LMFDB - Embedded newform 675.2.q.a.368.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(143,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("675.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.q (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
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} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			368.3
Root			$-0.0499037 - 0.186243i$ of defining polynomial
Character	$\chi$	$=$	675.368
Dual form			675.2.q.a.332.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0499037 - 0.186243i) q^{2} +(1.69985 + 0.981412i) q^{4} +(2.35868 + 0.632007i) q^{7} +(0.540289 - 0.540289i) q^{8} +O(q^{10})$	\(q+(0.0499037 - 0.186243i) q^{2} +(1.69985 + 0.981412i) q^{4} +(2.35868 + 0.632007i) q^{7} +(0.540289 - 0.540289i) q^{8} +(2.14390 - 1.23778i) q^{11} +(-1.57505 + 0.422032i) q^{13} +(0.235414 - 0.407749i) q^{14} +(1.88916 + 3.27212i) q^{16} +(-0.403949 - 0.403949i) q^{17} -4.28779i q^{19} +(-0.123539 - 0.461055i) q^{22} +(1.82845 + 6.82387i) q^{23} +0.314402i q^{26} +(3.38916 + 3.38916i) q^{28} +(-3.20524 - 5.55164i) q^{29} +(-1.97194 + 3.41550i) q^{31} +(2.17978 - 0.584071i) q^{32} +(-0.0953913 + 0.0550742i) q^{34} +(0.171954 - 0.171954i) q^{37} +(-0.798571 - 0.213977i) q^{38} +(6.52359 + 3.76639i) q^{41} +(-1.32695 + 4.95226i) q^{43} +4.85908 q^{44} +1.36214 q^{46} +(0.780885 - 2.91430i) q^{47} +(-0.898221 - 0.518588i) q^{49} +(-3.09154 - 0.828375i) q^{52} +(6.12030 - 6.12030i) q^{53} +(1.61584 - 0.932904i) q^{56} +(-1.19391 + 0.319907i) q^{58} +(-2.27234 + 3.93581i) q^{59} +(-0.235795 - 0.408408i) q^{61} +(0.537706 + 0.537706i) q^{62} +7.12153i q^{64} +(0.443446 + 1.65496i) q^{67} +(-0.290215 - 1.08310i) q^{68} -3.50583i q^{71} +(-6.88847 - 6.88847i) q^{73} +(-0.0234441 - 0.0406064i) q^{74} +(4.20809 - 7.28862i) q^{76} +(5.83906 - 1.56457i) q^{77} +(6.50159 - 3.75369i) q^{79} +(1.02702 - 1.02702i) q^{82} +(-10.6660 - 2.85794i) q^{83} +(0.856104 + 0.494272i) q^{86} +(0.489565 - 1.82708i) q^{88} +2.90124 q^{89} -3.98176 q^{91} +(-3.58893 + 13.3941i) q^{92} +(-0.503800 - 0.290869i) q^{94} +(-1.41681 - 0.379633i) q^{97} +(-0.141408 + 0.141408i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} + 2 q^{7}+O(q^{10}) $ 16 * q - 6 * q^2 + 2 * q^7	$ 16 q - 6 q^{2} + 2 q^{7} + 2 q^{13} - 8 q^{16} + 10 q^{22} + 18 q^{23} + 16 q^{28} - 4 q^{31} + 30 q^{32} - 4 q^{37} - 30 q^{38} + 24 q^{41} + 2 q^{43} + 32 q^{46} - 12 q^{47} + 14 q^{52} - 36 q^{56} + 6 q^{58} + 8 q^{61} - 4 q^{67} + 42 q^{68} + 8 q^{73} + 24 q^{76} - 6 q^{77} - 32 q^{82} - 66 q^{83} + 48 q^{86} - 18 q^{88} - 40 q^{91} - 60 q^{92} - 28 q^{97}+O(q^{100}) $ 16 * q - 6 * q^2 + 2 * q^7 + 2 * q^13 - 8 * q^16 + 10 * q^22 + 18 * q^23 + 16 * q^28 - 4 * q^31 + 30 * q^32 - 4 * q^37 - 30 * q^38 + 24 * q^41 + 2 * q^43 + 32 * q^46 - 12 * q^47 + 14 * q^52 - 36 * q^56 + 6 * q^58 + 8 * q^61 - 4 * q^67 + 42 * q^68 + 8 * q^73 + 24 * q^76 - 6 * q^77 - 32 * q^82 - 66 * q^83 + 48 * q^86 - 18 * q^88 - 40 * q^91 - 60 * q^92 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.0499037	−	0.186243i	0.0352872	−	0.131694i	−0.946035	−	0.324064i	$-0.894951\pi$
$2$	0.0499037	−	0.186243i	0.0352872	−	0.131694i	0.981322	+	0.192370i	$0.0616174\pi$
$3$		0			0
$3$		0			0
$4$	1.69985	+	0.981412i	0.849927	+	0.490706i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.35868	+	0.632007i	0.891499	+	0.238876i	0.675362	−	0.737487i	$-0.263988\pi$
$7$	2.35868	+	0.632007i	0.891499	+	0.238876i	0.216137	+	0.976363i	$0.430654\pi$
$8$	0.540289	−	0.540289i	0.191021	−	0.191021i
$9$		0			0
$10$		0			0
$11$	2.14390	−	1.23778i	0.646409	−	0.373204i	−0.140670	−	0.990057i	$-0.544926\pi$
$11$	2.14390	−	1.23778i	0.646409	−	0.373204i	0.787079	+	0.616852i	$0.211592\pi$
$12$		0			0
$13$	−1.57505	+	0.422032i	−0.436839	+	0.117051i	−0.470535	−	0.882381i	$-0.655939\pi$
$13$	−1.57505	+	0.422032i	−0.436839	+	0.117051i	0.0336956	+	0.999432i	$0.489272\pi$
$14$	0.235414	−	0.407749i	0.0629170	−	0.108975i
$15$		0			0
$16$	1.88916	+	3.27212i	0.472290	+	0.818031i
$17$	−0.403949	−	0.403949i	−0.0979721	−	0.0979721i	0.656422	−	0.754394i	$-0.272069\pi$
$17$	−0.403949	−	0.403949i	−0.0979721	−	0.0979721i	−0.754394	+	0.656422i	$0.772069\pi$
$18$		0			0
$19$		−	4.28779i		−	0.983687i	−0.870684	−	0.491843i	$-0.836323\pi$
$19$		−	4.28779i		−	0.983687i	0.870684	−	0.491843i	$-0.163677\pi$
$20$		0			0
$21$		0			0
$22$	−0.123539	−	0.461055i	−0.0263387	−	0.0982973i
$23$	1.82845	+	6.82387i	0.381258	+	1.42288i	0.843981	+	0.536373i	$0.180206\pi$
$23$	1.82845	+	6.82387i	0.381258	+	1.42288i	−0.462723	+	0.886503i	$0.653128\pi$
$24$		0			0
$25$		0			0
$26$			0.314402i			0.0616594i
$27$		0			0
$28$	3.38916	+	3.38916i	0.640491	+	0.640491i
$29$	−3.20524	−	5.55164i	−0.595199	−	1.03091i	−0.993519	−	0.113668i	$-0.963740\pi$
$29$	−3.20524	−	5.55164i	−0.595199	−	1.03091i	0.398320	−	0.917247i	$-0.369593\pi$
$30$		0			0
$31$	−1.97194	+	3.41550i	−0.354171	+	0.613442i	−0.986976	−	0.160869i	$-0.948570\pi$
$31$	−1.97194	+	3.41550i	−0.354171	+	0.613442i	0.632805	+	0.774312i	$0.281904\pi$
$32$	2.17978	−	0.584071i	0.385335	−	0.103250i
$33$		0			0
$34$	−0.0953913	+	0.0550742i	−0.0163595	+	0.00944515i
$35$		0			0
$36$		0			0
$37$	0.171954	−	0.171954i	0.0282691	−	0.0282691i	−0.692831	−	0.721100i	$-0.743637\pi$
$37$	0.171954	−	0.171954i	0.0282691	−	0.0282691i	0.721100	+	0.692831i	$0.243637\pi$
$38$	−0.798571	−	0.213977i	−0.129545	−	0.0347116i
$39$		0			0
$40$		0			0
$41$	6.52359	+	3.76639i	1.01881	+	0.588212i	0.913760	−	0.406255i	$-0.133165\pi$
$41$	6.52359	+	3.76639i	1.01881	+	0.588212i	0.105053	+	0.994467i	$0.466499\pi$
$42$		0			0
$43$	−1.32695	+	4.95226i	−0.202359	+	0.755213i	0.787880	+	0.615829i	$0.211179\pi$
$43$	−1.32695	+	4.95226i	−0.202359	+	0.755213i	−0.990238	+	0.139384i	$0.955488\pi$
$44$	4.85908			0.732534
$45$		0			0
$46$	1.36214			0.200837
$47$	0.780885	−	2.91430i	0.113904	−	0.425095i	−0.885299	−	0.465023i	$-0.846046\pi$
$47$	0.780885	−	2.91430i	0.113904	−	0.425095i	0.999203	+	0.0399279i	$0.0127128\pi$
$48$		0			0
$49$	−0.898221	−	0.518588i	−0.128317	−	0.0740841i
$50$		0			0
$51$		0			0
$52$	−3.09154	−	0.828375i	−0.428719	−	0.114875i
$53$	6.12030	−	6.12030i	0.840688	−	0.840688i	−0.148260	−	0.988948i	$-0.547367\pi$
$53$	6.12030	−	6.12030i	0.840688	−	0.840688i	0.988948	+	0.148260i	$0.0473672\pi$
$54$		0			0
$55$		0			0
$56$	1.61584	−	0.932904i	0.215925	−	0.124665i
$57$		0			0
$58$	−1.19391	+	0.319907i	−0.156768	+	0.0420058i
$59$	−2.27234	+	3.93581i	−0.295833	+	0.512399i	−0.975178	−	0.221421i	$-0.928931\pi$
$59$	−2.27234	+	3.93581i	−0.295833	+	0.512399i	0.679345	+	0.733819i	$0.262264\pi$
$60$		0			0
$61$	−0.235795	−	0.408408i	−0.0301904	−	0.0522913i	0.850535	−	0.525918i	$-0.176278\pi$
$61$	−0.235795	−	0.408408i	−0.0301904	−	0.0522913i	−0.880726	+	0.473626i	$0.842945\pi$
$62$	0.537706	+	0.537706i	0.0682888	+	0.0682888i
$63$		0			0
$64$			7.12153i			0.890191i
$65$		0			0
$66$		0			0
$67$	0.443446	+	1.65496i	0.0541756	+	0.202186i	0.987709	−	0.156305i	$-0.0499582\pi$
$67$	0.443446	+	1.65496i	0.0541756	+	0.202186i	−0.933533	+	0.358491i	$0.883291\pi$
$68$	−0.290215	−	1.08310i	−0.0351937	−	0.131345i
$69$		0			0
