LMFDB - Embedded newform 1134.2.k.a.647.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(647,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("1134.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.k (of order $6$, degree $2$, 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:	$9.05503558921$
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			647.2
Root			$1.58110 - 0.707199i$ of defining polynomial
Character	$\chi$	$=$	1134.647
Dual form			1134.2.k.a.971.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.450129 - 0.779646i) q^{5} +(-2.62906 - 0.296732i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.450129 - 0.779646i) q^{5} +(-2.62906 - 0.296732i) q^{7} +1.00000i q^{8} +(0.779646 + 0.450129i) q^{10} +(2.70900 + 1.56404i) q^{11} -2.29824i q^{13} +(2.42520 - 1.05755i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.57638 + 4.46242i) q^{17} +(2.38111 - 1.37474i) q^{19} -0.900258 q^{20} -3.12809 q^{22} +(1.48584 - 0.857850i) q^{23} +(2.09477 - 3.62824i) q^{25} +(1.14912 + 1.99033i) q^{26} +(-1.57151 + 2.12847i) q^{28} +2.14301i q^{29} +(-8.66298 - 5.00158i) q^{31} +(0.866025 + 0.500000i) q^{32} -5.15276i q^{34} +(0.952070 + 2.18330i) q^{35} +(-4.73701 - 8.20475i) q^{37} +(-1.37474 + 2.38111i) q^{38} +(0.779646 - 0.450129i) q^{40} -2.44268 q^{41} +0.546311 q^{43} +(2.70900 - 1.56404i) q^{44} +(-0.857850 + 1.48584i) q^{46} +(-3.93034 - 6.80755i) q^{47} +(6.82390 + 1.56025i) q^{49} +4.18954i q^{50} +(-1.99033 - 1.14912i) q^{52} +(-12.0733 - 6.97054i) q^{53} -2.81608i q^{55} +(0.296732 - 2.62906i) q^{56} +(-1.07151 - 1.85590i) q^{58} +(-3.99222 + 6.91472i) q^{59} +(-6.28224 + 3.62705i) q^{61} +10.0032 q^{62} -1.00000 q^{64} +(-1.79181 + 1.03450i) q^{65} +(-1.83525 + 3.17875i) q^{67} +(2.57638 + 4.46242i) q^{68} +(-1.91617 - 1.41476i) q^{70} -14.1484i q^{71} +(-10.9190 - 6.30409i) q^{73} +(8.20475 + 4.73701i) q^{74} -2.74947i q^{76} +(-6.65803 - 4.91581i) q^{77} +(3.27402 + 5.67077i) q^{79} +(-0.450129 + 0.779646i) q^{80} +(2.11542 - 1.22134i) q^{82} -0.368874 q^{83} +4.63881 q^{85} +(-0.473119 + 0.273155i) q^{86} +(-1.56404 + 2.70900i) q^{88} +(6.00244 + 10.3965i) q^{89} +(-0.681960 + 6.04220i) q^{91} -1.71570i q^{92} +(6.80755 + 3.93034i) q^{94} +(-2.14361 - 1.23762i) q^{95} -10.2401i q^{97} +(-6.68980 + 2.06074i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 4 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 - 4 * q^7	$ 16 q + 8 q^{4} - 4 q^{7} - 12 q^{11} - 8 q^{16} - 18 q^{17} + 6 q^{23} - 8 q^{25} + 12 q^{26} - 2 q^{28} - 6 q^{31} + 30 q^{35} - 2 q^{37} + 12 q^{41} + 4 q^{43} - 12 q^{44} + 6 q^{46} + 18 q^{47} - 2 q^{49} + 6 q^{52} - 36 q^{53} - 6 q^{56} + 6 q^{58} - 30 q^{59} + 60 q^{61} + 36 q^{62} - 16 q^{64} + 42 q^{65} + 14 q^{67} + 18 q^{68} + 18 q^{70} - 18 q^{74} + 24 q^{77} - 16 q^{79} + 24 q^{85} - 24 q^{86} - 24 q^{89} - 12 q^{91} - 66 q^{95} - 24 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 - 4 * q^7 - 12 * q^11 - 8 * q^16 - 18 * q^17 + 6 * q^23 - 8 * q^25 + 12 * q^26 - 2 * q^28 - 6 * q^31 + 30 * q^35 - 2 * q^37 + 12 * q^41 + 4 * q^43 - 12 * q^44 + 6 * q^46 + 18 * q^47 - 2 * q^49 + 6 * q^52 - 36 * q^53 - 6 * q^56 + 6 * q^58 - 30 * q^59 + 60 * q^61 + 36 * q^62 - 16 * q^64 + 42 * q^65 + 14 * q^67 + 18 * q^68 + 18 * q^70 - 18 * q^74 + 24 * q^77 - 16 * q^79 + 24 * q^85 - 24 * q^86 - 24 * q^89 - 12 * q^91 - 66 * q^95 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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
$5$	−0.450129	−	0.779646i	−0.201304	−	0.348668i	0.747645	−	0.664099i	$-0.231185\pi$
$5$	−0.450129	−	0.779646i	−0.201304	−	0.348668i	−0.948949	+	0.315430i	$0.897851\pi$
$6$		0			0
$7$	−2.62906	−	0.296732i	−0.993691	−	0.112154i
$7$	−2.62906	−	0.296732i	−0.993691	−	0.112154i
$8$			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	0.849310	−	0.527894i	$-0.177018\pi$
$11$	2.70900	+	1.56404i	0.816795	+	0.471577i	−0.0325150	+	0.999471i	$0.510352\pi$
$12$		0			0
$13$		−	2.29824i		−	0.637417i	−0.947853	−	0.318708i	$-0.896751\pi$
$13$		−	2.29824i		−	0.637417i	0.947853	−	0.318708i	$-0.103249\pi$
$14$	2.42520	−	1.05755i	0.648161	−	0.282643i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.57638	+	4.46242i	−0.624863	+	1.08230i	0.363704	+	0.931515i	$0.381512\pi$
$17$	−2.57638	+	4.46242i	−0.624863	+	1.08230i	−0.988567	+	0.150780i	$0.951821\pi$
$18$		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	$0.231199\pi$
$20$	−0.900258			−0.201304
$21$		0			0
$22$	−3.12809			−0.666910
$23$	1.48584	−	0.857850i	0.309819	−	0.178874i	−0.337027	−	0.941495i	$-0.609421\pi$
$23$	1.48584	−	0.857850i	0.309819	−	0.178874i	0.646845	+	0.762621i	$0.276088\pi$
$24$		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
$29$			2.14301i			0.397948i	0.980005	+	0.198974i	$0.0637609\pi$
$29$			2.14301i			0.397948i	−0.980005	+	0.198974i	$0.936239\pi$
$30$		0			0
$31$	−8.66298	−	5.00158i	−1.55592	−	0.898309i	−0.997640	−	0.0686548i	$-0.978129\pi$
$31$	−8.66298	−	5.00158i	−1.55592	−	0.898309i	−0.558277	−	0.829655i	$-0.688537\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$		−	5.15276i		−	0.883690i
$35$	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
$41$	−2.44268			−0.381482			−0.190741	−	0.981640i	$-0.561089\pi$
$41$	−2.44268			−0.381482			−0.190741	+	0.981640i	$0.561089\pi$
$42$		0			0
$43$	0.546311			0.0833116			0.0416558	−	0.999132i	$-0.486737\pi$
$43$	0.546311			0.0833116			0.0416558	+	0.999132i	$0.486737\pi$
$44$	2.70900	−	1.56404i	0.408397	−	0.235788i
$45$		0			0
$46$	−0.857850	+	1.48584i	−0.126483	+	0.219075i
$47$	−3.93034	−	6.80755i	−0.573299	−	0.992983i	−0.996224	−	0.0868184i	$-0.972330\pi$
$47$	−3.93034	−	6.80755i	−0.573299	−	0.992983i	0.422925	−	0.906165i	$-0.361003\pi$
$48$		0			0
$49$	6.82390	+	1.56025i	0.974843	+	0.222893i
$50$			4.18954i			0.592490i
$51$		0			0
$52$	−1.99033	−	1.14912i	−0.276009	−	0.159354i
$53$	−12.0733	−	6.97054i	−1.65840	−	0.957478i	−0.973454	−	0.228885i	$-0.926492\pi$
$53$	−12.0733	−	6.97054i	−1.65840	−	0.957478i	−0.684947	−	0.728593i	$-0.740175\pi$
$54$		0			0
$55$		−	2.81608i		−	0.379721i
$56$	0.296732	−	2.62906i	0.0396524	−	0.351323i
$57$		0			0
$58$	−1.07151	−	1.85590i	−0.140696	−	0.243692i
$59$	−3.99222	+	6.91472i	−0.519742	+	0.900220i	0.479994	+	0.877272i	$0.340639\pi$
$59$	−3.99222	+	6.91472i	−0.519742	+	0.900220i	−0.999737	+	0.0229484i	$0.992695\pi$
$60$		0			0
$61$	−6.28224	+	3.62705i	−0.804359	+	0.464397i	−0.844993	−	0.534777i	$-0.820395\pi$
$61$	−6.28224	+	3.62705i	−0.804359	+	0.464397i	0.0406343	+	0.999174i	$0.487062\pi$
