LMFDB - Embedded newform 289.2.c.c.251.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,2,Mod(38,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("289.38");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$289 = 17^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	289.c (of order $4$ , degree $2$ , not 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:	$2.30767661842$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} + 1$ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$2^{3}$
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.4
Root			$0.382683 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	289.251
Dual form			289.2.c.c.38.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.414214i q^{2} +(1.84776 + 1.84776i) q^{3} +1.82843 q^{4} +(-1.30656 - 1.30656i) q^{5} +(-0.765367 + 0.765367i) q^{6} +(-0.765367 + 0.765367i) q^{7} +1.58579i q^{8} +3.82843i q^{9} +(0.541196 - 0.541196i) q^{10} +(-0.765367 + 0.765367i) q^{11} +(3.37849 + 3.37849i) q^{12} +1.41421 q^{13} +(-0.317025 - 0.317025i) q^{14} -4.82843i q^{15} +3.00000 q^{16} -1.58579 q^{18} -4.82843i q^{19} +(-2.38896 - 2.38896i) q^{20} -2.82843 q^{21} +(-0.317025 - 0.317025i) q^{22} +(-2.93015 + 2.93015i) q^{23} +(-2.93015 + 2.93015i) q^{24} -1.58579i q^{25} +0.585786i q^{26} +(-1.53073 + 1.53073i) q^{27} +(-1.39942 + 1.39942i) q^{28} +(-3.15432 - 3.15432i) q^{29} +2.00000 q^{30} +(-2.29610 - 2.29610i) q^{31} +4.41421i q^{32} -2.82843 q^{33} +2.00000 q^{35} +7.00000i q^{36} +(2.70598 + 2.70598i) q^{37} +2.00000 q^{38} +(2.61313 + 2.61313i) q^{39} +(2.07193 - 2.07193i) q^{40} +(5.76745 - 5.76745i) q^{41} -1.17157i q^{42} -4.82843i q^{43} +(-1.39942 + 1.39942i) q^{44} +(5.00208 - 5.00208i) q^{45} +(-1.21371 - 1.21371i) q^{46} -10.8284 q^{47} +(5.54328 + 5.54328i) q^{48} +5.82843i q^{49} +0.656854 q^{50} +2.58579 q^{52} +1.41421i q^{53} +(-0.634051 - 0.634051i) q^{54} +2.00000 q^{55} +(-1.21371 - 1.21371i) q^{56} +(8.92177 - 8.92177i) q^{57} +(1.30656 - 1.30656i) q^{58} +6.00000i q^{59} -8.82843i q^{60} +(6.53281 - 6.53281i) q^{61} +(0.951076 - 0.951076i) q^{62} +(-2.93015 - 2.93015i) q^{63} +4.17157 q^{64} +(-1.84776 - 1.84776i) q^{65} -1.17157i q^{66} -6.82843 q^{67} -10.8284 q^{69} +0.828427i q^{70} +(-9.23880 - 9.23880i) q^{71} -6.07107 q^{72} +(3.78837 + 3.78837i) q^{73} +(-1.12085 + 1.12085i) q^{74} +(2.93015 - 2.93015i) q^{75} -8.82843i q^{76} -1.17157i q^{77} +(-1.08239 + 1.08239i) q^{78} +(-2.93015 + 2.93015i) q^{79} +(-3.91969 - 3.91969i) q^{80} +5.82843 q^{81} +(2.38896 + 2.38896i) q^{82} -0.343146i q^{83} -5.17157 q^{84} +2.00000 q^{86} -11.6569i q^{87} +(-1.21371 - 1.21371i) q^{88} -9.41421 q^{89} +(2.07193 + 2.07193i) q^{90} +(-1.08239 + 1.08239i) q^{91} +(-5.35757 + 5.35757i) q^{92} -8.48528i q^{93} -4.48528i q^{94} +(-6.30864 + 6.30864i) q^{95} +(-8.15640 + 8.15640i) q^{96} +(4.55374 + 4.55374i) q^{97} -2.41421 q^{98} +(-2.93015 - 2.93015i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q - 8 q^{4} + 24 q^{16} - 24 q^{18} + 16 q^{30} + 16 q^{35} + 16 q^{38} - 64 q^{47} - 40 q^{50} + 32 q^{52} + 16 q^{55} + 56 q^{64} - 32 q^{67} - 64 q^{69} + 8 q^{72} + 24 q^{81} - 64 q^{84} + 16 q^{86}+ \cdots - 8 q^{98}+O(q^{100})$ 8 * q - 8 * q^4 + 24 * q^16 - 24 * q^18 + 16 * q^30 + 16 * q^35 + 16 * q^38 - 64 * q^47 - 40 * q^50 + 32 * q^52 + 16 * q^55 + 56 * q^64 - 32 * q^67 - 64 * q^69 + 8 * q^72 + 24 * q^81 - 64 * q^84 + 16 * q^86 - 64 * q^89 - 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$ .

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$			0.414214i			0.292893i	0.989219	+	0.146447i	$0.0467837\pi$
$2$			0.414214i			0.292893i	−0.989219	+	0.146447i	$0.953216\pi$
$3$	1.84776	+	1.84776i	1.06680	+	1.06680i	0.997603	+	0.0692015i	$0.0220451\pi$
$3$	1.84776	+	1.84776i	1.06680	+	1.06680i	0.0692015	+	0.997603i	$0.477955\pi$
$4$	1.82843			0.914214
$5$	−1.30656	−	1.30656i	−0.584313	−	0.584313i	0.351773	−	0.936085i	$-0.385579\pi$
$5$	−1.30656	−	1.30656i	−0.584313	−	0.584313i	−0.936085	+	0.351773i	$0.885579\pi$
$6$	−0.765367	+	0.765367i	−0.312460	+	0.312460i
$7$	−0.765367	+	0.765367i	−0.289281	+	0.289281i	−0.836796	−	0.547515i	$-0.815574\pi$
$7$	−0.765367	+	0.765367i	−0.289281	+	0.289281i	0.547515	+	0.836796i	$0.315574\pi$
$8$			1.58579i			0.560660i
$9$			3.82843i			1.27614i
$10$	0.541196	−	0.541196i	0.171141	−	0.171141i
$11$	−0.765367	+	0.765367i	−0.230767	+	0.230767i	−0.813013	−	0.582246i	$-0.802174\pi$
$11$	−0.765367	+	0.765367i	−0.230767	+	0.230767i	0.582246	+	0.813013i	$0.302174\pi$
$12$	3.37849	+	3.37849i	0.975287	+	0.975287i
$13$	1.41421			0.392232			0.196116	−	0.980581i	$-0.437167\pi$
$13$	1.41421			0.392232			0.196116	+	0.980581i	$0.437167\pi$
$14$	−0.317025	−	0.317025i	−0.0847286	−	0.0847286i
$15$		−	4.82843i		−	1.24669i
$16$	3.00000			0.750000
$17$		0			0
$17$		0			0
$18$	−1.58579			−0.373773
$19$		−	4.82843i		−	1.10772i	−0.832611	−	0.553859i	$-0.813155\pi$
$19$		−	4.82843i		−	1.10772i	0.832611	−	0.553859i	$-0.186845\pi$
$20$	−2.38896	−	2.38896i	−0.534187	−	0.534187i
$21$	−2.82843			−0.617213
$22$	−0.317025	−	0.317025i	−0.0675900	−	0.0675900i
$23$	−2.93015	+	2.93015i	−0.610979	+	0.610979i	−0.943201	−	0.332222i	$-0.892202\pi$
$23$	−2.93015	+	2.93015i	−0.610979	+	0.610979i	0.332222	+	0.943201i	$0.392202\pi$
$24$	−2.93015	+	2.93015i	−0.598115	+	0.598115i
$25$		−	1.58579i		−	0.317157i
$26$			0.585786i			0.114882i
$27$	−1.53073	+	1.53073i	−0.294590	+	0.294590i
$28$	−1.39942	+	1.39942i	−0.264465	+	0.264465i
$29$	−3.15432	−	3.15432i	−0.585743	−	0.585743i	0.350733	−	0.936476i	$-0.385933\pi$
$29$	−3.15432	−	3.15432i	−0.585743	−	0.585743i	−0.936476	+	0.350733i	$0.885933\pi$
$30$	2.00000			0.365148
$31$	−2.29610	−	2.29610i	−0.412392	−	0.412392i	0.470179	−	0.882571i	$-0.344189\pi$
$31$	−2.29610	−	2.29610i	−0.412392	−	0.412392i	−0.882571	+	0.470179i	$0.844189\pi$
$32$			4.41421i			0.780330i
$33$	−2.82843			−0.492366
$34$		0			0
$35$	2.00000			0.338062
$36$			7.00000i			1.16667i
$37$	2.70598	+	2.70598i	0.444860	+	0.444860i	0.893642	−	0.448781i	$-0.148142\pi$
$37$	2.70598	+	2.70598i	0.444860	+	0.444860i	−0.448781	+	0.893642i	$0.648142\pi$
$38$	2.00000			0.324443
$39$	2.61313	+	2.61313i	0.418435	+	0.418435i
$40$	2.07193	−	2.07193i	0.327601	−	0.327601i
$41$	5.76745	−	5.76745i	0.900724	−	0.900724i	−0.0947747	−	0.995499i	$-0.530213\pi$
$41$	5.76745	−	5.76745i	0.900724	−	0.900724i	0.995499	+	0.0947747i	$0.0302131\pi$
$42$		−	1.17157i		−	0.180778i
$43$		−	4.82843i		−	0.736328i	−0.929761	−	0.368164i	$-0.879986\pi$
$43$		−	4.82843i		−	0.736328i	0.929761	−	0.368164i	$-0.120014\pi$
$44$	−1.39942	+	1.39942i	−0.210970	+	0.210970i
$45$	5.00208	−	5.00208i	0.745666	−	0.745666i
$46$	−1.21371	−	1.21371i	−0.178952	−	0.178952i
$47$	−10.8284			−1.57949			−0.789744	−	0.613436i	$-0.789787\pi$
$47$	−10.8284			−1.57949			−0.789744	+	0.613436i	$0.789787\pi$
$48$	5.54328	+	5.54328i	0.800103	+	0.800103i
$49$			5.82843i			0.832632i
$50$	0.656854			0.0928932
$51$		0			0
$52$	2.58579			0.358584
$53$			1.41421i			0.194257i	0.995272	+	0.0971286i	$0.0309658\pi$
$53$			1.41421i			0.194257i	−0.995272	+	0.0971286i	$0.969034\pi$
$54$	−0.634051	−	0.634051i	−0.0862834	−	0.0862834i
$55$	2.00000			0.269680
$56$	−1.21371	−	1.21371i	−0.162189	−	0.162189i
$57$	8.92177	−	8.92177i	1.18172	−	1.18172i
$58$	1.30656	−	1.30656i	0.171560	−	0.171560i
$59$			6.00000i			0.781133i	0.920575	+	0.390567i	$0.127721\pi$
$59$			6.00000i			0.781133i	−0.920575	+	0.390567i	$0.872279\pi$
$60$		−	8.82843i		−	1.13975i
$61$	6.53281	−	6.53281i	0.836441	−	0.836441i	−0.151947	−	0.988389i	$-0.548554\pi$
$61$	6.53281	−	6.53281i	0.836441	−	0.836441i	0.988389	+	0.151947i	$0.0485544\pi$
$62$	0.951076	−	0.951076i	0.120787	−	0.120787i
$63$	−2.93015	−	2.93015i	−0.369164	−	0.369164i
