LMFDB - Embedded newform 400.2.y.d.289.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(129,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("400.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.y (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			289.6
Character	$\chi$	$=$	400.289
Dual form			400.2.y.d.209.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.811472 + 0.263663i) q^{3} +(-0.390840 - 2.20165i) q^{5} +1.47738i q^{7} +(-1.83808 - 1.33545i) q^{9} +O(q^{10})$	\(q+(0.811472 + 0.263663i) q^{3} +(-0.390840 - 2.20165i) q^{5} +1.47738i q^{7} +(-1.83808 - 1.33545i) q^{9} +(3.08437 - 2.24093i) q^{11} +(3.25413 - 4.47892i) q^{13} +(0.263337 - 1.88962i) q^{15} +(4.28068 - 1.39088i) q^{17} +(2.12946 + 6.55380i) q^{19} +(-0.389530 + 1.19885i) q^{21} +(-2.45619 - 3.38065i) q^{23} +(-4.69449 + 1.72098i) q^{25} +(-2.64400 - 3.63915i) q^{27} +(-0.819316 + 2.52160i) q^{29} +(-1.82585 - 5.61939i) q^{31} +(3.09373 - 1.00521i) q^{33} +(3.25266 - 0.577418i) q^{35} +(-2.29696 + 3.16150i) q^{37} +(3.82156 - 2.77653i) q^{39} +(5.71537 + 4.15246i) q^{41} +7.36296i q^{43} +(-2.22178 + 4.56875i) q^{45} +(-2.89510 - 0.940676i) q^{47} +4.81736 q^{49} +3.84037 q^{51} +(-0.514416 - 0.167144i) q^{53} +(-6.13922 - 5.91485i) q^{55} +5.87969i q^{57} +(4.07951 + 2.96394i) q^{59} +(0.605160 - 0.439675i) q^{61} +(1.97295 - 2.71554i) q^{63} +(-11.1328 - 5.41389i) q^{65} +(-12.6695 + 4.11658i) q^{67} +(-1.10177 - 3.39091i) q^{69} +(1.19221 - 3.66925i) q^{71} +(-2.63370 - 3.62497i) q^{73} +(-4.26321 + 0.158766i) q^{75} +(3.31069 + 4.55677i) q^{77} +(-5.13548 + 15.8054i) q^{79} +(0.920236 + 2.83219i) q^{81} +(1.71513 - 0.557280i) q^{83} +(-4.73528 - 8.88092i) q^{85} +(-1.32970 + 1.83018i) q^{87} +(-10.4814 + 7.61517i) q^{89} +(6.61705 + 4.80757i) q^{91} -5.04139i q^{93} +(13.5969 - 7.24980i) q^{95} +(-7.33111 - 2.38202i) q^{97} -8.66196 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{5} + 10 q^{9}+O(q^{10}) $ 32 * q + 2 * q^5 + 10 * q^9	$ 32 q + 2 q^{5} + 10 q^{9} - 6 q^{11} - 12 q^{15} + 6 q^{19} - 4 q^{21} + 30 q^{23} + 6 q^{25} - 2 q^{29} - 6 q^{31} - 8 q^{35} - 40 q^{37} + 12 q^{39} - 12 q^{45} + 20 q^{47} - 60 q^{49} + 60 q^{51} - 30 q^{53} + 28 q^{55} + 30 q^{59} + 14 q^{61} + 20 q^{63} - 26 q^{65} - 4 q^{69} - 12 q^{71} + 40 q^{73} - 16 q^{75} - 16 q^{79} - 52 q^{81} - 30 q^{83} + 60 q^{85} - 110 q^{87} + 24 q^{89} + 4 q^{91} - 68 q^{95} + 30 q^{97} - 92 q^{99}+O(q^{100}) $ 32 * q + 2 * q^5 + 10 * q^9 - 6 * q^11 - 12 * q^15 + 6 * q^19 - 4 * q^21 + 30 * q^23 + 6 * q^25 - 2 * q^29 - 6 * q^31 - 8 * q^35 - 40 * q^37 + 12 * q^39 - 12 * q^45 + 20 * q^47 - 60 * q^49 + 60 * q^51 - 30 * q^53 + 28 * q^55 + 30 * q^59 + 14 * q^61 + 20 * q^63 - 26 * q^65 - 4 * q^69 - 12 * q^71 + 40 * q^73 - 16 * q^75 - 16 * q^79 - 52 * q^81 - 30 * q^83 + 60 * q^85 - 110 * q^87 + 24 * q^89 + 4 * q^91 - 68 * q^95 + 30 * q^97 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$	$1$

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
$3$	0.811472	+	0.263663i	0.468504	+	0.152226i	0.533749	−	0.845643i	$-0.320783\pi$
$3$	0.811472	+	0.263663i	0.468504	+	0.152226i	−0.0652450	+	0.997869i	$0.520783\pi$
$4$		0			0
$5$	−0.390840	−	2.20165i	−0.174789	−	0.984606i
$5$	−0.390840	−	2.20165i	−0.174789	−	0.984606i
$6$		0			0
$7$			1.47738i			0.558395i	0.960234	+	0.279198i	$0.0900685\pi$
$7$			1.47738i			0.558395i	−0.960234	+	0.279198i	$0.909932\pi$
$8$		0			0
$9$	−1.83808	−	1.33545i	−0.612694	−	0.445148i
$10$		0			0
$11$	3.08437	−	2.24093i	0.929973	−	0.675665i	−0.0160132	−	0.999872i	$-0.505097\pi$
$11$	3.08437	−	2.24093i	0.929973	−	0.675665i	0.945986	+	0.324207i	$0.105097\pi$
$12$		0			0
$13$	3.25413	−	4.47892i	0.902533	−	1.24223i	−0.0671205	−	0.997745i	$-0.521381\pi$
$13$	3.25413	−	4.47892i	0.902533	−	1.24223i	0.969653	−	0.244485i	$-0.0786188\pi$
$14$		0			0
$15$	0.263337	−	1.88962i	0.0679934	−	0.487899i
$16$		0			0
$17$	4.28068	−	1.39088i	1.03822	−	0.337337i	0.260183	−	0.965559i	$-0.416217\pi$
$17$	4.28068	−	1.39088i	1.03822	−	0.337337i	0.778034	+	0.628223i	$0.216217\pi$
$18$		0			0
$19$	2.12946	+	6.55380i	0.488531	+	1.50355i	0.826800	+	0.562496i	$0.190159\pi$
$19$	2.12946	+	6.55380i	0.488531	+	1.50355i	−0.338269	+	0.941050i	$0.609841\pi$
$20$		0			0
$21$	−0.389530	+	1.19885i	−0.0850023	+	0.261610i
$22$		0			0
$23$	−2.45619	−	3.38065i	−0.512151	−	0.704915i	0.472130	−	0.881529i	$-0.343485\pi$
$23$	−2.45619	−	3.38065i	−0.512151	−	0.704915i	−0.984280	+	0.176614i	$0.943485\pi$
$24$		0			0
$25$	−4.69449	+	1.72098i	−0.938898	+	0.344197i
$26$		0			0
$27$	−2.64400	−	3.63915i	−0.508837	−	0.700355i
$28$		0			0
$29$	−0.819316	+	2.52160i	−0.152143	+	0.468249i	−0.997860	−	0.0653829i	$-0.979173\pi$
$29$	−0.819316	+	2.52160i	−0.152143	+	0.468249i	0.845717	+	0.533632i	$0.179173\pi$
$30$		0			0
$31$	−1.82585	−	5.61939i	−0.327933	−	1.00927i	−0.970099	−	0.242708i	$-0.921964\pi$
$31$	−1.82585	−	5.61939i	−0.327933	−	1.00927i	0.642167	−	0.766565i	$-0.278036\pi$
$32$		0			0
$33$	3.09373	−	1.00521i	0.538549	−	0.174985i
$34$		0			0
$35$	3.25266	−	0.577418i	0.549799	−	0.0976014i
$36$		0			0
