LMFDB - Embedded newform 1650.2.d.i.1451.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1650,2,Mod(1451,1650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1650.1451"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1650, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1650.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,-12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$13.1753163335$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3x^{10} - 5x^{8} - 46x^{6} - 45x^{4} + 243x^{2} + 729 $ x^12 + 3x^10 - 5x^8 - 46x^6 - 45x^4 + 243*x^2 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5}\cdot 3 $
Twist minimal:	no (minimal twist has level 330)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1451.12
Root			$-1.71007 - 0.275064i$ of defining polynomial
Character	$\chi$	$=$	1650.1451
Dual form			1650.2.d.i.1451.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +(1.71007 + 0.275064i) q^{3} +1.00000 q^{4} +(-1.71007 - 0.275064i) q^{6} -2.37039i q^{7} -1.00000 q^{8} +(2.84868 + 0.940756i) q^{9} +(-2.83537 - 1.72066i) q^{11} +(1.71007 + 0.275064i) q^{12} +3.93020i q^{13} +2.37039i q^{14} +1.00000 q^{16} +0.381275 q^{17} +(-2.84868 - 0.940756i) q^{18} -5.33478i q^{19} +(0.652007 - 4.05352i) q^{21} +(2.83537 + 1.72066i) q^{22} -1.38613i q^{23} +(-1.71007 - 0.275064i) q^{24} -3.93020i q^{26} +(4.61267 + 2.39233i) q^{27} -2.37039i q^{28} +6.97475 q^{29} +7.69736 q^{31} -1.00000 q^{32} +(-4.37539 - 3.72236i) q^{33} -0.381275 q^{34} +(2.84868 + 0.940756i) q^{36} -1.08106 q^{37} +5.33478i q^{38} +(-1.08106 + 6.72092i) q^{39} +5.89370 q^{41} +(-0.652007 + 4.05352i) q^{42} -4.74077i q^{43} +(-2.83537 - 1.72066i) q^{44} +1.38613i q^{46} -12.0557i q^{47} +(1.71007 + 0.275064i) q^{48} +1.38127 q^{49} +(0.652007 + 0.104875i) q^{51} +3.93020i q^{52} +9.49318i q^{53} +(-4.61267 - 2.39233i) q^{54} +2.37039i q^{56} +(1.46741 - 9.12285i) q^{57} -6.97475 q^{58} -8.18210i q^{59} -13.7061i q^{61} -7.69736 q^{62} +(2.22995 - 6.75247i) q^{63} +1.00000 q^{64} +(4.37539 + 3.72236i) q^{66} -5.67074 q^{67} +0.381275 q^{68} +(0.381275 - 2.37039i) q^{69} -2.04869i q^{71} +(-2.84868 - 0.940756i) q^{72} +11.9451i q^{73} +1.08106 q^{74} -5.33478i q^{76} +(-4.07863 + 6.72092i) q^{77} +(1.08106 - 6.72092i) q^{78} -11.1436i q^{79} +(7.22995 + 5.35983i) q^{81} -5.89370 q^{82} -0.762550 q^{83} +(0.652007 - 4.05352i) q^{84} +4.74077i q^{86} +(11.9273 + 1.91850i) q^{87} +(2.83537 + 1.72066i) q^{88} +1.88151i q^{89} +9.31608 q^{91} -1.38613i q^{92} +(13.1630 + 2.11726i) q^{93} +12.0557i q^{94} +(-1.71007 - 0.275064i) q^{96} -3.28567 q^{97} -1.38127 q^{98} +(-6.45833 - 7.56901i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 12 q^{4} - 12 q^{8} - 6 q^{9} + 12 q^{16} - 4 q^{17} + 6 q^{18} + 12 q^{31} - 12 q^{32} - 18 q^{33} + 4 q^{34} - 6 q^{36} + 8 q^{49} - 14 q^{57} - 12 q^{62} - 22 q^{63} + 12 q^{64} + 18 q^{66}+ \cdots + 28 q^{99}+O(q^{100}) $ 12 * q - 12 * q^2 + 12 * q^4 - 12 * q^8 - 6 * q^9 + 12 * q^16 - 4 * q^17 + 6 * q^18 + 12 * q^31 - 12 * q^32 - 18 * q^33 + 4 * q^34 - 6 * q^36 + 8 * q^49 - 14 * q^57 - 12 * q^62 - 22 * q^63 + 12 * q^64 + 18 * q^66 - 4 * q^68 - 4 * q^69 + 6 * q^72 + 40 * q^77 + 38 * q^81 + 8 * q^83 + 14 * q^87 + 40 * q^91 - 8 * q^98 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1650\mathbb{Z}\right)^\times$.

$n$	$551$	$727$	$1201$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	1.71007	+	0.275064i	0.987309	+	0.158808i
$3$	1.71007	+	0.275064i	0.987309	+	0.158808i
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−1.71007	−	0.275064i	−0.698133	−	0.112294i
$7$		−	2.37039i		−	0.895921i	−0.894053	−	0.447961i	$-0.852150\pi$
$7$		−	2.37039i		−	0.895921i	0.894053	−	0.447961i	$-0.147850\pi$
$8$	−1.00000			−0.353553
$9$	2.84868	+	0.940756i	0.949560	+	0.313585i
$10$		0			0
$11$	−2.83537	−	1.72066i	−0.854896	−	0.518800i
$11$	−2.83537	−	1.72066i	−0.854896	−	0.518800i
$12$	1.71007	+	0.275064i	0.493655	+	0.0794040i
$13$			3.93020i			1.09004i	0.838423	+	0.545021i	$0.183478\pi$
$13$			3.93020i			1.09004i	−0.838423	+	0.545021i	$0.816522\pi$
$14$			2.37039i			0.633512i
$15$		0			0
$16$	1.00000			0.250000
$17$	0.381275			0.0924727			0.0462364	−	0.998931i	$-0.485277\pi$
$17$	0.381275			0.0924727			0.0462364	+	0.998931i	$0.485277\pi$
$18$	−2.84868	−	0.940756i	−0.671440	−	0.221738i
$19$		−	5.33478i		−	1.22388i	−0.790903	−	0.611942i	$-0.790389\pi$
$19$		−	5.33478i		−	1.22388i	0.790903	−	0.611942i	$-0.209611\pi$
$20$		0			0
$21$	0.652007	−	4.05352i	0.142280	−	0.884552i
$22$	2.83537	+	1.72066i	0.604503	+	0.366847i
$23$		−	1.38613i		−	0.289029i	−0.989503	−	0.144514i	$-0.953838\pi$
$23$		−	1.38613i		−	0.289029i	0.989503	−	0.144514i	$-0.0461620\pi$
$24$	−1.71007	−	0.275064i	−0.349067	−	0.0561471i
$25$		0			0
$26$		−	3.93020i		−	0.770775i
$27$	4.61267	+	2.39233i	0.887710	+	0.460404i
$28$		−	2.37039i		−	0.447961i
$29$	6.97475			1.29518			0.647589	−	0.761989i	$-0.275777\pi$
$29$	6.97475			1.29518			0.647589	+	0.761989i	$0.275777\pi$
$30$		0			0
$31$	7.69736			1.38249			0.691243	−	0.722622i	$-0.257063\pi$
$31$	7.69736			1.38249			0.691243	+	0.722622i	$0.257063\pi$
$32$	−1.00000			−0.176777
$33$	−4.37539	−	3.72236i	−0.761657	−	0.647980i
$34$	−0.381275			−0.0653881
$35$		0			0
$36$	2.84868	+	0.940756i	0.474780	+	0.156793i
$37$	−1.08106			−0.177724			−0.0888622	−	0.996044i	$-0.528323\pi$
$37$	−1.08106			−0.177724			−0.0888622	+	0.996044i	$0.528323\pi$
$38$			5.33478i			0.865416i
$39$	−1.08106	+	6.72092i	−0.173107	+	1.07621i
$40$		0			0
$41$	5.89370			0.920441			0.460220	−	0.887805i	$-0.347770\pi$
$41$	5.89370			0.920441			0.460220	+	0.887805i	$0.347770\pi$
$42$	−0.652007	+	4.05352i	−0.100607	+	0.625472i
$43$		−	4.74077i		−	0.722961i	−0.932380	−	0.361480i	$-0.882271\pi$
$43$		−	4.74077i		−	0.722961i	0.932380	−	0.361480i	$-0.117729\pi$
$44$	−2.83537	−	1.72066i	−0.427448	−	0.259400i
$45$		0			0
$46$			1.38613i			0.204374i
$47$		−	12.0557i		−	1.75850i	−0.476357	−	0.879252i	$-0.658043\pi$
$47$		−	12.0557i		−	1.75850i	0.476357	−	0.879252i	$-0.341957\pi$
$48$	1.71007	+	0.275064i	0.246827	+	0.0397020i
$49$	1.38127			0.197325
$50$		0			0
$51$	0.652007	+	0.104875i	0.0912992	+	0.0146854i
$52$			3.93020i			0.545021i
$53$			9.49318i			1.30399i	0.758224	+	0.651994i	$0.226067\pi$
$53$			9.49318i			1.30399i	−0.758224	+	0.651994i	$0.773933\pi$
$54$	−4.61267	−	2.39233i	−0.627706	−	0.325555i
$55$		0			0
$56$			2.37039i			0.316756i
$57$	1.46741	−	9.12285i	0.194363	−	1.20835i
$58$	−6.97475			−0.915830
$59$		−	8.18210i		−	1.06522i	−0.846361	−	0.532609i	$-0.821212\pi$
$59$		−	8.18210i		−	1.06522i	0.846361	−	0.532609i	$-0.178788\pi$
$60$		0			0
$61$		−	13.7061i		−	1.75488i	−0.479683	−	0.877442i	$-0.659248\pi$
$61$		−	13.7061i		−	1.75488i	0.479683	−	0.877442i	$-0.340752\pi$
$62$	−7.69736			−0.977566
$63$	2.22995	−	6.75247i	0.280948	−	0.850731i
$64$	1.00000			0.125000
$65$		0			0
$66$	4.37539	+	3.72236i	0.538573	+	0.458191i
