LMFDB - Embedded newform 504.2.r.d.337.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(169,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

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

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

chi := DirichletCharacter("504.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.r (of order $3$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.508277025.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 15x^{5} + 21x^{4} + 3x^{3} - 22x^{2} + 3x + 19 $ x^8 - 3x^7 + 5x^6 - 15x^5 + 21x^4 + 3x^3 - 22x^2 + 3*x + 19
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			337.2
Root			$1.86526 - 0.199842i$ of defining polynomial
Character	$\chi$	$=$	504.337
Dual form			504.2.r.d.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.60570 + 0.649414i) q^{3} +(-0.468293 + 0.811107i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(2.15652 - 2.08552i) q^{9} +O(q^{10})$	\(q+(-1.60570 + 0.649414i) q^{3} +(-0.468293 + 0.811107i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(2.15652 - 2.08552i) q^{9} +(-2.48741 - 4.30833i) q^{11} +(-0.622156 + 1.07761i) q^{13} +(0.225193 - 1.60651i) q^{15} +5.22446 q^{17} +5.18622 q^{19} +(1.36526 + 1.06587i) q^{21} +(1.00266 - 1.73666i) q^{23} +(2.06140 + 3.57046i) q^{25} +(-2.10836 + 4.74919i) q^{27} +(-3.43925 - 5.95695i) q^{29} +(2.86526 - 4.96277i) q^{31} +(6.79192 + 5.30251i) q^{33} +0.936586 q^{35} +9.73051 q^{37} +(0.299182 - 2.13435i) q^{39} +(5.73705 - 9.93686i) q^{41} +(-4.80184 - 8.31704i) q^{43} +(0.681697 + 2.72581i) q^{45} +(0.984753 + 1.70564i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-8.38890 + 3.39284i) q^{51} -7.63418 q^{53} +4.65935 q^{55} +(-8.32750 + 3.36800i) q^{57} +(-2.43925 + 4.22490i) q^{59} +(1.52178 + 2.63580i) q^{61} +(-2.88438 - 0.824844i) q^{63} +(-0.582703 - 1.00927i) q^{65} +(0.573990 - 0.994179i) q^{67} +(-0.482159 + 3.43969i) q^{69} -8.83749 q^{71} +6.10698 q^{73} +(-5.62869 - 4.39437i) q^{75} +(-2.48741 + 4.30833i) q^{77} +(6.05414 + 10.4861i) q^{79} +(0.301193 - 8.99496i) q^{81} +(0.431332 + 0.747088i) q^{83} +(-2.44658 + 4.23760i) q^{85} +(9.39091 + 7.33156i) q^{87} -10.8480 q^{89} +1.24431 q^{91} +(-1.37784 + 9.82944i) q^{93} +(-2.42867 + 4.20658i) q^{95} +(-3.78521 - 6.55618i) q^{97} +(-14.3493 - 4.10345i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 4 q^{5} - 4 q^{7} + 10 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 4 * q^5 - 4 * q^7 + 10 * q^9	$ 8 q - 4 q^{3} + 4 q^{5} - 4 q^{7} + 10 q^{9} - 6 q^{11} - 3 q^{13} + 4 q^{15} - 16 q^{17} - 4 q^{19} - q^{21} - 5 q^{23} - 14 q^{25} + 5 q^{27} + q^{29} + 11 q^{31} - 8 q^{35} + 54 q^{37} - 12 q^{39} + 2 q^{41} - 11 q^{43} + 26 q^{45} + 7 q^{47} - 4 q^{49} + 17 q^{51} - 8 q^{53} + 12 q^{55} - 13 q^{57} + 9 q^{59} - 7 q^{61} - 5 q^{63} - 9 q^{65} - 12 q^{67} + 4 q^{69} - 24 q^{71} + 26 q^{73} - 23 q^{75} - 6 q^{77} - 22 q^{79} + 34 q^{81} - 6 q^{83} - 11 q^{85} + 37 q^{87} - 28 q^{89} + 6 q^{91} - 13 q^{93} - 23 q^{95} - q^{97} - 42 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + 4 * q^5 - 4 * q^7 + 10 * q^9 - 6 * q^11 - 3 * q^13 + 4 * q^15 - 16 * q^17 - 4 * q^19 - q^21 - 5 * q^23 - 14 * q^25 + 5 * q^27 + q^29 + 11 * q^31 - 8 * q^35 + 54 * q^37 - 12 * q^39 + 2 * q^41 - 11 * q^43 + 26 * q^45 + 7 * q^47 - 4 * q^49 + 17 * q^51 - 8 * q^53 + 12 * q^55 - 13 * q^57 + 9 * q^59 - 7 * q^61 - 5 * q^63 - 9 * q^65 - 12 * q^67 + 4 * q^69 - 24 * q^71 + 26 * q^73 - 23 * q^75 - 6 * q^77 - 22 * q^79 + 34 * q^81 - 6 * q^83 - 11 * q^85 + 37 * q^87 - 28 * q^89 + 6 * q^91 - 13 * q^93 - 23 * q^95 - q^97 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	−1.60570	+	0.649414i	−0.927049	+	0.374939i
$3$	−1.60570	+	0.649414i	−0.927049	+	0.374939i
$4$		0			0
$5$	−0.468293	+	0.811107i	−0.209427	+	0.362738i	−0.951534	−	0.307543i	$-0.900493\pi$
$5$	−0.468293	+	0.811107i	−0.209427	+	0.362738i	0.742107	+	0.670281i	$0.233827\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$		0			0
$9$	2.15652	−	2.08552i	0.718841	−	0.695174i
$10$		0			0
$11$	−2.48741	−	4.30833i	−0.749983	−	1.29901i	−0.947830	−	0.318776i	$-0.896728\pi$
$11$	−2.48741	−	4.30833i	−0.749983	−	1.29901i	0.197847	−	0.980233i	$-0.436605\pi$
$12$		0			0
$13$	−0.622156	+	1.07761i	−0.172555	+	0.298874i	−0.939312	−	0.343063i	$-0.888536\pi$
$13$	−0.622156	+	1.07761i	−0.172555	+	0.298874i	0.766757	+	0.641937i	$0.221869\pi$
$14$		0			0
$15$	0.225193	−	1.60651i	0.0581445	−	0.414799i
$16$		0			0
$17$	5.22446			1.26712			0.633559	−	0.773694i	$-0.281593\pi$
$17$	5.22446			1.26712			0.633559	+	0.773694i	$0.281593\pi$
$18$		0			0
$19$	5.18622			1.18980			0.594900	−	0.803800i	$-0.297192\pi$
$19$	5.18622			1.18980			0.594900	+	0.803800i	$0.297192\pi$
$20$		0			0
$21$	1.36526	+	1.06587i	0.297923	+	0.232591i
$22$		0			0
$23$	1.00266	−	1.73666i	0.209069	−	0.362118i	−0.742352	−	0.670010i	$-0.766290\pi$
$23$	1.00266	−	1.73666i	0.209069	−	0.362118i	0.951422	+	0.307891i	$0.0996233\pi$
$24$		0			0
$25$	2.06140	+	3.57046i	0.412281	+	0.714091i
$26$		0			0
$27$	−2.10836	+	4.74919i	−0.405754	+	0.913983i
$28$		0			0
$29$	−3.43925	−	5.95695i	−0.638652	−	1.10618i	−0.985729	−	0.168341i	$-0.946159\pi$
$29$	−3.43925	−	5.95695i	−0.638652	−	1.10618i	0.347077	−	0.937837i	$-0.387174\pi$
$30$		0			0
$31$	2.86526	−	4.96277i	0.514615	−	0.891340i	−0.485241	−	0.874381i	$-0.661268\pi$
$31$	2.86526	−	4.96277i	0.514615	−	0.891340i	0.999856	−	0.0169594i	$-0.00539860\pi$
$32$		0			0
$33$	6.79192	+	5.30251i	1.18232	+	0.923048i
$34$		0			0
$35$	0.936586			0.158312
$36$		0			0
$37$	9.73051			1.59969			0.799843	−	0.600209i	$-0.204916\pi$
$37$	9.73051			1.59969			0.799843	+	0.600209i	$0.204916\pi$
$38$		0			0
$39$	0.299182	−	2.13435i	0.0479075	−	0.341769i
$40$		0			0
$41$	5.73705	−	9.93686i	0.895976	−	1.55188i	0.0633848	−	0.997989i	$-0.479810\pi$
$41$	5.73705	−	9.93686i	0.895976	−	1.55188i	0.832592	−	0.553887i	$-0.186856\pi$
$42$		0			0
$43$	−4.80184	−	8.31704i	−0.732274	−	1.26834i	−0.955909	−	0.293663i	$-0.905126\pi$
$43$	−4.80184	−	8.31704i	−0.732274	−	1.26834i	0.223635	−	0.974673i	$-0.428208\pi$
$44$		0			0
$45$	0.681697	+	2.72581i	0.101621	+	0.406339i
$46$		0			0
$47$	0.984753	+	1.70564i	0.143641	+	0.248793i	0.928865	−	0.370418i	$-0.120786\pi$
$47$	0.984753	+	1.70564i	0.143641	+	0.248793i	−0.785224	+	0.619212i	$0.787452\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$	−8.38890	+	3.39284i	−1.17468	+	0.475092i
$52$		0			0
$53$	−7.63418			−1.04864			−0.524318	−	0.851523i	$-0.675680\pi$
$53$	−7.63418			−1.04864			−0.524318	+	0.851523i	$0.675680\pi$
$54$		0			0
$55$	4.65935			0.628267
$56$		0			0
$57$	−8.32750	+	3.36800i	−1.10300	+	0.446103i
$58$		0			0
$59$	−2.43925	+	4.22490i	−0.317563	+	0.550035i	−0.979979	−	0.199101i	$-0.936198\pi$
