LMFDB - Embedded newform 552.2.q.a.193.2

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			193.2
Character	$\chi$	$=$	552.193
Dual form			552.2.q.a.409.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 - 0.755750i) q^{3} +(0.140637 + 0.978155i) q^{5} +(-1.46137 + 3.19994i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.654861 - 0.755750i) q^{3} +(0.140637 + 0.978155i) q^{5} +(-1.46137 + 3.19994i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-2.56792 - 0.754009i) q^{11} +(-2.78119 - 6.08995i) q^{13} +(0.647142 - 0.746842i) q^{15} +(-2.27588 - 1.46262i) q^{17} +(-3.51497 + 2.25894i) q^{19} +(3.37535 - 0.991091i) q^{21} +(-4.79553 + 0.0536132i) q^{23} +(3.86046 - 1.13353i) q^{25} +(0.841254 - 0.540641i) q^{27} +(-6.35703 - 4.08541i) q^{29} +(-1.84529 + 2.12958i) q^{31} +(1.11179 + 2.43447i) q^{33} +(-3.33556 - 0.979409i) q^{35} +(-1.16609 + 8.11031i) q^{37} +(-2.78119 + 6.08995i) q^{39} +(1.44358 + 10.0403i) q^{41} +(5.00415 + 5.77510i) q^{43} -0.988213 q^{45} -3.24988 q^{47} +(-3.52002 - 4.06233i) q^{49} +(0.385010 + 2.67781i) q^{51} +(5.25681 - 11.5108i) q^{53} +(0.376392 - 2.61786i) q^{55} +(4.00901 + 1.17715i) q^{57} +(-4.84553 - 10.6102i) q^{59} +(-7.57149 + 8.73797i) q^{61} +(-2.95940 - 1.90189i) q^{63} +(5.56578 - 3.57691i) q^{65} +(4.87902 - 1.43261i) q^{67} +(3.18092 + 3.58911i) q^{69} +(-9.33765 + 2.74178i) q^{71} +(11.2331 - 7.21905i) q^{73} +(-3.38473 - 2.17523i) q^{75} +(6.16545 - 7.11531i) q^{77} +(-0.111424 - 0.243984i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(0.0290859 - 0.202297i) q^{83} +(1.11059 - 2.43186i) q^{85} +(1.07542 + 7.47970i) q^{87} +(-0.0502774 - 0.0580232i) q^{89} +23.5518 q^{91} +2.81784 q^{93} +(-2.70393 - 3.12050i) q^{95} +(0.758963 + 5.27870i) q^{97} +(1.11179 - 2.43447i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9	$ 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9} - 15 q^{11} + 5 q^{13} - 15 q^{17} + 5 q^{19} + 9 q^{21} + 14 q^{23} + 5 q^{25} - 3 q^{27} + 13 q^{29} - 29 q^{31} - 15 q^{33} + 8 q^{35} - 3 q^{37} + 5 q^{39} + 24 q^{41} + 2 q^{43} + 22 q^{45} + 38 q^{47} + 15 q^{49} + 7 q^{51} - 7 q^{53} + 46 q^{55} - 6 q^{57} - 43 q^{59} - 22 q^{61} - 2 q^{63} + 44 q^{65} + 31 q^{67} + 3 q^{69} + 19 q^{71} - 50 q^{73} + 5 q^{75} + 16 q^{77} - 84 q^{79} - 3 q^{81} - 73 q^{83} - 8 q^{85} + 2 q^{87} + 19 q^{89} + 18 q^{91} + 26 q^{93} - 67 q^{95} - 29 q^{97} - 15 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9 - 15 * q^11 + 5 * q^13 - 15 * q^17 + 5 * q^19 + 9 * q^21 + 14 * q^23 + 5 * q^25 - 3 * q^27 + 13 * q^29 - 29 * q^31 - 15 * q^33 + 8 * q^35 - 3 * q^37 + 5 * q^39 + 24 * q^41 + 2 * q^43 + 22 * q^45 + 38 * q^47 + 15 * q^49 + 7 * q^51 - 7 * q^53 + 46 * q^55 - 6 * q^57 - 43 * q^59 - 22 * q^61 - 2 * q^63 + 44 * q^65 + 31 * q^67 + 3 * q^69 + 19 * q^71 - 50 * q^73 + 5 * q^75 + 16 * q^77 - 84 * q^79 - 3 * q^81 - 73 * q^83 - 8 * q^85 + 2 * q^87 + 19 * q^89 + 18 * q^91 + 26 * q^93 - 67 * q^95 - 29 * q^97 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$1$	$1$

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
$3$	−0.654861	−	0.755750i	−0.378084	−	0.436332i
$3$	−0.654861	−	0.755750i	−0.378084	−	0.436332i
$4$		0			0
$5$	0.140637	+	0.978155i	0.0628950	+	0.437444i	0.996801	+	0.0799251i	$0.0254681\pi$
$5$	0.140637	+	0.978155i	0.0628950	+	0.437444i	−0.933906	+	0.357519i	$0.883623\pi$
$6$		0			0
$7$	−1.46137	+	3.19994i	−0.552344	+	1.20946i	0.403334	+	0.915053i	$0.367851\pi$
$7$	−1.46137	+	3.19994i	−0.552344	+	1.20946i	−0.955679	+	0.294412i	$0.904876\pi$
$8$		0			0
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$		0			0
$11$	−2.56792	−	0.754009i	−0.774257	−	0.227342i	−0.129345	−	0.991600i	$-0.541288\pi$
$11$	−2.56792	−	0.754009i	−0.774257	−	0.227342i	−0.644911	+	0.764257i	$0.723106\pi$
$12$		0			0
$13$	−2.78119	−	6.08995i	−0.771363	−	1.68905i	−0.723629	−	0.690189i	$-0.757527\pi$
$13$	−2.78119	−	6.08995i	−0.771363	−	1.68905i	−0.0477338	−	0.998860i	$-0.515200\pi$
$14$		0			0
$15$	0.647142	−	0.746842i	0.167091	−	0.192834i
$16$		0			0
$17$	−2.27588	−	1.46262i	−0.551982	−	0.354737i	0.234727	−	0.972061i	$-0.424580\pi$
$17$	−2.27588	−	1.46262i	−0.551982	−	0.354737i	−0.786709	+	0.617324i	$0.788217\pi$
$18$		0			0
$19$	−3.51497	+	2.25894i	−0.806390	+	0.518235i	−0.877695	−	0.479219i	$-0.840920\pi$
$19$	−3.51497	+	2.25894i	−0.806390	+	0.518235i	0.0713052	+	0.997455i	$0.477284\pi$
$20$		0			0
$21$	3.37535	−	0.991091i	0.736561	−	0.216274i
$22$		0			0
$23$	−4.79553	+	0.0536132i	−0.999938	+	0.0111791i
$23$	−4.79553	+	0.0536132i	−0.999938	+	0.0111791i
$24$		0			0
$25$	3.86046	−	1.13353i	0.772091	−	0.226707i
$26$		0			0
$27$	0.841254	−	0.540641i	0.161899	−	0.104046i
$28$		0			0
$29$	−6.35703	−	4.08541i	−1.18047	−	0.758642i	−0.204997	−	0.978763i	$-0.565719\pi$
$29$	−6.35703	−	4.08541i	−1.18047	−	0.758642i	−0.975473	+	0.220121i	$0.929355\pi$
$30$		0			0
$31$	−1.84529	+	2.12958i	−0.331424	+	0.382484i	−0.896865	−	0.442305i	$-0.854161\pi$
$31$	−1.84529	+	2.12958i	−0.331424	+	0.382484i	0.565440	+	0.824789i	$0.308706\pi$
$32$		0			0
$33$	1.11179	+	2.43447i	0.193537	+	0.423788i
$34$		0			0
$35$	−3.33556	−	0.979409i	−0.563813	−	0.165550i
$36$		0			0
$37$	−1.16609	+	8.11031i	−0.191703	+	1.33333i	0.635795	+	0.771858i	$0.280672\pi$
$37$	−1.16609	+	8.11031i	−0.191703	+	1.33333i	−0.827498	+	0.561468i	$0.810237\pi$
$38$		0			0
$39$	−2.78119	+	6.08995i	−0.445347	+	0.975173i
$40$		0			0
$41$	1.44358	+	10.0403i	0.225449	+	1.56803i	0.716932	+	0.697144i	$0.245546\pi$
$41$	1.44358	+	10.0403i	0.225449	+	1.56803i	−0.491483	+	0.870887i	$0.663545\pi$
$42$		0			0
$43$	5.00415	+	5.77510i	0.763126	+	0.880694i	0.995771	−	0.0918676i	$-0.0292837\pi$
$43$	5.00415	+	5.77510i	0.763126	+	0.880694i	−0.232646	+	0.972562i	$0.574738\pi$
$44$		0			0
$45$	−0.988213			−0.147314
$46$		0			0
$47$	−3.24988			−0.474044			−0.237022	−	0.971504i	$-0.576171\pi$
$47$	−3.24988			−0.474044			−0.237022	+	0.971504i	$0.576171\pi$
$48$		0			0
$49$	−3.52002	−	4.06233i	−0.502861	−	0.580332i
$50$		0			0
$51$	0.385010	+	2.67781i	0.0539122	+	0.374968i
$52$		0			0
$53$	5.25681	−	11.5108i	0.722079	−	1.58113i	−0.0888889	−	0.996042i	$-0.528332\pi$
$53$	5.25681	−	11.5108i	0.722079	−	1.58113i	0.810968	−	0.585091i	$-0.198941\pi$
$54$		0			0
$55$	0.376392	−	2.61786i	0.0507527	−	0.352993i
$56$		0			0
$57$	4.00901	+	1.17715i	0.531006	+	0.155917i
$58$		0			0
$59$	−4.84553	−	10.6102i	−0.630834	−	1.38133i	−0.907371	−	0.420331i	$-0.861914\pi$
$59$	−4.84553	−	10.6102i	−0.630834	−	1.38133i	0.276536	−	0.961003i	$-0.410813\pi$
$60$		0			0
$61$	−7.57149	+	8.73797i	−0.969430	+	1.11878i	0.0234572	+	0.999725i	$0.492533\pi$
$61$	−7.57149	+	8.73797i	−0.969430	+	1.11878i	−0.992887	+	0.119057i	$0.962013\pi$
$62$		0			0
$63$	−2.95940	−	1.90189i	−0.372849	−	0.239616i
$64$		0			0
$65$	5.56578	−	3.57691i	0.690350	−	0.443661i
$66$		0			0
$67$	4.87902	−	1.43261i	0.596067	−	0.175021i	0.0302369	−	0.999543i	$-0.490374\pi$