$67$	−5.67074			−0.692791			−0.346395	−	0.938089i	$-0.612594\pi$
$67$	−5.67074			−0.692791			−0.346395	+	0.938089i	$0.612594\pi$
$68$	0.381275			0.0462364
$69$	0.381275	−	2.37039i	0.0459001	−	0.285361i
$70$		0			0
$71$		−	2.04869i		−	0.243134i	−0.992583	−	0.121567i	$-0.961208\pi$
$71$		−	2.04869i		−	0.243134i	0.992583	−	0.121567i	$-0.0387920\pi$
$72$	−2.84868	−	0.940756i	−0.335720	−	0.110869i
$73$			11.9451i			1.39807i	0.715087	+	0.699035i	$0.246387\pi$
$73$			11.9451i			1.39807i	−0.715087	+	0.699035i	$0.753613\pi$
$74$	1.08106			0.125670
$75$		0			0
$76$		−	5.33478i		−	0.611942i
$77$	−4.07863	+	6.72092i	−0.464804	+	0.765919i
$78$	1.08106	−	6.72092i	0.122405	−	0.760994i
$79$		−	11.1436i		−	1.25375i	−0.779120	−	0.626874i	$-0.784334\pi$
$79$		−	11.1436i		−	1.25375i	0.779120	−	0.626874i	$-0.215666\pi$
$80$		0			0
$81$	7.22995	+	5.35983i	0.803328	+	0.595536i
$82$	−5.89370			−0.650850
$83$	−0.762550			−0.0837007			−0.0418504	−	0.999124i	$-0.513325\pi$
$83$	−0.762550			−0.0837007			−0.0418504	+	0.999124i	$0.513325\pi$
$84$	0.652007	−	4.05352i	0.0711398	−	0.442276i
$85$		0			0
$86$			4.74077i			0.511210i
$87$	11.9273	+	1.91850i	1.27874	+	0.205685i
$88$	2.83537	+	1.72066i	0.302251	+	0.183423i
$89$			1.88151i			0.199440i	0.995016	+	0.0997200i	$0.0317947\pi$
$89$			1.88151i			0.199440i	−0.995016	+	0.0997200i	$0.968205\pi$
$90$		0			0
$91$	9.31608			0.976591
$92$		−	1.38613i		−	0.144514i
$93$	13.1630	+	2.11726i	1.36494	+	0.219550i
$94$			12.0557i			1.24345i
$95$		0			0
$96$	−1.71007	−	0.275064i	−0.174533	−	0.0280736i
$97$	−3.28567			−0.333609			−0.166805	−	0.985990i	$-0.553345\pi$
$97$	−3.28567			−0.333609			−0.166805	+	0.985990i	$0.553345\pi$
$98$	−1.38127			−0.139530
$99$	−6.45833	−	7.56901i	−0.649087	−	0.760714i
$100$		0			0
$101$	3.50863			0.349122			0.174561	−	0.984646i	$-0.444149\pi$
$101$	3.50863			0.349122			0.174561	+	0.984646i	$0.444149\pi$
$102$	−0.652007	−	0.104875i	−0.0645583	−	0.0103842i
$103$	−14.6271			−1.44126			−0.720628	−	0.693322i	$-0.756146\pi$
$103$	−14.6271			−1.44126			−0.720628	+	0.693322i	$0.756146\pi$
$104$		−	3.93020i		−	0.385388i
$105$		0			0
$106$		−	9.49318i		−	0.922059i
$107$	9.31608			0.900620			0.450310	−	0.892872i	$-0.351313\pi$
$107$	9.31608			0.900620			0.450310	+	0.892872i	$0.351313\pi$
$108$	4.61267	+	2.39233i	0.443855	+	0.230202i
$109$			8.37130i			0.801825i	0.916116	+	0.400912i	$0.131307\pi$
$109$			8.37130i			0.801825i	−0.916116	+	0.400912i	$0.868693\pi$
$110$		0			0
$111$	−1.84868	−	0.297359i	−0.175469	−	0.0282241i
$112$		−	2.37039i		−	0.223980i
$113$		−	6.45667i		−	0.607392i	−0.952769	−	0.303696i	$-0.901779\pi$
$113$		−	6.45667i		−	0.607392i	0.952769	−	0.303696i	$-0.0982207\pi$
$114$	−1.46741	+	9.12285i	−0.137435	+	0.854433i
$115$		0			0
$116$	6.97475			0.647589
$117$	−3.69736	+	11.1959i	−0.341821	+	1.03506i
$118$			8.18210i			0.753223i
$119$		−	0.903768i		−	0.0828483i
$120$		0			0
$121$	5.07863	+	9.75743i	0.461694	+	0.887039i
$122$			13.7061i			1.24089i
$123$	10.0786	+	1.62114i	0.908760	+	0.146173i
$124$	7.69736			0.691243
$125$		0			0
$126$	−2.22995	+	6.75247i	−0.198660	+	0.601558i
$127$			17.4965i			1.55256i	0.630388	+	0.776280i	$0.282896\pi$
$127$			17.4965i			1.55256i	−0.630388	+	0.776280i	$0.717104\pi$
$128$	−1.00000			−0.0883883
$129$	1.30401	−	8.10705i	0.114812	−	0.713786i
$130$		0			0
$131$	−19.4398			−1.69846			−0.849231	−	0.528021i	$-0.822934\pi$
$131$	−19.4398			−1.69846			−0.849231	+	0.528021i	$0.822934\pi$
$132$	−4.37539	−	3.72236i	−0.380829	−	0.323990i
$133$	−12.6455			−1.09650
$134$	5.67074			0.489877
$135$		0			0
$136$	−0.381275			−0.0326941
$137$		−	6.98517i		−	0.596783i	−0.954444	−	0.298391i	$-0.903550\pi$
$137$		−	6.98517i		−	0.596783i	0.954444	−	0.298391i	$-0.0964501\pi$
$138$	−0.381275	+	2.37039i	−0.0324563	+	0.201781i
$139$			5.54453i			0.470281i	0.971961	+	0.235141i	$0.0755550\pi$
$139$			5.54453i			0.470281i	−0.971961	+	0.235141i	$0.924445\pi$
$140$		0			0
$141$	3.31608	−	20.6161i	0.279265	−	1.73619i
$142$			2.04869i			0.171922i
$143$	6.76255	−	11.1436i	0.565513	−	0.931872i
$144$	2.84868	+	0.940756i	0.237390	+	0.0783964i
$145$		0			0
$146$		−	11.9451i		−	0.988585i
$147$	2.36208	+	0.379939i	0.194821	+	0.0313368i
$148$	−1.08106			−0.0888622
$149$	2.20461			0.180609			0.0903045	−	0.995914i	$-0.471216\pi$
$149$	2.20461			0.180609			0.0903045	+	0.995914i	$0.471216\pi$
$150$		0			0
$151$			5.07053i			0.412634i	0.978485	+	0.206317i	$0.0661478\pi$
$151$			5.07053i			0.412634i	−0.978485	+	0.206317i	$0.933852\pi$
$152$			5.33478i			0.432708i
$153$	1.08613	+	0.358687i	0.0878084	+	0.0289981i
$154$	4.07863	−	6.72092i	0.328666	−	0.541587i
$155$		0			0
$156$	−1.08106	+	6.72092i	−0.0865537	+	0.538104i
$157$	−10.2604			−0.818871			−0.409435	−	0.912339i	$-0.634274\pi$
$157$	−10.2604			−0.818871			−0.409435	+	0.912339i	$0.634274\pi$
$158$			11.1436i			0.886534i
$159$	−2.61123	+	16.2340i	−0.207084	+	1.28744i
$160$		0			0
$161$	−3.28567			−0.258947
$162$	−7.22995	−	5.35983i	−0.568039	−	0.421108i
$163$	1.52697			0.119602			0.0598008	−	0.998210i	$-0.480953\pi$
$163$	1.52697			0.119602			0.0598008	+	0.998210i	$0.480953\pi$
$164$	5.89370			0.460220
$165$		0			0
$166$	0.762550			0.0591853
$167$	22.3295			1.72791			0.863955	−	0.503568i	$-0.167980\pi$
$167$	22.3295			1.72791			0.863955	+	0.503568i	$0.167980\pi$
$168$	−0.652007	+	4.05352i	−0.0503034	+	0.312736i
$169$	−2.44646			−0.188190
$170$		0			0
$171$	5.01873	−	15.1971i	0.383792	−	1.16215i
$172$		−	4.74077i		−	0.361480i
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$	−11.9273	−	1.91850i	−0.904207	−	0.145441i
$175$		0			0
$176$	−2.83537	−	1.72066i	−0.213724	−	0.129700i
$177$	2.25060	−	13.9920i	0.169165	−	1.05170i
$178$		−	1.88151i		−	0.141025i
$179$			5.06247i			0.378387i	0.981940	+	0.189193i	$0.0605873\pi$
$179$			5.06247i			0.378387i	−0.981940	+	0.189193i	$0.939413\pi$
$180$		0			0
$181$	−9.39472			−0.698304			−0.349152	−	0.937066i	$-0.613530\pi$
$181$	−9.39472			−0.698304			−0.349152	+	0.937066i	$0.613530\pi$
$182$	−9.31608			−0.690554
$183$	3.77005	−	23.4384i	0.278690	−	1.73261i
$184$			1.38613i			0.102187i
$185$		0			0
$186$	−13.1630	−	2.11726i	−0.965160	−	0.155245i
$187$	−1.08106	−	0.656046i	−0.0790546	−	0.0479748i
$188$		−	12.0557i		−	0.879252i
$189$	5.67074	−	10.9338i	0.412485	−	0.795318i
$190$		0			0
$191$			4.57360i			0.330934i	0.986215	+	0.165467i	$0.0529131\pi$
$191$			4.57360i			0.330934i	−0.986215	+	0.165467i	$0.947087\pi$
$192$	1.71007	+	0.275064i	0.123414	+	0.0198510i
$193$		−	7.92173i		−	0.570218i	−0.958495	−	0.285109i	$-0.907970\pi$
$193$		−	7.92173i		−	0.570218i	0.958495	−	0.285109i	$-0.0920299\pi$
$194$	3.28567			0.235897
$195$		0			0
$196$	1.38127			0.0986625
$197$	21.5520			1.53552			0.767758	−	0.640740i	$-0.221372\pi$
$197$	21.5520			1.53552			0.767758	+	0.640740i	$0.221372\pi$
$198$	6.45833	+	7.56901i	0.458974	+	0.537906i
$199$	1.06519			0.0755093			0.0377547	−	0.999287i	$-0.487979\pi$
