2.17006i
$125$	6.02320	−	10.4325i	0.538732	−	0.933110i
$126$		0			0
$127$	−1.17217	−	2.03025i	−0.104013	−	0.180156i	0.809322	−	0.587366i	$-0.199835\pi$
$127$	−1.17217	−	2.03025i	−0.104013	−	0.180156i	−0.913335	+	0.407210i	$0.866502\pi$
$128$	−20.6570	+	17.3333i	−1.82584	+	1.53206i
$129$		0			0
$130$	−2.44503	+	13.8665i	−0.214443	+	1.21617i
$131$	13.1012	+	10.9932i	1.14466	+	0.960480i	0.999581	−	0.0289402i	$-0.00921323\pi$
$131$	13.1012	+	10.9932i	1.14466	+	0.960480i	0.145075	+	0.989421i	$0.453658\pi$
$132$		0			0
$133$	−2.72675	−	0.992455i	−0.236439	−	0.0860568i
$134$	−33.7689			−2.91719
$135$		0			0
$136$	23.9120			2.05044
$137$	13.0872	+	4.76337i	1.11812	+	0.406962i	0.833965	−	0.551817i	$-0.186065\pi$
$137$	13.0872	+	4.76337i	1.11812	+	0.406962i	0.284154	+	0.958779i	$0.408287\pi$
$138$		0			0
$139$	6.06450	+	5.08872i	0.514384	+	0.431619i	0.862669	−	0.505770i	$-0.168791\pi$
$139$	6.06450	+	5.08872i	0.514384	+	0.431619i	−0.348285	+	0.937389i	$0.613236\pi$
$140$	0.773013	−	4.38398i	0.0653315	−	0.370514i
$141$		0			0
$142$	−5.87611	+	4.93064i	−0.493112	+	0.413770i
$143$	−2.98439	−	5.16911i	−0.249567	−	0.432263i
$144$		0			0
$145$	−2.18670	+	3.78748i	−0.181596	+	0.314533i
$146$	−4.66675	−	26.4665i	−0.386223	−	2.19038i
$147$		0			0
$148$	24.2773	−	8.83622i	1.99558	−	0.726333i
$149$	0.684223	−	0.249037i	0.0560537	−	0.0204019i	−0.313841	−	0.949476i	$-0.601616\pi$
$149$	0.684223	−	0.249037i	0.0560537	−	0.0204019i	0.369895	+	0.929074i	$0.379394\pi$
$150$		0			0
$151$	0.753996	+	4.27612i	0.0613593	+	0.347986i	0.999995	+	0.00307656i	$0.000979301\pi$
$151$	0.753996	+	4.27612i	0.0613593	+	0.347986i	−0.938636	+	0.344910i	$0.887910\pi$
$152$	26.0087	−	45.0484i	2.10958	−	3.65390i
$153$		0			0
$154$	1.29842	+	2.24893i	0.104630	+	0.181224i
$155$	−5.91187	+	4.96064i	−0.474852	+	0.398449i
$156$		0			0
$157$	−2.69559	+	15.2874i	−0.215131	+	1.22007i	0.665547	+	0.746356i	$0.268198\pi$
$157$	−2.69559	+	15.2874i	−0.215131	+	1.22007i	−0.880679	+	0.473714i	$0.842913\pi$
$158$	−11.0059	−	9.23504i	−0.875582	−	0.734700i
$159$		0			0
$160$	29.7788	+	10.8386i	2.35422	+	0.856865i
$161$	2.32568			0.183289
$162$		0			0
$163$	8.49738			0.665566			0.332783	−	0.943003i	$-0.392012\pi$
$163$	8.49738			0.665566			0.332783	+	0.943003i	$0.392012\pi$
$164$	−57.7027	−	21.0021i	−4.50582	−	1.63999i
$165$		0			0
$166$	−5.65327	−	4.74366i	−0.438779	−	0.368179i
$167$	−4.01856	+	22.7904i	−0.310965	+	1.76357i	0.283038	+	0.959109i	$0.408658\pi$
$167$	−4.01856	+	22.7904i	−0.310965	+	1.76357i	−0.594003	+	0.804463i	$0.702453\pi$
$168$		0			0
$169$	−2.53771	+	2.12939i	−0.195209	+	0.163799i
$170$	−6.02737	−	10.4397i	−0.462278	−	0.800689i
$171$		0			0
$172$	23.9397	−	41.4648i	1.82539	−	3.16166i
$173$	0.447748	+	2.53931i	0.0340417	+	0.193060i	0.997086	−	0.0762821i	$-0.0243049\pi$
$173$	0.447748	+	2.53931i	0.0340417	+	0.193060i	−0.963045	+	0.269342i	$0.913194\pi$
$174$		0			0
$175$	1.03636	−	0.377203i	0.0783411	−	0.0285138i
$176$	−24.5797	+	8.94628i	−1.85276	+	0.674351i
$177$		0			0
$178$	5.26985	+	29.8868i	0.394992	+	2.24011i
$179$	−4.44806	+	7.70427i	−0.332464	+	0.575844i	−0.982994	−	0.183636i	$-0.941213\pi$
$179$	−4.44806	+	7.70427i	−0.332464	+	0.575844i	0.650530	+	0.759480i	$0.274547\pi$
$180$		0			0
$181$	−3.95592	−	6.85185i	−0.294041	−	0.509294i	0.680720	−	0.732543i	$-0.261667\pi$
$181$	−3.95592	−	6.85185i	−0.294041	−	0.509294i	−0.974761	+	0.223250i	$0.928334\pi$
$182$	−3.22861	+	2.70912i	−0.239320	+	0.200814i
$183$		0			0
$184$	−7.23952	+	41.0573i	−0.533704	+	3.02679i
$185$	−6.22455	−	5.22302i	−0.457638	−	0.384004i
$186$		0			0
$187$	4.80191	+	1.74775i	0.351151	+	0.127808i
$188$	−36.3296			−2.64961
$189$		0			0
$190$	−26.2235			−1.90245
$191$	−14.9386	−	5.43721i	−1.08092	−	0.393423i	−0.260671	−	0.965428i	$-0.583944\pi$
$191$	−14.9386	−	5.43721i	−1.08092	−	0.393423i	−0.820250	+	0.572005i	$0.806166\pi$
$192$		0			0
$193$	−3.51215	−	2.94704i	−0.252810	−	0.212133i	0.507571	−	0.861610i	$-0.330543\pi$
$193$	−3.51215	−	2.94704i	−0.252810	−	0.212133i	−0.760381	+	0.649477i	$0.774988\pi$
$194$	3.23603	−	18.3525i	0.232334	−	1.31763i
$195$		0			0
$196$	−27.4927	+	23.0691i	−1.96376	+	1.64779i
$197$	1.49708	+	2.59303i	0.106663	+	0.184745i	0.914416	−	0.404775i	$-0.132650\pi$
$197$	1.49708	+	2.59303i	0.106663	+	0.184745i	−0.807754	+	0.589520i	$0.799317\pi$
$198$		0			0
$199$	−7.44425	+	12.8938i	−0.527709	+	0.914018i	0.471770	+	0.881722i	$0.343615\pi$
$199$	−7.44425	+	12.8938i	−0.527709	+	0.914018i	−0.999478	+	0.0322965i	$0.989718\pi$
$200$	3.43307	+	19.4699i	0.242755	+	1.37673i
$201$		0			0
$202$	−9.48050	+	3.45062i	−0.667046	+	0.242785i
$203$	−1.23013	+	0.447732i	−0.0863385	+	0.0314246i
$204$		0			0
$205$	3.35366	+	19.0196i	0.234230	+	1.32838i
$206$	10.3885	−	17.9935i	0.723803	−	1.25366i
$207$		0			0
$208$	−21.2264	−	36.7652i	−1.47179	−	2.54921i
$209$	8.51559	−	7.14543i	0.589036	−	0.494260i
$210$		0			0
$211$	2.41006	−	13.6681i	0.165915	−	0.940951i	−0.782201	−	0.623026i	$-0.785903\pi$
$211$	2.41006	−	13.6681i	0.165915	−	0.940951i	0.948116	−	0.317925i	$-0.102986\pi$
$212$	22.1314	+	18.5704i	1.51999	+	1.27542i
$213$		0			0
$214$	27.3658	+	9.96034i	1.87069	+	0.680874i
$215$	−15.0587			−1.02700
$216$		0			0
$217$	−2.31003			−0.156815
$218$	31.0874	+	11.3149i	2.10550	+	0.766340i
$219$		0			0
$220$	13.0639	+	10.9619i	0.880767	+	0.739051i
$221$	−1.44017	+	8.16762i	−0.0968764	+	0.549414i
$222$		0			0
$223$	−5.21828	+	4.37866i	−0.349442	+	0.293216i	−0.800566	−	0.599245i	$-0.795468\pi$
$223$	−5.21828	+	4.37866i	−0.349442	+	0.293216i	0.451124	+	0.892461i	$0.351023\pi$
$224$	4.74283	+	8.21483i	0.316894	+	0.548876i
$225$		0			0
$226$	2.62925	−	4.55400i	0.174895	−	0.302928i
$227$	1.69148	+	9.59286i	0.112267	+	0.636700i	0.988067	+	0.154025i	$0.0492237\pi$
$227$	1.69148	+	9.59286i	0.112267	+	0.636700i	−0.875799	+	0.482675i	$0.839665\pi$
$228$		0			0
$229$	13.1978	−	4.80362i	0.872138	−	0.317432i	0.133105	−	0.991102i	$-0.457505\pi$
$229$	13.1978	−	4.80362i	0.872138	−	0.317432i	0.739032	+	0.673670i	$0.235283\pi$
$230$	19.7500	−	7.18840i	1.30227	−	0.473989i
$231$		0			0
$232$	−4.07498	−	23.1104i	−0.267536	−	1.51727i
$233$	2.66167	−	4.61014i	0.174372	−	0.302020i	−0.765572	−	0.643350i	$-0.777544\pi$
$233$	2.66167	−	4.61014i	0.174372	−	0.302020i	0.939944	+	0.341330i	$0.110877\pi$
$234$		0			0
$235$	5.71307	+	9.89532i	0.372679	+	0.645499i
$236$	8.92597	−	7.48978i	0.581031	−	0.487543i
$237$		0			0
$238$	0.626578	−	3.55350i	0.0406150	−	0.230339i
