LMFDB - Embedded newform 378.2.l.a.143.7

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			143.7
Root			$1.58110 + 0.707199i$ of defining polynomial
Character	$\chi$	$=$	378.143
Dual form			378.2.l.a.341.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(0.450129 - 0.779646i) q^{5} +(1.57151 - 2.12847i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(0.450129 - 0.779646i) q^{5} +(1.57151 - 2.12847i) q^{7} -1.00000i q^{8} +(0.779646 + 0.450129i) q^{10} +(2.70900 - 1.56404i) q^{11} +(-1.99033 + 1.14912i) q^{13} +(2.12847 + 1.57151i) q^{14} +1.00000 q^{16} +(2.57638 - 4.46242i) q^{17} +(2.38111 - 1.37474i) q^{19} +(-0.450129 + 0.779646i) q^{20} +(1.56404 + 2.70900i) q^{22} +(1.48584 + 0.857850i) q^{23} +(2.09477 + 3.62824i) q^{25} +(-1.14912 - 1.99033i) q^{26} +(-1.57151 + 2.12847i) q^{28} +(1.85590 + 1.07151i) q^{29} +10.0032i q^{31} +1.00000i q^{32} +(4.46242 + 2.57638i) q^{34} +(-0.952070 - 2.18330i) q^{35} +(-4.73701 - 8.20475i) q^{37} +(1.37474 + 2.38111i) q^{38} +(-0.779646 - 0.450129i) q^{40} +(-1.22134 - 2.11542i) q^{41} +(-0.273155 + 0.473119i) q^{43} +(-2.70900 + 1.56404i) q^{44} +(-0.857850 + 1.48584i) q^{46} -7.86068 q^{47} +(-2.06074 - 6.68980i) q^{49} +(-3.62824 + 2.09477i) q^{50} +(1.99033 - 1.14912i) q^{52} +(12.0733 + 6.97054i) q^{53} -2.81608i q^{55} +(-2.12847 - 1.57151i) q^{56} +(-1.07151 + 1.85590i) q^{58} -7.98443 q^{59} -7.25411i q^{61} -10.0032 q^{62} -1.00000 q^{64} +2.06901i q^{65} +3.67050 q^{67} +(-2.57638 + 4.46242i) q^{68} +(2.18330 - 0.952070i) q^{70} +14.1484i q^{71} +(-10.9190 - 6.30409i) q^{73} +(8.20475 - 4.73701i) q^{74} +(-2.38111 + 1.37474i) q^{76} +(0.928202 - 8.22392i) q^{77} -6.54804 q^{79} +(0.450129 - 0.779646i) q^{80} +(2.11542 - 1.22134i) q^{82} +(-0.184437 + 0.319454i) q^{83} +(-2.31940 - 4.01733i) q^{85} +(-0.473119 - 0.273155i) q^{86} +(-1.56404 - 2.70900i) q^{88} +(-6.00244 - 10.3965i) q^{89} +(-0.681960 + 6.04220i) q^{91} +(-1.48584 - 0.857850i) q^{92} -7.86068i q^{94} -2.47523i q^{95} +(8.86815 + 5.12003i) q^{97} +(6.68980 - 2.06074i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

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

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	0.450129	−	0.779646i	0.201304	−	0.348668i	−0.747645	−	0.664099i	$-0.768815\pi$
$5$	0.450129	−	0.779646i	0.201304	−	0.348668i	0.948949	+	0.315430i	$0.102149\pi$
$6$		0			0
$7$	1.57151	−	2.12847i	0.593974	−	0.804485i
$7$	1.57151	−	2.12847i	0.593974	−	0.804485i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	0.779646	+	0.450129i	0.246546	+	0.142343i
$11$	2.70900	−	1.56404i	0.816795	−	0.471577i	−0.0325150	−	0.999471i	$-0.510352\pi$
$11$	2.70900	−	1.56404i	0.816795	−	0.471577i	0.849310	+	0.527894i	$0.177018\pi$
$12$		0			0
$13$	−1.99033	+	1.14912i	−0.552019	+	0.318708i	−0.749936	−	0.661511i	$-0.769916\pi$
$13$	−1.99033	+	1.14912i	−0.552019	+	0.318708i	0.197917	+	0.980219i	$0.436582\pi$
$14$	2.12847	+	1.57151i	0.568856	+	0.420003i
$15$		0			0
$16$	1.00000			0.250000
$17$	2.57638	−	4.46242i	0.624863	−	1.08230i	−0.363704	−	0.931515i	$-0.618488\pi$
$17$	2.57638	−	4.46242i	0.624863	−	1.08230i	0.988567	−	0.150780i	$-0.0481787\pi$
$18$		0			0
$19$	2.38111	−	1.37474i	0.546264	−	0.315386i	−0.201350	−	0.979519i	$-0.564533\pi$
$19$	2.38111	−	1.37474i	0.546264	−	0.315386i	0.747614	+	0.664134i	$0.231199\pi$
$20$	−0.450129	+	0.779646i	−0.100652	+	0.174334i
$21$		0			0
$22$	1.56404	+	2.70900i	0.333455	+	0.577561i
$23$	1.48584	+	0.857850i	0.309819	+	0.178874i	0.646845	−	0.762621i	$-0.276088\pi$
$23$	1.48584	+	0.857850i	0.309819	+	0.178874i	−0.337027	+	0.941495i	$0.609421\pi$
$24$		0			0
$25$	2.09477	+	3.62824i	0.418954	+	0.725649i
$26$	−1.14912	−	1.99033i	−0.225361	−	0.390336i
$27$		0			0
$28$	−1.57151	+	2.12847i	−0.296987	+	0.402242i
$29$	1.85590	+	1.07151i	0.344633	+	0.198974i	0.662319	−	0.749222i	$-0.269572\pi$
$29$	1.85590	+	1.07151i	0.344633	+	0.198974i	−0.317686	+	0.948196i	$0.602906\pi$
$30$		0			0
$31$			10.0032i			1.79662i	0.439363	+	0.898309i	$0.355204\pi$
$31$			10.0032i			1.79662i	−0.439363	+	0.898309i	$0.644796\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	4.46242	+	2.57638i	0.765298	+	0.441845i
$35$	−0.952070	−	2.18330i	−0.160929	−	0.369046i
$36$		0			0
$37$	−4.73701	−	8.20475i	−0.778760	−	1.34885i	−0.932657	−	0.360766i	$-0.882515\pi$
$37$	−4.73701	−	8.20475i	−0.778760	−	1.34885i	0.153896	−	0.988087i	$-0.450818\pi$
$38$	1.37474	+	2.38111i	0.223012	+	0.386267i
$39$		0			0
$40$	−0.779646	−	0.450129i	−0.123273	−	0.0711716i
$41$	−1.22134	−	2.11542i	−0.190741	−	0.330373i	0.754755	−	0.656007i	$-0.227756\pi$
$41$	−1.22134	−	2.11542i	−0.190741	−	0.330373i	−0.945496	+	0.325634i	$0.894422\pi$
$42$		0			0
$43$	−0.273155	+	0.473119i	−0.0416558	+	0.0721499i	−0.886102	−	0.463491i	$-0.846597\pi$
$43$	−0.273155	+	0.473119i	−0.0416558	+	0.0721499i	0.844446	+	0.535641i	$0.179930\pi$
$44$	−2.70900	+	1.56404i	−0.408397	+	0.235788i
$45$		0			0
$46$	−0.857850	+	1.48584i	−0.126483	+	0.219075i
$47$	−7.86068			−1.14660			−0.573299	−	0.819346i	$-0.694337\pi$
$47$	−7.86068			−1.14660			−0.573299	+	0.819346i	$0.694337\pi$
$48$		0			0
$49$	−2.06074	−	6.68980i	−0.294391	−	0.955685i
$50$	−3.62824	+	2.09477i	−0.513111	+	0.296245i
$51$		0			0
$52$	1.99033	−	1.14912i	0.276009	−	0.159354i
$53$	12.0733	+	6.97054i	1.65840	+	0.957478i	0.973454	+	0.228885i	$0.0735079\pi$
$53$	12.0733	+	6.97054i	1.65840	+	0.957478i	0.684947	+	0.728593i	$0.259825\pi$
$54$		0			0
$55$		−	2.81608i		−	0.379721i
$56$	−2.12847	−	1.57151i	−0.284428	−	0.210001i
$57$		0			0
$58$	−1.07151	+	1.85590i	−0.140696	+	0.243692i
$59$	−7.98443			−1.03948			−0.519742	−	0.854323i	$-0.673972\pi$
$59$	−7.98443			−1.03948			−0.519742	+	0.854323i	$0.673972\pi$
$60$		0			0
$61$		−	7.25411i		−	0.928793i	−0.885627	−	0.464397i	$-0.846271\pi$
$61$		−	7.25411i		−	0.928793i	0.885627	−	0.464397i	$-0.153729\pi$
$62$	−10.0032			−1.27040
$63$		0			0
$64$	−1.00000			−0.125000
$65$			2.06901i			0.256629i
$66$		0			0
$67$	3.67050			0.448423			0.224212	−	0.974540i	$-0.428019\pi$
$67$	3.67050			0.448423			0.224212	+	0.974540i	$0.428019\pi$
$68$	−2.57638	+	4.46242i	−0.312432	+	0.541148i
$69$		0			0
$70$	2.18330	−	0.952070i	0.260955	−	0.113794i
$71$			14.1484i			1.67911i	0.543275	+	0.839555i	$0.317184\pi$
$71$			14.1484i			1.67911i	−0.543275	+	0.839555i	$0.682816\pi$
$72$		0			0
$73$	−10.9190	−	6.30409i	−1.27797	−	0.737838i	−0.301498	−	0.953467i	$-0.597487\pi$
$73$	−10.9190	−	6.30409i	−1.27797	−	0.737838i	−0.976475	+	0.215629i	$0.930820\pi$
$74$	8.20475	−	4.73701i	0.953783	−	0.550667i
$75$		0			0
$76$	−2.38111	+	1.37474i	−0.273132	+	0.157693i
$77$	0.928202	−	8.22392i	0.105778	−	0.937203i
$78$		0			0
$79$	−6.54804			−0.736712			−0.368356	−	0.929685i	$-0.620079\pi$
$79$	−6.54804			−0.736712			−0.368356	+	0.929685i	$0.620079\pi$
$80$	0.450129	−	0.779646i	0.0503259	−	0.0871671i
$81$		0			0
$82$	2.11542	−	1.22134i	0.233609	−	0.134874i
$83$	−0.184437	+	0.319454i	−0.0202446	+	0.0350646i	−0.875970	−	0.482365i	$-0.839778\pi$
$83$	−0.184437	+	0.319454i	−0.0202446	+	0.0350646i	0.855726	+	0.517430i	$0.173111\pi$
$84$		0			0
$85$	−2.31940	−	4.01733i	−0.251575	−	0.435740i
$86$	−0.473119	−	0.273155i	−0.0510177	−	0.0294551i
$87$		0			0
$88$	−1.56404	−	2.70900i	−0.166728	−	0.288781i