$59$	−2.43925	+	4.22490i	−0.317563	+	0.550035i	0.662416	+	0.749136i	$0.269531\pi$
$60$		0			0
$61$	1.52178	+	2.63580i	0.194844	+	0.337480i	0.946849	−	0.321677i	$-0.104247\pi$
$61$	1.52178	+	2.63580i	0.194844	+	0.337480i	−0.752005	+	0.659157i	$0.770913\pi$
$62$		0			0
$63$	−2.88438	−	0.824844i	−0.363397	−	0.103921i
$64$		0			0
$65$	−0.582703	−	1.00927i	−0.0722754	−	0.125185i
$66$		0			0
$67$	0.573990	−	0.994179i	0.0701240	−	0.121458i	−0.828831	−	0.559498i	$-0.810994\pi$
$67$	0.573990	−	0.994179i	0.0701240	−	0.121458i	0.898955	+	0.438040i	$0.144327\pi$
$68$		0			0
$69$	−0.482159	+	3.43969i	−0.0580451	+	0.414090i
$70$		0			0
$71$	−8.83749			−1.04882			−0.524409	−	0.851467i	$-0.675714\pi$
$71$	−8.83749			−1.04882			−0.524409	+	0.851467i	$0.675714\pi$
$72$		0			0
$73$	6.10698			0.714768			0.357384	−	0.933958i	$-0.383669\pi$
$73$	6.10698			0.714768			0.357384	+	0.933958i	$0.383669\pi$
$74$		0			0
$75$	−5.62869	−	4.39437i	−0.649945	−	0.507418i
$76$		0			0
$77$	−2.48741	+	4.30833i	−0.283467	+	0.490979i
$78$		0			0
$79$	6.05414	+	10.4861i	0.681144	+	1.17978i	0.974632	+	0.223813i	$0.0718505\pi$
$79$	6.05414	+	10.4861i	0.681144	+	1.17978i	−0.293488	+	0.955963i	$0.594816\pi$
$80$		0			0
$81$	0.301193	−	8.99496i	0.0334659	−	0.999440i
$82$		0			0
$83$	0.431332	+	0.747088i	0.0473448	+	0.0820036i	0.888727	−	0.458438i	$-0.151591\pi$
$83$	0.431332	+	0.747088i	0.0473448	+	0.0820036i	−0.841382	+	0.540441i	$0.818257\pi$
$84$		0			0
$85$	−2.44658	+	4.23760i	−0.265369	+	0.459632i
$86$		0			0
$87$	9.39091	+	7.33156i	1.00681	+	0.786026i
$88$		0			0
$89$	−10.8480			−1.14989			−0.574943	−	0.818194i	$-0.694976\pi$
$89$	−10.8480			−1.14989			−0.574943	+	0.818194i	$0.694976\pi$
$90$		0			0
$91$	1.24431			0.130439
$92$		0			0
$93$	−1.37784	+	9.82944i	−0.142876	+	1.01927i
$94$		0			0
$95$	−2.42867	+	4.20658i	−0.249176	+	0.431586i
$96$		0			0
$97$	−3.78521	−	6.55618i	−0.384330	−	0.665680i	0.607346	−	0.794438i	$-0.292234\pi$
$97$	−3.78521	−	6.55618i	−0.384330	−	0.665680i	−0.991676	+	0.128758i	$0.958901\pi$
$98$		0			0
$99$	−14.3493	−	4.10345i	−1.44216	−	0.412413i
$100$		0			0
$101$	−2.52970	−	4.38156i	−0.251714	−	0.435982i	0.712284	−	0.701892i	$-0.247661\pi$
$101$	−2.52970	−	4.38156i	−0.251714	−	0.435982i	−0.963998	+	0.265910i	$0.914328\pi$
$102$		0			0
$103$	−0.119496	+	0.206973i	−0.0117743	+	0.0203936i	−0.871853	−	0.489769i	$-0.837081\pi$
$103$	−0.119496	+	0.206973i	−0.0117743	+	0.0203936i	0.860078	+	0.510162i	$0.170415\pi$
$104$		0			0
$105$	−1.50387	+	0.608232i	−0.146763	+	0.0593573i
$106$		0			0
$107$	9.25496			0.894710			0.447355	−	0.894356i	$-0.352366\pi$
$107$	9.25496			0.894710			0.447355	+	0.894356i	$0.352366\pi$
$108$		0			0
$109$	−10.5453			−1.01005			−0.505026	−	0.863104i	$-0.668517\pi$
$109$	−10.5453			−1.01005			−0.505026	+	0.863104i	$0.668517\pi$
$110$		0			0
$111$	−15.6243	+	6.31913i	−1.48299	+	0.599785i
$112$		0			0
$113$	5.06406	−	8.77122i	0.476387	−	0.825127i	−0.523247	−	0.852181i	$-0.675279\pi$
$113$	5.06406	−	8.77122i	0.476387	−	0.825127i	0.999634	+	0.0270545i	$0.00861278\pi$
$114$		0			0
$115$	0.939078	+	1.62653i	0.0875695	+	0.151675i
$116$		0			0
$117$	0.905677	+	3.62141i	0.0837299	+	0.334799i
$118$		0			0
$119$	−2.61223	−	4.52452i	−0.239463	−	0.414762i
$120$		0			0
$121$	−6.87445	+	11.9069i	−0.624950	+	1.08245i
$122$		0			0
$123$	−2.75883	+	19.6813i	−0.248755	+	1.77460i
$124$		0			0
$125$	−8.54429			−0.764225
$126$		0			0
$127$	6.52720			0.579196			0.289598	−	0.957148i	$-0.406478\pi$
$127$	6.52720			0.579196			0.289598	+	0.957148i	$0.406478\pi$
$128$		0			0
$129$	13.1115	+	10.2363i	1.15440	+	0.901252i
$130$		0			0
$131$	1.76748	−	3.06136i	0.154425	−	0.267472i	−0.778424	−	0.627738i	$-0.783981\pi$
$131$	1.76748	−	3.06136i	0.154425	−	0.267472i	0.932850	+	0.360266i	$0.117314\pi$
$132$		0			0
$133$	−2.59311	−	4.49140i	−0.224851	−	0.389454i
$134$		0			0
$135$	−2.86478	−	3.93412i	−0.246561	−	0.338595i
$136$		0			0
$137$	−2.48603	−	4.30593i	−0.212396	−	0.367881i	0.740068	−	0.672532i	$-0.234793\pi$
$137$	−2.48603	−	4.30593i	−0.212396	−	0.367881i	−0.952464	+	0.304651i	$0.901460\pi$
$138$		0			0
$139$	−4.87566	+	8.44490i	−0.413548	+	0.716287i	−0.995275	−	0.0970976i	$-0.969044\pi$
$139$	−4.87566	+	8.44490i	−0.413548	+	0.716287i	0.581726	+	0.813385i	$0.302377\pi$
$140$		0			0
$141$	−2.68888	−	2.09923i	−0.226445	−	0.176787i
$142$		0			0
$143$	6.19024			0.517654
$144$		0			0
$145$	6.44230			0.535004
$146$		0			0
$147$	0.240440	−	1.71528i	0.0198311	−	0.141474i
$148$		0			0
$149$	6.39108	−	11.0697i	0.523578	−	0.906863i	−0.476046	−	0.879421i	$-0.657930\pi$
$149$	6.39108	−	11.0697i	0.523578	−	0.906863i	0.999623	−	0.0274426i	$-0.00873635\pi$
$150$		0			0
$151$	−11.4781	−	19.8807i	−0.934078	−	1.61787i	−0.776271	−	0.630400i	$-0.782891\pi$
$151$	−11.4781	−	19.8807i	−0.934078	−	1.61787i	−0.157807	−	0.987470i	$-0.550442\pi$
$152$		0			0
$153$	11.2667	−	10.8957i	0.910857	−	0.880868i
$154$		0			0
$155$	2.68356	+	4.64806i	0.215549	+	0.373341i
$156$		0			0
$157$	−8.25489	+	14.2979i	−0.658812	+	1.14110i	0.322112	+	0.946702i	$0.395607\pi$
$157$	−8.25489	+	14.2979i	−0.658812	+	1.14110i	−0.980924	+	0.194394i	$0.937726\pi$
$158$		0			0
$159$	12.2582	−	4.95774i	0.972137	−	0.393174i
$160$		0			0
$161$	−2.00532			−0.158041
$162$		0			0
$163$	17.2245			1.34912			0.674562	−	0.738218i	$-0.264333\pi$
$163$	17.2245			1.34912			0.674562	+	0.738218i	$0.264333\pi$
$164$		0			0
$165$	−7.48151	+	3.02585i	−0.582435	+	0.235562i
$166$		0			0
$167$	−6.56406	+	11.3693i	−0.507943	+	0.879782i	0.492015	+	0.870587i	$0.336260\pi$
$167$	−6.56406	+	11.3693i	−0.507943	+	0.879782i	−0.999958	+	0.00919564i	$0.997073\pi$
$168$		0			0
$169$	5.72584	+	9.91745i	0.440449	+	0.762881i
$170$		0			0
$171$	11.1842	−	10.8160i	0.855278	−	0.827119i
$172$		0			0
$173$	9.49412	+	16.4443i	0.721824	+	1.25024i	0.960268	+	0.279080i	$0.0900295\pi$
$173$	9.49412	+	16.4443i	0.721824	+	1.25024i	−0.238444	+	0.971156i	$0.576637\pi$
$174$		0			0
$175$	2.06140	−	3.57046i	0.155827	−	0.269901i
$176$		0			0
$177$	1.17298	−	8.36799i	0.0881669	−	0.628976i
$178$		0			0
$179$	7.61835			0.569422			0.284711	−	0.958613i	$-0.408102\pi$
$179$	7.61835			0.569422			0.284711	+	0.958613i	$0.408102\pi$
$180$		0			0
$181$	−9.27737			−0.689581			−0.344791	−	0.938680i	$-0.612050\pi$
$181$	−9.27737			−0.689581			−0.344791	+	0.938680i	$0.612050\pi$
$182$		0			0
$183$	−4.15524	−	3.24403i	−0.307165	−	0.239806i
$184$		0			0
$185$	−4.55673	+	7.89249i	−0.335018	+	0.580267i
$186$		0			0
$187$	−12.9954	−	22.5087i	−0.950317	−	1.64600i
$188$		0			0
$189$	5.16710	−	0.548705i	0.375851	−	0.0399124i
$190$		0			0
$191$	−4.80119	−	8.31591i	−0.347402	−	0.601718i	0.638385	−	0.769717i	$-0.279603\pi$
$191$	−4.80119	−	8.31591i	−0.347402	−	0.601718i	−0.985787	+	0.167999i	$0.946269\pi$
$192$		0			0
$193$	7.54155	−	13.0624i	0.542853	−	0.940249i	−0.455886	−	0.890038i	$-0.650677\pi$
