LMFDB - Embedded newform 378.2.l.a.341.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(143,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("378.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.l (of order $6$, degree $2$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.6
Root			$-1.68301 - 0.409224i$ of defining polynomial
Character	$\chi$	$=$	378.341
Dual form			378.2.l.a.143.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(-0.714925 - 1.23829i) q^{5} +(0.327442 - 2.62541i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-0.714925 - 1.23829i) q^{5} +(0.327442 - 2.62541i) q^{7} -1.00000i q^{8} +(1.23829 - 0.714925i) q^{10} +(-2.96133 - 1.70972i) q^{11} +(-5.48813 - 3.16857i) q^{13} +(2.62541 + 0.327442i) q^{14} +1.00000 q^{16} +(1.14201 + 1.97802i) q^{17} +(-1.87673 - 1.08353i) q^{19} +(0.714925 + 1.23829i) q^{20} +(1.70972 - 2.96133i) q^{22} +(6.97507 - 4.02706i) q^{23} +(1.47776 - 2.55956i) q^{25} +(3.16857 - 5.48813i) q^{26} +(-0.327442 + 2.62541i) q^{28} +(0.298879 - 0.172558i) q^{29} +4.34228i q^{31} +1.00000i q^{32} +(-1.97802 + 1.14201i) q^{34} +(-3.48511 + 1.47150i) q^{35} +(1.07786 - 1.86690i) q^{37} +(1.08353 - 1.87673i) q^{38} +(-1.23829 + 0.714925i) q^{40} +(-0.202180 + 0.350186i) q^{41} +(2.90883 + 5.03824i) q^{43} +(2.96133 + 1.70972i) q^{44} +(4.02706 + 6.97507i) q^{46} +5.51829 q^{47} +(-6.78556 - 1.71934i) q^{49} +(2.55956 + 1.47776i) q^{50} +(5.48813 + 3.16857i) q^{52} +(-8.56310 + 4.94391i) q^{53} +4.88930i q^{55} +(-2.62541 - 0.327442i) q^{56} +(0.172558 + 0.298879i) q^{58} -11.0296 q^{59} -11.4797i q^{61} -4.34228 q^{62} -1.00000 q^{64} +9.06117i q^{65} +4.25366 q^{67} +(-1.14201 - 1.97802i) q^{68} +(-1.47150 - 3.48511i) q^{70} -3.55393i q^{71} +(-0.201057 + 0.116080i) q^{73} +(1.86690 + 1.07786i) q^{74} +(1.87673 + 1.08353i) q^{76} +(-5.45839 + 7.21486i) q^{77} +14.5620 q^{79} +(-0.714925 - 1.23829i) q^{80} +(-0.350186 - 0.202180i) q^{82} +(-0.811624 - 1.40577i) q^{83} +(1.63290 - 2.82827i) q^{85} +(-5.03824 + 2.90883i) q^{86} +(-1.70972 + 2.96133i) q^{88} +(2.02974 - 3.51562i) q^{89} +(-10.1159 + 13.3711i) q^{91} +(-6.97507 + 4.02706i) q^{92} +5.51829i q^{94} +3.09858i q^{95} +(-9.18719 + 5.30423i) q^{97} +(1.71934 - 6.78556i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 2 q^{7}+O(q^{10}) $ 16 * q - 16 * q^4 + 2 * q^7	$ 16 q - 16 q^{4} + 2 q^{7} - 12 q^{11} + 6 q^{13} + 6 q^{14} + 16 q^{16} + 18 q^{17} + 6 q^{23} - 8 q^{25} - 12 q^{26} - 2 q^{28} - 6 q^{29} - 30 q^{35} - 2 q^{37} + 6 q^{41} - 2 q^{43} + 12 q^{44} + 6 q^{46} + 36 q^{47} - 8 q^{49} + 12 q^{50} - 6 q^{52} + 36 q^{53} - 6 q^{56} + 6 q^{58} - 60 q^{59} - 36 q^{62} - 16 q^{64} - 28 q^{67} - 18 q^{68} - 18 q^{70} - 18 q^{74} + 42 q^{77} + 32 q^{79} - 12 q^{85} - 24 q^{86} + 24 q^{89} - 12 q^{91} - 6 q^{92} + 6 q^{97} + 24 q^{98}+O(q^{100}) $ 16 * q - 16 * q^4 + 2 * q^7 - 12 * q^11 + 6 * q^13 + 6 * q^14 + 16 * q^16 + 18 * q^17 + 6 * q^23 - 8 * q^25 - 12 * q^26 - 2 * q^28 - 6 * q^29 - 30 * q^35 - 2 * q^37 + 6 * q^41 - 2 * q^43 + 12 * q^44 + 6 * q^46 + 36 * q^47 - 8 * q^49 + 12 * q^50 - 6 * q^52 + 36 * q^53 - 6 * q^56 + 6 * q^58 - 60 * q^59 - 36 * q^62 - 16 * q^64 - 28 * q^67 - 18 * q^68 - 18 * q^70 - 18 * q^74 + 42 * q^77 + 32 * q^79 - 12 * q^85 - 24 * q^86 + 24 * q^89 - 12 * q^91 - 6 * q^92 + 6 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−0.714925	−	1.23829i	−0.319724	−	0.553779i	0.660706	−	0.750645i	$-0.270257\pi$
$5$	−0.714925	−	1.23829i	−0.319724	−	0.553779i	−0.980430	+	0.196866i	$0.936924\pi$
$6$		0			0
$7$	0.327442	−	2.62541i	0.123762	−	0.992312i
$7$	0.327442	−	2.62541i	0.123762	−	0.992312i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.23829	−	0.714925i	0.391581	−	0.226079i
$11$	−2.96133	−	1.70972i	−0.892874	−	0.515501i	−0.0179923	−	0.999838i	$-0.505727\pi$
$11$	−2.96133	−	1.70972i	−0.892874	−	0.515501i	−0.874881	+	0.484337i	$0.839061\pi$
$12$		0			0
$13$	−5.48813	−	3.16857i	−1.52213	−	0.878804i	−0.999658	−	0.0261501i	$-0.991675\pi$
$13$	−5.48813	−	3.16857i	−1.52213	−	0.878804i	−0.522476	−	0.852654i	$-0.674991\pi$
$14$	2.62541	+	0.327442i	0.701671	+	0.0875127i
$15$		0			0
$16$	1.00000			0.250000
$17$	1.14201	+	1.97802i	0.276978	+	0.479739i	0.970632	−	0.240569i	$-0.0773339\pi$
$17$	1.14201	+	1.97802i	0.276978	+	0.479739i	−0.693655	+	0.720308i	$0.744001\pi$
$18$		0			0
$19$	−1.87673	−	1.08353i	−0.430553	−	0.248580i	0.269029	−	0.963132i	$-0.413297\pi$
$19$	−1.87673	−	1.08353i	−0.430553	−	0.248580i	−0.699582	+	0.714552i	$0.746630\pi$
$20$	0.714925	+	1.23829i	0.159862	+	0.276889i
$21$		0			0
$22$	1.70972	−	2.96133i	0.364514	−	0.631357i
$23$	6.97507	−	4.02706i	1.45440	−	0.839699i	0.455675	−	0.890146i	$-0.349398\pi$
$23$	6.97507	−	4.02706i	1.45440	−	0.839699i	0.998727	+	0.0504469i	$0.0160646\pi$
$24$		0			0
$25$	1.47776	−	2.55956i	0.295553	−	0.511912i
$26$	3.16857	−	5.48813i	0.621408	−	1.07631i
$27$		0			0
$28$	−0.327442	+	2.62541i	−0.0618808	+	0.496156i
$29$	0.298879	−	0.172558i	0.0555003	−	0.0320431i	−0.471993	−	0.881602i	$-0.656465\pi$
$29$	0.298879	−	0.172558i	0.0555003	−	0.0320431i	0.527493	+	0.849559i	$0.323132\pi$
$30$		0			0
$31$			4.34228i			0.779896i	0.920837	+	0.389948i	$0.127507\pi$
$31$			4.34228i			0.779896i	−0.920837	+	0.389948i	$0.872493\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−1.97802	+	1.14201i	−0.339227	+	0.195853i
$35$	−3.48511	+	1.47150i	−0.589091	+	0.248730i
$36$		0			0
$37$	1.07786	−	1.86690i	0.177199	−	0.306917i	−0.763721	−	0.645546i	$-0.776630\pi$
$37$	1.07786	−	1.86690i	0.177199	−	0.306917i	0.940920	+	0.338629i	$0.109963\pi$
$38$	1.08353	−	1.87673i	0.175772	−	0.304447i
$39$		0			0
$40$	−1.23829	+	0.714925i	−0.195790	+	0.113040i
$41$	−0.202180	+	0.350186i	−0.0315752	+	0.0546898i	−0.881381	−	0.472406i	$-0.843386\pi$
$41$	−0.202180	+	0.350186i	−0.0315752	+	0.0546898i	0.849806	+	0.527096i	$0.176719\pi$
$42$		0			0
$43$	2.90883	+	5.03824i	0.443592	+	0.768325i	0.997953	−	0.0639521i	$-0.0203705\pi$
$43$	2.90883	+	5.03824i	0.443592	+	0.768325i	−0.554361	+	0.832277i	$0.687037\pi$
$44$	2.96133	+	1.70972i	0.446437	+	0.257750i
$45$		0			0
$46$	4.02706	+	6.97507i	0.593757	+	1.02842i
$47$	5.51829			0.804926			0.402463	−	0.915436i	$-0.368154\pi$
$47$	5.51829			0.804926			0.402463	+	0.915436i	$0.368154\pi$
$48$		0			0
$49$	−6.78556	−	1.71934i	−0.969366	−	0.245620i
$50$	2.55956	+	1.47776i	0.361977	+	0.208987i
$51$		0			0
$52$	5.48813	+	3.16857i	0.761067	+	0.439402i
$53$	−8.56310	+	4.94391i	−1.17623	+	0.679098i	−0.955140	−	0.296155i	$-0.904296\pi$
$53$	−8.56310	+	4.94391i	−1.17623	+	0.679098i	−0.221093	+	0.975253i	$0.570962\pi$
$54$		0			0
$55$			4.88930i			0.659273i
$56$	−2.62541	−	0.327442i	−0.350835	−	0.0437563i
$57$		0			0
$58$	0.172558	+	0.298879i	0.0226579	+	0.0392447i
$59$	−11.0296			−1.43593			−0.717966	−	0.696079i	$-0.754926\pi$
$59$	−11.0296			−1.43593			−0.717966	+	0.696079i	$0.754926\pi$
$60$		0			0
$61$		−	11.4797i		−	1.46983i	−0.678159	−	0.734915i	$-0.737222\pi$
$61$		−	11.4797i		−	1.46983i	0.678159	−	0.734915i	$-0.262778\pi$
$62$	−4.34228			−0.551470
$63$		0			0
$64$	−1.00000			−0.125000
$65$			9.06117i			1.12390i
$66$		0			0
$67$	4.25366			0.519667			0.259833	−	0.965653i	$-0.416332\pi$
$67$	4.25366			0.519667			0.259833	+	0.965653i	$0.416332\pi$
$68$	−1.14201	−	1.97802i	−0.138489	−	0.239870i
$69$		0			0
$70$	−1.47150	−	3.48511i	−0.175878	−	0.416550i
$71$		−	3.55393i		−	0.421773i	−0.977511	−	0.210887i	$-0.932365\pi$
$71$		−	3.55393i		−	0.421773i	0.977511	−	0.210887i	$-0.0676351\pi$
$72$		0			0
$73$	−0.201057	+	0.116080i	−0.0235320	+	0.0135862i	−0.511720	−	0.859152i	$-0.670991\pi$