$199$	1.06519			0.0755093			0.0377547	+	0.999287i	$0.487979\pi$
$200$		0			0
$201$	−9.69736	−	1.55981i	−0.683999	−	0.110021i
$202$	−3.50863			−0.246866
$203$		−	16.5328i		−	1.16038i
$204$	0.652007	+	0.104875i	0.0456496	+	0.00734271i
$205$		0			0
$206$	14.6271			1.01912
$207$	1.30401	−	3.94865i	0.0906352	−	0.274450i
$208$			3.93020i			0.272510i
$209$	−9.17937	+	15.1261i	−0.634950	+	1.04629i
$210$		0			0
$211$			18.7766i			1.29264i	0.763068	+	0.646318i	$0.223692\pi$
$211$			18.7766i			1.29264i	−0.763068	+	0.646318i	$0.776308\pi$
$212$			9.49318i			0.651994i
$213$	0.563519	−	3.50340i	0.0386117	−	0.240049i
$214$	−9.31608			−0.636834
$215$		0			0
$216$	−4.61267	−	2.39233i	−0.313853	−	0.162777i
$217$		−	18.2457i		−	1.23860i
$218$		−	8.37130i		−	0.566976i
$219$	−3.28567	+	20.4270i	−0.222025	+	1.38033i
$220$		0			0
$221$			1.49849i			0.100799i
$222$	1.84868	+	0.297359i	0.124075	+	0.0199574i
$223$	−14.6271			−0.979506			−0.489753	−	0.871861i	$-0.662913\pi$
$223$	−14.6271			−0.979506			−0.489753	+	0.871861i	$0.662913\pi$
$224$			2.37039i			0.158378i
$225$		0			0
$226$			6.45667i			0.429491i
$227$	−16.7108			−1.10914			−0.554568	−	0.832139i	$-0.687116\pi$
$227$	−16.7108			−1.10914			−0.554568	+	0.832139i	$0.687116\pi$
$228$	1.46741	−	9.12285i	0.0971813	−	0.604176i
$229$	18.1573			1.19987			0.599933	−	0.800050i	$-0.295194\pi$
$229$	18.1573			1.19987			0.599933	+	0.800050i	$0.295194\pi$
$230$		0			0
$231$	−8.82343	+	10.3714i	−0.580539	+	0.682385i
$232$	−6.97475			−0.457915
$233$	−1.54009			−0.100895			−0.0504473	−	0.998727i	$-0.516065\pi$
$233$	−1.54009			−0.100895			−0.0504473	+	0.998727i	$0.516065\pi$
$234$	3.69736	−	11.1959i	0.241704	−	0.731898i
$235$		0			0
$236$		−	8.18210i		−	0.532609i
$237$	3.06519	−	19.0563i	0.199105	−	1.23784i
$238$			0.903768i			0.0585826i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$		−	10.1411i		−	0.653244i	−0.945155	−	0.326622i	$-0.894090\pi$
$241$		−	10.1411i		−	0.653244i	0.945155	−	0.326622i	$-0.105910\pi$
$242$	−5.07863	−	9.75743i	−0.326467	−	0.627231i
$243$	10.8894	+	11.1544i	0.698558	+	0.715554i
$244$		−	13.7061i		−	0.877442i
$245$		0			0
$246$	−10.0786	−	1.62114i	−0.642590	−	0.103360i
$247$	20.9668			1.33408
$248$	−7.69736			−0.488783
$249$	−1.30401	−	0.209750i	−0.0826385	−	0.0132924i
$250$		0			0
$251$			20.7833i			1.31183i	0.754836	+	0.655914i	$0.227717\pi$
$251$			20.7833i			1.31183i	−0.754836	+	0.655914i	$0.772283\pi$
$252$	2.22995	−	6.75247i	0.140474	−	0.425366i
$253$	−2.38507	+	3.93020i	−0.149948	+	0.247089i
$254$		−	17.4965i		−	1.09783i
$255$		0			0
$256$	1.00000			0.0625000
$257$			20.4270i			1.27420i	0.770781	+	0.637101i	$0.219866\pi$
$257$			20.4270i			1.27420i	−0.770781	+	0.637101i	$0.780134\pi$
$258$	−1.30401	+	8.10705i	−0.0811843	+	0.504723i
$259$			2.56252i			0.159227i
$260$		0			0
$261$	19.8688	+	6.56154i	1.22985	+	0.406149i
$262$	19.4398			1.20099
$263$	23.0921			1.42392			0.711959	−	0.702221i	$-0.247808\pi$
$263$	23.0921			1.42392			0.711959	+	0.702221i	$0.247808\pi$
$264$	4.37539	+	3.72236i	0.269287	+	0.229096i
$265$		0			0
$266$	12.6455			0.775345
$267$	−0.517536	+	3.21752i	−0.0316727	+	0.196909i
$268$	−5.67074			−0.346395
$269$		−	23.2150i		−	1.41544i	−0.706492	−	0.707721i	$-0.749723\pi$
$269$		−	23.2150i		−	1.41544i	0.706492	−	0.707721i	$-0.250277\pi$
$270$		0			0
$271$			2.82677i			0.171714i	0.996307	+	0.0858569i	$0.0273628\pi$
$271$			2.82677i			0.171714i	−0.996307	+	0.0858569i	$0.972637\pi$
$272$	0.381275			0.0231182
$273$	15.9312	+	2.56252i	0.964198	+	0.155091i
$274$			6.98517i			0.421989i
$275$		0			0
$276$	0.381275	−	2.37039i	0.0229501	−	0.142680i
$277$			11.7906i			0.708428i	0.935164	+	0.354214i	$0.115252\pi$
$277$			11.7906i			0.708428i	−0.935164	+	0.354214i	$0.884748\pi$
$278$		−	5.54453i		−	0.332539i
$279$	21.9273	+	7.24134i	1.31275	+	0.433528i
$280$		0			0
$281$	8.73345			0.520994			0.260497	−	0.965475i	$-0.416114\pi$
$281$	8.73345			0.520994			0.260497	+	0.965475i	$0.416114\pi$
$282$	−3.31608	+	20.6161i	−0.197470	+	1.22767i
$283$			28.6310i			1.70194i	0.525217	+	0.850969i	$0.323984\pi$
$283$			28.6310i			1.70194i	−0.525217	+	0.850969i	$0.676016\pi$
$284$		−	2.04869i		−	0.121567i
$285$		0			0
$286$	−6.76255	+	11.1436i	−0.399878	+	0.658933i
$287$		−	13.9703i		−	0.824643i
$288$	−2.84868	−	0.940756i	−0.167860	−	0.0554346i
$289$	−16.8546			−0.991449
$290$		0			0
$291$	−5.61873	−	0.903768i	−0.329375	−	0.0529798i
$292$			11.9451i			0.699035i
$293$	−25.3947			−1.48358			−0.741788	−	0.670635i	$-0.766022\pi$
$293$	−25.3947			−1.48358			−0.741788	+	0.670635i	$0.766022\pi$
$294$	−2.36208	−	0.379939i	−0.137759	−	0.0221585i
$295$		0			0
$296$	1.08106			0.0628350
$297$	−8.96224	−	14.7200i	−0.520042	−	0.854141i
$298$	−2.20461			−0.127710
$299$	5.44778			0.315053
$300$		0			0
$301$	−11.2375			−0.647716
$302$		−	5.07053i		−	0.291776i
$303$	6.00000	+	0.965096i	0.344691	+	0.0554433i
$304$		−	5.33478i		−	0.305971i
$305$		0			0
$306$	−1.08613	−	0.358687i	−0.0620899	−	0.0205048i
$307$		−	23.8902i		−	1.36349i	−0.731591	−	0.681744i	$-0.761222\pi$
$307$		−	23.8902i		−	1.36349i	0.731591	−	0.681744i	$-0.238778\pi$
$308$	−4.07863	+	6.72092i	−0.232402	+	0.382960i
$309$	−25.0134	−	4.02340i	−1.42297	−	0.228883i
$310$		0			0
$311$			8.93134i			0.506450i	0.967407	+	0.253225i	$0.0814913\pi$
$311$			8.93134i			0.506450i	−0.967407	+	0.253225i	$0.918509\pi$
$312$	1.08106	−	6.72092i	0.0612027	−	0.380497i
$313$	20.5208			1.15991			0.579953	−	0.814650i	$-0.303071\pi$
$313$	20.5208			1.15991			0.579953	+	0.814650i	$0.303071\pi$
$314$	10.2604			0.579029
$315$		0			0
$316$		−	11.1436i		−	0.626874i
$317$		−	22.9350i		−	1.28816i	−0.764959	−	0.644079i	$-0.777241\pi$
$317$		−	22.9350i		−	1.28816i	0.764959	−	0.644079i	$-0.222759\pi$
$318$	2.61123	−	16.2340i	0.146430	−	0.910358i
$319$	−19.7760	−	12.0012i	−1.10724	−	0.671938i
$320$		0			0
$321$	15.9312	+	2.56252i	0.889191	+	0.143026i
$322$	3.28567			0.183103
$323$		−	2.03402i		−	0.113176i
$324$	7.22995	+	5.35983i	0.401664	+	0.297768i
$325$		0			0
$326$	−1.52697			−0.0845712
$327$	−2.30264	+	14.3155i	−0.127336	+	0.791649i
$328$	−5.89370			−0.325425
$329$	−28.5766			−1.57548
$330$		0			0
$331$	−26.9985			−1.48397			−0.741985	−	0.670417i	$-0.766115\pi$
$331$	−26.9985			−1.48397			−0.741985	+	0.670417i	$0.766115\pi$
$332$	−0.762550			−0.0418504
$333$	−3.07958	−	1.01701i	−0.168760	−	0.0557318i
$334$	−22.3295			−1.22182
$335$		0			0
$336$	0.652007	−	4.05352i	0.0355699	−	0.221138i
$337$		−	0.0613278i		−	0.00334074i	−0.999999	−	0.00167037i	$-0.999468\pi$
$337$		−	0.0613278i		−	0.00334074i	0.999999	−	0.00167037i	$-0.000531695\pi$
$338$	2.44646			0.133070
$339$	1.77599	−	11.0414i	0.0964588	−	0.599684i
$340$		0			0
$341$	−21.8249	−	13.2446i	−1.18188	−	0.717233i
$342$	−5.01873	+	15.1971i	−0.271382	+	0.821764i
$343$		−	19.8668i		−	1.07271i
$344$			4.74077i			0.255605i
$345$		0			0
$346$	−6.00000			−0.322562
$347$	−19.3947			−1.04116			−0.520582	−	0.853812i	$-0.674285\pi$