$89$	−6.00244	−	10.3965i	−0.636258	−	1.10203i	−0.986247	−	0.165277i	$-0.947148\pi$
$89$	−6.00244	−	10.3965i	−0.636258	−	1.10203i	0.349990	−	0.936754i	$-0.386185\pi$
$90$		0			0
$91$	−0.681960	+	6.04220i	−0.0714888	+	0.633395i
$92$	−1.48584	−	0.857850i	−0.154909	−	0.0894370i
$93$		0			0
$94$		−	7.86068i		−	0.810767i
$95$		−	2.47523i		−	0.253953i
$96$		0			0
$97$	8.86815	+	5.12003i	0.900424	+	0.519860i	0.877338	−	0.479873i	$-0.159317\pi$
$97$	8.86815	+	5.12003i	0.900424	+	0.519860i	0.0230864	+	0.999733i	$0.492651\pi$
$98$	6.68980	−	2.06074i	0.675771	−	0.208166i
$99$		0			0
$100$	−2.09477	−	3.62824i	−0.209477	−	0.362824i
$101$	1.35969	+	2.35506i	0.135294	+	0.234337i	0.925710	−	0.378234i	$-0.123469\pi$
$101$	1.35969	+	2.35506i	0.135294	+	0.234337i	−0.790415	+	0.612571i	$0.790135\pi$
$102$		0			0
$103$	1.18861	+	0.686242i	0.117117	+	0.0676174i	0.557414	−	0.830235i	$-0.311794\pi$
$103$	1.18861	+	0.686242i	0.117117	+	0.0676174i	−0.440297	+	0.897852i	$0.645127\pi$
$104$	1.14912	+	1.99033i	0.112680	+	0.195168i
$105$		0			0
$106$	−6.97054	+	12.0733i	−0.677039	+	1.17267i
$107$	−12.3585	+	7.13519i	−1.19474	+	0.689785i	−0.959378	−	0.282122i	$-0.908962\pi$
$107$	−12.3585	+	7.13519i	−1.19474	+	0.689785i	−0.235364	+	0.971907i	$0.575628\pi$
$108$		0			0
$109$	−2.64583	+	4.58271i	−0.253425	+	0.438944i	−0.964466	−	0.264206i	$-0.914890\pi$
$109$	−2.64583	+	4.58271i	−0.253425	+	0.438944i	0.711042	+	0.703150i	$0.248224\pi$
$110$	2.81608			0.268503
$111$		0			0
$112$	1.57151	−	2.12847i	0.148493	−	0.201121i
$113$	2.30371	−	1.33005i	0.216715	−	0.125121i	−0.387713	−	0.921780i	$-0.626735\pi$
$113$	2.30371	−	1.33005i	0.216715	−	0.125121i	0.604428	+	0.796659i	$0.293402\pi$
$114$		0			0
$115$	1.33764	−	0.772286i	0.124735	−	0.0720160i
$116$	−1.85590	−	1.07151i	−0.172316	−	0.0994869i
$117$		0			0
$118$		−	7.98443i		−	0.735026i
$119$	−5.44931	−	12.4964i	−0.499537	−	1.14555i
$120$		0			0
$121$	−0.607537	+	1.05229i	−0.0552307	+	0.0956623i
$122$	7.25411			0.656756
$123$		0			0
$124$		−	10.0032i		−	0.898309i
$125$	8.27295			0.739955
$126$		0			0
$127$	6.10587			0.541808			0.270904	−	0.962606i	$-0.412677\pi$
$127$	6.10587			0.541808			0.270904	+	0.962606i	$0.412677\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−2.06901			−0.181464
$131$	3.97879	−	6.89147i	0.347629	−	0.602111i	−0.638199	−	0.769871i	$-0.720320\pi$
$131$	3.97879	−	6.89147i	0.347629	−	0.602111i	0.985828	+	0.167761i	$0.0536536\pi$
$132$		0			0
$133$	0.815855	−	7.22852i	0.0707436	−	0.626792i
$134$			3.67050i			0.317083i
$135$		0			0
$136$	−4.46242	−	2.57638i	−0.382649	−	0.220923i
$137$	−18.9140	+	10.9200i	−1.61593	+	0.932957i	−0.627970	+	0.778237i	$0.716114\pi$
$137$	−18.9140	+	10.9200i	−1.61593	+	0.932957i	−0.987958	+	0.154719i	$0.950553\pi$
$138$		0			0
$139$	−11.7109	+	6.76127i	−0.993302	+	0.573483i	−0.906260	−	0.422721i	$-0.861075\pi$
$139$	−11.7109	+	6.76127i	−0.993302	+	0.573483i	−0.0870425	+	0.996205i	$0.527742\pi$
$140$	0.952070	+	2.18330i	0.0804646	+	0.184523i
$141$		0			0
$142$	−14.1484			−1.18731
$143$	−3.59454	+	6.22593i	−0.300591	+	0.520639i
$144$		0			0
$145$	1.67079	−	0.964632i	0.138752	−	0.0801083i
$146$	6.30409	−	10.9190i	0.521730	−	0.903663i
$147$		0			0
$148$	4.73701	+	8.20475i	0.389380	+	0.674426i
$149$	4.41192	+	2.54722i	0.361438	+	0.208676i	0.669711	−	0.742621i	$-0.266418\pi$
$149$	4.41192	+	2.54722i	0.361438	+	0.208676i	−0.308273	+	0.951298i	$0.599751\pi$
$150$		0			0
$151$	10.5877	+	18.3385i	0.861618	+	1.49237i	0.870366	+	0.492405i	$0.163882\pi$
$151$	10.5877	+	18.3385i	0.861618	+	1.49237i	−0.00874783	+	0.999962i	$0.502785\pi$
$152$	−1.37474	−	2.38111i	−0.111506	−	0.193134i
$153$		0			0
$154$	8.22392	+	0.928202i	0.662703	+	0.0747966i
$155$	7.79892	+	4.50271i	0.626424	+	0.361666i
$156$		0			0
$157$		−	0.359924i		−	0.0287250i	−0.999897	−	0.0143625i	$-0.995428\pi$
$157$		−	0.359924i		−	0.0287250i	0.999897	−	0.0143625i	$-0.00457189\pi$
$158$		−	6.54804i		−	0.520934i
$159$		0			0
$160$	0.779646	+	0.450129i	0.0616364	+	0.0355858i
$161$	4.16091	−	1.81444i	0.327926	−	0.142998i
$162$		0			0
$163$	6.18640	+	10.7152i	0.484557	+	0.839277i	0.999843	−	0.0177416i	$-0.00564762\pi$
$163$	6.18640	+	10.7152i	0.484557	+	0.839277i	−0.515286	+	0.857018i	$0.672314\pi$
$164$	1.22134	+	2.11542i	0.0953705	+	0.165186i
$165$		0			0
$166$	−0.319454	−	0.184437i	−0.0247944	−	0.0143151i
$167$	7.40866	+	12.8322i	0.573299	+	0.992984i	0.996224	+	0.0868188i	$0.0276701\pi$
$167$	7.40866	+	12.8322i	0.573299	+	0.992984i	−0.422925	+	0.906165i	$0.638997\pi$
$168$		0			0
$169$	−3.85905	+	6.68407i	−0.296850	+	0.514159i
$170$	4.01733	−	2.31940i	0.308115	−	0.177890i
$171$		0			0
$172$	0.273155	−	0.473119i	0.0208279	−	0.0360750i
$173$	−4.63544			−0.352426			−0.176213	−	0.984352i	$-0.556385\pi$
$173$	−4.63544			−0.352426			−0.176213	+	0.984352i	$0.556385\pi$
$174$		0			0
$175$	11.0145	+	1.24317i	0.832621	+	0.0939746i
$176$	2.70900	−	1.56404i	0.204199	−	0.117894i
$177$		0			0
$178$	10.3965	−	6.00244i	0.779253	−	0.449902i
$179$	5.25855	+	3.03602i	0.393042	+	0.226923i	0.683477	−	0.729972i	$-0.260467\pi$
$179$	5.25855	+	3.03602i	0.393042	+	0.226923i	−0.290435	+	0.956895i	$0.593800\pi$
$180$		0			0
$181$			7.12701i			0.529746i	0.964283	+	0.264873i	$0.0853301\pi$
$181$			7.12701i			0.529746i	−0.964283	+	0.264873i	$0.914670\pi$
$182$	−6.04220	−	0.681960i	−0.447878	−	0.0505502i
$183$		0			0
$184$	0.857850	−	1.48584i	0.0632415	−	0.109538i
$185$	−8.52907			−0.627070
$186$		0			0
$187$		−	16.1183i		−	1.17868i
$188$	7.86068			0.573299
$189$		0			0
$190$	2.47523			0.179572
$191$			14.4006i			1.04199i	0.853558	+	0.520997i	$0.174440\pi$
$191$			14.4006i			1.04199i	−0.853558	+	0.520997i	$0.825560\pi$
$192$		0			0
$193$	17.8115			1.28210			0.641048	−	0.767501i	$-0.278500\pi$
$193$	17.8115			1.28210			0.641048	+	0.767501i	$0.278500\pi$
$194$	−5.12003	+	8.86815i	−0.367597	+	0.636696i
$195$		0			0
$196$	2.06074	+	6.68980i	0.147195	+	0.477843i
$197$		−	19.1025i		−	1.36100i	−0.732750	−	0.680498i	$-0.761764\pi$
$197$		−	19.1025i		−	1.36100i	0.732750	−	0.680498i	$-0.238236\pi$
$198$		0			0
$199$	11.6008	+	6.69771i	0.822357	+	0.474788i	0.851229	−	0.524795i	$-0.175858\pi$
$199$	11.6008	+	6.69771i	0.822357	+	0.474788i	−0.0288716	+	0.999583i	$0.509191\pi$
$200$	3.62824	−	2.09477i	0.256556	−	0.148122i
$201$		0			0
$202$	−2.35506	+	1.35969i	−0.165701	+	0.0956677i
$203$	5.19723	−	2.26635i	0.364774	−	0.159066i
$204$		0			0
$205$	−2.19904			−0.153587
$206$	−0.686242	+	1.18861i	−0.0478127	+	0.0828141i
$207$		0			0
$208$	−1.99033	+	1.14912i	−0.138005	+	0.0796771i
$209$	4.30029	−	7.44832i	0.297457	−	0.515211i
$210$		0			0
$211$	−9.37193	−	16.2327i	−0.645190	−	1.11750i	−0.984258	−	0.176740i	$-0.943445\pi$
$211$	−9.37193	−	16.2327i	−0.645190	−	1.11750i	0.339067	−	0.940762i	$-0.389889\pi$
$212$	−12.0733	−	6.97054i	−0.829200	−	0.478739i
$213$		0			0
$214$	−7.13519	−	12.3585i	−0.487752	−	0.844810i
$215$	0.245910	+	0.425929i	0.0167709	+	0.0290481i
$216$		0			0
$217$	21.2914	+	15.7200i	1.44535	+	1.06714i
$218$	−4.58271	−	2.64583i	−0.310380	−	0.179198i
$219$		0			0
$220$			2.81608i			0.189860i
$221$			11.8423i			0.796597i
$222$		0			0
$223$	2.21609	+	1.27946i	0.148400	+	0.0856789i	0.572362	−	0.820001i	$-0.306027\pi$
$223$	2.21609	+	1.27946i	0.148400	+	0.0856789i	−0.423961	+	0.905680i	$0.639361\pi$
$224$	2.12847	+	1.57151i	0.142214	+	0.105001i