$70$		0			0
$71$		−	3.50583i		−	0.416065i	−0.978122	−	0.208032i	$-0.933294\pi$
$71$		−	3.50583i		−	0.416065i	0.978122	−	0.208032i	$-0.0667060\pi$
$72$		0			0
$73$	−6.88847	−	6.88847i	−0.806234	−	0.806234i	0.177827	−	0.984062i	$-0.443093\pi$
$73$	−6.88847	−	6.88847i	−0.806234	−	0.806234i	−0.984062	+	0.177827i	$0.943093\pi$
$74$	−0.0234441	−	0.0406064i	−0.00272533	−	0.00472040i
$75$		0			0
$76$	4.20809	−	7.28862i	0.482701	−	0.836062i
$77$	5.83906	−	1.56457i	0.665422	−	0.178299i
$78$		0			0
$79$	6.50159	−	3.75369i	0.731485	−	0.422323i	−0.0874799	−	0.996166i	$-0.527881\pi$
$79$	6.50159	−	3.75369i	0.731485	−	0.422323i	0.818965	+	0.573843i	$0.194548\pi$
$80$		0			0
$81$		0			0
$82$	1.02702	−	1.02702i	0.113415	−	0.113415i
$83$	−10.6660	−	2.85794i	−1.17074	−	0.313700i	−0.379495	−	0.925194i	$-0.623902\pi$
$83$	−10.6660	−	2.85794i	−1.17074	−	0.313700i	−0.791249	+	0.611493i	$0.790569\pi$
$84$		0			0
$85$		0			0
$86$	0.856104	+	0.494272i	0.0923161	+	0.0532987i
$87$		0			0
$88$	0.489565	−	1.82708i	0.0521878	−	0.194767i
$89$	2.90124			0.307531			0.153765	−	0.988107i	$-0.450860\pi$
$89$	2.90124			0.307531			0.153765	+	0.988107i	$0.450860\pi$
$90$		0			0
$91$	−3.98176			−0.417402
$92$	−3.58893	+	13.3941i	−0.374171	+	1.39643i
$93$		0			0
$94$	−0.503800	−	0.290869i	−0.0519630	−	0.0300008i
$95$		0			0
$96$		0			0
$97$	−1.41681	−	0.379633i	−0.143855	−	0.0385459i	0.186173	−	0.982517i	$-0.440392\pi$
$97$	−1.41681	−	0.379633i	−0.143855	−	0.0385459i	−0.330028	+	0.943971i	$0.607058\pi$
$98$	−0.141408	+	0.141408i	−0.0142844	+	0.0142844i
$99$		0			0
$100$		0			0
$101$	−15.3563	+	8.86596i	−1.52801	+	0.882196i	−0.528563	+	0.848894i	$0.677269\pi$
$101$	−15.3563	+	8.86596i	−1.52801	+	0.882196i	−0.999445	+	0.0333015i	$0.989398\pi$
$102$		0			0
$103$	10.2381	−	2.74330i	1.00879	−	0.270305i	0.283668	−	0.958922i	$-0.408449\pi$
$103$	10.2381	−	2.74330i	1.00879	−	0.270305i	0.725125	+	0.688617i	$0.241782\pi$
$104$	−0.622960	+	1.07900i	−0.0610863	+	0.105805i
$105$		0			0
$106$	−0.834438	−	1.44529i	−0.0810478	−	0.140379i
$107$	−10.4591	−	10.4591i	−1.01112	−	1.01112i	−0.999937	−	0.0111806i	$-0.996441\pi$
$107$	−10.4591	−	10.4591i	−1.01112	−	1.01112i	−0.0111806	−	0.999937i	$-0.503559\pi$
$108$		0			0
$109$		−	0.343204i		−	0.0328730i	−0.999865	−	0.0164365i	$-0.994768\pi$
$109$		−	0.343204i		−	0.0328730i	0.999865	−	0.0164365i	$-0.00523214\pi$
$110$		0			0
$111$		0			0
$112$	2.38793	+	8.91187i	0.225638	+	0.842092i
$113$	1.39133	+	5.19250i	0.130885	+	0.488469i	0.999981	−	0.00617426i	$-0.00196534\pi$
$113$	1.39133	+	5.19250i	0.130885	+	0.488469i	−0.869096	+	0.494643i	$0.835299\pi$
$114$		0			0
$115$		0			0
$116$		−	12.5827i		−	1.16827i
$117$		0			0
$118$	0.619619	+	0.619619i	0.0570405	+	0.0570405i
$119$	−0.697490	−	1.20809i	−0.0639388	−	0.110745i
$120$		0			0
$121$	−2.43581	+	4.21894i	−0.221437	+	0.383540i
$122$	−0.0878302	+	0.0235340i	−0.00795177	+	0.00213067i
$123$		0			0
$124$	−6.70403	+	3.87057i	−0.602039	+	0.347588i
$125$		0			0
$126$		0			0
$127$	3.59190	−	3.59190i	0.318729	−	0.318729i	−0.529550	−	0.848279i	$-0.677639\pi$
$127$	3.59190	−	3.59190i	0.318729	−	0.318729i	0.848279	+	0.529550i	$0.177639\pi$
$128$	5.68590	+	1.52353i	0.502567	+	0.134662i
$129$		0			0
$130$		0			0
$131$	−14.5188	−	8.38241i	−1.26851	−	0.732375i	−0.293804	−	0.955866i	$-0.594921\pi$
$131$	−14.5188	−	8.38241i	−1.26851	−	0.732375i	−0.974706	+	0.223491i	$0.928255\pi$
$132$		0			0
$133$	2.70992	−	10.1135i	0.234980	−	0.876956i
$134$	0.330355			0.0285383
$135$		0			0
$136$	−0.436499			−0.0374295
$137$	−1.65517	+	6.17718i	−0.141411	+	0.527752i	0.858478	+	0.512850i	$0.171410\pi$
$137$	−1.65517	+	6.17718i	−0.141411	+	0.527752i	−0.999889	+	0.0149021i	$0.995256\pi$
$138$		0			0
$139$	−9.09433	−	5.25061i	−0.771371	−	0.445351i	0.0619924	−	0.998077i	$-0.480255\pi$
$139$	−9.09433	−	5.25061i	−0.771371	−	0.445351i	−0.833364	+	0.552725i	$0.813588\pi$
$140$		0			0
$141$		0			0
$142$	−0.652936	−	0.174954i	−0.0547931	−	0.0146818i
$143$	−2.85435	+	2.85435i	−0.238693	+	0.238693i
$144$		0			0
$145$		0			0
$146$	−1.62669	+	0.939170i	−0.134626	+	0.0777262i
$147$		0			0
$148$	0.461055	−	0.123539i	0.0378985	−	0.0101549i
$149$	−4.96581	+	8.60103i	−0.406815	+	0.704624i	−0.994531	−	0.104443i	$-0.966694\pi$
$149$	−4.96581	+	8.60103i	−0.406815	+	0.704624i	0.587716	+	0.809067i	$0.300027\pi$
$150$		0			0
$151$	−6.95939	−	12.0540i	−0.566347	−	0.980942i	−0.996923	−	0.0783879i	$-0.975023\pi$
$151$	−6.95939	−	12.0540i	−0.566347	−	0.980942i	0.430576	−	0.902555i	$-0.358311\pi$
$152$	−2.31665	−	2.31665i	−0.187905	−	0.187905i
$153$		0			0
$154$		−	1.16556i		−	0.0939236i
$155$		0			0
$156$		0			0
$157$	−5.42234	−	20.2365i	−0.432750	−	1.61505i	−0.746394	−	0.665504i	$-0.768216\pi$
$157$	−5.42234	−	20.2365i	−0.432750	−	1.61505i	0.313644	−	0.949541i	$-0.398450\pi$
$158$	−0.374646	−	1.39820i	−0.0298052	−	0.111235i
$159$		0			0
$160$		0			0
$161$			17.2510i			1.35957i
$162$		0			0
$163$	2.42872	+	2.42872i	0.190232	+	0.190232i	0.795796	−	0.605564i	$-0.207052\pi$
$163$	2.42872	+	2.42872i	0.190232	+	0.190232i	−0.605564	+	0.795796i	$0.707052\pi$
$164$	7.39277	+	12.8046i	0.577278	+	0.999875i
$165$		0			0
$166$	−1.06454	+	1.84385i	−0.0826247	+	0.143110i
$167$	−8.23252	+	2.20590i	−0.637052	+	0.170697i	−0.562868	−	0.826547i	$-0.690302\pi$
$167$	−8.23252	+	2.20590i	−0.637052	+	0.170697i	−0.0741841	+	0.997245i	$0.523635\pi$
$168$		0			0
$169$	−8.95567	+	5.17056i	−0.688898	+	0.397735i
$170$		0			0
$171$		0			0
$172$	−7.11584	+	7.11584i	−0.542577	+	0.542577i
$173$	−17.0726	−	4.57458i	−1.29800	−	0.347799i	−0.457308	−	0.889308i	$-0.651186\pi$
$173$	−17.0726	−	4.57458i	−1.29800	−	0.347799i	−0.840695	+	0.541509i	$0.817853\pi$
$174$		0			0
$175$		0			0
$176$	8.10033	+	4.67673i	0.610585	+	0.352521i
$177$		0			0
$178$	0.144783	−	0.540336i	0.0108519	−	0.0404999i
$179$	−8.30788			−0.620960			−0.310480	−	0.950580i	$-0.600490\pi$
$179$	−8.30788			−0.620960			−0.310480	+	0.950580i	$0.600490\pi$
$180$		0			0
$181$	−4.73429			−0.351897			−0.175948	−	0.984399i	$-0.556299\pi$
$181$	−4.73429			−0.351897			−0.175948	+	0.984399i	$0.556299\pi$
$182$	−0.198705	+	0.741576i	−0.0147290	+	0.0549693i
$183$		0			0
$184$	4.67475	+	2.69897i	0.344627	+	0.198971i
$185$		0			0
$186$		0			0
$187$	−1.36603	−	0.366025i	−0.0998937	−	0.0267664i
$188$	4.18752	−	4.18752i	0.305406	−	0.305406i
$189$		0			0
$190$		0			0
$191$	3.34902	−	1.93356i	0.242327	−	0.139907i	−0.373919	−	0.927461i	$-0.621986\pi$
$191$	3.34902	−	1.93356i	0.242327	−	0.139907i	0.616246	+	0.787554i	$0.288653\pi$
$192$		0			0
$193$	−16.5901	+	4.44530i	−1.19418	+	0.319979i	−0.800536	−	0.599284i	$-0.795452\pi$
$193$	−16.5901	+	4.44530i	−1.19418	+	0.319979i	−0.393643	+	0.919263i	$0.628785\pi$
$194$	−0.141408	+	0.244926i	−0.0101525	+	0.0175847i
$195$		0			0
$196$	−1.01790	−	1.76305i	−0.0727070	−	0.125932i
$197$	11.0386	+	11.0386i	0.786469	+	0.786469i	0.980913	−	0.194445i	$-0.0622905\pi$
$197$	11.0386	+	11.0386i	0.786469	+	0.786469i	−0.194445	+	0.980913i	$0.562291\pi$
$198$		0			0
$199$			3.60138i			0.255295i	0.991820	+	0.127648i	$0.0407427\pi$
$199$			3.60138i			0.255295i	−0.991820	+	0.127648i	$0.959257\pi$
$200$		0			0