$73$	−0.201057	+	0.116080i	−0.0235320	+	0.0135862i	0.488188	+	0.872739i	$0.337658\pi$
$74$	1.86690	+	1.07786i	0.217023	+	0.125298i
$75$		0			0
$76$	1.87673	+	1.08353i	0.215276	+	0.124290i
$77$	−5.45839	+	7.21486i	−0.622041	+	0.822210i
$78$		0			0
$79$	14.5620			1.63835			0.819177	−	0.573541i	$-0.194431\pi$
$79$	14.5620			1.63835			0.819177	+	0.573541i	$0.194431\pi$
$80$	−0.714925	−	1.23829i	−0.0799311	−	0.138445i
$81$		0			0
$82$	−0.350186	−	0.202180i	−0.0386716	−	0.0223270i
$83$	−0.811624	−	1.40577i	−0.0890873	−	0.154304i	0.818038	−	0.575164i	$-0.195062\pi$
$83$	−0.811624	−	1.40577i	−0.0890873	−	0.154304i	−0.907126	+	0.420860i	$0.861728\pi$
$84$		0			0
$85$	1.63290	−	2.82827i	0.177113	−	0.306769i
$86$	−5.03824	+	2.90883i	−0.543287	+	0.313667i
$87$		0			0
$88$	−1.70972	+	2.96133i	−0.182257	+	0.315679i
$89$	2.02974	−	3.51562i	0.215152	−	0.372655i	−0.738167	−	0.674618i	$-0.764309\pi$
$89$	2.02974	−	3.51562i	0.215152	−	0.372655i	0.953320	+	0.301963i	$0.0976419\pi$
$90$		0			0
$91$	−10.1159	+	13.3711i	−1.06043	+	1.40167i
$92$	−6.97507	+	4.02706i	−0.727201	+	0.419850i
$93$		0			0
$94$			5.51829i			0.569169i
$95$			3.09858i			0.317908i
$96$		0			0
$97$	−9.18719	+	5.30423i	−0.932818	+	0.538563i	−0.887702	−	0.460419i	$-0.847699\pi$
$97$	−9.18719	+	5.30423i	−0.932818	+	0.538563i	−0.0451164	+	0.998982i	$0.514366\pi$
$98$	1.71934	−	6.78556i	0.173680	−	0.685445i
$99$		0			0
$100$	−1.47776	+	2.55956i	−0.147776	+	0.255956i
$101$	4.02443	−	6.97052i	0.400446	−	0.693593i	−0.593334	−	0.804957i	$-0.702189\pi$
$101$	4.02443	−	6.97052i	0.400446	−	0.693593i	0.993780	+	0.111364i	$0.0355219\pi$
$102$		0			0
$103$	−2.43692	+	1.40695i	−0.240117	+	0.138631i	−0.615230	−	0.788347i	$-0.710937\pi$
$103$	−2.43692	+	1.40695i	−0.240117	+	0.138631i	0.375114	+	0.926979i	$0.377604\pi$
$104$	−3.16857	+	5.48813i	−0.310704	+	0.538156i
$105$		0			0
$106$	−4.94391	−	8.56310i	−0.480195	−	0.831722i
$107$	13.7019	+	7.91078i	1.32461	+	0.764764i	0.984460	−	0.175607i	$-0.0561888\pi$
$107$	13.7019	+	7.91078i	1.32461	+	0.764764i	0.340150	+	0.940371i	$0.389522\pi$
$108$		0			0
$109$	5.10675	+	8.84514i	0.489138	+	0.847211i	0.999922	−	0.0124977i	$-0.00397826\pi$
$109$	5.10675	+	8.84514i	0.489138	+	0.847211i	−0.510784	+	0.859709i	$0.670645\pi$
$110$	−4.88930			−0.466176
$111$		0			0
$112$	0.327442	−	2.62541i	0.0309404	−	0.248078i
$113$	−7.28808	−	4.20778i	−0.685605	−	0.395834i	0.116359	−	0.993207i	$-0.462878\pi$
$113$	−7.28808	−	4.20778i	−0.685605	−	0.395834i	−0.801963	+	0.597373i	$0.796211\pi$
$114$		0			0
$115$	−9.97330	−	5.75809i	−0.930015	−	0.536945i
$116$	−0.298879	+	0.172558i	−0.0277502	+	0.0160216i
$117$		0			0
$118$		−	11.0296i		−	1.01536i
$119$	5.56705	−	2.35055i	0.510330	−	0.215475i
$120$		0			0
$121$	0.346305	+	0.599818i	0.0314823	+	0.0545289i
$122$	11.4797			1.03933
$123$		0			0
$124$		−	4.34228i		−	0.389948i
$125$	−11.3752			−1.01743
$126$		0			0
$127$	5.77773			0.512691			0.256345	−	0.966585i	$-0.417482\pi$
$127$	5.77773			0.512691			0.256345	+	0.966585i	$0.417482\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−9.06117			−0.794718
$131$	−2.22833	−	3.85959i	−0.194690	−	0.337214i	0.752109	−	0.659039i	$-0.229037\pi$
$131$	−2.22833	−	3.85959i	−0.194690	−	0.337214i	−0.946799	+	0.321825i	$0.895704\pi$
$132$		0			0
$133$	−3.45924	+	4.57241i	−0.299954	+	0.396478i
$134$			4.25366i			0.367460i
$135$		0			0
$136$	1.97802	−	1.14201i	0.169613	−	0.0979264i
$137$	−8.36293	−	4.82834i	−0.714493	−	0.412513i	0.0982292	−	0.995164i	$-0.468682\pi$
$137$	−8.36293	−	4.82834i	−0.714493	−	0.412513i	−0.812723	+	0.582651i	$0.802016\pi$
$138$		0			0
$139$	16.0680	+	9.27686i	1.36287	+	0.786853i	0.990005	−	0.141033i	$-0.0450423\pi$
$139$	16.0680	+	9.27686i	1.36287	+	0.786853i	0.372864	+	0.927886i	$0.378376\pi$
$140$	3.48511	−	1.47150i	0.294545	−	0.124365i
$141$		0			0
$142$	3.55393			0.298239
$143$	10.8348	+	18.7664i	0.906049	+	1.56932i
$144$		0			0
$145$	−0.427352	−	0.246732i	−0.0354896	−	0.0204899i
$146$	−0.116080	−	0.201057i	−0.00960689	−	0.0166396i
$147$		0			0
$148$	−1.07786	+	1.86690i	−0.0885993	+	0.153458i
$149$	5.63517	−	3.25347i	0.461651	−	0.266535i	−0.251087	−	0.967965i	$-0.580788\pi$
$149$	5.63517	−	3.25347i	0.461651	−	0.266535i	0.712738	+	0.701430i	$0.247455\pi$
$150$		0			0
$151$	−2.87950	+	4.98745i	−0.234331	+	0.405873i	−0.959078	−	0.283142i	$-0.908623\pi$
$151$	−2.87950	+	4.98745i	−0.234331	+	0.405873i	0.724747	+	0.689015i	$0.241956\pi$
$152$	−1.08353	+	1.87673i	−0.0878862	+	0.152223i
$153$		0			0
$154$	−7.21486	−	5.45839i	−0.581390	−	0.439850i
$155$	5.37699	−	3.10441i	0.431890	−	0.249352i
$156$		0			0
$157$		−	7.96361i		−	0.635565i	−0.948164	−	0.317783i	$-0.897062\pi$
$157$		−	7.96361i		−	0.635565i	0.948164	−	0.317783i	$-0.102938\pi$
$158$			14.5620i			1.15849i
$159$		0			0
$160$	1.23829	−	0.714925i	0.0978952	−	0.0565198i
$161$	−8.28874	−	19.6310i	−0.653245	−	1.54714i
$162$		0			0
$163$	5.69256	−	9.85980i	0.445876	−	0.772279i	−0.552237	−	0.833687i	$-0.686226\pi$
$163$	5.69256	−	9.85980i	0.445876	−	0.772279i	0.998113	+	0.0614080i	$0.0195591\pi$
$164$	0.202180	−	0.350186i	0.0157876	−	0.0273449i
$165$		0			0
$166$	1.40577	−	0.811624i	0.109109	−	0.0629942i
$167$	5.66418	−	9.81065i	0.438308	−	0.759171i	−0.559252	−	0.828998i	$-0.688911\pi$
$167$	5.66418	−	9.81065i	0.438308	−	0.759171i	0.997559	+	0.0698271i	$0.0222447\pi$
$168$		0			0
$169$	13.5797	+	23.5208i	1.04459	+	1.80929i
$170$	2.82827	+	1.63290i	0.216918	+	0.125238i
$171$		0			0
$172$	−2.90883	−	5.03824i	−0.221796	−	0.384162i
$173$	21.6914			1.64917			0.824584	−	0.565739i	$-0.191409\pi$
$173$	21.6914			1.64917			0.824584	+	0.565739i	$0.191409\pi$
$174$		0			0
$175$	−6.23602	−	4.71785i	−0.471399	−	0.356636i
$176$	−2.96133	−	1.70972i	−0.223218	−	0.128875i
$177$		0			0
$178$	3.51562	+	2.02974i	0.263507	+	0.152136i
$179$	18.0057	−	10.3956i	1.34581	−	0.777002i	0.358155	−	0.933662i	$-0.383406\pi$
$179$	18.0057	−	10.3956i	1.34581	−	0.777002i	0.987653	+	0.156660i	$0.0500726\pi$
$180$		0			0
$181$		−	21.5301i		−	1.60032i	−0.599788	−	0.800159i	$-0.704748\pi$
$181$		−	21.5301i		−	1.60032i	0.599788	−	0.800159i	$-0.295252\pi$
$182$	−13.3711	−	10.1159i	−0.991130	−	0.749837i
$183$		0			0
$184$	−4.02706	−	6.97507i	−0.296879	−	0.514209i
$185$	−3.08235			−0.226619
$186$		0			0
$187$		−	7.81007i		−	0.571129i
$188$	−5.51829			−0.402463
$189$		0			0
$190$	−3.09858			−0.224795
$191$		−	7.36938i		−	0.533230i	−0.963803	−	0.266615i	$-0.914095\pi$
$191$		−	7.36938i		−	0.533230i	0.963803	−	0.266615i	$-0.0859052\pi$
$192$		0			0
$193$	−2.82559			−0.203390			−0.101695	−	0.994816i	$-0.532427\pi$
$193$	−2.82559			−0.203390			−0.101695	+	0.994816i	$0.532427\pi$
$194$	−5.30423	−	9.18719i	−0.380821	−	0.659602i
$195$		0			0
$196$	6.78556	+	1.71934i	0.484683	+	0.122810i
$197$			26.0883i			1.85871i	0.369183	+	0.929357i	$0.379637\pi$
$197$			26.0883i			1.85871i	−0.369183	+	0.929357i	$0.620363\pi$
$198$		0			0
$199$	13.3511	−	7.70826i	0.946434	−	0.546424i	0.0544625	−	0.998516i	$-0.482655\pi$
$199$	13.3511	−	7.70826i	0.946434	−	0.546424i	0.891971	+	0.452092i	$0.149322\pi$
$200$	−2.55956	−	1.47776i	−0.180988	−	0.104494i
$201$		0			0
$202$	6.97052	+	4.02443i	0.490444	+	0.283158i
$203$	−0.355169	−	0.841182i	−0.0249280	−	0.0590394i
$204$		0			0
$205$	0.578174			0.0403814
$206$	−1.40695	−	2.43692i	−0.0980272	−	0.169788i
$207$		0			0
$208$	−5.48813	−	3.16857i	−0.380533	−	0.219701i
$209$	3.70508	+	6.41739i	0.256286	+	0.443900i
$210$		0			0
$211$	4.42465	−	7.66371i	0.304605	−	0.527592i	−0.672568	−	0.740035i	$-0.734809\pi$
