LMFDB - Embedded newform 147.2.c.b.146.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,2,Mod(146,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("147.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	147.c (of order $2$, degree $1$, 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:	$1.17380090971$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.3288334336.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 8x^{6} - 8x^{5} + 14x^{4} + 8x^{3} - 16x^{2} + 7 $ x^8 + 8x^6 - 8x^5 + 14x^4 + 8x^3 - 16*x^2 + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.3
Root			$0.707107 - 1.43164i$ of defining polynomial
Character	$\chi$	$=$	147.146
Dual form			147.2.c.b.146.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.25928i q^{2} +(-1.64533 + 0.541196i) q^{3} +0.414214 q^{4} +2.32685 q^{5} +(0.681517 + 2.07193i) q^{6} -3.04017i q^{8} +(2.41421 - 1.78089i) q^{9} +O(q^{10})$	\(q-1.25928i q^{2} +(-1.64533 + 0.541196i) q^{3} +0.414214 q^{4} +2.32685 q^{5} +(0.681517 + 2.07193i) q^{6} -3.04017i q^{8} +(2.41421 - 1.78089i) q^{9} -2.93015i q^{10} +1.78089i q^{11} +(-0.681517 + 0.224171i) q^{12} -4.46088i q^{13} +(-3.82843 + 1.25928i) q^{15} -3.00000 q^{16} +0.963811 q^{17} +(-2.24264 - 3.04017i) q^{18} +2.16478i q^{19} +0.963811 q^{20} +2.24264 q^{22} +4.29945i q^{23} +(1.64533 + 5.00208i) q^{24} +0.414214 q^{25} -5.61750 q^{26} +(-3.00836 + 4.23671i) q^{27} +7.86123i q^{29} +(1.58579 + 4.82106i) q^{30} +1.08239i q^{31} -2.30250i q^{32} +(-0.963811 - 2.93015i) q^{33} -1.21371i q^{34} +(1.00000 - 0.737669i) q^{36} -5.07107 q^{37} +2.72607 q^{38} +(2.41421 + 7.33962i) q^{39} -7.07401i q^{40} -4.25447 q^{41} +2.00000 q^{43} +0.737669i q^{44} +(5.61750 - 4.14386i) q^{45} +5.41421 q^{46} +0.564588 q^{47} +(4.93599 - 1.62359i) q^{48} -0.521611i q^{50} +(-1.58579 + 0.521611i) q^{51} -1.84776i q^{52} -6.08034i q^{53} +(5.33521 + 3.78837i) q^{54} +4.14386i q^{55} +(-1.17157 - 3.56178i) q^{57} +9.89949 q^{58} -9.30739 q^{59} +(-1.58579 + 0.521611i) q^{60} +7.52235i q^{61} +1.36303 q^{62} -8.89949 q^{64} -10.3798i q^{65} +(-3.68988 + 1.21371i) q^{66} -14.4853 q^{67} +0.399224 q^{68} +(-2.32685 - 7.07401i) q^{69} -7.86123i q^{71} +(-5.41421 - 7.33962i) q^{72} +6.43996i q^{73} +6.38589i q^{74} +(-0.681517 + 0.224171i) q^{75} +0.896683i q^{76} +(9.24264 - 3.04017i) q^{78} +4.82843 q^{79} -6.98054 q^{80} +(2.65685 - 8.59890i) q^{81} +5.35757i q^{82} +14.5257 q^{83} +2.24264 q^{85} -2.51856i q^{86} +(-4.25447 - 12.9343i) q^{87} +5.41421 q^{88} +8.34357 q^{89} +(-5.21828 - 7.07401i) q^{90} +1.78089i q^{92} +(-0.585786 - 1.78089i) q^{93} -0.710974i q^{94} +5.03712i q^{95} +(1.24611 + 3.78837i) q^{96} +13.8310i q^{97} +(3.17157 + 4.29945i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 + 8 * q^9	$ 8 q - 8 q^{4} + 8 q^{9} - 8 q^{15} - 24 q^{16} + 16 q^{18} - 16 q^{22} - 8 q^{25} + 24 q^{30} + 8 q^{36} + 16 q^{37} + 8 q^{39} + 16 q^{43} + 32 q^{46} - 24 q^{51} - 32 q^{57} - 24 q^{60} + 8 q^{64} - 48 q^{67} - 32 q^{72} + 40 q^{78} + 16 q^{79} - 24 q^{81} - 16 q^{85} + 32 q^{88} - 16 q^{93} + 48 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 + 8 * q^9 - 8 * q^15 - 24 * q^16 + 16 * q^18 - 16 * q^22 - 8 * q^25 + 24 * q^30 + 8 * q^36 + 16 * q^37 + 8 * q^39 + 16 * q^43 + 32 * q^46 - 24 * q^51 - 32 * q^57 - 24 * q^60 + 8 * q^64 - 48 * q^67 - 32 * q^72 + 40 * q^78 + 16 * q^79 - 24 * q^81 - 16 * q^85 + 32 * q^88 - 16 * q^93 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	1.25928i		−	0.890446i	−0.895420	−	0.445223i	$-0.853124\pi$
$2$		−	1.25928i		−	0.890446i	0.895420	−	0.445223i	$-0.146876\pi$
$3$	−1.64533	+	0.541196i	−0.949931	+	0.312460i
$3$	−1.64533	+	0.541196i	−0.949931	+	0.312460i
$4$	0.414214			0.207107
$5$	2.32685			1.04060			0.520299	−	0.853984i	$-0.325821\pi$
$5$	2.32685			1.04060			0.520299	+	0.853984i	$0.325821\pi$
$6$	0.681517	+	2.07193i	0.278228	+	0.845862i
$7$		0			0
$7$		0			0
$8$		−	3.04017i		−	1.07486i
$9$	2.41421	−	1.78089i	0.804738	−	0.593630i
$10$		−	2.93015i		−	0.926595i
$11$			1.78089i			0.536959i	0.963285	+	0.268479i	$0.0865211\pi$
$11$			1.78089i			0.536959i	−0.963285	+	0.268479i	$0.913479\pi$
$12$	−0.681517	+	0.224171i	−0.196737	+	0.0647125i
$13$		−	4.46088i		−	1.23723i	−0.785695	−	0.618613i	$-0.787695\pi$
$13$		−	4.46088i		−	1.23723i	0.785695	−	0.618613i	$-0.212305\pi$
$14$		0			0
$15$	−3.82843	+	1.25928i	−0.988496	+	0.325145i
$16$	−3.00000			−0.750000
$17$	0.963811			0.233759			0.116879	−	0.993146i	$-0.462711\pi$
$17$	0.963811			0.233759			0.116879	+	0.993146i	$0.462711\pi$
$18$	−2.24264	−	3.04017i	−0.528595	−	0.716575i
$19$			2.16478i			0.496636i	0.968679	+	0.248318i	$0.0798777\pi$
$19$			2.16478i			0.496636i	−0.968679	+	0.248318i	$0.920122\pi$
$20$	0.963811			0.215515
$21$		0			0
$22$	2.24264			0.478133
$23$			4.29945i			0.896498i	0.893909	+	0.448249i	$0.147952\pi$
$23$			4.29945i			0.896498i	−0.893909	+	0.448249i	$0.852048\pi$
$24$	1.64533	+	5.00208i	0.335851	+	1.02105i
$25$	0.414214			0.0828427
$26$	−5.61750			−1.10168
$27$	−3.00836	+	4.23671i	−0.578960	+	0.815356i
$28$		0			0
$29$			7.86123i			1.45979i	0.683557	+	0.729897i	$0.260432\pi$
$29$			7.86123i			1.45979i	−0.683557	+	0.729897i	$0.739568\pi$
$30$	1.58579	+	4.82106i	0.289524	+	0.880202i
$31$			1.08239i			0.194403i	0.995265	+	0.0972017i	$0.0309892\pi$
$31$			1.08239i			0.194403i	−0.995265	+	0.0972017i	$0.969011\pi$
$32$		−	2.30250i		−	0.407029i
$33$	−0.963811	−	2.93015i	−0.167778	−	0.510074i
$34$		−	1.21371i		−	0.208149i
$35$		0			0
$36$	1.00000	−	0.737669i	0.166667	−	0.122945i
$37$	−5.07107			−0.833678			−0.416839	−	0.908980i	$-0.636862\pi$
$37$	−5.07107			−0.833678			−0.416839	+	0.908980i	$0.636862\pi$
$38$	2.72607			0.442227
$39$	2.41421	+	7.33962i	0.386584	+	1.17528i
$40$		−	7.07401i		−	1.11850i
$41$	−4.25447			−0.664436			−0.332218	−	0.943203i	$-0.607797\pi$
$41$	−4.25447			−0.664436			−0.332218	+	0.943203i	$0.607797\pi$
$42$		0			0
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$			0.737669i			0.111208i
$45$	5.61750	−	4.14386i	0.837408	−	0.617730i
$46$	5.41421			0.798282
$47$	0.564588			0.0823536			0.0411768	−	0.999152i	$-0.486889\pi$
$47$	0.564588			0.0823536			0.0411768	+	0.999152i	$0.486889\pi$
$48$	4.93599	−	1.62359i	0.712448	−	0.234345i
$49$		0			0
$50$		−	0.521611i		−	0.0737669i
$51$	−1.58579	+	0.521611i	−0.222055	+	0.0730401i
$52$		−	1.84776i		−	0.256238i
$53$		−	6.08034i		−	0.835199i	−0.908631	−	0.417600i	$-0.862871\pi$
$53$		−	6.08034i		−	0.835199i	0.908631	−	0.417600i	$-0.137129\pi$
$54$	5.33521	+	3.78837i	0.726030	+	0.515532i
$55$			4.14386i			0.558758i
$56$		0			0
$57$	−1.17157	−	3.56178i	−0.155179	−	0.471770i
$58$	9.89949			1.29987
$59$	−9.30739			−1.21172			−0.605859	−	0.795572i	$-0.707171\pi$
$59$	−9.30739			−1.21172			−0.605859	+	0.795572i	$0.707171\pi$
$60$	−1.58579	+	0.521611i	−0.204724	+	0.0673397i
$61$			7.52235i			0.963139i	0.876408	+	0.481569i	$0.159933\pi$
$61$			7.52235i			0.963139i	−0.876408	+	0.481569i	$0.840067\pi$
$62$	1.36303			0.173106