$64$	4.17157			0.521447
$65$	−1.84776	−	1.84776i	−0.229186	−	0.229186i
$66$		−	1.17157i		−	0.144211i
$67$	−6.82843			−0.834225			−0.417113	−	0.908855i	$-0.636958\pi$
$67$	−6.82843			−0.834225			−0.417113	+	0.908855i	$0.636958\pi$
$68$		0			0
$69$	−10.8284			−1.30359
$70$			0.828427i			0.0990160i
$71$	−9.23880	−	9.23880i	−1.09644	−	1.09644i	−0.994823	−	0.101620i	$-0.967597\pi$
$71$	−9.23880	−	9.23880i	−1.09644	−	1.09644i	−0.101620	−	0.994823i	$-0.532403\pi$
$72$	−6.07107			−0.715482
$73$	3.78837	+	3.78837i	0.443395	+	0.443395i	0.893151	−	0.449756i	$-0.148489\pi$
$73$	3.78837	+	3.78837i	0.443395	+	0.443395i	−0.449756	+	0.893151i	$0.648489\pi$
$74$	−1.12085	+	1.12085i	−0.130297	+	0.130297i
$75$	2.93015	−	2.93015i	0.338345	−	0.338345i
$76$		−	8.82843i		−	1.01269i
$77$		−	1.17157i		−	0.133513i
$78$	−1.08239	+	1.08239i	−0.122557	+	0.122557i
$79$	−2.93015	+	2.93015i	−0.329668	+	0.329668i	−0.852460	−	0.522792i	$-0.824890\pi$
$79$	−2.93015	+	2.93015i	−0.329668	+	0.329668i	0.522792	+	0.852460i	$0.324890\pi$
$80$	−3.91969	−	3.91969i	−0.438235	−	0.438235i
$81$	5.82843			0.647603
$82$	2.38896	+	2.38896i	0.263816	+	0.263816i
$83$		−	0.343146i		−	0.0376651i	−0.999823	−	0.0188326i	$-0.994005\pi$
$83$		−	0.343146i		−	0.0376651i	0.999823	−	0.0188326i	$-0.00599495\pi$
$84$	−5.17157			−0.564265
$85$		0			0
$86$	2.00000			0.215666
$87$		−	11.6569i		−	1.24975i
$88$	−1.21371	−	1.21371i	−0.129382	−	0.129382i
$89$	−9.41421			−0.997905			−0.498952	−	0.866629i	$-0.666282\pi$
$89$	−9.41421			−0.997905			−0.498952	+	0.866629i	$0.666282\pi$
$90$	2.07193	+	2.07193i	0.218401	+	0.218401i
$91$	−1.08239	+	1.08239i	−0.113466	+	0.113466i
$92$	−5.35757	+	5.35757i	−0.558565	+	0.558565i
$93$		−	8.48528i		−	0.879883i
$94$		−	4.48528i		−	0.462621i
$95$	−6.30864	+	6.30864i	−0.647253	+	0.647253i
$96$	−8.15640	+	8.15640i	−0.832459	+	0.832459i
$97$	4.55374	+	4.55374i	0.462362	+	0.462362i	0.899429	−	0.437067i	$-0.143983\pi$
$97$	4.55374	+	4.55374i	0.462362	+	0.462362i	−0.437067	+	0.899429i	$0.643983\pi$
$98$	−2.41421			−0.243872
$99$	−2.93015	−	2.93015i	−0.294491	−	0.294491i
$100$		−	2.89949i		−	0.289949i
$101$	13.4142			1.33476			0.667382	−	0.744715i	$-0.267415\pi$
$101$	13.4142			1.33476			0.667382	+	0.744715i	$0.267415\pi$
$102$		0			0
$103$	−4.48528			−0.441948			−0.220974	−	0.975280i	$-0.570924\pi$
$103$	−4.48528			−0.441948			−0.220974	+	0.975280i	$0.570924\pi$
$104$			2.24264i			0.219909i
$105$	3.69552	+	3.69552i	0.360646	+	0.360646i
$106$	−0.585786			−0.0568966
$107$	4.46088	+	4.46088i	0.431250	+	0.431250i	0.889053	−	0.457803i	$-0.151364\pi$
$107$	4.46088	+	4.46088i	0.431250	+	0.431250i	−0.457803	+	0.889053i	$0.651364\pi$
$108$	−2.79884	+	2.79884i	−0.269318	+	0.269318i
$109$	−3.02301	+	3.02301i	−0.289551	+	0.289551i	−0.836903	−	0.547351i	$-0.815636\pi$
$109$	−3.02301	+	3.02301i	−0.289551	+	0.289551i	0.547351	+	0.836903i	$0.315636\pi$
$110$			0.828427i			0.0789874i
$111$			10.0000i			0.949158i
$112$	−2.29610	+	2.29610i	−0.216961	+	0.216961i
$113$	11.4420	−	11.4420i	1.07638	−	1.07638i	0.0795455	−	0.996831i	$-0.474653\pi$
$113$	11.4420	−	11.4420i	1.07638	−	1.07638i	0.996831	−	0.0795455i	$-0.0253469\pi$
$114$	3.69552	+	3.69552i	0.346117	+	0.346117i
$115$	7.65685			0.714005
$116$	−5.76745	−	5.76745i	−0.535494	−	0.535494i
$117$			5.41421i			0.500544i
$118$	−2.48528			−0.228789
$119$		0			0
$120$	7.65685			0.698972
$121$			9.82843i			0.893493i
$122$	2.70598	+	2.70598i	0.244988	+	0.244988i
$123$	21.3137			1.92179
$124$	−4.19825	−	4.19825i	−0.377014	−	0.377014i
$125$	−8.60474	+	8.60474i	−0.769632	+	0.769632i
$126$	1.21371	−	1.21371i	0.108126	−	0.108126i
$127$			17.3137i			1.53634i	0.640244	+	0.768172i	$0.278833\pi$
$127$			17.3137i			1.53634i	−0.640244	+	0.768172i	$0.721167\pi$
$128$			10.5563i			0.933058i
$129$	8.92177	−	8.92177i	0.785518	−	0.785518i
$130$	0.765367	−	0.765367i	0.0671271	−	0.0671271i
$131$	0.131316	+	0.131316i	0.0114731	+	0.0114731i	0.712820	−	0.701347i	$-0.247418\pi$
$131$	0.131316	+	0.131316i	0.0114731	+	0.0114731i	−0.701347	+	0.712820i	$0.747418\pi$
$132$	−5.17157			−0.450128
$133$	3.69552	+	3.69552i	0.320442	+	0.320442i
$134$		−	2.82843i		−	0.244339i
$135$	4.00000			0.344265
$136$		0			0
$137$	8.72792			0.745677			0.372838	−	0.927896i	$-0.378385\pi$
$137$	8.72792			0.745677			0.372838	+	0.927896i	$0.378385\pi$
$138$		−	4.48528i		−	0.381813i
$139$	10.5838	+	10.5838i	0.897708	+	0.897708i	0.995233	−	0.0975252i	$-0.0310926\pi$
$139$	10.5838	+	10.5838i	0.897708	+	0.897708i	−0.0975252	+	0.995233i	$0.531093\pi$
$140$	3.65685			0.309061
$141$	−20.0083	−	20.0083i	−1.68500	−	1.68500i
$142$	3.82683	−	3.82683i	0.321141	−	0.321141i
$143$	−1.08239	+	1.08239i	−0.0905142	+	0.0905142i
$144$			11.4853i			0.957107i
$145$			8.24264i			0.684514i
$146$	−1.56920	+	1.56920i	−0.129868	+	0.129868i
$147$	−10.7695	+	10.7695i	−0.888256	+	0.888256i
$148$	4.94769	+	4.94769i	0.406697	+	0.406697i
$149$	−16.9706			−1.39028			−0.695141	−	0.718873i	$-0.744658\pi$
$149$	−16.9706			−1.39028			−0.695141	+	0.718873i	$0.744658\pi$
$150$	1.21371	+	1.21371i	0.0990989	+	0.0990989i
$151$		−	12.8284i		−	1.04396i	−0.852957	−	0.521981i	$-0.825193\pi$
$151$		−	12.8284i		−	1.04396i	0.852957	−	0.521981i	$-0.174807\pi$
$152$	7.65685			0.621053
$153$		0			0
$154$	0.485281			0.0391051
$155$			6.00000i			0.481932i
$156$	4.77791	+	4.77791i	0.382539	+	0.382539i
$157$	−1.65685			−0.132231			−0.0661157	−	0.997812i	$-0.521061\pi$
$157$	−1.65685			−0.132231			−0.0661157	+	0.997812i	$0.521061\pi$
$158$	−1.21371	−	1.21371i	−0.0965575	−	0.0965575i
$159$	−2.61313	+	2.61313i	−0.207234	+	0.207234i
$160$	5.76745	−	5.76745i	0.455957	−	0.455957i
$161$		−	4.48528i		−	0.353490i
$162$			2.41421i			0.189679i
$163$	−4.01254	+	4.01254i	−0.314287	+	0.314287i	−0.846568	−	0.532281i	$-0.821335\pi$
$163$	−4.01254	+	4.01254i	−0.314287	+	0.314287i	0.532281	+	0.846568i	$0.321335\pi$
$164$	10.5454	−	10.5454i	0.823454	−	0.823454i
$165$	3.69552	+	3.69552i	0.287696	+	0.287696i
$166$	0.142136			0.0110319
$167$	7.07401	+	7.07401i	0.547403	+	0.547403i	0.925689	−	0.378286i	$-0.123486\pi$
$167$	7.07401	+	7.07401i	0.547403	+	0.547403i	−0.378286	+	0.925689i	$0.623486\pi$
$168$		−	4.48528i		−	0.346047i
$169$	−11.0000			−0.846154
$170$		0			0
$171$	18.4853			1.41360
$172$		−	8.82843i		−	0.673161i
$173$	2.38896	+	2.38896i	0.181629	+	0.181629i	0.792065	−	0.610436i	$-0.209006\pi$
$173$	2.38896	+	2.38896i	0.181629	+	0.181629i	−0.610436	+	0.792065i	$0.709006\pi$
$174$	4.82843			0.366042
$175$	1.21371	+	1.21371i	0.0917477	+	0.0917477i
$176$	−2.29610	+	2.29610i	−0.173075	+	0.173075i
$177$	−11.0866	+	11.0866i	−0.833316	+	0.833316i
$178$		−	3.89949i		−	0.292280i
$179$			6.00000i			0.448461i	0.974536	+	0.224231i	$0.0719869\pi$
$179$			6.00000i			0.448461i	−0.974536	+	0.224231i	$0.928013\pi$
$180$	9.14594	−	9.14594i	0.681698	−	0.681698i
$181$	−8.82892	+	8.82892i	−0.656248	+	0.656248i	−0.954490	−	0.298242i	$-0.903600\pi$
$181$	−8.82892	+	8.82892i	−0.656248	+	0.656248i	0.298242	+	0.954490i	$0.403600\pi$
$182$	−0.448342	−	0.448342i	−0.0332333	−	0.0332333i
$183$	24.1421			1.78464
$184$	−4.64659	−	4.64659i	−0.342551	−	0.342551i
$185$		−	7.07107i		−	0.519875i
$186$	3.51472			0.257712
$187$		0			0
$188$	−19.7990			−1.44399
$189$		−	2.34315i		−	0.170439i
$190$	−2.61313	−	2.61313i	−0.189576	−	0.189576i
$191$	−20.0000			−1.44715			−0.723575	−	0.690246i	$-0.757502\pi$
$191$	−20.0000			−1.44715			−0.723575	+	0.690246i	$0.757502\pi$
$192$	7.70806	+	7.70806i	0.556281	+	0.556281i
$193$	−3.91969	+	3.91969i	−0.282145	+	0.282145i	−0.833964	−	0.551819i	$-0.813934\pi$
$193$	−3.91969	+	3.91969i	−0.282145	+	0.282145i	0.551819	+	0.833964i	$0.313934\pi$
$194$	−1.88622	+	1.88622i	−0.135423	+	0.135423i
$195$		−	6.82843i		−	0.488994i
$196$			10.6569i			0.761204i
