LMFDB - Embedded newform 552.2.q.d.169.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			169.3
Character	$\chi$	$=$	552.169
Dual form			552.2.q.d.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{3} +(0.920354 + 1.06214i) q^{5} +(-3.86124 - 2.48147i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{3} +(0.920354 + 1.06214i) q^{5} +(-3.86124 - 2.48147i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(-0.178583 - 1.24207i) q^{11} +(-3.62146 + 2.32737i) q^{13} +(0.583832 - 1.27841i) q^{15} +(-3.37097 + 0.989806i) q^{17} +(-0.828102 - 0.243153i) q^{19} +(-0.653207 + 4.54315i) q^{21} +(-2.01477 - 4.35209i) q^{23} +(0.430474 - 2.99401i) q^{25} +(0.959493 + 0.281733i) q^{27} +(-0.901084 + 0.264582i) q^{29} +(-3.62070 + 7.92822i) q^{31} +(-1.05564 + 0.678421i) q^{33} +(-0.918029 - 6.38503i) q^{35} +(2.07281 - 2.39215i) q^{37} +(3.62146 + 2.32737i) q^{39} +(-5.66411 - 6.53673i) q^{41} +(0.334255 + 0.731917i) q^{43} -1.40542 q^{45} -0.337617 q^{47} +(5.84360 + 12.7957i) q^{49} +(2.30071 + 2.65516i) q^{51} +(-5.96078 - 3.83076i) q^{53} +(1.15490 - 1.33283i) q^{55} +(0.122827 + 0.854277i) q^{57} +(-4.99396 + 3.20942i) q^{59} +(-2.75838 + 6.04002i) q^{61} +(4.40395 - 1.29312i) q^{63} +(-5.80502 - 1.70451i) q^{65} +(1.63901 - 11.3995i) q^{67} +(-3.12184 + 3.64062i) q^{69} +(1.21442 - 8.44651i) q^{71} +(14.6178 + 4.29216i) q^{73} +(-2.90227 + 0.852184i) q^{75} +(-2.39262 + 5.23910i) q^{77} +(-9.38569 + 6.03182i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(3.65282 - 4.21558i) q^{83} +(-4.15380 - 2.66949i) q^{85} +(0.614996 + 0.709743i) q^{87} +(4.27501 + 9.36096i) q^{89} +19.7586 q^{91} +8.71585 q^{93} +(-0.503883 - 1.10335i) q^{95} +(-2.32141 - 2.67905i) q^{97} +(1.05564 + 0.678421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9	$ 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9} - 15 q^{11} - 5 q^{13} - 2 q^{15} + 9 q^{17} - 3 q^{19} + 7 q^{21} + 18 q^{23} - 19 q^{25} + 3 q^{27} - 21 q^{29} + 17 q^{31} - 7 q^{33} - 36 q^{35} + 9 q^{37} + 5 q^{39} + 18 q^{41} + 50 q^{43} + 2 q^{45} + 74 q^{47} - 17 q^{49} + 13 q^{51} + 43 q^{53} - 42 q^{55} - 8 q^{57} + 7 q^{59} - 10 q^{61} + 4 q^{63} - 4 q^{65} + 33 q^{67} + 15 q^{69} + 3 q^{71} + 30 q^{73} - 25 q^{75} - 82 q^{77} - 40 q^{79} - 3 q^{81} + 9 q^{83} - 54 q^{85} + 10 q^{87} + 25 q^{89} - 30 q^{91} + 38 q^{93} - 49 q^{95} - 69 q^{97} + 7 q^{99}+O(q^{100}) $ 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9 - 15 * q^11 - 5 * q^13 - 2 * q^15 + 9 * q^17 - 3 * q^19 + 7 * q^21 + 18 * q^23 - 19 * q^25 + 3 * q^27 - 21 * q^29 + 17 * q^31 - 7 * q^33 - 36 * q^35 + 9 * q^37 + 5 * q^39 + 18 * q^41 + 50 * q^43 + 2 * q^45 + 74 * q^47 - 17 * q^49 + 13 * q^51 + 43 * q^53 - 42 * q^55 - 8 * q^57 + 7 * q^59 - 10 * q^61 + 4 * q^63 - 4 * q^65 + 33 * q^67 + 15 * q^69 + 3 * q^71 + 30 * q^73 - 25 * q^75 - 82 * q^77 - 40 * q^79 - 3 * q^81 + 9 * q^83 - 54 * q^85 + 10 * q^87 + 25 * q^89 - 30 * q^91 + 38 * q^93 - 49 * q^95 - 69 * q^97 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$		0			0
$5$	0.920354	+	1.06214i	0.411595	+	0.475006i	0.923258	−	0.384180i	$-0.125516\pi$
$5$	0.920354	+	1.06214i	0.411595	+	0.475006i	−0.511663	+	0.859186i	$0.670970\pi$
$6$		0			0
$7$	−3.86124	−	2.48147i	−1.45941	−	0.937908i	−0.998732	−	0.0503422i	$-0.983969\pi$
$7$	−3.86124	−	2.48147i	−1.45941	−	0.937908i	−0.460681	−	0.887566i	$-0.652395\pi$
$8$		0			0
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$		0			0
$11$	−0.178583	−	1.24207i	−0.0538449	−	0.374499i	−0.998871	−	0.0475045i	$-0.984873\pi$
$11$	−0.178583	−	1.24207i	−0.0538449	−	0.374499i	0.945026	−	0.326995i	$-0.106036\pi$
$12$		0			0
$13$	−3.62146	+	2.32737i	−1.00441	+	0.645496i	−0.935941	−	0.352157i	$-0.885448\pi$
$13$	−3.62146	+	2.32737i	−1.00441	+	0.645496i	−0.0684702	+	0.997653i	$0.521812\pi$
$14$		0			0
$15$	0.583832	−	1.27841i	0.150745	−	0.330085i
$16$		0			0
$17$	−3.37097	+	0.989806i	−0.817580	+	0.240063i	−0.663674	−	0.748022i	$-0.731004\pi$
$17$	−3.37097	+	0.989806i	−0.817580	+	0.240063i	−0.153906	+	0.988085i	$0.549185\pi$
$18$		0			0
$19$	−0.828102	−	0.243153i	−0.189980	−	0.0557830i	0.185359	−	0.982671i	$-0.440655\pi$
$19$	−0.828102	−	0.243153i	−0.189980	−	0.0557830i	−0.375338	+	0.926888i	$0.622473\pi$
$20$		0			0
$21$	−0.653207	+	4.54315i	−0.142541	+	0.991397i
$22$		0			0
$23$	−2.01477	−	4.35209i	−0.420108	−	0.907474i
$23$	−2.01477	−	4.35209i	−0.420108	−	0.907474i
$24$		0			0
$25$	0.430474	−	2.99401i	0.0860947	−	0.598802i
$26$		0			0
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$		0			0
$29$	−0.901084	+	0.264582i	−0.167327	+	0.0491317i	−0.364323	−	0.931273i	$-0.618700\pi$
$29$	−0.901084	+	0.264582i	−0.167327	+	0.0491317i	0.196996	+	0.980404i	$0.436881\pi$
$30$		0			0
$31$	−3.62070	+	7.92822i	−0.650296	+	1.42395i	0.240998	+	0.970526i	$0.422525\pi$
$31$	−3.62070	+	7.92822i	−0.650296	+	1.42395i	−0.891295	+	0.453425i	$0.850202\pi$
$32$		0			0
$33$	−1.05564	+	0.678421i	−0.183764	+	0.118098i
$34$		0			0
$35$	−0.918029	−	6.38503i	−0.155175	−	1.07927i
$36$		0			0
$37$	2.07281	−	2.39215i	0.340768	−	0.393268i	−0.559337	−	0.828941i	$-0.688944\pi$
$37$	2.07281	−	2.39215i	0.340768	−	0.393268i	0.900105	+	0.435673i	$0.143490\pi$
$38$		0			0
$39$	3.62146	+	2.32737i	0.579897	+	0.372677i
$40$		0			0
$41$	−5.66411	−	6.53673i	−0.884586	−	1.02087i	−0.999622	−	0.0275048i	$-0.991244\pi$
$41$	−5.66411	−	6.53673i	−0.884586	−	1.02087i	0.115036	−	0.993361i	$-0.463302\pi$
$42$		0			0
$43$	0.334255	+	0.731917i	0.0509735	+	0.111616i	0.933405	−	0.358824i	$-0.116822\pi$
$43$	0.334255	+	0.731917i	0.0509735	+	0.111616i	−0.882432	+	0.470441i	$0.844095\pi$
$44$		0			0
$45$	−1.40542			−0.209507
$46$		0			0
$47$	−0.337617			−0.0492466			−0.0246233	−	0.999697i	$-0.507839\pi$
$47$	−0.337617			−0.0492466			−0.0246233	+	0.999697i	$0.507839\pi$
$48$		0			0
$49$	5.84360	+	12.7957i	0.834801	+	1.82796i
$50$		0			0
$51$	2.30071	+	2.65516i	0.322164	+	0.371797i
$52$		0			0
$53$	−5.96078	−	3.83076i	−0.818776	−	0.526195i	0.0629170	−	0.998019i	$-0.479960\pi$
$53$	−5.96078	−	3.83076i	−0.818776	−	0.526195i	−0.881693	+	0.471823i	$0.843596\pi$
$54$		0			0
$55$	1.15490	−	1.33283i	0.155727	−	0.179718i
$56$		0			0
$57$	0.122827	+	0.854277i	0.0162688	+	0.113152i
$58$		0			0
$59$	−4.99396	+	3.20942i	−0.650158	+	0.417831i	−0.823724	−	0.566991i	$-0.808107\pi$
$59$	−4.99396	+	3.20942i	−0.650158	+	0.417831i	0.173566	+	0.984822i	$0.444471\pi$
$60$		0			0
$61$	−2.75838	+	6.04002i	−0.353175	+	0.773345i	0.646768	+	0.762687i	$0.276120\pi$
$61$	−2.75838	+	6.04002i	−0.353175	+	0.773345i	−0.999943	+	0.0106587i	$0.996607\pi$
$62$		0			0
$63$	4.40395	−	1.29312i	0.554845	−	0.162917i
$64$		0			0
$65$	−5.80502	−	1.70451i	−0.720024	−	0.211418i
$66$		0			0
$67$	1.63901	−	11.3995i	0.200236	−	1.39267i	−0.603345	−	0.797480i	$-0.706166\pi$
$67$	1.63901	−	11.3995i	0.200236	−	1.39267i	0.803582	−	0.595195i	$-0.202925\pi$
$68$		0			0
$69$	−3.12184	+	3.64062i	−0.375825	+	0.438279i
$70$		0			0
