LMFDB - Embedded newform 639.2.f.d.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [639,2,Mod(199,639)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(639, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("639.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 639 = 3^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	639.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.10244068916$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 213)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			289.1
Character	$\chi$	$=$	639.289
Dual form			639.2.f.d.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.782687 - 2.40886i) q^{2} +(-3.57199 + 2.59520i) q^{4} +(-1.75584 - 1.27569i) q^{5} +(-1.09908 - 3.38262i) q^{7} +(4.94904 + 3.59569i) q^{8} +O(q^{10})$	\(q+(-0.782687 - 2.40886i) q^{2} +(-3.57199 + 2.59520i) q^{4} +(-1.75584 - 1.27569i) q^{5} +(-1.09908 - 3.38262i) q^{7} +(4.94904 + 3.59569i) q^{8} +(-1.69869 + 5.22804i) q^{10} +(-1.39620 - 4.29705i) q^{11} +(1.03454 - 3.18399i) q^{13} +(-7.28803 + 5.29507i) q^{14} +(2.05921 - 6.33761i) q^{16} +(-1.83970 + 5.66201i) q^{17} +(0.463228 + 1.42567i) q^{19} +9.58251 q^{20} +(-9.25822 + 6.72649i) q^{22} +0.643154 q^{23} +(-0.0895063 - 0.275472i) q^{25} -8.47953 q^{26} +(12.7045 + 9.23035i) q^{28} +(-1.83594 - 1.33389i) q^{29} +(2.48741 + 7.65546i) q^{31} -4.64346 q^{32} +15.0789 q^{34} +(-2.38537 + 7.34141i) q^{35} -5.26585 q^{37} +(3.07168 - 2.23171i) q^{38} +(-4.10272 - 12.6269i) q^{40} +9.34473 q^{41} +(4.39288 + 3.19162i) q^{43} +(16.1389 + 11.7256i) q^{44} +(-0.503389 - 1.54927i) q^{46} +(-4.12115 + 12.6836i) q^{47} +(-4.57102 + 3.32104i) q^{49} +(-0.593519 + 0.431217i) q^{50} +(4.56774 + 14.0580i) q^{52} +(-7.85328 - 5.70574i) q^{53} +(-3.03021 + 9.32603i) q^{55} +(6.72346 - 20.6927i) q^{56} +(-1.77619 + 5.46655i) q^{58} +(-2.85724 - 2.07591i) q^{59} +(4.37475 - 13.4641i) q^{61} +(16.4941 - 11.9837i) q^{62} +(-0.484054 - 1.48977i) q^{64} +(-5.87828 + 4.27082i) q^{65} +(-7.81267 + 5.67624i) q^{67} +(-8.12268 - 24.9990i) q^{68} +19.5515 q^{70} +(0.269484 - 8.42184i) q^{71} +(-1.44187 - 4.43763i) q^{73} +(4.12151 + 12.6847i) q^{74} +(-5.35455 - 3.89031i) q^{76} +(-13.0007 + 9.44560i) q^{77} +(-11.8733 - 8.62648i) q^{79} +(-11.7005 + 8.50089i) q^{80} +(-7.31400 - 22.5102i) q^{82} +(0.964168 + 0.700509i) q^{83} +(10.4532 - 7.59468i) q^{85} +(4.24992 - 13.0799i) q^{86} +(8.54102 - 26.2866i) q^{88} +(10.7803 + 7.83238i) q^{89} -11.9073 q^{91} +(-2.29734 + 1.66912i) q^{92} +33.7786 q^{94} +(1.00536 - 3.09418i) q^{95} -5.92770 q^{97} +(11.5776 + 8.41162i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} - 7 q^{4} + 2 q^{5} - 4 q^{7} - 8 q^{8}+O(q^{10}) $ 24 * q - 3 * q^2 - 7 * q^4 + 2 * q^5 - 4 * q^7 - 8 * q^8	$ 24 q - 3 q^{2} - 7 q^{4} + 2 q^{5} - 4 q^{7} - 8 q^{8} - 8 q^{10} + 5 q^{11} - 8 q^{13} - 29 q^{14} + 5 q^{16} + 2 q^{19} + 2 q^{20} - 11 q^{22} - 6 q^{23} - 12 q^{25} - 24 q^{26} - 25 q^{28} - 2 q^{29} - 24 q^{31} + 36 q^{32} + 102 q^{34} - 22 q^{35} + 10 q^{37} + 27 q^{38} - 56 q^{40} - 2 q^{41} - 18 q^{43} - 9 q^{44} - 11 q^{46} + 36 q^{47} - 6 q^{49} - 3 q^{50} - 35 q^{52} - 6 q^{53} - 9 q^{55} + 100 q^{56} + 64 q^{58} - 3 q^{61} + 36 q^{62} + 66 q^{64} + 3 q^{65} - 18 q^{67} - 76 q^{68} + 130 q^{70} + 10 q^{71} - 9 q^{73} - 7 q^{74} - 24 q^{76} - 39 q^{77} - 20 q^{79} - 51 q^{80} + 20 q^{82} - 17 q^{83} + 25 q^{85} + 69 q^{86} + 13 q^{88} + 28 q^{89} - 38 q^{91} + 81 q^{92} - 56 q^{94} - 35 q^{95} - 34 q^{98}+O(q^{100}) $ 24 * q - 3 * q^2 - 7 * q^4 + 2 * q^5 - 4 * q^7 - 8 * q^8 - 8 * q^10 + 5 * q^11 - 8 * q^13 - 29 * q^14 + 5 * q^16 + 2 * q^19 + 2 * q^20 - 11 * q^22 - 6 * q^23 - 12 * q^25 - 24 * q^26 - 25 * q^28 - 2 * q^29 - 24 * q^31 + 36 * q^32 + 102 * q^34 - 22 * q^35 + 10 * q^37 + 27 * q^38 - 56 * q^40 - 2 * q^41 - 18 * q^43 - 9 * q^44 - 11 * q^46 + 36 * q^47 - 6 * q^49 - 3 * q^50 - 35 * q^52 - 6 * q^53 - 9 * q^55 + 100 * q^56 + 64 * q^58 - 3 * q^61 + 36 * q^62 + 66 * q^64 + 3 * q^65 - 18 * q^67 - 76 * q^68 + 130 * q^70 + 10 * q^71 - 9 * q^73 - 7 * q^74 - 24 * q^76 - 39 * q^77 - 20 * q^79 - 51 * q^80 + 20 * q^82 - 17 * q^83 + 25 * q^85 + 69 * q^86 + 13 * q^88 + 28 * q^89 - 38 * q^91 + 81 * q^92 - 56 * q^94 - 35 * q^95 - 34 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.782687	−	2.40886i	−0.553443	−	1.70332i	−0.700019	−	0.714124i	$-0.746825\pi$
$2$	−0.782687	−	2.40886i	−0.553443	−	1.70332i	0.146575	−	0.989200i	$-0.453175\pi$
$3$		0			0
$3$		0			0
$4$	−3.57199	+	2.59520i	−1.78600	+	1.29760i
$5$	−1.75584	−	1.27569i	−0.785234	−	0.570506i	0.121311	−	0.992615i	$-0.461290\pi$
$5$	−1.75584	−	1.27569i	−0.785234	−	0.570506i	−0.906545	+	0.422108i	$0.861290\pi$
$6$		0			0
$7$	−1.09908	−	3.38262i	−0.415413	−	1.27851i	−0.911881	−	0.410455i	$-0.865370\pi$
$7$	−1.09908	−	3.38262i	−0.415413	−	1.27851i	0.496468	−	0.868055i	$-0.334630\pi$
$8$	4.94904	+	3.59569i	1.74975	+	1.27127i
$9$		0			0
$10$	−1.69869	+	5.22804i	−0.537174	+	1.65325i
$11$	−1.39620	−	4.29705i	−0.420969	−	1.29561i	−0.906802	−	0.421557i	$-0.861484\pi$
$11$	−1.39620	−	4.29705i	−0.420969	−	1.29561i	0.485833	−	0.874052i	$-0.338516\pi$
$12$		0			0
$13$	1.03454	−	3.18399i	0.286930	−	0.883081i	−0.698883	−	0.715236i	$-0.746319\pi$
$13$	1.03454	−	3.18399i	0.286930	−	0.883081i	0.985813	−	0.167845i	$-0.0536808\pi$
$14$	−7.28803	+	5.29507i	−1.94781	+	1.41517i
$15$		0			0
$16$	2.05921	−	6.33761i	0.514803	−	1.58440i
$17$	−1.83970	+	5.66201i	−0.446192	+	1.37324i	0.434978	+	0.900441i	$0.356756\pi$
$17$	−1.83970	+	5.66201i	−0.446192	+	1.37324i	−0.881171	+	0.472798i	$0.843244\pi$
$18$		0			0
$19$	0.463228	+	1.42567i	0.106272	+	0.327071i	0.990027	−	0.140879i	$-0.0449928\pi$
$19$	0.463228	+	1.42567i	0.106272	+	0.327071i	−0.883755	+	0.467950i	$0.844993\pi$
$20$	9.58251			2.14272
$21$		0			0
$22$	−9.25822	+	6.72649i	−1.97386	+	1.43409i
$23$	0.643154			0.134107			0.0670535	−	0.997749i	$-0.478640\pi$
$23$	0.643154			0.134107			0.0670535	+	0.997749i	$0.478640\pi$
$24$		0			0
$25$	−0.0895063	−	0.275472i	−0.0179013	−	0.0550944i
$26$	−8.47953			−1.66297
$27$		0			0
$28$	12.7045	+	9.23035i	2.40092	+	1.74437i
$29$	−1.83594	−	1.33389i	−0.340926	−	0.247697i	0.404126	−	0.914703i	$-0.367576\pi$
$29$	−1.83594	−	1.33389i	−0.340926	−	0.247697i	−0.745052	+	0.667006i	$0.767576\pi$
$30$		0			0
$31$	2.48741	+	7.65546i	0.446752	+	1.37496i	0.880551	+	0.473951i	$0.157173\pi$
$31$	2.48741	+	7.65546i	0.446752	+	1.37496i	−0.433800	+	0.901009i	$0.642827\pi$
$32$	−4.64346			−0.820855
$33$		0			0
$34$	15.0789			2.58601
$35$	−2.38537	+	7.34141i	−0.403201	+	1.24093i
$36$		0			0
$37$	−5.26585			−0.865700			−0.432850	−	0.901466i	$-0.642492\pi$
$37$	−5.26585			−0.865700			−0.432850	+	0.901466i	$0.642492\pi$
$38$	3.07168	−	2.23171i	0.498292	−	0.362031i
$39$		0			0
$40$	−4.10272	−	12.6269i	−0.648698	−	1.99649i
$41$	9.34473			1.45940			0.729701	−	0.683767i	$-0.239659\pi$
$41$	9.34473			1.45940			0.729701	+	0.683767i	$0.239659\pi$
$42$		0			0
$43$	4.39288	+	3.19162i	0.669909	+	0.486717i	0.869995	−	0.493061i	$-0.164122\pi$
$43$	4.39288	+	3.19162i	0.669909	+	0.486717i	−0.200086	+	0.979778i	$0.564122\pi$
$44$	16.1389	+	11.7256i	2.43303	+	1.76770i
$45$		0			0
$46$	−0.503389	−	1.54927i	−0.0742206	−	0.228428i
$47$	−4.12115	+	12.6836i	−0.601131	+	1.85009i	−0.0796609	+	0.996822i	$0.525384\pi$
$47$	−4.12115	+	12.6836i	−0.601131	+	1.85009i	−0.521470	+	0.853269i	$0.674616\pi$
$48$		0			0
$49$	−4.57102	+	3.32104i	−0.653003	+	0.474434i
$50$	−0.593519	+	0.431217i	−0.0839363	+	0.0609833i
$51$		0			0
$52$	4.56774	+	14.0580i	0.633431	+	1.94950i
$53$	−7.85328	−	5.70574i	−1.07873	−	0.783744i	−0.101270	−	0.994859i	$-0.532291\pi$