$211$	4.42465	−	7.66371i	0.304605	−	0.527592i	0.977173	+	0.212443i	$0.0681421\pi$
$212$	8.56310	−	4.94391i	0.588116	−	0.339549i
$213$		0			0
$214$	−7.91078	+	13.7019i	−0.540770	+	0.936641i
$215$	4.15919	−	7.20393i	0.283655	−	0.491304i
$216$		0			0
$217$	11.4003	+	1.42185i	0.773901	+	0.0965212i
$218$	−8.84514	+	5.10675i	−0.599069	+	0.345873i
$219$		0			0
$220$		−	4.88930i		−	0.329636i
$221$		−	14.4741i		−	0.973637i
$222$		0			0
$223$	−6.88961	+	3.97772i	−0.461363	+	0.266368i	−0.712617	−	0.701553i	$-0.752490\pi$
$223$	−6.88961	+	3.97772i	−0.461363	+	0.266368i	0.251254	+	0.967921i	$0.419157\pi$
$224$	2.62541	+	0.327442i	0.175418	+	0.0218782i
$225$		0			0
$226$	4.20778	−	7.28808i	0.279897	−	0.484796i
$227$	−4.61984	+	8.00180i	−0.306630	+	0.531098i	−0.977623	−	0.210365i	$-0.932535\pi$
$227$	−4.61984	+	8.00180i	−0.306630	+	0.531098i	0.670993	+	0.741464i	$0.265868\pi$
$228$		0			0
$229$	−7.31319	+	4.22227i	−0.483269	+	0.279016i	−0.721778	−	0.692125i	$-0.756675\pi$
$229$	−7.31319	+	4.22227i	−0.483269	+	0.279016i	0.238509	+	0.971140i	$0.423341\pi$
$230$	5.75809	−	9.97330i	0.379677	−	0.657620i
$231$		0			0
$232$	−0.172558	−	0.298879i	−0.0113290	−	0.0196223i
$233$	−14.4176	−	8.32399i	−0.944526	−	0.545323i	−0.0531500	−	0.998587i	$-0.516926\pi$
$233$	−14.4176	−	8.32399i	−0.944526	−	0.545323i	−0.891376	+	0.453264i	$0.850259\pi$
$234$		0			0
$235$	−3.94517	−	6.83323i	−0.257354	−	0.445751i
$236$	11.0296			0.717966
$237$		0			0
$238$	2.35055	+	5.56705i	0.152364	+	0.360858i
$239$	23.6325	+	13.6442i	1.52866	+	0.882572i	0.999418	+	0.0341012i	$0.0108569\pi$
$239$	23.6325	+	13.6442i	1.52866	+	0.882572i	0.529242	+	0.848471i	$0.322476\pi$
$240$		0			0
$241$	−21.9018	−	12.6450i	−1.41082	−	0.814537i	−0.415354	−	0.909660i	$-0.636342\pi$
$241$	−21.9018	−	12.6450i	−1.41082	−	0.814537i	−0.995466	+	0.0951223i	$0.969676\pi$
$242$	−0.599818	+	0.346305i	−0.0385578	+	0.0222613i
$243$		0			0
$244$			11.4797i			0.734915i
$245$	2.72213	+	9.63167i	0.173911	+	0.615345i
$246$		0			0
$247$	6.86651	+	11.8931i	0.436906	+	0.756743i
$248$	4.34228			0.275735
$249$		0			0
$250$		−	11.3752i		−	0.719432i
$251$	8.19337			0.517161			0.258581	−	0.965990i	$-0.416745\pi$
$251$	8.19337			0.517161			0.258581	+	0.965990i	$0.416745\pi$
$252$		0			0
$253$	−27.5406			−1.73146
$254$			5.77773i			0.362527i
$255$		0			0
$256$	1.00000			0.0625000
$257$	3.31723	+	5.74560i	0.206923	+	0.358401i	0.950744	−	0.309978i	$-0.100322\pi$
$257$	3.31723	+	5.74560i	0.206923	+	0.358401i	−0.743821	+	0.668379i	$0.766988\pi$
$258$		0			0
$259$	−4.54845	−	3.44112i	−0.282627	−	0.213821i
$260$		−	9.06117i		−	0.561950i
$261$		0			0
$262$	3.85959	−	2.22833i	0.238446	−	0.137667i
$263$	−5.23590	−	3.02295i	−0.322860	−	0.186403i	0.329807	−	0.944048i	$-0.393016\pi$
$263$	−5.23590	−	3.02295i	−0.322860	−	0.186403i	−0.652666	+	0.757645i	$0.726350\pi$
$264$		0			0
$265$	12.2440	+	7.06905i	0.752140	+	0.434248i
$266$	−4.57241	−	3.45924i	−0.280352	−	0.212100i
$267$		0			0
$268$	−4.25366			−0.259833
$269$	−3.41069	−	5.90750i	−0.207954	−	0.360186i	0.743116	−	0.669163i	$-0.233347\pi$
$269$	−3.41069	−	5.90750i	−0.207954	−	0.360186i	−0.951070	+	0.308976i	$0.900014\pi$
$270$		0			0
$271$	−4.39780	−	2.53907i	−0.267148	−	0.154238i	0.360443	−	0.932781i	$-0.382625\pi$
$271$	−4.39780	−	2.53907i	−0.267148	−	0.154238i	−0.627591	+	0.778543i	$0.715959\pi$
$272$	1.14201	+	1.97802i	0.0692444	+	0.119935i
$273$		0			0
$274$	4.82834	−	8.36293i	0.291691	−	0.505223i
$275$	−8.75228	+	5.05313i	−0.527783	+	0.304715i
$276$		0			0
$277$	0.989567	−	1.71398i	0.0594573	−	0.102983i	−0.834765	−	0.550607i	$-0.814396\pi$
$277$	0.989567	−	1.71398i	0.0594573	−	0.102983i	0.894222	+	0.447624i	$0.147730\pi$
$278$	−9.27686	+	16.0680i	−0.556389	+	0.963694i
$279$		0			0
$280$	1.47150	+	3.48511i	0.0879392	+	0.208275i
$281$	15.2703	−	8.81631i	0.910950	−	0.525937i	0.0302131	−	0.999543i	$-0.490381\pi$
$281$	15.2703	−	8.81631i	0.910950	−	0.525937i	0.880737	+	0.473606i	$0.157048\pi$
$282$		0			0
$283$		−	5.15385i		−	0.306365i	−0.988198	−	0.153182i	$-0.951048\pi$
$283$		−	5.15385i		−	0.306365i	0.988198	−	0.153182i	$-0.0489522\pi$
$284$			3.55393i			0.210887i
$285$		0			0
$286$	−18.7664	+	10.8348i	−1.10968	+	0.640673i
$287$	0.853179	+	0.645471i	0.0503616	+	0.0381009i
$288$		0			0
$289$	5.89164	−	10.2046i	0.346567	−	0.600271i
$290$	0.246732	−	0.427352i	0.0144886	−	0.0250949i
$291$		0			0
$292$	0.201057	−	0.116080i	0.0117660	−	0.00679310i
$293$	−1.03248	+	1.78831i	−0.0603183	+	0.104474i	−0.894608	−	0.446852i	$-0.852545\pi$
$293$	−1.03248	+	1.78831i	−0.0603183	+	0.104474i	0.834289	+	0.551327i	$0.185878\pi$
$294$		0			0
$295$	7.88534	+	13.6578i	0.459102	+	0.795188i
$296$	−1.86690	−	1.07786i	−0.108511	−	0.0626491i
$297$		0			0
$298$	3.25347	+	5.63517i	0.188468	+	0.326437i
$299$	−51.0401			−2.95173
$300$		0			0
$301$	14.1799	−	5.98714i	0.817317	−	0.345093i
$302$	−4.98745	−	2.87950i	−0.286995	−	0.165697i
$303$		0			0
$304$	−1.87673	−	1.08353i	−0.107638	−	0.0621449i
$305$	−14.2152	+	8.20716i	−0.813961	+	0.469941i
$306$		0			0
$307$			1.09119i			0.0622772i	0.999515	+	0.0311386i	$0.00991333\pi$
$307$			1.09119i			0.0622772i	−0.999515	+	0.0311386i	$0.990087\pi$
$308$	5.45839	−	7.21486i	0.311021	−	0.411105i
$309$		0			0
$310$	3.10441	+	5.37699i	0.176318	+	0.305392i
$311$	−15.2220			−0.863161			−0.431580	−	0.902075i	$-0.642044\pi$
$311$	−15.2220			−0.863161			−0.431580	+	0.902075i	$0.642044\pi$
$312$		0			0
$313$			11.5704i			0.653996i	0.945025	+	0.326998i	$0.106037\pi$
$313$			11.5704i			0.653996i	−0.945025	+	0.326998i	$0.893963\pi$
$314$	7.96361			0.449412
$315$		0			0
$316$	−14.5620			−0.819177
$317$			17.1604i			0.963824i	0.876220	+	0.481912i	$0.160058\pi$
$317$			17.1604i			0.963824i	−0.876220	+	0.481912i	$0.839942\pi$
$318$		0			0
$319$	−1.18010			−0.0660731
$320$	0.714925	+	1.23829i	0.0399655	+	0.0692223i
$321$		0			0
$322$	19.6310	−	8.28874i	1.09400	−	0.461914i
$323$		−	4.94962i		−	0.275404i
$324$		0			0
$325$	−16.2203	+	9.36481i	−0.899742	+	0.519466i
$326$	9.85980	+	5.69256i	0.546084	+	0.315282i
$327$		0			0
$328$	0.350186	+	0.202180i	0.0193358	+	0.0111635i
$329$	1.80692	−	14.4878i	0.0996189	−	0.798738i
$330$		0			0
$331$	−26.4931			−1.45619			−0.728096	−	0.685475i	$-0.759595\pi$
$331$	−26.4931			−1.45619			−0.728096	+	0.685475i	$0.759595\pi$
$332$	0.811624	+	1.40577i	0.0445436	+	0.0771519i
$333$		0			0
$334$	9.81065	+	5.66418i	0.536815	+	0.309930i
$335$	−3.04105	−	5.26725i	−0.166150	−	0.287780i
$336$		0			0
$337$	4.06451	−	7.03993i	0.221408	−	0.383490i	−0.733828	−	0.679335i	$-0.762268\pi$
$337$	4.06451	−	7.03993i	0.221408	−	0.383490i	0.955236	+	0.295846i	$0.0956015\pi$
$338$	−23.5208	+	13.5797i	−1.27936	+	0.738640i
$339$		0			0
$340$	−1.63290	+	2.82827i	−0.0885565	+	0.153384i
$341$	7.42410	−	12.8589i	0.402037	−	0.696349i
$342$		0			0
$343$	−6.73586	+	17.2519i	−0.363702	+	0.931515i
$344$	5.03824	−	2.90883i	0.271644	−	0.156834i
$345$		0			0
$346$			21.6914i			1.16614i
$347$			25.6171i			1.37520i	0.726090	+	0.687599i	$0.241335\pi$
$347$			25.6171i			1.37520i	−0.726090	+	0.687599i	$0.758665\pi$
$348$		0			0
$349$	9.11932	−	5.26504i	0.488146	−	0.281831i	−0.235659	−	0.971836i	$-0.575725\pi$
$349$	9.11932	−	5.26504i	0.488146	−	0.281831i	0.723805	+	0.690005i	$0.242391\pi$
$350$	4.71785	−	6.23602i	0.252179	−	0.333329i
$351$		0			0
$352$	1.70972	−	2.96133i	0.0911285	−	0.157839i
$353$	−6.42186	+	11.1230i	−0.341801	+	0.592017i	−0.984767	−	0.173878i	$-0.944370\pi$
$353$	−6.42186	+	11.1230i	−0.341801	+	0.592017i	0.642966	+	0.765895i	$0.277704\pi$
$354$		0			0
$355$	−4.40078	+	2.54079i	−0.233569	+	0.134851i