$239$	−13.6153	−	11.4246i	−0.880700	−	0.738995i	0.0856227	−	0.996328i	$-0.472712\pi$
$239$	−13.6153	−	11.4246i	−0.880700	−	0.738995i	−0.966323	+	0.257332i	$0.917156\pi$
$240$		0			0
$241$	1.88577	+	0.686364i	0.121473	+	0.0442126i	0.402041	−	0.915621i	$-0.368301\pi$
$241$	1.88577	+	0.686364i	0.121473	+	0.0442126i	−0.280568	+	0.959834i	$0.590523\pi$
$242$	19.8075			1.27327
$243$		0			0
$244$	36.3726			2.32852
$245$	10.6069	+	3.86059i	0.677649	+	0.246644i
$246$		0			0
$247$	13.8207	+	11.5970i	0.879391	+	0.737896i
$248$	7.19080	−	40.7810i	0.456616	−	2.58960i
$249$		0			0
$250$	24.9626	−	20.9461i	1.57877	−	1.32475i
$251$	11.7822	+	20.4073i	0.743683	+	1.28810i	0.950808	+	0.309782i	$0.100256\pi$
$251$	11.7822	+	20.4073i	0.743683	+	1.28810i	−0.207125	+	0.978314i	$0.566411\pi$
$252$		0			0
$253$	−4.45473	+	7.71582i	−0.280067	+	0.485090i
$254$	−1.10120	−	6.24523i	−0.0690956	−	0.391860i
$255$		0			0
$256$	−23.4802	+	8.54611i	−1.46751	+	0.534132i
$257$	5.52029	−	2.00922i	0.344346	−	0.125332i	−0.164057	−	0.986451i	$-0.552458\pi$
$257$	5.52029	−	2.00922i	0.344346	−	0.125332i	0.508403	+	0.861119i	$0.330236\pi$
$258$		0			0
$259$	−0.422349	−	2.39526i	−0.0262435	−	0.148834i
$260$	−13.8390	+	23.9698i	−0.858257	+	1.48654i
$261$		0			0
$262$	23.1315	+	40.0650i	1.42907	+	2.47522i
$263$	−16.8362	+	14.1273i	−1.03817	+	0.871125i	−0.991800	−	0.127800i	$-0.959209\pi$
$263$	−16.8362	+	14.1273i	−1.03817	+	0.871125i	−0.0463663	+	0.998925i	$0.514764\pi$
$264$		0			0
$265$	1.57784	−	8.94838i	0.0969260	−	0.549695i
$266$	−6.01300	−	5.04550i	−0.368680	−	0.309360i
$267$		0			0
$268$	−62.3768	−	22.7033i	−3.81027	−	1.38682i
$269$	30.6026			1.86587			0.932937	−	0.360041i	$-0.117237\pi$
$269$	30.6026			1.86587			0.932937	+	0.360041i	$0.117237\pi$
$270$		0			0
$271$	−16.0823			−0.976928			−0.488464	−	0.872584i	$-0.662443\pi$
$271$	−16.0823			−0.976928			−0.488464	+	0.872584i	$0.662443\pi$
$272$	34.1535	+	12.4309i	2.07086	+	0.753732i
$273$		0			0
$274$	28.8599	+	24.2163i	1.74349	+	1.46296i
$275$	−0.733660	+	4.16079i	−0.0442414	+	0.250905i
$276$		0			0
$277$	−15.9441	+	13.3787i	−0.957990	+	0.803849i	−0.980625	−	0.195895i	$-0.937239\pi$
$277$	−15.9441	+	13.3787i	−0.957990	+	0.803849i	0.0226353	+	0.999744i	$0.492794\pi$
$278$	10.7075	+	18.5459i	0.642194	+	1.11231i
$279$		0			0
$280$	3.75631	−	6.50612i	0.224483	−	0.388815i
$281$	−2.12897	−	12.0740i	−0.127004	−	0.720275i	−0.980097	−	0.198517i	$-0.936387\pi$
$281$	−2.12897	−	12.0740i	−0.127004	−	0.720275i	0.853093	−	0.521758i	$-0.174724\pi$
$282$		0			0
$283$	−4.29682	+	1.56391i	−0.255419	+	0.0929650i	−0.466556	−	0.884491i	$-0.654506\pi$
$283$	−4.29682	+	1.56391i	−0.255419	+	0.0929650i	0.211137	+	0.977456i	$0.432283\pi$
$284$	−14.1691	+	5.15712i	−0.840779	+	0.306019i
$285$		0			0
$286$	−2.80371	−	15.9006i	−0.165787	−	0.940224i
$287$	−2.89045	+	5.00641i	−0.170618	+	0.295519i
$288$		0			0
$289$	4.94976	+	8.57324i	0.291162	+	0.504308i
$290$	−9.06257	+	7.60440i	−0.532172	+	0.446546i
$291$		0			0
$292$	9.17348	−	52.0254i	0.536837	−	3.04456i
$293$	−20.0117	−	16.7918i	−1.16910	−	0.980988i	−0.169106	−	0.985598i	$-0.554088\pi$
$293$	−20.0117	−	16.7918i	−1.16910	−	0.980988i	−0.999989	+	0.00460992i	$0.998533\pi$
$294$		0			0
$295$	−3.44371	−	1.25341i	−0.200500	−	0.0729762i
$296$	43.6004			2.53422
$297$		0			0
$298$	1.96965			0.114099
$299$	−13.5879	−	4.94560i	−0.785810	−	0.286011i
$300$		0			0
$301$	−3.45294	−	2.89736i	−0.199024	−	0.167001i
$302$	−2.03961	+	11.5672i	−0.117366	+	0.665617i
$303$		0			0
$304$	60.5670	−	50.8217i	3.47375	−	2.91483i
$305$	−5.71984	−	9.90705i	−0.327517	−	0.567276i
$306$		0			0
$307$	−1.64638	+	2.85162i	−0.0939641	+	0.162751i	−0.909176	−	0.416412i	$-0.863287\pi$
$307$	−1.64638	+	2.85162i	−0.0939641	+	0.162751i	0.815212	+	0.579163i	$0.196621\pi$
$308$	0.886412	+	5.02709i	0.0505080	+	0.286445i
$309$		0			0
$310$	−19.6171	+	7.14003i	−1.11417	+	0.405526i
$311$	32.6944	−	11.8998i	1.85393	−	0.674775i	0.870861	−	0.491529i	$-0.163562\pi$
$311$	32.6944	−	11.8998i	1.85393	−	0.674775i	0.983067	−	0.183246i	$-0.0586606\pi$
$312$		0			0
$313$	1.84550	+	10.4664i	0.104314	+	0.591594i	0.991492	+	0.130167i	$0.0415514\pi$
$313$	1.84550	+	10.4664i	0.104314	+	0.591594i	−0.887178	+	0.461427i	$0.847337\pi$
$314$	−20.9957	+	36.3657i	−1.18486	+	2.05223i
$315$		0			0
$316$	−14.1209	−	24.4580i	−0.794360	−	1.37587i
$317$	11.8739	−	9.96335i	0.666902	−	0.559598i	−0.245244	−	0.969461i	$-0.578868\pi$
$317$	11.8739	−	9.96335i	0.666902	−	0.559598i	0.912147	+	0.409864i	$0.134424\pi$
$318$		0			0
$319$	0.870840	−	4.93878i	0.0487577	−	0.276519i
$320$	30.7195	+	25.7767i	1.71727	+	1.44096i
$321$		0			0
$322$	5.91172	+	2.15169i	0.329447	+	0.119909i
$323$	−15.4461			−0.859446
$324$		0			0
$325$	−6.85710			−0.380363
$326$	21.5997	+	7.86166i	1.19630	+	0.435417i
$327$		0			0
$328$	−79.3851	−	66.6120i	−4.38331	−	3.67803i
$329$	−0.593904	+	3.36820i	−0.0327430	+	0.185695i
$330$		0			0
$331$	−11.1615	+	9.36559i	−0.613490	+	0.514780i	−0.895750	−	0.444559i	$-0.853361\pi$
$331$	−11.1615	+	9.36559i	−0.613490	+	0.514780i	0.282259	+	0.959338i	$0.408916\pi$
$332$	−7.25330	−	12.5631i	−0.398077	−	0.689489i
$333$		0			0
$334$	−31.3002	+	54.2136i	−1.71267	+	2.96644i
$335$	3.62532	+	20.5602i	0.198072	+	1.12332i
$336$		0			0
$337$	19.3716	−	7.05067i	1.05524	−	0.384074i	0.244599	−	0.969624i	$-0.421344\pi$
$337$	19.3716	−	7.05067i	1.05524	−	0.384074i	0.810636	+	0.585550i	$0.199121\pi$
$338$	−8.42077	+	3.06491i	−0.458030	+	0.166709i
$339$		0			0
$340$	−4.11479	−	23.3361i	−0.223156	−	1.26558i
$341$	4.42475	−	7.66390i	0.239614	−	0.415023i
$342$		0			0
$343$	3.44142	+	5.96071i	0.185819	+	0.321848i
$344$	61.8982	−	51.9388i	3.33733	−	2.80035i
$345$		0			0
$346$	−1.21119	+	6.86899i	−0.0651138	+	0.369279i
$347$	16.2275	+	13.6165i	0.871140	+	0.730973i	0.964338	−	0.264674i	$-0.0852645\pi$
$347$	16.2275	+	13.6165i	0.871140	+	0.730973i	−0.0931979	+	0.995648i	$0.529709\pi$
$348$		0			0
$349$	4.34699	+	1.58218i	0.232689	+	0.0846919i	0.455733	−	0.890116i	$-0.349377\pi$
$349$	4.34699	+	1.58218i	0.232689	+	0.0846919i	−0.223044	+	0.974808i	$0.571599\pi$
$350$	2.98333			0.159466
$351$		0			0
$352$	−36.3387			−1.93686
$353$	−12.8206	−	4.66632i	−0.682372	−	0.248363i	−0.0225065	−	0.999747i	$-0.507165\pi$
$353$	−12.8206	−	4.66632i	−0.682372	−	0.248363i	−0.659866	+	0.751383i	$0.729387\pi$
$354$		0			0
$355$	3.63286	+	3.04833i	0.192812	+	0.161788i
$356$	−10.3590	+	58.7488i	−0.549026	+	3.11368i