$201$		0			0
$202$	0.884888	+	3.30245i	0.0622605	+	0.232359i
$203$	−4.05148	−	15.1203i	−0.284358	−	1.06124i
$204$		0			0
$205$		0			0
$206$		−	2.04368i		−	0.142390i
$207$		0			0
$208$	−4.35646	−	4.35646i	−0.302066	−	0.302066i
$209$	−5.30734	−	9.19258i	−0.367116	−	0.635864i
$210$		0			0
$211$	9.56007	−	16.5585i	0.658142	−	1.13994i	−0.322954	−	0.946415i	$-0.604676\pi$
$211$	9.56007	−	16.5585i	0.658142	−	1.13994i	0.981096	−	0.193521i	$-0.0619909\pi$
$212$	16.4102	−	4.39709i	1.12705	−	0.301993i
$213$		0			0
$214$	−2.46988	+	1.42599i	−0.168837	+	0.0974783i
$215$		0			0
$216$		0			0
$217$	−6.80981	+	6.80981i	−0.462280	+	0.462280i
$218$	−0.0639194	−	0.0171272i	−0.00432917	−	0.00116000i
$219$		0			0
$220$		0			0
$221$	0.806719	+	0.465759i	0.0542658	+	0.0313304i
$222$		0			0
$223$	1.08126	−	4.03530i	0.0724062	−	0.270224i	−0.920226	−	0.391386i	$-0.871996\pi$
$223$	1.08126	−	4.03530i	0.0724062	−	0.270224i	0.992633	+	0.121163i	$0.0386623\pi$
$224$	5.51055			0.368189
$225$		0			0
$226$	1.03650			0.0689469
$227$	3.55990	−	13.2857i	0.236279	−	0.881803i	−0.741290	−	0.671185i	$-0.765786\pi$
$227$	3.55990	−	13.2857i	0.236279	−	0.881803i	0.977568	−	0.210618i	$-0.0675478\pi$
$228$		0			0
$229$	13.2694	+	7.66109i	0.876866	+	0.506259i	0.869624	−	0.493715i	$-0.164361\pi$
$229$	13.2694	+	7.66109i	0.876866	+	0.506259i	0.00724242	+	0.999974i	$0.497695\pi$
$230$		0			0
$231$		0			0
$232$	−4.73125	−	1.26773i	−0.310622	−	0.0832308i
$233$	2.98562	−	2.98562i	0.195595	−	0.195595i	−0.602514	−	0.798108i	$-0.705834\pi$
$233$	2.98562	−	2.98562i	0.195595	−	0.195595i	0.798108	+	0.602514i	$0.205834\pi$
$234$		0			0
$235$		0			0
$236$	−7.72529	+	4.46020i	−0.502874	+	0.290334i
$237$		0			0
$238$	−0.259805	+	0.0696146i	−0.0168407	+	0.00451245i
$239$	2.59439	−	4.49362i	0.167817	−	0.290668i	−0.769835	−	0.638243i	$-0.779661\pi$
$239$	2.59439	−	4.49362i	0.167817	−	0.290668i	0.937652	+	0.347575i	$0.112995\pi$
$240$		0			0
$241$	1.85872	+	3.21939i	0.119730	+	0.207379i	0.919661	−	0.392714i	$-0.128464\pi$
$241$	1.85872	+	3.21939i	0.119730	+	0.207379i	−0.799930	+	0.600093i	$0.795130\pi$
$242$	0.664193	+	0.664193i	0.0426959	+	0.0426959i
$243$		0			0
$244$		−	0.925646i		−	0.0592584i
$245$		0			0
$246$		0			0
$247$	1.80959	+	6.75347i	0.115141	+	0.429713i
$248$	0.779940	+	2.91078i	0.0495262	+	0.184834i
$249$		0			0
$250$		0			0
$251$		−	3.97271i		−	0.250755i	−0.992109	−	0.125378i	$-0.959986\pi$
$251$		−	3.97271i		−	0.250755i	0.992109	−	0.125378i	$-0.0400142\pi$
$252$		0			0
$253$	12.3665	+	12.3665i	0.777472	+	0.777472i
$254$	−0.489717	−	0.848215i	−0.0307276	−	0.0532217i
$255$		0			0
$256$	−6.55403	+	11.3519i	−0.409627	+	0.709495i
$257$	−16.5120	+	4.42437i	−1.02999	+	0.275985i	−0.733959	−	0.679194i	$-0.762329\pi$
$257$	−16.5120	+	4.42437i	−1.02999	+	0.275985i	−0.296030	+	0.955179i	$0.595663\pi$
$258$		0			0
$259$	0.514262	−	0.296909i	0.0319547	−	0.0184491i
$260$		0			0
$261$		0			0
$262$	−2.28571	+	2.28571i	−0.141211	+	0.141211i
$263$	10.3436	+	2.77155i	0.637812	+	0.170901i	0.563212	−	0.826312i	$-0.309565\pi$
$263$	10.3436	+	2.77155i	0.637812	+	0.170901i	0.0746001	+	0.997214i	$0.476232\pi$
$264$		0			0
$265$		0			0
$266$	−1.74834	−	1.00941i	−0.107198	−	0.0618907i
$267$		0			0
$268$	−0.870407	+	3.24840i	−0.0531685	+	0.198428i
$269$	15.8925			0.968985			0.484492	−	0.874796i	$-0.339004\pi$
$269$	15.8925			0.968985			0.484492	+	0.874796i	$0.339004\pi$
$270$		0			0
$271$	0.974200			0.0591785			0.0295892	−	0.999562i	$-0.490580\pi$
$271$	0.974200			0.0591785			0.0295892	+	0.999562i	$0.490580\pi$
$272$	0.558646	−	2.08490i	0.0338729	−	0.126415i
$273$		0			0
$274$	1.06786	+	0.616528i	0.0645117	+	0.0372458i
$275$		0			0
$276$		0			0
$277$	23.0788	+	6.18395i	1.38667	+	0.371557i	0.873540	−	0.486753i	$-0.161819\pi$
$277$	23.0788	+	6.18395i	1.38667	+	0.371557i	0.513131	+	0.858310i	$0.328485\pi$
$278$	−1.43173	+	1.43173i	−0.0858695	+	0.0858695i
$279$		0			0
$280$		0			0
$281$	23.9241	−	13.8126i	1.42720	−	0.823991i	0.430296	−	0.902688i	$-0.358409\pi$
$281$	23.9241	−	13.8126i	1.42720	−	0.823991i	0.996899	+	0.0786961i	$0.0250757\pi$
$282$		0			0
$283$	16.4535	−	4.40870i	0.978058	−	0.262070i	0.265831	−	0.964020i	$-0.414354\pi$
$283$	16.4535	−	4.40870i	0.978058	−	0.262070i	0.712227	+	0.701950i	$0.247687\pi$
$284$	3.44066	−	5.95939i	0.204165	−	0.353625i
$285$		0			0
$286$	0.389161	+	0.674046i	0.0230115	+	0.0398572i
$287$	13.0067	+	13.0067i	0.767761	+	0.767761i
$288$		0			0
$289$		−	16.6736i		−	0.980803i
$290$		0			0
$291$		0			0
$292$	−4.94897	−	18.4698i	−0.289617	−	1.08086i
$293$	6.90146	+	25.7566i	0.403188	+	1.50472i	0.807374	+	0.590041i	$0.200888\pi$
$293$	6.90146	+	25.7566i	0.403188	+	1.50472i	−0.404186	+	0.914677i	$0.632445\pi$
$294$		0			0
$295$		0			0
$296$		−	0.185810i		−	0.0108000i
$297$		0			0
$298$	1.35407	+	1.35407i	0.0784392	+	0.0784392i
$299$	−5.75979	−	9.97625i	−0.333097	−	0.576941i
$300$		0			0
$301$	−6.25973	+	10.8422i	−0.360805	+	0.624933i
$302$	−2.59228	+	0.694599i	−0.149169	+	0.0399697i
$303$		0			0
$304$	14.0302	−	8.10033i	0.804686	−	0.464586i
$305$		0			0
$306$		0			0
$307$	12.3556	−	12.3556i	0.705171	−	0.705171i	−0.260345	−	0.965516i	$-0.583836\pi$
$307$	12.3556	−	12.3556i	0.705171	−	0.705171i	0.965516	+	0.260345i	$0.0838363\pi$
$308$	11.4610	+	3.07098i	0.653053	+	0.174985i
$309$		0			0
$310$		0			0
$311$	−7.49228	−	4.32567i	−0.424848	−	0.245286i	0.272301	−	0.962212i	$-0.412215\pi$
$311$	−7.49228	−	4.32567i	−0.424848	−	0.245286i	−0.697149	+	0.716926i	$0.745549\pi$
$312$		0			0
$313$	−4.85240	+	18.1094i	−0.274274	+	1.02360i	0.682052	+	0.731303i	$0.261088\pi$
$313$	−4.85240	+	18.1094i	−0.274274	+	1.02360i	−0.956326	+	0.292301i	$0.905579\pi$
$314$	−4.03949			−0.227962
$315$		0			0
$316$	14.7357			0.828946
$317$	5.02186	−	18.7418i	0.282056	−	1.05265i	−0.668908	−	0.743345i	$-0.733238\pi$
$317$	5.02186	−	18.7418i	0.282056	−	1.05265i	0.950964	−	0.309301i	$-0.100095\pi$
$318$		0			0
$319$	−13.7434	−	7.93476i	−0.769484	−	0.444262i
$320$		0			0
$321$		0			0
$322$	3.21287	+	0.860886i	0.179046	+	0.0479753i
$323$	−1.73205	+	1.73205i	−0.0963739	+	0.0963739i
$324$		0			0
$325$		0			0
$326$	0.573535	−	0.331131i	0.0317652	−	0.0183396i
$327$		0			0
$328$	5.55956	−	1.48968i	0.306975	−	0.0822538i
$329$	3.68372	−	6.38039i	0.203090	−	0.351763i
$330$		0			0
$331$	17.1969	+	29.7859i	0.945226	+	1.63718i	0.755298	+	0.655382i	$0.227492\pi$
$331$	17.1969	+	29.7859i	0.945226	+	1.63718i	0.189929	+	0.981798i	$0.439174\pi$
$332$	−15.3258	−	15.3258i	−0.841114	−	0.841114i
$333$		0			0
$334$			1.64333i			0.0899191i
$335$		0			0
$336$		0			0
$337$	8.28744	+	30.9291i	0.451445	+	1.68482i	0.698333	+	0.715773i	$0.253925\pi$
$337$	8.28744	+	30.9291i	0.451445	+	1.68482i	−0.246888	+	0.969044i	$0.579408\pi$
$338$	0.516060	+	1.92596i	0.0280700	+	0.104758i
$339$		0			0
$340$		0			0
$341$			9.76331i			0.528713i
$342$		0			0
$343$	−13.8776	−	13.8776i	−0.749320	−	0.749320i
$344$	1.95871	+	3.39259i	0.105607	+	0.182916i
$345$		0			0
$346$	−1.70397	+	2.95136i	−0.0916059	+	0.158666i
$347$	−15.5122	+	4.15647i	−0.832737	+	0.223131i	−0.649907	−	0.760014i	$-0.725192\pi$
$347$	−15.5122	+	4.15647i	−0.832737	+	0.223131i	−0.182829	+	0.983145i	$0.558526\pi$