$37$	−2.29696	+	3.16150i	−0.377618	+	0.519747i	−0.954952	−	0.296762i	$-0.904093\pi$
$37$	−2.29696	+	3.16150i	−0.377618	+	0.519747i	0.577334	+	0.816508i	$0.304093\pi$
$38$		0			0
$39$	3.82156	−	2.77653i	0.611939	−	0.444600i
$40$		0			0
$41$	5.71537	+	4.15246i	0.892591	+	0.648505i	0.936552	−	0.350528i	$-0.113998\pi$
$41$	5.71537	+	4.15246i	0.892591	+	0.648505i	−0.0439614	+	0.999033i	$0.513998\pi$
$42$		0			0
$43$			7.36296i			1.12284i	0.827531	+	0.561420i	$0.189745\pi$
$43$			7.36296i			1.12284i	−0.827531	+	0.561420i	$0.810255\pi$
$44$		0			0
$45$	−2.22178	+	4.56875i	−0.331204	+	0.681069i
$46$		0			0
$47$	−2.89510	−	0.940676i	−0.422294	−	0.137212i	0.0901581	−	0.995927i	$-0.471263\pi$
$47$	−2.89510	−	0.940676i	−0.422294	−	0.137212i	−0.512452	+	0.858716i	$0.671263\pi$
$48$		0			0
$49$	4.81736			0.688195
$50$		0			0
$51$	3.84037			0.537759
$52$		0			0
$53$	−0.514416	−	0.167144i	−0.0706604	−	0.0229590i	0.273473	−	0.961880i	$-0.411827\pi$
$53$	−0.514416	−	0.167144i	−0.0706604	−	0.0229590i	−0.344134	+	0.938921i	$0.611827\pi$
$54$		0			0
$55$	−6.13922	−	5.91485i	−0.827813	−	0.797558i
$56$		0			0
$57$			5.87969i			0.778783i
$58$		0			0
$59$	4.07951	+	2.96394i	0.531107	+	0.385872i	0.820772	−	0.571256i	$-0.193544\pi$
$59$	4.07951	+	2.96394i	0.531107	+	0.385872i	−0.289665	+	0.957128i	$0.593544\pi$
$60$		0			0
$61$	0.605160	−	0.439675i	0.0774829	−	0.0562946i	−0.548369	−	0.836236i	$-0.684751\pi$
$61$	0.605160	−	0.439675i	0.0774829	−	0.0562946i	0.625852	+	0.779942i	$0.284751\pi$
$62$		0			0
$63$	1.97295	−	2.71554i	0.248569	−	0.342126i
$64$		0			0
$65$	−11.1328	−	5.41389i	−1.38086	−	0.671511i
$66$		0			0
$67$	−12.6695	+	4.11658i	−1.54783	+	0.502920i	−0.953523	−	0.301319i	$-0.902573\pi$
$67$	−12.6695	+	4.11658i	−1.54783	+	0.502920i	−0.594306	+	0.804239i	$0.702573\pi$
$68$		0			0
$69$	−1.10177	−	3.39091i	−0.132638	−	0.408218i
$70$		0			0
$71$	1.19221	−	3.66925i	0.141490	−	0.435460i	−0.855053	−	0.518540i	$-0.826476\pi$
$71$	1.19221	−	3.66925i	0.141490	−	0.435460i	0.996543	+	0.0830799i	$0.0264757\pi$
$72$		0			0
$73$	−2.63370	−	3.62497i	−0.308251	−	0.424271i	0.626584	−	0.779354i	$-0.284453\pi$
$73$	−2.63370	−	3.62497i	−0.308251	−	0.424271i	−0.934835	+	0.355083i	$0.884453\pi$
$74$		0			0
$75$	−4.26321	+	0.158766i	−0.492273	+	0.0183327i
$76$		0			0
$77$	3.31069	+	4.55677i	0.377288	+	0.519293i
$78$		0			0
$79$	−5.13548	+	15.8054i	−0.577787	+	1.77825i	0.0487004	+	0.998813i	$0.484492\pi$
$79$	−5.13548	+	15.8054i	−0.577787	+	1.77825i	−0.626487	+	0.779432i	$0.715508\pi$
$80$		0			0
$81$	0.920236	+	2.83219i	0.102248	+	0.314688i
$82$		0			0
$83$	1.71513	−	0.557280i	0.188260	−	0.0611695i	−0.213370	−	0.976972i	$-0.568444\pi$
$83$	1.71513	−	0.557280i	0.188260	−	0.0611695i	0.401630	+	0.915802i	$0.368444\pi$
$84$		0			0
$85$	−4.73528	−	8.88092i	−0.513613	−	0.963271i
$86$		0			0
$87$	−1.32970	+	1.83018i	−0.142559	+	0.196216i
$88$		0			0
$89$	−10.4814	+	7.61517i	−1.11103	+	0.807207i	−0.982825	−	0.184541i	$-0.940920\pi$
$89$	−10.4814	+	7.61517i	−1.11103	+	0.807207i	−0.128200	+	0.991748i	$0.540920\pi$
$90$		0			0
$91$	6.61705	+	4.80757i	0.693655	+	0.503970i
$92$		0			0
$93$		−	5.04139i		−	0.522768i
$94$		0			0
$95$	13.5969	−	7.24980i	1.39501	−	0.743814i
$96$		0			0
$97$	−7.33111	−	2.38202i	−0.744361	−	0.241858i	−0.0878082	−	0.996137i	$-0.527986\pi$
$97$	−7.33111	−	2.38202i	−0.744361	−	0.241858i	−0.656553	+	0.754280i	$0.727986\pi$
$98$		0			0
$99$	−8.66196			−0.870560
$100$		0			0
$101$	3.89360			0.387428			0.193714	−	0.981058i	$-0.437947\pi$
$101$	3.89360			0.387428			0.193714	+	0.981058i	$0.437947\pi$
$102$		0			0
$103$	−7.73215	−	2.51233i	−0.761871	−	0.247547i	−0.0977898	−	0.995207i	$-0.531177\pi$
$103$	−7.73215	−	2.51233i	−0.761871	−	0.247547i	−0.664082	+	0.747660i	$0.731177\pi$
$104$		0			0
$105$	2.79168	+	0.389048i	0.272440	+	0.0379672i
$106$		0			0
$107$			11.8404i			1.14466i	0.820024	+	0.572329i	$0.193960\pi$
$107$			11.8404i			1.14466i	−0.820024	+	0.572329i	$0.806040\pi$
$108$		0			0
$109$	9.92787	+	7.21302i	0.950917	+	0.690882i	0.951024	−	0.309118i	$-0.100034\pi$
$109$	9.92787	+	7.21302i	0.950917	+	0.690882i	−0.000106210		1.00000i	$0.500034\pi$
$110$		0			0
$111$	−2.69749	+	1.95984i	−0.256034	+	0.186020i
$112$		0			0
$113$	9.31278	−	12.8179i	0.876072	−	1.20581i	−0.101421	−	0.994844i	$-0.532339\pi$
$113$	9.31278	−	12.8179i	0.876072	−	1.20581i	0.977493	−	0.210967i	$-0.0676611\pi$
$114$		0			0
$115$	−6.48302	+	6.72895i	−0.604545	+	0.627478i
$116$		0			0
$117$	−11.9627	+	3.88692i	−1.10595	+	0.359346i
$118$		0			0
$119$	2.05485	+	6.32416i	0.188367	+	0.579735i
$120$		0			0
$121$	1.09241	−	3.36208i	0.0993097	−	0.305644i
$122$		0			0
$123$	3.54301	+	4.87654i	0.319463	+	0.439703i
$124$		0			0
$125$	5.62379	+	9.66297i	0.503007	+	0.864282i
$126$		0			0
$127$	−1.02802	−	1.41495i	−0.0912218	−	0.125556i	0.760967	−	0.648791i	$-0.224725\pi$
$127$	−1.02802	−	1.41495i	−0.0912218	−	0.125556i	−0.852189	+	0.523235i	$0.824725\pi$
$128$		0			0
$129$	−1.94134	+	5.97483i	−0.170926	+	0.526055i
$130$		0			0
$131$	5.62036	+	17.2977i	0.491053	+	1.51131i	0.823019	+	0.568014i	$0.192288\pi$