$193$	7.54155	−	13.0624i	0.542853	−	0.940249i	0.998739	−	0.0502103i	$-0.0159892\pi$
$194$		0			0
$195$	1.59108	+	1.24217i	0.113940	+	0.0889535i
$196$		0			0
$197$	−11.0712			−0.788788			−0.394394	−	0.918942i	$-0.629045\pi$
$197$	−11.0712			−0.788788			−0.394394	+	0.918942i	$0.629045\pi$
$198$		0			0
$199$	18.3368			1.29986			0.649929	−	0.759995i	$-0.274799\pi$
$199$	18.3368			1.29986			0.649929	+	0.759995i	$0.274799\pi$
$200$		0			0
$201$	−0.276020	+	1.96911i	−0.0194689	+	0.138890i
$202$		0			0
$203$	−3.43925	+	5.95695i	−0.241388	+	0.418096i
$204$		0			0
$205$	5.37324	+	9.30672i	0.375283	+	0.650010i
$206$		0			0
$207$	−1.45958	−	5.83622i	−0.101448	−	0.405645i
$208$		0			0
$209$	−12.9003	−	22.3439i	−0.892331	−	1.54556i
$210$		0			0
$211$	−1.30911	+	2.26744i	−0.0901227	+	0.156097i	−0.907563	−	0.419917i	$-0.862059\pi$
$211$	−1.30911	+	2.26744i	−0.0901227	+	0.156097i	0.817440	+	0.576014i	$0.195393\pi$
$212$		0			0
$213$	14.1903	−	5.73919i	0.972305	−	0.393243i
$214$		0			0
$215$	8.99468			0.613432
$216$		0			0
$217$	−5.73051			−0.389013
$218$		0			0
$219$	−9.80595	+	3.96595i	−0.662625	+	0.267994i
$220$		0			0
$221$	−3.25043	+	5.62991i	−0.218648	+	0.378709i
$222$		0			0
$223$	12.5442	+	21.7272i	0.840023	+	1.45496i	0.889875	+	0.456205i	$0.150792\pi$
$223$	12.5442	+	21.7272i	0.840023	+	1.45496i	−0.0498520	+	0.998757i	$0.515875\pi$
$224$		0			0
$225$	11.8917	+	3.40067i	0.792782	+	0.226711i
$226$		0			0
$227$	12.7781	+	22.1323i	0.848113	+	1.46898i	0.882890	+	0.469581i	$0.155595\pi$
$227$	12.7781	+	22.1323i	0.848113	+	1.46898i	−0.0347761	+	0.999395i	$0.511072\pi$
$228$		0			0
$229$	−2.73657	+	4.73987i	−0.180837	+	0.313220i	−0.942166	−	0.335147i	$-0.891214\pi$
$229$	−2.73657	+	4.73987i	−0.180837	+	0.313220i	0.761329	+	0.648366i	$0.224547\pi$
$230$		0			0
$231$	1.19615	−	8.53323i	0.0787006	−	0.561445i
$232$		0			0
$233$	10.6774			0.699500			0.349750	−	0.936843i	$-0.386267\pi$
$233$	10.6774			0.699500			0.349750	+	0.936843i	$0.386267\pi$
$234$		0			0
$235$	−1.84461			−0.120329
$236$		0			0
$237$	−16.5309	−	12.9058i	−1.07380	−	0.838323i
$238$		0			0
$239$	−2.50000	+	4.33013i	−0.161712	+	0.280093i	−0.935483	−	0.353373i	$-0.885035\pi$
$239$	−2.50000	+	4.33013i	−0.161712	+	0.280093i	0.773771	+	0.633465i	$0.218368\pi$
$240$		0			0
$241$	−10.1684	−	17.6121i	−0.655003	−	1.13450i	−0.981893	−	0.189436i	$-0.939334\pi$
$241$	−10.1684	−	17.6121i	−0.655003	−	1.13450i	0.326890	−	0.945062i	$-0.393999\pi$
$242$		0			0
$243$	5.35782	+	14.6388i	0.343705	+	0.939078i
$244$		0			0
$245$	−0.468293	−	0.811107i	−0.0299181	−	0.0518197i
$246$		0			0
$247$	−3.22664	+	5.58871i	−0.205306	+	0.355601i
$248$		0			0
$249$	−1.17776	−	0.919485i	−0.0746373	−	0.0582700i
$250$		0			0
$251$	19.8151			1.25072			0.625358	−	0.780338i	$-0.284953\pi$
$251$	19.8151			1.25072			0.625358	+	0.780338i	$0.284953\pi$
$252$		0			0
$253$	−9.97613			−0.627194
$254$		0			0
$255$	1.17651	−	8.39314i	0.0736759	−	0.525599i
$256$		0			0
$257$	0.969506	−	1.67923i	0.0604761	−	0.104748i	−0.834202	−	0.551459i	$-0.814071\pi$
$257$	0.969506	−	1.67923i	0.0604761	−	0.104748i	0.894678	+	0.446711i	$0.147405\pi$
$258$		0			0
$259$	−4.86526	−	8.42687i	−0.302312	−	0.523620i
$260$		0			0
$261$	−19.8402	−	5.67368i	−1.22808	−	0.351192i
$262$		0			0
$263$	6.67768	+	11.5661i	0.411763	+	0.713195i	0.995083	−	0.0990481i	$-0.0315798\pi$
$263$	6.67768	+	11.5661i	0.411763	+	0.713195i	−0.583320	+	0.812243i	$0.698246\pi$
$264$		0			0
$265$	3.57503	−	6.19214i	0.219613	−	0.380380i
$266$		0			0
$267$	17.4186	−	7.04484i	1.06600	−	0.431137i
$268$		0			0
$269$	4.15040			0.253055			0.126527	−	0.991963i	$-0.459617\pi$
$269$	4.15040			0.253055			0.126527	+	0.991963i	$0.459617\pi$
$270$		0			0
$271$	−16.6050			−1.00868			−0.504341	−	0.863505i	$-0.668264\pi$
$271$	−16.6050			−1.00868			−0.504341	+	0.863505i	$0.668264\pi$
$272$		0			0
$273$	−1.99799	+	0.808074i	−0.120924	+	0.0489068i
$274$		0			0
$275$	10.2551	−	17.7624i	0.618407	−	1.07111i
$276$		0			0
$277$	−8.55414	−	14.8162i	−0.513968	−	0.890219i	−0.999869	−	0.0162051i	$-0.994842\pi$
$277$	−8.55414	−	14.8162i	−0.513968	−	0.890219i	0.485900	−	0.874014i	$-0.338492\pi$
$278$		0			0
$279$	−4.17097	−	16.6779i	−0.249710	−	0.998479i
$280$		0			0
$281$	7.49007	+	12.9732i	0.446820	+	0.773916i	0.998177	−	0.0603541i	$-0.0192230\pi$
$281$	7.49007	+	12.9732i	0.446820	+	0.773916i	−0.551357	+	0.834270i	$0.685890\pi$
$282$		0			0
$283$	9.00580	−	15.5985i	0.535339	−	0.927235i	−0.463807	−	0.885936i	$-0.653517\pi$
$283$	9.00580	−	15.5985i	0.535339	−	0.927235i	0.999147	−	0.0412990i	$-0.0131496\pi$
$284$		0			0
$285$	1.16790	−	8.33171i	0.0691803	−	0.493528i
$286$		0			0
$287$	−11.4741			−0.677294
$288$		0			0
$289$	10.2950			0.605588
$290$		0			0
$291$	10.3356	+	8.06907i	0.605883	+	0.473017i
$292$		0			0
$293$	13.8362	−	23.9650i	0.808320	−	1.40005i	−0.105707	−	0.994397i	$-0.533710\pi$
$293$	13.8362	−	23.9650i	0.808320	−	1.40005i	0.914027	−	0.405654i	$-0.132956\pi$
$294$		0			0
$295$	−2.28456	−	3.95698i	−0.133012	−	0.230384i
$296$		0			0
$297$	25.7054	−	2.72971i	1.49158	−	0.158394i
$298$		0			0
$299$	1.24762	+	2.16095i	0.0721519	+	0.124971i
$300$		0			0
$301$	−4.80184	+	8.31704i	−0.276774	+	0.479386i
$302$		0			0
$303$	6.90737	+	5.39264i	0.396818	+	0.309799i
$304$		0			0
$305$	−2.85056			−0.163222
$306$		0			0
$307$	−6.10040			−0.348168			−0.174084	−	0.984731i	$-0.555696\pi$
$307$	−6.10040			−0.348168			−0.174084	+	0.984731i	$0.555696\pi$
$308$		0			0
$309$	0.0574631	−	0.409938i	0.00326896	−	0.0233205i
$310$		0			0
$311$	−13.3277	+	23.0842i	−0.755743	+	1.30898i	0.189262	+	0.981927i	$0.439391\pi$
$311$	−13.3277	+	23.0842i	−0.755743	+	1.30898i	−0.945004	+	0.327058i	$0.893943\pi$
$312$		0			0
$313$	−12.0681	−	20.9026i	−0.682130	−	1.18148i	−0.974330	−	0.225126i	$-0.927721\pi$
$313$	−12.0681	−	20.9026i	−0.682130	−	1.18148i	0.292200	−	0.956357i	$-0.405613\pi$
$314$		0			0
$315$	2.01977	−	1.95327i	0.113801	−	0.110054i
$316$		0			0
$317$	8.80046	+	15.2428i	0.494283	+	0.856124i	0.999978	−	0.00658868i	$-0.00209726\pi$
$317$	8.80046	+	15.2428i	0.494283	+	0.856124i	−0.505695	+	0.862712i	$0.668764\pi$
$318$		0			0
$319$	−17.1097	+	29.6348i	−0.957957	+	1.65923i
$320$		0			0
$321$	−14.8607	+	6.01029i	−0.829441	+	0.335462i
$322$		0			0
$323$	27.0952			1.50762
$324$		0			0
$325$	−5.13006			−0.284565
$326$		0			0
$327$	16.9325	−	6.84823i	0.936368	−	0.378708i
$328$		0			0
$329$	0.984753	−	1.70564i	0.0542912	−	0.0940351i
$330$		0			0
$331$	−12.1497	−	21.0440i	−0.667810	−	1.15668i	−0.978515	−	0.206175i	$-0.933898\pi$
$331$	−12.1497	−	21.0440i	−0.667810	−	1.15668i	0.310705	−	0.950506i	$-0.399435\pi$
$332$		0			0
$333$	20.9841	−	20.2932i	1.14992	−	1.11206i
$334$		0			0
$335$	0.537591	+	0.931135i	0.0293717	+	0.0508733i
$336$		0			0
