LMFDB - Embedded newform 639.2.f.d.199.1

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			199.1
Character	$\chi$	$=$	639.199
Dual form			639.2.f.d.289.1

$q$-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 $\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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	0.146575	+	0.989200i	$0.453175\pi$
$2$	−0.782687	+	2.40886i	−0.553443	+	1.70332i	−0.700019	+	0.714124i	$0.746825\pi$
$3$		0			0
$3$		0			0
$4$	−3.57199	−	2.59520i	−1.78600	−	1.29760i
$5$	−1.75584	+	1.27569i	−0.785234	+	0.570506i	−0.906545	−	0.422108i	$-0.861290\pi$
$5$	−1.75584	+	1.27569i	−0.785234	+	0.570506i	0.121311	+	0.992615i	$0.461290\pi$
$6$		0			0
$7$	−1.09908	+	3.38262i	−0.415413	+	1.27851i	0.496468	+	0.868055i	$0.334630\pi$
$7$	−1.09908	+	3.38262i	−0.415413	+	1.27851i	−0.911881	+	0.410455i	$0.865370\pi$
$8$	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	0.485833	+	0.874052i	$0.338516\pi$
$11$	−1.39620	+	4.29705i	−0.420969	+	1.29561i	−0.906802	+	0.421557i	$0.861484\pi$
$12$		0			0
$13$	1.03454	+	3.18399i	0.286930	+	0.883081i	0.985813	+	0.167845i	$0.0536808\pi$
$13$	1.03454	+	3.18399i	0.286930	+	0.883081i	−0.698883	+	0.715236i	$0.746319\pi$
$14$	−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	−0.881171	−	0.472798i	$-0.843244\pi$
$17$	−1.83970	−	5.66201i	−0.446192	−	1.37324i	0.434978	−	0.900441i	$-0.356756\pi$
$18$		0			0
$19$	0.463228	−	1.42567i	0.106272	−	0.327071i	−0.883755	−	0.467950i	$-0.844993\pi$
$19$	0.463228	−	1.42567i	0.106272	−	0.327071i	0.990027	+	0.140879i	$0.0449928\pi$
$20$	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	−0.745052	−	0.667006i	$-0.767576\pi$
$29$	−1.83594	+	1.33389i	−0.340926	+	0.247697i	0.404126	+	0.914703i	$0.367576\pi$
$30$		0			0
$31$	2.48741	−	7.65546i	0.446752	−	1.37496i	−0.433800	−	0.901009i	$-0.642827\pi$
$31$	2.48741	−	7.65546i	0.446752	−	1.37496i	0.880551	−	0.473951i	$-0.157173\pi$
$32$	−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	−0.200086	−	0.979778i	$-0.564122\pi$
$43$	4.39288	−	3.19162i	0.669909	−	0.486717i	0.869995	+	0.493061i	$0.164122\pi$
$44$	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	−0.521470	−	0.853269i	$-0.674616\pi$
$47$	−4.12115	−	12.6836i	−0.601131	−	1.85009i	−0.0796609	−	0.996822i	$-0.525384\pi$
$48$		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	−0.977461	−	0.211115i	$-0.932291\pi$
$53$	−7.85328	+	5.70574i	−1.07873	+	0.783744i	−0.101270	+	0.994859i	$0.532291\pi$
$54$		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	−0.758032	−	0.652217i	$-0.773839\pi$
$59$	−2.85724	+	2.07591i	−0.371981	+	0.270260i	0.386051	+	0.922478i	$0.373839\pi$
$60$		0			0
$61$	4.37475	+	13.4641i	0.560129	+	1.72390i	0.681998	+	0.731354i	$0.261111\pi$
$61$	4.37475	+	13.4641i	0.560129	+	1.72390i	−0.121869	+	0.992546i	$0.538889\pi$
$62$	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	−0.00260970	−	0.999997i	$-0.500831\pi$
$67$	−7.81267	−	5.67624i	−0.954469	−	0.693463i	−0.951860	+	0.306534i	$0.900831\pi$
$68$	−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	−0.999294	−	0.0375809i	$-0.988035\pi$
$73$	−1.44187	+	4.43763i	−0.168759	+	0.519386i	0.830535	+	0.556966i	$0.188035\pi$