$357$		0			0
$358$	−18.4346	+	15.4684i	−0.974297	+	0.817532i
$359$	−14.1223	−	24.4606i	−0.745349	−	1.29098i	−0.950032	−	0.312153i	$-0.898950\pi$
$359$	−14.1223	−	24.4606i	−0.745349	−	1.29098i	0.204683	−	0.978828i	$-0.434384\pi$
$360$		0			0
$361$	−7.30050	+	12.6448i	−0.384237	+	0.665517i
$362$	−3.71642	−	21.0769i	−0.195331	−	1.10778i
$363$		0			0
$364$	−7.78514	+	2.83356i	−0.408052	+	0.148519i
$365$	−15.6131	+	5.68270i	−0.817226	+	0.297446i
$366$		0			0
$367$	6.05688	+	34.3503i	0.316167	+	1.79307i	0.565601	+	0.824679i	$0.308644\pi$
$367$	6.05688	+	34.3503i	0.316167	+	1.79307i	−0.249434	+	0.968392i	$0.580245\pi$
$368$	−31.6842	+	54.8786i	−1.65165	+	2.86075i
$369$		0			0
$370$	−10.9901	−	19.0354i	−0.571348	−	0.989604i
$371$	2.08350	−	1.74827i	0.108170	−	0.0907655i
$372$		0			0
$373$	0.531266	−	3.01296i	0.0275079	−	0.156005i	−0.967960	−	0.251105i	$-0.919206\pi$
$373$	0.531266	−	3.01296i	0.0275079	−	0.156005i	0.995468	+	0.0951001i	$0.0303171\pi$
$374$	10.5891	+	8.88533i	0.547551	+	0.459450i
$375$		0			0
$376$	−57.6131	−	20.9694i	−2.97117	−	1.08142i
$377$	8.13924			0.419192
$378$		0			0
$379$	−7.67705			−0.394344			−0.197172	−	0.980369i	$-0.563176\pi$
$379$	−7.67705			−0.394344			−0.197172	+	0.980369i	$0.563176\pi$
$380$	−48.4390	−	17.6304i	−2.48487	−	0.904419i
$381$		0			0
$382$	−32.9425	−	27.6420i	−1.68548	−	1.41429i
$383$	−1.79933	+	10.2045i	−0.0919416	+	0.521427i	0.903700	+	0.428166i	$0.140840\pi$
$383$	−1.79933	+	10.2045i	−0.0919416	+	0.521427i	−0.995642	+	0.0932607i	$0.970271\pi$
$384$		0			0
$385$	1.22987	−	1.03198i	0.0626798	−	0.0525946i
$386$	−6.20106	−	10.7406i	−0.315626	−	0.546680i
$387$		0			0
$388$	18.3161	−	31.7244i	0.929858	−	1.61056i
$389$	0.0741393	+	0.420465i	0.00375901	+	0.0213184i	0.986630	−	0.162979i	$-0.0521102\pi$
$389$	0.0741393	+	0.420465i	0.00375901	+	0.0213184i	−0.982871	+	0.184297i	$0.940999\pi$
$390$		0			0
$391$	11.6331	−	4.23411i	0.588313	−	0.214128i
$392$	−56.9146	+	20.7152i	−2.87462	+	1.04628i
$393$		0			0
$394$	1.40645	+	7.97637i	0.0708559	+	0.401844i
$395$	−4.44119	+	7.69238i	−0.223461	+	0.387045i
$396$		0			0
$397$	13.5445	+	23.4598i	0.679781	+	1.17741i	0.975047	+	0.221999i	$0.0712583\pi$
$397$	13.5445	+	23.4598i	0.679781	+	1.17741i	−0.295266	+	0.955415i	$0.595408\pi$
$398$	−30.8519	+	25.8879i	−1.54647	+	1.29764i
$399$		0			0
$400$	−5.21814	+	29.5936i	−0.260907	+	1.47968i
$401$	−22.4914	−	18.8725i	−1.12317	−	0.942450i	−0.124408	−	0.992231i	$-0.539703\pi$
$401$	−22.4914	−	18.8725i	−1.12317	−	0.942450i	−0.998760	+	0.0497810i	$0.984148\pi$
$402$		0			0
$403$	13.4965	+	4.91232i	0.672308	+	0.244700i
$404$	−19.8319			−0.986675
$405$		0			0
$406$	−3.54115			−0.175744
$407$	8.75565	+	3.18680i	0.434001	+	0.157964i
$408$		0			0
$409$	−15.4618	−	12.9740i	−0.764536	−	0.641522i	0.174767	−	0.984610i	$-0.444083\pi$
$409$	−15.4618	−	12.9740i	−0.764536	−	0.641522i	−0.939303	+	0.343088i	$0.888527\pi$
$410$	−9.07187	+	51.4491i	−0.448028	+	2.54089i
$411$		0			0
$412$	31.2865	−	26.2525i	1.54138	−	1.29337i
$413$	−0.548476	−	0.949988i	−0.0269887	−	0.0467459i
$414$		0			0
$415$	−2.28126	+	3.95126i	−0.111983	+	0.193960i
$416$	−10.2413	−	58.0813i	−0.502121	−	2.84767i
$417$		0			0
$418$	28.2569	−	10.2847i	1.38209	−	0.503039i
$419$	22.9006	−	8.33514i	1.11877	−	0.407198i	0.284566	−	0.958657i	$-0.408151\pi$
$419$	22.9006	−	8.33514i	1.11877	−	0.407198i	0.834203	+	0.551458i	$0.185928\pi$
$420$		0			0
$421$	−4.54516	−	25.7769i	−0.221518	−	1.25629i	−0.869232	−	0.494405i	$-0.835386\pi$
$421$	−4.54516	−	25.7769i	−0.221518	−	1.25629i	0.647714	−	0.761884i	$-0.275725\pi$
$422$	18.7717	−	32.5136i	0.913794	−	1.58274i
$423$		0			0
$424$	24.3781	+	42.2240i	1.18390	+	2.05058i
$425$	4.49715	−	3.77356i	0.218144	−	0.183045i
$426$		0			0
$427$	0.594608	−	3.37219i	0.0287751	−	0.163192i
$428$	43.8527	+	36.7967i	2.11970	+	1.77864i
$429$		0			0
$430$	−38.2782	−	13.9321i	−1.84594	−	0.671867i
$431$	−31.9185			−1.53746			−0.768731	−	0.639572i	$-0.779111\pi$
$431$	−31.9185			−1.53746			−0.768731	+	0.639572i	$0.779111\pi$
$432$		0			0
$433$	0.0123080			0.000591484			0.000295742	−	1.00000i	$-0.499906\pi$
$433$	0.0123080			0.000591484			0.000295742		1.00000i	$0.499906\pi$
$434$	−5.87193	−	2.13721i	−0.281862	−	0.102589i
$435$		0			0
$436$	49.8164	+	41.8009i	2.38577	+	2.00190i
$437$	4.67642	−	26.5213i	0.223703	−	1.26868i
$438$		0			0
$439$	4.06372	−	3.40986i	0.193951	−	0.162744i	−0.540641	−	0.841253i	$-0.681818\pi$
$439$	4.06372	−	3.40986i	0.193951	−	0.162744i	0.734592	+	0.678510i	$0.237374\pi$
$440$	14.3901	+	24.9244i	0.686020	+	1.18822i
$441$		0			0
$442$	−11.2174	+	19.4291i	−0.533557	+	0.924147i
$443$	−7.06684	−	40.0781i	−0.335756	−	1.90417i	−0.419639	−	0.907691i	$-0.637843\pi$
$443$	−7.06684	−	40.0781i	−0.335756	−	1.90417i	0.0838834	−	0.996476i	$-0.473268\pi$
$444$		0			0
$445$	17.6308	−	6.41709i	0.835780	−	0.304199i
$446$	−17.3156	+	6.30235i	−0.819916	+	0.298425i
$447$		0			0
$448$	2.08438	+	11.8211i	0.0984778	+	0.558496i
$449$	7.71401	−	13.3611i	0.364047	−	0.630547i	−0.624576	−	0.780964i	$-0.714728\pi$
$449$	7.71401	−	13.3611i	0.364047	−	0.630547i	0.988623	+	0.150417i	$0.0480615\pi$
$450$		0			0
$451$	−11.0731	−	19.1791i	−0.521410	−	0.903109i
$452$	7.91838	−	6.64431i	0.372449	−	0.312522i
$453$		0			0
$454$	−4.57556	+	25.9493i	−0.214742	+	1.21786i
$455$	1.99606	+	1.67489i	0.0935767	+	0.0785202i
$456$		0			0
$457$	−2.24469	−	0.816999i	−0.105002	−	0.0382176i	0.288985	−	0.957334i	$-0.406682\pi$
$457$	−2.24469	−	0.816999i	−0.105002	−	0.0382176i	−0.393987	+	0.919116i	$0.628904\pi$
$458$	37.9922			1.77526
$459$		0			0
$460$	41.3143			1.92629
$461$	30.5248	+	11.1101i	1.42168	+	0.517451i	0.934536	−	0.355869i	$-0.115815\pi$
$461$	30.5248	+	11.1101i	1.42168	+	0.517451i	0.487148	+	0.873319i	$0.338037\pi$
$462$		0			0
$463$	25.9525	+	21.7767i	1.20611	+	1.01205i	0.999434	+	0.0336404i	$0.0107101\pi$
$463$	25.9525	+	21.7767i	1.20611	+	1.01205i	0.206679	+	0.978409i	$0.433734\pi$
$464$	6.19383	−	35.1270i	0.287541	−	1.63073i
$465$		0			0
$466$	11.0310	−	9.25612i	0.511002	−	0.428781i
$467$	−6.90133	−	11.9535i	−0.319356	−	0.553140i	0.660998	−	0.750388i	$-0.270133\pi$
$467$	−6.90133	−	11.9535i	−0.319356	−	0.553140i	−0.980354	+	0.197247i	$0.936800\pi$
$468$		0			0
$469$	−3.12459	+	5.41195i	−0.144280	+	0.249901i
$470$	5.36719	+	30.4389i	0.247570	+	1.40404i
$471$		0			0
$472$	18.4783	−	6.72556i	0.850534	−	0.309569i
$473$	16.2264	−	5.90593i	0.746091	−	0.271555i
$474$		0			0