$53$	−7.85328	−	5.70574i	−1.07873	−	0.783744i	−0.977461	+	0.211115i	$0.932291\pi$
$54$		0			0
$55$	−3.03021	+	9.32603i	−0.408594	+	1.25752i
$56$	6.72346	−	20.6927i	0.898459	−	2.76517i
$57$		0			0
$58$	−1.77619	+	5.46655i	−0.233225	+	0.717794i
$59$	−2.85724	−	2.07591i	−0.371981	−	0.270260i	0.386051	−	0.922478i	$-0.373839\pi$
$59$	−2.85724	−	2.07591i	−0.371981	−	0.270260i	−0.758032	+	0.652217i	$0.773839\pi$
$60$		0			0
$61$	4.37475	−	13.4641i	0.560129	−	1.72390i	−0.121869	−	0.992546i	$-0.538889\pi$
$61$	4.37475	−	13.4641i	0.560129	−	1.72390i	0.681998	−	0.731354i	$-0.261111\pi$
$62$	16.4941	−	11.9837i	2.09475	−	1.52193i
$63$		0			0
$64$	−0.484054	−	1.48977i	−0.0605068	−	0.186221i
$65$	−5.87828	+	4.27082i	−0.729111	+	0.529730i
$66$		0			0
$67$	−7.81267	+	5.67624i	−0.954469	+	0.693463i	−0.951860	−	0.306534i	$-0.900831\pi$
$67$	−7.81267	+	5.67624i	−0.954469	+	0.693463i	−0.00260970	+	0.999997i	$0.500831\pi$
$68$	−8.12268	−	24.9990i	−0.985020	−	3.03158i
$69$		0			0
$70$	19.5515			2.33685
$71$	0.269484	−	8.42184i	0.0319818	−	0.999488i
$71$	0.269484	−	8.42184i	0.0319818	−	0.999488i
$72$		0			0
$73$	−1.44187	−	4.43763i	−0.168759	−	0.519386i	0.830535	−	0.556966i	$-0.188035\pi$
$73$	−1.44187	−	4.43763i	−0.168759	−	0.519386i	−0.999294	+	0.0375809i	$0.988035\pi$
$74$	4.12151	+	12.6847i	0.479116	+	1.47457i
$75$		0			0
$76$	−5.35455	−	3.89031i	−0.614209	−	0.446249i
$77$	−13.0007	+	9.44560i	−1.48157	+	1.07643i
$78$		0			0
$79$	−11.8733	−	8.62648i	−1.33585	−	0.970555i	−0.999586	−	0.0287887i	$-0.990835\pi$
$79$	−11.8733	−	8.62648i	−1.33585	−	0.970555i	−0.336269	−	0.941766i	$-0.609165\pi$
$80$	−11.7005	+	8.50089i	−1.30815	+	0.950428i
$81$		0			0
$82$	−7.31400	−	22.5102i	−0.807696	−	2.48583i
$83$	0.964168	+	0.700509i	0.105831	+	0.0768909i	0.639442	−	0.768839i	$-0.279165\pi$
$83$	0.964168	+	0.700509i	0.105831	+	0.0768909i	−0.533611	+	0.845730i	$0.679165\pi$
$84$		0			0
$85$	10.4532	−	7.59468i	1.13381	−	0.823759i
$86$	4.24992	−	13.0799i	0.458280	−	1.41044i
$87$		0			0
$88$	8.54102	−	26.2866i	0.910476	−	2.80216i
$89$	10.7803	+	7.83238i	1.14271	+	0.830231i	0.987495	−	0.157649i	$-0.0503915\pi$
$89$	10.7803	+	7.83238i	1.14271	+	0.830231i	0.155220	+	0.987880i	$0.450391\pi$
$90$		0			0
$91$	−11.9073			−1.24822
$92$	−2.29734	+	1.66912i	−0.239514	+	0.174017i
$93$		0			0
$94$	33.7786			3.48400
$95$	1.00536	−	3.09418i	0.103148	−	0.317456i
$96$		0			0
$97$	−5.92770			−0.601867			−0.300933	−	0.953645i	$-0.597298\pi$
$97$	−5.92770			−0.601867			−0.300933	+	0.953645i	$0.597298\pi$
$98$	11.5776	+	8.41162i	1.16952	+	0.849702i
$99$		0			0
$100$	1.03462	+	0.751697i	0.103462	+	0.0751697i
$101$	−2.71138			−0.269792			−0.134896	−	0.990860i	$-0.543070\pi$
$101$	−2.71138			−0.269792			−0.134896	+	0.990860i	$0.543070\pi$
$102$		0			0
$103$	1.31379			0.129451			0.0647256	−	0.997903i	$-0.479383\pi$
$103$	1.31379			0.129451			0.0647256	+	0.997903i	$0.479383\pi$
$104$	16.5686	−	12.0378i	1.62469	−	1.18041i
$105$		0			0
$106$	−7.59769	+	23.3833i	−0.737953	+	2.27119i
$107$	−1.64615	+	5.06632i	−0.159139	+	0.489779i	−0.998557	−	0.0537075i	$-0.982896\pi$
$107$	−1.64615	+	5.06632i	−0.159139	+	0.489779i	0.839418	+	0.543487i	$0.182896\pi$
$108$		0			0
$109$	5.47687	−	3.97918i	0.524589	−	0.381136i	−0.293741	−	0.955885i	$-0.594900\pi$
$109$	5.47687	−	3.97918i	0.524589	−	0.381136i	0.818330	+	0.574749i	$0.194900\pi$
$110$	24.8368			2.36810
$111$		0			0
$112$	−23.7010			−2.23953
$113$	0.510911	+	0.371199i	0.0480625	+	0.0349194i	0.611557	−	0.791200i	$-0.290543\pi$
$113$	0.510911	+	0.371199i	0.0480625	+	0.0349194i	−0.563495	+	0.826120i	$0.690543\pi$
$114$		0			0
$115$	−1.12927	−	0.820466i	−0.105305	−	0.0765089i
$116$	10.0197			0.930305
$117$		0			0
$118$	−2.76425	+	8.50749i	−0.254470	+	0.783178i
$119$	21.1744			1.94105
$120$		0			0
$121$	−7.61608	+	5.53340i	−0.692371	+	0.503037i
$122$	−35.8572			−3.24636
$123$		0			0
$124$	−28.7525	−	20.8899i	−2.58205	−	1.87597i
$125$	−3.54761	+	10.9184i	−0.317308	+	0.976573i
$126$		0			0
$127$	3.21307	−	9.88881i	0.285114	−	0.877490i	−0.701251	−	0.712915i	$-0.747375\pi$
$127$	3.21307	−	9.88881i	0.285114	−	0.877490i	0.986365	−	0.164575i	$-0.0526253\pi$
$128$	−10.7230	+	7.79075i	−0.947792	+	0.688612i
$129$		0			0
$130$	14.8887	+	10.8173i	1.30582	+	0.948736i
$131$	−4.52537	−	13.9277i	−0.395384	−	1.21687i	−0.928662	−	0.370926i	$-0.879040\pi$
$131$	−4.52537	−	13.9277i	−0.395384	−	1.21687i	0.533279	−	0.845939i	$-0.320960\pi$
$132$		0			0
$133$	4.31337	−	3.13385i	0.374017	−	0.271739i
$134$	19.7882	+	14.3769i	1.70944	+	1.24198i
$135$		0			0
$136$	−29.4636	+	21.4065i	−2.52648	+	1.83560i
$137$	1.44196	+	1.04765i	0.123195	+	0.0895067i	0.647677	−	0.761915i	$-0.275741\pi$
$137$	1.44196	+	1.04765i	0.123195	+	0.0895067i	−0.524481	+	0.851422i	$0.675741\pi$
$138$		0			0
$139$	−2.94739	−	9.07113i	−0.249994	−	0.769403i	−0.994775	−	0.102094i	$-0.967446\pi$
$139$	−2.94739	−	9.07113i	−0.249994	−	0.769403i	0.744781	−	0.667309i	$-0.232554\pi$
$140$	−10.5319	−	32.4140i	−0.890112	−	2.73948i
$141$		0			0
$142$	−20.4980	+	5.94252i	−1.72015	+	0.498685i
$143$	−15.1262			−1.26492
$144$		0			0
$145$	1.52199	+	4.68419i	0.126394	+	0.389001i
$146$	−9.56112	+	6.94656i	−0.791284	+	0.574901i
$147$		0			0
$148$	18.8096	−	13.6659i	1.54614	−	1.12333i
$149$	−1.56593	−	4.81942i	−0.128286	−	0.394822i	0.866200	−	0.499698i	$-0.166556\pi$
$149$	−1.56593	−	4.81942i	−0.128286	−	0.394822i	−0.994485	+	0.104875i	$0.966556\pi$
$150$		0			0
$151$	−15.9438	+	11.5839i	−1.29749	+	0.942682i	−0.999928	−	0.0120197i	$-0.996174\pi$
$151$	−15.9438	+	11.5839i	−1.29749	+	0.942682i	−0.297563	+	0.954702i	$0.596174\pi$
$152$	−2.83373	+	8.72132i	−0.229846	+	0.707392i
$153$		0			0
$154$	32.9287	+	23.9241i	2.65347	+	1.92786i
$155$	5.39851	−	16.6149i	0.433619	−	1.33454i
$156$		0			0
$157$	−3.53643	+	10.8840i	−0.282238	+	0.868640i	0.704975	+	0.709232i	$0.250958\pi$
$157$	−3.53643	+	10.8840i	−0.282238	+	0.868640i	−0.987213	+	0.159407i	$0.949042\pi$
$158$	−11.4869	+	35.3531i	−0.913849	+	2.81254i
$159$		0			0
$160$	8.15315	+	5.92361i	0.644563	+	0.468303i
$161$	−0.706878	−	2.17555i	−0.0557098	−	0.171457i
$162$		0			0
$163$	−15.1240	+	10.9883i	−1.18461	+	0.860667i	−0.992684	−	0.120743i	$-0.961472\pi$
$163$	−15.1240	+	10.9883i	−1.18461	+	0.860667i	−0.191923	+	0.981410i	$0.561472\pi$
$164$	−33.3793	+	24.2515i	−2.60648	+	1.89372i
$165$		0			0
$166$	0.932789	−	2.87083i	0.0723985	−	0.222820i
$167$	−4.87908	−	15.0163i	−0.377554	−	1.16199i	−0.941739	−	0.336344i	$-0.890809\pi$
$167$	−4.87908	−	15.0163i	−0.377554	−	1.16199i	0.564185	−	0.825649i	$-0.309191\pi$
$168$		0			0
$169$	1.44968	+	1.05325i	0.111514	+	0.0810195i
$170$	−26.4761	−	19.2360i	−2.03063	−	1.47534i
$171$		0			0
$172$	−23.9742			−1.82802
$173$	−4.17912	−	12.8620i	−0.317733	−	0.977880i	−0.974615	−	0.223887i	$-0.928125\pi$
$173$	−4.17912	−	12.8620i	−0.317733	−	0.977880i	0.656882	−	0.753993i	$-0.271875\pi$
$174$		0			0
$175$	−0.833443	+	0.605532i	−0.0630024	+	0.0457739i
$176$	−30.1081			−2.26948
$177$		0			0
$178$	10.4295	−	32.0987i	0.781724	−	2.40590i
$179$	5.94196			0.444123			0.222061	−	0.975033i	$-0.428721\pi$
$179$	5.94196			0.444123			0.222061	+	0.975033i	$0.428721\pi$
$180$		0			0
$181$	2.13198			0.158469			0.0792344	−	0.996856i	$-0.474752\pi$
$181$	2.13198			0.158469			0.0792344	+	0.996856i	$0.474752\pi$
$182$	9.31968	+	28.6830i	0.690821	+	2.12613i
$183$		0			0
$184$	3.18300	+	2.31258i	0.234654	+	0.170486i
$185$	9.24597	+	6.71759i	0.679777	+	0.493887i
$186$		0			0
$187$	26.8985			1.96701
$188$	−18.1958	−	56.0009i	−1.32706	−	4.08428i
$189$		0			0
$190$	−8.24034			−0.597817
$191$	−6.33601	+	4.60338i	−0.458457	+	0.333089i	−0.792926	−	0.609318i	$-0.791443\pi$