$74$	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	−0.336269	+	0.941766i	$0.609165\pi$
$79$	−11.8733	+	8.62648i	−1.33585	+	0.970555i	−0.999586	+	0.0287887i	$0.990835\pi$
$80$	−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	−0.533611	−	0.845730i	$-0.679165\pi$
$83$	0.964168	−	0.700509i	0.105831	−	0.0768909i	0.639442	+	0.768839i	$0.279165\pi$
$84$		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	0.155220	−	0.987880i	$-0.450391\pi$
$89$	10.7803	−	7.83238i	1.14271	−	0.830231i	0.987495	+	0.157649i	$0.0503915\pi$
$90$		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	0.839418	−	0.543487i	$-0.182896\pi$
$107$	−1.64615	−	5.06632i	−0.159139	−	0.489779i	−0.998557	+	0.0537075i	$0.982896\pi$
$108$		0			0
$109$	5.47687	+	3.97918i	0.524589	+	0.381136i	0.818330	−	0.574749i	$-0.194900\pi$
$109$	5.47687	+	3.97918i	0.524589	+	0.381136i	−0.293741	+	0.955885i	$0.594900\pi$
$110$	24.8368			2.36810
$111$		0			0
$112$	−23.7010			−2.23953
$113$	0.510911	−	0.371199i	0.0480625	−	0.0349194i	−0.563495	−	0.826120i	$-0.690543\pi$
$113$	0.510911	−	0.371199i	0.0480625	−	0.0349194i	0.611557	+	0.791200i	$0.290543\pi$
$114$		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	0.986365	+	0.164575i	$0.0526253\pi$
$127$	3.21307	+	9.88881i	0.285114	+	0.877490i	−0.701251	+	0.712915i	$0.747375\pi$
$128$	−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	0.533279	+	0.845939i	$0.320960\pi$
$131$	−4.52537	+	13.9277i	−0.395384	+	1.21687i	−0.928662	+	0.370926i	$0.879040\pi$
$132$		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	−0.524481	−	0.851422i	$-0.675741\pi$
$137$	1.44196	−	1.04765i	0.123195	−	0.0895067i	0.647677	+	0.761915i	$0.275741\pi$
$138$		0			0
$139$	−2.94739	+	9.07113i	−0.249994	+	0.769403i	0.744781	+	0.667309i	$0.232554\pi$
$139$	−2.94739	+	9.07113i	−0.249994	+	0.769403i	−0.994775	+	0.102094i	$0.967446\pi$
$140$	−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	−0.994485	−	0.104875i	$-0.966556\pi$
$149$	−1.56593	+	4.81942i	−0.128286	+	0.394822i	0.866200	+	0.499698i	$0.166556\pi$
$150$		0			0
$151$	−15.9438	−	11.5839i	−1.29749	−	0.942682i	−0.297563	−	0.954702i	$-0.596174\pi$
$151$	−15.9438	−	11.5839i	−1.29749	−	0.942682i	−0.999928	+	0.0120197i	$0.996174\pi$
$152$	−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	−0.987213	−	0.159407i	$-0.949042\pi$
$157$	−3.53643	−	10.8840i	−0.282238	−	0.868640i	0.704975	−	0.709232i	$-0.250958\pi$
$158$	−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	−0.191923	−	0.981410i	$-0.561472\pi$
$163$	−15.1240	−	10.9883i	−1.18461	−	0.860667i	−0.992684	+	0.120743i	$0.961472\pi$
$164$	−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	0.564185	+	0.825649i	$0.309191\pi$
$167$	−4.87908	+	15.0163i	−0.377554	+	1.16199i	−0.941739	+	0.336344i	$0.890809\pi$
$168$		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	0.656882	+	0.753993i	$0.271875\pi$
$173$	−4.17912	+	12.8620i	−0.317733	+	0.977880i	−0.974615	+	0.223887i	$0.928125\pi$
$174$		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	0.334469	−	0.942407i	$-0.391443\pi$
$191$	−6.33601	−	4.60338i	−0.458457	−	0.333089i	−0.792926	+	0.609318i	$0.791443\pi$