$356$	−2.02974	+	3.51562i	−0.107576	+	0.186327i
$357$		0			0
$358$	10.3956	+	18.0057i	0.549424	+	0.951630i
$359$	−25.6881	−	14.8311i	−1.35577	−	0.782753i	−0.366718	−	0.930332i	$-0.619518\pi$
$359$	−25.6881	−	14.8311i	−1.35577	−	0.782753i	−0.989050	+	0.147579i	$0.952852\pi$
$360$		0			0
$361$	−7.15191	−	12.3875i	−0.376416	−	0.651972i
$362$	21.5301			1.13160
$363$		0			0
$364$	10.1159	−	13.3711i	0.530215	−	0.700835i
$365$	0.287482	+	0.165978i	0.0150475	+	0.00868767i
$366$		0			0
$367$	20.7828	+	11.9989i	1.08485	+	0.626340i	0.932201	−	0.361940i	$-0.117885\pi$
$367$	20.7828	+	11.9989i	1.08485	+	0.626340i	0.152651	+	0.988280i	$0.451219\pi$
$368$	6.97507	−	4.02706i	0.363600	−	0.209925i
$369$		0			0
$370$		−	3.08235i		−	0.160244i
$371$	10.1759	+	24.1005i	0.528305	+	1.25124i
$372$		0			0
$373$	5.91948	+	10.2528i	0.306499	+	0.530872i	0.977594	−	0.210500i	$-0.0675091\pi$
$373$	5.91948	+	10.2528i	0.306499	+	0.530872i	−0.671095	+	0.741371i	$0.734176\pi$
$374$	7.81007			0.403849
$375$		0			0
$376$		−	5.51829i		−	0.284584i
$377$	−2.18705			−0.112639
$378$		0			0
$379$	−13.1379			−0.674850			−0.337425	−	0.941352i	$-0.609556\pi$
$379$	−13.1379			−0.674850			−0.337425	+	0.941352i	$0.609556\pi$
$380$		−	3.09858i		−	0.158954i
$381$		0			0
$382$	7.36938			0.377050
$383$	8.77603	+	15.2005i	0.448434	+	0.776711i	0.998284	−	0.0585527i	$-0.0186486\pi$
$383$	8.77603	+	15.2005i	0.448434	+	0.776711i	−0.549850	+	0.835263i	$0.685315\pi$
$384$		0			0
$385$	12.8364	+	1.60096i	0.654204	+	0.0815926i
$386$		−	2.82559i		−	0.143819i
$387$		0			0
$388$	9.18719	−	5.30423i	0.466409	−	0.269281i
$389$	−18.9148	−	10.9205i	−0.959020	−	0.553691i	−0.0631489	−	0.998004i	$-0.520114\pi$
$389$	−18.9148	−	10.9205i	−0.959020	−	0.553691i	−0.895871	+	0.444313i	$0.853448\pi$
$390$		0			0
$391$	15.9312	+	9.19786i	0.805674	+	0.465156i
$392$	−1.71934	+	6.78556i	−0.0868399	+	0.342723i
$393$		0			0
$394$	−26.0883			−1.31431
$395$	−10.4107	−	18.0319i	−0.523821	−	0.907285i
$396$		0			0
$397$	33.7636	+	19.4935i	1.69455	+	0.978348i	0.950757	+	0.309937i	$0.100308\pi$
$397$	33.7636	+	19.4935i	1.69455	+	0.978348i	0.743792	+	0.668411i	$0.233025\pi$
$398$	7.70826	+	13.3511i	0.386380	+	0.669230i
$399$		0			0
$400$	1.47776	−	2.55956i	0.0738882	−	0.127978i
$401$	20.0899	−	11.5989i	1.00324	−	0.579223i	0.0940373	−	0.995569i	$-0.470023\pi$
$401$	20.0899	−	11.5989i	1.00324	−	0.579223i	0.909206	+	0.416346i	$0.136689\pi$
$402$		0			0
$403$	13.7588	−	23.8310i	0.685376	−	1.18711i
$404$	−4.02443	+	6.97052i	−0.200223	+	0.346796i
$405$		0			0
$406$	0.841182	−	0.355169i	0.0417471	−	0.0176267i
$407$	−6.38377	+	3.68567i	−0.316432	+	0.182692i
$408$		0			0
$409$			24.6187i			1.21732i	0.793432	+	0.608659i	$0.208292\pi$
$409$			24.6187i			1.21732i	−0.793432	+	0.608659i	$0.791708\pi$
$410$			0.578174i			0.0285540i
$411$		0			0
$412$	2.43692	−	1.40695i	0.120058	−	0.0693157i
$413$	−3.61156	+	28.9572i	−0.177713	+	1.42489i
$414$		0			0
$415$	−1.16050	+	2.01005i	−0.0569667	+	0.0986693i
$416$	3.16857	−	5.48813i	0.155352	−	0.269078i
$417$		0			0
$418$	−6.41739	+	3.70508i	−0.313885	+	0.181222i
$419$	−8.53996	+	14.7916i	−0.417204	+	0.722619i	−0.995657	−	0.0930969i	$-0.970323\pi$
$419$	−8.53996	+	14.7916i	−0.417204	+	0.722619i	0.578453	+	0.815716i	$0.303657\pi$
$420$		0			0
$421$	−7.35652	−	12.7419i	−0.358535	−	0.621000i	0.629182	−	0.777258i	$-0.283390\pi$
$421$	−7.35652	−	12.7419i	−0.358535	−	0.621000i	−0.987716	+	0.156258i	$0.950057\pi$
$422$	7.66371	+	4.42465i	0.373064	+	0.215388i
$423$		0			0
$424$	4.94391	+	8.56310i	0.240097	+	0.415861i
$425$	6.75047			0.327446
$426$		0			0
$427$	−30.1391	−	3.75896i	−1.45853	−	0.181909i
$428$	−13.7019	−	7.91078i	−0.662305	−	0.382382i
$429$		0			0
$430$	7.20393	+	4.15919i	0.347404	+	0.200574i
$431$	8.32286	−	4.80521i	0.400898	−	0.231459i	−0.285973	−	0.958238i	$-0.592317\pi$
$431$	8.32286	−	4.80521i	0.400898	−	0.231459i	0.686871	+	0.726779i	$0.258984\pi$
$432$		0			0
$433$		−	9.04314i		−	0.434585i	−0.976106	−	0.217293i	$-0.930277\pi$
$433$		−	9.04314i		−	0.434585i	0.976106	−	0.217293i	$-0.0697226\pi$
$434$	−1.42185	+	11.4003i	−0.0682508	+	0.547230i
$435$		0			0
$436$	−5.10675	−	8.84514i	−0.244569	−	0.423606i
$437$	−17.4538			−0.834929
$438$		0			0
$439$			0.913795i			0.0436131i	0.999762	+	0.0218065i	$0.00694178\pi$
$439$			0.913795i			0.0436131i	−0.999762	+	0.0218065i	$0.993058\pi$
$440$	4.88930			0.233088
$441$		0			0
$442$	14.4741			0.688465
$443$		−	29.3616i		−	1.39501i	−0.716578	−	0.697507i	$-0.754293\pi$
$443$		−	29.3616i		−	1.39501i	0.716578	−	0.697507i	$-0.245707\pi$
$444$		0			0
$445$	−5.80446			−0.275158
$446$	−3.97772	−	6.88961i	−0.188351	−	0.326233i
$447$		0			0
$448$	−0.327442	+	2.62541i	−0.0154702	+	0.124039i
$449$			3.36736i			0.158915i	0.996838	+	0.0794577i	$0.0253189\pi$
$449$			3.36736i			0.158915i	−0.996838	+	0.0794577i	$0.974681\pi$
$450$		0			0
$451$	1.19744	−	0.691343i	0.0563853	−	0.0325541i
$452$	7.28808	+	4.20778i	0.342802	+	0.197917i
$453$		0			0
$454$	−8.00180	−	4.61984i	−0.375543	−	0.216820i
$455$	23.7893	+	2.96701i	1.11526	+	0.139096i
$456$		0			0
$457$	−15.1139			−0.706996			−0.353498	−	0.935435i	$-0.615008\pi$
$457$	−15.1139			−0.706996			−0.353498	+	0.935435i	$0.615008\pi$
$458$	−4.22227	−	7.31319i	−0.197294	−	0.341723i
$459$		0			0
$460$	9.97330	+	5.75809i	0.465008	+	0.268472i
$461$	−5.19445	−	8.99706i	−0.241930	−	0.419035i	0.719334	−	0.694664i	$-0.244447\pi$
$461$	−5.19445	−	8.99706i	−0.241930	−	0.419035i	−0.961264	+	0.275629i	$0.911114\pi$
$462$		0			0
$463$	−2.65722	+	4.60244i	−0.123492	+	0.213894i	−0.921142	−	0.389226i	$-0.872743\pi$
$463$	−2.65722	+	4.60244i	−0.123492	+	0.213894i	0.797651	+	0.603120i	$0.206076\pi$
$464$	0.298879	−	0.172558i	0.0138751	−	0.00801078i
$465$		0			0
$466$	8.32399	−	14.4176i	0.385601	−	0.667881i
$467$	−9.74994	+	16.8874i	−0.451173	+	0.781455i	−0.998459	−	0.0554907i	$-0.982328\pi$
$467$	−9.74994	+	16.8874i	−0.451173	+	0.781455i	0.547286	+	0.836946i	$0.315661\pi$
$468$		0			0
$469$	1.39283	−	11.1676i	0.0643148	−	0.515672i
$470$	6.83323	−	3.94517i	0.315193	−	0.181977i
$471$		0			0
$472$			11.0296i			0.507678i
$473$		−	19.8932i		−	0.914689i
$474$		0			0
$475$	−5.54674	+	3.20241i	−0.254502	+	0.146937i
$476$	−5.56705	+	2.35055i	−0.255165	+	0.107737i
$477$		0			0
$478$	−13.6442	+	23.6325i	−0.624073	+	1.08093i
$479$	13.9012	−	24.0776i	0.635163	−	1.10013i	−0.351318	−	0.936256i	$-0.614266\pi$
$479$	13.9012	−	24.0776i	0.635163	−	1.10013i	0.986481	−	0.163878i	$-0.0524003\pi$
$480$		0			0
$481$	−11.8308	+	6.83054i	−0.539440	+	0.311446i
$482$	12.6450	−	21.9018i	0.575965	−	0.997600i
$483$		0			0
$484$	−0.346305	−	0.599818i	−0.0157411	−	0.0272645i
$485$	13.1363	+	7.58425i	0.596489	+	0.344383i
$486$		0			0
$487$	3.73838	+	6.47506i	0.169402	+	0.293413i	0.938210	−	0.346067i	$-0.112483\pi$
$487$	3.73838	+	6.47506i	0.169402	+	0.293413i	−0.768808	+	0.639480i	$0.779150\pi$
$488$	−11.4797			−0.519664
$489$		0			0
$490$	−9.63167	+	2.72213i	−0.435115	+	0.122973i
$491$	−19.1466	−	11.0543i	−0.864073	−	0.498873i	0.00130103	−	0.999999i	$-0.499586\pi$
$491$	−19.1466	−	11.0543i	−0.864073	−	0.498873i	−0.865374	+	0.501126i	$0.832919\pi$
$492$		0			0
$493$	0.682643	+	0.394124i	0.0307447	+	0.0177505i
$494$	−11.8931	+	6.86651i	−0.535098	+	0.308939i
$495$		0			0
$496$			4.34228i			0.194974i
$497$	−9.33052	−	1.16371i	−0.418531	−	0.0521994i
$498$		0			0
$499$	−16.4521	−	28.4959i	−0.736498	−	1.27565i	−0.954063	−	0.299606i	$-0.903145\pi$
$499$	−16.4521	−	28.4959i	−0.736498	−	1.27565i	0.217565	−	0.976046i	$-0.430189\pi$
$500$	11.3752			0.508715