$191$	−6.33601	+	4.60338i	−0.458457	+	0.333089i	0.334469	+	0.942407i	$0.391443\pi$
$192$		0			0
$193$	1.35804			0.0977542			0.0488771	−	0.998805i	$-0.484436\pi$
$193$	1.35804			0.0977542			0.0488771	+	0.998805i	$0.484436\pi$
$194$	4.63953	+	14.2790i	0.333099	+	1.02517i
$195$		0			0
$196$	7.70886	−	23.7254i	0.550633	−	1.69467i
$197$	−0.709836	+	2.18465i	−0.0505737	+	0.155650i	−0.973154	−	0.230156i	$-0.926076\pi$
$197$	−0.709836	+	2.18465i	−0.0505737	+	0.155650i	0.922580	+	0.385806i	$0.126076\pi$
$198$		0			0
$199$	−9.18339	+	6.67212i	−0.650993	+	0.472974i	−0.863609	−	0.504162i	$-0.831802\pi$
$199$	−9.18339	+	6.67212i	−0.650993	+	0.472974i	0.212616	+	0.977136i	$0.431802\pi$
$200$	0.547542	−	1.68516i	0.0387170	−	0.119159i
$201$		0			0
$202$	2.12216	+	6.53134i	0.149315	+	0.459543i
$203$	−2.49420	+	7.67635i	−0.175058	+	0.538774i
$204$		0			0
$205$	−16.4078	−	11.9210i	−1.14597	−	0.832597i
$206$	−1.02828	−	3.16473i	−0.0716439	−	0.220497i
$207$		0			0
$208$	−18.0486	−	13.1131i	−1.25144	−	0.909226i
$209$	5.47941	−	3.98103i	0.379019	−	0.275373i
$210$		0			0
$211$	2.42561	+	7.46526i	0.166986	+	0.513930i	0.999177	−	0.0405590i	$-0.0129139\pi$
$211$	2.42561	+	7.46526i	0.166986	+	0.513930i	−0.832191	+	0.554489i	$0.812914\pi$
$212$	42.8594			2.94360
$213$		0			0
$214$	13.4925			0.922327
$215$	−3.64167	−	11.2079i	−0.248360	−	0.764374i
$216$		0			0
$217$	23.1616	−	16.8279i	1.57231	−	1.14235i
$218$	−13.8720	−	10.0786i	−0.939529	−	0.682608i
$219$		0			0
$220$	−13.3791	−	41.1765i	−0.902016	−	2.77612i
$221$	16.1246	+	11.7152i	1.08466	+	0.788048i
$222$		0			0
$223$	−2.94593	+	9.06664i	−0.197274	+	0.607147i	0.802668	+	0.596425i	$0.203413\pi$
$223$	−2.94593	+	9.06664i	−0.197274	+	0.607147i	−0.999943	+	0.0107216i	$0.996587\pi$
$224$	5.10353	+	15.7070i	0.340994	+	1.04947i
$225$		0			0
$226$	0.494283	−	1.52125i	0.0328792	−	0.101192i
$227$	−1.99373	+	1.44853i	−0.132329	+	0.0961424i	−0.651981	−	0.758236i	$-0.726062\pi$
$227$	−1.99373	+	1.44853i	−0.132329	+	0.0961424i	0.519652	+	0.854378i	$0.326062\pi$
$228$		0			0
$229$	−5.54393	+	17.0625i	−0.366353	+	1.12752i	0.582776	+	0.812633i	$0.301966\pi$
$229$	−5.54393	+	17.0625i	−0.366353	+	1.12752i	−0.949129	+	0.314886i	$0.898034\pi$
$230$	−1.09252	+	3.36244i	−0.0720388	+	0.221713i
$231$		0			0
$232$	−4.28990	−	13.2030i	−0.281646	−	0.866816i
$233$	8.31888			0.544988			0.272494	−	0.962157i	$-0.412151\pi$
$233$	8.31888			0.544988			0.272494	+	0.962157i	$0.412151\pi$
$234$		0			0
$235$	23.4164	−	17.0130i	1.52752	−	1.10981i
$236$	15.5934			1.01505
$237$		0			0
$238$	−16.5729	−	51.0062i	−1.07426	−	3.30624i
$239$	−3.56419			−0.230548			−0.115274	−	0.993334i	$-0.536775\pi$
$239$	−3.56419			−0.230548			−0.115274	+	0.993334i	$0.536775\pi$
$240$		0			0
$241$	5.81624	+	4.22575i	0.374657	+	0.272204i	0.759139	−	0.650928i	$-0.225620\pi$
$241$	5.81624	+	4.22575i	0.374657	+	0.272204i	−0.384482	+	0.923132i	$0.625620\pi$
$242$	19.2902	+	14.0152i	1.24002	+	0.900929i
$243$		0			0
$244$	19.3155	+	59.4470i	1.23655	+	3.80570i
$245$	12.2626			0.783428
$246$		0			0
$247$	5.01855			0.319323
$248$	−15.2163	+	46.8311i	−0.966239	+	2.97378i
$249$		0			0
$250$	29.0777			1.83903
$251$	9.99778	−	7.26381i	0.631054	−	0.458488i	−0.225711	−	0.974194i	$-0.572471\pi$
$251$	9.99778	−	7.26381i	0.631054	−	0.458488i	0.856765	+	0.515707i	$0.172471\pi$
$252$		0			0
$253$	−0.897969	−	2.76367i	−0.0564549	−	0.173750i
$254$	−26.3356			−1.65244
$255$		0			0
$256$	24.6251	+	17.8912i	1.53907	+	1.11820i
$257$	−21.9731	−	15.9644i	−1.37064	−	0.995832i	−0.997686	−	0.0679834i	$-0.978344\pi$
$257$	−21.9731	−	15.9644i	−1.37064	−	0.995832i	−0.372958	−	0.927848i	$-0.621656\pi$
$258$		0			0
$259$	5.78758	+	17.8123i	0.359623	+	1.10681i
$260$	9.91352	−	30.5107i	0.614810	−	1.89219i
$261$		0			0
$262$	−30.0079	+	21.8020i	−1.85389	+	1.34693i
$263$	11.6289	−	8.44888i	0.717068	−	0.520980i	−0.168378	−	0.985722i	$-0.553853\pi$
$263$	11.6289	−	8.44888i	0.717068	−	0.520980i	0.885446	+	0.464742i	$0.153853\pi$
$264$		0			0
$265$	6.51032	+	20.0367i	0.399926	+	1.23085i
$266$	−10.9250	−	7.93750i	−0.669857	−	0.486680i
$267$		0			0
$268$	13.1758	−	40.5509i	0.804840	−	2.47704i
$269$	4.20111	−	12.9297i	0.256146	−	0.788336i	−0.737456	−	0.675395i	$-0.763973\pi$
$269$	4.20111	−	12.9297i	0.256146	−	0.788336i	0.993602	−	0.112941i	$-0.0360270\pi$
$270$		0			0
$271$	8.79331	−	27.0630i	0.534156	−	1.64396i	−0.211310	−	0.977419i	$-0.567773\pi$
$271$	8.79331	−	27.0630i	0.534156	−	1.64396i	0.745466	−	0.666543i	$-0.232227\pi$
$272$	32.0953	+	23.3186i	1.94606	+	1.41390i
$273$		0			0
$274$	1.39504	−	4.29348i	0.0842772	−	0.259379i
$275$	−1.05875	+	0.769226i	−0.0638450	+	0.0463861i
$276$		0			0
$277$	−3.17310	−	9.76580i	−0.190653	−	0.586770i	0.809347	−	0.587331i	$-0.199821\pi$
$277$	−3.17310	−	9.76580i	−0.190653	−	0.586770i	−1.00000		0.000561047i	$0.999821\pi$
$278$	−19.5442	+	14.1997i	−1.17218	+	0.851642i
$279$		0			0
$280$	−38.2027	+	27.7559i	−2.28305	+	1.65873i
$281$	5.80690	+	17.8718i	0.346410	+	1.06614i	0.960824	+	0.277158i	$0.0893925\pi$
$281$	5.80690	+	17.8718i	0.346410	+	1.06614i	−0.614414	+	0.788984i	$0.710607\pi$
$282$		0			0
$283$	−13.9726			−0.830583			−0.415291	−	0.909688i	$-0.636320\pi$
$283$	−13.9726			−0.830583			−0.415291	+	0.909688i	$0.636320\pi$
$284$	20.8938	+	30.7821i	1.23982	+	1.82658i
$285$		0			0
$286$	11.8391	+	36.4370i	0.700060	+	2.15456i
$287$	−10.2706	−	31.6097i	−0.606254	−	1.86586i
$288$		0			0
$289$	−14.9206	−	10.8404i	−0.877681	−	0.637672i
$290$	10.0923	−	7.33251i	0.592642	−	0.430580i
$291$		0			0
$292$	16.6669	+	12.1092i	0.975358	+	0.708639i
$293$	4.29240	−	3.11861i	0.250765	−	0.182191i	−0.455301	−	0.890338i	$-0.650468\pi$
$293$	4.29240	−	3.11861i	0.250765	−	0.182191i	0.706066	+	0.708146i	$0.250468\pi$
$294$		0			0
$295$	2.36864	+	7.28991i	0.137907	+	0.424435i
$296$	−26.0609	−	18.9343i	−1.51476	−	1.10054i
$297$		0			0
$298$	−10.3837	+	7.54420i	−0.601512	+	0.437024i
$299$	0.665371	−	2.04780i	0.0384794	−	0.118427i
$300$		0			0
$301$	5.96790	−	18.3673i	0.343984	−	1.05867i
$302$	40.3830	+	29.3400i	2.32378	+	1.68833i
$303$		0			0
$304$	9.98922			0.572921
$305$	−24.8574	+	18.0599i	−1.42333	+	1.03411i
$306$		0			0
$307$	−24.9808			−1.42573			−0.712865	−	0.701301i	$-0.752603\pi$
$307$	−24.9808			−1.42573			−0.712865	+	0.701301i	$0.752603\pi$
$308$	21.9253	−	67.4792i	1.24931	−	3.84498i
$309$		0			0
$310$	−44.2484			−2.51314
$311$	−20.8375	−	15.1394i	−1.18159	−	0.858474i	−0.189239	−	0.981931i	$-0.560602\pi$
$311$	−20.8375	−	15.1394i	−1.18159	−	0.858474i	−0.992350	+	0.123457i	$0.960602\pi$
$312$		0			0
$313$	3.43769	+	2.49763i	0.194310	+	0.141174i	0.680686	−	0.732575i	$-0.261682\pi$
$313$	3.43769	+	2.49763i	0.194310	+	0.141174i	−0.486376	+	0.873749i	$0.661682\pi$
$314$	28.9861			1.63578
$315$		0			0
$316$	64.7989			3.64522
$317$	22.7219	−	16.5085i	1.27619	−	0.927207i	0.276760	−	0.960939i	$-0.410739\pi$
$317$	22.7219	−	16.5085i	1.27619	−	0.927207i	0.999431	+	0.0337317i	$0.0107392\pi$
$318$		0			0
$319$	−3.16846	+	9.75151i	−0.177399	+	0.545980i
$320$	−1.05056	+	3.23329i	−0.0587281	+	0.180746i
$321$		0			0
$322$	−4.68733	+	3.40555i	−0.261215	+	0.189784i
$323$	−8.92435			−0.496564
$324$		0			0
$325$	−0.969700			−0.0537893
$326$	38.3066	+	27.8314i	2.12161	+	1.54144i
$327$		0			0
$328$	46.2474	+	33.6007i	2.55359	+	1.85529i
$329$	47.4332			2.61508
$330$		0			0
$331$	2.20820	−	6.79613i	0.121374	−	0.373549i	−0.871849	−	0.489774i	$-0.837079\pi$
$331$	2.20820	−	6.79613i	0.121374	−	0.373549i	0.993223	+	0.116225i	$0.0370793\pi$
$332$	−5.26196			−0.288788
$333$		0			0
$334$	−32.3533	+	23.5061i	−1.77030	+	1.28619i