$63$		0			0
$64$	−8.89949			−1.11244
$65$		−	10.3798i		−	1.28745i
$66$	−3.68988	+	1.21371i	−0.454193	+	0.149397i
$67$	−14.4853			−1.76966			−0.884829	−	0.465915i	$-0.845725\pi$
$67$	−14.4853			−1.76966			−0.884829	+	0.465915i	$0.845725\pi$
$68$	0.399224			0.0484130
$69$	−2.32685	−	7.07401i	−0.280119	−	0.851611i
$70$		0			0
$71$		−	7.86123i		−	0.932957i	−0.884533	−	0.466478i	$-0.845523\pi$
$71$		−	7.86123i		−	0.932957i	0.884533	−	0.466478i	$-0.154477\pi$
$72$	−5.41421	−	7.33962i	−0.638071	−	0.864983i
$73$			6.43996i			0.753740i	0.926266	+	0.376870i	$0.123000\pi$
$73$			6.43996i			0.753740i	−0.926266	+	0.376870i	$0.877000\pi$
$74$			6.38589i			0.742345i
$75$	−0.681517	+	0.224171i	−0.0786949	+	0.0258850i
$76$			0.896683i			0.102857i
$77$		0			0
$78$	9.24264	−	3.04017i	1.04652	−	0.344232i
$79$	4.82843			0.543240			0.271620	−	0.962405i	$-0.412441\pi$
$79$	4.82843			0.543240			0.271620	+	0.962405i	$0.412441\pi$
$80$	−6.98054			−0.780448
$81$	2.65685	−	8.59890i	0.295206	−	0.955434i
$82$			5.35757i			0.591644i
$83$	14.5257			1.59440			0.797199	−	0.603716i	$-0.206314\pi$
$83$	14.5257			1.59440			0.797199	+	0.603716i	$0.206314\pi$
$84$		0			0
$85$	2.24264			0.243249
$86$		−	2.51856i		−	0.271583i
$87$	−4.25447	−	12.9343i	−0.456127	−	1.38670i
$88$	5.41421			0.577157
$89$	8.34357			0.884417			0.442209	−	0.896912i	$-0.354195\pi$
$89$	8.34357			0.884417			0.442209	+	0.896912i	$0.354195\pi$
$90$	−5.21828	−	7.07401i	−0.550055	−	0.745666i
$91$		0			0
$92$			1.78089i			0.185671i
$93$	−0.585786	−	1.78089i	−0.0607432	−	0.184670i
$94$		−	0.710974i		−	0.0733314i
$95$			5.03712i			0.516798i
$96$	1.24611	+	3.78837i	0.127180	+	0.386649i
$97$			13.8310i			1.40432i	0.712017	+	0.702162i	$0.247782\pi$
$97$			13.8310i			1.40432i	−0.712017	+	0.702162i	$0.752218\pi$
$98$		0			0
$99$	3.17157	+	4.29945i	0.318755	+	0.432111i
$100$	0.171573			0.0171573
$101$	12.9973			1.29328			0.646638	−	0.762797i	$-0.276174\pi$
$101$	12.9973			1.29328			0.646638	+	0.762797i	$0.276174\pi$
$102$	0.656854	+	1.99695i	0.0650383	+	0.197727i
$103$		−	16.1271i		−	1.58905i	−0.607231	−	0.794525i	$-0.707720\pi$
$103$		−	16.1271i		−	1.58905i	0.607231	−	0.794525i	$-0.292280\pi$
$104$	−13.5619			−1.32985
$105$		0			0
$106$	−7.65685			−0.743699
$107$			8.90446i			0.860826i	0.902632	+	0.430413i	$0.141632\pi$
$107$			8.90446i			0.860826i	−0.902632	+	0.430413i	$0.858368\pi$
$108$	−1.24611	+	1.75490i	−0.119907	+	0.168866i
$109$	9.41421			0.901718			0.450859	−	0.892595i	$-0.351118\pi$
$109$	9.41421			0.901718			0.450859	+	0.892595i	$0.351118\pi$
$110$	5.21828			0.497543
$111$	8.34357	−	2.74444i	0.791937	−	0.260491i
$112$		0			0
$113$		−	11.1175i		−	1.04584i	−0.852381	−	0.522921i	$-0.824842\pi$
$113$		−	11.1175i		−	1.04584i	0.852381	−	0.522921i	$-0.175158\pi$
$114$	−4.48528	+	1.47534i	−0.420085	+	0.138178i
$115$			10.0042i			0.932893i
$116$			3.25623i			0.302333i
$117$	−7.94435	−	10.7695i	−0.734455	−	0.995643i
$118$			11.7206i			1.07897i
$119$		0			0
$120$	3.82843	+	11.6391i	0.349486	+	1.06250i
$121$	7.82843			0.711675
$122$	9.47275			0.857622
$123$	7.00000	−	2.30250i	0.631169	−	0.207610i
$124$			0.448342i			0.0402623i
$125$	−10.6704			−0.954391
$126$		0			0
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$			6.60195i			0.583536i
$129$	−3.29066	+	1.08239i	−0.289726	+	0.0952993i
$130$	−13.0711			−1.14641
$131$	−16.4533			−1.43753			−0.718765	−	0.695253i	$-0.755292\pi$
$131$	−16.4533			−1.43753			−0.718765	+	0.695253i	$0.755292\pi$
$132$	−0.399224	−	1.21371i	−0.0347480	−	0.105640i
$133$		0			0
$134$			18.2410i			1.57578i
$135$	−7.00000	+	9.85818i	−0.602464	+	0.848457i
$136$		−	2.93015i		−	0.251258i
$137$		−	9.33657i		−	0.797677i	−0.917021	−	0.398839i	$-0.869413\pi$
$137$		−	9.33657i		−	0.797677i	0.917021	−	0.398839i	$-0.130587\pi$
$138$	−8.90816	+	2.93015i	−0.758313	+	0.249431i
$139$		−	17.3952i		−	1.47544i	−0.675106	−	0.737721i	$-0.735902\pi$
$139$		−	17.3952i		−	1.47544i	0.675106	−	0.737721i	$-0.264098\pi$
$140$		0			0
$141$	−0.928932	+	0.305553i	−0.0782302	+	0.0257322i
$142$	−9.89949			−0.830747
$143$	7.94435			0.664340
$144$	−7.24264	+	5.34267i	−0.603553	+	0.445223i
$145$			18.2919i			1.51906i
$146$	8.10971			0.671165
$147$		0			0
$148$	−2.10051			−0.172660
$149$			7.55568i			0.618985i	0.950902	+	0.309493i	$0.100159\pi$
$149$			7.55568i			0.618985i	−0.950902	+	0.309493i	$0.899841\pi$
$150$	0.282294	+	0.858221i	0.0230492	+	0.0700735i
$151$	−0.485281			−0.0394916			−0.0197458	−	0.999805i	$-0.506286\pi$
$151$	−0.485281			−0.0394916			−0.0197458	+	0.999805i	$0.506286\pi$
$152$	6.58132			0.533815
$153$	2.32685	−	1.71644i	0.188114	−	0.138766i
$154$		0			0
$155$			2.51856i			0.202296i
$156$	1.00000	+	3.04017i	0.0800641	+	0.243408i
$157$			6.43996i			0.513965i	0.966416	+	0.256982i	$0.0827282\pi$
$157$			6.43996i			0.513965i	−0.966416	+	0.256982i	$0.917272\pi$
$158$		−	6.08034i		−	0.483726i
$159$	3.29066	+	10.0042i	0.260966	+	0.793382i
$160$		−	5.35757i		−	0.423553i
$161$		0			0
$162$	−10.8284	−	3.34572i	−0.850762	−	0.262865i
$163$	−9.17157			−0.718373			−0.359187	−	0.933266i	$-0.616946\pi$
$163$	−9.17157			−0.718373			−0.359187	+	0.933266i	$0.616946\pi$
$164$	−1.76226			−0.137609
$165$	−2.24264	−	6.81801i	−0.174589	−	0.530781i
$166$		−	18.2919i		−	1.41973i
$167$	6.01673			0.465588			0.232794	−	0.972526i	$-0.425213\pi$
$167$	6.01673			0.465588			0.232794	+	0.972526i	$0.425213\pi$
$168$		0			0
$169$	−6.89949			−0.530730
$170$		−	2.82411i		−	0.216600i
$171$	3.85525	+	5.22625i	0.294818	+	0.399661i
$172$	0.828427			0.0631670
$173$	−18.2155			−1.38490			−0.692451	−	0.721465i	$-0.743469\pi$
$173$	−18.2155			−1.38490			−0.692451	+	0.721465i	$0.743469\pi$
$174$	−16.2879	+	5.35757i	−1.23478	+	0.406156i
$175$		0			0
$176$		−	5.34267i		−	0.402719i
$177$	15.3137	−	5.03712i	1.15105	−	0.378613i
$178$		−	10.5069i		−	0.787525i
$179$			12.8984i			0.964068i	0.876152	+	0.482034i	$0.160102\pi$
$179$			12.8984i			0.964068i	−0.876152	+	0.482034i	$0.839898\pi$
$180$	2.32685	−	1.71644i	0.173433	−	0.127936i
$181$			3.11586i			0.231600i	0.993273	+	0.115800i	$0.0369432\pi$
$181$			3.11586i			0.231600i	−0.993273	+	0.115800i	$0.963057\pi$
$182$		0			0
$183$	−4.07107	−	12.3767i	−0.300942	−	0.914915i
$184$	13.0711			0.963612
$185$	−11.7996			−0.867523
$186$	−2.24264	+	0.737669i	−0.164438	+	0.0540885i
$187$			1.71644i			0.125519i
$188$	0.233860			0.0170560
$189$		0			0
$190$	6.34315			0.460180
$191$		−	11.4230i		−	0.826540i	−0.910608	−	0.413270i	$-0.864387\pi$
$191$		−	11.4230i		−	0.826540i	0.910608	−	0.413270i	$-0.135613\pi$
$192$	14.6426	−	4.81637i	1.05674	−	0.347592i
$193$	5.31371			0.382489			0.191245	−	0.981542i	$-0.438748\pi$
$193$	5.31371			0.382489			0.191245	+	0.981542i	$0.438748\pi$
$194$	17.4171			1.25047
$195$	5.61750	+	17.0782i	0.402278	+	1.22299i
$196$		0			0
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	5.41421	−	3.99390i	0.384771	−	0.283834i
$199$		−	17.2095i		−	1.21995i	−0.792421	−	0.609974i	$-0.791180\pi$
$199$		−	17.2095i		−	1.21995i	0.792421	−	0.609974i	$-0.208820\pi$