$71$	1.21442	−	8.44651i	0.144126	−	1.00242i	−0.781481	−	0.623929i	$-0.785535\pi$
$71$	1.21442	−	8.44651i	0.144126	−	1.00242i	0.925607	−	0.378487i	$-0.123556\pi$
$72$		0			0
$73$	14.6178	+	4.29216i	1.71088	+	0.502359i	0.983040	−	0.183389i	$-0.0587068\pi$
$73$	14.6178	+	4.29216i	1.71088	+	0.502359i	0.727839	+	0.685749i	$0.240525\pi$
$74$		0			0
$75$	−2.90227	+	0.852184i	−0.335126	+	0.0984017i
$76$		0			0
$77$	−2.39262	+	5.23910i	−0.272664	+	0.597051i
$78$		0			0
$79$	−9.38569	+	6.03182i	−1.05597	+	0.678633i	−0.948887	−	0.315617i	$-0.897789\pi$
$79$	−9.38569	+	6.03182i	−1.05597	+	0.678633i	−0.107086	+	0.994250i	$0.534152\pi$
$80$		0			0
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$		0			0
$83$	3.65282	−	4.21558i	0.400949	−	0.462720i	−0.518991	−	0.854780i	$-0.673692\pi$
$83$	3.65282	−	4.21558i	0.400949	−	0.462720i	0.919940	+	0.392060i	$0.128238\pi$
$84$		0			0
$85$	−4.15380	−	2.66949i	−0.450543	−	0.289546i
$86$		0			0
$87$	0.614996	+	0.709743i	0.0659345	+	0.0760925i
$88$		0			0
$89$	4.27501	+	9.36096i	0.453150	+	0.992260i	0.988996	+	0.147944i	$0.0472656\pi$
$89$	4.27501	+	9.36096i	0.453150	+	0.992260i	−0.535846	+	0.844316i	$0.680007\pi$
$90$		0			0
$91$	19.7586			2.07127
$92$		0			0
$93$	8.71585			0.903792
$94$		0			0
$95$	−0.503883	−	1.10335i	−0.0516973	−	0.113201i
$96$		0			0
$97$	−2.32141	−	2.67905i	−0.235703	−	0.272016i	0.625559	−	0.780177i	$-0.284871\pi$
$97$	−2.32141	−	2.67905i	−0.235703	−	0.272016i	−0.861262	+	0.508161i	$0.830326\pi$
$98$		0			0
$99$	1.05564	+	0.678421i	0.106096	+	0.0681839i
$100$		0			0
$101$	10.4850	−	12.1003i	1.04329	−	1.20402i	0.0647671	−	0.997900i	$-0.479370\pi$
$101$	10.4850	−	12.1003i	1.04329	−	1.20402i	0.978526	−	0.206124i	$-0.0660850\pi$
$102$		0			0
$103$	−0.465791	−	3.23965i	−0.0458957	−	0.319212i	−0.999817	−	0.0191534i	$-0.993903\pi$
$103$	−0.465791	−	3.23965i	−0.0458957	−	0.319212i	0.953921	−	0.300058i	$-0.0970062\pi$
$104$		0			0
$105$	−5.42667	+	3.48751i	−0.529588	+	0.340346i
$106$		0			0
$107$	7.93245	−	17.3696i	0.766859	−	1.67919i	0.0334103	−	0.999442i	$-0.489363\pi$
$107$	7.93245	−	17.3696i	0.766859	−	1.67919i	0.733449	−	0.679745i	$-0.237910\pi$
$108$		0			0
$109$	7.30751	−	2.14568i	0.699933	−	0.205519i	0.0876426	−	0.996152i	$-0.472067\pi$
$109$	7.30751	−	2.14568i	0.699933	−	0.205519i	0.612290	+	0.790633i	$0.290248\pi$
$110$		0			0
$111$	−3.03706	−	0.891761i	−0.288265	−	0.0846422i
$112$		0			0
$113$	0.129805	−	0.902813i	0.0122110	−	0.0849295i	−0.982805	−	0.184649i	$-0.940885\pi$
$113$	0.129805	−	0.902813i	0.0122110	−	0.0849295i	0.995016	+	0.0997190i	$0.0317944\pi$
$114$		0			0
$115$	2.76825	−	6.14544i	0.258141	−	0.573065i
$116$		0			0
$117$	0.612642	−	4.26102i	0.0566387	−	0.393931i
$118$		0			0
$119$	15.4723	+	4.54308i	1.41834	+	0.416463i
$120$		0			0
$121$	9.04357	−	2.65543i	0.822143	−	0.241403i
$122$		0			0
$123$	−3.59306	+	7.86771i	−0.323976	+	0.709408i
$124$		0			0
$125$	9.48783	−	6.09746i	0.848617	−	0.545373i
$126$		0			0
$127$	2.42807	+	16.8876i	0.215456	+	1.49853i	0.754527	+	0.656269i	$0.227867\pi$
$127$	2.42807	+	16.8876i	0.215456	+	1.49853i	−0.539071	+	0.842261i	$0.681224\pi$
$128$		0			0
$129$	0.526921	−	0.608099i	0.0463928	−	0.0535401i
$130$		0			0
$131$	10.3087	+	6.62500i	0.900676	+	0.578829i	0.906991	−	0.421151i	$-0.138374\pi$
$131$	10.3087	+	6.62500i	0.900676	+	0.578829i	−0.00631473	+	0.999980i	$0.502010\pi$
$132$		0			0
$133$	2.59413	+	2.99378i	0.224939	+	0.259594i
$134$		0			0
$135$	0.583832	+	1.27841i	0.0502483	+	0.110028i
$136$		0			0
$137$	−0.853655			−0.0729327			−0.0364663	−	0.999335i	$-0.511610\pi$
$137$	−0.853655			−0.0729327			−0.0364663	+	0.999335i	$0.511610\pi$
$138$		0			0
$139$	−13.6216			−1.15537			−0.577684	−	0.816261i	$-0.696043\pi$
$139$	−13.6216			−1.15537			−0.577684	+	0.816261i	$0.696043\pi$
$140$		0			0
$141$	0.140251	+	0.307108i	0.0118113	+	0.0258631i
$142$		0			0
$143$	3.53749	+	4.08248i	0.295820	+	0.341394i
$144$		0			0
$145$	−1.11034	−	0.713572i	−0.0922088	−	0.0592590i
$146$		0			0
$147$	9.21186	−	10.6311i	0.759782	−	0.876835i
$148$		0			0
$149$	−0.225161	−	1.56603i	−0.0184459	−	0.128294i	0.978518	−	0.206163i	$-0.0660976\pi$
$149$	−0.225161	−	1.56603i	−0.0184459	−	0.128294i	−0.996964	+	0.0778686i	$0.975189\pi$
$150$		0			0
$151$	−8.36691	+	5.37709i	−0.680889	+	0.437581i	−0.834836	−	0.550498i	$-0.814438\pi$
$151$	−8.36691	+	5.37709i	−0.680889	+	0.437581i	0.153947	+	0.988079i	$0.450801\pi$
$152$		0			0
$153$	1.45947	−	3.19579i	0.117991	−	0.258365i
$154$		0			0
$155$	−11.7532	+	3.45106i	−0.944043	+	0.277196i
$156$		0			0
$157$	−6.42491	−	1.88653i	−0.512764	−	0.150561i	0.0151066	−	0.999886i	$-0.495191\pi$
$157$	−6.42491	−	1.88653i	−0.512764	−	0.150561i	−0.527871	+	0.849325i	$0.677009\pi$
$158$		0			0
$159$	−1.00839	+	7.01347i	−0.0799701	+	0.556205i
$160$		0			0
$161$	−3.02008	+	21.8041i	−0.238016	+	1.71840i
$162$		0			0
$163$	1.28349	−	8.92688i	0.100531	−	0.699208i	−0.875760	−	0.482746i	$-0.839639\pi$
$163$	1.28349	−	8.92688i	0.100531	−	0.699208i	0.976291	−	0.216461i	$-0.0694515\pi$
$164$		0			0
$165$	−1.69215	−	0.496859i	−0.131733	−	0.0386804i
$166$		0			0
$167$	−19.7075	+	5.78663i	−1.52501	+	0.447783i	−0.933519	−	0.358529i	$-0.883279\pi$
$167$	−19.7075	+	5.78663i	−1.52501	+	0.447783i	−0.591491	+	0.806312i	$0.701460\pi$
$168$		0			0
$169$	2.29790	−	5.03170i	0.176762	−	0.387054i
$170$		0			0
$171$	0.726054	−	0.466606i	0.0555227	−	0.0356823i
$172$		0			0
$173$	−2.76834	−	19.2542i	−0.210473	−	1.46387i	−0.771582	−	0.636130i	$-0.780534\pi$
$173$	−2.76834	−	19.2542i	−0.210473	−	1.46387i	0.561109	−	0.827742i	$-0.310375\pi$
$174$		0			0
$175$	−9.09171	+	10.4924i	−0.687269	+	0.793151i
$176$		0			0
$177$	4.99396	+	3.20942i	0.375369	+	0.241235i
$178$		0			0
$179$	4.03388	+	4.65534i	0.301506	+	0.347957i	0.886205	−	0.463294i	$-0.153333\pi$
$179$	4.03388	+	4.65534i	0.301506	+	0.347957i	−0.584699	+	0.811251i	$0.698787\pi$
$180$		0			0
$181$	−0.693275	−	1.51806i	−0.0515307	−	0.112837i	0.882115	−	0.471033i	$-0.156119\pi$
$181$	−0.693275	−	1.51806i	−0.0515307	−	0.112837i	−0.933646	+	0.358197i	$0.883392\pi$
$182$		0			0
$183$	6.64007			0.490848
$184$		0			0
$185$	4.44854			0.327063
$186$		0			0
$187$	1.83141	+	4.01023i	0.133926	+	0.293257i
$188$		0			0
$189$	−3.00573	−	3.46879i	−0.218634	−	0.252318i
$190$		0			0
$191$	10.9202	+	7.01800i	0.790160	+	0.507805i	0.872391	−	0.488809i	$-0.162568\pi$
$191$	10.9202	+	7.01800i	0.790160	+	0.507805i	−0.0822315	+	0.996613i	$0.526205\pi$
$192$		0			0
$193$	−7.58714	+	8.75603i	−0.546134	+	0.630273i	−0.959978	−	0.280075i	$-0.909641\pi$
$193$	−7.58714	+	8.75603i	−0.546134	+	0.630273i	0.413844	+	0.910348i	$0.364186\pi$
$194$		0			0
$195$	0.861018	+	5.98851i	0.0616588	+	0.428846i
$196$		0			0
$197$	−21.8184	+	14.0219i	−1.55450	+	0.999016i	−0.570406	+	0.821363i	$0.693214\pi$
$197$	−21.8184	+	14.0219i	−1.55450	+	0.999016i	−0.984093	+	0.177653i	$0.943149\pi$
$198$		0			0
$199$	−7.41830	+	16.2438i	−0.525869	+	1.15149i	0.441300	+	0.897360i	$0.354517\pi$