$475$	−2.21762	−	12.5767i	−0.101751	−	0.577060i
$476$	3.54645	−	6.14264i	0.162551	−	0.281547i
$477$		0			0
$478$	−24.0392	−	41.6372i	−1.09953	−	1.90444i
$479$	−4.51286	+	3.78674i	−0.206198	+	0.173020i	−0.740038	−	0.672565i	$-0.765193\pi$
$479$	−4.51286	+	3.78674i	−0.206198	+	0.173020i	0.533841	+	0.845585i	$0.320748\pi$
$480$		0			0
$481$	−2.62596	+	14.8926i	−0.119734	+	0.679042i
$482$	4.15848	+	3.48938i	0.189413	+	0.158937i
$483$		0			0
$484$	36.5876	+	13.3168i	1.66307	+	0.605309i
$485$	−11.5213			−0.523155
$486$		0			0
$487$	29.0299			1.31547			0.657736	−	0.753249i	$-0.271514\pi$
$487$	29.0299			1.31547			0.657736	+	0.753249i	$0.271514\pi$
$488$	57.6814	+	20.9943i	2.61111	+	0.950368i
$489$		0			0
$490$	23.3902	+	19.6267i	1.05666	+	0.886644i
$491$	−0.761188	+	4.31691i	−0.0343519	+	0.194820i	−0.997154	−	0.0753869i	$-0.975981\pi$
$491$	−0.761188	+	4.31691i	−0.0343519	+	0.194820i	0.962802	+	0.270206i	$0.0870919\pi$
$492$		0			0
$493$	−5.33803	+	4.47914i	−0.240413	+	0.201730i
$494$	24.4019	+	42.2654i	1.09789	+	1.90161i
$495$		0			0
$496$	31.4710	−	54.5093i	1.41309	−	2.44754i
$497$	0.246497	+	1.39795i	0.0110569	+	0.0627068i
$498$		0			0
$499$	−33.2120	+	12.0882i	−1.48677	+	0.541142i	−0.952598	−	0.304231i	$-0.901600\pi$
$499$	−33.2120	+	12.0882i	−1.48677	+	0.541142i	−0.534177	+	0.845373i	$0.679378\pi$
$500$	60.1922	−	21.9082i	2.69188	−	0.979764i
$501$		0			0
$502$	11.0688	+	62.7746i	0.494027	+	2.80177i
$503$	−4.18829	+	7.25434i	−0.186747	+	0.323455i	−0.944164	−	0.329477i	$-0.893128\pi$
$503$	−4.18829	+	7.25434i	−0.186747	+	0.323455i	0.757417	+	0.652932i	$0.226461\pi$
$504$		0			0
$505$	3.11870	+	5.40175i	0.138780	+	0.240375i
$506$	−18.4622	+	15.4916i	−0.820745	+	0.688687i
$507$		0			0
$508$	2.16465	−	12.2763i	0.0960406	−	0.544673i
$509$	2.94389	+	2.47021i	0.130485	+	0.109490i	0.705695	−	0.708516i	$-0.250635\pi$
$509$	2.94389	+	2.47021i	0.130485	+	0.109490i	−0.575209	+	0.818006i	$0.695079\pi$
$510$		0			0
$511$	−4.67343	−	1.70099i	−0.206740	−	0.0752473i
$512$	−13.6601			−0.603699
$513$		0			0
$514$	15.8911			0.700925
$515$	−12.0706	−	4.39333i	−0.531894	−	0.193593i
$516$		0			0
$517$	−10.0369	−	8.42200i	−0.441425	−	0.370399i
$518$	1.14248	−	6.47933i	0.0501977	−	0.284685i
$519$		0			0
$520$	−35.7819	+	30.0245i	−1.56914	+	1.31666i
$521$	9.82615	+	17.0194i	0.430491	+	0.745633i	0.996916	−	0.0784810i	$-0.0250070\pi$
$521$	9.82615	+	17.0194i	0.430491	+	0.745633i	−0.566424	+	0.824114i	$0.691674\pi$
$522$		0			0
$523$	19.8051	−	34.3035i	0.866018	−	1.49999i	−1.41543e−5	−	1.00000i	$-0.500005\pi$
$523$	19.8051	−	34.3035i	0.866018	−	1.49999i	0.866032	−	0.499988i	$-0.166662\pi$
$524$	15.7915	+	89.5582i	0.689856	+	3.91237i
$525$		0			0
$526$	−55.8669	+	20.3339i	−2.43591	+	0.886599i
$527$	−11.5548	+	4.20562i	−0.503337	+	0.183200i
$528$		0			0
$529$	−0.245870	−	1.39440i	−0.0106900	−	0.0606259i
$530$	12.2897	−	21.2864i	0.533830	−	0.924620i
$531$		0			0
$532$	−7.71483	−	13.3625i	−0.334480	−	0.579337i
$533$	27.5339	−	23.1037i	1.19262	−	1.00073i
$534$		0			0
$535$	3.12645	−	17.7310i	0.135168	−	0.766576i
$536$	−85.8156	−	72.0078i	−3.70667	−	3.11026i
$537$		0			0
$538$	77.7896	+	28.3131i	3.35375	+	1.22066i
$539$	−12.9435			−0.557514
$540$		0			0
$541$	−41.8257			−1.79823			−0.899115	−	0.437713i	$-0.855788\pi$
$541$	−41.8257			−1.79823			−0.899115	+	0.437713i	$0.855788\pi$
$542$	−40.8800	−	14.8791i	−1.75595	−	0.639112i
$543$		0			0
$544$	38.6796	+	32.4561i	1.65838	+	1.39154i
$545$	3.55162	−	20.1423i	0.152135	−	0.862800i
$546$		0			0
$547$	−13.0490	+	10.9495i	−0.557937	+	0.468165i	−0.877618	−	0.479360i	$-0.840869\pi$
$547$	−13.0490	+	10.9495i	−0.557937	+	0.468165i	0.319681	+	0.947525i	$0.396424\pi$
$548$	37.0280	+	64.1343i	1.58176	+	2.73968i
$549$		0			0
$550$	−5.71442	+	9.89767i	−0.243664	+	0.422038i
$551$	2.63227	+	14.9283i	0.112138	+	0.635968i
$552$		0			0
$553$	−2.49840	+	0.909345i	−0.106243	+	0.0386693i
$554$	−52.9066	+	19.2564i	−2.24779	+	0.818128i
$555$		0			0
$556$	7.30985	+	41.4562i	0.310007	+	1.75813i
$557$	−16.8840	+	29.2439i	−0.715398	+	1.23911i	0.247408	+	0.968911i	$0.420421\pi$
$557$	−16.8840	+	29.2439i	−0.715398	+	1.23911i	−0.962806	+	0.270194i	$0.912912\pi$
$558$		0			0
$559$	14.0127	+	24.2707i	0.592674	+	1.02654i
$560$	8.74740	−	7.33994i	0.369645	−	0.310169i
$561$		0			0
$562$	5.75902	−	32.6610i	0.242929	−	1.37772i
$563$	17.3978	+	14.5985i	0.733232	+	0.615254i	0.931011	−	0.364992i	$-0.118928\pi$
$563$	17.3978	+	14.5985i	0.733232	+	0.615254i	−0.197779	+	0.980247i	$0.563373\pi$
$564$		0			0
$565$	−3.05497	−	1.11192i	−0.128524	−	0.0467787i
$566$	−12.3691			−0.519913
$567$		0			0
$568$	−25.4466			−1.06772
$569$	10.2158	+	3.71825i	0.428269	+	0.155877i	0.547156	−	0.837031i	$-0.315710\pi$
$569$	10.2158	+	3.71825i	0.428269	+	0.155877i	−0.118887	+	0.992908i	$0.537933\pi$
$570$		0			0
$571$	11.4016	+	9.56706i	0.477141	+	0.400369i	0.849391	−	0.527763i	$-0.176969\pi$
$571$	11.4016	+	9.56706i	0.477141	+	0.400369i	−0.372250	+	0.928132i	$0.621414\pi$
$572$	5.51128	−	31.2560i	0.230438	−	1.30688i
$573$		0			0
$574$	−11.9792	+	10.0517i	−0.500002	+	0.419551i
$575$	5.11772	+	8.86416i	0.213424	+	0.369661i
$576$		0			0
$577$	18.5582	−	32.1437i	0.772586	−	1.33816i	−0.163555	−	0.986534i	$-0.552296\pi$
$577$	18.5582	−	32.1437i	0.772586	−	1.33816i	0.936141	−	0.351624i	$-0.114371\pi$
$578$	4.65010	+	26.3720i	0.193419	+	1.09693i
$579$		0			0
$580$	−21.8526	+	7.95369i	−0.907379	+	0.330259i
$581$	−1.28333	+	0.467093i	−0.0532414	+	0.0193783i
$582$		0			0
$583$	1.80931	+	10.2611i	0.0749338	+	0.424971i
$584$	44.5768	−	77.2093i	1.84460	−	3.19494i
$585$		0			0
$586$	−35.3328	−	61.1981i	−1.45958	−	2.52807i
$587$	−11.2174	+	9.41248i	−0.462990	+	0.388495i	−0.844230	−	0.535982i	$-0.819942\pi$
$587$	−11.2174	+	9.41248i	−0.462990	+	0.388495i	0.381240	+	0.924476i	$0.375497\pi$
$588$		0			0
$589$	−4.64495	+	26.3428i	−0.191392	+	1.08544i
$590$	−7.59403	−	6.37215i	−0.312641	−	0.262337i
$591$		0			0
$592$	62.2744	+	22.6660i	2.55946	+	0.931568i
$593$	36.4392			1.49638			0.748189	−	0.663485i	$-0.230924\pi$
$593$	36.4392			1.49638			0.748189	+	0.663485i	$0.230924\pi$
$594$		0			0
$595$	−2.23081			−0.0914544
$596$	3.63827	+	1.32422i	0.149029	+	0.0542422i
$597$		0			0
$598$	−29.9639	−	25.1427i	−1.22532	−	1.02816i
$599$	4.77444	−	27.0772i	0.195078	−	1.10634i	−0.717229	−	0.696838i	$-0.754590\pi$
$599$	4.77444	−	27.0772i	0.195078	−	1.10634i	0.912307	−	0.409506i	$-0.134299\pi$
$600$		0			0
$601$	34.6076	−	29.0392i	1.41167	−	1.18453i	0.456045	−	0.889957i	$-0.349266\pi$
