LMFDB - Embedded newform 378.2.t.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(17,378)]

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([5, 1]))

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

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

chi := DirichletCharacter("378.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.t (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:	$\Z[a_1, \ldots, a_{7}]$
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			17.2
Root			$-1.68301 - 0.409224i$ of defining polynomial
Character	$\chi$	$=$	378.17
Dual form			378.2.t.a.89.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.42985 q^{5} +(-2.43739 - 1.02913i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.42985 q^{5} +(-2.43739 - 1.02913i) q^{7} -1.00000i q^{8} +(1.23829 + 0.714925i) q^{10} +3.41945i q^{11} +(5.48813 + 3.16857i) q^{13} +(1.59628 + 2.10995i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.14201 + 1.97802i) q^{17} +(-1.87673 + 1.08353i) q^{19} +(-0.714925 - 1.23829i) q^{20} +(1.70972 - 2.96133i) q^{22} +8.05411i q^{23} -2.95553 q^{25} +(-3.16857 - 5.48813i) q^{26} +(-0.327442 - 2.62541i) q^{28} +(0.298879 - 0.172558i) q^{29} +(-3.76052 + 2.17114i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.97802 - 1.14201i) q^{34} +(3.48511 + 1.47150i) q^{35} +(1.07786 + 1.86690i) q^{37} +2.16707 q^{38} +1.42985i q^{40} +(0.202180 - 0.350186i) q^{41} +(2.90883 + 5.03824i) q^{43} +(-2.96133 + 1.70972i) q^{44} +(4.02706 - 6.97507i) q^{46} +(2.75915 - 4.77898i) q^{47} +(4.88178 + 5.01680i) q^{49} +(2.55956 + 1.47776i) q^{50} +6.33715i q^{52} +(8.56310 + 4.94391i) q^{53} -4.88930i q^{55} +(-1.02913 + 2.43739i) q^{56} -0.345115 q^{58} +(-5.51480 - 9.55191i) q^{59} +(-9.94175 - 5.73987i) q^{61} +4.34228 q^{62} -1.00000 q^{64} +(-7.84721 - 4.53059i) q^{65} +(-2.12683 - 3.68377i) q^{67} -2.28402 q^{68} +(-2.28244 - 3.01691i) q^{70} -3.55393i q^{71} +(-0.201057 - 0.116080i) q^{73} -2.15571i q^{74} +(-1.87673 - 1.08353i) q^{76} +(3.51906 - 8.33454i) q^{77} +(-7.28100 + 12.6111i) q^{79} +(0.714925 - 1.23829i) q^{80} +(-0.350186 + 0.202180i) q^{82} +(0.811624 + 1.40577i) q^{83} +(1.63290 - 2.82827i) q^{85} -5.81766i q^{86} +3.41945 q^{88} +(-2.02974 - 3.51562i) q^{89} +(-10.1159 - 13.3711i) q^{91} +(-6.97507 + 4.02706i) q^{92} +(-4.77898 + 2.75915i) q^{94} +(2.68345 - 1.54929i) q^{95} +(9.18719 - 5.30423i) q^{97} +(-1.71934 - 6.78556i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 + 2 * q^7	$ 16 q + 8 q^{4} + 2 q^{7} - 6 q^{13} + 6 q^{14} - 8 q^{16} - 18 q^{17} + 16 q^{25} + 12 q^{26} - 2 q^{28} - 6 q^{29} + 6 q^{31} + 30 q^{35} - 2 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{44} + 6 q^{46} + 18 q^{47} + 10 q^{49} + 12 q^{50} - 36 q^{53} - 12 q^{58} - 30 q^{59} - 60 q^{61} + 36 q^{62} - 16 q^{64} - 42 q^{65} + 14 q^{67} - 36 q^{68} + 18 q^{77} - 16 q^{79} - 12 q^{85} - 24 q^{89} - 12 q^{91} - 6 q^{92} + 66 q^{95} - 6 q^{97} - 24 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^13 + 6 * q^14 - 8 * q^16 - 18 * q^17 + 16 * q^25 + 12 * q^26 - 2 * q^28 - 6 * q^29 + 6 * q^31 + 30 * q^35 - 2 * q^37 - 6 * q^41 - 2 * q^43 - 12 * q^44 + 6 * q^46 + 18 * q^47 + 10 * q^49 + 12 * q^50 - 36 * q^53 - 12 * q^58 - 30 * q^59 - 60 * q^61 + 36 * q^62 - 16 * q^64 - 42 * q^65 + 14 * q^67 - 36 * q^68 + 18 * q^77 - 16 * q^79 - 12 * q^85 - 24 * q^89 - 12 * q^91 - 6 * q^92 + 66 * q^95 - 6 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.42985			−0.639449			−0.319724	−	0.947511i	$-0.603590\pi$
$5$	−1.42985			−0.639449			−0.319724	+	0.947511i	$0.603590\pi$
$6$		0			0
$7$	−2.43739	−	1.02913i	−0.921248	−	0.388975i
$7$	−2.43739	−	1.02913i	−0.921248	−	0.388975i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.23829	+	0.714925i	0.391581	+	0.226079i
$11$			3.41945i			1.03100i	0.856889	+	0.515501i	$0.172394\pi$
$11$			3.41945i			1.03100i	−0.856889	+	0.515501i	$0.827606\pi$
$12$		0			0
$13$	5.48813	+	3.16857i	1.52213	+	0.878804i	0.999658	+	0.0261501i	$0.00832479\pi$
$13$	5.48813	+	3.16857i	1.52213	+	0.878804i	0.522476	+	0.852654i	$0.325009\pi$
$14$	1.59628	+	2.10995i	0.426623	+	0.563908i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.14201	+	1.97802i	−0.276978	+	0.479739i	−0.970632	−	0.240569i	$-0.922666\pi$
$17$	−1.14201	+	1.97802i	−0.276978	+	0.479739i	0.693655	+	0.720308i	$0.255999\pi$
$18$		0			0
$19$	−1.87673	+	1.08353i	−0.430553	+	0.248580i	−0.699582	−	0.714552i	$-0.746630\pi$
$19$	−1.87673	+	1.08353i	−0.430553	+	0.248580i	0.269029	+	0.963132i	$0.413297\pi$
$20$	−0.714925	−	1.23829i	−0.159862	−	0.276889i
$21$		0			0
$22$	1.70972	−	2.96133i	0.364514	−	0.631357i
$23$			8.05411i			1.67940i	0.543052	+	0.839699i	$0.317269\pi$
$23$			8.05411i			1.67940i	−0.543052	+	0.839699i	$0.682731\pi$
$24$		0			0
$25$	−2.95553			−0.591106
$26$	−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
$31$	−3.76052	+	2.17114i	−0.675410	+	0.389948i	−0.798123	−	0.602494i	$-0.794174\pi$
$31$	−3.76052	+	2.17114i	−0.675410	+	0.389948i	0.122713	+	0.992442i	$0.460840\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		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	0.940920	−	0.338629i	$-0.109963\pi$
$37$	1.07786	+	1.86690i	0.177199	+	0.306917i	−0.763721	+	0.645546i	$0.776630\pi$
$38$	2.16707			0.351545
$39$		0			0
$40$			1.42985i			0.226079i
$41$	0.202180	−	0.350186i	0.0315752	−	0.0546898i	−0.849806	−	0.527096i	$-0.823281\pi$
$41$	0.202180	−	0.350186i	0.0315752	−	0.0546898i	0.881381	+	0.472406i	$0.156614\pi$
$42$		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
$47$	2.75915	−	4.77898i	0.402463	−	0.697086i	−0.591560	−	0.806261i	$-0.701488\pi$
$47$	2.75915	−	4.77898i	0.402463	−	0.697086i	0.994023	+	0.109175i	$0.0348209\pi$
$48$		0			0
$49$	4.88178	+	5.01680i	0.697396	+	0.716686i
$50$	2.55956	+	1.47776i	0.361977	+	0.208987i
$51$		0			0
$52$			6.33715i			0.878804i
$53$	8.56310	+	4.94391i	1.17623	+	0.679098i	0.955140	−	0.296155i	$-0.0957044\pi$
$53$	8.56310	+	4.94391i	1.17623	+	0.679098i	0.221093	+	0.975253i	$0.429038\pi$
$54$		0			0
$55$		−	4.88930i		−	0.659273i
$56$	−1.02913	+	2.43739i	−0.137524	+	0.325710i
$57$		0			0
$58$	−0.345115			−0.0453158
$59$	−5.51480	−	9.55191i	−0.717966	−	1.24355i	−0.961805	−	0.273737i	$-0.911740\pi$
$59$	−5.51480	−	9.55191i	−0.717966	−	1.24355i	0.243839	−	0.969816i	$-0.421593\pi$
$60$		0			0
$61$	−9.94175	−	5.73987i	−1.27291	−	0.734915i	−0.297376	−	0.954760i	$-0.596112\pi$