$131$	5.62036	+	17.2977i	0.491053	+	1.51131i	−0.331966	+	0.943291i	$0.607712\pi$
$132$		0			0
$133$	−9.68243	+	3.14601i	−0.839573	+	0.272794i
$134$		0			0
$135$	−6.97874	+	7.24347i	−0.600634	+	0.623419i
$136$		0			0
$137$	−3.11657	+	4.28959i	−0.266267	+	0.366485i	−0.921125	−	0.389267i	$-0.872728\pi$
$137$	−3.11657	+	4.28959i	−0.266267	+	0.366485i	0.654858	+	0.755752i	$0.272728\pi$
$138$		0			0
$139$	13.5667	−	9.85680i	1.15071	−	0.836043i	0.162138	−	0.986768i	$-0.448161\pi$
$139$	13.5667	−	9.85680i	1.15071	−	0.836043i	0.988576	+	0.150725i	$0.0481609\pi$
$140$		0			0
$141$	−2.10127	−	1.52666i	−0.176959	−	0.128568i
$142$		0			0
$143$		−	21.1069i		−	1.76505i
$144$		0			0
$145$	5.87188	+	0.818303i	0.487633	+	0.0679564i
$146$		0			0
$147$	3.90915	+	1.27016i	0.322422	+	0.104761i
$148$		0			0
$149$	7.18189			0.588364			0.294182	−	0.955749i	$-0.404953\pi$
$149$	7.18189			0.588364			0.294182	+	0.955749i	$0.404953\pi$
$150$		0			0
$151$	−8.05871			−0.655809			−0.327904	−	0.944711i	$-0.606342\pi$
$151$	−8.05871			−0.655809			−0.327904	+	0.944711i	$0.606342\pi$
$152$		0			0
$153$	−9.72567	−	3.16006i	−0.786274	−	0.255476i
$154$		0			0
$155$	−11.6583	+	6.21616i	−0.936417	+	0.499294i
$156$		0			0
$157$		−	14.9319i		−	1.19170i	−0.803097	−	0.595848i	$-0.796816\pi$
$157$		−	14.9319i		−	1.19170i	0.803097	−	0.595848i	$-0.203184\pi$
$158$		0			0
$159$	−0.373364	−	0.271265i	−0.0296097	−	0.0215127i
$160$		0			0
$161$	4.99449	−	3.62871i	0.393621	−	0.285983i
$162$		0			0
$163$	10.2806	−	14.1500i	0.805236	−	1.10831i	−0.186805	−	0.982397i	$-0.559813\pi$
$163$	10.2806	−	14.1500i	0.805236	−	1.10831i	0.992041	−	0.125915i	$-0.0401868\pi$
$164$		0			0
$165$	−3.42228	−	6.41842i	−0.266424	−	0.499673i
$166$		0			0
$167$	3.25153	−	1.05649i	0.251611	−	0.0817534i	−0.180496	−	0.983576i	$-0.557770\pi$
$167$	3.25153	−	1.05649i	0.251611	−	0.0817534i	0.432107	+	0.901822i	$0.357770\pi$
$168$		0			0
$169$	−5.45418	−	16.7862i	−0.419552	−	1.29125i
$170$		0			0
$171$	4.83812	−	14.8902i	0.369980	−	1.13868i
$172$		0			0
$173$	13.4866	+	18.5627i	1.02536	+	1.41129i	0.908373	+	0.418160i	$0.137325\pi$
$173$	13.4866	+	18.5627i	1.02536	+	1.41129i	0.116991	+	0.993133i	$0.462675\pi$
$174$		0			0
$175$	−2.54254	−	6.93552i	−0.192198	−	0.524276i
$176$		0			0
$177$	2.52893	+	3.48077i	0.190086	+	0.261631i
$178$		0			0
$179$	7.38769	−	22.7370i	0.552182	−	1.69944i	−0.151090	−	0.988520i	$-0.548278\pi$
$179$	7.38769	−	22.7370i	0.552182	−	1.69944i	0.703272	−	0.710921i	$-0.251722\pi$
$180$		0			0
$181$	3.28318	+	10.1046i	0.244037	+	0.751068i	0.995793	+	0.0916270i	$0.0292068\pi$
$181$	3.28318	+	10.1046i	0.244037	+	0.751068i	−0.751757	+	0.659440i	$0.770793\pi$
$182$		0			0
$183$	0.606997	−	0.197225i	0.0448705	−	0.0145793i
$184$		0			0
$185$	7.85824	+	3.82145i	0.577749	+	0.280959i
$186$		0			0
$187$	10.0863	−	13.8827i	0.737586	−	1.01520i
$188$		0			0
$189$	5.37639	−	3.90618i	0.391075	−	0.284132i
$190$		0			0
$191$	4.34494	+	3.15678i	0.314389	+	0.228417i	0.733777	−	0.679390i	$-0.237755\pi$
$191$	4.34494	+	3.15678i	0.314389	+	0.228417i	−0.419389	+	0.907807i	$0.637755\pi$
$192$		0			0
$193$			7.03850i			0.506642i	0.967382	+	0.253321i	$0.0815229\pi$
$193$			7.03850i			0.506642i	−0.967382	+	0.253321i	$0.918477\pi$
$194$		0			0
$195$	−7.60655	−	7.32854i	−0.544716	−	0.524808i
$196$		0			0
$197$	−7.70939	−	2.50493i	−0.549271	−	0.178469i	0.0212168	−	0.999775i	$-0.493246\pi$
$197$	−7.70939	−	2.50493i	−0.549271	−	0.178469i	−0.570488	+	0.821306i	$0.693246\pi$
$198$		0			0
$199$	−20.8870			−1.48064			−0.740320	−	0.672254i	$-0.765326\pi$
$199$	−20.8870			−1.48064			−0.740320	+	0.672254i	$0.765326\pi$
$200$		0			0
$201$	−11.3664			−0.801721
$202$		0			0
$203$	−3.72534	−	1.21044i	−0.261468	−	0.0849561i
$204$		0			0
$205$	6.90845	−	14.2062i	0.482507	−	0.992202i
$206$		0			0
$207$			9.49402i			0.659880i
$208$		0			0
$209$	21.2546	+	15.4424i	1.47021	+	1.06817i
$210$		0			0
$211$	2.70666	−	1.96650i	0.186334	−	0.135380i	−0.490708	−	0.871324i	$-0.663262\pi$
$211$	2.70666	−	1.96650i	0.186334	−	0.135380i	0.677042	+	0.735945i	$0.263262\pi$
$212$		0			0
$213$	1.93489	−	2.66315i	0.132577	−	0.182476i
$214$		0			0
$215$	16.2106	−	2.87774i	1.10556	−	0.196260i
$216$		0			0
$217$	8.30196	−	2.69747i	0.563573	−	0.183116i
$218$		0			0
$219$	−1.18140	−	3.63597i	−0.0798315	−	0.245696i
$220$		0			0
$221$	7.70024	−	23.6989i	0.517974	−	1.59416i
$222$		0			0
$223$	1.41196	+	1.94339i	0.0945515	+	0.130139i	0.853672	−	0.520811i	$-0.174371\pi$
$223$	1.41196	+	1.94339i	0.0945515	+	0.130139i	−0.759120	+	0.650950i	$0.774371\pi$
$224$		0			0
$225$	10.9271	+	3.10592i	0.728476	+	0.207061i
$226$		0			0
$227$	−5.43578	−	7.48171i	−0.360785	−	0.496578i	0.589582	−	0.807709i	$-0.299292\pi$
$227$	−5.43578	−	7.48171i	−0.360785	−	0.496578i	−0.950367	+	0.311130i	$0.899292\pi$
$228$		0			0
$229$	−7.81805	+	24.0615i	−0.516631	+	1.59003i	0.263662	+	0.964615i	$0.415069\pi$
$229$	−7.81805	+	24.0615i	−0.516631	+	1.59003i	−0.780294	+	0.625413i	$0.784931\pi$
$230$		0			0
$231$	1.48508	+	4.57060i	0.0977110	+	0.300724i
$232$		0			0