$199$	−7.41830	+	16.2438i	−0.525869	+	1.15149i	−0.967169	+	0.254133i	$0.918210\pi$
$200$		0			0
$201$	−11.0502	+	3.24465i	−0.779425	+	0.228860i
$202$		0			0
$203$	4.13586	+	1.21440i	0.290280	+	0.0852340i
$204$		0			0
$205$	1.72997	−	12.0322i	0.120826	−	0.840366i
$206$		0			0
$207$	4.60848	+	1.32735i	0.320312	+	0.0922575i
$208$		0			0
$209$	−0.154128	+	1.07199i	−0.0106613	+	0.0741508i
$210$		0			0
$211$	−4.23283	−	1.24287i	−0.291400	−	0.0855629i	0.132765	−	0.991148i	$-0.457614\pi$
$211$	−4.23283	−	1.24287i	−0.291400	−	0.0855629i	−0.424166	+	0.905585i	$0.639433\pi$
$212$		0			0
$213$	−8.18771	+	2.40413i	−0.561012	+	0.164728i
$214$		0			0
$215$	−0.469769	+	1.02865i	−0.0320380	+	0.0701534i
$216$		0			0
$217$	33.6540	−	21.6281i	2.28458	−	1.46821i
$218$		0			0
$219$	−2.16815	−	15.0798i	−0.146510	−	1.01900i
$220$		0			0
$221$	9.90417	−	11.4300i	0.666227	−	0.768867i
$222$		0			0
$223$	−13.4322	−	8.63234i	−0.899486	−	0.578064i	0.00715203	−	0.999974i	$-0.497723\pi$
$223$	−13.4322	−	8.63234i	−0.899486	−	0.578064i	−0.906638	+	0.421910i	$0.861360\pi$
$224$		0			0
$225$	1.98082	+	2.28599i	0.132055	+	0.152399i
$226$		0			0
$227$	−5.43890	−	11.9095i	−0.360993	−	0.790464i	−0.999778	−	0.0210785i	$-0.993290\pi$
$227$	−5.43890	−	11.9095i	−0.360993	−	0.790464i	0.638785	−	0.769385i	$-0.279437\pi$
$228$		0			0
$229$	25.0459			1.65508			0.827541	−	0.561406i	$-0.189739\pi$
$229$	25.0459			1.65508			0.827541	+	0.561406i	$0.189739\pi$
$230$		0			0
$231$	5.75958			0.378952
$232$		0			0
$233$	−7.10911	−	15.5668i	−0.465733	−	1.01981i	−0.986143	−	0.165897i	$-0.946948\pi$
$233$	−7.10911	−	15.5668i	−0.465733	−	1.01981i	0.520410	−	0.853917i	$-0.325779\pi$
$234$		0			0
$235$	−0.310727	−	0.358599i	−0.0202696	−	0.0233924i
$236$		0			0
$237$	9.38569	+	6.03182i	0.609666	+	0.391809i
$238$		0			0
$239$	−5.75494	+	6.64156i	−0.372256	+	0.429607i	−0.910709	−	0.413049i	$-0.864464\pi$
$239$	−5.75494	+	6.64156i	−0.372256	+	0.429607i	0.538452	+	0.842656i	$0.319009\pi$
$240$		0			0
$241$	−1.54816	−	10.7677i	−0.0997257	−	0.693607i	−0.976941	−	0.213510i	$-0.931510\pi$
$241$	−1.54816	−	10.7677i	−0.0997257	−	0.693607i	0.877215	−	0.480097i	$-0.159399\pi$
$242$		0			0
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$		0			0
$245$	−8.21271	+	17.9833i	−0.524691	+	1.14891i
$246$		0			0
$247$	3.56484	−	1.04673i	0.226825	−	0.0666019i
$248$		0			0
$249$	−5.35206	−	1.57151i	−0.339173	−	0.0995902i
$250$		0			0
$251$	4.44555	−	30.9195i	0.280601	−	1.95162i	−0.0256542	−	0.999671i	$-0.508167\pi$
$251$	4.44555	−	30.9195i	0.280601	−	1.95162i	0.306255	−	0.951950i	$-0.400924\pi$
$252$		0			0
$253$	−5.04581	+	3.27970i	−0.317228	+	0.206193i
$254$		0			0
$255$	−0.702698	+	4.88737i	−0.0440047	+	0.306059i
$256$		0			0
$257$	−3.23177	−	0.948933i	−0.201592	−	0.0591928i	0.179378	−	0.983780i	$-0.442592\pi$
$257$	−3.23177	−	0.948933i	−0.201592	−	0.0591928i	−0.380970	+	0.924588i	$0.624410\pi$
$258$		0			0
$259$	−13.9397	+	4.09307i	−0.866171	+	0.254331i
$260$		0			0
$261$	0.390127	−	0.854258i	0.0241482	−	0.0528773i
$262$		0			0
$263$	−16.7606	+	10.7714i	−1.03351	+	0.664194i	−0.943372	−	0.331736i	$-0.892366\pi$
$263$	−16.7606	+	10.7714i	−1.03351	+	0.664194i	−0.0901332	+	0.995930i	$0.528729\pi$
$264$		0			0
$265$	−1.41720	−	9.85687i	−0.0870581	−	0.605502i
$266$		0			0
$267$	6.73913	−	7.77737i	0.412428	−	0.475967i
$268$		0			0
$269$	14.4516	+	9.28749i	0.881131	+	0.566268i	0.901138	−	0.433532i	$-0.142733\pi$
$269$	14.4516	+	9.28749i	0.881131	+	0.566268i	−0.0200078	+	0.999800i	$0.506369\pi$
$270$		0			0
$271$	0.286004	+	0.330067i	0.0173735	+	0.0200501i	0.764370	−	0.644778i	$-0.223050\pi$
$271$	0.286004	+	0.330067i	0.0173735	+	0.0200501i	−0.746996	+	0.664828i	$0.768505\pi$
$272$		0			0
$273$	−8.20803	−	17.9731i	−0.496772	−	1.08778i
$274$		0			0
$275$	−3.79565			−0.228887
$276$		0			0
$277$	−21.2409			−1.27624			−0.638122	−	0.769935i	$-0.720288\pi$
$277$	−21.2409			−1.27624			−0.638122	+	0.769935i	$0.720288\pi$
$278$		0			0
$279$	−3.62070	−	7.92822i	−0.216765	−	0.474650i
$280$		0			0
$281$	−18.6827	−	21.5610i	−1.11452	−	1.28622i	−0.954205	−	0.299154i	$-0.903296\pi$
$281$	−18.6827	−	21.5610i	−1.11452	−	1.28622i	−0.160311	−	0.987067i	$-0.551250\pi$
$282$		0			0
$283$	−8.18052	−	5.25730i	−0.486282	−	0.312514i	0.274427	−	0.961608i	$-0.411512\pi$
$283$	−8.18052	−	5.25730i	−0.486282	−	0.312514i	−0.760708	+	0.649094i	$0.775148\pi$
$284$		0			0
$285$	−0.794322	+	0.916697i	−0.0470516	+	0.0543004i
$286$		0			0
$287$	5.64980	+	39.2952i	0.333497	+	2.31953i
$288$		0			0
$289$	−3.91759	+	2.51768i	−0.230447	+	0.148099i
$290$		0			0
$291$	−1.47260	+	3.22454i	−0.0863253	+	0.189026i
$292$		0			0
$293$	−7.46237	+	2.19115i	−0.435956	+	0.128008i	−0.492344	−	0.870401i	$-0.663860\pi$
$293$	−7.46237	+	2.19115i	−0.435956	+	0.128008i	0.0563878	+	0.998409i	$0.482042\pi$
$294$		0			0
$295$	−8.00508	−	2.35050i	−0.466074	−	0.136852i
$296$		0			0
$297$	0.178583	−	1.24207i	0.0103624	−	0.0720724i
$298$		0			0
$299$	17.4253	+	11.0718i	1.00773	+	0.640299i
$300$		0			0
$301$	0.525590	−	3.65556i	0.0302945	−	0.210703i
$302$		0			0
$303$	−15.3624	−	4.51082i	−0.882548	−	0.259140i
$304$		0			0
$305$	−8.95406	+	2.62915i	−0.512708	+	0.150545i
$306$		0			0
$307$	−13.1591	+	28.8144i	−0.751028	+	1.64452i	0.0134798	+	0.999909i	$0.495709\pi$
$307$	−13.1591	+	28.8144i	−0.751028	+	1.64452i	−0.764508	+	0.644614i	$0.777018\pi$
$308$		0			0
$309$	−2.75339	+	1.76950i	−0.156635	+	0.100663i
$310$		0			0
$311$	−0.915069	−	6.36444i	−0.0518888	−	0.360894i	−0.999179	−	0.0405172i	$-0.987099\pi$
$311$	−0.915069	−	6.36444i	−0.0518888	−	0.360894i	0.947290	−	0.320377i	$-0.103810\pi$
$312$		0			0
$313$	−5.44849	+	6.28789i	−0.307967	+	0.355413i	−0.888543	−	0.458793i	$-0.848282\pi$
$313$	−5.44849	+	6.28789i	−0.307967	+	0.355413i	0.580576	+	0.814206i	$0.302827\pi$
$314$		0			0
$315$	5.42667	+	3.48751i	0.305758	+	0.196499i
$316$		0			0
$317$	8.78845	+	10.1424i	0.493608	+	0.569654i	0.946826	−	0.321745i	$-0.104270\pi$
$317$	8.78845	+	10.1424i	0.493608	+	0.569654i	−0.453218	+	0.891400i	$0.649724\pi$
$318$		0			0
$319$	0.489549	+	1.07196i	0.0274095	+	0.0600184i
$320$		0			0
$321$	−19.0952			−1.06579
$322$		0			0
$323$	3.03218			0.168715
$324$		0			0
$325$	5.40922	+	11.8445i	0.300050	+	0.657017i
$326$		0			0
$327$	−4.98743	−	5.75580i	−0.275805	−	0.318296i
$328$		0			0
$329$	1.30362	+	0.837788i	0.0718711	+	0.0461887i
$330$		0			0
$331$	−16.4912	+	19.0318i	−0.906438	+	1.04608i	0.0922940	+	0.995732i	$0.470580\pi$
$331$	−16.4912	+	19.0318i	−0.906438	+	1.04608i	−0.998731	+	0.0503529i	$0.983965\pi$
$332$		0			0
$333$	0.450465	+	3.13306i	0.0246854	+	0.171690i
$334$		0			0
$335$	13.6164	−	8.75074i	0.743945	−	0.478104i
$336$		0			0
$337$	9.56211	−	20.9381i	0.520881	−	1.14057i	−0.448223	−	0.893922i	$-0.647943\pi$
$337$	9.56211	−	20.9381i	0.520881	−	1.14057i	0.969105	−	0.246650i	$-0.0793296\pi$
$338$		0			0
$339$	−0.875151	+	0.256967i	−0.0475317	+	0.0139566i
