LMFDB - Embedded newform 585.2.bs.b.334.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(289,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("585.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bs (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			334.2
Character	$\chi$	$=$	585.334
Dual form			585.2.bs.b.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.85914 - 1.07337i) q^{2} +(1.30426 + 2.25904i) q^{4} +(2.16557 - 0.557052i) q^{5} +(0.635729 - 0.367038i) q^{7} -1.30633i q^{8} +O(q^{10})$	\(q+(-1.85914 - 1.07337i) q^{2} +(1.30426 + 2.25904i) q^{4} +(2.16557 - 0.557052i) q^{5} +(0.635729 - 0.367038i) q^{7} -1.30633i q^{8} +(-4.62401 - 1.28883i) q^{10} +(0.110220 - 0.190906i) q^{11} +(-0.632595 - 3.54962i) q^{13} -1.57588 q^{14} +(1.20633 - 2.08943i) q^{16} +(-0.710116 + 0.409986i) q^{17} +(1.61059 + 2.78963i) q^{19} +(4.08287 + 4.16558i) q^{20} +(-0.409827 + 0.236613i) q^{22} +(6.92086 + 3.99576i) q^{23} +(4.37939 - 2.41267i) q^{25} +(-2.63399 + 7.27824i) q^{26} +(1.65831 + 0.957426i) q^{28} +(1.51840 - 2.62994i) q^{29} -5.27667 q^{31} +(-6.74812 + 3.89603i) q^{32} +1.76027 q^{34} +(1.17226 - 1.14898i) q^{35} +(4.44748 + 2.56775i) q^{37} -6.91507i q^{38} +(-0.727696 - 2.82896i) q^{40} +(5.87981 - 10.1841i) q^{41} +(4.62010 - 2.66741i) q^{43} +0.575020 q^{44} +(-8.57789 - 14.8573i) q^{46} -5.80713i q^{47} +(-3.23057 + 5.59550i) q^{49} +(-10.7316 - 0.215233i) q^{50} +(7.19368 - 6.05869i) q^{52} +4.27058i q^{53} +(0.132344 - 0.474818i) q^{55} +(-0.479475 - 0.830474i) q^{56} +(-5.64581 + 3.25961i) q^{58} +(-1.08650 - 1.88188i) q^{59} +(-6.03816 - 10.4584i) q^{61} +(9.81005 + 5.66383i) q^{62} +11.9022 q^{64} +(-3.34725 - 7.33457i) q^{65} +(-1.38164 - 0.797691i) q^{67} +(-1.85235 - 1.06945i) q^{68} +(-3.41267 + 0.877845i) q^{70} +(-4.41778 - 7.65181i) q^{71} -7.86235i q^{73} +(-5.51231 - 9.54761i) q^{74} +(-4.20126 + 7.27680i) q^{76} -0.161819i q^{77} +13.9175 q^{79} +(1.44848 - 5.19680i) q^{80} +(-21.8628 + 12.6225i) q^{82} -4.38199i q^{83} +(-1.30942 + 1.28342i) q^{85} -11.4525 q^{86} +(-0.249387 - 0.143984i) q^{88} +(-2.16344 + 3.74719i) q^{89} +(-1.70501 - 2.02441i) q^{91} +20.8460i q^{92} +(-6.23322 + 10.7962i) q^{94} +(5.04182 + 5.14395i) q^{95} +(-7.48331 + 4.32049i) q^{97} +(12.0121 - 6.93520i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{4} - 4 q^{5}+O(q^{10}) $ 24 * q + 8 * q^4 - 4 * q^5	$ 24 q + 8 q^{4} - 4 q^{5} - 4 q^{10} - 4 q^{11} - 24 q^{14} + 16 q^{16} - 16 q^{19} + 16 q^{20} - 16 q^{25} + 48 q^{26} + 12 q^{29} + 8 q^{31} - 32 q^{34} - 10 q^{35} - 48 q^{40} + 40 q^{41} - 40 q^{44} - 24 q^{46} - 16 q^{49} - 20 q^{50} + 20 q^{55} + 24 q^{56} - 12 q^{59} + 20 q^{61} + 48 q^{64} - 14 q^{65} - 56 q^{70} - 4 q^{71} + 12 q^{74} + 8 q^{76} + 136 q^{79} + 4 q^{80} - 4 q^{85} - 48 q^{86} + 64 q^{89} + 60 q^{91} - 48 q^{94} + 28 q^{95}+O(q^{100}) $ 24 * q + 8 * q^4 - 4 * q^5 - 4 * q^10 - 4 * q^11 - 24 * q^14 + 16 * q^16 - 16 * q^19 + 16 * q^20 - 16 * q^25 + 48 * q^26 + 12 * q^29 + 8 * q^31 - 32 * q^34 - 10 * q^35 - 48 * q^40 + 40 * q^41 - 40 * q^44 - 24 * q^46 - 16 * q^49 - 20 * q^50 + 20 * q^55 + 24 * q^56 - 12 * q^59 + 20 * q^61 + 48 * q^64 - 14 * q^65 - 56 * q^70 - 4 * q^71 + 12 * q^74 + 8 * q^76 + 136 * q^79 + 4 * q^80 - 4 * q^85 - 48 * q^86 + 64 * q^89 + 60 * q^91 - 48 * q^94 + 28 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.85914	−	1.07337i	−1.31461	−	0.758989i	−0.331752	−	0.943366i	$-0.607640\pi$
$2$	−1.85914	−	1.07337i	−1.31461	−	0.758989i	−0.982856	+	0.184377i	$0.940973\pi$
$3$		0			0
$3$		0			0
$4$	1.30426	+	2.25904i	0.652130	+	1.12952i
$5$	2.16557	−	0.557052i	0.968472	−	0.249121i
$5$	2.16557	−	0.557052i	0.968472	−	0.249121i
$6$		0			0
$7$	0.635729	−	0.367038i	0.240283	−	0.138727i	−0.375024	−	0.927015i	$-0.622365\pi$
$7$	0.635729	−	0.367038i	0.240283	−	0.138727i	0.615307	+	0.788288i	$0.289032\pi$
$8$		−	1.30633i		−	0.461859i
$9$		0			0
$10$	−4.62401	−	1.28883i	−1.46224	−	0.407563i
$11$	0.110220	−	0.190906i	0.0332325	−	0.0575603i	−0.848931	−	0.528504i	$-0.822753\pi$
$11$	0.110220	−	0.190906i	0.0332325	−	0.0575603i	0.882163	+	0.470944i	$0.156086\pi$
$12$		0			0
$13$	−0.632595	−	3.54962i	−0.175450	−	0.984488i
$13$	−0.632595	−	3.54962i	−0.175450	−	0.984488i
$14$	−1.57588			−0.421171
$15$		0			0
$16$	1.20633	−	2.08943i	0.301584	−	0.522358i
$17$	−0.710116	+	0.409986i	−0.172228	+	0.0994361i	−0.583636	−	0.812015i	$-0.698371\pi$
$17$	−0.710116	+	0.409986i	−0.172228	+	0.0994361i	0.411408	+	0.911451i	$0.365037\pi$
$18$		0			0
$19$	1.61059	+	2.78963i	0.369495	+	0.639985i	0.989487	−	0.144624i	$-0.0461972\pi$
$19$	1.61059	+	2.78963i	0.369495	+	0.639985i	−0.619991	+	0.784609i	$0.712864\pi$
$20$	4.08287	+	4.16558i	0.912957	+	0.931451i
$21$		0			0
$22$	−0.409827	+	0.236613i	−0.0873753	+	0.0504462i
$23$	6.92086	+	3.99576i	1.44310	+	0.833174i	0.998055	−	0.0623347i	$-0.0198546\pi$
$23$	6.92086	+	3.99576i	1.44310	+	0.833174i	0.445044	+	0.895509i	$0.353188\pi$
$24$		0			0
$25$	4.37939	−	2.41267i	0.875877	−	0.482534i
$26$	−2.63399	+	7.27824i	−0.516568	+	1.42738i
$27$		0			0
$28$	1.65831	+	0.957426i	0.313391	+	0.180937i
$29$	1.51840	−	2.62994i	0.281959	−	0.488367i	−0.689908	−	0.723897i	$-0.742349\pi$
$29$	1.51840	−	2.62994i	0.281959	−	0.488367i	0.971867	+	0.235530i	$0.0756824\pi$
$30$		0			0
$31$	−5.27667			−0.947718			−0.473859	−	0.880601i	$-0.657139\pi$
$31$	−5.27667			−0.947718			−0.473859	+	0.880601i	$0.657139\pi$
$32$	−6.74812	+	3.89603i	−1.19291	+	0.688727i
$33$		0			0
$34$	1.76027			0.301884
$35$	1.17226	−	1.14898i	0.198147	−	0.194213i
$36$		0			0
$37$	4.44748	+	2.56775i	0.731161	+	0.422136i	0.818847	−	0.574012i	$-0.194614\pi$
$37$	4.44748	+	2.56775i	0.731161	+	0.422136i	−0.0876857	+	0.996148i	$0.527947\pi$
$38$		−	6.91507i		−	1.12177i
$39$		0			0
$40$	−0.727696	−	2.82896i	−0.115059	−	0.447297i
$41$	5.87981	−	10.1841i	0.918273	−	1.59050i	0.116235	−	0.993222i	$-0.462917\pi$
$41$	5.87981	−	10.1841i	0.918273	−	1.59050i	0.802038	−	0.597273i	$-0.203749\pi$
$42$		0			0
$43$	4.62010	−	2.66741i	0.704558	−	0.406777i	−0.104485	−	0.994526i	$-0.533319\pi$
$43$	4.62010	−	2.66741i	0.704558	−	0.406777i	0.809043	+	0.587750i	$0.199986\pi$
$44$	0.575020			0.0866875
$45$		0			0
$46$	−8.57789	−	14.8573i	−1.26474	−	2.19059i
$47$		−	5.80713i		−	0.847057i	−0.905883	−	0.423528i	$-0.860791\pi$
$47$		−	5.80713i		−	0.847057i	0.905883	−	0.423528i	$-0.139209\pi$
$48$		0			0
$49$	−3.23057	+	5.59550i	−0.461509	+	0.799358i
$50$	−10.7316	−	0.215233i	−1.51767	−	0.0304386i
$51$		0			0
$52$	7.19368	−	6.05869i	0.997584	−	0.840189i
$53$			4.27058i			0.586610i	0.956019	+	0.293305i	$0.0947551\pi$
$53$			4.27058i			0.586610i	−0.956019	+	0.293305i	$0.905245\pi$
$54$		0			0
$55$	0.132344	−	0.474818i	0.0178452	−	0.0640245i
$56$	−0.479475	−	0.830474i	−0.0640725	−	0.110977i
$57$		0			0
$58$	−5.64581	+	3.25961i	−0.741331	+	0.428008i
$59$	−1.08650	−	1.88188i	−0.141451	−	0.245000i	0.786592	−	0.617473i	$-0.211843\pi$
$59$	−1.08650	−	1.88188i	−0.141451	−	0.245000i	−0.928043	+	0.372473i	$0.878510\pi$
$60$		0			0
$61$	−6.03816	−	10.4584i	−0.773107	−	1.33906i	−0.935852	−	0.352393i	$-0.885368\pi$
$61$	−6.03816	−	10.4584i	−0.773107	−	1.33906i	0.162745	−	0.986668i	$-0.447965\pi$
$62$	9.81005	+	5.66383i	1.24588	+	0.719308i
$63$		0			0
$64$	11.9022			1.48778
$65$	−3.34725	−	7.33457i	−0.415176	−	0.909741i
$66$		0			0
$67$	−1.38164	−	0.797691i	−0.168794	−	0.0974535i	0.413223	−	0.910630i	$-0.364403\pi$
