LMFDB - Embedded newform 729.2.e.t.163.2

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			163.2
Root			$-1.37340i$ of defining polynomial
Character	$\chi$	$=$	729.163
Dual form			729.2.e.t.568.2

$q$-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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	2.54193	−	0.925187i	1.79742	−	0.654206i	0.798800	−	0.601596i	$-0.205468\pi$
$2$	2.54193	−	0.925187i	1.79742	−	0.654206i	0.998615	−	0.0526096i	$-0.0167539\pi$
$3$		0			0
$3$		0			0
$4$	4.07335	−	3.41794i	2.03667	−	1.70897i
$5$	0.290407	+	1.64698i	0.129874	+	0.736551i	0.978293	+	0.207226i	$0.0664436\pi$
$5$	0.290407	+	1.64698i	0.129874	+	0.736551i	−0.848419	+	0.529325i	$0.822445\pi$
$6$		0			0
$7$	0.383475	+	0.321774i	0.144940	+	0.121619i	0.712375	−	0.701799i	$-0.247620\pi$
$7$	0.383475	+	0.321774i	0.144940	+	0.121619i	−0.567435	+	0.823418i	$0.692064\pi$
$8$	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	−0.892550	−	0.450948i	$-0.851086\pi$
$11$	0.333008	−	1.88858i	0.100406	−	0.569429i	0.992956	−	0.118482i	$-0.0378027\pi$
$12$		0			0
$13$	−2.92473	−	1.06452i	−0.811175	−	0.295243i	−0.0970658	−	0.995278i	$-0.530946\pi$
$13$	−2.92473	−	1.06452i	−0.811175	−	0.295243i	−0.714109	+	0.700034i	$0.753168\pi$
$14$	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	0.981134	−	0.193329i	$-0.0619285\pi$
$17$	1.33234	+	2.30767i	0.323139	+	0.559693i	−0.657995	+	0.753022i	$0.728595\pi$
$18$		0			0
$19$	−2.89832	+	5.02003i	−0.664920	+	1.15167i	0.314387	+	0.949295i	$0.398201\pi$
$19$	−2.89832	+	5.02003i	−0.664920	+	1.15167i	−0.979307	+	0.202380i	$0.935132\pi$
$20$	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	−0.191308	−	0.981530i	$-0.561273\pi$
$23$	3.55894	−	2.98631i	0.742091	−	0.622688i	0.933398	+	0.358842i	$0.116828\pi$
$24$		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	−0.559946	−	0.828529i	$-0.689178\pi$
$29$	−2.45736	+	0.894407i	−0.456321	+	0.166087i	0.103625	+	0.994616i	$0.466956\pi$
$30$		0			0
$31$	−3.53499	+	2.96621i	−0.634903	+	0.532747i	−0.902448	−	0.430798i	$-0.858232\pi$
$31$	−3.53499	+	2.96621i	−0.634903	+	0.532747i	0.267545	+	0.963545i	$0.413788\pi$
$32$	−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	0.993650	−	0.112519i	$-0.0358919\pi$
$37$	2.42934	+	4.20773i	0.399381	+	0.691747i	−0.594269	+	0.804266i	$0.702559\pi$
$38$	−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	−0.699543	−	0.714590i	$-0.746613\pi$
$41$	−10.8517	−	3.94970i	−1.69475	−	0.616840i	−0.995211	+	0.0977502i	$0.968835\pi$
$42$		0			0
$43$	−1.56359	+	8.86754i	−0.238445	+	1.35229i	0.596792	+	0.802396i	$0.296442\pi$
$43$	−1.56359	+	8.86754i	−0.238445	+	1.35229i	−0.835236	+	0.549891i	$0.814669\pi$
$44$	−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	0.175589	−	0.984464i	$-0.443817\pi$
$47$	−5.23380	−	4.39168i	−0.763428	−	0.640592i	−0.939017	+	0.343872i	$0.888262\pi$
$48$		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	0.999507	−	0.0313973i	$-0.00999570\pi$
$59$	0.380517	+	2.15802i	0.0495392	+	0.280950i	−0.949968	+	0.312348i	$0.898885\pi$
$60$		0			0
$61$	5.24000	+	4.39688i	0.670914	+	0.562963i	0.913336	−	0.407208i	$-0.133497\pi$
$61$	5.24000	+	4.39688i	0.670914	+	0.562963i	−0.242422	+	0.970171i	$0.577942\pi$