$200$		−	1.25928i		−	0.0890446i
$201$	23.8331	−	7.83938i	1.68105	−	0.552947i
$202$		−	16.3672i		−	1.15159i
$203$		0			0
$204$	−0.656854	+	0.216058i	−0.0459890	+	0.0151271i
$205$	−9.89949			−0.691411
$206$	−20.3085			−1.41496
$207$	7.65685	+	10.3798i	0.532188	+	0.721446i
$208$			13.3827i			0.927920i
$209$	−3.85525			−0.266673
$210$		0			0
$211$	21.7990			1.50070			0.750352	−	0.661038i	$-0.229884\pi$
$211$	21.7990			1.50070			0.750352	+	0.661038i	$0.229884\pi$
$212$		−	2.51856i		−	0.172975i
$213$	4.25447	+	12.9343i	0.291511	+	0.886245i
$214$	11.2132			0.766519
$215$	4.65369			0.317379
$216$	12.8803	+	9.14594i	0.876396	+	0.622302i
$217$		0			0
$218$		−	11.8551i		−	0.802931i
$219$	−3.48528	−	10.5959i	−0.235513	−	0.716001i
$220$			1.71644i			0.115723i
$221$		−	4.29945i		−	0.289212i
$222$	−3.45602	−	10.5069i	−0.231953	−	0.705177i
$223$			0.896683i			0.0600463i	0.999549	+	0.0300232i	$0.00955811\pi$
$223$			0.896683i			0.0600463i	−0.999549	+	0.0300232i	$0.990442\pi$
$224$		0			0
$225$	1.00000	−	0.737669i	0.0666667	−	0.0491779i
$226$	−14.0000			−0.931266
$227$	−17.8163			−1.18251			−0.591255	−	0.806484i	$-0.701367\pi$
$227$	−17.8163			−1.18251			−0.591255	+	0.806484i	$0.701367\pi$
$228$	−0.485281	−	1.47534i	−0.0321385	−	0.0977067i
$229$		−	10.7695i		−	0.711671i	−0.934549	−	0.355835i	$-0.884196\pi$
$229$		−	10.7695i		−	0.711671i	0.934549	−	0.355835i	$-0.115804\pi$
$230$	12.5980			0.830690
$231$		0			0
$232$	23.8995			1.56908
$233$		−	17.9355i		−	1.17499i	−0.809227	−	0.587496i	$-0.800114\pi$
$233$		−	17.9355i		−	1.17499i	0.809227	−	0.587496i	$-0.199886\pi$
$234$	−13.5619	+	10.0042i	−0.886566	+	0.653993i
$235$	1.31371			0.0856969
$236$	−3.85525			−0.250955
$237$	−7.94435	+	2.61313i	−0.516041	+	0.169741i
$238$		0			0
$239$			14.3737i			0.929757i	0.885375	+	0.464878i	$0.153902\pi$
$239$			14.3737i			0.929757i	−0.885375	+	0.464878i	$0.846098\pi$
$240$	11.4853	−	3.77784i	0.741372	−	0.243859i
$241$		−	11.8519i		−	0.763449i	−0.924276	−	0.381725i	$-0.875330\pi$
$241$		−	11.8519i		−	0.763449i	0.924276	−	0.381725i	$-0.124670\pi$
$242$		−	9.85818i		−	0.633708i
$243$	0.282294	+	15.5859i	0.0181092	+	0.999836i
$244$			3.11586i			0.199473i
$245$		0			0
$246$	−2.89949	−	8.81496i	−0.184865	−	0.562021i
$247$	9.65685			0.614451
$248$	3.29066			0.208957
$249$	−23.8995	+	7.86123i	−1.51457	+	0.498185i
$250$			13.4370i			0.849834i
$251$	−12.0335			−0.759545			−0.379772	−	0.925080i	$-0.623998\pi$
$251$	−12.0335			−0.759545			−0.379772	+	0.925080i	$0.623998\pi$
$252$		0			0
$253$	−7.65685			−0.481382
$254$		−	2.51856i		−	0.158029i
$255$	−3.68988	+	1.21371i	−0.231069	+	0.0760054i
$256$	−9.48528			−0.592830
$257$	10.8358			0.675918			0.337959	−	0.941161i	$-0.390264\pi$
$257$	10.8358			0.675918			0.337959	+	0.941161i	$0.390264\pi$
$258$	1.36303	+	4.14386i	0.0848589	+	0.257985i
$259$		0			0
$260$		−	4.29945i		−	0.266641i
$261$	14.0000	+	18.9787i	0.866578	+	1.17475i
$262$			20.7193i			1.28004i
$263$		−	2.82411i		−	0.174142i	−0.996202	−	0.0870711i	$-0.972249\pi$
$263$		−	2.82411i		−	0.174142i	0.996202	−	0.0870711i	$-0.0277507\pi$
$264$	−8.90816	+	2.93015i	−0.548259	+	0.180338i
$265$		−	14.1480i		−	0.869106i
$266$		0			0
$267$	−13.7279	+	4.51551i	−0.840135	+	0.276345i
$268$	−6.00000			−0.366508
$269$	17.9817			1.09636			0.548181	−	0.836359i	$-0.315320\pi$
$269$	17.9817			1.09636			0.548181	+	0.836359i	$0.315320\pi$
$270$	12.4142	+	8.81496i	0.755505	+	0.536461i
$271$		−	5.41196i		−	0.328753i	−0.986398	−	0.164377i	$-0.947439\pi$
$271$		−	5.41196i		−	0.328753i	0.986398	−	0.164377i	$-0.0525612\pi$
$272$	−2.89143			−0.175319
$273$		0			0
$274$	−11.7574			−0.710288
$275$			0.737669i			0.0444831i
$276$	−0.963811	−	2.93015i	−0.0580146	−	0.176374i
$277$	−0.485281			−0.0291577			−0.0145789	−	0.999894i	$-0.504641\pi$
$277$	−0.485281			−0.0291577			−0.0145789	+	0.999894i	$0.504641\pi$
$278$	−21.9054			−1.31380
$279$	1.92762	+	2.61313i	0.115404	+	0.156444i
$280$		0			0
$281$		−	1.34877i		−	0.0804611i	−0.999190	−	0.0402306i	$-0.987191\pi$
$281$		−	1.34877i		−	0.0804611i	0.999190	−	0.0402306i	$-0.0128092\pi$
$282$	0.384776	+	1.16979i	0.0229131	+	0.0696597i
$283$		−	17.2095i		−	1.02300i	−0.859284	−	0.511499i	$-0.829090\pi$
$283$		−	17.2095i		−	1.02300i	0.859284	−	0.511499i	$-0.170910\pi$
$284$		−	3.25623i		−	0.193222i
$285$	−2.72607	−	8.28772i	−0.161478	−	0.490922i
$286$		−	10.0042i		−	0.591559i
$287$		0			0
$288$	−4.10051	−	5.55873i	−0.241625	−	0.327551i
$289$	−16.0711			−0.945357
$290$	23.0346			1.35264
$291$	−7.48528	−	22.7565i	−0.438795	−	1.33401i
$292$			2.66752i			0.156105i
$293$	6.74668			0.394145			0.197073	−	0.980389i	$-0.436857\pi$
$293$	6.74668			0.394145			0.197073	+	0.980389i	$0.436857\pi$
$294$		0			0
$295$	−21.6569			−1.26091
$296$			15.4169i			0.896090i
$297$	−7.54513	−	5.35757i	−0.437813	−	0.310878i
$298$	9.51472			0.551173
$299$	19.1794			1.10917
$300$	−0.282294	+	0.0928546i	−0.0162982	+	0.00536096i
$301$		0			0
$302$			0.611105i			0.0351652i
$303$	−21.3848	+	7.03407i	−1.22852	+	0.404097i
$304$		−	6.49435i		−	0.372477i
$305$			17.5034i			1.00224i
$306$	−2.16148	−	2.93015i	−0.123564	−	0.167506i
$307$		−	9.81845i		−	0.560369i	−0.959946	−	0.280184i	$-0.909604\pi$
$307$		−	9.81845i		−	0.560369i	0.959946	−	0.280184i	$-0.0903956\pi$
$308$		0			0
$309$	8.72792	+	26.5344i	0.496514	+	1.50949i
$310$	3.17157			0.180133
$311$	17.2517			0.978256			0.489128	−	0.872212i	$-0.337315\pi$
$311$	17.2517			0.978256			0.489128	+	0.872212i	$0.337315\pi$
$312$	22.3137	−	7.33962i	1.26326	−	0.415524i
$313$		−	0.0543929i		−	0.00307447i	−0.999999	−	0.00153724i	$-0.999511\pi$
$313$		−	0.0543929i		−	0.00307447i	0.999999	−	0.00153724i	$-0.000489317\pi$
$314$	8.10971			0.457658
$315$		0			0
$316$	2.00000			0.112509
$317$			34.3956i			1.93185i	0.258822	+	0.965925i	$0.416666\pi$
$317$			34.3956i			1.93185i	−0.258822	+	0.965925i	$0.583334\pi$
$318$	12.5980	−	4.14386i	0.706463	−	0.232376i
$319$	−14.0000			−0.783850
$320$	−20.7078			−1.15760
$321$	−4.81906	−	14.6508i	−0.268973	−	0.817725i
$322$		0			0
$323$			2.08644i			0.116093i
$324$	1.10051	−	3.56178i	0.0611392	−	0.197877i
$325$		−	1.84776i		−	0.102495i
$326$			11.5496i			0.639672i
$327$	−15.4895	+	5.09494i	−0.856570	+	0.281751i
$328$			12.9343i			0.714178i
$329$		0			0
$330$	−8.58579	+	2.82411i	−0.472632	+	0.155462i
$331$	18.8284			1.03490			0.517452	−	0.855712i	$-0.326881\pi$
$331$	18.8284			1.03490			0.517452	+	0.855712i	$0.326881\pi$
$332$	6.01673			0.330211
$333$	−12.2426	+	9.03102i	−0.670893	+	0.494897i
$334$		−	7.57675i		−	0.414581i
$335$	−33.7050			−1.84150
$336$		0			0
$337$	6.10051			0.332316			0.166158	−	0.986099i	$-0.446864\pi$
$337$	6.10051			0.332316			0.166158	+	0.986099i	$0.446864\pi$
$338$			8.68840i			0.472586i
$339$	6.01673	+	18.2919i	0.326784	+	0.993479i
$340$	0.928932			0.0503784
$341$	−1.92762			−0.104387
$342$	6.58132	−	4.85483i	0.355877	−	0.262519i
$343$		0			0
$344$		−	6.08034i		−	0.327830i
$345$	−5.41421	−	16.4601i	−0.291491	−	0.886184i