$340$		0			0
$341$	10.4940	+	3.08132i	0.568283	+	0.166863i
$342$		0			0
$343$	4.61615	−	32.1060i	0.249249	−	1.73356i
$344$		0			0
$345$	−6.74006	+	0.0348157i	−0.362873	+	0.00187442i
$346$		0			0
$347$	−2.30746	+	16.0487i	−0.123871	+	0.861541i	0.829234	+	0.558902i	$0.188777\pi$
$347$	−2.30746	+	16.0487i	−0.123871	+	0.861541i	−0.953105	+	0.302640i	$0.902132\pi$
$348$		0			0
$349$	−17.1494	−	5.03551i	−0.917985	−	0.269545i	−0.211587	−	0.977359i	$-0.567863\pi$
$349$	−17.1494	−	5.03551i	−0.917985	−	0.269545i	−0.706399	+	0.707814i	$0.749681\pi$
$350$		0			0
$351$	−4.13046	+	1.21281i	−0.220467	+	0.0647351i
$352$		0			0
$353$	−2.31391	+	5.06675i	−0.123157	+	0.269676i	−0.961161	−	0.275988i	$-0.910995\pi$
$353$	−2.31391	+	5.06675i	−0.123157	+	0.269676i	0.838004	+	0.545664i	$0.183722\pi$
$354$		0			0
$355$	10.0891	−	6.48388i	0.535475	−	0.344129i
$356$		0			0
$357$	−2.29490	−	15.9614i	−0.121459	−	0.844765i
$358$		0			0
$359$	−24.6060	+	28.3968i	−1.29865	+	1.49873i	−0.551288	+	0.834315i	$0.685863\pi$
$359$	−24.6060	+	28.3968i	−1.29865	+	1.49873i	−0.747366	+	0.664412i	$0.768682\pi$
$360$		0			0
$361$	−15.3572	−	9.86947i	−0.808273	−	0.519446i
$362$		0			0
$363$	−6.17230	−	7.12321i	−0.323962	−	0.373872i
$364$		0			0
$365$	8.89461	+	19.4765i	0.465565	+	1.01945i
$366$		0			0
$367$	37.1438			1.93889			0.969447	−	0.245303i	$-0.0788873\pi$
$367$	37.1438			1.93889			0.969447	+	0.245303i	$0.0788873\pi$
$368$		0			0
$369$	8.64934			0.450266
$370$		0			0
$371$	13.5101	+	29.5830i	0.701410	+	1.53587i
$372$		0			0
$373$	−20.0927	−	23.1882i	−1.04036	−	1.20064i	−0.979281	−	0.202506i	$-0.935091\pi$
$373$	−20.0927	−	23.1882i	−1.04036	−	1.20064i	−0.0610789	−	0.998133i	$-0.519454\pi$
$374$		0			0
$375$	−9.48783	−	6.09746i	−0.489949	−	0.314871i
$376$		0			0
$377$	2.64746	−	3.05533i	0.136351	−	0.157357i
$378$		0			0
$379$	−1.95054	−	13.5663i	−0.100193	−	0.696855i	−0.976565	−	0.215221i	$-0.930953\pi$
$379$	−1.95054	−	13.5663i	−0.100193	−	0.696855i	0.876373	−	0.481634i	$-0.159956\pi$
$380$		0			0
$381$	14.3528	−	9.22400i	0.735317	−	0.472560i
$382$		0			0
$383$	1.80510	−	3.95261i	0.0922362	−	0.201969i	−0.857891	−	0.513832i	$-0.828226\pi$
$383$	1.80510	−	3.95261i	0.0922362	−	0.201969i	0.950127	+	0.311863i	$0.100953\pi$
$384$		0			0
$385$	−7.76673	+	2.28052i	−0.395829	+	0.116226i
$386$		0			0
$387$	−0.772037	−	0.226691i	−0.0392448	−	0.0115233i
$388$		0			0
$389$	−2.14863	+	14.9440i	−0.108940	+	0.757693i	0.859982	+	0.510325i	$0.170475\pi$
$389$	−2.14863	+	14.9440i	−0.108940	+	0.757693i	−0.968921	+	0.247368i	$0.920434\pi$
$390$		0			0
$391$	11.0994	+	12.6765i	0.561323	+	0.641080i
$392$		0			0
$393$	1.74392	−	12.1293i	0.0879693	−	0.611840i
$394$		0			0
$395$	−15.0448	−	4.41756i	−0.756987	−	0.222272i
$396$		0			0
$397$	−21.8608	+	6.41892i	−1.09716	+	0.322157i	−0.779725	−	0.626122i	$-0.784641\pi$
$397$	−21.8608	+	6.41892i	−1.09716	+	0.322157i	−0.317439	+	0.948279i	$0.602823\pi$
$398$		0			0
$399$	1.64560	−	3.60336i	0.0823831	−	0.180394i
$400$		0			0
$401$	22.2756	−	14.3156i	1.11239	−	0.714889i	0.150577	−	0.988598i	$-0.451887\pi$
$401$	22.2756	−	14.3156i	1.11239	−	0.714889i	0.961813	+	0.273709i	$0.0882505\pi$
$402$		0			0
$403$	−5.33969	−	37.1384i	−0.265989	−	1.84999i
$404$		0			0
$405$	0.920354	−	1.06214i	0.0457327	−	0.0527784i
$406$		0			0
$407$	−3.34140	−	2.14739i	−0.165627	−	0.106442i
$408$		0			0
$409$	14.6253	+	16.8785i	0.723176	+	0.834590i	0.991685	−	0.128687i	$-0.0410764\pi$
$409$	14.6253	+	16.8785i	0.723176	+	0.834590i	−0.268509	+	0.963277i	$0.586531\pi$
$410$		0			0
$411$	0.354621	+	0.776512i	0.0174922	+	0.0383025i
$412$		0			0
$413$	27.2470			1.34074
$414$		0			0
$415$	7.83944			0.384823
$416$		0			0
$417$	5.65861	+	12.3906i	0.277103	+	0.606771i
$418$		0			0
$419$	5.86316	+	6.76645i	0.286434	+	0.330563i	0.880672	−	0.473727i	$-0.157092\pi$
$419$	5.86316	+	6.76645i	0.286434	+	0.330563i	−0.594238	+	0.804290i	$0.702546\pi$
$420$		0			0
$421$	8.15530	+	5.24109i	0.397465	+	0.255435i	0.724071	−	0.689725i	$-0.242269\pi$
$421$	8.15530	+	5.24109i	0.397465	+	0.255435i	−0.326606	+	0.945161i	$0.605905\pi$
$422$		0			0
$423$	0.221092	−	0.255154i	0.0107499	−	0.0124060i
$424$		0			0
$425$	1.51238	+	10.5188i	0.0733610	+	0.510237i
$426$		0			0
$427$	25.6389	−	16.4771i	1.24075	−	0.797385i
$428$		0			0
$429$	2.24403	−	4.91374i	0.108343	−	0.237238i
$430$		0			0
$431$	2.54611	−	0.747606i	0.122642	−	0.0360109i	−0.219836	−	0.975537i	$-0.570552\pi$
$431$	2.54611	−	0.747606i	0.122642	−	0.0360109i	0.342478	+	0.939526i	$0.388734\pi$
$432$		0			0
$433$	13.3062	+	3.90706i	0.639456	+	0.187761i	0.585359	−	0.810774i	$-0.300954\pi$
$433$	13.3062	+	3.90706i	0.639456	+	0.187761i	0.0540973	+	0.998536i	$0.482772\pi$
$434$		0			0
$435$	−0.187836	+	1.30643i	−0.00900606	+	0.0626385i
$436$		0			0
$437$	0.610210	+	4.09387i	0.0291903	+	0.195836i
$438$		0			0
$439$	1.42291	−	9.89658i	0.0679120	−	0.472338i	−0.927278	−	0.374374i	$-0.877858\pi$
$439$	1.42291	−	9.89658i	0.0679120	−	0.472338i	0.995190	−	0.0979644i	$-0.0312331\pi$
$440$		0			0
$441$	−13.4971	−	3.96311i	−0.642719	−	0.188719i
$442$		0			0
$443$	7.72771	−	2.26906i	0.367155	−	0.107806i	−0.0929505	−	0.995671i	$-0.529630\pi$
$443$	7.72771	−	2.26906i	0.367155	−	0.107806i	0.460105	+	0.887864i	$0.347812\pi$
$444$		0			0
$445$	−6.00818	+	13.1561i	−0.284815	+	0.623658i
$446$		0			0
$447$	−1.33098	+	0.855366i	−0.0629530	+	0.0404574i
$448$		0			0
$449$	−1.23348	−	8.57902i	−0.0582114	−	0.404869i	−0.998005	−	0.0631277i	$-0.979892\pi$
$449$	−1.23348	−	8.57902i	−0.0582114	−	0.404869i	0.939794	−	0.341741i	$-0.111017\pi$
$450$		0			0
$451$	−7.10759	+	8.20259i	−0.334683	+	0.386245i
$452$		0			0
$453$	8.36691	+	5.37709i	0.393112	+	0.252638i
$454$		0			0
$455$	18.1849	+	20.9865i	0.852522	+	0.983863i
$456$		0			0
$457$	0.0715348	+	0.156639i	0.00334626	+	0.00732728i	0.911298	−	0.411748i	$-0.135082\pi$
$457$	0.0715348	+	0.156639i	0.00334626	+	0.00732728i	−0.907951	+	0.419075i	$0.862354\pi$
$458$		0			0
$459$	−3.51328			−0.163986
$460$		0			0
$461$	19.2423			0.896202			0.448101	−	0.893983i	$-0.352101\pi$
$461$	19.2423			0.896202			0.448101	+	0.893983i	$0.352101\pi$
$462$		0			0
$463$	0.274230	+	0.600481i	0.0127446	+	0.0279067i	0.915897	−	0.401413i	$-0.131481\pi$
$463$	0.274230	+	0.600481i	0.0127446	+	0.0279067i	−0.903153	+	0.429319i	$0.858753\pi$
$464$		0			0
$465$	8.02167	+	9.25750i	0.371996	+	0.429306i
$466$		0			0
$467$	−2.11760	−	1.36090i	−0.0979907	−	0.0629748i	0.490728	−	0.871313i	$-0.336731\pi$
$467$	−2.11760	−	1.36090i	−0.0979907	−	0.0629748i	−0.588718	+	0.808338i	$0.700367\pi$
$468$		0			0
$469$	−34.6162	+	39.9492i	−1.59843	+	1.84468i
$470$		0			0
$471$	0.952962	+	6.62800i	0.0439102	+	0.305402i
$472$		0			0
$473$	0.849403	−	0.545878i	0.0390556	−	0.0250995i
$474$		0			0
$475$	−1.08448	+	2.37467i	−0.0497592	+	0.108958i
$476$		0			0
$477$	6.79858	−	1.99624i	0.311285	−	0.0914017i
$478$		0			0
$479$	−22.0216	−	6.46613i	−1.00619	−	0.295445i	−0.263198	−	0.964742i	$-0.584777\pi$