$197$	−10.5454	+	10.5454i	−0.751326	+	0.751326i	−0.974727	−	0.223401i	$-0.928284\pi$
$197$	−10.5454	+	10.5454i	−0.751326	+	0.751326i	0.223401	+	0.974727i	$0.428284\pi$
$198$	1.21371	−	1.21371i	0.0862545	−	0.0862545i
$199$	−1.21371	−	1.21371i	−0.0860375	−	0.0860375i	0.662778	−	0.748816i	$-0.269377\pi$
$199$	−1.21371	−	1.21371i	−0.0860375	−	0.0860375i	−0.748816	+	0.662778i	$0.769377\pi$
$200$	2.51472			0.177817
$201$	−12.6173	−	12.6173i	−0.889955	−	0.889955i
$202$			5.55635i			0.390943i
$203$	4.82843			0.338889
$204$		0			0
$205$	−15.0711			−1.05261
$206$		−	1.85786i		−	0.129444i
$207$	−11.2179	−	11.2179i	−0.779696	−	0.779696i
$208$	4.24264			0.294174
$209$	3.69552	+	3.69552i	0.255624	+	0.255624i
$210$	−1.53073	+	1.53073i	−0.105631	+	0.105631i
$211$	−10.5838	+	10.5838i	−0.728620	+	0.728620i	−0.970345	−	0.241725i	$-0.922287\pi$
$211$	−10.5838	+	10.5838i	−0.728620	+	0.728620i	0.241725	+	0.970345i	$0.422287\pi$
$212$			2.58579i			0.177593i
$213$		−	34.1421i		−	2.33938i
$214$	−1.84776	+	1.84776i	−0.126310	+	0.126310i
$215$	−6.30864	+	6.30864i	−0.430246	+	0.430246i
$216$	−2.42742	−	2.42742i	−0.165165	−	0.165165i
$217$	3.51472			0.238595
$218$	−1.25217	−	1.25217i	−0.0848077	−	0.0848077i
$219$			14.0000i			0.946032i
$220$	3.65685			0.246545
$221$		0			0
$222$	−4.14214			−0.278002
$223$		−	0.828427i		−	0.0554756i	−0.999615	−	0.0277378i	$-0.991170\pi$
$223$		−	0.828427i		−	0.0554756i	0.999615	−	0.0277378i	$-0.00883035\pi$
$224$	−3.37849	−	3.37849i	−0.225735	−	0.225735i
$225$	6.07107			0.404738
$226$	4.73945	+	4.73945i	0.315263	+	0.315263i
$227$	3.56420	−	3.56420i	0.236564	−	0.236564i	−0.578861	−	0.815426i	$-0.696503\pi$
$227$	3.56420	−	3.56420i	0.236564	−	0.236564i	0.815426	+	0.578861i	$0.196503\pi$
$228$	16.3128	−	16.3128i	1.08034	−	1.08034i
$229$		−	22.8284i		−	1.50854i	−0.656562	−	0.754272i	$-0.727990\pi$
$229$		−	22.8284i		−	1.50854i	0.656562	−	0.754272i	$-0.272010\pi$
$230$			3.17157i			0.209127i
$231$	2.16478	−	2.16478i	0.142432	−	0.142432i
$232$	5.00208	−	5.00208i	0.328403	−	0.328403i
$233$	7.16687	+	7.16687i	0.469517	+	0.469517i	0.901758	−	0.432241i	$-0.142277\pi$
$233$	7.16687	+	7.16687i	0.469517	+	0.469517i	−0.432241	+	0.901758i	$0.642277\pi$
$234$	−2.24264			−0.146606
$235$	14.1480	+	14.1480i	0.922915	+	0.922915i
$236$			10.9706i			0.714123i
$237$	−10.8284			−0.703382
$238$		0			0
$239$	9.17157			0.593260			0.296630	−	0.954993i	$-0.404137\pi$
$239$	9.17157			0.593260			0.296630	+	0.954993i	$0.404137\pi$
$240$		−	14.4853i		−	0.935021i
$241$	−8.69760	−	8.69760i	−0.560262	−	0.560262i	0.369120	−	0.929382i	$-0.379659\pi$
$241$	−8.69760	−	8.69760i	−0.560262	−	0.560262i	−0.929382	+	0.369120i	$0.879659\pi$
$242$	−4.07107			−0.261698
$243$	15.3617	+	15.3617i	0.985455	+	0.985455i
$244$	11.9448	−	11.9448i	0.764686	−	0.764686i
$245$	7.61521	−	7.61521i	0.486518	−	0.486518i
$246$			8.82843i			0.562880i
$247$		−	6.82843i		−	0.434482i
$248$	3.64113	−	3.64113i	0.231212	−	0.231212i
$249$	0.634051	−	0.634051i	0.0401813	−	0.0401813i
$250$	−3.56420	−	3.56420i	−0.225420	−	0.225420i
$251$	−3.51472			−0.221847			−0.110924	−	0.993829i	$-0.535381\pi$
$251$	−3.51472			−0.221847			−0.110924	+	0.993829i	$0.535381\pi$
$252$	−5.35757	−	5.35757i	−0.337495	−	0.337495i
$253$		−	4.48528i		−	0.281987i
$254$	−7.17157			−0.449985
$255$		0			0
$256$	3.97056			0.248160
$257$			22.1421i			1.38119i	0.723242	+	0.690594i	$0.242651\pi$
$257$			22.1421i			1.38119i	−0.723242	+	0.690594i	$0.757349\pi$
$258$	3.69552	+	3.69552i	0.230073	+	0.230073i
$259$	−4.14214			−0.257380
$260$	−3.37849	−	3.37849i	−0.209525	−	0.209525i
$261$	12.0761	−	12.0761i	0.747491	−	0.747491i
$262$	−0.0543929	+	0.0543929i	−0.00336041	+	0.00336041i
$263$			6.48528i			0.399900i	0.979806	+	0.199950i	$0.0640779\pi$
$263$			6.48528i			0.399900i	−0.979806	+	0.199950i	$0.935922\pi$
$264$		−	4.48528i		−	0.276050i
$265$	1.84776	−	1.84776i	0.113507	−	0.113507i
$266$	−1.53073	+	1.53073i	−0.0938553	+	0.0938553i
$267$	−17.3952	−	17.3952i	−1.06457	−	1.06457i
$268$	−12.4853			−0.762660
$269$	4.49935	+	4.49935i	0.274330	+	0.274330i	0.830841	−	0.556511i	$-0.187860\pi$
$269$	4.49935	+	4.49935i	0.274330	+	0.274330i	−0.556511	+	0.830841i	$0.687860\pi$
$270$			1.65685i			0.100833i
$271$	6.14214			0.373108			0.186554	−	0.982445i	$-0.440268\pi$
$271$	6.14214			0.373108			0.186554	+	0.982445i	$0.440268\pi$
$272$		0			0
$273$	−4.00000			−0.242091
$274$			3.61522i			0.218404i
$275$	1.21371	+	1.21371i	0.0731894	+	0.0731894i
$276$	−19.7990			−1.19176
$277$	−15.5859	−	15.5859i	−0.936466	−	0.936466i	0.0616329	−	0.998099i	$-0.480369\pi$
$277$	−15.5859	−	15.5859i	−0.936466	−	0.936466i	−0.998099	+	0.0616329i	$0.980369\pi$
$278$	−4.38396	+	4.38396i	−0.262933	+	0.262933i
$279$	8.79045	−	8.79045i	0.526271	−	0.526271i
$280$			3.17157i			0.189538i
$281$		−	17.8995i		−	1.06779i	−0.845549	−	0.533897i	$-0.820727\pi$
$281$		−	17.8995i		−	1.06779i	0.845549	−	0.533897i	$-0.179273\pi$
$282$	8.28772	−	8.28772i	0.493527	−	0.493527i
$283$	16.1815	−	16.1815i	0.961890	−	0.961890i	−0.0374103	−	0.999300i	$-0.511911\pi$
$283$	16.1815	−	16.1815i	0.961890	−	0.961890i	0.999300	+	0.0374103i	$0.0119108\pi$
$284$	−16.8925	−	16.8925i	−1.00238	−	1.00238i
$285$	−23.3137			−1.38098
$286$	−0.448342	−	0.448342i	−0.0265110	−	0.0265110i
$287$			8.82843i			0.521126i
$288$	−16.8995			−0.995812
$289$		0			0
$290$	−3.41421			−0.200490
$291$			16.8284i			0.986500i
$292$	6.92676	+	6.92676i	0.405358	+	0.405358i
$293$	23.6569			1.38205			0.691024	−	0.722832i	$-0.257160\pi$
$293$	23.6569			1.38205			0.691024	+	0.722832i	$0.257160\pi$
$294$	−4.46088	−	4.46088i	−0.260164	−	0.260164i
$295$	7.83938	−	7.83938i	0.456426	−	0.456426i
$296$	−4.29111	+	4.29111i	−0.249416	+	0.249416i
$297$		−	2.34315i		−	0.135963i
$298$		−	7.02944i		−	0.407204i
$299$	−4.14386	+	4.14386i	−0.239646	+	0.239646i
$300$	5.35757	−	5.35757i	0.309319	−	0.309319i
$301$	3.69552	+	3.69552i	0.213006	+	0.213006i
$302$	5.31371			0.305770
$303$	24.7862	+	24.7862i	1.42393	+	1.42393i
$304$		−	14.4853i		−	0.830788i
$305$	−17.0711			−0.977486
$306$		0			0
$307$	2.14214			0.122258			0.0611291	−	0.998130i	$-0.480530\pi$
$307$	2.14214			0.122258			0.0611291	+	0.998130i	$0.480530\pi$
$308$		−	2.14214i		−	0.122060i
$309$	−8.28772	−	8.28772i	−0.471472	−	0.471472i
$310$	−2.48528			−0.141154
$311$	3.19278	+	3.19278i	0.181046	+	0.181046i	0.791812	−	0.610765i	$-0.209138\pi$
$311$	3.19278	+	3.19278i	0.181046	+	0.181046i	−0.610765	+	0.791812i	$0.709138\pi$
$312$	−4.14386	+	4.14386i	−0.234600	+	0.234600i
$313$	9.01462	−	9.01462i	0.509537	−	0.509537i	−0.404848	−	0.914384i	$-0.632675\pi$
$313$	9.01462	−	9.01462i	0.509537	−	0.509537i	0.914384	+	0.404848i	$0.132675\pi$
$314$		−	0.686292i		−	0.0387297i
$315$			7.65685i			0.431415i
$316$	−5.35757	+	5.35757i	−0.301387	+	0.301387i
$317$	−4.10540	+	4.10540i	−0.230582	+	0.230582i	−0.812936	−	0.582354i	$-0.802132\pi$
$317$	−4.10540	+	4.10540i	−0.230582	+	0.230582i	0.582354	+	0.812936i	$0.302132\pi$
$318$	−1.08239	−	1.08239i	−0.0606975	−	0.0606975i
$319$	4.82843			0.270340
$320$	−5.45042	−	5.45042i	−0.304688	−	0.304688i
$321$			16.4853i			0.920119i
$322$	1.85786			0.103535
$323$		0			0
$324$	10.6569			0.592047
$325$		−	2.24264i		−	0.124399i
$326$	−1.66205	−	1.66205i	−0.0920524	−	0.0920524i
$327$	−11.1716			−0.617789
$328$	9.14594	+	9.14594i	0.505000	+	0.505000i
$329$	8.28772	−	8.28772i	0.456917	−	0.456917i
$330$	−1.53073	+	1.53073i	−0.0842641	+	0.0842641i
$331$			17.7990i			0.978321i	0.872194	+	0.489160i	$0.162697\pi$
$331$			17.7990i			0.978321i	−0.872194	+	0.489160i	$0.837303\pi$
$332$		−	0.627417i		−	0.0344340i
$333$	−10.3596	+	10.3596i	−0.567705	+	0.567705i
$334$	−2.93015	+	2.93015i	−0.160331	+	0.160331i
$335$	8.92177	+	8.92177i	0.487448	+	0.487448i
$336$	−8.48528			−0.462910