$347$	−19.3947			−1.04116			−0.520582	+	0.853812i	$0.674285\pi$
$348$	11.9273	+	1.91850i	0.639371	+	0.102842i
$349$			18.5124i			0.990944i	0.868624	+	0.495472i	$0.165005\pi$
$349$			18.5124i			0.990944i	−0.868624	+	0.495472i	$0.834995\pi$
$350$		0			0
$351$	−9.40232	+	18.1287i	−0.501859	+	0.967640i
$352$	2.83537	+	1.72066i	0.151126	+	0.0917117i
$353$			31.0966i			1.65510i	0.561390	+	0.827552i	$0.310267\pi$
$353$			31.0966i			1.65510i	−0.561390	+	0.827552i	$0.689733\pi$
$354$	−2.25060	+	13.9920i	−0.119618	+	0.743664i
$355$		0			0
$356$			1.88151i			0.0997200i
$357$	0.248594	−	1.54551i	0.0131570	−	0.0817969i
$358$		−	5.06247i		−	0.267560i
$359$	−13.9495			−0.736227			−0.368113	−	0.929781i	$-0.619996\pi$
$359$	−13.9495			−0.736227			−0.368113	+	0.929781i	$0.619996\pi$
$360$		0			0
$361$	−9.45991			−0.497890
$362$	9.39472			0.493776
$363$	6.00091	+	18.0828i	0.314966	+	0.949103i
$364$	9.31608			0.488296
$365$		0			0
$366$	−3.77005	+	23.4384i	−0.197063	+	1.22514i
$367$	−12.4650			−0.650670			−0.325335	−	0.945599i	$-0.605477\pi$
$367$	−12.4650			−0.650670			−0.325335	+	0.945599i	$0.605477\pi$
$368$		−	1.38613i		−	0.0722572i
$369$	16.7893	+	5.54453i	0.874014	+	0.288637i
$370$		0			0
$371$	22.5025			1.16827
$372$	13.1630	+	2.11726i	0.682471	+	0.109775i
$373$		−	2.43171i		−	0.125909i	−0.998016	−	0.0629547i	$-0.979948\pi$
$373$		−	2.43171i		−	0.125909i	0.998016	−	0.0629547i	$-0.0200524\pi$
$374$	1.08106	+	0.656046i	0.0559000	+	0.0339233i
$375$		0			0
$376$			12.0557i			0.621725i
$377$			27.4122i			1.41180i
$378$	−5.67074	+	10.9338i	−0.291671	+	0.562375i
$379$	0.553535			0.0284332			0.0142166	−	0.999899i	$-0.495475\pi$
$379$	0.553535			0.0284332			0.0142166	+	0.999899i	$0.495475\pi$
$380$		0			0
$381$	−4.81264	+	29.9202i	−0.246559	+	1.53286i
$382$		−	4.57360i		−	0.234006i
$383$		−	1.38613i		−	0.0708281i	−0.999373	−	0.0354140i	$-0.988725\pi$
$383$		−	1.38613i		−	0.0708281i	0.999373	−	0.0354140i	$-0.0112750\pi$
$384$	−1.71007	−	0.275064i	−0.0872667	−	0.0140368i
$385$		0			0
$386$			7.92173i			0.403205i
$387$	4.45991	−	13.5049i	0.226710	−	0.686495i
$388$	−3.28567			−0.166805
$389$		−	5.87304i		−	0.297775i	−0.988854	−	0.148887i	$-0.952431\pi$
$389$		−	5.87304i		−	0.297775i	0.988854	−	0.148887i	$-0.0475692\pi$
$390$		0			0
$391$		−	0.528498i		−	0.0267273i
$392$	−1.38127			−0.0697649
$393$	−33.2434	−	5.34718i	−1.67691	−	0.269730i
$394$	−21.5520			−1.08577
$395$		0			0
$396$	−6.45833	−	7.56901i	−0.324543	−	0.380357i
$397$	25.0680			1.25813			0.629064	−	0.777354i	$-0.283438\pi$
$397$	25.0680			1.25813			0.629064	+	0.777354i	$0.283438\pi$
$398$	−1.06519			−0.0533931
$399$	−21.6247	−	3.47831i	−1.08259	−	0.174134i
$400$		0			0
$401$			20.3876i			1.01811i	0.860735	+	0.509054i	$0.170005\pi$
$401$			20.3876i			1.01811i	−0.860735	+	0.509054i	$0.829995\pi$
$402$	9.69736	+	1.55981i	0.483660	+	0.0777965i
$403$			30.2522i			1.50697i
$404$	3.50863			0.174561
$405$		0			0
$406$			16.5328i			0.820511i
$407$	3.06519	+	1.86013i	0.151936	+	0.0922033i
$408$	−0.652007	−	0.104875i	−0.0322791	−	0.00519208i
$409$			13.4418i			0.664656i	0.943164	+	0.332328i	$0.107834\pi$
$409$			13.4418i			0.664656i	−0.943164	+	0.332328i	$0.892166\pi$
$410$		0			0
$411$	1.92137	−	11.9451i	0.0947740	−	0.589209i
$412$	−14.6271			−0.720628
$413$	−19.3947			−0.954352
$414$	−1.30401	+	3.94865i	−0.0640888	+	0.194066i
$415$		0			0
$416$		−	3.93020i		−	0.192694i
$417$	−1.52510	+	9.48154i	−0.0746844	+	0.464313i
$418$	9.17937	−	15.1261i	0.448977	−	0.739841i
$419$			32.0723i			1.56684i	0.621495	+	0.783418i	$0.286526\pi$
$419$			32.0723i			1.56684i	−0.621495	+	0.783418i	$0.713474\pi$
$420$		0			0
$421$	−27.2643			−1.32878			−0.664391	−	0.747385i	$-0.731309\pi$
$421$	−27.2643			−1.32878			−0.664391	+	0.747385i	$0.731309\pi$
$422$		−	18.7766i		−	0.914031i
$423$	11.3415	−	34.3428i	0.551441	−	1.66981i
$424$		−	9.49318i		−	0.461030i
$425$		0			0
$426$	−0.563519	+	3.50340i	−0.0273026	+	0.169740i
$427$	−32.4887			−1.57224
$428$	9.31608			0.450310
$429$	14.6296	−	17.1961i	0.706325	−	0.830238i
$430$		0			0
$431$	−0.445917			−0.0214791			−0.0107395	−	0.999942i	$-0.503419\pi$
$431$	−0.445917			−0.0214791			−0.0107395	+	0.999942i	$0.503419\pi$
$432$	4.61267	+	2.39233i	0.221927	+	0.115101i
$433$	−34.9163			−1.67797			−0.838984	−	0.544156i	$-0.816850\pi$
$433$	−34.9163			−1.67797			−0.838984	+	0.544156i	$0.816850\pi$
$434$			18.2457i			0.875822i
$435$		0			0
$436$			8.37130i			0.400912i
$437$	−7.39472			−0.353737
$438$	3.28567	−	20.4270i	0.156995	−	0.976040i
$439$			0.473999i			0.0226227i	0.999936	+	0.0113114i	$0.00360059\pi$
$439$			0.473999i			0.0226227i	−0.999936	+	0.0113114i	$0.996399\pi$
$440$		0			0
$441$	3.93481	+	1.29944i	0.187372	+	0.0618782i
$442$		−	1.49849i		−	0.0712757i
$443$			15.3020i			0.727018i	0.931591	+	0.363509i	$0.118421\pi$
$443$			15.3020i			0.727018i	−0.931591	+	0.363509i	$0.881579\pi$
$444$	−1.84868	−	0.297359i	−0.0877345	−	0.0141120i
$445$		0			0
$446$	14.6271			0.692615
$447$	3.77005	+	0.606409i	0.178317	+	0.0286822i
$448$		−	2.37039i		−	0.111990i
$449$			16.6985i			0.788053i	0.919099	+	0.394026i	$0.128918\pi$
$449$			16.6985i			0.788053i	−0.919099	+	0.394026i	$0.871082\pi$
$450$		0			0
$451$	−16.7108	−	10.1411i	−0.786881	−	0.477524i
$452$		−	6.45667i		−	0.303696i
$453$	−1.39472	+	8.67097i	−0.0655297	+	0.407398i
$454$	16.7108			0.784277
$455$		0			0
$456$	−1.46741	+	9.12285i	−0.0687175	+	0.427217i
$457$			22.3304i			1.04457i	0.852770	+	0.522287i	$0.174921\pi$
$457$			22.3304i			1.04457i	−0.852770	+	0.522287i	$0.825079\pi$
$458$	−18.1573			−0.848433
$459$	1.75870	+	0.912135i	0.0820889	+	0.0425748i
$460$		0			0
$461$	−40.9992			−1.90952			−0.954761	−	0.297374i	$-0.903889\pi$
$461$	−40.9992			−1.90952			−0.954761	+	0.297374i	$0.903889\pi$
$462$	8.82343	−	10.3714i	0.410503	−	0.482519i
$463$	3.73159			0.173422			0.0867108	−	0.996234i	$-0.472364\pi$
$463$	3.73159			0.173422			0.0867108	+	0.996234i	$0.472364\pi$
$464$	6.97475			0.323795
$465$		0			0
$466$	1.54009			0.0713433
$467$			19.6887i			0.911087i	0.890214	+	0.455543i	$0.150555\pi$
$467$			19.6887i			0.911087i	−0.890214	+	0.455543i	$0.849445\pi$
$468$	−3.69736	+	11.1959i	−0.170911	+	0.517530i
$469$			13.4418i			0.620686i
$470$		0			0
$471$	−17.5460	−	2.82227i	−0.808479	−	0.130043i
$472$			8.18210i			0.376612i
$473$	−8.15727	+	13.4418i	−0.375072	+	0.618056i
$474$	−3.06519	+	19.0563i	−0.140789	+	0.875284i
$475$		0			0
$476$		−	0.903768i		−	0.0414242i
$477$	−8.93077	+	27.0430i	−0.408912	+	1.23822i
$478$		0			0
$479$	27.8990			1.27474			0.637369	−	0.770559i	$-0.280023\pi$
$479$	27.8990			1.27474			0.637369	+	0.770559i	$0.280023\pi$
$480$		0			0
$481$		−	4.24876i		−	0.193727i
$482$			10.1411i			0.461913i
$483$	−5.61873	−	0.903768i	−0.255661	−	0.0411229i
$484$	5.07863	+	9.75743i	0.230847	+	0.443520i
$485$		0			0
$486$	−10.8894	−	11.1544i	−0.493955	−	0.505973i
$487$	−3.28567			−0.148888			−0.0744439	−	0.997225i	$-0.523718\pi$