$62$	10.0032			1.27040
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.79181	+	1.03450i	−0.222247	+	0.128314i
$66$		0			0
$67$	−1.83525	+	3.17875i	−0.224212	+	0.388346i	−0.956083	−	0.293097i	$-0.905314\pi$
$67$	−1.83525	+	3.17875i	−0.224212	+	0.388346i	0.731871	+	0.681443i	$0.238647\pi$
$68$	2.57638	+	4.46242i	0.312432	+	0.541148i
$69$		0			0
$70$	−1.91617	−	1.41476i	−0.229026	−	0.169096i
$71$		−	14.1484i		−	1.67911i	−0.543275	−	0.839555i	$-0.682816\pi$
$71$		−	14.1484i		−	1.67911i	0.543275	−	0.839555i	$-0.317184\pi$
$72$		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
$76$		−	2.74947i		−	0.315386i
$77$	−6.65803	−	4.91581i	−0.758752	−	0.560208i
$78$		0			0
$79$	3.27402	+	5.67077i	0.368356	+	0.638011i	0.989309	−	0.145837i	$-0.0465875\pi$
$79$	3.27402	+	5.67077i	0.368356	+	0.638011i	−0.620953	+	0.783848i	$0.713254\pi$
$80$	−0.450129	+	0.779646i	−0.0503259	+	0.0871671i
$81$		0			0
$82$	2.11542	−	1.22134i	0.233609	−	0.134874i
$83$	−0.368874			−0.0404891			−0.0202446	−	0.999795i	$-0.506444\pi$
$83$	−0.368874			−0.0404891			−0.0202446	+	0.999795i	$0.506444\pi$
$84$		0			0
$85$	4.63881			0.503149
$86$	−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	$0.0528518\pi$
$89$	6.00244	+	10.3965i	0.636258	+	1.10203i	−0.349990	+	0.936754i	$0.613815\pi$
$90$		0			0
$91$	−0.681960	+	6.04220i	−0.0714888	+	0.633395i
$92$		−	1.71570i		−	0.178874i
$93$		0			0
$94$	6.80755	+	3.93034i	0.702145	+	0.405384i
$95$	−2.14361	−	1.23762i	−0.219930	−	0.126977i
$96$		0			0
$97$		−	10.2401i		−	1.03972i	−0.854251	−	0.519860i	$-0.825984\pi$
$97$		−	10.2401i		−	1.03972i	0.854251	−	0.519860i	$-0.174016\pi$
$98$	−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	$-0.876531\pi$
$101$	−1.35969	+	2.35506i	−0.135294	+	0.234337i	0.790415	+	0.612571i	$0.209865\pi$
$102$		0			0
$103$	−1.18861	+	0.686242i	−0.117117	+	0.0676174i	−0.557414	−	0.830235i	$-0.688206\pi$
$103$	−1.18861	+	0.686242i	−0.117117	+	0.0676174i	0.440297	+	0.897852i	$0.354873\pi$
$104$	2.29824			0.225361
$105$		0			0
$106$	13.9411			1.35408
$107$	12.3585	−	7.13519i	1.19474	−	0.689785i	0.235364	−	0.971907i	$-0.424372\pi$
$107$	12.3585	−	7.13519i	1.19474	−	0.689785i	0.959378	+	0.282122i	$0.0910385\pi$
$108$		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	$0.248224\pi$
$110$	1.40804	+	2.43880i	0.134252	+	0.232531i
$111$		0			0
$112$	1.05755	+	2.42520i	0.0999293	+	0.229160i
$113$		−	2.66010i		−	0.250241i	−0.992142	−	0.125121i	$-0.960068\pi$
$113$		−	2.66010i		−	0.250241i	0.992142	−	0.125121i	$-0.0399318\pi$
$114$		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
$119$	8.09759	−	10.9675i	0.742305	−	1.00539i
$120$		0			0
$121$	−0.607537	−	1.05229i	−0.0552307	−	0.0956623i
$122$	3.62705	−	6.28224i	0.328378	−	0.568767i
$123$		0			0
$124$	−8.66298	+	5.00158i	−0.777959	+	0.449155i
$125$	−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	$0.412677\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	1.03450	−	1.79181i	0.0907320	−	0.157152i
$131$	−3.97879	−	6.89147i	−0.347629	−	0.602111i	0.638199	−	0.769871i	$-0.279680\pi$
$131$	−3.97879	−	6.89147i	−0.347629	−	0.602111i	−0.985828	+	0.167761i	$0.946346\pi$
$132$		0			0
$133$	−6.66801	+	2.90771i	−0.578190	+	0.252130i
$134$		−	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	−0.987958	−	0.154719i	$-0.950553\pi$
$137$	−18.9140	−	10.9200i	−1.61593	−	0.932957i	−0.627970	−	0.778237i	$-0.716114\pi$
$138$		0			0
$139$		−	13.5225i		−	1.14697i	−0.819217	−	0.573483i	$-0.805592\pi$
$139$		−	13.5225i		−	1.14697i	0.819217	−	0.573483i	$-0.194408\pi$
$140$	2.36683	+	0.267135i	0.200034	+	0.0225770i
$141$		0			0
$142$	7.07421	+	12.2529i	0.593655	+	1.02824i
$143$	3.59454	−	6.22593i	0.300591	−	0.520639i
$144$		0			0
$145$	1.67079	−	0.964632i	0.138752	−	0.0801083i
$146$	12.6082			1.04346
$147$		0			0
$148$	−9.47403			−0.778760
$149$	4.41192	−	2.54722i	0.361438	−	0.208676i	−0.308273	−	0.951298i	$-0.599751\pi$
$149$	4.41192	−	2.54722i	0.361438	−	0.208676i	0.669711	+	0.742621i	$0.266418\pi$
$150$		0			0
$151$	10.5877	−	18.3385i	0.861618	−	1.49237i	−0.00874783	−	0.999962i	$-0.502785\pi$
$151$	10.5877	−	18.3385i	0.861618	−	1.49237i	0.870366	−	0.492405i	$-0.163882\pi$
$152$	1.37474	+	2.38111i	0.111506	+	0.193134i
$153$		0			0
$154$	8.22392	+	0.928202i	0.662703	+	0.0747966i
$155$			9.00541i			0.723332i
$156$		0			0
$157$	0.311703	+	0.179962i	0.0248766	+	0.0143625i	0.512387	−	0.858755i	$-0.328761\pi$
$157$	0.311703	+	0.179962i	0.0248766	+	0.0143625i	−0.487510	+	0.873117i	$0.662095\pi$
$158$	−5.67077	−	3.27402i	−0.451142	−	0.260467i
$159$		0			0
$160$		−	0.900258i		−	0.0711716i
$161$	−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
$167$	14.8173			1.14660			0.573299	−	0.819346i	$-0.305663\pi$
$167$	14.8173			1.14660			0.573299	+	0.819346i	$0.305663\pi$
$168$		0			0
$169$	7.71810			0.593700
$170$	−4.01733	+	2.31940i	−0.308115	+	0.177890i
$171$		0			0
$172$	0.273155	−	0.473119i	0.0208279	−	0.0360750i
$173$	−2.31772	−	4.01441i	−0.176213	−	0.305210i	0.764367	−	0.644781i	$-0.223051\pi$
$173$	−2.31772	−	4.01441i	−0.176213	−	0.305210i	−0.940580	+	0.339571i	$0.889718\pi$
$174$		0			0
$175$	−6.58388	+	8.91728i	−0.497695	+	0.674083i
$176$		−	3.12809i		−	0.235788i
$177$		0			0
$178$	−10.3965	−	6.00244i	−0.779253	−	0.449902i
$179$	−5.25855	−	3.03602i	−0.393042	−	0.226923i	0.290435	−	0.956895i	$-0.406200\pi$
$179$	−5.25855	−	3.03602i	−0.393042	−	0.226923i	−0.683477	+	0.729972i	$0.739533\pi$
$180$		0			0
$181$			7.12701i			0.529746i	0.964283	+	0.264873i	$0.0853301\pi$
$181$			7.12701i			0.529746i	−0.964283	+	0.264873i	$0.914670\pi$
$182$	−2.43051	−	5.57368i	−0.180161	−	0.413149i
$183$		0			0
$184$	0.857850	+	1.48584i	0.0632415	+	0.109538i
$185$	−4.26453	+	7.38639i	−0.313535	+	0.543058i
$186$		0			0
$187$	−13.9588	+	8.05913i	−1.02077	+	0.589342i
$188$	−7.86068			−0.573299
$189$		0			0
$190$	2.47523			0.179572
$191$	−12.4713	+	7.20032i	−0.902394	+	0.520997i	−0.877976	−	0.478705i	$-0.841106\pi$
$191$	−12.4713	+	7.20032i	−0.902394	+	0.520997i	−0.0244176	+	0.999702i	$0.507773\pi$
$192$		0			0
$193$	−8.90573	+	15.4252i	−0.641048	+	1.11033i	0.344151	+	0.938914i	$0.388167\pi$
$193$	−8.90573	+	15.4252i	−0.641048	+	1.11033i	−0.985199	+	0.171414i	$0.945166\pi$
$194$	5.12003	+	8.86815i	0.367597	+	0.636696i
$195$		0			0
$196$	4.76317	−	5.12955i	0.340226	−	0.366396i
$197$			19.1025i			1.36100i	0.732750	+	0.680498i	$0.238236\pi$
$197$			19.1025i			1.36100i	−0.732750	+	0.680498i	$0.761764\pi$
$198$		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
$202$		−	2.71939i		−	0.191335i