$225$		0			0
$226$	1.33005	+	2.30371i	0.0884736	+	0.153241i
$227$	4.36455	+	7.55962i	0.289685	+	0.501749i	0.973735	−	0.227686i	$-0.0731161\pi$
$227$	4.36455	+	7.55962i	0.289685	+	0.501749i	−0.684049	+	0.729436i	$0.739783\pi$
$228$		0			0
$229$	−3.40979	−	1.96865i	−0.225325	−	0.130092i	0.383088	−	0.923712i	$-0.374861\pi$
$229$	−3.40979	−	1.96865i	−0.225325	−	0.130092i	−0.608414	+	0.793620i	$0.708194\pi$
$230$	0.772286	+	1.33764i	0.0509230	+	0.0882013i
$231$		0			0
$232$	1.07151	−	1.85590i	0.0703478	−	0.121846i
$233$	3.92147	−	2.26406i	0.256904	−	0.148324i	−0.366018	−	0.930608i	$-0.619279\pi$
$233$	3.92147	−	2.26406i	0.256904	−	0.148324i	0.622921	+	0.782284i	$0.285946\pi$
$234$		0			0
$235$	−3.53832	+	6.12855i	−0.230815	+	0.399782i
$236$	7.98443			0.519742
$237$		0			0
$238$	12.4964	−	5.44931i	0.810024	−	0.353226i
$239$	7.55315	−	4.36081i	0.488573	−	0.282078i	−0.235409	−	0.971896i	$-0.575643\pi$
$239$	7.55315	−	4.36081i	0.488573	−	0.282078i	0.723982	+	0.689819i	$0.242310\pi$
$240$		0			0
$241$	−17.1314	+	9.89079i	−1.10353	+	0.637122i	−0.937145	−	0.348939i	$-0.886542\pi$
$241$	−17.1314	+	9.89079i	−1.10353	+	0.637122i	−0.166382	+	0.986061i	$0.553209\pi$
$242$	−1.05229	−	0.607537i	−0.0676435	−	0.0390540i
$243$		0			0
$244$			7.25411i			0.464397i
$245$	−6.14327	−	1.40463i	−0.392479	−	0.0897383i
$246$		0			0
$247$	−3.15947	+	5.47236i	−0.201032	+	0.348198i
$248$	10.0032			0.635201
$249$		0			0
$250$			8.27295i			0.523227i
$251$	−3.80791			−0.240353			−0.120176	−	0.992753i	$-0.538346\pi$
$251$	−3.80791			−0.240353			−0.120176	+	0.992753i	$0.538346\pi$
$252$		0			0
$253$	5.36686			0.337411
$254$			6.10587i			0.383116i
$255$		0			0
$256$	1.00000			0.0625000
$257$	7.53771	−	13.0557i	0.470189	−	0.814392i	−0.529230	−	0.848479i	$-0.677519\pi$
$257$	7.53771	−	13.0557i	0.470189	−	0.814392i	0.999419	+	0.0340869i	$0.0108523\pi$
$258$		0			0
$259$	−24.9078	−	2.81124i	−1.54769	−	0.174682i
$260$		−	2.06901i		−	0.128314i
$261$		0			0
$262$	6.89147	+	3.97879i	0.425756	+	0.245811i
$263$	6.59852	−	3.80965i	0.406882	−	0.234913i	−0.282567	−	0.959248i	$-0.591186\pi$
$263$	6.59852	−	3.80965i	0.406882	−	0.234913i	0.689449	+	0.724334i	$0.257853\pi$
$264$		0			0
$265$	10.8691	−	6.27529i	0.667684	−	0.385488i
$266$	7.22852	+	0.815855i	0.443209	+	0.0500233i
$267$		0			0
$268$	−3.67050			−0.224212
$269$	4.32720	−	7.49493i	0.263834	−	0.456974i	−0.703424	−	0.710771i	$-0.748346\pi$
$269$	4.32720	−	7.49493i	0.263834	−	0.456974i	0.967257	+	0.253797i	$0.0816796\pi$
$270$		0			0
$271$	−15.6611	+	9.04193i	−0.951343	+	0.549258i	−0.893498	−	0.449068i	$-0.851756\pi$
$271$	−15.6611	+	9.04193i	−0.951343	+	0.549258i	−0.0578449	+	0.998326i	$0.518423\pi$
$272$	2.57638	−	4.46242i	0.156216	−	0.270574i
$273$		0			0
$274$	−10.9200	−	18.9140i	−0.659700	−	1.14263i
$275$	11.3495	+	6.55262i	0.684398	+	0.395138i
$276$		0			0
$277$	−4.99073	−	8.64419i	−0.299864	−	0.519379i	0.676241	−	0.736681i	$-0.263608\pi$
$277$	−4.99073	−	8.64419i	−0.299864	−	0.519379i	−0.976105	+	0.217301i	$0.930275\pi$
$278$	−6.76127	−	11.7109i	−0.405514	−	0.702371i
$279$		0			0
$280$	−2.18330	+	0.952070i	−0.130477	+	0.0568971i
$281$	13.0297	+	7.52272i	0.777289	+	0.448768i	0.835469	−	0.549538i	$-0.185196\pi$
$281$	13.0297	+	7.52272i	0.777289	+	0.448768i	−0.0581797	+	0.998306i	$0.518530\pi$
$282$		0			0
$283$		−	4.02933i		−	0.239519i	−0.992803	−	0.119759i	$-0.961788\pi$
$283$		−	4.02933i		−	0.239519i	0.992803	−	0.119759i	$-0.0382123\pi$
$284$		−	14.1484i		−	0.839555i
$285$		0			0
$286$	−6.22593	−	3.59454i	−0.368147	−	0.212550i
$287$	−6.42194	−	0.724819i	−0.379075	−	0.0427847i
$288$		0			0
$289$	−4.77544	−	8.27131i	−0.280908	−	0.486548i
$290$	0.964632	+	1.67079i	0.0566451	+	0.0981123i
$291$		0			0
$292$	10.9190	+	6.30409i	0.638987	+	0.368919i
$293$	−6.59608	−	11.4248i	−0.385347	−	0.667441i	0.606470	−	0.795106i	$-0.292585\pi$
$293$	−6.59608	−	11.4248i	−0.385347	−	0.667441i	−0.991817	+	0.127665i	$0.959252\pi$
$294$		0			0
$295$	−3.59402	+	6.22503i	−0.209252	+	0.362435i
$296$	−8.20475	+	4.73701i	−0.476891	+	0.275333i
$297$		0			0
$298$	−2.54722	+	4.41192i	−0.147557	+	0.255575i
$299$	−3.94309			−0.228035
$300$		0			0
$301$	0.577752	+	1.32491i	0.0333011	+	0.0763666i
$302$	−18.3385	+	10.5877i	−1.05526	+	0.609256i
$303$		0			0
$304$	2.38111	−	1.37474i	0.136566	−	0.0788465i
$305$	−5.65564	−	3.26528i	−0.323841	−	0.186970i
$306$		0			0
$307$		−	28.7690i		−	1.64194i	−0.570974	−	0.820968i	$-0.693434\pi$
$307$		−	28.7690i		−	1.64194i	0.570974	−	0.820968i	$-0.306566\pi$
$308$	−0.928202	+	8.22392i	−0.0528892	+	0.468602i
$309$		0			0
$310$	−4.50271	+	7.79892i	−0.255737	+	0.442949i
$311$	−30.8457			−1.74910			−0.874550	−	0.484936i	$-0.838843\pi$
$311$	−30.8457			−1.74910			−0.874550	+	0.484936i	$0.838843\pi$
$312$		0			0
$313$		−	18.3661i		−	1.03811i	−0.854740	−	0.519056i	$-0.826283\pi$
$313$		−	18.3661i		−	1.03811i	0.854740	−	0.519056i	$-0.173717\pi$
$314$	0.359924			0.0203117
$315$		0			0
$316$	6.54804			0.368356
$317$		−	17.4560i		−	0.980426i	−0.871603	−	0.490213i	$-0.836919\pi$
$317$		−	17.4560i		−	0.980426i	0.871603	−	0.490213i	$-0.163081\pi$
$318$		0			0
$319$	6.70353			0.375326
$320$	−0.450129	+	0.779646i	−0.0251630	+	0.0435835i
$321$		0			0
$322$	1.81444	+	4.16091i	0.101115	+	0.231878i
$323$		−	14.1673i		−	0.788292i
$324$		0			0
$325$	−8.33857	−	4.81428i	−0.462541	−	0.267048i
$326$	−10.7152	+	6.18640i	−0.593458	+	0.342633i
$327$		0			0
$328$	−2.11542	+	1.22134i	−0.116804	+	0.0674371i
$329$	−12.3531	+	16.7312i	−0.681049	+	0.922420i
$330$		0			0
$331$	10.4294			0.573254			0.286627	−	0.958042i	$-0.407466\pi$
$331$	10.4294			0.573254			0.286627	+	0.958042i	$0.407466\pi$
$332$	0.184437	−	0.319454i	0.0101223	−	0.0175323i
$333$		0			0
$334$	−12.8322	+	7.40866i	−0.702145	+	0.405384i
$335$	1.65220	−	2.86169i	0.0902693	−	0.156351i
$336$		0			0
$337$	−15.8312	−	27.4204i	−0.862380	−	1.49369i	−0.869626	−	0.493712i	$-0.835640\pi$
$337$	−15.8312	−	27.4204i	−0.862380	−	1.49369i	0.00724616	−	0.999974i	$-0.497693\pi$
$338$	−6.68407	−	3.85905i	−0.363566	−	0.209905i
$339$		0			0
$340$	2.31940	+	4.01733i	0.125787	+	0.217870i
$341$	15.6454	+	27.0986i	0.847244	+	1.46747i
$342$		0			0
$343$	−17.4775	−	6.12685i	−0.943694	−	0.330819i
$344$	0.473119	+	0.273155i	0.0255089	+	0.0147275i
$345$		0			0
$346$		−	4.63544i		−	0.249203i
$347$		−	12.5252i		−	0.672389i	−0.941793	−	0.336195i	$-0.890860\pi$
$347$		−	12.5252i		−	0.672389i	0.941793	−	0.336195i	$-0.109140\pi$
$348$		0			0
$349$	12.2560	+	7.07599i	0.656047	+	0.378769i	0.790769	−	0.612115i	$-0.209681\pi$
$349$	12.2560	+	7.07599i	0.656047	+	0.378769i	−0.134722	+	0.990883i	$0.543014\pi$
$350$	−1.24317	+	11.0145i	−0.0664501	+	0.588752i
$351$		0			0
$352$	1.56404	+	2.70900i	0.0833638	+	0.144390i
$353$	2.48267	+	4.30012i	0.132139	+	0.228872i	0.924501	−	0.381180i	$-0.124482\pi$
$353$	2.48267	+	4.30012i	0.132139	+	0.228872i	−0.792362	+	0.610052i	$0.791149\pi$
$354$		0			0
$355$	11.0308	+	6.36862i	0.585452	+	0.338011i
$356$	6.00244	+	10.3965i	0.318129	+	0.551015i
$357$		0			0
$358$	−3.03602	+	5.25855i	−0.160459	+	0.277923i
$359$	−15.0013	+	8.66098i	−0.791736	+	0.457109i	−0.840573	−	0.541698i	$-0.817782\pi$
$359$	−15.0013	+	8.66098i	−0.791736	+	0.457109i	0.0488375	+	0.998807i	$0.484448\pi$
$360$		0			0