$501$		0			0
$502$			8.19337i			0.365688i
$503$	25.6142			1.14208			0.571039	−	0.820923i	$-0.306540\pi$
$503$	25.6142			1.14208			0.571039	+	0.820923i	$0.306540\pi$
$504$		0			0
$505$	−11.5087			−0.512129
$506$		−	27.5406i		−	1.22433i
$507$		0			0
$508$	−5.77773			−0.256345
$509$	10.7358	+	18.5950i	0.475857	+	0.824209i	0.999617	−	0.0276567i	$-0.00880451\pi$
$509$	10.7358	+	18.5950i	0.475857	+	0.824209i	−0.523760	+	0.851866i	$0.675471\pi$
$510$		0			0
$511$	0.238924	+	0.565868i	0.0105694	+	0.0250325i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−5.74560	+	3.31723i	−0.253428	+	0.146317i
$515$	3.48443	+	2.01173i	0.153542	+	0.0886476i
$516$		0			0
$517$	−16.3415	−	9.43475i	−0.718697	−	0.414940i
$518$	3.44112	−	4.54845i	0.151194	−	0.199847i
$519$		0			0
$520$	9.06117			0.397359
$521$	3.23087	+	5.59604i	0.141547	+	0.245167i	0.928079	−	0.372382i	$-0.121459\pi$
$521$	3.23087	+	5.59604i	0.141547	+	0.245167i	−0.786532	+	0.617549i	$0.788126\pi$
$522$		0			0
$523$	11.7830	+	6.80291i	0.515234	+	0.297470i	0.734982	−	0.678086i	$-0.237190\pi$
$523$	11.7830	+	6.80291i	0.515234	+	0.297470i	−0.219749	+	0.975557i	$0.570524\pi$
$524$	2.22833	+	3.85959i	0.0973452	+	0.168607i
$525$		0			0
$526$	3.02295	−	5.23590i	0.131807	−	0.228296i
$527$	−8.58910	+	4.95892i	−0.374147	+	0.216014i
$528$		0			0
$529$	20.9344	−	36.2594i	0.910190	−	1.57649i
$530$	−7.06905	+	12.2440i	−0.307060	+	0.531843i
$531$		0			0
$532$	3.45924	−	4.57241i	0.149977	−	0.198239i
$533$	2.21918	−	1.28124i	0.0961233	−	0.0554968i
$534$		0			0
$535$		−	22.6225i		−	0.978055i
$536$		−	4.25366i		−	0.183730i
$537$		0			0
$538$	5.90750	−	3.41069i	0.254690	−	0.147045i
$539$	17.1547	+	16.6930i	0.738904	+	0.719017i
$540$		0			0
$541$	−14.9288	+	25.8574i	−0.641838	+	1.11170i	0.343184	+	0.939268i	$0.388494\pi$
$541$	−14.9288	+	25.8574i	−0.641838	+	1.11170i	−0.985022	+	0.172428i	$0.944839\pi$
$542$	2.53907	−	4.39780i	0.109063	−	0.188902i
$543$		0			0
$544$	−1.97802	+	1.14201i	−0.0848067	+	0.0489632i
$545$	7.30188	−	12.6472i	0.312778	−	0.541748i
$546$		0			0
$547$	−9.07207	−	15.7133i	−0.387894	−	0.671852i	0.604272	−	0.796778i	$-0.293464\pi$
$547$	−9.07207	−	15.7133i	−0.387894	−	0.671852i	−0.992166	+	0.124926i	$0.960131\pi$
$548$	8.36293	+	4.82834i	0.357247	+	0.206256i
$549$		0			0
$550$	−5.05313	−	8.75228i	−0.215466	−	0.373199i
$551$	−0.747888			−0.0318611
$552$		0			0
$553$	4.76822	−	38.2312i	0.202765	−	1.62576i
$554$	1.71398	+	0.989567i	0.0728201	+	0.0420427i
$555$		0			0
$556$	−16.0680	−	9.27686i	−0.681435	−	0.393426i
$557$	32.5079	−	18.7684i	1.37740	−	0.795245i	0.385558	−	0.922684i	$-0.374009\pi$
$557$	32.5079	−	18.7684i	1.37740	−	0.795245i	0.991846	+	0.127439i	$0.0406757\pi$
$558$		0			0
$559$		−	36.8674i		−	1.55932i
$560$	−3.48511	+	1.47150i	−0.147273	+	0.0621824i
$561$		0			0
$562$	8.81631	+	15.2703i	0.371894	+	0.644139i
$563$	−7.10681			−0.299516			−0.149758	−	0.988723i	$-0.547850\pi$
$563$	−7.10681			−0.299516			−0.149758	+	0.988723i	$0.547850\pi$
$564$		0			0
$565$			12.0330i			0.506231i
$566$	5.15385			0.216633
$567$		0			0
$568$	−3.55393			−0.149119
$569$			41.1650i			1.72572i	0.505439	+	0.862862i	$0.331331\pi$
$569$			41.1650i			1.72572i	−0.505439	+	0.862862i	$0.668669\pi$
$570$		0			0
$571$	4.42585			0.185216			0.0926080	−	0.995703i	$-0.470480\pi$
$571$	4.42585			0.185216			0.0926080	+	0.995703i	$0.470480\pi$
$572$	−10.8348	−	18.7664i	−0.453024	−	0.784661i
$573$		0			0
$574$	−0.645471	+	0.853179i	−0.0269414	+	0.0356110i
$575$		−	23.8042i		−	0.992702i
$576$		0			0
$577$	2.37542	−	1.37145i	0.0988900	−	0.0570941i	−0.449739	−	0.893160i	$-0.648483\pi$
$577$	2.37542	−	1.37145i	0.0988900	−	0.0570941i	0.548629	+	0.836066i	$0.315150\pi$
$578$	10.2046	+	5.89164i	0.424456	+	0.245060i
$579$		0			0
$580$	0.427352	+	0.246732i	0.0177448	+	0.0102450i
$581$	−3.95649	+	1.67054i	−0.164143	+	0.0693055i
$582$		0			0
$583$	33.8109			1.40030
$584$	0.116080	+	0.201057i	0.00480344	+	0.00831981i
$585$		0			0
$586$	−1.78831	−	1.03248i	−0.0738745	−	0.0426515i
$587$	−9.90248	−	17.1516i	−0.408719	−	0.707922i	0.586027	−	0.810291i	$-0.300691\pi$
$587$	−9.90248	−	17.1516i	−0.408719	−	0.707922i	−0.994747	+	0.102369i	$0.967358\pi$
$588$		0			0
$589$	4.70501	−	8.14931i	0.193866	−	0.335786i
$590$	−13.6578	+	7.88534i	−0.562283	+	0.324634i
$591$		0			0
$592$	1.07786	−	1.86690i	0.0442996	−	0.0767292i
$593$	−0.434850	+	0.753183i	−0.0178572	+	0.0309295i	−0.874816	−	0.484456i	$-0.839018\pi$
$593$	−0.434850	+	0.753183i	−0.0178572	+	0.0309295i	0.856959	+	0.515385i	$0.172351\pi$
$594$		0			0
$595$	−6.89068	−	5.21313i	−0.282490	−	0.213717i
$596$	−5.63517	+	3.25347i	−0.230826	+	0.133267i
$597$		0			0
$598$		−	51.0401i		−	2.08719i
$599$		−	2.69365i		−	0.110059i	−0.998485	−	0.0550297i	$-0.982475\pi$
$599$		−	2.69365i		−	0.110059i	0.998485	−	0.0550297i	$-0.0175254\pi$
$600$		0			0
$601$	0.115325	−	0.0665827i	0.00470419	−	0.00271596i	−0.497646	−	0.867380i	$-0.665802\pi$
$601$	0.115325	−	0.0665827i	0.00470419	−	0.00271596i	0.502350	+	0.864664i	$0.332469\pi$
$602$	5.98714	+	14.1799i	0.244018	+	0.577931i
$603$		0			0
$604$	2.87950	−	4.98745i	0.117165	−	0.202936i
$605$	0.495165	−	0.857650i	0.0201313	−	0.0348684i
$606$		0			0
$607$	−38.3860	+	22.1622i	−1.55804	+	0.899534i	−0.560594	+	0.828091i	$0.689427\pi$
$607$	−38.3860	+	22.1622i	−1.55804	+	0.899534i	−0.997445	+	0.0714432i	$0.977240\pi$
$608$	1.08353	−	1.87673i	0.0439431	−	0.0761117i
$609$		0			0
$610$	−8.20716	−	14.2152i	−0.332298	−	0.575557i
$611$	−30.2851	−	17.4851i	−1.22520	−	0.707372i
$612$		0			0
$613$	3.29901	+	5.71406i	0.133246	+	0.230789i	0.924926	−	0.380147i	$-0.124127\pi$
$613$	3.29901	+	5.71406i	0.133246	+	0.230789i	−0.791680	+	0.610936i	$0.790793\pi$
$614$	−1.09119			−0.0440367
$615$		0			0
$616$	7.21486	+	5.45839i	0.290695	+	0.219925i
$617$	7.99450	+	4.61563i	0.321846	+	0.185818i	0.652215	−	0.758034i	$-0.273840\pi$
$617$	7.99450	+	4.61563i	0.321846	+	0.185818i	−0.330369	+	0.943852i	$0.607173\pi$
$618$		0			0
$619$	−5.66289	−	3.26947i	−0.227611	−	0.131411i	0.381859	−	0.924221i	$-0.375284\pi$
$619$	−5.66289	−	3.26947i	−0.227611	−	0.131411i	−0.609469	+	0.792810i	$0.708617\pi$
$620$	−5.37699	+	3.10441i	−0.215945	+	0.124676i
$621$		0			0
$622$		−	15.2220i		−	0.610347i
$623$	−8.56532	−	6.48007i	−0.343162	−	0.259619i
$624$		0			0
$625$	0.743610	+	1.28797i	0.0297444	+	0.0515188i
$626$	−11.5704			−0.462445
$627$		0			0
$628$			7.96361i			0.317783i
$629$	4.92368			0.196320
$630$		0			0
$631$	13.8837			0.552699			0.276350	−	0.961057i	$-0.410875\pi$
$631$	13.8837			0.552699			0.276350	+	0.961057i	$0.410875\pi$
$632$		−	14.5620i		−	0.579245i
$633$		0			0
$634$	−17.1604			−0.681526
$635$	−4.13064	−	7.15449i	−0.163920	−	0.283917i
$636$		0			0
$637$	31.7922	+	30.9365i	1.25965	+	1.22575i
$638$		−	1.18010i		−	0.0467207i
$639$		0			0
$640$	−1.23829	+	0.714925i	−0.0489476	+	0.0282599i
$641$	13.1940	+	7.61757i	0.521133	+	0.300876i	0.737398	−	0.675459i	$-0.236054\pi$
$641$	13.1940	+	7.61757i	0.521133	+	0.300876i	−0.216265	+	0.976335i	$0.569388\pi$
$642$		0			0
$643$	−16.5813	−	9.57324i	−0.653904	−	0.377532i	0.136046	−	0.990702i	$-0.456560\pi$
$643$	−16.5813	−	9.57324i	−0.653904	−	0.377532i	−0.789950	+	0.613171i	$0.789894\pi$
$644$	8.28874	+	19.6310i	0.326622	+	0.773571i
$645$		0			0
$646$	4.94962			0.194740
$647$	−0.793991	−	1.37523i	−0.0312150	−	0.0540660i	0.849996	−	0.526789i	$-0.176604\pi$
$647$	−0.793991	−	1.37523i	−0.0312150	−	0.0540660i	−0.881211	+	0.472723i	$0.843271\pi$
$648$		0			0
$649$	32.6622	+	18.8576i	1.28211	+	0.740224i
$650$	−9.36481	−	16.2203i	−0.367318	−	0.636213i