$233$	−9.08630	+	2.95232i	−0.595263	+	0.193413i	−0.591127	−	0.806579i	$-0.701317\pi$
$233$	−9.08630	+	2.95232i	−0.595263	+	0.193413i	−0.00413648	+	0.999991i	$0.501317\pi$
$234$		0			0
$235$	−0.939513	+	6.74164i	−0.0612870	+	0.439776i
$236$		0			0
$237$	−8.33460	+	11.4716i	−0.541390	+	0.745160i
$238$		0			0
$239$	10.8401	−	7.87578i	0.701187	−	0.509442i	−0.179132	−	0.983825i	$-0.557329\pi$
$239$	10.8401	−	7.87578i	0.701187	−	0.509442i	0.880318	+	0.474383i	$0.157329\pi$
$240$		0			0
$241$	7.92795	+	5.75999i	0.510684	+	0.371034i	0.813083	−	0.582148i	$-0.197787\pi$
$241$	7.92795	+	5.75999i	0.510684	+	0.371034i	−0.302399	+	0.953181i	$0.597787\pi$
$242$		0			0
$243$			16.0356i			1.02868i
$244$		0			0
$245$	−1.88282	−	10.6061i	−0.120289	−	0.677600i
$246$		0			0
$247$	36.2835	+	11.7892i	2.30866	+	0.750130i
$248$		0			0
$249$	1.53872			0.0975122
$250$		0			0
$251$	7.90855			0.499183			0.249592	−	0.968351i	$-0.419704\pi$
$251$	7.90855			0.499183			0.249592	+	0.968351i	$0.419704\pi$
$252$		0			0
$253$	−15.1516	−	4.92305i	−0.952572	−	0.309510i
$254$		0			0
$255$	−1.50097	−	8.45514i	−0.0939944	−	0.529481i
$256$		0			0
$257$		−	17.6996i		−	1.10407i	−0.833820	−	0.552036i	$-0.813851\pi$
$257$		−	17.6996i		−	1.10407i	0.833820	−	0.552036i	$-0.186149\pi$
$258$		0			0
$259$	−4.67072	−	3.39347i	−0.290224	−	0.210860i
$260$		0			0
$261$	4.87342	−	3.54075i	0.301657	−	0.219167i
$262$		0			0
$263$	14.0885	−	19.3911i	0.868733	−	1.19571i	−0.110683	−	0.993856i	$-0.535304\pi$
$263$	14.0885	−	19.3911i	0.868733	−	1.19571i	0.979416	−	0.201853i	$-0.0646962\pi$
$264$		0			0
$265$	−0.166937	+	1.19789i	−0.0102549	+	0.0735856i
$266$		0			0
$267$	−10.5132	+	3.41594i	−0.643397	+	0.209052i
$268$		0			0
$269$	−5.79732	−	17.8423i	−0.353469	−	1.08787i	−0.956892	−	0.290444i	$-0.906197\pi$
$269$	−5.79732	−	17.8423i	−0.353469	−	1.08787i	0.603423	−	0.797421i	$-0.293803\pi$
$270$		0			0
$271$	−8.62619	+	26.5487i	−0.524004	+	1.61272i	0.242274	+	0.970208i	$0.422107\pi$
$271$	−8.62619	+	26.5487i	−0.524004	+	1.61272i	−0.766277	+	0.642510i	$0.777893\pi$
$272$		0			0
$273$	4.10197	+	5.64588i	0.248263	+	0.341704i
$274$		0			0
$275$	−10.6229	+	15.8282i	−0.640588	+	0.954474i
$276$		0			0
$277$	−1.30649	−	1.79823i	−0.0784995	−	0.108045i	0.767962	−	0.640496i	$-0.221271\pi$
$277$	−1.30649	−	1.79823i	−0.0784995	−	0.108045i	−0.846461	+	0.532451i	$0.821271\pi$
$278$		0			0
$279$	−4.14833	+	12.7672i	−0.248354	+	0.764354i
$280$		0			0
$281$	−7.95505	−	24.4831i	−0.474559	−	1.46054i	−0.846552	−	0.532306i	$-0.821325\pi$
$281$	−7.95505	−	24.4831i	−0.474559	−	1.46054i	0.371993	−	0.928235i	$-0.378675\pi$
$282$		0			0
$283$	−11.7512	+	3.81819i	−0.698535	+	0.226968i	−0.636692	−	0.771118i	$-0.719698\pi$
$283$	−11.7512	+	3.81819i	−0.698535	+	0.226968i	−0.0618429	+	0.998086i	$0.519698\pi$
$284$		0			0
$285$	12.9450	−	2.29802i	0.766795	−	0.136123i
$286$		0			0
$287$	−6.13474	+	8.44375i	−0.362122	+	0.498419i
$288$		0			0
$289$	2.63636	−	1.91542i	0.155080	−	0.112672i
$290$		0			0
$291$	−5.32094	−	3.86589i	−0.311919	−	0.226622i
$292$		0			0
$293$			15.9980i			0.934614i	0.884095	+	0.467307i	$0.154776\pi$
$293$			15.9980i			0.934614i	−0.884095	+	0.467307i	$0.845224\pi$
$294$		0			0
$295$	4.93110	−	10.1401i	0.287100	−	0.590377i
$296$		0			0
$297$	−16.3101	−	5.29948i	−0.946410	−	0.307507i
$298$		0			0
$299$	−23.1344			−1.33790
$300$		0			0
$301$	−10.8778			−0.626989
$302$		0			0
$303$	3.15955	+	1.02660i	0.181511	+	0.0589766i
$304$		0			0
$305$	−1.20453	−	1.16051i	−0.0689711	−	0.0664504i
$306$		0			0
$307$		−	25.8788i		−	1.47698i	−0.674265	−	0.738490i	$-0.735539\pi$
$307$		−	25.8788i		−	1.47698i	0.674265	−	0.738490i	$-0.264461\pi$
$308$		0			0
$309$	−5.61201	−	4.07737i	−0.319256	−	0.231953i
$310$		0			0
$311$	−9.49496	+	6.89849i	−0.538410	+	0.391178i	−0.823494	−	0.567325i	$-0.807978\pi$
$311$	−9.49496	+	6.89849i	−0.538410	+	0.391178i	0.285084	+	0.958502i	$0.407978\pi$
$312$		0			0
$313$	−1.69099	+	2.32745i	−0.0955803	+	0.131555i	−0.854129	−	0.520062i	$-0.825909\pi$
$313$	−1.69099	+	2.32745i	−0.0955803	+	0.131555i	0.758548	+	0.651617i	$0.225909\pi$
$314$		0			0
$315$	−6.74976	−	3.28240i	−0.380306	−	0.184943i
$316$		0			0
$317$	23.1001	−	7.50568i	1.29743	−	0.421561i	0.422744	−	0.906249i	$-0.361067\pi$
$317$	23.1001	−	7.50568i	1.29743	−	0.421561i	0.874687	+	0.484688i	$0.161067\pi$
$318$		0			0
$319$	3.12364	+	9.61357i	0.174890	+	0.538256i
$320$		0			0
$321$	−3.12189	+	9.60818i	−0.174247	+	0.536277i
$322$		0			0
$323$	18.2310	+	25.0929i	1.01440	+	1.39621i
$324$		0			0
$325$	−7.56831	+	26.6265i	−0.419815	+	1.47698i
$326$		0			0
$327$	6.15438	+	8.47078i	0.340338	+	0.468435i
$328$		0			0
$329$	1.38973	−	4.27715i	0.0766184	−	0.235807i
$330$		0			0
$331$	−3.99163	−	12.2850i	−0.219400	−	0.675243i	−0.998812	−	0.0487317i	$-0.984482\pi$
$331$	−3.99163	−	12.2850i	−0.219400	−	0.675243i	0.779412	−	0.626512i	$-0.215518\pi$
$332$		0			0
$333$	8.44401	−	2.74362i	0.462729	−	0.150350i
$334$		0			0
$335$	14.0150	+	26.2849i	0.765722	+	1.43610i
$336$		0			0
$337$	−6.18433	+	8.51200i	−0.336882	+	0.463678i	−0.943528	−	0.331294i	$-0.892515\pi$