$361$	−5.72021	+	9.90769i	−0.301063	+	0.521457i
$362$	−7.12701			−0.374587
$363$		0			0
$364$	0.681960	−	6.04220i	0.0357444	−	0.316698i
$365$	−9.82992	+	5.67531i	−0.514522	+	0.297059i
$366$		0			0
$367$	1.18799	−	0.685884i	0.0620124	−	0.0358029i	−0.468673	−	0.883372i	$-0.655268\pi$
$367$	1.18799	−	0.685884i	0.0620124	−	0.0358029i	0.530686	+	0.847569i	$0.321934\pi$
$368$	1.48584	+	0.857850i	0.0774547	+	0.0447185i
$369$		0			0
$370$		−	8.52907i		−	0.443405i
$371$	33.8099	−	14.7434i	1.75532	−	0.765441i
$372$		0			0
$373$	2.40488	−	4.16537i	0.124520	−	0.215675i	−0.797025	−	0.603946i	$-0.793594\pi$
$373$	2.40488	−	4.16537i	0.124520	−	0.215675i	0.921545	+	0.388271i	$0.126928\pi$
$374$	16.1183			0.833456
$375$		0			0
$376$			7.86068i			0.405384i
$377$	−4.92515			−0.253658
$378$		0			0
$379$	19.5669			1.00508			0.502542	−	0.864553i	$-0.332398\pi$
$379$	19.5669			1.00508			0.502542	+	0.864553i	$0.332398\pi$
$380$			2.47523i			0.126977i
$381$		0			0
$382$	−14.4006			−0.736801
$383$	−15.7349	+	27.2536i	−0.804014	+	1.39259i	0.112940	+	0.993602i	$0.463973\pi$
$383$	−15.7349	+	27.2536i	−0.804014	+	1.39259i	−0.916955	+	0.398992i	$0.869360\pi$
$384$		0			0
$385$	−5.99394	−	4.42549i	−0.305479	−	0.225544i
$386$			17.8115i			0.906579i
$387$		0			0
$388$	−8.86815	−	5.12003i	−0.450212	−	0.259930i
$389$	−3.52130	+	2.03303i	−0.178537	+	0.103078i	−0.586605	−	0.809873i	$-0.699536\pi$
$389$	−3.52130	+	2.03303i	−0.178537	+	0.103078i	0.408068	+	0.912952i	$0.366203\pi$
$390$		0			0
$391$	7.65617	−	4.42029i	0.387189	−	0.223544i
$392$	−6.68980	+	2.06074i	−0.337886	+	0.104083i
$393$		0			0
$394$	19.1025			0.962369
$395$	−2.94746	+	5.10515i	−0.148303	+	0.256868i
$396$		0			0
$397$	−3.81692	+	2.20370i	−0.191566	+	0.110601i	−0.592715	−	0.805412i	$-0.701944\pi$
$397$	−3.81692	+	2.20370i	−0.191566	+	0.110601i	0.401150	+	0.916013i	$0.368611\pi$
$398$	−6.69771	+	11.6008i	−0.335726	+	0.581494i
$399$		0			0
$400$	2.09477	+	3.62824i	0.104738	+	0.181412i
$401$	−16.0586	−	9.27141i	−0.801926	−	0.462992i	0.0422180	−	0.999108i	$-0.486558\pi$
$401$	−16.0586	−	9.27141i	−0.801926	−	0.462992i	−0.844144	+	0.536116i	$0.819891\pi$
$402$		0			0
$403$	−11.4948	−	19.9096i	−0.572597	−	0.991768i
$404$	−1.35969	−	2.35506i	−0.0676472	−	0.117168i
$405$		0			0
$406$	2.26635	+	5.19723i	0.112477	+	0.257934i
$407$	−25.6652	−	14.8178i	−1.27218	−	0.734491i
$408$		0			0
$409$			24.8902i			1.23074i	0.788238	+	0.615370i	$0.210994\pi$
$409$			24.8902i			1.23074i	−0.788238	+	0.615370i	$0.789006\pi$
$410$		−	2.19904i		−	0.108603i
$411$		0			0
$412$	−1.18861	−	0.686242i	−0.0585584	−	0.0338087i
$413$	−12.5476	+	16.9946i	−0.617426	+	0.836249i
$414$		0			0
$415$	0.166041	+	0.287591i	0.00815062	+	0.0141173i
$416$	−1.14912	−	1.99033i	−0.0563402	−	0.0975841i
$417$		0			0
$418$	7.44832	+	4.30029i	0.364309	+	0.210334i
$419$	2.57422	+	4.45869i	0.125759	+	0.217821i	0.922029	−	0.387120i	$-0.126530\pi$
$419$	2.57422	+	4.45869i	0.125759	+	0.217821i	−0.796270	+	0.604941i	$0.793197\pi$
$420$		0			0
$421$	−13.5022	+	23.3864i	−0.658055	+	1.13978i	0.323063	+	0.946377i	$0.395287\pi$
$421$	−13.5022	+	23.3864i	−0.658055	+	1.13978i	−0.981119	+	0.193408i	$0.938046\pi$
$422$	16.2327	−	9.37193i	0.790193	−	0.456218i
$423$		0			0
$424$	6.97054	−	12.0733i	0.338520	−	0.586333i
$425$	21.5877			1.04715
$426$		0			0
$427$	−15.4401	−	11.3999i	−0.747200	−	0.551679i
$428$	12.3585	−	7.13519i	0.597371	−	0.344892i
$429$		0			0
$430$	−0.425929	+	0.245910i	−0.0205401	+	0.0118588i
$431$	8.10874	+	4.68159i	0.390584	+	0.225504i	0.682413	−	0.730966i	$-0.260930\pi$
$431$	8.10874	+	4.68159i	0.390584	+	0.225504i	−0.291829	+	0.956471i	$0.594264\pi$
$432$		0			0
$433$		−	21.0373i		−	1.01099i	−0.862830	−	0.505494i	$-0.831310\pi$
$433$		−	21.0373i		−	1.01099i	0.862830	−	0.505494i	$-0.168690\pi$
$434$	−15.7200	+	21.2914i	−0.754585	+	1.02202i
$435$		0			0
$436$	2.64583	−	4.58271i	0.126712	−	0.219472i
$437$	4.71727			0.225657
$438$		0			0
$439$			20.4229i			0.974730i	0.873198	+	0.487365i	$0.162042\pi$
$439$			20.4229i			0.974730i	−0.873198	+	0.487365i	$0.837958\pi$
$440$	−2.81608			−0.134252
$441$		0			0
$442$	−11.8423			−0.563279
$443$		−	32.3649i		−	1.53770i	−0.639427	−	0.768852i	$-0.720828\pi$
$443$		−	32.3649i		−	1.53770i	0.639427	−	0.768852i	$-0.279172\pi$
$444$		0			0
$445$	−10.8075			−0.512324
$446$	−1.27946	+	2.21609i	−0.0605841	+	0.104935i
$447$		0			0
$448$	−1.57151	+	2.12847i	−0.0742467	+	0.100561i
$449$		−	21.5693i		−	1.01792i	−0.860791	−	0.508958i	$-0.830031\pi$
$449$		−	21.5693i		−	1.01792i	0.860791	−	0.508958i	$-0.169969\pi$
$450$		0			0
$451$	−6.61721	−	3.82045i	−0.311592	−	0.179898i
$452$	−2.30371	+	1.33005i	−0.108358	+	0.0625603i
$453$		0			0
$454$	−7.55962	+	4.36455i	−0.354790	+	0.204838i
$455$	4.40381	+	3.25146i	0.206454	+	0.152431i
$456$		0			0
$457$	21.0700			0.985611			0.492806	−	0.870139i	$-0.335971\pi$
$457$	21.0700			0.985611			0.492806	+	0.870139i	$0.335971\pi$
$458$	1.96865	−	3.40979i	0.0919887	−	0.159329i
$459$		0			0
$460$	−1.33764	+	0.772286i	−0.0623677	+	0.0360080i
$461$	−15.8412	+	27.4378i	−0.737800	+	1.27791i	0.215684	+	0.976463i	$0.430802\pi$
$461$	−15.8412	+	27.4378i	−0.737800	+	1.27791i	−0.953484	+	0.301444i	$0.902531\pi$
$462$		0			0
$463$	4.40058	+	7.62202i	0.204512	+	0.354225i	0.949977	−	0.312319i	$-0.101106\pi$
$463$	4.40058	+	7.62202i	0.204512	+	0.354225i	−0.745465	+	0.666545i	$0.767773\pi$
$464$	1.85590	+	1.07151i	0.0861582	+	0.0497434i
$465$		0			0
$466$	2.26406	+	3.92147i	0.104881	+	0.181658i
$467$	−9.49444	−	16.4449i	−0.439350	−	0.760977i	0.558289	−	0.829646i	$-0.311458\pi$
$467$	−9.49444	−	16.4449i	−0.439350	−	0.760977i	−0.997639	+	0.0686693i	$0.978125\pi$
$468$		0			0
$469$	5.76822	−	7.81254i	0.266352	−	0.360750i
$470$	−6.12855	−	3.53832i	−0.282689	−	0.163211i
$471$		0			0
$472$			7.98443i			0.367513i
$473$			1.70891i			0.0785756i
$474$		0			0
$475$	9.97575	+	5.75950i	0.457719	+	0.264264i
$476$	5.44931	+	12.4964i	0.249769	+	0.572774i
$477$		0			0
$478$	4.36081	+	7.55315i	0.199459	+	0.345473i
$479$	−12.0701	−	20.9060i	−0.551495	−	0.955218i	−0.998167	−	0.0605197i	$-0.980724\pi$
$479$	−12.0701	−	20.9060i	−0.551495	−	0.955218i	0.446672	−	0.894698i	$-0.352609\pi$
$480$		0			0
$481$	18.8565	+	10.8868i	0.859781	+	0.496395i
$482$	−9.89079	−	17.1314i	−0.450513	−	0.780312i
$483$		0			0
$484$	0.607537	−	1.05229i	0.0276153	−	0.0478312i
$485$	7.98362	−	4.60935i	0.362518	−	0.209300i
$486$		0			0
$487$	7.05542	−	12.2204i	0.319712	−	0.553757i	−0.660716	−	0.750636i	$-0.729747\pi$
$487$	7.05542	−	12.2204i	0.319712	−	0.553757i	0.980428	+	0.196879i	$0.0630806\pi$
$488$	−7.25411			−0.328378
$489$		0			0
$490$	1.40463	−	6.14327i	0.0634546	−	0.277525i
$491$	18.8344	−	10.8740i	0.849982	−	0.490738i	−0.0106626	−	0.999943i	$-0.503394\pi$
$491$	18.8344	−	10.8740i	0.849982	−	0.490738i	0.860645	+	0.509206i	$0.170061\pi$
$492$		0			0
$493$	9.56302	−	5.52121i	0.430697	−	0.248663i
$494$	−5.47236	−	3.15947i	−0.246213	−	0.142151i
$495$		0			0
$496$			10.0032i			0.449155i
$497$	30.1144	+	22.2343i	1.35082	+	0.997347i
$498$		0			0
$499$	4.21233	−	7.29596i	0.188570	−	0.326612i	−0.756204	−	0.654336i	$-0.772948\pi$
$499$	4.21233	−	7.29596i	0.188570	−	0.326612i	0.944774	+	0.327724i	$0.106282\pi$
$500$	−8.27295			−0.369978
$501$		0			0
$502$		−	3.80791i		−	0.169955i
$503$	8.71316			0.388501			0.194250	−	0.980952i	$-0.437773\pi$