$61$	−9.94175	−	5.73987i	−1.27291	−	0.734915i	−0.975535	+	0.219845i	$0.929445\pi$
$62$	4.34228			0.551470
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−7.84721	−	4.53059i	−0.973326	−	0.561950i
$66$		0			0
$67$	−2.12683	−	3.68377i	−0.259833	−	0.450045i	0.706364	−	0.707849i	$-0.250334\pi$
$67$	−2.12683	−	3.68377i	−0.259833	−	0.450045i	−0.966197	+	0.257804i	$0.917001\pi$
$68$	−2.28402			−0.276978
$69$		0			0
$70$	−2.28244	−	3.01691i	−0.272804	−	0.360590i
$71$		−	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	0.488188	−	0.872739i	$-0.337658\pi$
$73$	−0.201057	−	0.116080i	−0.0235320	−	0.0135862i	−0.511720	+	0.859152i	$0.670991\pi$
$74$		−	2.15571i		−	0.250597i
$75$		0			0
$76$	−1.87673	−	1.08353i	−0.215276	−	0.124290i
$77$	3.51906	−	8.33454i	0.401034	−	0.949808i
$78$		0			0
$79$	−7.28100	+	12.6111i	−0.819177	+	1.41886i	0.0871130	+	0.996198i	$0.472236\pi$
$79$	−7.28100	+	12.6111i	−0.819177	+	1.41886i	−0.906290	+	0.422657i	$0.861097\pi$
$80$	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	0.907126	−	0.420860i	$-0.138272\pi$
$83$	0.811624	+	1.40577i	0.0890873	+	0.154304i	−0.818038	+	0.575164i	$0.804938\pi$
$84$		0			0
$85$	1.63290	−	2.82827i	0.177113	−	0.306769i
$86$		−	5.81766i		−	0.627334i
$87$		0			0
$88$	3.41945			0.364514
$89$	−2.02974	−	3.51562i	−0.215152	−	0.372655i	0.738167	−	0.674618i	$-0.235691\pi$
$89$	−2.02974	−	3.51562i	−0.215152	−	0.372655i	−0.953320	+	0.301963i	$0.902358\pi$
$90$		0			0
$91$	−10.1159	−	13.3711i	−1.06043	−	1.40167i
$92$	−6.97507	+	4.02706i	−0.727201	+	0.419850i
$93$		0			0
$94$	−4.77898	+	2.75915i	−0.492914	+	0.284584i
$95$	2.68345	−	1.54929i	0.275316	−	0.158954i
$96$		0			0
$97$	9.18719	−	5.30423i	0.932818	−	0.538563i	0.0451164	−	0.998982i	$-0.485634\pi$
$97$	9.18719	−	5.30423i	0.932818	−	0.538563i	0.887702	+	0.460419i	$0.152301\pi$
$98$	−1.71934	−	6.78556i	−0.173680	−	0.685445i
$99$		0			0
$100$	−1.47776	−	2.55956i	−0.147776	−	0.255956i
$101$	8.04886			0.800892			0.400446	−	0.916320i	$-0.368855\pi$
$101$	8.04886			0.800892			0.400446	+	0.916320i	$0.368855\pi$
$102$		0			0
$103$			2.81391i			0.277263i	0.990344	+	0.138631i	$0.0442703\pi$
$103$			2.81391i			0.277263i	−0.990344	+	0.138631i	$0.955730\pi$
$104$	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	$-0.943811\pi$
$107$	−13.7019	+	7.91078i	−1.32461	+	0.764764i	−0.340150	+	0.940371i	$0.610478\pi$
$108$		0			0
$109$	5.10675	−	8.84514i	0.489138	−	0.847211i	−0.510784	−	0.859709i	$-0.670645\pi$
$109$	5.10675	−	8.84514i	0.489138	−	0.847211i	0.999922	+	0.0124977i	$0.00397826\pi$
$110$	−2.44465	+	4.23425i	−0.233088	+	0.403720i
$111$		0			0
$112$	2.10995	−	1.59628i	0.199372	−	0.150834i
$113$	−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
$115$		−	11.5162i		−	1.07389i
$116$	0.298879	+	0.172558i	0.0277502	+	0.0160216i
$117$		0			0
$118$			11.0296i			1.01536i
$119$	4.81916	−	3.64593i	0.441772	−	0.334222i
$120$		0			0
$121$	−0.692610			−0.0629646
$122$	5.73987	+	9.94175i	0.519664	+	0.900084i
$123$		0			0
$124$	−3.76052	−	2.17114i	−0.337705	−	0.194974i
$125$	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	$0.417482\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	4.53059	+	7.84721i	0.397359	+	0.688246i
$131$	−4.45667			−0.389381			−0.194690	−	0.980865i	$-0.562370\pi$
$131$	−4.45667			−0.389381			−0.194690	+	0.980865i	$0.562370\pi$
$132$		0			0
$133$	5.68944	−	0.709590i	0.493337	−	0.0615292i
$134$			4.25366i			0.367460i
$135$		0			0
$136$	1.97802	+	1.14201i	0.169613	+	0.0979264i
$137$			9.65668i			0.825026i	0.910952	+	0.412513i	$0.135349\pi$
$137$			9.65668i			0.825026i	−0.910952	+	0.412513i	$0.864651\pi$
$138$		0			0
$139$	−16.0680	−	9.27686i	−1.36287	−	0.786853i	−0.372864	−	0.927886i	$-0.621624\pi$
$139$	−16.0680	−	9.27686i	−1.36287	−	0.786853i	−0.990005	+	0.141033i	$0.954958\pi$
$140$	0.468194	+	3.75394i	0.0395696	+	0.317266i
$141$		0			0
$142$	−1.77696	+	3.07779i	−0.149119	+	0.258282i
$143$	−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
$149$			6.50694i			0.533069i	0.963825	+	0.266535i	$0.0858786\pi$
$149$			6.50694i			0.533069i	−0.963825	+	0.266535i	$0.914121\pi$
$150$		0			0
$151$	5.75901			0.468661			0.234331	−	0.972157i	$-0.424710\pi$
$151$	5.75901			0.468661			0.234331	+	0.972157i	$0.424710\pi$
$152$	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
$157$	6.89669	−	3.98180i	0.550415	−	0.317783i	−0.198874	−	0.980025i	$-0.563728\pi$
$157$	6.89669	−	3.98180i	0.550415	−	0.317783i	0.749290	+	0.662243i	$0.230395\pi$
$158$	12.6111	−	7.28100i	1.00328	−	0.579245i
$159$		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	0.998113	−	0.0614080i	$-0.0195591\pi$
$163$	5.69256	+	9.85980i	0.445876	+	0.772279i	−0.552237	+	0.833687i	$0.686226\pi$
$164$	0.404360			0.0315752
$165$		0			0
$166$		−	1.62325i		−	0.125988i
$167$	−5.66418	+	9.81065i	−0.438308	+	0.759171i	−0.997559	−	0.0698271i	$-0.977755\pi$
$167$	−5.66418	+	9.81065i	−0.438308	+	0.759171i	0.559252	+	0.828998i	$0.311089\pi$
$168$		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
$173$	10.8457	−	18.7853i	0.824584	−	1.42822i	−0.0776528	−	0.996980i	$-0.524743\pi$
$173$	10.8457	−	18.7853i	0.824584	−	1.42822i	0.902237	−	0.431241i	$-0.141924\pi$
$174$		0			0
$175$	7.20378	+	3.04163i	0.544555	+	0.229925i
$176$	−2.96133	−	1.70972i	−0.223218	−	0.128875i
$177$		0			0
$178$			4.05949i			0.304271i
$179$	−18.0057	−	10.3956i	−1.34581	−	0.777002i	−0.358155	−	0.933662i	$-0.616594\pi$
$179$	−18.0057	−	10.3956i	−1.34581	−	0.777002i	−0.987653	+	0.156660i	$0.949927\pi$
$180$		0			0
$181$			21.5301i			1.60032i	0.599788	+	0.800159i	$0.295252\pi$
$181$			21.5301i			1.60032i	−0.599788	+	0.800159i	$0.704748\pi$
$182$	2.07505	+	16.6376i	0.153813	+	1.23326i
$183$		0			0
$184$	8.05411			0.593757
$185$	−1.54117	−	2.66939i	−0.113309	−	0.196258i
$186$		0			0
$187$	−6.76372	−	3.90503i	−0.494612	−	0.285564i
$188$	5.51829			0.402463
$189$		0			0
$190$	−3.09858			−0.224795
$191$	6.38207	+	3.68469i	0.461791	+	0.266615i	0.712797	−	0.701371i	$-0.247428\pi$
$191$	6.38207	+	3.68469i	0.461791	+	0.266615i	−0.251006	+	0.967985i	$0.580761\pi$
$192$		0			0
$193$	1.41279	+	2.44703i	0.101695	+	0.176141i	0.912383	−	0.409337i	$-0.134240\pi$
$193$	1.41279	+	2.44703i	0.101695	+	0.176141i	−0.810688	+	0.585478i	$0.800907\pi$
$194$	−10.6085			−0.761643
$195$		0			0
$196$	−1.90379	+	6.73614i	−0.135985	+	0.481153i