$67$	−1.38164	−	0.797691i	−0.168794	−	0.0974535i	−0.582017	+	0.813176i	$0.697736\pi$
$68$	−1.85235	−	1.06945i	−0.224630	−	0.129690i
$69$		0			0
$70$	−3.41267	+	0.877845i	−0.407892	+	0.104922i
$71$	−4.41778	−	7.65181i	−0.524294	−	0.908103i	−0.999600	−	0.0282829i	$-0.990996\pi$
$71$	−4.41778	−	7.65181i	−0.524294	−	0.908103i	0.475306	−	0.879820i	$-0.342337\pi$
$72$		0			0
$73$		−	7.86235i		−	0.920218i	−0.887862	−	0.460109i	$-0.847810\pi$
$73$		−	7.86235i		−	0.920218i	0.887862	−	0.460109i	$-0.152190\pi$
$74$	−5.51231	−	9.54761i	−0.640794	−	1.10989i
$75$		0			0
$76$	−4.20126	+	7.27680i	−0.481918	+	0.834706i
$77$		−	0.161819i		−	0.0184410i
$78$		0			0
$79$	13.9175			1.56585			0.782923	−	0.622118i	$-0.213728\pi$
$79$	13.9175			1.56585			0.782923	+	0.622118i	$0.213728\pi$
$80$	1.44848	−	5.19680i	0.161945	−	0.581020i
$81$		0			0
$82$	−21.8628	+	12.6225i	−2.41434	+	1.39392i
$83$		−	4.38199i		−	0.480986i	−0.970651	−	0.240493i	$-0.922691\pi$
$83$		−	4.38199i		−	0.480986i	0.970651	−	0.240493i	$-0.0773091\pi$
$84$		0			0
$85$	−1.30942	+	1.28342i	−0.142027	+	0.139207i
$86$	−11.4525			−1.23496
$87$		0			0
$88$	−0.249387	−	0.143984i	−0.0265847	−	0.0153487i
$89$	−2.16344	+	3.74719i	−0.229324	+	0.397201i	−0.957608	−	0.288074i	$-0.906985\pi$
$89$	−2.16344	+	3.74719i	−0.229324	+	0.397201i	0.728284	+	0.685276i	$0.240318\pi$
$90$		0			0
$91$	−1.70501	−	2.02441i	−0.178733	−	0.212216i
$92$			20.8460i			2.17335i
$93$		0			0
$94$	−6.23322	+	10.7962i	−0.642907	+	1.11355i
$95$	5.04182	+	5.14395i	0.517280	+	0.527758i
$96$		0			0
$97$	−7.48331	+	4.32049i	−0.759815	+	0.438679i	−0.829229	−	0.558908i	$-0.811220\pi$
$97$	−7.48331	+	4.32049i	−0.759815	+	0.438679i	0.0694143	+	0.997588i	$0.477887\pi$
$98$	12.0121	−	6.93520i	1.21341	−	0.700561i
$99$		0			0
$100$	11.1622	+	6.74648i	1.11622	+	0.674648i
$101$	2.86187	−	4.95690i	0.284766	−	0.493230i	−0.687786	−	0.725913i	$-0.741417\pi$
$101$	2.86187	−	4.95690i	0.284766	−	0.493230i	0.972552	+	0.232684i	$0.0747507\pi$
$102$		0			0
$103$			7.85100i			0.773582i	0.922167	+	0.386791i	$0.126417\pi$
$103$			7.85100i			0.773582i	−0.922167	+	0.386791i	$0.873583\pi$
$104$	−4.63699	+	0.826381i	−0.454695	+	0.0810333i
$105$		0			0
$106$	4.58393	−	7.93960i	0.445230	−	0.771162i
$107$	10.1208	+	5.84322i	0.978411	+	0.564886i	0.901790	−	0.432175i	$-0.142254\pi$
$107$	10.1208	+	5.84322i	0.978411	+	0.564886i	0.0766207	+	0.997060i	$0.475587\pi$
$108$		0			0
$109$	−13.2496			−1.26908			−0.634541	−	0.772889i	$-0.718811\pi$
$109$	−13.2496			−1.26908			−0.634541	+	0.772889i	$0.718811\pi$
$110$	−0.755702	+	0.740698i	−0.0720534	+	0.0706228i
$111$		0			0
$112$		−	1.77108i		−	0.167352i
$113$	−13.0045	+	7.50816i	−1.22336	+	0.706309i	−0.965633	−	0.259908i	$-0.916308\pi$
$113$	−13.0045	+	7.50816i	−1.22336	+	0.706309i	−0.257729	+	0.966217i	$0.582974\pi$
$114$		0			0
$115$	17.2135	+	4.79782i	1.60516	+	0.447399i
$116$	7.92153			0.735495
$117$		0			0
$118$			4.66489i			0.429438i
$119$	−0.300961	+	0.521279i	−0.0275890	+	0.0477856i
$120$		0			0
$121$	5.47570	+	9.48420i	0.497791	+	0.862200i
$122$			25.9248i			2.34712i
$123$		0			0
$124$	−6.88214	−	11.9202i	−0.618035	−	1.07047i
$125$	8.13989	−	7.66435i	0.728054	−	0.685520i
$126$		0			0
$127$	15.4827	+	8.93894i	1.37387	+	0.793203i	0.991413	−	0.130771i	$-0.0417454\pi$
$127$	15.4827	+	8.93894i	1.37387	+	0.793203i	0.382455	+	0.923974i	$0.375079\pi$
$128$	−8.63163	−	4.98347i	−0.762935	−	0.440481i
$129$		0			0
$130$	−1.64973	+	17.2288i	−0.144691	+	1.51107i
$131$	−8.13522			−0.710778			−0.355389	−	0.934719i	$-0.615652\pi$
$131$	−8.13522			−0.710778			−0.355389	+	0.934719i	$0.615652\pi$
$132$		0			0
$133$	2.04780	+	1.18230i	0.177567	+	0.102518i
$134$	1.71244	+	2.96603i	0.147932	+	0.256226i
$135$		0			0
$136$	0.535578	+	0.927648i	0.0459254	+	0.0795452i
$137$	9.22293	−	5.32486i	0.787968	−	0.454933i	−0.0512789	−	0.998684i	$-0.516330\pi$
$137$	9.22293	−	5.32486i	0.787968	−	0.454933i	0.839247	+	0.543751i	$0.182996\pi$
$138$		0			0
$139$	1.23172	+	2.13340i	0.104473	+	0.180953i	0.913523	−	0.406787i	$-0.133351\pi$
$139$	1.23172	+	2.13340i	0.104473	+	0.180953i	−0.809050	+	0.587740i	$0.800018\pi$
$140$	4.12452	+	1.14961i	0.348586	+	0.0971596i
$141$		0			0
$142$			18.9677i			1.59173i
$143$	−0.747369	−	0.270472i	−0.0624981	−	0.0226180i
$144$		0			0
$145$	1.82318	−	6.54114i	0.151407	−	0.543212i
$146$	−8.43923	+	14.6172i	−0.698436	+	1.20973i
$147$		0			0
$148$			13.3961i			1.10115i
$149$	8.15299	+	14.1214i	0.667919	+	1.15687i	0.978485	+	0.206318i	$0.0661482\pi$
$149$	8.15299	+	14.1214i	0.667919	+	1.15687i	−0.310566	+	0.950552i	$0.600518\pi$
$150$		0			0
$151$	21.1259			1.71920			0.859602	−	0.510964i	$-0.170711\pi$
$151$	21.1259			1.71920			0.859602	+	0.510964i	$0.170711\pi$
$152$	3.64419	−	2.10397i	0.295583	−	0.170655i
$153$		0			0
$154$	−0.173692	+	0.300844i	−0.0139965	+	0.0242427i
$155$	−11.4270	+	2.93938i	−0.917838	+	0.236097i
$156$		0			0
$157$		−	17.3604i		−	1.38551i	−0.721173	−	0.692755i	$-0.756397\pi$
$157$		−	17.3604i		−	1.38551i	0.721173	−	0.692755i	$-0.243603\pi$
$158$	−25.8746	−	14.9387i	−2.05847	−	1.18846i
$159$		0			0
$160$	−12.4432	+	12.1962i	−0.983724	+	0.964192i
$161$	5.86639			0.462336
$162$		0			0
$163$	6.80671	−	3.92986i	0.533143	−	0.307810i	−0.209153	−	0.977883i	$-0.567071\pi$
$163$	6.80671	−	3.92986i	0.533143	−	0.307810i	0.742295	+	0.670073i	$0.233737\pi$
$164$	30.6752			2.39533
$165$		0			0
$166$	−4.70351	+	8.14672i	−0.365063	+	0.632308i
$167$	1.69535	+	0.978812i	0.131190	+	0.0757428i	0.564159	−	0.825666i	$-0.309201\pi$
$167$	1.69535	+	0.978812i	0.131190	+	0.0757428i	−0.432969	+	0.901409i	$0.642534\pi$
$168$		0			0
$169$	−12.1996	+	4.49095i	−0.938434	+	0.345458i
$170$	3.81199	−	0.980562i	0.292366	−	0.0752056i
$171$		0			0
$172$	12.0516	+	6.95800i	0.918926	+	0.530542i
$173$	−17.9850	+	10.3837i	−1.36738	+	0.789456i	−0.990593	−	0.136845i	$-0.956304\pi$
$173$	−17.9850	+	10.3837i	−1.36738	+	0.789456i	−0.376785	+	0.926301i	$0.622971\pi$
$174$		0			0
$175$	1.89856	−	3.14121i	0.143518	−	0.237453i
$176$	−0.265923	−	0.460593i	−0.0200447	−	0.0347185i
$177$		0			0
$178$	8.04426	−	4.64436i	0.602943	−	0.348109i
$179$	−12.8863	+	22.3197i	−0.963166	+	1.66825i	−0.248701	+	0.968580i	$0.580004\pi$
$179$	−12.8863	+	22.3197i	−0.963166	+	1.66825i	−0.714465	+	0.699671i	$0.753330\pi$
$180$		0			0
$181$	−11.8750			−0.882659			−0.441329	−	0.897345i	$-0.645493\pi$
$181$	−11.8750			−0.882659			−0.441329	+	0.897345i	$0.645493\pi$
$182$	0.996891	+	5.59377i	0.0738945	+	0.414637i
$183$		0			0
$184$	5.21980	−	9.04096i	0.384809	−	0.666508i
$185$	11.0617	+	3.08317i	0.813272	+	0.226679i
$186$		0			0
$187$			0.180754i			0.0132180i
$188$	13.1186	−	7.57400i	0.956769	−	0.552391i
$189$		0			0
$190$	−3.85205	−	14.9751i	−0.279457	−	1.08641i
$191$	10.9611	+	18.9852i	0.793120	+	1.37372i	0.924026	+	0.382329i	$0.124878\pi$
$191$	10.9611	+	18.9852i	0.793120	+	1.37372i	−0.130907	+	0.991395i	$0.541789\pi$
$192$		0			0
$193$	−18.0972	−	10.4484i	−1.30267	−	0.752095i	−0.321806	−	0.946806i	$-0.604290\pi$
$193$	−18.0972	−	10.4484i	−1.30267	−	0.752095i	−0.980861	+	0.194711i	$0.937623\pi$
$194$	18.5500			1.33181
$195$		0			0
$196$	−16.8540			−1.20386
$197$	−3.28615	−	1.89726i	−0.234129	−	0.135174i	0.378347	−	0.925664i	$-0.376493\pi$
$197$	−3.28615	−	1.89726i	−0.234129	−	0.135174i	−0.612475	+	0.790490i	$0.709826\pi$
$198$		0			0
$199$	−0.193666	−	0.335440i	−0.0137286	−	0.0237787i	0.859079	−	0.511842i	$-0.171037\pi$