$67$	4.87902	−	1.43261i	0.596067	−	0.175021i	0.565831	+	0.824522i	$0.308556\pi$
$68$		0			0
$69$	3.18092	+	3.58911i	0.382938	+	0.432078i
$70$		0			0
$71$	−9.33765	+	2.74178i	−1.10817	+	0.325389i	−0.784095	−	0.620640i	$-0.786873\pi$
$71$	−9.33765	+	2.74178i	−1.10817	+	0.325389i	−0.324079	+	0.946030i	$0.605055\pi$
$72$		0			0
$73$	11.2331	−	7.21905i	1.31473	−	0.844926i	0.319997	−	0.947419i	$-0.396318\pi$
$73$	11.2331	−	7.21905i	1.31473	−	0.844926i	0.994734	+	0.102492i	$0.0326817\pi$
$74$		0			0
$75$	−3.38473	−	2.17523i	−0.390835	−	0.251174i
$76$		0			0
$77$	6.16545	−	7.11531i	0.702619	−	0.810865i
$78$		0			0
$79$	−0.111424	−	0.243984i	−0.0125362	−	0.0274504i	0.903260	−	0.429093i	$-0.141167\pi$
$79$	−0.111424	−	0.243984i	−0.0125362	−	0.0274504i	−0.915797	+	0.401643i	$0.868439\pi$
$80$		0			0
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$		0			0
$83$	0.0290859	−	0.202297i	0.00319259	−	0.0222050i	−0.988163	−	0.153408i	$-0.950975\pi$
$83$	0.0290859	−	0.202297i	0.00319259	−	0.0222050i	0.991355	+	0.131203i	$0.0418841\pi$
$84$		0			0
$85$	1.11059	−	2.43186i	0.120461	−	0.263772i
$86$		0			0
$87$	1.07542	+	7.47970i	0.115297	+	0.801908i
$88$		0			0
$89$	−0.0502774	−	0.0580232i	−0.00532939	−	0.00615044i	0.753079	−	0.657931i	$-0.228568\pi$
$89$	−0.0502774	−	0.0580232i	−0.00532939	−	0.00615044i	−0.758408	+	0.651780i	$0.774023\pi$
$90$		0			0
$91$	23.5518			2.46890
$92$		0			0
$93$	2.81784			0.292196
$94$		0			0
$95$	−2.70393	−	3.12050i	−0.277417	−	0.320156i
$96$		0			0
$97$	0.758963	+	5.27870i	0.0770610	+	0.535971i	0.991384	+	0.130986i	$0.0418142\pi$
$97$	0.758963	+	5.27870i	0.0770610	+	0.535971i	−0.914323	+	0.404985i	$0.867277\pi$
$98$		0			0
$99$	1.11179	−	2.43447i	0.111739	−	0.244674i
$100$		0			0
$101$	−0.272469	+	1.89506i	−0.0271116	+	0.188566i	−0.998877	−	0.0473850i	$-0.984911\pi$
$101$	−0.272469	+	1.89506i	−0.0271116	+	0.188566i	0.971765	+	0.235951i	$0.0758203\pi$
$102$		0			0
$103$	−8.93565	−	2.62374i	−0.880456	−	0.258525i	−0.189899	−	0.981804i	$-0.560816\pi$
$103$	−8.93565	−	2.62374i	−0.880456	−	0.258525i	−0.690557	+	0.723278i	$0.742634\pi$
$104$		0			0
$105$	1.44414	+	3.16223i	0.140934	+	0.308602i
$106$		0			0
$107$	2.47357	−	2.85465i	0.239129	−	0.275970i	−0.623482	−	0.781838i	$-0.714282\pi$
$107$	2.47357	−	2.85465i	0.239129	−	0.275970i	0.862611	+	0.505868i	$0.168828\pi$
$108$		0			0
$109$	8.53625	+	5.48591i	0.817624	+	0.525455i	0.881323	−	0.472514i	$-0.156653\pi$
$109$	8.53625	+	5.48591i	0.817624	+	0.525455i	−0.0636989	+	0.997969i	$0.520290\pi$
$110$		0			0
$111$	6.89299	−	4.42985i	0.654253	−	0.420463i
$112$		0			0
$113$	−11.9422	+	3.50655i	−1.12343	+	0.329869i	−0.790122	−	0.612950i	$-0.789983\pi$
$113$	−11.9422	+	3.50655i	−1.12343	+	0.329869i	−0.333307	+	0.942818i	$0.608165\pi$
$114$		0			0
$115$	−0.726873	−	4.68323i	−0.0677813	−	0.436714i
$116$		0			0
$117$	6.42377	−	1.88619i	0.593878	−	0.174378i
$118$		0			0
$119$	8.00619	−	5.14526i	0.733926	−	0.471665i
$120$		0			0
$121$	−3.22811	−	2.07458i	−0.293465	−	0.188598i
$122$		0			0
$123$	6.64261	−	7.66598i	0.598944	−	0.691218i
$124$		0			0
$125$	3.70429	+	8.11126i	0.331322	+	0.725493i
$126$		0			0
$127$	17.7320	+	5.20659i	1.57346	+	0.462010i	0.948006	−	0.318251i	$-0.103095\pi$
$127$	17.7320	+	5.20659i	1.57346	+	0.462010i	0.625454	+	0.780261i	$0.284914\pi$
$128$		0			0
$129$	1.08751	−	7.56377i	0.0957495	−	0.665953i
$130$		0			0
$131$	−3.18111	+	6.96566i	−0.277935	+	0.608593i	−0.996192	−	0.0871849i	$-0.972213\pi$
$131$	−3.18111	+	6.96566i	−0.277935	+	0.608593i	0.718257	+	0.695778i	$0.244940\pi$
$132$		0			0
$133$	−2.09181	−	14.5488i	−0.181383	−	1.26154i
$134$		0			0
$135$	0.647142	+	0.746842i	0.0556971	+	0.0642779i
$136$		0			0
$137$	−5.56006			−0.475028			−0.237514	−	0.971384i	$-0.576333\pi$
$137$	−5.56006			−0.475028			−0.237514	+	0.971384i	$0.576333\pi$
$138$		0			0
$139$	−1.39414			−0.118250			−0.0591248	−	0.998251i	$-0.518831\pi$
$139$	−1.39414			−0.118250			−0.0591248	+	0.998251i	$0.518831\pi$
$140$		0			0
$141$	2.12822	+	2.45610i	0.179228	+	0.206841i
$142$		0			0
$143$	2.54999	+	17.7355i	0.213241	+	1.48312i
$144$		0			0
$145$	3.10213	−	6.79272i	0.257618	−	0.564104i
$146$		0			0
$147$	−0.764975	+	5.32051i	−0.0630940	+	0.438829i
$148$		0			0
$149$	15.4249	+	4.52915i	1.26366	+	0.371043i	0.843854	−	0.536573i	$-0.180281\pi$
$149$	15.4249	+	4.52915i	1.26366	+	0.371043i	0.419802	+	0.907616i	$0.362100\pi$
$150$		0			0
$151$	−0.893752	−	1.95704i	−0.0727325	−	0.159262i	0.869774	−	0.493451i	$-0.164265\pi$
$151$	−0.893752	−	1.95704i	−0.0727325	−	0.159262i	−0.942506	+	0.334189i	$0.891538\pi$
$152$		0			0
$153$	1.77162	−	2.04456i	0.143227	−	0.165293i
$154$		0			0
$155$	−2.34258	−	1.50548i	−0.188160	−	0.120923i
$156$		0			0
$157$	3.50862	−	2.25485i	0.280018	−	0.179957i	−0.393092	−	0.919499i	$-0.628594\pi$
$157$	3.50862	−	2.25485i	0.280018	−	0.179957i	0.673110	+	0.739542i	$0.264958\pi$
$158$		0			0
$159$	−12.1418	+	3.56515i	−0.962905	+	0.282735i
$160$		0			0
$161$	6.83646	−	15.4238i	0.538789	−	1.21556i
$162$		0			0
$163$	4.16404	−	1.22267i	0.326153	−	0.0957671i	−0.114557	−	0.993417i	$-0.536545\pi$
$163$	4.16404	−	1.22267i	0.326153	−	0.0957671i	0.440710	+	0.897650i	$0.354727\pi$
$164$		0			0
$165$	−2.22493	+	1.42988i	−0.173211	+	0.111316i
$166$		0			0
$167$	8.09678	+	5.20348i	0.626547	+	0.402658i	0.815030	−	0.579419i	$-0.196721\pi$
$167$	8.09678	+	5.20348i	0.626547	+	0.402658i	−0.188482	+	0.982077i	$0.560357\pi$
$168$		0			0
$169$	−20.8393	+	24.0499i	−1.60303	+	1.84999i
$170$		0			0
$171$	−1.73571	−	3.80068i	−0.132733	−	0.290645i
$172$		0			0
$173$	−9.63446	−	2.82893i	−0.732495	−	0.215080i	−0.105847	−	0.994382i	$-0.533755\pi$
$173$	−9.63446	−	2.82893i	−0.732495	−	0.215080i	−0.626648	+	0.779303i	$0.715574\pi$
$174$		0			0
$175$	−2.01430	+	14.0098i	−0.152267	+	1.05904i
$176$		0			0
$177$	−4.84553	+	10.6102i	−0.364212	+	0.797514i
$178$		0			0
$179$	−2.61293	−	18.1733i	−0.195299	−	1.35834i	−0.817703	−	0.575641i	$-0.804753\pi$
$179$	−2.61293	−	18.1733i	−0.195299	−	1.35834i	0.622403	−	0.782697i	$-0.286156\pi$
$180$		0			0
$181$	−10.9012	−	12.5806i	−0.810277	−	0.935109i	0.188621	−	0.982050i	$-0.439598\pi$
$181$	−10.9012	−	12.5806i	−0.810277	−	0.935109i	−0.998898	+	0.0469407i	$0.985053\pi$
$182$		0			0
$183$	11.5620			0.854687
$184$		0			0
$185$	−8.09713			−0.595313
$186$		0			0
$187$	4.74144	+	5.47192i	0.346729	+	0.400146i
$188$		0			0
$189$	0.500641	+	3.48204i	0.0364163	+	0.253281i
$190$		0			0
$191$	−1.56519	+	3.42729i	−0.113253	+	0.247990i	−0.957768	−	0.287543i	$-0.907162\pi$
$191$	−1.56519	+	3.42729i	−0.113253	+	0.247990i	0.844515	+	0.535532i	$0.179889\pi$
$192$		0			0
$193$	−1.00573	+	6.99500i	−0.0723939	+	0.503511i	0.921073	+	0.389390i	$0.127314\pi$
$193$	−1.00573	+	6.99500i	−0.0723939	+	0.503511i	−0.993467	+	0.114121i	$0.963595\pi$
$194$		0			0
$195$	−6.34805	−	1.86396i	−0.454594	−	0.133481i
$196$		0			0
$197$	−3.41105	−	7.46917i	−0.243028	−	0.532156i	0.748333	−	0.663324i	$-0.230855\pi$
$197$	−3.41105	−	7.46917i	−0.243028	−	0.532156i	−0.991360	+	0.131168i	$0.958127\pi$