$197$			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	0.891971	−	0.452092i	$-0.149322\pi$
$199$	13.3511	+	7.70826i	0.946434	+	0.546424i	0.0544625	+	0.998516i	$0.482655\pi$
$200$			2.95553i			0.208987i
$201$		0			0
$202$	−6.97052	−	4.02443i	−0.490444	−	0.283158i
$203$	−0.906069	+	0.113005i	−0.0635936	+	0.00793142i
$204$		0			0
$205$	−0.289087	+	0.500713i	−0.0201907	+	0.0349713i
$206$	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	$0.0681421\pi$
$212$			9.88782i			0.679098i
$213$		0			0
$214$	15.8216			1.08154
$215$	−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
$220$	4.23425	−	2.44465i	0.285473	−	0.164818i
$221$	−12.5350	+	7.23707i	−0.843194	+	0.486818i
$222$		0			0
$223$	6.88961	−	3.97772i	0.461363	−	0.266368i	−0.251254	−	0.967921i	$-0.580843\pi$
$223$	6.88961	−	3.97772i	0.461363	−	0.266368i	0.712617	+	0.701553i	$0.247510\pi$
$224$	−2.62541	+	0.327442i	−0.175418	+	0.0218782i
$225$		0			0
$226$	4.20778	+	7.28808i	0.279897	+	0.484796i
$227$	−9.23968			−0.613259			−0.306630	−	0.951829i	$-0.599201\pi$
$227$	−9.23968			−0.613259			−0.306630	+	0.951829i	$0.599201\pi$
$228$		0			0
$229$			8.44454i			0.558031i	0.960287	+	0.279016i	$0.0900081\pi$
$229$			8.44454i			0.558031i	−0.960287	+	0.279016i	$0.909992\pi$
$230$	−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	$-0.483074\pi$
$233$	14.4176	−	8.32399i	0.944526	−	0.545323i	0.891376	+	0.453264i	$0.149741\pi$
$234$		0			0
$235$	−3.94517	+	6.83323i	−0.257354	+	0.445751i
$236$	5.51480	−	9.55191i	0.358983	−	0.621776i
$237$		0			0
$238$	−5.99648	+	0.747884i	−0.388694	+	0.0484781i
$239$	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
$241$		−	25.2900i		−	1.62907i	−0.580111	−	0.814537i	$-0.696991\pi$
$241$		−	25.2900i		−	1.62907i	0.580111	−	0.814537i	$-0.303009\pi$
$242$	0.599818	+	0.346305i	0.0385578	+	0.0222613i
$243$		0			0
$244$		−	11.4797i		−	0.734915i
$245$	−6.98021	−	7.17327i	−0.445949	−	0.458284i
$246$		0			0
$247$	−13.7330			−0.873811
$248$	2.17114	+	3.76052i	0.137868	+	0.238794i
$249$		0			0
$250$	−9.85123	−	5.68761i	−0.623046	−	0.359716i
$251$	−8.19337			−0.517161			−0.258581	−	0.965990i	$-0.583255\pi$
$251$	−8.19337			−0.517161			−0.258581	+	0.965990i	$0.583255\pi$
$252$		0			0
$253$	−27.5406			−1.73146
$254$	−5.00366	−	2.88886i	−0.313958	−	0.181264i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.63445			0.413846			0.206923	−	0.978357i	$-0.433655\pi$
$257$	6.63445			0.413846			0.206923	+	0.978357i	$0.433655\pi$
$258$		0			0
$259$	−0.705872	−	5.65963i	−0.0438607	−	0.351672i
$260$		−	9.06117i		−	0.561950i
$261$		0			0
$262$	3.85959	+	2.22833i	0.238446	+	0.137667i
$263$			6.04590i			0.372806i	0.982473	+	0.186403i	$0.0596830\pi$
$263$			6.04590i			0.372806i	−0.982473	+	0.186403i	$0.940317\pi$
$264$		0			0
$265$	−12.2440	−	7.06905i	−0.752140	−	0.434248i
$266$	−5.28199	−	2.23020i	−0.323860	−	0.136742i
$267$		0			0
$268$	2.12683	−	3.68377i	0.129917	−	0.225022i
$269$	3.41069	−	5.90750i	0.207954	−	0.360186i	−0.743116	−	0.669163i	$-0.766653\pi$
$269$	3.41069	−	5.90750i	0.207954	−	0.360186i	0.951070	+	0.308976i	$0.0999863\pi$
$270$		0			0
$271$	−4.39780	+	2.53907i	−0.267148	+	0.154238i	−0.627591	−	0.778543i	$-0.715959\pi$
$271$	−4.39780	+	2.53907i	−0.267148	+	0.154238i	0.360443	+	0.932781i	$0.382625\pi$
$272$	−1.14201	−	1.97802i	−0.0692444	−	0.119935i
$273$		0			0
$274$	4.82834	−	8.36293i	0.291691	−	0.505223i
$275$		−	10.1063i		−	0.609431i
$276$		0			0
$277$	−1.97913			−0.118915			−0.0594573	−	0.998231i	$-0.518937\pi$
$277$	−1.97913			−0.118915			−0.0594573	+	0.998231i	$0.518937\pi$
$278$	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
$283$	4.46337	−	2.57693i	0.265320	−	0.153182i	−0.361439	−	0.932396i	$-0.617714\pi$
$283$	4.46337	−	2.57693i	0.265320	−	0.153182i	0.626759	+	0.779213i	$0.284381\pi$
$284$	3.07779	−	1.77696i	0.182633	−	0.105443i
$285$		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
$290$	0.493463			0.0289772
$291$		0			0
$292$		−	0.232161i		−	0.0135862i
$293$	1.03248	−	1.78831i	0.0603183	−	0.104474i	−0.834289	−	0.551327i	$-0.814122\pi$
$293$	1.03248	−	1.78831i	0.0603183	−	0.104474i	0.894608	+	0.446852i	$0.147455\pi$
$294$		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
$299$	−25.5201	+	44.2020i	−1.47586	+	2.55627i
$300$		0			0
$301$	−1.90495	−	15.2737i	−0.109799	−	0.880364i
$302$	−4.98745	−	2.87950i	−0.286995	−	0.165697i
$303$		0			0
$304$		−	2.16707i		−	0.124290i
$305$	14.2152	+	8.20716i	0.813961	+	0.469941i
$306$		0			0
$307$		−	1.09119i		−	0.0622772i	−0.999515	−	0.0311386i	$-0.990087\pi$
$307$		−	1.09119i		−	0.0622772i	0.999515	−	0.0311386i	$-0.00991333\pi$
$308$	8.97745	−	1.11967i	0.511538	−	0.0637992i
$309$		0			0
$310$	−6.20881			−0.352637
$311$	−7.61100	−	13.1826i	−0.431580	−	0.747519i	0.565429	−	0.824797i	$-0.308711\pi$
$311$	−7.61100	−	13.1826i	−0.431580	−	0.747519i	−0.997010	+	0.0772777i	$0.975377\pi$
$312$		0			0
$313$	10.0202	+	5.78518i	0.566377	+	0.326998i	0.755701	−	0.654917i	$-0.227296\pi$
$313$	10.0202	+	5.78518i	0.566377	+	0.326998i	−0.189324	+	0.981915i	$0.560630\pi$
$314$	−7.96361			−0.449412
$315$		0			0
$316$	−14.5620			−0.819177
$317$	−14.8613	−	8.58020i	−0.834696	−	0.481912i	0.0207618	−	0.999784i	$-0.493391\pi$
$317$	−14.8613	−	8.58020i	−0.834696	−	0.481912i	−0.855458	+	0.517872i	$0.826724\pi$
$318$		0			0
$319$	0.590051	+	1.02200i	0.0330365	+	0.0572210i
$320$	1.42985			0.0799311
$321$		0			0
$322$	−16.9938	+	12.8566i	−0.947027	+	0.716471i
$323$		−	4.94962i		−	0.275404i
$324$		0			0
$325$	−16.2203	−	9.36481i	−0.899742	−	0.519466i
$326$		−	11.3851i		−	0.630563i
$327$		0			0
$328$	−0.350186	−	0.202180i	−0.0193358	−	0.0111635i
$329$	−11.6433	+	8.80874i	−0.641918	+	0.485641i
$330$		0			0
$331$	13.2466	−	22.9437i	0.728096	−	1.26110i	−0.229591	−	0.973287i	$-0.573739\pi$
$331$	13.2466	−	22.9437i	0.728096	−	1.26110i	0.957687	−	0.287812i	$-0.0929280\pi$
$332$	−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	$0.0956015\pi$
$338$		−	27.1594i		−	1.47728i
$339$		0			0
$340$	3.26580			0.177113
$341$	−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
$346$	−18.7853	+	10.8457i	−1.00991	+	0.583069i
$347$	22.1851	−	12.8086i	1.19096	−	0.687599i	0.232433	−	0.972612i	$-0.425331\pi$
$347$	22.1851	−	12.8086i	1.19096	−	0.687599i	0.958524	+	0.285013i	$0.0919979\pi$
$348$		0			0
$349$	−9.11932	+	5.26504i	−0.488146	+	0.281831i	−0.723805	−	0.690005i	$-0.757609\pi$
$349$	−9.11932	+	5.26504i	−0.488146	+	0.281831i	0.235659	+	0.971836i	$0.424275\pi$