$199$	−0.193666	−	0.335440i	−0.0137286	−	0.0237787i	−0.872808	+	0.488064i	$0.837703\pi$
$200$	−3.15175	−	5.72094i	−0.222862	−	0.404532i
$201$		0			0
$202$	−10.6412	+	6.14370i	−0.748712	+	0.432269i
$203$		−	2.22924i		−	0.156462i
$204$		0			0
$205$	7.06006	−	25.3298i	0.493096	−	1.76911i
$206$	8.42705	−	14.5961i	0.587141	−	1.01696i
$207$		0			0
$208$	−8.17982	−	2.96027i	−0.567169	−	0.205258i
$209$	0.710076			0.0491170
$210$		0			0
$211$	−4.52279	+	7.83370i	−0.311362	+	0.539294i	−0.978657	−	0.205499i	$-0.934118\pi$
$211$	−4.52279	+	7.83370i	−0.311362	+	0.539294i	0.667296	+	0.744793i	$0.267452\pi$
$212$	−9.64743	+	5.56995i	−0.662588	+	0.382545i
$213$		0			0
$214$	−12.5439	−	21.7267i	−0.857484	−	1.48521i
$215$	8.51925	−	8.35010i	0.581008	−	0.569472i
$216$		0			0
$217$	−3.35453	+	1.93674i	−0.227720	+	0.131474i
$218$	24.6328	+	14.2218i	1.66835	+	0.963220i
$219$		0			0
$220$	1.24525	−	0.320316i	0.0839544	−	0.0215957i
$221$	1.90451	+	2.26129i	0.128111	+	0.152111i
$222$		0			0
$223$	−12.4345	−	7.17903i	−0.832672	−	0.480744i	0.0220944	−	0.999756i	$-0.492967\pi$
$223$	−12.4345	−	7.17903i	−0.832672	−	0.480744i	−0.854767	+	0.519012i	$0.826300\pi$
$224$	−2.85998	+	4.95364i	−0.191091	+	0.330979i
$225$		0			0
$226$	32.2362			2.14432
$227$	−21.4099	+	12.3610i	−1.42102	+	0.820429i	−0.996387	−	0.0849341i	$-0.972932\pi$
$227$	−21.4099	+	12.3610i	−1.42102	+	0.820429i	−0.424638	+	0.905363i	$0.639599\pi$
$228$		0			0
$229$	1.20021			0.0793124			0.0396562	−	0.999213i	$-0.487374\pi$
$229$	1.20021			0.0793124			0.0396562	+	0.999213i	$0.487374\pi$
$230$	−26.8523	−	27.3963i	−1.77059	−	1.80646i
$231$		0			0
$232$	−3.43558	−	1.98353i	−0.225557	−	0.130225i
$233$		−	20.5107i		−	1.34370i	−0.740687	−	0.671851i	$-0.765500\pi$
$233$		−	20.5107i		−	1.34370i	0.740687	−	0.671851i	$-0.234500\pi$
$234$		0			0
$235$	−3.23487	−	12.5757i	−0.211020	−	0.820351i
$236$	2.83416	−	4.90892i	0.184488	−	0.319543i
$237$		0			0
$238$	1.11905	−	0.646086i	0.0725375	−	0.0418796i
$239$	−29.0377			−1.87829			−0.939146	−	0.343518i	$-0.888381\pi$
$239$	−29.0377			−1.87829			−0.939146	+	0.343518i	$0.888381\pi$
$240$		0			0
$241$	7.22083	+	12.5068i	0.465134	+	0.805636i	0.999208	−	0.0398019i	$-0.0126727\pi$
$241$	7.22083	+	12.5068i	0.465134	+	0.805636i	−0.534073	+	0.845438i	$0.679339\pi$
$242$		−	23.5099i		−	1.51127i
$243$		0			0
$244$	15.7507	−	27.2809i	1.00833	−	1.74648i
$245$	−3.87903	+	13.9170i	−0.247822	+	0.889128i
$246$		0			0
$247$	8.88328	−	7.48170i	0.565229	−	0.476049i
$248$			6.89309i			0.437712i
$249$		0			0
$250$	−23.3599	+	5.51194i	−1.47741	+	0.348606i
$251$	−2.57837	−	4.46587i	−0.162745	−	0.281883i	0.773107	−	0.634276i	$-0.218702\pi$
$251$	−2.57837	−	4.46587i	−0.162745	−	0.281883i	−0.935852	+	0.352392i	$0.885368\pi$
$252$		0			0
$253$	1.52563	−	0.880822i	0.0959155	−	0.0553768i
$254$	−19.1896	−	33.2374i	−1.20406	−	2.08550i
$255$		0			0
$256$	−1.20398	−	2.08535i	−0.0752487	−	0.130335i
$257$	8.13546	+	4.69701i	0.507476	+	0.292991i	0.731795	−	0.681524i	$-0.238683\pi$
$257$	8.13546	+	4.69701i	0.507476	+	0.292991i	−0.224320	+	0.974516i	$0.572016\pi$
$258$		0			0
$259$	3.76986			0.234247
$260$	12.2034	−	17.1278i	0.756824	−	1.06222i
$261$		0			0
$262$	15.1245	+	8.73213i	0.934394	+	0.539473i
$263$	9.13306	+	5.27297i	0.563168	+	0.325145i	0.754416	−	0.656396i	$-0.227920\pi$
$263$	9.13306	+	5.27297i	0.563168	+	0.325145i	−0.191248	+	0.981542i	$0.561253\pi$
$264$		0			0
$265$	2.37894	+	9.24824i	0.146137	+	0.568115i
$266$	−2.53809	−	4.39611i	−0.155621	−	0.269543i
$267$		0			0
$268$		−	4.16158i		−	0.254209i
$269$	8.87299	+	15.3685i	0.540996	+	0.937032i	0.998847	+	0.0480034i	$0.0152858\pi$
$269$	8.87299	+	15.3685i	0.540996	+	0.937032i	−0.457851	+	0.889029i	$0.651381\pi$
$270$		0			0
$271$	−9.64364	+	16.7033i	−0.585809	+	1.01465i	0.408965	+	0.912550i	$0.365890\pi$
$271$	−9.64364	+	16.7033i	−0.585809	+	1.01465i	−0.994774	+	0.102101i	$0.967443\pi$
$272$			1.97832i			0.119953i
$273$		0			0
$274$	−22.8622			−1.38116
$275$	0.0221013	−	1.10197i	0.00133276	−	0.0664516i
$276$		0			0
$277$	10.0045	−	5.77610i	0.601112	−	0.347052i	−0.168367	−	0.985724i	$-0.553849\pi$
$277$	10.0045	−	5.77610i	0.601112	−	0.347052i	0.769479	+	0.638672i	$0.220516\pi$
$278$		−	5.28838i		−	0.317176i
$279$		0			0
$280$	−1.50095	−	1.53136i	−0.0896991	−	0.0915161i
$281$	−17.4749			−1.04246			−0.521232	−	0.853415i	$-0.674528\pi$
$281$	−17.4749			−1.04246			−0.521232	+	0.853415i	$0.674528\pi$
$282$		0			0
$283$	12.4472	+	7.18642i	0.739912	+	0.427188i	0.822037	−	0.569434i	$-0.192838\pi$
$283$	12.4472	+	7.18642i	0.739912	+	0.427188i	−0.0821255	+	0.996622i	$0.526171\pi$
$284$	11.5239	−	19.9599i	0.683815	−	1.18440i
$285$		0			0
$286$	1.09914	+	1.30505i	0.0649937	+	0.0771692i
$287$		−	8.63247i		−	0.509558i
$288$		0			0
$289$	−8.16382	+	14.1402i	−0.480225	+	0.831774i
$290$	−10.4106	+	10.2039i	−0.611333	+	0.599195i
$291$		0			0
$292$	17.7614	−	10.2545i	1.03941	−	0.600101i
$293$	5.19452	−	2.99906i	0.303467	−	0.175207i	−0.340532	−	0.940233i	$-0.610607\pi$
$293$	5.19452	−	2.99906i	0.303467	−	0.175207i	0.643999	+	0.765026i	$0.277274\pi$
$294$		0			0
$295$	−3.40120	−	3.47010i	−0.198026	−	0.202037i
$296$	3.35434	−	5.80989i	0.194967	−	0.337693i
$297$		0			0
$298$		−	35.0048i		−	2.02777i
$299$	9.80534	−	27.0942i	0.567058	−	1.56690i
$300$		0			0
$301$	1.95809	−	3.39150i	0.112862	−	0.195483i
$302$	−39.2760	−	22.6760i	−2.26008	−	1.30486i
$303$		0			0
$304$	7.77166			0.445735
$305$	−18.9019	−	19.2848i	−1.08232	−	1.10425i
$306$		0			0
$307$			13.2035i			0.753566i	0.926301	+	0.376783i	$0.122970\pi$
$307$			13.2035i			0.753566i	−0.926301	+	0.376783i	$0.877030\pi$
$308$	0.365557	−	0.211054i	0.0208295	−	0.0120259i
$309$		0			0
$310$	24.3994	+	6.80072i	1.38579	+	0.386255i
$311$	19.1493			1.08586			0.542929	−	0.839779i	$-0.317315\pi$
$311$	19.1493			1.08586			0.542929	+	0.839779i	$0.317315\pi$
$312$		0			0
$313$			22.9820i			1.29902i	0.760353	+	0.649510i	$0.225026\pi$
$313$			22.9820i			1.29902i	−0.760353	+	0.649510i	$0.774974\pi$
$314$	−18.6342	+	32.2753i	−1.05159	+	1.82140i
$315$		0			0
$316$	18.1521	+	31.4403i	1.02113	+	1.76866i
$317$		−	4.61063i		−	0.258959i	−0.991582	−	0.129479i	$-0.958669\pi$
$317$		−	4.61063i		−	0.258959i	0.991582	−	0.129479i	$-0.0413306\pi$
$318$		0			0
$319$	−0.334714	−	0.579742i	−0.0187404	−	0.0324593i
$320$	25.7751	−	6.63016i	1.44087	−	0.370637i
$321$		0			0
$322$	−10.9064	−	6.29682i	−0.607791	−	0.350908i
$323$	−2.28742	−	1.32064i	−0.127275	−	0.0734824i
$324$		0			0
$325$	−11.3344	−	14.0189i	−0.628722	−	0.777630i
$326$	−16.8728			−0.934498
$327$		0			0
$328$	−13.3039	−	7.68100i	−0.734584	−	0.424112i
$329$	−2.13144	−	3.69176i	−0.117510	−	0.203533i
$330$		0			0
$331$	3.79252	+	6.56884i	0.208456	+	0.361056i	0.951228	−	0.308488i	$-0.0998229\pi$
$331$	3.79252	+	6.56884i	0.208456	+	0.361056i	−0.742772	+	0.669544i	$0.766490\pi$
$332$	9.89911	−	5.71525i	0.543284	−	0.313665i
$333$		0			0
$334$	−2.10126	−	3.63949i	−0.114976	−	0.199144i
$335$	−3.43640	−	0.957810i	−0.187750	−	0.0523308i
$336$		0			0
$337$		−	10.1761i		−	0.554329i	−0.960822	−	0.277165i	$-0.910605\pi$
$337$		−	10.1761i		−	0.554329i	0.960822	−	0.277165i	$-0.0893947\pi$
$338$	27.5013	+	4.74548i	1.49587	+	0.258120i
$339$		0			0
$340$	−4.60714	−	1.28412i	−0.249857	−	0.0696414i
$341$	−0.581592	+	1.00735i	−0.0314950	+	0.0545509i
$342$		0			0
$343$			9.88150i			0.533551i
$344$	−3.48453	−	6.03539i	−0.187873	−	0.325406i
$345$		0			0
$346$	44.5822			2.39675