$651$		0			0
$652$	−5.69256	+	9.85980i	−0.222938	+	0.386140i
$653$	15.5572	−	8.98197i	0.608802	−	0.351492i	−0.163695	−	0.986511i	$-0.552341\pi$
$653$	15.5572	−	8.98197i	0.608802	−	0.351492i	0.772496	+	0.635019i	$0.219008\pi$
$654$		0			0
$655$	−3.18619	+	5.51863i	−0.124495	+	0.215631i
$656$	−0.202180	+	0.350186i	−0.00789380	+	0.0136725i
$657$		0			0
$658$	14.4878	+	1.80692i	0.564793	+	0.0704412i
$659$	−10.0955	+	5.82866i	−0.393266	+	0.227052i	−0.683574	−	0.729881i	$-0.739576\pi$
$659$	−10.0955	+	5.82866i	−0.393266	+	0.227052i	0.290308	+	0.956933i	$0.406242\pi$
$660$		0			0
$661$			18.2195i			0.708657i	0.935121	+	0.354328i	$0.115290\pi$
$661$			18.2195i			0.708657i	−0.935121	+	0.354328i	$0.884710\pi$
$662$		−	26.4931i		−	1.02968i
$663$		0			0
$664$	−1.40577	+	0.811624i	−0.0545546	+	0.0314971i
$665$	8.13505	+	1.01461i	0.315464	+	0.0393448i
$666$		0			0
$667$	1.38980	−	2.40720i	0.0538132	−	0.0932072i
$668$	−5.66418	+	9.81065i	−0.219154	+	0.379585i
$669$		0			0
$670$	5.26725	−	3.04105i	0.203491	−	0.117486i
$671$	−19.6272	+	33.9953i	−0.757699	+	1.31237i
$672$		0			0
$673$	2.41106	+	4.17608i	0.0929395	+	0.160976i	0.908747	−	0.417348i	$-0.137040\pi$
$673$	2.41106	+	4.17608i	0.0929395	+	0.160976i	−0.815807	+	0.578324i	$0.803707\pi$
$674$	7.03993	+	4.06451i	0.271168	+	0.156559i
$675$		0			0
$676$	−13.5797	−	23.5208i	−0.522297	−	0.904645i
$677$	−23.1290			−0.888920			−0.444460	−	0.895799i	$-0.646604\pi$
$677$	−23.1290			−0.888920			−0.444460	+	0.895799i	$0.646604\pi$
$678$		0			0
$679$	10.9175	+	25.8570i	0.418975	+	0.992300i
$680$	−2.82827	−	1.63290i	−0.108459	−	0.0626189i
$681$		0			0
$682$	12.8589	+	7.42410i	0.492393	+	0.284283i
$683$	6.80041	−	3.92622i	0.260210	−	0.150233i	−0.364220	−	0.931313i	$-0.618664\pi$
$683$	6.80041	−	3.92622i	0.260210	−	0.150233i	0.624431	+	0.781080i	$0.285331\pi$
$684$		0			0
$685$			13.8076i			0.527562i
$686$	−17.2519	−	6.73586i	−0.658681	−	0.257176i
$687$		0			0
$688$	2.90883	+	5.03824i	0.110898	+	0.192081i
$689$	62.6606			2.38718
$690$		0			0
$691$		−	17.1676i		−	0.653085i	−0.945182	−	0.326543i	$-0.894116\pi$
$691$		−	17.1676i		−	0.653085i	0.945182	−	0.326543i	$-0.105884\pi$
$692$	−21.6914			−0.824584
$693$		0			0
$694$	−25.6171			−0.972412
$695$		−	26.5290i		−	1.00630i
$696$		0			0
$697$	−0.923564			−0.0349825
$698$	5.26504	+	9.11932i	0.199285	+	0.345171i
$699$		0			0
$700$	6.23602	+	4.71785i	0.235699	+	0.178318i
$701$		−	34.9404i		−	1.31968i	−0.751406	−	0.659840i	$-0.770624\pi$
$701$		−	34.9404i		−	1.31968i	0.751406	−	0.659840i	$-0.229376\pi$
$702$		0			0
$703$	−4.04570	+	2.33579i	−0.152587	+	0.0880959i
$704$	2.96133	+	1.70972i	0.111609	+	0.0644376i
$705$		0			0
$706$	−11.1230	−	6.42186i	−0.418619	−	0.241690i
$707$	−16.9827	−	12.8482i	−0.638701	−	0.483207i
$708$		0			0
$709$	−24.3336			−0.913867			−0.456933	−	0.889501i	$-0.651052\pi$
$709$	−24.3336			−0.913867			−0.456933	+	0.889501i	$0.651052\pi$
$710$	−2.54079	−	4.40078i	−0.0953542	−	0.165158i
$711$		0			0
$712$	−3.51562	−	2.02974i	−0.131753	−	0.0760678i
$713$	17.4866	+	30.2877i	0.654879	+	1.13428i
$714$		0			0
$715$	15.4921	−	26.8331i	0.579372	−	1.00350i
$716$	−18.0057	+	10.3956i	−0.672904	+	0.388501i
$717$		0			0
$718$	14.8311	−	25.6881i	0.553490	−	0.958673i
$719$	−8.76887	+	15.1881i	−0.327024	+	0.566422i	−0.981920	−	0.189297i	$-0.939379\pi$
$719$	−8.76887	+	15.1881i	−0.327024	+	0.566422i	0.654896	+	0.755719i	$0.272712\pi$
$720$		0			0
$721$	2.89588	+	6.85860i	0.107848	+	0.255428i
$722$	12.3875	−	7.15191i	0.461014	−	0.266167i
$723$		0			0
$724$			21.5301i			0.800159i
$725$		−	1.02000i		−	0.0378818i
$726$		0			0
$727$	−33.8627	+	19.5507i	−1.25590	+	0.725094i	−0.972275	−	0.233841i	$-0.924870\pi$
$727$	−33.8627	+	19.5507i	−1.25590	+	0.725094i	−0.283625	+	0.958935i	$0.591537\pi$
$728$	13.3711	+	10.1159i	0.495565	+	0.374919i
$729$		0			0
$730$	−0.165978	+	0.287482i	−0.00614311	+	0.0106402i
$731$	−6.64381	+	11.5074i	−0.245730	+	0.425617i
$732$		0			0
$733$	20.3073	−	11.7245i	0.750069	−	0.433053i	−0.0756499	−	0.997134i	$-0.524103\pi$
$733$	20.3073	−	11.7245i	0.750069	−	0.433053i	0.825719	+	0.564082i	$0.190770\pi$
$734$	−11.9989	+	20.7828i	−0.442889	+	0.767107i
$735$		0			0
$736$	4.02706	+	6.97507i	0.148439	+	0.257104i
$737$	−12.5965	−	7.27257i	−0.463997	−	0.267889i
$738$		0			0
$739$	13.3662	+	23.1509i	0.491682	+	0.851618i	0.999954	−	0.00957820i	$-0.00304888\pi$
$739$	13.3662	+	23.1509i	0.491682	+	0.851618i	−0.508272	+	0.861197i	$0.669716\pi$
$740$	3.08235			0.113309
$741$		0			0
$742$	−24.1005	+	10.1759i	−0.884757	+	0.373568i
$743$	11.0914	+	6.40360i	0.406903	+	0.234925i	0.689458	−	0.724326i	$-0.257849\pi$
$743$	11.0914	+	6.40360i	0.406903	+	0.234925i	−0.282555	+	0.959251i	$0.591182\pi$
$744$		0			0
$745$	−8.05745	−	4.65197i	−0.295202	−	0.170435i
$746$	−10.2528	+	5.91948i	−0.375383	+	0.216727i
$747$		0			0
$748$			7.81007i			0.285564i
$749$	25.2556	−	33.3827i	0.922821	−	1.21978i
$750$		0			0
$751$	5.12417	+	8.87532i	0.186984	+	0.323865i	0.944243	−	0.329249i	$-0.106796\pi$
$751$	5.12417	+	8.87532i	0.186984	+	0.323865i	−0.757260	+	0.653114i	$0.773462\pi$
$752$	5.51829			0.201231
$753$		0			0
$754$		−	2.18705i		−	0.0796475i
$755$	8.23452			0.299685
$756$		0			0
$757$	11.0844			0.402868			0.201434	−	0.979502i	$-0.435440\pi$
$757$	11.0844			0.402868			0.201434	+	0.979502i	$0.435440\pi$
$758$		−	13.1379i		−	0.477191i
$759$		0			0
$760$	3.09858			0.112397
$761$	8.14993	+	14.1161i	0.295435	+	0.511708i	0.975086	−	0.221827i	$-0.0712022\pi$
$761$	8.14993	+	14.1161i	0.295435	+	0.511708i	−0.679651	+	0.733536i	$0.737869\pi$
$762$		0			0
$763$	24.8943	−	10.5110i	0.901234	−	0.380525i
$764$			7.36938i			0.266615i
$765$		0			0
$766$	−15.2005	+	8.77603i	−0.549217	+	0.317091i
$767$	60.5319	+	34.9481i	2.18568	+	1.26190i
$768$		0			0
$769$	41.4043	+	23.9048i	1.49308	+	0.862029i	0.999968	−	0.00793771i	$-0.00252668\pi$
$769$	41.4043	+	23.9048i	1.49308	+	0.862029i	0.493110	+	0.869967i	$0.335860\pi$
$770$	−1.60096	+	12.8364i	−0.0576947	+	0.462592i
$771$		0			0
$772$	2.82559			0.101695
$773$	6.25441	+	10.8330i	0.224956	+	0.389635i	0.956306	−	0.292367i	$-0.0944429\pi$
$773$	6.25441	+	10.8330i	0.224956	+	0.389635i	−0.731350	+	0.682002i	$0.761110\pi$
$774$		0			0
$775$	11.1143	+	6.41686i	0.399239	+	0.230501i
$776$	5.30423	+	9.18719i	0.190411	+	0.329801i
$777$		0			0
$778$	10.9205	−	18.9148i	0.391518	−	0.678130i
$779$	0.758876	−	0.438137i	0.0271896	−	0.0156979i
$780$		0			0
$781$	−6.07623	+	10.5243i	−0.217425	+	0.376590i
$782$	−9.19786	+	15.9312i	−0.328915	+	0.569697i
$783$		0			0
$784$	−6.78556	−	1.71934i	−0.242342	−	0.0614051i
$785$	−9.86123	+	5.69338i	−0.351962	+	0.203206i
$786$		0			0
$787$		−	0.261017i		−	0.00930426i	−0.999989	−	0.00465213i	$-0.998519\pi$
$787$		−	0.261017i		−	0.00930426i	0.999989	−	0.00465213i	$-0.00148082\pi$
$788$		−	26.0883i		−	0.929357i
$789$		0			0
$790$	18.0319	−	10.4107i	0.641548	−	0.370398i
$791$	−13.4336	+	17.7564i	−0.477643	+	0.631345i
$792$		0			0
$793$	−36.3744	+	63.0024i	−1.29169	+	2.23728i
$794$	−19.4935	+	33.7636i	−0.691797	+	1.19823i
$795$		0			0
$796$	−13.3511	+	7.70826i	−0.473217	+	0.273212i
$797$	−1.85220	+	3.20810i	−0.0656083	+	0.113637i	−0.896964	−	0.442104i	$-0.854232\pi$
$797$	−1.85220	+	3.20810i	−0.0656083	+	0.113637i	0.831355	+	0.555741i	$0.187565\pi$
$798$		0			0
$799$	6.30194	+	10.9153i	0.222946	+	0.386155i
$800$	2.55956	+	1.47776i	0.0904942	+	0.0522468i
$801$		0			0
$802$	11.5989	+	20.0899i	0.409573	+	0.709400i
$803$	0.793862			0.0280148
$804$		0			0
$805$	−18.3830	+	24.2986i	−0.647917	+	0.856412i
$806$	23.8310	+	13.7588i	0.839411	+	0.484634i