$62$	−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	−0.495309	−	0.868717i	$-0.664945\pi$
$67$	−11.7307	−	4.26964i	−1.43314	−	0.521620i	−0.937829	+	0.347097i	$0.887167\pi$
$68$	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	0.769544	−	0.638594i	$-0.220484\pi$
$71$	−1.41784	−	2.45578i	−0.168267	−	0.291447i	−0.937811	+	0.347147i	$0.887150\pi$
$72$		0			0
$73$	−4.96749	+	8.60394i	−0.581400	+	1.00701i	0.413913	+	0.910316i	$0.364162\pi$
$73$	−4.96749	+	8.60394i	−0.581400	+	1.00701i	−0.995314	+	0.0966986i	$0.969172\pi$
$74$	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	−0.607158	−	0.794581i	$-0.707690\pi$
$79$	−4.99091	+	1.81654i	−0.561521	+	0.204377i	0.0456370	+	0.998958i	$0.485468\pi$
$80$	22.8109			2.55033
$81$		0			0
$82$	−31.2385			−3.44972
$83$	−2.56362	+	0.933082i	−0.281394	+	0.102419i	−0.478862	−	0.877890i	$-0.658950\pi$
$83$	−2.56362	+	0.933082i	−0.281394	+	0.102419i	0.197468	+	0.980309i	$0.436728\pi$
$84$		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	−0.399003	−	0.916950i	$-0.630644\pi$
$89$	5.60945	−	9.71585i	0.594600	−	1.02988i	0.993603	−	0.112928i	$-0.0360230\pi$
$90$		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	0.861881	+	0.507111i	$0.169287\pi$
$97$	−1.19629	+	6.78448i	−0.121465	+	0.688860i	−0.983345	+	0.181748i	$0.941824\pi$
$98$	−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	0.489480	−	0.872015i	$-0.337187\pi$
$101$	−2.85708	−	2.39737i	−0.284290	−	0.238547i	−0.773769	+	0.633467i	$0.781631\pi$
$102$		0			0
$103$	1.33376	+	7.56411i	0.131419	+	0.745314i	0.977287	+	0.211921i	$0.0679720\pi$
$103$	1.33376	+	7.56411i	0.131419	+	0.745314i	−0.845868	+	0.533393i	$0.820917\pi$
$104$	−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	0.996560	−	0.0828742i	$-0.0264100\pi$
$113$	0.337563	+	1.91442i	0.0317553	+	0.180093i	−0.964805	+	0.262967i	$0.915299\pi$
$114$		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	−0.913335	−	0.407210i	$-0.866502\pi$
$127$	−1.17217	+	2.03025i	−0.104013	+	0.180156i	0.809322	+	0.587366i	$0.199835\pi$
$128$	−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	0.145075	−	0.989421i	$-0.453658\pi$
$131$	13.1012	−	10.9932i	1.14466	−	0.960480i	0.999581	+	0.0289402i	$0.00921323\pi$
$132$		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	0.284154	−	0.958779i	$-0.408287\pi$
$137$	13.0872	−	4.76337i	1.11812	−	0.406962i	0.833965	+	0.551817i	$0.186065\pi$
$138$		0			0
$139$	6.06450	−	5.08872i	0.514384	−	0.431619i	−0.348285	−	0.937389i	$-0.613236\pi$
$139$	6.06450	−	5.08872i	0.514384	−	0.431619i	0.862669	+	0.505770i	$0.168791\pi$
$140$	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	0.369895	−	0.929074i	$-0.379394\pi$
$149$	0.684223	+	0.249037i	0.0560537	+	0.0204019i	−0.313841	+	0.949476i	$0.601616\pi$
$150$		0			0
$151$	0.753996	−	4.27612i	0.0613593	−	0.347986i	−0.938636	−	0.344910i	$-0.887910\pi$
$151$	0.753996	−	4.27612i	0.0613593	−	0.347986i	0.999995	−	0.00307656i	$-0.000979301\pi$
$152$	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	−0.880679	−	0.473714i	$-0.842913\pi$
$157$	−2.69559	−	15.2874i	−0.215131	−	1.22007i	0.665547	−	0.746356i	$-0.268198\pi$
$158$	−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	−0.594003	−	0.804463i	$-0.702453\pi$
$167$	−4.01856	−	22.7904i	−0.310965	−	1.76357i	0.283038	−	0.959109i	$-0.408658\pi$