$337$	−11.4722	+	19.8704i	−0.624929	+	1.08241i	0.363626	+	0.931545i	$0.381539\pi$
$337$	−11.4722	+	19.8704i	−0.624929	+	1.08241i	−0.988555	+	0.150863i	$0.951795\pi$
$338$		0			0
$339$	−2.43520	+	17.3726i	−0.132262	+	0.943549i
$340$		0			0
$341$	−28.5083			−1.54381
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	−2.56417	−	2.00187i	−0.138050	−	0.107777i
$346$		0			0
$347$	6.36930	−	11.0319i	0.341922	−	0.592226i	−0.642868	−	0.765977i	$-0.722256\pi$
$347$	6.36930	−	11.0319i	0.341922	−	0.592226i	0.984790	+	0.173751i	$0.0555888\pi$
$348$		0			0
$349$	3.99468	+	6.91899i	0.213830	+	0.370365i	0.952910	−	0.303253i	$-0.0980727\pi$
$349$	3.99468	+	6.91899i	0.213830	+	0.370365i	−0.739080	+	0.673618i	$0.764739\pi$
$350$		0			0
$351$	−3.80603	−	5.22672i	−0.203151	−	0.278982i
$352$		0			0
$353$	10.9781	+	19.0147i	0.584307	+	1.01205i	0.994961	+	0.100259i	$0.0319671\pi$
$353$	10.9781	+	19.0147i	0.584307	+	1.01205i	−0.410654	+	0.911791i	$0.634700\pi$
$354$		0			0
$355$	4.13854	−	7.16815i	0.219651	−	0.380446i
$356$		0			0
$357$	7.13273	+	5.56858i	0.377504	+	0.294721i
$358$		0			0
$359$	20.4673			1.08022			0.540112	−	0.841593i	$-0.318382\pi$
$359$	20.4673			1.08022			0.540112	+	0.841593i	$0.318382\pi$
$360$		0			0
$361$	7.89688			0.415625
$362$		0			0
$363$	3.30578	−	23.5832i	0.173509	−	1.23780i
$364$		0			0
$365$	−2.85985	+	4.95341i	−0.149692	+	0.259273i
$366$		0			0
$367$	9.94174	+	17.2196i	0.518955	+	0.898856i	0.999757	+	0.0220269i	$0.00701195\pi$
$367$	9.94174	+	17.2196i	0.518955	+	0.898856i	−0.480803	+	0.876829i	$0.659655\pi$
$368$		0			0
$369$	−8.35146	−	33.3938i	−0.434760	−	1.73841i
$370$		0			0
$371$	3.81709	+	6.61139i	0.198173	+	0.343246i
$372$		0			0
$373$	−17.1438	+	29.6939i	−0.887672	+	1.53749i	−0.0450513	+	0.998985i	$0.514345\pi$
$373$	−17.1438	+	29.6939i	−0.887672	+	1.53749i	−0.842620	+	0.538508i	$0.818988\pi$
$374$		0			0
$375$	13.7195	−	5.54878i	0.708474	−	0.286538i
$376$		0			0
$377$	8.55900			0.440811
$378$		0			0
$379$	18.6248			0.956694			0.478347	−	0.878171i	$-0.341236\pi$
$379$	18.6248			0.956694			0.478347	+	0.878171i	$0.341236\pi$
$380$		0			0
$381$	−10.4807	+	4.23885i	−0.536943	+	0.217163i
$382$		0			0
$383$	−16.4360	+	28.4680i	−0.839842	+	1.45465i	0.0501852	+	0.998740i	$0.484019\pi$
$383$	−16.4360	+	28.4680i	−0.839842	+	1.45465i	−0.890027	+	0.455908i	$0.849314\pi$
$384$		0			0
$385$	−2.32968	−	4.03512i	−0.118731	−	0.205649i
$386$		0			0
$387$	−27.7007	−	7.92154i	−1.40810	−	0.402674i
$388$		0			0
$389$	10.8250	+	18.7495i	0.548850	+	0.950635i	0.998354	+	0.0573571i	$0.0182674\pi$
$389$	10.8250	+	18.7495i	0.548850	+	0.950635i	−0.449504	+	0.893278i	$0.648399\pi$
$390$		0			0
$391$	5.23836	−	9.07311i	0.264915	−	0.458847i
$392$		0			0
$393$	−0.849943	+	6.06343i	−0.0428739	+	0.305860i
$394$		0			0
$395$	−11.3404			−0.570600
$396$		0			0
$397$	16.2721			0.816673			0.408336	−	0.912832i	$-0.366109\pi$
$397$	16.2721			0.816673			0.408336	+	0.912832i	$0.366109\pi$
$398$		0			0
$399$	7.08052	+	5.52782i	0.354470	+	0.276737i
$400$		0			0
$401$	4.57133	−	7.91777i	0.228281	−	0.395395i	−0.729018	−	0.684495i	$-0.760023\pi$
$401$	4.57133	−	7.91777i	0.228281	−	0.395395i	0.957299	+	0.289100i	$0.0933561\pi$
$402$		0			0
$403$	3.56528	+	6.17524i	0.177599	+	0.307611i
$404$		0			0
$405$	7.15483	+	4.45658i	0.355526	+	0.221449i
$406$		0			0
$407$	−24.2038	−	41.9222i	−1.19974	−	2.07801i
$408$		0			0
$409$	11.0976	−	19.2217i	0.548743	−	0.950450i	−0.449618	−	0.893221i	$-0.648440\pi$
$409$	11.0976	−	19.2217i	0.548743	−	0.950450i	0.998361	−	0.0572294i	$-0.0182266\pi$
$410$		0			0
$411$	6.78815	+	5.29956i	0.334835	+	0.261408i
$412$		0			0
$413$	4.87849			0.240055
$414$		0			0
$415$	−0.807958			−0.0396611
$416$		0			0
$417$	2.34461	−	16.7263i	0.114816	−	0.819089i
$418$		0			0
$419$	−13.9601	+	24.1795i	−0.681994	+	1.18125i	0.292378	+	0.956303i	$0.405553\pi$
$419$	−13.9601	+	24.1795i	−0.681994	+	1.18125i	−0.974372	+	0.224945i	$0.927780\pi$
$420$		0			0
$421$	−12.0441	−	20.8611i	−0.586996	−	1.01671i	−0.994623	−	0.103558i	$-0.966977\pi$
$421$	−12.0441	−	20.8611i	−0.586996	−	1.01671i	0.407628	−	0.913148i	$-0.366356\pi$
$422$		0			0
$423$	5.68080	+	1.62453i	0.276210	+	0.0789875i
$424$		0			0
$425$	10.7697	+	18.6537i	0.522408	+	0.904838i
$426$		0			0
$427$	1.52178	−	2.63580i	0.0736442	−	0.127555i
$428$		0			0
$429$	−9.93965	+	4.02003i	−0.479891	+	0.194089i
$430$		0			0
$431$	−26.1623			−1.26020			−0.630098	−	0.776516i	$-0.716985\pi$
$431$	−26.1623			−1.26020			−0.630098	+	0.776516i	$0.716985\pi$
$432$		0			0
$433$	−18.5630			−0.892082			−0.446041	−	0.895013i	$-0.647166\pi$
$433$	−18.5630			−0.892082			−0.446041	+	0.895013i	$0.647166\pi$
$434$		0			0
$435$	−10.3444	+	4.18372i	−0.495975	+	0.200594i
$436$		0			0
$437$	5.20002	−	9.00670i	0.248751	−	0.430849i
$438$		0			0
$439$	−3.85395	−	6.67524i	−0.183939	−	0.318592i	0.759279	−	0.650765i	$-0.225552\pi$
$439$	−3.85395	−	6.67524i	−0.183939	−	0.318592i	−0.943218	+	0.332173i	$0.892218\pi$
$440$		0			0
$441$	0.727853	+	2.91037i	0.0346597	+	0.138589i
$442$		0			0
$443$	−16.5204	−	28.6142i	−0.784909	−	1.35950i	−0.929053	−	0.369945i	$-0.879376\pi$
$443$	−16.5204	−	28.6142i	−0.784909	−	1.35950i	0.144145	−	0.989557i	$-0.453957\pi$
$444$		0			0
$445$	5.08004	−	8.79889i	0.240817	−	0.417107i
$446$		0			0
$447$	−3.07334	+	21.9250i	−0.145364	+	1.03702i
$448$		0			0
$449$	19.9283			0.940477			0.470238	−	0.882540i	$-0.344168\pi$
$449$	19.9283			0.940477			0.470238	+	0.882540i	$0.344168\pi$
$450$		0			0
$451$	−57.0816			−2.68787
$452$		0			0
$453$	31.3412	+	24.4683i	1.47254	+	1.14962i
$454$		0			0
$455$	−0.582703	+	1.00927i	−0.0273175	+	0.0473154i
$456$		0			0
$457$	16.9326	+	29.3282i	0.792075	+	1.37191i	0.924680	+	0.380745i	$0.124333\pi$
$457$	16.9326	+	29.3282i	0.792075	+	1.37191i	−0.132605	+	0.991169i	$0.542334\pi$
$458$		0			0
$459$	−11.0150	+	24.8120i	−0.514138	+	1.15812i
$460$		0			0
$461$	7.25351	+	12.5634i	0.337830	+	0.585138i	0.984024	−	0.178035i	$-0.0569739\pi$
$461$	7.25351	+	12.5634i	0.337830	+	0.585138i	−0.646195	+	0.763173i	$0.723641\pi$
$462$		0			0
$463$	−12.5348	+	21.7110i	−0.582544	+	1.00900i	0.412633	+	0.910897i	$0.364609\pi$
$463$	−12.5348	+	21.7110i	−0.582544	+	1.00900i	−0.995177	+	0.0980981i	$0.968724\pi$
$464$		0			0
$465$	−7.32750	−	5.72064i	−0.339805	−	0.265288i
$466$		0			0
$467$	−0.102955			−0.00476419			−0.00238209	−	0.999997i	$-0.500758\pi$
$467$	−0.102955			−0.00476419			−0.00238209	+	0.999997i	$0.500758\pi$
$468$		0			0
$469$	−1.14798			−0.0530088
$470$		0			0
$471$	3.96961	−	28.3189i	0.182910	−	1.30487i
$472$		0			0
$473$	−23.8883	+	41.3758i	−1.09839	+	1.90246i
$474$		0			0
$475$	10.6909	+	18.5172i	0.490532	+	0.849626i
$476$		0			0
$477$	−16.4633	+	15.9213i	−0.753802	+	0.728984i
$478$		0			0
$479$	−2.62668	−	4.54954i	−0.120016	−	0.207874i	0.799758	−	0.600323i	$-0.204961\pi$