$192$		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	0.922580	−	0.385806i	$-0.126076\pi$
$197$	−0.709836	−	2.18465i	−0.0505737	−	0.155650i	−0.973154	+	0.230156i	$0.926076\pi$
$198$		0			0
$199$	−9.18339	−	6.67212i	−0.650993	−	0.472974i	0.212616	−	0.977136i	$-0.431802\pi$
$199$	−9.18339	−	6.67212i	−0.650993	−	0.472974i	−0.863609	+	0.504162i	$0.831802\pi$
$200$	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	−0.832191	−	0.554489i	$-0.812914\pi$
$211$	2.42561	−	7.46526i	0.166986	−	0.513930i	0.999177	+	0.0405590i	$0.0129139\pi$
$212$	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	−0.999943	−	0.0107216i	$-0.996587\pi$
$223$	−2.94593	−	9.06664i	−0.197274	−	0.607147i	0.802668	−	0.596425i	$-0.203413\pi$
$224$	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	0.519652	−	0.854378i	$-0.326062\pi$
$227$	−1.99373	−	1.44853i	−0.132329	−	0.0961424i	−0.651981	+	0.758236i	$0.726062\pi$
$228$		0			0
$229$	−5.54393	−	17.0625i	−0.366353	−	1.12752i	−0.949129	−	0.314886i	$-0.898034\pi$
$229$	−5.54393	−	17.0625i	−0.366353	−	1.12752i	0.582776	−	0.812633i	$-0.301966\pi$
$230$	−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	−0.384482	−	0.923132i	$-0.625620\pi$
$241$	5.81624	−	4.22575i	0.374657	−	0.272204i	0.759139	+	0.650928i	$0.225620\pi$
$242$	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	0.856765	−	0.515707i	$-0.172471\pi$
$251$	9.99778	+	7.26381i	0.631054	+	0.458488i	−0.225711	+	0.974194i	$0.572471\pi$
$252$		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	−0.372958	+	0.927848i	$0.621656\pi$
$257$	−21.9731	+	15.9644i	−1.37064	+	0.995832i	−0.997686	+	0.0679834i	$0.978344\pi$
$258$		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	0.885446	−	0.464742i	$-0.153853\pi$
$263$	11.6289	+	8.44888i	0.717068	+	0.520980i	−0.168378	+	0.985722i	$0.553853\pi$
$264$		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	0.993602	+	0.112941i	$0.0360270\pi$
$269$	4.20111	+	12.9297i	0.256146	+	0.788336i	−0.737456	+	0.675395i	$0.763973\pi$
$270$		0			0
$271$	8.79331	+	27.0630i	0.534156	+	1.64396i	0.745466	+	0.666543i	$0.232227\pi$
$271$	8.79331	+	27.0630i	0.534156	+	1.64396i	−0.211310	+	0.977419i	$0.567773\pi$
$272$	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	−1.00000		0.000561047i	$-0.999821\pi$
$277$	−3.17310	+	9.76580i	−0.190653	+	0.586770i	0.809347	+	0.587331i	$0.199821\pi$
$278$	−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	−0.614414	−	0.788984i	$-0.710607\pi$
$281$	5.80690	−	17.8718i	0.346410	−	1.06614i	0.960824	−	0.277158i	$-0.0893925\pi$
$282$		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	0.706066	−	0.708146i	$-0.250468\pi$
$293$	4.29240	+	3.11861i	0.250765	+	0.182191i	−0.455301	+	0.890338i	$0.650468\pi$
$294$		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	−0.992350	−	0.123457i	$-0.960602\pi$
$311$	−20.8375	+	15.1394i	−1.18159	+	0.858474i	−0.189239	+	0.981931i	$0.560602\pi$
$312$		0			0
$313$	3.43769	−	2.49763i	0.194310	−	0.141174i	−0.486376	−	0.873749i	$-0.661682\pi$
$313$	3.43769	−	2.49763i	0.194310	−	0.141174i	0.680686	+	0.732575i	$0.261682\pi$
$314$	28.9861			1.63578
$315$		0			0