$503$	8.71316			0.388501			0.194250	+	0.980952i	$0.437773\pi$
$504$		0			0
$505$	2.44815			0.108941
$506$			5.36686i			0.238586i
$507$		0			0
$508$	−6.10587			−0.270904
$509$	14.9177	−	25.8382i	0.661214	−	1.14526i	−0.319082	−	0.947727i	$-0.603375\pi$
$509$	14.9177	−	25.8382i	0.661214	−	1.14526i	0.980297	−	0.197530i	$-0.0632920\pi$
$510$		0			0
$511$	−30.5773	+	13.3338i	−1.35266	+	0.589853i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	13.0557	+	7.53771i	0.575862	+	0.332474i
$515$	1.07005	−	0.617794i	0.0471521	−	0.0272233i
$516$		0			0
$517$	−21.2946	+	12.2944i	−0.936536	+	0.540709i
$518$	2.81124	−	24.9078i	0.123519	−	1.09439i
$519$		0			0
$520$	2.06901			0.0907320
$521$	9.89004	−	17.1301i	0.433291	−	0.750482i	−0.563864	−	0.825868i	$-0.690686\pi$
$521$	9.89004	−	17.1301i	0.433291	−	0.750482i	0.997154	+	0.0753863i	$0.0240190\pi$
$522$		0			0
$523$	−10.5932	+	6.11597i	−0.463207	+	0.267433i	−0.713392	−	0.700766i	$-0.752842\pi$
$523$	−10.5932	+	6.11597i	−0.463207	+	0.267433i	0.250185	+	0.968198i	$0.419509\pi$
$524$	−3.97879	+	6.89147i	−0.173814	+	0.301055i
$525$		0			0
$526$	3.80965	+	6.59852i	0.166109	+	0.287709i
$527$	44.6382	+	25.7719i	1.94447	+	1.12264i
$528$		0			0
$529$	−10.0282	−	17.3693i	−0.436008	−	0.755188i
$530$	6.27529	+	10.8691i	0.272581	+	0.472124i
$531$		0			0
$532$	−0.815855	+	7.22852i	−0.0353718	+	0.313396i
$533$	4.86174	+	2.80693i	0.210585	+	0.121581i
$534$		0			0
$535$			12.8470i			0.555425i
$536$		−	3.67050i		−	0.158542i
$537$		0			0
$538$	7.49493	+	4.32720i	0.323129	+	0.186559i
$539$	−16.0457	−	14.8996i	−0.691136	−	0.641771i
$540$		0			0
$541$	−0.348944	−	0.604389i	−0.0150023	−	0.0259847i	0.858427	−	0.512936i	$-0.171442\pi$
$541$	−0.348944	−	0.604389i	−0.0150023	−	0.0259847i	−0.873429	+	0.486951i	$0.838109\pi$
$542$	−9.04193	−	15.6611i	−0.388384	−	0.672701i
$543$		0			0
$544$	4.46242	+	2.57638i	0.191325	+	0.110461i
$545$	2.38193	+	4.12562i	0.102031	+	0.176722i
$546$		0			0
$547$	21.0049	−	36.3815i	0.898103	−	1.55556i	0.0681854	−	0.997673i	$-0.478279\pi$
$547$	21.0049	−	36.3815i	0.898103	−	1.55556i	0.829917	−	0.557887i	$-0.188388\pi$
$548$	18.9140	−	10.9200i	0.807964	−	0.466478i
$549$		0			0
$550$	−6.55262	+	11.3495i	−0.279404	+	0.483943i
$551$	5.89215			0.251014
$552$		0			0
$553$	−10.2903	+	13.9373i	−0.437587	+	0.592673i
$554$	8.64419	−	4.99073i	0.367257	−	0.212036i
$555$		0			0
$556$	11.7109	−	6.76127i	0.496651	−	0.286742i
$557$	−4.85612	−	2.80368i	−0.205760	−	0.118796i	0.393579	−	0.919291i	$-0.371237\pi$
$557$	−4.85612	−	2.80368i	−0.205760	−	0.118796i	−0.599340	+	0.800495i	$0.704570\pi$
$558$		0			0
$559$		−	1.25555i		−	0.0531042i
$560$	−0.952070	−	2.18330i	−0.0402323	−	0.0922614i
$561$		0			0
$562$	−7.52272	+	13.0297i	−0.317327	+	0.549626i
$563$	35.1896			1.48306			0.741532	−	0.670918i	$-0.234100\pi$
$563$	35.1896			1.48306			0.741532	+	0.670918i	$0.234100\pi$
$564$		0			0
$565$		−	2.39478i		−	0.100749i
$566$	4.02933			0.169365
$567$		0			0
$568$	14.1484			0.593655
$569$		−	8.81739i		−	0.369644i	−0.982772	−	0.184822i	$-0.940829\pi$
$569$		−	8.81739i		−	0.369644i	0.982772	−	0.184822i	$-0.0591709\pi$
$570$		0			0
$571$	−11.8828			−0.497280			−0.248640	−	0.968596i	$-0.579984\pi$
$571$	−11.8828			−0.497280			−0.248640	+	0.968596i	$0.579984\pi$
$572$	3.59454	−	6.22593i	0.150295	−	0.260319i
$573$		0			0
$574$	0.724819	−	6.42194i	0.0302534	−	0.268047i
$575$			7.18799i			0.299760i
$576$		0			0
$577$	15.8314	+	9.14028i	0.659071	+	0.380515i	0.791923	−	0.610621i	$-0.209080\pi$
$577$	15.8314	+	9.14028i	0.659071	+	0.380515i	−0.132852	+	0.991136i	$0.542413\pi$
$578$	8.27131	−	4.77544i	0.344041	−	0.198632i
$579$		0			0
$580$	−1.67079	+	0.964632i	−0.0693758	+	0.0400542i
$581$	0.390103	+	0.894591i	0.0161842	+	0.0371139i
$582$		0			0
$583$	43.6089			1.80610
$584$	−6.30409	+	10.9190i	−0.260865	+	0.451832i
$585$		0			0
$586$	11.4248	−	6.59608i	0.471952	−	0.272482i
$587$	1.75389	−	3.03782i	0.0723907	−	0.125384i	−0.827558	−	0.561380i	$-0.810270\pi$
$587$	1.75389	−	3.03782i	0.0723907	−	0.125384i	0.899949	+	0.435996i	$0.143604\pi$
$588$		0			0
$589$	13.7517	+	23.8186i	0.566628	+	0.981429i
$590$	−6.22503	−	3.59402i	−0.256280	−	0.147964i
$591$		0			0
$592$	−4.73701	−	8.20475i	−0.194690	−	0.337213i
$593$	24.2336	+	41.9738i	0.995155	+	1.72366i	0.582727	+	0.812668i	$0.301986\pi$
$593$	24.2336	+	41.9738i	0.995155	+	1.72366i	0.412428	+	0.910990i	$0.364681\pi$
$594$		0			0
$595$	−12.1957	−	1.37648i	−0.499975	−	0.0564302i
$596$	−4.41192	−	2.54722i	−0.180719	−	0.104338i
$597$		0			0
$598$		−	3.94309i		−	0.161245i
$599$			25.1463i			1.02745i	0.857955	+	0.513724i	$0.171734\pi$
$599$			25.1463i			1.02745i	−0.857955	+	0.513724i	$0.828266\pi$
$600$		0			0
$601$	11.2731	+	6.50854i	0.459840	+	0.265489i	0.711977	−	0.702203i	$-0.247800\pi$
$601$	11.2731	+	6.50854i	0.459840	+	0.265489i	−0.252137	+	0.967692i	$0.581133\pi$
$602$	−1.32491	+	0.577752i	−0.0539993	+	0.0235474i
$603$		0			0
$604$	−10.5877	−	18.3385i	−0.430809	−	0.746183i
$605$	0.546940	+	0.947328i	0.0222363	+	0.0385144i
$606$		0			0
$607$	−7.10546	−	4.10234i	−0.288402	−	0.166509i	0.348819	−	0.937190i	$-0.386583\pi$
$607$	−7.10546	−	4.10234i	−0.288402	−	0.166509i	−0.637221	+	0.770681i	$0.719916\pi$
$608$	1.37474	+	2.38111i	0.0557529	+	0.0965668i
$609$		0			0
$610$	3.26528	−	5.65564i	0.132207	−	0.228990i
$611$	15.6454	−	9.03286i	0.632944	−	0.365430i
$612$		0			0
$613$	2.35051	−	4.07120i	0.0949361	−	0.164434i	−0.814646	−	0.579959i	$-0.803069\pi$
$613$	2.35051	−	4.07120i	0.0949361	−	0.164434i	0.909582	+	0.415525i	$0.136402\pi$
$614$	28.7690			1.16102
$615$		0			0
$616$	−8.22392	−	0.928202i	−0.331351	−	0.0373983i
$617$	−17.0178	+	9.82521i	−0.685109	+	0.395548i	−0.801777	−	0.597623i	$-0.796112\pi$
$617$	−17.0178	+	9.82521i	−0.685109	+	0.395548i	0.116668	+	0.993171i	$0.462779\pi$
$618$		0			0
$619$	30.0586	−	17.3544i	1.20816	−	0.697531i	0.245802	−	0.969320i	$-0.420949\pi$
$619$	30.0586	−	17.3544i	1.20816	−	0.697531i	0.962357	+	0.271789i	$0.0876153\pi$
$620$	−7.79892	−	4.50271i	−0.313212	−	0.180833i
$621$		0			0
$622$		−	30.8457i		−	1.23680i
$623$	−31.5615	−	3.56223i	−1.26449	−	0.142718i
$624$		0			0
$625$	−6.74995	+	11.6912i	−0.269998	+	0.467650i
$626$	18.3661			0.734057
$627$		0			0
$628$			0.359924i			0.0143625i
$629$	−48.8174			−1.94648
$630$		0			0
$631$	22.9139			0.912188			0.456094	−	0.889932i	$-0.349248\pi$
$631$	22.9139			0.912188			0.456094	+	0.889932i	$0.349248\pi$
$632$			6.54804i			0.260467i
$633$		0			0
$634$	17.4560			0.693266
$635$	2.74843	−	4.76041i	0.109068	−	0.188911i
$636$		0			0
$637$	11.7889	+	10.9469i	0.467094	+	0.433732i
$638$			6.70353i			0.265395i
$639$		0			0
$640$	−0.779646	−	0.450129i	−0.0308182	−	0.0177929i
$641$	−11.9968	+	6.92634i	−0.473844	+	0.273574i	−0.717848	−	0.696200i	$-0.754873\pi$
$641$	−11.9968	+	6.92634i	−0.473844	+	0.273574i	0.244003	+	0.969774i	$0.421539\pi$
$642$		0			0
$643$	−27.9684	+	16.1476i	−1.10297	+	0.636797i	−0.936998	−	0.349334i	$-0.886408\pi$
$643$	−27.9684	+	16.1476i	−1.10297	+	0.636797i	−0.165967	+	0.986131i	$0.553075\pi$
$644$	−4.16091	+	1.81444i	−0.163963	+	0.0714990i
$645$		0			0
$646$	14.1673			0.557407
$647$	8.96715	−	15.5316i	0.352535	−	0.610609i	−0.634158	−	0.773204i	$-0.718653\pi$
$647$	8.96715	−	15.5316i	0.352535	−	0.610609i	0.986693	+	0.162595i	$0.0519864\pi$