$479$	−2.62668	−	4.54954i	−0.120016	−	0.207874i	−0.919774	+	0.392449i	$0.871628\pi$
$480$		0			0
$481$	−6.05390	+	10.4857i	−0.276034	+	0.478105i
$482$		0			0
$483$	3.21994	−	1.30228i	0.146512	−	0.0592559i
$484$		0			0
$485$	7.09036			0.321957
$486$		0			0
$487$	−30.7319			−1.39260			−0.696299	−	0.717752i	$-0.745171\pi$
$487$	−30.7319			−1.39260			−0.696299	+	0.717752i	$0.745171\pi$
$488$		0			0
$489$	−27.6573	+	11.1858i	−1.25070	+	0.505839i
$490$		0			0
$491$	2.35920	−	4.08626i	0.106469	−	0.184410i	−0.807868	−	0.589363i	$-0.799379\pi$
$491$	2.35920	−	4.08626i	0.106469	−	0.184410i	0.914338	+	0.404953i	$0.132712\pi$
$492$		0			0
$493$	−17.9682	−	31.1219i	−0.809248	−	1.40166i
$494$		0			0
$495$	10.0480	−	9.71719i	0.451624	−	0.436755i
$496$		0			0
$497$	4.41875	+	7.65349i	0.198208	+	0.343306i
$498$		0			0
$499$	−12.3566	+	21.4023i	−0.553158	+	0.958098i	0.444886	+	0.895587i	$0.353244\pi$
$499$	−12.3566	+	21.4023i	−0.553158	+	0.958098i	−0.998044	+	0.0625105i	$0.980089\pi$
$500$		0			0
$501$	3.15652	−	22.5184i	0.141023	−	1.00605i
$502$		0			0
$503$	−19.4083			−0.865371			−0.432686	−	0.901545i	$-0.642434\pi$
$503$	−19.4083			−0.865371			−0.432686	+	0.901545i	$0.642434\pi$
$504$		0			0
$505$	4.73856			0.210863
$506$		0			0
$507$	−15.6345	−	12.2060i	−0.694352	−	0.542087i
$508$		0			0
$509$	−2.72850	+	4.72591i	−0.120939	+	0.209472i	−0.920138	−	0.391594i	$-0.871924\pi$
$509$	−2.72850	+	4.72591i	−0.120939	+	0.209472i	0.799199	+	0.601066i	$0.205257\pi$
$510$		0			0
$511$	−3.05349	−	5.28880i	−0.135078	−	0.233963i
$512$		0			0
$513$	−10.9344	+	24.6304i	−0.482766	+	1.08746i
$514$		0			0
$515$	−0.111918	−	0.193848i	−0.00493170	−	0.00854196i
$516$		0			0
$517$	4.89897	−	8.48527i	0.215457	−	0.373182i
$518$		0			0
$519$	−25.9238	−	20.2389i	−1.13793	−	0.888391i
$520$		0			0
$521$	−24.7683			−1.08512			−0.542558	−	0.840018i	$-0.682544\pi$
$521$	−24.7683			−1.08512			−0.542558	+	0.840018i	$0.682544\pi$
$522$		0			0
$523$	−32.7530			−1.43219			−0.716094	−	0.698004i	$-0.754072\pi$
$523$	−32.7530			−1.43219			−0.716094	+	0.698004i	$0.754072\pi$
$524$		0			0
$525$	−0.991287	+	7.07177i	−0.0432633	+	0.308637i
$526$		0			0
$527$	14.9694	−	25.9278i	0.652078	−	1.12943i
$528$		0			0
$529$	9.48934	+	16.4360i	0.412580	+	0.714610i
$530$		0			0
$531$	3.55083	+	14.1982i	0.154093	+	0.616149i
$532$		0			0
$533$	7.13868	+	12.3646i	0.309211	+	0.535569i
$534$		0			0
$535$	−4.33403	+	7.50676i	−0.187377	+	0.324546i
$536$		0			0
$537$	−12.2328	+	4.94746i	−0.527883	+	0.213499i
$538$		0			0
$539$	4.97483			0.214281
$540$		0			0
$541$	37.8575			1.62762			0.813811	−	0.581130i	$-0.197389\pi$
$541$	37.8575			1.62762			0.813811	+	0.581130i	$0.197389\pi$
$542$		0			0
$543$	14.8966	−	6.02485i	0.639276	−	0.258551i
$544$		0			0
$545$	4.93827	−	8.55333i	0.211532	−	0.366385i
$546$		0			0
$547$	−1.74835	−	3.02824i	−0.0747543	−	0.129478i	0.826225	−	0.563340i	$-0.190484\pi$
$547$	−1.74835	−	3.02824i	−0.0747543	−	0.129478i	−0.900979	+	0.433862i	$0.857151\pi$
$548$		0			0
$549$	8.77878	+	2.51046i	0.374669	+	0.107144i
$550$		0			0
$551$	−17.8367	−	30.8941i	−0.759869	−	1.31613i
$552$		0			0
$553$	6.05414	−	10.4861i	0.257448	−	0.445913i
$554$		0			0
$555$	2.19124	−	15.6322i	0.0930129	−	0.663548i
$556$		0			0
$557$	−34.1226			−1.44582			−0.722911	−	0.690941i	$-0.757197\pi$
$557$	−34.1226			−1.44582			−0.722911	+	0.690941i	$0.757197\pi$
$558$		0			0
$559$	11.9500			0.505431
$560$		0			0
$561$	35.4841	+	27.7027i	1.49814	+	1.16961i
$562$		0			0
$563$	−7.65071	+	13.2514i	−0.322439	+	0.558481i	−0.980991	−	0.194055i	$-0.937836\pi$
$563$	−7.65071	+	13.2514i	−0.322439	+	0.558481i	0.658552	+	0.752535i	$0.271169\pi$
$564$		0			0
$565$	4.74293	+	8.21500i	0.199537	+	0.345608i
$566$		0			0
$567$	−7.94046	+	4.23664i	−0.333468	+	0.177922i
$568$		0			0
$569$	−16.4953	−	28.5707i	−0.691520	−	1.19775i	−0.971340	−	0.237695i	$-0.923608\pi$
$569$	−16.4953	−	28.5707i	−0.691520	−	1.19775i	0.279820	−	0.960053i	$-0.409725\pi$
$570$		0			0
$571$	10.7150	−	18.5590i	0.448410	−	0.776668i	−0.549873	−	0.835248i	$-0.685324\pi$
$571$	10.7150	−	18.5590i	0.448410	−	0.776668i	0.998283	+	0.0585801i	$0.0186573\pi$
$572$		0			0
$573$	13.1097	+	10.2349i	0.547667	+	0.427568i
$574$		0			0
$575$	8.26755			0.344781
$576$		0			0
$577$	−38.4188			−1.59939			−0.799697	−	0.600404i	$-0.795007\pi$
$577$	−38.4188			−1.59939			−0.799697	+	0.600404i	$0.795007\pi$
$578$		0			0
$579$	−3.62658	+	25.8718i	−0.150715	+	1.07519i
$580$		0			0
$581$	0.431332	−	0.747088i	0.0178947	−	0.0309944i
$582$		0			0
$583$	18.9894	+	32.8905i	0.786459	+	1.36219i
$584$		0			0
$585$	−3.36147	−	0.961278i	−0.138980	−	0.0397439i
$586$		0			0
$587$	8.43772	+	14.6146i	0.348262	+	0.603207i	0.985941	−	0.167095i	$-0.0534387\pi$
$587$	8.43772	+	14.6146i	0.348262	+	0.603207i	−0.637679	+	0.770302i	$0.720105\pi$
$588$		0			0
$589$	14.8599	−	25.7380i	0.612290	−	1.06052i
$590$		0			0
$591$	17.7769	−	7.18976i	0.731245	−	0.295747i
$592$		0			0
$593$	21.7817			0.894467			0.447233	−	0.894417i	$-0.352409\pi$
$593$	21.7817			0.894467			0.447233	+	0.894417i	$0.352409\pi$
$594$		0			0
$595$	4.89316			0.200600
$596$		0			0
$597$	−29.4433	+	11.9081i	−1.20503	+	0.487368i
$598$		0			0
$599$	13.3778	−	23.1710i	0.546601	−	0.946740i	−0.451904	−	0.892067i	$-0.649255\pi$
$599$	13.3778	−	23.1710i	0.546601	−	0.946740i	0.998504	−	0.0546732i	$-0.0174117\pi$
$600$		0			0
$601$	12.5615	+	21.7571i	0.512393	+	0.887491i	0.999897	+	0.0143699i	$0.00457423\pi$
$601$	12.5615	+	21.7571i	0.512393	+	0.887491i	−0.487504	+	0.873121i	$0.662092\pi$
$602$		0			0
$603$	−0.835561	−	3.34104i	−0.0340267	−	0.136058i
$604$		0			0
$605$	−6.43852	−	11.1518i	−0.261763	−	0.453387i
$606$		0			0
$607$	−4.31975	+	7.48203i	−0.175333	+	0.303686i	−0.940277	−	0.340411i	$-0.889434\pi$
$607$	−4.31975	+	7.48203i	−0.175333	+	0.303686i	0.764943	+	0.644098i	$0.222767\pi$
$608$		0			0
$609$	1.65386	−	11.7985i	0.0670179	−	0.478101i
$610$		0			0
$611$	−2.45068			−0.0991440
$612$		0			0
$613$	46.1789			1.86515			0.932575	−	0.360977i	$-0.117557\pi$
$613$	46.1789			1.86515			0.932575	+	0.360977i	$0.117557\pi$
$614$		0			0
$615$	−14.6717	−	11.4543i	−0.591620	−	0.461883i
$616$		0			0
$617$	5.76222	−	9.98046i	0.231978	−	0.401798i	−0.726412	−	0.687260i	$-0.758814\pi$
$617$	5.76222	−	9.98046i	0.231978	−	0.401798i	0.958390	+	0.285461i	$0.0921468\pi$
$618$		0			0
$619$	−19.6325	−	34.0045i	−0.789096	−	1.36675i	−0.926521	−	0.376242i	$-0.877216\pi$
$619$	−19.6325	−	34.0045i	−0.789096	−	1.36675i	0.137425	−	0.990512i	$-0.456117\pi$
$620$		0			0
$621$	6.13376	+	8.42333i	0.246139	+	0.338016i
$622$		0			0
$623$	5.42400	+	9.39464i	0.217308	+	0.376388i
$624$		0			0
$625$	−6.30578	+	10.9219i	−0.252231	+	0.436877i
$626$		0			0
$627$	35.2244	+	27.5000i	1.40673	+	1.09824i
$628$		0			0
$629$	50.8367			2.02699