$335$	20.9589			1.14511
$336$		0			0
$337$	−10.6125	−	7.71047i	−0.578102	−	0.420016i	0.259937	−	0.965626i	$-0.416298\pi$
$337$	−10.6125	−	7.71047i	−0.578102	−	0.420016i	−0.838040	+	0.545610i	$0.816298\pi$
$338$	1.40250	−	4.31645i	0.0762859	−	0.234784i
$339$		0			0
$340$	−17.6289	+	54.2563i	−0.956063	+	2.94246i
$341$	29.4230	−	21.3770i	1.59334	−	1.15763i
$342$		0			0
$343$	−3.88427	−	2.82209i	−0.209731	−	0.152378i
$344$	10.2645	+	31.5909i	0.553425	+	1.70327i
$345$		0			0
$346$	−27.7119	+	20.1339i	−1.48980	+	1.08240i
$347$	0.354610	+	0.257639i	0.0190364	+	0.0138308i	0.597263	−	0.802046i	$-0.296255\pi$
$347$	0.354610	+	0.257639i	0.0190364	+	0.0138308i	−0.578226	+	0.815876i	$0.696255\pi$
$348$		0			0
$349$	21.9577	−	15.9532i	1.17537	−	0.853956i	0.183727	−	0.982977i	$-0.441184\pi$
$349$	21.9577	−	15.9532i	1.17537	−	0.853956i	0.991642	+	0.129022i	$0.0411837\pi$
$350$	2.11097	+	1.53371i	0.112836	+	0.0819802i
$351$		0			0
$352$	6.48317	+	19.9532i	0.345554	+	1.06351i
$353$	−4.40515	−	13.5577i	−0.234463	−	0.721602i	−0.997192	−	0.0748844i	$-0.976141\pi$
$353$	−4.40515	−	13.5577i	−0.234463	−	0.721602i	0.762730	−	0.646718i	$-0.223859\pi$
$354$		0			0
$355$	−11.2168	+	14.4436i	−0.595328	+	0.766587i
$356$	−58.8339			−3.11819
$357$		0			0
$358$	−4.65069	−	14.3134i	−0.245797	−	0.756485i
$359$	−6.51656	+	4.73456i	−0.343931	+	0.249880i	−0.746319	−	0.665589i	$-0.768180\pi$
$359$	−6.51656	+	4.73456i	−0.343931	+	0.249880i	0.402388	+	0.915469i	$0.368180\pi$
$360$		0			0
$361$	13.5534	−	9.84710i	0.713335	−	0.518268i
$362$	−1.66867	−	5.13565i	−0.0877035	−	0.269924i
$363$		0			0
$364$	42.5327	−	30.9018i	2.22932	−	1.61970i
$365$	−3.12935	+	9.63115i	−0.163798	+	0.504117i
$366$		0			0
$367$	11.5454	+	8.38823i	0.602665	+	0.437862i	0.846824	−	0.531873i	$-0.178512\pi$
$367$	11.5454	+	8.38823i	0.602665	+	0.437862i	−0.244159	+	0.969735i	$0.578512\pi$
$368$	1.32439	−	4.07606i	0.0690387	−	0.212479i
$369$		0			0
$370$	8.94506	−	27.5300i	0.465031	−	1.43122i
$371$	−10.6690	+	32.8357i	−0.553905	+	1.70475i
$372$		0			0
$373$	17.4128	+	12.6511i	0.901601	+	0.655051i	0.938877	−	0.344254i	$-0.111868\pi$
$373$	17.4128	+	12.6511i	0.901601	+	0.655051i	−0.0372760	+	0.999305i	$0.511868\pi$
$374$	−21.0531	−	64.7948i	−1.08863	−	3.35046i
$375$		0			0
$376$	−66.0020	+	47.9532i	−3.40379	+	2.47300i
$377$	−6.14646	+	4.46566i	−0.316559	+	0.229993i
$378$		0			0
$379$	4.98647	−	15.3468i	0.256138	−	0.788311i	−0.737465	−	0.675385i	$-0.763978\pi$
$379$	4.98647	−	15.3468i	0.256138	−	0.788311i	0.993603	−	0.112926i	$-0.0360225\pi$
$380$	4.43889	+	13.6615i	0.227710	+	0.700820i
$381$		0			0
$382$	16.0480	+	11.6596i	0.821088	+	0.596555i
$383$	6.31683	+	4.58944i	0.322775	+	0.234510i	0.737359	−	0.675502i	$-0.236073\pi$
$383$	6.31683	+	4.58944i	0.322775	+	0.234510i	−0.414584	+	0.910011i	$0.636073\pi$
$384$		0			0
$385$	34.8769			1.77749
$386$	−1.06292	−	3.27134i	−0.0541014	−	0.166507i
$387$		0			0
$388$	21.1737	−	15.3836i	1.07493	−	0.780983i
$389$	−26.8665			−1.36218			−0.681092	−	0.732198i	$-0.738494\pi$
$389$	−26.8665			−1.36218			−0.681092	+	0.732198i	$0.738494\pi$
$390$		0			0
$391$	−1.18321	+	3.64155i	−0.0598375	+	0.184161i
$392$	−34.5636			−1.74572
$393$		0			0
$394$	5.81810			0.293112
$395$	9.84292	+	30.2934i	0.495251	+	1.52423i
$396$		0			0
$397$	−3.46099	−	2.51456i	−0.173702	−	0.126202i	0.497537	−	0.867443i	$-0.334238\pi$
$397$	−3.46099	−	2.51456i	−0.173702	−	0.126202i	−0.671239	+	0.741241i	$0.734238\pi$
$398$	23.2600	+	16.8993i	1.16592	+	0.847088i
$399$		0			0
$400$	−1.93015			−0.0965074
$401$	9.00045	+	27.7005i	0.449461	+	1.38330i	0.877517	+	0.479546i	$0.159199\pi$
$401$	9.00045	+	27.7005i	0.449461	+	1.38330i	−0.428056	+	0.903752i	$0.640801\pi$
$402$		0			0
$403$	26.9483			1.34239
$404$	9.68502	−	7.03658i	0.481848	−	0.350083i
$405$		0			0
$406$	20.4434			1.01459
$407$	7.35215	+	22.6276i	0.364433	+	1.12161i
$408$		0			0
$409$	−6.59198	+	20.2880i	−0.325952	+	1.00318i	0.645057	+	0.764135i	$0.276834\pi$
$409$	−6.59198	+	20.2880i	−0.325952	+	1.00318i	−0.971009	+	0.239043i	$0.923166\pi$
$410$	−15.8738	+	48.8546i	−0.783952	+	2.41276i
$411$		0			0
$412$	−4.69283	+	3.40954i	−0.231199	+	0.167976i
$413$	−3.88167	+	11.9465i	−0.191004	+	0.587851i
$414$		0			0
$415$	−0.799290	−	2.45996i	−0.0392356	−	0.120755i
$416$	−4.80385	+	14.7847i	−0.235528	+	0.724881i
$417$		0			0
$418$	−13.8784	−	10.0833i	−0.678816	−	0.493188i
$419$	1.50635	+	4.63607i	0.0735900	+	0.226487i	0.981085	−	0.193575i	$-0.0620083\pi$
$419$	1.50635	+	4.63607i	0.0735900	+	0.226487i	−0.907495	+	0.420062i	$0.862008\pi$
$420$		0			0
$421$	−9.26713	−	6.73296i	−0.451652	−	0.328145i	0.338596	−	0.940932i	$-0.390048\pi$
$421$	−9.26713	−	6.73296i	−0.451652	−	0.328145i	−0.790248	+	0.612787i	$0.790048\pi$
$422$	16.0843	−	11.6859i	0.782972	−	0.568862i
$423$		0			0
$424$	−18.3501	−	56.4759i	−0.891161	−	2.74271i
$425$	1.72439			0.0836452
$426$		0			0
$427$	−50.3521			−2.43671
$428$	−7.26810	−	22.3689i	−0.351317	−	1.08124i
$429$		0			0
$430$	−24.1481	+	17.5446i	−1.16452	+	0.846076i
$431$	−7.48437	−	5.43771i	−0.360509	−	0.261925i	0.392755	−	0.919643i	$-0.371522\pi$
$431$	−7.48437	−	5.43771i	−0.360509	−	0.261925i	−0.753264	+	0.657718i	$0.771522\pi$
$432$		0			0
$433$	1.53452	+	4.72276i	0.0737443	+	0.226962i	0.981134	−	0.193329i	$-0.0619283\pi$
$433$	1.53452	+	4.72276i	0.0737443	+	0.226962i	−0.907390	+	0.420290i	$0.861928\pi$
$434$	−58.6645	−	42.6222i	−2.81598	−	2.04593i
$435$		0			0
$436$	−9.23655	+	28.4272i	−0.442351	+	1.36142i
$437$	0.297927	+	0.916926i	0.0142518	+	0.0438625i
$438$		0			0
$439$	−4.30073	+	13.2363i	−0.205263	+	0.631734i	0.794440	+	0.607343i	$0.207765\pi$
$439$	−4.30073	+	13.2363i	−0.205263	+	0.631734i	−0.999703	+	0.0243907i	$0.992235\pi$
$440$	−48.5301	+	35.2592i	−2.31358	+	1.68092i
$441$		0			0
$442$	15.5998	−	48.0112i	0.742006	−	2.28366i
$443$	−3.50747	+	10.7949i	−0.166645	+	0.512880i	−0.999154	−	0.0411314i	$-0.986904\pi$
$443$	−3.50747	+	10.7949i	−0.166645	+	0.512880i	0.832509	+	0.554012i	$0.186904\pi$
$444$		0			0
$445$	−8.93685	−	27.5048i	−0.423647	−	1.30385i
$446$	24.1460			1.14335
$447$		0			0
$448$	−4.50730	+	3.27474i	−0.212950	+	0.154717i
$449$	−21.0714			−0.994420			−0.497210	−	0.867630i	$-0.665642\pi$
$449$	−21.0714			−0.994420			−0.497210	+	0.867630i	$0.665642\pi$
$450$		0			0
$451$	−13.0471	−	40.1547i	−0.614362	−	1.89081i
$452$	−2.78831			−0.131151
$453$		0			0
$454$	5.04978	+	3.66888i	0.236998	+	0.172189i
$455$	20.9073	+	15.1900i	0.980147	+	0.712119i
$456$		0			0
$457$	−2.20912	−	6.79899i	−0.103338	−	0.318043i	0.885998	−	0.463688i	$-0.153474\pi$
$457$	−2.20912	−	6.79899i	−0.103338	−	0.318043i	−0.989337	+	0.145645i	$0.953474\pi$
$458$	45.4403			2.12329
$459$		0			0
$460$	6.16304			0.287353
$461$	7.66833	−	23.6007i	0.357150	−	1.09919i	−0.597603	−	0.801792i	$-0.703880\pi$
$461$	7.66833	−	23.6007i	0.357150	−	1.09919i	0.954752	−	0.297402i	$-0.0961200\pi$
$462$		0			0
$463$	−8.64890			−0.401948			−0.200974	−	0.979597i	$-0.564411\pi$
$463$	−8.64890			−0.401948			−0.200974	+	0.979597i	$0.564411\pi$
$464$	−12.2343	+	8.88872i	−0.567962	+	0.412648i
$465$		0			0
$466$	−6.51108	−	20.0391i	−0.301620	−	0.928291i
$467$	−18.1959			−0.842007			−0.421003	−	0.907059i	$-0.638322\pi$
$467$	−18.1959			−0.842007			−0.421003	+	0.907059i	$0.638322\pi$
$468$		0			0
$469$	27.7873	+	20.1886i	1.28310	+	0.932225i
$470$	−59.3097	−	43.0910i	−2.73575	−	1.98764i
$471$		0			0
$472$	−6.67629	−	20.5475i	−0.307301	−	0.945775i
$473$	7.58121	−	23.3326i	0.348584	−	1.07283i
$474$		0			0
$475$	0.351270	−	0.255213i	0.0161174	−	0.0117100i
$476$	−75.6348	+	54.9519i	−3.46671	+	2.51872i
$477$		0			0
$478$	2.78964	+	8.58564i	0.127595	+	0.392698i