$316$	64.7989			3.64522
$317$	22.7219	+	16.5085i	1.27619	+	0.927207i	0.999431	−	0.0337317i	$-0.0107392\pi$
$317$	22.7219	+	16.5085i	1.27619	+	0.927207i	0.276760	+	0.960939i	$0.410739\pi$
$318$		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	0.993223	−	0.116225i	$-0.0370793\pi$
$331$	2.20820	+	6.79613i	0.121374	+	0.373549i	−0.871849	+	0.489774i	$0.837079\pi$
$332$	−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	−0.838040	−	0.545610i	$-0.816298\pi$
$337$	−10.6125	+	7.71047i	−0.578102	+	0.420016i	0.259937	+	0.965626i	$0.416298\pi$
$338$	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	−0.578226	−	0.815876i	$-0.696255\pi$
$347$	0.354610	−	0.257639i	0.0190364	−	0.0138308i	0.597263	+	0.802046i	$0.296255\pi$
$348$		0			0
$349$	21.9577	+	15.9532i	1.17537	+	0.853956i	0.991642	−	0.129022i	$-0.0411837\pi$
$349$	21.9577	+	15.9532i	1.17537	+	0.853956i	0.183727	+	0.982977i	$0.441184\pi$
$350$	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	0.762730	+	0.646718i	$0.223859\pi$
$353$	−4.40515	+	13.5577i	−0.234463	+	0.721602i	−0.997192	+	0.0748844i	$0.976141\pi$
$354$		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	0.402388	−	0.915469i	$-0.368180\pi$
$359$	−6.51656	−	4.73456i	−0.343931	−	0.249880i	−0.746319	+	0.665589i	$0.768180\pi$
$360$		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	−0.244159	−	0.969735i	$-0.578512\pi$
$367$	11.5454	−	8.38823i	0.602665	−	0.437862i	0.846824	+	0.531873i	$0.178512\pi$
$368$	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	−0.0372760	−	0.999305i	$-0.511868\pi$
$373$	17.4128	−	12.6511i	0.901601	−	0.655051i	0.938877	+	0.344254i	$0.111868\pi$
$374$	−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	0.993603	+	0.112926i	$0.0360225\pi$
$379$	4.98647	+	15.3468i	0.256138	+	0.788311i	−0.737465	+	0.675385i	$0.763978\pi$
$380$	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	−0.414584	−	0.910011i	$-0.636073\pi$
$383$	6.31683	−	4.58944i	0.322775	−	0.234510i	0.737359	+	0.675502i	$0.236073\pi$
$384$		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	−0.671239	−	0.741241i	$-0.734238\pi$
$397$	−3.46099	+	2.51456i	−0.173702	+	0.126202i	0.497537	+	0.867443i	$0.334238\pi$
$398$	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	−0.428056	−	0.903752i	$-0.640801\pi$
$401$	9.00045	−	27.7005i	0.449461	−	1.38330i	0.877517	−	0.479546i	$-0.159199\pi$
$402$		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	−0.971009	−	0.239043i	$-0.923166\pi$
$409$	−6.59198	−	20.2880i	−0.325952	−	1.00318i	0.645057	−	0.764135i	$-0.276834\pi$
$410$	−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	−0.907495	−	0.420062i	$-0.862008\pi$
$419$	1.50635	−	4.63607i	0.0735900	−	0.226487i	0.981085	+	0.193575i	$0.0620083\pi$
$420$		0			0
$421$	−9.26713	+	6.73296i	−0.451652	+	0.328145i	−0.790248	−	0.612787i	$-0.790048\pi$
$421$	−9.26713	+	6.73296i	−0.451652	+	0.328145i	0.338596	+	0.940932i	$0.390048\pi$
$422$	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	−0.753264	−	0.657718i	$-0.771522\pi$
$431$	−7.48437	+	5.43771i	−0.360509	+	0.261925i	0.392755	+	0.919643i	$0.371522\pi$
$432$		0			0