$630$		0			0
$631$	22.8387			0.909193			0.454596	−	0.890698i	$-0.349784\pi$
$631$	22.8387			0.909193			0.454596	+	0.890698i	$0.349784\pi$
$632$		0			0
$633$	0.629523	−	4.49098i	0.0250213	−	0.178500i
$634$		0			0
$635$	−3.05664	+	5.29426i	−0.121299	+	0.210096i
$636$		0			0
$637$	−0.622156	−	1.07761i	−0.0246507	−	0.0426963i
$638$		0			0
$639$	−19.0583	+	18.4308i	−0.753933	+	0.729111i
$640$		0			0
$641$	9.04899	+	15.6733i	0.357413	+	0.619058i	0.987528	−	0.157444i	$-0.0503254\pi$
$641$	9.04899	+	15.6733i	0.357413	+	0.619058i	−0.630114	+	0.776502i	$0.716992\pi$
$642$		0			0
$643$	15.0416	−	26.0529i	0.593184	−	1.02742i	−0.400616	−	0.916246i	$-0.631204\pi$
$643$	15.0416	−	26.0529i	0.593184	−	1.02742i	0.993800	−	0.111179i	$-0.0354627\pi$
$644$		0			0
$645$	−14.4427	+	5.84127i	−0.568682	+	0.230000i
$646$		0			0
$647$	−25.1323			−0.988054			−0.494027	−	0.869447i	$-0.664476\pi$
$647$	−25.1323			−0.988054			−0.494027	+	0.869447i	$0.664476\pi$
$648$		0			0
$649$	24.2697			0.952668
$650$		0			0
$651$	9.20147	−	3.72147i	0.360634	−	0.145856i
$652$		0			0
$653$	−5.24884	+	9.09125i	−0.205403	+	0.355768i	−0.950261	−	0.311455i	$-0.899184\pi$
$653$	−5.24884	+	9.09125i	−0.205403	+	0.355768i	0.744858	+	0.667223i	$0.232517\pi$
$654$		0			0
$655$	1.65539	+	2.86722i	0.0646815	+	0.112032i
$656$		0			0
$657$	13.1698	−	12.7362i	0.513804	−	0.496888i
$658$		0			0
$659$	4.04138	+	6.99988i	0.157430	+	0.272677i	0.933941	−	0.357427i	$-0.116346\pi$
$659$	4.04138	+	6.99988i	0.157430	+	0.272677i	−0.776511	+	0.630103i	$0.783012\pi$
$660$		0			0
$661$	13.4530	−	23.3012i	0.523260	−	0.906312i	−0.476374	−	0.879243i	$-0.658049\pi$
$661$	13.4530	−	23.3012i	0.523260	−	0.906312i	0.999634	−	0.0270695i	$-0.00861755\pi$
$662$		0			0
$663$	1.56307	−	11.1508i	0.0607045	−	0.433062i
$664$		0			0
$665$	4.85734			0.188360
$666$		0			0
$667$	−13.7936			−0.534090
$668$		0			0
$669$	−34.2521	−	26.7409i	−1.32426	−	1.03386i
$670$		0			0
$671$	7.57060	−	13.1127i	0.292260	−	0.506209i
$672$		0			0
$673$	6.11160	+	10.5856i	0.235585	+	0.408045i	0.959443	−	0.281904i	$-0.0909661\pi$
$673$	6.11160	+	10.5856i	0.235585	+	0.408045i	−0.723858	+	0.689949i	$0.757633\pi$
$674$		0			0
$675$	−21.3030	+	2.26220i	−0.819951	+	0.0870723i
$676$		0			0
$677$	−3.34015	−	5.78531i	−0.128372	−	0.222348i	0.794674	−	0.607037i	$-0.207642\pi$
$677$	−3.34015	−	5.78531i	−0.128372	−	0.222348i	−0.923046	+	0.384689i	$0.874309\pi$
$678$		0			0
$679$	−3.78521	+	6.55618i	−0.145263	+	0.251603i
$680$		0			0
$681$	−34.8908	−	27.2396i	−1.33702	−	1.04382i
$682$		0			0
$683$	19.2125			0.735146			0.367573	−	0.929995i	$-0.380189\pi$
$683$	19.2125			0.735146			0.367573	+	0.929995i	$0.380189\pi$
$684$		0			0
$685$	4.65677			0.177926
$686$		0			0
$687$	1.31596	−	9.38796i	0.0502070	−	0.358173i
$688$		0			0
$689$	4.74966	−	8.22664i	0.180947	−	0.313410i
$690$		0			0
$691$	5.72706	+	9.91955i	0.217867	+	0.377357i	0.954156	−	0.299310i	$-0.0967566\pi$
$691$	5.72706	+	9.91955i	0.217867	+	0.377357i	−0.736288	+	0.676668i	$0.763423\pi$
$692$		0			0
$693$	3.62094	+	14.4786i	0.137548	+	0.549995i
$694$		0			0
$695$	−4.56648	−	7.90937i	−0.173216	−	0.300020i
$696$		0			0
$697$	29.9730	−	51.9147i	1.13531	−	1.96641i
$698$		0			0
$699$	−17.1447	+	6.93405i	−0.648471	+	0.262270i
$700$		0			0
$701$	−4.29596			−0.162256			−0.0811281	−	0.996704i	$-0.525852\pi$
$701$	−4.29596			−0.162256			−0.0811281	+	0.996704i	$0.525852\pi$
$702$		0			0
$703$	50.4646			1.90331
$704$		0			0
$705$	2.96189	−	1.19792i	0.111551	−	0.0451161i
$706$		0			0
$707$	−2.52970	+	4.38156i	−0.0951390	+	0.164786i
$708$		0			0
$709$	−6.44506	−	11.1632i	−0.242049	−	0.419242i	0.719248	−	0.694753i	$-0.244486\pi$
$709$	−6.44506	−	11.1632i	−0.242049	−	0.419242i	−0.961298	+	0.275511i	$0.911153\pi$
$710$		0			0
$711$	34.9248	+	9.98743i	1.30978	+	0.374558i
$712$		0			0
$713$	−5.74576	−	9.95195i	−0.215180	−	0.372703i
$714$		0			0
$715$	−2.89885	+	5.02095i	−0.108411	+	0.187773i
$716$		0			0
$717$	1.20220	−	8.57640i	0.0448969	−	0.320292i
$718$		0			0
$719$	5.46489			0.203806			0.101903	−	0.994794i	$-0.467507\pi$
$719$	5.46489			0.203806			0.101903	+	0.994794i	$0.467507\pi$
$720$		0			0
$721$	0.238992			0.00890051
$722$		0			0
$723$	27.7649	+	21.6763i	1.03259	+	0.806150i
$724$		0			0
$725$	14.1793	−	24.5594i	0.526608	−	0.912111i
$726$		0			0
$727$	24.9300	+	43.1800i	0.924601	+	1.60146i	0.792201	+	0.610260i	$0.208935\pi$
$727$	24.9300	+	43.1800i	0.924601	+	1.60146i	0.132401	+	0.991196i	$0.457731\pi$
$728$		0			0
$729$	−18.1097	−	20.0260i	−0.670728	−	0.741703i
$730$		0			0
$731$	−25.0870	−	43.4520i	−0.927878	−	1.60713i
$732$		0			0
$733$	17.6123	−	30.5054i	0.650525	−	1.12674i	−0.332471	−	0.943114i	$-0.607882\pi$
$733$	17.6123	−	30.5054i	0.650525	−	1.12674i	0.982996	−	0.183629i	$-0.0587844\pi$
$734$		0			0
$735$	1.27868	+	0.998277i	0.0471648	+	0.0368220i
$736$		0			0
$737$	−5.71100			−0.210367
$738$		0			0
$739$	−35.7209			−1.31401			−0.657007	−	0.753885i	$-0.728178\pi$
$739$	−35.7209			−1.31401			−0.657007	+	0.753885i	$0.728178\pi$
$740$		0			0
$741$	1.55163	−	11.0692i	0.0570004	−	0.406637i
$742$		0			0
$743$	−6.53043	+	11.3110i	−0.239578	+	0.414962i	−0.960593	−	0.277958i	$-0.910342\pi$
$743$	−6.53043	+	11.3110i	−0.239578	+	0.414962i	0.721015	+	0.692919i	$0.243676\pi$
$744$		0			0
$745$	5.98580	+	10.3677i	0.219303	+	0.379843i
$746$		0			0
$747$	2.48825	+	0.711562i	0.0910402	+	0.0260347i
$748$		0			0
$749$	−4.62748	−	8.01503i	−0.169084	−	0.292863i
$750$		0			0
$751$	1.11223	−	1.92644i	0.0405859	−	0.0702968i	−0.845019	−	0.534736i	$-0.820411\pi$
$751$	1.11223	−	1.92644i	0.0405859	−	0.0702968i	0.885605	+	0.464440i	$0.153744\pi$
$752$		0			0
$753$	−31.8170	+	12.8682i	−1.15948	+	0.468943i
$754$		0			0
$755$	21.5005			0.782484
$756$		0			0
$757$	4.27335			0.155317			0.0776587	−	0.996980i	$-0.475256\pi$
$757$	4.27335			0.155317			0.0776587	+	0.996980i	$0.475256\pi$
$758$		0			0
$759$	16.0186	−	6.47863i	0.581440	−	0.235159i
$760$		0			0
$761$	−25.2206	+	43.6833i	−0.914245	+	1.58352i	−0.106242	+	0.994340i	$0.533882\pi$
$761$	−25.2206	+	43.6833i	−0.914245	+	1.58352i	−0.808003	+	0.589179i	$0.799451\pi$
$762$		0			0
$763$	5.27263	+	9.13246i	0.190882	+	0.330617i
$764$		0			0
$765$	3.56150	+	14.2409i	0.128766	+	0.514880i
$766$		0			0
$767$	−3.03519	−	5.25710i	−0.109594	−	0.189823i
$768$		0			0
$769$	1.03493	−	1.79255i	0.0373205	−	0.0646411i	−0.846762	−	0.531972i	$-0.821451\pi$
$769$	1.03493	−	1.79255i	0.0373205	−	0.0646411i	0.884082	+	0.467331i	$0.154784\pi$
$770$		0			0
$771$	−0.466215	+	3.32595i	−0.0167903	+	0.119781i
$772$		0			0
$773$	−28.3739			−1.02054			−0.510269	−	0.860015i	$-0.670454\pi$
$773$	−28.3739			−1.02054			−0.510269	+	0.860015i	$0.670454\pi$
$774$		0			0
$775$	23.6258			0.848664
$776$		0			0
$777$	13.2847	+	10.3714i	0.476584	+	0.372073i
$778$		0			0