$337$	−6.18433	+	8.51200i	−0.336882	+	0.463678i	0.606646	+	0.794972i	$0.292515\pi$
$338$		0			0
$339$	10.9367	−	7.94596i	0.593999	−	0.431565i
$340$		0			0
$341$	−18.2243	−	13.2407i	−0.986899	−	0.717024i
$342$		0			0
$343$			17.4587i			0.942680i
$344$		0			0
$345$	−7.03497	+	3.75102i	−0.378750	+	0.201948i
$346$		0			0
$347$	−23.0903	−	7.50251i	−1.23955	−	0.402756i	−0.385388	−	0.922755i	$-0.625932\pi$
$347$	−23.0903	−	7.50251i	−1.23955	−	0.402756i	−0.854167	+	0.519999i	$0.825932\pi$
$348$		0			0
$349$	1.62888			0.0871919			0.0435959	−	0.999049i	$-0.486119\pi$
$349$	1.62888			0.0871919			0.0435959	+	0.999049i	$0.486119\pi$
$350$		0			0
$351$	−24.9034			−1.32924
$352$		0			0
$353$	9.80968	+	3.18736i	0.522116	+	0.169646i	0.558206	−	0.829703i	$-0.311490\pi$
$353$	9.80968	+	3.18736i	0.522116	+	0.169646i	−0.0360892	+	0.999349i	$0.511490\pi$
$354$		0			0
$355$	−8.54436	−	1.19074i	−0.453487	−	0.0631978i
$356$		0			0
$357$			5.67367i			0.300282i
$358$		0			0
$359$	3.45296	+	2.50872i	0.182240	+	0.132405i	0.675165	−	0.737666i	$-0.264072\pi$
$359$	3.45296	+	2.50872i	0.182240	+	0.132405i	−0.492925	+	0.870072i	$0.664072\pi$
$360$		0			0
$361$	−23.0464	+	16.7442i	−1.21297	+	0.881273i
$362$		0			0
$363$	1.77291	−	2.44021i	0.0930539	−	0.128078i
$364$		0			0
$365$	−6.95155	+	7.21525i	−0.363861	+	0.377664i
$366$		0			0
$367$	27.6401	−	8.98081i	1.44280	−	0.468794i	0.520031	−	0.854147i	$-0.325920\pi$
$367$	27.6401	−	8.98081i	1.44280	−	0.468794i	0.922769	+	0.385353i	$0.125920\pi$
$368$		0			0
$369$	−4.95994	−	15.2651i	−0.258204	−	0.794671i
$370$		0			0
$371$	0.246934	−	0.759985i	0.0128202	−	0.0394564i
$372$		0			0
$373$	−10.0442	−	13.8247i	−0.520070	−	0.715814i	0.465507	−	0.885044i	$-0.345872\pi$
$373$	−10.0442	−	13.8247i	−0.520070	−	0.715814i	−0.985577	+	0.169230i	$0.945872\pi$
$374$		0			0
$375$	2.01578	+	9.32402i	0.104094	+	0.481490i
$376$		0			0
$377$	8.62787	+	11.8753i	0.444358	+	0.611607i
$378$		0			0
$379$	0.737344	−	2.26931i	0.0378748	−	0.116567i	−0.930332	−	0.366720i	$-0.880481\pi$
$379$	0.737344	−	2.26931i	0.0378748	−	0.116567i	0.968206	+	0.250153i	$0.0804809\pi$
$380$		0			0
$381$	−0.461139	−	1.41924i	−0.0236248	−	0.0727098i
$382$		0			0
$383$	−20.0821	+	6.52507i	−1.02615	+	0.333415i	−0.773266	−	0.634082i	$-0.781378\pi$
$383$	−20.0821	+	6.52507i	−1.02615	+	0.333415i	−0.252881	+	0.967497i	$0.581378\pi$
$384$		0			0
$385$	8.73845	−	9.06994i	0.445353	−	0.462247i
$386$		0			0
$387$	9.83282	−	13.5337i	0.499830	−	0.687958i
$388$		0			0
$389$	−18.8160	+	13.6707i	−0.954011	+	0.693130i	−0.951752	−	0.306868i	$-0.900719\pi$
$389$	−18.8160	+	13.6707i	−0.954011	+	0.693130i	−0.00225922	+	0.999997i	$0.500719\pi$
$390$		0			0
$391$	−15.2162	−	11.0552i	−0.769517	−	0.559087i
$392$		0			0
$393$			15.5185i			0.782803i
$394$		0			0
$395$	36.8050	+	5.12913i	1.85186	+	0.258075i
$396$		0			0
$397$	28.1348	+	9.14155i	1.41204	+	0.458801i	0.913065	−	0.407813i	$-0.133709\pi$
$397$	28.1348	+	9.14155i	1.41204	+	0.458801i	0.498979	+	0.866614i	$0.333709\pi$
$398$		0			0
$399$	−8.68650			−0.434869
$400$		0			0
$401$	25.3875			1.26779			0.633895	−	0.773419i	$-0.281455\pi$
$401$	25.3875			1.26779			0.633895	+	0.773419i	$0.281455\pi$
$402$		0			0
$403$	−31.1104	−	10.1084i	−1.54972	−	0.503534i
$404$		0			0
$405$	5.87582	−	3.13297i	0.291972	−	0.155678i
$406$		0			0
$407$			14.8985i			0.738494i
$408$		0			0
$409$	9.22081	+	6.69931i	0.455940	+	0.331260i	0.791936	−	0.610604i	$-0.209073\pi$
$409$	9.22081	+	6.69931i	0.455940	+	0.331260i	−0.335997	+	0.941863i	$0.609073\pi$
$410$		0			0
$411$	−3.66002	+	2.65916i	−0.180535	+	0.131167i
$412$		0			0
$413$	−4.37885	+	6.02697i	−0.215469	+	0.296568i
$414$		0			0
$415$	−1.89728	−	3.55831i	−0.0931337	−	0.174670i
$416$		0			0
$417$	13.6079	−	4.42147i	0.666381	−	0.216520i
$418$		0			0
$419$	−7.11888	−	21.9097i	−0.347780	−	1.07036i	−0.960079	−	0.279730i	$-0.909755\pi$
$419$	−7.11888	−	21.9097i	−0.347780	−	1.07036i	0.612299	−	0.790627i	$-0.290245\pi$
$420$		0			0
$421$	−10.6097	+	32.6533i	−0.517085	+	1.59142i	0.262372	+	0.964967i	$0.415495\pi$
$421$	−10.6097	+	32.6533i	−0.517085	+	1.59142i	−0.779456	+	0.626456i	$0.784505\pi$
$422$		0			0
$423$	4.06522	+	5.59529i	0.197658	+	0.272052i
$424$		0			0
$425$	−17.7019	+	13.8964i	−0.858669	+	0.674075i
$426$		0			0
$427$	0.649565	+	0.894049i	0.0314346	+	0.0432661i
$428$		0			0
$429$	5.56512	−	17.1277i	0.268687	−	0.826932i
$430$		0			0
$431$	−6.47896	−	19.9402i	−0.312080	−	0.960484i	−0.976940	−	0.213516i	$-0.931509\pi$
$431$	−6.47896	−	19.9402i	−0.312080	−	0.960484i	0.664859	−	0.746969i	$-0.268491\pi$
$432$		0			0
$433$	−19.7657	+	6.42227i	−0.949880	+	0.308635i	−0.742667	−	0.669661i	$-0.766439\pi$
$433$	−19.7657	+	6.42227i	−0.949880	+	0.308635i	−0.207213	+	0.978296i	$0.566439\pi$
$434$		0			0
$435$	4.54911	+	2.21223i	0.218113	+	0.106068i
$436$		0			0
$437$	16.9258	−	23.2963i	0.809670	−	1.11441i
$438$		0			0
$439$	−8.37149	+	6.08225i	−0.399550	+	0.290290i	−0.769358	−	0.638818i	$-0.779424\pi$
$439$	−8.37149	+	6.08225i	−0.399550	+	0.290290i	0.369808	+	0.929108i	$0.379424\pi$
$440$		0			0
$441$	−8.85471	−	6.43332i	−0.421653	−	0.306349i