$346$			22.9385i			1.23318i
$347$			6.38589i			0.342813i	0.985200	+	0.171406i	$0.0548311\pi$
$347$			6.38589i			0.342813i	−0.985200	+	0.171406i	$0.945169\pi$
$348$	−1.76226	−	5.35757i	−0.0944670	−	0.287196i
$349$			28.9845i			1.55150i	0.631038	+	0.775752i	$0.282629\pi$
$349$			28.9845i			1.55150i	−0.631038	+	0.775752i	$0.717371\pi$
$350$		0			0
$351$	18.8995	+	13.4200i	1.00878	+	0.716305i
$352$	4.10051			0.218558
$353$	−25.5953			−1.36230			−0.681150	−	0.732144i	$-0.738520\pi$
$353$	−25.5953			−1.36230			−0.681150	+	0.732144i	$0.738520\pi$
$354$	−6.34315	−	19.2842i	−0.337134	−	1.02495i
$355$		−	18.2919i		−	0.970832i
$356$	3.45602			0.183169
$357$		0			0
$358$	16.2426			0.858450
$359$		−	2.21301i		−	0.116798i	−0.998293	−	0.0583990i	$-0.981400\pi$
$359$		−	2.21301i		−	0.116798i	0.998293	−	0.0583990i	$-0.0185996\pi$
$360$	−12.5980	−	17.0782i	−0.663975	−	0.900099i
$361$	14.3137			0.753353
$362$	3.92374			0.206227
$363$	−12.8803	+	4.23671i	−0.676042	+	0.222370i
$364$		0			0
$365$			14.9848i			0.784340i
$366$	−15.5858	+	5.12661i	−0.814682	+	0.267972i
$367$			34.5278i			1.80233i	0.433471	+	0.901167i	$0.357289\pi$
$367$			34.5278i			1.80233i	−0.433471	+	0.901167i	$0.642711\pi$
$368$		−	12.8984i		−	0.672373i
$369$	−10.2712	+	7.57675i	−0.534697	+	0.394430i
$370$			14.8590i			0.772482i
$371$		0			0
$372$	−0.242641	−	0.737669i	−0.0125803	−	0.0382464i
$373$	−9.17157			−0.474886			−0.237443	−	0.971401i	$-0.576309\pi$
$373$	−9.17157			−0.474886			−0.237443	+	0.971401i	$0.576309\pi$
$374$	2.16148			0.111768
$375$	17.5563	−	5.77479i	0.906606	−	0.298209i
$376$		−	1.71644i		−	0.0885188i
$377$	35.0681			1.80610
$378$		0			0
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$			2.08644i			0.107032i
$381$	−3.29066	+	1.08239i	−0.168585	+	0.0554526i
$382$	−14.3848			−0.735989
$383$	15.0903			0.771076			0.385538	−	0.922692i	$-0.374016\pi$
$383$	15.0903			0.771076			0.385538	+	0.922692i	$0.374016\pi$
$384$	−3.57295	−	10.8624i	−0.182331	−	0.554319i
$385$		0			0
$386$		−	6.69145i		−	0.340586i
$387$	4.82843	−	3.56178i	0.245443	−	0.181056i
$388$			5.72899i			0.290845i
$389$			3.68835i			0.187007i	0.995619	+	0.0935033i	$0.0298066\pi$
$389$			3.68835i			0.187007i	−0.995619	+	0.0935033i	$0.970193\pi$
$390$	21.5062	−	7.07401i	1.08901	−	0.358206i
$391$			4.14386i			0.209564i
$392$		0			0
$393$	27.0711	−	8.90446i	1.36555	−	0.449170i
$394$		0			0
$395$	11.2350			0.565295
$396$	1.31371	+	1.78089i	0.0660163	+	0.0894931i
$397$			22.6758i			1.13807i	0.822314	+	0.569034i	$0.192683\pi$
$397$			22.6758i			1.13807i	−0.822314	+	0.569034i	$0.807317\pi$
$398$	−21.6716			−1.08630
$399$		0			0
$400$	−1.24264			−0.0621320
$401$		−	33.6579i		−	1.68080i	−0.541969	−	0.840399i	$-0.682321\pi$
$401$		−	33.6579i		−	1.68080i	0.541969	−	0.840399i	$-0.317679\pi$
$402$	−9.87197	−	30.0125i	−0.492369	−	1.49689i
$403$	4.82843			0.240521
$404$	5.38364			0.267846
$405$	6.18209	−	20.0083i	0.307191	−	0.994222i
$406$		0			0
$407$		−	9.03102i		−	0.447651i
$408$	1.58579	+	4.82106i	0.0785081	+	0.238678i
$409$		−	30.1438i		−	1.49052i	−0.666777	−	0.745258i	$-0.732327\pi$
$409$		−	30.1438i		−	1.49052i	0.666777	−	0.745258i	$-0.267673\pi$
$410$			12.4662i			0.615664i
$411$	5.05292	+	15.3617i	0.249242	+	0.757738i
$412$		−	6.68006i		−	0.329103i
$413$		0			0
$414$	13.0711	−	9.64212i	0.642408	−	0.473885i
$415$	33.7990			1.65913
$416$	−10.2712			−0.503587
$417$	9.41421	+	28.6208i	0.461016	+	1.40157i
$418$			4.85483i			0.237458i
$419$	3.52452			0.172184			0.0860920	−	0.996287i	$-0.472562\pi$
$419$	3.52452			0.172184			0.0860920	+	0.996287i	$0.472562\pi$
$420$		0			0
$421$	−31.7990			−1.54979			−0.774894	−	0.632091i	$-0.782197\pi$
$421$	−31.7990			−1.54979			−0.774894	+	0.632091i	$0.782197\pi$
$422$		−	27.4510i		−	1.33630i
$423$	1.36303	−	1.00547i	0.0662730	−	0.0488876i
$424$	−18.4853			−0.897725
$425$	0.399224			0.0193652
$426$	16.2879	−	5.35757i	0.789152	−	0.259575i
$427$		0			0
$428$			3.68835i			0.178283i
$429$	−13.0711	+	4.29945i	−0.631077	+	0.207579i
$430$		−	5.86030i		−	0.282609i
$431$		−	26.9665i		−	1.29893i	−0.760391	−	0.649465i	$-0.774993\pi$
$431$		−	26.9665i		−	1.29893i	0.760391	−	0.649465i	$-0.225007\pi$
$432$	9.02509	−	12.7101i	0.434220	−	0.611517i
$433$			6.25425i			0.300560i	0.988643	+	0.150280i	$0.0480175\pi$
$433$			6.25425i			0.300560i	−0.988643	+	0.150280i	$0.951982\pi$
$434$		0			0
$435$	−9.89949	−	30.0962i	−0.474644	−	1.44300i
$436$	3.89949			0.186752
$437$	−9.30739			−0.445233
$438$	−13.3431	+	4.38895i	−0.637560	+	0.209712i
$439$		−	12.9887i		−	0.619917i	−0.950750	−	0.309959i	$-0.899685\pi$
$439$		−	12.9887i		−	0.619917i	0.950750	−	0.309959i	$-0.100315\pi$
$440$	12.5980			0.600588
$441$		0			0
$442$	−5.41421			−0.257528
$443$		−	4.91056i		−	0.233308i	−0.993173	−	0.116654i	$-0.962783\pi$
$443$		−	4.91056i		−	0.233308i	0.993173	−	0.116654i	$-0.0372168\pi$
$444$	3.45602	−	1.13679i	0.164016	−	0.0539494i
$445$	19.4142			0.920322
$446$	1.12918			0.0534680
$447$	−4.08910	−	12.4316i	−0.193408	−	0.587994i
$448$		0			0
$449$		−	26.8399i		−	1.26665i	−0.773884	−	0.633327i	$-0.781689\pi$
$449$		−	26.8399i		−	1.26665i	0.773884	−	0.633327i	$-0.218311\pi$
$450$	−0.928932	−	1.25928i	−0.0437903	−	0.0593630i
$451$		−	7.57675i		−	0.356775i
$452$		−	4.60500i		−	0.216601i
$453$	0.798447	−	0.262632i	0.0375143	−	0.0123395i
$454$			22.4357i			1.05296i
$455$		0			0
$456$	−10.8284	+	3.56178i	−0.507088	+	0.166796i
$457$	10.6274			0.497130			0.248565	−	0.968615i	$-0.420041\pi$
$457$	10.6274			0.497130			0.248565	+	0.968615i	$0.420041\pi$
$458$	−13.5619			−0.633704
$459$	−2.89949	+	4.08339i	−0.135337	+	0.190596i
$460$			4.14386i			0.193208i
$461$	−0.729951			−0.0339972			−0.0169986	−	0.999856i	$-0.505411\pi$
$461$	−0.729951			−0.0339972			−0.0169986	+	0.999856i	$0.505411\pi$
$462$		0			0
$463$	−12.0000			−0.557687			−0.278844	−	0.960337i	$-0.589951\pi$
$463$	−12.0000			−0.557687			−0.278844	+	0.960337i	$0.589951\pi$
$464$		−	23.5837i		−	1.09485i
$465$	−1.36303	−	4.14386i	−0.0632092	−	0.192167i
$466$	−22.5858			−1.04627
$467$	−1.92762			−0.0891997			−0.0445999	−	0.999005i	$-0.514201\pi$
$467$	−1.92762			−0.0891997			−0.0445999	+	0.999005i	$0.514201\pi$
$468$	−3.29066	−	4.46088i	−0.152111	−	0.206204i
$469$		0			0
$470$		−	1.65433i		−	0.0763084i
$471$	−3.48528	−	10.5959i	−0.160593	−	0.488231i
$472$			28.2960i			1.30243i
$473$			3.56178i			0.163771i
$474$	3.29066	+	10.0042i	0.151145	+	0.459506i
$475$			0.896683i			0.0411426i
$476$		0			0
$477$	−10.8284	−	14.6792i	−0.495800	−	0.672116i
$478$	18.1005			0.827898
$479$	−23.8331			−1.08896			−0.544480	−	0.838774i	$-0.683273\pi$
$479$	−23.8331			−1.08896			−0.544480	+	0.838774i	$0.683273\pi$
$480$	2.89949	+	8.81496i	0.132343	+	0.402346i
$481$			22.6215i			1.03145i
$482$	−14.9249			−0.679810
$483$		0			0
$484$	3.24264			0.147393
$485$			32.1826i			1.46134i
$486$	19.6270	−	0.355487i	0.890299	−	0.0161252i
$487$	−0.485281			−0.0219902			−0.0109951	−	0.999940i	$-0.503500\pi$
$487$	−0.485281			−0.0219902			−0.0109951	+	0.999940i	$0.503500\pi$