$601$	34.6076	−	29.0392i	1.41167	−	1.18453i	0.955628	−	0.294578i	$-0.0951789\pi$
$602$	−6.09653	−	10.5595i	−0.248476	−	0.430373i
$603$		0			0
$604$	−11.5443	+	19.9953i	−0.469729	+	0.813595i
$605$	−2.12646	−	12.0598i	−0.0864529	−	0.490299i
$606$		0			0
$607$	−16.1037	+	5.86126i	−0.653628	+	0.237901i	−0.647483	−	0.762080i	$-0.724178\pi$
$607$	−16.1037	+	5.86126i	−0.653628	+	0.237901i	−0.00614504	+	0.999981i	$0.501956\pi$
$608$	103.216	−	37.5675i	4.18596	−	1.52356i
$609$		0			0
$610$	−5.37355	−	30.4749i	−0.217569	−	1.23389i
$611$	10.6324	−	18.4159i	0.430143	−	0.745029i
$612$		0			0
$613$	0.234380	+	0.405959i	0.00946653	+	0.0163965i	0.870720	−	0.491779i	$-0.163653\pi$
$613$	0.234380	+	0.405959i	0.00946653	+	0.0163965i	−0.861253	+	0.508176i	$0.830320\pi$
$614$	−6.82327	+	5.72541i	−0.275365	+	0.231059i
$615$		0			0
$616$	−1.49593	+	8.48383i	−0.0602726	+	0.341823i
$617$	−1.63539	−	1.37225i	−0.0658383	−	0.0552449i	0.609275	−	0.792959i	$-0.291461\pi$
$617$	−1.63539	−	1.37225i	−0.0658383	−	0.0552449i	−0.675113	+	0.737714i	$0.735905\pi$
$618$		0			0
$619$	−8.02272	−	2.92003i	−0.322460	−	0.117366i	0.175718	−	0.984441i	$-0.443775\pi$
$619$	−8.02272	−	2.92003i	−0.322460	−	0.117366i	−0.498178	+	0.867075i	$0.665998\pi$
$620$	−41.0363			−1.64806
$621$		0			0
$622$	94.1163			3.77372
$623$	5.27739	+	1.92081i	0.211434	+	0.0769557i
$624$		0			0
$625$	−6.99443	−	5.86902i	−0.279777	−	0.234761i
$626$	−4.99221	+	28.3122i	−0.199529	+	1.13158i
$627$		0			0
$628$	−63.2316	+	53.0576i	−2.52322	+	2.11723i
$629$	−6.47339	−	11.2122i	−0.258111	−	0.447061i
$630$		0			0
$631$	5.93539	−	10.2804i	0.236284	−	0.409256i	−0.723361	−	0.690470i	$-0.757404\pi$
$631$	5.93539	−	10.2804i	0.236284	−	0.409256i	0.959645	+	0.281214i	$0.0907370\pi$
$632$	−8.27630	−	46.9372i	−0.329214	−	1.86706i
$633$		0			0
$634$	39.4005	−	14.3406i	1.56479	−	0.569538i
$635$	−3.68418	+	1.34093i	−0.146202	+	0.0532133i
$636$		0			0
$637$	−3.64784	−	20.6880i	−0.144533	−	0.819686i
$638$	6.78291	−	11.7483i	0.268538	−	0.465121i
$639$		0			0
$640$	22.5486	+	39.0554i	0.891313	+	1.54380i
$641$	4.06284	−	3.40913i	0.160472	−	0.134652i	−0.559016	−	0.829157i	$-0.688821\pi$
$641$	4.06284	−	3.40913i	0.160472	−	0.134652i	0.719488	+	0.694505i	$0.244376\pi$
$642$		0			0
$643$	−0.143063	+	0.811352i	−0.00564187	+	0.0319966i	−0.987499	−	0.157627i	$-0.949616\pi$
$643$	−0.143063	+	0.811352i	−0.00564187	+	0.0319966i	0.981857	+	0.189624i	$0.0607268\pi$
$644$	9.47330	+	7.94904i	0.373300	+	0.313236i
$645$		0			0
$646$	−39.2630	−	14.2906i	−1.54478	−	0.562254i
$647$	−40.8373			−1.60548			−0.802740	−	0.596329i	$-0.796626\pi$
$647$	−40.8373			−1.60548			−0.802740	+	0.596329i	$0.796626\pi$
$648$		0			0
$649$	4.20232			0.164955
$650$	−17.4303	−	6.34409i	−0.683671	−	0.248836i
$651$		0			0
$652$	34.6128	+	29.0436i	1.35554	+	1.13743i
$653$	0.185692	−	1.05311i	0.00726668	−	0.0412114i	−0.980959	−	0.194216i	$-0.937784\pi$
$653$	0.185692	−	1.05311i	0.00726668	−	0.0412114i	0.988225	+	0.153004i	$0.0488949\pi$
$654$		0			0
$655$	21.9102	−	18.3849i	0.856103	−	0.718356i
$656$	−78.7569	−	136.411i	−3.07494	−	5.32595i
$657$		0			0
$658$	−4.62587	+	8.01225i	−0.180335	+	0.312350i
$659$	−4.97750	−	28.2288i	−0.193896	−	1.09964i	−0.913982	−	0.405754i	$-0.867009\pi$
$659$	−4.97750	−	28.2288i	−0.193896	−	1.09964i	0.720086	−	0.693884i	$-0.244102\pi$
$660$		0			0
$661$	4.22459	−	1.53763i	0.164318	−	0.0598067i	−0.258552	−	0.965997i	$-0.583245\pi$
$661$	4.22459	−	1.53763i	0.164318	−	0.0598067i	0.422869	+	0.906191i	$0.361023\pi$
$662$	−37.0366	+	13.4802i	−1.43947	+	0.523924i
$663$		0			0
$664$	−4.25119	−	24.1097i	−0.164978	−	0.935638i
$665$	−2.42642	+	4.20268i	−0.0940924	+	0.162973i
$666$		0			0
$667$	−6.07464	−	10.5216i	−0.235211	−	0.407397i
$668$	−94.2651	+	79.0978i	−3.64723	+	3.06039i
$669$		0			0
$670$	−9.80672	+	55.6167i	−0.378867	+	2.14866i
$671$	10.0488	+	8.43198i	0.387931	+	0.325513i
$672$		0			0
$673$	−16.9695	−	6.17640i	−0.654127	−	0.238083i	−0.00642810	−	0.999979i	$-0.502046\pi$
$673$	−16.9695	−	6.17640i	−0.654127	−	0.238083i	−0.647699	+	0.761897i	$0.724268\pi$
$674$	55.7643			2.14796
$675$		0			0
$676$	−17.6151			−0.677505
$677$	−14.7900	−	5.38311i	−0.568425	−	0.206890i	0.0417888	−	0.999126i	$-0.486694\pi$
$677$	−14.7900	−	5.38311i	−0.568425	−	0.206890i	−0.610214	+	0.792237i	$0.708917\pi$
$678$		0			0
$679$	−2.64181	−	2.21675i	−0.101384	−	0.0850709i
$680$	6.94420	−	39.3825i	0.266298	−	1.51025i
$681$		0			0
$682$	18.3380	−	15.3874i	0.702196	−	0.589213i
$683$	1.38059	+	2.39125i	0.0528268	+	0.0914987i	0.891230	−	0.453552i	$-0.149844\pi$
$683$	1.38059	+	2.39125i	0.0528268	+	0.0914987i	−0.838403	+	0.545051i	$0.816510\pi$
$684$		0			0
$685$	11.6458	−	20.1711i	0.444963	−	0.770698i
$686$	3.23307	+	18.3357i	0.123439	+	0.700058i
$687$		0			0
$688$	115.410	−	42.0058i	4.39996	−	1.60146i
$689$	−15.8907	+	5.78374i	−0.605387	+	0.220343i
$690$		0			0
$691$	−5.99530	−	34.0010i	−0.228072	−	1.29346i	−0.856725	−	0.515774i	$-0.827504\pi$
$691$	−5.99530	−	34.0010i	−0.228072	−	1.29346i	0.628653	−	0.777686i	$-0.283607\pi$
$692$	−6.85537	+	11.8738i	−0.260602	+	0.451376i
$693$		0			0
$694$	28.6514	+	49.6257i	1.08759	+	1.88377i
$695$	10.1422	−	8.51029i	0.384714	−	0.322814i
$696$		0			0
$697$	−5.34351	+	30.3046i	−0.202400	+	1.14787i
$698$	9.58594	+	8.04356i	0.362833	+	0.304453i
$699$		0			0
$700$	5.51069	+	2.00573i	0.208285	+	0.0758094i
$701$	−20.7410			−0.783378			−0.391689	−	0.920098i	$-0.628109\pi$
$701$	−20.7410			−0.783378			−0.391689	+	0.920098i	$0.628109\pi$
$702$		0			0
$703$	−28.1640			−1.06222
$704$	−43.2110	−	15.7275i	−1.62858	−	0.592754i
$705$		0			0
$706$	−28.2719	−	23.7229i	−1.06403	−	0.892824i
$707$	−0.324206	+	1.83866i	−0.0121930	+	0.0691501i
$708$		0			0
$709$	21.2249	−	17.8098i	0.797117	−	0.668861i	−0.150379	−	0.988628i	$-0.548049\pi$
$709$	21.2249	−	17.8098i	0.797117	−	0.668861i	0.947496	+	0.319768i	$0.103605\pi$
$710$	6.41419	+	11.1097i	0.240720	+	0.416940i
$711$		0			0
$712$	−50.3376	+	87.1873i	−1.88648	+	3.26748i
$713$	−3.72282	−	21.1131i	−0.139421	−	0.790693i
$714$		0			0
$715$	−9.38009	+	3.41407i	−0.350796	+	0.127679i
$716$	−44.4513	+	16.1789i	−1.66122	+	0.604635i
$717$		0			0
$718$	−13.2674	−	75.2429i	−0.495133	−	2.80804i
$719$	−16.5657	+	28.6927i	−0.617797	+	1.07006i	0.372090	+	0.928197i	$0.378641\pi$
$719$	−16.5657	+	28.6927i	−0.617797	+	1.07006i	−0.989887	+	0.141859i	$0.954692\pi$
$720$		0			0
$721$	−1.92247	−	3.32981i	−0.0715965	−	0.124009i