$337$	−24.3764	−	24.3764i	−1.32786	−	1.32786i	−0.907230	−	0.420634i	$-0.861808\pi$
$337$	−24.3764	−	24.3764i	−1.32786	−	1.32786i	−0.420634	−	0.907230i	$-0.638192\pi$
$338$		−	4.55635i		−	0.247833i
$339$	42.2843			2.29657
$340$		0			0
$341$	3.51472			0.190333
$342$			7.65685i			0.414035i
$343$	−9.81845	−	9.81845i	−0.530147	−	0.530147i
$344$	7.65685			0.412830
$345$	14.1480	+	14.1480i	0.761704	+	0.761704i
$346$	−0.989538	+	0.989538i	−0.0531979	+	0.0531979i
$347$	2.74444	−	2.74444i	0.147329	−	0.147329i	−0.629595	−	0.776924i	$-0.716779\pi$
$347$	2.74444	−	2.74444i	0.147329	−	0.147329i	0.776924	+	0.629595i	$0.216779\pi$
$348$		−	21.3137i		−	1.14253i
$349$			4.24264i			0.227103i	0.993532	+	0.113552i	$0.0362227\pi$
$349$			4.24264i			0.227103i	−0.993532	+	0.113552i	$0.963777\pi$
$350$	−0.502734	+	0.502734i	−0.0268723	+	0.0268723i
$351$	−2.16478	+	2.16478i	−0.115548	+	0.115548i
$352$	−3.37849	−	3.37849i	−0.180074	−	0.180074i
$353$	14.0000			0.745145			0.372572	−	0.928003i	$-0.378476\pi$
$353$	14.0000			0.745145			0.372572	+	0.928003i	$0.378476\pi$
$354$	−4.59220	−	4.59220i	−0.244073	−	0.244073i
$355$			24.1421i			1.28133i
$356$	−17.2132			−0.912298
$357$		0			0
$358$	−2.48528			−0.131351
$359$		−	23.1716i		−	1.22295i	−0.791264	−	0.611474i	$-0.790577\pi$
$359$		−	23.1716i		−	1.22295i	0.791264	−	0.611474i	$-0.209423\pi$
$360$	7.93223	+	7.93223i	0.418065	+	0.418065i
$361$	−4.31371			−0.227037
$362$	−3.65706	−	3.65706i	−0.192211	−	0.192211i
$363$	−18.1606	+	18.1606i	−0.953182	+	0.953182i
$364$	−1.97908	+	1.97908i	−0.103732	+	0.103732i
$365$		−	9.89949i		−	0.518163i
$366$			10.0000i			0.522708i
$367$	18.6089	−	18.6089i	0.971377	−	0.971377i	−0.0282246	−	0.999602i	$-0.508985\pi$
$367$	18.6089	−	18.6089i	0.971377	−	0.971377i	0.999602	+	0.0282246i	$0.00898536\pi$
$368$	−8.79045	+	8.79045i	−0.458234	+	0.458234i
$369$	22.0803	+	22.0803i	1.14945	+	1.14945i
$370$	2.92893			0.152268
$371$	−1.08239	−	1.08239i	−0.0561950	−	0.0561950i
$372$		−	15.5147i		−	0.804401i
$373$	19.5563			1.01259			0.506295	−	0.862361i	$-0.331015\pi$
$373$	19.5563			1.01259			0.506295	+	0.862361i	$0.331015\pi$
$374$		0			0
$375$	−31.7990			−1.64209
$376$		−	17.1716i		−	0.885556i
$377$	−4.46088	−	4.46088i	−0.229747	−	0.229747i
$378$	0.970563			0.0499204
$379$	−0.765367	−	0.765367i	−0.0393143	−	0.0393143i	0.687176	−	0.726491i	$-0.258850\pi$
$379$	−0.765367	−	0.765367i	−0.0393143	−	0.0393143i	−0.726491	+	0.687176i	$0.758850\pi$
$380$	−11.5349	+	11.5349i	−0.591728	+	0.591728i
$381$	−31.9916	+	31.9916i	−1.63898	+	1.63898i
$382$		−	8.28427i		−	0.423860i
$383$			5.51472i			0.281789i	0.990025	+	0.140894i	$0.0449978\pi$
$383$			5.51472i			0.281789i	−0.990025	+	0.140894i	$0.955002\pi$
$384$	−19.5056	+	19.5056i	−0.995390	+	0.995390i
$385$	−1.53073	+	1.53073i	−0.0780134	+	0.0780134i
$386$	−1.62359	−	1.62359i	−0.0826385	−	0.0826385i
$387$	18.4853			0.939660
$388$	8.32618	+	8.32618i	0.422698	+	0.422698i
$389$		−	16.1421i		−	0.818439i	−0.912436	−	0.409219i	$-0.865801\pi$
$389$		−	16.1421i		−	0.818439i	0.912436	−	0.409219i	$-0.134199\pi$
$390$	2.82843			0.143223
$391$		0			0
$392$	−9.24264			−0.466824
$393$			0.485281i			0.0244792i
$394$	−4.36803	−	4.36803i	−0.220058	−	0.220058i
$395$	7.65685			0.385258
$396$	−5.35757	−	5.35757i	−0.269228	−	0.269228i
$397$	−19.2814	+	19.2814i	−0.967707	+	0.967707i	−0.999495	−	0.0317879i	$-0.989880\pi$
$397$	−19.2814	+	19.2814i	−0.967707	+	0.967707i	0.0317879	+	0.999495i	$0.489880\pi$
$398$	0.502734	−	0.502734i	0.0251998	−	0.0251998i
$399$			13.6569i			0.683698i
$400$		−	4.75736i		−	0.237868i
$401$	12.0761	−	12.0761i	0.603051	−	0.603051i	−0.338070	−	0.941121i	$-0.609774\pi$
$401$	12.0761	−	12.0761i	0.603051	−	0.603051i	0.941121	+	0.338070i	$0.109774\pi$
$402$	5.22625	−	5.22625i	0.260662	−	0.260662i
$403$	−3.24718	−	3.24718i	−0.161753	−	0.161753i
$404$	24.5269			1.22026
$405$	−7.61521	−	7.61521i	−0.378403	−	0.378403i
$406$			2.00000i			0.0992583i
$407$	−4.14214			−0.205318
$408$		0			0
$409$	19.3137			0.955001			0.477501	−	0.878631i	$-0.341543\pi$
$409$	19.3137			0.955001			0.477501	+	0.878631i	$0.341543\pi$
$410$		−	6.24264i		−	0.308302i
$411$	16.1271	+	16.1271i	0.795491	+	0.795491i
$412$	−8.20101			−0.404035
$413$	−4.59220	−	4.59220i	−0.225967	−	0.225967i
$414$	4.64659	−	4.64659i	0.228368	−	0.228368i
$415$	−0.448342	+	0.448342i	−0.0220082	+	0.0220082i
$416$			6.24264i			0.306071i
$417$			39.1127i			1.91536i
$418$	−1.53073	+	1.53073i	−0.0748706	+	0.0748706i
$419$	−19.0572	+	19.0572i	−0.931008	+	0.931008i	−0.997769	−	0.0667615i	$-0.978733\pi$
$419$	−19.0572	+	19.0572i	−0.931008	+	0.931008i	0.0667615	+	0.997769i	$0.478733\pi$
$420$	6.75699	+	6.75699i	0.329707	+	0.329707i
$421$	−17.4142			−0.848717			−0.424358	−	0.905494i	$-0.639500\pi$
$421$	−17.4142			−0.848717			−0.424358	+	0.905494i	$0.639500\pi$
$422$	−4.38396	−	4.38396i	−0.213408	−	0.213408i
$423$		−	41.4558i		−	2.01565i
$424$	−2.24264			−0.108912
$425$		0			0
$426$	14.1421			0.685189
$427$			10.0000i			0.483934i
$428$	8.15640	+	8.15640i	0.394255	+	0.394255i
$429$	−4.00000			−0.193122
$430$	−2.61313	−	2.61313i	−0.126016	−	0.126016i
$431$	28.1647	−	28.1647i	1.35665	−	1.35665i	0.478631	−	0.878016i	$-0.341133\pi$
$431$	28.1647	−	28.1647i	1.35665	−	1.35665i	0.878016	−	0.478631i	$-0.158867\pi$
$432$	−4.59220	+	4.59220i	−0.220942	+	0.220942i
$433$			15.1716i			0.729099i	0.931184	+	0.364550i	$0.118777\pi$
$433$			15.1716i			0.729099i	−0.931184	+	0.364550i	$0.881223\pi$
$434$			1.45584i			0.0698828i
$435$	−15.2304	+	15.2304i	−0.730242	+	0.730242i
$436$	−5.52735	+	5.52735i	−0.264712	+	0.264712i
$437$	14.1480	+	14.1480i	0.676792	+	0.676792i
$438$	−5.79899			−0.277086
$439$	7.70806	+	7.70806i	0.367886	+	0.367886i	0.866706	−	0.498820i	$-0.166233\pi$
$439$	7.70806	+	7.70806i	0.367886	+	0.367886i	−0.498820	+	0.866706i	$0.666233\pi$
$440$			3.17157i			0.151199i
$441$	−22.3137			−1.06256
$442$		0			0
$443$	15.7990			0.750633			0.375316	−	0.926897i	$-0.377534\pi$
$443$	15.7990			0.750633			0.375316	+	0.926897i	$0.377534\pi$
$444$			18.2843i			0.867733i
$445$	12.3003	+	12.3003i	0.583088	+	0.583088i
$446$	0.343146			0.0162484
$447$	−31.3575	−	31.3575i	−1.48316	−	1.48316i
$448$	−3.19278	+	3.19278i	−0.150845	+	0.150845i
$449$	13.2898	−	13.2898i	0.627184	−	0.627184i	−0.320174	−	0.947359i	$-0.603741\pi$
$449$	13.2898	−	13.2898i	0.627184	−	0.627184i	0.947359	+	0.320174i	$0.103741\pi$
$450$			2.51472i			0.118545i
$451$			8.82843i			0.415714i
$452$	20.9209	−	20.9209i	0.984038	−	0.984038i
$453$	23.7038	−	23.7038i	1.11370	−	1.11370i
$454$	1.47634	+	1.47634i	0.0692881	+	0.0692881i
$455$	2.82843			0.132599
$456$	14.1480	+	14.1480i	0.662542	+	0.662542i
$457$		−	18.8284i		−	0.880757i	−0.897812	−	0.440378i	$-0.854844\pi$
$457$		−	18.8284i		−	0.880757i	0.897812	−	0.440378i	$-0.145156\pi$
$458$	9.45584			0.441843
$459$		0			0
$460$	14.0000			0.652753
$461$		−	24.0416i		−	1.11973i	−0.828584	−	0.559865i	$-0.810853\pi$
$461$		−	24.0416i		−	1.11973i	0.828584	−	0.559865i	$-0.189147\pi$
$462$	0.896683	+	0.896683i	0.0417175	+	0.0417175i
$463$	30.6274			1.42338			0.711688	−	0.702495i	$-0.247931\pi$
$463$	30.6274			1.42338			0.711688	+	0.702495i	$0.247931\pi$
$464$	−9.46297	−	9.46297i	−0.439307	−	0.439307i
$465$	−11.0866	+	11.0866i	−0.514127	+	0.514127i
$466$	−2.96861	+	2.96861i	−0.137518	+	0.137518i
$467$		−	12.6274i		−	0.584327i	−0.956368	−	0.292164i	$-0.905625\pi$
$467$		−	12.6274i		−	0.584327i	0.956368	−	0.292164i	$-0.0943752\pi$
$468$			9.89949i			0.457604i
$469$	5.22625	−	5.22625i	0.241326	−	0.241326i
$470$	−5.86030	+	5.86030i	−0.270316	+	0.270316i
$471$	−3.06147	−	3.06147i	−0.141065	−	0.141065i
$472$	−9.51472			−0.437950
$473$	3.69552	+	3.69552i	0.169920	+	0.169920i
$474$		−	4.48528i		−	0.206016i
$475$	−7.65685			−0.351321