$198$		0			0
$199$	−12.5320	+	14.4627i	−0.888372	+	1.02524i	0.111134	+	0.993805i	$0.464552\pi$
$199$	−12.5320	+	14.4627i	−0.888372	+	1.02524i	−0.999506	+	0.0314305i	$0.989994\pi$
$200$		0			0
$201$	−4.27777	−	2.74916i	−0.301731	−	0.193911i
$202$		0			0
$203$	22.3630	−	14.3718i	1.56958	−	1.00871i
$204$		0			0
$205$	−9.61794	+	2.82408i	−0.671746	+	0.197242i
$206$		0			0
$207$	0.629408	−	4.75435i	0.0437469	−	0.330450i
$208$		0			0
$209$	10.7294	−	3.15044i	0.742170	−	0.217921i
$210$		0			0
$211$	19.9634	−	12.8297i	1.37434	−	0.883232i	0.375290	−	0.926907i	$-0.377543\pi$
$211$	19.9634	−	12.8297i	1.37434	−	0.883232i	0.999046	+	0.0436755i	$0.0139068\pi$
$212$		0			0
$213$	8.18696	+	5.26144i	0.560961	+	0.360508i
$214$		0			0
$215$	−4.94517	+	5.70703i	−0.337258	+	0.389216i
$216$		0			0
$217$	−4.11789	−	9.01692i	−0.279541	−	0.612109i
$218$		0			0
$219$	−12.8119	−	3.76191i	−0.865747	−	0.254206i
$220$		0			0
$221$	−2.57763	+	17.9278i	−0.173390	+	1.20596i
$222$		0			0
$223$	−1.04380	+	2.28561i	−0.0698983	+	0.153056i	−0.941356	−	0.337414i	$-0.890448\pi$
$223$	−1.04380	+	2.28561i	−0.0698983	+	0.153056i	0.871458	+	0.490470i	$0.163175\pi$
$224$		0			0
$225$	0.572594	+	3.98248i	0.0381730	+	0.265499i
$226$		0			0
$227$	−11.9884	−	13.8354i	−0.795701	−	0.918288i	0.202437	−	0.979295i	$-0.435114\pi$
$227$	−11.9884	−	13.8354i	−0.795701	−	0.918288i	−0.998137	+	0.0610077i	$0.980569\pi$
$228$		0			0
$229$	−20.7105			−1.36859			−0.684293	−	0.729207i	$-0.739889\pi$
$229$	−20.7105			−1.36859			−0.684293	+	0.729207i	$0.739889\pi$
$230$		0			0
$231$	−9.41491			−0.619456
$232$		0			0
$233$	9.35257	+	10.7934i	0.612707	+	0.707102i	0.974305	−	0.225232i	$-0.0723142\pi$
$233$	9.35257	+	10.7934i	0.612707	+	0.707102i	−0.361598	+	0.932334i	$0.617769\pi$
$234$		0			0
$235$	−0.457055	−	3.17888i	−0.0298150	−	0.207368i
$236$		0			0
$237$	−0.111424	+	0.243984i	−0.00723776	+	0.0158485i
$238$		0			0
$239$	0.229732	−	1.59782i	0.0148601	−	0.103354i	−0.981041	−	0.193798i	$-0.937919\pi$
$239$	0.229732	−	1.59782i	0.0148601	−	0.103354i	0.995902	+	0.0904436i	$0.0288285\pi$
$240$		0			0
$241$	1.98713	+	0.583475i	0.128003	+	0.0375850i	0.345106	−	0.938564i	$-0.387843\pi$
$241$	1.98713	+	0.583475i	0.128003	+	0.0375850i	−0.217104	+	0.976149i	$0.569661\pi$
$242$		0			0
$243$	0.415415	+	0.909632i	0.0266489	+	0.0583529i
$244$		0			0
$245$	3.47854	−	4.01444i	0.222235	−	0.256473i
$246$		0			0
$247$	23.5326	+	15.1235i	1.49734	+	0.962285i
$248$		0			0
$249$	−0.171933	+	0.110495i	−0.0108958	+	0.00700232i
$250$		0			0
$251$	14.1573	−	4.15697i	0.893604	−	0.262386i	0.197479	−	0.980307i	$-0.436724\pi$
$251$	14.1573	−	4.15697i	0.893604	−	0.262386i	0.696124	+	0.717921i	$0.254906\pi$
$252$		0			0
$253$	12.3550	+	3.47820i	0.776750	+	0.218673i
$254$		0			0
$255$	−2.56516	+	0.753199i	−0.160637	+	0.0471672i
$256$		0			0
$257$	−12.2586	+	7.87814i	−0.764672	+	0.491425i	−0.863914	−	0.503639i	$-0.831994\pi$
$257$	−12.2586	+	7.87814i	−0.764672	+	0.491425i	0.0992428	+	0.995063i	$0.468358\pi$
$258$		0			0
$259$	−24.2485	−	15.5835i	−1.50673	−	0.968314i
$260$		0			0
$261$	4.94853	−	5.71091i	0.306306	−	0.353496i
$262$		0			0
$263$	3.81210	+	8.34734i	0.235064	+	0.514719i	0.989998	−	0.141082i	$-0.0450582\pi$
$263$	3.81210	+	8.34734i	0.235064	+	0.514719i	−0.754934	+	0.655801i	$0.772331\pi$
$264$		0			0
$265$	11.9987	+	3.52313i	0.737072	+	0.216424i
$266$		0			0
$267$	−0.0109263	+	0.0759942i	−0.000668679	+	0.00465077i
$268$		0			0
$269$	−10.1523	+	22.2304i	−0.618996	+	1.35541i	0.297251	+	0.954799i	$0.403930\pi$
$269$	−10.1523	+	22.2304i	−0.618996	+	1.35541i	−0.916247	+	0.400613i	$0.868797\pi$
$270$		0			0
$271$	−4.08598	−	28.4186i	−0.248205	−	1.72631i	−0.608575	−	0.793496i	$-0.708259\pi$
$271$	−4.08598	−	28.4186i	−0.248205	−	1.72631i	0.360370	−	0.932810i	$-0.382651\pi$
$272$		0			0
$273$	−15.4232	−	17.7993i	−0.933453	−	1.07726i
$274$		0			0
$275$	−10.7680			−0.649337
$276$		0			0
$277$	−29.8731			−1.79490			−0.897450	−	0.441117i	$-0.854583\pi$
$277$	−29.8731			−1.79490			−0.897450	+	0.441117i	$0.854583\pi$
$278$		0			0
$279$	−1.84529	−	2.12958i	−0.110475	−	0.127495i
$280$		0			0
$281$	1.17830	+	8.19527i	0.0702916	+	0.488889i	0.994309	+	0.106537i	$0.0339764\pi$
$281$	1.17830	+	8.19527i	0.0702916	+	0.488889i	−0.924017	+	0.382351i	$0.875114\pi$
$282$		0			0
$283$	−1.61516	+	3.53670i	−0.0960111	+	0.210235i	−0.951543	−	0.307514i	$-0.900503\pi$
$283$	−1.61516	+	3.53670i	−0.0960111	+	0.210235i	0.855532	+	0.517749i	$0.173230\pi$
$284$		0			0
$285$	−0.587619	+	4.08698i	−0.0348076	+	0.242092i
$286$		0			0
$287$	−34.2380	−	10.0532i	−2.02100	−	0.593420i
$288$		0			0
$289$	−4.02168	−	8.80626i	−0.236570	−	0.518015i
$290$		0			0
$291$	3.49236	−	4.03040i	0.204726	−	0.236266i
$292$		0			0
$293$	9.34886	+	6.00815i	0.546166	+	0.351000i	0.784446	−	0.620197i	$-0.212947\pi$
$293$	9.34886	+	6.00815i	0.546166	+	0.351000i	−0.238280	+	0.971196i	$0.576584\pi$
$294$		0			0
$295$	9.69698	−	6.23187i	0.564580	−	0.362834i
$296$		0			0
$297$	−2.56792	+	0.754009i	−0.149006	+	0.0437520i
$298$		0			0
$299$	13.6638	+	29.0555i	0.790197	+	1.68032i
$300$		0			0
$301$	−25.7929	+	7.57347i	−1.48668	+	0.436528i
$302$		0			0
$303$	1.61062	−	1.03508i	0.0925277	−	0.0594640i
$304$		0			0
$305$	−9.61192	−	6.17720i	−0.550377	−	0.353706i
$306$		0			0
$307$	3.59849	−	4.15288i	0.205376	−	0.237017i	−0.643712	−	0.765268i	$-0.722606\pi$
$307$	3.59849	−	4.15288i	0.205376	−	0.237017i	0.849088	+	0.528251i	$0.177152\pi$
$308$		0			0
$309$	3.86871	+	8.47130i	0.220083	+	0.481915i
$310$		0			0
$311$	−12.9732	−	3.80929i	−0.735645	−	0.216005i	−0.107614	−	0.994193i	$-0.534321\pi$
$311$	−12.9732	−	3.80929i	−0.735645	−	0.216005i	−0.628032	+	0.778188i	$0.716139\pi$
$312$		0			0
$313$	3.26996	−	22.7431i	0.184829	−	1.28552i	−0.660319	−	0.750985i	$-0.729579\pi$
$313$	3.26996	−	22.7431i	0.184829	−	1.28552i	0.845149	−	0.534531i	$-0.179512\pi$
$314$		0			0
$315$	1.44414	−	3.16223i	0.0813681	−	0.178171i
$316$		0			0
$317$	−0.461835	−	3.21214i	−0.0259393	−	0.180412i	0.972733	−	0.231928i	$-0.0745035\pi$
$317$	−0.461835	−	3.21214i	−0.0259393	−	0.180412i	−0.998672	+	0.0515168i	$0.983594\pi$
$318$		0			0
$319$	13.2439	+	15.2843i	0.741515	+	0.855754i
$320$		0			0
$321$	−3.77724			−0.210825
$322$		0			0
$323$	11.3036			0.628950
$324$		0			0
$325$	−17.6398	−	20.3574i	−0.978481	−	1.12923i
$326$		0			0
$327$	−1.44408	−	10.0438i	−0.0798576	−	0.555422i
$328$		0			0
$329$	4.74926	−	10.3994i	0.261835	−	0.573339i
$330$		0			0
$331$	−2.90410	+	20.1984i	−0.159624	+	1.11021i	0.739705	+	0.672932i	$0.234965\pi$
$331$	−2.90410	+	20.1984i	−0.159624	+	1.11021i	−0.899328	+	0.437274i	$0.855944\pi$
$332$		0			0
$333$	−7.86181	−	2.30843i	−0.430824	−	0.126501i
$334$		0			0
$335$	2.08749	+	4.57096i	0.114052	+	0.249738i
$336$		0			0
$337$	8.78876	−	10.1428i	0.478754	−	0.552512i	−0.464072	−	0.885798i	$-0.653612\pi$
$337$	8.78876	−	10.1428i	0.478754	−	0.552512i	0.942826	+	0.333286i	$0.108157\pi$