$348$		0			0
$349$	15.1664	−	8.75630i	0.811837	−	0.468714i	−0.0357566	−	0.999361i	$-0.511384\pi$
$349$	15.1664	−	8.75630i	0.811837	−	0.468714i	0.847593	+	0.530646i	$0.178051\pi$
$350$		0			0
$351$		0			0
$352$	3.95028	−	3.95028i	0.210550	−	0.210550i
$353$	18.4846	+	4.95294i	0.983837	+	0.263618i	0.714660	−	0.699472i	$-0.246582\pi$
$353$	18.4846	+	4.95294i	0.983837	+	0.263618i	0.269177	+	0.963091i	$0.413248\pi$
$354$		0			0
$355$		0			0
$356$	4.93169	+	2.84731i	0.261379	+	0.150907i
$357$		0			0
$358$	−0.414594	+	1.54728i	−0.0219120	+	0.0817766i
$359$	−23.0127			−1.21457			−0.607283	−	0.794486i	$-0.707741\pi$
$359$	−23.0127			−1.21457			−0.607283	+	0.794486i	$0.707741\pi$
$360$		0			0
$361$	0.614846			0.0323603
$362$	−0.236258	+	0.881728i	−0.0124175	+	0.0463426i
$363$		0			0
$364$	−6.76842	−	3.90775i	−0.354762	−	0.204822i
$365$		0			0
$366$		0			0
$367$	−26.1875	−	7.01692i	−1.36698	−	0.366280i	−0.500603	−	0.865677i	$-0.666888\pi$
$367$	−26.1875	−	7.01692i	−1.36698	−	0.366280i	−0.866373	+	0.499397i	$0.833555\pi$
$368$	−18.8743	+	18.8743i	−0.983891	+	0.983891i
$369$		0			0
$370$		0			0
$371$	18.3039	−	10.5678i	0.950293	−	0.548652i
$372$		0			0
$373$	−28.9771	+	7.76440i	−1.50038	+	0.402025i	−0.913227	−	0.407451i	$-0.866418\pi$
$373$	−28.9771	+	7.76440i	−1.50038	+	0.402025i	−0.587152	+	0.809477i	$0.699751\pi$
$374$	−0.136339	+	0.236147i	−0.00704994	+	0.0122109i
$375$		0			0
$376$	−1.15266	−	1.99647i	−0.0594440	−	0.102960i
$377$	7.39138	+	7.39138i	0.380675	+	0.380675i
$378$		0			0
$379$			20.0943i			1.03218i	0.856535	+	0.516089i	$0.172612\pi$
$379$			20.0943i			1.03218i	−0.856535	+	0.516089i	$0.827388\pi$
$380$		0			0
$381$		0			0
$382$	−0.192983	−	0.720223i	−0.00987388	−	0.0368498i
$383$	−7.14181	−	26.6536i	−0.364929	−	1.36194i	−0.867516	−	0.497409i	$-0.834285\pi$
$383$	−7.14181	−	26.6536i	−0.364929	−	1.36194i	0.502587	−	0.864527i	$-0.332382\pi$
$384$		0			0
$385$		0			0
$386$			3.31162i			0.168557i
$387$		0			0
$388$	−2.03579	−	2.03579i	−0.103352	−	0.103352i
$389$	6.71184	+	11.6253i	0.340304	+	0.589424i	0.984489	−	0.175446i	$-0.0561367\pi$
$389$	6.71184	+	11.6253i	0.340304	+	0.589424i	−0.644185	+	0.764870i	$0.722803\pi$
$390$		0			0
$391$	2.01790	−	3.49510i	0.102049	−	0.176755i
$392$	−0.765487	+	0.205111i	−0.0386629	+	0.0103597i
$393$		0			0
$394$	2.60673	−	1.50500i	0.131325	−	0.0758207i
$395$		0			0
$396$		0			0
$397$	12.8716	−	12.8716i	0.646008	−	0.646008i	−0.306018	−	0.952026i	$-0.598997\pi$
$397$	12.8716	−	12.8716i	0.646008	−	0.646008i	0.952026	+	0.306018i	$0.0989967\pi$
$398$	0.670732	+	0.179722i	0.0336208	+	0.00900866i
$399$		0			0
$400$		0			0
$401$	21.7606	+	12.5635i	1.08667	+	0.627391i	0.932689	−	0.360682i	$-0.117456\pi$
$401$	21.7606	+	12.5635i	1.08667	+	0.627391i	0.153985	+	0.988073i	$0.450789\pi$
$402$		0			0
$403$	1.66445	−	6.21180i	0.0829120	−	0.309432i
$404$	−34.8046			−1.73159
$405$		0			0
$406$	−3.01824			−0.149793
$407$	0.155811	−	0.581494i	0.00772325	−	0.0288236i
$408$		0			0
$409$	9.81878	+	5.66888i	0.485508	+	0.280308i	0.722709	−	0.691153i	$-0.242897\pi$
$409$	9.81878	+	5.66888i	0.485508	+	0.280308i	−0.237201	+	0.971461i	$0.576230\pi$
$410$		0			0
$411$		0			0
$412$	20.0957	+	5.38461i	0.990042	+	0.265281i
$413$	−7.84719	+	7.84719i	−0.386135	+	0.386135i
$414$		0			0
$415$		0			0
$416$	−3.18676	+	1.83988i	−0.156244	+	0.0902074i
$417$		0			0
$418$	−1.97691	+	0.529711i	−0.0966938	+	0.0259090i
$419$	4.26264	−	7.38311i	0.208244	−	0.360688i	−0.742918	−	0.669383i	$-0.766559\pi$
$419$	4.26264	−	7.38311i	0.208244	−	0.360688i	0.951161	+	0.308694i	$0.0998920\pi$
$420$		0			0
$421$	1.10329	+	1.91095i	0.0537710	+	0.0931341i	0.891658	−	0.452710i	$-0.149543\pi$
$421$	1.10329	+	1.91095i	0.0537710	+	0.0931341i	−0.837887	+	0.545844i	$0.816209\pi$
$422$	−2.60683	−	2.60683i	−0.126898	−	0.126898i
$423$		0			0
$424$		−	6.61346i		−	0.321178i
$425$		0			0
$426$		0			0
$427$	−0.298048	−	1.11233i	−0.0144235	−	0.0538294i
$428$	−7.51426	−	28.0436i	−0.363215	−	1.35554i
$429$		0			0
$430$		0			0
$431$			1.95738i			0.0942838i	0.998888	+	0.0471419i	$0.0150113\pi$
$431$			1.95738i			0.0942838i	−0.998888	+	0.0471419i	$0.984989\pi$
$432$		0			0
$433$	9.71652	+	9.71652i	0.466946	+	0.466946i	0.900924	−	0.433978i	$-0.142890\pi$
$433$	9.71652	+	9.71652i	0.466946	+	0.466946i	−0.433978	+	0.900924i	$0.642890\pi$
$434$	0.928445	+	1.60811i	0.0445668	+	0.0771919i
$435$		0			0
$436$	0.336825	−	0.583398i	0.0161310	−	0.0279397i
$437$	29.2593	−	7.84002i	1.39966	−	0.375039i
$438$		0			0
$439$	4.68008	−	2.70205i	0.223368	−	0.128962i	−0.384141	−	0.923275i	$-0.625502\pi$
$439$	4.68008	−	2.70205i	0.223368	−	0.128962i	0.607509	+	0.794313i	$0.292169\pi$
$440$		0			0
$441$		0			0
$442$	0.127003	−	0.127003i	0.00604090	−	0.00604090i
$443$	26.0848	+	6.98940i	1.23933	+	0.332077i	0.818204	−	0.574927i	$-0.194970\pi$
$443$	26.0848	+	6.98940i	1.23933	+	0.332077i	0.421122	+	0.907004i	$0.361636\pi$
$444$		0			0
$445$		0			0
$446$	−0.697588	−	0.402752i	−0.0330317	−	0.0190709i
$447$		0			0
$448$	−4.50086	+	16.7974i	−0.212646	+	0.793604i
$449$	23.8541			1.12574			0.562872	−	0.826544i	$-0.309696\pi$
$449$	23.8541			1.12574			0.562872	+	0.826544i	$0.309696\pi$
$450$		0			0
$451$	18.6479			0.878093
$452$	−2.73093	+	10.1920i	−0.128452	+	0.479389i
$453$		0			0
$454$	−2.29672	−	1.32601i	−0.107790	−	0.0622328i
$455$		0			0
$456$		0			0
$457$	−19.1467	−	5.13035i	−0.895647	−	0.239988i	−0.218501	−	0.975837i	$-0.570117\pi$
$457$	−19.1467	−	5.13035i	−0.895647	−	0.239988i	−0.677146	+	0.735849i	$0.736783\pi$
$458$	2.08902	−	2.08902i	0.0976133	−	0.0976133i
$459$		0			0
$460$		0			0
$461$	1.14371	−	0.660321i	0.0532679	−	0.0307542i	−0.473130	−	0.880993i	$-0.656876\pi$
$461$	1.14371	−	0.660321i	0.0532679	−	0.0307542i	0.526397	+	0.850239i	$0.323542\pi$
$462$		0			0
$463$	14.8827	−	3.98780i	0.691656	−	0.185329i	0.104166	−	0.994560i	$-0.466783\pi$
$463$	14.8827	−	3.98780i	0.691656	−	0.185329i	0.587490	+	0.809231i	$0.300116\pi$
$464$	12.1104	−	20.9759i	0.562213	−	0.973782i
$465$		0			0
$466$	−0.407058	−	0.705045i	−0.0188566	−	0.0326606i
$467$	1.77645	+	1.77645i	0.0822044	+	0.0822044i	0.747013	−	0.664809i	$-0.231487\pi$
$467$	1.77645	+	1.77645i	0.0822044	+	0.0822044i	−0.664809	+	0.747013i	$0.731487\pi$
$468$		0			0
$469$			4.18380i			0.193190i
$470$		0			0
$471$		0			0
$472$	0.898753	+	3.35419i	0.0413685	+	0.154389i
$473$	3.28495	+	12.2596i	0.151042	+	0.563697i
$474$		0			0
$475$		0			0
$476$		−	2.73810i		−	0.125501i
$477$		0			0
$478$	−0.707436	−	0.707436i	−0.0323574	−	0.0323574i
$479$	18.9907	+	32.8928i	0.867705	+	1.50291i	0.864336	+	0.502915i	$0.167739\pi$
$479$	18.9907	+	32.8928i	0.867705	+	1.50291i	0.00336919	+	0.999994i	$0.498928\pi$
$480$		0			0
$481$	−0.198266	+	0.343406i	−0.00904014	+	0.0156580i
$482$	0.692346	−	0.185513i	0.0315355	−	0.00844991i
$483$		0			0
$484$	−8.28104	+	4.78106i	−0.376411	+	0.217321i
$485$		0			0
$486$		0			0
$487$	−23.6900	+	23.6900i	−1.07350	+	1.07350i	−0.0764213	+	0.997076i	$0.524349\pi$
$487$	−23.6900	+	23.6900i	−1.07350	+	1.07350i	−0.997076	+	0.0764213i	$0.975651\pi$
$488$	−0.348056	−	0.0932612i	−0.0157557	−	0.00422174i
$489$		0			0
$490$		0			0