$168$		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	−0.963045	−	0.269342i	$-0.913194\pi$
$173$	0.447748	−	2.53931i	0.0340417	−	0.193060i	0.997086	+	0.0762821i	$0.0243049\pi$
$174$		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	0.650530	−	0.759480i	$-0.274547\pi$
$179$	−4.44806	−	7.70427i	−0.332464	−	0.575844i	−0.982994	+	0.183636i	$0.941213\pi$
$180$		0			0
$181$	−3.95592	+	6.85185i	−0.294041	+	0.509294i	−0.974761	−	0.223250i	$-0.928334\pi$
$181$	−3.95592	+	6.85185i	−0.294041	+	0.509294i	0.680720	+	0.732543i	$0.261667\pi$
$182$	−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	−0.820250	−	0.572005i	$-0.806166\pi$
$191$	−14.9386	+	5.43721i	−1.08092	+	0.393423i	−0.260671	+	0.965428i	$0.583944\pi$
$192$		0			0
$193$	−3.51215	+	2.94704i	−0.252810	+	0.212133i	−0.760381	−	0.649477i	$-0.774988\pi$
$193$	−3.51215	+	2.94704i	−0.252810	+	0.212133i	0.507571	+	0.861610i	$0.330543\pi$
$194$	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	−0.807754	−	0.589520i	$-0.799317\pi$
$197$	1.49708	−	2.59303i	0.106663	−	0.184745i	0.914416	+	0.404775i	$0.132650\pi$
$198$		0			0
$199$	−7.44425	−	12.8938i	−0.527709	−	0.914018i	−0.999478	−	0.0322965i	$-0.989718\pi$
$199$	−7.44425	−	12.8938i	−0.527709	−	0.914018i	0.471770	−	0.881722i	$-0.343615\pi$
$200$	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	0.948116	+	0.317925i	$0.102986\pi$
$211$	2.41006	+	13.6681i	0.165915	+	0.940951i	−0.782201	+	0.623026i	$0.785903\pi$
$212$	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	0.451124	−	0.892461i	$-0.351023\pi$
$223$	−5.21828	−	4.37866i	−0.349442	−	0.293216i	−0.800566	+	0.599245i	$0.795468\pi$
$224$	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	−0.875799	−	0.482675i	$-0.839665\pi$
$227$	1.69148	−	9.59286i	0.112267	−	0.636700i	0.988067	−	0.154025i	$-0.0492237\pi$
$228$		0			0
$229$	13.1978	+	4.80362i	0.872138	+	0.317432i	0.739032	−	0.673670i	$-0.235283\pi$
$229$	13.1978	+	4.80362i	0.872138	+	0.317432i	0.133105	+	0.991102i	$0.457505\pi$
$230$	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	0.939944	−	0.341330i	$-0.110877\pi$
$233$	2.66167	+	4.61014i	0.174372	+	0.302020i	−0.765572	+	0.643350i	$0.777544\pi$
$234$		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	−0.966323	−	0.257332i	$-0.917156\pi$
$239$	−13.6153	+	11.4246i	−0.880700	+	0.738995i	0.0856227	+	0.996328i	$0.472712\pi$
$240$		0			0
$241$	1.88577	−	0.686364i	0.121473	−	0.0442126i	−0.280568	−	0.959834i	$-0.590523\pi$
$241$	1.88577	−	0.686364i	0.121473	−	0.0442126i	0.402041	+	0.915621i	$0.368301\pi$
$242$	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	−0.207125	−	0.978314i	$-0.566411\pi$
$251$	11.7822	−	20.4073i	0.743683	−	1.28810i	0.950808	−	0.309782i	$-0.100256\pi$
$252$		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	0.508403	−	0.861119i	$-0.330236\pi$
$257$	5.52029	+	2.00922i	0.344346	+	0.125332i	−0.164057	+	0.986451i	$0.552458\pi$
$258$		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	−0.0463663	−	0.998925i	$-0.514764\pi$
$263$	−16.8362	−	14.1273i	−1.03817	−	0.871125i	−0.991800	+	0.127800i	$0.959209\pi$
$264$		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	0.0226353	−	0.999744i	$-0.492794\pi$