$479$	−7.57306	−	5.50215i	−0.346022	−	0.251400i	0.401176	−	0.916001i	$-0.368601\pi$
$479$	−7.57306	−	5.50215i	−0.346022	−	0.251400i	−0.747198	+	0.664601i	$0.768601\pi$
$480$		0			0
$481$	−5.44774	+	16.7664i	−0.248396	+	0.764483i
$482$	5.62695	−	17.3180i	0.256301	−	0.788812i
$483$		0			0
$484$	12.8442	−	39.5305i	0.583830	−	1.79684i
$485$	10.4081	+	7.56191i	0.472606	+	0.343369i
$486$		0			0
$487$	8.04898	−	24.7722i	0.364734	−	1.12254i	−0.585413	−	0.810735i	$-0.699068\pi$
$487$	8.04898	−	24.7722i	0.364734	−	1.12254i	0.950147	−	0.311801i	$-0.100932\pi$
$488$	70.0635	−	50.9041i	3.17162	−	2.30432i
$489$		0			0
$490$	−9.59777	−	29.5389i	−0.433583	−	1.33443i
$491$	3.04866	−	2.21498i	0.137584	−	0.0999606i	−0.516864	−	0.856067i	$-0.672901\pi$
$491$	3.04866	−	2.21498i	0.137584	−	0.0999606i	0.654448	+	0.756107i	$0.272901\pi$
$492$		0			0
$493$	10.9301	−	7.94117i	0.492266	−	0.357652i
$494$	−3.92796	−	12.0890i	−0.176727	−	0.543910i
$495$		0			0
$496$	53.6394			2.40848
$497$	−28.7841	+	8.34471i	−1.29114	+	0.374311i
$498$		0			0
$499$	−11.0808	−	34.1032i	−0.496046	−	1.52667i	−0.815321	−	0.579009i	$-0.803440\pi$
$499$	−11.0808	−	34.1032i	−0.496046	−	1.52667i	0.319276	−	0.947662i	$-0.396560\pi$
$500$	−15.6635	−	48.2073i	−0.700493	−	2.15589i
$501$		0			0
$502$	−25.3227	−	18.3980i	−1.13021	−	0.821142i
$503$	−33.0790	+	24.0333i	−1.47492	+	1.07159i	−0.495767	+	0.868455i	$0.665113\pi$
$503$	−33.0790	+	24.0333i	−1.47492	+	1.07159i	−0.979151	+	0.203135i	$0.934887\pi$
$504$		0			0
$505$	4.76074	+	3.45888i	0.211850	+	0.153918i
$506$	−5.95447	+	4.32617i	−0.264708	+	0.192322i
$507$		0			0
$508$	14.1864	+	43.6613i	0.629420	+	1.93716i
$509$	11.2844	+	8.19860i	0.500173	+	0.363397i	0.809083	−	0.587695i	$-0.199964\pi$
$509$	11.2844	+	8.19860i	0.500173	+	0.363397i	−0.308910	+	0.951091i	$0.599964\pi$
$510$		0			0
$511$	−13.4261	+	9.75462i	−0.593935	+	0.431519i
$512$	15.6320	−	48.1103i	0.690843	−	2.12620i
$513$		0			0
$514$	−21.2580	+	65.4253i	−0.937649	+	2.88579i
$515$	−2.30679	−	1.67598i	−0.101649	−	0.0738527i
$516$		0			0
$517$	60.2559			2.65005
$518$	38.3777	−	27.8830i	1.68622	−	1.22511i
$519$		0			0
$520$	−44.4484			−1.94919
$521$	−4.07494	+	12.5414i	−0.178526	+	0.549447i	−0.999777	−	0.0211202i	$-0.993277\pi$
$521$	−4.07494	+	12.5414i	−0.178526	+	0.549447i	0.821251	+	0.570568i	$0.193277\pi$
$522$		0			0
$523$	2.13668			0.0934304			0.0467152	−	0.998908i	$-0.485125\pi$
$523$	2.13668			0.0934304			0.0467152	+	0.998908i	$0.485125\pi$
$524$	52.3097	+	38.0052i	2.28516	+	1.66027i
$525$		0			0
$526$	−29.4540	−	21.3996i	−1.28425	−	0.933065i
$527$	−47.9213			−2.08749
$528$		0			0
$529$	−22.5864			−0.982015
$530$	43.1702	−	31.3650i	1.87519	−	1.36241i
$531$		0			0
$532$	−7.27435	+	22.3882i	−0.315383	+	0.970650i
$533$	9.66752	−	29.7536i	0.418747	−	1.28877i
$534$		0			0
$535$	9.35341	−	6.79565i	0.404383	−	0.293802i
$536$	−59.0752			−2.55166
$537$		0			0
$538$	−34.4340			−1.48455
$539$	20.6527	+	15.0051i	0.889575	+	0.646314i
$540$		0			0
$541$	25.0862	+	18.2262i	1.07854	+	0.783605i	0.977428	−	0.211270i	$-0.0677600\pi$
$541$	25.0862	+	18.2262i	1.07854	+	0.783605i	0.101112	+	0.994875i	$0.467760\pi$
$542$	−72.0736			−3.09583
$543$		0			0
$544$	8.54256	−	26.2913i	0.366259	−	1.12723i
$545$	−14.6927			−0.629366
$546$		0			0
$547$	−28.5199	+	20.7209i	−1.21942	+	0.885962i	−0.996052	−	0.0887723i	$-0.971706\pi$
$547$	−28.5199	+	20.7209i	−1.21942	+	0.885962i	−0.223369	+	0.974734i	$0.571706\pi$
$548$	−7.86955			−0.336170
$549$		0			0
$550$	2.68163	+	1.94832i	0.114345	+	0.0830766i
$551$	1.05123	−	3.23534i	0.0447838	−	0.137830i
$552$		0			0
$553$	−16.1304	+	49.6441i	−0.685933	+	2.11108i
$554$	−21.0409	+	15.2871i	−0.893944	+	0.649488i
$555$		0			0
$556$	34.0695	+	24.7529i	1.44487	+	1.04976i
$557$	−1.78186	−	5.48400i	−0.0754998	−	0.232365i	0.906183	−	0.422885i	$-0.138983\pi$
$557$	−1.78186	−	5.48400i	−0.0754998	−	0.232365i	−0.981683	+	0.190520i	$0.938983\pi$
$558$		0			0
$559$	14.7067	−	10.6851i	0.622028	−	0.451930i
$560$	41.6150	+	30.2351i	1.75856	+	1.27767i
$561$		0			0
$562$	38.5057	−	27.9760i	1.62427	−	1.18010i
$563$	3.83831	+	2.78870i	0.161766	+	0.117530i	0.665723	−	0.746199i	$-0.268123\pi$
$563$	3.83831	+	2.78870i	0.161766	+	0.117530i	−0.503958	+	0.863728i	$0.668123\pi$
$564$		0			0
$565$	−0.423542	−	1.30353i	−0.0178186	−	0.0548399i
$566$	10.9362	+	33.6580i	0.459681	+	1.41475i
$567$		0			0
$568$	31.6160	−	40.7110i	1.32658	−	1.70820i
$569$	−17.4633			−0.732099			−0.366050	−	0.930595i	$-0.619290\pi$
$569$	−17.4633			−0.732099			−0.366050	+	0.930595i	$0.619290\pi$
$570$		0			0
$571$	12.4957	+	38.4577i	0.522927	+	1.60940i	0.768379	+	0.639995i	$0.221064\pi$
$571$	12.4957	+	38.4577i	0.522927	+	1.60940i	−0.245452	+	0.969409i	$0.578936\pi$
$572$	54.0307	−	39.2556i	2.25914	−	1.64136i
$573$		0			0
$574$	−68.1047	+	49.4810i	−2.84263	+	2.06530i
$575$	−0.0575664	−	0.177171i	−0.00240068	−	0.00738855i
$576$		0			0
$577$	15.1024	−	10.9725i	0.628720	−	0.456792i	−0.227236	−	0.973840i	$-0.572969\pi$
$577$	15.1024	−	10.9725i	0.628720	−	0.456792i	0.855957	+	0.517048i	$0.172969\pi$
$578$	−14.4350	+	44.4263i	−0.600416	+	1.84789i
$579$		0			0
$580$	−17.5929	−	12.7820i	−0.730507	−	0.530745i
$581$	1.30986	−	4.03133i	0.0543421	−	0.167248i
$582$		0			0
$583$	−13.5531	+	41.7123i	−0.561313	+	1.72755i
$584$	8.82045	−	27.1466i	0.364993	−	1.12333i
$585$		0			0
$586$	−10.8719	−	7.89891i	−0.449115	−	0.326301i
$587$	5.90314	+	18.1680i	0.243648	+	0.749873i	0.995856	+	0.0909464i	$0.0289892\pi$
$587$	5.90314	+	18.1680i	0.243648	+	0.749873i	−0.752207	+	0.658926i	$0.771011\pi$
$588$		0			0
$589$	−9.76191	+	7.09244i	−0.402233	+	0.292239i
$590$	15.7065	−	11.4114i	0.646627	−	0.469802i
$591$		0			0
$592$	−10.8435	+	33.3729i	−0.445665	+	1.37162i
$593$	−1.87301	−	5.76454i	−0.0769154	−	0.236721i	0.905205	−	0.424975i	$-0.139717\pi$
$593$	−1.87301	−	5.76454i	−0.0769154	−	0.236721i	−0.982120	+	0.188254i	$0.939717\pi$
$594$		0			0
$595$	−37.1788	−	27.0120i	−1.52418	−	1.10738i
$596$	18.1009	+	13.1510i	0.741440	+	0.538688i
$597$		0			0
$598$	−5.45365			−0.223016
$599$	5.15395	+	15.8622i	0.210585	+	0.648113i	0.999438	+	0.0335311i	$0.0106753\pi$
$599$	5.15395	+	15.8622i	0.210585	+	0.648113i	−0.788853	+	0.614582i	$0.789325\pi$
$600$		0			0
$601$	27.3150	−	19.8455i	1.11420	−	0.809516i	0.130883	−	0.991398i	$-0.458219\pi$
$601$	27.3150	−	19.8455i	1.11420	−	0.809516i	0.983320	+	0.181881i	$0.0582187\pi$
$602$	−48.9153			−1.99364
$603$		0			0
$604$	26.8887	−	82.7550i	1.09409	−	3.36725i
$605$	20.4315			0.830659
$606$		0			0
$607$	30.7668			1.24878			0.624392	−	0.781111i	$-0.285347\pi$
$607$	30.7668			1.24878			0.624392	+	0.781111i	$0.285347\pi$
$608$	−2.15098	−	6.62003i	−0.0872337	−	0.268478i
$609$		0			0
$610$	62.9594	+	45.7427i	2.54915	+	1.85207i
$611$	36.1210	+	26.2434i	1.46130	+	1.06170i
$612$		0			0
$613$	−17.7891			−0.718495			−0.359248	−	0.933242i	$-0.616967\pi$
$613$	−17.7891			−0.718495			−0.359248	+	0.933242i	$0.616967\pi$
$614$	19.5522	+	60.1754i	0.789061	+	2.42848i
$615$		0			0
$616$	−98.3047			−3.96081
$617$	−5.60055	+	4.06904i	−0.225470	+	0.163813i	−0.694785	−	0.719217i	$-0.744501\pi$
$617$	−5.60055	+	4.06904i	−0.225470	+	0.163813i	0.469316	+	0.883030i	$0.344501\pi$
$618$		0			0
$619$	−1.30608			−0.0524959			−0.0262480	−	0.999655i	$-0.508356\pi$
$619$	−1.30608			−0.0524959			−0.0262480	+	0.999655i	$0.508356\pi$
$620$	23.8356	+	73.3585i	0.957262	+	2.94615i
$621$		0			0
$622$	−20.1594	+	62.0442i	−0.808317	+	2.48775i
$623$	14.6455	−	45.0742i	0.586760	−	1.80586i
$624$		0			0
$625$	18.9859	−	13.7941i	0.759436	−	0.551763i
$626$	3.32581	−	10.2358i	0.132926	−	0.409105i
$627$		0			0