$488$	22.8692			1.03524
$489$	15.0903	−	4.96362i	0.682405	−	0.224463i
$490$		0			0
$491$			12.4662i			0.562593i	0.959621	+	0.281297i	$0.0907645\pi$
$491$			12.4662i			0.562593i	−0.959621	+	0.281297i	$0.909235\pi$
$492$	2.89949	−	0.953728i	0.130719	−	0.0429974i
$493$			7.57675i			0.341239i
$494$		−	12.1607i		−	0.547135i
$495$	7.37976	+	10.0042i	0.331696	+	0.449654i
$496$		−	3.24718i		−	0.145803i
$497$		0			0
$498$	9.89949	+	30.0962i	0.443607	+	1.34864i
$499$	−9.17157			−0.410576			−0.205288	−	0.978702i	$-0.565813\pi$
$499$	−9.17157			−0.410576			−0.205288	+	0.978702i	$0.565813\pi$
$500$	−4.41983			−0.197661
$501$	−9.89949	+	3.25623i	−0.442277	+	0.145478i
$502$			15.1535i			0.676333i
$503$	8.50894			0.379395			0.189697	−	0.981843i	$-0.439249\pi$
$503$	8.50894			0.379395			0.189697	+	0.981843i	$0.439249\pi$
$504$		0			0
$505$	30.2426			1.34578
$506$			9.64212i			0.428645i
$507$	11.3519	−	3.73398i	0.504157	−	0.165832i
$508$	0.828427			0.0367555
$509$	−36.2657			−1.60745			−0.803725	−	0.595001i	$-0.797152\pi$
$509$	−36.2657			−1.60745			−0.803725	+	0.595001i	$0.797152\pi$
$510$	1.52840	+	4.64659i	0.0676786	+	0.205755i
$511$		0			0
$512$			25.1485i			1.11142i
$513$	−9.17157	−	6.51246i	−0.404935	−	0.287532i
$514$		−	13.6453i		−	0.601868i
$515$		−	37.5253i		−	1.65356i
$516$	−1.36303	+	0.448342i	−0.0600043	+	0.0197371i
$517$			1.00547i			0.0442205i
$518$		0			0
$519$	29.9706	−	9.85818i	1.31556	−	0.432726i
$520$	−31.5563			−1.38384
$521$	−1.52840			−0.0669604			−0.0334802	−	0.999439i	$-0.510659\pi$
$521$	−1.52840			−0.0669604			−0.0334802	+	0.999439i	$0.510659\pi$
$522$	23.8995	−	17.6299i	1.04605	−	0.771641i
$523$		−	41.9957i		−	1.83634i	−0.396181	−	0.918172i	$-0.629665\pi$
$523$		−	41.9957i		−	1.83634i	0.396181	−	0.918172i	$-0.370335\pi$
$524$	−6.81517			−0.297722
$525$		0			0
$526$	−3.55635			−0.155064
$527$			1.04322i			0.0454435i
$528$	2.89143	+	8.79045i	0.125834	+	0.382555i
$529$	4.51472			0.196292
$530$	−17.8163			−0.773892
$531$	−22.4700	+	16.5754i	−0.975116	+	0.719313i
$532$		0			0
$533$			18.9787i			0.822059i
$534$	5.68629	+	17.2873i	0.246070	+	0.748095i
$535$			20.7193i			0.895773i
$536$			44.0377i			1.90214i
$537$	−6.98054	−	21.2220i	−0.301232	−	0.915798i
$538$		−	22.6440i		−	0.976251i
$539$		0			0
$540$	−2.89949	+	4.08339i	−0.124774	+	0.175721i
$541$	−14.9706			−0.643635			−0.321817	−	0.946802i	$-0.604294\pi$
$541$	−14.9706			−0.643635			−0.321817	+	0.946802i	$0.604294\pi$
$542$	−6.81517			−0.292737
$543$	−1.68629	−	5.12661i	−0.0723657	−	0.220004i
$544$		−	2.21918i		−	0.0951464i
$545$	21.9054			0.938325
$546$		0			0
$547$	21.7990			0.932058			0.466029	−	0.884770i	$-0.345684\pi$
$547$	21.7990			0.932058			0.466029	+	0.884770i	$0.345684\pi$
$548$		−	3.86733i		−	0.165204i
$549$	13.3965	+	18.1606i	0.571748	+	0.775074i
$550$	0.928932			0.0396098
$551$	−17.0179			−0.724986
$552$	−21.5062	+	7.07401i	−0.915365	+	0.301090i
$553$		0			0
$554$			0.611105i			0.0259634i
$555$	19.4142	−	6.38589i	0.824087	−	0.271066i
$556$		−	7.20533i		−	0.305574i
$557$			27.2720i			1.15555i	0.816195	+	0.577777i	$0.196080\pi$
$557$			27.2720i			1.15555i	−0.816195	+	0.577777i	$0.803920\pi$
$558$	3.29066	−	2.42742i	0.139305	−	0.102761i
$559$		−	8.92177i		−	0.377351i
$560$		0			0
$561$	−0.928932	−	2.82411i	−0.0392195	−	0.119234i
$562$	−1.69848			−0.0716463
$563$	43.8109			1.84641			0.923204	−	0.384311i	$-0.125561\pi$
$563$	43.8109			1.84641			0.923204	+	0.384311i	$0.125561\pi$
$564$	−0.384776	+	0.126564i	−0.0162020	+	0.00532931i
$565$		−	25.8686i		−	1.08830i
$566$	−21.6716			−0.910924
$567$		0			0
$568$	−23.8995			−1.00280
$569$			35.7444i			1.49848i	0.662297	+	0.749241i	$0.269582\pi$
$569$			35.7444i			1.49848i	−0.662297	+	0.749241i	$0.730418\pi$
$570$	−10.4366	+	3.43289i	−0.437139	+	0.143788i
$571$	25.1127			1.05093			0.525467	−	0.850814i	$-0.323891\pi$
$571$	25.1127			1.05093			0.525467	+	0.850814i	$0.323891\pi$
$572$	3.29066			0.137589
$573$	6.18209	+	18.7946i	0.258261	+	0.785156i
$574$		0			0
$575$			1.78089i			0.0742683i
$576$	−21.4853	+	15.8490i	−0.895220	+	0.660376i
$577$		−	1.13679i		−	0.0473250i	−0.999720	−	0.0236625i	$-0.992467\pi$
$577$		−	1.13679i		−	0.0473250i	0.999720	−	0.0236625i	$-0.00753271\pi$
$578$			20.2380i			0.841789i
$579$	−8.74280	+	2.87576i	−0.363338	+	0.119512i
$580$			7.57675i			0.314607i
$581$		0			0
$582$	−28.6569	+	9.42607i	−1.18786	+	0.390723i
$583$	10.8284			0.448468
$584$	19.5786			0.810167
$585$	−18.4853	−	25.0590i	−0.764272	−	1.03606i
$586$		−	8.49596i		−	0.350965i
$587$		0			0			−	1.00000i	$-0.5\pi$
$587$		0			0				1.00000i	$0.5\pi$
$588$		0			0
$589$	−2.34315			−0.0965476
$590$			27.2720i			1.12277i
$591$		0			0
$592$	15.2132			0.625259
$593$	25.3614			1.04147			0.520735	−	0.853718i	$-0.325658\pi$
$593$	25.3614			1.04147			0.520735	+	0.853718i	$0.325658\pi$
$594$	−6.74668	+	9.50143i	−0.276820	+	0.389848i
$595$		0			0
$596$			3.12967i			0.128196i
$597$	9.31371	+	28.3153i	0.381185	+	1.15887i
$598$		−	24.1522i		−	0.987656i
$599$		−	40.7815i		−	1.66629i	−0.553057	−	0.833144i	$-0.686539\pi$
$599$		−	40.7815i		−	1.66629i	0.553057	−	0.833144i	$-0.313461\pi$
$600$	0.681517	+	2.07193i	0.0278228	+	0.0845862i
$601$			13.8310i			0.564178i	0.959388	+	0.282089i	$0.0910274\pi$
$601$			13.8310i			0.564178i	−0.959388	+	0.282089i	$0.908973\pi$
$602$		0			0
$603$	−34.9706	+	25.7967i	−1.42411	+	1.05052i
$604$	−0.201010			−0.00817899
$605$	18.2155			0.740567
$606$	8.85786	+	26.9294i	0.359826	+	1.09393i
$607$			38.7485i			1.57276i	0.617746	+	0.786378i	$0.288046\pi$
$607$			38.7485i			1.57276i	−0.617746	+	0.786378i	$0.711954\pi$
$608$	4.98442			0.202145
$609$		0			0
$610$	22.0416			0.892440
$611$		−	2.51856i		−	0.101890i
$612$	0.963811	−	0.710974i	0.0389598	−	0.0287394i
$613$	−38.3848			−1.55035			−0.775173	−	0.631749i	$-0.782337\pi$
$613$	−38.3848			−1.55035			−0.775173	+	0.631749i	$0.782337\pi$
$614$	−12.3642			−0.498978
$615$	16.2879	−	5.35757i	0.656792	−	0.216038i
$616$		0			0
$617$		−	17.0712i		−	0.687262i	−0.939105	−	0.343631i	$-0.888343\pi$
$617$		−	17.0712i		−	0.687262i	0.939105	−	0.343631i	$-0.111657\pi$
$618$	33.4142	−	10.9909i	1.34412	−	0.442119i
$619$		−	24.7862i		−	0.996243i	−0.867107	−	0.498121i	$-0.834023\pi$
$619$		−	24.7862i		−	0.996243i	0.867107	−	0.498121i	$-0.165977\pi$
$620$			1.04322i			0.0418968i
$621$	−18.2155	−	12.9343i	−0.730965	−	0.519036i
$622$		−	21.7248i		−	0.871084i
$623$		0			0
$624$	−7.24264	−	22.0189i	−0.289938	−	0.881460i
$625$	−26.8995			−1.07598
$626$	−0.0684960			−0.00273765
$627$	6.34315	−	2.08644i	0.253321	−	0.0833245i
$628$			2.66752i			0.106446i
$629$	−4.88755			−0.194879
$630$		0			0
$631$	7.79899			0.310473			0.155236	−	0.987877i	$-0.450386\pi$
$631$	7.79899			0.310473			0.155236	+	0.987877i	$0.450386\pi$
$632$		−	14.6792i		−	0.583909i
$633$	−35.8665	+	11.7975i	−1.42557	+	0.468910i
$634$	43.3137			1.72021
$635$	4.65369			0.184676
$636$	1.36303	+	4.14386i	0.0540479	+	0.164315i
$637$		0			0
$638$			17.6299i			0.697975i