$433$	1.53452	−	4.72276i	0.0737443	−	0.226962i	−0.907390	−	0.420290i	$-0.861928\pi$
$433$	1.53452	−	4.72276i	0.0737443	−	0.226962i	0.981134	+	0.193329i	$0.0619283\pi$
$434$	−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	−0.999703	−	0.0243907i	$-0.992235\pi$
$439$	−4.30073	−	13.2363i	−0.205263	−	0.631734i	0.794440	−	0.607343i	$-0.207765\pi$
$440$	−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	0.832509	−	0.554012i	$-0.186904\pi$
$443$	−3.50747	−	10.7949i	−0.166645	−	0.512880i	−0.999154	+	0.0411314i	$0.986904\pi$
$444$		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	−0.989337	−	0.145645i	$-0.953474\pi$
$457$	−2.20912	+	6.79899i	−0.103338	+	0.318043i	0.885998	+	0.463688i	$0.153474\pi$
$458$	45.4403			2.12329
$459$		0			0
$460$	6.16304			0.287353
$461$	7.66833	+	23.6007i	0.357150	+	1.09919i	0.954752	+	0.297402i	$0.0961200\pi$
$461$	7.66833	+	23.6007i	0.357150	+	1.09919i	−0.597603	+	0.801792i	$0.703880\pi$
$462$		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	−0.747198	−	0.664601i	$-0.768601\pi$
$479$	−7.57306	+	5.50215i	−0.346022	+	0.251400i	0.401176	+	0.916001i	$0.368601\pi$
$480$		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	0.950147	+	0.311801i	$0.100932\pi$
$487$	8.04898	+	24.7722i	0.364734	+	1.12254i	−0.585413	+	0.810735i	$0.699068\pi$
$488$	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	0.654448	−	0.756107i	$-0.272901\pi$
$491$	3.04866	+	2.21498i	0.137584	+	0.0999606i	−0.516864	+	0.856067i	$0.672901\pi$
$492$		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	0.319276	+	0.947662i	$0.396560\pi$
$499$	−11.0808	+	34.1032i	−0.496046	+	1.52667i	−0.815321	+	0.579009i	$0.803440\pi$
$500$	−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	−0.979151	−	0.203135i	$-0.934887\pi$
$503$	−33.0790	−	24.0333i	−1.47492	−	1.07159i	−0.495767	−	0.868455i	$-0.665113\pi$
$504$		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	−0.308910	−	0.951091i	$-0.599964\pi$
$509$	11.2844	−	8.19860i	0.500173	−	0.363397i	0.809083	+	0.587695i	$0.199964\pi$
$510$		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	0.821251	−	0.570568i	$-0.193277\pi$
$521$	−4.07494	−	12.5414i	−0.178526	−	0.549447i	−0.999777	+	0.0211202i	$0.993277\pi$
$522$		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	0.101112	−	0.994875i	$-0.467760\pi$
$541$	25.0862	−	18.2262i	1.07854	−	0.783605i	0.977428	+	0.211270i	$0.0677600\pi$
$542$	−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	−0.223369	−	0.974734i	$-0.571706\pi$
$547$	−28.5199	−	20.7209i	−1.21942	−	0.885962i	−0.996052	+	0.0887723i	$0.971706\pi$
$548$	−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	−0.981683	−	0.190520i	$-0.938983\pi$
$557$	−1.78186	+	5.48400i	−0.0754998	+	0.232365i	0.906183	+	0.422885i	$0.138983\pi$
$558$		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	−0.503958	−	0.863728i	$-0.668123\pi$
$563$	3.83831	−	2.78870i	0.161766	−	0.117530i	0.665723	+	0.746199i	$0.268123\pi$
$564$		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	−0.245452	−	0.969409i	$-0.578936\pi$
$571$	12.4957	−	38.4577i	0.522927	−	1.60940i	0.768379	−	0.639995i	$-0.221064\pi$
$572$	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	0.855957	−	0.517048i	$-0.172969\pi$