$487$	−3.28567			−0.148888			−0.0744439	+	0.997225i	$0.523718\pi$
$488$			13.7061i			0.620445i
$489$	2.61123	+	0.420015i	0.118084	+	0.0189937i
$490$		0			0
$491$	−40.9992			−1.85027			−0.925134	−	0.379642i	$-0.876047\pi$
$491$	−40.9992			−1.85027			−0.925134	+	0.379642i	$0.876047\pi$
$492$	10.0786	+	1.62114i	0.454380	+	0.0730867i
$493$	2.65930			0.119769
$494$	−20.9668			−0.943339
$495$		0			0
$496$	7.69736			0.345622
$497$	−4.85618			−0.217829
$498$	1.30401	+	0.209750i	0.0584342	+	0.00939911i
$499$	−9.15882			−0.410005			−0.205002	−	0.978761i	$-0.565720\pi$
$499$	−9.15882			−0.410005			−0.205002	+	0.978761i	$0.565720\pi$
$500$		0			0
$501$	38.1851	+	6.14204i	1.70598	+	0.274406i
$502$		−	20.7833i		−	0.927603i
$503$	30.6322			1.36582			0.682910	−	0.730502i	$-0.260714\pi$
$503$	30.6322			1.36582			0.682910	+	0.730502i	$0.260714\pi$
$504$	−2.22995	+	6.75247i	−0.0993301	+	0.300779i
$505$		0			0
$506$	2.38507	−	3.93020i	0.106029	−	0.174719i
$507$	−4.18363	−	0.672934i	−0.185801	−	0.0298860i
$508$			17.4965i			0.776280i
$509$			21.1368i			0.936874i	0.883497	+	0.468437i	$0.155183\pi$
$509$			21.1368i			0.936874i	−0.883497	+	0.468437i	$0.844817\pi$
$510$		0			0
$511$	28.3145			1.25256
$512$	−1.00000			−0.0441942
$513$	12.7625	−	24.6076i	0.563480	−	1.08645i
$514$		−	20.4270i		−	0.900996i
$515$		0			0
$516$	1.30401	−	8.10705i	0.0574060	−	0.356893i
$517$	−20.7438	+	34.1824i	−0.912311	+	1.50334i
$518$		−	2.56252i		−	0.112591i
$519$	10.2604	+	1.65038i	0.450382	+	0.0724437i
$520$		0			0
$521$		−	9.14719i		−	0.400746i	−0.979720	−	0.200373i	$-0.935785\pi$
$521$		−	9.14719i		−	0.400746i	0.979720	−	0.200373i	$-0.0642154\pi$
$522$	−19.8688	−	6.56154i	−0.869635	−	0.287191i
$523$		−	3.42868i		−	0.149926i	−0.997186	−	0.0749628i	$-0.976116\pi$
$523$		−	3.42868i		−	0.149926i	0.997186	−	0.0749628i	$-0.0238838\pi$
$524$	−19.4398			−0.849231
$525$		0			0
$526$	−23.0921			−1.00686
$527$	2.93481			0.127842
$528$	−4.37539	−	3.72236i	−0.190414	−	0.161995i
$529$	21.0786			0.916462
$530$		0			0
$531$	7.69736	−	23.3082i	0.334037	−	1.01149i
$532$	−12.6455			−0.548252
$533$			23.1634i			1.00332i
$534$	0.517536	−	3.21752i	0.0223960	−	0.139236i
$535$		0			0
$536$	5.67074			0.244939
$537$	−1.39250	+	8.65718i	−0.0600909	+	0.373585i
$538$			23.2150i			1.00087i
$539$	−3.91642	−	2.37671i	−0.168692	−	0.102372i
$540$		0			0
$541$		−	29.5007i		−	1.26833i	−0.773196	−	0.634167i	$-0.781343\pi$
$541$		−	29.5007i		−	1.26833i	0.773196	−	0.634167i	$-0.218657\pi$
$542$		−	2.82677i		−	0.121420i
$543$	−16.0656	−	2.58415i	−0.689442	−	0.110896i
$544$	−0.381275			−0.0163470
$545$		0			0
$546$	−15.9312	−	2.56252i	−0.681791	−	0.109666i
$547$			3.11963i			0.133386i	0.997774	+	0.0666928i	$0.0212448\pi$
$547$			3.11963i			0.133386i	−0.997774	+	0.0666928i	$0.978755\pi$
$548$		−	6.98517i		−	0.298391i
$549$	12.8941	−	39.0442i	0.550306	−	1.66637i
$550$		0			0
$551$		−	37.2088i		−	1.58515i
$552$	−0.381275	+	2.37039i	−0.0162281	+	0.100890i
$553$	−26.4145			−1.12326
$554$		−	11.7906i		−	0.500934i
$555$		0			0
$556$			5.54453i			0.235141i
$557$	−26.1573			−1.10832			−0.554160	−	0.832410i	$-0.686960\pi$
$557$	−26.1573			−1.10832			−0.554160	+	0.832410i	$0.686960\pi$
$558$	−21.9273	−	7.24134i	−0.928257	−	0.306550i
$559$	18.6322			0.788057
$560$		0			0
$561$	−1.66823	−	1.41924i	−0.0704325	−	0.0599205i
$562$	−8.73345			−0.368398
$563$	−3.44646			−0.145251			−0.0726256	−	0.997359i	$-0.523138\pi$
$563$	−3.44646			−0.145251			−0.0726256	+	0.997359i	$0.523138\pi$
$564$	3.31608	−	20.6161i	0.139632	−	0.868094i
$565$		0			0
$566$		−	28.6310i		−	1.20345i
$567$	12.7049	−	17.1378i	0.533554	−	0.719719i
$568$			2.04869i			0.0859610i
$569$	9.17937			0.384819			0.192410	−	0.981315i	$-0.438370\pi$
$569$	9.17937			0.384819			0.192410	+	0.981315i	$0.438370\pi$
$570$		0			0
$571$			28.1504i			1.17806i	0.808112	+	0.589029i	$0.200490\pi$
$571$			28.1504i			1.17806i	−0.808112	+	0.589029i	$0.799510\pi$
$572$	6.76255	−	11.1436i	0.282756	−	0.465936i
$573$	−1.25803	+	7.82117i	−0.0525550	+	0.326734i
$574$			13.9703i			0.583110i
$575$		0			0
$576$	2.84868	+	0.940756i	0.118695	+	0.0391982i
$577$	25.5227			1.06252			0.531262	−	0.847208i	$-0.321718\pi$
$577$	25.5227			1.06252			0.531262	+	0.847208i	$0.321718\pi$
$578$	16.8546			0.701060
$579$	2.17898	−	13.5467i	0.0905553	−	0.562982i
$580$		0			0
$581$			1.80754i			0.0749893i
$582$	5.61873	+	0.903768i	0.232904	+	0.0374624i
$583$	16.3346	−	26.9167i	0.676509	−	1.11477i
$584$		−	11.9451i		−	0.494293i
$585$		0			0
$586$	25.3947			1.04905
$587$		−	28.0055i		−	1.15591i	−0.816068	−	0.577956i	$-0.803850\pi$
$587$		−	28.0055i		−	1.15591i	0.816068	−	0.577956i	$-0.196150\pi$
$588$	2.36208	+	0.379939i	0.0974104	+	0.0156684i
$589$		−	41.0637i		−	1.69200i
$590$		0			0
$591$	36.8554	+	5.92817i	1.51603	+	0.243852i
$592$	−1.08106			−0.0444311
$593$	−22.7108			−0.932621			−0.466310	−	0.884621i	$-0.654417\pi$
$593$	−22.7108			−0.932621			−0.466310	+	0.884621i	$0.654417\pi$
$594$	8.96224	+	14.7200i	0.367725	+	0.603969i
$595$		0			0
$596$	2.20461			0.0903045
$597$	1.82155	+	0.292995i	0.0745511	+	0.0119915i
$598$	−5.44778			−0.222776
$599$		−	29.1812i		−	1.19231i	−0.802869	−	0.596156i	$-0.796694\pi$
$599$		−	29.1812i		−	1.19231i	0.802869	−	0.596156i	$-0.203306\pi$
$600$		0			0
$601$		−	2.24377i		−	0.0915252i	−0.998952	−	0.0457626i	$-0.985428\pi$
$601$		−	2.24377i		−	0.0915252i	0.998952	−	0.0457626i	$-0.0145718\pi$
$602$	11.2375			0.458004
$603$	−16.1541	−	5.33478i	−0.657847	−	0.217249i
$604$			5.07053i			0.206317i
$605$		0			0
$606$	−6.00000	−	0.965096i	−0.243733	−	0.0392044i
$607$		−	2.37039i		−	0.0962110i	−0.998842	−	0.0481055i	$-0.984682\pi$
$607$		−	2.37039i		−	0.0962110i	0.998842	−	0.0481055i	$-0.0153184\pi$
$608$			5.33478i			0.216354i
$609$	4.54759	−	28.2723i	0.184277	−	1.14565i
$610$		0			0
$611$	47.3813			1.91684
$612$	1.08613	+	0.358687i	0.0439042	+	0.0144991i
$613$		−	24.3918i		−	0.985174i	−0.870263	−	0.492587i	$-0.836051\pi$
$613$		−	24.3918i		−	0.985174i	0.870263	−	0.492587i	$-0.163949\pi$
$614$			23.8902i			0.964132i
$615$		0			0
$616$	4.07863	−	6.72092i	0.164333	−	0.270793i
$617$		−	14.8825i		−	0.599145i	−0.954073	−	0.299573i	$-0.903156\pi$
$617$		−	14.8825i		−	0.599145i	0.954073	−	0.299573i	$-0.0968441\pi$
$618$	25.0134	+	4.02340i	1.00619	+	0.161845i
$619$	10.2876			0.413496			0.206748	−	0.978394i	$-0.433712\pi$
$619$	10.2876			0.413496			0.206748	+	0.978394i	$0.433712\pi$
$620$		0			0
$621$	3.31608	−	6.39378i	0.133070	−	0.256574i
$622$		−	8.93134i		−	0.358114i
$623$	4.45991			0.178683
$624$	−1.08106	+	6.72092i	−0.0432768	+	0.269052i
$625$		0			0
$626$	−20.5208			−0.820178
$627$	−19.8580	+	23.3417i	−0.793052	+	0.932180i
$628$	−10.2604			−0.409435
$629$	−0.412179			−0.0164347
$630$		0			0
$631$	−12.3026			−0.489760			−0.244880	−	0.969553i	$-0.578749\pi$
$631$	−12.3026			−0.489760			−0.244880	+	0.969553i	$0.578749\pi$
$632$			11.1436i			0.443267i
$633$	−5.16476	+	32.1093i	−0.205281	+	1.27623i
$634$			22.9350i			0.910866i