$648$		0			0
$649$	−21.6298	+	12.4880i	−0.849046	+	0.490197i
$650$	4.81428	−	8.33857i	0.188831	−	0.327066i
$651$		0			0
$652$	−6.18640	−	10.7152i	−0.242278	−	0.419638i
$653$	−6.49080	−	3.74747i	−0.254005	−	0.146650i	0.367592	−	0.929987i	$-0.380182\pi$
$653$	−6.49080	−	3.74747i	−0.254005	−	0.146650i	−0.621597	+	0.783338i	$0.713516\pi$
$654$		0			0
$655$	−3.58194	−	6.20410i	−0.139958	−	0.242414i
$656$	−1.22134	−	2.11542i	−0.0476852	−	0.0825932i
$657$		0			0
$658$	−16.7312	−	12.3531i	−0.652250	−	0.481574i
$659$	9.32497	+	5.38377i	0.363249	+	0.209722i	0.670505	−	0.741905i	$-0.266077\pi$
$659$	9.32497	+	5.38377i	0.363249	+	0.209722i	−0.307256	+	0.951627i	$0.599411\pi$
$660$		0			0
$661$		−	11.6409i		−	0.452778i	−0.974037	−	0.226389i	$-0.927308\pi$
$661$		−	11.6409i		−	0.452778i	0.974037	−	0.226389i	$-0.0726920\pi$
$662$			10.4294i			0.405352i
$663$		0			0
$664$	0.319454	+	0.184437i	0.0123972	+	0.00715754i
$665$	−5.26845	−	3.88984i	−0.204302	−	0.150842i
$666$		0			0
$667$	1.83838	+	3.18417i	0.0711825	+	0.123292i
$668$	−7.40866	−	12.8322i	−0.286650	−	0.496492i
$669$		0			0
$670$	2.86169	+	1.65220i	0.110557	+	0.0638301i
$671$	−11.3457	−	19.6514i	−0.437997	−	0.758634i
$672$		0			0
$673$	−0.550931	+	0.954241i	−0.0212368	+	0.0367833i	−0.876449	−	0.481496i	$-0.840094\pi$
$673$	−0.550931	+	0.954241i	−0.0212368	+	0.0367833i	0.855212	+	0.518279i	$0.173427\pi$
$674$	27.4204	−	15.8312i	1.05619	−	0.609794i
$675$		0			0
$676$	3.85905	−	6.68407i	0.148425	−	0.257080i
$677$	11.2324			0.431695			0.215847	−	0.976427i	$-0.430749\pi$
$677$	11.2324			0.431695			0.215847	+	0.976427i	$0.430749\pi$
$678$		0			0
$679$	24.8342	−	10.8294i	0.953048	−	0.415594i
$680$	−4.01733	+	2.31940i	−0.154057	+	0.0889451i
$681$		0			0
$682$	−27.0986	+	15.6454i	−1.03766	+	0.599092i
$683$	−37.6792	−	21.7541i	−1.44175	−	0.832396i	−0.443786	−	0.896133i	$-0.646365\pi$
$683$	−37.6792	−	21.7541i	−1.44175	−	0.832396i	−0.997967	+	0.0637365i	$0.979698\pi$
$684$		0			0
$685$			19.6616i			0.751231i
$686$	6.12685	−	17.4775i	0.233924	−	0.667293i
$687$		0			0
$688$	−0.273155	+	0.473119i	−0.0104139	+	0.0180375i
$689$	−32.0399			−1.22062
$690$		0			0
$691$			32.2260i			1.22593i	0.790108	+	0.612967i	$0.210024\pi$
$691$			32.2260i			1.22593i	−0.790108	+	0.612967i	$0.789976\pi$
$692$	4.63544			0.176213
$693$		0			0
$694$	12.5252			0.475451
$695$			12.1738i			0.461777i
$696$		0			0
$697$	−12.5865			−0.476748
$698$	−7.07599	+	12.2560i	−0.267830	+	0.463895i
$699$		0			0
$700$	−11.0145	−	1.24317i	−0.416310	−	0.0469873i
$701$			21.8995i			0.827133i	0.910474	+	0.413566i	$0.135717\pi$
$701$			21.8995i			0.827133i	−0.910474	+	0.413566i	$0.864283\pi$
$702$		0			0
$703$	−22.5587	−	13.0243i	−0.850818	−	0.491220i
$704$	−2.70900	+	1.56404i	−0.102099	+	0.0589471i
$705$		0			0
$706$	−4.30012	+	2.48267i	−0.161837	+	0.0934366i
$707$	7.14942	+	0.806927i	0.268882	+	0.0303476i
$708$		0			0
$709$	−18.0470			−0.677770			−0.338885	−	0.940828i	$-0.610050\pi$
$709$	−18.0470			−0.677770			−0.338885	+	0.940828i	$0.610050\pi$
$710$	−6.36862	+	11.0308i	−0.239010	+	0.413977i
$711$		0			0
$712$	−10.3965	+	6.00244i	−0.389627	+	0.224951i
$713$	−8.58120	+	14.8631i	−0.321369	+	0.556627i
$714$		0			0
$715$	3.23602	+	5.60494i	0.121020	+	0.209613i
$716$	−5.25855	−	3.03602i	−0.196521	−	0.113462i
$717$		0			0
$718$	−8.66098	−	15.0013i	−0.323225	−	0.559842i
$719$	4.65944	+	8.07039i	0.173768	+	0.300975i	0.939734	−	0.341906i	$-0.111072\pi$
$719$	4.65944	+	8.07039i	0.173768	+	0.300975i	−0.765966	+	0.642881i	$0.777739\pi$
$720$		0			0
$721$	3.32854	−	1.45147i	0.123961	−	0.0540557i
$722$	−9.90769	−	5.72021i	−0.368726	−	0.212884i
$723$		0			0
$724$		−	7.12701i		−	0.264873i
$725$			8.97823i			0.333443i
$726$		0			0
$727$	−6.73516	−	3.88855i	−0.249793	−	0.144218i	0.369876	−	0.929081i	$-0.379400\pi$
$727$	−6.73516	−	3.88855i	−0.249793	−	0.144218i	−0.619670	+	0.784863i	$0.712733\pi$
$728$	6.04220	+	0.681960i	0.223939	+	0.0252751i
$729$		0			0
$730$	−5.67531	−	9.82992i	−0.210053	−	0.363822i
$731$	1.40750	+	2.43787i	0.0520583	+	0.0901677i
$732$		0			0
$733$	31.2841	+	18.0619i	1.15550	+	0.667131i	0.950222	−	0.311572i	$-0.100856\pi$
$733$	31.2841	+	18.0619i	1.15550	+	0.667131i	0.205282	+	0.978703i	$0.434189\pi$
$734$	0.685884	+	1.18799i	0.0253164	+	0.0438494i
$735$		0			0
$736$	−0.857850	+	1.48584i	−0.0316208	+	0.0547688i
$737$	9.94341	−	5.74083i	0.366270	−	0.211466i
$738$		0			0
$739$	12.0693	−	20.9046i	0.443975	−	0.768987i	−0.554005	−	0.832513i	$-0.686901\pi$
$739$	12.0693	−	20.9046i	0.443975	−	0.768987i	0.997980	+	0.0635263i	$0.0202347\pi$
$740$	8.52907			0.313535
$741$		0			0
$742$	14.7434	+	33.8099i	0.541248	+	1.24120i
$743$	−10.5762	+	6.10618i	−0.388003	+	0.224014i	−0.681295	−	0.732009i	$-0.738583\pi$
$743$	−10.5762	+	6.10618i	−0.388003	+	0.224014i	0.293291	+	0.956023i	$0.405249\pi$
$744$		0			0
$745$	3.97186	−	2.29316i	0.145518	−	0.0840147i
$746$	4.16537	+	2.40488i	0.152505	+	0.0880488i
$747$		0			0
$748$			16.1183i			0.589342i
$749$	−4.23447	+	37.5177i	−0.154724	+	1.37087i
$750$		0			0
$751$	11.7190	−	20.2980i	0.427634	−	0.740684i	−0.569028	−	0.822318i	$-0.692680\pi$
$751$	11.7190	−	20.2980i	0.427634	−	0.740684i	0.996662	+	0.0816339i	$0.0260138\pi$
$752$	−7.86068			−0.286650
$753$		0			0
$754$		−	4.92515i		−	0.179364i
$755$	19.0634			0.693788
$756$		0			0
$757$	3.52341			0.128060			0.0640302	−	0.997948i	$-0.479605\pi$
$757$	3.52341			0.128060			0.0640302	+	0.997948i	$0.479605\pi$
$758$			19.5669i			0.710702i
$759$		0			0
$760$	−2.47523			−0.0897861
$761$	−10.7021	+	18.5365i	−0.387950	+	0.671949i	−0.992174	−	0.124866i	$-0.960150\pi$
$761$	−10.7021	+	18.5365i	−0.387950	+	0.671949i	0.604224	+	0.796815i	$0.293483\pi$
$762$		0			0
$763$	5.59621	+	12.8333i	0.202596	+	0.464597i
$764$		−	14.4006i		−	0.520997i
$765$		0			0
$766$	−27.2536	−	15.7349i	−0.984712	−	0.568524i
$767$	15.8917	−	9.17506i	0.573815	−	0.331292i
$768$		0			0
$769$	−23.4043	+	13.5125i	−0.843982	+	0.487273i	−0.858616	−	0.512620i	$-0.828675\pi$
$769$	−23.4043	+	13.5125i	−0.843982	+	0.487273i	0.0146339	+	0.999893i	$0.495342\pi$
$770$	4.42549	−	5.99394i	0.159484	−	0.216007i
$771$		0			0
$772$	−17.8115			−0.641048
$773$	−8.10280	+	14.0345i	−0.291437	+	0.504784i	−0.974150	−	0.225903i	$-0.927467\pi$
$773$	−8.10280	+	14.0345i	−0.291437	+	0.504784i	0.682712	+	0.730687i	$0.260800\pi$
$774$		0			0
$775$	−36.2939	+	20.9543i	−1.30371	+	0.752700i
$776$	5.12003	−	8.86815i	0.183798	−	0.318348i
$777$		0			0
$778$	−2.03303	−	3.52130i	−0.0728875	−	0.126245i
$779$	−5.81628	−	3.35803i	−0.208390	−	0.120314i
$780$		0			0
$781$	22.1288	+	38.3281i	0.791829	+	1.37149i
$782$	4.42029	+	7.65617i	0.158069	+	0.273784i
$783$		0			0
$784$	−2.06074	−	6.68980i	−0.0735977	−	0.238921i
$785$	−0.280613	−	0.162012i	−0.0100155	−	0.00578246i
$786$		0			0
$787$		−	38.2571i		−	1.36372i	−0.731483	−	0.681860i	$-0.761171\pi$
$787$		−	38.2571i		−	1.36372i	0.731483	−	0.681860i	$-0.238829\pi$
$788$			19.1025i			0.680498i
$789$		0			0
$790$	−5.10515	−	2.94746i	−0.181633	−	0.104866i
$791$	0.789335	−	6.99356i	0.0280655	−	0.248662i
$792$		0			0
$793$	8.33583	+	14.4381i	0.296014	+	0.512712i
$794$	−2.20370	−	3.81692i	−0.0782064	−	0.135457i
$795$		0			0
$796$	−11.6008	−	6.69771i	−0.411179	−	0.237394i