$442$		0			0
$443$			22.6484i			1.07606i	0.842926	+	0.538029i	$0.180831\pi$
$443$			22.6484i			1.07606i	−0.842926	+	0.538029i	$0.819169\pi$
$444$		0			0
$445$	20.8625	+	20.1000i	0.988976	+	0.952831i
$446$		0			0
$447$	5.82791	+	1.89360i	0.275650	+	0.0895643i
$448$		0			0
$449$	−39.0991			−1.84520			−0.922601	−	0.385755i	$-0.873941\pi$
$449$	−39.0991			−1.84520			−0.922601	+	0.385755i	$0.873941\pi$
$450$		0			0
$451$	26.9337			1.26826
$452$		0			0
$453$	−6.53942	−	2.12479i	−0.307249	−	0.0998312i
$454$		0			0
$455$	7.99835	−	16.4474i	0.374969	−	0.771066i
$456$		0			0
$457$		−	11.2189i		−	0.524799i	−0.964959	−	0.262399i	$-0.915486\pi$
$457$		−	11.2189i		−	0.524799i	0.964959	−	0.262399i	$-0.0845138\pi$
$458$		0			0
$459$	−16.3797	−	11.9005i	−0.764539	−	0.555470i
$460$		0			0
$461$	−14.0125	+	10.1807i	−0.652626	+	0.474160i	−0.864165	−	0.503209i	$-0.832153\pi$
$461$	−14.0125	+	10.1807i	−0.652626	+	0.474160i	0.211539	+	0.977370i	$0.432153\pi$
$462$		0			0
$463$	−5.30456	+	7.30109i	−0.246524	+	0.339311i	−0.914290	−	0.405060i	$-0.867251\pi$
$463$	−5.30456	+	7.30109i	−0.246524	+	0.339311i	0.667766	+	0.744371i	$0.267251\pi$
$464$		0			0
$465$	−11.0994	+	1.97038i	−0.514720	+	0.0913741i
$466$		0			0
$467$	−22.6434	+	7.35727i	−1.04781	+	0.340454i	−0.781808	−	0.623519i	$-0.785702\pi$
$467$	−22.6434	+	7.35727i	−1.04781	+	0.340454i	−0.266001	+	0.963973i	$0.585702\pi$
$468$		0			0
$469$	−6.08173	−	18.7176i	−0.280828	−	0.864301i
$470$		0			0
$471$	3.93700	−	12.1168i	0.181407	−	0.558314i
$472$		0			0
$473$	16.4998	+	22.7101i	0.758664	+	1.04421i
$474$		0			0
$475$	−21.2757	−	27.1020i	−0.976196	−	1.24352i
$476$		0			0
$477$	0.722327	+	0.994198i	0.0330731	+	0.0455212i
$478$		0			0
$479$	0.743104	−	2.28704i	0.0339533	−	0.104498i	−0.932644	−	0.360799i	$-0.882504\pi$
$479$	0.743104	−	2.28704i	0.0339533	−	0.104498i	0.966597	+	0.256302i	$0.0825040\pi$
$480$		0			0
$481$	6.68549	+	20.5758i	0.304832	+	0.938177i
$482$		0			0
$483$	5.00965	−	1.62773i	0.227947	−	0.0740645i
$484$		0			0
$485$	−2.37908	+	17.0715i	−0.108028	+	0.775177i
$486$		0			0
$487$	8.25243	−	11.3585i	0.373953	−	0.514702i	−0.580017	−	0.814605i	$-0.696954\pi$
$487$	8.25243	−	11.3585i	0.373953	−	0.514702i	0.953970	+	0.299902i	$0.0969540\pi$
$488$		0			0
$489$	12.0732	−	8.77171i	0.545970	−	0.396670i
$490$		0			0
$491$	1.82781	+	1.32798i	0.0824880	+	0.0599311i	0.628265	−	0.777999i	$-0.283765\pi$
$491$	1.82781	+	1.32798i	0.0824880	+	0.0599311i	−0.545777	+	0.837931i	$0.683765\pi$
$492$		0			0
$493$			11.9337i			0.537467i
$494$		0			0
$495$	3.38544	+	19.0706i	0.152164	+	0.857159i
$496$		0			0
$497$	5.42086	+	1.76135i	0.243159	+	0.0790071i
$498$		0			0
$499$	34.0514			1.52435			0.762176	−	0.647370i	$-0.224131\pi$
$499$	34.0514			1.52435			0.762176	+	0.647370i	$0.224131\pi$
$500$		0			0
$501$	2.91708			0.130326
$502$		0			0
$503$	−26.6609	−	8.66264i	−1.18875	−	0.386248i	−0.353139	−	0.935571i	$-0.614886\pi$
$503$	−26.6609	−	8.66264i	−1.18875	−	0.386248i	−0.835610	+	0.549323i	$0.814886\pi$
$504$		0			0
$505$	−1.52178	−	8.57233i	−0.0677181	−	0.381464i
$506$		0			0
$507$		−	15.0596i		−	0.668821i
$508$		0			0
$509$	−15.8622	−	11.5246i	−0.703081	−	0.510818i	0.177854	−	0.984057i	$-0.443085\pi$
$509$	−15.8622	−	11.5246i	−0.703081	−	0.510818i	−0.880934	+	0.473239i	$0.843085\pi$
$510$		0			0
$511$	5.35545	−	3.89096i	0.236911	−	0.172126i
$512$		0			0
$513$	18.2200	−	25.0776i	0.804432	−	1.10721i
$514$		0			0
$515$	−2.50922	+	18.0054i	−0.110570	+	0.793412i
$516$		0			0
$517$	−11.0376	+	3.58632i	−0.485431	+	0.157726i
$518$		0			0
$519$	6.04968	+	18.6190i	0.265551	+	0.817283i
$520$		0			0
$521$	1.04871	−	3.22761i	0.0459450	−	0.141404i	−0.925452	−	0.378864i	$-0.876315\pi$
$521$	1.04871	−	3.22761i	0.0459450	−	0.141404i	0.971397	+	0.237460i	$0.0763148\pi$
$522$		0			0
$523$	13.3150	+	18.3266i	0.582226	+	0.801366i	0.993937	−	0.109949i	$-0.0350687\pi$
$523$	13.3150	+	18.3266i	0.582226	+	0.801366i	−0.411711	+	0.911314i	$0.635069\pi$
$524$		0			0
$525$	−0.234556	−	6.29836i	−0.0102369	−	0.274883i
$526$		0			0
$527$	−15.6318	−	21.5153i	−0.680930	−	0.937220i
$528$		0			0
$529$	1.71144	−	5.26726i	0.0744103	−	0.229011i
$530$		0			0
$531$	−3.54030	−	10.8959i	−0.153636	−	0.472843i
$532$		0			0
$533$	37.1971	−	12.0861i	1.61118	−	0.523506i
$534$		0			0
$535$	26.0685	−	4.62772i	1.12704	−	0.200074i
$536$		0			0
$537$	11.9898	−	16.5026i	0.517398	−	0.712138i
$538$		0			0
$539$	14.8585	−	10.7954i	0.640002	−	0.464989i
$540$		0			0
$541$	17.7933	+	12.9276i	0.764994	+	0.555801i	0.900438	−	0.434984i	$-0.143246\pi$
$541$	17.7933	+	12.9276i	0.764994	+	0.555801i	−0.135444	+	0.990785i	$0.543246\pi$
$542$		0			0
$543$			9.06524i			0.389027i
$544$		0			0
$545$	12.0003	−	24.6768i	0.514037	−	1.05704i
$546$		0			0
$547$	−17.0702	−	5.54645i	−0.729870	−	0.237149i	−0.0795726	−	0.996829i	$-0.525356\pi$
$547$	−17.0702	−	5.54645i	−0.729870	−	0.237149i	−0.650297	+	0.759680i	$0.725356\pi$
$548$		0			0
$549$	−1.69950			−0.0725327
$550$		0			0
$551$	−18.2707			−0.778360
$552$		0			0
$553$	−23.3505	−	7.58704i	−0.992964	−	0.322634i
$554$		0			0