$491$	−18.9114	−	10.9185i	−0.853460	−	0.492746i	0.00835660	−	0.999965i	$-0.497340\pi$
$491$	−18.9114	−	10.9185i	−0.853460	−	0.492746i	−0.861817	+	0.507220i	$0.830673\pi$
$492$		0			0
$493$	−0.947827	+	3.53734i	−0.0426880	+	0.159314i
$494$	1.34809			0.0606535
$495$		0			0
$496$	−14.9013			−0.669086
$497$	2.21571	−	8.26913i	0.0993881	−	0.370921i
$498$		0			0
$499$	2.74862	+	1.58691i	0.123045	+	0.0710401i	0.560259	−	0.828317i	$-0.310702\pi$
$499$	2.74862	+	1.58691i	0.123045	+	0.0710401i	−0.437214	+	0.899357i	$0.644035\pi$
$500$		0			0
$501$		0			0
$502$	−0.739889	−	0.198253i	−0.0330229	−	0.00884845i
$503$	7.00484	−	7.00484i	0.312330	−	0.312330i	−0.533481	−	0.845812i	$-0.679117\pi$
$503$	7.00484	−	7.00484i	0.312330	−	0.312330i	0.845812	+	0.533481i	$0.179117\pi$
$504$		0			0
$505$		0			0
$506$	2.92030	−	1.68603i	0.129823	−	0.0749534i
$507$		0			0
$508$	9.63084	−	2.58058i	0.427299	−	0.114495i
$509$	8.36206	−	14.4835i	0.370642	−	0.641971i	−0.619023	−	0.785373i	$-0.712471\pi$
$509$	8.36206	−	14.4835i	0.370642	−	0.641971i	0.989664	+	0.143403i	$0.0458044\pi$
$510$		0			0
$511$	−11.8942	−	20.6013i	−0.526167	−	0.911347i
$512$	10.1119	+	10.1119i	0.446886	+	0.446886i
$513$		0			0
$514$			3.29603i			0.145382i
$515$		0			0
$516$		0			0
$517$	−1.93313	−	7.21452i	−0.0850188	−	0.317294i
$518$	−0.0296337	−	0.110595i	−0.00130203	−	0.00485925i
$519$		0			0
$520$		0			0
$521$		−	1.34092i		−	0.0587466i	−0.999569	−	0.0293733i	$-0.990649\pi$
$521$		−	1.34092i		−	0.0587466i	0.999569	−	0.0293733i	$-0.00935116\pi$
$522$		0			0
$523$	9.19187	+	9.19187i	0.401933	+	0.401933i	0.878914	−	0.476981i	$-0.158269\pi$
$523$	9.19187	+	9.19187i	0.401933	+	0.401933i	−0.476981	+	0.878914i	$0.658269\pi$
$524$	−16.4532	−	28.4978i	−0.718761	−	1.24493i
$525$		0			0
$526$	1.03237	−	1.78811i	0.0450133	−	0.0779653i
$527$	2.17625	−	0.583126i	0.0947991	−	0.0254014i
$528$		0			0
$529$	−23.3034	+	13.4542i	−1.01319	+	0.584967i
$530$		0			0
$531$		0			0
$532$	14.5320	−	14.5320i	0.630043	−	0.630043i
$533$	−11.8645	−	3.17908i	−0.513908	−	0.137701i
$534$		0			0
$535$		0			0
$536$	1.13375	+	0.654569i	0.0489704	+	0.0282731i
$537$		0			0
$538$	0.793096	−	2.95987i	0.0341928	−	0.127609i
$539$	−2.56759			−0.110594
$540$		0			0
$541$	−34.0389			−1.46345			−0.731724	−	0.681601i	$-0.761284\pi$
$541$	−34.0389			−1.46345			−0.731724	+	0.681601i	$0.761284\pi$
$542$	0.0486162	−	0.181438i	0.00208824	−	0.00779343i
$543$		0			0
$544$	−1.11646	−	0.644587i	−0.0478677	−	0.0276364i
$545$		0			0
$546$		0			0
$547$	9.12437	+	2.44487i	0.390130	+	0.104535i	0.448552	−	0.893757i	$-0.351940\pi$
$547$	9.12437	+	2.44487i	0.390130	+	0.104535i	−0.0584215	+	0.998292i	$0.518607\pi$
$548$	−8.87591	+	8.87591i	−0.379160	+	0.379160i
$549$		0			0
$550$		0			0
$551$	−23.8043	+	13.7434i	−1.01410	+	0.585489i
$552$		0			0
$553$	17.7075	−	4.74472i	0.753001	−	0.201766i
$554$	2.30343	−	3.98967i	0.0978636	−	0.169505i
$555$		0			0
$556$	−10.3060	−	17.8506i	−0.437073	−	0.757033i
$557$	−1.48579	−	1.48579i	−0.0629551	−	0.0629551i	0.674928	−	0.737883i	$-0.264175\pi$
$557$	−1.48579	−	1.48579i	−0.0629551	−	0.0629551i	−0.737883	+	0.674928i	$0.764175\pi$
$558$		0			0
$559$		−	8.36006i		−	0.353593i
$560$		0			0
$561$		0			0
$562$	−1.37860	−	5.14501i	−0.0581527	−	0.217029i
$563$	−5.52969	−	20.6371i	−0.233049	−	0.869750i	−0.979019	−	0.203770i	$-0.934681\pi$
$563$	−5.52969	−	20.6371i	−0.233049	−	0.869750i	0.745970	−	0.665979i	$-0.231986\pi$
$564$		0			0
$565$		0			0
$566$		−	3.28436i		−	0.138052i
$567$		0			0
$568$	−1.89416	−	1.89416i	−0.0794771	−	0.0794771i
$569$	5.82589	+	10.0907i	0.244234	+	0.423026i	0.961916	−	0.273345i	$-0.0881301\pi$
$569$	5.82589	+	10.0907i	0.244234	+	0.423026i	−0.717682	+	0.696371i	$0.754797\pi$
$570$		0			0
$571$	10.5623	−	18.2945i	0.442020	−	0.765601i	−0.555819	−	0.831303i	$-0.687595\pi$
$571$	10.5623	−	18.2945i	0.442020	−	0.765601i	0.997839	+	0.0657023i	$0.0209288\pi$
$572$	−7.65328	+	2.05069i	−0.320000	+	0.0857436i
$573$		0			0
$574$	3.07149	−	1.77332i	0.128201	−	0.0740171i
$575$		0			0
$576$		0			0
$577$	−30.1119	+	30.1119i	−1.25357	+	1.25357i	−0.299469	+	0.954106i	$0.596809\pi$
$577$	−30.1119	+	30.1119i	−1.25357	+	1.25357i	−0.954106	+	0.299469i	$0.903191\pi$
$578$	−3.10535	−	0.832076i	−0.129166	−	0.0346098i
$579$		0			0
$580$		0			0
$581$	−23.3515	−	13.4820i	−0.968782	−	0.559327i
$582$		0			0
$583$	5.54571	−	20.6969i	0.229680	−	0.857177i
$584$	−7.44353			−0.308015
$585$		0			0
$586$	5.14140			0.212389
$587$	−2.28631	+	8.53262i	−0.0943661	+	0.352179i	−0.996923	−	0.0783924i	$-0.975021\pi$
$587$	−2.28631	+	8.53262i	−0.0943661	+	0.352179i	0.902556	+	0.430571i	$0.141688\pi$
$588$		0			0
$589$	14.6450	+	8.45527i	0.603435	+	0.348393i
$590$		0			0
$591$		0			0
$592$	0.887505	+	0.237806i	0.0364762	+	0.00977377i
$593$	−24.5829	+	24.5829i	−1.00950	+	1.00950i	−0.00954475	+	0.999954i	$0.503038\pi$
$593$	−24.5829	+	24.5829i	−1.00950	+	1.00950i	−0.999954	+	0.00954475i	$0.996962\pi$
$594$		0			0
$595$		0			0
$596$	−16.8823	+	9.74700i	−0.691526	+	0.399253i
$597$		0			0
$598$	−2.14544	+	0.574869i	−0.0877336	+	0.0235082i
$599$	−18.8291	+	32.6129i	−0.769335	+	1.33253i	0.168590	+	0.985686i	$0.446079\pi$
$599$	−18.8291	+	32.6129i	−0.769335	+	1.33253i	−0.937924	+	0.346840i	$0.887255\pi$
$600$		0			0
$601$	11.1158	+	19.2532i	0.453424	+	0.785354i	0.998596	−	0.0529703i	$-0.0168689\pi$
$601$	11.1158	+	19.2532i	0.453424	+	0.785354i	−0.545172	+	0.838324i	$0.683536\pi$
$602$	1.70690	+	1.70690i	0.0695679	+	0.0695679i
$603$		0			0
$604$		−	27.3201i		−	1.11164i
$605$		0			0
$606$		0			0
$607$	−5.59982	−	20.8988i	−0.227290	−	0.848257i	−0.981474	−	0.191594i	$-0.938634\pi$
$607$	−5.59982	−	20.8988i	−0.227290	−	0.848257i	0.754184	−	0.656663i	$-0.228032\pi$
$608$	−2.50437	−	9.34645i	−0.101566	−	0.379049i
$609$		0			0
$610$		0			0
$611$			4.91972i			0.199031i
$612$		0			0
$613$	−15.7726	−	15.7726i	−0.637051	−	0.637051i	0.312776	−	0.949827i	$-0.398741\pi$
$613$	−15.7726	−	15.7726i	−0.637051	−	0.637051i	−0.949827	+	0.312776i	$0.898741\pi$
$614$	−1.68455	−	2.91773i	−0.0679830	−	0.117750i
$615$		0			0
$616$	2.30946	−	4.00010i	0.0930507	−	0.161169i
$617$	−40.8914	+	10.9568i	−1.64622	+	0.441104i	−0.958552	−	0.284917i	$-0.908034\pi$
$617$	−40.8914	+	10.9568i	−1.64622	+	0.441104i	−0.687672	+	0.726021i	$0.741367\pi$
$618$		0			0
$619$	−27.5855	+	15.9265i	−1.10876	+	0.640141i	−0.938507	−	0.345260i	$-0.887791\pi$
$619$	−27.5855	+	15.9265i	−1.10876	+	0.640141i	−0.170250	+	0.985401i	$0.554457\pi$
$620$		0			0
$621$		0			0
$622$	−1.17952	+	1.17952i	−0.0472944	+	0.0472944i
$623$	6.84311	+	1.83361i	0.274163	+	0.0734619i
$624$		0			0
$625$		0			0
$626$	3.13060	+	1.80745i	0.125124	+	0.0722403i
$627$		0			0
$628$	10.6431	−	39.7206i	0.424706	−	1.58502i
$629$	−0.138922			−0.00553917
$630$		0			0
$631$	15.7931			0.628713			0.314356	−	0.949305i	$-0.398211\pi$
$631$	15.7931			0.628713			0.314356	+	0.949305i	$0.398211\pi$
$632$	1.48466	−	5.54081i	0.0590564	−	0.220402i
$633$		0			0
$634$	−3.23993	−	1.87057i	−0.128674	−	0.0742899i
$635$		0			0
$636$		0			0
$637$	1.63360	+	0.437722i	0.0647256	+	0.0173432i
$638$	−2.16364	+	2.16364i	−0.0856594	+	0.0856594i
$639$		0			0