$277$	−15.9441	−	13.3787i	−0.957990	−	0.803849i	−0.980625	+	0.195895i	$0.937239\pi$
$278$	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	0.853093	+	0.521758i	$0.174724\pi$
$281$	−2.12897	+	12.0740i	−0.127004	+	0.720275i	−0.980097	+	0.198517i	$0.936387\pi$
$282$		0			0
$283$	−4.29682	−	1.56391i	−0.255419	−	0.0929650i	0.211137	−	0.977456i	$-0.432283\pi$
$283$	−4.29682	−	1.56391i	−0.255419	−	0.0929650i	−0.466556	+	0.884491i	$0.654506\pi$
$284$	−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	−0.999989	−	0.00460992i	$-0.998533\pi$
$293$	−20.0117	+	16.7918i	−1.16910	+	0.980988i	−0.169106	+	0.985598i	$0.554088\pi$
$294$		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	0.815212	−	0.579163i	$-0.196621\pi$
$307$	−1.64638	−	2.85162i	−0.0939641	−	0.162751i	−0.909176	+	0.416412i	$0.863287\pi$
$308$	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	0.983067	+	0.183246i	$0.0586606\pi$
$311$	32.6944	+	11.8998i	1.85393	+	0.674775i	0.870861	+	0.491529i	$0.163562\pi$
$312$		0			0
$313$	1.84550	−	10.4664i	0.104314	−	0.591594i	−0.887178	−	0.461427i	$-0.847337\pi$
$313$	1.84550	−	10.4664i	0.104314	−	0.591594i	0.991492	−	0.130167i	$-0.0415514\pi$
$314$	−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	0.912147	−	0.409864i	$-0.134424\pi$
$317$	11.8739	+	9.96335i	0.666902	+	0.559598i	−0.245244	+	0.969461i	$0.578868\pi$
$318$		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	0.282259	−	0.959338i	$-0.408916\pi$
$331$	−11.1615	−	9.36559i	−0.613490	−	0.514780i	−0.895750	+	0.444559i	$0.853361\pi$
$332$	−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	0.810636	−	0.585550i	$-0.199121\pi$
$337$	19.3716	+	7.05067i	1.05524	+	0.384074i	0.244599	+	0.969624i	$0.421344\pi$
$338$	−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	−0.0931979	−	0.995648i	$-0.529709\pi$
$347$	16.2275	−	13.6165i	0.871140	−	0.730973i	0.964338	+	0.264674i	$0.0852645\pi$
$348$		0			0
$349$	4.34699	−	1.58218i	0.232689	−	0.0846919i	−0.223044	−	0.974808i	$-0.571599\pi$
$349$	4.34699	−	1.58218i	0.232689	−	0.0846919i	0.455733	+	0.890116i	$0.349377\pi$
$350$	2.98333			0.159466
$351$		0			0
$352$	−36.3387			−1.93686
$353$	−12.8206	+	4.66632i	−0.682372	+	0.248363i	−0.659866	−	0.751383i	$-0.729387\pi$
$353$	−12.8206	+	4.66632i	−0.682372	+	0.248363i	−0.0225065	+	0.999747i	$0.507165\pi$
$354$		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	0.204683	+	0.978828i	$0.434384\pi$
$359$	−14.1223	+	24.4606i	−0.745349	+	1.29098i	−0.950032	+	0.312153i	$0.898950\pi$
$360$		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	−0.249434	−	0.968392i	$-0.580245\pi$
$367$	6.05688	−	34.3503i	0.316167	−	1.79307i	0.565601	−	0.824679i	$-0.308644\pi$
$368$	−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	0.995468	−	0.0951001i	$-0.0303171\pi$
$373$	0.531266	+	3.01296i	0.0275079	+	0.156005i	−0.967960	+	0.251105i	$0.919206\pi$
$374$	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	−0.995642	−	0.0932607i	$-0.970271\pi$
$383$	−1.79933	−	10.2045i	−0.0919416	−	0.521427i	0.903700	−	0.428166i	$-0.140840\pi$
$384$		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	−0.982871	−	0.184297i	$-0.940999\pi$
$389$	0.0741393	−	0.420465i	0.00375901	−	0.0213184i	0.986630	+	0.162979i	$0.0521102\pi$