$807$		0			0
$808$	−6.97052	−	4.02443i	−0.245222	−	0.141579i
$809$	−5.94276	+	3.43105i	−0.208936	+	0.120629i	−0.600817	−	0.799387i	$-0.705158\pi$
$809$	−5.94276	+	3.43105i	−0.208936	+	0.120629i	0.391881	+	0.920016i	$0.371825\pi$
$810$		0			0
$811$			23.1945i			0.814470i	0.913323	+	0.407235i	$0.133507\pi$
$811$			23.1945i			0.814470i	−0.913323	+	0.407235i	$0.866493\pi$
$812$	0.355169	+	0.841182i	0.0124640	+	0.0295197i
$813$		0			0
$814$	−3.68567	−	6.38377i	−0.129183	−	0.223751i
$815$	−16.2790			−0.570229
$816$		0			0
$817$		−	12.6073i		−	0.441072i
$818$	−24.6187			−0.860774
$819$		0			0
$820$	−0.578174			−0.0201907
$821$		−	3.79377i		−	0.132403i	−0.997806	−	0.0662017i	$-0.978912\pi$
$821$		−	3.79377i		−	0.132403i	0.997806	−	0.0662017i	$-0.0210881\pi$
$822$		0			0
$823$	−14.9079			−0.519656			−0.259828	−	0.965655i	$-0.583666\pi$
$823$	−14.9079			−0.519656			−0.259828	+	0.965655i	$0.583666\pi$
$824$	1.40695	+	2.43692i	0.0490136	+	0.0848940i
$825$		0			0
$826$	−28.9572	−	3.61156i	−1.00755	−	0.125662i
$827$		−	21.9819i		−	0.764384i	−0.924083	−	0.382192i	$-0.875169\pi$
$827$		−	21.9819i		−	0.764384i	0.924083	−	0.382192i	$-0.124831\pi$
$828$		0			0
$829$	12.2406	−	7.06713i	0.425135	−	0.245452i	−0.272137	−	0.962259i	$-0.587730\pi$
$829$	12.2406	−	7.06713i	0.425135	−	0.245452i	0.697272	+	0.716807i	$0.254397\pi$
$830$	−2.01005	−	1.16050i	−0.0697697	−	0.0402816i
$831$		0			0
$832$	5.48813	+	3.16857i	0.190267	+	0.109851i
$833$	−4.34828	−	15.3855i	−0.150659	−	0.533074i
$834$		0			0
$835$	−16.1979			−0.560550
$836$	−3.70508	−	6.41739i	−0.128143	−	0.221950i
$837$		0			0
$838$	−14.7916	−	8.53996i	−0.510969	−	0.295008i
$839$	−8.92488	−	15.4583i	−0.308121	−	0.533681i	0.669830	−	0.742514i	$-0.266367\pi$
$839$	−8.92488	−	15.4583i	−0.308121	−	0.533681i	−0.977951	+	0.208833i	$0.933034\pi$
$840$		0			0
$841$	−14.4404	+	25.0116i	−0.497946	+	0.862469i
$842$	12.7419	−	7.35652i	0.439114	−	0.253522i
$843$		0			0
$844$	−4.42465	+	7.66371i	−0.152303	+	0.263796i
$845$	19.4170	−	33.6312i	0.667964	−	1.15695i
$846$		0			0
$847$	1.68816	−	0.712787i	0.0580060	−	0.0244917i
$848$	−8.56310	+	4.94391i	−0.294058	+	0.169775i
$849$		0			0
$850$			6.75047i			0.231539i
$851$		−	17.3624i		−	0.595174i
$852$		0			0
$853$	35.2392	−	20.3454i	1.20657	−	0.696612i	0.244559	−	0.969634i	$-0.421357\pi$
$853$	35.2392	−	20.3454i	1.20657	−	0.696612i	0.962008	+	0.273022i	$0.0880233\pi$
$854$	3.75896	−	30.1391i	0.128629	−	1.03134i
$855$		0			0
$856$	7.91078	−	13.7019i	0.270385	−	0.468320i
$857$	−2.72896	+	4.72669i	−0.0932194	+	0.161461i	−0.908864	−	0.417092i	$-0.863049\pi$
$857$	−2.72896	+	4.72669i	−0.0932194	+	0.161461i	0.815645	+	0.578553i	$0.196382\pi$
$858$		0			0
$859$	38.8822	−	22.4487i	1.32664	−	0.765938i	0.341865	−	0.939749i	$-0.388941\pi$
$859$	38.8822	−	22.4487i	1.32664	−	0.765938i	0.984779	+	0.173810i	$0.0556080\pi$
$860$	−4.15919	+	7.20393i	−0.141827	+	0.245652i
$861$		0			0
$862$	4.80521	+	8.32286i	0.163666	+	0.283478i
$863$	−19.6689	−	11.3559i	−0.669539	−	0.386558i	0.126363	−	0.991984i	$-0.459670\pi$
$863$	−19.6689	−	11.3559i	−0.669539	−	0.386558i	−0.795902	+	0.605426i	$0.793003\pi$
$864$		0			0
$865$	−15.5077	−	26.8602i	−0.527279	−	0.913274i
$866$	9.04314			0.307298
$867$		0			0
$868$	−11.4003	−	1.42185i	−0.386950	−	0.0482606i
$869$	−43.1229	−	24.8970i	−1.46284	−	0.844573i
$870$		0			0
$871$	−23.3446	−	13.4780i	−0.791002	−	0.456685i
$872$	8.84514	−	5.10675i	0.299534	−	0.172936i
$873$		0			0
$874$		−	17.4538i		−	0.590384i
$875$	−3.72473	+	29.8646i	−0.125919	+	1.00961i
$876$		0			0
$877$	15.2445	+	26.4043i	0.514771	+	0.891610i	0.999853	+	0.0171413i	$0.00545653\pi$
$877$	15.2445	+	26.4043i	0.514771	+	0.891610i	−0.485082	+	0.874469i	$0.661210\pi$
$878$	−0.913795			−0.0308391
$879$		0			0
$880$			4.88930i			0.164818i
$881$	−29.3810			−0.989871			−0.494935	−	0.868930i	$-0.664808\pi$
$881$	−29.3810			−0.989871			−0.494935	+	0.868930i	$0.664808\pi$
$882$		0			0
$883$	14.1682			0.476798			0.238399	−	0.971167i	$-0.423377\pi$
$883$	14.1682			0.476798			0.238399	+	0.971167i	$0.423377\pi$
$884$			14.4741i			0.486818i
$885$		0			0
$886$	29.3616			0.986424
$887$	16.3537	+	28.3254i	0.549103	+	0.951074i	0.998336	+	0.0576593i	$0.0183637\pi$
$887$	16.3537	+	28.3254i	0.549103	+	0.951074i	−0.449234	+	0.893414i	$0.648303\pi$
$888$		0			0
$889$	1.89187	−	15.1689i	0.0634514	−	0.508749i
$890$		−	5.80446i		−	0.194566i
$891$		0			0
$892$	6.88961	−	3.97772i	0.230681	−	0.133184i
$893$	−10.3564	−	5.97926i	−0.346563	−	0.200088i
$894$		0			0
$895$	−25.7454	−	14.8641i	−0.860575	−	0.496853i
$896$	−2.62541	−	0.327442i	−0.0877088	−	0.0109391i
$897$		0			0
$898$	−3.36736			−0.112370
$899$	0.749293	+	1.29781i	0.0249903	+	0.0432845i
$900$		0			0
$901$	−19.5583	−	11.2920i	−0.651580	−	0.376190i
$902$	0.691343	+	1.19744i	0.0230192	+	0.0398704i
$903$		0			0
$904$	−4.20778	+	7.28808i	−0.139949	+	0.242398i
$905$	−26.6604	+	15.3924i	−0.886222	+	0.511661i
$906$		0			0
$907$	−28.3467	+	49.0980i	−0.941238	+	1.63027i	−0.178123	+	0.984008i	$0.557002\pi$
$907$	−28.3467	+	49.0980i	−0.941238	+	1.63027i	−0.763115	+	0.646263i	$0.776331\pi$
$908$	4.61984	−	8.00180i	0.153315	−	0.265549i
$909$		0			0
$910$	−2.96701	+	23.7893i	−0.0983555	+	0.788608i
$911$	−0.621795	+	0.358994i	−0.0206010	+	0.0118940i	−0.510265	−	0.860017i	$-0.670453\pi$
$911$	−0.621795	+	0.358994i	−0.0206010	+	0.0118940i	0.489664	+	0.871911i	$0.337119\pi$
$912$		0			0
$913$			5.55061i			0.183698i
$914$		−	15.1139i		−	0.499922i
$915$		0			0
$916$	7.31319	−	4.22227i	0.241635	−	0.139508i
$917$	−10.8627	+	4.58650i	−0.358717	+	0.151460i
$918$		0			0
$919$	18.9720	−	32.8605i	0.625829	−	1.08397i	−0.362550	−	0.931964i	$-0.618094\pi$
$919$	18.9720	−	32.8605i	0.625829	−	1.08397i	0.988380	−	0.152004i	$-0.0485727\pi$
$920$	−5.75809	+	9.97330i	−0.189839	+	0.328810i
$921$		0			0
$922$	8.99706	−	5.19445i	0.296302	−	0.171070i
$923$	−11.2609	+	19.5044i	−0.370656	+	0.641996i
$924$		0			0
$925$	−3.18563	−	5.51768i	−0.104743	−	0.181420i
$926$	−4.60244	−	2.65722i	−0.151246	−	0.0873217i
$927$		0			0
$928$	0.172558	+	0.298879i	0.00566448	+	0.00981117i
$929$	−42.8700			−1.40652			−0.703259	−	0.710934i	$-0.748273\pi$
$929$	−42.8700			−1.40652			−0.703259	+	0.710934i	$0.748273\pi$
$930$		0			0
$931$	10.8717	+	10.5791i	0.356307	+	0.346717i
$932$	14.4176	+	8.32399i	0.472263	+	0.272661i
$933$		0			0
$934$	−16.8874	−	9.74994i	−0.552572	−	0.319028i
$935$	−9.67111	+	5.58362i	−0.316279	+	0.182604i
$936$		0			0
$937$		−	8.64637i		−	0.282464i	−0.989976	−	0.141232i	$-0.954894\pi$
$937$		−	8.64637i		−	0.282464i	0.989976	−	0.141232i	$-0.0451064\pi$
$938$	11.1676	+	1.39283i	0.364635	+	0.0454774i
$939$		0			0
$940$	3.94517	+	6.83323i	0.128677	+	0.222875i
$941$	−10.0921			−0.328991			−0.164496	−	0.986378i	$-0.552600\pi$
$941$	−10.0921			−0.328991			−0.164496	+	0.986378i	$0.552600\pi$
$942$		0			0
$943$			3.25676i			0.106055i
$944$	−11.0296			−0.358983
$945$		0			0
$946$	19.8932			0.646783
$947$			58.2693i			1.89350i	0.321973	+	0.946749i	$0.395654\pi$
$947$			58.2693i			1.89350i	−0.321973	+	0.946749i	$0.604346\pi$
$948$		0			0
$949$	1.47124			0.0477584
$950$	−3.20241	−	5.54674i	−0.103900	−	0.179960i
$951$		0			0
$952$	−2.35055	−	5.56705i	−0.0761819	−	0.180429i
$953$			46.9356i			1.52039i	0.649694	+	0.760196i	$0.274897\pi$
$953$			46.9356i			1.52039i	−0.649694	+	0.760196i	$0.725103\pi$
$954$		0			0
$955$	−9.12541	+	5.26856i	−0.295291	+	0.170487i
$956$	−23.6325	−	13.6442i	−0.764330	−	0.441286i
$957$		0			0
$958$	24.0776	+	13.9012i	0.777912	+	0.449128i
$959$	−15.4148	+	20.3751i	−0.497768	+	0.657947i