$628$	−15.6141	−	48.0554i	−0.623072	−	1.91762i
$629$	9.68757	−	29.8153i	0.386269	−	1.18881i
$630$		0			0
$631$	19.0994	+	13.8765i	0.760334	+	0.552415i	0.899013	−	0.437922i	$-0.144285\pi$
$631$	19.0994	+	13.8765i	0.760334	+	0.552415i	−0.138679	+	0.990337i	$0.544285\pi$
$632$	−27.7435	−	85.3856i	−1.10358	−	3.39646i
$633$		0			0
$634$	−57.5508	−	41.8131i	−2.28563	−	1.66061i
$635$	−18.2567	+	13.2643i	−0.724494	+	0.526376i
$636$		0			0
$637$	5.84526	+	17.9899i	0.231598	+	0.712784i
$638$	25.9700			1.02816
$639$		0			0
$640$	28.7665			1.13710
$641$	−10.1859	−	31.3490i	−0.402320	−	1.23821i	−0.923113	−	0.384530i	$-0.874364\pi$
$641$	−10.1859	−	31.3490i	−0.402320	−	1.23821i	0.520793	−	0.853683i	$-0.325636\pi$
$642$		0			0
$643$	12.2578	−	8.90584i	0.483402	−	0.351212i	−0.319240	−	0.947674i	$-0.603427\pi$
$643$	12.2578	−	8.90584i	0.483402	−	0.351212i	0.802641	+	0.596462i	$0.203427\pi$
$644$	8.17095	+	5.93654i	0.321980	+	0.233933i
$645$		0			0
$646$	6.98498	+	21.4976i	0.274820	+	0.845810i
$647$	−23.5428	−	17.1048i	−0.925563	−	0.672461i	0.0193396	−	0.999813i	$-0.493844\pi$
$647$	−23.5428	−	17.1048i	−0.925563	−	0.672461i	−0.944902	+	0.327352i	$0.893844\pi$
$648$		0			0
$649$	−4.93101	+	15.1761i	−0.193559	+	0.595713i
$650$	0.758972	+	2.33587i	0.0297693	+	0.0916205i
$651$		0			0
$652$	25.5062	−	78.5000i	0.998899	−	3.07430i
$653$	31.2994	−	22.7404i	1.22484	−	0.889899i	0.228348	−	0.973579i	$-0.426667\pi$
$653$	31.2994	−	22.7404i	1.22484	−	0.889899i	0.996493	+	0.0836804i	$0.0266675\pi$
$654$		0			0
$655$	−9.82157	+	30.2277i	−0.383760	+	1.18109i
$656$	19.2428	−	59.2232i	0.751305	−	2.31228i
$657$		0			0
$658$	−37.1254	−	114.260i	−1.44730	−	4.45432i
$659$	30.8004			1.19981			0.599907	−	0.800070i	$-0.295204\pi$
$659$	30.8004			1.19981			0.599907	+	0.800070i	$0.295204\pi$
$660$		0			0
$661$	16.0583	−	11.6670i	0.624595	−	0.453795i	−0.229929	−	0.973208i	$-0.573849\pi$
$661$	16.0583	−	11.6670i	0.624595	−	0.453795i	0.854523	+	0.519413i	$0.173849\pi$
$662$	−18.0993			−0.703449
$663$		0			0
$664$	2.25289	+	6.93370i	0.0874293	+	0.269080i
$665$	−11.5714			−0.448720
$666$		0			0
$667$	−1.18079	−	0.857898i	−0.0457206	−	0.0332179i
$668$	56.3983	+	40.9757i	2.18211	+	1.58540i
$669$		0			0
$670$	−16.4043	−	50.4871i	−0.633752	−	1.95049i
$671$	−63.9639			−2.46930
$672$		0			0
$673$	−16.2733			−0.627291			−0.313645	−	0.949540i	$-0.601550\pi$
$673$	−16.2733			−0.627291			−0.313645	+	0.949540i	$0.601550\pi$
$674$	−10.2672	+	31.5991i	−0.395476	+	1.21715i
$675$		0			0
$676$	−7.91165			−0.304294
$677$	−1.06916	+	0.776794i	−0.0410913	+	0.0298546i	−0.608141	−	0.793829i	$-0.708085\pi$
$677$	−1.06916	+	0.776794i	−0.0410913	+	0.0298546i	0.567050	+	0.823683i	$0.308085\pi$
$678$		0			0
$679$	6.51501	+	20.0511i	0.250023	+	0.769492i
$680$	79.0413			3.03110
$681$		0			0
$682$	−74.5233	−	54.1444i	−2.85365	−	2.07329i
$683$	11.2204	+	8.15206i	0.429335	+	0.311930i	0.781383	−	0.624052i	$-0.214515\pi$
$683$	11.2204	+	8.15206i	0.429335	+	0.311930i	−0.352048	+	0.935982i	$0.614515\pi$
$684$		0			0
$685$	−1.19538	−	3.67900i	−0.0456731	−	0.140567i
$686$	−3.75786	+	11.5655i	−0.143476	+	0.441573i
$687$		0			0
$688$	29.2731	−	21.2682i	1.11603	−	0.810841i
$689$	−26.2916	+	19.1020i	−1.00163	+	0.727727i
$690$		0			0
$691$	4.38779	+	13.5042i	0.166919	+	0.513725i	0.999173	−	0.0406707i	$-0.0129495\pi$
$691$	4.38779	+	13.5042i	0.166919	+	0.513725i	−0.832253	+	0.554396i	$0.812949\pi$
$692$	48.3073	+	35.0973i	1.83637	+	1.33420i
$693$		0			0
$694$	0.343069	−	1.05586i	0.0130227	−	0.0400798i
$695$	−6.39682	+	19.6874i	−0.242645	+	0.746785i
$696$		0			0
$697$	−17.1915	+	52.9099i	−0.651174	+	2.00411i
$698$	−55.6151	−	40.4068i	−2.10506	−	1.52942i
$699$		0			0
$700$	1.40557	−	4.32591i	0.0531256	−	0.163504i
$701$	0.143056	−	0.103936i	0.00540315	−	0.00392562i	−0.585080	−	0.810975i	$-0.698937\pi$
$701$	0.143056	−	0.103936i	0.00540315	−	0.00392562i	0.590484	+	0.807050i	$0.298937\pi$
$702$		0			0
$703$	−2.43929	−	7.50735i	−0.0919995	−	0.283145i
$704$	−5.72576	+	4.16001i	−0.215798	+	0.156786i
$705$		0			0
$706$	−29.2107	+	21.2228i	−1.09936	+	0.798732i
$707$	2.98002	+	9.17156i	0.112075	+	0.344932i
$708$		0			0
$709$	−15.7997			−0.593369			−0.296684	−	0.954976i	$-0.595881\pi$
$709$	−15.7997			−0.593369			−0.296684	+	0.954976i	$0.595881\pi$
$710$	43.5719	+	15.7150i	1.63523	+	0.589773i
$711$		0			0
$712$	25.1896	+	77.5256i	0.944019	+	2.90539i
$713$	1.59979	+	4.92364i	0.0599125	+	0.184392i
$714$		0			0
$715$	26.5591	+	19.2964i	0.993256	+	0.721643i
$716$	−21.2246	+	15.4206i	−0.793201	+	0.576294i
$717$		0			0
$718$	16.5053	+	11.9918i	0.615974	+	0.447531i
$719$	6.93601	−	5.03931i	0.258670	−	0.187934i	−0.450891	−	0.892579i	$-0.648894\pi$
$719$	6.93601	−	5.03931i	0.258670	−	0.187934i	0.709560	+	0.704645i	$0.248894\pi$
$720$		0			0
$721$	−1.44396	−	4.44404i	−0.0537757	−	0.165505i
$722$	−34.3284	−	24.9410i	−1.27757	−	0.928209i
$723$		0			0
$724$	−7.61541	+	5.53292i	−0.283025	+	0.205629i
$725$	−0.203121	+	0.625143i	−0.00754373	+	0.0232172i
$726$		0			0
$727$	3.64613	−	11.2216i	0.135227	−	0.416187i	−0.860398	−	0.509623i	$-0.829785\pi$
$727$	3.64613	−	11.2216i	0.135227	−	0.416187i	0.995625	+	0.0934355i	$0.0297849\pi$
$728$	−58.9296	−	42.8149i	−2.18408	−	1.58683i
$729$		0			0
$730$	25.6494			0.949328
$731$	−26.1526	+	19.0009i	−0.967287	+	0.702775i
$732$		0			0
$733$	49.0297			1.81095			0.905477	−	0.424394i	$-0.139513\pi$
$733$	49.0297			1.81095			0.905477	+	0.424394i	$0.139513\pi$
$734$	11.1697	−	34.3767i	0.412280	−	1.26887i
$735$		0			0
$736$	−2.98646			−0.110082
$737$	35.2991	+	25.6463i	1.30026	+	0.944693i
$738$		0			0
$739$	42.2553	+	30.7002i	1.55439	+	1.12933i	0.940431	+	0.339985i	$0.110422\pi$
$739$	42.2553	+	30.7002i	1.55439	+	1.12933i	0.613954	+	0.789342i	$0.289578\pi$
$740$	−50.4600			−1.85495
$741$		0			0
$742$	87.4473			3.21029
$743$	−10.0859	+	7.32784i	−0.370016	+	0.268833i	−0.757218	−	0.653163i	$-0.773442\pi$
$743$	−10.0859	+	7.32784i	−0.370016	+	0.268833i	0.387201	+	0.921995i	$0.373442\pi$
$744$		0			0
$745$	−3.39858	+	10.4598i	−0.124514	+	0.383216i
$746$	16.8461	−	51.8469i	0.616779	−	1.89825i
$747$		0			0
$748$	−96.0812	+	69.8071i	−3.51308	+	2.55240i
$749$	18.9467			0.692296
$750$		0			0
$751$	20.7916			0.758696			0.379348	−	0.925254i	$-0.376148\pi$
$751$	20.7916			0.758696			0.379348	+	0.925254i	$0.376148\pi$
$752$	71.8973	+	52.2364i	2.62182	+	1.90487i
$753$		0			0
$754$	15.5679	+	11.3108i	0.566951	+	0.411914i
$755$	42.7722			1.55664
$756$		0			0
$757$	14.2535	−	43.8678i	0.518052	−	1.59440i	−0.259606	−	0.965715i	$-0.583593\pi$
$757$	14.2535	−	43.8678i	0.518052	−	1.59440i	0.777659	−	0.628687i	$-0.216407\pi$
$758$	−40.8712			−1.48451
$759$		0			0
$760$	16.1013	−	11.6983i	0.584054	−	0.424340i
$761$	47.4504			1.72008			0.860038	−	0.510230i	$-0.170440\pi$
$761$	47.4504			1.72008			0.860038	+	0.510230i	$0.170440\pi$
$762$		0			0
$763$	−19.4796	−	14.1527i	−0.705208	−	0.512363i
$764$	10.6855	−	32.8865i	0.386586	−	1.18979i
$765$		0			0
$766$	6.11124	−	18.8085i	0.220808	−	0.679578i
$767$	−9.56562	+	6.94983i	−0.345394	+	0.250944i
$768$		0			0
$769$	−14.7327	−	10.7040i	−0.531276	−	0.385995i	0.289559	−	0.957160i	$-0.406491\pi$
$769$	−14.7327	−	10.7040i	−0.531276	−	0.385995i	−0.820835	+	0.571166i	$0.806491\pi$
$770$	−27.2977	−	84.0136i	−0.983740	−	3.02764i
$771$		0			0
$772$	−4.85092	+	3.52440i	−0.174589	+	0.126846i
$773$	0.606297	+	0.440501i	0.0218070	+	0.0158437i	0.598635	−	0.801022i	$-0.295710\pi$
$773$	0.606297	+	0.440501i	0.0218070	+	0.0158437i	−0.576828	+	0.816865i	$0.695710\pi$
$774$		0			0
$775$	1.88623	−	1.37042i	0.0677552	−	0.0492271i
$776$	−29.3364	−	21.3142i	−1.05312	−	0.765134i