$555$	5.36916	+	5.17293i	0.227908	+	0.219579i
$556$		0			0
$557$			20.5801i			0.872009i	0.899945	+	0.436004i	$0.143607\pi$
$557$			20.5801i			0.872009i	−0.899945	+	0.436004i	$0.856393\pi$
$558$		0			0
$559$	32.9781	+	23.9600i	1.39483	+	1.01340i
$560$		0			0
$561$	11.8451	−	8.60599i	0.500102	−	0.363345i
$562$		0			0
$563$	−9.35024	+	12.8695i	−0.394066	+	0.542385i	−0.959242	−	0.282585i	$-0.908808\pi$
$563$	−9.35024	+	12.8695i	−0.394066	+	0.542385i	0.565177	+	0.824970i	$0.308808\pi$
$564$		0			0
$565$	−31.8604	−	15.4937i	−1.34038	−	0.651824i
$566$		0			0
$567$	−4.18421	+	1.35953i	−0.175721	+	0.0570951i
$568$		0			0
$569$	−7.60203	−	23.3967i	−0.318694	−	0.980839i	−0.974207	−	0.225655i	$-0.927548\pi$
$569$	−7.60203	−	23.3967i	−0.318694	−	0.980839i	0.655513	−	0.755184i	$-0.272452\pi$
$570$		0			0
$571$	−1.46436	+	4.50683i	−0.0612815	+	0.188605i	−0.977010	−	0.213192i	$-0.931614\pi$
$571$	−1.46436	+	4.50683i	−0.0612815	+	0.188605i	0.915729	+	0.401797i	$0.131614\pi$
$572$		0			0
$573$	2.69347	+	3.70724i	0.112521	+	0.154872i
$574$		0			0
$575$	17.3486	+	11.6434i	0.723486	+	0.485562i
$576$		0			0
$577$	2.04571	+	2.81568i	0.0851642	+	0.117218i	0.849473	−	0.527632i	$-0.176920\pi$
$577$	2.04571	+	2.81568i	0.0851642	+	0.117218i	−0.764309	+	0.644850i	$0.776920\pi$
$578$		0			0
$579$	−1.85579	+	5.71154i	−0.0771241	+	0.237364i
$580$		0			0
$581$	0.823312	+	2.53390i	0.0341568	+	0.105124i
$582$		0			0
$583$	−1.96121	+	0.637234i	−0.0812248	+	0.0263915i
$584$		0			0
$585$	13.2331	+	24.8185i	0.547122	+	1.02612i
$586$		0			0
$587$	3.88361	−	5.34534i	0.160294	−	0.220626i	−0.721314	−	0.692608i	$-0.756462\pi$
$587$	3.88361	−	5.34534i	0.160294	−	0.220626i	0.881608	+	0.471983i	$0.156462\pi$
$588$		0			0
$589$	32.9403	−	23.9325i	1.35728	−	0.986123i
$590$		0			0
$591$	−5.59550	−	4.06537i	−0.230168	−	0.167227i
$592$		0			0
$593$		−	12.0096i		−	0.493176i	−0.969120	−	0.246588i	$-0.920691\pi$
$593$		−	12.0096i		−	0.493176i	0.969120	−	0.246588i	$-0.0793095\pi$
$594$		0			0
$595$	13.1205	−	6.99578i	0.537886	−	0.286799i
$596$		0			0
$597$	−16.9492	−	5.50714i	−0.693686	−	0.225392i
$598$		0			0
$599$	−6.99933			−0.285985			−0.142992	−	0.989724i	$-0.545672\pi$
$599$	−6.99933			−0.285985			−0.142992	+	0.989724i	$0.545672\pi$
$600$		0			0
$601$	−40.2796			−1.64304			−0.821519	−	0.570181i	$-0.806873\pi$
$601$	−40.2796			−1.64304			−0.821519	+	0.570181i	$0.806873\pi$
$602$		0			0
$603$	28.7851	+	9.35284i	1.17222	+	0.380877i
$604$		0			0
$605$	−7.82907	−	1.09106i	−0.318297	−	0.0443577i
$606$		0			0
$607$			18.1182i			0.735394i	0.929946	+	0.367697i	$0.119854\pi$
$607$			18.1182i			0.735394i	−0.929946	+	0.367697i	$0.880146\pi$
$608$		0			0
$609$	−2.70386	−	1.96447i	−0.109566	−	0.0796045i
$610$		0			0
$611$	−13.6342	+	9.90586i	−0.551582	+	0.400748i
$612$		0			0
$613$	24.9960	−	34.4040i	1.00958	−	1.38956i	0.0903167	−	0.995913i	$-0.471212\pi$
$613$	24.9960	−	34.4040i	1.00958	−	1.38956i	0.919260	−	0.393650i	$-0.128788\pi$
$614$		0			0
$615$	9.35166	−	9.70640i	0.377095	−	0.391400i
$616$		0			0
$617$	6.03204	−	1.95993i	0.242841	−	0.0789038i	−0.185068	−	0.982726i	$-0.559250\pi$
$617$	6.03204	−	1.95993i	0.242841	−	0.0789038i	0.427909	+	0.903822i	$0.359250\pi$
$618$		0			0
$619$	−3.48148	−	10.7149i	−0.139932	−	0.430668i	0.856392	−	0.516326i	$-0.172701\pi$
$619$	−3.48148	−	10.7149i	−0.139932	−	0.430668i	−0.996325	+	0.0856583i	$0.972701\pi$
$620$		0			0
$621$	−5.80855	+	17.8769i	−0.233089	+	0.717374i
$622$		0			0
$623$	−11.2505	−	15.4849i	−0.450741	−	0.620391i
$624$		0			0
$625$	19.0764	−	16.1583i	0.763057	−	0.646331i
$626$		0			0
$627$	13.1759	+	18.1351i	0.526197	+	0.724248i
$628$		0			0
$629$	−5.43530	+	16.7281i	−0.216719	+	0.666994i
$630$		0			0
$631$	1.28691	+	3.96070i	0.0512310	+	0.157673i	0.973399	−	0.229117i	$-0.0735839\pi$
$631$	1.28691	+	3.96070i	0.0512310	+	0.157673i	−0.922168	+	0.386790i	$0.873584\pi$
$632$		0			0
$633$	2.71487	−	0.882115i	0.107906	−	0.0350609i
$634$		0			0
$635$	−2.71342	+	2.81635i	−0.107679	+	0.111763i
$636$		0			0
$637$	15.6763	−	21.5766i	0.621118	−	0.854896i
$638$		0			0
$639$	−7.09147	+	5.15225i	−0.280534	+	0.203820i
$640$		0			0
$641$	−24.5529	−	17.8387i	−0.969782	−	0.704588i	−0.0143803	−	0.999897i	$-0.504578\pi$
$641$	−24.5529	−	17.8387i	−0.969782	−	0.704588i	−0.955402	+	0.295309i	$0.904578\pi$
$642$		0			0
$643$		−	11.1954i		−	0.441505i	−0.975330	−	0.220752i	$-0.929149\pi$
$643$		−	11.1954i		−	0.441505i	0.975330	−	0.220752i	$-0.0708512\pi$
$644$		0			0
$645$	13.9132	+	1.93894i	0.547832	+	0.0763457i
$646$		0			0
$647$	3.38313	+	1.09925i	0.133005	+	0.0432159i	0.374763	−	0.927121i	$-0.377724\pi$
$647$	3.38313	+	1.09925i	0.133005	+	0.0432159i	−0.241758	+	0.970337i	$0.577724\pi$
$648$		0			0
$649$	19.2247			0.754635
$650$		0			0
$651$	7.44803			0.291911
$652$		0			0
$653$	−25.7568	−	8.36890i	−1.00794	−	0.327500i	−0.241907	−	0.970299i	$-0.577773\pi$
$653$	−25.7568	−	8.36890i	−1.00794	−	0.327500i	−0.766035	+	0.642799i	$0.777773\pi$
$654$		0			0
$655$	35.8867	−	19.1347i	1.40221	−	0.747653i
$656$		0			0
$657$			10.1802i			0.397166i
$658$		0			0