$476$		0			0
$477$	−5.41421			−0.247900
$478$			3.79899i			0.173762i
$479$	24.4692	+	24.4692i	1.11803	+	1.11803i	0.992031	+	0.125996i	$0.0402126\pi$
$479$	24.4692	+	24.4692i	1.11803	+	1.11803i	0.125996	+	0.992031i	$0.459787\pi$
$480$	21.3137			0.972833
$481$	3.82683	+	3.82683i	0.174489	+	0.174489i
$482$	3.60266	−	3.60266i	0.164097	−	0.164097i
$483$	8.28772	−	8.28772i	0.377104	−	0.377104i
$484$			17.9706i			0.816844i
$485$		−	11.8995i		−	0.540328i
$486$	−6.36304	+	6.36304i	−0.288633	+	0.288633i
$487$	−3.11586	+	3.11586i	−0.141193	+	0.141193i	−0.774170	−	0.632977i	$-0.781833\pi$
$487$	−3.11586	+	3.11586i	−0.141193	+	0.141193i	0.632977	+	0.774170i	$0.281833\pi$
$488$	10.3596	+	10.3596i	0.468959	+	0.468959i
$489$	−14.8284			−0.670565
$490$	3.15432	+	3.15432i	0.142498	+	0.142498i
$491$			25.1127i			1.13332i	0.823952	+	0.566660i	$0.191765\pi$
$491$			25.1127i			1.13332i	−0.823952	+	0.566660i	$0.808235\pi$
$492$	38.9706			1.75693
$493$		0			0
$494$	2.82843			0.127257
$495$			7.65685i			0.344150i
$496$	−6.88830	−	6.88830i	−0.309294	−	0.309294i
$497$	14.1421			0.634361
$498$	0.262632	+	0.262632i	0.0117688	+	0.0117688i
$499$	−26.1857	+	26.1857i	−1.17223	+	1.17223i	−0.190554	+	0.981677i	$0.561028\pi$
$499$	−26.1857	+	26.1857i	−1.17223	+	1.17223i	−0.981677	+	0.190554i	$0.938972\pi$
$500$	−15.7331	+	15.7331i	−0.703608	+	0.703608i
$501$			26.1421i			1.16794i
$502$		−	1.45584i		−	0.0649775i
$503$	10.5838	−	10.5838i	0.471909	−	0.471909i	−0.430623	−	0.902532i	$-0.641706\pi$
$503$	10.5838	−	10.5838i	0.471909	−	0.471909i	0.902532	+	0.430623i	$0.141706\pi$
$504$	4.64659	−	4.64659i	0.206976	−	0.206976i
$505$	−17.5265	−	17.5265i	−0.779920	−	0.779920i
$506$	1.85786			0.0825921
$507$	−20.3253	−	20.3253i	−0.902680	−	0.902680i
$508$			31.6569i			1.40455i
$509$	3.02944			0.134277			0.0671387	−	0.997744i	$-0.478613\pi$
$509$	3.02944			0.134277			0.0671387	+	0.997744i	$0.478613\pi$
$510$		0			0
$511$	−5.79899			−0.256532
$512$			22.7574i			1.00574i
$513$	7.39104	+	7.39104i	0.326322	+	0.326322i
$514$	−9.17157			−0.404541
$515$	5.86030	+	5.86030i	0.258236	+	0.258236i
$516$	16.3128	−	16.3128i	0.718131	−	0.718131i
$517$	8.28772	−	8.28772i	0.364493	−	0.364493i
$518$		−	1.71573i		−	0.0753848i
$519$			8.82843i			0.387525i
$520$	2.93015	−	2.93015i	0.128496	−	0.128496i
$521$	2.20325	−	2.20325i	0.0965260	−	0.0965260i	−0.657195	−	0.753721i	$-0.728257\pi$
$521$	2.20325	−	2.20325i	0.0965260	−	0.0965260i	0.753721	+	0.657195i	$0.228257\pi$
$522$	5.00208	+	5.00208i	0.218935	+	0.218935i
$523$	−6.82843			−0.298586			−0.149293	−	0.988793i	$-0.547700\pi$
$523$	−6.82843			−0.298586			−0.149293	+	0.988793i	$0.547700\pi$
$524$	0.240102	+	0.240102i	0.0104889	+	0.0104889i
$525$			4.48528i			0.195754i
$526$	−2.68629			−0.117128
$527$		0			0
$528$	−8.48528			−0.369274
$529$			5.82843i			0.253410i
$530$	0.765367	+	0.765367i	0.0332454	+	0.0332454i
$531$	−22.9706			−0.996838
$532$	6.75699	+	6.75699i	0.292952	+	0.292952i
$533$	8.15640	−	8.15640i	0.353293	−	0.353293i
$534$	7.20533	−	7.20533i	0.311805	−	0.311805i
$535$		−	11.6569i		−	0.503970i
$536$		−	10.8284i		−	0.467717i
$537$	−11.0866	+	11.0866i	−0.478420	+	0.478420i
$538$	−1.86369	+	1.86369i	−0.0803494	+	0.0803494i
$539$	−4.46088	−	4.46088i	−0.192144	−	0.192144i
$540$	7.31371			0.314732
$541$	−12.9728	−	12.9728i	−0.557743	−	0.557743i	0.370921	−	0.928664i	$-0.379042\pi$
$541$	−12.9728	−	12.9728i	−0.557743	−	0.557743i	−0.928664	+	0.370921i	$0.879042\pi$
$542$			2.54416i			0.109281i
$543$	−32.6274			−1.40018
$544$		0			0
$545$	7.89949			0.338377
$546$		−	1.65685i		−	0.0709068i
$547$	−17.5265	−	17.5265i	−0.749380	−	0.749380i	0.224983	−	0.974363i	$-0.427767\pi$
$547$	−17.5265	−	17.5265i	−0.749380	−	0.749380i	−0.974363	+	0.224983i	$0.927767\pi$
$548$	15.9584			0.681708
$549$	25.0104	+	25.0104i	1.06742	+	1.06742i
$550$	−0.502734	+	0.502734i	−0.0214367	+	0.0214367i
$551$	−15.2304	+	15.2304i	−0.648837	+	0.648837i
$552$		−	17.1716i		−	0.730871i
$553$		−	4.48528i		−	0.190734i
$554$	6.45589	−	6.45589i	0.274285	−	0.274285i
$555$	13.0656	−	13.0656i	0.554605	−	0.554605i
$556$	19.3517	+	19.3517i	0.820697	+	0.820697i
$557$	28.2426			1.19668			0.598340	−	0.801243i	$-0.295827\pi$
$557$	28.2426			1.19668			0.598340	+	0.801243i	$0.295827\pi$
$558$	3.64113	+	3.64113i	0.154141	+	0.154141i
$559$		−	6.82843i		−	0.288812i
$560$	6.00000			0.253546
$561$		0			0
$562$	7.41421			0.312750
$563$		−	38.7696i		−	1.63394i	−0.576679	−	0.816971i	$-0.695652\pi$
$563$		−	38.7696i		−	1.63394i	0.576679	−	0.816971i	$-0.304348\pi$
$564$	−36.5838	−	36.5838i	−1.54045	−	1.54045i
$565$	−29.8995			−1.25788
$566$	6.70259	+	6.70259i	0.281731	+	0.281731i
$567$	−4.46088	+	4.46088i	−0.187340	+	0.187340i
$568$	14.6508	−	14.6508i	0.614732	−	0.614732i
$569$		−	36.0416i		−	1.51094i	−0.655181	−	0.755472i	$-0.727408\pi$
$569$		−	36.0416i		−	1.51094i	0.655181	−	0.755472i	$-0.272592\pi$
$570$		−	9.65685i		−	0.404481i
$571$	−33.3910	+	33.3910i	−1.39737	+	1.39737i	−0.589873	+	0.807496i	$0.700822\pi$
$571$	−33.3910	+	33.3910i	−1.39737	+	1.39737i	−0.807496	+	0.589873i	$0.799178\pi$
$572$	−1.97908	+	1.97908i	−0.0827493	+	0.0827493i
$573$	−36.9552	−	36.9552i	−1.54382	−	1.54382i
$574$	−3.65685			−0.152634
$575$	4.64659	+	4.64659i	0.193776	+	0.193776i
$576$			15.9706i			0.665440i
$577$	12.9289			0.538238			0.269119	−	0.963107i	$-0.413267\pi$
$577$	12.9289			0.538238			0.269119	+	0.963107i	$0.413267\pi$
$578$		0			0
$579$	−14.4853			−0.601988
$580$			15.0711i			0.625792i
$581$	0.262632	+	0.262632i	0.0108958	+	0.0108958i
$582$	−6.97056			−0.288939
$583$	−1.08239	−	1.08239i	−0.0448281	−	0.0448281i
$584$	−6.00755	+	6.00755i	−0.248594	+	0.248594i
$585$	7.07401	−	7.07401i	0.292474	−	0.292474i
$586$			9.79899i			0.404793i
$587$		−	22.6863i		−	0.936363i	−0.883632	−	0.468182i	$-0.844909\pi$
$587$		−	22.6863i		−	0.936363i	0.883632	−	0.468182i	$-0.155091\pi$
$588$	−19.6913	+	19.6913i	−0.812055	+	0.812055i
$589$	−11.0866	+	11.0866i	−0.456814	+	0.456814i
$590$	3.24718	+	3.24718i	0.133684	+	0.133684i
$591$	−38.9706			−1.60303
$592$	8.11794	+	8.11794i	0.333645	+	0.333645i
$593$		−	27.0711i		−	1.11168i	−0.831291	−	0.555838i	$-0.812398\pi$
$593$		−	27.0711i		−	1.11168i	0.831291	−	0.555838i	$-0.187602\pi$
$594$	0.970563			0.0398227
$595$		0			0
$596$	−31.0294			−1.27102
$597$		−	4.48528i		−	0.183570i
$598$	−1.71644	−	1.71644i	−0.0701906	−	0.0701906i
$599$	−34.6274			−1.41484			−0.707419	−	0.706794i	$-0.750141\pi$
$599$	−34.6274			−1.41484			−0.707419	+	0.706794i	$0.750141\pi$
$600$	4.64659	+	4.64659i	0.189696	+	0.189696i
$601$	14.3722	−	14.3722i	0.586254	−	0.586254i	−0.350361	−	0.936615i	$-0.613941\pi$
$601$	14.3722	−	14.3722i	0.586254	−	0.586254i	0.936615	+	0.350361i	$0.113941\pi$
$602$	−1.53073	+	1.53073i	−0.0623880	+	0.0623880i
$603$		−	26.1421i		−	1.06459i
$604$		−	23.4558i		−	0.954405i
$605$	12.8415	−	12.8415i	0.522080	−	0.522080i
$606$	−10.2668	+	10.2668i	−0.417060	+	0.417060i
$607$	−24.2835	−	24.2835i	−0.985637	−	0.985637i	0.0142614	−	0.999898i	$-0.495460\pi$
$607$	−24.2835	−	24.2835i	−0.985637	−	0.985637i	−0.999898	+	0.0142614i	$0.995460\pi$
$608$	21.3137			0.864385
$609$	8.92177	+	8.92177i	0.361528	+	0.361528i
$610$		−	7.07107i		−	0.286299i
$611$	−15.3137			−0.619526
$612$		0			0
$613$	−17.3137			−0.699294			−0.349647	−	0.936881i	$-0.613698\pi$
$613$	−17.3137			−0.699294			−0.349647	+	0.936881i	$0.613698\pi$
$614$			0.887302i			0.0358086i
$615$	−27.8477	−	27.8477i	−1.12293	−	1.12293i
$616$	1.85786			0.0748555
$617$	2.38896	+	2.38896i	0.0961757	+	0.0961757i	0.753558	−	0.657382i	$-0.228336\pi$
$617$	2.38896	+	2.38896i	0.0961757	+	0.0961757i	−0.657382	+	0.753558i	$0.728336\pi$
$618$	3.43289	−	3.43289i	0.138091	−	0.138091i
$619$	−6.81138	+	6.81138i	−0.273772	+	0.273772i	−0.830617	−	0.556844i	$-0.812012\pi$