$722$	−30.2562	+	25.3879i	−1.12602	+	0.944842i
$723$		0			0
$724$	7.30541	−	41.4310i	0.271503	−	1.53977i
$725$	−4.41344	−	3.70332i	−0.163911	−	0.137538i
$726$		0			0
$727$	0.0776238	+	0.0282527i	0.00287891	+	0.00104784i	0.343459	−	0.939168i	$-0.388401\pi$
$727$	0.0776238	+	0.0282527i	0.00287891	+	0.00104784i	−0.340580	+	0.940215i	$0.610624\pi$
$728$	−13.9816			−0.518191
$729$		0			0
$730$	−44.9449			−1.66349
$731$	−22.5466	−	8.20630i	−0.833917	−	0.303521i
$732$		0			0
$733$	−24.4502	−	20.5162i	−0.903089	−	0.757782i	0.0677025	−	0.997706i	$-0.478433\pi$
$733$	−24.4502	−	20.5162i	−0.903089	−	0.757782i	−0.970792	+	0.239924i	$0.922878\pi$
$734$	−16.3843	+	92.9198i	−0.604754	+	3.42973i
$735$		0			0
$736$	−67.4381	+	56.5873i	−2.48580	+	2.08584i
$737$	−11.9700	−	20.7327i	−0.440921	−	0.763698i
$738$		0			0
$739$	17.8960	−	30.9967i	0.658314	−	1.14023i	−0.322738	−	0.946488i	$-0.604603\pi$
$739$	17.8960	−	30.9967i	0.658314	−	1.14023i	0.981052	−	0.193745i	$-0.0620634\pi$
$740$	−7.50277	−	42.5503i	−0.275807	−	1.56418i
$741$		0			0
$742$	6.91359	−	2.51634i	0.253806	−	0.0923778i
$743$	−18.5861	+	6.76477i	−0.681856	+	0.248175i	−0.659644	−	0.751578i	$-0.729293\pi$
$743$	−18.5861	+	6.76477i	−0.681856	+	0.248175i	−0.0222120	+	0.999753i	$0.507071\pi$
$744$		0			0
$745$	−0.211455	−	1.19922i	−0.00774711	−	0.0439361i
$746$	4.13799	−	7.16721i	0.151503	−	0.262410i
$747$		0			0
$748$	13.5861	+	23.5319i	0.496758	+	0.860411i
$749$	4.12840	−	3.46414i	0.150848	−	0.126577i
$750$		0			0
$751$	5.31026	−	30.1160i	0.193774	−	1.09895i	−0.720380	−	0.693580i	$-0.756032\pi$
$751$	5.31026	−	30.1160i	0.193774	−	1.09895i	0.914154	−	0.405367i	$-0.132856\pi$
$752$	−71.3876	−	59.9013i	−2.60324	−	2.18438i
$753$		0			0
$754$	20.6894	+	7.53031i	0.753462	+	0.274238i
$755$	7.26165			0.264278
$756$		0			0
$757$	25.4129			0.923647			0.461824	−	0.886972i	$-0.347195\pi$
$757$	25.4129			0.923647			0.461824	+	0.886972i	$0.347195\pi$
$758$	−19.5145	−	7.10271i	−0.708799	−	0.257982i
$759$		0			0
$760$	−66.6405	−	55.9181i	−2.41731	−	2.02836i
$761$	8.12986	−	46.1067i	0.294707	−	1.67137i	−0.373684	−	0.927556i	$-0.621905\pi$
$761$	8.12986	−	46.1067i	0.294707	−	1.67137i	0.668391	−	0.743810i	$-0.266983\pi$
$762$		0			0
$763$	4.68984	−	3.93524i	0.169784	−	0.142465i
$764$	−42.2661	−	73.2070i	−1.52913	−	2.64854i
$765$		0			0
$766$	−14.0149	+	24.2744i	−0.506377	+	0.877071i
$767$	1.18434	+	6.71670i	0.0427639	+	0.242526i
$768$		0			0
$769$	−13.6870	+	4.98167i	−0.493567	+	0.179644i	−0.576798	−	0.816887i	$-0.695698\pi$
$769$	−13.6870	+	4.98167i	−0.493567	+	0.179644i	0.0832316	+	0.996530i	$0.473476\pi$
$770$	4.08101	−	1.48537i	0.147069	−	0.0535289i
$771$		0			0
$772$	−4.23337	−	24.0086i	−0.152362	−	0.864089i
$773$	12.1767	−	21.0906i	0.437964	−	0.758576i	−0.559568	−	0.828784i	$-0.689033\pi$
$773$	12.1767	−	21.0906i	0.437964	−	0.758576i	0.997532	+	0.0702080i	$0.0223663\pi$
$774$		0			0
$775$	−5.08328	−	8.80451i	−0.182597	−	0.316267i
$776$	47.3578	−	39.7379i	1.70005	−	1.42651i
$777$		0			0
$778$	−0.200552	+	1.13738i	−0.00719012	+	0.0407772i
$779$	51.2794	+	43.0285i	1.83727	+	1.54166i
$780$		0			0
$781$	−5.11009	−	1.85992i	−0.182853	−	0.0665532i
$782$	33.4879			1.19753
$783$		0			0
$784$	−92.0601			−3.28786
$785$	24.3952	+	8.87914i	0.870703	+	0.316910i
$786$		0			0
$787$	−21.1177	−	17.7198i	−0.752764	−	0.631644i	0.183468	−	0.983026i	$-0.441268\pi$
$787$	−21.1177	−	17.7198i	−0.752764	−	0.631644i	−0.936232	+	0.351381i	$0.885712\pi$
$788$	−2.76467	+	15.6792i	−0.0984874	+	0.558550i
$789$		0			0
$790$	−18.4061	+	15.4445i	−0.654859	+	0.549492i
$791$	−0.486562	−	0.842750i	−0.0173001	−	0.0299647i
$792$		0			0
$793$	−10.6451	+	18.4378i	−0.378017	+	0.654744i
$794$	12.7245	+	72.1644i	0.451577	+	2.56102i
$795$		0			0
$796$	−74.3933	+	27.0770i	−2.63680	+	0.959717i
$797$	−6.21787	+	2.26312i	−0.220248	+	0.0801638i	−0.449787	−	0.893136i	$-0.648500\pi$
$797$	−6.21787	+	2.26312i	−0.220248	+	0.0801638i	0.229539	+	0.973299i	$0.426278\pi$
$798$		0			0
$799$	3.16138	+	17.9291i	0.111842	+	0.634286i
$800$	−20.8735	+	36.1539i	−0.737989	+	1.27823i
$801$		0			0
$802$	−39.7110	−	68.7815i	−1.40224	−	2.42876i
$803$	14.5950	−	12.2467i	0.515048	−	0.432177i
$804$		0			0
$805$	0.675393	−	3.83034i	0.0238045	−	0.135002i
$806$	29.7623	+	24.9735i	1.04833	+	0.879655i
$807$		0			0
$808$	−31.4504	−	11.4470i	−1.10642	−	0.402704i
$809$	8.61362			0.302839			0.151419	−	0.988470i	$-0.451616\pi$
$809$	8.61362			0.302839			0.151419	+	0.988470i	$0.451616\pi$
$810$		0			0
$811$	−9.58716			−0.336651			−0.168325	−	0.985732i	$-0.553836\pi$
$811$	−9.58716			−0.336651			−0.168325	+	0.985732i	$0.553836\pi$
$812$	−6.54108	−	2.38076i	−0.229547	−	0.0835483i
$813$		0			0
$814$	19.3079	+	16.2012i	0.676740	+	0.567852i
$815$	2.46770	−	13.9950i	0.0864396	−	0.490223i
$816$		0			0
$817$	−39.9836	+	33.5502i	−1.39885	+	1.17377i
$818$	−27.2994	−	47.2840i	−0.954502	−	1.65325i
$819$		0			0
$820$	−51.3472	+	88.9359i	−1.79312	+	3.10578i
$821$	2.40737	+	13.6529i	0.0840177	+	0.476488i	0.997564	+	0.0697537i	$0.0222213\pi$
$821$	2.40737	+	13.6529i	0.0840177	+	0.476488i	−0.913547	+	0.406734i	$0.866668\pi$
$822$		0			0
$823$	−44.9415	+	16.3574i	−1.56656	+	0.570182i	−0.972228	−	0.234037i	$-0.924806\pi$
$823$	−44.9415	+	16.3574i	−1.56656	+	0.570182i	−0.594334	+	0.804218i	$0.702584\pi$
$824$	64.7686	−	23.5738i	2.25632	−	0.821234i
$825$		0			0
$826$	−0.515271	−	2.92225i	−0.0179286	−	0.101678i
$827$	−21.2209	+	36.7556i	−0.737921	+	1.27812i	0.215508	+	0.976502i	$0.430859\pi$
$827$	−21.2209	+	36.7556i	−0.737921	+	1.27812i	−0.953430	+	0.301615i	$0.902474\pi$
$828$		0			0
$829$	−13.0018	−	22.5199i	−0.451573	−	0.782147i	0.546911	−	0.837191i	$-0.315804\pi$
$829$	−13.0018	−	22.5199i	−0.451573	−	0.782147i	−0.998484	+	0.0550437i	$0.982470\pi$
$830$	−9.45445	+	7.93322i	−0.328169	+	0.275366i
$831$		0			0
$832$	12.9597	−	73.4981i	0.449296	−	2.54809i
$833$	13.7773	+	11.5605i	0.477354	+	0.400548i
$834$		0			0
$835$	36.3682	+	13.2369i	1.25857	+	0.458083i
$836$	59.1096			2.04435
$837$		0			0
$838$	65.9233			2.27728
$839$	1.18051	+	0.429672i	0.0407558	+	0.0148339i	0.362318	−	0.932055i	$-0.381986\pi$
$839$	1.18051	+	0.429672i	0.0407558	+	0.0148339i	−0.321562	+	0.946889i	$0.604208\pi$
$840$		0			0
$841$	−16.9766	−	14.2451i	−0.585401	−	0.491210i
$842$	12.2950	−	69.7282i	0.423712	−	2.40299i
$843$		0			0
$844$	56.5338	−	47.4375i	1.94597	−	1.63287i
$845$	2.77009	+	4.79794i	0.0952941	+	0.165054i
$846$		0			0