$203$	0.635899	−	5.63411i	0.0446314	−	0.395437i
$204$		0			0
$205$	1.09952	+	1.90442i	0.0767937	+	0.133011i
$206$	0.686242	−	1.18861i	0.0478127	−	0.0828141i
$207$		0			0
$208$	−1.99033	+	1.14912i	−0.138005	+	0.0796771i
$209$	8.60058			0.594915
$210$		0			0
$211$	18.7439			1.29038			0.645190	−	0.764022i	$-0.276778\pi$
$211$	18.7439			1.29038			0.645190	+	0.764022i	$0.276778\pi$
$212$	−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
$218$		−	5.29166i		−	0.358396i
$219$		0			0
$220$	−2.43880	−	1.40804i	−0.164424	−	0.0949302i
$221$	10.2557	+	5.92113i	0.689873	+	0.398298i
$222$		0			0
$223$		−	2.55892i		−	0.171358i	−0.996323	−	0.0856789i	$-0.972694\pi$
$223$		−	2.55892i		−	0.171358i	0.996323	−	0.0856789i	$-0.0273059\pi$
$224$	−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	$-0.926884\pi$
$227$	−4.36455	+	7.55962i	−0.289685	+	0.501749i	0.684049	+	0.729436i	$0.260217\pi$
$228$		0			0
$229$	3.40979	−	1.96865i	0.225325	−	0.130092i	−0.383088	−	0.923712i	$-0.625139\pi$
$229$	3.40979	−	1.96865i	0.225325	−	0.130092i	0.608414	+	0.793620i	$0.291806\pi$
$230$	1.54457			0.101846
$231$		0			0
$232$	−2.14301			−0.140696
$233$	−3.92147	+	2.26406i	−0.256904	+	0.148324i	−0.622921	−	0.782284i	$-0.714054\pi$
$233$	−3.92147	+	2.26406i	−0.256904	+	0.148324i	0.366018	+	0.930608i	$0.380721\pi$
$234$		0			0
$235$	−3.53832	+	6.12855i	−0.230815	+	0.399782i
$236$	3.99222	+	6.91472i	0.259871	+	0.450110i
$237$		0			0
$238$	−1.52898	+	13.5469i	−0.0991094	+	0.878115i
$239$		−	8.72163i		−	0.564155i	−0.959392	−	0.282078i	$-0.908976\pi$
$239$		−	8.72163i		−	0.564155i	0.959392	−	0.282078i	$-0.0910235\pi$
$240$		0			0
$241$	17.1314	+	9.89079i	1.10353	+	0.637122i	0.937145	−	0.348939i	$-0.113458\pi$
$241$	17.1314	+	9.89079i	1.10353	+	0.637122i	0.166382	+	0.986061i	$0.446791\pi$
$242$	1.05229	+	0.607537i	0.0676435	+	0.0390540i
$243$		0			0
$244$			7.25411i			0.464397i
$245$	−1.85519	−	6.02254i	−0.118524	−	0.384766i
$246$		0			0
$247$	−3.15947	−	5.47236i	−0.201032	−	0.348198i
$248$	5.00158	−	8.66298i	0.317600	−	0.550100i
$249$		0			0
$250$	7.16459	−	4.13648i	0.453128	−	0.261614i
$251$	3.80791			0.240353			0.120176	−	0.992753i	$-0.461654\pi$
$251$	3.80791			0.240353			0.120176	+	0.992753i	$0.461654\pi$
$252$		0			0
$253$	5.36686			0.337411
$254$	−5.28784	+	3.05293i	−0.331788	+	0.191558i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.53771	−	13.0557i	−0.470189	−	0.814392i	0.529230	−	0.848479i	$-0.322481\pi$
$257$	−7.53771	−	13.0557i	−0.470189	−	0.814392i	−0.999419	+	0.0340869i	$0.989148\pi$
$258$		0			0
$259$	10.0193	+	22.9764i	0.622568	+	1.42768i
$260$			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	0.689449	−	0.724334i	$-0.257853\pi$
$263$	6.59852	+	3.80965i	0.406882	+	0.234913i	−0.282567	+	0.959248i	$0.591186\pi$
$264$		0			0
$265$			12.5506i			0.770976i
$266$	4.32081	−	5.85215i	0.264926	−	0.358819i
$267$		0			0
$268$	1.83525	+	3.17875i	0.112106	+	0.194173i
$269$	−4.32720	+	7.49493i	−0.263834	+	0.456974i	−0.967257	−	0.253797i	$-0.918320\pi$
$269$	−4.32720	+	7.49493i	−0.263834	+	0.456974i	0.703424	+	0.710771i	$0.251654\pi$
$270$		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	$0.518423\pi$
$272$	5.15276			0.312432
$273$		0			0
$274$	21.8400			1.31940
$275$	11.3495	−	6.55262i	0.684398	−	0.395138i
$276$		0			0
$277$	−4.99073	+	8.64419i	−0.299864	+	0.519379i	−0.976105	−	0.217301i	$-0.930275\pi$
$277$	−4.99073	+	8.64419i	−0.299864	+	0.519379i	0.676241	+	0.736681i	$0.263608\pi$
$278$	6.76127	+	11.7109i	0.405514	+	0.702371i
$279$		0			0
$280$	−2.18330	+	0.952070i	−0.130477	+	0.0568971i
$281$			15.0454i			0.897536i	0.893648	+	0.448768i	$0.148137\pi$
$281$			15.0454i			0.897536i	−0.893648	+	0.448768i	$0.851863\pi$
$282$		0			0
$283$	3.48950	+	2.01467i	0.207429	+	0.119759i	0.600116	−	0.799913i	$-0.295121\pi$
$283$	3.48950	+	2.01467i	0.207429	+	0.119759i	−0.392687	+	0.919672i	$0.628454\pi$
$284$	−12.2529	−	7.07421i	−0.727076	−	0.419777i
$285$		0			0
$286$			7.18909i			0.425100i
$287$	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
$293$	−13.1922			−0.770695			−0.385347	−	0.922772i	$-0.625918\pi$
$293$	−13.1922			−0.770695			−0.385347	+	0.922772i	$0.625918\pi$
$294$		0			0
$295$	7.18805			0.418504
$296$	8.20475	−	4.73701i	0.476891	−	0.275333i
$297$		0			0
$298$	−2.54722	+	4.41192i	−0.147557	+	0.255575i
$299$	−1.97154	−	3.41481i	−0.114017	−	0.197484i
$300$		0			0
$301$	−1.43628	−	0.162108i	−0.0827859	−	0.00934372i
$302$			21.1755i			1.21851i
$303$		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	$-0.306566\pi$
$308$	−7.58623	+	3.30812i	−0.432265	+	0.188497i
$309$		0			0
$310$	−4.50271	−	7.79892i	−0.255737	−	0.442949i
$311$	−15.4228	+	26.7132i	−0.874550	+	1.51476i	−0.0173077	+	0.999850i	$0.505509\pi$
$311$	−15.4228	+	26.7132i	−0.874550	+	1.51476i	−0.857242	+	0.514914i	$0.827824\pi$
$312$		0			0
$313$	−15.9055	+	9.18304i	−0.899032	+	0.519056i	−0.876886	−	0.480698i	$-0.840383\pi$
$313$	−15.9055	+	9.18304i	−0.899032	+	0.519056i	−0.0221460	+	0.999755i	$0.507050\pi$
$314$	−0.359924			−0.0203117
$315$		0			0
$316$	6.54804			0.368356
$317$	15.1173	−	8.72800i	0.849074	−	0.490213i	−0.0112642	−	0.999937i	$-0.503586\pi$
$317$	15.1173	−	8.72800i	0.849074	−	0.490213i	0.860338	+	0.509723i	$0.170252\pi$
$318$		0			0
$319$	−3.35176	+	5.80543i	−0.187663	+	0.325042i
$320$	0.450129	+	0.779646i	0.0251630	+	0.0435835i
$321$		0			0
$322$	2.69623	−	3.65181i	0.150255	−	0.203507i
$323$			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
$328$		−	2.44268i		−	0.134874i
$329$	8.31308	+	19.0637i	0.458315	+	1.05102i
$330$		0			0
$331$	−5.21472	−	9.03216i	−0.286627	−	0.496452i	0.686375	−	0.727247i	$-0.259201\pi$
$331$	−5.21472	−	9.03216i	−0.286627	−	0.496452i	−0.973002	+	0.230795i	$0.925867\pi$
$332$	−0.184437	+	0.319454i	−0.0101223	+	0.0175323i
$333$		0			0
$334$	−12.8322	+	7.40866i	−0.702145	+	0.405384i
$335$	3.30440			0.180539
$336$		0			0
$337$	31.6624			1.72476			0.862380	−	0.506262i	$-0.168973\pi$
$337$	31.6624			1.72476			0.862380	+	0.506262i	$0.168973\pi$
$338$	−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
$344$			0.546311i			0.0294551i
$345$		0			0
$346$	4.01441	+	2.31772i	0.215816	+	0.124601i
$347$	−10.8472	−	6.26261i	−0.582306	−	0.336195i	0.179743	−	0.983714i	$-0.442473\pi$
$347$	−10.8472	−	6.26261i	−0.582306	−	0.336195i	−0.762049	+	0.647519i	$0.775807\pi$
$348$		0			0
$349$		−	14.1520i		−	0.757538i	−0.925491	−	0.378769i	$-0.876348\pi$
$349$		−	14.1520i		−	0.757538i	0.925491	−	0.378769i	$-0.123652\pi$