$619$	−6.81138	+	6.81138i	−0.273772	+	0.273772i	0.556844	+	0.830617i	$0.312012\pi$
$620$			10.9706i			0.440588i
$621$		−	8.97056i		−	0.359976i
$622$	−1.32249	+	1.32249i	−0.0530272	+	0.0530272i
$623$	7.20533	−	7.20533i	0.288675	−	0.288675i
$624$	7.83938	+	7.83938i	0.313826	+	0.313826i
$625$	14.5563			0.582254
$626$	3.73398	+	3.73398i	0.149240	+	0.149240i
$627$			13.6569i			0.545402i
$628$	−3.02944			−0.120888
$629$		0			0
$630$	−3.17157			−0.126358
$631$		−	6.68629i		−	0.266177i	−0.991104	−	0.133089i	$-0.957511\pi$
$631$		−	6.68629i		−	0.266177i	0.991104	−	0.133089i	$-0.0424895\pi$
$632$	−4.64659	−	4.64659i	−0.184832	−	0.184832i
$633$	−39.1127			−1.55459
$634$	−1.70051	−	1.70051i	−0.0675359	−	0.0675359i
$635$	22.6215	−	22.6215i	0.897705	−	0.897705i
$636$	−4.77791	+	4.77791i	−0.189456	+	0.189456i
$637$			8.24264i			0.326585i
$638$			2.00000i			0.0791808i
$639$	35.3701	−	35.3701i	1.39922	−	1.39922i
$640$	13.7925	−	13.7925i	0.545198	−	0.545198i
$641$	−10.5998	−	10.5998i	−0.418665	−	0.418665i	0.466078	−	0.884743i	$-0.345666\pi$
$641$	−10.5998	−	10.5998i	−0.418665	−	0.418665i	−0.884743	+	0.466078i	$0.845666\pi$
$642$	−6.82843			−0.269497
$643$	−28.3504	−	28.3504i	−1.11803	−	1.11803i	−0.992030	−	0.126002i	$-0.959785\pi$
$643$	−28.3504	−	28.3504i	−1.11803	−	1.11803i	−0.126002	−	0.992030i	$-0.540215\pi$
$644$		−	8.20101i		−	0.323165i
$645$	−23.3137			−0.917976
$646$		0			0
$647$	2.82843			0.111197			0.0555985	−	0.998453i	$-0.482293\pi$
$647$	2.82843			0.111197			0.0555985	+	0.998453i	$0.482293\pi$
$648$			9.24264i			0.363085i
$649$	−4.59220	−	4.59220i	−0.180260	−	0.180260i
$650$	0.928932			0.0364357
$651$	6.49435	+	6.49435i	0.254534	+	0.254534i
$652$	−7.33664	+	7.33664i	−0.287325	+	0.287325i
$653$	12.5244	−	12.5244i	0.490119	−	0.490119i	−0.418225	−	0.908344i	$-0.637348\pi$
$653$	12.5244	−	12.5244i	0.490119	−	0.490119i	0.908344	+	0.418225i	$0.137348\pi$
$654$		−	4.62742i		−	0.180946i
$655$		−	0.343146i		−	0.0134078i
$656$	17.3023	−	17.3023i	0.675543	−	0.675543i
$657$	−14.5035	+	14.5035i	−0.565836	+	0.565836i
$658$	3.43289	+	3.43289i	0.133828	+	0.133828i
$659$	−8.48528			−0.330540			−0.165270	−	0.986248i	$-0.552849\pi$
$659$	−8.48528			−0.330540			−0.165270	+	0.986248i	$0.552849\pi$
$660$	6.75699	+	6.75699i	0.263015	+	0.263015i
$661$			41.2132i			1.60301i	0.597990	+	0.801504i	$0.295966\pi$
$661$			41.2132i			1.60301i	−0.597990	+	0.801504i	$0.704034\pi$
$662$	−7.37258			−0.286544
$663$		0			0
$664$	0.544156			0.0211173
$665$		−	9.65685i		−	0.374477i
$666$	−4.29111	−	4.29111i	−0.166277	−	0.166277i
$667$	18.4853			0.715753
$668$	12.9343	+	12.9343i	0.500444	+	0.500444i
$669$	1.53073	−	1.53073i	0.0591816	−	0.0591816i
$670$	−3.69552	+	3.69552i	−0.142770	+	0.142770i
$671$			10.0000i			0.386046i
$672$		−	12.4853i		−	0.481630i
$673$	−0.224171	+	0.224171i	−0.00864115	+	0.00864115i	−0.711414	−	0.702773i	$-0.751945\pi$
$673$	−0.224171	+	0.224171i	−0.00864115	+	0.00864115i	0.702773	+	0.711414i	$0.251945\pi$
$674$	10.0970	−	10.0970i	0.388923	−	0.388923i
$675$	2.42742	+	2.42742i	0.0934313	+	0.0934313i
$676$	−20.1127			−0.773565
$677$	31.0564	+	31.0564i	1.19360	+	1.19360i	0.976050	+	0.217545i	$0.0698048\pi$
$677$	31.0564	+	31.0564i	1.19360	+	1.19360i	0.217545	+	0.976050i	$0.430195\pi$
$678$			17.5147i			0.672649i
$679$	−6.97056			−0.267506
$680$		0			0
$681$	13.1716			0.504736
$682$			1.45584i			0.0557472i
$683$	22.1187	+	22.1187i	0.846349	+	0.846349i	0.989675	−	0.143326i	$-0.0457799\pi$
$683$	22.1187	+	22.1187i	0.846349	+	0.846349i	−0.143326	+	0.989675i	$0.545780\pi$
$684$	33.7990			1.29234
$685$	−11.4036	−	11.4036i	−0.435708	−	0.435708i
$686$	4.06694	−	4.06694i	0.155276	−	0.155276i
$687$	42.1814	−	42.1814i	1.60932	−	1.60932i
$688$		−	14.4853i		−	0.552246i
$689$			2.00000i			0.0761939i
$690$	−5.86030	+	5.86030i	−0.223098	+	0.223098i
$691$	28.7988	−	28.7988i	1.09556	−	1.09556i	0.100634	−	0.994924i	$-0.467913\pi$
$691$	28.7988	−	28.7988i	1.09556	−	1.09556i	0.994924	−	0.100634i	$-0.0320870\pi$
$692$	4.36803	+	4.36803i	0.166048	+	0.166048i
$693$	4.48528			0.170382
$694$	1.13679	+	1.13679i	0.0431518	+	0.0431518i
$695$		−	27.6569i		−	1.04908i
$696$	18.4853			0.700683
$697$		0			0
$698$	−1.75736			−0.0665170
$699$			26.4853i			1.00177i
$700$	2.21918	+	2.21918i	0.0838770	+	0.0838770i
$701$	21.6985			0.819540			0.409770	−	0.912189i	$-0.365609\pi$
$701$	21.6985			0.819540			0.409770	+	0.912189i	$0.365609\pi$
$702$	−0.896683	−	0.896683i	−0.0338431	−	0.0338431i
$703$	13.0656	−	13.0656i	0.492780	−	0.492780i
$704$	−3.19278	+	3.19278i	−0.120333	+	0.120333i
$705$			52.2843i			1.96914i
$706$			5.79899i			0.218248i
$707$	−10.2668	+	10.2668i	−0.386123	+	0.386123i
$708$	−20.2710	+	20.2710i	−0.761829	+	0.761829i
$709$	−8.19486	−	8.19486i	−0.307765	−	0.307765i	0.536277	−	0.844042i	$-0.319830\pi$
$709$	−8.19486	−	8.19486i	−0.307765	−	0.307765i	−0.844042	+	0.536277i	$0.819830\pi$
$710$	−10.0000			−0.375293
$711$	−11.2179	−	11.2179i	−0.420703	−	0.420703i
$712$		−	14.9289i		−	0.559485i
$713$	13.4558			0.503925
$714$		0			0
$715$	2.82843			0.105777
$716$			10.9706i			0.409989i
$717$	16.9469	+	16.9469i	0.632892	+	0.632892i
$718$	9.59798			0.358193
$719$	−9.94977	−	9.94977i	−0.371064	−	0.371064i	0.496801	−	0.867865i	$-0.334508\pi$
$719$	−9.94977	−	9.94977i	−0.371064	−	0.371064i	−0.867865	+	0.496801i	$0.834508\pi$
$720$	15.0062	−	15.0062i	0.559250	−	0.559250i
$721$	3.43289	−	3.43289i	0.127847	−	0.127847i
$722$		−	1.78680i		−	0.0664977i
$723$		−	32.1421i		−	1.19538i
$724$	−16.1430	+	16.1430i	−0.599951	+	0.599951i
$725$	−5.00208	+	5.00208i	−0.185773	+	0.185773i
$726$	−7.52235	−	7.52235i	−0.279181	−	0.279181i
$727$	−19.1127			−0.708851			−0.354425	−	0.935084i	$-0.615324\pi$
$727$	−19.1127			−0.708851			−0.354425	+	0.935084i	$0.615324\pi$
$728$	−1.71644	−	1.71644i	−0.0636156	−	0.0636156i
$729$			39.2843i			1.45497i
$730$	4.10051			0.151767
$731$		0			0
$732$	44.1421			1.63154
$733$			12.0416i			0.444768i	0.974959	+	0.222384i	$0.0713838\pi$
$733$			12.0416i			0.444768i	−0.974959	+	0.222384i	$0.928616\pi$
$734$	7.70806	+	7.70806i	0.284510	+	0.284510i
$735$	28.1421			1.03804
$736$	−12.9343	−	12.9343i	−0.476765	−	0.476765i
$737$	5.22625	−	5.22625i	0.192511	−	0.192511i
$738$	−9.14594	+	9.14594i	−0.336667	+	0.336667i
$739$		−	34.2843i		−	1.26117i	−0.776121	−	0.630584i	$-0.782816\pi$
$739$		−	34.2843i		−	1.26117i	0.776121	−	0.630584i	$-0.217184\pi$
$740$		−	12.9289i		−	0.475277i
$741$	12.6173	−	12.6173i	0.463508	−	0.463508i
$742$	0.448342	−	0.448342i	0.0164591	−	0.0164591i
$743$	34.8448	+	34.8448i	1.27833	+	1.27833i	0.941601	+	0.336730i	$0.109321\pi$
$743$	34.8448	+	34.8448i	1.27833	+	1.27833i	0.336730	+	0.941601i	$0.390679\pi$
$744$	13.4558			0.493315
$745$	22.1731	+	22.1731i	0.812360	+	0.812360i
$746$			8.10051i			0.296581i
$747$	1.31371			0.0480661
$748$		0			0
$749$	−6.82843			−0.249505
$750$		−	13.1716i		−	0.480958i
$751$	18.5320	+	18.5320i	0.676242	+	0.676242i	0.959148	−	0.282906i	$-0.0912984\pi$
$751$	18.5320	+	18.5320i	0.676242	+	0.676242i	−0.282906	+	0.959148i	$0.591298\pi$
$752$	−32.4853			−1.18462
$753$	−6.49435	−	6.49435i	−0.236667	−	0.236667i
$754$	1.84776	−	1.84776i	0.0672914	−	0.0672914i
$755$	−16.7611	+	16.7611i	−0.610001	+	0.610001i
$756$		−	4.28427i		−	0.155817i
$757$			53.4558i			1.94289i	0.237274	+	0.971443i	$0.423746\pi$
$757$			53.4558i			1.94289i	−0.237274	+	0.971443i	$0.576254\pi$
$758$	0.317025	−	0.317025i	0.0115149	−	0.0115149i
$759$	8.28772	−	8.28772i	0.300825	−	0.300825i
$760$	−10.0042	−	10.0042i	−0.362889	−	0.362889i
$761$	21.6985			0.786569			0.393285	−	0.919417i	$-0.371339\pi$
$761$	21.6985			0.786569			0.393285	+	0.919417i	$0.371339\pi$
$762$	−13.2513	−	13.2513i	−0.480045	−	0.480045i
$763$		−	4.62742i		−	0.167524i