$338$		0			0
$339$	10.4706	+	6.72902i	0.568683	+	0.365470i
$340$		0			0
$341$	6.34428	−	4.07722i	0.343562	−	0.220794i
$342$		0			0
$343$	−5.48417	+	1.61030i	−0.296117	+	0.0869479i
$344$		0			0
$345$	−3.06335	+	3.61620i	−0.164925	+	0.194690i
$346$		0			0
$347$	13.3371	−	3.91612i	0.715971	−	0.210228i	0.0965965	−	0.995324i	$-0.469204\pi$
$347$	13.3371	−	3.91612i	0.715971	−	0.210228i	0.619375	+	0.785095i	$0.287386\pi$
$348$		0			0
$349$	−3.60710	+	2.31814i	−0.193083	+	0.124087i	−0.633611	−	0.773652i	$-0.718428\pi$
$349$	−3.60710	+	2.31814i	−0.193083	+	0.124087i	0.440527	+	0.897739i	$0.354792\pi$
$350$		0			0
$351$	−5.63216	−	3.61957i	−0.300623	−	0.193198i
$352$		0			0
$353$	−0.801481	+	0.924959i	−0.0426586	+	0.0492306i	−0.776678	−	0.629898i	$-0.783097\pi$
$353$	−0.801481	+	0.924959i	−0.0426586	+	0.0492306i	0.734019	+	0.679129i	$0.237642\pi$
$354$		0			0
$355$	−3.99511	−	8.74806i	−0.212038	−	0.464299i
$356$		0			0
$357$	−9.13147	−	2.68124i	−0.483288	−	0.141906i
$358$		0			0
$359$	−3.31893	+	23.0836i	−0.175166	+	1.21831i	0.692595	+	0.721327i	$0.256467\pi$
$359$	−3.31893	+	23.0836i	−0.175166	+	1.21831i	−0.867761	+	0.496981i	$0.834442\pi$
$360$		0			0
$361$	−0.640642	+	1.40281i	−0.0337180	+	0.0738322i
$362$		0			0
$363$	0.546099	+	3.79820i	0.0286628	+	0.199354i
$364$		0			0
$365$	8.64114	+	9.97241i	0.452298	+	0.521980i
$366$		0			0
$367$	−29.7120			−1.55095			−0.775477	−	0.631376i	$-0.782490\pi$
$367$	−29.7120			−1.55095			−0.775477	+	0.631376i	$0.782490\pi$
$368$		0			0
$369$	−10.1435			−0.528052
$370$		0			0
$371$	29.1518	+	33.6430i	1.51349	+	1.74666i
$372$		0			0
$373$	1.21649	+	8.46090i	0.0629877	+	0.438089i	0.996774	+	0.0802581i	$0.0255744\pi$
$373$	1.21649	+	8.46090i	0.0629877	+	0.438089i	−0.933786	+	0.357831i	$0.883516\pi$
$374$		0			0
$375$	3.70429	−	8.11126i	0.191289	−	0.418864i
$376$		0			0
$377$	−7.19988	+	50.0763i	−0.370813	+	2.57906i
$378$		0			0
$379$	−33.8464	−	9.93820i	−1.73857	−	0.510491i	−0.750027	−	0.661407i	$-0.769959\pi$
$379$	−33.8464	−	9.93820i	−1.73857	−	0.510491i	−0.988547	+	0.150916i	$0.951778\pi$
$380$		0			0
$381$	−7.67712	−	16.8105i	−0.393311	−	0.861230i
$382$		0			0
$383$	23.7847	−	27.4490i	1.21534	−	1.40258i	0.325976	−	0.945378i	$-0.394307\pi$
$383$	23.7847	−	27.4490i	1.21534	−	1.40258i	0.889364	−	0.457199i	$-0.151147\pi$
$384$		0			0
$385$	7.82697	+	5.03009i	0.398899	+	0.256357i
$386$		0			0
$387$	−6.42848	+	4.13133i	−0.326778	+	0.210007i
$388$		0			0
$389$	−31.5424	+	9.26168i	−1.59926	+	0.469586i	−0.955341	−	0.295506i	$-0.904512\pi$
$389$	−31.5424	+	9.26168i	−1.59926	+	0.469586i	−0.643921	+	0.765092i	$0.722693\pi$
$390$		0			0
$391$	10.9925	+	6.89202i	0.555913	+	0.348544i
$392$		0			0
$393$	7.34748	−	2.15742i	0.370631	−	0.108827i
$394$		0			0
$395$	0.222984	−	0.143303i	0.0112195	−	0.00721037i
$396$		0			0
$397$	24.8126	+	15.9461i	1.24531	+	0.800311i	0.986203	−	0.165538i	$-0.0529360\pi$
$397$	24.8126	+	15.9461i	1.24531	+	0.800311i	0.259105	+	0.965849i	$0.416572\pi$
$398$		0			0
$399$	−9.62544	+	11.1084i	−0.481875	+	0.556113i
$400$		0			0
$401$	−3.08219	−	6.74905i	−0.153917	−	0.337032i	0.816928	−	0.576740i	$-0.195675\pi$
$401$	−3.08219	−	6.74905i	−0.153917	−	0.337032i	−0.970845	+	0.239708i	$0.922948\pi$
$402$		0			0
$403$	18.1011	+	5.31498i	0.901682	+	0.264758i
$404$		0			0
$405$	0.140637	−	0.978155i	0.00698833	−	0.0486049i
$406$		0			0
$407$	9.10966	−	19.9474i	0.451549	−	0.988755i
$408$		0			0
$409$	1.82996	+	12.7276i	0.0904855	+	0.629341i	0.983714	+	0.179739i	$0.0575252\pi$
$409$	1.82996	+	12.7276i	0.0904855	+	0.629341i	−0.893229	+	0.449602i	$0.851566\pi$
$410$		0			0
$411$	3.64107	+	4.20202i	0.179601	+	0.207270i
$412$		0			0
$413$	41.0332			2.01911
$414$		0			0
$415$	0.201968			0.00991423
$416$		0			0
$417$	0.912969	+	1.05362i	0.0447083	+	0.0515961i
$418$		0			0
$419$	0.881670	+	6.13215i	0.0430724	+	0.299575i	0.999958	+	0.00911171i	$0.00290039\pi$
$419$	0.881670	+	6.13215i	0.0430724	+	0.299575i	−0.956886	+	0.290463i	$0.906191\pi$
$420$		0			0
$421$	−3.36983	+	7.37889i	−0.164235	+	0.359625i	−0.973800	−	0.227405i	$-0.926976\pi$
$421$	−3.36983	+	7.37889i	−0.164235	+	0.359625i	0.809565	+	0.587030i	$0.199703\pi$
$422$		0			0
$423$	0.462506	−	3.21680i	0.0224878	−	0.156406i
$424$		0			0
$425$	−10.4439	−	3.06659i	−0.506602	−	0.148752i
$426$		0			0
$427$	−16.8963	−	36.9977i	−0.817669	−	1.79044i
$428$		0			0
$429$	11.7337	−	13.5415i	0.566511	−	0.653788i
$430$		0			0
$431$	16.8562	+	10.8328i	0.811934	+	0.521798i	0.879490	−	0.475917i	$-0.157884\pi$
$431$	16.8562	+	10.8328i	0.811934	+	0.521798i	−0.0675559	+	0.997715i	$0.521520\pi$
$432$		0			0
$433$	19.1447	−	12.3036i	0.920037	−	0.591272i	0.00736833	−	0.999973i	$-0.497655\pi$
$433$	19.1447	−	12.3036i	0.920037	−	0.591272i	0.912668	+	0.408701i	$0.134018\pi$
$434$		0			0
$435$	−7.16505	+	2.10385i	−0.343538	+	0.100872i
$436$		0			0
$437$	16.7351	−	11.0212i	0.800546	−	0.527218i
$438$		0			0
$439$	−9.94984	+	2.92154i	−0.474880	+	0.139437i	−0.510410	−	0.859931i	$-0.670506\pi$
$439$	−9.94984	+	2.92154i	−0.474880	+	0.139437i	0.0355298	+	0.999369i	$0.488688\pi$
$440$		0			0
$441$	4.52193	−	2.90607i	0.215330	−	0.138384i
$442$		0			0
$443$	−7.91872	−	5.08905i	−0.376230	−	0.241788i	0.338836	−	0.940845i	$-0.389967\pi$
$443$	−7.91872	−	5.08905i	−0.376230	−	0.241788i	−0.715066	+	0.699057i	$0.753603\pi$
$444$		0			0
$445$	0.0496847	−	0.0573392i	0.00235528	−	0.00271814i
$446$		0			0
$447$	−6.67824	−	14.6233i	−0.315870	−	0.691659i
$448$		0			0
$449$	2.66953	+	0.783845i	0.125983	+	0.0369920i	0.344116	−	0.938927i	$-0.388179\pi$
$449$	2.66953	+	0.783845i	0.125983	+	0.0369920i	−0.218133	+	0.975919i	$0.569997\pi$
$450$		0			0
$451$	3.86349	−	26.8711i	0.181924	−	1.26531i
$452$		0			0
$453$	−0.893752	+	1.95704i	−0.0419921	+	0.0919499i
$454$		0			0
$455$	3.31227	+	23.0373i	0.155282	+	1.08001i
$456$		0			0
$457$	0.552335	+	0.637428i	0.0258371	+	0.0298176i	0.768521	−	0.639824i	$-0.220993\pi$
$457$	0.552335	+	0.637428i	0.0258371	+	0.0298176i	−0.742684	+	0.669642i	$0.766448\pi$
$458$		0			0
$459$	−2.70534			−0.126275
$460$		0			0
$461$	4.27505			0.199109			0.0995544	−	0.995032i	$-0.468258\pi$
$461$	4.27505			0.199109			0.0995544	+	0.995032i	$0.468258\pi$
$462$		0			0
$463$	−14.4169	−	16.6380i	−0.670010	−	0.773233i	0.314368	−	0.949301i	$-0.398207\pi$
$463$	−14.4169	−	16.6380i	−0.670010	−	0.773233i	−0.984378	+	0.176068i	$0.943662\pi$
$464$		0			0
$465$	0.396293	+	2.75628i	0.0183777	+	0.127820i
$466$		0			0
$467$	11.1976	−	24.5193i	0.518162	−	1.13462i	−0.451968	−	0.892034i	$-0.649278\pi$
$467$	11.1976	−	24.5193i	0.518162	−	1.13462i	0.970131	−	0.242583i	$-0.0779948\pi$
$468$		0			0
$469$	−2.54576	+	17.7062i	−0.117552	+	0.817595i
$470$		0			0
$471$	−4.00176	−	1.17502i	−0.184391	−	0.0541422i
$472$		0			0
$473$	−8.49578	−	18.6032i	−0.390636	−	0.855374i
$474$		0			0
$475$	−11.0088	+	12.7049i	−0.505120	+	0.582939i
$476$		0			0
$477$	10.6455	+	6.84147i	0.487425	+	0.313249i
$478$		0			0