$640$		0			0
$641$	8.57453	−	4.95051i	0.338673	−	0.195533i	−0.321012	−	0.947075i	$-0.604023\pi$
$641$	8.57453	−	4.95051i	0.338673	−	0.195533i	0.659685	+	0.751542i	$0.270690\pi$
$642$		0			0
$643$	−45.6232	+	12.2247i	−1.79920	+	0.482095i	−0.993853	−	0.110706i	$-0.964689\pi$
$643$	−45.6232	+	12.2247i	−1.79920	+	0.482095i	−0.805349	+	0.592801i	$0.798022\pi$
$644$	−16.9303	+	29.3241i	−0.667147	+	1.15553i
$645$		0			0
$646$	0.236147	+	0.409018i	0.00929107	+	0.0160926i
$647$	9.75824	+	9.75824i	0.383636	+	0.383636i	0.872410	−	0.488774i	$-0.162556\pi$
$647$	9.75824	+	9.75824i	0.383636	+	0.383636i	−0.488774	+	0.872410i	$0.662556\pi$
$648$		0			0
$649$			11.2506i			0.441625i
$650$		0			0
$651$		0			0
$652$	1.74490	+	6.51206i	0.0683356	+	0.255032i
$653$	−0.802065	−	2.99335i	−0.0313872	−	0.117139i	0.948455	−	0.316912i	$-0.102646\pi$
$653$	−0.802065	−	2.99335i	−0.0313872	−	0.117139i	−0.979842	+	0.199773i	$0.935979\pi$
$654$		0			0
$655$		0			0
$656$			28.4613i			1.11123i
$657$		0			0
$658$	−1.00447	−	1.00447i	−0.0391584	−	0.0391584i
$659$	13.5644	+	23.4942i	0.528393	+	0.915204i	0.999452	+	0.0331023i	$0.0105387\pi$
$659$	13.5644	+	23.4942i	0.528393	+	0.915204i	−0.471059	+	0.882102i	$0.656128\pi$
$660$		0			0
$661$	−9.54526	+	16.5329i	−0.371268	+	0.643055i	−0.989761	−	0.142736i	$-0.954410\pi$
$661$	−9.54526	+	16.5329i	−0.371268	+	0.643055i	0.618493	+	0.785790i	$0.287743\pi$
$662$	6.40560	−	1.71638i	0.248961	−	0.0667088i
$663$		0			0
$664$	−7.30683	+	4.21860i	−0.283560	+	0.163713i
$665$		0			0
$666$		0			0
$667$	32.0231	−	32.0231i	1.23994	−	1.23994i
$668$	−16.1590	−	4.32979i	−0.625210	−	0.167524i
$669$		0			0
$670$		0			0
$671$	−1.01104	−	0.583723i	−0.0390307	−	0.0225344i
$672$		0			0
$673$	−0.0359820	+	0.134287i	−0.00138701	+	0.00517638i	−0.966616	−	0.256230i	$-0.917520\pi$
$673$	−0.0359820	+	0.134287i	−0.00138701	+	0.00517638i	0.965229	+	0.261406i	$0.0841862\pi$
$674$	6.17391			0.237810
$675$		0			0
$676$	−20.2978			−0.780684
$677$	−2.09108	+	7.80401i	−0.0803667	+	0.299933i	−0.994397	−	0.105714i	$-0.966287\pi$
$677$	−2.09108	+	7.80401i	−0.0803667	+	0.299933i	0.914030	+	0.405647i	$0.132954\pi$
$678$		0			0
$679$	−3.10188	−	1.79087i	−0.119039	−	0.0687272i
$680$		0			0
$681$		0			0
$682$	1.81835	+	0.487225i	0.0696281	+	0.0186568i
$683$	35.0271	−	35.0271i	1.34027	−	1.34027i	0.444490	−	0.895784i	$-0.353385\pi$
$683$	35.0271	−	35.0271i	1.34027	−	1.34027i	0.895784	−	0.444490i	$-0.146615\pi$
$684$		0			0
$685$		0			0
$686$	−3.27715	+	1.89206i	−0.125122	+	0.0722393i
$687$		0			0
$688$	−18.7112	+	5.01366i	−0.713359	+	0.191144i
$689$	−7.05680	+	12.2227i	−0.268843	+	0.465649i
$690$		0			0
$691$	−20.5195	−	35.5408i	−0.780597	−	1.35203i	−0.931594	−	0.363500i	$-0.881582\pi$
$691$	−20.5195	−	35.5408i	−0.780597	−	1.35203i	0.150997	−	0.988534i	$-0.451752\pi$
$692$	−24.5313	−	24.5313i	−0.932541	−	0.932541i
$693$		0			0
$694$			3.09646i			0.117540i
$695$		0			0
$696$		0			0
$697$	−1.11377	−	4.15663i	−0.0421869	−	0.157444i
$698$	−0.873943	−	3.26160i	−0.0330792	−	0.123453i
$699$		0			0
$700$		0			0
$701$		−	37.2173i		−	1.40568i	−0.711348	−	0.702840i	$-0.751915\pi$
$701$		−	37.2173i		−	1.40568i	0.711348	−	0.702840i	$-0.248085\pi$
$702$		0			0
$703$	−0.737304	−	0.737304i	−0.0278080	−	0.0278080i
$704$	8.81487	+	15.2678i	0.332223	+	0.575427i
$705$		0			0
$706$	1.84490	−	3.19546i	0.0694337	−	0.120263i
$707$	−41.8240	+	11.2067i	−1.57295	+	0.421471i
$708$		0			0
$709$	13.3449	−	7.70466i	0.501177	−	0.289355i	−0.228023	−	0.973656i	$-0.573226\pi$
$709$	13.3449	−	7.70466i	0.501177	−	0.289355i	0.729199	+	0.684301i	$0.239893\pi$
$710$		0			0
$711$		0			0
$712$	1.56751	−	1.56751i	0.0587448	−	0.0587448i
$713$	−26.9125	−	7.21120i	−1.00788	−	0.270061i
$714$		0			0
$715$		0			0
$716$	−14.1222	−	8.15345i	−0.527771	−	0.304709i
$717$		0			0
$718$	−1.14842	+	4.28596i	−0.0428587	+	0.159951i
$719$	−11.9324			−0.445002			−0.222501	−	0.974932i	$-0.571422\pi$
$719$	−11.9324			−0.445002			−0.222501	+	0.974932i	$0.571422\pi$
$720$		0			0
$721$	25.8823			0.963908
$722$	0.0306831	−	0.114511i	0.00114191	−	0.00426165i
$723$		0			0
$724$	−8.04760	−	4.64628i	−0.299087	−	0.172678i
$725$		0			0
$726$		0			0
$727$	4.20134	+	1.12575i	0.155819	+	0.0417516i	0.335885	−	0.941903i	$-0.390965\pi$
$727$	4.20134	+	1.12575i	0.155819	+	0.0417516i	−0.180066	+	0.983654i	$0.557631\pi$
$728$	−2.15130	+	2.15130i	−0.0797326	+	0.0797326i
$729$		0			0
$730$		0			0
$731$	2.53649	−	1.46444i	0.0938153	−	0.0541643i
$732$		0			0
$733$	47.6943	−	12.7796i	1.76163	−	0.472027i	0.774583	−	0.632473i	$-0.217960\pi$
$733$	47.6943	−	12.7796i	1.76163	−	0.472027i	0.987045	+	0.160446i	$0.0512932\pi$
$734$	−2.61370	+	4.52707i	−0.0964736	+	0.167097i
$735$		0			0
$736$	7.97125	+	13.8066i	0.293824	+	0.508918i
$737$	2.99918	+	2.99918i	0.110476	+	0.110476i
$738$		0			0
$739$			16.1890i			0.595523i	0.954640	+	0.297761i	$0.0962400\pi$
$739$			16.1890i			0.595523i	−0.954640	+	0.297761i	$0.903760\pi$
$740$		0			0
$741$		0			0
$742$	−1.05474	−	3.93635i	−0.0387208	−	0.144508i
$743$	5.14520	+	19.2021i	0.188759	+	0.704458i	0.993795	+	0.111232i	$0.0354796\pi$
$743$	5.14520	+	19.2021i	0.188759	+	0.704458i	−0.805035	+	0.593227i	$0.797854\pi$
$744$		0			0
$745$		0			0
$746$			5.78426i			0.211777i
$747$		0			0
$748$	−1.96282	−	1.96282i	−0.0717679	−	0.0717679i
$749$	−18.0595	−	31.2799i	−0.659878	−	1.14294i
$750$		0			0
$751$	7.95061	−	13.7709i	0.290122	−	0.502506i	−0.683716	−	0.729748i	$-0.739637\pi$
$751$	7.95061	−	13.7709i	0.290122	−	0.502506i	0.973838	+	0.227242i	$0.0729708\pi$
$752$	11.0112	−	2.95043i	0.401536	−	0.107591i
$753$		0			0
$754$	1.74545	−	1.00774i	0.0635655	−	0.0366996i
$755$		0			0
$756$		0			0
$757$	−21.3482	+	21.3482i	−0.775914	+	0.775914i	−0.979133	−	0.203219i	$-0.934860\pi$
$757$	−21.3482	+	21.3482i	−0.775914	+	0.775914i	0.203219	+	0.979133i	$0.434860\pi$
$758$	3.74243	+	1.00278i	0.135931	+	0.0364227i
$759$		0			0
$760$		0			0
$761$	−4.74778	−	2.74113i	−0.172107	−	0.0993659i	0.411472	−	0.911422i	$-0.365015\pi$
$761$	−4.74778	−	2.74113i	−0.172107	−	0.0993659i	−0.583579	+	0.812056i	$0.698348\pi$
$762$		0			0
$763$	0.216908	−	0.809511i	0.00785259	−	0.0293063i
$764$	7.59046			0.274613
$765$		0			0
$766$	−5.32045			−0.192236
$767$	1.91800	−	7.15808i	0.0692550	−	0.258463i
$768$		0			0
$769$	7.13004	+	4.11653i	0.257116	+	0.148446i	0.623018	−	0.782207i	$-0.285906\pi$
$769$	7.13004	+	4.11653i	0.257116	+	0.148446i	−0.365902	+	0.930653i	$0.619240\pi$
$770$		0			0
$771$		0			0
$772$	−32.5634	−	8.72533i	−1.17198	−	0.314031i
$773$	14.0889	−	14.0889i	0.506743	−	0.506743i	−0.406782	−	0.913525i	$-0.633349\pi$
$773$	14.0889	−	14.0889i	0.506743	−	0.506743i	0.913525	+	0.406782i	$0.133349\pi$
$774$		0			0
$775$		0			0
$776$	−0.970598	+	0.560375i	−0.0348424	+	0.0201163i
$777$		0			0
$778$	2.50007	−	0.669891i	0.0896318	−	0.0240168i
$779$	16.1495	−	27.9718i	0.578616	−	1.00219i
$780$		0			0
$781$	−4.33944	−	7.51612i	−0.155277	−	0.268948i
$782$	−0.550238	−	0.550238i	−0.0196765	−	0.0196765i
$783$		0			0
$784$		−	3.91879i		−	0.139957i
$785$		0			0
$786$		0			0
$787$	5.21175	+	19.4505i	0.185779	+	0.693336i	0.994462	+	0.105092i	$0.0335138\pi$