$764$	−36.5685			−1.32300
$765$		0			0
$766$	−2.28427			−0.0825341
$767$			8.48528i			0.306386i
$768$	7.33664	+	7.33664i	0.264738	+	0.264738i
$769$	12.7279			0.458981			0.229490	−	0.973311i	$-0.426294\pi$
$769$	12.7279			0.458981			0.229490	+	0.973311i	$0.426294\pi$
$770$	−0.634051	−	0.634051i	−0.0228496	−	0.0228496i
$771$	−40.9133	+	40.9133i	−1.47346	+	1.47346i
$772$	−7.16687	+	7.16687i	−0.257941	+	0.257941i
$773$			4.82843i			0.173666i	0.996223	+	0.0868332i	$0.0276747\pi$
$773$			4.82843i			0.173666i	−0.996223	+	0.0868332i	$0.972325\pi$
$774$			7.65685i			0.275220i
$775$	−3.64113	+	3.64113i	−0.130793	+	0.130793i
$776$	−7.22126	+	7.22126i	−0.259228	+	0.259228i
$777$	−7.65367	−	7.65367i	−0.274574	−	0.274574i
$778$	6.68629			0.239715
$779$	−27.8477	−	27.8477i	−0.997747	−	0.997747i
$780$		−	12.4853i		−	0.447045i
$781$	14.1421			0.506045
$782$		0			0
$783$	9.65685			0.345108
$784$			17.4853i			0.624474i
$785$	2.16478	+	2.16478i	0.0772645	+	0.0772645i
$786$	−0.201010			−0.00716979
$787$	35.1074	+	35.1074i	1.25144	+	1.25144i	0.955073	+	0.296372i	$0.0957768\pi$
$787$	35.1074	+	35.1074i	1.25144	+	1.25144i	0.296372	+	0.955073i	$0.404223\pi$
$788$	−19.2814	+	19.2814i	−0.686872	+	0.686872i
$789$	−11.9832	+	11.9832i	−0.426615	+	0.426615i
$790$			3.17157i			0.112839i
$791$			17.5147i			0.622752i
$792$	4.64659	−	4.64659i	0.165110	−	0.165110i
$793$	9.23880	−	9.23880i	0.328079	−	0.328079i
$794$	−7.98663	−	7.98663i	−0.283435	−	0.283435i
$795$	6.82843			0.242179
$796$	−2.21918	−	2.21918i	−0.0786567	−	0.0786567i
$797$		−	17.2132i		−	0.609723i	−0.952397	−	0.304861i	$-0.901390\pi$
$797$		−	17.2132i		−	0.609723i	0.952397	−	0.304861i	$-0.0986102\pi$
$798$	−5.65685			−0.200250
$799$		0			0
$800$	7.00000			0.247487
$801$		−	36.0416i		−	1.27347i
$802$	5.00208	+	5.00208i	0.176630	+	0.176630i
$803$	−5.79899			−0.204642
$804$	−23.0698	−	23.0698i	−0.813609	−	0.813609i
$805$	−5.86030	+	5.86030i	−0.206549	+	0.206549i
$806$	1.34502	−	1.34502i	0.0473765	−	0.0473765i
$807$			16.6274i			0.585313i
$808$			21.2721i			0.748349i
$809$	−21.0523	+	21.0523i	−0.740158	+	0.740158i	−0.972608	−	0.232450i	$-0.925326\pi$
$809$	−21.0523	+	21.0523i	−0.740158	+	0.740158i	0.232450	+	0.972608i	$0.425326\pi$
$810$	3.15432	−	3.15432i	0.110832	−	0.110832i
$811$	31.3031	+	31.3031i	1.09920	+	1.09920i	0.994504	+	0.104697i	$0.0333873\pi$
$811$	31.3031	+	31.3031i	1.09920	+	1.09920i	0.104697	+	0.994504i	$0.466613\pi$
$812$	8.82843			0.309817
$813$	11.3492	+	11.3492i	0.398033	+	0.398033i
$814$		−	1.71573i		−	0.0601363i
$815$	10.4853			0.367283
$816$		0			0
$817$	−23.3137			−0.815643
$818$			8.00000i			0.279713i
$819$	−4.14386	−	4.14386i	−0.144798	−	0.144798i
$820$	−27.5563			−0.962309
$821$	10.1739	+	10.1739i	0.355073	+	0.355073i	0.861993	−	0.506920i	$-0.169216\pi$
$821$	10.1739	+	10.1739i	0.355073	+	0.355073i	−0.506920	+	0.861993i	$0.669216\pi$
$822$	−6.68006	+	6.68006i	−0.232994	+	0.232994i
$823$	−16.6298	+	16.6298i	−0.579679	+	0.579679i	−0.934815	−	0.355135i	$-0.884435\pi$
$823$	−16.6298	+	16.6298i	−0.579679	+	0.579679i	0.355135	+	0.934815i	$0.384435\pi$
$824$		−	7.11270i		−	0.247783i
$825$			4.48528i			0.156157i
$826$	1.90215	−	1.90215i	0.0661843	−	0.0661843i
$827$	−24.5461	+	24.5461i	−0.853553	+	0.853553i	−0.990569	−	0.137016i	$-0.956249\pi$
$827$	−24.5461	+	24.5461i	−0.853553	+	0.853553i	0.137016	+	0.990569i	$0.456249\pi$
$828$	−20.5111	−	20.5111i	−0.712809	−	0.712809i
$829$	13.9411			0.484195			0.242098	−	0.970252i	$-0.422165\pi$
$829$	13.9411			0.484195			0.242098	+	0.970252i	$0.422165\pi$
$830$	−0.185709	−	0.185709i	−0.00644606	−	0.00644606i
$831$		−	57.5980i		−	1.99805i
$832$	5.89949			0.204528
$833$		0			0
$834$	−16.2010			−0.560995
$835$		−	18.4853i		−	0.639710i
$836$	6.75699	+	6.75699i	0.233695	+	0.233695i
$837$	7.02944			0.242973
$838$	−7.89377	−	7.89377i	−0.272686	−	0.272686i
$839$	2.74444	−	2.74444i	0.0947487	−	0.0947487i	−0.658144	−	0.752892i	$-0.728658\pi$
$839$	2.74444	−	2.74444i	0.0947487	−	0.0947487i	0.752892	+	0.658144i	$0.228658\pi$
$840$	−5.86030	+	5.86030i	−0.202200	+	0.202200i
$841$		−	9.10051i		−	0.313811i
$842$		−	7.21320i		−	0.248583i
$843$	33.0740	−	33.0740i	1.13913	−	1.13913i
$844$	−19.3517	+	19.3517i	−0.666114	+	0.666114i
$845$	14.3722	+	14.3722i	0.494418	+	0.494418i
$846$	17.1716			0.590371
$847$	−7.52235	−	7.52235i	−0.258471	−	0.258471i
$848$			4.24264i			0.145693i
$849$	59.7990			2.05230
$850$		0			0
$851$	−15.8579			−0.543601
$852$		−	62.4264i		−	2.13869i
$853$	−30.1053	−	30.1053i	−1.03079	−	1.03079i	−0.999511	−	0.0312765i	$-0.990043\pi$
$853$	−30.1053	−	30.1053i	−1.03079	−	1.03079i	−0.0312765	−	0.999511i	$-0.509957\pi$
$854$	−4.14214			−0.141741
$855$	−24.1522	−	24.1522i	−0.825987	−	0.825987i
$856$	−7.07401	+	7.07401i	−0.241785	+	0.241785i
$857$	2.70598	−	2.70598i	0.0924345	−	0.0924345i	−0.659377	−	0.751812i	$-0.729180\pi$
$857$	2.70598	−	2.70598i	0.0924345	−	0.0924345i	0.751812	+	0.659377i	$0.229180\pi$
$858$		−	1.65685i		−	0.0565641i
$859$		−	1.02944i		−	0.0351239i	−0.999846	−	0.0175620i	$-0.994410\pi$
$859$		−	1.02944i		−	0.0351239i	0.999846	−	0.0175620i	$-0.00559044\pi$
$860$	−11.5349	+	11.5349i	−0.393337	+	0.393337i
$861$	−16.3128	+	16.3128i	−0.555939	+	0.555939i
$862$	11.6662	+	11.6662i	0.397353	+	0.397353i
$863$	−34.6274			−1.17873			−0.589365	−	0.807867i	$-0.700622\pi$
$863$	−34.6274			−1.17873			−0.589365	+	0.807867i	$0.700622\pi$
$864$	−6.75699	−	6.75699i	−0.229877	−	0.229877i
$865$		−	6.24264i		−	0.212256i
$866$	−6.28427			−0.213548
$867$		0			0
$868$	6.42641			0.218126
$869$		−	4.48528i		−	0.152153i
$870$	−6.30864	−	6.30864i	−0.213883	−	0.213883i
$871$	−9.65685			−0.327210
$872$	−4.79384	−	4.79384i	−0.162340	−	0.162340i
$873$	−17.4337	+	17.4337i	−0.590040	+	0.590040i
$874$	−5.86030	+	5.86030i	−0.198228	+	0.198228i
$875$		−	13.1716i		−	0.445280i
$876$			25.5980i			0.864876i
$877$	−26.6181	+	26.6181i	−0.898828	+	0.898828i	−0.995333	−	0.0965044i	$-0.969234\pi$
$877$	−26.6181	+	26.6181i	−0.898828	+	0.898828i	0.0965044	+	0.995333i	$0.469234\pi$
$878$	−3.19278	+	3.19278i	−0.107751	+	0.107751i
$879$	43.7122	+	43.7122i	1.47437	+	1.47437i
$880$	6.00000			0.202260
$881$	13.1041	+	13.1041i	0.441488	+	0.441488i	0.892512	−	0.451024i	$-0.148941\pi$
$881$	13.1041	+	13.1041i	0.441488	+	0.441488i	−0.451024	+	0.892512i	$0.648941\pi$
$882$		−	9.24264i		−	0.311216i
$883$	−8.00000			−0.269221			−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000			−0.269221			−0.134611	+	0.990899i	$0.542978\pi$
$884$		0			0
$885$	28.9706			0.973835
$886$			6.54416i			0.219855i
$887$	−34.5503	−	34.5503i	−1.16009	−	1.16009i	−0.984456	−	0.175629i	$-0.943804\pi$
$887$	−34.5503	−	34.5503i	−1.16009	−	1.16009i	−0.175629	−	0.984456i	$-0.556196\pi$
$888$	−15.8579			−0.532155
$889$	−13.2513	−	13.2513i	−0.444436	−	0.444436i
$890$	−5.09494	+	5.09494i	−0.170783	+	0.170783i
$891$	−4.46088	+	4.46088i	−0.149445	+	0.149445i
$892$		−	1.51472i		−	0.0507165i
$893$			52.2843i			1.74963i
$894$	12.9887	−	12.9887i	0.434407	−	0.434407i
$895$	7.83938	−	7.83938i	0.262041	−	0.262041i
$896$	−8.07948	−	8.07948i	−0.269916	−	0.269916i
$897$	−15.3137			−0.511310
$898$	5.50482	+	5.50482i	0.183698	+	0.183698i
$899$			14.4853i			0.483111i
$900$	11.1005			0.370017
$901$		0			0
$902$	−3.65685			−0.121760
$903$			13.6569i			0.454472i
$904$	18.1446	+	18.1446i	0.603482	+	0.603482i
$905$	23.0711			0.766908
$906$	9.81845	+	9.81845i	0.326196	+	0.326196i
$907$	17.7122	−	17.7122i	0.588125	−	0.588125i	−0.348999	−	0.937123i	$-0.613478\pi$
$907$	17.7122	−	17.7122i	0.588125	−	0.588125i	0.937123	+	0.348999i	$0.113478\pi$
$908$	6.51688	−	6.51688i	0.216270	−	0.216270i
$909$			51.3553i			1.70335i
$910$			1.17157i			0.0388373i
$911$	−5.99162	+	5.99162i	−0.198511	+	0.198511i	−0.799362	−	0.600850i	$-0.794829\pi$