$779$	29.7536	−	51.5347i	1.06603	−	1.84642i
$780$		0			0
$781$	21.9825	+	38.0748i	0.786595	+	1.36242i
$782$		0			0
$783$	35.5419	−	3.77426i	1.27016	−	0.134881i
$784$		0			0
$785$	−7.73141	−	13.3912i	−0.275946	−	0.477952i
$786$		0			0
$787$	1.72536	−	2.98841i	0.0615025	−	0.106525i	−0.833635	−	0.552316i	$-0.813744\pi$
$787$	1.72536	−	2.98841i	0.0615025	−	0.106525i	0.895137	+	0.445791i	$0.147077\pi$
$788$		0			0
$789$	−18.2335	−	14.2350i	−0.649129	−	0.506781i
$790$		0			0
$791$	−10.1281			−0.360115
$792$		0			0
$793$	−3.78714			−0.134485
$794$		0			0
$795$	−1.71916	+	12.2644i	−0.0609723	+	0.434973i
$796$		0			0
$797$	11.2230	−	19.4388i	0.397540	−	0.688559i	−0.595882	−	0.803072i	$-0.703197\pi$
$797$	11.2230	−	19.4388i	0.397540	−	0.688559i	0.993422	+	0.114513i	$0.0365308\pi$
$798$		0			0
$799$	5.14480	+	8.91106i	0.182010	+	0.315251i
$800$		0			0
$801$	−23.3940	+	22.6237i	−0.826585	+	0.799371i
$802$		0			0
$803$	−15.1906	−	26.3108i	−0.536064	−	0.928490i
$804$		0			0
$805$	0.939078	−	1.62653i	0.0330982	−	0.0573277i
$806$		0			0
$807$	−6.66429	+	2.69533i	−0.234594	+	0.0948801i
$808$		0			0
$809$	18.2366			0.641164			0.320582	−	0.947221i	$-0.396122\pi$
$809$	18.2366			0.641164			0.320582	+	0.947221i	$0.396122\pi$
$810$		0			0
$811$	16.8280			0.590910			0.295455	−	0.955357i	$-0.404529\pi$
$811$	16.8280			0.590910			0.295455	+	0.955357i	$0.404529\pi$
$812$		0			0
$813$	26.6626	−	10.7835i	0.935097	−	0.378194i
$814$		0			0
$815$	−8.06610	+	13.9709i	−0.282543	+	0.489379i
$816$		0			0
$817$	−24.9034	−	43.1340i	−0.871260	−	1.50907i
$818$		0			0
$819$	2.68339	−	2.59504i	0.0937653	−	0.0906781i
$820$		0			0
$821$	18.6149	+	32.2420i	0.649665	+	1.12525i	0.983203	+	0.182516i	$0.0584241\pi$
$821$	18.6149	+	32.2420i	0.649665	+	1.12525i	−0.333538	+	0.942737i	$0.608243\pi$
$822$		0			0
$823$	6.13747	−	10.6304i	0.213939	−	0.370553i	−0.739005	−	0.673700i	$-0.764704\pi$
$823$	6.13747	−	10.6304i	0.213939	−	0.370553i	0.952944	+	0.303147i	$0.0980374\pi$
$824$		0			0
$825$	−4.93148	+	35.1808i	−0.171692	+	1.22484i
$826$		0			0
$827$	−8.60355			−0.299175			−0.149587	−	0.988749i	$-0.547795\pi$
$827$	−8.60355			−0.299175			−0.149587	+	0.988749i	$0.547795\pi$
$828$		0			0
$829$	−44.2887			−1.53821			−0.769105	−	0.639123i	$-0.779298\pi$
$829$	−44.2887			−1.53821			−0.769105	+	0.639123i	$0.779298\pi$
$830$		0			0
$831$	23.3572	+	18.2352i	0.810252	+	0.632571i
$832$		0			0
$833$	−2.61223	+	4.52452i	−0.0905084	+	0.156765i
$834$		0			0
$835$	−6.14781	−	10.6483i	−0.212754	−	0.368500i
$836$		0			0
$837$	17.5282	+	24.0710i	0.605862	+	0.832014i
$838$		0			0
$839$	−23.6154	−	40.9030i	−0.815293	−	1.41213i	−0.909117	−	0.416540i	$-0.863242\pi$
$839$	−23.6154	−	40.9030i	−0.815293	−	1.41213i	0.0938240	−	0.995589i	$-0.470091\pi$
$840$		0			0
$841$	−9.15684	+	15.8601i	−0.315753	+	0.546900i
$842$		0			0
$843$	−20.4518	−	15.9669i	−0.704396	−	0.549928i
$844$		0			0
$845$	−10.7255			−0.368968
$846$		0			0
$847$	13.7489			0.472418
$848$		0			0
$849$	−4.33071	+	30.8950i	−0.148629	+	1.06031i
$850$		0			0
$851$	9.75640	−	16.8986i	0.334445	−	0.579276i
$852$		0			0
$853$	11.9825	+	20.7543i	0.410273	+	0.710614i	0.994919	−	0.100674i	$-0.0321000\pi$
$853$	11.9825	+	20.7543i	0.410273	+	0.710614i	−0.584646	+	0.811288i	$0.698767\pi$
$854$		0			0
$855$	3.53543	+	14.1366i	0.120909	+	0.483463i
$856$		0			0
$857$	−6.50903	−	11.2740i	−0.222344	−	0.385111i	0.733175	−	0.680040i	$-0.238038\pi$
$857$	−6.50903	−	11.2740i	−0.222344	−	0.385111i	−0.955519	+	0.294928i	$0.904704\pi$
$858$		0			0
$859$	0.0473685	−	0.0820447i	0.00161619	−	0.00279933i	−0.865216	−	0.501399i	$-0.832819\pi$
$859$	0.0473685	−	0.0820447i	0.00161619	−	0.00279933i	0.866832	+	0.498600i	$0.166152\pi$
$860$		0			0
$861$	18.4239	−	7.45143i	0.627885	−	0.253944i
$862$		0			0
$863$	−25.8729			−0.880723			−0.440361	−	0.897821i	$-0.645150\pi$
$863$	−25.8729			−0.880723			−0.440361	+	0.897821i	$0.645150\pi$
$864$		0			0
$865$	−17.7841			−0.604678
$866$		0			0
$867$	−16.5306	+	6.68571i	−0.561410	+	0.227059i
$868$		0			0
$869$	30.1183	−	52.1664i	1.02169	−	1.76962i
$870$		0			0
$871$	0.714223	+	1.23707i	0.0242005	+	0.0419165i
$872$		0			0
$873$	−21.8360	−	6.24442i	−0.739036	−	0.211342i
$874$		0			0
$875$	4.27215	+	7.39958i	0.144425	+	0.250151i
$876$		0			0
$877$	26.9042	−	46.5994i	0.908489	−	1.57355i	0.0923254	−	0.995729i	$-0.470570\pi$
$877$	26.9042	−	46.5994i	0.908489	−	1.57355i	0.816164	−	0.577821i	$-0.196097\pi$
$878$		0			0
$879$	−6.65355	+	47.4660i	−0.224419	+	1.60099i
$880$		0			0
$881$	−42.8689			−1.44429			−0.722144	−	0.691743i	$-0.756843\pi$
$881$	−42.8689			−1.44429			−0.722144	+	0.691743i	$0.756843\pi$
$882$		0			0
$883$	34.5967			1.16427			0.582136	−	0.813092i	$-0.302217\pi$
$883$	34.5967			1.16427			0.582136	+	0.813092i	$0.302217\pi$
$884$		0			0
$885$	6.23804	+	4.87009i	0.209689	+	0.163706i
$886$		0			0
$887$	10.2278	−	17.7150i	0.343415	−	0.594812i	−0.641650	−	0.766998i	$-0.721750\pi$
$887$	10.2278	−	17.7150i	0.343415	−	0.594812i	0.985064	+	0.172186i	$0.0550829\pi$
$888$		0			0
$889$	−3.26360	−	5.65272i	−0.109458	−	0.189586i
$890$		0			0
$891$	−39.5024	+	21.0765i	−1.32338	+	0.706091i
$892$		0			0
$893$	5.10714	+	8.84583i	0.170904	+	0.296015i
$894$		0			0
$895$	−3.56762	+	6.17930i	−0.119252	+	0.206551i
$896$		0			0
$897$	−3.40665	−	2.65960i	−0.113745	−	0.0888016i
$898$		0			0
$899$	−39.4173			−1.31464
$900$		0			0
$901$	−39.8845			−1.32874
$902$		0			0
$903$	2.30911	−	16.4730i	0.0768423	−	0.548188i
$904$		0			0
$905$	4.34453	−	7.52494i	0.144417	−	0.250137i
$906$		0			0
$907$	3.92456	+	6.79754i	0.130313	+	0.225709i	0.923797	−	0.382882i	$-0.125068\pi$
$907$	3.92456	+	6.79754i	0.130313	+	0.225709i	−0.793484	+	0.608591i	$0.791735\pi$
$908$		0			0
$909$	−14.5932	−	4.17321i	−0.484026	−	0.138417i
$910$		0			0
$911$	3.87189	+	6.70631i	0.128282	+	0.222190i	0.923011	−	0.384774i	$-0.125721\pi$
$911$	3.87189	+	6.70631i	0.128282	+	0.222190i	−0.794729	+	0.606964i	$0.792387\pi$
$912$		0			0
$913$	2.14580	−	3.71663i	0.0710156	−	0.123003i
$914$		0			0
$915$	4.57713	−	1.85119i	0.151315	−	0.0611985i
$916$		0			0
$917$	−3.53495			−0.116734
$918$		0			0
$919$	19.3702			0.638963			0.319482	−	0.947592i	$-0.396491\pi$
$919$	19.3702			0.638963			0.319482	+	0.947592i	$0.396491\pi$
$920$		0			0
$921$	9.79539	−	3.96168i	0.322769	−	0.130542i
$922$		0			0
$923$	5.49830	−	9.52334i	0.180979	−	0.313464i
$924$		0			0
$925$	20.0585	+	34.7424i	0.659520	+	1.14232i
$926$		0			0
$927$	0.173951	+	0.695553i	0.00571329	+	0.0228450i
$928$		0			0
$929$	1.77989	+	3.08287i	0.0583964	+	0.101146i	0.893746	−	0.448574i	$-0.148068\pi$
$929$	1.77989	+	3.08287i	0.0583964	+	0.101146i	−0.835349	+	0.549720i	$0.814735\pi$
$930$		0			0
$931$	−2.59311	+	4.49140i	−0.0849858	+	0.147200i
$932$		0			0
$933$	6.40900	−	45.7214i	0.209821	−	1.49685i