$577$	15.1024	+	10.9725i	0.628720	+	0.456792i	−0.227236	+	0.973840i	$0.572969\pi$
$578$	−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	−0.752207	−	0.658926i	$-0.771011\pi$
$587$	5.90314	−	18.1680i	0.243648	−	0.749873i	0.995856	−	0.0909464i	$-0.0289892\pi$
$588$		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	−0.982120	−	0.188254i	$-0.939717\pi$
$593$	−1.87301	+	5.76454i	−0.0769154	+	0.236721i	0.905205	+	0.424975i	$0.139717\pi$
$594$		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	−0.788853	−	0.614582i	$-0.789325\pi$
$599$	5.15395	−	15.8622i	0.210585	−	0.648113i	0.999438	−	0.0335311i	$-0.0106753\pi$
$600$		0			0
$601$	27.3150	+	19.8455i	1.11420	+	0.809516i	0.983320	−	0.181881i	$-0.0582187\pi$
$601$	27.3150	+	19.8455i	1.11420	+	0.809516i	0.130883	+	0.991398i	$0.458219\pi$
$602$	−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	0.469316	−	0.883030i	$-0.344501\pi$
$617$	−5.60055	−	4.06904i	−0.225470	−	0.163813i	−0.694785	+	0.719217i	$0.744501\pi$
$618$		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	−0.138679	−	0.990337i	$-0.544285\pi$
$631$	19.0994	−	13.8765i	0.760334	−	0.552415i	0.899013	+	0.437922i	$0.144285\pi$
$632$	−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	0.520793	+	0.853683i	$0.325636\pi$
$641$	−10.1859	+	31.3490i	−0.402320	+	1.23821i	−0.923113	+	0.384530i	$0.874364\pi$
$642$		0			0
$643$	12.2578	+	8.90584i	0.483402	+	0.351212i	0.802641	−	0.596462i	$-0.203427\pi$
$643$	12.2578	+	8.90584i	0.483402	+	0.351212i	−0.319240	+	0.947674i	$0.603427\pi$
$644$	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	−0.944902	−	0.327352i	$-0.893844\pi$
$647$	−23.5428	+	17.1048i	−0.925563	+	0.672461i	0.0193396	+	0.999813i	$0.493844\pi$
$648$		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	0.996493	−	0.0836804i	$-0.0266675\pi$
$653$	31.2994	+	22.7404i	1.22484	+	0.889899i	0.228348	+	0.973579i	$0.426667\pi$
$654$		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	0.854523	−	0.519413i	$-0.173849\pi$
$661$	16.0583	+	11.6670i	0.624595	+	0.453795i	−0.229929	+	0.973208i	$0.573849\pi$
$662$	−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	0.567050	−	0.823683i	$-0.308085\pi$
$677$	−1.06916	−	0.776794i	−0.0410913	−	0.0298546i	−0.608141	+	0.793829i	$0.708085\pi$
$678$		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	−0.352048	−	0.935982i	$-0.614515\pi$
$683$	11.2204	−	8.15206i	0.429335	−	0.311930i	0.781383	+	0.624052i	$0.214515\pi$
$684$		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	−0.832253	−	0.554396i	$-0.812949\pi$
$691$	4.38779	−	13.5042i	0.166919	−	0.513725i	0.999173	+	0.0406707i	$0.0129495\pi$
$692$	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	0.590484	−	0.807050i	$-0.298937\pi$
$701$	0.143056	+	0.103936i	0.00540315	+	0.00392562i	−0.585080	+	0.810975i	$0.698937\pi$
$702$		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	0.709560	−	0.704645i	$-0.248894\pi$
$719$	6.93601	+	5.03931i	0.258670	+	0.187934i	−0.450891	+	0.892579i	$0.648894\pi$
$720$		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	0.995625	−	0.0934355i	$-0.0297849\pi$