$911$	−5.99162	+	5.99162i	−0.198511	+	0.198511i	0.600850	+	0.799362i	$0.294829\pi$
$912$	26.7653	−	26.7653i	0.886288	−	0.886288i
$913$	0.262632	+	0.262632i	0.00869186	+	0.00869186i
$914$	7.79899			0.257968
$915$	−31.5432	−	31.5432i	−1.04279	−	1.04279i
$916$		−	41.7401i		−	1.37913i
$917$	−0.201010			−0.00663794
$918$		0			0
$919$	−3.31371			−0.109309			−0.0546546	−	0.998505i	$-0.517406\pi$
$919$	−3.31371			−0.109309			−0.0546546	+	0.998505i	$0.517406\pi$
$920$			12.1421i			0.400314i
$921$	3.95815	+	3.95815i	0.130425	+	0.130425i
$922$	9.95837			0.327961
$923$	−13.0656	−	13.0656i	−0.430060	−	0.430060i
$924$	3.95815	−	3.95815i	0.130214	−	0.130214i
$925$	4.29111	−	4.29111i	0.141091	−	0.141091i
$926$			12.6863i			0.416897i
$927$		−	17.1716i		−	0.563988i
$928$	13.9239	−	13.9239i	0.457073	−	0.457073i
$929$	14.8205	−	14.8205i	0.486246	−	0.486246i	−0.420873	−	0.907119i	$-0.638276\pi$
$929$	14.8205	−	14.8205i	0.486246	−	0.486246i	0.907119	+	0.420873i	$0.138276\pi$
$930$	−4.59220	−	4.59220i	−0.150584	−	0.150584i
$931$	28.1421			0.922321
$932$	13.1041	+	13.1041i	0.429239	+	0.429239i
$933$			11.7990i			0.386282i
$934$	5.23045			0.171145
$935$		0			0
$936$	−8.58579			−0.280635
$937$		−	3.55635i		−	0.116181i	−0.998311	−	0.0580904i	$-0.981499\pi$
$937$		−	3.55635i		−	0.116181i	0.998311	−	0.0580904i	$-0.0185012\pi$
$938$	2.16478	+	2.16478i	0.0706827	+	0.0706827i
$939$	33.3137			1.08715
$940$	25.8686	+	25.8686i	0.843742	+	0.843742i
$941$	−13.2129	+	13.2129i	−0.430727	+	0.430727i	−0.888876	−	0.458148i	$-0.848513\pi$
$941$	−13.2129	+	13.2129i	−0.430727	+	0.430727i	0.458148	+	0.888876i	$0.348513\pi$
$942$	1.26810	−	1.26810i	0.0413170	−	0.0413170i
$943$			33.7990i			1.10065i
$944$			18.0000i			0.585850i
$945$	−3.06147	+	3.06147i	−0.0995895	+	0.0995895i
$946$	−1.53073	+	1.53073i	−0.0497684	+	0.0497684i
$947$	10.5069	+	10.5069i	0.341428	+	0.341428i	0.856904	−	0.515476i	$-0.172385\pi$
$947$	10.5069	+	10.5069i	0.341428	+	0.341428i	−0.515476	+	0.856904i	$0.672385\pi$
$948$	−19.7990			−0.643041
$949$	5.35757	+	5.35757i	0.173914	+	0.173914i
$950$		−	3.17157i		−	0.102899i
$951$	−15.1716			−0.491972
$952$		0			0
$953$	−9.69848			−0.314165			−0.157082	−	0.987586i	$-0.550209\pi$
$953$	−9.69848			−0.314165			−0.157082	+	0.987586i	$0.550209\pi$
$954$		−	2.24264i		−	0.0726082i
$955$	26.1313	+	26.1313i	0.845588	+	0.845588i
$956$	16.7696			0.542366
$957$	8.92177	+	8.92177i	0.288400	+	0.288400i
$958$	−10.1355	+	10.1355i	−0.327462	+	0.327462i
$959$	−6.68006	+	6.68006i	−0.215710	+	0.215710i
$960$		−	20.1421i		−	0.650085i
$961$		−	20.4558i		−	0.659866i
$962$	−1.58513	+	1.58513i	−0.0511065	+	0.0511065i
$963$	−17.0782	+	17.0782i	−0.550336	+	0.550336i
$964$	−15.9029	−	15.9029i	−0.512199	−	0.512199i
$965$	10.2426			0.329722
$966$	3.43289	+	3.43289i	0.110451	+	0.110451i
$967$			32.3431i			1.04009i	0.854140	+	0.520043i	$0.174084\pi$
$967$			32.3431i			1.04009i	−0.854140	+	0.520043i	$0.825916\pi$
$968$	−15.5858			−0.500946
$969$		0			0
$970$	4.92893			0.158258
$971$			55.7401i			1.78879i	0.447283	+	0.894393i	$0.352392\pi$
$971$			55.7401i			1.78879i	−0.447283	+	0.894393i	$0.647608\pi$
$972$	28.0878	+	28.0878i	0.900917	+	0.900917i
$973$	−16.2010			−0.519381
$974$	−1.29063	−	1.29063i	−0.0413545	−	0.0413545i
$975$	4.14386	−	4.14386i	0.132710	−	0.132710i
$976$	19.5984	−	19.5984i	0.627331	−	0.627331i
$977$		−	1.61522i		−	0.0516756i	−0.999666	−	0.0258378i	$-0.991775\pi$
$977$		−	1.61522i		−	0.0516756i	0.999666	−	0.0258378i	$-0.00822534\pi$
$978$		−	6.14214i		−	0.196404i
$979$	7.20533	−	7.20533i	0.230283	−	0.230283i
$980$	13.9239	−	13.9239i	0.444781	−	0.444781i
$981$	−11.5734	−	11.5734i	−0.369509	−	0.369509i
$982$	−10.4020			−0.331942
$983$	−16.6298	−	16.6298i	−0.530409	−	0.530409i	0.390285	−	0.920694i	$-0.372377\pi$
$983$	−16.6298	−	16.6298i	−0.530409	−	0.530409i	−0.920694	+	0.390285i	$0.872377\pi$
$984$			33.7990i			1.07747i
$985$	27.5563			0.878018
$986$		0			0
$987$	30.6274			0.974881
$988$		−	12.4853i		−	0.397210i
$989$	14.1480	+	14.1480i	0.449881	+	0.449881i
$990$	−3.17157			−0.100799
$991$	−22.6758	−	22.6758i	−0.720322	−	0.720322i	0.248349	−	0.968671i	$-0.420112\pi$
$991$	−22.6758	−	22.6758i	−0.720322	−	0.720322i	−0.968671	+	0.248349i	$0.920112\pi$
$992$	10.1355	−	10.1355i	0.321802	−	0.321802i
$993$	−32.8882	+	32.8882i	−1.04368	+	1.04368i
$994$			5.85786i			0.185800i
$995$			3.17157i			0.100546i
$996$	1.15932	−	1.15932i	0.0367343	−	0.0367343i
$997$	−5.45042	+	5.45042i	−0.172617	+	0.172617i	−0.788128	−	0.615511i	$-0.788950\pi$
$997$	−5.45042	+	5.45042i	−0.172617	+	0.172617i	0.615511	+	0.788128i	$0.288950\pi$
$998$	−10.8465	−	10.8465i	−0.343338	−	0.343338i
$999$	−8.28427			−0.262103

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.c.c.251.4		8
17.2	even	8		289.2.a.f.1.2		4
17.3	odd	16		289.2.d.c.134.1		4
17.4	even	4	inner	289.2.c.c.38.2		8
17.5	odd	16		17.2.d.a.2.1	✓	4
17.6	odd	16		289.2.d.a.179.1		4
17.7	odd	16		289.2.d.c.110.1		4
17.8	even	8		289.2.b.b.288.3		4
17.9	even	8		289.2.b.b.288.4		4
17.10	odd	16		289.2.d.b.110.1		4
17.11	odd	16		17.2.d.a.9.1	yes	4
17.12	odd	16		289.2.d.a.155.1		4
17.13	even	4	inner	289.2.c.c.38.1		8
17.14	odd	16		289.2.d.b.134.1		4
17.15	even	8		289.2.a.f.1.1		4
17.16	even	2	inner	289.2.c.c.251.3		8
51.2	odd	8		2601.2.a.bb.1.3		4
51.5	even	16		153.2.l.c.19.1		4
51.11	even	16		153.2.l.c.145.1		4
51.32	odd	8		2601.2.a.bb.1.4		4
68.11	even	16		272.2.v.d.145.1		4
68.15	odd	8		4624.2.a.bp.1.4		4
68.19	odd	8		4624.2.a.bp.1.1		4
68.39	even	16		272.2.v.d.257.1		4
85.19	even	8		7225.2.a.u.1.3		4
85.22	even	16		425.2.n.b.274.1		4
85.28	even	16		425.2.n.b.349.1		4
85.39	odd	16		425.2.m.a.376.1		4
85.49	even	8		7225.2.a.u.1.4		4
85.62	even	16		425.2.n.a.349.1		4
85.73	even	16		425.2.n.a.274.1		4
85.79	odd	16		425.2.m.a.26.1		4
119.5	even	48		833.2.v.a.410.1		8
119.11	odd	48		833.2.v.b.128.1		8
119.39	odd	48		833.2.v.b.716.1		8
119.45	even	48		833.2.v.a.128.1		8
119.62	even	16		833.2.l.a.638.1		4
119.73	even	48		833.2.v.a.716.1		8
119.79	odd	48		833.2.v.b.655.1		8
119.90	even	16		833.2.l.a.393.1		4
119.96	even	48		833.2.v.a.655.1		8
119.107	odd	48		833.2.v.b.410.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.2.d.a.2.1	✓	4	17.5	odd	16
17.2.d.a.9.1	yes	4	17.11	odd	16
153.2.l.c.19.1		4	51.5	even	16
153.2.l.c.145.1		4	51.11	even	16
272.2.v.d.145.1		4	68.11	even	16
272.2.v.d.257.1		4	68.39	even	16
289.2.a.f.1.1		4	17.15	even	8
289.2.a.f.1.2		4	17.2	even	8
289.2.b.b.288.3		4	17.8	even	8
289.2.b.b.288.4		4	17.9	even	8
289.2.c.c.38.1		8	17.13	even	4	inner
289.2.c.c.38.2		8	17.4	even	4	inner
289.2.c.c.251.3		8	17.16	even	2	inner
289.2.c.c.251.4		8	1.1	even	1	trivial
289.2.d.a.155.1		4	17.12	odd	16
289.2.d.a.179.1		4	17.6	odd	16
289.2.d.b.110.1		4	17.10	odd	16
289.2.d.b.134.1		4	17.14	odd	16
289.2.d.c.110.1		4	17.7	odd	16
289.2.d.c.134.1		4	17.3	odd	16
425.2.m.a.26.1		4	85.79	odd	16
425.2.m.a.376.1		4	85.39	odd	16
425.2.n.a.274.1		4	85.73	even	16
425.2.n.a.349.1		4	85.62	even	16
425.2.n.b.274.1		4	85.22	even	16
425.2.n.b.349.1		4	85.28	even	16
833.2.l.a.393.1		4	119.90	even	16
833.2.l.a.638.1		4	119.62	even	16
833.2.v.a.128.1		8	119.45	even	48
833.2.v.a.410.1		8	119.5	even	48
833.2.v.a.655.1		8	119.96	even	48
833.2.v.a.716.1		8	119.73	even	48
833.2.v.b.128.1		8	119.11	odd	48
833.2.v.b.410.1		8	119.107	odd	48
833.2.v.b.655.1		8	119.79	odd	48
833.2.v.b.716.1		8	119.39	odd	48
2601.2.a.bb.1.3		4	51.2	odd	8
2601.2.a.bb.1.4		4	51.32	odd	8
4624.2.a.bp.1.1		4	68.19	odd	8
4624.2.a.bp.1.4		4	68.15	odd	8
7225.2.a.u.1.3		4	85.19	even	8
7225.2.a.u.1.4		4	85.49	even	8

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	289.2.c.c.251.4

Level	$289$
Weight	$2$
Character	289.251
Analytic conductor	$2.308$
Analytic rank	$0$
Dimension	$8$
Inner twists	$4$