$787$	5.21175	+	19.4505i	0.185779	+	0.693336i	−0.808684	+	0.588244i	$0.799820\pi$
$788$	7.93062	+	29.5975i	0.282516	+	1.05437i
$789$		0			0
$790$		0			0
$791$			13.1268i			0.466735i
$792$		0			0
$793$	0.543749	+	0.543749i	0.0193091	+	0.0193091i
$794$	−1.75491	−	3.03959i	−0.0622793	−	0.107871i
$795$		0			0
$796$	−3.53444	+	6.12183i	−0.125275	+	0.216982i
$797$	42.7605	−	11.4576i	1.51465	−	0.405850i	0.596676	−	0.802483i	$-0.296488\pi$
$797$	42.7605	−	11.4576i	1.51465	−	0.405850i	0.917978	+	0.396632i	$0.129821\pi$
$798$		0			0
$799$	−1.49267	+	0.861793i	−0.0528068	+	0.0304880i
$800$		0			0
$801$		0			0
$802$	3.42580	−	3.42580i	0.120969	−	0.120969i
$803$	−23.2946	−	6.24176i	−0.822047	−	0.220267i
$804$		0			0
$805$		0			0
$806$	−1.07384	−	0.619983i	−0.0378245	−	0.0218380i
$807$		0			0
$808$	−3.50665	+	13.0870i	−0.123364	+	0.460399i
$809$	35.4591			1.24667			0.623337	−	0.781953i	$-0.285777\pi$
$809$	35.4591			1.24667			0.623337	+	0.781953i	$0.285777\pi$
$810$		0			0
$811$	−9.68119			−0.339952			−0.169976	−	0.985448i	$-0.554369\pi$
$811$	−9.68119			−0.339952			−0.169976	+	0.985448i	$0.554369\pi$
$812$	7.95233	−	29.6785i	0.279072	−	1.04151i
$813$		0			0
$814$	−0.100524	−	0.0580373i	−0.00352335	−	0.00203421i
$815$		0			0
$816$		0			0
$817$	21.2343	+	5.68970i	0.742893	+	0.199058i
$818$	1.54578	−	1.54578i	0.0540470	−	0.0540470i
$819$		0			0
$820$		0			0
$821$	−14.6602	+	8.46408i	−0.511645	+	0.295398i	−0.733510	−	0.679679i	$-0.762119\pi$
$821$	−14.6602	+	8.46408i	−0.511645	+	0.295398i	0.221865	+	0.975077i	$0.428786\pi$
$822$		0			0
$823$	34.3102	−	9.19340i	1.19598	−	0.320462i	0.394733	−	0.918796i	$-0.370837\pi$
$823$	34.3102	−	9.19340i	1.19598	−	0.320462i	0.801247	+	0.598334i	$0.204170\pi$
$824$	4.04938	−	7.01372i	0.141067	−	0.244335i
$825$		0			0
$826$	1.06988	+	1.85309i	0.0372259	+	0.0644772i
$827$	31.4545	+	31.4545i	1.09378	+	1.09378i	0.995121	+	0.0986577i	$0.0314549\pi$
$827$	31.4545	+	31.4545i	1.09378	+	1.09378i	0.0986577	+	0.995121i	$0.468545\pi$
$828$		0			0
$829$			17.3376i			0.602161i	0.953599	+	0.301081i	$0.0973474\pi$
$829$			17.3376i			0.602161i	−0.953599	+	0.301081i	$0.902653\pi$
$830$		0			0
$831$		0			0
$832$	−3.00551	−	11.2167i	−0.104197	−	0.388870i
$833$	0.153353	+	0.572320i	0.00531335	+	0.0198297i
$834$		0			0
$835$		0			0
$836$		−	20.8347i		−	0.720584i
$837$		0			0
$838$	−1.16233	−	1.16233i	−0.0401521	−	0.0401521i
$839$	−12.8988	−	22.3413i	−0.445315	−	0.771308i	0.552759	−	0.833341i	$-0.313575\pi$
$839$	−12.8988	−	22.3413i	−0.445315	−	0.771308i	−0.998074	+	0.0620331i	$0.980242\pi$
$840$		0			0
$841$	−6.04717	+	10.4740i	−0.208523	+	0.361173i
$842$	0.410960	−	0.110116i	0.0141626	−	0.00379486i
$843$		0			0
$844$	32.5015	−	18.7647i	1.11875	−	0.645909i
$845$		0			0
$846$		0			0
$847$	−8.41170	+	8.41170i	−0.289030	+	0.289030i
$848$	31.5886	+	8.46415i	1.08476	+	0.290660i
$849$		0			0
$850$		0			0
$851$	1.48780	+	0.858984i	0.0510013	+	0.0294456i
$852$		0			0
$853$	−3.67518	+	13.7160i	−0.125836	+	0.469626i	−0.999868	−	0.0162423i	$-0.994830\pi$
$853$	−3.67518	+	13.7160i	−0.125836	+	0.469626i	0.874032	+	0.485868i	$0.161496\pi$
$854$	−0.222037			−0.00759796
$855$		0			0
$856$	−11.3019			−0.386289
$857$	−12.9182	+	48.2115i	−0.441278	+	1.64687i	0.284303	+	0.958735i	$0.408238\pi$
$857$	−12.9182	+	48.2115i	−0.441278	+	1.64687i	−0.725581	+	0.688137i	$0.758429\pi$
$858$		0			0
$859$	−35.6374	−	20.5752i	−1.21593	−	0.702018i	−0.251886	−	0.967757i	$-0.581051\pi$
$859$	−35.6374	−	20.5752i	−1.21593	−	0.702018i	−0.964045	+	0.265739i	$0.914384\pi$
$860$		0			0
$861$		0			0
$862$	0.364549	+	0.0976806i	0.0124166	+	0.00332701i
$863$	−20.5637	+	20.5637i	−0.699996	+	0.699996i	−0.964410	−	0.264413i	$-0.914822\pi$
$863$	−20.5637	+	20.5637i	−0.699996	+	0.699996i	0.264413	+	0.964410i	$0.414822\pi$
$864$		0			0
$865$		0			0
$866$	2.29452	−	1.32474i	0.0779711	−	0.0450166i
$867$		0			0
$868$	−18.2589	+	4.89246i	−0.619748	+	0.166061i
$869$	9.29248	−	16.0950i	0.315226	−	0.545987i
$870$		0			0
$871$	−1.39690	−	2.41950i	−0.0473320	−	0.0819815i
$872$	−0.185430	−	0.185430i	−0.00627944	−	0.00627944i
$873$		0			0
$874$		−	5.84059i		−	0.197561i
$875$		0			0
$876$		0			0
$877$	12.9568	+	48.3556i	0.437521	+	1.63285i	0.734959	+	0.678111i	$0.237201\pi$
$877$	12.9568	+	48.3556i	0.437521	+	1.63285i	−0.297438	+	0.954741i	$0.596132\pi$
$878$	−0.269684	−	1.00647i	−0.00910140	−	0.0339669i
$879$		0			0
$880$		0			0
$881$			25.4215i			0.856471i	0.903667	+	0.428235i	$0.140865\pi$
$881$			25.4215i			0.856471i	−0.903667	+	0.428235i	$0.859135\pi$
$882$		0			0
$883$	27.7207	+	27.7207i	0.932874	+	0.932874i	0.997885	−	0.0650103i	$-0.0207080\pi$
$883$	27.7207	+	27.7207i	0.932874	+	0.932874i	−0.0650103	+	0.997885i	$0.520708\pi$
$884$	0.914203	+	1.58345i	0.0307480	+	0.0532571i
$885$		0			0
$886$	2.60346	−	4.50932i	0.0874648	−	0.151493i
$887$	19.9334	−	5.34114i	0.669298	−	0.179338i	0.0918595	−	0.995772i	$-0.470719\pi$
$887$	19.9334	−	5.34114i	0.669298	−	0.179338i	0.577439	+	0.816434i	$0.304052\pi$
$888$		0			0
$889$	10.7423	−	6.20205i	0.360284	−	0.208010i
$890$		0			0
$891$		0			0
$892$	5.79827	−	5.79827i	0.194140	−	0.194140i
$893$	−12.4959	−	3.34827i	−0.418160	−	0.112046i
$894$		0			0
$895$		0			0
$896$	12.4484	+	7.18706i	0.415870	+	0.240103i
$897$		0			0
$898$	1.19041	−	4.44266i	0.0397244	−	0.148253i
$899$	25.2822			0.843209
$900$		0			0
$901$	−4.94459			−0.164728
$902$	0.930596	−	3.47303i	0.0309855	−	0.115639i
$903$		0			0
$904$	3.55717	+	2.05373i	0.118310	+	0.0683061i
$905$		0			0
$906$		0			0
$907$	−38.0242	−	10.1886i	−1.26257	−	0.338305i	−0.435392	−	0.900241i	$-0.643390\pi$
$907$	−38.0242	−	10.1886i	−1.26257	−	0.338305i	−0.827181	+	0.561935i	$0.810057\pi$
$908$	19.0901	−	19.0901i	0.633526	−	0.633526i
$909$		0			0
$910$		0			0
$911$	42.5747	−	24.5805i	1.41056	−	0.814389i	0.415122	−	0.909766i	$-0.363739\pi$
$911$	42.5747	−	24.5805i	1.41056	−	0.814389i	0.995441	+	0.0953768i	$0.0304056\pi$
$912$		0			0
$913$	−26.4043	+	7.07501i	−0.873854	+	0.234149i
$914$	−1.91099	+	3.30992i	−0.0632098	+	0.109483i
$915$		0			0
$916$	15.0374	+	26.0455i	0.496848	+	0.860567i
$917$	−28.9474	−	28.9474i	−0.955928	−	0.955928i
$918$		0			0
$919$		−	7.00522i		−	0.231081i	−0.993303	−	0.115540i	$-0.963140\pi$
$919$		−	7.00522i		−	0.231081i	0.993303	−	0.115540i	$-0.0368600\pi$
$920$		0			0
$921$		0			0
$922$	−0.0659049	−	0.245960i	−0.00217046	−	0.00810028i
$923$	1.47957	+	5.52184i	0.0487007	+	0.181753i
$924$		0			0
$925$		0			0
$926$		−	2.97080i		−	0.0976265i
$927$		0			0
$928$	−10.2293	−	10.2293i	−0.335793	−	0.335793i
$929$	−1.96179	−	3.39791i	−0.0643641	−	0.111482i	0.832048	−	0.554704i	$-0.187169\pi$
$929$	−1.96179	−	3.39791i	−0.0643641	−	0.111482i	−0.896412	+	0.443222i	$0.853835\pi$
$930$		0			0
$931$	−2.22360	+	3.85139i	−0.0728755	+	0.126224i
$932$	8.00525	−	2.14500i	0.262221	−	0.0702618i
$933$		0			0
$934$	0.419503	−	0.242200i	0.0137266	−	0.00792504i
$935$		0			0
$936$		0			0
$937$	28.6351	−	28.6351i	0.935468	−	0.935468i	−0.0625728	−	0.998040i	$-0.519931\pi$
$937$	28.6351	−	28.6351i	0.935468	−	0.935468i	0.998040	+	0.0625728i	$0.0199305\pi$
$938$	0.779203	+	0.208787i	0.0254419	+	0.00681713i
$939$		0			0
$940$		0			0