$727$	3.64613	+	11.2216i	0.135227	+	0.416187i	−0.860398	+	0.509623i	$0.829785\pi$
$728$	−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	0.613954	−	0.789342i	$-0.289578\pi$
$739$	42.2553	−	30.7002i	1.55439	−	1.12933i	0.940431	−	0.339985i	$-0.110422\pi$
$740$	−50.4600			−1.85495
$741$		0			0
$742$	87.4473			3.21029
$743$	−10.0859	−	7.32784i	−0.370016	−	0.268833i	0.387201	−	0.921995i	$-0.373442\pi$
$743$	−10.0859	−	7.32784i	−0.370016	−	0.268833i	−0.757218	+	0.653163i	$0.773442\pi$
$744$		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	0.777659	+	0.628687i	$0.216407\pi$
$757$	14.2535	+	43.8678i	0.518052	+	1.59440i	−0.259606	+	0.965715i	$0.583593\pi$
$758$	−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	−0.820835	−	0.571166i	$-0.806491\pi$
$769$	−14.7327	+	10.7040i	−0.531276	+	0.385995i	0.289559	+	0.957160i	$0.406491\pi$
$770$	−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	−0.576828	−	0.816865i	$-0.695710\pi$
$773$	0.606297	−	0.440501i	0.0218070	−	0.0158437i	0.598635	+	0.801022i	$0.295710\pi$
$774$		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	0.568548	−	0.822650i	$-0.307505\pi$
$787$	−1.07018	−	0.777532i	−0.0381478	−	0.0277160i	−0.606696	+	0.794934i	$0.707505\pi$
$788$	−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	0.958324	−	0.285685i	$-0.0922210\pi$
$797$	0.426355	+	1.31219i	0.0151023	+	0.0464800i	−0.943221	+	0.332165i	$0.892221\pi$
$798$		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	−0.524152	+	0.851625i	$0.675618\pi$
$809$	−42.5525	+	30.9162i	−1.49607	+	1.08696i	−0.971915	+	0.235332i	$0.924382\pi$
$810$		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	−0.999721	−	0.0236149i	$-0.992482\pi$
$821$	−5.07301	+	15.6131i	−0.177049	+	0.544902i	0.822672	+	0.568516i	$0.192482\pi$
$822$		0			0
$823$	−16.5635	+	12.0341i	−0.577368	+	0.419483i	−0.837774	−	0.546017i	$-0.816144\pi$
$823$	−16.5635	+	12.0341i	−0.577368	+	0.419483i	0.260406	+	0.965499i	$0.416144\pi$
$824$	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	−0.974211	−	0.225640i	$-0.927553\pi$
$827$	−1.53651	+	4.72890i	−0.0534298	+	0.164440i	0.920781	+	0.390080i	$0.127553\pi$
$828$		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	0.980670	+	0.195670i	$0.0626882\pi$
$839$	8.75637	+	26.9493i	0.302303	+	0.930394i	−0.678366	+	0.734724i	$0.737312\pi$
$840$		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	0.163974	−	0.986465i	$-0.447569\pi$
$857$	33.7486	−	24.5198i	1.15283	−	0.837579i	0.988854	+	0.148886i	$0.0475686\pi$
$858$		0			0
$859$	−12.8870	+	39.6622i	−0.439700	+	1.35326i	0.448493	+	0.893787i	$0.351961\pi$
$859$	−12.8870	+	39.6622i	−0.439700	+	1.35326i	−0.888193	+	0.459471i	$0.848039\pi$
$860$	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	−0.446984	−	0.894542i	$-0.647502\pi$
$863$	12.9385	−	39.8207i	0.440432	−	1.35551i	0.887416	−	0.460969i	$-0.152498\pi$
$864$		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	−0.616718	−	0.787184i	$-0.711538\pi$
$877$	10.2143	−	31.4364i	0.344912	−	1.06153i	0.961631	−	0.274347i	$-0.0884617\pi$
$878$	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	−0.705316	−	0.708893i	$-0.749195\pi$