$635$		0			0
$636$	−2.61123	+	16.2340i	−0.103542	+	0.643720i
$637$			5.42869i			0.215092i
$638$	19.7760	+	12.0012i	0.782939	+	0.475132i
$639$	1.92731	−	5.83605i	0.0762434	−	0.230871i
$640$		0			0
$641$			31.7993i			1.25600i	0.778214	+	0.627999i	$0.216126\pi$
$641$			31.7993i			1.25600i	−0.778214	+	0.627999i	$0.783874\pi$
$642$	−15.9312	−	2.56252i	−0.628753	−	0.101134i
$643$	18.3162			0.722322			0.361161	−	0.932504i	$-0.382381\pi$
$643$	18.3162			0.722322			0.361161	+	0.932504i	$0.382381\pi$
$644$	−3.28567			−0.129474
$645$		0			0
$646$			2.03402i			0.0800274i
$647$			15.3565i			0.603725i	0.953351	+	0.301862i	$0.0976083\pi$
$647$			15.3565i			0.603725i	−0.953351	+	0.301862i	$0.902392\pi$
$648$	−7.22995	−	5.35983i	−0.284019	−	0.210554i
$649$	−14.0786	+	23.1993i	−0.552635	+	0.910651i
$650$		0			0
$651$	5.01873	−	31.2014i	0.196700	−	1.22288i
$652$	1.52697			0.0598008
$653$		−	41.9214i		−	1.64051i	−0.571998	−	0.820255i	$-0.693831\pi$
$653$		−	41.9214i		−	1.64051i	0.571998	−	0.820255i	$-0.306169\pi$
$654$	2.30264	−	14.3155i	0.0900404	−	0.559781i
$655$		0			0
$656$	5.89370			0.230110
$657$	−11.2375	+	34.0278i	−0.438415	+	1.32755i
$658$	28.5766			1.11403
$659$	−2.20461			−0.0858796			−0.0429398	−	0.999078i	$-0.513672\pi$
$659$	−2.20461			−0.0858796			−0.0429398	+	0.999078i	$0.513672\pi$
$660$		0			0
$661$	49.7093			1.93347			0.966733	−	0.255787i	$-0.0823347\pi$
$661$	49.7093			1.93347			0.966733	+	0.255787i	$0.0823347\pi$
$662$	26.9985			1.04932
$663$	−0.412179	+	2.56252i	−0.0160077	+	0.0995199i
$664$	0.762550			0.0295927
$665$		0			0
$666$	3.07958	+	1.01701i	0.119331	+	0.0394083i
$667$		−	9.66793i		−	0.374344i
$668$	22.3295			0.863955
$669$	−25.0134	−	4.02340i	−0.967076	−	0.155553i
$670$		0			0
$671$	−23.5836	+	38.8618i	−0.910433	+	1.50024i
$672$	−0.652007	+	4.05352i	−0.0251517	+	0.156368i
$673$		−	7.92173i		−	0.305360i	−0.988276	−	0.152680i	$-0.951210\pi$
$673$		−	7.92173i		−	0.305360i	0.988276	−	0.152680i	$-0.0487904\pi$
$674$			0.0613278i			0.00236226i
$675$		0			0
$676$	−2.44646			−0.0940948
$677$	−39.6824			−1.52512			−0.762559	−	0.646919i	$-0.776057\pi$
$677$	−39.6824			−1.52512			−0.762559	+	0.646919i	$0.776057\pi$
$678$	−1.77599	+	11.0414i	−0.0682067	+	0.424041i
$679$			7.78830i			0.298888i
$680$		0			0
$681$	−28.5766	−	4.59654i	−1.09506	−	0.176140i
$682$	21.8249	+	13.2446i	0.835717	+	0.507161i
$683$		−	15.0922i		−	0.577488i	−0.957406	−	0.288744i	$-0.906762\pi$
$683$		−	15.0922i		−	0.577488i	0.957406	−	0.288744i	$-0.0932376\pi$
$684$	5.01873	−	15.1971i	0.191896	−	0.581075i
$685$		0			0
$686$			19.8668i			0.758520i
$687$	31.0502	+	4.99441i	1.18464	+	0.190548i
$688$		−	4.74077i		−	0.180740i
$689$	−37.3101			−1.42140
$690$		0			0
$691$	40.1573			1.52765			0.763827	−	0.645421i	$-0.223318\pi$
$691$	40.1573			1.52765			0.763827	+	0.645421i	$0.223318\pi$
$692$	6.00000			0.228086
$693$	−17.9415	+	15.3087i	−0.681540	+	0.581531i
$694$	19.3947			0.736213
$695$		0			0
$696$	−11.9273	−	1.91850i	−0.452104	−	0.0727206i
$697$	2.24712			0.0851157
$698$		−	18.5124i		−	0.700703i
$699$	−2.63366	−	0.423623i	−0.0996143	−	0.0160229i
$700$		0			0
$701$	38.8371			1.46686			0.733428	−	0.679767i	$-0.237919\pi$
$701$	38.8371			1.46686			0.733428	+	0.679767i	$0.237919\pi$
$702$	9.40232	−	18.1287i	0.354868	−	0.684225i
$703$			5.76719i			0.217514i
$704$	−2.83537	−	1.72066i	−0.106862	−	0.0648499i
$705$		0			0
$706$		−	31.0966i		−	1.17033i
$707$		−	8.31680i		−	0.312785i
$708$	2.25060	−	13.9920i	0.0845826	−	0.525850i
$709$	−10.0000			−0.375558			−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000			−0.375558			−0.187779	+	0.982211i	$0.560129\pi$
$710$		0			0
$711$	10.4834	−	31.7444i	0.393157	−	1.19051i
$712$		−	1.88151i		−	0.0705127i
$713$		−	10.6696i		−	0.399578i
$714$	−0.248594	+	1.54551i	−0.00930339	+	0.0578392i
$715$		0			0
$716$			5.06247i			0.189193i
$717$		0			0
$718$	13.9495			0.520591
$719$			27.8944i			1.04029i	0.854079	+	0.520143i	$0.174121\pi$
$719$			27.8944i			1.04029i	−0.854079	+	0.520143i	$0.825879\pi$
$720$		0			0
$721$			34.6720i			1.29125i
$722$	9.45991			0.352061
$723$	2.78944	−	17.3419i	0.103740	−	0.644954i
$724$	−9.39472			−0.349152
$725$		0			0
$726$	−6.00091	−	18.0828i	−0.222715	−	0.671117i
$727$	1.12356			0.0416705			0.0208353	−	0.999783i	$-0.493367\pi$
$727$	1.12356			0.0416705			0.0208353	+	0.999783i	$0.493367\pi$
$728$	−9.31608			−0.345277
$729$	15.5535	+	22.0701i	0.576057	+	0.817410i
$730$		0			0
$731$		−	1.80754i		−	0.0668542i
$732$	3.77005	−	23.4384i	0.139345	−	0.866307i
$733$			21.2721i			0.785704i	0.919602	+	0.392852i	$0.128512\pi$
$733$			21.2721i			0.785704i	−0.919602	+	0.392852i	$0.871488\pi$
$734$	12.4650			0.460093
$735$		0			0
$736$			1.38613i			0.0510935i
$737$	16.0786	+	9.75743i	0.592264	+	0.359420i
$738$	−16.7893	−	5.54453i	−0.618021	−	0.204097i
$739$			11.1981i			0.411927i	0.978560	+	0.205964i	$0.0660329\pi$
$739$			11.1981i			0.411927i	−0.978560	+	0.205964i	$0.933967\pi$
$740$		0			0
$741$	35.8546	+	5.76719i	1.31715	+	0.211863i
$742$	−22.5025			−0.826093
$743$	13.3797			0.490855			0.245427	−	0.969415i	$-0.421072\pi$
$743$	13.3797			0.490855			0.245427	+	0.969415i	$0.421072\pi$
$744$	−13.1630	−	2.11726i	−0.482580	−	0.0776227i
$745$		0			0
$746$			2.43171i			0.0890313i
$747$	−2.17226	−	0.717374i	−0.0794788	−	0.0262473i
$748$	−1.08106	−	0.656046i	−0.0395273	−	0.0239874i
$749$		−	22.0827i		−	0.806885i
$750$		0			0
$751$	−2.59029			−0.0945210			−0.0472605	−	0.998883i	$-0.515049\pi$
$751$	−2.59029			−0.0945210			−0.0472605	+	0.998883i	$0.515049\pi$
$752$		−	12.0557i		−	0.439626i
$753$	−5.71672	+	35.5408i	−0.208329	+	1.29518i
$754$		−	27.4122i		−	0.998292i
$755$		0			0
$756$	5.67074	−	10.9338i	0.206243	−	0.397659i
$757$	29.8382			1.08449			0.542243	−	0.840222i	$-0.317575\pi$
$757$	29.8382			1.08449			0.542243	+	0.840222i	$0.317575\pi$
$758$	−0.553535			−0.0201053
$759$	−5.15969	+	6.06487i	−0.187285	+	0.220141i
$760$		0			0
$761$	−29.2543			−1.06047			−0.530234	−	0.847852i	$-0.677896\pi$
$761$	−29.2543			−1.06047			−0.530234	+	0.847852i	$0.677896\pi$
$762$	4.81264	−	29.9202i	0.174344	−	1.08389i
$763$	19.8432			0.718372
$764$			4.57360i			0.165467i
$765$		0			0
$766$			1.38613i			0.0500830i
$767$	32.1573			1.16113
$768$	1.71007	+	0.275064i	0.0617068	+	0.00992551i
$769$		−	45.8700i		−	1.65412i	−0.562117	−	0.827058i	$-0.690013\pi$
$769$		−	45.8700i		−	1.65412i	0.562117	−	0.827058i	$-0.309987\pi$
$770$		0			0
$771$	−5.61873	+	34.9316i	−0.202353	+	1.25803i
$772$		−	7.92173i		−	0.285109i
$773$			29.0080i			1.04335i	0.853145	+	0.521673i	$0.174692\pi$
$773$			29.0080i			1.04335i	−0.853145	+	0.521673i	$0.825308\pi$
$774$	−4.45991	+	13.5049i	−0.160308	+	0.485425i
$775$		0			0
$776$	3.28567			0.117949
$777$	−0.704855	+	4.38208i	−0.0252865	+	0.157206i
$778$			5.87304i			0.210559i
$779$		−	31.4416i		−	1.12651i
$780$		0			0
$781$	−3.52510	+	5.80878i	−0.126138	+	0.207855i
$782$			0.528498i			0.0188990i