$797$	−4.38709	−	7.59866i	−0.155399	−	0.269158i	0.777805	−	0.628505i	$-0.216333\pi$
$797$	−4.38709	−	7.59866i	−0.155399	−	0.269158i	−0.933204	+	0.359347i	$0.883000\pi$
$798$		0			0
$799$	−20.2521	+	35.0776i	−0.716467	+	1.24096i
$800$	−3.62824	+	2.09477i	−0.128278	+	0.0740612i
$801$		0			0
$802$	9.27141	−	16.0586i	0.327385	−	0.567047i
$803$	−39.4395			−1.39179
$804$		0			0
$805$	0.458323	−	4.06077i	0.0161538	−	0.143123i
$806$	19.9096	−	11.4948i	0.701286	−	0.404887i
$807$		0			0
$808$	2.35506	−	1.35969i	0.0828506	−	0.0478338i
$809$	−26.6053	−	15.3606i	−0.935394	−	0.540050i	−0.0468805	−	0.998901i	$-0.514928\pi$
$809$	−26.6053	−	15.3606i	−0.935394	−	0.540050i	−0.888513	+	0.458851i	$0.848261\pi$
$810$		0			0
$811$		−	8.70634i		−	0.305721i	−0.988248	−	0.152861i	$-0.951151\pi$
$811$		−	8.70634i		−	0.305721i	0.988248	−	0.152861i	$-0.0488485\pi$
$812$	−5.19723	+	2.26635i	−0.182387	+	0.0795332i
$813$		0			0
$814$	14.8178	−	25.6652i	0.519363	−	0.899564i
$815$	11.1387			0.390172
$816$		0			0
$817$			1.50206i			0.0525506i
$818$	−24.8902			−0.870265
$819$		0			0
$820$	2.19904			0.0767937
$821$		−	52.4347i		−	1.82998i	−0.403473	−	0.914992i	$-0.632197\pi$
$821$		−	52.4347i		−	1.82998i	0.403473	−	0.914992i	$-0.367803\pi$
$822$		0			0
$823$	8.36398			0.291550			0.145775	−	0.989318i	$-0.453432\pi$
$823$	8.36398			0.291550			0.145775	+	0.989318i	$0.453432\pi$
$824$	0.686242	−	1.18861i	0.0239064	−	0.0414070i
$825$		0			0
$826$	−16.9946	−	12.5476i	−0.591317	−	0.436586i
$827$			26.4934i			0.921267i	0.887590	+	0.460634i	$0.152378\pi$
$827$			26.4934i			0.921267i	−0.887590	+	0.460634i	$0.847622\pi$
$828$		0			0
$829$	−5.14134	−	2.96835i	−0.178566	−	0.103095i	0.408053	−	0.912958i	$-0.366208\pi$
$829$	−5.14134	−	2.96835i	−0.178566	−	0.103095i	−0.586619	+	0.809863i	$0.699541\pi$
$830$	−0.287591	+	0.166041i	−0.00998243	+	0.00576336i
$831$		0			0
$832$	1.99033	−	1.14912i	0.0690024	−	0.0398385i
$833$	−35.1619	−	8.03958i	−1.21829	−	0.278555i
$834$		0			0
$835$	13.3394			0.461629
$836$	−4.30029	+	7.44832i	−0.148729	+	0.257606i
$837$		0			0
$838$	−4.45869	+	2.57422i	−0.154023	+	0.0889251i
$839$	3.80537	−	6.59110i	0.131376	−	0.227550i	−0.792831	−	0.609441i	$-0.791394\pi$
$839$	3.80537	−	6.59110i	0.131376	−	0.227550i	0.924207	+	0.381891i	$0.124727\pi$
$840$		0			0
$841$	−12.2037	−	21.1375i	−0.420819	−	0.728880i
$842$	−23.3864	−	13.5022i	−0.805950	−	0.465315i
$843$		0			0
$844$	9.37193	+	16.2327i	0.322595	+	0.558751i
$845$	3.47414	+	6.01739i	0.119514	+	0.207004i
$846$		0			0
$847$	1.28500	+	2.94680i	0.0441533	+	0.101253i
$848$	12.0733	+	6.97054i	0.414600	+	0.239369i
$849$		0			0
$850$			21.5877i			0.740450i
$851$		−	16.2546i		−	0.557200i
$852$		0			0
$853$	−24.8764	−	14.3624i	−0.851751	−	0.491759i	0.00949029	−	0.999955i	$-0.496979\pi$
$853$	−24.8764	−	14.3624i	−0.851751	−	0.491759i	−0.861241	+	0.508196i	$0.830312\pi$
$854$	11.3999	−	15.4401i	0.390096	−	0.528350i
$855$		0			0
$856$	7.13519	+	12.3585i	0.243876	+	0.422405i
$857$	20.1198	+	34.8486i	0.687280	+	1.19040i	0.972714	+	0.232006i	$0.0745288\pi$
$857$	20.1198	+	34.8486i	0.687280	+	1.19040i	−0.285434	+	0.958398i	$0.592138\pi$
$858$		0			0
$859$	−13.3256	−	7.69355i	−0.454664	−	0.262501i	0.255134	−	0.966906i	$-0.417881\pi$
$859$	−13.3256	−	7.69355i	−0.454664	−	0.262501i	−0.709798	+	0.704405i	$0.751214\pi$
$860$	−0.245910	−	0.425929i	−0.00838547	−	0.0145241i
$861$		0			0
$862$	−4.68159	+	8.10874i	−0.159455	+	0.276185i
$863$	−16.6494	+	9.61252i	−0.566751	+	0.327214i	−0.755851	−	0.654744i	$-0.772776\pi$
$863$	−16.6494	+	9.61252i	−0.566751	+	0.327214i	0.189099	+	0.981958i	$0.439443\pi$
$864$		0			0
$865$	−2.08655	+	3.61400i	−0.0709447	+	0.122880i
$866$	21.0373			0.714876
$867$		0			0
$868$	−21.2914	−	15.7200i	−0.722676	−	0.533572i
$869$	−17.7386	+	10.2414i	−0.601742	+	0.347416i
$870$		0			0
$871$	−7.30552	+	4.21785i	−0.247538	+	0.142916i
$872$	4.58271	+	2.64583i	0.155190	+	0.0895991i
$873$		0			0
$874$			4.71727i			0.159564i
$875$	13.0010	−	17.6087i	0.439514	−	0.595283i
$876$		0			0
$877$	5.39035	−	9.33636i	0.182019	−	0.315267i	−0.760549	−	0.649281i	$-0.775070\pi$
$877$	5.39035	−	9.33636i	0.182019	−	0.315267i	0.942568	+	0.334014i	$0.108403\pi$
$878$	−20.4229			−0.689238
$879$		0			0
$880$		−	2.81608i		−	0.0949302i
$881$	44.2875			1.49208			0.746041	−	0.665900i	$-0.231952\pi$
$881$	44.2875			1.49208			0.746041	+	0.665900i	$0.231952\pi$
$882$		0			0
$883$	−47.6098			−1.60220			−0.801098	−	0.598533i	$-0.795751\pi$
$883$	−47.6098			−1.60220			−0.801098	+	0.598533i	$0.795751\pi$
$884$		−	11.8423i		−	0.398298i
$885$		0			0
$886$	32.3649			1.08732
$887$	−0.989965	+	1.71467i	−0.0332398	+	0.0575730i	−0.882167	−	0.470937i	$-0.843916\pi$
$887$	−0.989965	+	1.71467i	−0.0332398	+	0.0575730i	0.848927	+	0.528510i	$0.177249\pi$
$888$		0			0
$889$	9.59541	−	12.9961i	0.321820	−	0.435876i
$890$		−	10.8075i		−	0.362268i
$891$		0			0
$892$	−2.21609	−	1.27946i	−0.0742001	−	0.0428395i
$893$	−18.7172	+	10.8064i	−0.626346	+	0.361621i
$894$		0			0
$895$	4.73405	−	2.73320i	0.158242	−	0.0913609i
$896$	−2.12847	−	1.57151i	−0.0711071	−	0.0525003i
$897$		0			0
$898$	21.5693			0.719776
$899$	−10.7184	+	18.5649i	−0.357480	+	0.619173i
$900$		0			0
$901$	62.2109	−	35.9175i	2.07255	−	1.19659i
$902$	3.82045	−	6.61721i	0.127207	−	0.220329i
$903$		0			0
$904$	−1.33005	−	2.30371i	−0.0442368	−	0.0766204i
$905$	5.55654	+	3.20807i	0.184706	+	0.106640i
$906$		0			0
$907$	−17.0252	−	29.4886i	−0.565314	−	0.979152i	−0.997020	−	0.0771381i	$-0.975422\pi$
$907$	−17.0252	−	29.4886i	−0.565314	−	0.979152i	0.431707	−	0.902014i	$-0.357912\pi$
$908$	−4.36455	−	7.55962i	−0.144843	−	0.250875i
$909$		0			0
$910$	−3.25146	+	4.40381i	−0.107785	+	0.145985i
$911$	6.58371	+	3.80111i	0.218128	+	0.125936i	0.605083	−	0.796162i	$-0.293140\pi$
$911$	6.58371	+	3.80111i	0.218128	+	0.125936i	−0.386955	+	0.922099i	$0.626473\pi$
$912$		0			0
$913$			1.15387i			0.0381875i
$914$			21.0700i			0.696932i
$915$		0			0
$916$	3.40979	+	1.96865i	0.112663	+	0.0650459i
$917$	−8.41556	−	19.2987i	−0.277906	−	0.637300i
$918$		0			0
$919$	−4.11136	−	7.12109i	−0.135621	−	0.234903i	0.790213	−	0.612832i	$-0.209970\pi$
$919$	−4.11136	−	7.12109i	−0.135621	−	0.234903i	−0.925835	+	0.377929i	$0.876636\pi$
$920$	−0.772286	−	1.33764i	−0.0254615	−	0.0441006i
$921$		0			0
$922$	−27.4378	−	15.8412i	−0.903617	−	0.521704i
$923$	−16.2582	−	28.1601i	−0.535146	−	0.926900i
$924$		0			0
$925$	19.8459	−	34.3741i	0.652529	−	1.13021i
$926$	−7.62202	+	4.40058i	−0.250475	+	0.144612i
$927$		0			0
$928$	−1.07151	+	1.85590i	−0.0351739	+	0.0609230i
$929$	−5.07963			−0.166657			−0.0833287	−	0.996522i	$-0.526555\pi$
$929$	−5.07963			−0.166657			−0.0833287	+	0.996522i	$0.526555\pi$
$930$		0			0
$931$	−14.1035	−	13.0962i	−0.462225	−	0.429210i
$932$	−3.92147	+	2.26406i	−0.128452	+	0.0741618i
$933$		0			0
$934$	16.4449	−	9.49444i	0.538092	−	0.310668i
$935$	−12.5665	−	7.25530i	−0.410970	−	0.237274i
$936$		0			0
$937$			10.8127i			0.353236i	0.984280	+	0.176618i	$0.0565157\pi$
$937$			10.8127i			0.353236i	−0.984280	+	0.176618i	$0.943484\pi$
$938$	7.81254	+	5.76822i	0.255089	+	0.188339i
$939$		0			0
$940$	3.53832	−	6.12855i	0.115407	−	0.199891i
$941$	19.1639			0.624724			0.312362	−	0.949963i	$-0.398880\pi$
$941$	19.1639			0.624724			0.312362	+	0.949963i	$0.398880\pi$
$942$		0			0
$943$		−	4.19090i		−	0.136474i