$479$	−22.0216	−	6.46613i	−1.00619	−	0.295445i	−0.742995	+	0.669297i	$0.766596\pi$
$480$		0			0
$481$	−1.93918	+	13.4873i	−0.0884189	+	0.614967i
$482$		0			0
$483$	21.0883	−	6.31058i	0.959550	−	0.287141i
$484$		0			0
$485$	0.709020	−	4.93134i	0.0321949	−	0.223921i
$486$		0			0
$487$	32.1962	+	9.45365i	1.45895	+	0.428386i	0.912490	−	0.409100i	$-0.134157\pi$
$487$	32.1962	+	9.45365i	1.45895	+	0.428386i	0.546459	+	0.837486i	$0.315975\pi$
$488$		0			0
$489$	−8.65336	+	2.54086i	−0.391319	+	0.114901i
$490$		0			0
$491$	6.24324	−	13.6708i	0.281753	−	0.616954i	−0.714853	−	0.699275i	$-0.753506\pi$
$491$	6.24324	−	13.6708i	0.281753	−	0.616954i	0.996606	+	0.0823216i	$0.0262335\pi$
$492$		0			0
$493$	2.77564	−	1.78380i	0.125009	−	0.0803381i
$494$		0			0
$495$	0.250984	+	1.74563i	0.0112809	+	0.0784604i
$496$		0			0
$497$	−25.6490	+	29.6005i	−1.15051	+	1.32776i
$498$		0			0
$499$	9.05829	+	5.82141i	0.405505	+	0.260602i	0.727456	−	0.686154i	$-0.240702\pi$
$499$	9.05829	+	5.82141i	0.405505	+	0.260602i	−0.321952	+	0.946756i	$0.604339\pi$
$500$		0			0
$501$	13.4505	+	15.5227i	0.600923	+	0.693502i
$502$		0			0
$503$	−16.6793	−	36.5226i	−0.743695	−	1.62846i	−0.777380	−	0.629031i	$-0.783452\pi$
$503$	−16.6793	−	36.5226i	−0.743695	−	1.62846i	0.0336854	−	0.999432i	$-0.489276\pi$
$504$		0			0
$505$	22.5021			1.00133
$506$		0			0
$507$	−5.53158			−0.245666
$508$		0			0
$509$	−18.4482	−	40.3960i	−0.817704	−	1.79052i	−0.569906	−	0.821710i	$-0.693020\pi$
$509$	−18.4482	−	40.3960i	−0.817704	−	1.79052i	−0.247798	−	0.968812i	$-0.579707\pi$
$510$		0			0
$511$	−45.7919	−	52.8466i	−2.02571	−	2.33780i
$512$		0			0
$513$	−0.726054	−	0.466606i	−0.0320561	−	0.0206012i
$514$		0			0
$515$	3.01228	−	3.47636i	0.132737	−	0.153187i
$516$		0			0
$517$	0.0602928	+	0.419345i	0.00265167	+	0.0184428i
$518$		0			0
$519$	−16.3643	+	10.5167i	−0.718311	+	0.461630i
$520$		0			0
$521$	−1.77542	+	3.88762i	−0.0777824	+	0.170320i	−0.944528	−	0.328431i	$-0.893480\pi$
$521$	−1.77542	+	3.88762i	−0.0777824	+	0.170320i	0.866746	+	0.498750i	$0.166208\pi$
$522$		0			0
$523$	13.9135	−	4.08538i	0.608395	−	0.178641i	0.0369991	−	0.999315i	$-0.488220\pi$
$523$	13.9135	−	4.08538i	0.608395	−	0.178641i	0.571396	+	0.820674i	$0.306402\pi$
$524$		0			0
$525$	13.3211	+	3.91141i	0.581378	+	0.170708i
$526$		0			0
$527$	4.35786	−	30.3096i	0.189831	−	1.32031i
$528$		0			0
$529$	−14.8814	+	17.5369i	−0.647018	+	0.762474i
$530$		0			0
$531$	0.844827	−	5.87590i	0.0366624	−	0.254993i
$532$		0			0
$533$	35.7257	+	10.4900i	1.54745	+	0.454373i
$534$		0			0
$535$	25.7497	−	7.56080i	1.11326	−	0.326882i
$536$		0			0
$537$	2.55891	−	5.60324i	0.110425	−	0.241798i
$538$		0			0
$539$	14.8496	−	9.54328i	0.639619	−	0.411058i
$540$		0			0
$541$	−3.80884	−	26.4910i	−0.163755	−	1.13894i	−0.891477	−	0.453067i	$-0.850330\pi$
$541$	−3.80884	−	26.4910i	−0.163755	−	1.13894i	0.727722	−	0.685872i	$-0.240579\pi$
$542$		0			0
$543$	−1.09288	+	1.26125i	−0.0469000	+	0.0541254i
$544$		0			0
$545$	9.00452	+	5.78685i	0.385711	+	0.247882i
$546$		0			0
$547$	3.85932	+	4.45389i	0.165013	+	0.190435i	0.832234	−	0.554425i	$-0.187062\pi$
$547$	3.85932	+	4.45389i	0.165013	+	0.190435i	−0.667221	+	0.744860i	$0.732516\pi$
$548$		0			0
$549$	−2.75838	−	6.04002i	−0.117725	−	0.257782i
$550$		0			0
$551$	0.810523			0.0345294
$552$		0			0
$553$	51.2082			2.17760
$554$		0			0
$555$	−1.84799	−	4.04653i	−0.0784427	−	0.171766i
$556$		0			0
$557$	8.50794	+	9.81869i	0.360493	+	0.416031i	0.906805	−	0.421551i	$-0.138514\pi$
$557$	8.50794	+	9.81869i	0.360493	+	0.416031i	−0.546312	+	0.837582i	$0.683969\pi$
$558$		0			0
$559$	−2.91393	−	1.87267i	−0.123246	−	0.0792055i
$560$		0			0
$561$	2.88704	−	3.33182i	0.121891	−	0.140669i
$562$		0			0
$563$	4.99447	+	34.7373i	0.210492	+	1.46400i	0.771519	+	0.636206i	$0.219497\pi$
$563$	4.99447	+	34.7373i	0.210492	+	1.46400i	−0.561027	+	0.827798i	$0.689594\pi$
$564$		0			0
$565$	1.07838	−	0.693036i	0.0453680	−	0.0291562i
$566$		0			0
$567$	−1.90670	+	4.17509i	−0.0800739	+	0.175337i
$568$		0			0
$569$	−12.2843	+	3.60701i	−0.514986	+	0.151214i	−0.528891	−	0.848690i	$-0.677392\pi$
$569$	−12.2843	+	3.60701i	−0.514986	+	0.151214i	0.0139047	+	0.999903i	$0.495574\pi$
$570$		0			0
$571$	13.2239	+	3.88290i	0.553405	+	0.162494i	0.546465	−	0.837482i	$-0.315973\pi$
$571$	13.2239	+	3.88290i	0.553405	+	0.162494i	0.00693920	+	0.999976i	$0.497791\pi$
$572$		0			0
$573$	1.84737	−	12.8488i	0.0771751	−	0.536765i
$574$		0			0
$575$	−13.8975	+	4.15877i	−0.579566	+	0.173433i
$576$		0			0
$577$	−4.66355	+	32.4357i	−0.194146	+	1.35032i	0.626741	+	0.779227i	$0.284388\pi$
$577$	−4.66355	+	32.4357i	−0.194146	+	1.35032i	−0.820888	+	0.571090i	$0.806521\pi$
$578$		0			0
$579$	11.1166	+	3.26412i	0.461989	+	0.135652i
$580$		0			0
$581$	−24.5653	+	7.21301i	−1.01914	+	0.299246i
$582$		0			0
$583$	−3.69359	+	8.08784i	−0.152973	+	0.334964i
$584$		0			0
$585$	5.08966	−	3.27093i	0.210432	−	0.135236i
$586$		0			0
$587$	−4.22632	−	29.3947i	−0.174439	−	1.21325i	−0.869366	−	0.494169i	$-0.835472\pi$
$587$	−4.22632	−	29.3947i	−0.174439	−	1.21325i	0.694927	−	0.719081i	$-0.255437\pi$
$588$		0			0
$589$	4.92607	−	5.68499i	0.202975	−	0.234246i
$590$		0			0
$591$	21.8184	+	14.0219i	0.897491	+	0.576782i
$592$		0			0
$593$	11.3825	+	13.1361i	0.467425	+	0.539437i	0.939694	−	0.342018i	$-0.111110\pi$
$593$	11.3825	+	13.1361i	0.467425	+	0.539437i	−0.472269	+	0.881455i	$0.656565\pi$
$594$		0			0
$595$	9.41459	+	20.6151i	0.385960	+	0.845136i
$596$		0			0
$597$	17.8576			0.730861
$598$		0			0
$599$	38.4297			1.57020			0.785098	−	0.619371i	$-0.212612\pi$
$599$	38.4297			1.57020			0.785098	+	0.619371i	$0.212612\pi$
$600$		0			0
$601$	2.98804	+	6.54290i	0.121885	+	0.266890i	0.960733	−	0.277475i	$-0.0894977\pi$
$601$	2.98804	+	6.54290i	0.121885	+	0.266890i	−0.838848	+	0.544366i	$0.816770\pi$
$602$		0			0
$603$	7.54187	+	8.70379i	0.307129	+	0.354446i
$604$		0			0
$605$	11.1437	+	7.16164i	0.453057	+	0.291162i
$606$		0			0
$607$	15.3693	−	17.7371i	0.623820	−	0.719926i	−0.352608	−	0.935771i	$-0.614705\pi$
$607$	15.3693	−	17.7371i	0.623820	−	0.719926i	0.976428	+	0.215845i	$0.0692505\pi$
$608$		0			0
$609$	−0.613443	−	4.26659i	−0.0248580	−	0.172891i
$610$		0			0
$611$	1.22267	−	0.785760i	0.0494638	−	0.0317884i
$612$		0			0
$613$	12.2491	−	26.8219i	0.494738	−	1.08333i	−0.483406	−	0.875396i	$-0.660600\pi$
$613$	12.2491	−	26.8219i	0.494738	−	1.08333i	0.978144	−	0.207929i	$-0.0666723\pi$
$614$		0			0
$615$	−11.6635	+	3.42472i	−0.470319	+	0.138098i
$616$		0			0
$617$	3.27376	+	0.961262i	0.131796	+	0.0386989i	0.346966	−	0.937878i	$-0.387212\pi$
$617$	3.27376	+	0.961262i	0.131796	+	0.0386989i	−0.215169	+	0.976577i	$0.569030\pi$
$618$		0			0
$619$	2.59750	−	18.0660i	0.104402	−	0.726135i	−0.868629	−	0.495463i	$-0.834999\pi$
$619$	2.59750	−	18.0660i	0.104402	−	0.726135i	0.973032	−	0.230672i	$-0.0740924\pi$
$620$		0			0
$621$	−0.707029	−	4.74343i	−0.0283721	−	0.190347i