$350$	−4.71785	−	6.23602i	−0.252179	−	0.333329i
$351$		0			0
$352$	1.70972	+	2.96133i	0.0911285	+	0.157839i
$353$	−12.8437			−0.683602			−0.341801	−	0.939772i	$-0.611037\pi$
$353$	−12.8437			−0.683602			−0.341801	+	0.939772i	$0.611037\pi$
$354$		0			0
$355$			5.08158i			0.269702i
$356$	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	$-0.380482\pi$
$359$	25.6881	−	14.8311i	1.35577	−	0.782753i	0.989050	+	0.147579i	$0.0471482\pi$
$360$		0			0
$361$	−7.15191	+	12.3875i	−0.376416	+	0.651972i
$362$	10.7650	−	18.6456i	0.565798	−	0.979991i
$363$		0			0
$364$	6.52176	−	15.4461i	0.341833	−	0.809597i
$365$	0.287482	+	0.165978i	0.0150475	+	0.00868767i
$366$		0			0
$367$			23.9979i			1.25268i	0.779550	+	0.626340i	$0.215448\pi$
$367$			23.9979i			1.25268i	−0.779550	+	0.626340i	$0.784552\pi$
$368$	−6.97507	−	4.02706i	−0.363600	−	0.209925i
$369$		0			0
$370$			3.08235i			0.160244i
$371$	−15.7837	−	20.8628i	−0.819450	−	1.08314i
$372$		0			0
$373$	−11.8390			−0.612998			−0.306499	−	0.951871i	$-0.599158\pi$
$373$	−11.8390			−0.612998			−0.306499	+	0.951871i	$0.599158\pi$
$374$	3.90503	+	6.76372i	0.201925	+	0.349744i
$375$		0			0
$376$	−4.77898	−	2.75915i	−0.246457	−	0.142292i
$377$	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	$0.609556\pi$
$380$	2.68345	+	1.54929i	0.137658	+	0.0794769i
$381$		0			0
$382$	−3.68469	−	6.38207i	−0.188525	−	0.326535i
$383$	17.5521			0.896868			0.448434	−	0.893816i	$-0.351982\pi$
$383$	17.5521			0.896868			0.448434	+	0.893816i	$0.351982\pi$
$384$		0			0
$385$	−5.03173	+	11.9171i	−0.256441	+	0.607354i
$386$		−	2.82559i		−	0.143819i
$387$		0			0
$388$	9.18719	+	5.30423i	0.466409	+	0.269281i
$389$			21.8410i			1.10738i	0.832722	+	0.553691i	$0.186781\pi$
$389$			21.8410i			1.10738i	−0.832722	+	0.553691i	$0.813219\pi$
$390$		0			0
$391$	−15.9312	−	9.19786i	−0.805674	−	0.465156i
$392$	5.01680	−	4.88178i	0.253387	−	0.246567i
$393$		0			0
$394$	13.0441	−	22.5931i	0.657154	−	1.13822i
$395$	10.4107	−	18.0319i	0.523821	−	0.907285i
$396$		0			0
$397$	33.7636	−	19.4935i	1.69455	−	0.978348i	0.743792	−	0.668411i	$-0.233025\pi$
$397$	33.7636	−	19.4935i	1.69455	−	0.978348i	0.950757	−	0.309937i	$-0.100308\pi$
$398$	−7.70826	−	13.3511i	−0.386380	−	0.669230i
$399$		0			0
$400$	1.47776	−	2.55956i	0.0738882	−	0.127978i
$401$			23.1979i			1.15845i	0.815169	+	0.579223i	$0.196644\pi$
$401$			23.1979i			1.15845i	−0.815169	+	0.579223i	$0.803356\pi$
$402$		0			0
$403$	−27.5177			−1.37075
$404$	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
$409$	−21.3205	+	12.3094i	−1.05423	+	0.608659i	−0.923830	−	0.382803i	$-0.874959\pi$
$409$	−21.3205	+	12.3094i	−1.05423	+	0.608659i	−0.130398	+	0.991462i	$0.541626\pi$
$410$	0.500713	−	0.289087i	0.0247285	−	0.0142770i
$411$		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
$416$	6.33715			0.310704
$417$		0			0
$418$			7.41017i			0.362443i
$419$	8.53996	−	14.7916i	0.417204	−	0.722619i	−0.578453	−	0.815716i	$-0.696343\pi$
$419$	8.53996	−	14.7916i	0.417204	−	0.722619i	0.995657	+	0.0930969i	$0.0296766\pi$
$420$		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
$425$	3.37524	−	5.84608i	0.163723	−	0.283577i
$426$		0			0
$427$	18.3249	+	24.2217i	0.886803	+	1.17217i
$428$	−13.7019	−	7.91078i	−0.662305	−	0.382382i
$429$		0			0
$430$			8.31838i			0.401148i
$431$	−8.32286	−	4.80521i	−0.400898	−	0.231459i	0.285973	−	0.958238i	$-0.407683\pi$
$431$	−8.32286	−	4.80521i	−0.400898	−	0.231459i	−0.686871	+	0.726779i	$0.741016\pi$
$432$		0			0
$433$			9.04314i			0.434585i	0.976106	+	0.217293i	$0.0697226\pi$
$433$			9.04314i			0.434585i	−0.976106	+	0.217293i	$0.930277\pi$
$434$	−10.5838	−	4.46878i	−0.508041	−	0.214508i
$435$		0			0
$436$	10.2135			0.489138
$437$	−8.72690	−	15.1154i	−0.417464	−	0.723069i
$438$		0			0
$439$	0.791370	+	0.456897i	0.0377700	+	0.0218065i	0.518766	−	0.854916i	$-0.326392\pi$
$439$	0.791370	+	0.456897i	0.0377700	+	0.0218065i	−0.480996	+	0.876723i	$0.659725\pi$
$440$	−4.88930			−0.233088
$441$		0			0
$442$	14.4741			0.688465
$443$	25.4279	+	14.6808i	1.20812	+	0.697507i	0.962348	−	0.271821i	$-0.0876259\pi$
$443$	25.4279	+	14.6808i	1.20812	+	0.697507i	0.245770	+	0.969328i	$0.420959\pi$
$444$		0			0
$445$	2.90223	+	5.02681i	0.137579	+	0.238294i
$446$	−7.95544			−0.376701
$447$		0			0
$448$	2.43739	+	1.02913i	0.115156	+	0.0486219i
$449$			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
$452$		−	8.41555i		−	0.395834i
$453$		0			0
$454$	8.00180	+	4.61984i	0.375543	+	0.216820i
$455$	14.4642	+	19.1186i	0.678090	+	0.896295i
$456$		0			0
$457$	7.55693	−	13.0890i	0.353498	−	0.612277i	−0.633362	−	0.773856i	$-0.718325\pi$
$457$	7.55693	−	13.0890i	0.353498	−	0.612277i	0.986860	+	0.161579i	$0.0516588\pi$
$458$	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	0.961264	−	0.275629i	$-0.0888863\pi$
$461$	5.19445	+	8.99706i	0.241930	+	0.419035i	−0.719334	+	0.694664i	$0.755553\pi$
$462$		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	$0.206076\pi$
$464$			0.345115i			0.0160216i
$465$		0			0
$466$	−16.6480			−0.771203
$467$	9.74994	+	16.8874i	0.451173	+	0.781455i	0.998459	−	0.0554907i	$-0.0176723\pi$
$467$	9.74994	+	16.8874i	0.451173	+	0.781455i	−0.547286	+	0.836946i	$0.684339\pi$
$468$		0			0
$469$	1.39283	+	11.1676i	0.0643148	+	0.515672i
$470$	6.83323	−	3.94517i	0.315193	−	0.181977i
$471$		0			0
$472$	−9.55191	+	5.51480i	−0.439662	+	0.253839i
$473$	−17.2280	+	9.94659i	−0.792144	+	0.457345i
$474$		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
$479$	27.8024			1.27033			0.635163	−	0.772378i	$-0.280933\pi$
$479$	27.8024			1.27033			0.635163	+	0.772378i	$0.280933\pi$
$480$		0			0
$481$			13.6611i			0.622891i
$482$	−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	−0.768808	−	0.639480i	$-0.779150\pi$
$487$	3.73838	−	6.47506i	0.169402	−	0.293413i	0.938210	+	0.346067i	$0.112483\pi$
$488$	−5.73987	+	9.94175i	−0.259832	+	0.450042i
$489$		0			0
$490$	2.45840	+	9.70234i	0.111059	+	0.438307i
$491$	−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
$493$			0.788249i			0.0355009i
$494$	11.8931	+	6.86651i	0.535098	+	0.308939i
$495$		0			0
$496$		−	4.34228i		−	0.194974i
$497$	−3.65746	+	8.66232i	−0.164059	+	0.388558i
$498$		0			0
$499$	32.9042			1.47300			0.736498	−	0.676439i	$-0.236478\pi$
$499$	32.9042			1.47300			0.736498	+	0.676439i	$0.236478\pi$
$500$	5.68761	+	9.85123i	0.254358	+	0.440560i
$501$		0			0