$777$		0			0
$778$	21.0280	+	64.7176i	0.753891	+	2.32024i
$779$	4.32874	+	13.3225i	0.155093	+	0.477328i
$780$		0			0
$781$	−36.5653	+	10.6006i	−1.30841	+	0.379318i
$782$	9.69807			0.346802
$783$		0			0
$784$	11.6347	+	35.8081i	0.415526	+	1.27886i
$785$	20.0941	−	14.5992i	0.717187	−	0.521067i
$786$		0			0
$787$	−1.07018	+	0.777532i	−0.0381478	+	0.0277160i	−0.606696	−	0.794934i	$-0.707505\pi$
$787$	−1.07018	+	0.777532i	−0.0381478	+	0.0277160i	0.568548	+	0.822650i	$0.307505\pi$
$788$	−3.13408	−	9.64572i	−0.111647	−	0.343615i
$789$		0			0
$790$	65.2687	−	47.4205i	2.32216	−	1.68715i
$791$	0.694092	−	2.13620i	0.0246791	−	0.0759544i
$792$		0			0
$793$	−38.3437	−	27.8583i	−1.36163	−	0.989279i
$794$	−3.34835	+	10.3052i	−0.118829	+	0.365717i
$795$		0			0
$796$	15.4875	−	47.6655i	0.548939	−	1.68946i
$797$	0.426355	−	1.31219i	0.0151023	−	0.0464800i	−0.943221	−	0.332165i	$-0.892221\pi$
$797$	0.426355	−	1.31219i	0.0151023	−	0.0464800i	0.958324	+	0.285685i	$0.0922210\pi$
$798$		0			0
$799$	−64.2329	−	46.6680i	−2.27240	−	1.65099i
$800$	0.415619	+	1.27914i	0.0146943	+	0.0452245i
$801$		0			0
$802$	59.6823	−	43.3617i	2.10745	−	1.53115i
$803$	−17.0556	+	12.3916i	−0.601878	+	0.437290i
$804$		0			0
$805$	−1.53416	+	4.72166i	−0.0540721	+	0.166417i
$806$	−21.0921	−	64.9147i	−0.742936	−	2.28652i
$807$		0			0
$808$	−13.4187	−	9.74927i	−0.472069	−	0.342978i
$809$	−42.5525	−	30.9162i	−1.49607	−	1.08696i	−0.971915	−	0.235332i	$-0.924382\pi$
$809$	−42.5525	−	30.9162i	−1.49607	−	1.08696i	−0.524152	−	0.851625i	$-0.675618\pi$
$810$		0			0
$811$	−49.5489			−1.73990			−0.869949	−	0.493142i	$-0.835848\pi$
$811$	−49.5489			−1.73990			−0.869949	+	0.493142i	$0.835848\pi$
$812$	−11.0124	−	33.8928i	−0.386461	−	1.18940i
$813$		0			0
$814$	48.7524	−	35.4207i	1.70877	−	1.24149i
$815$	40.5730			1.42121
$816$		0			0
$817$	−2.51528	+	7.74125i	−0.0879986	+	0.270832i
$818$	54.0305			1.88913
$819$		0			0
$820$	89.5460			3.12708
$821$	−5.07301	−	15.6131i	−0.177049	−	0.544902i	0.822672	−	0.568516i	$-0.192482\pi$
$821$	−5.07301	−	15.6131i	−0.177049	−	0.544902i	−0.999721	+	0.0236149i	$0.992482\pi$
$822$		0			0
$823$	−16.5635	−	12.0341i	−0.577368	−	0.419483i	0.260406	−	0.965499i	$-0.416144\pi$
$823$	−16.5635	−	12.0341i	−0.577368	−	0.419483i	−0.837774	+	0.546017i	$0.816144\pi$
$824$	6.50198	+	4.72396i	0.226507	+	0.164567i
$825$		0			0
$826$	31.8157			1.10701
$827$	−1.53651	−	4.72890i	−0.0534298	−	0.164440i	0.920781	−	0.390080i	$-0.127553\pi$
$827$	−1.53651	−	4.72890i	−0.0534298	−	0.164440i	−0.974211	+	0.225640i	$0.927553\pi$
$828$		0			0
$829$	13.2021			0.458529			0.229265	−	0.973364i	$-0.426368\pi$
$829$	13.2021			0.458529			0.229265	+	0.973364i	$0.426368\pi$
$830$	−5.30012	+	3.85076i	−0.183970	+	0.133662i
$831$		0			0
$832$	−5.24418			−0.181809
$833$	−10.3945	−	31.9909i	−0.360147	−	1.10842i
$834$		0			0
$835$	−10.5892	+	32.5903i	−0.366455	+	1.12783i
$836$	−9.24084	+	28.4404i	−0.319601	+	0.983631i
$837$		0			0
$838$	9.98866	−	7.25718i	0.345052	−	0.250695i
$839$	8.75637	−	26.9493i	0.302303	−	0.930394i	−0.678366	−	0.734724i	$-0.737312\pi$
$839$	8.75637	−	26.9493i	0.302303	−	0.930394i	0.980670	−	0.195670i	$-0.0626882\pi$
$840$		0			0
$841$	−7.37007	−	22.6827i	−0.254140	−	0.782164i
$842$	−8.96553	+	27.5931i	−0.308972	+	0.950920i
$843$		0			0
$844$	−28.0381	−	20.3709i	−0.965112	−	0.701195i
$845$	−1.20178	−	3.69869i	−0.0413423	−	0.127239i
$846$		0			0
$847$	27.0881	+	19.6806i	0.930757	+	0.676235i
$848$	−52.3323	+	38.0217i	−1.79710	+	1.30567i
$849$		0			0
$850$	−1.34966	−	4.15382i	−0.0462929	−	0.142475i
$851$	−3.38675			−0.116096
$852$		0			0
$853$	28.0372			0.959974			0.479987	−	0.877276i	$-0.340641\pi$
$853$	28.0372			0.959974			0.479987	+	0.877276i	$0.340641\pi$
$854$	39.4099	+	121.291i	1.34858	+	4.15050i
$855$		0			0
$856$	−26.3637	+	19.1544i	−0.901094	+	0.654683i
$857$	33.7486	+	24.5198i	1.15283	+	0.837579i	0.988854	−	0.148886i	$-0.0475686\pi$
$857$	33.7486	+	24.5198i	1.15283	+	0.837579i	0.163974	+	0.986465i	$0.447569\pi$
$858$		0			0
$859$	−12.8870	−	39.6622i	−0.439700	−	1.35326i	−0.888193	−	0.459471i	$-0.848039\pi$
$859$	−12.8870	−	39.6622i	−0.439700	−	1.35326i	0.448493	−	0.893787i	$-0.351961\pi$
$860$	42.0949	+	30.5837i	1.43542	+	1.04290i
$861$		0			0
$862$	−7.24079	+	22.2848i	−0.246622	+	0.759025i
$863$	12.9385	+	39.8207i	0.440432	+	1.35551i	0.887416	+	0.460969i	$0.152498\pi$
$863$	12.9385	+	39.8207i	0.440432	+	1.35551i	−0.446984	+	0.894542i	$0.647502\pi$
$864$		0			0
$865$	−9.07009	+	27.9149i	−0.308392	+	0.949134i
$866$	10.1754	−	7.39290i	0.345776	−	0.251221i
$867$		0			0
$868$	−39.0613	+	120.218i	−1.32583	+	4.08047i
$869$	−20.4909	+	63.0645i	−0.695106	+	2.13932i
$870$		0			0
$871$	9.99057	+	30.7478i	0.338517	+	1.04185i
$872$	41.4131			1.40243
$873$		0			0
$874$	1.97557	−	1.43533i	0.0668245	−	0.0485508i
$875$	40.8320			1.38037
$876$		0			0
$877$	10.2143	+	31.4364i	0.344912	+	1.06153i	0.961631	+	0.274347i	$0.0884617\pi$
$877$	10.2143	+	31.4364i	0.344912	+	1.06153i	−0.616718	+	0.787184i	$0.711538\pi$
$878$	35.2505			1.18965
$879$		0			0
$880$	52.8649	+	38.4086i	1.78207	+	1.29475i
$881$	−7.39288	−	5.37124i	−0.249072	−	0.180962i	0.456243	−	0.889855i	$-0.349195\pi$
$881$	−7.39288	−	5.37124i	−0.249072	−	0.180962i	−0.705316	+	0.708893i	$0.749195\pi$
$882$		0			0
$883$	−16.1893	−	49.8257i	−0.544815	−	1.67677i	−0.721429	−	0.692488i	$-0.756515\pi$
$883$	−16.1893	−	49.8257i	−0.544815	−	1.67677i	0.176614	−	0.984280i	$-0.443485\pi$
$884$	−88.0001			−2.95976
$885$		0			0
$886$	28.7487			0.965830
$887$	2.07842	−	6.39671i	0.0697864	−	0.214780i	−0.910081	−	0.414431i	$-0.863981\pi$
$887$	2.07842	−	6.39671i	0.0697864	−	0.214780i	0.979867	+	0.199650i	$0.0639806\pi$
$888$		0			0
$889$	−36.9815			−1.24032
$890$	−59.2605	+	43.0553i	−1.98642	+	1.44322i
$891$		0			0
$892$	−13.0069	−	40.0312i	−0.435505	−	1.34035i
$893$	−19.9916			−0.668995
$894$		0			0
$895$	−10.4331	−	7.58010i	−0.348740	−	0.253375i
$896$	38.1386	+	27.7093i	1.27412	+	0.925704i
$897$		0			0
$898$	16.4923	+	50.7581i	0.550355	+	1.69382i
$899$	5.64480	−	17.3729i	0.188265	−	0.579419i
$900$		0			0
$901$	46.7536	−	33.9685i	1.55759	−	1.13165i
$902$	−86.5155	+	62.8572i	−2.88065	+	2.09292i
$903$		0			0
$904$	1.19381	+	3.67416i	0.0397054	+	0.122201i
$905$	−3.74341	−	2.71975i	−0.124435	−	0.0904074i
$906$		0			0
$907$	0.0779976	−	0.240052i	0.00258987	−	0.00797080i	−0.949753	−	0.313000i	$-0.898666\pi$
$907$	0.0779976	−	0.240052i	0.00258987	−	0.00797080i	0.952343	+	0.305029i	$0.0986661\pi$
$908$	3.36236	−	10.3483i	0.111584	−	0.343420i
$909$		0			0
$910$	20.2268	−	62.2518i	0.670513	−	2.06363i
$911$	−14.1115	−	10.2526i	−0.467534	−	0.339683i	0.328946	−	0.944349i	$-0.393307\pi$
$911$	−14.1115	−	10.2526i	−0.467534	−	0.339683i	−0.796479	+	0.604666i	$0.793307\pi$
$912$		0			0
$913$	1.66395	−	5.12112i	0.0550688	−	0.169484i
$914$	−14.6488	+	10.6430i	−0.484539	+	0.352038i
$915$		0			0
$916$	−24.4777	−	75.3346i	−0.808765	−	2.48912i
$917$	−42.1382	+	30.6152i	−1.39153	+	1.01100i
$918$		0			0
$919$	−6.74505	+	4.90057i	−0.222499	+	0.161655i	−0.693451	−	0.720504i	$-0.743911\pi$
$919$	−6.74505	+	4.90057i	−0.222499	+	0.161655i	0.470952	+	0.882159i	$0.343911\pi$
$920$	−2.63869	−	8.12104i	−0.0869949	−	0.267743i
$921$		0			0
$922$	−62.8528			−2.06995
$923$	−26.5363	−	9.57078i	−0.873453	−	0.315026i
$924$		0			0
$925$	0.471326	+	1.45059i	0.0154971	+	0.0476952i
$926$	6.76938	+	20.8340i	0.222456	+	0.684648i
$927$		0			0
$928$	8.52512	+	6.19386i	0.279851	+	0.203323i
$929$	23.7369	−	17.2459i	0.778782	−	0.565818i	−0.125831	−	0.992052i	$-0.540160\pi$
$929$	23.7369	−	17.2459i	0.778782	−	0.565818i	0.904613	+	0.426234i	$0.140160\pi$