$479$	−22.8407	+	14.6788i	−1.04362	+	0.670693i	−0.945879	−	0.324519i	$-0.894798\pi$
$479$	−22.8407	+	14.6788i	−1.04362	+	0.670693i	−0.0977396	+	0.995212i	$0.531161\pi$
$480$		0			0
$481$	52.6345	−	15.4549i	2.39993	−	0.704682i
$482$		0			0
$483$	−16.1334	+	4.93377i	−0.734097	+	0.224494i
$484$		0			0
$485$	−5.05665	+	1.48477i	−0.229611	+	0.0674197i
$486$		0			0
$487$	−1.28138	+	0.823492i	−0.0580648	+	0.0373160i	−0.569351	−	0.822094i	$-0.692806\pi$
$487$	−1.28138	+	0.823492i	−0.0580648	+	0.0373160i	0.511286	+	0.859410i	$0.329169\pi$
$488$		0			0
$489$	−3.65090	−	2.34629i	−0.165099	−	0.106103i
$490$		0			0
$491$	−17.2597	+	19.9187i	−0.778917	+	0.898919i	−0.997031	−	0.0770048i	$-0.975464\pi$
$491$	−17.2597	+	19.9187i	−0.778917	+	0.898919i	0.218113	+	0.975923i	$0.430010\pi$
$492$		0			0
$493$	8.49242	+	18.5958i	0.382479	+	0.837513i
$494$		0			0
$495$	2.53765	+	0.745122i	0.114059	+	0.0334907i
$496$		0			0
$497$	4.87217	−	33.8867i	0.218547	−	1.52003i
$498$		0			0
$499$	7.50494	−	16.4335i	0.335967	−	0.735665i	−0.663960	−	0.747768i	$-0.731125\pi$
$499$	7.50494	−	16.4335i	0.335967	−	0.735665i	0.999927	+	0.0121031i	$0.00385262\pi$
$500$		0			0
$501$	−1.36973	−	9.52669i	−0.0611951	−	0.425621i
$502$		0			0
$503$	−10.6843	−	12.3304i	−0.476391	−	0.549784i	0.465787	−	0.884897i	$-0.345771\pi$
$503$	−10.6843	−	12.3304i	−0.476391	−	0.549784i	−0.942178	+	0.335112i	$0.891226\pi$
$504$		0			0
$505$	−1.89198			−0.0841921
$506$		0			0
$507$	31.8225			1.41329
$508$		0			0
$509$	−0.568106	−	0.655629i	−0.0251809	−	0.0290603i	0.743019	−	0.669270i	$-0.233393\pi$
$509$	−0.568106	−	0.655629i	−0.0251809	−	0.0290603i	−0.768200	+	0.640210i	$0.778848\pi$
$510$		0			0
$511$	6.68495	+	46.4949i	0.295725	+	2.05681i
$512$		0			0
$513$	−1.73571	+	3.80068i	−0.0766335	+	0.167804i
$514$		0			0
$515$	1.30974	−	9.10944i	0.0577141	−	0.401410i
$516$		0			0
$517$	8.34543	+	2.45044i	0.367032	+	0.107770i
$518$		0			0
$519$	4.17127	+	9.13380i	0.183098	+	0.400929i
$520$		0			0
$521$	10.7654	−	12.4240i	0.471642	−	0.544304i	−0.469225	−	0.883078i	$-0.655467\pi$
$521$	10.7654	−	12.4240i	0.471642	−	0.544304i	0.940868	+	0.338774i	$0.110012\pi$
$522$		0			0
$523$	4.73878	+	3.04543i	0.207212	+	0.133167i	0.640131	−	0.768266i	$-0.278880\pi$
$523$	4.73878	+	3.04543i	0.207212	+	0.133167i	−0.432919	+	0.901433i	$0.642516\pi$
$524$		0			0
$525$	11.9069	−	7.65213i	0.519662	−	0.333966i
$526$		0			0
$527$	7.31442	−	2.14771i	0.318621	−	0.0935556i
$528$		0			0
$529$	22.9943	−	0.514208i	0.999750	−	0.0223569i
$530$		0			0
$531$	11.1918	−	3.28622i	0.485684	−	0.142610i
$532$		0			0
$533$	57.1301	−	36.7153i	2.47458	−	1.59032i
$534$		0			0
$535$	3.14017	+	2.01806i	0.135761	+	0.0872484i
$536$		0			0
$537$	−12.0234	+	13.8757i	−0.518847	+	0.598781i
$538$		0			0
$539$	5.97611	+	13.0859i	0.257409	+	0.563648i
$540$		0			0
$541$	−14.0958	−	4.13890i	−0.606026	−	0.177945i	−0.0356982	−	0.999363i	$-0.511366\pi$
$541$	−14.0958	−	4.13890i	−0.606026	−	0.177945i	−0.570327	+	0.821417i	$0.693184\pi$
$542$		0			0
$543$	−2.36905	+	16.4771i	−0.101666	+	0.707100i
$544$		0			0
$545$	−4.16556	+	9.12129i	−0.178433	+	0.390713i
$546$		0			0
$547$	2.63293	+	18.3125i	0.112576	+	0.782984i	0.965398	+	0.260782i	$0.0839803\pi$
$547$	2.63293	+	18.3125i	0.112576	+	0.782984i	−0.852822	+	0.522202i	$0.825111\pi$
$548$		0			0
$549$	−7.57149	−	8.73797i	−0.323143	−	0.372927i
$550$		0			0
$551$	31.5735			1.34507
$552$		0			0
$553$	0.943567			0.0401246
$554$		0			0
$555$	5.30249	+	6.11940i	0.225078	+	0.259754i
$556$		0			0
$557$	−0.861964	−	5.99509i	−0.0365226	−	0.254020i	0.963378	−	0.268148i	$-0.0864118\pi$
$557$	−0.861964	−	5.99509i	−0.0365226	−	0.254020i	−0.999900	+	0.0141283i	$0.995503\pi$
$558$		0			0
$559$	21.2526	−	46.5367i	0.898889	−	1.96829i
$560$		0			0
$561$	1.03041	−	7.16669i	0.0435041	−	0.302578i
$562$		0			0
$563$	−24.1909	−	7.10308i	−1.01952	−	0.299359i	−0.271079	−	0.962557i	$-0.587381\pi$
$563$	−24.1909	−	7.10308i	−1.01952	−	0.299359i	−0.748444	+	0.663198i	$0.769199\pi$
$564$		0			0
$565$	−5.10947	−	11.1882i	−0.214957	−	0.470690i
$566$		0			0
$567$	2.30370	−	2.65861i	0.0967462	−	0.111651i
$568$		0			0
$569$	29.9636	+	19.2564i	1.25614	+	0.807271i	0.987751	−	0.156040i	$-0.0498729\pi$
$569$	29.9636	+	19.2564i	1.25614	+	0.807271i	0.268387	+	0.963311i	$0.413509\pi$
$570$		0			0
$571$	−20.9173	+	13.4427i	−0.875360	+	0.562560i	−0.899388	−	0.437152i	$-0.855987\pi$
$571$	−20.9173	+	13.4427i	−0.875360	+	0.562560i	0.0240279	+	0.999711i	$0.492351\pi$
$572$		0			0
$573$	3.61515	−	1.06150i	0.151025	−	0.0443450i
$574$		0			0
$575$	−18.4522	+	5.64286i	−0.769509	+	0.235324i
$576$		0			0
$577$	−13.3798	+	3.92866i	−0.557008	+	0.163552i	−0.548107	−	0.836408i	$-0.684651\pi$
$577$	−13.3798	+	3.92866i	−0.557008	+	0.163552i	−0.00890093	+	0.999960i	$0.502833\pi$
$578$		0			0
$579$	5.94508	−	3.82067i	0.247069	−	0.158782i
$580$		0			0
$581$	0.604834	+	0.388703i	0.0250927	+	0.0161261i
$582$		0			0
$583$	−22.1783	+	25.5952i	−0.918533	+	1.06004i
$584$		0			0
$585$	2.74841	+	6.01817i	0.113633	+	0.248821i
$586$		0			0
$587$	−21.5463	−	6.32656i	−0.889311	−	0.261125i	−0.195002	−	0.980803i	$-0.562471\pi$
$587$	−21.5463	−	6.32656i	−0.889311	−	0.261125i	−0.694308	+	0.719678i	$0.744290\pi$
$588$		0			0
$589$	1.67557	−	11.6538i	0.0690405	−	0.480187i
$590$		0			0
$591$	−3.41105	+	7.46917i	−0.140312	+	0.307240i
$592$		0			0
$593$	−1.22518	−	8.52129i	−0.0503120	−	0.349928i	−0.999391	−	0.0348899i	$-0.988892\pi$
$593$	−1.22518	−	8.52129i	−0.0503120	−	0.349928i	0.949079	−	0.315038i	$-0.102017\pi$
$594$		0			0
$595$	6.15883	+	7.10767i	0.252487	+	0.291386i
$596$		0			0
$597$	19.1369			0.783223
$598$		0			0
$599$	47.3402			1.93427			0.967133	−	0.254270i	$-0.0818351\pi$
$599$	47.3402			1.93427			0.967133	+	0.254270i	$0.0818351\pi$
$600$		0			0
$601$	−3.94220	−	4.54954i	−0.160806	−	0.185580i	0.669629	−	0.742696i	$-0.266453\pi$
$601$	−3.94220	−	4.54954i	−0.160806	−	0.185580i	−0.830434	+	0.557116i	$0.811908\pi$
$602$		0			0
$603$	0.723671	+	5.03324i	0.0294702	+	0.204969i
$604$		0			0
$605$	1.57527	−	3.44935i	0.0640437	−	0.140236i
$606$		0			0
$607$	0.583890	−	4.06104i	0.0236994	−	0.164833i	−0.974535	−	0.224237i	$-0.928011\pi$
$607$	0.583890	−	4.06104i	0.0236994	−	0.164833i	0.998234	+	0.0594043i	$0.0189201\pi$
$608$		0			0
$609$	−25.5062	−	7.48929i	−1.03356	−	0.303481i
$610$		0			0
$611$	9.03853	+	19.7916i	0.365660	+	0.800683i
$612$		0			0
$613$	25.8304	−	29.8099i	1.04328	−	1.20401i	0.0647507	−	0.997901i	$-0.479375\pi$
$613$	25.8304	−	29.8099i	1.04328	−	1.20401i	0.978529	−	0.206108i	$-0.0660798\pi$
$614$		0			0
$615$	8.43271	+	5.41937i	0.340040	+	0.218530i
$616$		0			0
$617$	−6.13347	+	3.94174i	−0.246924	+	0.158689i	−0.658249	−	0.752800i	$-0.728703\pi$
$617$	−6.13347	+	3.94174i	−0.246924	+	0.158689i	0.411325	+	0.911489i	$0.365066\pi$
$618$		0			0
$619$	4.92585	−	1.44636i	0.197987	−	0.0581341i	−0.181236	−	0.983440i	$-0.558010\pi$
$619$	4.92585	−	1.44636i	0.197987	−	0.0581341i	0.379222	+	0.925306i	$0.376192\pi$