$350$	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	$-0.875518\pi$
$353$	−2.48267	+	4.30012i	−0.132139	+	0.228872i	0.792362	+	0.610052i	$0.208851\pi$
$354$		0			0
$355$	−11.0308	+	6.36862i	−0.585452	+	0.338011i
$356$	12.0049			0.636258
$357$		0			0
$358$	6.07205			0.320918
$359$	15.0013	−	8.66098i	0.791736	−	0.457109i	−0.0488375	−	0.998807i	$-0.515552\pi$
$359$	15.0013	−	8.66098i	0.791736	−	0.457109i	0.840573	+	0.541698i	$0.182218\pi$
$360$		0			0
$361$	−5.72021	+	9.90769i	−0.301063	+	0.521457i
$362$	−3.56350	−	6.17217i	−0.187294	−	0.324402i
$363$		0			0
$364$	4.89172	+	3.61170i	0.256396	+	0.189304i
$365$			11.3506i			0.594118i
$366$		0			0
$367$	−1.18799	−	0.685884i	−0.0620124	−	0.0358029i	0.468673	−	0.883372i	$-0.344732\pi$
$367$	−1.18799	−	0.685884i	−0.0620124	−	0.0358029i	−0.530686	+	0.847569i	$0.678066\pi$
$368$	−1.48584	−	0.857850i	−0.0774547	−	0.0447185i
$369$		0			0
$370$		−	8.52907i		−	0.443405i
$371$	29.6731	+	21.9085i	1.54055	+	1.13743i
$372$		0			0
$373$	2.40488	+	4.16537i	0.124520	+	0.215675i	0.921545	−	0.388271i	$-0.126928\pi$
$373$	2.40488	+	4.16537i	0.124520	+	0.215675i	−0.797025	+	0.603946i	$0.793594\pi$
$374$	8.05913	−	13.9588i	0.416728	−	0.721794i
$375$		0			0
$376$	6.80755	−	3.93034i	0.351073	−	0.202692i
$377$	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	$0.332398\pi$
$380$	−2.14361	+	1.23762i	−0.109965	+	0.0634884i
$381$		0			0
$382$	7.20032	−	12.4713i	0.368401	−	0.638089i
$383$	15.7349	+	27.2536i	0.804014	+	1.39259i	0.916955	+	0.398992i	$0.130640\pi$
$383$	15.7349	+	27.2536i	0.804014	+	1.39259i	−0.112940	+	0.993602i	$0.536027\pi$
$384$		0			0
$385$	−0.835621	+	7.40365i	−0.0425872	+	0.377325i
$386$		−	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	0.408068	−	0.912952i	$-0.366203\pi$
$389$	−3.52130	−	2.03303i	−0.178537	−	0.103078i	−0.586605	+	0.809873i	$0.699536\pi$
$390$		0			0
$391$			8.84058i			0.447087i
$392$	−1.56025	+	6.82390i	−0.0788045	+	0.344659i
$393$		0			0
$394$	−9.55124	−	16.5432i	−0.481185	−	0.833436i
$395$	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	$0.368611\pi$
$398$	−13.3954			−0.671452
$399$		0			0
$400$	−4.18954			−0.209477
$401$	−16.0586	+	9.27141i	−0.801926	+	0.462992i	−0.844144	−	0.536116i	$-0.819891\pi$
$401$	−16.0586	+	9.27141i	−0.801926	+	0.462992i	0.0422180	+	0.999108i	$0.486558\pi$
$402$		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
$407$		−	29.6356i		−	1.46898i
$408$		0			0
$409$	−21.5555	−	12.4451i	−1.06585	−	0.615370i	−0.138807	−	0.990319i	$-0.544327\pi$
$409$	−21.5555	−	12.4451i	−1.06585	−	0.615370i	−0.927045	+	0.374949i	$0.877660\pi$
$410$	−1.90442	−	1.09952i	−0.0940527	−	0.0543014i
$411$		0			0
$412$			1.37248i			0.0676174i
$413$	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
$419$	5.14845			0.251518			0.125759	−	0.992061i	$-0.459863\pi$
$419$	5.14845			0.251518			0.125759	+	0.992061i	$0.459863\pi$
$420$		0			0
$421$	27.0043			1.31611			0.658055	−	0.752970i	$-0.271379\pi$
$421$	27.0043			1.31611			0.658055	+	0.752970i	$0.271379\pi$
$422$	−16.2327	+	9.37193i	−0.790193	+	0.456218i
$423$		0			0
$424$	6.97054	−	12.0733i	0.338520	−	0.586333i
$425$	10.7938	+	18.6955i	0.523577	+	0.906863i
$426$		0			0
$427$	17.5926	−	7.67160i	0.851368	−	0.371255i
$428$		−	14.2704i		−	0.689785i
$429$		0			0
$430$	0.425929	+	0.245910i	0.0205401	+	0.0118588i
$431$	−8.10874	−	4.68159i	−0.390584	−	0.225504i	0.291829	−	0.956471i	$-0.405736\pi$
$431$	−8.10874	−	4.68159i	−0.390584	−	0.225504i	−0.682413	+	0.730966i	$0.739070\pi$
$432$		0			0
$433$		−	21.0373i		−	1.01099i	−0.862830	−	0.505494i	$-0.831310\pi$
$433$		−	21.0373i		−	1.01099i	0.862830	−	0.505494i	$-0.168690\pi$
$434$	−26.2989	−	2.96825i	−1.26239	−	0.142481i
$435$		0			0
$436$	2.64583	+	4.58271i	0.126712	+	0.219472i
$437$	2.35863	−	4.08527i	0.112829	−	0.195425i
$438$		0			0
$439$	17.6867	−	10.2114i	0.844141	−	0.487365i	−0.0145289	−	0.999894i	$-0.504625\pi$
$439$	17.6867	−	10.2114i	0.844141	−	0.487365i	0.858670	+	0.512530i	$0.171292\pi$
$440$	2.81608			0.134252
$441$		0			0
$442$	−11.8423			−0.563279
$443$	28.0288	−	16.1825i	1.33169	−	0.768852i	0.346131	−	0.938186i	$-0.387495\pi$
$443$	28.0288	−	16.1825i	1.33169	−	0.768852i	0.985559	+	0.169334i	$0.0541618\pi$
$444$		0			0
$445$	5.40375	−	9.35956i	0.256162	−	0.443686i
$446$	1.27946	+	2.21609i	0.0605841	+	0.104935i
$447$		0			0
$448$	2.62906	+	0.296732i	0.124211	+	0.0140192i
$449$			21.5693i			1.01792i	0.860791	+	0.508958i	$0.169969\pi$
$449$			21.5693i			1.01792i	−0.860791	+	0.508958i	$0.830031\pi$
$450$		0			0
$451$	−6.61721	−	3.82045i	−0.311592	−	0.179898i
$452$	−2.30371	−	1.33005i	−0.108358	−	0.0625603i
$453$		0			0
$454$		−	8.72909i		−	0.409677i
$455$	5.01775	−	2.18808i	0.235236	−	0.102579i
$456$		0			0
$457$	−10.5350	−	18.2471i	−0.492806	−	0.853564i	0.507160	−	0.861852i	$-0.330695\pi$
$457$	−10.5350	−	18.2471i	−0.492806	−	0.853564i	−0.999966	+	0.00828760i	$0.997362\pi$
$458$	−1.96865	+	3.40979i	−0.0919887	+	0.159329i
$459$		0			0
$460$	−1.33764	+	0.772286i	−0.0623677	+	0.0360080i
$461$	−31.6825			−1.47560			−0.737800	−	0.675019i	$-0.764135\pi$
$461$	−31.6825			−1.47560			−0.737800	+	0.675019i	$0.764135\pi$
$462$		0			0
$463$	−8.80115			−0.409024			−0.204512	−	0.978864i	$-0.565561\pi$
$463$	−8.80115			−0.409024			−0.204512	+	0.978864i	$0.565561\pi$
$464$	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	0.997639	−	0.0686693i	$-0.0218753\pi$
$467$	9.49444	+	16.4449i	0.439350	+	0.760977i	−0.558289	+	0.829646i	$0.688542\pi$
$468$		0			0
$469$	5.76822	−	7.81254i	0.266352	−	0.360750i
$470$		−	7.07664i		−	0.326421i
$471$		0			0
$472$	−6.91472	−	3.99222i	−0.318276	−	0.183757i
$473$	1.47996	+	0.854453i	0.0680485	+	0.0392878i
$474$		0			0
$475$		−	11.5190i		−	0.528528i
$476$	−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	−0.446672	−	0.894698i	$-0.647391\pi$
$479$	12.0701	−	20.9060i	0.551495	−	0.955218i	0.998167	−	0.0605197i	$-0.0192758\pi$
$480$		0			0
$481$	−18.8565	+	10.8868i	−0.859781	+	0.496395i
$482$	−19.7816			−0.901026
$483$		0			0
$484$	−1.21507			−0.0552307
$485$	−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	$0.0630806\pi$
$488$	−3.62705	−	6.28224i	−0.164189	−	0.284384i
$489$		0			0
$490$	4.61791	+	4.28808i	0.208616	+	0.193716i
$491$		−	21.7480i		−	0.981475i	−0.871307	−	0.490738i	$-0.836727\pi$
$491$		−	21.7480i		−	0.981475i	0.871307	−	0.490738i	$-0.163273\pi$
$492$		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
$497$	−4.19828	+	37.1970i	−0.188319	+	1.66852i
$498$		0			0
$499$	4.21233	+	7.29596i	0.188570	+	0.326612i	0.944774	−	0.327724i	$-0.106282\pi$