$390$		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	−0.295266	−	0.955415i	$-0.595408\pi$
$397$	13.5445	−	23.4598i	0.679781	−	1.17741i	0.975047	−	0.221999i	$-0.0712583\pi$
$398$	−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	−0.998760	−	0.0497810i	$-0.984148\pi$
$401$	−22.4914	+	18.8725i	−1.12317	+	0.942450i	−0.124408	+	0.992231i	$0.539703\pi$
$402$		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	−0.939303	−	0.343088i	$-0.888527\pi$
$409$	−15.4618	+	12.9740i	−0.764536	+	0.641522i	0.174767	+	0.984610i	$0.444083\pi$
$410$	−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	0.834203	−	0.551458i	$-0.185928\pi$
$419$	22.9006	+	8.33514i	1.11877	+	0.407198i	0.284566	+	0.958657i	$0.408151\pi$
$420$		0			0
$421$	−4.54516	+	25.7769i	−0.221518	+	1.25629i	0.647714	+	0.761884i	$0.275725\pi$
$421$	−4.54516	+	25.7769i	−0.221518	+	1.25629i	−0.869232	+	0.494405i	$0.835386\pi$
$422$	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	0.734592	−	0.678510i	$-0.237374\pi$
$439$	4.06372	+	3.40986i	0.193951	+	0.162744i	−0.540641	+	0.841253i	$0.681818\pi$
$440$	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	0.0838834	+	0.996476i	$0.473268\pi$
$443$	−7.06684	+	40.0781i	−0.335756	+	1.90417i	−0.419639	+	0.907691i	$0.637843\pi$
$444$		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	0.988623	−	0.150417i	$-0.0480615\pi$
$449$	7.71401	+	13.3611i	0.364047	+	0.630547i	−0.624576	+	0.780964i	$0.714728\pi$
$450$		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	−0.393987	−	0.919116i	$-0.628904\pi$
$457$	−2.24469	+	0.816999i	−0.105002	+	0.0382176i	0.288985	+	0.957334i	$0.406682\pi$
$458$	37.9922			1.77526
$459$		0			0
$460$	41.3143			1.92629
$461$	30.5248	−	11.1101i	1.42168	−	0.517451i	0.487148	−	0.873319i	$-0.338037\pi$
$461$	30.5248	−	11.1101i	1.42168	−	0.517451i	0.934536	+	0.355869i	$0.115815\pi$
$462$		0			0
$463$	25.9525	−	21.7767i	1.20611	−	1.01205i	0.206679	−	0.978409i	$-0.433734\pi$
$463$	25.9525	−	21.7767i	1.20611	−	1.01205i	0.999434	−	0.0336404i	$-0.0107101\pi$
$464$	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	−0.980354	−	0.197247i	$-0.936800\pi$
$467$	−6.90133	+	11.9535i	−0.319356	+	0.553140i	0.660998	+	0.750388i	$0.270133\pi$
$468$		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	0.533841	−	0.845585i	$-0.320748\pi$
$479$	−4.51286	−	3.78674i	−0.206198	−	0.173020i	−0.740038	+	0.672565i	$0.765193\pi$
$480$		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	0.962802	−	0.270206i	$-0.0870919\pi$
$491$	−0.761188	−	4.31691i	−0.0343519	−	0.194820i	−0.997154	+	0.0753869i	$0.975981\pi$
$492$		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	−0.534177	−	0.845373i	$-0.679378\pi$
$499$	−33.2120	−	12.0882i	−1.48677	−	0.541142i	−0.952598	+	0.304231i	$0.901600\pi$
$500$	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	0.757417	−	0.652932i	$-0.226461\pi$
$503$	−4.18829	−	7.25434i	−0.186747	−	0.323455i	−0.944164	+	0.329477i	$0.893128\pi$
$504$		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	−0.575209	−	0.818006i	$-0.695079\pi$
$509$	2.94389	−	2.47021i	0.130485	−	0.109490i	0.705695	+	0.708516i	$0.250635\pi$
$510$		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	−0.566424	−	0.824114i	$-0.691674\pi$
$521$	9.82615	−	17.0194i	0.430491	−	0.745633i	0.996916	+	0.0784810i	$0.0250070\pi$