$639$	−14.0000	−	18.9787i	−0.553831	−	0.750786i
$640$			15.3617i			0.607226i
$641$			6.38589i			0.252228i	0.992016	+	0.126114i	$0.0402505\pi$
$641$			6.38589i			0.252228i	−0.992016	+	0.126114i	$0.959750\pi$
$642$	−18.4494	+	6.06854i	−0.728140	+	0.239506i
$643$		−	35.6871i		−	1.40736i	−0.710517	−	0.703681i	$-0.751539\pi$
$643$		−	35.6871i		−	1.40736i	0.710517	−	0.703681i	$-0.248461\pi$
$644$		0			0
$645$	−7.65685	+	2.51856i	−0.301488	+	0.0991682i
$646$	2.62742			0.103374
$647$	13.7272			0.539673			0.269836	−	0.962906i	$-0.413030\pi$
$647$	13.7272			0.539673			0.269836	+	0.962906i	$0.413030\pi$
$648$	−26.1421	−	8.07729i	−1.02696	−	0.317306i
$649$		−	16.5754i		−	0.650643i
$650$	−2.32685			−0.0912664
$651$		0			0
$652$	−3.79899			−0.148780
$653$		−	2.21301i		−	0.0866017i	−0.999062	−	0.0433008i	$-0.986213\pi$
$653$		−	2.21301i		−	0.0866017i	0.999062	−	0.0433008i	$-0.0137874\pi$
$654$	6.41595	+	19.5056i	0.250884	+	0.762729i
$655$	−38.2843			−1.49589
$656$	12.7634			0.498327
$657$	11.4689	+	15.5474i	0.447443	+	0.606563i
$658$		0			0
$659$		−	50.4236i		−	1.96423i	−0.188293	−	0.982113i	$-0.560296\pi$
$659$		−	50.4236i		−	1.96423i	0.188293	−	0.982113i	$-0.439704\pi$
$660$	−0.928932	−	2.82411i	−0.0361586	−	0.109928i
$661$		−	19.4287i		−	0.755688i	−0.925869	−	0.377844i	$-0.876666\pi$
$661$		−	19.4287i		−	0.755688i	0.925869	−	0.377844i	$-0.123334\pi$
$662$		−	23.7103i		−	0.921526i
$663$	2.32685	+	7.07401i	0.0903672	+	0.274732i
$664$		−	44.1605i		−	1.71376i
$665$		0			0
$666$	11.3726	+	15.4169i	0.440679	+	0.597393i
$667$	−33.7990			−1.30870
$668$	2.49221			0.0964265
$669$	−0.485281	−	1.47534i	−0.0187621	−	0.0570399i
$670$			42.4441i			1.63976i
$671$	−13.3965			−0.517166
$672$		0			0
$673$	−7.89949			−0.304503			−0.152252	−	0.988342i	$-0.548652\pi$
$673$	−7.89949			−0.304503			−0.152252	+	0.988342i	$0.548652\pi$
$674$		−	7.68224i		−	0.295909i
$675$	−1.24611	+	1.75490i	−0.0479626	+	0.0675463i
$676$	−2.85786			−0.109918
$677$	−1.19767			−0.0460302			−0.0230151	−	0.999735i	$-0.507327\pi$
$677$	−1.19767			−0.0460302			−0.0230151	+	0.999735i	$0.507327\pi$
$678$	23.0346	−	7.57675i	0.884639	−	0.290983i
$679$		0			0
$680$		−	6.81801i		−	0.261459i
$681$	29.3137	−	9.64212i	1.12330	−	0.369487i
$682$			2.42742i			0.0929506i
$683$			28.6208i			1.09515i	0.836758	+	0.547573i	$0.184448\pi$
$683$			28.6208i			1.09515i	−0.836758	+	0.547573i	$0.815552\pi$
$684$	1.59689	+	2.16478i	0.0610588	+	0.0827726i
$685$		−	21.7248i		−	0.830061i
$686$		0			0
$687$	5.82843	+	17.7194i	0.222368	+	0.676038i
$688$	−6.00000			−0.228748
$689$	−27.1237			−1.03333
$690$	−20.7279	+	6.81801i	−0.789099	+	0.259557i
$691$			20.4567i			0.778208i	0.921194	+	0.389104i	$0.127215\pi$
$691$			20.4567i			0.778208i	−0.921194	+	0.389104i	$0.872785\pi$
$692$	−7.54513			−0.286823
$693$		0			0
$694$	8.04163			0.305256
$695$		−	40.4760i		−	1.53534i
$696$	−39.3225	+	12.9343i	−1.49052	+	0.490274i
$697$	−4.10051			−0.155318
$698$	36.4996			1.38153
$699$	9.70661	+	29.5098i	0.367138	+	1.11616i
$700$		0			0
$701$			1.34877i			0.0509425i	0.999676	+	0.0254713i	$0.00810863\pi$
$701$			1.34877i			0.0509425i	−0.999676	+	0.0254713i	$0.991891\pi$
$702$	16.8995	−	23.7998i	0.637830	−	0.898264i
$703$		−	10.9778i		−	0.414034i
$704$		−	15.8490i		−	0.597333i
$705$	−2.16148	+	0.710974i	−0.0814061	+	0.0267768i
$706$			32.2317i			1.21305i
$707$		0			0
$708$	6.34315	−	2.08644i	0.238390	−	0.0784134i
$709$	28.7279			1.07890			0.539450	−	0.842018i	$-0.318632\pi$
$709$	28.7279			1.07890			0.539450	+	0.842018i	$0.318632\pi$
$710$	−23.0346			−0.864473
$711$	11.6569	−	8.59890i	0.437166	−	0.322484i
$712$		−	25.3659i		−	0.950627i
$713$	−4.65369			−0.174282
$714$		0			0
$715$	18.4853			0.691310
$716$			5.34267i			0.199665i
$717$	−7.77899	−	23.6494i	−0.290512	−	0.883205i
$718$	−2.78680			−0.104002
$719$	−6.91204			−0.257776			−0.128888	−	0.991659i	$-0.541141\pi$
$719$	−6.91204			−0.257776			−0.128888	+	0.991659i	$0.541141\pi$
$720$	−16.8525	+	12.4316i	−0.628056	+	0.463298i
$721$		0			0
$722$		−	18.0250i		−	0.670820i
$723$	6.41421	+	19.5003i	0.238547	+	0.725224i
$724$			1.29063i			0.0479659i
$725$			3.25623i			0.120933i
$726$	5.33521	+	16.2200i	0.198008	+	0.601979i
$727$			29.9037i			1.10907i	0.832161	+	0.554533i	$0.187103\pi$
$727$			29.9037i			1.10907i	−0.832161	+	0.554533i	$0.812897\pi$
$728$		0			0
$729$	−8.89949	−	25.4912i	−0.329611	−	0.944117i
$730$	18.8701			0.698412
$731$	1.92762			0.0712957
$732$	−1.68629	−	5.12661i	−0.0623271	−	0.189485i
$733$			15.0991i			0.557698i	0.960335	+	0.278849i	$0.0899529\pi$
$733$			15.0991i			0.557698i	−0.960335	+	0.278849i	$0.910047\pi$
$734$	43.4801			1.60488
$735$		0			0
$736$	9.89949			0.364900
$737$		−	25.7967i		−	0.950234i
$738$	9.54124	+	12.9343i	0.351218	+	0.476119i
$739$	39.1127			1.43878			0.719392	−	0.694604i	$-0.244421\pi$
$739$	39.1127			1.43878			0.719392	+	0.694604i	$0.244421\pi$
$740$	−4.88755			−0.179670
$741$	−15.8887	+	5.22625i	−0.583686	+	0.191991i
$742$		0			0
$743$			3.25623i			0.119459i	0.998215	+	0.0597297i	$0.0190239\pi$
$743$			3.25623i			0.119459i	−0.998215	+	0.0597297i	$0.980976\pi$
$744$	−5.41421	+	1.78089i	−0.198495	+	0.0652906i
$745$			17.5809i			0.644115i
$746$			11.5496i			0.422860i
$747$	35.0681	−	25.8686i	1.28307	−	0.946484i
$748$			0.710974i			0.0259958i
$749$		0			0
$750$	−7.27208	−	22.1084i	−0.265539	−	0.807283i
$751$	−34.7696			−1.26876			−0.634379	−	0.773022i	$-0.718744\pi$
$751$	−34.7696			−1.26876			−0.634379	+	0.773022i	$0.718744\pi$
$752$	−1.69376			−0.0617652
$753$	19.7990	−	6.51246i	0.721515	−	0.237327i
$754$		−	44.1605i		−	1.60823i
$755$	−1.12918			−0.0410949
$756$		0			0
$757$	25.8995			0.941333			0.470667	−	0.882311i	$-0.344013\pi$
$757$	25.8995			0.941333			0.470667	+	0.882311i	$0.344013\pi$
$758$			15.1114i			0.548869i
$759$	12.5980	−	4.14386i	0.457280	−	0.150413i
$760$	15.3137			0.555487
$761$	37.3949			1.35556			0.677782	−	0.735263i	$-0.262941\pi$
$761$	37.3949			1.35556			0.677782	+	0.735263i	$0.262941\pi$
$762$	1.36303	+	4.14386i	0.0493775	+	0.150116i
$763$		0			0
$764$		−	4.73157i		−	0.171182i
$765$	5.41421	−	3.99390i	0.195751	−	0.144400i
$766$		−	19.0029i		−	0.686601i
$767$			41.5192i			1.49917i
$768$	15.6064	−	5.13340i	0.563148	−	0.185236i
$769$			21.4077i			0.771983i	0.922502	+	0.385991i	$0.126141\pi$
$769$			21.4077i			0.771983i	−0.922502	+	0.385991i	$0.873859\pi$
$770$		0			0
$771$	−17.8284	+	5.86428i	−0.642075	+	0.211197i
$772$	2.20101			0.0792161
$773$	−30.5797			−1.09988			−0.549938	−	0.835205i	$-0.685349\pi$
$773$	−30.5797			−1.09988			−0.549938	+	0.835205i	$0.685349\pi$
$774$	−4.48528	−	6.08034i	−0.161220	−	0.218553i
$775$			0.448342i			0.0161049i
$776$	42.0486			1.50946
$777$		0			0
$778$	4.64466			0.166519
$779$		−	9.21001i		−	0.329983i
$780$	2.32685	+	7.07401i	0.0833145	+	0.253290i
$781$	14.0000			0.500959
$782$	5.21828			0.186605
$783$	−33.3058	−	23.6494i	−1.19025	−	0.845162i
$784$		0			0
$785$			14.9848i			0.534830i
$786$	−11.2132	−	34.0901i	−0.399962	−	1.21595i