$499$	4.21233	+	7.29596i	0.188570	+	0.326612i	−0.756204	+	0.654336i	$0.772948\pi$
$500$	−4.13648	+	7.16459i	−0.184989	+	0.320410i
$501$		0			0
$502$	−3.29774	+	1.90395i	−0.147186	+	0.0849776i
$503$	−8.71316			−0.388501			−0.194250	−	0.980952i	$-0.562227\pi$
$503$	−8.71316			−0.388501			−0.194250	+	0.980952i	$0.562227\pi$
$504$		0			0
$505$	2.44815			0.108941
$506$	−4.64783	+	2.68343i	−0.206621	+	0.119293i
$507$		0			0
$508$	3.05293	−	5.28784i	0.135452	−	0.234610i
$509$	−14.9177	−	25.8382i	−0.661214	−	1.14526i	−0.980297	−	0.197530i	$-0.936708\pi$
$509$	−14.9177	−	25.8382i	−0.661214	−	1.14526i	0.319082	−	0.947727i	$-0.396625\pi$
$510$		0			0
$511$	26.8361	+	19.8138i	1.18716	+	0.876513i
$512$		−	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
$517$		−	24.5889i		−	1.08142i
$518$	−20.1652	−	14.8885i	−0.886006	−	0.654163i
$519$		0			0
$520$	−1.03450	−	1.79181i	−0.0453660	−	0.0785762i
$521$	−9.89004	+	17.1301i	−0.433291	+	0.750482i	−0.997154	−	0.0753863i	$-0.975981\pi$
$521$	−9.89004	+	17.1301i	−0.433291	+	0.750482i	0.563864	+	0.825868i	$0.309314\pi$
$522$		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	$0.419509\pi$
$524$	−7.95758			−0.347629
$525$		0			0
$526$	−7.61931			−0.332218
$527$	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
$533$			5.61385i			0.243163i
$534$		0			0
$535$	−11.1258	−	6.42351i	−0.481012	−	0.277713i
$536$	−3.17875	−	1.83525i	−0.137301	−	0.0792708i
$537$		0			0
$538$		−	8.65440i		−	0.373118i
$539$	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
$545$	4.76386			0.204061
$546$		0			0
$547$	−42.0097			−1.79621			−0.898103	−	0.439786i	$-0.855054\pi$
$547$	−42.0097			−1.79621			−0.898103	+	0.439786i	$0.855054\pi$
$548$	−18.9140	+	10.9200i	−0.807964	+	0.466478i
$549$		0			0
$550$	−6.55262	+	11.3495i	−0.279404	+	0.483943i
$551$	2.94608	+	5.10275i	0.125507	+	0.217385i
$552$		0			0
$553$	−6.92489	−	15.8803i	−0.294476	−	0.675298i
$554$		−	9.98145i		−	0.424071i
$555$		0			0
$556$	−11.7109	−	6.76127i	−0.496651	−	0.286742i
$557$	4.85612	+	2.80368i	0.205760	+	0.118796i	0.599340	−	0.800495i	$-0.295430\pi$
$557$	4.85612	+	2.80368i	0.205760	+	0.118796i	−0.393579	+	0.919291i	$0.628763\pi$
$558$		0			0
$559$		−	1.25555i		−	0.0531042i
$560$	1.41476	−	1.91617i	0.0597846	−	0.0809729i
$561$		0			0
$562$	−7.52272	−	13.0297i	−0.317327	−	0.549626i
$563$	17.5948	−	30.4751i	0.741532	−	1.28437i	−0.210266	−	0.977644i	$-0.567433\pi$
$563$	17.5948	−	30.4751i	0.741532	−	1.28437i	0.951798	−	0.306727i	$-0.0992338\pi$
$564$		0			0
$565$	−2.07394	+	1.19739i	−0.0872512	+	0.0503745i
$566$	−4.02933			−0.169365
$567$		0			0
$568$	14.1484			0.593655
$569$	7.63608	−	4.40869i	0.320121	−	0.184822i	−0.331325	−	0.943517i	$-0.607496\pi$
$569$	7.63608	−	4.40869i	0.320121	−	0.184822i	0.651447	+	0.758695i	$0.274162\pi$
$570$		0			0
$571$	5.94140	−	10.2908i	0.248640	−	0.430657i	−0.714509	−	0.699626i	$-0.753350\pi$
$571$	5.94140	−	10.2908i	0.248640	−	0.430657i	0.963149	+	0.268970i	$0.0866831\pi$
$572$	−3.59454	−	6.22593i	−0.150295	−	0.260319i
$573$		0			0
$574$	−5.92397	+	2.58326i	−0.247262	+	0.107823i
$575$		−	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
$580$		−	1.92926i		−	0.0801083i
$581$	0.969790	+	0.109456i	0.0402337	+	0.00454102i
$582$		0			0
$583$	−21.8045	−	37.7664i	−0.903049	−	1.56413i
$584$	6.30409	−	10.9190i	0.260865	−	0.451832i
$585$		0			0
$586$	11.4248	−	6.59608i	0.471952	−	0.272482i
$587$	3.50777			0.144781			0.0723907	−	0.997376i	$-0.476937\pi$
$587$	3.50777			0.144781			0.0723907	+	0.997376i	$0.476937\pi$
$588$		0			0
$589$	−27.5034			−1.13326
$590$	−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	$-0.698014\pi$
$593$	−24.2336	−	41.9738i	−0.995155	−	1.72366i	−0.412428	−	0.910990i	$-0.635319\pi$
$594$		0			0
$595$	−12.1957	−	1.37648i	−0.499975	−	0.0564302i
$596$		−	5.09444i		−	0.208676i
$597$		0			0
$598$	3.41481	+	1.97154i	0.139642	+	0.0806224i
$599$	21.7773	+	12.5731i	0.889796	+	0.513724i	0.873876	−	0.486149i	$-0.161599\pi$
$599$	21.7773	+	12.5731i	0.889796	+	0.513724i	0.0159203	+	0.999873i	$0.494932\pi$
$600$		0			0
$601$		−	13.0171i		−	0.530978i	−0.964114	−	0.265489i	$-0.914467\pi$
$601$		−	13.0171i		−	0.530978i	0.964114	−	0.265489i	$-0.0855334\pi$
$602$	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	$-0.613417\pi$
$607$	7.10546	−	4.10234i	0.288402	−	0.166509i	0.637221	+	0.770681i	$0.280084\pi$
$608$	2.74947			0.111506
$609$		0			0
$610$	−6.53057			−0.264415
$611$	−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	$0.136402\pi$
$614$	14.3845	+	24.9147i	0.580512	+	1.00548i
$615$		0			0
$616$	4.91581	−	6.65803i	0.198064	−	0.268260i
$617$			19.6504i			0.791096i	0.918445	+	0.395548i	$0.129445\pi$
$617$			19.6504i			0.791096i	−0.918445	+	0.395548i	$0.870555\pi$
$618$		0			0
$619$	−30.0586	−	17.3544i	−1.20816	−	0.697531i	−0.245802	−	0.969320i	$-0.579051\pi$
$619$	−30.0586	−	17.3544i	−1.20816	−	0.697531i	−0.962357	+	0.271789i	$0.912385\pi$
$620$	7.79892	+	4.50271i	0.313212	+	0.180833i
$621$		0			0
$622$		−	30.8457i		−	1.23680i
$623$	−12.6958	−	29.1142i	−0.508646	−	1.16644i
$624$		0			0
$625$	−6.74995	−	11.6912i	−0.269998	−	0.467650i
$626$	9.18304	−	15.9055i	0.367028	−	0.635712i
$627$		0			0
$628$	0.311703	−	0.179962i	0.0124383	−	0.00718126i
$629$	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	$0.349248\pi$
$632$	−5.67077	+	3.27402i	−0.225571	+	0.130233i
$633$		0			0
$634$	−8.72800	+	15.1173i	−0.346633	+	0.600386i
$635$	−2.74843	−	4.76041i	−0.109068	−	0.188911i
$636$		0			0
$637$	3.58582	−	15.6829i	0.142076	−	0.621381i
$638$		−	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	0.244003	−	0.969774i	$-0.421539\pi$
$641$	−11.9968	−	6.92634i	−0.473844	−	0.273574i	−0.717848	+	0.696200i	$0.754873\pi$
$642$		0			0
$643$		−	32.2951i		−	1.27359i	−0.771031	−	0.636797i	$-0.780259\pi$
$643$		−	32.2951i		−	1.27359i	0.771031	−	0.636797i	$-0.219741\pi$
$644$	−0.509102	+	4.51068i	−0.0200614	+	0.177746i
$645$		0			0
$646$	−7.08367	−	12.2693i	−0.278703	−	0.482729i
$647$	−8.96715	+	15.5316i	−0.352535	+	0.610609i	−0.986693	−	0.162595i	$-0.948014\pi$
$647$	−8.96715	+	15.5316i	−0.352535	+	0.610609i	0.634158	+	0.773204i	$0.281347\pi$
$648$		0			0
$649$	−21.6298	+	12.4880i	−0.849046	+	0.490197i
$650$	9.62855			0.377663
$651$		0			0
$652$	12.3728			0.484557
$653$	−6.49080	+	3.74747i	−0.254005	+	0.146650i	−0.621597	−	0.783338i	$-0.713516\pi$
$653$	−6.49080	+	3.74747i	−0.254005	+	0.146650i	0.367592	+	0.929987i	$0.380182\pi$
$654$		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