$347$	11.3421	−	6.54836i	0.608875	−	0.351534i	−0.163650	−	0.986518i	$-0.552327\pi$
$347$	11.3421	−	6.54836i	0.608875	−	0.351534i	0.772525	+	0.634984i	$0.218993\pi$
$348$		0			0
$349$	3.08193	−	5.33806i	0.164972	−	0.285740i	−0.771673	−	0.636019i	$-0.780580\pi$
$349$	3.08193	−	5.33806i	0.164972	−	0.285740i	0.936645	+	0.350279i	$0.113913\pi$
$350$	−6.90137	+	3.80207i	−0.368894	+	0.203229i
$351$		0			0
$352$			1.71767i			0.0915524i
$353$	3.04903	+	1.76036i	0.162284	+	0.0936944i	0.578942	−	0.815369i	$-0.303466\pi$
$353$	3.04903	+	1.76036i	0.162284	+	0.0936944i	−0.416659	+	0.909063i	$0.636799\pi$
$354$		0			0
$355$	−13.8295	−	14.1096i	−0.733992	−	0.748860i
$356$	−11.2867			−0.598196
$357$		0			0
$358$	47.9147	−	27.6636i	2.53237	−	1.46206i
$359$	10.0828			0.532152			0.266076	−	0.963952i	$-0.414273\pi$
$359$	10.0828			0.532152			0.266076	+	0.963952i	$0.414273\pi$
$360$		0			0
$361$	4.31198	−	7.46857i	0.226946	−	0.393083i
$362$	22.0772	+	12.7463i	1.16035	+	0.669929i
$363$		0			0
$364$	2.34946	−	6.49204i	0.123145	−	0.340275i
$365$	−4.37973	−	17.0265i	−0.229246	−	0.891206i
$366$		0			0
$367$	−5.16742	−	2.98341i	−0.269737	−	0.155733i	0.359031	−	0.933326i	$-0.383107\pi$
$367$	−5.16742	−	2.98341i	−0.269737	−	0.155733i	−0.628768	+	0.777593i	$0.716441\pi$
$368$	16.6978	−	9.64045i	0.870431	−	0.502543i
$369$		0			0
$370$	−17.2558	−	17.6054i	−0.897087	−	0.915260i
$371$	1.56747	+	2.71493i	0.0813788	+	0.140952i
$372$		0			0
$373$	−23.2753	+	13.4380i	−1.20515	+	0.695794i	−0.961696	−	0.274118i	$-0.911614\pi$
$373$	−23.2753	+	13.4380i	−1.20515	+	0.695794i	−0.243455	+	0.969912i	$0.578281\pi$
$374$	0.194016	−	0.336046i	0.0100323	−	0.0173765i
$375$		0			0
$376$	−7.58605			−0.391221
$377$	−10.2958	−	3.72605i	−0.530262	−	0.191901i
$378$		0			0
$379$	−9.26453	+	16.0466i	−0.475887	+	0.824261i	−0.999618	−	0.0276228i	$-0.991206\pi$
$379$	−9.26453	+	16.0466i	−0.475887	+	0.824261i	0.523731	+	0.851884i	$0.324540\pi$
$380$	−5.04457	+	18.0987i	−0.258781	+	0.928445i
$381$		0			0
$382$		−	47.0615i		−	2.40788i
$383$	−22.9850	+	13.2704i	−1.17448	+	0.678085i	−0.954731	−	0.297472i	$-0.903857\pi$
$383$	−22.9850	+	13.2704i	−1.17448	+	0.678085i	−0.219747	+	0.975557i	$0.570523\pi$
$384$		0			0
$385$	−0.0901417	−	0.350431i	−0.00459405	−	0.0178596i
$386$	22.4301	+	38.8501i	1.14166	+	1.97742i
$387$		0			0
$388$	−19.5204	−	11.2701i	−0.990996	−	0.572152i
$389$	15.8937			0.805841			0.402920	−	0.915235i	$-0.367995\pi$
$389$	15.8937			0.805841			0.402920	+	0.915235i	$0.367995\pi$
$390$		0			0
$391$	−6.55282			−0.331390
$392$	7.30960	+	4.22020i	0.369190	+	0.213152i
$393$		0			0
$394$	4.07294	+	7.05454i	0.205192	+	0.355403i
$395$	30.1394	−	7.75279i	1.51648	−	0.390085i
$396$		0			0
$397$	−27.5216	+	15.8896i	−1.38127	+	0.797477i	−0.992310	−	0.123777i	$-0.960499\pi$
$397$	−27.5216	+	15.8896i	−1.38127	+	0.797477i	−0.388961	+	0.921254i	$0.627166\pi$
$398$			0.831504i			0.0416795i
$399$		0			0
$400$	0.241895	−	12.0609i	0.0120947	−	0.603046i
$401$	−4.31681	+	7.47694i	−0.215571	+	0.373380i	−0.953449	−	0.301554i	$-0.902495\pi$
$401$	−4.31681	+	7.47694i	−0.215571	+	0.373380i	0.737878	+	0.674934i	$0.235828\pi$
$402$		0			0
$403$	3.33800	+	18.7302i	0.166277	+	0.933017i
$404$	14.9305			0.742818
$405$		0			0
$406$	−2.39280	+	4.14446i	−0.118753	+	0.205686i
$407$	0.980399	−	0.566034i	0.0485966	−	0.0280572i
$408$		0			0
$409$	−6.57277	−	11.3844i	−0.325003	−	0.562921i	0.656510	−	0.754317i	$-0.272032\pi$
$409$	−6.57277	−	11.3844i	−0.325003	−	0.562921i	−0.981513	+	0.191396i	$0.938699\pi$
$410$	−40.3140	+	39.5135i	−1.99096	+	1.95143i
$411$		0			0
$412$	−17.7357	+	10.2397i	−0.873778	+	0.504476i
$413$	−1.38144	−	0.797577i	−0.0679764	−	0.0392462i
$414$		0			0
$415$	−2.44100	−	9.48951i	−0.119824	−	0.465822i
$416$	18.0983	+	21.4887i	0.887340	+	1.05357i
$417$		0			0
$418$	−1.32013	−	0.762176i	−0.0645695	−	0.0372792i
$419$	−16.7664	+	29.0403i	−0.819093	+	1.41871i	0.0872581	+	0.996186i	$0.472190\pi$
$419$	−16.7664	+	29.0403i	−0.819093	+	1.41871i	−0.906351	+	0.422525i	$0.861144\pi$
$420$		0			0
$421$	12.4700			0.607749			0.303874	−	0.952712i	$-0.401720\pi$
$421$	12.4700			0.607749			0.303874	+	0.952712i	$0.401720\pi$
$422$	16.8170	−	9.70928i	0.818637	−	0.472640i
$423$		0			0
$424$	5.57881			0.270931
$425$	−2.12071	+	3.50876i	−0.102870	+	0.170200i
$426$		0			0
$427$	−7.67727	−	4.43247i	−0.371529	−	0.214502i
$428$			30.4843i			1.47351i
$429$		0			0
$430$	−24.8012	+	6.37965i	−1.19602	+	0.307654i
$431$	8.18051	−	14.1691i	0.394041	−	0.682500i	−0.598937	−	0.800796i	$-0.704410\pi$
$431$	8.18051	−	14.1691i	0.394041	−	0.682500i	0.992978	+	0.118297i	$0.0377434\pi$
$432$		0			0
$433$	10.4479	−	6.03208i	0.502093	−	0.289883i	−0.227485	−	0.973782i	$-0.573050\pi$
$433$	10.4479	−	6.03208i	0.502093	−	0.289883i	0.729577	+	0.683898i	$0.239717\pi$
$434$	8.31538			0.399151
$435$		0			0
$436$	−17.2809	−	29.9314i	−0.827606	−	1.43346i
$437$			25.7422i			1.23142i
$438$		0			0
$439$	−9.21872	+	15.9673i	−0.439986	+	0.762077i	−0.997688	−	0.0679637i	$-0.978350\pi$
$439$	−9.21872	+	15.9673i	−0.439986	+	0.762077i	0.557702	+	0.830041i	$0.311683\pi$
$440$	−0.620271	−	0.172885i	−0.0295703	−	0.00824197i
$441$		0			0
$442$	−1.11354	−	6.24829i	−0.0529656	−	0.297201i
$443$			7.40466i			0.351806i	0.984407	+	0.175903i	$0.0562845\pi$
$443$			7.40466i			0.351806i	−0.984407	+	0.175903i	$0.943715\pi$
$444$		0			0
$445$	−2.59770	+	9.31995i	−0.123143	+	0.441808i
$446$	15.4116	+	26.6936i	0.729759	+	1.26398i
$447$		0			0
$448$	7.56659	−	4.36857i	0.357488	−	0.206396i
$449$	−7.74065	−	13.4072i	−0.365304	−	0.632725i	0.623521	−	0.781807i	$-0.285702\pi$
$449$	−7.74065	−	13.4072i	−0.365304	−	0.632725i	−0.988825	+	0.149082i	$0.952368\pi$
$450$		0			0
$451$	−1.29614	−	2.24498i	−0.0610329	−	0.105712i
$452$	−33.9225	−	19.5852i	−1.59558	−	0.921210i
$453$		0			0
$454$	53.0719			2.49079
$455$	−4.82001	−	3.43423i	−0.225966	−	0.160999i
$456$		0			0
$457$	−19.4185	−	11.2113i	−0.908358	−	0.524441i	−0.0284555	−	0.999595i	$-0.509059\pi$
$457$	−19.4185	−	11.2113i	−0.908358	−	0.524441i	−0.879902	+	0.475154i	$0.842392\pi$
$458$	−2.23136	−	1.28828i	−0.104265	−	0.0601972i
$459$		0			0
$460$	11.6123	+	45.1435i	0.541427	+	2.10483i
$461$	−4.52049	−	7.82973i	−0.210540	−	0.364667i	0.741343	−	0.671126i	$-0.234189\pi$
$461$	−4.52049	−	7.82973i	−0.210540	−	0.364667i	−0.951884	+	0.306459i	$0.900856\pi$
$462$		0			0
$463$			38.6693i			1.79711i	0.438857	+	0.898557i	$0.355383\pi$
$463$			38.6693i			1.79711i	−0.438857	+	0.898557i	$0.644617\pi$
$464$	−3.66339	−	6.34517i	−0.170068	−	0.294567i
$465$		0			0
$466$	−22.0156	+	38.1322i	−1.01986	+	1.76644i
$467$		−	2.14046i		−	0.0990485i	−0.998773	−	0.0495242i	$-0.984229\pi$
$467$		−	2.14046i		−	0.0990485i	0.998773	−	0.0495242i	$-0.0157705\pi$
$468$		0			0
$469$	−1.17113			−0.0540779
$470$	−7.48440	+	26.8523i	−0.345229	+	1.23860i
$471$		0			0
$472$	−2.45836	+	1.41934i	−0.113155	+	0.0653303i
$473$		−	1.17600i		−	0.0540728i
$474$		0			0
$475$	13.7839	+	8.33103i	0.632447	+	0.382254i
$476$	−1.57012			−0.0719665
$477$		0			0
$478$	53.9850	+	31.1683i	2.46922	+	1.42560i
$479$	1.18648	−	2.05505i	0.0542118	−	0.0938975i	−0.837646	−	0.546213i	$-0.816069\pi$
$479$	1.18648	−	2.05505i	0.0542118	−	0.0938975i	0.891858	+	0.452316i	$0.149402\pi$
$480$		0			0
$481$	6.30110	−	17.4112i	0.287306	−	0.793883i
$482$		−	31.0026i		−	1.41213i
$483$		0			0
$484$	−14.2835	+	24.7397i	−0.649249	+	1.12453i
$485$	−13.7989	+	13.5249i	−0.626576	+	0.614135i
$486$		0			0