$783$	32.1723	+	16.6859i	1.14974	+	0.596305i
$784$	1.38127			0.0493312
$785$		0			0
$786$	33.2434	+	5.34718i	1.18575	+	0.190728i
$787$		−	20.5842i		−	0.733748i	−0.930271	−	0.366874i	$-0.880428\pi$
$787$		−	20.5842i		−	0.733748i	0.930271	−	0.366874i	$-0.119572\pi$
$788$	21.5520			0.767758
$789$	39.4891	+	6.35179i	1.40585	+	0.226130i
$790$		0			0
$791$	−15.3048			−0.544176
$792$	6.45833	+	7.56901i	0.229487	+	0.268953i
$793$	53.8676			1.91290
$794$	−25.0680			−0.889631
$795$		0			0
$796$	1.06519			0.0377547
$797$		−	13.5322i		−	0.479335i	−0.970855	−	0.239667i	$-0.922962\pi$
$797$		−	13.5322i		−	0.479335i	0.970855	−	0.239667i	$-0.0770384\pi$
$798$	21.6247	+	3.47831i	0.765505	+	0.123131i
$799$		−	4.59654i		−	0.162614i
$800$		0			0
$801$	−1.77005	+	5.35983i	−0.0625415	+	0.189380i
$802$		−	20.3876i		−	0.719911i
$803$	20.5535	−	33.8688i	0.725319	−	1.19521i
$804$	−9.69736	−	1.55981i	−0.342000	−	0.0550104i
$805$		0			0
$806$		−	30.2522i		−	1.06559i
$807$	6.38560	−	39.6992i	0.224784	−	1.39748i
$808$	−3.50863			−0.123433
$809$	−29.4685			−1.03606			−0.518028	−	0.855363i	$-0.673334\pi$
$809$	−29.4685			−1.03606			−0.518028	+	0.855363i	$0.673334\pi$
$810$		0			0
$811$		−	55.5626i		−	1.95107i	−0.219853	−	0.975533i	$-0.570558\pi$
$811$		−	55.5626i		−	1.95107i	0.219853	−	0.975533i	$-0.429442\pi$
$812$		−	16.5328i		−	0.580189i
$813$	−0.777541	+	4.83397i	−0.0272695	+	0.169535i
$814$	−3.06519	−	1.86013i	−0.107435	−	0.0651976i
$815$		0			0
$816$	0.652007	+	0.104875i	0.0228248	+	0.00367136i
$817$	−25.2910			−0.884819
$818$		−	13.4418i		−	0.469983i
$819$	26.5385	+	8.76417i	0.927332	+	0.306245i
$820$		0			0
$821$	−10.0800			−0.351793			−0.175897	−	0.984409i	$-0.556282\pi$
$821$	−10.0800			−0.351793			−0.175897	+	0.984409i	$0.556282\pi$
$822$	−1.92137	+	11.9451i	−0.0670153	+	0.416634i
$823$	−23.8065			−0.829843			−0.414921	−	0.909857i	$-0.636191\pi$
$823$	−23.8065			−0.829843			−0.414921	+	0.909857i	$0.636191\pi$
$824$	14.6271			0.509561
$825$		0			0
$826$	19.3947			0.674829
$827$	−45.4216			−1.57946			−0.789732	−	0.613452i	$-0.789780\pi$
$827$	−45.4216			−1.57946			−0.789732	+	0.613452i	$0.789780\pi$
$828$	1.30401	−	3.94865i	0.0453176	−	0.137225i
$829$	24.1842			0.839951			0.419975	−	0.907536i	$-0.362039\pi$
$829$	24.1842			0.839951			0.419975	+	0.907536i	$0.362039\pi$
$830$		0			0
$831$	−3.24317	+	20.1627i	−0.112504	+	0.699438i
$832$			3.93020i			0.136255i
$833$	0.526645			0.0182472
$834$	1.52510	−	9.48154i	0.0528099	−	0.328319i
$835$		0			0
$836$	−9.17937	+	15.1261i	−0.317475	+	0.523146i
$837$	35.5054	+	18.4146i	1.22725	+	0.636502i
$838$		−	32.0723i		−	1.10792i
$839$		−	43.2069i		−	1.49167i	−0.666132	−	0.745834i	$-0.732051\pi$
$839$		−	43.2069i		−	1.49167i	0.666132	−	0.745834i	$-0.267949\pi$
$840$		0			0
$841$	19.6472			0.677488
$842$	27.2643			0.939591
$843$	14.9348	+	2.40225i	0.514382	+	0.0827380i
$844$			18.7766i			0.646318i
$845$		0			0
$846$	−11.3415	+	34.3428i	−0.389928	+	1.18073i
$847$	23.1289	−	12.0383i	0.794717	−	0.413642i
$848$			9.49318i			0.325997i
$849$	−7.87535	+	48.9610i	−0.270281	+	1.68034i
$850$		0			0
$851$			1.49849i			0.0513674i
$852$	0.563519	−	3.50340i	0.0193058	−	0.120024i
$853$		−	16.7178i		−	0.572405i	−0.958169	−	0.286203i	$-0.907607\pi$
$853$		−	16.7178i		−	0.572405i	0.958169	−	0.286203i	$-0.0923931\pi$
$854$	32.4887			1.11174
$855$		0			0
$856$	−9.31608			−0.318417
$857$	−44.6441			−1.52501			−0.762506	−	0.646981i	$-0.776031\pi$
$857$	−44.6441			−1.52501			−0.762506	+	0.646981i	$0.776031\pi$
$858$	−14.6296	+	17.1961i	−0.499447	+	0.587067i
$859$	−16.8681			−0.575531			−0.287766	−	0.957701i	$-0.592912\pi$
$859$	−16.8681			−0.575531			−0.287766	+	0.957701i	$0.592912\pi$
$860$		0			0
$861$	3.84273	−	23.8902i	0.130960	−	0.814177i
$862$	0.445917			0.0151880
$863$		−	14.9370i		−	0.508460i	−0.967144	−	0.254230i	$-0.918178\pi$
$863$		−	14.9370i		−	0.508460i	0.967144	−	0.254230i	$-0.0818220\pi$
$864$	−4.61267	−	2.39233i	−0.156926	−	0.0813886i
$865$		0			0
$866$	34.9163			1.18650
$867$	−28.8226	−	4.63610i	−0.978867	−	0.157450i
$868$		−	18.2457i		−	0.619300i
$869$	−19.1743	+	31.5961i	−0.650444	+	1.07182i
$870$		0			0
$871$		−	22.2871i		−	0.755171i
$872$		−	8.37130i		−	0.283488i
$873$	−9.35982	−	3.09101i	−0.316782	−	0.104615i
$874$	7.39472			0.250130
$875$		0			0
$876$	−3.28567	+	20.4270i	−0.111012	+	0.690164i
$877$		−	38.9231i		−	1.31434i	−0.753742	−	0.657170i	$-0.771753\pi$
$877$		−	38.9231i		−	1.31434i	0.753742	−	0.657170i	$-0.228247\pi$
$878$		−	0.473999i		−	0.0159967i
$879$	−43.4268	−	6.98517i	−1.46475	−	0.235604i
$880$		0			0
$881$			5.84117i			0.196794i	0.995147	+	0.0983970i	$0.0313715\pi$
$881$			5.84117i			0.196794i	−0.995147	+	0.0983970i	$0.968628\pi$
$882$	−3.93481	−	1.29944i	−0.132492	−	0.0437545i
$883$	22.7255			0.764772			0.382386	−	0.924003i	$-0.375102\pi$
$883$	22.7255			0.764772			0.382386	+	0.924003i	$0.375102\pi$
$884$			1.49849i			0.0503995i
$885$		0			0
$886$		−	15.3020i		−	0.514080i
$887$	22.9467			0.770475			0.385238	−	0.922817i	$-0.374120\pi$
$887$	22.9467			0.770475			0.385238	+	0.922817i	$0.374120\pi$
$888$	1.84868	+	0.297359i	0.0620376	+	0.00997871i
$889$	41.4734			1.39097
$890$		0			0
$891$	−11.2771	−	27.6374i	−0.377798	−	0.925888i
$892$	−14.6271			−0.489753
$893$	−64.3145			−2.15220
$894$	−3.77005	−	0.606409i	−0.126089	−	0.0202814i
$895$		0			0
$896$			2.37039i			0.0791890i
$897$	9.31608	+	1.49849i	0.311055	+	0.0500330i
$898$		−	16.6985i		−	0.557238i
$899$	53.6872			1.79057
$900$		0			0
$901$			3.61951i			0.120583i
$902$	16.7108	+	10.1411i	0.556409	+	0.337661i
$903$	−19.2168	−	3.09101i	−0.639496	−	0.102863i
$904$			6.45667i			0.214746i
$905$		0			0
$906$	1.39472	−	8.67097i	0.0463365	−	0.288074i
$907$	10.9381			0.363192			0.181596	−	0.983373i	$-0.441874\pi$
$907$	10.9381			0.363192			0.181596	+	0.983373i	$0.441874\pi$
$908$	−16.7108			−0.554568
$909$	9.99496	+	3.30076i	0.331512	+	0.109479i
$910$		0			0
$911$		−	42.3031i		−	1.40157i	−0.713375	−	0.700783i	$-0.752834\pi$
$911$		−	42.3031i		−	1.40157i	0.713375	−	0.700783i	$-0.247166\pi$
$912$	1.46741	−	9.12285i	0.0485906	−	0.302088i
$913$	2.16211	+	1.31209i	0.0715554	+	0.0434239i
$914$		−	22.3304i		−	0.738625i
$915$		0			0
$916$	18.1573			0.599933
$917$			46.0798i			1.52169i
$918$	−1.75870	−	0.912135i	−0.0580457	−	0.0301049i
$919$		−	1.00250i		−	0.0330693i	−0.999863	−	0.0165347i	$-0.994737\pi$
$919$		−	1.00250i		−	0.0330693i	0.999863	−	0.0165347i	$-0.00526338\pi$
$920$		0			0
$921$	6.57134	−	40.8540i	0.216533	−	1.34618i
$922$	40.9992			1.35024
$923$	8.05175			0.265026
$924$	−8.82343	+	10.3714i	−0.290270	+	0.341192i
$925$		0			0
$926$	−3.73159			−0.122628
$927$	−41.6681	−	13.7606i	−1.36856	−	0.451957i
$928$	−6.97475			−0.228957
$929$			52.0745i			1.70851i	0.519855	+	0.854254i	$0.325986\pi$
$929$			52.0745i			1.70851i	−0.519855	+	0.854254i	$0.674014\pi$
$930$		0			0
$931$		−	7.36880i		−	0.241503i
$932$	−1.54009			−0.0504473
$933$	−2.45669	+	15.2732i	−0.0804283	+	0.500023i