$502$	7.09567	+	4.09669i	0.316695	+	0.182844i
$503$	−25.6142			−1.14208			−0.571039	−	0.820923i	$-0.693460\pi$
$503$	−25.6142			−1.14208			−0.571039	+	0.820923i	$0.693460\pi$
$504$		0			0
$505$	−11.5087			−0.512129
$506$	23.8509	+	13.7703i	1.06030	+	0.612165i
$507$		0			0
$508$	2.88886	+	5.00366i	0.128173	+	0.222002i
$509$	21.4717			0.951715			0.475857	−	0.879522i	$-0.342138\pi$
$509$	21.4717			0.951715			0.475857	+	0.879522i	$0.342138\pi$
$510$		0			0
$511$	0.370594	+	0.489848i	0.0163941	+	0.0216696i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−5.74560	−	3.31723i	−0.253428	−	0.146317i
$515$		−	4.02347i		−	0.177295i
$516$		0			0
$517$	16.3415	+	9.43475i	0.718697	+	0.414940i
$518$	−2.21851	+	5.25432i	−0.0974759	+	0.230862i
$519$		0			0
$520$	−4.53059	+	7.84721i	−0.198679	+	0.344123i
$521$	−3.23087	+	5.59604i	−0.141547	+	0.245167i	−0.928079	−	0.372382i	$-0.878541\pi$
$521$	−3.23087	+	5.59604i	−0.141547	+	0.245167i	0.786532	+	0.617549i	$0.211874\pi$
$522$		0			0
$523$	11.7830	−	6.80291i	0.515234	−	0.297470i	−0.219749	−	0.975557i	$-0.570524\pi$
$523$	11.7830	−	6.80291i	0.515234	−	0.297470i	0.734982	+	0.678086i	$0.237190\pi$
$524$	−2.22833	−	3.85959i	−0.0973452	−	0.168607i
$525$		0			0
$526$	3.02295	−	5.23590i	0.131807	−	0.228296i
$527$		−	9.91784i		−	0.432028i
$528$		0			0
$529$	−41.8687			−1.82038
$530$	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
$535$	19.5916	−	11.3112i	0.847020	−	0.489027i
$536$	−3.68377	+	2.12683i	−0.159115	+	0.0918650i
$537$		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	−0.985022	−	0.172428i	$-0.944839\pi$
$541$	−14.9288	−	25.8574i	−0.641838	−	1.11170i	0.343184	−	0.939268i	$-0.388494\pi$
$542$	5.07815			0.218125
$543$		0			0
$544$			2.28402i			0.0979264i
$545$	−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
$551$	−0.373944	+	0.647690i	−0.0159305	+	0.0275925i
$552$		0			0
$553$	30.7251	−	23.2450i	1.30656	−	0.988479i
$554$	1.71398	+	0.989567i	0.0728201	+	0.0420427i
$555$		0			0
$556$		−	18.5537i		−	0.786853i
$557$	−32.5079	−	18.7684i	−1.37740	−	0.795245i	−0.385558	−	0.922684i	$-0.625991\pi$
$557$	−32.5079	−	18.7684i	−1.37740	−	0.795245i	−0.991846	+	0.127439i	$0.959324\pi$
$558$		0			0
$559$			36.8674i			1.55932i
$560$	−3.01691	+	2.28244i	−0.127488	+	0.0964507i
$561$		0			0
$562$	−17.6326			−0.743787
$563$	−3.55341	−	6.15468i	−0.149758	−	0.259389i	0.781380	−	0.624056i	$-0.214516\pi$
$563$	−3.55341	−	6.15468i	−0.149758	−	0.259389i	−0.931138	+	0.364667i	$0.881183\pi$
$564$		0			0
$565$	10.4209	+	6.01649i	0.438409	+	0.253116i
$566$	−5.15385			−0.216633
$567$		0			0
$568$	−3.55393			−0.149119
$569$	−35.6499	−	20.5825i	−1.49452	−	0.862862i	−0.494541	−	0.869154i	$-0.664664\pi$
$569$	−35.6499	−	20.5825i	−1.49452	−	0.862862i	−0.999980	+	0.00629202i	$0.997997\pi$
$570$		0			0
$571$	−2.21293	−	3.83290i	−0.0926080	−	0.160402i	0.816000	−	0.578052i	$-0.196187\pi$
$571$	−2.21293	−	3.83290i	−0.0926080	−	0.160402i	−0.908608	+	0.417650i	$0.862854\pi$
$572$	−21.6695			−0.906049
$573$		0			0
$574$	1.06161	−	0.132405i	0.0443108	−	0.00552646i
$575$		−	23.8042i		−	0.992702i
$576$		0			0
$577$	2.37542	+	1.37145i	0.0988900	+	0.0570941i	0.548629	−	0.836066i	$-0.315150\pi$
$577$	2.37542	+	1.37145i	0.0988900	+	0.0570941i	−0.449739	+	0.893160i	$0.648483\pi$
$578$		−	11.7833i		−	0.490119i
$579$		0			0
$580$	−0.427352	−	0.246732i	−0.0177448	−	0.0102450i
$581$	−0.531520	−	4.26169i	−0.0220512	−	0.176805i
$582$		0			0
$583$	−16.9054	+	29.2811i	−0.700151	+	1.21270i
$584$	−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	0.994747	−	0.102369i	$-0.0326422\pi$
$587$	9.90248	+	17.1516i	0.408719	+	0.707922i	−0.586027	+	0.810291i	$0.699309\pi$
$588$		0			0
$589$	4.70501	−	8.14931i	0.193866	−	0.335786i
$590$		−	15.7707i		−	0.649268i
$591$		0			0
$592$	−2.15571			−0.0885993
$593$	0.434850	+	0.753183i	0.0178572	+	0.0309295i	0.874816	−	0.484456i	$-0.160982\pi$
$593$	0.434850	+	0.753183i	0.0178572	+	0.0309295i	−0.856959	+	0.515385i	$0.827649\pi$
$594$		0			0
$595$	−6.89068	+	5.21313i	−0.282490	+	0.213717i
$596$	−5.63517	+	3.25347i	−0.230826	+	0.133267i
$597$		0			0
$598$	44.2020	−	25.5201i	1.80756	−	1.04359i
$599$	−2.33277	+	1.34682i	−0.0953143	+	0.0550297i	−0.546899	−	0.837198i	$-0.684192\pi$
$599$	−2.33277	+	1.34682i	−0.0953143	+	0.0550297i	0.451585	+	0.892228i	$0.350859\pi$
$600$		0			0
$601$	−0.115325	+	0.0665827i	−0.00470419	+	0.00271596i	−0.502350	−	0.864664i	$-0.667531\pi$
$601$	−0.115325	+	0.0665827i	−0.00470419	+	0.00271596i	0.497646	+	0.867380i	$0.334198\pi$
$602$	−5.98714	+	14.1799i	−0.244018	+	0.577931i
$603$		0			0
$604$	2.87950	+	4.98745i	0.117165	+	0.202936i
$605$	0.990329			0.0402626
$606$		0			0
$607$			44.3243i			1.79907i	0.436851	+	0.899534i	$0.356094\pi$
$607$			44.3243i			1.79907i	−0.436851	+	0.899534i	$0.643906\pi$
$608$	−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	−0.791680	−	0.610936i	$-0.790793\pi$
$613$	3.29901	−	5.71406i	0.133246	−	0.230789i	0.924926	+	0.380147i	$0.124127\pi$
$614$	−0.545593	+	0.944994i	−0.0220183	+	0.0381369i
$615$		0			0
$616$	−8.33454	−	3.51906i	−0.335808	−	0.141787i
$617$	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
$619$		−	6.53894i		−	0.262822i	−0.991328	−	0.131411i	$-0.958049\pi$
$619$		−	6.53894i		−	0.262822i	0.991328	−	0.131411i	$-0.0419508\pi$
$620$	5.37699	+	3.10441i	0.215945	+	0.124676i
$621$		0			0
$622$			15.2220i			0.610347i
$623$	1.32925	+	10.6578i	0.0532552	+	0.426996i
$624$		0			0
$625$	−1.48722			−0.0594888
$626$	−5.78518	−	10.0202i	−0.231222	−	0.400489i
$627$		0			0
$628$	6.89669	+	3.98180i	0.275208	+	0.158891i
$629$	−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	$0.410875\pi$
$632$	12.6111	+	7.28100i	0.501641	+	0.289623i
$633$		0			0
$634$	8.58020	+	14.8613i	0.340763	+	0.590219i
$635$	−8.26129			−0.327839
$636$		0			0
$637$	10.8957	+	43.0011i	0.431704	+	1.70377i
$638$		−	1.18010i		−	0.0467207i
$639$		0			0
$640$	−1.23829	−	0.714925i	−0.0489476	−	0.0282599i
$641$		−	15.2351i		−	0.601752i	−0.953663	−	0.300876i	$-0.902721\pi$
$641$		−	15.2351i		−	0.601752i	0.953663	−	0.300876i	$-0.0972790\pi$
$642$		0			0
$643$	16.5813	+	9.57324i	0.653904	+	0.377532i	0.789950	−	0.613171i	$-0.210106\pi$
$643$	16.5813	+	9.57324i	0.653904	+	0.377532i	−0.136046	+	0.990702i	$0.543440\pi$
$644$	21.1454	−	2.63726i	0.833244	−	0.103923i
$645$		0			0
$646$	−2.47481	+	4.28649i	−0.0973700	+	0.168650i