$847$	1.83275	−	3.17442i	0.0629742	−	0.109074i
$848$	12.8687	+	72.9817i	0.441911	+	2.50620i
$849$		0			0
$850$	14.9227	−	5.43142i	0.511844	−	0.186296i
$851$	21.2115	−	7.72034i	0.727119	−	0.264650i
$852$		0			0
$853$	0.252545	+	1.43225i	0.00864696	+	0.0490394i	0.988826	−	0.149075i	$-0.0476295\pi$
$853$	0.252545	+	1.43225i	0.00864696	+	0.0490394i	−0.980179	+	0.198114i	$0.936518\pi$
$854$	4.63136	−	8.02175i	0.158482	−	0.274499i
$855$		0			0
$856$	48.3044	+	83.6657i	1.65101	+	2.85964i
$857$	40.0715	−	33.6240i	1.36882	−	1.14857i	0.395670	−	0.918393i	$-0.370512\pi$
$857$	40.0715	−	33.6240i	1.36882	−	1.14857i	0.973148	−	0.230182i	$-0.0739322\pi$
$858$		0			0
$859$	−3.64736	+	20.6852i	−0.124446	+	0.705771i	0.857189	+	0.515003i	$0.172209\pi$
$859$	−3.64736	+	20.6852i	−0.124446	+	0.705771i	−0.981635	+	0.190768i	$0.938902\pi$
$860$	−61.3394	−	51.4698i	−2.09165	−	1.75511i
$861$		0			0
$862$	−81.1347	−	29.5306i	−2.76346	−	1.00582i
$863$	−12.9813			−0.441890			−0.220945	−	0.975286i	$-0.570914\pi$
$863$	−12.9813			−0.441890			−0.220945	+	0.975286i	$0.570914\pi$
$864$		0			0
$865$	4.31221			0.146619
$866$	0.0312860	+	0.0113872i	0.00106314	+	0.000386952i
$867$		0			0
$868$	−9.40955	−	7.89555i	−0.319381	−	0.267992i
$869$	1.76868	−	10.0307i	0.0599983	−	0.340267i
$870$		0			0
$871$	29.7642	−	24.9751i	1.00852	−	0.846250i
$872$	54.8735	+	95.0438i	1.85825	+	3.21859i
$873$		0			0
$874$	36.4243	−	63.0887i	1.23207	−	2.13401i
$875$	−1.04715	−	5.93871i	−0.0354003	−	0.200765i
$876$		0			0
$877$	−29.1734	+	10.6182i	−0.985115	+	0.358553i	−0.783827	−	0.620979i	$-0.786735\pi$
$877$	−29.1734	+	10.6182i	−0.985115	+	0.358553i	−0.201288	+	0.979532i	$0.564513\pi$
$878$	13.4844	−	4.90793i	0.455078	−	0.165635i
$879$		0			0
$880$	7.59621	+	43.0803i	0.256068	+	1.45224i
$881$	9.64783	−	16.7105i	0.325044	−	0.562992i	−0.656478	−	0.754346i	$-0.727954\pi$
$881$	9.64783	−	16.7105i	0.325044	−	0.562992i	0.981521	+	0.191353i	$0.0612877\pi$
$882$		0			0
$883$	4.91194	+	8.50773i	0.165300	+	0.286308i	0.936762	−	0.349968i	$-0.113807\pi$
$883$	4.91194	+	8.50773i	0.165300	+	0.286308i	−0.771462	+	0.636276i	$0.780474\pi$
$884$	−33.7828	+	28.3471i	−1.13624	+	0.953417i
$885$		0			0
$886$	19.1163	−	108.414i	0.642224	−	3.64223i
$887$	−33.7927	−	28.3555i	−1.13465	−	0.952084i	−0.135399	−	0.990791i	$-0.543231\pi$
$887$	−33.7927	−	28.3555i	−1.13465	−	0.952084i	−0.999251	+	0.0387076i	$0.987676\pi$
$888$		0			0
$889$	−1.10278	−	0.401378i	−0.0369860	−	0.0134618i
$890$	50.7533			1.70125
$891$		0			0
$892$	−36.2219			−1.21280
$893$	37.2156	+	13.5454i	1.24537	+	0.453278i
$894$		0			0
$895$	11.3970	+	9.56323i	0.380960	+	0.319664i
$896$	−2.34405	+	13.2938i	−0.0783093	+	0.444114i
$897$		0			0
$898$	31.9699	−	26.8260i	1.06685	−	0.895194i
$899$	6.03376	+	10.4508i	0.201237	+	0.348553i
$900$		0			0
$901$	7.23887	−	12.5381i	0.241162	−	0.417704i
$902$	−10.4027	−	58.9966i	−0.346372	−	1.96437i
$903$		0			0
$904$	16.3924	−	5.96635i	0.545204	−	0.198438i
$905$	−12.4337	+	4.52548i	−0.413309	+	0.150432i
$906$		0			0
$907$	−7.36483	−	41.7680i	−0.244545	−	1.38689i	−0.821546	−	0.570142i	$-0.806888\pi$
$907$	−7.36483	−	41.7680i	−0.244545	−	1.38689i	0.577001	−	0.816743i	$-0.304223\pi$
$908$	−25.8979	+	44.8564i	−0.859451	+	1.48861i
$909$		0			0
$910$	3.52426	+	6.10419i	0.116828	+	0.202352i
$911$	−28.1218	+	23.5970i	−0.931716	+	0.781802i	−0.976125	−	0.217211i	$-0.930304\pi$
$911$	−28.1218	+	23.5970i	−0.931716	+	0.781802i	0.0444090	+	0.999013i	$0.485860\pi$
$912$		0			0
$913$	0.908497	−	5.15234i	0.0300668	−	0.170518i
$914$	−4.94996	−	4.15351i	−0.163730	−	0.137386i
$915$		0			0
$916$	70.1779	+	25.5427i	2.31874	+	0.843953i
$917$	8.56130			0.282719
$918$		0			0
$919$	−14.0589			−0.463761			−0.231881	−	0.972744i	$-0.574488\pi$
$919$	−14.0589			−0.463761			−0.231881	+	0.972744i	$0.574488\pi$
$920$	65.5181	+	23.8466i	2.16007	+	0.786200i
$921$		0			0
$922$	67.3131	+	56.4824i	2.21684	+	1.86015i
$923$	1.53260	−	8.69180i	0.0504461	−	0.286094i
$924$		0			0
$925$	8.19996	−	6.88058i	0.269613	−	0.226232i
$926$	45.8218	+	79.3657i	1.50580	+	2.60812i
$927$		0			0
$928$	24.7764	−	42.9140i	0.813325	−	1.40872i
$929$	3.21553	+	18.2362i	0.105498	+	0.598309i	0.991020	+	0.133712i	$0.0426898\pi$
$929$	3.21553	+	18.2362i	0.105498	+	0.598309i	−0.885522	+	0.464597i	$0.846199\pi$
$930$		0			0
$931$	36.7644	−	13.3812i	1.20490	−	0.438550i
$932$	26.5991	−	9.68128i	0.871282	−	0.317121i
$933$		0			0
$934$	−6.48352	−	36.7699i	−0.212147	−	1.20315i
$935$	4.27302	−	7.40108i	0.139743	−	0.242041i
$936$		0			0
$937$	−2.23409	−	3.86955i	−0.0729845	−	0.126413i	0.827224	−	0.561873i	$-0.189919\pi$
$937$	−2.23409	−	3.86955i	−0.0729845	−	0.126413i	−0.900208	+	0.435460i	$0.856586\pi$
$938$	−12.9495	+	10.8660i	−0.422818	+	0.354786i
$939$		0			0
$940$	−10.5503	+	59.8340i	−0.344114	+	1.95157i
$941$	1.53505	+	1.28806i	0.0500410	+	0.0419894i	0.667465	−	0.744641i	$-0.267379\pi$
$941$	1.53505	+	1.28806i	0.0500410	+	0.0419894i	−0.617424	+	0.786630i	$0.711824\pi$
$942$		0			0
$943$	−50.4157	−	18.3498i	−1.64176	−	0.597552i
$944$	29.8889			0.972801
$945$		0			0
$946$	46.7105			1.51869
$947$	−11.8249	−	4.30392i	−0.384258	−	0.139859i	0.142666	−	0.989771i	$-0.454433\pi$
$947$	−11.8249	−	4.30392i	−0.384258	−	0.139859i	−0.526924	+	0.849912i	$0.676655\pi$
$948$		0			0
$949$	23.6876	+	19.8763i	0.768932	+	0.645210i
$950$	5.99879	−	34.0209i	0.194627	−	1.10378i
$951$		0			0
$952$	9.16966	−	7.69426i	0.297190	−	0.249372i
$953$	−9.98205	−	17.2894i	−0.323350	−	0.560059i	0.657827	−	0.753169i	$-0.271476\pi$
$953$	−9.98205	−	17.2894i	−0.323350	−	0.560059i	−0.981177	+	0.193110i	$0.938143\pi$
$954$		0			0
$955$	−13.2932	+	23.0246i	−0.430159	+	0.745058i
$956$	−16.4112	−	93.0726i	−0.530777	−	3.01018i
$957$		0			0
$958$	−14.9748	+	5.45038i	−0.483814	+	0.176094i
$959$	6.55136	−	2.38450i	0.211554	−	0.0769995i
$960$		0			0
$961$	−1.68533	−	9.55799i	−0.0543655	−	0.308322i
$962$	−20.4534	+	35.4263i	−0.659444	+	1.14219i
$963$		0			0
$964$	5.33544	+	9.24125i	0.171843	+	0.297640i
$965$	−5.87366	+	4.92858i	−0.189080	+	0.158657i
$966$		0			0
$967$	−5.59296	+	31.7193i	−0.179858	+	1.02002i	0.752529	+	0.658559i	$0.228834\pi$
$967$	−5.59296	+	31.7193i	−0.179858	+	1.02002i	−0.932386	+	0.361463i	$0.882277\pi$
$968$	50.3358	+	42.2368i	1.61785	+	1.35754i
$969$		0			0
$970$	−29.2863	−	10.6593i	−0.940327	−	0.342251i
$971$	6.62934			0.212746			0.106373	−	0.994326i	$-0.466076\pi$
$971$	6.62934			0.212746			0.106373	+	0.994326i	$0.466076\pi$