$522$		0			0
$523$	19.8051	+	34.3035i	0.866018	+	1.49999i	0.866032	+	0.499988i	$0.166662\pi$
$523$	19.8051	+	34.3035i	0.866018	+	1.49999i	−1.41543e−5		1.00000i	$0.500005\pi$
$524$	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	0.319681	−	0.947525i	$-0.396424\pi$
$547$	−13.0490	−	10.9495i	−0.557937	−	0.468165i	−0.877618	+	0.479360i	$0.840869\pi$
$548$	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	−0.962806	−	0.270194i	$-0.912912\pi$
$557$	−16.8840	−	29.2439i	−0.715398	−	1.23911i	0.247408	−	0.968911i	$-0.420421\pi$
$558$		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	−0.197779	−	0.980247i	$-0.563373\pi$
$563$	17.3978	−	14.5985i	0.733232	−	0.615254i	0.931011	+	0.364992i	$0.118928\pi$
$564$		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	−0.118887	−	0.992908i	$-0.537933\pi$
$569$	10.2158	−	3.71825i	0.428269	−	0.155877i	0.547156	+	0.837031i	$0.315710\pi$
$570$		0			0
$571$	11.4016	−	9.56706i	0.477141	−	0.400369i	−0.372250	−	0.928132i	$-0.621414\pi$
$571$	11.4016	−	9.56706i	0.477141	−	0.400369i	0.849391	+	0.527763i	$0.176969\pi$
$572$	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	0.936141	+	0.351624i	$0.114371\pi$
$577$	18.5582	+	32.1437i	0.772586	+	1.33816i	−0.163555	+	0.986534i	$0.552296\pi$
$578$	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	0.381240	−	0.924476i	$-0.375497\pi$
$587$	−11.2174	−	9.41248i	−0.462990	−	0.388495i	−0.844230	+	0.535982i	$0.819942\pi$
$588$		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	0.912307	+	0.409506i	$0.134299\pi$
$599$	4.77444	+	27.0772i	0.195078	+	1.10634i	−0.717229	+	0.696838i	$0.754590\pi$
$600$		0			0
$601$	34.6076	+	29.0392i	1.41167	+	1.18453i	0.955628	+	0.294578i	$0.0951789\pi$
$601$	34.6076	+	29.0392i	1.41167	+	1.18453i	0.456045	+	0.889957i	$0.349266\pi$
$602$	−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	−0.00614504	−	0.999981i	$-0.501956\pi$
$607$	−16.1037	−	5.86126i	−0.653628	−	0.237901i	−0.647483	+	0.762080i	$0.724178\pi$
$608$	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	−0.861253	−	0.508176i	$-0.830320\pi$
$613$	0.234380	−	0.405959i	0.00946653	−	0.0163965i	0.870720	+	0.491779i	$0.163653\pi$
$614$	−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	−0.675113	−	0.737714i	$-0.735905\pi$
$617$	−1.63539	+	1.37225i	−0.0658383	+	0.0552449i	0.609275	+	0.792959i	$0.291461\pi$
$618$		0			0
$619$	−8.02272	+	2.92003i	−0.322460	+	0.117366i	−0.498178	−	0.867075i	$-0.665998\pi$
$619$	−8.02272	+	2.92003i	−0.322460	+	0.117366i	0.175718	+	0.984441i	$0.443775\pi$
$620$	−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	0.959645	−	0.281214i	$-0.0907370\pi$
$631$	5.93539	+	10.2804i	0.236284	+	0.409256i	−0.723361	+	0.690470i	$0.757404\pi$
$632$	−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	0.719488	−	0.694505i	$-0.244376\pi$
$641$	4.06284	+	3.40913i	0.160472	+	0.134652i	−0.559016	+	0.829157i	$0.688821\pi$
$642$		0			0
$643$	−0.143063	−	0.811352i	−0.00564187	−	0.0319966i	0.981857	−	0.189624i	$-0.0607268\pi$
$643$	−0.143063	−	0.811352i	−0.00564187	−	0.0319966i	−0.987499	+	0.157627i	$0.949616\pi$
$644$	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	0.988225	−	0.153004i	$-0.0488949\pi$