$647$	0.793991	−	1.37523i	0.0312150	−	0.0540660i	−0.849996	−	0.526789i	$-0.823396\pi$
$647$	0.793991	−	1.37523i	0.0312150	−	0.0540660i	0.881211	+	0.472723i	$0.156729\pi$
$648$		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
$653$			17.9639i			0.702983i	0.936191	+	0.351492i	$0.114325\pi$
$653$			17.9639i			0.702983i	−0.936191	+	0.351492i	$0.885675\pi$
$654$		0			0
$655$	6.37237			0.248989
$656$	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
$661$	−15.7786	+	9.10975i	−0.613715	+	0.354328i	−0.774418	−	0.632674i	$-0.781957\pi$
$661$	−15.7786	+	9.10975i	−0.613715	+	0.354328i	0.160703	+	0.987003i	$0.448624\pi$
$662$	−22.9437	+	13.2466i	−0.891732	+	0.514842i
$663$		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
$668$	−11.3284			−0.438308
$669$		0			0
$670$		−	6.08209i		−	0.234972i
$671$	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
$677$	−11.5645	+	20.0303i	−0.444460	+	0.769827i	−0.998014	−	0.0629856i	$-0.979938\pi$
$677$	−11.5645	+	20.0303i	−0.444460	+	0.769827i	0.553554	+	0.832813i	$0.313271\pi$
$678$		0			0
$679$	−27.8516	+	3.47366i	−1.06884	+	0.133307i
$680$	−2.82827	−	1.63290i	−0.108459	−	0.0626189i
$681$		0			0
$682$			14.8482i			0.568567i
$683$	−6.80041	−	3.92622i	−0.260210	−	0.150233i	0.364220	−	0.931313i	$-0.381336\pi$
$683$	−6.80041	−	3.92622i	−0.260210	−	0.150233i	−0.624431	+	0.781080i	$0.714669\pi$
$684$		0			0
$685$		−	13.8076i		−	0.527562i
$686$	−2.79253	+	18.3085i	−0.106619	+	0.699022i
$687$		0			0
$688$	−5.81766			−0.221796
$689$	31.3303	+	54.2656i	1.19359	+	2.06736i
$690$		0			0
$691$	−14.8676	−	8.58379i	−0.565589	−	0.326543i	0.189797	−	0.981823i	$-0.439217\pi$
$691$	−14.8676	−	8.58379i	−0.565589	−	0.326543i	−0.755386	+	0.655281i	$0.772550\pi$
$692$	21.6914			0.824584
$693$		0			0
$694$	−25.6171			−0.972412
$695$	22.9748	+	13.2645i	0.871485	+	0.503152i
$696$		0			0
$697$	0.461782	+	0.799830i	0.0174912	+	0.0302957i
$698$	10.5301			0.398570
$699$		0			0
$700$	0.967765	+	7.75947i	0.0365781	+	0.293281i
$701$		−	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
$704$		−	3.41945i		−	0.128875i
$705$		0			0
$706$	11.1230	+	6.42186i	0.418619	+	0.241690i
$707$	−19.6183	−	8.28334i	−0.737820	−	0.311527i
$708$		0			0
$709$	12.1668	−	21.0735i	0.456933	−	0.791432i	−0.541864	−	0.840466i	$-0.682281\pi$
$709$	12.1668	−	21.0735i	0.456933	−	0.791432i	0.998797	+	0.0490345i	$0.0156144\pi$
$710$	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
$716$		−	20.7912i		−	0.777002i
$717$		0			0
$718$	−29.6621			−1.10698
$719$	8.76887	+	15.1881i	0.327024	+	0.566422i	0.981920	−	0.189297i	$-0.0606210\pi$
$719$	8.76887	+	15.1881i	0.327024	+	0.566422i	−0.654896	+	0.755719i	$0.727288\pi$
$720$		0			0
$721$	2.89588	−	6.85860i	0.107848	−	0.255428i
$722$	12.3875	−	7.15191i	0.461014	−	0.266167i
$723$		0			0
$724$	−18.6456	+	10.7650i	−0.692958	+	0.400079i
$725$	−0.883344	+	0.509999i	−0.0328066	+	0.0189409i
$726$		0			0
$727$	33.8627	−	19.5507i	1.25590	−	0.725094i	0.283625	−	0.958935i	$-0.408463\pi$
$727$	33.8627	−	19.5507i	1.25590	−	0.725094i	0.972275	+	0.233841i	$0.0751296\pi$
$728$	−13.3711	+	10.1159i	−0.495565	+	0.374919i
$729$		0			0
$730$	−0.165978	−	0.287482i	−0.00614311	−	0.0106402i
$731$	−13.2876			−0.491461
$732$		0			0
$733$		−	23.4489i		−	0.866105i	−0.901369	−	0.433053i	$-0.857436\pi$
$733$		−	23.4489i		−	0.866105i	0.901369	−	0.433053i	$-0.142564\pi$
$734$	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	−0.508272	−	0.861197i	$-0.669716\pi$
$739$	13.3662	−	23.1509i	0.491682	−	0.851618i	0.999954	+	0.00957820i	$0.00304888\pi$
$740$	1.54117	−	2.66939i	0.0566547	−	0.0981288i
$741$		0			0
$742$	3.23769	+	25.9596i	0.118859	+	0.953006i
$743$	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
$745$		−	9.30395i		−	0.340870i
$746$	10.2528	+	5.91948i	0.375383	+	0.216727i
$747$		0			0
$748$		−	7.81007i		−	0.285564i
$749$	41.5381	−	5.18065i	1.51777	−	0.189297i
$750$		0			0
$751$	−10.2483			−0.373967			−0.186984	−	0.982363i	$-0.559871\pi$
$751$	−10.2483			−0.373967			−0.186984	+	0.982363i	$0.559871\pi$
$752$	2.75915	+	4.77898i	0.100616	+	0.174272i
$753$		0			0
$754$	−1.89404	−	1.09352i	−0.0689768	−	0.0398238i
$755$	−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	$0.435440\pi$
$758$	11.3778	+	6.56897i	0.413260	+	0.238596i
$759$		0			0
$760$	−1.54929	−	2.68345i	−0.0561987	−	0.0973390i
$761$	16.2999			0.590870			0.295435	−	0.955363i	$-0.404535\pi$
$761$	16.2999			0.590870			0.295435	+	0.955363i	$0.404535\pi$
$762$		0			0
$763$	−21.5500	+	16.3036i	−0.780161	+	0.590229i
$764$			7.36938i			0.266615i
$765$		0			0
$766$	−15.2005	−	8.77603i	−0.549217	−	0.317091i
$767$		−	69.8962i		−	2.52380i
$768$		0			0
$769$	−41.4043	−	23.9048i	−1.49308	−	0.862029i	−0.493110	−	0.869967i	$-0.664140\pi$
$769$	−41.4043	−	23.9048i	−1.49308	−	0.862029i	−0.999968	+	0.00793771i	$0.997473\pi$
$770$	10.3162	−	7.80468i	0.371769	−	0.281261i
$771$		0			0
$772$	−1.41279	+	2.44703i	−0.0508476	+	0.0880706i
$773$	−6.25441	+	10.8330i	−0.224956	+	0.389635i	−0.956306	−	0.292367i	$-0.905557\pi$
$773$	−6.25441	+	10.8330i	−0.224956	+	0.389635i	0.731350	+	0.682002i	$0.238890\pi$
$774$		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
$779$			0.876275i			0.0313958i
$780$		0			0
$781$	12.1525			0.434849
$782$	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
$787$	0.226048	−	0.130509i	0.00805773	−	0.00465213i	−0.495966	−	0.868342i	$-0.665186\pi$
$787$	0.226048	−	0.130509i	0.00805773	−	0.00465213i	0.504023	+	0.863690i	$0.331853\pi$
$788$	−22.5931	+	13.0441i	−0.804846	+	0.464678i
$789$		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
$794$	−38.9869			−1.38359
$795$		0			0
$796$			15.4165i			0.546424i
$797$	1.85220	−	3.20810i	0.0656083	−	0.113637i	−0.831355	−	0.555741i	$-0.812435\pi$
$797$	1.85220	−	3.20810i	0.0656083	−	0.113637i	0.896964	+	0.442104i	$0.145768\pi$
$798$		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
$803$	0.396931	−	0.687504i	0.0140074	−	0.0242615i
$804$		0			0
$805$	−11.8517	+	28.0695i	−0.417716	+	0.989318i
$806$	23.8310	+	13.7588i	0.839411	+	0.484634i
$807$		0			0
$808$		−	8.04886i		−	0.283158i
$809$	5.94276	+	3.43105i	0.208936	+	0.120629i	0.600817	−	0.799387i	$-0.294842\pi$
$809$	5.94276	+	3.43105i	0.208936	+	0.120629i	−0.391881	+	0.920016i	$0.628175\pi$
$810$		0			0
$811$		−	23.1945i		−	0.814470i	−0.913323	−	0.407235i	$-0.866493\pi$
$811$		−	23.1945i		−	0.814470i	0.913323	−	0.407235i	$-0.133507\pi$