$487$	−0.772529	+	0.446020i	−0.0350066	+	0.0202111i	−0.517401	−	0.855743i	$-0.673100\pi$
$487$	−0.772529	+	0.446020i	−0.0350066	+	0.0202111i	0.482395	+	0.875954i	$0.339767\pi$
$488$	−13.6622	+	7.88786i	−0.618457	+	0.357066i
$489$		0			0
$490$	22.1498	−	21.7100i	1.00063	−	0.980760i
$491$	11.1110	−	19.2448i	0.501432	−	0.868506i	−0.498566	−	0.866852i	$-0.666140\pi$
$491$	11.1110	−	19.2448i	0.501432	−	0.868506i	0.999999	−	0.00165479i	$-0.000526736\pi$
$492$		0			0
$493$			2.49008i			0.112148i
$494$	−24.5459	+	4.37444i	−1.10437	+	0.196815i
$495$		0			0
$496$	−6.36543	+	11.0252i	−0.285816	+	0.495048i
$497$	−5.61702	−	3.24299i	−0.251958	−	0.145468i
$498$		0			0
$499$	8.17294			0.365871			0.182936	−	0.983125i	$-0.441440\pi$
$499$	8.17294			0.365871			0.182936	+	0.983125i	$0.441440\pi$
$500$	27.9306	+	8.39205i	1.24910	+	0.375304i
$501$		0			0
$502$			11.0702i			0.494088i
$503$	−7.52730	+	4.34589i	−0.335626	+	0.193774i	−0.658336	−	0.752724i	$-0.728739\pi$
$503$	−7.52730	+	4.34589i	−0.335626	+	0.193774i	0.322710	+	0.946498i	$0.395406\pi$
$504$		0			0
$505$	3.43632	−	12.3287i	0.152914	−	0.548620i
$506$	−3.78180			−0.168122
$507$		0			0
$508$			46.6348i			2.06908i
$509$	2.74976	−	4.76273i	0.121881	−	0.211104i	−0.798628	−	0.601824i	$-0.794441\pi$
$509$	2.74976	−	4.76273i	0.121881	−	0.211104i	0.920509	+	0.390720i	$0.127774\pi$
$510$		0			0
$511$	−2.88578	−	4.99832i	−0.127659	−	0.221113i
$512$			25.1032i			1.10941i
$513$		0			0
$514$	−10.0833	−	17.4648i	−0.444755	−	0.770337i
$515$	4.37341	+	17.0019i	0.192716	+	0.749193i
$516$		0			0
$517$	−1.10862	−	0.640059i	−0.0487569	−	0.0281498i
$518$	−7.00868	−	4.04646i	−0.307944	−	0.177791i
$519$		0			0
$520$	−9.58140	+	4.37263i	−0.420172	+	0.191753i
$521$	1.98624			0.0870189			0.0435095	−	0.999053i	$-0.486146\pi$
$521$	1.98624			0.0870189			0.0435095	+	0.999053i	$0.486146\pi$
$522$		0			0
$523$	−17.6311	−	10.1793i	−0.770954	−	0.445111i	0.0622607	−	0.998060i	$-0.480169\pi$
$523$	−17.6311	−	10.1793i	−0.770954	−	0.445111i	−0.833215	+	0.552949i	$0.813502\pi$
$524$	−10.6104	−	18.3778i	−0.463519	−	0.802839i
$525$		0			0
$526$	−11.3197	−	19.6064i	−0.493564	−	0.854878i
$527$	3.74705	−	2.16336i	0.163224	−	0.0942374i
$528$		0			0
$529$	20.4322	+	35.3896i	0.888357	+	1.53868i
$530$	5.50405	−	19.7472i	0.239081	−	0.857765i
$531$		0			0
$532$			6.16809i			0.267421i
$533$	−39.8694	−	14.4287i	−1.72694	−	0.624976i
$534$		0			0
$535$	25.1722	+	7.01612i	1.08829	+	0.303333i
$536$	−1.04205	+	1.80489i	−0.0450097	+	0.0779592i
$537$		0			0
$538$		−	38.0961i		−	1.64244i
$539$	0.712143	+	1.23347i	0.0306742	+	0.0531292i
$540$		0			0
$541$	−0.604941			−0.0260084			−0.0130042	−	0.999915i	$-0.504139\pi$
$541$	−0.604941			−0.0260084			−0.0130042	+	0.999915i	$0.504139\pi$
$542$	35.8577	−	20.7024i	1.54022	−	0.889246i
$543$		0			0
$544$	3.19463	−	5.53326i	0.136969	−	0.237237i
$545$	−28.6930	+	7.38072i	−1.22907	+	0.316155i
$546$		0			0
$547$		−	21.2353i		−	0.907958i	−0.891012	−	0.453979i	$-0.850004\pi$
$547$		−	21.2353i		−	0.907958i	0.891012	−	0.453979i	$-0.149996\pi$
$548$	24.0582	+	13.8900i	1.02771	+	0.593351i
$549$		0			0
$550$	−1.22392	+	2.02500i	−0.0521881	+	0.0863462i
$551$	9.78207			0.416730
$552$		0			0
$553$	8.84779	−	5.10827i	0.376246	−	0.217226i
$554$	−24.7996			−1.05364
$555$		0			0
$556$	−3.21297	+	5.56502i	−0.136260	+	0.236009i
$557$	37.4735	+	21.6354i	1.58780	+	0.916720i	0.993668	+	0.112355i	$0.0358395\pi$
$557$	37.4735	+	21.6354i	1.58780	+	0.916720i	0.594137	+	0.804364i	$0.297494\pi$
$558$		0			0
$559$	−12.3910	−	14.7122i	−0.524082	−	0.622260i
$560$	−0.986586	−	3.83541i	−0.0416909	−	0.162075i
$561$		0			0
$562$	32.4882	+	18.7571i	1.37043	+	0.791220i
$563$	19.8331	−	11.4507i	0.835866	−	0.482587i	−0.0199909	−	0.999800i	$-0.506364\pi$
$563$	19.8331	−	11.4507i	0.835866	−	0.482587i	0.855857	+	0.517213i	$0.173030\pi$
$564$		0			0
$565$	−23.9798	+	23.5036i	−1.00884	+	0.988806i
$566$	−15.4274	−	26.7211i	−0.648463	−	1.12317i
$567$		0			0
$568$	−9.99582	+	5.77109i	−0.419415	+	0.242150i
$569$	18.6978	−	32.3855i	0.783852	−	1.35767i	−0.145831	−	0.989310i	$-0.546586\pi$
$569$	18.6978	−	32.3855i	0.783852	−	1.35767i	0.929683	−	0.368362i	$-0.120081\pi$
$570$		0			0
$571$	−14.3597			−0.600935			−0.300467	−	0.953792i	$-0.597143\pi$
$571$	−14.3597			−0.600935			−0.300467	+	0.953792i	$0.597143\pi$
$572$	−0.363755	−	2.04110i	−0.0152093	−	0.0853428i
$573$		0			0
$574$	−9.26586	+	16.0489i	−0.386749	+	0.669870i
$575$	39.9496	+	0.801232i	1.66601	+	0.0334137i
$576$		0			0
$577$			16.7453i			0.697117i	0.937287	+	0.348558i	$0.113329\pi$
$577$			16.7453i			0.697117i	−0.937287	+	0.348558i	$0.886671\pi$
$578$	30.3553	−	17.5257i	1.26262	−	0.728971i
$579$		0			0
$580$	17.1546	−	4.41270i	0.712307	−	0.183227i
$581$	−1.60836	−	2.78576i	−0.0667260	−	0.115573i
$582$		0			0
$583$	0.815280	+	0.470702i	0.0337654	+	0.0194945i
$584$	−10.2708			−0.425011
$585$		0			0
$586$	−12.8764			−0.531921
$587$	−2.52788	−	1.45947i	−0.104337	−	0.0602388i	0.446924	−	0.894572i	$-0.352520\pi$
$587$	−2.52788	−	1.45947i	−0.104337	−	0.0602388i	−0.551260	+	0.834333i	$0.685853\pi$
$588$		0			0
$589$	−8.49857	−	14.7199i	−0.350177	−	0.606525i
$590$	2.59859	+	10.1022i	0.106982	+	0.415899i
$591$		0			0
$592$	10.7303	−	6.19514i	0.441013	−	0.254619i
$593$			37.4573i			1.53819i	0.639137	+	0.769093i	$0.279292\pi$
$593$			37.4573i			1.53819i	−0.639137	+	0.769093i	$0.720708\pi$
$594$		0			0
$595$	−0.361372	+	1.29652i	−0.0148148	+	0.0531520i
$596$	−21.2672	+	36.8359i	−0.871140	+	1.50886i
$597$		0			0
$598$	−47.3116	+	39.8469i	−1.93472	+	1.62946i
$599$	−25.0853			−1.02496			−0.512479	−	0.858700i	$-0.671273\pi$
$599$	−25.0853			−1.02496			−0.512479	+	0.858700i	$0.671273\pi$
$600$		0			0
$601$	0.697943	−	1.20887i	0.0284697	−	0.0493109i	−0.851440	−	0.524453i	$-0.824270\pi$
$601$	0.697943	−	1.20887i	0.0284697	−	0.0493109i	0.879909	+	0.475142i	$0.157603\pi$
$602$	−7.28070	+	4.20351i	−0.296739	+	0.171322i
$603$		0			0
$604$	27.5537	+	47.7244i	1.12114	+	1.94188i
$605$	17.1412	+	17.4884i	0.696889	+	0.711006i
$606$		0			0
$607$	−0.517866	+	0.298990i	−0.0210195	+	0.0121356i	−0.510473	−	0.859894i	$-0.670530\pi$
$607$	−0.517866	+	0.298990i	−0.0210195	+	0.0121356i	0.489453	+	0.872029i	$0.337196\pi$
$608$	−21.7369	−	12.5498i	−0.881549	−	0.508963i
$609$		0			0
$610$	14.4415	+	56.1420i	0.584718	+	2.27312i
$611$	−20.6131	+	3.67356i	−0.833918	+	0.148616i
$612$		0			0
$613$	−23.9930	−	13.8524i	−0.969070	−	0.559493i	−0.0701171	−	0.997539i	$-0.522337\pi$
$613$	−23.9930	−	13.8524i	−0.969070	−	0.559493i	−0.898952	+	0.438046i	$0.855671\pi$
$614$	14.1723	−	24.5472i	0.571949	−	0.990644i
$615$		0			0
$616$	−0.211390			−0.00851714
$617$	9.95360	−	5.74671i	0.400717	−	0.231354i	−0.286076	−	0.958207i	$-0.592351\pi$
$617$	9.95360	−	5.74671i	0.400717	−	0.231354i	0.686793	+	0.726853i	$0.259018\pi$
$618$		0			0
$619$	13.7729			0.553581			0.276791	−	0.960930i	$-0.410729\pi$
$619$	13.7729			0.553581			0.276791	+	0.960930i	$0.410729\pi$
$620$	−21.5439	−	21.9804i	−0.865226	−	0.882753i
$621$		0			0
$622$	−35.6012	−	20.5544i	−1.42748	−	0.824154i
$623$			3.17626i			0.127254i
$624$		0			0
$625$	13.3581	−	21.1320i	0.534322	−	0.845281i
$626$	24.6683	−	42.7267i	0.985943	−	1.70770i
$627$		0			0
$628$	39.2179	−	22.6424i	1.56496	−	0.903532i
$629$	−4.21097			−0.167902
$630$		0			0
$631$	−15.4209	−	26.7097i	−0.613895	−	1.06330i	−0.990577	−	0.136955i	$-0.956268\pi$
$631$	−15.4209	−	26.7097i	−0.613895	−	1.06330i	0.376682	−	0.926343i	$-0.377065\pi$