$620$		0			0
$621$	−4.00527	+	2.63776i	−0.160726	+	0.105850i
$622$		0			0
$623$	0.259144	−	0.0760917i	0.0103824	−	0.00304855i
$624$		0			0
$625$	9.51054	−	6.11205i	0.380422	−	0.244482i
$626$		0			0
$627$	−9.40722	−	6.04566i	−0.375688	−	0.241440i
$628$		0			0
$629$	14.5162	−	16.7525i	0.578797	−	0.667967i
$630$		0			0
$631$	−11.1633	−	24.4441i	−0.444402	−	0.973105i	−0.990769	−	0.135559i	$-0.956717\pi$
$631$	−11.1633	−	24.4441i	−0.444402	−	0.973105i	0.546367	−	0.837546i	$-0.316010\pi$
$632$		0			0
$633$	−22.7693	−	6.68566i	−0.904997	−	0.265731i
$634$		0			0
$635$	−2.59906	+	18.0769i	−0.103141	+	0.717359i
$636$		0			0
$637$	−14.9495	+	32.7349i	−0.592322	+	1.29700i
$638$		0			0
$639$	−1.38499	−	9.63280i	−0.0547893	−	0.381068i
$640$		0			0
$641$	3.54445	+	4.09052i	0.139997	+	0.161566i	0.821418	−	0.570326i	$-0.193183\pi$
$641$	3.54445	+	4.09052i	0.139997	+	0.161566i	−0.681421	+	0.731892i	$0.738638\pi$
$642$		0			0
$643$	7.63902			0.301254			0.150627	−	0.988591i	$-0.451871\pi$
$643$	7.63902			0.301254			0.150627	+	0.988591i	$0.451871\pi$
$644$		0			0
$645$	7.55148			0.297339
$646$		0			0
$647$	−23.7151	−	27.3687i	−0.932336	−	1.07597i	−0.996948	−	0.0780631i	$-0.975126\pi$
$647$	−23.7151	−	27.3687i	−0.932336	−	1.07597i	0.0646120	−	0.997910i	$-0.479419\pi$
$648$		0			0
$649$	4.44272	+	30.8998i	0.174392	+	1.21292i
$650$		0			0
$651$	−4.11789	+	9.01692i	−0.161393	+	0.353401i
$652$		0			0
$653$	−2.80855	+	19.5339i	−0.109907	+	0.764419i	0.858098	+	0.513487i	$0.171646\pi$
$653$	−2.80855	+	19.5339i	−0.109907	+	0.764419i	−0.968005	+	0.250933i	$0.919263\pi$
$654$		0			0
$655$	−7.26088	−	2.13199i	−0.283706	−	0.0833036i
$656$		0			0
$657$	5.54694	+	12.1461i	0.216407	+	0.473865i
$658$		0			0
$659$	−29.3489	+	33.8705i	−1.14327	+	1.31941i	−0.202924	+	0.979194i	$0.565044\pi$
$659$	−29.3489	+	33.8705i	−1.14327	+	1.31941i	−0.940349	+	0.340213i	$0.889501\pi$
$660$		0			0
$661$	−1.22820	−	0.789315i	−0.0477713	−	0.0307008i	0.516537	−	0.856265i	$-0.327221\pi$
$661$	−1.22820	−	0.789315i	−0.0477713	−	0.0307008i	−0.564309	+	0.825564i	$0.690857\pi$
$662$		0			0
$663$	15.2369	−	9.79218i	0.591753	−	0.380297i
$664$		0			0
$665$	13.9368	−	4.09222i	0.540447	−	0.158690i
$666$		0			0
$667$	30.7044	+	19.2509i	1.18888	+	0.745398i
$668$		0			0
$669$	2.41090	−	0.707904i	0.0932107	−	0.0273691i
$670$		0			0
$671$	26.0315	−	16.7294i	1.00493	−	0.645832i
$672$		0			0
$673$	9.97688	+	6.41175i	0.384581	+	0.247155i	0.718618	−	0.695405i	$-0.244775\pi$
$673$	9.97688	+	6.41175i	0.384581	+	0.247155i	−0.334038	+	0.942560i	$0.608411\pi$
$674$		0			0
$675$	2.63479	−	3.04071i	0.101413	−	0.117037i
$676$		0			0
$677$	−3.44521	−	7.54397i	−0.132410	−	0.289938i	0.831801	−	0.555075i	$-0.187310\pi$
$677$	−3.44521	−	7.54397i	−0.132410	−	0.289938i	−0.964211	+	0.265136i	$0.914583\pi$
$678$		0			0
$679$	−18.0007	−	5.28547i	−0.690802	−	0.202838i
$680$		0			0
$681$	−2.60534	+	18.1205i	−0.0998367	+	0.694380i
$682$		0			0
$683$	−9.21185	+	20.1711i	−0.352482	+	0.771827i	0.647471	+	0.762090i	$0.275827\pi$
$683$	−9.21185	+	20.1711i	−0.352482	+	0.771827i	−0.999953	+	0.00973683i	$0.996901\pi$
$684$		0			0
$685$	−0.781953	−	5.43860i	−0.0298769	−	0.207798i
$686$		0			0
$687$	13.5625	+	15.6519i	0.517440	+	0.597158i
$688$		0			0
$689$	−84.7205			−3.22760
$690$		0			0
$691$	−45.8495			−1.74420			−0.872098	−	0.489332i	$-0.837241\pi$
$691$	−45.8495			−1.74420			−0.872098	+	0.489332i	$0.837241\pi$
$692$		0			0
$693$	6.16545	+	7.11531i	0.234206	+	0.270288i
$694$		0			0
$695$	−0.196069	−	1.36369i	−0.00743731	−	0.0517276i
$696$		0			0
$697$	11.3997	−	24.9619i	0.431795	−	0.945499i
$698$		0			0
$699$	2.03251	−	14.1364i	0.0768765	−	0.534688i
$700$		0			0
$701$	−32.2605	−	9.47253i	−1.21846	−	0.357772i	−0.391577	−	0.920145i	$-0.628070\pi$
$701$	−32.2605	−	9.47253i	−1.21846	−	0.357772i	−0.826884	+	0.562373i	$0.809889\pi$
$702$		0			0
$703$	−14.2219	−	31.1416i	−0.536389	−	1.17453i
$704$		0			0
$705$	−2.10313	+	2.42715i	−0.0792086	+	0.0914116i
$706$		0			0
$707$	−5.66591	−	3.64126i	−0.213089	−	0.136944i
$708$		0			0
$709$	8.34680	−	5.36416i	0.313470	−	0.201455i	−0.374439	−	0.927251i	$-0.622165\pi$
$709$	8.34680	−	5.36416i	0.313470	−	0.201455i	0.687910	+	0.725796i	$0.258528\pi$
$710$		0			0
$711$	0.257358	−	0.0755672i	0.00965169	−	0.00283399i
$712$		0			0
$713$	8.73498	−	10.3114i	0.327128	−	0.386165i
$714$		0			0
$715$	−16.9895	+	4.98856i	−0.635371	+	0.186562i
$716$		0			0
$717$	−1.35799	+	0.872730i	−0.0507152	+	0.0325927i
$718$		0			0
$719$	−7.99340	−	5.13704i	−0.298103	−	0.191579i	0.383036	−	0.923734i	$-0.374879\pi$
$719$	−7.99340	−	5.13704i	−0.298103	−	0.191579i	−0.681139	+	0.732154i	$0.738515\pi$
$720$		0			0
$721$	21.4541	−	24.7593i	0.798992	−	0.922086i
$722$		0			0
$723$	−0.860335	−	1.88387i	−0.0319962	−	0.0700619i
$724$		0			0
$725$	−29.1720	−	8.56566i	−1.08342	−	0.318121i
$726$		0			0
$727$	−1.59666	+	11.1050i	−0.0592167	+	0.411861i	0.938554	+	0.345131i	$0.112166\pi$
$727$	−1.59666	+	11.1050i	−0.0592167	+	0.411861i	−0.997771	+	0.0667299i	$0.978743\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$		0			0
$731$	−2.94207	−	20.4626i	−0.108817	−	0.756836i
$732$		0			0
$733$	−1.93434	−	2.23235i	−0.0714466	−	0.0824537i	0.718901	−	0.695113i	$-0.244645\pi$
$733$	−1.93434	−	2.23235i	−0.0714466	−	0.0824537i	−0.790348	+	0.612659i	$0.790100\pi$
$734$		0			0
$735$	−5.31187			−0.195931
$736$		0			0
$737$	−13.6091			−0.501299
$738$		0			0
$739$	18.2157	+	21.0220i	0.670074	+	0.773307i	0.984388	−	0.176012i	$-0.0563198\pi$
$739$	18.2157	+	21.0220i	0.670074	+	0.773307i	−0.314314	+	0.949319i	$0.601774\pi$
$740$		0			0
$741$	−3.98101	−	27.6885i	−0.146246	−	1.01716i
$742$		0			0
$743$	7.13615	−	15.6260i	0.261800	−	0.573262i	−0.732392	−	0.680883i	$-0.761596\pi$
$743$	7.13615	−	15.6260i	0.261800	−	0.573262i	0.994192	+	0.107621i	$0.0343234\pi$
$744$		0			0
$745$	−2.26090	+	15.7249i	−0.0828329	+	0.576115i
$746$		0			0
$747$	0.196099	+	0.0575797i	0.00717487	+	0.00210673i
$748$		0			0
$749$	5.51993	+	12.0870i	0.201694	+	0.441648i
$750$		0			0
$751$	3.22457	−	3.72136i	0.117666	−	0.135794i	−0.693860	−	0.720110i	$-0.744091\pi$
$751$	3.22457	−	3.72136i	0.117666	−	0.135794i	0.811527	+	0.584315i	$0.198637\pi$
$752$		0			0
$753$	−12.4127	−	7.97717i	−0.452345	−	0.290704i
$754$		0			0
$755$	1.78860	−	1.14946i	0.0650937	−	0.0418332i
$756$		0			0
$757$	32.4127	−	9.51722i	1.17806	−	0.345909i	0.366634	−	0.930365i	$-0.380510\pi$
$757$	32.4127	−	9.51722i	1.17806	−	0.345909i	0.811425	+	0.584456i	$0.198692\pi$
$758$		0			0
$759$	−5.46213	−	11.6150i	−0.198263	−	0.421598i
$760$		0			0
$761$	−21.6554	+	6.35859i	−0.785007	+	0.230499i	−0.649585	−	0.760289i	$-0.725057\pi$
$761$	−21.6554	+	6.35859i	−0.785007	+	0.230499i	−0.135422	+	0.990788i	$0.543239\pi$
$762$		0			0
$763$	−30.0292	+	19.2986i	−1.08713	+	0.698656i
$764$		0			0
$765$	2.24905	+	1.44538i	0.0813147	+	0.0522578i
$766$		0			0
$767$	−51.1395	+	59.0181i	−1.84654	+	2.13102i
$768$		0			0