$930$		0			0
$931$	−6.85213	−	4.97836i	−0.224569	−	0.163159i
$932$	−29.7150	+	21.5892i	−0.973346	+	0.707177i
$933$		0			0
$934$	14.2417	+	43.8315i	0.466003	+	1.43421i
$935$	−47.2294	−	34.3142i	−1.54457	−	1.12219i
$936$		0			0
$937$	−13.6311	+	9.90356i	−0.445308	+	0.323535i	−0.787740	−	0.616007i	$-0.788749\pi$
$937$	−13.6311	+	9.90356i	−0.445308	+	0.323535i	0.342432	+	0.939542i	$0.388749\pi$
$938$	26.8829	−	82.7372i	0.877759	−	2.70147i
$939$		0			0
$940$	−39.4910	+	121.541i	−1.28805	+	3.96422i
$941$	−16.2910	−	11.8361i	−0.531071	−	0.385846i	0.289687	−	0.957121i	$-0.406449\pi$
$941$	−16.2910	−	11.8361i	−0.531071	−	0.385846i	−0.820758	+	0.571275i	$0.806449\pi$
$942$		0			0
$943$	6.01010			0.195716
$944$	−19.0400	+	13.8333i	−0.619698	+	0.450237i
$945$		0			0
$946$	−62.1387			−2.02030
$947$	6.96087	−	21.4234i	0.226198	−	0.696166i	−0.771970	−	0.635659i	$-0.780728\pi$
$947$	6.96087	−	21.4234i	0.226198	−	0.696166i	0.998168	−	0.0605066i	$-0.0192716\pi$
$948$		0			0
$949$	−15.6211			−0.507082
$950$	−0.889708	−	0.646411i	−0.0288659	−	0.0209723i
$951$		0			0
$952$	104.793	+	76.1365i	3.39636	+	2.46760i
$953$	−36.3130			−1.17629			−0.588147	−	0.808754i	$-0.700142\pi$
$953$	−36.3130			−1.17629			−0.588147	+	0.808754i	$0.700142\pi$
$954$		0			0
$955$	16.9975			0.550026
$956$	12.7312	−	9.24979i	0.411758	−	0.299160i
$957$		0			0
$958$	−7.32659	+	22.5489i	−0.236711	+	0.728523i
$959$	1.95896	−	6.02907i	0.0632582	−	0.194689i
$960$		0			0
$961$	−27.3393	+	19.8631i	−0.881912	+	0.640747i
$962$	44.6519			1.43964
$963$		0			0
$964$	−31.7422			−1.02235
$965$	−2.38451	−	1.73244i	−0.0767600	−	0.0557694i
$966$		0			0
$967$	9.75598	+	7.08814i	0.313731	+	0.227939i	0.733496	−	0.679694i	$-0.237887\pi$
$967$	9.75598	+	7.08814i	0.313731	+	0.227939i	−0.419765	+	0.907633i	$0.637887\pi$
$968$	−57.5887			−1.85097
$969$		0			0
$970$	10.0693	−	30.9902i	0.323307	−	0.995037i
$971$	−17.1567			−0.550585			−0.275292	−	0.961361i	$-0.588775\pi$
$971$	−17.1567			−0.550585			−0.275292	+	0.961361i	$0.588775\pi$
$972$		0			0
$973$	−27.4448	+	19.9398i	−0.879838	+	0.639240i
$974$	−65.9727			−2.11390
$975$		0			0
$976$	−76.3216	−	55.4509i	−2.44299	−	1.77494i
$977$	0.437743	−	1.34723i	0.0140046	−	0.0431019i	−0.943810	−	0.330489i	$-0.892786\pi$
$977$	0.437743	−	1.34723i	0.0140046	−	0.0431019i	0.957815	+	0.287387i	$0.0927865\pi$
$978$		0			0
$979$	18.6046	−	57.2592i	0.594607	−	1.83001i
$980$	−43.8018	+	31.8239i	−1.39920	+	1.01658i
$981$		0			0
$982$	−7.72173	−	5.61016i	−0.246410	−	0.179027i
$983$	11.2301	+	34.5628i	0.358186	+	1.10238i	0.954139	+	0.299364i	$0.0967744\pi$
$983$	11.2301	+	34.5628i	0.358186	+	1.10238i	−0.595953	+	0.803019i	$0.703226\pi$
$984$		0			0
$985$	4.03329	−	2.93036i	0.128511	−	0.0933690i
$986$	−27.6840	−	20.1136i	−0.881639	−	0.640548i
$987$		0			0
$988$	−17.9262	+	13.0242i	−0.570309	+	0.414354i
$989$	2.82530	+	2.05270i	0.0898394	+	0.0652722i
$990$		0			0
$991$	13.9661	+	42.9833i	0.443649	+	1.36541i	0.883959	+	0.467565i	$0.154868\pi$
$991$	13.9661	+	42.9833i	0.443649	+	1.36541i	−0.440310	+	0.897846i	$0.645132\pi$
$992$	−11.5502	−	35.5478i	−0.366718	−	1.12864i
$993$		0			0
$994$	42.6302	+	62.8056i	1.35215	+	1.99207i
$995$	24.6361			0.781017
$996$		0			0
$997$	−17.5543	−	54.0267i	−0.555952	−	1.71104i	−0.693416	−	0.720537i	$-0.743895\pi$
$997$	−17.5543	−	54.0267i	−0.555952	−	1.71104i	0.137465	−	0.990507i	$-0.456105\pi$
$998$	−73.4773	+	53.3844i	−2.32588	+	1.68985i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	639.2.f.d.289.1		24
3.2	odd	2		213.2.e.c.76.6	✓	24
71.57	even	5	inner	639.2.f.d.199.1		24
213.128	odd	10		213.2.e.c.199.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
213.2.e.c.76.6	✓	24	3.2	odd	2
213.2.e.c.199.6	yes	24	213.128	odd	10
639.2.f.d.199.1		24	71.57	even	5	inner
639.2.f.d.289.1		24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 639 = 3^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	639.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.782687 - 2.40886i) q^{2} +(-3.57199 + 2.59520i) q^{4} +(-1.75584 - 1.27569i) q^{5} +(-1.09908 - 3.38262i) q^{7} +(4.94904 + 3.59569i) q^{8} +O(q^{10})\)	\(q+(-0.782687 - 2.40886i) q^{2} +(-3.57199 + 2.59520i) q^{4} +(-1.75584 - 1.27569i) q^{5} +(-1.09908 - 3.38262i) q^{7} +(4.94904 + 3.59569i) q^{8} +(-1.69869 + 5.22804i) q^{10} +(-1.39620 - 4.29705i) q^{11} +(1.03454 - 3.18399i) q^{13} +(-7.28803 + 5.29507i) q^{14} +(2.05921 - 6.33761i) q^{16} +(-1.83970 + 5.66201i) q^{17} +(0.463228 + 1.42567i) q^{19} +9.58251 q^{20} +(-9.25822 + 6.72649i) q^{22} +0.643154 q^{23} +(-0.0895063 - 0.275472i) q^{25} -8.47953 q^{26} +(12.7045 + 9.23035i) q^{28} +(-1.83594 - 1.33389i) q^{29} +(2.48741 + 7.65546i) q^{31} -4.64346 q^{32} +15.0789 q^{34} +(-2.38537 + 7.34141i) q^{35} -5.26585 q^{37} +(3.07168 - 2.23171i) q^{38} +(-4.10272 - 12.6269i) q^{40} +9.34473 q^{41} +(4.39288 + 3.19162i) q^{43} +(16.1389 + 11.7256i) q^{44} +(-0.503389 - 1.54927i) q^{46} +(-4.12115 + 12.6836i) q^{47} +(-4.57102 + 3.32104i) q^{49} +(-0.593519 + 0.431217i) q^{50} +(4.56774 + 14.0580i) q^{52} +(-7.85328 - 5.70574i) q^{53} +(-3.03021 + 9.32603i) q^{55} +(6.72346 - 20.6927i) q^{56} +(-1.77619 + 5.46655i) q^{58} +(-2.85724 - 2.07591i) q^{59} +(4.37475 - 13.4641i) q^{61} +(16.4941 - 11.9837i) q^{62} +(-0.484054 - 1.48977i) q^{64} +(-5.87828 + 4.27082i) q^{65} +(-7.81267 + 5.67624i) q^{67} +(-8.12268 - 24.9990i) q^{68} +19.5515 q^{70} +(0.269484 - 8.42184i) q^{71} +(-1.44187 - 4.43763i) q^{73} +(4.12151 + 12.6847i) q^{74} +(-5.35455 - 3.89031i) q^{76} +(-13.0007 + 9.44560i) q^{77} +(-11.8733 - 8.62648i) q^{79} +(-11.7005 + 8.50089i) q^{80} +(-7.31400 - 22.5102i) q^{82} +(0.964168 + 0.700509i) q^{83} +(10.4532 - 7.59468i) q^{85} +(4.24992 - 13.0799i) q^{86} +(8.54102 - 26.2866i) q^{88} +(10.7803 + 7.83238i) q^{89} -11.9073 q^{91} +(-2.29734 + 1.66912i) q^{92} +33.7786 q^{94} +(1.00536 - 3.09418i) q^{95} -5.92770 q^{97} +(11.5776 + 8.41162i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} - 7 q^{4} + 2 q^{5} - 4 q^{7} - 8 q^{8}+O(q^{10}) \) 24 * q - 3 * q^2 - 7 * q^4 + 2 * q^5 - 4 * q^7 - 8 * q^8	\( 24 q - 3 q^{2} - 7 q^{4} + 2 q^{5} - 4 q^{7} - 8 q^{8} - 8 q^{10} + 5 q^{11} - 8 q^{13} - 29 q^{14} + 5 q^{16} + 2 q^{19} + 2 q^{20} - 11 q^{22} - 6 q^{23} - 12 q^{25} - 24 q^{26} - 25 q^{28} - 2 q^{29} - 24 q^{31} + 36 q^{32} + 102 q^{34} - 22 q^{35} + 10 q^{37} + 27 q^{38} - 56 q^{40} - 2 q^{41} - 18 q^{43} - 9 q^{44} - 11 q^{46} + 36 q^{47} - 6 q^{49} - 3 q^{50} - 35 q^{52} - 6 q^{53} - 9 q^{55} + 100 q^{56} + 64 q^{58} - 3 q^{61} + 36 q^{62} + 66 q^{64} + 3 q^{65} - 18 q^{67} - 76 q^{68} + 130 q^{70} + 10 q^{71} - 9 q^{73} - 7 q^{74} - 24 q^{76} - 39 q^{77} - 20 q^{79} - 51 q^{80} + 20 q^{82} - 17 q^{83} + 25 q^{85} + 69 q^{86} + 13 q^{88} + 28 q^{89} - 38 q^{91} + 81 q^{92} - 56 q^{94} - 35 q^{95} - 34 q^{98}+O(q^{100}) \) 24 * q - 3 * q^2 - 7 * q^4 + 2 * q^5 - 4 * q^7 - 8 * q^8 - 8 * q^10 + 5 * q^11 - 8 * q^13 - 29 * q^14 + 5 * q^16 + 2 * q^19 + 2 * q^20 - 11 * q^22 - 6 * q^23 - 12 * q^25 - 24 * q^26 - 25 * q^28 - 2 * q^29 - 24 * q^31 + 36 * q^32 + 102 * q^34 - 22 * q^35 + 10 * q^37 + 27 * q^38 - 56 * q^40 - 2 * q^41 - 18 * q^43 - 9 * q^44 - 11 * q^46 + 36 * q^47 - 6 * q^49 - 3 * q^50 - 35 * q^52 - 6 * q^53 - 9 * q^55 + 100 * q^56 + 64 * q^58 - 3 * q^61 + 36 * q^62 + 66 * q^64 + 3 * q^65 - 18 * q^67 - 76 * q^68 + 130 * q^70 + 10 * q^71 - 9 * q^73 - 7 * q^74 - 24 * q^76 - 39 * q^77 - 20 * q^79 - 51 * q^80 + 20 * q^82 - 17 * q^83 + 25 * q^85 + 69 * q^86 + 13 * q^88 + 28 * q^89 - 38 * q^91 + 81 * q^92 - 56 * q^94 - 35 * q^95 - 34 * q^98

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