$941$	50.0184	+	28.8781i	1.63055	+	0.941400i	0.983922	+	0.178596i	$0.0571557\pi$
$941$	50.0184	+	28.8781i	1.63055	+	0.941400i	0.646630	+	0.762804i	$0.276178\pi$
$942$		0			0
$943$	−13.7733	+	51.4028i	−0.448521	+	1.67390i
$944$	−17.1713			−0.558877
$945$		0			0
$946$	2.44720			0.0795653
$947$	2.14989	−	8.02351i	0.0698622	−	0.260729i	−0.922157	−	0.386816i	$-0.873575\pi$
$947$	2.14989	−	8.02351i	0.0698622	−	0.260729i	0.992019	+	0.126086i	$0.0402417\pi$
$948$		0			0
$949$	13.7568	+	7.94250i	0.446565	+	0.257824i
$950$		0			0
$951$		0			0
$952$	−1.02956	−	0.275870i	−0.0333683	−	0.00894101i
$953$	27.2237	−	27.2237i	0.881861	−	0.881861i	−0.111862	−	0.993724i	$-0.535682\pi$
$953$	27.2237	−	27.2237i	0.881861	−	0.881861i	0.993724	+	0.111862i	$0.0356816\pi$
$954$		0			0
$955$		0			0
$956$	8.82018	−	5.09233i	0.285265	−	0.164698i
$957$		0			0
$958$	7.07375	−	1.89541i	0.228543	−	0.0612378i
$959$	−7.80805	+	13.5239i	−0.252135	+	0.436711i
$960$		0			0
$961$	7.72289	+	13.3764i	0.249126	+	0.431498i
$962$	0.0540628	+	0.0540628i	0.00174306	+	0.00174306i
$963$		0			0
$964$			7.29666i			0.235010i
$965$		0			0
$966$		0			0
$967$	−12.2085	−	45.5627i	−0.392598	−	1.46520i	−0.825832	−	0.563916i	$-0.809294\pi$
$967$	−12.2085	−	45.5627i	−0.392598	−	1.46520i	0.433234	−	0.901282i	$-0.357372\pi$
$968$	0.963408	+	3.59549i	0.0309651	+	0.115563i
$969$		0			0
$970$		0			0
$971$		−	20.4752i		−	0.657080i	−0.944490	−	0.328540i	$-0.893443\pi$
$971$		−	20.4752i		−	0.657080i	0.944490	−	0.328540i	$-0.106557\pi$
$972$		0			0
$973$	−18.1322	−	18.1322i	−0.581292	−	0.581292i
$974$	3.22988	+	5.59432i	0.103492	+	0.179254i
$975$		0			0
$976$	0.890908	−	1.54310i	0.0285173	−	0.0493934i
$977$	34.9400	−	9.36214i	1.11783	−	0.299521i	0.347824	−	0.937560i	$-0.386921\pi$
$977$	34.9400	−	9.36214i	1.11783	−	0.299521i	0.770005	+	0.638038i	$0.220254\pi$
$978$		0			0
$979$	6.21996	−	3.59109i	0.198791	−	0.114772i
$980$		0			0
$981$		0			0
$982$	−2.97725	+	2.97725i	−0.0950077	+	0.0950077i
$983$	19.0596	+	5.10700i	0.607906	+	0.162888i	0.549624	−	0.835412i	$-0.314771\pi$
$983$	19.0596	+	5.10700i	0.607906	+	0.162888i	0.0582820	+	0.998300i	$0.481438\pi$
$984$		0			0
$985$		0			0
$986$	0.611505	+	0.353052i	0.0194743	+	0.0112435i
$987$		0			0
$988$	−3.55190	+	13.2559i	−0.113001	+	0.421725i
$989$	−36.2199			−1.15172
$990$		0			0
$991$	53.0916			1.68651			0.843255	−	0.537513i	$-0.180636\pi$
$991$	53.0916			1.68651			0.843255	+	0.537513i	$0.180636\pi$
$992$	−2.30351	+	8.59681i	−0.0731364	+	0.272949i
$993$		0			0
$994$	−1.42950	−	0.825320i	−0.0453409	−	0.0261776i
$995$		0			0
$996$		0			0
$997$	36.6745	+	9.82689i	1.16149	+	0.311221i	0.787562	−	0.616236i	$-0.211343\pi$
$997$	36.6745	+	9.82689i	1.16149	+	0.311221i	0.373930	+	0.927457i	$0.378010\pi$
$998$	0.432718	−	0.432718i	0.0136974	−	0.0136974i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.q.a.368.3		16
3.2	odd	2		225.2.p.b.68.2		16
5.2	odd	4	inner	675.2.q.a.557.3		16
5.3	odd	4		135.2.m.a.17.2		16
5.4	even	2		135.2.m.a.98.2		16
9.2	odd	6	inner	675.2.q.a.143.3		16
9.7	even	3		225.2.p.b.218.2		16
15.2	even	4		225.2.p.b.32.2		16
15.8	even	4		45.2.l.a.32.3	yes	16
15.14	odd	2		45.2.l.a.23.3	yes	16
45.2	even	12	inner	675.2.q.a.332.3		16
45.4	even	6		405.2.f.a.323.4		16
45.7	odd	12		225.2.p.b.182.2		16
45.13	odd	12		405.2.f.a.242.5		16
45.14	odd	6		405.2.f.a.323.5		16
45.23	even	12		405.2.f.a.242.4		16
45.29	odd	6		135.2.m.a.8.2		16
45.34	even	6		45.2.l.a.38.3	yes	16
45.38	even	12		135.2.m.a.62.2		16
45.43	odd	12		45.2.l.a.2.3	✓	16
60.23	odd	4		720.2.cu.c.257.1		16
60.59	even	2		720.2.cu.c.113.2		16
180.43	even	12		720.2.cu.c.497.2		16
180.79	odd	6		720.2.cu.c.353.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.3	✓	16	45.43	odd	12
45.2.l.a.23.3	yes	16	15.14	odd	2
45.2.l.a.32.3	yes	16	15.8	even	4
45.2.l.a.38.3	yes	16	45.34	even	6
135.2.m.a.8.2		16	45.29	odd	6
135.2.m.a.17.2		16	5.3	odd	4
135.2.m.a.62.2		16	45.38	even	12
135.2.m.a.98.2		16	5.4	even	2
225.2.p.b.32.2		16	15.2	even	4
225.2.p.b.68.2		16	3.2	odd	2
225.2.p.b.182.2		16	45.7	odd	12
225.2.p.b.218.2		16	9.7	even	3
405.2.f.a.242.4		16	45.23	even	12
405.2.f.a.242.5		16	45.13	odd	12
405.2.f.a.323.4		16	45.4	even	6
405.2.f.a.323.5		16	45.14	odd	6
675.2.q.a.143.3		16	9.2	odd	6	inner
675.2.q.a.332.3		16	45.2	even	12	inner
675.2.q.a.368.3		16	1.1	even	1	trivial
675.2.q.a.557.3		16	5.2	odd	4	inner
720.2.cu.c.113.2		16	60.59	even	2
720.2.cu.c.257.1		16	60.23	odd	4
720.2.cu.c.353.1		16	180.79	odd	6
720.2.cu.c.497.2		16	180.43	even	12

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.q (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0499037 - 0.186243i) q^{2} +(1.69985 + 0.981412i) q^{4} +(2.35868 + 0.632007i) q^{7} +(0.540289 - 0.540289i) q^{8} +O(q^{10})\)	\(q+(0.0499037 - 0.186243i) q^{2} +(1.69985 + 0.981412i) q^{4} +(2.35868 + 0.632007i) q^{7} +(0.540289 - 0.540289i) q^{8} +(2.14390 - 1.23778i) q^{11} +(-1.57505 + 0.422032i) q^{13} +(0.235414 - 0.407749i) q^{14} +(1.88916 + 3.27212i) q^{16} +(-0.403949 - 0.403949i) q^{17} -4.28779i q^{19} +(-0.123539 - 0.461055i) q^{22} +(1.82845 + 6.82387i) q^{23} +0.314402i q^{26} +(3.38916 + 3.38916i) q^{28} +(-3.20524 - 5.55164i) q^{29} +(-1.97194 + 3.41550i) q^{31} +(2.17978 - 0.584071i) q^{32} +(-0.0953913 + 0.0550742i) q^{34} +(0.171954 - 0.171954i) q^{37} +(-0.798571 - 0.213977i) q^{38} +(6.52359 + 3.76639i) q^{41} +(-1.32695 + 4.95226i) q^{43} +4.85908 q^{44} +1.36214 q^{46} +(0.780885 - 2.91430i) q^{47} +(-0.898221 - 0.518588i) q^{49} +(-3.09154 - 0.828375i) q^{52} +(6.12030 - 6.12030i) q^{53} +(1.61584 - 0.932904i) q^{56} +(-1.19391 + 0.319907i) q^{58} +(-2.27234 + 3.93581i) q^{59} +(-0.235795 - 0.408408i) q^{61} +(0.537706 + 0.537706i) q^{62} +7.12153i q^{64} +(0.443446 + 1.65496i) q^{67} +(-0.290215 - 1.08310i) q^{68} -3.50583i q^{71} +(-6.88847 - 6.88847i) q^{73} +(-0.0234441 - 0.0406064i) q^{74} +(4.20809 - 7.28862i) q^{76} +(5.83906 - 1.56457i) q^{77} +(6.50159 - 3.75369i) q^{79} +(1.02702 - 1.02702i) q^{82} +(-10.6660 - 2.85794i) q^{83} +(0.856104 + 0.494272i) q^{86} +(0.489565 - 1.82708i) q^{88} +2.90124 q^{89} -3.98176 q^{91} +(-3.58893 + 13.3941i) q^{92} +(-0.503800 - 0.290869i) q^{94} +(-1.41681 - 0.379633i) q^{97} +(-0.141408 + 0.141408i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 2 q^{7}+O(q^{10}) \) 16 * q - 6 * q^2 + 2 * q^7	\( 16 q - 6 q^{2} + 2 q^{7} + 2 q^{13} - 8 q^{16} + 10 q^{22} + 18 q^{23} + 16 q^{28} - 4 q^{31} + 30 q^{32} - 4 q^{37} - 30 q^{38} + 24 q^{41} + 2 q^{43} + 32 q^{46} - 12 q^{47} + 14 q^{52} - 36 q^{56} + 6 q^{58} + 8 q^{61} - 4 q^{67} + 42 q^{68} + 8 q^{73} + 24 q^{76} - 6 q^{77} - 32 q^{82} - 66 q^{83} + 48 q^{86} - 18 q^{88} - 40 q^{91} - 60 q^{92} - 28 q^{97}+O(q^{100}) \) 16 * q - 6 * q^2 + 2 * q^7 + 2 * q^13 - 8 * q^16 + 10 * q^22 + 18 * q^23 + 16 * q^28 - 4 * q^31 + 30 * q^32 - 4 * q^37 - 30 * q^38 + 24 * q^41 + 2 * q^43 + 32 * q^46 - 12 * q^47 + 14 * q^52 - 36 * q^56 + 6 * q^58 + 8 * q^61 - 4 * q^67 + 42 * q^68 + 8 * q^73 + 24 * q^76 - 6 * q^77 - 32 * q^82 - 66 * q^83 + 48 * q^86 - 18 * q^88 - 40 * q^91 - 60 * q^92 - 28 * q^97

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