$972$		0			0
$973$	3.96300			0.127048
$974$	73.7920	+	26.8581i	2.36445	+	0.860589i
$975$		0			0
$976$	71.4722	+	59.9723i	2.28777	+	1.91967i
$977$	−2.05888	+	11.6765i	−0.0658696	+	0.373565i	0.933998	+	0.357279i	$0.116295\pi$
$977$	−2.05888	+	11.6765i	−0.0658696	+	0.373565i	−0.999867	+	0.0162861i	$0.994816\pi$
$978$		0			0
$979$	−16.4812	+	13.8294i	−0.526742	+	0.441989i
$980$	30.0102	+	51.9792i	0.958642	+	1.66042i
$981$		0			0
$982$	−5.92884	+	10.2690i	−0.189197	+	0.327698i
$983$	9.04099	+	51.2740i	0.288363	+	1.63539i	0.693020	+	0.720918i	$0.256280\pi$
$983$	9.04099	+	51.2740i	0.288363	+	1.63539i	−0.404657	+	0.914469i	$0.632609\pi$
$984$		0			0
$985$	4.70542	−	1.71263i	0.149927	−	0.0545690i
$986$	−17.7129	+	6.44698i	−0.564095	+	0.205314i
$987$		0			0
$988$	16.6588	+	94.4768i	0.529987	+	3.00571i
$989$	20.9165	−	36.2284i	0.665105	−	1.15200i
$990$		0			0
$991$	−0.735575	−	1.27405i	−0.0233663	−	0.0404716i	0.854106	−	0.520099i	$-0.174105\pi$
$991$	−0.735575	−	1.27405i	−0.0233663	−	0.0404716i	−0.877472	+	0.479628i	$0.840772\pi$
$992$	66.9843	−	56.2065i	2.12675	−	1.78456i
$993$		0			0
$994$	−0.666790	+	3.78155i	−0.0211493	+	0.119944i
$995$	19.0740	+	16.0050i	0.604685	+	0.507391i
$996$		0			0
$997$	24.8279	+	9.03661i	0.786307	+	0.286192i	0.703800	−	0.710398i	$-0.251485\pi$
$997$	24.8279	+	9.03661i	0.786307	+	0.286192i	0.0825071	+	0.996590i	$0.473707\pi$
$998$	−95.6065			−3.02637
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.t.568.2		12
3.2	odd	2		729.2.e.k.568.1		12
9.2	odd	6		729.2.e.l.82.2		12
9.4	even	3		729.2.e.j.325.1		12
9.5	odd	6		729.2.e.u.325.2		12
9.7	even	3		729.2.e.s.82.1		12
27.2	odd	18		729.2.e.u.406.2		12
27.4	even	9		729.2.c.d.244.6		12
27.5	odd	18		729.2.c.a.487.1		12
27.7	even	9	inner	729.2.e.t.163.2		12
27.11	odd	18		729.2.e.l.649.2		12
27.13	even	9		729.2.a.b.1.1	✓	6
27.14	odd	18		729.2.a.e.1.6	yes	6
27.16	even	9		729.2.e.s.649.1		12
27.20	odd	18		729.2.e.k.163.1		12
27.22	even	9		729.2.c.d.487.6		12
27.23	odd	18		729.2.c.a.244.1		12
27.25	even	9		729.2.e.j.406.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.b.1.1	✓	6	27.13	even	9
729.2.a.e.1.6	yes	6	27.14	odd	18
729.2.c.a.244.1		12	27.23	odd	18
729.2.c.a.487.1		12	27.5	odd	18
729.2.c.d.244.6		12	27.4	even	9
729.2.c.d.487.6		12	27.22	even	9
729.2.e.j.325.1		12	9.4	even	3
729.2.e.j.406.1		12	27.25	even	9
729.2.e.k.163.1		12	27.20	odd	18
729.2.e.k.568.1		12	3.2	odd	2
729.2.e.l.82.2		12	9.2	odd	6
729.2.e.l.649.2		12	27.11	odd	18
729.2.e.s.82.1		12	9.7	even	3
729.2.e.s.649.1		12	27.16	even	9
729.2.e.t.163.2		12	27.7	even	9	inner
729.2.e.t.568.2		12	1.1	even	1	trivial
729.2.e.u.325.2		12	9.5	odd	6
729.2.e.u.406.2		12	27.2	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)

\(f(q)\)	\(=\)	\(q+(2.54193 + 0.925187i) q^{2} +(4.07335 + 3.41794i) q^{4} +(0.290407 - 1.64698i) q^{5} +(0.383475 - 0.321774i) q^{7} +(4.48686 + 7.77147i) q^{8} +O(q^{10})\)	\(q+(2.54193 + 0.925187i) q^{2} +(4.07335 + 3.41794i) q^{4} +(0.290407 - 1.64698i) q^{5} +(0.383475 - 0.321774i) q^{7} +(4.48686 + 7.77147i) q^{8} +(2.26195 - 3.91782i) q^{10} +(0.333008 + 1.88858i) q^{11} +(-2.92473 + 1.06452i) q^{13} +(1.27247 - 0.463140i) q^{14} +(2.36851 + 13.4325i) q^{16} +(1.33234 - 2.30767i) q^{17} +(-2.89832 - 5.02003i) q^{19} +(6.81220 - 5.71612i) q^{20} +(-0.900809 + 5.10874i) q^{22} +(3.55894 + 2.98631i) q^{23} +(2.07026 + 0.753515i) q^{25} -8.41934 q^{26} +2.66183 q^{28} +(-2.45736 - 0.894407i) q^{29} +(-3.53499 - 2.96621i) q^{31} +(-3.29045 + 18.6611i) q^{32} +(5.52173 - 4.63328i) q^{34} +(-0.418591 - 0.725020i) q^{35} +(2.42934 - 4.20773i) q^{37} +(-2.72285 - 15.4421i) q^{38} +(14.1024 - 5.13287i) q^{40} +(-10.8517 + 3.94970i) q^{41} +(-1.56359 - 8.86754i) q^{43} +(-5.09861 + 8.83106i) q^{44} +(6.28369 + 10.8837i) q^{46} +(-5.23380 + 4.39168i) q^{47} +(-1.17202 + 6.64687i) q^{49} +(4.56532 + 3.83076i) q^{50} +(-15.5519 - 5.66043i) q^{52} +5.43322 q^{53} +3.20716 q^{55} +(4.22125 + 1.53641i) q^{56} +(-5.41895 - 4.54704i) q^{58} +(0.380517 - 2.15802i) q^{59} +(5.24000 - 4.39688i) q^{61} +(-6.24140 - 10.8104i) q^{62} +(-11.9893 + 20.7661i) q^{64} +(0.903872 + 5.12611i) q^{65} +(-11.7307 + 4.26964i) q^{67} +(13.3146 - 4.84610i) q^{68} +(-0.393249 - 2.23022i) q^{70} +(-1.41784 + 2.45578i) q^{71} +(-4.96749 - 8.60394i) q^{73} +(10.0681 - 8.44817i) q^{74} +(5.35234 - 30.3546i) q^{76} +(0.735397 + 0.617071i) q^{77} +(-4.99091 - 1.81654i) q^{79} +22.8109 q^{80} -31.2385 q^{82} +(-2.56362 - 0.933082i) q^{83} +(-3.41377 - 2.86449i) q^{85} +(4.22960 - 23.9873i) q^{86} +(-13.1829 + 11.0618i) q^{88} +(5.60945 + 9.71585i) q^{89} +(-0.779029 + 1.34932i) q^{91} +(4.28977 + 24.3285i) q^{92} +(-17.3671 + 6.32110i) q^{94} +(-9.10957 + 3.31561i) q^{95} +(-1.19629 - 6.78448i) q^{97} +(-9.12879 + 15.8115i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8	\( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8} - 6 q^{10} - 15 q^{11} - 3 q^{13} - 21 q^{14} + 9 q^{16} - 9 q^{17} - 12 q^{19} - 3 q^{20} + 33 q^{22} + 15 q^{23} - 12 q^{25} - 48 q^{26} + 6 q^{28} - 6 q^{29} - 12 q^{31} - 27 q^{32} + 27 q^{34} + 30 q^{35} - 3 q^{37} - 39 q^{38} + 24 q^{40} - 39 q^{41} + 24 q^{43} - 33 q^{44} + 3 q^{46} - 42 q^{47} - 30 q^{49} - 15 q^{50} - 45 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} - 30 q^{58} + 15 q^{59} - 3 q^{61} - 30 q^{62} - 6 q^{64} - 6 q^{65} - 3 q^{67} + 36 q^{68} - 75 q^{70} - 12 q^{73} + 60 q^{74} + 30 q^{76} + 33 q^{77} + 33 q^{79} + 42 q^{80} - 42 q^{82} - 33 q^{83} - 18 q^{85} - 30 q^{86} - 42 q^{88} - 9 q^{89} - 18 q^{91} + 33 q^{92} - 66 q^{94} + 12 q^{95} + 15 q^{97} + 18 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8 - 6 * q^10 - 15 * q^11 - 3 * q^13 - 21 * q^14 + 9 * q^16 - 9 * q^17 - 12 * q^19 - 3 * q^20 + 33 * q^22 + 15 * q^23 - 12 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 - 12 * q^31 - 27 * q^32 + 27 * q^34 + 30 * q^35 - 3 * q^37 - 39 * q^38 + 24 * q^40 - 39 * q^41 + 24 * q^43 - 33 * q^44 + 3 * q^46 - 42 * q^47 - 30 * q^49 - 15 * q^50 - 45 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 - 30 * q^58 + 15 * q^59 - 3 * q^61 - 30 * q^62 - 6 * q^64 - 6 * q^65 - 3 * q^67 + 36 * q^68 - 75 * q^70 - 12 * q^73 + 60 * q^74 + 30 * q^76 + 33 * q^77 + 33 * q^79 + 42 * q^80 - 42 * q^82 - 33 * q^83 - 18 * q^85 - 30 * q^86 - 42 * q^88 - 9 * q^89 - 18 * q^91 + 33 * q^92 - 66 * q^94 + 12 * q^95 + 15 * q^97 + 18 * q^98

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