$632$		−	18.1810i		−	0.723200i
$633$		0			0
$634$	−4.94893	+	8.57179i	−0.196547	+	0.340429i
$635$	38.5083	+	10.7332i	1.52816	+	0.425935i
$636$		0			0
$637$	21.9056	+	7.92760i	0.867930	+	0.314103i
$638$			1.43709i			0.0568950i
$639$		0			0
$640$	−21.4684	−	5.98379i	−0.848615	−	0.236530i
$641$	−7.56498	−	13.1029i	−0.298799	−	0.517535i	0.677063	−	0.735925i	$-0.263253\pi$
$641$	−7.56498	−	13.1029i	−0.298799	−	0.517535i	−0.975861	+	0.218391i	$0.929919\pi$
$642$		0			0
$643$	1.55601	−	0.898362i	0.0613630	−	0.0354279i	−0.469005	−	0.883196i	$-0.655387\pi$
$643$	1.55601	−	0.898362i	0.0613630	−	0.0354279i	0.530368	+	0.847768i	$0.322054\pi$
$644$	7.65129	+	13.2524i	0.301503	+	0.522219i
$645$		0			0
$646$	2.83508	+	4.91050i	0.111545	+	0.193201i
$647$	−34.8534	−	20.1226i	−1.37023	−	0.791103i	−0.379273	−	0.925285i	$-0.623826\pi$
$647$	−34.8534	−	20.1226i	−1.37023	−	0.791103i	−0.990957	+	0.134182i	$0.957159\pi$
$648$		0			0
$649$	−0.479016			−0.0188030
$650$	6.02474	+	38.2292i	0.236310	+	1.49947i
$651$		0			0
$652$	17.7554	+	10.2511i	0.695356	+	0.401464i
$653$	8.55859	+	4.94130i	0.334923	+	0.193368i	0.658025	−	0.752996i	$-0.271392\pi$
$653$	8.55859	+	4.94130i	0.334923	+	0.193368i	−0.323101	+	0.946364i	$0.604726\pi$
$654$		0			0
$655$	−17.6174	+	4.53174i	−0.688369	+	0.177070i
$656$	−14.1860	−	24.5710i	−0.553872	−	0.959335i
$657$		0			0
$658$			9.15131i			0.356755i
$659$	−13.1170	−	22.7193i	−0.510965	−	0.885017i	−0.999919	−	0.0127075i	$-0.995955\pi$
$659$	−13.1170	−	22.7193i	−0.510965	−	0.885017i	0.488955	−	0.872309i	$-0.337378\pi$
$660$		0			0
$661$	19.9501	−	34.5545i	0.775968	−	1.34402i	−0.158281	−	0.987394i	$-0.550595\pi$
$661$	19.9501	−	34.5545i	0.775968	−	1.34402i	0.934249	−	0.356622i	$-0.116072\pi$
$662$		−	16.2832i		−	0.632863i
$663$		0			0
$664$	−5.72434			−0.222148
$665$	5.09326	+	1.41962i	0.197508	+	0.0550505i
$666$		0			0
$667$	21.0172	−	12.1343i	0.813790	−	0.469842i
$668$			5.10650i			0.197576i
$669$		0			0
$670$	5.36064	+	5.46924i	0.207100	+	0.211295i
$671$	−2.66210			−0.102769
$672$		0			0
$673$	−12.1025	−	6.98740i	−0.466518	−	0.269344i	0.248263	−	0.968693i	$-0.420140\pi$
$673$	−12.1025	−	6.98740i	−0.466518	−	0.269344i	−0.714781	+	0.699348i	$0.753474\pi$
$674$	−10.9228	+	18.9188i	−0.420730	+	0.728726i
$675$		0			0
$676$	−26.0567	−	21.7022i	−1.00218	−	0.834699i
$677$		−	37.3636i		−	1.43600i	−0.696043	−	0.718000i	$-0.745058\pi$
$677$		−	37.3636i		−	1.43600i	0.696043	−	0.718000i	$-0.254942\pi$
$678$		0			0
$679$	−3.17157	+	5.49332i	−0.121714	+	0.210814i
$680$	1.67658	+	1.71054i	0.0642939	+	0.0655963i
$681$		0			0
$682$	2.16252	−	1.24853i	0.0828071	−	0.0478087i
$683$	−20.2586	+	11.6963i	−0.775176	+	0.447548i	−0.834718	−	0.550678i	$-0.814369\pi$
$683$	−20.2586	+	11.6963i	−0.775176	+	0.447548i	0.0595422	+	0.998226i	$0.481036\pi$
$684$		0			0
$685$	17.0067	−	16.6690i	0.649791	−	0.636890i
$686$	10.6065	−	18.3711i	0.404959	−	0.701410i
$687$		0			0
$688$		−	12.8712i		−	0.490709i
$689$	15.1590	−	2.70155i	0.577510	−	0.102921i
$690$		0			0
$691$	18.0692	−	31.2968i	0.687386	−	1.19059i	−0.285294	−	0.958440i	$-0.592091\pi$
$691$	18.0692	−	31.2968i	0.687386	−	1.19059i	0.972681	−	0.232148i	$-0.0745753\pi$
$692$	−46.9143	−	27.0860i	−1.78342	−	1.02966i
$693$		0			0
$694$	−28.1153			−1.06724
$695$	3.85579	+	3.93390i	0.146259	+	0.149221i
$696$		0			0
$697$			9.64256i			0.365238i
$698$	−11.4595	+	6.61612i	−0.433747	+	0.250424i
$699$		0			0
$700$	9.57233	+	0.191984i	0.361800	+	0.00725630i
$701$	−44.5949			−1.68433			−0.842163	−	0.539223i	$-0.818718\pi$
$701$	−44.5949			−1.68433			−0.842163	+	0.539223i	$0.818718\pi$
$702$		0			0
$703$			16.5424i			0.623909i
$704$	1.31186	−	2.27221i	0.0494425	−	0.0856370i
$705$		0			0
$706$	−3.77904	−	6.54549i	−0.142226	−	0.246343i
$707$		−	4.20166i		−	0.158020i
$708$		0			0
$709$	−14.9101	−	25.8251i	−0.559962	−	0.969882i	−0.997499	−	0.0706821i	$-0.977482\pi$
$709$	−14.9101	−	25.8251i	−0.559962	−	0.969882i	0.437537	−	0.899200i	$-0.355851\pi$
$710$	10.5660	+	41.0759i	0.396534	+	1.54155i
$711$		0			0
$712$	4.89508	+	2.82618i	0.183451	+	0.105915i
$713$	−36.5191	−	21.0843i	−1.36765	−	0.789614i
$714$		0			0
$715$	−1.76915	−	0.169403i	−0.0661623	−	0.00633530i
$716$	−67.2282			−2.51244
$717$		0			0
$718$	−18.7454	−	10.8226i	−0.699571	−	0.403897i
$719$	5.02234	+	8.69895i	0.187302	+	0.324416i	0.944350	−	0.328943i	$-0.106692\pi$
$719$	5.02234	+	8.69895i	0.187302	+	0.324416i	−0.757048	+	0.653359i	$0.773359\pi$
$720$		0			0
$721$	2.88162	+	4.99111i	0.107317	+	0.185879i
$722$	−16.0331	+	9.25673i	−0.596691	+	0.344500i
$723$		0			0
$724$	−15.4880	−	26.8260i	−0.575608	−	0.996982i
$725$	0.304470	−	15.1809i	0.0113077	−	0.563805i
$726$		0			0
$727$			24.9360i			0.924827i	0.886664	+	0.462413i	$0.153016\pi$
$727$			24.9360i			0.924827i	−0.886664	+	0.462413i	$0.846984\pi$
$728$	−2.64456	+	2.22731i	−0.0980138	+	0.0825495i
$729$		0			0
$730$	−10.1332	+	36.3556i	−0.375047	+	1.34558i
$731$	−2.18720	+	3.78835i	−0.0808966	+	0.140117i
$732$		0			0
$733$		−	28.9043i		−	1.06760i	−0.845609	−	0.533802i	$-0.820763\pi$
$733$		−	28.9043i		−	1.06760i	0.845609	−	0.533802i	$-0.179237\pi$
$734$	6.40463	+	11.0931i	0.236399	+	0.409455i
$735$		0			0
$736$	−62.2704			−2.29532
$737$	−0.304568	+	0.175842i	−0.0112189	+	0.00647724i
$738$		0			0
$739$	10.1747	−	17.6232i	0.374284	−	0.648278i	−0.615936	−	0.787796i	$-0.711222\pi$
$739$	10.1747	−	17.6232i	0.374284	−	0.648278i	0.990220	+	0.139518i	$0.0445553\pi$
$740$	7.46230	+	29.0101i	0.274320	+	1.06643i
$741$		0			0
$742$		−	6.72991i		−	0.247063i
$743$	23.6364	+	13.6465i	0.867135	+	0.500640i	0.866395	−	0.499359i	$-0.166431\pi$
$743$	23.6364	+	13.6465i	0.867135	+	0.500640i	0.000739676		1.00000i	$0.499765\pi$
$744$		0			0
$745$	25.5222	+	26.0392i	0.935062	+	0.954004i
$746$	57.6960			2.11240
$747$		0			0
$748$	−0.408331	+	0.235750i	−0.0149300	+	0.00861987i
$749$	8.57875			0.313461
$750$		0			0
$751$	3.59994	−	6.23528i	0.131364	−	0.227528i	−0.792839	−	0.609431i	$-0.791398\pi$
$751$	3.59994	−	6.23528i	0.131364	−	0.227528i	0.924202	+	0.381903i	$0.124731\pi$
$752$	−12.1336	−	7.00534i	−0.442467	−	0.255459i
$753$		0			0
$754$	15.1419	+	17.9785i	0.551435	+	0.654738i
$755$	45.7497	−	11.7682i	1.66500	−	0.428290i
$756$		0			0
$757$	17.3694	+	10.0282i	0.631303	+	0.364483i	0.781256	−	0.624210i	$-0.214579\pi$
$757$	17.3694	+	10.0282i	0.631303	+	0.364483i	−0.149954	+	0.988693i	$0.547912\pi$
$758$	34.4481	−	19.8886i	1.25121	−	0.722387i
$759$		0			0
$760$	6.71972	−	6.58630i	0.243750	−	0.238910i
$761$	13.6739	+	23.6839i	0.495678	+	0.858539i	0.999988	−	0.00498368i	$-0.00158636\pi$
$761$	13.6739	+	23.6839i	0.495678	+	0.858539i	−0.504310	+	0.863523i	$0.668253\pi$
$762$		0			0
$763$	−8.42316	+	4.86311i	−0.304939	+	0.176057i
$764$	−28.5923	+	49.5233i	−1.03443	+	1.79169i
$765$		0			0
$766$	56.9763			2.05864
$767$	−5.99265	+	5.04715i	−0.216382	+	0.182242i
$768$		0			0
$769$	15.7783	−	27.3289i	0.568982	−	0.985505i	−0.427685	−	0.903928i	$-0.640671\pi$
$769$	15.7783	−	27.3289i	0.568982	−	0.985505i	0.996667	−	0.0815776i	$-0.0259959\pi$
$770$	−0.208557	+	0.748255i	−0.00751588	+	0.0269652i
$771$		0			0
$772$		−	54.5099i		−	1.96185i
$773$	−21.1167	+	12.1917i	−0.759516	+	0.438506i	−0.829122	−	0.559068i	$-0.811159\pi$
$773$	−21.1167	+	12.1917i	−0.759516	+	0.438506i	0.0696062	+	0.997575i	$0.477826\pi$
$774$		0			0
$775$	−23.1086	+	12.7309i	−0.830085	+	0.457306i
$776$	5.64400	+	9.77570i	0.202608	+	0.350927i
$777$		0			0