$622$		0			0
$623$	6.72211	−	46.7533i	0.269315	−	1.87313i
$624$		0			0
$625$	0.697176	+	0.204709i	0.0278871	+	0.00818838i
$626$		0			0
$627$	1.03914	−	0.305119i	0.0414993	−	0.0121853i
$628$		0			0
$629$	−4.61962	+	10.1156i	−0.184196	+	0.403334i
$630$		0			0
$631$	−1.97567	+	1.26969i	−0.0786503	+	0.0505455i	−0.579375	−	0.815061i	$-0.696703\pi$
$631$	−1.97567	+	1.26969i	−0.0786503	+	0.0505455i	0.500725	+	0.865607i	$0.333067\pi$
$632$		0			0
$633$	0.627827	+	4.36663i	0.0249539	+	0.173558i
$634$		0			0
$635$	−15.7024	+	18.1215i	−0.623129	+	0.719130i
$636$		0			0
$637$	−50.9427	−	32.7389i	−2.01842	−	1.29716i
$638$		0			0
$639$	5.58817	+	6.44909i	0.221064	+	0.255122i
$640$		0			0
$641$	−4.80863	−	10.5294i	−0.189929	−	0.415887i	0.790580	−	0.612358i	$-0.209779\pi$
$641$	−4.80863	−	10.5294i	−0.189929	−	0.415887i	−0.980510	+	0.196471i	$0.937052\pi$
$642$		0			0
$643$	−26.5443			−1.04681			−0.523403	−	0.852086i	$-0.675338\pi$
$643$	−26.5443			−1.04681			−0.523403	+	0.852086i	$0.675338\pi$
$644$		0			0
$645$	1.13084			0.0445269
$646$		0			0
$647$	13.9766	+	30.6045i	0.549477	+	1.20319i	0.957026	+	0.290003i	$0.0936564\pi$
$647$	13.9766	+	30.6045i	0.549477	+	1.20319i	−0.407549	+	0.913183i	$0.633616\pi$
$648$		0			0
$649$	4.87817	+	5.62971i	0.191485	+	0.220985i
$650$		0			0
$651$	−33.6540	−	21.6281i	−1.31901	−	0.847673i
$652$		0			0
$653$	16.7634	−	19.3460i	0.656003	−	0.757068i	−0.326115	−	0.945330i	$-0.605740\pi$
$653$	16.7634	−	19.3460i	0.656003	−	0.757068i	0.982119	+	0.188262i	$0.0602853\pi$
$654$		0			0
$655$	2.45094	+	17.0467i	0.0957663	+	0.666069i
$656$		0			0
$657$	−12.8164	+	8.23660i	−0.500015	+	0.321340i
$658$		0			0
$659$	8.33292	−	18.2465i	0.324604	−	0.710785i	−0.675031	−	0.737789i	$-0.735870\pi$
$659$	8.33292	−	18.2465i	0.324604	−	0.710785i	0.999635	+	0.0270049i	$0.00859698\pi$
$660$		0			0
$661$	−10.0634	+	2.95487i	−0.391420	+	0.114931i	−0.471520	−	0.881856i	$-0.656294\pi$
$661$	−10.0634	+	2.95487i	−0.391420	+	0.114931i	0.0800996	+	0.996787i	$0.474476\pi$
$662$		0			0
$663$	−14.5115	−	4.26095i	−0.563578	−	0.165482i
$664$		0			0
$665$	−0.792316	+	5.51068i	−0.0307247	+	0.213695i
$666$		0			0
$667$	2.96696	+	3.38853i	0.114881	+	0.131204i
$668$		0			0
$669$	−2.27232	+	15.8043i	−0.0878531	+	0.611031i
$670$		0			0
$671$	7.99475	+	2.34747i	0.308634	+	0.0906231i
$672$		0			0
$673$	−20.1297	+	5.91061i	−0.775943	+	0.227837i	−0.645645	−	0.763637i	$-0.723412\pi$
$673$	−20.1297	+	5.91061i	−0.775943	+	0.227837i	−0.130298	+	0.991475i	$0.541593\pi$
$674$		0			0
$675$	1.25655	−	2.75145i	0.0483645	−	0.105903i
$676$		0			0
$677$	−42.2534	+	27.1546i	−1.62393	+	1.04364i	−0.670549	+	0.741865i	$0.733941\pi$
$677$	−42.2534	+	27.1546i	−1.62393	+	1.04364i	−0.953380	+	0.301771i	$0.902422\pi$
$678$		0			0
$679$	2.31554	+	16.1050i	0.0888624	+	0.618052i
$680$		0			0
$681$	−8.57389	+	9.89480i	−0.328552	+	0.379170i
$682$		0			0
$683$	−6.60797	−	4.24668i	−0.252847	−	0.162495i	0.408078	−	0.912947i	$-0.366199\pi$
$683$	−6.60797	−	4.24668i	−0.252847	−	0.162495i	−0.660924	+	0.750452i	$0.729836\pi$
$684$		0			0
$685$	−0.785665	−	0.906705i	−0.0300187	−	0.0346434i
$686$		0			0
$687$	−10.4045	−	22.7826i	−0.396955	−	0.869209i
$688$		0			0
$689$	30.5023			1.16204
$690$		0			0
$691$	−6.72066			−0.255666			−0.127833	−	0.991796i	$-0.540802\pi$
$691$	−6.72066			−0.255666			−0.127833	+	0.991796i	$0.540802\pi$
$692$		0			0
$693$	−2.39262	−	5.23910i	−0.0908879	−	0.199017i
$694$		0			0
$695$	−12.5367	−	14.4681i	−0.475543	−	0.548806i
$696$		0			0
$697$	25.5636	+	16.4288i	0.968292	+	0.622283i
$698$		0			0
$699$	−11.2068	+	12.9333i	−0.423880	+	0.489184i
$700$		0			0
$701$	−4.47599	−	31.1312i	−0.169056	−	1.17581i	−0.880841	−	0.473411i	$-0.843022\pi$
$701$	−4.47599	−	31.1312i	−0.169056	−	1.17581i	0.711786	−	0.702397i	$-0.247887\pi$
$702$		0			0
$703$	−2.29816	+	1.47694i	−0.0866767	+	0.0557037i
$704$		0			0
$705$	−0.197112	+	0.431615i	−0.00742366	+	0.0162556i
$706$		0			0
$707$	−70.5115	+	20.7041i	−2.65186	+	0.778656i
$708$		0			0
$709$	−21.0447	−	6.17927i	−0.790349	−	0.232067i	−0.138446	−	0.990370i	$-0.544211\pi$
$709$	−21.0447	−	6.17927i	−0.790349	−	0.232067i	−0.651903	+	0.758303i	$0.726029\pi$
$710$		0			0
$711$	1.58778	−	11.0432i	0.0595463	−	0.414154i
$712$		0			0
$713$	41.7992	−	0.215913i	1.56539	−	0.00808602i
$714$		0			0
$715$	−1.08044	+	7.51466i	−0.0404063	+	0.281032i
$716$		0			0
$717$	8.43206	+	2.47588i	0.314901	+	0.0924633i
$718$		0			0
$719$	14.9460	−	4.38854i	0.557392	−	0.163665i	0.00910986	−	0.999959i	$-0.497100\pi$
$719$	14.9460	−	4.38854i	0.557392	−	0.163665i	0.548282	+	0.836293i	$0.315282\pi$
$720$		0			0
$721$	−6.24055	+	13.6649i	−0.232410	+	0.508908i
$722$		0			0
$723$	−9.15150	+	5.88131i	−0.340348	+	0.218728i
$724$		0			0
$725$	0.404269	+	2.81175i	0.0150142	+	0.104426i
$726$		0			0
$727$	7.32600	−	8.45466i	0.271706	−	0.313566i	−0.603455	−	0.797397i	$-0.706210\pi$
$727$	7.32600	−	8.45466i	0.271706	−	0.313566i	0.875161	+	0.483831i	$0.160755\pi$
$728$		0			0
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$		0			0
$731$	−1.85122	−	2.13642i	−0.0684699	−	0.0790184i
$732$		0			0
$733$	13.9700	+	30.5901i	0.515994	+	1.12987i	0.970934	+	0.239348i	$0.0769337\pi$
$733$	13.9700	+	30.5901i	0.515994	+	1.12987i	−0.454939	+	0.890522i	$0.650339\pi$
$734$		0			0
$735$	19.7699			0.729224
$736$		0			0
$737$	−14.4518			−0.532337
$738$		0			0
$739$	20.5884	+	45.0822i	0.757355	+	1.65838i	0.752680	+	0.658386i	$0.228761\pi$
$739$	20.5884	+	45.0822i	0.757355	+	1.65838i	0.00467464	+	0.999989i	$0.498512\pi$
$740$		0			0
$741$	−2.43303	−	2.80786i	−0.0893795	−	0.103149i
$742$		0			0
$743$	−35.9022	−	23.0729i	−1.31712	−	0.846463i	−0.322158	−	0.946686i	$-0.604408\pi$
$743$	−35.9022	−	23.0729i	−1.31712	−	0.846463i	−0.994965	+	0.100223i	$0.968045\pi$
$744$		0			0
$745$	1.45612	−	1.68046i	0.0533482	−	0.0615671i
$746$		0			0
$747$	0.793833	+	5.52123i	0.0290448	+	0.202011i
$748$		0			0
$749$	−73.7314	+	47.3843i	−2.69409	+	1.73138i
$750$		0			0
$751$	14.7598	−	32.3195i	0.538594	−	1.17936i	−0.423314	−	0.905983i	$-0.639133\pi$
$751$	14.7598	−	32.3195i	0.538594	−	1.17936i	0.961908	−	0.273373i	$-0.0881394\pi$
$752$		0			0
$753$	−29.9721	+	8.80060i	−1.09224	+	0.320712i
$754$		0			0
$755$	−13.4118	−	3.93805i	−0.488104	−	0.143320i
$756$		0			0
$757$	0.396979	−	2.76105i	0.0144284	−	0.100352i	−0.981335	−	0.192308i	$-0.938403\pi$
$757$	0.396979	−	2.76105i	0.0144284	−	0.100352i	0.995763	+	0.0919559i	$0.0293119\pi$
$758$		0			0
$759$	5.07943	+	3.22740i	0.184372	+	0.117147i
$760$		0			0
$761$	−1.56477	+	10.8832i	−0.0567229	+	0.394516i	0.941605	+	0.336718i	$0.109317\pi$
$761$	−1.56477	+	10.8832i	−0.0567229	+	0.394516i	−0.998328	+	0.0577979i	$0.981592\pi$
$762$		0			0
$763$	−33.5405	−	9.84839i	−1.21425	−	0.356536i
$764$		0			0
$765$	4.73762	−	1.39109i	0.171289	−	0.0502950i
$766$		0			0
$767$	10.6159	−	23.2455i	0.383317	−	0.839348i
$768$		0			0
$769$	−30.0160	+	19.2901i	−1.08241	+	0.695619i	−0.955112	−	0.296246i	$-0.904265\pi$