$934$		0			0
$935$	24.3426			0.796089
$936$		0			0
$937$	−34.2230			−1.11802			−0.559008	−	0.829162i	$-0.688818\pi$
$937$	−34.2230			−1.11802			−0.559008	+	0.829162i	$0.688818\pi$
$938$		0			0
$939$	32.9521	+	25.7260i	1.07535	+	0.839536i
$940$		0			0
$941$	6.02033	−	10.4275i	0.196257	−	0.339928i	−0.751055	−	0.660240i	$-0.770455\pi$
$941$	6.02033	−	10.4275i	0.196257	−	0.339928i	0.947312	+	0.320312i	$0.103788\pi$
$942$		0			0
$943$	−11.5046	−	19.9266i	−0.374642	−	0.648899i
$944$		0			0
$945$	−1.97466	+	4.44803i	−0.0642356	+	0.144694i
$946$		0			0
$947$	11.3623	+	19.6802i	0.369227	+	0.639519i	0.989445	−	0.144910i	$-0.0462893\pi$
$947$	11.3623	+	19.6802i	0.369227	+	0.639519i	−0.620218	+	0.784429i	$0.712956\pi$
$948$		0			0
$949$	−3.79949	+	6.58092i	−0.123337	+	0.213626i
$950$		0			0
$951$	−24.0298	−	18.7603i	−0.779219	−	0.608343i
$952$		0			0
$953$	−6.74488			−0.218488			−0.109244	−	0.994015i	$-0.534843\pi$
$953$	−6.74488			−0.218488			−0.109244	+	0.994015i	$0.534843\pi$
$954$		0			0
$955$	8.99346			0.291022
$956$		0			0
$957$	8.22768	−	58.6957i	0.265963	−	1.89736i
$958$		0			0
$959$	−2.48603	+	4.30593i	−0.0802782	+	0.139046i
$960$		0			0
$961$	−0.919395	−	1.59244i	−0.0296579	−	0.0513690i
$962$		0			0
$963$	19.9585	−	19.3014i	0.643155	−	0.621979i
$964$		0			0
$965$	7.06331	+	12.2340i	0.227376	+	0.393827i
$966$		0			0
$967$	12.8267	−	22.2165i	0.412479	−	0.714434i	−0.582681	−	0.812701i	$-0.697996\pi$
$967$	12.8267	−	22.2165i	0.412479	−	0.714434i	0.995160	+	0.0982664i	$0.0313297\pi$
$968$		0			0
$969$	−43.5067	+	17.5960i	−1.39764	+	0.565265i
$970$		0			0
$971$	40.9298			1.31350			0.656750	−	0.754108i	$-0.271931\pi$
$971$	40.9298			1.31350			0.656750	+	0.754108i	$0.271931\pi$
$972$		0			0
$973$	9.75133			0.312613
$974$		0			0
$975$	8.23732	−	3.33153i	0.263805	−	0.106694i
$976$		0			0
$977$	−22.2365	+	38.5147i	−0.711408	+	1.23220i	0.252920	+	0.967487i	$0.418609\pi$
$977$	−22.2365	+	38.5147i	−0.711408	+	1.23220i	−0.964329	+	0.264708i	$0.914724\pi$
$978$		0			0
$979$	26.9835	+	46.7367i	0.862395	+	1.49371i
$980$		0			0
$981$	−22.7411	+	21.9924i	−0.726067	+	0.702162i
$982$		0			0
$983$	28.4550	+	49.2855i	0.907573	+	1.57196i	0.817425	+	0.576035i	$0.195401\pi$
$983$	28.4550	+	49.2855i	0.907573	+	1.57196i	0.0901483	+	0.995928i	$0.471266\pi$
$984$		0			0
$985$	5.18455	−	8.97990i	0.165193	−	0.286123i
$986$		0			0
$987$	−0.473547	+	3.37826i	−0.0150732	+	0.107531i
$988$		0			0
$989$	−19.2585			−0.612384
$990$		0			0
$991$	−44.7331			−1.42099			−0.710496	−	0.703701i	$-0.751530\pi$
$991$	−44.7331			−1.42099			−0.710496	+	0.703701i	$0.751530\pi$
$992$		0			0
$993$	33.1750	+	25.9000i	1.05278	+	0.821912i
$994$		0			0
$995$	−8.58698	+	14.8731i	−0.272225	+	0.471508i
$996$		0			0
$997$	9.36681	+	16.2238i	0.296650	+	0.513812i	0.975367	−	0.220587i	$-0.0707973\pi$
$997$	9.36681	+	16.2238i	0.296650	+	0.513812i	−0.678718	+	0.734399i	$0.737464\pi$
$998$		0			0
$999$	−20.5154	+	46.2121i	−0.649079	+	1.46209i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.r.d.337.2	yes	8
3.2	odd	2		1512.2.r.d.1009.3		8
4.3	odd	2		1008.2.r.m.337.3		8
9.2	odd	6		1512.2.r.d.505.3		8
9.4	even	3		4536.2.a.x.1.3		4
9.5	odd	6		4536.2.a.ba.1.2		4
9.7	even	3	inner	504.2.r.d.169.2	✓	8
12.11	even	2		3024.2.r.l.1009.3		8
36.7	odd	6		1008.2.r.m.673.3		8
36.11	even	6		3024.2.r.l.2017.3		8
36.23	even	6		9072.2.a.cl.1.2		4
36.31	odd	6		9072.2.a.ce.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.r.d.169.2	✓	8	9.7	even	3	inner
504.2.r.d.337.2	yes	8	1.1	even	1	trivial
1008.2.r.m.337.3		8	4.3	odd	2
1008.2.r.m.673.3		8	36.7	odd	6
1512.2.r.d.505.3		8	9.2	odd	6
1512.2.r.d.1009.3		8	3.2	odd	2
3024.2.r.l.1009.3		8	12.11	even	2
3024.2.r.l.2017.3		8	36.11	even	6
4536.2.a.x.1.3		4	9.4	even	3
4536.2.a.ba.1.2		4	9.5	odd	6
9072.2.a.ce.1.3		4	36.31	odd	6
9072.2.a.cl.1.2		4	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.r (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.60570 + 0.649414i) q^{3} +(-0.468293 + 0.811107i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(2.15652 - 2.08552i) q^{9} +O(q^{10})\)	\(q+(-1.60570 + 0.649414i) q^{3} +(-0.468293 + 0.811107i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(2.15652 - 2.08552i) q^{9} +(-2.48741 - 4.30833i) q^{11} +(-0.622156 + 1.07761i) q^{13} +(0.225193 - 1.60651i) q^{15} +5.22446 q^{17} +5.18622 q^{19} +(1.36526 + 1.06587i) q^{21} +(1.00266 - 1.73666i) q^{23} +(2.06140 + 3.57046i) q^{25} +(-2.10836 + 4.74919i) q^{27} +(-3.43925 - 5.95695i) q^{29} +(2.86526 - 4.96277i) q^{31} +(6.79192 + 5.30251i) q^{33} +0.936586 q^{35} +9.73051 q^{37} +(0.299182 - 2.13435i) q^{39} +(5.73705 - 9.93686i) q^{41} +(-4.80184 - 8.31704i) q^{43} +(0.681697 + 2.72581i) q^{45} +(0.984753 + 1.70564i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-8.38890 + 3.39284i) q^{51} -7.63418 q^{53} +4.65935 q^{55} +(-8.32750 + 3.36800i) q^{57} +(-2.43925 + 4.22490i) q^{59} +(1.52178 + 2.63580i) q^{61} +(-2.88438 - 0.824844i) q^{63} +(-0.582703 - 1.00927i) q^{65} +(0.573990 - 0.994179i) q^{67} +(-0.482159 + 3.43969i) q^{69} -8.83749 q^{71} +6.10698 q^{73} +(-5.62869 - 4.39437i) q^{75} +(-2.48741 + 4.30833i) q^{77} +(6.05414 + 10.4861i) q^{79} +(0.301193 - 8.99496i) q^{81} +(0.431332 + 0.747088i) q^{83} +(-2.44658 + 4.23760i) q^{85} +(9.39091 + 7.33156i) q^{87} -10.8480 q^{89} +1.24431 q^{91} +(-1.37784 + 9.82944i) q^{93} +(-2.42867 + 4.20658i) q^{95} +(-3.78521 - 6.55618i) q^{97} +(-14.3493 - 4.10345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 4 q^{5} - 4 q^{7} + 10 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 4 * q^5 - 4 * q^7 + 10 * q^9	\( 8 q - 4 q^{3} + 4 q^{5} - 4 q^{7} + 10 q^{9} - 6 q^{11} - 3 q^{13} + 4 q^{15} - 16 q^{17} - 4 q^{19} - q^{21} - 5 q^{23} - 14 q^{25} + 5 q^{27} + q^{29} + 11 q^{31} - 8 q^{35} + 54 q^{37} - 12 q^{39} + 2 q^{41} - 11 q^{43} + 26 q^{45} + 7 q^{47} - 4 q^{49} + 17 q^{51} - 8 q^{53} + 12 q^{55} - 13 q^{57} + 9 q^{59} - 7 q^{61} - 5 q^{63} - 9 q^{65} - 12 q^{67} + 4 q^{69} - 24 q^{71} + 26 q^{73} - 23 q^{75} - 6 q^{77} - 22 q^{79} + 34 q^{81} - 6 q^{83} - 11 q^{85} + 37 q^{87} - 28 q^{89} + 6 q^{91} - 13 q^{93} - 23 q^{95} - q^{97} - 42 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + 4 * q^5 - 4 * q^7 + 10 * q^9 - 6 * q^11 - 3 * q^13 + 4 * q^15 - 16 * q^17 - 4 * q^19 - q^21 - 5 * q^23 - 14 * q^25 + 5 * q^27 + q^29 + 11 * q^31 - 8 * q^35 + 54 * q^37 - 12 * q^39 + 2 * q^41 - 11 * q^43 + 26 * q^45 + 7 * q^47 - 4 * q^49 + 17 * q^51 - 8 * q^53 + 12 * q^55 - 13 * q^57 + 9 * q^59 - 7 * q^61 - 5 * q^63 - 9 * q^65 - 12 * q^67 + 4 * q^69 - 24 * q^71 + 26 * q^73 - 23 * q^75 - 6 * q^77 - 22 * q^79 + 34 * q^81 - 6 * q^83 - 11 * q^85 + 37 * q^87 - 28 * q^89 + 6 * q^91 - 13 * q^93 - 23 * q^95 - q^97 - 42 * q^99

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