$787$		−	14.0711i		−	0.501580i	−0.968041	−	0.250790i	$-0.919310\pi$
$787$		−	14.0711i		−	0.501580i	0.968041	−	0.250790i	$-0.0806904\pi$
$788$		0			0
$789$	1.52840	+	4.64659i	0.0544124	+	0.165423i
$790$		−	14.1480i		−	0.503364i
$791$		0			0
$792$	13.0711	−	9.64212i	0.464460	−	0.342618i
$793$	33.5563			1.19162
$794$	28.5552			1.01339
$795$	7.65685	+	23.2781i	0.271561	+	0.825591i
$796$		−	7.12840i		−	0.252660i
$797$	−30.8136			−1.09147			−0.545737	−	0.837957i	$-0.683750\pi$
$797$	−30.8136			−1.09147			−0.545737	+	0.837957i	$0.683750\pi$
$798$		0			0
$799$	0.544156			0.0192509
$800$		−	0.953728i		−	0.0337194i
$801$	20.1432	−	14.8590i	0.711724	−	0.525017i
$802$	−42.3848			−1.49666
$803$	−11.4689			−0.404728
$804$	9.87197	−	3.24718i	0.348158	−	0.114519i
$805$		0			0
$806$		−	6.08034i		−	0.214171i
$807$	−29.5858	+	9.73162i	−1.04147	+	0.342569i
$808$		−	39.5139i		−	1.39009i
$809$			5.03712i			0.177096i	0.996072	+	0.0885479i	$0.0282226\pi$
$809$			5.03712i			0.177096i	−0.996072	+	0.0885479i	$0.971777\pi$
$810$	−25.1961	−	7.78498i	−0.885300	−	0.273536i
$811$		−	38.8255i		−	1.36335i	−0.731657	−	0.681673i	$-0.761253\pi$
$811$		−	38.8255i		−	1.36335i	0.731657	−	0.681673i	$-0.238747\pi$
$812$		0			0
$813$	2.92893	+	8.90446i	0.102722	+	0.312293i
$814$	−11.3726			−0.398609
$815$	−21.3408			−0.747537
$816$	4.75736	−	1.56483i	0.166541	−	0.0547801i
$817$			4.32957i			0.151472i
$818$	−37.9595			−1.32722
$819$		0			0
$820$	−4.10051			−0.143196
$821$		−	12.7718i		−	0.445739i	−0.974848	−	0.222869i	$-0.928458\pi$
$821$		−	12.7718i		−	0.445739i	0.974848	−	0.222869i	$-0.0715423\pi$
$822$	19.3447	−	6.36304i	0.674725	−	0.221936i
$823$	13.5147			0.471093			0.235547	−	0.971863i	$-0.424312\pi$
$823$	13.5147			0.471093			0.235547	+	0.971863i	$0.424312\pi$
$824$	−49.0291			−1.70801
$825$	−0.399224	−	1.21371i	−0.0138992	−	0.0422559i
$826$		0			0
$827$			32.0036i			1.11287i	0.830890	+	0.556437i	$0.187832\pi$
$827$			32.0036i			1.11287i	−0.830890	+	0.556437i	$0.812168\pi$
$828$	3.17157	+	4.29945i	0.110220	+	0.149416i
$829$			50.6005i			1.75743i	0.477350	+	0.878713i	$0.341598\pi$
$829$			50.6005i			1.75743i	−0.477350	+	0.878713i	$0.658402\pi$
$830$		−	42.5624i		−	1.47736i
$831$	0.798447	−	0.262632i	0.0276978	−	0.00911062i
$832$			39.6996i			1.37634i
$833$		0			0
$834$	36.0416	−	11.8551i	1.24802	−	0.410510i
$835$	14.0000			0.484490
$836$	−1.59689			−0.0552298
$837$	−4.58579	−	3.25623i	−0.158508	−	0.112552i
$838$		−	4.43835i		−	0.153320i
$839$	43.5770			1.50444			0.752222	−	0.658909i	$-0.228982\pi$
$839$	43.5770			1.50444			0.752222	+	0.658909i	$0.228982\pi$
$840$		0			0
$841$	−32.7990			−1.13100
$842$			40.0438i			1.38000i
$843$	0.729951	+	2.21918i	0.0251409	+	0.0764325i
$844$	9.02944			0.310806
$845$	−16.0541			−0.552277
$846$	−1.26617	−	1.71644i	−0.0435317	−	0.0590125i
$847$		0			0
$848$			18.2410i			0.626399i
$849$	9.31371	+	28.3153i	0.319646	+	0.971777i
$850$		−	0.502734i		−	0.0172437i
$851$		−	21.8028i		−	0.747391i
$852$	1.76226	+	5.35757i	0.0603740	+	0.183547i
$853$		−	12.0376i		−	0.412161i	−0.978535	−	0.206080i	$-0.933929\pi$
$853$		−	12.0376i		−	0.412161i	0.978535	−	0.206080i	$-0.0660708\pi$
$854$		0			0
$855$	8.97056	+	12.1607i	0.306787	+	0.415887i
$856$	27.0711			0.925270
$857$	4.48833			0.153318			0.0766592	−	0.997057i	$-0.475575\pi$
$857$	4.48833			0.153318			0.0766592	+	0.997057i	$0.475575\pi$
$858$	5.41421	+	16.4601i	0.184838	+	0.561940i
$859$			43.1869i			1.47352i	0.676155	+	0.736759i	$0.263645\pi$
$859$			43.1869i			1.47352i	−0.676155	+	0.736759i	$0.736355\pi$
$860$	1.92762			0.0657314
$861$		0			0
$862$	−33.9584			−1.15663
$863$			28.4418i			0.968171i	0.875021	+	0.484086i	$0.160848\pi$
$863$			28.4418i			0.968171i	−0.875021	+	0.484086i	$0.839152\pi$
$864$	9.75504	+	6.92676i	0.331873	+	0.235653i
$865$	−42.3848			−1.44113
$866$	7.87585			0.267632
$867$	26.4422	−	8.69760i	0.898024	−	0.295386i
$868$		0			0
$869$			8.59890i			0.291698i
$870$	−37.8995	+	12.4662i	−1.28491	+	0.422645i
$871$			64.6172i			2.18947i
$872$		−	28.6208i		−	0.969223i
$873$	24.6315	+	33.3910i	0.833650	+	1.13011i
$874$			11.7206i			0.396455i
$875$		0			0
$876$	−1.44365	−	4.38895i	−0.0487764	−	0.148289i
$877$	−38.8701			−1.31255			−0.656274	−	0.754522i	$-0.727869\pi$
$877$	−38.8701			−1.31255			−0.656274	+	0.754522i	$0.727869\pi$
$878$	−16.3564			−0.552002
$879$	−11.1005	+	3.65128i	−0.374411	+	0.123154i
$880$		−	12.4316i		−	0.419068i
$881$	−39.3225			−1.32481			−0.662405	−	0.749146i	$-0.730464\pi$
$881$	−39.3225			−1.32481			−0.662405	+	0.749146i	$0.730464\pi$
$882$		0			0
$883$	−12.0000			−0.403832			−0.201916	−	0.979403i	$-0.564717\pi$
$883$	−12.0000			−0.403832			−0.201916	+	0.979403i	$0.564717\pi$
$884$		−	1.78089i		−	0.0598978i
$885$	35.6326	−	11.7206i	1.19778	−	0.393984i
$886$	−6.18377			−0.207748
$887$	−36.9957			−1.24219			−0.621097	−	0.783734i	$-0.713313\pi$
$887$	−36.9957			−1.24219			−0.621097	+	0.783734i	$0.713313\pi$
$888$	−8.34357	−	25.3659i	−0.279992	−	0.851224i
$889$		0			0
$890$		−	24.4479i		−	0.819497i
$891$	15.3137	+	4.73157i	0.513029	+	0.158513i
$892$			0.371418i			0.0124360i
$893$			1.22221i			0.0408997i
$894$	−15.6548	+	5.14933i	−0.523576	+	0.172219i
$895$			30.0125i			1.00321i
$896$		0			0
$897$	−31.5563	+	10.3798i	−1.05364	+	0.346571i
$898$	−33.7990			−1.12789
$899$	−8.50894			−0.283789
$900$	0.414214	−	0.305553i	0.0138071	−	0.0101851i
$901$		−	5.86030i		−	0.195235i
$902$	−9.54124			−0.317689
$903$		0			0
$904$	−33.7990			−1.12414
$905$			7.25013i			0.241002i
$906$	−0.330728	−	1.00547i	−0.0109877	−	0.0334045i
$907$	−48.2843			−1.60325			−0.801626	−	0.597825i	$-0.796032\pi$
$907$	−48.2843			−1.60325			−0.801626	+	0.597825i	$0.796032\pi$
$908$	−7.37976			−0.244906
$909$	31.3782	−	23.1467i	1.04075	−	0.767728i
$910$		0			0
$911$			50.4236i			1.67061i	0.549787	+	0.835305i	$0.314709\pi$
$911$			50.4236i			1.67061i	−0.549787	+	0.835305i	$0.685291\pi$
$912$	3.51472	+	10.6853i	0.116384	+	0.353827i
$913$			25.8686i			0.856127i
$914$		−	13.3829i		−	0.442667i
$915$	−9.47275	−	28.7988i	−0.313159	−	0.952058i
$916$		−	4.46088i		−	0.147392i
$917$		0			0
$918$	5.14214	+	3.65128i	0.169716	+	0.120510i
$919$	44.4264			1.46549			0.732746	−	0.680502i	$-0.238238\pi$
$919$	44.4264			1.46549			0.732746	+	0.680502i	$0.238238\pi$
$920$	30.4144			1.00273
$921$	5.31371	+	16.1546i	0.175093	+	0.532312i
$922$			0.919213i			0.0302727i
$923$	−35.0681			−1.15428
$924$		0			0
$925$	−2.10051			−0.0690642
$926$			15.1114i			0.496590i
$927$	−28.7206	−	38.9343i	−0.943308	−	1.27877i
$928$	18.1005			0.594178
$929$	−29.2167			−0.958569			−0.479284	−	0.877660i	$-0.659104\pi$
$929$	−29.2167			−0.958569			−0.479284	+	0.877660i	$0.659104\pi$
$930$	−5.21828	+	1.71644i	−0.171114	+	0.0562844i
$931$		0			0
$932$		−	7.42912i		−	0.243349i
$933$	−28.3848	+	9.33657i	−0.929276	+	0.305666i
$934$			2.42742i			0.0794275i
$935$			3.99390i			0.130614i
$936$	−32.7412	+	24.1522i	−1.07018	+	0.789439i
$937$		−	12.0376i		−	0.393252i	−0.980479	−	0.196626i	$-0.937001\pi$