$881$	−7.39288	+	5.37124i	−0.249072	+	0.180962i	0.456243	+	0.889855i	$0.349195\pi$
$882$		0			0
$883$	−16.1893	+	49.8257i	−0.544815	+	1.67677i	0.176614	+	0.984280i	$0.443485\pi$
$883$	−16.1893	+	49.8257i	−0.544815	+	1.67677i	−0.721429	+	0.692488i	$0.756515\pi$
$884$	−88.0001			−2.95976
$885$		0			0
$886$	28.7487			0.965830
$887$	2.07842	+	6.39671i	0.0697864	+	0.214780i	0.979867	−	0.199650i	$-0.0639806\pi$
$887$	2.07842	+	6.39671i	0.0697864	+	0.214780i	−0.910081	+	0.414431i	$0.863981\pi$
$888$		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	0.952343	−	0.305029i	$-0.0986661\pi$
$907$	0.0779976	+	0.240052i	0.00258987	+	0.00797080i	−0.949753	+	0.313000i	$0.898666\pi$
$908$	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	−0.796479	−	0.604666i	$-0.793307\pi$
$911$	−14.1115	+	10.2526i	−0.467534	+	0.339683i	0.328946	+	0.944349i	$0.393307\pi$
$912$		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	0.470952	−	0.882159i	$-0.343911\pi$
$919$	−6.74505	−	4.90057i	−0.222499	−	0.161655i	−0.693451	+	0.720504i	$0.743911\pi$
$920$	−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	0.904613	−	0.426234i	$-0.140160\pi$
$929$	23.7369	+	17.2459i	0.778782	+	0.565818i	−0.125831	+	0.992052i	$0.540160\pi$
$930$		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	0.342432	−	0.939542i	$-0.388749\pi$
$937$	−13.6311	−	9.90356i	−0.445308	−	0.323535i	−0.787740	+	0.616007i	$0.788749\pi$
$938$	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	−0.820758	−	0.571275i	$-0.806449\pi$
$941$	−16.2910	+	11.8361i	−0.531071	+	0.385846i	0.289687	+	0.957121i	$0.406449\pi$
$942$		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	0.998168	+	0.0605066i	$0.0192716\pi$
$947$	6.96087	+	21.4234i	0.226198	+	0.696166i	−0.771970	+	0.635659i	$0.780728\pi$
$948$		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	−0.419765	−	0.907633i	$-0.637887\pi$
$967$	9.75598	−	7.08814i	0.313731	−	0.227939i	0.733496	+	0.679694i	$0.237887\pi$
$968$	−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	0.957815	−	0.287387i	$-0.0927865\pi$
$977$	0.437743	+	1.34723i	0.0140046	+	0.0431019i	−0.943810	+	0.330489i	$0.892786\pi$
$978$		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	−0.595953	−	0.803019i	$-0.703226\pi$
$983$	11.2301	−	34.5628i	0.358186	−	1.10238i	0.954139	−	0.299364i	$-0.0967744\pi$
$984$		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	−0.440310	−	0.897846i	$-0.645132\pi$
$991$	13.9661	−	42.9833i	0.443649	−	1.36541i	0.883959	−	0.467565i	$-0.154868\pi$
$992$	−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	0.137465	+	0.990507i	$0.456105\pi$
$997$	−17.5543	+	54.0267i	−0.555952	+	1.71104i	−0.693416	+	0.720537i	$0.743895\pi$
$998$	−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.199.1		24
3.2	odd	2		213.2.e.c.199.6	yes	24
71.5	even	5	inner	639.2.f.d.289.1		24
213.5	odd	10		213.2.e.c.76.6	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
213.2.e.c.76.6	✓	24	213.5	odd	10
213.2.e.c.199.6	yes	24	3.2	odd	2
639.2.f.d.199.1		24	1.1	even	1	trivial
639.2.f.d.289.1		24	71.5	even	5	inner

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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