$960$		0			0
$961$	12.1446			0.391761
$962$	−6.83054	−	11.8308i	−0.220225	−	0.381441i
$963$		0			0
$964$	21.9018	+	12.6450i	0.705410	+	0.407269i
$965$	2.02008	+	3.49889i	0.0650288	+	0.112633i
$966$		0			0
$967$	6.43145	−	11.1396i	0.206822	−	0.358226i	−0.743890	−	0.668302i	$-0.767021\pi$
$967$	6.43145	−	11.1396i	0.206822	−	0.358226i	0.950712	+	0.310077i	$0.100355\pi$
$968$	0.599818	−	0.346305i	0.0192789	−	0.0111307i
$969$		0			0
$970$	−7.58425	+	13.1363i	−0.243516	+	0.421782i
$971$	−17.3742	+	30.0930i	−0.557565	+	0.965731i	0.440134	+	0.897932i	$0.354931\pi$
$971$	−17.3742	+	30.0930i	−0.557565	+	0.965731i	−0.997699	+	0.0677990i	$0.978402\pi$
$972$		0			0
$973$	29.6169	−	39.1474i	0.949474	−	1.25501i
$974$	−6.47506	+	3.73838i	−0.207474	+	0.119785i
$975$		0			0
$976$		−	11.4797i		−	0.367458i
$977$			20.3667i			0.651590i	0.945441	+	0.325795i	$0.105632\pi$
$977$			20.3667i			0.651590i	−0.945441	+	0.325795i	$0.894368\pi$
$978$		0			0
$979$	−12.0215	+	6.94060i	−0.384208	+	0.221822i
$980$	−2.72213	−	9.63167i	−0.0869553	−	0.307673i
$981$		0			0
$982$	11.0543	−	19.1466i	0.352756	−	0.610992i
$983$	14.6682	−	25.4061i	0.467843	−	0.810328i	−0.531482	−	0.847070i	$-0.678365\pi$
$983$	14.6682	−	25.4061i	0.467843	−	0.810328i	0.999325	+	0.0367416i	$0.0116978\pi$
$984$		0			0
$985$	32.3048	−	18.6512i	1.02932	−	0.594276i
$986$	−0.394124	+	0.682643i	−0.0125515	+	0.0217398i
$987$		0			0
$988$	−6.86651	−	11.8931i	−0.218453	−	0.378371i
$989$	40.5786	+	23.4280i	1.29032	+	0.744968i
$990$		0			0
$991$	−14.8114	−	25.6540i	−0.470498	−	0.814927i	0.528933	−	0.848664i	$-0.322592\pi$
$991$	−14.8114	−	25.6540i	−0.470498	−	0.814927i	−0.999431	+	0.0337371i	$0.989259\pi$
$992$	−4.34228			−0.137868
$993$		0			0
$994$	1.16371	−	9.33052i	0.0369105	−	0.295946i
$995$	−19.0901	−	11.0217i	−0.605196	−	0.349410i
$996$		0			0
$997$	23.4011	+	13.5106i	0.741120	+	0.427886i	0.822477	−	0.568799i	$-0.192592\pi$
$997$	23.4011	+	13.5106i	0.741120	+	0.427886i	−0.0813562	+	0.996685i	$0.525925\pi$
$998$	28.4959	−	16.4521i	0.902022	−	0.520783i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.l.a.341.6		16
3.2	odd	2		126.2.l.a.5.3	✓	16
4.3	odd	2		3024.2.ca.c.2609.3		16
7.2	even	3		2646.2.m.b.881.6		16
7.3	odd	6		378.2.t.a.17.2		16
7.4	even	3		2646.2.t.b.2285.3		16
7.5	odd	6		2646.2.m.a.881.7		16
7.6	odd	2		2646.2.l.a.1097.7		16
9.2	odd	6		378.2.t.a.89.2		16
9.4	even	3		1134.2.k.b.971.2		16
9.5	odd	6		1134.2.k.a.971.7		16
9.7	even	3		126.2.t.a.47.6	yes	16
12.11	even	2		1008.2.ca.c.257.3		16
21.2	odd	6		882.2.m.b.293.1		16
21.5	even	6		882.2.m.a.293.4		16
21.11	odd	6		882.2.t.a.815.7		16
21.17	even	6		126.2.t.a.59.6	yes	16
21.20	even	2		882.2.l.b.509.2		16
28.3	even	6		3024.2.df.c.17.3		16
36.7	odd	6		1008.2.df.c.929.6		16
36.11	even	6		3024.2.df.c.1601.3		16
63.2	odd	6		2646.2.m.a.1763.7		16
63.11	odd	6		2646.2.l.a.521.3		16
63.16	even	3		882.2.m.a.587.4		16
63.20	even	6		2646.2.t.b.1979.3		16
63.25	even	3		882.2.l.b.227.6		16
63.31	odd	6		1134.2.k.a.647.7		16
63.34	odd	6		882.2.t.a.803.7		16
63.38	even	6	inner	378.2.l.a.143.2		16
63.47	even	6		2646.2.m.b.1763.6		16
63.52	odd	6		126.2.l.a.101.7	yes	16
63.59	even	6		1134.2.k.b.647.2		16
63.61	odd	6		882.2.m.b.587.1		16
84.59	odd	6		1008.2.df.c.689.6		16
252.115	even	6		1008.2.ca.c.353.3		16
252.227	odd	6		3024.2.ca.c.2033.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.3	✓	16	3.2	odd	2
126.2.l.a.101.7	yes	16	63.52	odd	6
126.2.t.a.47.6	yes	16	9.7	even	3
126.2.t.a.59.6	yes	16	21.17	even	6
378.2.l.a.143.2		16	63.38	even	6	inner
378.2.l.a.341.6		16	1.1	even	1	trivial
378.2.t.a.17.2		16	7.3	odd	6
378.2.t.a.89.2		16	9.2	odd	6
882.2.l.b.227.6		16	63.25	even	3
882.2.l.b.509.2		16	21.20	even	2
882.2.m.a.293.4		16	21.5	even	6
882.2.m.a.587.4		16	63.16	even	3
882.2.m.b.293.1		16	21.2	odd	6
882.2.m.b.587.1		16	63.61	odd	6
882.2.t.a.803.7		16	63.34	odd	6
882.2.t.a.815.7		16	21.11	odd	6
1008.2.ca.c.257.3		16	12.11	even	2
1008.2.ca.c.353.3		16	252.115	even	6
1008.2.df.c.689.6		16	84.59	odd	6
1008.2.df.c.929.6		16	36.7	odd	6
1134.2.k.a.647.7		16	63.31	odd	6
1134.2.k.a.971.7		16	9.5	odd	6
1134.2.k.b.647.2		16	63.59	even	6
1134.2.k.b.971.2		16	9.4	even	3
2646.2.l.a.521.3		16	63.11	odd	6
2646.2.l.a.1097.7		16	7.6	odd	2
2646.2.m.a.881.7		16	7.5	odd	6
2646.2.m.a.1763.7		16	63.2	odd	6
2646.2.m.b.881.6		16	7.2	even	3
2646.2.m.b.1763.6		16	63.47	even	6
2646.2.t.b.1979.3		16	63.20	even	6
2646.2.t.b.2285.3		16	7.4	even	3
3024.2.ca.c.2033.3		16	252.227	odd	6
3024.2.ca.c.2609.3		16	4.3	odd	2
3024.2.df.c.17.3		16	28.3	even	6
3024.2.df.c.1601.3		16	36.11	even	6

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-0.714925 - 1.23829i) q^{5} +(0.327442 - 2.62541i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-0.714925 - 1.23829i) q^{5} +(0.327442 - 2.62541i) q^{7} -1.00000i q^{8} +(1.23829 - 0.714925i) q^{10} +(-2.96133 - 1.70972i) q^{11} +(-5.48813 - 3.16857i) q^{13} +(2.62541 + 0.327442i) q^{14} +1.00000 q^{16} +(1.14201 + 1.97802i) q^{17} +(-1.87673 - 1.08353i) q^{19} +(0.714925 + 1.23829i) q^{20} +(1.70972 - 2.96133i) q^{22} +(6.97507 - 4.02706i) q^{23} +(1.47776 - 2.55956i) q^{25} +(3.16857 - 5.48813i) q^{26} +(-0.327442 + 2.62541i) q^{28} +(0.298879 - 0.172558i) q^{29} +4.34228i q^{31} +1.00000i q^{32} +(-1.97802 + 1.14201i) q^{34} +(-3.48511 + 1.47150i) q^{35} +(1.07786 - 1.86690i) q^{37} +(1.08353 - 1.87673i) q^{38} +(-1.23829 + 0.714925i) q^{40} +(-0.202180 + 0.350186i) q^{41} +(2.90883 + 5.03824i) q^{43} +(2.96133 + 1.70972i) q^{44} +(4.02706 + 6.97507i) q^{46} +5.51829 q^{47} +(-6.78556 - 1.71934i) q^{49} +(2.55956 + 1.47776i) q^{50} +(5.48813 + 3.16857i) q^{52} +(-8.56310 + 4.94391i) q^{53} +4.88930i q^{55} +(-2.62541 - 0.327442i) q^{56} +(0.172558 + 0.298879i) q^{58} -11.0296 q^{59} -11.4797i q^{61} -4.34228 q^{62} -1.00000 q^{64} +9.06117i q^{65} +4.25366 q^{67} +(-1.14201 - 1.97802i) q^{68} +(-1.47150 - 3.48511i) q^{70} -3.55393i q^{71} +(-0.201057 + 0.116080i) q^{73} +(1.86690 + 1.07786i) q^{74} +(1.87673 + 1.08353i) q^{76} +(-5.45839 + 7.21486i) q^{77} +14.5620 q^{79} +(-0.714925 - 1.23829i) q^{80} +(-0.350186 - 0.202180i) q^{82} +(-0.811624 - 1.40577i) q^{83} +(1.63290 - 2.82827i) q^{85} +(-5.03824 + 2.90883i) q^{86} +(-1.70972 + 2.96133i) q^{88} +(2.02974 - 3.51562i) q^{89} +(-10.1159 + 13.3711i) q^{91} +(-6.97507 + 4.02706i) q^{92} +5.51829i q^{94} +3.09858i q^{95} +(-9.18719 + 5.30423i) q^{97} +(1.71934 - 6.78556i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 16 * q - 16 * q^4 + 2 * q^7	\( 16 q - 16 q^{4} + 2 q^{7} - 12 q^{11} + 6 q^{13} + 6 q^{14} + 16 q^{16} + 18 q^{17} + 6 q^{23} - 8 q^{25} - 12 q^{26} - 2 q^{28} - 6 q^{29} - 30 q^{35} - 2 q^{37} + 6 q^{41} - 2 q^{43} + 12 q^{44} + 6 q^{46} + 36 q^{47} - 8 q^{49} + 12 q^{50} - 6 q^{52} + 36 q^{53} - 6 q^{56} + 6 q^{58} - 60 q^{59} - 36 q^{62} - 16 q^{64} - 28 q^{67} - 18 q^{68} - 18 q^{70} - 18 q^{74} + 42 q^{77} + 32 q^{79} - 12 q^{85} - 24 q^{86} + 24 q^{89} - 12 q^{91} - 6 q^{92} + 6 q^{97} + 24 q^{98}+O(q^{100}) \) 16 * q - 16 * q^4 + 2 * q^7 - 12 * q^11 + 6 * q^13 + 6 * q^14 + 16 * q^16 + 18 * q^17 + 6 * q^23 - 8 * q^25 - 12 * q^26 - 2 * q^28 - 6 * q^29 - 30 * q^35 - 2 * q^37 + 6 * q^41 - 2 * q^43 + 12 * q^44 + 6 * q^46 + 36 * q^47 - 8 * q^49 + 12 * q^50 - 6 * q^52 + 36 * q^53 - 6 * q^56 + 6 * q^58 - 60 * q^59 - 36 * q^62 - 16 * q^64 - 28 * q^67 - 18 * q^68 - 18 * q^70 - 18 * q^74 + 42 * q^77 + 32 * q^79 - 12 * q^85 - 24 * q^86 + 24 * q^89 - 12 * q^91 - 6 * q^92 + 6 * q^97 + 24 * q^98

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