$769$	4.98137	+	10.9077i	0.179633	+	0.393341i	0.977933	−	0.208919i	$-0.0669945\pi$
$769$	4.98137	+	10.9077i	0.179633	+	0.393341i	−0.798300	+	0.602260i	$0.794267\pi$
$770$		0			0
$771$	13.9816	+	4.10536i	0.503535	+	0.147851i
$772$		0			0
$773$	1.51909	−	10.5655i	0.0546379	−	0.380015i	−0.944094	−	0.329675i	$-0.893061\pi$
$773$	1.51909	−	10.5655i	0.0546379	−	0.380015i	0.998732	−	0.0503392i	$-0.0160302\pi$
$774$		0			0
$775$	−4.70972	+	10.3129i	−0.169178	+	0.370449i
$776$		0			0
$777$	4.10211	+	28.5308i	0.147162	+	1.02354i
$778$		0			0
$779$	−27.7545	−	32.0304i	−0.994409	−	1.14761i
$780$		0			0
$781$	26.0456			0.931987
$782$		0			0
$783$	−7.55661			−0.270051
$784$		0			0
$785$	2.69904	+	3.11486i	0.0963328	+	0.111174i
$786$		0			0
$787$	3.69112	+	25.6723i	0.131574	+	0.915120i	0.943503	+	0.331363i	$0.107509\pi$
$787$	3.69112	+	25.6723i	0.131574	+	0.915120i	−0.811929	+	0.583756i	$0.801582\pi$
$788$		0			0
$789$	3.81210	−	8.34734i	0.135714	−	0.297173i
$790$		0			0
$791$	6.23118	−	43.3388i	0.221555	−	1.54095i
$792$		0			0
$793$	74.2716	+	21.8081i	2.63746	+	0.774428i
$794$		0			0
$795$	−5.19485	−	11.3751i	−0.184242	−	0.403435i
$796$		0			0
$797$	−26.9604	+	31.1139i	−0.954985	+	1.10211i	0.0397067	+	0.999211i	$0.487358\pi$
$797$	−26.9604	+	31.1139i	−0.954985	+	1.10211i	−0.994692	+	0.102900i	$0.967188\pi$
$798$		0			0
$799$	7.39633	+	4.75333i	0.261663	+	0.168161i
$800$		0			0
$801$	0.0645878	−	0.0415080i	0.00228210	−	0.00146661i
$802$		0			0
$803$	−34.2888	+	10.0681i	−1.21003	+	0.355296i
$804$		0			0
$805$	16.0483	+	4.51796i	0.565628	+	0.159237i
$806$		0			0
$807$	23.4490	−	6.88524i	0.825443	−	0.242372i
$808$		0			0
$809$	−21.7740	+	13.9933i	−0.765532	+	0.491978i	−0.864204	−	0.503142i	$-0.832177\pi$
$809$	−21.7740	+	13.9933i	−0.765532	+	0.491978i	0.0986712	+	0.995120i	$0.468541\pi$
$810$		0			0
$811$	−17.9853	−	11.5584i	−0.631548	−	0.405871i	0.185334	−	0.982676i	$-0.440663\pi$
$811$	−17.9853	−	11.5584i	−0.631548	−	0.405871i	−0.816882	+	0.576804i	$0.804300\pi$
$812$		0			0
$813$	−18.8016	+	21.6982i	−0.659400	+	0.760989i
$814$		0			0
$815$	1.78158	+	3.90112i	0.0624061	+	0.136650i
$816$		0			0
$817$	−30.6350	−	8.99525i	−1.07178	−	0.314704i
$818$		0			0
$819$	−3.35178	+	23.3121i	−0.117121	+	0.814591i
$820$		0			0
$821$	−19.0960	+	41.8144i	−0.666454	+	1.45933i	0.209929	+	0.977717i	$0.432677\pi$
$821$	−19.0960	+	41.8144i	−0.666454	+	1.45933i	−0.876383	+	0.481614i	$0.840051\pi$
$822$		0			0
$823$	−1.93798	−	13.4790i	−0.0675538	−	0.469847i	−0.995316	−	0.0966749i	$-0.969179\pi$
$823$	−1.93798	−	13.4790i	−0.0675538	−	0.469847i	0.927762	−	0.373172i	$-0.121730\pi$
$824$		0			0
$825$	7.05156	+	8.13794i	0.245504	+	0.283327i
$826$		0			0
$827$	38.0002			1.32140			0.660699	−	0.750651i	$-0.270260\pi$
$827$	38.0002			1.32140			0.660699	+	0.750651i	$0.270260\pi$
$828$		0			0
$829$	−52.9128			−1.83774			−0.918869	−	0.394563i	$-0.870896\pi$
$829$	−52.9128			−1.83774			−0.918869	+	0.394563i	$0.870896\pi$
$830$		0			0
$831$	19.5627	+	22.5766i	0.678623	+	0.783173i
$832$		0			0
$833$	2.06952	+	14.3938i	0.0717045	+	0.498716i
$834$		0			0
$835$	−3.95110	+	8.65170i	−0.136733	+	0.299405i
$836$		0			0
$837$	−0.401020	+	2.78916i	−0.0138613	+	0.0964074i
$838$		0			0
$839$	−18.9373	−	5.56048i	−0.653787	−	0.191969i	−0.0620156	−	0.998075i	$-0.519753\pi$
$839$	−18.9373	−	5.56048i	−0.653787	−	0.191969i	−0.591771	+	0.806106i	$0.701571\pi$
$840$		0			0
$841$	11.6741	+	25.5628i	0.402557	+	0.881476i
$842$		0			0
$843$	5.42195	−	6.25726i	0.186742	−	0.215511i
$844$		0			0
$845$	−26.4553	−	17.0018i	−0.910089	−	0.584879i
$846$		0			0
$847$	11.3560	−	7.29805i	0.390196	−	0.250764i
$848$		0			0
$849$	3.73056	−	1.09539i	0.128033	−	0.0375938i
$850$		0			0
$851$	5.15718	−	38.9558i	0.176786	−	1.33539i
$852$		0			0
$853$	−40.2429	+	11.8164i	−1.37789	+	0.404585i	−0.885034	−	0.465526i	$-0.845865\pi$
$853$	−40.2429	+	11.8164i	−1.37789	+	0.404585i	−0.492856	+	0.870111i	$0.664047\pi$
$854$		0			0
$855$	3.47354	−	2.23231i	0.118793	−	0.0763434i
$856$		0			0
$857$	−1.14991	−	0.739001i	−0.0392801	−	0.0252438i	0.520853	−	0.853646i	$-0.325614\pi$
$857$	−1.14991	−	0.739001i	−0.0392801	−	0.0252438i	−0.560134	+	0.828402i	$0.689250\pi$
$858$		0			0
$859$	−4.92402	+	5.68262i	−0.168005	+	0.193889i	−0.833509	−	0.552506i	$-0.813672\pi$
$859$	−4.92402	+	5.68262i	−0.168005	+	0.193889i	0.665503	+	0.746395i	$0.268217\pi$
$860$		0			0
$861$	14.8234	+	32.4588i	0.505181	+	1.10619i
$862$		0			0
$863$	40.7035	+	11.9516i	1.38556	+	0.406838i	0.887702	−	0.460418i	$-0.152300\pi$
$863$	40.7035	+	11.9516i	1.38556	+	0.406838i	0.497862	+	0.867256i	$0.334119\pi$
$864$		0			0
$865$	1.41217	−	9.82185i	0.0480152	−	0.333953i
$866$		0			0
$867$	−4.02168	+	8.80626i	−0.136584	+	0.299076i
$868$		0			0
$869$	0.102161	+	0.710547i	0.00346558	+	0.0241037i
$870$		0			0
$871$	−22.2940	−	25.7287i	−0.755404	−	0.871782i
$872$		0			0
$873$	−5.33298			−0.180494
$874$		0			0
$875$	−31.3689			−1.06046
$876$		0			0
$877$	−5.11071	−	5.89808i	−0.172577	−	0.199164i	0.662872	−	0.748733i	$-0.269337\pi$
$877$	−5.11071	−	5.89808i	−0.172577	−	0.199164i	−0.835448	+	0.549569i	$0.814792\pi$
$878$		0			0
$879$	−1.58155	−	10.9999i	−0.0533442	−	0.371017i
$880$		0			0
$881$	9.79235	−	21.4422i	0.329913	−	0.722408i	−0.669886	−	0.742464i	$-0.733657\pi$
$881$	9.79235	−	21.4422i	0.329913	−	0.722408i	0.999799	+	0.0200560i	$0.00638445\pi$
$882$		0			0
$883$	−2.28357	+	15.8826i	−0.0768481	+	0.534491i	0.914638	+	0.404275i	$0.132476\pi$
$883$	−2.28357	+	15.8826i	−0.0768481	+	0.534491i	−0.991486	+	0.130216i	$0.958433\pi$
$884$		0			0
$885$	−11.0599	−	3.24748i	−0.371775	−	0.109163i
$886$		0			0
$887$	−22.4745	−	49.2123i	−0.754621	−	1.65239i	−0.757880	−	0.652394i	$-0.773765\pi$
$887$	−22.4745	−	49.2123i	−0.754621	−	1.65239i	0.00325906	−	0.999995i	$-0.498963\pi$
$888$		0			0
$889$	−42.5737	+	49.1327i	−1.42788	+	1.64786i
$890$		0			0
$891$	2.25147	+	1.44693i	0.0754271	+	0.0484741i
$892$		0			0
$893$	11.4232	−	7.34127i	0.382264	−	0.245666i
$894$		0			0
$895$	17.4088	−	5.11170i	0.581913	−	0.170865i
$896$		0			0
$897$	13.0108	−	29.3537i	0.434417	−	0.980091i
$898$		0			0
$899$	20.4308	−	5.99902i	0.681405	−	0.200078i
$900$		0			0
$901$	−28.7998	+	18.5085i	−0.959461	+	0.616608i
$902$		0			0
$903$	22.6144	+	14.5334i	0.752560	+	0.483641i
$904$		0			0
$905$	10.7727	−	12.4323i	0.358096	−	0.413264i
$906$		0			0
$907$	−19.5794	−	42.8730i	−0.650124	−	1.42357i	−0.891445	−	0.453128i	$-0.850308\pi$
$907$	−19.5794	−	42.8730i	−0.650124	−	1.42357i	0.241321	−	0.970445i	$-0.422419\pi$
$908$		0			0
$909$	−1.83700	−	0.539390i	−0.0609293	−	0.0178905i
$910$		0			0
$911$	3.44310	−	23.9473i	0.114075	−	0.793410i	−0.849809	−	0.527090i	$-0.823283\pi$
$911$	3.44310	−	23.9473i	0.114075	−	0.793410i	0.963885	−	0.266320i	$-0.0858078\pi$
$912$		0			0
$913$	−0.227224	+	0.497551i	−0.00752002	+	0.0164665i
$914$		0			0
$915$	1.62605	+	11.3094i	0.0537555	+	0.373878i
$916$		0			0
$917$	−17.6410	−	20.3588i	−0.582556	−	0.672305i
$918$		0			0