$934$		−	19.6887i		−	0.644236i
$935$		0			0
$936$	3.69736	−	11.1959i	0.120852	−	0.365949i
$937$			15.1874i			0.496151i	0.968741	+	0.248075i	$0.0797981\pi$
$937$			15.1874i			0.496151i	−0.968741	+	0.248075i	$0.920202\pi$
$938$		−	13.4418i		−	0.438891i
$939$	35.0921	+	5.64454i	1.14519	+	0.184203i
$940$		0			0
$941$	−8.69094			−0.283317			−0.141658	−	0.989916i	$-0.545243\pi$
$941$	−8.69094			−0.283317			−0.141658	+	0.989916i	$0.545243\pi$
$942$	17.5460	+	2.82227i	0.571681	+	0.0919545i
$943$		−	8.16945i		−	0.266034i
$944$		−	8.18210i		−	0.266305i
$945$		0			0
$946$	8.15727	−	13.4418i	0.265216	−	0.437032i
$947$			41.4474i			1.34686i	0.739251	+	0.673429i	$0.235179\pi$
$947$			41.4474i			1.34686i	−0.739251	+	0.673429i	$0.764821\pi$
$948$	3.06519	−	19.0563i	0.0995527	−	0.618919i
$949$	−46.9467			−1.52395
$950$		0			0
$951$	6.30859	−	39.2205i	0.204570	−	1.27181i
$952$			0.903768i			0.0292913i
$953$	−15.0652			−0.488009			−0.244005	−	0.969774i	$-0.578461\pi$
$953$	−15.0652			−0.488009			−0.244005	+	0.969774i	$0.578461\pi$
$954$	8.93077	−	27.0430i	0.289144	−	0.875551i
$955$		0			0
$956$		0			0
$957$	−30.5172	−	25.9626i	−0.986482	−	0.839250i
$958$	−27.8990			−0.901376
$959$	−16.5575			−0.534671
$960$		0			0
$961$	28.2493			0.911269
$962$			4.24876i			0.136986i
$963$	26.5385	+	8.76417i	0.855193	+	0.282421i
$964$		−	10.1411i		−	0.326622i
$965$		0			0
$966$	5.61873	+	0.903768i	0.180780	+	0.0290783i
$967$			18.7093i			0.601650i	0.953679	+	0.300825i	$0.0972620\pi$
$967$			18.7093i			0.601650i	−0.953679	+	0.300825i	$0.902738\pi$
$968$	−5.07863	−	9.75743i	−0.163234	−	0.313616i
$969$	0.559485	−	3.47831i	0.0179732	−	0.111740i
$970$		0			0
$971$		−	14.4214i		−	0.462803i	−0.972858	−	0.231402i	$-0.925669\pi$
$971$		−	14.4214i		−	0.462803i	0.972858	−	0.231402i	$-0.0743311\pi$
$972$	10.8894	+	11.1544i	0.349279	+	0.357777i
$973$	13.1427			0.421335
$974$	3.28567			0.105280
$975$		0			0
$976$		−	13.7061i		−	0.438721i
$977$			10.2859i			0.329076i	0.986371	+	0.164538i	$0.0526133\pi$
$977$			10.2859i			0.329076i	−0.986371	+	0.164538i	$0.947387\pi$
$978$	−2.61123	−	0.420015i	−0.0834979	−	0.0134306i
$979$	3.23745	−	5.33478i	0.103469	−	0.170500i
$980$		0			0
$981$	−7.87535	+	23.8471i	−0.251441	+	0.761381i
$982$	40.9992			1.30834
$983$			39.8874i			1.27221i	0.771603	+	0.636105i	$0.219455\pi$
$983$			39.8874i			1.27221i	−0.771603	+	0.636105i	$0.780545\pi$
$984$	−10.0786	−	1.62114i	−0.321295	−	0.0516801i
$985$		0			0
$986$	−2.65930			−0.0846893
$987$	−48.8681	−	7.86040i	−1.55549	−	0.250199i
$988$	20.9668			0.667041
$989$	−6.57134			−0.208956
$990$		0			0
$991$	10.8929			0.346025			0.173013	−	0.984920i	$-0.444650\pi$
$991$	10.8929			0.346025			0.173013	+	0.984920i	$0.444650\pi$
$992$	−7.69736			−0.244391
$993$	−46.1693	−	7.42629i	−1.46514	−	0.235666i
$994$	4.85618			0.154029
$995$		0			0
$996$	−1.30401	−	0.209750i	−0.0413193	−	0.00664618i
$997$		−	21.5812i		−	0.683483i	−0.939794	−	0.341742i	$-0.888983\pi$
$997$		−	21.5812i		−	0.683483i	0.939794	−	0.341742i	$-0.111017\pi$
$998$	9.15882			0.289917
$999$	−4.98656	−	2.58624i	−0.157768	−	0.0818249i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1650.2.d.i.1451.12		12
3.2	odd	2		1650.2.d.j.1451.11		12
5.2	odd	4		330.2.f.a.329.7	yes	24
5.3	odd	4		330.2.f.a.329.18	yes	24
5.4	even	2		1650.2.d.j.1451.1		12
11.10	odd	2		1650.2.d.j.1451.12		12
15.2	even	4		330.2.f.a.329.17	yes	24
15.8	even	4		330.2.f.a.329.8	yes	24
15.14	odd	2	inner	1650.2.d.i.1451.2		12
33.32	even	2	inner	1650.2.d.i.1451.11		12
55.32	even	4		330.2.f.a.329.19	yes	24
55.43	even	4		330.2.f.a.329.6	yes	24
55.54	odd	2	inner	1650.2.d.i.1451.1		12
165.32	odd	4		330.2.f.a.329.5	✓	24
165.98	odd	4		330.2.f.a.329.20	yes	24
165.164	even	2		1650.2.d.j.1451.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.f.a.329.5	✓	24	165.32	odd	4
330.2.f.a.329.6	yes	24	55.43	even	4
330.2.f.a.329.7	yes	24	5.2	odd	4
330.2.f.a.329.8	yes	24	15.8	even	4
330.2.f.a.329.17	yes	24	15.2	even	4
330.2.f.a.329.18	yes	24	5.3	odd	4
330.2.f.a.329.19	yes	24	55.32	even	4
330.2.f.a.329.20	yes	24	165.98	odd	4
1650.2.d.i.1451.1		12	55.54	odd	2	inner
1650.2.d.i.1451.2		12	15.14	odd	2	inner
1650.2.d.i.1451.11		12	33.32	even	2	inner
1650.2.d.i.1451.12		12	1.1	even	1	trivial
1650.2.d.j.1451.1		12	5.4	even	2
1650.2.d.j.1451.2		12	165.164	even	2
1650.2.d.j.1451.11		12	3.2	odd	2
1650.2.d.j.1451.12		12	11.10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1650.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.71007 + 0.275064i) q^{3} +1.00000 q^{4} +(-1.71007 - 0.275064i) q^{6} -2.37039i q^{7} -1.00000 q^{8} +(2.84868 + 0.940756i) q^{9} +(-2.83537 - 1.72066i) q^{11} +(1.71007 + 0.275064i) q^{12} +3.93020i q^{13} +2.37039i q^{14} +1.00000 q^{16} +0.381275 q^{17} +(-2.84868 - 0.940756i) q^{18} -5.33478i q^{19} +(0.652007 - 4.05352i) q^{21} +(2.83537 + 1.72066i) q^{22} -1.38613i q^{23} +(-1.71007 - 0.275064i) q^{24} -3.93020i q^{26} +(4.61267 + 2.39233i) q^{27} -2.37039i q^{28} +6.97475 q^{29} +7.69736 q^{31} -1.00000 q^{32} +(-4.37539 - 3.72236i) q^{33} -0.381275 q^{34} +(2.84868 + 0.940756i) q^{36} -1.08106 q^{37} +5.33478i q^{38} +(-1.08106 + 6.72092i) q^{39} +5.89370 q^{41} +(-0.652007 + 4.05352i) q^{42} -4.74077i q^{43} +(-2.83537 - 1.72066i) q^{44} +1.38613i q^{46} -12.0557i q^{47} +(1.71007 + 0.275064i) q^{48} +1.38127 q^{49} +(0.652007 + 0.104875i) q^{51} +3.93020i q^{52} +9.49318i q^{53} +(-4.61267 - 2.39233i) q^{54} +2.37039i q^{56} +(1.46741 - 9.12285i) q^{57} -6.97475 q^{58} -8.18210i q^{59} -13.7061i q^{61} -7.69736 q^{62} +(2.22995 - 6.75247i) q^{63} +1.00000 q^{64} +(4.37539 + 3.72236i) q^{66} -5.67074 q^{67} +0.381275 q^{68} +(0.381275 - 2.37039i) q^{69} -2.04869i q^{71} +(-2.84868 - 0.940756i) q^{72} +11.9451i q^{73} +1.08106 q^{74} -5.33478i q^{76} +(-4.07863 + 6.72092i) q^{77} +(1.08106 - 6.72092i) q^{78} -11.1436i q^{79} +(7.22995 + 5.35983i) q^{81} -5.89370 q^{82} -0.762550 q^{83} +(0.652007 - 4.05352i) q^{84} +4.74077i q^{86} +(11.9273 + 1.91850i) q^{87} +(2.83537 + 1.72066i) q^{88} +1.88151i q^{89} +9.31608 q^{91} -1.38613i q^{92} +(13.1630 + 2.11726i) q^{93} +12.0557i q^{94} +(-1.71007 - 0.275064i) q^{96} -3.28567 q^{97} -1.38127 q^{98} +(-6.45833 - 7.56901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 12 q^{4} - 12 q^{8} - 6 q^{9} + 12 q^{16} - 4 q^{17} + 6 q^{18} + 12 q^{31} - 12 q^{32} - 18 q^{33} + 4 q^{34} - 6 q^{36} + 8 q^{49} - 14 q^{57} - 12 q^{62} - 22 q^{63} + 12 q^{64} + 18 q^{66}+ \cdots + 28 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^4 - 12 * q^8 - 6 * q^9 + 12 * q^16 - 4 * q^17 + 6 * q^18 + 12 * q^31 - 12 * q^32 - 18 * q^33 + 4 * q^34 - 6 * q^36 + 8 * q^49 - 14 * q^57 - 12 * q^62 - 22 * q^63 + 12 * q^64 + 18 * q^66 - 4 * q^68 - 4 * q^69 + 6 * q^72 + 40 * q^77 + 38 * q^81 + 8 * q^83 + 14 * q^87 + 40 * q^91 - 8 * q^98 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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