$778$	−29.5485	−	17.0598i	−1.05936	−	0.611624i
$779$	37.8800			1.35719
$780$		0			0
$781$	−1.94770			−0.0696943
$782$	12.1826	+	7.03362i	0.435648	+	0.251522i
$783$		0			0
$784$	7.79429	+	13.5001i	0.278367	+	0.482146i
$785$	−9.67064	−	37.5951i	−0.345160	−	1.34183i
$786$		0			0
$787$	3.24278	−	1.87222i	0.115593	−	0.0667374i	−0.441089	−	0.897463i	$-0.645408\pi$
$787$	3.24278	−	1.87222i	0.115593	−	0.0667374i	0.556682	+	0.830726i	$0.312074\pi$
$788$		−	9.89809i		−	0.352605i
$789$		0			0
$790$	−64.3549	−	17.9373i	−2.28965	−	0.638182i
$791$	−5.51157	+	9.54632i	−0.195969	+	0.339428i
$792$		0			0
$793$	−33.3037	+	28.0491i	−1.18265	+	0.996054i
$794$	68.2220			2.42111
$795$		0			0
$796$	0.505182	−	0.875000i	0.0179057	−	0.0310136i
$797$	7.56168	−	4.36574i	0.267848	−	0.154642i	−0.360061	−	0.932929i	$-0.617244\pi$
$797$	7.56168	−	4.36574i	0.267848	−	0.154642i	0.627909	+	0.778286i	$0.283911\pi$
$798$		0			0
$799$	2.38084	+	4.12373i	0.0842280	+	0.145887i
$800$	−20.1528	+	33.3432i	−0.712509	+	1.17886i
$801$		0			0
$802$	16.0511	−	9.26710i	0.566784	−	0.327233i
$803$	−1.50097	−	0.866585i	−0.0529680	−	0.0305811i
$804$		0			0
$805$	12.7041	−	3.26788i	0.447760	−	0.115178i
$806$	13.8987	−	38.4049i	0.489560	−	1.35275i
$807$		0			0
$808$	−6.47536	−	3.73855i	−0.227802	−	0.131522i
$809$	−14.1043	+	24.4294i	−0.495881	+	0.858891i	−0.999989	−	0.00474964i	$-0.998488\pi$
$809$	−14.1043	+	24.4294i	−0.495881	+	0.858891i	0.504108	+	0.863641i	$0.331821\pi$
$810$		0			0
$811$	−38.4805			−1.35123			−0.675617	−	0.737253i	$-0.736123\pi$
$811$	−38.4805			−1.35123			−0.675617	+	0.737253i	$0.736123\pi$
$812$	5.03594	−	2.90750i	0.176727	−	0.102033i
$813$		0			0
$814$	−2.43026			−0.0851806
$815$	12.5513	−	12.3021i	0.439652	−	0.430923i
$816$		0			0
$817$	14.8822	+	8.59223i	0.520662	+	0.300604i
$818$			28.2201i			0.986694i
$819$		0			0
$820$	66.4293	−	17.0877i	2.31981	−	0.596728i
$821$	0.237151	−	0.410758i	0.00827663	−	0.0143355i	−0.861857	−	0.507151i	$-0.830699\pi$
$821$	0.237151	−	0.410758i	0.00827663	−	0.0143355i	0.870134	+	0.492815i	$0.164032\pi$
$822$		0			0
$823$	−6.19717	+	3.57794i	−0.216020	+	0.124719i	−0.604106	−	0.796904i	$-0.706470\pi$
$823$	−6.19717	+	3.57794i	−0.216020	+	0.124719i	0.388086	+	0.921623i	$0.373136\pi$
$824$	10.2560			0.357286
$825$		0			0
$826$	1.71219	+	2.96561i	0.0595749	+	0.103187i
$827$		−	25.1309i		−	0.873888i	−0.899489	−	0.436944i	$-0.856061\pi$
$827$		−	25.1309i		−	0.873888i	0.899489	−	0.436944i	$-0.143939\pi$
$828$		0			0
$829$	−10.7461	+	18.6129i	−0.373229	+	0.646452i	−0.990060	−	0.140644i	$-0.955083\pi$
$829$	−10.7461	+	18.6129i	−0.373229	+	0.646452i	0.616831	+	0.787096i	$0.288416\pi$
$830$	−5.64764	+	20.2624i	−0.196032	+	0.703318i
$831$		0			0
$832$	−7.52929	−	42.2484i	−0.261031	−	1.46470i
$833$		−	5.29794i		−	0.183563i
$834$		0			0
$835$	4.21665	+	1.17529i	0.145923	+	0.0406725i
$836$	0.926123	+	1.60409i	0.0320306	+	0.0554787i
$837$		0			0
$838$	62.3421	−	35.9932i	2.15357	−	1.24337i
$839$	2.71708	+	4.70613i	0.0938041	+	0.162474i	0.909109	−	0.416559i	$-0.136764\pi$
$839$	2.71708	+	4.70613i	0.0938041	+	0.162474i	−0.815305	+	0.579032i	$0.803431\pi$
$840$		0			0
$841$	9.88895	+	17.1282i	0.340998	+	0.590626i
$842$	−23.1834	−	13.3849i	−0.798951	−	0.461275i
$843$		0			0
$844$	−23.5956			−0.812193
$845$	−23.9175	+	16.5213i	−0.822787	+	0.568350i
$846$		0			0
$847$	6.96213	+	4.01959i	0.239221	+	0.138115i
$848$	8.92310	+	5.15175i	0.306420	+	0.176912i
$849$		0			0
$850$	7.70890	−	4.24695i	0.264413	−	0.145669i
$851$	20.5203	+	35.5421i	0.703425	+	1.21837i
$852$		0			0
$853$			15.2149i			0.520948i	0.965481	+	0.260474i	$0.0838788\pi$
$853$			15.2149i			0.520948i	−0.965481	+	0.260474i	$0.916121\pi$
$854$	9.51539	+	16.4811i	0.325610	+	0.563973i
$855$		0			0
$856$	7.63320	−	13.2211i	0.260897	−	0.451888i
$857$		−	15.2698i		−	0.521606i	−0.965392	−	0.260803i	$-0.916013\pi$
$857$		−	15.2698i		−	0.521606i	0.965392	−	0.260803i	$-0.0839872\pi$
$858$		0			0
$859$	44.0769			1.50388			0.751942	−	0.659229i	$-0.229117\pi$
$859$	44.0769			1.50388			0.751942	+	0.659229i	$0.229117\pi$
$860$	29.9746	+	8.35466i	1.02212	+	0.284892i
$861$		0			0
$862$	−30.4174	+	17.5615i	−1.03602	+	0.598146i
$863$		−	5.21492i		−	0.177518i	−0.996053	−	0.0887590i	$-0.971710\pi$
$863$		−	5.21492i		−	0.177518i	0.996053	−	0.0887590i	$-0.0282901\pi$
$864$		0			0
$865$	−33.1636	+	32.5052i	−1.12760	+	1.10521i
$866$	−25.8987			−0.880073
$867$		0			0
$868$	−8.75036	−	5.05202i	−0.297006	−	0.171477i
$869$	1.53399	−	2.65694i	0.0520369	−	0.0901306i
$870$		0			0
$871$	−1.95748	+	5.40892i	−0.0663268	+	0.183274i
$872$			17.3084i			0.586137i
$873$		0			0
$874$	27.6310	−	47.8582i	0.934631	−	1.61883i
$875$	2.36165	−	7.86010i	0.0798384	−	0.265720i
$876$		0			0
$877$	19.6246	−	11.3303i	0.662677	−	0.382596i	−0.130619	−	0.991433i	$-0.541697\pi$
$877$	19.6246	−	11.3303i	0.662677	−	0.382596i	0.793296	+	0.608836i	$0.208363\pi$
$878$	34.2777	−	19.7903i	1.15682	−	0.667889i
$879$		0			0
$880$	−0.832450	−	0.849313i	−0.0280619	−	0.0286303i
$881$	−17.4269	+	30.1842i	−0.587126	+	1.01693i	0.407481	+	0.913214i	$0.366407\pi$
$881$	−17.4269	+	30.1842i	−0.587126	+	1.01693i	−0.994607	+	0.103718i	$0.966926\pi$
$882$		0			0
$883$		−	43.7622i		−	1.47271i	−0.676593	−	0.736357i	$-0.736545\pi$
$883$		−	43.7622i		−	1.47271i	0.676593	−	0.736357i	$-0.263455\pi$
$884$	−2.62437	+	7.25168i	−0.0882672	+	0.243900i
$885$		0			0
$886$	7.94797	−	13.7663i	0.267017	−	0.462487i
$887$	16.0143	+	9.24583i	0.537706	+	0.310445i	0.744149	−	0.668014i	$-0.232855\pi$
$887$	16.0143	+	9.24583i	0.537706	+	0.310445i	−0.206443	+	0.978459i	$0.566189\pi$
$888$		0			0
$889$	13.1237			0.440156
$890$	14.8333	−	14.5388i	0.497212	−	0.487340i
$891$		0			0
$892$		−	37.4533i		−	1.25403i
$893$	16.1997	−	9.35292i	0.542103	−	0.312984i
$894$		0			0
$895$	−15.4729	+	55.5132i	−0.517202	+	1.85560i
$896$	−7.31650			−0.244427
$897$		0			0
$898$			33.2344i			1.10905i
$899$	−8.01207	+	13.8773i	−0.267218	+	0.462834i
$900$		0			0
$901$	−1.75088	−	3.03261i	−0.0583302	−	0.101031i
$902$			5.56497i			0.185293i
$903$		0			0
$904$	9.80817	+	16.9882i	0.326215	+	0.565021i
$905$	−25.7161	+	6.61497i	−0.854831	+	0.219889i
$906$		0			0
$907$	−38.0177	−	21.9495i	−1.26236	−	0.728822i	−0.288826	−	0.957381i	$-0.593265\pi$
$907$	−38.0177	−	21.9495i	−1.26236	−	0.728822i	−0.973530	+	0.228560i	$0.926598\pi$
$908$	−55.8481	−	32.2439i	−1.85338	−	1.07005i
$909$		0			0
$910$	5.27486	+	11.5584i	0.174860	+	0.383156i
$911$	21.1250			0.699902			0.349951	−	0.936768i	$-0.386198\pi$
$911$	21.1250			0.699902			0.349951	+	0.936768i	$0.386198\pi$
$912$		0			0
$913$	−0.836548	−	0.482981i	−0.0276857	−	0.0159844i
$914$	24.0677	+	41.6865i	0.796090	+	1.37887i
$915$		0			0
$916$	1.56539	+	2.71133i	0.0517219	+	0.0895850i
$917$	−5.17180	+	2.98594i	−0.170788	+	0.0986044i
$918$		0			0
$919$	9.06440	+	15.7000i	0.299007	+	0.517895i	0.975909	−	0.218178i	$-0.0700112\pi$
$919$	9.06440	+	15.7000i	0.299007	+	0.517895i	−0.676902	+	0.736073i	$0.736678\pi$
$920$	6.26756	−	22.4865i	0.206635	−	0.741359i
$921$		0			0
$922$			19.4087i			0.639192i
$923$	−24.3664	+	20.5219i	−0.802030	+	0.675488i
$924$		0			0
$925$	25.6724	+	0.514887i	0.844102	+	0.0169294i
$926$	41.5066	−	71.8915i	1.36399	−	2.36250i
$927$		0			0
$928$			23.6629i			0.776771i
$929$	6.16891	+	10.6849i	0.202395	+	0.350559i	0.949300	−	0.314372i	$-0.101794\pi$
$929$	6.16891	+	10.6849i	0.202395	+	0.350559i	−0.746904	+	0.664931i	$0.768461\pi$
$930$		0			0