$769$	−30.0160	+	19.2901i	−1.08241	+	0.695619i	−0.127293	+	0.991865i	$0.540629\pi$
$770$		0			0
$771$	0.479345	+	3.33392i	0.0172632	+	0.120068i
$772$		0			0
$773$	29.2161	−	33.7172i	1.05083	−	1.21272i	0.0743235	−	0.997234i	$-0.476320\pi$
$773$	29.2161	−	33.7172i	1.05083	−	1.21272i	0.976506	−	0.215488i	$-0.0691343\pi$
$774$		0			0
$775$	22.1785	+	14.2533i	0.796677	+	0.511993i
$776$		0			0
$777$	9.51395	+	10.9797i	0.341311	+	0.393894i
$778$		0			0
$779$	3.10104	+	6.79032i	0.111106	+	0.243289i
$780$		0			0
$781$	−10.7081			−0.383164
$782$		0			0
$783$	−0.939125			−0.0335616
$784$		0			0
$785$	−3.90943	−	8.56046i	−0.139534	−	0.305536i
$786$		0			0
$787$	14.4830	+	16.7142i	0.516262	+	0.595798i	0.952691	−	0.303940i	$-0.0983024\pi$
$787$	14.4830	+	16.7142i	0.516262	+	0.595798i	−0.436429	+	0.899739i	$0.643757\pi$
$788$		0			0
$789$	16.7606	+	10.7714i	0.596695	+	0.383472i
$790$		0			0
$791$	−2.74151	+	3.16388i	−0.0974770	+	0.112494i
$792$		0			0
$793$	−4.06798	−	28.2934i	−0.144458	−	1.00473i
$794$		0			0
$795$	−8.37739	+	5.38382i	−0.297116	+	0.190945i
$796$		0			0
$797$	18.2663	−	39.9975i	0.647024	−	1.41679i	−0.247110	−	0.968987i	$-0.579481\pi$
$797$	18.2663	−	39.9975i	0.647024	−	1.41679i	0.894135	−	0.447798i	$-0.147792\pi$
$798$		0			0
$799$	1.13810	−	0.334176i	0.0402630	−	0.0118223i
$800$		0			0
$801$	−9.87408	−	2.89929i	−0.348883	−	0.102441i
$802$		0			0
$803$	2.72069	−	18.9228i	0.0960111	−	0.667772i
$804$		0			0
$805$	−25.9386	+	16.8597i	−0.914217	+	0.594226i
$806$		0			0
$807$	2.44478	−	17.0038i	0.0860603	−	0.598563i
$808$		0			0
$809$	−27.5486	−	8.08901i	−0.968558	−	0.284394i	−0.241065	−	0.970509i	$-0.577497\pi$
$809$	−27.5486	−	8.08901i	−0.968558	−	0.284394i	−0.727494	+	0.686115i	$0.759315\pi$
$810$		0			0
$811$	49.4405	−	14.5171i	1.73609	−	0.509763i	0.748010	−	0.663688i	$-0.231010\pi$
$811$	49.4405	−	14.5171i	1.73609	−	0.509763i	0.988082	+	0.153925i	$0.0491915\pi$
$812$		0			0
$813$	0.181429	−	0.397274i	0.00636298	−	0.0139330i
$814$		0			0
$815$	10.6629	−	6.85264i	0.373505	−	0.240037i
$816$		0			0
$817$	−0.0988299	−	0.687377i	−0.00345762	−	0.0240483i
$818$		0			0
$819$	−12.9391	+	14.9326i	−0.452130	+	0.521786i
$820$		0			0
$821$	6.82622	+	4.38694i	0.238237	+	0.153105i	0.654312	−	0.756225i	$-0.272958\pi$
$821$	6.82622	+	4.38694i	0.238237	+	0.153105i	−0.416075	+	0.909330i	$0.636595\pi$
$822$		0			0
$823$	−4.65470	−	5.37181i	−0.162253	−	0.187250i	0.668802	−	0.743441i	$-0.266808\pi$
$823$	−4.65470	−	5.37181i	−0.162253	−	0.187250i	−0.831054	+	0.556191i	$0.812262\pi$
$824$		0			0
$825$	1.57677	+	3.45265i	0.0548962	+	0.120206i
$826$		0			0
$827$	−0.982351			−0.0341597			−0.0170799	−	0.999854i	$-0.505437\pi$
$827$	−0.982351			−0.0341597			−0.0170799	+	0.999854i	$0.505437\pi$
$828$		0			0
$829$	−8.13718			−0.282616			−0.141308	−	0.989966i	$-0.545131\pi$
$829$	−8.13718			−0.282616			−0.141308	+	0.989966i	$0.545131\pi$
$830$		0			0
$831$	8.82380	+	19.3214i	0.306094	+	0.670253i
$832$		0			0
$833$	−32.3639	−	37.3499i	−1.12134	−	1.29410i
$834$		0			0
$835$	−24.2841	−	15.6064i	−0.840385	−	0.540083i
$836$		0			0
$837$	−5.70767	+	6.58700i	−0.197286	+	0.227680i
$838$		0			0
$839$	−3.93399	−	27.3615i	−0.135816	−	0.944624i	−0.937775	−	0.347244i	$-0.887118\pi$
$839$	−3.93399	−	27.3615i	−0.135816	−	0.944624i	0.801959	−	0.597380i	$-0.203791\pi$
$840$		0			0
$841$	−23.6544	+	15.2018i	−0.815669	+	0.524199i
$842$		0			0
$843$	−11.8515	+	25.9511i	−0.408187	+	0.893804i
$844$		0			0
$845$	7.45928	−	2.19024i	0.256607	−	0.0753466i
$846$		0			0
$847$	−41.5088	−	12.1881i	−1.42626	−	0.418788i
$848$		0			0
$849$	−1.38390	+	9.62523i	−0.0474953	+	0.330337i
$850$		0			0
$851$	−14.5871	−	4.20144i	−0.500040	−	0.144024i
$852$		0			0
$853$	−4.79769	+	33.3687i	−0.164270	+	1.14252i	0.726202	+	0.687482i	$0.241284\pi$
$853$	−4.79769	+	33.3687i	−0.164270	+	1.14252i	−0.890471	+	0.455039i	$0.849625\pi$
$854$		0			0
$855$	1.16383	+	0.341731i	0.0398021	+	0.0116870i
$856$		0			0
$857$	23.5078	−	6.90251i	0.803011	−	0.235785i	0.145626	−	0.989340i	$-0.453481\pi$
$857$	23.5078	−	6.90251i	0.803011	−	0.235785i	0.657385	+	0.753554i	$0.271662\pi$
$858$		0			0
$859$	−15.8760	+	34.7637i	−0.541683	+	1.18612i	0.418875	+	0.908044i	$0.362424\pi$
$859$	−15.8760	+	34.7637i	−0.541683	+	1.18612i	−0.960559	+	0.278078i	$0.910303\pi$
$860$		0			0
$861$	33.3972	−	21.4631i	1.13817	−	0.731460i
$862$		0			0
$863$	2.29422	+	15.9566i	0.0780961	+	0.543170i	0.990882	+	0.134732i	$0.0430174\pi$
$863$	2.29422	+	15.9566i	0.0780961	+	0.543170i	−0.912786	+	0.408438i	$0.866074\pi$
$864$		0			0
$865$	17.9029	−	20.6611i	0.608718	−	0.702498i
$866$		0			0
$867$	3.91759	+	2.51768i	0.133048	+	0.0855050i
$868$		0			0
$869$	9.16809	+	10.5805i	0.311006	+	0.358920i
$870$		0			0
$871$	20.5953	+	45.0975i	0.697846	+	1.52807i
$872$		0			0
$873$	3.54489			0.119976
$874$		0			0
$875$	−51.7655			−1.74999
$876$		0			0
$877$	−10.2185	−	22.3753i	−0.345053	−	0.755560i	0.654947	−	0.755674i	$-0.272691\pi$
$877$	−10.2185	−	22.3753i	−0.345053	−	0.755560i	−1.00000		0.000114659i	$0.999964\pi$
$878$		0			0
$879$	5.09312	+	5.87778i	0.171787	+	0.198252i
$880$		0			0
$881$	−44.1182	−	28.3530i	−1.48638	−	0.955237i	−0.996513	−	0.0834393i	$-0.973410\pi$
$881$	−44.1182	−	28.3530i	−1.48638	−	0.955237i	−0.489865	−	0.871798i	$-0.662954\pi$
$882$		0			0
$883$	10.4788	−	12.0932i	0.352640	−	0.406968i	−0.551521	−	0.834161i	$-0.685952\pi$
$883$	10.4788	−	12.0932i	0.352640	−	0.406968i	0.904160	+	0.427193i	$0.140498\pi$
$884$		0			0
$885$	1.18734	+	8.25811i	0.0399119	+	0.277593i
$886$		0			0
$887$	−2.07530	+	1.33371i	−0.0696816	+	0.0447816i	−0.575018	−	0.818141i	$-0.695005\pi$
$887$	−2.07530	+	1.33371i	−0.0696816	+	0.0447816i	0.505336	+	0.862923i	$0.331368\pi$
$888$		0			0
$889$	32.5307	−	71.2322i	1.09104	−	2.38905i
$890$		0			0
$891$	−1.20402	+	0.353531i	−0.0403360	+	0.0118437i
$892$		0			0
$893$	0.279582	+	0.0820925i	0.00935584	+	0.00274712i
$894$		0			0
$895$	−1.23205	+	8.56912i	−0.0411830	+	0.286434i
$896$		0			0
$897$	2.83253	−	20.4500i	0.0945754	−	0.682806i
$898$		0			0
$899$	1.16489	−	8.10196i	0.0388511	−	0.270216i
$900$		0			0
$901$	23.8853	+	7.01336i	0.795735	+	0.233649i
$902$		0			0
$903$	−3.54355	+	1.04048i	−0.117922	+	0.0346250i
$904$		0			0
$905$	0.974342	−	2.13351i	0.0323882	−	0.0709203i
$906$		0			0
$907$	−13.7491	+	8.83600i	−0.456531	+	0.293394i	−0.748623	−	0.662996i	$-0.769285\pi$
$907$	−13.7491	+	8.83600i	−0.456531	+	0.293394i	0.292093	+	0.956390i	$0.405648\pi$
$908$		0			0
$909$	2.27860	+	15.8480i	0.0755764	+	0.525646i
$910$		0			0
$911$	−20.8007	+	24.0053i	−0.689158	+	0.795331i	−0.987245	−	0.159208i	$-0.949106\pi$
$911$	−20.8007	+	24.0053i	−0.689158	+	0.795331i	0.298087	+	0.954539i	$0.403651\pi$
$912$		0			0
$913$	−5.88839	−	3.78424i	−0.194877	−	0.125240i
$914$		0			0
$915$	6.11121	+	7.05271i	0.202030	+	0.233156i
$916$		0			0
$917$	−23.3647	−	51.1615i	−0.771570	−	1.68950i
$918$		0			0