$659$			10.7675i			0.419444i	0.977761	+	0.209722i	$0.0672559\pi$
$659$			10.7675i			0.419444i	−0.977761	+	0.209722i	$0.932744\pi$
$660$		0			0
$661$	10.0813	+	5.82044i	0.392117	+	0.226389i	0.683077	−	0.730346i	$-0.260641\pi$
$661$	10.0813	+	5.82044i	0.392117	+	0.226389i	−0.290960	+	0.956735i	$0.593975\pi$
$662$	9.03216	+	5.21472i	0.351045	+	0.202676i
$663$		0			0
$664$		−	0.368874i		−	0.0143151i
$665$	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
$671$	−22.6915			−0.875995
$672$		0			0
$673$	1.10186			0.0424737			0.0212368	−	0.999774i	$-0.493240\pi$
$673$	1.10186			0.0424737			0.0212368	+	0.999774i	$0.493240\pi$
$674$	−27.4204	+	15.8312i	−1.05619	+	0.609794i
$675$		0			0
$676$	3.85905	−	6.68407i	0.148425	−	0.257080i
$677$	5.61618	+	9.72751i	0.215847	+	0.373859i	0.953534	−	0.301284i	$-0.0974153\pi$
$677$	5.61618	+	9.72751i	0.215847	+	0.373859i	−0.737687	+	0.675143i	$0.764082\pi$
$678$		0			0
$679$	−3.03855	+	26.9217i	−0.116609	+	1.03316i
$680$			4.63881i			0.177890i
$681$		0			0
$682$	27.0986	+	15.6454i	1.03766	+	0.599092i
$683$	37.6792	+	21.7541i	1.44175	+	0.832396i	0.997967	−	0.0637365i	$-0.0203017\pi$
$683$	37.6792	+	21.7541i	1.44175	+	0.832396i	0.443786	+	0.896133i	$0.353635\pi$
$684$		0			0
$685$			19.6616i			0.751231i
$686$	18.1994	−	3.43272i	0.694855	−	0.131062i
$687$		0			0
$688$	−0.273155	−	0.473119i	−0.0104139	−	0.0180375i
$689$	−16.0200	+	27.7474i	−0.610312	+	1.05709i
$690$		0			0
$691$	27.9085	−	16.1130i	1.06169	−	0.612967i	0.135791	−	0.990738i	$-0.456642\pi$
$691$	27.9085	−	16.1130i	1.06169	−	0.612967i	0.925899	+	0.377770i	$0.123309\pi$
$692$	−4.63544			−0.176213
$693$		0			0
$694$	12.5252			0.475451
$695$	−10.5428	+	6.08689i	−0.399911	+	0.230889i
$696$		0			0
$697$	6.29326	−	10.9002i	0.238374	−	0.412876i
$698$	7.07599	+	12.2560i	0.267830	+	0.463895i
$699$		0			0
$700$	4.43065	+	10.1605i	0.167463	+	0.384029i
$701$		−	21.8995i		−	0.827133i	−0.910474	−	0.413566i	$-0.864283\pi$
$701$		−	21.8995i		−	0.827133i	0.910474	−	0.413566i	$-0.135717\pi$
$702$		0			0
$703$	−22.5587	−	13.0243i	−0.850818	−	0.491220i
$704$	−2.70900	−	1.56404i	−0.102099	−	0.0589471i
$705$		0			0
$706$		−	4.96535i		−	0.186873i
$707$	4.27353	−	5.78812i	0.160723	−	0.217685i
$708$		0			0
$709$	9.02351	+	15.6292i	0.338885	+	0.586966i	0.984223	−	0.176931i	$-0.0566168\pi$
$709$	9.02351	+	15.6292i	0.338885	+	0.586966i	−0.645338	+	0.763897i	$0.723284\pi$
$710$	6.36862	−	11.0308i	0.239010	−	0.413977i
$711$		0			0
$712$	−10.3965	+	6.00244i	−0.389627	+	0.224951i
$713$	−17.1624			−0.642737
$714$		0			0
$715$	−6.47203			−0.242040
$716$	−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	0.765966	−	0.642881i	$-0.222261\pi$
$719$	−4.65944	−	8.07039i	−0.173768	−	0.300975i	−0.939734	+	0.341906i	$0.888928\pi$
$720$		0			0
$721$	3.32854	−	1.45147i	0.123961	−	0.0540557i
$722$		−	11.4404i		−	0.425768i
$723$		0			0
$724$	6.17217	+	3.56350i	0.229387	+	0.132437i
$725$	7.77537	+	4.48911i	0.288770	+	0.166722i
$726$		0			0
$727$			7.77710i			0.288437i	0.989546	+	0.144218i	$0.0460667\pi$
$727$			7.77710i			0.288437i	−0.989546	+	0.144218i	$0.953933\pi$
$728$	−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	$-0.899144\pi$
$733$	−31.2841	+	18.0619i	−1.15550	+	0.667131i	−0.205282	+	0.978703i	$0.565811\pi$
$734$	1.37177			0.0506329
$735$		0			0
$736$	1.71570			0.0632415
$737$	−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	$0.0202347\pi$
$740$	4.26453	+	7.38639i	0.156767	+	0.271529i
$741$		0			0
$742$	−36.6519	−	4.13676i	−1.34554	−	0.151865i
$743$			12.2124i			0.448028i	0.974586	+	0.224014i	$0.0719161\pi$
$743$			12.2124i			0.448028i	−0.974586	+	0.224014i	$0.928084\pi$
$744$		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
$749$	−34.6085	+	15.0917i	−1.26457	+	0.551438i
$750$		0			0
$751$	11.7190	+	20.2980i	0.427634	+	0.740684i	0.996662	−	0.0816339i	$-0.0260138\pi$
$751$	11.7190	+	20.2980i	0.427634	+	0.740684i	−0.569028	+	0.822318i	$0.692680\pi$
$752$	−3.93034	+	6.80755i	−0.143325	+	0.248246i
$753$		0			0
$754$	−4.26531	+	2.46258i	−0.155333	+	0.0896818i
$755$	−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	$0.479605\pi$
$758$	−16.9454	+	9.78346i	−0.615486	+	0.355351i
$759$		0			0
$760$	1.23762	−	2.14361i	0.0448931	−	0.0777571i
$761$	10.7021	+	18.5365i	0.387950	+	0.671949i	0.992174	−	0.124866i	$-0.0398500\pi$
$761$	10.7021	+	18.5365i	0.387950	+	0.671949i	−0.604224	+	0.796815i	$0.706517\pi$
$762$		0			0
$763$	8.31588	−	11.2631i	0.301055	−	0.407752i
$764$			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
$769$		−	27.0250i		−	0.974546i	−0.873250	−	0.487273i	$-0.837992\pi$
$769$		−	27.0250i		−	0.974546i	0.873250	−	0.487273i	$-0.162008\pi$
$770$	−2.97816	−	6.82956i	−0.107325	−	0.246120i
$771$		0			0
$772$	8.90573	+	15.4252i	0.320524	+	0.555164i
$773$	8.10280	−	14.0345i	0.291437	−	0.504784i	−0.682712	−	0.730687i	$-0.739200\pi$
$773$	8.10280	−	14.0345i	0.291437	−	0.504784i	0.974150	+	0.225903i	$0.0725332\pi$
$774$		0			0
$775$	−36.2939	+	20.9543i	−1.30371	+	0.752700i
$776$	10.2401			0.367597
$777$		0			0
$778$	4.06605			0.145775
$779$	−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
$785$		−	0.324024i		−	0.0115649i
$786$		0			0
$787$	33.1317	+	19.1286i	1.18102	+	0.681860i	0.956249	−	0.292553i	$-0.0945047\pi$
$787$	33.1317	+	19.1286i	1.18102	+	0.681860i	0.224767	+	0.974413i	$0.427838\pi$
$788$	16.5432	+	9.55124i	0.589328	+	0.340249i
$789$		0			0
$790$			5.89492i			0.209732i
$791$	−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
$797$	−8.77418			−0.310797			−0.155399	−	0.987852i	$-0.549666\pi$
$797$	−8.77418			−0.310797			−0.155399	+	0.987852i	$0.549666\pi$
$798$		0			0
$799$	40.5042			1.43293
$800$	3.62824	−	2.09477i	0.128278	−	0.0740612i
$801$		0			0
$802$	9.27141	−	16.0586i	0.327385	−	0.567047i
$803$	−19.7197	−	34.1556i	−0.695895	−	1.20532i
$804$		0			0
$805$	3.28757	+	2.42730i	0.115872	+	0.0855513i
$806$		−	22.9896i		−	0.809775i
$807$		0			0
$808$	−2.35506	−	1.35969i	−0.0828506	−	0.0478338i
$809$	26.6053	+	15.3606i	0.935394	+	0.540050i	0.888513	−	0.458851i	$-0.151739\pi$
$809$	26.6053	+	15.3606i	0.935394	+	0.540050i	0.0468805	+	0.998901i	$0.485072\pi$
$810$		0			0
$811$		−	8.70634i		−	0.305721i	−0.988248	−	0.152861i	$-0.951151\pi$
$811$		−	8.70634i		−	0.305721i	0.988248	−	0.152861i	$-0.0488485\pi$
$812$	−4.56133	−	3.36776i	−0.160071	−	0.118185i
$813$		0			0
$814$	14.8178	+	25.6652i	0.519363	+	0.899564i
$815$	5.56936	−	9.64641i	0.195086	−	0.337899i
$816$		0			0
$817$	1.30083	−	0.751032i	0.0455101	−	0.0262753i
$818$	24.8902			0.870265