$937$		−	12.0376i		−	0.393252i	0.980479	−	0.196626i	$-0.0629985\pi$
$938$		0			0
$939$	0.0294373	+	0.0894943i	0.000960648	+	0.00292054i
$940$	0.544156			0.0177484
$941$	30.0151			0.978466			0.489233	−	0.872153i	$-0.337277\pi$
$941$	30.0151			0.978466			0.489233	+	0.872153i	$0.337277\pi$
$942$	−13.3431	+	4.38895i	−0.434743	+	0.143000i
$943$		−	18.2919i		−	0.595666i
$944$	27.9222			0.908789
$945$		0			0
$946$	4.48528			0.145829
$947$		−	2.21301i		−	0.0719131i	−0.999353	−	0.0359565i	$-0.988552\pi$
$947$		−	2.21301i		−	0.0719131i	0.999353	−	0.0359565i	$-0.0114478\pi$
$948$	−3.29066	+	1.08239i	−0.106876	+	0.0351545i
$949$	28.7279			0.932548
$950$	1.12918			0.0366353
$951$	−18.6148	−	56.5921i	−0.603625	−	1.83512i
$952$		0			0
$953$			22.2349i			0.720260i	0.932902	+	0.360130i	$0.117268\pi$
$953$			22.2349i			0.720260i	−0.932902	+	0.360130i	$0.882732\pi$
$954$	−18.4853	+	13.6360i	−0.598483	+	0.441483i
$955$		−	26.5796i		−	0.860096i
$956$			5.95378i			0.192559i
$957$	23.0346	−	7.57675i	0.744603	−	0.244921i
$958$			30.0125i			0.969659i
$959$		0			0
$960$	34.0711	−	11.2070i	1.09964	−	0.361703i
$961$	29.8284			0.962207
$962$	28.4867			0.918449
$963$	15.8579	+	21.4973i	0.511013	+	0.692739i
$964$		−	4.90923i		−	0.158116i
$965$	12.3642			0.398017
$966$		0			0
$967$	10.2010			0.328042			0.164021	−	0.986457i	$-0.447553\pi$
$967$	10.2010			0.328042			0.164021	+	0.986457i	$0.447553\pi$
$968$		−	23.7998i		−	0.764953i
$969$	−1.12918	−	3.43289i	−0.0362743	−	0.110280i
$970$	40.5269			1.30124
$971$	38.1249			1.22348			0.611742	−	0.791057i	$-0.290469\pi$
$971$	38.1249			1.22348			0.611742	+	0.791057i	$0.290469\pi$
$972$	0.116930	+	6.45589i	0.00375053	+	0.207073i
$973$		0			0
$974$			0.611105i			0.0195811i
$975$	1.00000	+	3.04017i	0.0320256	+	0.0973634i
$976$		−	22.5671i		−	0.722354i
$977$			3.68835i			0.118001i	0.998258	+	0.0590003i	$0.0187913\pi$
$977$			3.68835i			0.118001i	−0.998258	+	0.0590003i	$0.981209\pi$
$978$	−6.25059	−	19.0029i	−0.199872	−	0.607644i
$979$			14.8590i			0.474896i
$980$		0			0
$981$	22.7279	−	16.7657i	0.725647	−	0.535287i
$982$	15.6985			0.500959
$983$	6.25059			0.199363			0.0996814	−	0.995019i	$-0.468218\pi$
$983$	6.25059			0.199363			0.0996814	+	0.995019i	$0.468218\pi$
$984$	−7.00000	−	21.2812i	−0.223152	−	0.678420i
$985$		0			0
$986$	9.54124			0.303855
$987$		0			0
$988$	4.00000			0.127257
$989$			8.59890i			0.273429i
$990$	12.5980	−	9.29319i	0.400392	−	0.295357i
$991$	−14.4853			−0.460140			−0.230070	−	0.973174i	$-0.573896\pi$
$991$	−14.4853			−0.460140			−0.230070	+	0.973174i	$0.573896\pi$
$992$	2.49221			0.0791278
$993$	−30.9790	+	10.1899i	−0.983087	+	0.323366i
$994$		0			0
$995$		−	40.0438i		−	1.26947i
$996$	−9.89949	+	3.25623i	−0.313678	+	0.103178i
$997$		−	14.9903i		−	0.474748i	−0.971418	−	0.237374i	$-0.923713\pi$
$997$		−	14.9903i		−	0.474748i	0.971418	−	0.237374i	$-0.0762867\pi$
$998$			11.5496i			0.365596i
$999$	15.2556	−	21.4847i	0.482666	−	0.679745i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.2.c.b.146.3	✓	8
3.2	odd	2	inner	147.2.c.b.146.6	yes	8
4.3	odd	2		2352.2.k.h.881.7		8
7.2	even	3		147.2.g.b.80.4		16
7.3	odd	6		147.2.g.b.68.5		16
7.4	even	3		147.2.g.b.68.6		16
7.5	odd	6		147.2.g.b.80.3		16
7.6	odd	2	inner	147.2.c.b.146.4	yes	8
12.11	even	2		2352.2.k.h.881.1		8
21.2	odd	6		147.2.g.b.80.5		16
21.5	even	6		147.2.g.b.80.6		16
21.11	odd	6		147.2.g.b.68.3		16
21.17	even	6		147.2.g.b.68.4		16
21.20	even	2	inner	147.2.c.b.146.5	yes	8
28.27	even	2		2352.2.k.h.881.2		8
84.83	odd	2		2352.2.k.h.881.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.c.b.146.3	✓	8	1.1	even	1	trivial
147.2.c.b.146.4	yes	8	7.6	odd	2	inner
147.2.c.b.146.5	yes	8	21.20	even	2	inner
147.2.c.b.146.6	yes	8	3.2	odd	2	inner
147.2.g.b.68.3		16	21.11	odd	6
147.2.g.b.68.4		16	21.17	even	6
147.2.g.b.68.5		16	7.3	odd	6
147.2.g.b.68.6		16	7.4	even	3
147.2.g.b.80.3		16	7.5	odd	6
147.2.g.b.80.4		16	7.2	even	3
147.2.g.b.80.5		16	21.2	odd	6
147.2.g.b.80.6		16	21.5	even	6
2352.2.k.h.881.1		8	12.11	even	2
2352.2.k.h.881.2		8	28.27	even	2
2352.2.k.h.881.7		8	4.3	odd	2
2352.2.k.h.881.8		8	84.83	odd	2

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	147.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.25928i q^{2} +(-1.64533 + 0.541196i) q^{3} +0.414214 q^{4} +2.32685 q^{5} +(0.681517 + 2.07193i) q^{6} -3.04017i q^{8} +(2.41421 - 1.78089i) q^{9} +O(q^{10})\)	\(q-1.25928i q^{2} +(-1.64533 + 0.541196i) q^{3} +0.414214 q^{4} +2.32685 q^{5} +(0.681517 + 2.07193i) q^{6} -3.04017i q^{8} +(2.41421 - 1.78089i) q^{9} -2.93015i q^{10} +1.78089i q^{11} +(-0.681517 + 0.224171i) q^{12} -4.46088i q^{13} +(-3.82843 + 1.25928i) q^{15} -3.00000 q^{16} +0.963811 q^{17} +(-2.24264 - 3.04017i) q^{18} +2.16478i q^{19} +0.963811 q^{20} +2.24264 q^{22} +4.29945i q^{23} +(1.64533 + 5.00208i) q^{24} +0.414214 q^{25} -5.61750 q^{26} +(-3.00836 + 4.23671i) q^{27} +7.86123i q^{29} +(1.58579 + 4.82106i) q^{30} +1.08239i q^{31} -2.30250i q^{32} +(-0.963811 - 2.93015i) q^{33} -1.21371i q^{34} +(1.00000 - 0.737669i) q^{36} -5.07107 q^{37} +2.72607 q^{38} +(2.41421 + 7.33962i) q^{39} -7.07401i q^{40} -4.25447 q^{41} +2.00000 q^{43} +0.737669i q^{44} +(5.61750 - 4.14386i) q^{45} +5.41421 q^{46} +0.564588 q^{47} +(4.93599 - 1.62359i) q^{48} -0.521611i q^{50} +(-1.58579 + 0.521611i) q^{51} -1.84776i q^{52} -6.08034i q^{53} +(5.33521 + 3.78837i) q^{54} +4.14386i q^{55} +(-1.17157 - 3.56178i) q^{57} +9.89949 q^{58} -9.30739 q^{59} +(-1.58579 + 0.521611i) q^{60} +7.52235i q^{61} +1.36303 q^{62} -8.89949 q^{64} -10.3798i q^{65} +(-3.68988 + 1.21371i) q^{66} -14.4853 q^{67} +0.399224 q^{68} +(-2.32685 - 7.07401i) q^{69} -7.86123i q^{71} +(-5.41421 - 7.33962i) q^{72} +6.43996i q^{73} +6.38589i q^{74} +(-0.681517 + 0.224171i) q^{75} +0.896683i q^{76} +(9.24264 - 3.04017i) q^{78} +4.82843 q^{79} -6.98054 q^{80} +(2.65685 - 8.59890i) q^{81} +5.35757i q^{82} +14.5257 q^{83} +2.24264 q^{85} -2.51856i q^{86} +(-4.25447 - 12.9343i) q^{87} +5.41421 q^{88} +8.34357 q^{89} +(-5.21828 - 7.07401i) q^{90} +1.78089i q^{92} +(-0.585786 - 1.78089i) q^{93} -0.710974i q^{94} +5.03712i q^{95} +(1.24611 + 3.78837i) q^{96} +13.8310i q^{97} +(3.17157 + 4.29945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 + 8 * q^9	\( 8 q - 8 q^{4} + 8 q^{9} - 8 q^{15} - 24 q^{16} + 16 q^{18} - 16 q^{22} - 8 q^{25} + 24 q^{30} + 8 q^{36} + 16 q^{37} + 8 q^{39} + 16 q^{43} + 32 q^{46} - 24 q^{51} - 32 q^{57} - 24 q^{60} + 8 q^{64} - 48 q^{67} - 32 q^{72} + 40 q^{78} + 16 q^{79} - 24 q^{81} - 16 q^{85} + 32 q^{88} - 16 q^{93} + 48 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 + 8 * q^9 - 8 * q^15 - 24 * q^16 + 16 * q^18 - 16 * q^22 - 8 * q^25 + 24 * q^30 + 8 * q^36 + 16 * q^37 + 8 * q^39 + 16 * q^43 + 32 * q^46 - 24 * q^51 - 32 * q^57 - 24 * q^60 + 8 * q^64 - 48 * q^67 - 32 * q^72 + 40 * q^78 + 16 * q^79 - 24 * q^81 - 16 * q^85 + 32 * q^88 - 16 * q^93 + 48 * q^99

Introduction

L-functions

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