$931$	−20.8125			−0.682102
$932$	46.3346	−	26.7513i	1.51774	−	0.876267i
$933$		0			0
$934$	−2.29751	+	3.97940i	−0.0751767	+	0.130210i
$935$	0.100689	+	0.391435i	0.00329289	+	0.0128013i
$936$		0			0
$937$		−	42.2147i		−	1.37909i	−0.724241	−	0.689547i	$-0.757810\pi$
$937$		−	42.2147i		−	1.37909i	0.724241	−	0.689547i	$-0.242190\pi$
$938$	2.17730	+	1.25706i	0.0710912	+	0.0410445i
$939$		0			0
$940$	24.1900	−	23.7097i	0.788992	−	0.773327i
$941$	3.55988			0.116049			0.0580245	−	0.998315i	$-0.481520\pi$
$941$	3.55988			0.116049			0.0580245	+	0.998315i	$0.481520\pi$
$942$		0			0
$943$	81.3868	−	46.9887i	2.65032	−	1.53016i
$944$	−5.24275			−0.170637
$945$		0			0
$946$	−1.26229	+	2.18635i	−0.0410406	+	0.0710845i
$947$	−1.55599	−	0.898350i	−0.0505628	−	0.0291924i	0.474506	−	0.880253i	$-0.342627\pi$
$947$	−1.55599	−	0.898350i	−0.0505628	−	0.0291924i	−0.525068	+	0.851060i	$0.675960\pi$
$948$		0			0
$949$	−27.9084	+	4.97368i	−0.905944	+	0.161453i
$950$	−16.6838	−	30.2838i	−0.541293	−	0.982535i
$951$		0			0
$952$	0.680965	+	0.393155i	0.0220702	+	0.0127422i
$953$	7.11822	−	4.10970i	0.230582	−	0.133126i	−0.380259	−	0.924880i	$-0.624165\pi$
$953$	7.11822	−	4.10970i	0.230582	−	0.133126i	0.610840	+	0.791754i	$0.290832\pi$
$954$		0			0
$955$	34.3129	+	35.0079i	1.11034	+	1.13283i
$956$	−37.8727	−	65.5974i	−1.22489	−	2.12157i
$957$		0			0
$958$	−4.41166	+	2.54708i	−0.142534	+	0.0822923i
$959$	3.90885	−	6.77033i	0.126223	−	0.218625i
$960$		0			0
$961$	−3.15676			−0.101831
$962$	−30.4033	+	25.6064i	−0.980243	+	0.825584i
$963$		0			0
$964$	−18.8357	+	32.6243i	−0.606656	+	1.05076i
$965$	−45.0111	−	12.5457i	−1.44896	−	0.403861i
$966$		0			0
$967$			54.7952i			1.76209i	0.473028	+	0.881047i	$0.343161\pi$
$967$			54.7952i			1.76209i	−0.473028	+	0.881047i	$0.656839\pi$
$968$	12.3895	−	7.15310i	0.398214	−	0.229909i
$969$		0			0
$970$	40.1713	−	10.3333i	1.28982	−	0.331783i
$971$	−2.13198	−	3.69271i	−0.0684186	−	0.118505i	0.829787	−	0.558081i	$-0.188462\pi$
$971$	−2.13198	−	3.69271i	−0.0684186	−	0.118505i	−0.898205	+	0.439576i	$0.855129\pi$
$972$		0			0
$973$	1.56608	+	0.904177i	0.0502062	+	0.0289866i
$974$	1.91498			0.0613600
$975$		0			0
$976$	−29.1362			−0.932626
$977$	15.0852	+	8.70945i	0.482618	+	0.278640i	0.721507	−	0.692407i	$-0.243450\pi$
$977$	15.0852	+	8.70945i	0.482618	+	0.278640i	−0.238889	+	0.971047i	$0.576783\pi$
$978$		0			0
$979$	0.476907	+	0.826027i	0.0152420	+	0.0263999i
$980$	−36.4985	+	9.38854i	−1.16590	+	0.299906i
$981$		0			0
$982$	−41.3137	+	23.8525i	−1.31837	+	0.761164i
$983$			36.2982i			1.15773i	0.815422	+	0.578867i	$0.196505\pi$
$983$			36.2982i			1.15773i	−0.815422	+	0.578867i	$0.803495\pi$
$984$		0			0
$985$	−8.17327	−	2.27810i	−0.260422	−	0.0725862i
$986$	2.67279	−	4.62940i	0.0851189	−	0.147430i
$987$		0			0
$988$	28.4876	+	10.3096i	0.906311	+	0.327993i
$989$	42.6334			1.35566
$990$		0			0
$991$	−3.94083	+	6.82572i	−0.125185	+	0.216826i	−0.921805	−	0.387654i	$-0.873286\pi$
$991$	−3.94083	+	6.82572i	−0.125185	+	0.216826i	0.796620	+	0.604480i	$0.206619\pi$
$992$	35.6076	−	20.5581i	1.13054	−	0.652719i
$993$		0			0
$994$	6.96187	+	12.0583i	0.220817	+	0.382466i
$995$	−0.606255	−	0.618536i	−0.0192196	−	0.0196089i
$996$		0			0
$997$	−47.2647	+	27.2883i	−1.49689	+	0.864229i	−0.999994	−	0.00358086i	$-0.998860\pi$
$997$	−47.2647	+	27.2883i	−1.49689	+	0.864229i	−0.496896	+	0.867810i	$0.665527\pi$
$998$	−15.1946	−	8.77261i	−0.480977	−	0.277692i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bs.b.334.2		24
3.2	odd	2		195.2.ba.a.139.11	yes	24
5.4	even	2	inner	585.2.bs.b.334.11		24
13.3	even	3	inner	585.2.bs.b.289.11		24
15.2	even	4		975.2.i.q.451.1		12
15.8	even	4		975.2.i.o.451.6		12
15.14	odd	2		195.2.ba.a.139.2	yes	24
39.29	odd	6		195.2.ba.a.94.2	✓	24
65.29	even	6	inner	585.2.bs.b.289.2		24
195.29	odd	6		195.2.ba.a.94.11	yes	24
195.68	even	12		975.2.i.o.601.6		12
195.107	even	12		975.2.i.q.601.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.ba.a.94.2	✓	24	39.29	odd	6
195.2.ba.a.94.11	yes	24	195.29	odd	6
195.2.ba.a.139.2	yes	24	15.14	odd	2
195.2.ba.a.139.11	yes	24	3.2	odd	2
585.2.bs.b.289.2		24	65.29	even	6	inner
585.2.bs.b.289.11		24	13.3	even	3	inner
585.2.bs.b.334.2		24	1.1	even	1	trivial
585.2.bs.b.334.11		24	5.4	even	2	inner
975.2.i.o.451.6		12	15.8	even	4
975.2.i.o.601.6		12	195.68	even	12
975.2.i.q.451.1		12	15.2	even	4
975.2.i.q.601.1		12	195.107	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.85914 - 1.07337i) q^{2} +(1.30426 + 2.25904i) q^{4} +(2.16557 - 0.557052i) q^{5} +(0.635729 - 0.367038i) q^{7} -1.30633i q^{8} +O(q^{10})\)	\(q+(-1.85914 - 1.07337i) q^{2} +(1.30426 + 2.25904i) q^{4} +(2.16557 - 0.557052i) q^{5} +(0.635729 - 0.367038i) q^{7} -1.30633i q^{8} +(-4.62401 - 1.28883i) q^{10} +(0.110220 - 0.190906i) q^{11} +(-0.632595 - 3.54962i) q^{13} -1.57588 q^{14} +(1.20633 - 2.08943i) q^{16} +(-0.710116 + 0.409986i) q^{17} +(1.61059 + 2.78963i) q^{19} +(4.08287 + 4.16558i) q^{20} +(-0.409827 + 0.236613i) q^{22} +(6.92086 + 3.99576i) q^{23} +(4.37939 - 2.41267i) q^{25} +(-2.63399 + 7.27824i) q^{26} +(1.65831 + 0.957426i) q^{28} +(1.51840 - 2.62994i) q^{29} -5.27667 q^{31} +(-6.74812 + 3.89603i) q^{32} +1.76027 q^{34} +(1.17226 - 1.14898i) q^{35} +(4.44748 + 2.56775i) q^{37} -6.91507i q^{38} +(-0.727696 - 2.82896i) q^{40} +(5.87981 - 10.1841i) q^{41} +(4.62010 - 2.66741i) q^{43} +0.575020 q^{44} +(-8.57789 - 14.8573i) q^{46} -5.80713i q^{47} +(-3.23057 + 5.59550i) q^{49} +(-10.7316 - 0.215233i) q^{50} +(7.19368 - 6.05869i) q^{52} +4.27058i q^{53} +(0.132344 - 0.474818i) q^{55} +(-0.479475 - 0.830474i) q^{56} +(-5.64581 + 3.25961i) q^{58} +(-1.08650 - 1.88188i) q^{59} +(-6.03816 - 10.4584i) q^{61} +(9.81005 + 5.66383i) q^{62} +11.9022 q^{64} +(-3.34725 - 7.33457i) q^{65} +(-1.38164 - 0.797691i) q^{67} +(-1.85235 - 1.06945i) q^{68} +(-3.41267 + 0.877845i) q^{70} +(-4.41778 - 7.65181i) q^{71} -7.86235i q^{73} +(-5.51231 - 9.54761i) q^{74} +(-4.20126 + 7.27680i) q^{76} -0.161819i q^{77} +13.9175 q^{79} +(1.44848 - 5.19680i) q^{80} +(-21.8628 + 12.6225i) q^{82} -4.38199i q^{83} +(-1.30942 + 1.28342i) q^{85} -11.4525 q^{86} +(-0.249387 - 0.143984i) q^{88} +(-2.16344 + 3.74719i) q^{89} +(-1.70501 - 2.02441i) q^{91} +20.8460i q^{92} +(-6.23322 + 10.7962i) q^{94} +(5.04182 + 5.14395i) q^{95} +(-7.48331 + 4.32049i) q^{97} +(12.0121 - 6.93520i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4} - 4 q^{5}+O(q^{10}) \) 24 * q + 8 * q^4 - 4 * q^5	\( 24 q + 8 q^{4} - 4 q^{5} - 4 q^{10} - 4 q^{11} - 24 q^{14} + 16 q^{16} - 16 q^{19} + 16 q^{20} - 16 q^{25} + 48 q^{26} + 12 q^{29} + 8 q^{31} - 32 q^{34} - 10 q^{35} - 48 q^{40} + 40 q^{41} - 40 q^{44} - 24 q^{46} - 16 q^{49} - 20 q^{50} + 20 q^{55} + 24 q^{56} - 12 q^{59} + 20 q^{61} + 48 q^{64} - 14 q^{65} - 56 q^{70} - 4 q^{71} + 12 q^{74} + 8 q^{76} + 136 q^{79} + 4 q^{80} - 4 q^{85} - 48 q^{86} + 64 q^{89} + 60 q^{91} - 48 q^{94} + 28 q^{95}+O(q^{100}) \) 24 * q + 8 * q^4 - 4 * q^5 - 4 * q^10 - 4 * q^11 - 24 * q^14 + 16 * q^16 - 16 * q^19 + 16 * q^20 - 16 * q^25 + 48 * q^26 + 12 * q^29 + 8 * q^31 - 32 * q^34 - 10 * q^35 - 48 * q^40 + 40 * q^41 - 40 * q^44 - 24 * q^46 - 16 * q^49 - 20 * q^50 + 20 * q^55 + 24 * q^56 - 12 * q^59 + 20 * q^61 + 48 * q^64 - 14 * q^65 - 56 * q^70 - 4 * q^71 + 12 * q^74 + 8 * q^76 + 136 * q^79 + 4 * q^80 - 4 * q^85 - 48 * q^86 + 64 * q^89 + 60 * q^91 - 48 * q^94 + 28 * q^95

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