$919$	44.9294			1.48209			0.741043	−	0.671458i	$-0.234332\pi$
$919$	44.9294			1.48209			0.741043	+	0.671458i	$0.234332\pi$
$920$		0			0
$921$	31.6770			1.04379
$922$		0			0
$923$	15.2602	+	33.4151i	0.502294	+	1.09987i
$924$		0			0
$925$	−6.26984	−	7.23578i	−0.206151	−	0.237911i
$926$		0			0
$927$	2.75339	+	1.76950i	0.0904331	+	0.0581179i
$928$		0			0
$929$	−15.8301	+	18.2690i	−0.519370	+	0.599385i	−0.953473	−	0.301478i	$-0.902520\pi$
$929$	−15.8301	+	18.2690i	−0.519370	+	0.599385i	0.434103	+	0.900863i	$0.357065\pi$
$930$		0			0
$931$	−1.72779	−	12.0170i	−0.0566260	−	0.393842i
$932$		0			0
$933$	−5.40917	+	3.47626i	−0.177088	+	0.113808i
$934$		0			0
$935$	−2.57390	+	5.63605i	−0.0841755	+	0.184319i
$936$		0			0
$937$	−6.13782	+	1.80223i	−0.200514	+	0.0588761i	−0.380447	−	0.924803i	$-0.624230\pi$
$937$	−6.13782	+	1.80223i	−0.200514	+	0.0588761i	0.179933	+	0.983679i	$0.442412\pi$
$938$		0			0
$939$	7.98305	+	2.34404i	0.260517	+	0.0764947i
$940$		0			0
$941$	5.72596	−	39.8249i	0.186661	−	1.29825i	−0.653918	−	0.756566i	$-0.726876\pi$
$941$	5.72596	−	39.8249i	0.186661	−	1.29825i	0.840579	−	0.541689i	$-0.182215\pi$
$942$		0			0
$943$	−17.0366	+	37.8207i	−0.554788	+	1.23161i
$944$		0			0
$945$	0.918029	−	6.38503i	0.0298635	−	0.207705i
$946$		0			0
$947$	−25.0373	−	7.35161i	−0.813603	−	0.238895i	−0.151644	−	0.988435i	$-0.548457\pi$
$947$	−25.0373	−	7.35161i	−0.813603	−	0.238895i	−0.661959	+	0.749540i	$0.730275\pi$
$948$		0			0
$949$	−62.9270	+	18.4770i	−2.04270	+	0.599790i
$950$		0			0
$951$	5.57501	−	12.2076i	0.180782	−	0.395857i
$952$		0			0
$953$	14.8521	−	9.54489i	0.481108	−	0.309189i	−0.277513	−	0.960722i	$-0.589510\pi$
$953$	14.8521	−	9.54489i	0.481108	−	0.309189i	0.758621	+	0.651533i	$0.225874\pi$
$954$		0			0
$955$	2.59633	+	18.0579i	0.0840154	+	0.584340i
$956$		0			0
$957$	0.771725	−	0.890619i	0.0249463	−	0.0287896i
$958$		0			0
$959$	3.29617	+	2.11832i	0.106439	+	0.0684042i
$960$		0			0
$961$	−29.4465	−	33.9831i	−0.949888	−	1.09623i
$962$		0			0
$963$	7.93245	+	17.3696i	0.255620	+	0.559729i
$964$		0			0
$965$	−16.2830			−0.524169
$966$		0			0
$967$	−24.8519			−0.799184			−0.399592	−	0.916693i	$-0.630848\pi$
$967$	−24.8519			−0.799184			−0.399592	+	0.916693i	$0.630848\pi$
$968$		0			0
$969$	−1.25961	−	2.75817i	−0.0404646	−	0.0886051i
$970$		0			0
$971$	26.9182	+	31.0653i	0.863848	+	0.996933i	0.999981	+	0.00624274i	$0.00198714\pi$
$971$	26.9182	+	31.0653i	0.863848	+	0.996933i	−0.136133	+	0.990691i	$0.543467\pi$
$972$		0			0
$973$	52.5962	+	33.8016i	1.68616	+	1.08363i
$974$		0			0
$975$	8.52710	−	9.84080i	0.273086	−	0.315158i
$976$		0			0
$977$	−5.80401	−	40.3678i	−0.185687	−	1.29148i	−0.843021	−	0.537880i	$-0.819225\pi$
$977$	−5.80401	−	40.3678i	−0.185687	−	1.29148i	0.657335	−	0.753599i	$-0.271684\pi$
$978$		0			0
$979$	10.8636	−	6.98158i	0.347201	−	0.223132i
$980$		0			0
$981$	−3.16381	+	6.92777i	−0.101013	+	0.221187i
$982$		0			0
$983$	−3.50328	+	1.02866i	−0.111737	+	0.0328091i	−0.337123	−	0.941461i	$-0.609454\pi$
$983$	−3.50328	+	1.02866i	−0.111737	+	0.0328091i	0.225386	+	0.974270i	$0.427636\pi$
$984$		0			0
$985$	−34.9739	−	10.2693i	−1.11436	−	0.327206i
$986$		0			0
$987$	0.220534	−	1.53385i	0.00701967	−	0.0488229i
$988$		0			0
$989$	2.51193	−	2.92935i	0.0798746	−	0.0931480i
$990$		0			0
$991$	5.34064	−	37.1450i	0.169651	−	1.17995i	−0.709955	−	0.704247i	$-0.751285\pi$
$991$	5.34064	−	37.1450i	0.169651	−	1.17995i	0.879606	−	0.475703i	$-0.157806\pi$
$992$		0			0
$993$	24.1627	+	7.09480i	0.766779	+	0.225147i
$994$		0			0
$995$	−24.0807	+	7.07074i	−0.763410	+	0.224157i
$996$		0			0
$997$	−14.7224	+	32.2375i	−0.466263	+	1.02097i	0.519752	+	0.854317i	$0.326024\pi$
$997$	−14.7224	+	32.2375i	−0.466263	+	1.02097i	−0.986015	+	0.166656i	$0.946703\pi$
$998$		0			0
$999$	2.66280	−	1.71128i	0.0842472	−	0.0541424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.d.169.3	yes	30
23.3	even	11	inner	552.2.q.d.49.3	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.d.49.3	✓	30	23.3	even	11	inner
552.2.q.d.169.3	yes	30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{3} +(0.920354 + 1.06214i) q^{5} +(-3.86124 - 2.48147i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{3} +(0.920354 + 1.06214i) q^{5} +(-3.86124 - 2.48147i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(-0.178583 - 1.24207i) q^{11} +(-3.62146 + 2.32737i) q^{13} +(0.583832 - 1.27841i) q^{15} +(-3.37097 + 0.989806i) q^{17} +(-0.828102 - 0.243153i) q^{19} +(-0.653207 + 4.54315i) q^{21} +(-2.01477 - 4.35209i) q^{23} +(0.430474 - 2.99401i) q^{25} +(0.959493 + 0.281733i) q^{27} +(-0.901084 + 0.264582i) q^{29} +(-3.62070 + 7.92822i) q^{31} +(-1.05564 + 0.678421i) q^{33} +(-0.918029 - 6.38503i) q^{35} +(2.07281 - 2.39215i) q^{37} +(3.62146 + 2.32737i) q^{39} +(-5.66411 - 6.53673i) q^{41} +(0.334255 + 0.731917i) q^{43} -1.40542 q^{45} -0.337617 q^{47} +(5.84360 + 12.7957i) q^{49} +(2.30071 + 2.65516i) q^{51} +(-5.96078 - 3.83076i) q^{53} +(1.15490 - 1.33283i) q^{55} +(0.122827 + 0.854277i) q^{57} +(-4.99396 + 3.20942i) q^{59} +(-2.75838 + 6.04002i) q^{61} +(4.40395 - 1.29312i) q^{63} +(-5.80502 - 1.70451i) q^{65} +(1.63901 - 11.3995i) q^{67} +(-3.12184 + 3.64062i) q^{69} +(1.21442 - 8.44651i) q^{71} +(14.6178 + 4.29216i) q^{73} +(-2.90227 + 0.852184i) q^{75} +(-2.39262 + 5.23910i) q^{77} +(-9.38569 + 6.03182i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(3.65282 - 4.21558i) q^{83} +(-4.15380 - 2.66949i) q^{85} +(0.614996 + 0.709743i) q^{87} +(4.27501 + 9.36096i) q^{89} +19.7586 q^{91} +8.71585 q^{93} +(-0.503883 - 1.10335i) q^{95} +(-2.32141 - 2.67905i) q^{97} +(1.05564 + 0.678421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9	\( 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9} - 15 q^{11} - 5 q^{13} - 2 q^{15} + 9 q^{17} - 3 q^{19} + 7 q^{21} + 18 q^{23} - 19 q^{25} + 3 q^{27} - 21 q^{29} + 17 q^{31} - 7 q^{33} - 36 q^{35} + 9 q^{37} + 5 q^{39} + 18 q^{41} + 50 q^{43} + 2 q^{45} + 74 q^{47} - 17 q^{49} + 13 q^{51} + 43 q^{53} - 42 q^{55} - 8 q^{57} + 7 q^{59} - 10 q^{61} + 4 q^{63} - 4 q^{65} + 33 q^{67} + 15 q^{69} + 3 q^{71} + 30 q^{73} - 25 q^{75} - 82 q^{77} - 40 q^{79} - 3 q^{81} + 9 q^{83} - 54 q^{85} + 10 q^{87} + 25 q^{89} - 30 q^{91} + 38 q^{93} - 49 q^{95} - 69 q^{97} + 7 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9 - 15 * q^11 - 5 * q^13 - 2 * q^15 + 9 * q^17 - 3 * q^19 + 7 * q^21 + 18 * q^23 - 19 * q^25 + 3 * q^27 - 21 * q^29 + 17 * q^31 - 7 * q^33 - 36 * q^35 + 9 * q^37 + 5 * q^39 + 18 * q^41 + 50 * q^43 + 2 * q^45 + 74 * q^47 - 17 * q^49 + 13 * q^51 + 43 * q^53 - 42 * q^55 - 8 * q^57 + 7 * q^59 - 10 * q^61 + 4 * q^63 - 4 * q^65 + 33 * q^67 + 15 * q^69 + 3 * q^71 + 30 * q^73 - 25 * q^75 - 82 * q^77 - 40 * q^79 - 3 * q^81 + 9 * q^83 - 54 * q^85 + 10 * q^87 + 25 * q^89 - 30 * q^91 + 38 * q^93 - 49 * q^95 - 69 * q^97 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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