$653$	0.185692	+	1.05311i	0.00726668	+	0.0412114i	−0.980959	+	0.194216i	$0.937784\pi$
$654$		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	0.720086	+	0.693884i	$0.244102\pi$
$659$	−4.97750	+	28.2288i	−0.193896	+	1.09964i	−0.913982	+	0.405754i	$0.867009\pi$
$660$		0			0
$661$	4.22459	+	1.53763i	0.164318	+	0.0598067i	0.422869	−	0.906191i	$-0.361023\pi$
$661$	4.22459	+	1.53763i	0.164318	+	0.0598067i	−0.258552	+	0.965997i	$0.583245\pi$
$662$	−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	−0.647699	−	0.761897i	$-0.724268\pi$
$673$	−16.9695	+	6.17640i	−0.654127	+	0.238083i	−0.00642810	+	0.999979i	$0.502046\pi$
$674$	55.7643			2.14796
$675$		0			0
$676$	−17.6151			−0.677505
$677$	−14.7900	+	5.38311i	−0.568425	+	0.206890i	−0.610214	−	0.792237i	$-0.708917\pi$
$677$	−14.7900	+	5.38311i	−0.568425	+	0.206890i	0.0417888	+	0.999126i	$0.486694\pi$
$678$		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	−0.838403	−	0.545051i	$-0.816510\pi$
$683$	1.38059	−	2.39125i	0.0528268	−	0.0914987i	0.891230	+	0.453552i	$0.149844\pi$
$684$		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	0.628653	+	0.777686i	$0.283607\pi$
$691$	−5.99530	+	34.0010i	−0.228072	+	1.29346i	−0.856725	+	0.515774i	$0.827504\pi$
$692$	−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	0.947496	−	0.319768i	$-0.103605\pi$
$709$	21.2249	+	17.8098i	0.797117	+	0.668861i	−0.150379	+	0.988628i	$0.548049\pi$
$710$	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	−0.989887	−	0.141859i	$-0.954692\pi$
$719$	−16.5657	−	28.6927i	−0.617797	−	1.07006i	0.372090	−	0.928197i	$-0.378641\pi$
$720$		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	−0.340580	−	0.940215i	$-0.610624\pi$
$727$	0.0776238	−	0.0282527i	0.00287891	−	0.00104784i	0.343459	+	0.939168i	$0.388401\pi$
$728$	−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	−0.970792	−	0.239924i	$-0.922878\pi$
$733$	−24.4502	+	20.5162i	−0.903089	+	0.757782i	0.0677025	+	0.997706i	$0.478433\pi$
$734$	−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	0.981052	+	0.193745i	$0.0620634\pi$
$739$	17.8960	+	30.9967i	0.658314	+	1.14023i	−0.322738	+	0.946488i	$0.604603\pi$
$740$	−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	−0.0222120	−	0.999753i	$-0.507071\pi$
$743$	−18.5861	−	6.76477i	−0.681856	−	0.248175i	−0.659644	+	0.751578i	$0.729293\pi$
$744$		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	0.914154	+	0.405367i	$0.132856\pi$
$751$	5.31026	+	30.1160i	0.193774	+	1.09895i	−0.720380	+	0.693580i	$0.756032\pi$
$752$	−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	0.668391	+	0.743810i	$0.266983\pi$
$761$	8.12986	+	46.1067i	0.294707	+	1.67137i	−0.373684	+	0.927556i	$0.621905\pi$
$762$		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	0.0832316	−	0.996530i	$-0.473476\pi$
$769$	−13.6870	−	4.98167i	−0.493567	−	0.179644i	−0.576798	+	0.816887i	$0.695698\pi$
$770$	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	0.997532	−	0.0702080i	$-0.0223663\pi$
$773$	12.1767	+	21.0906i	0.437964	+	0.758576i	−0.559568	+	0.828784i	$0.689033\pi$
$774$		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

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

Introduction

L-functions

Modular forms

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