$812$	−0.550900	−	0.728176i	−0.0193328	−	0.0255540i
$813$		0			0
$814$	7.37134			0.258365
$815$	−8.13951	−	14.0980i	−0.285114	−	0.493833i
$816$		0			0
$817$	−10.9182	−	6.30363i	−0.381980	−	0.220536i
$818$	24.6187			0.860774
$819$		0			0
$820$	−0.578174			−0.0201907
$821$	3.28550	+	1.89688i	0.114665	+	0.0662017i	0.556236	−	0.831025i	$-0.312245\pi$
$821$	3.28550	+	1.89688i	0.114665	+	0.0662017i	−0.441571	+	0.897226i	$0.645579\pi$
$822$		0			0
$823$	7.45395	+	12.9106i	0.259828	+	0.450036i	0.966196	−	0.257810i	$-0.0830007\pi$
$823$	7.45395	+	12.9106i	0.259828	+	0.450036i	−0.706368	+	0.707845i	$0.749667\pi$
$824$	2.81391			0.0980272
$825$		0			0
$826$	11.3509	−	26.8835i	0.394949	−	0.935395i
$827$		−	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	0.697272	−	0.716807i	$-0.254397\pi$
$829$	12.2406	+	7.06713i	0.425135	+	0.245452i	−0.272137	+	0.962259i	$0.587730\pi$
$830$			2.32100i			0.0805631i
$831$		0			0
$832$	−5.48813	−	3.16857i	−0.190267	−	0.109851i
$833$	−15.4983	+	3.92700i	−0.536985	+	0.136063i
$834$		0			0
$835$	8.09893	−	14.0278i	0.280275	−	0.485451i
$836$	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	0.977951	−	0.208833i	$-0.0669665\pi$
$839$	8.92488	+	15.4583i	0.308121	+	0.533681i	−0.669830	+	0.742514i	$0.733633\pi$
$840$		0			0
$841$	−14.4404	+	25.0116i	−0.497946	+	0.862469i
$842$			14.7130i			0.507045i
$843$		0			0
$844$	8.84930			0.304605
$845$	−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
$850$	−5.84608	+	3.37524i	−0.200519	+	0.115770i
$851$	−15.0362	+	8.68118i	−0.515436	+	0.297587i
$852$		0			0
$853$	−35.2392	+	20.3454i	−1.20657	+	0.696612i	−0.962008	−	0.273022i	$-0.911977\pi$
$853$	−35.2392	+	20.3454i	−1.20657	+	0.696612i	−0.244559	+	0.969634i	$0.578643\pi$
$854$	−3.75896	−	30.1391i	−0.128629	−	1.03134i
$855$		0			0
$856$	7.91078	+	13.7019i	0.270385	+	0.468320i
$857$	−5.45792			−0.186439			−0.0932194	−	0.995646i	$-0.529716\pi$
$857$	−5.45792			−0.186439			−0.0932194	+	0.995646i	$0.529716\pi$
$858$		0			0
$859$		−	44.8973i		−	1.53188i	−0.642914	−	0.765938i	$-0.722275\pi$
$859$		−	44.8973i		−	1.53188i	0.642914	−	0.765938i	$-0.277725\pi$
$860$	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	$-0.540330\pi$
$863$	19.6689	−	11.3559i	0.669539	−	0.386558i	0.795902	+	0.605426i	$0.206997\pi$
$864$		0			0
$865$	−15.5077	+	26.8602i	−0.527279	+	0.913274i
$866$	4.52157	−	7.83159i	0.153649	−	0.266128i
$867$		0			0
$868$	6.93149	+	9.16200i	0.235270	+	0.310978i
$869$	−43.1229	−	24.8970i	−1.46284	−	0.844573i
$870$		0			0
$871$		−	26.9560i		−	0.913371i
$872$	−8.84514	−	5.10675i	−0.299534	−	0.172936i
$873$		0			0
$874$			17.4538i			0.590384i
$875$	−27.7259	−	11.7066i	−0.937306	−	0.395755i
$876$		0			0
$877$	−30.4891			−1.02954			−0.514771	−	0.857327i	$-0.672123\pi$
$877$	−30.4891			−1.02954			−0.514771	+	0.857327i	$0.672123\pi$
$878$	−0.456897	−	0.791370i	−0.0154195	−	0.0267074i
$879$		0			0
$880$	4.23425	+	2.44465i	0.142737	+	0.0824091i
$881$	29.3810			0.989871			0.494935	−	0.868930i	$-0.335192\pi$
$881$	29.3810			0.989871			0.494935	+	0.868930i	$0.335192\pi$
$882$		0			0
$883$	14.1682			0.476798			0.238399	−	0.971167i	$-0.423377\pi$
$883$	14.1682			0.476798			0.238399	+	0.971167i	$0.423377\pi$
$884$	−12.5350	−	7.23707i	−0.421597	−	0.243409i
$885$		0			0
$886$	−14.6808	−	25.4279i	−0.493212	−	0.854268i
$887$	32.7073			1.09821			0.549103	−	0.835755i	$-0.314970\pi$
$887$	32.7073			1.09821			0.549103	+	0.835755i	$0.314970\pi$
$888$		0			0
$889$	−14.0826	−	5.94605i	−0.472315	−	0.199424i
$890$		−	5.80446i		−	0.194566i
$891$		0			0
$892$	6.88961	+	3.97772i	0.230681	+	0.133184i
$893$			11.9585i			0.400176i
$894$		0			0
$895$	25.7454	+	14.8641i	0.860575	+	0.496853i
$896$	−1.59628	−	2.10995i	−0.0533279	−	0.0704885i
$897$		0			0
$898$	1.68368	−	2.91622i	0.0561851	−	0.0973154i
$899$	−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
$905$		−	30.7848i		−	1.02332i
$906$		0			0
$907$	56.6934			1.88248			0.941238	−	0.337745i	$-0.109664\pi$
$907$	56.6934			1.88248			0.941238	+	0.337745i	$0.109664\pi$
$908$	−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
$913$	−4.80697	+	2.77530i	−0.159087	+	0.0918492i
$914$	−13.0890	+	7.55693i	−0.432945	+	0.249961i
$915$		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	0.988380	+	0.152004i	$0.0485727\pi$
$919$	18.9720	+	32.8605i	0.625829	+	1.08397i	−0.362550	+	0.931964i	$0.618094\pi$
$920$	−11.5162			−0.379677
$921$		0			0
$922$		−	10.3889i		−	0.342140i
$923$	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
$929$	−21.4350	+	37.1265i	−0.703259	+	1.21808i	0.264057	+	0.964507i	$0.414939\pi$
$929$	−21.4350	+	37.1265i	−0.703259	+	1.21808i	−0.967316	+	0.253574i	$0.918394\pi$
$930$		0			0
$931$	−14.5977	−	4.12564i	−0.478419	−	0.135212i
$932$	14.4176	+	8.32399i	0.472263	+	0.272661i
$933$		0			0
$934$		−	19.4999i		−	0.638055i
$935$	9.67111	+	5.58362i	0.316279	+	0.182604i
$936$		0			0
$937$			8.64637i			0.282464i	0.989976	+	0.141232i	$0.0451064\pi$
$937$			8.64637i			0.282464i	−0.989976	+	0.141232i	$0.954894\pi$
$938$	4.37757	−	10.3678i	0.142933	−	0.338522i
$939$		0			0
$940$	−7.89034			−0.257354
$941$	−5.04603	−	8.73997i	−0.164496	−	0.284915i	0.771980	−	0.635646i	$-0.219266\pi$
$941$	−5.04603	−	8.73997i	−0.164496	−	0.284915i	−0.936476	+	0.350731i	$0.885933\pi$
$942$		0			0
$943$	2.82044	+	1.62838i	0.0918460	+	0.0530273i
$944$	11.0296			0.358983
$945$		0			0
$946$	19.8932			0.646783
$947$	−50.4627	−	29.1346i	−1.63982	−	0.946749i	−0.980895	−	0.194537i	$-0.937680\pi$
$947$	−50.4627	−	29.1346i	−1.63982	−	0.946749i	−0.658922	−	0.752212i	$-0.728987\pi$
$948$		0			0
$949$	−0.735619	−	1.27413i	−0.0238792	−	0.0413600i
$950$	−6.40483			−0.207800
$951$		0			0
$952$	−3.64593	−	4.81916i	−0.118165	−	0.156190i
$953$			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
$956$			27.2885i			0.882572i
$957$		0			0
$958$	−24.0776	−	13.9012i	−0.777912	−	0.449128i
$959$	9.93800	−	23.5371i	0.320915	−	0.760054i
$960$		0			0
$961$	−6.07230	+	10.5175i	−0.195881	+	0.339275i
$962$	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	$0.100355\pi$
$968$			0.692610i			0.0222613i
$969$		0			0
$970$	15.1685			0.487031
$971$	17.3742	+	30.0930i	0.557565	+	0.965731i	0.997699	+	0.0677990i	$0.0215977\pi$
$971$	17.3742	+	30.0930i	0.557565	+	0.965731i	−0.440134	+	0.897932i	$0.645069\pi$
$972$		0			0
$973$	29.6169	+	39.1474i	0.949474	+	1.25501i
$974$	−6.47506	+	3.73838i	−0.207474	+	0.119785i
$975$		0			0