$819$		0			0
$820$	2.19904			0.0767937
$821$	45.4098	−	26.2173i	1.58481	−	0.914992i	0.590670	−	0.806914i	$-0.298864\pi$
$821$	45.4098	−	26.2173i	1.58481	−	0.914992i	0.994142	−	0.108078i	$-0.0344697\pi$
$822$		0			0
$823$	−4.18199	+	7.24342i	−0.145775	+	0.252490i	−0.929662	−	0.368414i	$-0.879901\pi$
$823$	−4.18199	+	7.24342i	−0.145775	+	0.252490i	0.783887	+	0.620904i	$0.213234\pi$
$824$	−0.686242	−	1.18861i	−0.0239064	−	0.0414070i
$825$		0			0
$826$	−2.36923	+	20.9915i	−0.0824361	+	0.730389i
$827$		−	26.4934i		−	0.921267i	−0.887590	−	0.460634i	$-0.847622\pi$
$827$		−	26.4934i		−	0.921267i	0.887590	−	0.460634i	$-0.152378\pi$
$828$		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
$832$			2.29824i			0.0796771i
$833$	−24.5434	+	26.4313i	−0.850379	+	0.915790i
$834$		0			0
$835$	−6.66970	−	11.5523i	−0.230815	−	0.399783i
$836$	4.30029	−	7.44832i	0.148729	−	0.257606i
$837$		0			0
$838$	−4.45869	+	2.57422i	−0.154023	+	0.0889251i
$839$	7.61075			0.262752			0.131376	−	0.991333i	$-0.458060\pi$
$839$	7.61075			0.262752			0.131376	+	0.991333i	$0.458060\pi$
$840$		0			0
$841$	24.4075			0.841638
$842$	−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
$848$			13.9411i			0.478739i
$849$		0			0
$850$	−18.6955	−	10.7938i	−0.641249	−	0.370225i
$851$	−14.0769	−	8.12730i	−0.482550	−	0.278600i
$852$		0			0
$853$			28.7248i			0.983517i	0.870732	+	0.491759i	$0.163646\pi$
$853$			28.7248i			0.983517i	−0.870732	+	0.491759i	$0.836354\pi$
$854$	−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	0.285434	+	0.958398i	$0.407862\pi$
$857$	−20.1198	+	34.8486i	−0.687280	+	1.19040i	−0.972714	+	0.232006i	$0.925471\pi$
$858$		0			0
$859$	13.3256	−	7.69355i	0.454664	−	0.262501i	−0.255134	−	0.966906i	$-0.582119\pi$
$859$	13.3256	−	7.69355i	0.454664	−	0.262501i	0.709798	+	0.704405i	$0.248786\pi$
$860$	−0.491820			−0.0167709
$861$		0			0
$862$	9.36317			0.318911
$863$	16.6494	−	9.61252i	0.566751	−	0.327214i	−0.189099	−	0.981958i	$-0.560557\pi$
$863$	16.6494	−	9.61252i	0.566751	−	0.327214i	0.755851	+	0.654744i	$0.227224\pi$
$864$		0			0
$865$	−2.08655	+	3.61400i	−0.0709447	+	0.122880i
$866$	10.5186	+	18.2188i	0.357438	+	0.619101i
$867$		0			0
$868$	24.2596	−	10.5789i	0.823425	−	0.359070i
$869$			20.4828i			0.694832i
$870$		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
$875$	21.7501	+	2.45485i	0.735287	+	0.0829889i
$876$		0			0
$877$	5.39035	+	9.33636i	0.182019	+	0.315267i	0.942568	−	0.334014i	$-0.108403\pi$
$877$	5.39035	+	9.33636i	0.182019	+	0.315267i	−0.760549	+	0.649281i	$0.775070\pi$
$878$	−10.2114	+	17.6867i	−0.344619	+	0.596898i
$879$		0			0
$880$	−2.43880	+	1.40804i	−0.0822120	+	0.0474651i
$881$	−44.2875			−1.49208			−0.746041	−	0.665900i	$-0.768048\pi$
$881$	−44.2875			−1.49208			−0.746041	+	0.665900i	$0.768048\pi$
$882$		0			0
$883$	−47.6098			−1.60220			−0.801098	−	0.598533i	$-0.795751\pi$
$883$	−47.6098			−1.60220			−0.801098	+	0.598533i	$0.795751\pi$
$884$	10.2557	−	5.92113i	0.344936	−	0.199149i
$885$		0			0
$886$	−16.1825	+	28.0288i	−0.543660	+	0.941647i
$887$	0.989965	+	1.71467i	0.0332398	+	0.0575730i	0.882167	−	0.470937i	$-0.156084\pi$
$887$	0.989965	+	1.71467i	0.0332398	+	0.0575730i	−0.848927	+	0.528510i	$0.822751\pi$
$888$		0			0
$889$	−16.0527	−	1.81180i	−0.538390	−	0.0607659i
$890$			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
$895$			5.46641i			0.182722i
$896$	−2.42520	+	1.05755i	−0.0810202	+	0.0353303i
$897$		0			0
$898$	−10.7846	−	18.6795i	−0.359888	−	0.623344i
$899$	10.7184	−	18.5649i	0.357480	−	0.619173i
$900$		0			0
$901$	62.2109	−	35.9175i	2.07255	−	1.19659i
$902$	7.64090			0.254414
$903$		0			0
$904$	2.66010			0.0884736
$905$	5.55654	−	3.20807i	0.184706	−	0.106640i
$906$		0			0
$907$	−17.0252	+	29.4886i	−0.565314	+	0.979152i	0.431707	+	0.902014i	$0.357912\pi$
$907$	−17.0252	+	29.4886i	−0.565314	+	0.979152i	−0.997020	+	0.0771381i	$0.975422\pi$
$908$	4.36455	+	7.55962i	0.144843	+	0.250875i
$909$		0			0
$910$	−3.25146	+	4.40381i	−0.107785	+	0.145985i
$911$			7.60222i			0.251873i	0.992038	+	0.125936i	$0.0401935\pi$
$911$			7.60222i			0.251873i	−0.992038	+	0.125936i	$0.959806\pi$
$912$		0			0
$913$	−0.999280	−	0.576934i	−0.0330713	−	0.0190937i
$914$	18.2471	+	10.5350i	0.603561	+	0.348466i
$915$		0			0
$916$		−	3.93729i		−	0.130092i
$917$	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
$923$	−32.5165			−1.07029
$924$		0			0
$925$	−39.6918			−1.30506
$926$	7.62202	−	4.40058i	0.250475	−	0.144612i
$927$		0			0
$928$	−1.07151	+	1.85590i	−0.0351739	+	0.0609230i
$929$	−2.53982	−	4.39909i	−0.0833287	−	0.144329i	0.821349	−	0.570426i	$-0.193222\pi$
$929$	−2.53982	−	4.39909i	−0.0833287	−	0.144329i	−0.904678	+	0.426096i	$0.859888\pi$
$930$		0			0
$931$	18.3934	−	5.66593i	0.602819	−	0.185693i
$932$			4.52812i			0.148324i
$933$		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	$0.943484\pi$
$938$	−1.08915	+	9.64997i	−0.0355621	+	0.315083i
$939$		0			0
$940$	3.53832	+	6.12855i	0.115407	+	0.199891i
$941$	9.58193	−	16.5964i	0.312362	−	0.541027i	−0.666511	−	0.745495i	$-0.732213\pi$
$941$	9.58193	−	16.5964i	0.312362	−	0.541027i	0.978873	+	0.204468i	$0.0655464\pi$
$942$		0			0
$943$	−3.62942	+	2.09545i	−0.118190	+	0.0682372i
$944$	7.98443			0.259871
$945$		0			0
$946$	−1.70891			−0.0555613
$947$	−21.9930	+	12.6977i	−0.714676	+	0.412618i	−0.812790	−	0.582557i	$-0.802052\pi$
$947$	−21.9930	+	12.6977i	−0.714676	+	0.412618i	0.0981139	+	0.995175i	$0.468719\pi$
$948$		0			0
$949$	−14.4883	+	25.0945i	−0.470310	+	0.814601i
$950$	5.75950	+	9.97575i	0.186863	+	0.323656i
$951$		0			0
$952$	10.9675	+	8.09759i	0.355458	+	0.262444i
$953$			18.4818i			0.598686i	0.954146	+	0.299343i	$0.0967674\pi$
$953$			18.4818i			0.598686i	−0.954146	+	0.299343i	$0.903233\pi$
$954$		0			0
$955$	11.2274	+	6.48215i	0.363310	+	0.209757i
$956$	−7.55315	−	4.36081i	−0.244286	−	0.141039i
$957$		0			0
$958$			24.1401i			0.779932i
$959$	46.4856	+	34.3216i	1.50110	+	1.10830i
$960$		0			0
$961$	34.5315	+	59.8103i	1.11392	+	1.92937i
$962$	10.8868	−	18.8565i	0.351004	−	0.607957i
$963$		0			0
$964$	17.1314	−	9.89079i	0.551764	−	0.318561i
$965$	16.0349			0.516182
$966$		0			0
$967$	19.2910			0.620357			0.310179	−	0.950678i	$-0.399611\pi$
$967$	19.2910			0.620357			0.310179	+	0.950678i	$0.399611\pi$
$968$	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	0.849949	−	0.526865i	$-0.176633\pi$
$971$	−0.975444	−	1.68952i	−0.0313035	−	0.0542192i	−0.881253	+	0.472645i	$0.843299\pi$
$972$		0			0
$973$	−4.01256	+	35.5515i	−0.128637	+	1.13973i
$974$			14.1108i			0.452141i