$944$	−7.98443			−0.259871
$945$		0			0
$946$	−1.70891			−0.0555613
$947$			25.3953i			0.825237i	0.910904	+	0.412618i	$0.135386\pi$
$947$			25.3953i			0.825237i	−0.910904	+	0.412618i	$0.864614\pi$
$948$		0			0
$949$	28.9766			0.940620
$950$	−5.75950	+	9.97575i	−0.186863	+	0.323656i
$951$		0			0
$952$	−12.4964	+	5.44931i	−0.405012	+	0.176613i
$953$		−	18.4818i		−	0.598686i	−0.954146	−	0.299343i	$-0.903233\pi$
$953$		−	18.4818i		−	0.598686i	0.954146	−	0.299343i	$-0.0967674\pi$
$954$		0			0
$955$	11.2274	+	6.48215i	0.363310	+	0.209757i
$956$	−7.55315	+	4.36081i	−0.244286	+	0.141039i
$957$		0			0
$958$	20.9060	−	12.0701i	0.675441	−	0.389966i
$959$	−6.48060	+	57.4185i	−0.209270	+	1.85414i
$960$		0			0
$961$	−69.0630			−2.22784
$962$	−10.8868	+	18.8565i	−0.351004	+	0.607957i
$963$		0			0
$964$	17.1314	−	9.89079i	0.551764	−	0.318561i
$965$	8.01745	−	13.8866i	0.258091	−	0.447026i
$966$		0			0
$967$	−9.64551	−	16.7065i	−0.310179	−	0.537245i	0.668222	−	0.743962i	$-0.267056\pi$
$967$	−9.64551	−	16.7065i	−0.310179	−	0.537245i	−0.978401	+	0.206717i	$0.933722\pi$
$968$	1.05229	+	0.607537i	0.0338217	+	0.0195270i
$969$		0			0
$970$	4.60935	+	7.98362i	0.147997	+	0.256339i
$971$	0.975444	+	1.68952i	0.0313035	+	0.0542192i	0.881253	−	0.472645i	$-0.156701\pi$
$971$	0.975444	+	1.68952i	0.0313035	+	0.0542192i	−0.849949	+	0.526865i	$0.823367\pi$
$972$		0			0
$973$	−4.01256	+	35.5515i	−0.128637	+	1.13973i
$974$	12.2204	+	7.05542i	0.391565	+	0.226070i
$975$		0			0
$976$		−	7.25411i		−	0.232198i
$977$		−	16.7265i		−	0.535129i	−0.963540	−	0.267564i	$-0.913781\pi$
$977$		−	16.7265i		−	0.535129i	0.963540	−	0.267564i	$-0.0862188\pi$
$978$		0			0
$979$	−32.5213	−	18.7762i	−1.03938	−	0.600089i
$980$	6.14327	+	1.40463i	0.196240	+	0.0448691i
$981$		0			0
$982$	10.8740	+	18.8344i	0.347004	+	0.601028i
$983$	16.1458	+	27.9653i	0.514970	+	0.891955i	0.999849	+	0.0173733i	$0.00553037\pi$
$983$	16.1458	+	27.9653i	0.514970	+	0.891955i	−0.484879	+	0.874581i	$0.661136\pi$
$984$		0			0
$985$	−14.8932	−	8.59858i	−0.474536	−	0.273974i
$986$	5.52121	+	9.56302i	0.175831	+	0.304549i
$987$		0			0
$988$	3.15947	−	5.47236i	0.100516	−	0.174099i
$989$	−0.811730	+	0.468652i	−0.0258115	+	0.0149023i
$990$		0			0
$991$	4.25134	−	7.36353i	0.135048	−	0.233910i	−0.790568	−	0.612375i	$-0.790214\pi$
$991$	4.25134	−	7.36353i	0.135048	−	0.233910i	0.925616	+	0.378464i	$0.123548\pi$
$992$	−10.0032			−0.317600
$993$		0			0
$994$	−22.2343	+	30.1144i	−0.705231	+	0.955172i
$995$	10.4437	−	6.02967i	0.331087	−	0.191153i
$996$		0			0
$997$	9.78395	−	5.64877i	0.309861	−	0.178898i	−0.337003	−	0.941503i	$-0.609413\pi$
$997$	9.78395	−	5.64877i	0.309861	−	0.178898i	0.646864	+	0.762605i	$0.276080\pi$
$998$	7.29596	+	4.21233i	0.230950	+	0.133339i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.l.a.143.7		16
3.2	odd	2		126.2.l.a.101.4	yes	16
4.3	odd	2		3024.2.ca.c.2033.6		16
7.2	even	3		2646.2.t.b.1979.6		16
7.3	odd	6		2646.2.m.a.1763.2		16
7.4	even	3		2646.2.m.b.1763.3		16
7.5	odd	6		378.2.t.a.89.7		16
7.6	odd	2		2646.2.l.a.521.6		16
9.2	odd	6		1134.2.k.a.647.2		16
9.4	even	3		126.2.t.a.59.3	yes	16
9.5	odd	6		378.2.t.a.17.7		16
9.7	even	3		1134.2.k.b.647.7		16
12.11	even	2		1008.2.ca.c.353.1		16
21.2	odd	6		882.2.t.a.803.2		16
21.5	even	6		126.2.t.a.47.3	yes	16
21.11	odd	6		882.2.m.b.587.5		16
21.17	even	6		882.2.m.a.587.8		16
21.20	even	2		882.2.l.b.227.1		16
28.19	even	6		3024.2.df.c.1601.6		16
36.23	even	6		3024.2.df.c.17.6		16
36.31	odd	6		1008.2.df.c.689.4		16
63.4	even	3		882.2.m.a.293.8		16
63.5	even	6	inner	378.2.l.a.341.3		16
63.13	odd	6		882.2.t.a.815.2		16
63.23	odd	6		2646.2.l.a.1097.2		16
63.31	odd	6		882.2.m.b.293.5		16
63.32	odd	6		2646.2.m.a.881.2		16
63.40	odd	6		126.2.l.a.5.8	✓	16
63.41	even	6		2646.2.t.b.2285.6		16
63.47	even	6		1134.2.k.b.971.7		16
63.58	even	3		882.2.l.b.509.5		16
63.59	even	6		2646.2.m.b.881.3		16
63.61	odd	6		1134.2.k.a.971.2		16
84.47	odd	6		1008.2.df.c.929.4		16
252.103	even	6		1008.2.ca.c.257.1		16
252.131	odd	6		3024.2.ca.c.2609.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.8	✓	16	63.40	odd	6
126.2.l.a.101.4	yes	16	3.2	odd	2
126.2.t.a.47.3	yes	16	21.5	even	6
126.2.t.a.59.3	yes	16	9.4	even	3
378.2.l.a.143.7		16	1.1	even	1	trivial
378.2.l.a.341.3		16	63.5	even	6	inner
378.2.t.a.17.7		16	9.5	odd	6
378.2.t.a.89.7		16	7.5	odd	6
882.2.l.b.227.1		16	21.20	even	2
882.2.l.b.509.5		16	63.58	even	3
882.2.m.a.293.8		16	63.4	even	3
882.2.m.a.587.8		16	21.17	even	6
882.2.m.b.293.5		16	63.31	odd	6
882.2.m.b.587.5		16	21.11	odd	6
882.2.t.a.803.2		16	21.2	odd	6
882.2.t.a.815.2		16	63.13	odd	6
1008.2.ca.c.257.1		16	252.103	even	6
1008.2.ca.c.353.1		16	12.11	even	2
1008.2.df.c.689.4		16	36.31	odd	6
1008.2.df.c.929.4		16	84.47	odd	6
1134.2.k.a.647.2		16	9.2	odd	6
1134.2.k.a.971.2		16	63.61	odd	6
1134.2.k.b.647.7		16	9.7	even	3
1134.2.k.b.971.7		16	63.47	even	6
2646.2.l.a.521.6		16	7.6	odd	2
2646.2.l.a.1097.2		16	63.23	odd	6
2646.2.m.a.881.2		16	63.32	odd	6
2646.2.m.a.1763.2		16	7.3	odd	6
2646.2.m.b.881.3		16	63.59	even	6
2646.2.m.b.1763.3		16	7.4	even	3
2646.2.t.b.1979.6		16	7.2	even	3
2646.2.t.b.2285.6		16	63.41	even	6
3024.2.ca.c.2033.6		16	4.3	odd	2
3024.2.ca.c.2609.6		16	252.131	odd	6
3024.2.df.c.17.6		16	36.23	even	6
3024.2.df.c.1601.6		16	28.19	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(0.450129 - 0.779646i) q^{5} +(1.57151 - 2.12847i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(0.450129 - 0.779646i) q^{5} +(1.57151 - 2.12847i) q^{7} -1.00000i q^{8} +(0.779646 + 0.450129i) q^{10} +(2.70900 - 1.56404i) q^{11} +(-1.99033 + 1.14912i) q^{13} +(2.12847 + 1.57151i) q^{14} +1.00000 q^{16} +(2.57638 - 4.46242i) q^{17} +(2.38111 - 1.37474i) q^{19} +(-0.450129 + 0.779646i) q^{20} +(1.56404 + 2.70900i) q^{22} +(1.48584 + 0.857850i) q^{23} +(2.09477 + 3.62824i) q^{25} +(-1.14912 - 1.99033i) q^{26} +(-1.57151 + 2.12847i) q^{28} +(1.85590 + 1.07151i) q^{29} +10.0032i q^{31} +1.00000i q^{32} +(4.46242 + 2.57638i) q^{34} +(-0.952070 - 2.18330i) q^{35} +(-4.73701 - 8.20475i) q^{37} +(1.37474 + 2.38111i) q^{38} +(-0.779646 - 0.450129i) q^{40} +(-1.22134 - 2.11542i) q^{41} +(-0.273155 + 0.473119i) q^{43} +(-2.70900 + 1.56404i) q^{44} +(-0.857850 + 1.48584i) q^{46} -7.86068 q^{47} +(-2.06074 - 6.68980i) q^{49} +(-3.62824 + 2.09477i) q^{50} +(1.99033 - 1.14912i) q^{52} +(12.0733 + 6.97054i) q^{53} -2.81608i q^{55} +(-2.12847 - 1.57151i) q^{56} +(-1.07151 + 1.85590i) q^{58} -7.98443 q^{59} -7.25411i q^{61} -10.0032 q^{62} -1.00000 q^{64} +2.06901i q^{65} +3.67050 q^{67} +(-2.57638 + 4.46242i) q^{68} +(2.18330 - 0.952070i) q^{70} +14.1484i q^{71} +(-10.9190 - 6.30409i) q^{73} +(8.20475 - 4.73701i) q^{74} +(-2.38111 + 1.37474i) q^{76} +(0.928202 - 8.22392i) q^{77} -6.54804 q^{79} +(0.450129 - 0.779646i) q^{80} +(2.11542 - 1.22134i) q^{82} +(-0.184437 + 0.319454i) q^{83} +(-2.31940 - 4.01733i) q^{85} +(-0.473119 - 0.273155i) q^{86} +(-1.56404 - 2.70900i) q^{88} +(-6.00244 - 10.3965i) q^{89} +(-0.681960 + 6.04220i) q^{91} +(-1.48584 - 0.857850i) q^{92} -7.86068i q^{94} -2.47523i q^{95} +(8.86815 + 5.12003i) q^{97} +(6.68980 - 2.06074i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 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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