$919$	38.6806			1.27595			0.637977	−	0.770055i	$-0.279772\pi$
$919$	38.6806			1.27595			0.637977	+	0.770055i	$0.279772\pi$
$920$		0			0
$921$	−5.49504			−0.181068
$922$		0			0
$923$	42.6671	+	49.2404i	1.40440	+	1.62077i
$924$		0			0
$925$	4.69167	+	32.6313i	0.154261	+	1.07291i
$926$		0			0
$927$	3.86871	−	8.47130i	0.127065	−	0.278234i
$928$		0			0
$929$	7.96965	−	55.4301i	0.261476	−	1.81860i	−0.260307	−	0.965526i	$-0.583824\pi$
$929$	7.96965	−	55.4301i	0.261476	−	1.81860i	0.521783	−	0.853078i	$-0.325267\pi$
$930$		0			0
$931$	21.5493	+	6.32745i	0.706251	+	0.207374i
$932$		0			0
$933$	5.61680	+	12.2991i	0.183886	+	0.402654i
$934$		0			0
$935$	−4.68556	+	5.40742i	−0.153234	+	0.176842i
$936$		0			0
$937$	24.1432	+	15.5159i	0.788723	+	0.506882i	0.871918	−	0.489652i	$-0.162876\pi$
$937$	24.1432	+	15.5159i	0.788723	+	0.506882i	−0.0831949	+	0.996533i	$0.526512\pi$
$938$		0			0
$939$	−19.3295	+	12.4223i	−0.630793	+	0.405386i
$940$		0			0
$941$	35.2803	−	10.3592i	1.15010	−	0.337701i	0.349524	−	0.936927i	$-0.386343\pi$
$941$	35.2803	−	10.3592i	1.15010	−	0.337701i	0.800580	+	0.599226i	$0.204525\pi$
$942$		0			0
$943$	−7.46101	−	48.0712i	−0.242964	−	1.56541i
$944$		0			0
$945$	−3.33556	+	0.979409i	−0.108506	+	0.0318602i
$946$		0			0
$947$	42.4724	−	27.2954i	1.38017	−	0.886980i	0.380877	−	0.924626i	$-0.375622\pi$
$947$	42.4724	−	27.2954i	1.38017	−	0.886980i	0.999291	+	0.0376451i	$0.0119856\pi$
$948$		0			0
$949$	−75.2050	−	48.3313i	−2.44126	−	1.56890i
$950$		0			0
$951$	−2.12513	+	2.45253i	−0.0689122	+	0.0795289i
$952$		0			0
$953$	−9.51412	−	20.8330i	−0.308193	−	0.674847i	0.690638	−	0.723201i	$-0.257330\pi$
$953$	−9.51412	−	20.8330i	−0.308193	−	0.674847i	−0.998830	+	0.0483534i	$0.984603\pi$
$954$		0			0
$955$	−3.57254	−	1.04899i	−0.115605	−	0.0339446i
$956$		0			0
$957$	2.87817	−	20.0181i	0.0930381	−	0.647094i
$958$		0			0
$959$	8.12528	−	17.7919i	0.262379	−	0.574530i
$960$		0			0
$961$	3.28175	+	22.8251i	0.105863	+	0.736293i
$962$		0			0
$963$	2.47357	+	2.85465i	0.0797097	+	0.0919898i
$964$		0			0
$965$	−6.98363			−0.224811
$966$		0			0
$967$	−15.4805			−0.497818			−0.248909	−	0.968527i	$-0.580072\pi$
$967$	−15.4805			−0.497818			−0.248909	+	0.968527i	$0.580072\pi$
$968$		0			0
$969$	−7.40229	−	8.54270i	−0.237796	−	0.274431i
$970$		0			0
$971$	−7.24445	−	50.3863i	−0.232486	−	1.61697i	−0.687291	−	0.726382i	$-0.741200\pi$
$971$	−7.24445	−	50.3863i	−0.232486	−	1.61697i	0.454806	−	0.890591i	$-0.349709\pi$
$972$		0			0
$973$	2.03735	−	4.46118i	0.0653145	−	0.143019i
$974$		0			0
$975$	−3.83350	+	26.6626i	−0.122770	+	0.853886i
$976$		0			0
$977$	−11.6483	−	3.42026i	−0.372663	−	0.109424i	0.0900373	−	0.995938i	$-0.471301\pi$
$977$	−11.6483	−	3.42026i	−0.372663	−	0.109424i	−0.462701	+	0.886515i	$0.653120\pi$
$978$		0			0
$979$	0.0853582	+	0.186908i	0.00272806	+	0.00597362i
$980$		0			0
$981$	−6.64491	+	7.66863i	−0.212156	+	0.244841i
$982$		0			0
$983$	−2.38840	−	1.53493i	−0.0761781	−	0.0489567i	0.501997	−	0.864869i	$-0.332599\pi$
$983$	−2.38840	−	1.53493i	−0.0761781	−	0.0489567i	−0.578175	+	0.815912i	$0.696235\pi$
$984$		0			0
$985$	6.82628	−	4.38698i	0.217503	−	0.139781i
$986$		0			0
$987$	−10.9695	+	3.22093i	−0.349162	+	0.102523i
$988$		0			0
$989$	−24.3072	−	27.4264i	−0.772923	−	0.872108i
$990$		0			0
$991$	19.6085	−	5.75757i	0.622884	−	0.182895i	0.0449642	−	0.998989i	$-0.485683\pi$
$991$	19.6085	−	5.75757i	0.622884	−	0.182895i	0.577920	+	0.816093i	$0.303864\pi$
$992$		0			0
$993$	17.1667	−	11.0324i	0.544770	−	0.350102i
$994$		0			0
$995$	−15.9093	−	10.2243i	−0.504357	−	0.324131i
$996$		0			0
$997$	25.1433	−	29.0169i	0.796296	−	0.918974i	−0.201876	−	0.979411i	$-0.564704\pi$
$997$	25.1433	−	29.0169i	0.796296	−	0.918974i	0.998172	+	0.0604366i	$0.0192493\pi$
$998$		0			0
$999$	3.40379	+	7.45326i	0.107691	+	0.235811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.a.193.2	✓	30
23.18	even	11	inner	552.2.q.a.409.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.a.193.2	✓	30	1.1	even	1	trivial
552.2.q.a.409.2	yes	30	23.18	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.654861 - 0.755750i) q^{3} +(0.140637 + 0.978155i) q^{5} +(-1.46137 + 3.19994i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.654861 - 0.755750i) q^{3} +(0.140637 + 0.978155i) q^{5} +(-1.46137 + 3.19994i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-2.56792 - 0.754009i) q^{11} +(-2.78119 - 6.08995i) q^{13} +(0.647142 - 0.746842i) q^{15} +(-2.27588 - 1.46262i) q^{17} +(-3.51497 + 2.25894i) q^{19} +(3.37535 - 0.991091i) q^{21} +(-4.79553 + 0.0536132i) q^{23} +(3.86046 - 1.13353i) q^{25} +(0.841254 - 0.540641i) q^{27} +(-6.35703 - 4.08541i) q^{29} +(-1.84529 + 2.12958i) q^{31} +(1.11179 + 2.43447i) q^{33} +(-3.33556 - 0.979409i) q^{35} +(-1.16609 + 8.11031i) q^{37} +(-2.78119 + 6.08995i) q^{39} +(1.44358 + 10.0403i) q^{41} +(5.00415 + 5.77510i) q^{43} -0.988213 q^{45} -3.24988 q^{47} +(-3.52002 - 4.06233i) q^{49} +(0.385010 + 2.67781i) q^{51} +(5.25681 - 11.5108i) q^{53} +(0.376392 - 2.61786i) q^{55} +(4.00901 + 1.17715i) q^{57} +(-4.84553 - 10.6102i) q^{59} +(-7.57149 + 8.73797i) q^{61} +(-2.95940 - 1.90189i) q^{63} +(5.56578 - 3.57691i) q^{65} +(4.87902 - 1.43261i) q^{67} +(3.18092 + 3.58911i) q^{69} +(-9.33765 + 2.74178i) q^{71} +(11.2331 - 7.21905i) q^{73} +(-3.38473 - 2.17523i) q^{75} +(6.16545 - 7.11531i) q^{77} +(-0.111424 - 0.243984i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(0.0290859 - 0.202297i) q^{83} +(1.11059 - 2.43186i) q^{85} +(1.07542 + 7.47970i) q^{87} +(-0.0502774 - 0.0580232i) q^{89} +23.5518 q^{91} +2.81784 q^{93} +(-2.70393 - 3.12050i) q^{95} +(0.758963 + 5.27870i) q^{97} +(1.11179 - 2.43447i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9	\( 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9} - 15 q^{11} + 5 q^{13} - 15 q^{17} + 5 q^{19} + 9 q^{21} + 14 q^{23} + 5 q^{25} - 3 q^{27} + 13 q^{29} - 29 q^{31} - 15 q^{33} + 8 q^{35} - 3 q^{37} + 5 q^{39} + 24 q^{41} + 2 q^{43} + 22 q^{45} + 38 q^{47} + 15 q^{49} + 7 q^{51} - 7 q^{53} + 46 q^{55} - 6 q^{57} - 43 q^{59} - 22 q^{61} - 2 q^{63} + 44 q^{65} + 31 q^{67} + 3 q^{69} + 19 q^{71} - 50 q^{73} + 5 q^{75} + 16 q^{77} - 84 q^{79} - 3 q^{81} - 73 q^{83} - 8 q^{85} + 2 q^{87} + 19 q^{89} + 18 q^{91} + 26 q^{93} - 67 q^{95} - 29 q^{97} - 15 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9 - 15 * q^11 + 5 * q^13 - 15 * q^17 + 5 * q^19 + 9 * q^21 + 14 * q^23 + 5 * q^25 - 3 * q^27 + 13 * q^29 - 29 * q^31 - 15 * q^33 + 8 * q^35 - 3 * q^37 + 5 * q^39 + 24 * q^41 + 2 * q^43 + 22 * q^45 + 38 * q^47 + 15 * q^49 + 7 * q^51 - 7 * q^53 + 46 * q^55 - 6 * q^57 - 43 * q^59 - 22 * q^61 - 2 * q^63 + 44 * q^65 + 31 * q^67 + 3 * q^69 + 19 * q^71 - 50 * q^73 + 5 * q^75 + 16 * q^77 - 84 * q^79 - 3 * q^81 - 73 * q^83 - 8 * q^85 + 2 * q^87 + 19 * q^89 + 18 * q^91 + 26 * q^93 - 67 * q^95 - 29 * q^97 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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