$975$		0			0
$976$	6.28224	+	3.62705i	0.201090	+	0.116099i
$977$	−14.4856	−	8.36326i	−0.463435	−	0.267564i	0.250052	−	0.968232i	$-0.419552\pi$
$977$	−14.4856	−	8.36326i	−0.463435	−	0.267564i	−0.713488	+	0.700668i	$0.752885\pi$
$978$		0			0
$979$			37.5523i			1.20018i
$980$	−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	0.484879	+	0.874581i	$0.338864\pi$
$983$	−16.1458	+	27.9653i	−0.514970	+	0.891955i	−0.999849	+	0.0173733i	$0.994470\pi$
$984$		0			0
$985$	14.8932	−	8.59858i	0.474536	−	0.273974i
$986$	11.0424			0.351662
$987$		0			0
$988$	−6.31894			−0.201032
$989$	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	$0.123548\pi$
$992$	−5.00158	−	8.66298i	−0.158800	−	0.275050i
$993$		0			0
$994$	−14.9627	−	34.3127i	−0.474588	−	1.08833i
$995$		−	12.0593i		−	0.382306i
$996$		0			0
$997$	−9.78395	−	5.64877i	−0.309861	−	0.178898i	0.337003	−	0.941503i	$-0.390587\pi$
$997$	−9.78395	−	5.64877i	−0.309861	−	0.178898i	−0.646864	+	0.762605i	$0.723920\pi$
$998$	−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	1134.2.k.a.647.2		16
3.2	odd	2		1134.2.k.b.647.7		16
7.5	odd	6		1134.2.k.b.971.7		16
9.2	odd	6		126.2.t.a.59.3	yes	16
9.4	even	3		126.2.l.a.101.4	yes	16
9.5	odd	6		378.2.l.a.143.7		16
9.7	even	3		378.2.t.a.17.7		16
21.5	even	6	inner	1134.2.k.a.971.2		16
36.7	odd	6		3024.2.df.c.17.6		16
36.11	even	6		1008.2.df.c.689.4		16
36.23	even	6		3024.2.ca.c.2033.6		16
36.31	odd	6		1008.2.ca.c.353.1		16
63.2	odd	6		882.2.l.b.509.5		16
63.4	even	3		882.2.m.b.587.5		16
63.5	even	6		378.2.t.a.89.7		16
63.11	odd	6		882.2.m.a.293.8		16
63.13	odd	6		882.2.l.b.227.1		16
63.16	even	3		2646.2.l.a.1097.2		16
63.20	even	6		882.2.t.a.815.2		16
63.23	odd	6		2646.2.t.b.1979.6		16
63.25	even	3		2646.2.m.a.881.2		16
63.31	odd	6		882.2.m.a.587.8		16
63.32	odd	6		2646.2.m.b.1763.3		16
63.34	odd	6		2646.2.t.b.2285.6		16
63.38	even	6		882.2.m.b.293.5		16
63.40	odd	6		126.2.t.a.47.3	yes	16
63.41	even	6		2646.2.l.a.521.6		16
63.47	even	6		126.2.l.a.5.8	✓	16
63.52	odd	6		2646.2.m.b.881.3		16
63.58	even	3		882.2.t.a.803.2		16
63.59	even	6		2646.2.m.a.1763.2		16
63.61	odd	6		378.2.l.a.341.3		16
252.47	odd	6		1008.2.ca.c.257.1		16
252.103	even	6		1008.2.df.c.929.4		16
252.131	odd	6		3024.2.df.c.1601.6		16
252.187	even	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	63.47	even	6
126.2.l.a.101.4	yes	16	9.4	even	3
126.2.t.a.47.3	yes	16	63.40	odd	6
126.2.t.a.59.3	yes	16	9.2	odd	6
378.2.l.a.143.7		16	9.5	odd	6
378.2.l.a.341.3		16	63.61	odd	6
378.2.t.a.17.7		16	9.7	even	3
378.2.t.a.89.7		16	63.5	even	6
882.2.l.b.227.1		16	63.13	odd	6
882.2.l.b.509.5		16	63.2	odd	6
882.2.m.a.293.8		16	63.11	odd	6
882.2.m.a.587.8		16	63.31	odd	6
882.2.m.b.293.5		16	63.38	even	6
882.2.m.b.587.5		16	63.4	even	3
882.2.t.a.803.2		16	63.58	even	3
882.2.t.a.815.2		16	63.20	even	6
1008.2.ca.c.257.1		16	252.47	odd	6
1008.2.ca.c.353.1		16	36.31	odd	6
1008.2.df.c.689.4		16	36.11	even	6
1008.2.df.c.929.4		16	252.103	even	6
1134.2.k.a.647.2		16	1.1	even	1	trivial
1134.2.k.a.971.2		16	21.5	even	6	inner
1134.2.k.b.647.7		16	3.2	odd	2
1134.2.k.b.971.7		16	7.5	odd	6
2646.2.l.a.521.6		16	63.41	even	6
2646.2.l.a.1097.2		16	63.16	even	3
2646.2.m.a.881.2		16	63.25	even	3
2646.2.m.a.1763.2		16	63.59	even	6
2646.2.m.b.881.3		16	63.52	odd	6
2646.2.m.b.1763.3		16	63.32	odd	6
2646.2.t.b.1979.6		16	63.23	odd	6
2646.2.t.b.2285.6		16	63.34	odd	6
3024.2.ca.c.2033.6		16	36.23	even	6
3024.2.ca.c.2609.6		16	252.187	even	6
3024.2.df.c.17.6		16	36.7	odd	6
3024.2.df.c.1601.6		16	252.131	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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.450129 - 0.779646i) q^{5} +(-2.62906 - 0.296732i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.450129 - 0.779646i) q^{5} +(-2.62906 - 0.296732i) q^{7} +1.00000i q^{8} +(0.779646 + 0.450129i) q^{10} +(2.70900 + 1.56404i) q^{11} -2.29824i q^{13} +(2.42520 - 1.05755i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.57638 + 4.46242i) q^{17} +(2.38111 - 1.37474i) q^{19} -0.900258 q^{20} -3.12809 q^{22} +(1.48584 - 0.857850i) q^{23} +(2.09477 - 3.62824i) q^{25} +(1.14912 + 1.99033i) q^{26} +(-1.57151 + 2.12847i) q^{28} +2.14301i q^{29} +(-8.66298 - 5.00158i) q^{31} +(0.866025 + 0.500000i) q^{32} -5.15276i q^{34} +(0.952070 + 2.18330i) q^{35} +(-4.73701 - 8.20475i) q^{37} +(-1.37474 + 2.38111i) q^{38} +(0.779646 - 0.450129i) q^{40} -2.44268 q^{41} +0.546311 q^{43} +(2.70900 - 1.56404i) q^{44} +(-0.857850 + 1.48584i) q^{46} +(-3.93034 - 6.80755i) q^{47} +(6.82390 + 1.56025i) q^{49} +4.18954i q^{50} +(-1.99033 - 1.14912i) q^{52} +(-12.0733 - 6.97054i) q^{53} -2.81608i q^{55} +(0.296732 - 2.62906i) q^{56} +(-1.07151 - 1.85590i) q^{58} +(-3.99222 + 6.91472i) q^{59} +(-6.28224 + 3.62705i) q^{61} +10.0032 q^{62} -1.00000 q^{64} +(-1.79181 + 1.03450i) q^{65} +(-1.83525 + 3.17875i) q^{67} +(2.57638 + 4.46242i) q^{68} +(-1.91617 - 1.41476i) q^{70} -14.1484i q^{71} +(-10.9190 - 6.30409i) q^{73} +(8.20475 + 4.73701i) q^{74} -2.74947i q^{76} +(-6.65803 - 4.91581i) q^{77} +(3.27402 + 5.67077i) q^{79} +(-0.450129 + 0.779646i) q^{80} +(2.11542 - 1.22134i) q^{82} -0.368874 q^{83} +4.63881 q^{85} +(-0.473119 + 0.273155i) q^{86} +(-1.56404 + 2.70900i) q^{88} +(6.00244 + 10.3965i) q^{89} +(-0.681960 + 6.04220i) q^{91} -1.71570i q^{92} +(6.80755 + 3.93034i) q^{94} +(-2.14361 - 1.23762i) q^{95} -10.2401i q^{97} +(-6.68980 + 2.06074i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 4 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 - 4 * q^7	\( 16 q + 8 q^{4} - 4 q^{7} - 12 q^{11} - 8 q^{16} - 18 q^{17} + 6 q^{23} - 8 q^{25} + 12 q^{26} - 2 q^{28} - 6 q^{31} + 30 q^{35} - 2 q^{37} + 12 q^{41} + 4 q^{43} - 12 q^{44} + 6 q^{46} + 18 q^{47} - 2 q^{49} + 6 q^{52} - 36 q^{53} - 6 q^{56} + 6 q^{58} - 30 q^{59} + 60 q^{61} + 36 q^{62} - 16 q^{64} + 42 q^{65} + 14 q^{67} + 18 q^{68} + 18 q^{70} - 18 q^{74} + 24 q^{77} - 16 q^{79} + 24 q^{85} - 24 q^{86} - 24 q^{89} - 12 q^{91} - 66 q^{95} - 24 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 - 4 * q^7 - 12 * q^11 - 8 * q^16 - 18 * q^17 + 6 * q^23 - 8 * q^25 + 12 * q^26 - 2 * q^28 - 6 * q^31 + 30 * q^35 - 2 * q^37 + 12 * q^41 + 4 * q^43 - 12 * q^44 + 6 * q^46 + 18 * q^47 - 2 * q^49 + 6 * q^52 - 36 * q^53 - 6 * q^56 + 6 * q^58 - 30 * q^59 + 60 * q^61 + 36 * q^62 - 16 * q^64 + 42 * q^65 + 14 * q^67 + 18 * q^68 + 18 * q^70 - 18 * q^74 + 24 * q^77 - 16 * q^79 + 24 * q^85 - 24 * q^86 - 24 * q^89 - 12 * q^91 - 66 * q^95 - 24 * q^98

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