$976$	9.94175	−	5.73987i	0.318228	−	0.183729i
$977$	17.6381	−	10.1834i	0.564293	−	0.325795i	−0.190574	−	0.981673i	$-0.561035\pi$
$977$	17.6381	−	10.1834i	0.564293	−	0.325795i	0.754867	+	0.655878i	$0.227701\pi$
$978$		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
$983$	29.3364			0.935686			0.467843	−	0.883811i	$-0.345031\pi$
$983$	29.3364			0.935686			0.467843	+	0.883811i	$0.345031\pi$
$984$		0			0
$985$		−	37.3023i		−	1.18855i
$986$	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	−0.999431	−	0.0337371i	$-0.989259\pi$
$991$	−14.8114	+	25.6540i	−0.470498	+	0.814927i	0.528933	+	0.848664i	$0.322592\pi$
$992$	−2.17114	+	3.76052i	−0.0689338	+	0.119397i
$993$		0			0
$994$	7.49861	−	5.67306i	0.237842	−	0.179938i
$995$	−19.0901	−	11.0217i	−0.605196	−	0.349410i
$996$		0			0
$997$			27.0213i			0.855772i	0.903833	+	0.427886i	$0.140742\pi$
$997$			27.0213i			0.855772i	−0.903833	+	0.427886i	$0.859258\pi$
$998$	−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.t.a.17.2		16
3.2	odd	2		126.2.t.a.59.6	yes	16
4.3	odd	2		3024.2.df.c.17.3		16
7.2	even	3		2646.2.l.a.1097.7		16
7.3	odd	6		2646.2.m.b.881.6		16
7.4	even	3		2646.2.m.a.881.7		16
7.5	odd	6		378.2.l.a.341.6		16
7.6	odd	2		2646.2.t.b.2285.3		16
9.2	odd	6		378.2.l.a.143.2		16
9.4	even	3		1134.2.k.a.647.7		16
9.5	odd	6		1134.2.k.b.647.2		16
9.7	even	3		126.2.l.a.101.7	yes	16
12.11	even	2		1008.2.df.c.689.6		16
21.2	odd	6		882.2.l.b.509.2		16
21.5	even	6		126.2.l.a.5.3	✓	16
21.11	odd	6		882.2.m.a.293.4		16
21.17	even	6		882.2.m.b.293.1		16
21.20	even	2		882.2.t.a.815.7		16
28.19	even	6		3024.2.ca.c.2609.3		16
36.7	odd	6		1008.2.ca.c.353.3		16
36.11	even	6		3024.2.ca.c.2033.3		16
63.2	odd	6		2646.2.t.b.1979.3		16
63.5	even	6		1134.2.k.a.971.7		16
63.11	odd	6		2646.2.m.b.1763.6		16
63.16	even	3		882.2.t.a.803.7		16
63.20	even	6		2646.2.l.a.521.3		16
63.25	even	3		882.2.m.b.587.1		16
63.34	odd	6		882.2.l.b.227.6		16
63.38	even	6		2646.2.m.a.1763.7		16
63.40	odd	6		1134.2.k.b.971.2		16
63.47	even	6	inner	378.2.t.a.89.2		16
63.52	odd	6		882.2.m.a.587.4		16
63.61	odd	6		126.2.t.a.47.6	yes	16
84.47	odd	6		1008.2.ca.c.257.3		16
252.47	odd	6		3024.2.df.c.1601.3		16
252.187	even	6		1008.2.df.c.929.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.3	✓	16	21.5	even	6
126.2.l.a.101.7	yes	16	9.7	even	3
126.2.t.a.47.6	yes	16	63.61	odd	6
126.2.t.a.59.6	yes	16	3.2	odd	2
378.2.l.a.143.2		16	9.2	odd	6
378.2.l.a.341.6		16	7.5	odd	6
378.2.t.a.17.2		16	1.1	even	1	trivial
378.2.t.a.89.2		16	63.47	even	6	inner
882.2.l.b.227.6		16	63.34	odd	6
882.2.l.b.509.2		16	21.2	odd	6
882.2.m.a.293.4		16	21.11	odd	6
882.2.m.a.587.4		16	63.52	odd	6
882.2.m.b.293.1		16	21.17	even	6
882.2.m.b.587.1		16	63.25	even	3
882.2.t.a.803.7		16	63.16	even	3
882.2.t.a.815.7		16	21.20	even	2
1008.2.ca.c.257.3		16	84.47	odd	6
1008.2.ca.c.353.3		16	36.7	odd	6
1008.2.df.c.689.6		16	12.11	even	2
1008.2.df.c.929.6		16	252.187	even	6
1134.2.k.a.647.7		16	9.4	even	3
1134.2.k.a.971.7		16	63.5	even	6
1134.2.k.b.647.2		16	9.5	odd	6
1134.2.k.b.971.2		16	63.40	odd	6
2646.2.l.a.521.3		16	63.20	even	6
2646.2.l.a.1097.7		16	7.2	even	3
2646.2.m.a.881.7		16	7.4	even	3
2646.2.m.a.1763.7		16	63.38	even	6
2646.2.m.b.881.6		16	7.3	odd	6
2646.2.m.b.1763.6		16	63.11	odd	6
2646.2.t.b.1979.3		16	63.2	odd	6
2646.2.t.b.2285.3		16	7.6	odd	2
3024.2.ca.c.2033.3		16	36.11	even	6
3024.2.ca.c.2609.3		16	28.19	even	6
3024.2.df.c.17.3		16	4.3	odd	2
3024.2.df.c.1601.3		16	252.47	odd	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.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.42985 q^{5} +(-2.43739 - 1.02913i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.42985 q^{5} +(-2.43739 - 1.02913i) q^{7} -1.00000i q^{8} +(1.23829 + 0.714925i) q^{10} +3.41945i q^{11} +(5.48813 + 3.16857i) q^{13} +(1.59628 + 2.10995i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.14201 + 1.97802i) q^{17} +(-1.87673 + 1.08353i) q^{19} +(-0.714925 - 1.23829i) q^{20} +(1.70972 - 2.96133i) q^{22} +8.05411i q^{23} -2.95553 q^{25} +(-3.16857 - 5.48813i) q^{26} +(-0.327442 - 2.62541i) q^{28} +(0.298879 - 0.172558i) q^{29} +(-3.76052 + 2.17114i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.97802 - 1.14201i) q^{34} +(3.48511 + 1.47150i) q^{35} +(1.07786 + 1.86690i) q^{37} +2.16707 q^{38} +1.42985i q^{40} +(0.202180 - 0.350186i) q^{41} +(2.90883 + 5.03824i) q^{43} +(-2.96133 + 1.70972i) q^{44} +(4.02706 - 6.97507i) q^{46} +(2.75915 - 4.77898i) q^{47} +(4.88178 + 5.01680i) q^{49} +(2.55956 + 1.47776i) q^{50} +6.33715i q^{52} +(8.56310 + 4.94391i) q^{53} -4.88930i q^{55} +(-1.02913 + 2.43739i) q^{56} -0.345115 q^{58} +(-5.51480 - 9.55191i) q^{59} +(-9.94175 - 5.73987i) q^{61} +4.34228 q^{62} -1.00000 q^{64} +(-7.84721 - 4.53059i) q^{65} +(-2.12683 - 3.68377i) q^{67} -2.28402 q^{68} +(-2.28244 - 3.01691i) q^{70} -3.55393i q^{71} +(-0.201057 - 0.116080i) q^{73} -2.15571i q^{74} +(-1.87673 - 1.08353i) q^{76} +(3.51906 - 8.33454i) q^{77} +(-7.28100 + 12.6111i) q^{79} +(0.714925 - 1.23829i) q^{80} +(-0.350186 + 0.202180i) q^{82} +(0.811624 + 1.40577i) q^{83} +(1.63290 - 2.82827i) q^{85} -5.81766i q^{86} +3.41945 q^{88} +(-2.02974 - 3.51562i) q^{89} +(-10.1159 - 13.3711i) q^{91} +(-6.97507 + 4.02706i) q^{92} +(-4.77898 + 2.75915i) q^{94} +(2.68345 - 1.54929i) q^{95} +(9.18719 - 5.30423i) q^{97} +(-1.71934 - 6.78556i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 + 2 * q^7	\( 16 q + 8 q^{4} + 2 q^{7} - 6 q^{13} + 6 q^{14} - 8 q^{16} - 18 q^{17} + 16 q^{25} + 12 q^{26} - 2 q^{28} - 6 q^{29} + 6 q^{31} + 30 q^{35} - 2 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{44} + 6 q^{46} + 18 q^{47} + 10 q^{49} + 12 q^{50} - 36 q^{53} - 12 q^{58} - 30 q^{59} - 60 q^{61} + 36 q^{62} - 16 q^{64} - 42 q^{65} + 14 q^{67} - 36 q^{68} + 18 q^{77} - 16 q^{79} - 12 q^{85} - 24 q^{89} - 12 q^{91} - 6 q^{92} + 66 q^{95} - 6 q^{97} - 24 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^13 + 6 * q^14 - 8 * q^16 - 18 * q^17 + 16 * q^25 + 12 * q^26 - 2 * q^28 - 6 * q^29 + 6 * q^31 + 30 * q^35 - 2 * q^37 - 6 * q^41 - 2 * q^43 - 12 * q^44 + 6 * q^46 + 18 * q^47 + 10 * q^49 + 12 * q^50 - 36 * q^53 - 12 * q^58 - 30 * q^59 - 60 * q^61 + 36 * q^62 - 16 * q^64 - 42 * q^65 + 14 * q^67 - 36 * q^68 + 18 * q^77 - 16 * q^79 - 12 * q^85 - 24 * q^89 - 12 * q^91 - 6 * q^92 + 66 * q^95 - 6 * q^97 - 24 * q^98

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