$659$	7.69424	+	5.59019i	0.299725	+	0.217763i	0.727475	−	0.686134i	$-0.240694\pi$
$659$	7.69424	+	5.59019i	0.299725	+	0.217763i	−0.427750	+	0.903897i	$0.640694\pi$
$660$		0			0
$661$	23.0789	−	16.7678i	0.897665	−	0.652191i	−0.0402006	−	0.999192i	$-0.512800\pi$
$661$	23.0789	−	16.7678i	0.897665	−	0.652191i	0.937865	+	0.347000i	$0.112800\pi$
$662$		0			0
$663$	12.4971	−	17.2007i	0.485345	−	0.668021i
$664$		0			0
$665$	10.7107	+	20.0877i	0.415342	+	0.778967i
$666$		0			0
$667$	10.5370	−	3.42369i	0.407996	−	0.132566i
$668$		0			0
$669$	0.633362	+	1.94929i	0.0244872	+	0.0753638i
$670$		0			0
$671$	0.881260	−	2.71224i	0.0340207	−	0.104705i
$672$		0			0
$673$	5.15474	+	7.09489i	0.198700	+	0.273488i	0.896727	−	0.442584i	$-0.145938\pi$
$673$	5.15474	+	7.09489i	0.198700	+	0.273488i	−0.698026	+	0.716072i	$0.745938\pi$
$674$		0			0
$675$	18.6751	+	12.5337i	0.718806	+	0.482421i
$676$		0			0
$677$	−9.94809	−	13.6924i	−0.382336	−	0.526241i	0.573865	−	0.818950i	$-0.305443\pi$
$677$	−9.94809	−	13.6924i	−0.382336	−	0.526241i	−0.956202	+	0.292709i	$0.905443\pi$
$678$		0			0
$679$	3.51914	−	10.8308i	0.135052	−	0.415648i
$680$		0			0
$681$	−2.43833	−	7.50441i	−0.0934370	−	0.287570i
$682$		0			0
$683$	4.89160	−	1.58938i	0.187172	−	0.0608158i	−0.213931	−	0.976849i	$-0.568627\pi$
$683$	4.89160	−	1.58938i	0.187172	−	0.0608158i	0.401103	+	0.916033i	$0.368627\pi$
$684$		0			0
$685$	10.6622	+	5.18504i	0.407384	+	0.198110i
$686$		0			0
$687$	−12.6883	+	17.4639i	−0.484087	+	0.666289i
$688$		0			0
$689$	−2.42260	+	1.76012i	−0.0922936	+	0.0670552i
$690$		0			0
$691$	−12.4920	−	9.07594i	−0.475216	−	0.345265i	0.324254	−	0.945970i	$-0.394887\pi$
$691$	−12.4920	−	9.07594i	−0.475216	−	0.345265i	−0.799471	+	0.600705i	$0.794887\pi$
$692$		0			0
$693$		−	12.7970i		−	0.486117i
$694$		0			0
$695$	−27.0036	−	26.0167i	−1.02430	−	0.986869i
$696$		0			0
$697$	30.2412	+	9.82596i	1.14547	+	0.372185i
$698$		0			0
$699$	−8.15169			−0.308325
$700$		0			0
$701$	−1.31123			−0.0495246			−0.0247623	−	0.999693i	$-0.507883\pi$
$701$	−1.31123			−0.0495246			−0.0247623	+	0.999693i	$0.507883\pi$
$702$		0			0
$703$	−25.6111	−	8.32155i	−0.965941	−	0.313853i
$704$		0			0
$705$	−2.53991	+	5.22294i	−0.0956586	+	0.196707i
$706$		0			0
$707$			5.75231i			0.216338i
$708$		0			0
$709$	0.280923	+	0.204102i	0.0105503	+	0.00766523i	0.593048	−	0.805167i	$-0.297924\pi$
$709$	0.280923	+	0.204102i	0.0105503	+	0.00766523i	−0.582498	+	0.812832i	$0.697924\pi$
$710$		0			0
$711$	30.5467	−	22.1935i	1.14559	−	0.832320i
$712$		0			0
$713$	−14.5126	+	19.9749i	−0.543501	+	0.748064i
$714$		0			0
$715$	−46.4700	+	8.24943i	−1.73788	+	0.308511i
$716$		0			0
$717$	10.8730	−	3.53284i	0.406059	−	0.131936i
$718$		0			0
$719$	−14.3344	−	44.1166i	−0.534581	−	1.64527i	−0.744552	−	0.667564i	$-0.767337\pi$
$719$	−14.3344	−	44.1166i	−0.534581	−	1.64527i	0.209971	−	0.977708i	$-0.432663\pi$
$720$		0			0
$721$	3.71165	−	11.4233i	0.138229	−	0.425426i
$722$		0			0
$723$	4.91461	+	6.76438i	0.182776	+	0.251570i
$724$		0			0
$725$	−0.493354	−	13.2476i	−0.0183227	−	0.492005i
$726$		0			0
$727$	−27.8742	−	38.3655i	−1.03380	−	1.42290i	−0.902058	−	0.431614i	$-0.857944\pi$
$727$	−27.8742	−	38.3655i	−1.03380	−	1.42290i	−0.131738	−	0.991285i	$-0.542056\pi$
$728$		0			0
$729$	−1.46729	+	4.51585i	−0.0543440	+	0.167254i
$730$		0			0
$731$	10.2410	+	31.5184i	0.378775	+	1.16575i
$732$		0			0
$733$	−48.5450	+	15.7732i	−1.79305	+	0.582597i	−0.999659	−	0.0261156i	$-0.991686\pi$
$733$	−48.5450	+	15.7732i	−1.79305	+	0.582597i	−0.793391	+	0.608713i	$0.791686\pi$
$734$		0			0
$735$	1.26859	−	9.10300i	0.0467927	−	0.335769i
$736$		0			0
$737$	−29.8526	+	41.0885i	−1.09963	+	1.51352i
$738$		0			0
$739$	4.09664	−	2.97638i	0.150697	−	0.109488i	−0.509882	−	0.860245i	$-0.670311\pi$
$739$	4.09664	−	2.97638i	0.150697	−	0.109488i	0.660579	+	0.750757i	$0.270311\pi$
$740$		0			0
$741$	26.3347	+	19.1332i	0.967428	+	0.702877i
$742$		0			0
$743$		−	7.49320i		−	0.274899i	−0.990509	−	0.137449i	$-0.956110\pi$
$743$		−	7.49320i		−	0.274899i	0.990509	−	0.137449i	$-0.0438905\pi$
$744$		0			0
$745$	−2.80697	−	15.8120i	−0.102840	−	0.579306i
$746$		0			0
$747$	−3.89677	−	1.26614i	−0.142575	−	0.0463256i
$748$		0			0
$749$	−17.4928			−0.639172
$750$		0			0
$751$	−22.1201			−0.807173			−0.403587	−	0.914941i	$-0.632237\pi$
$751$	−22.1201			−0.807173			−0.403587	+	0.914941i	$0.632237\pi$
$752$		0			0
$753$	6.41757	+	2.08519i	0.233869	+	0.0759887i
$754$		0			0
$755$	3.14967	+	17.7424i	0.114628	+	0.645713i
$756$		0			0
$757$			0.540763i			0.0196544i	0.999952	+	0.00982718i	$0.00312814\pi$
$757$			0.540763i			0.0196544i	−0.999952	+	0.00982718i	$0.996872\pi$
$758$		0			0
$759$	−10.9971	−	7.98984i	−0.399168	−	0.290013i
$760$		0			0
$761$	2.06457	−	1.50000i	0.0748407	−	0.0543749i	−0.549736	−	0.835339i	$-0.685272\pi$
$761$	2.06457	−	1.50000i	0.0748407	−	0.0543749i	0.624576	+	0.780964i	$0.285272\pi$
$762$		0			0
$763$	−10.6563	+	14.6672i	−0.385785	+	0.530988i
$764$		0			0
$765$	−3.15616	+	22.6476i	−0.114111	+	0.818824i
$766$		0			0
$767$	26.5505	−	8.62678i	0.958682	−	0.311495i
$768$		0			0
$769$	14.4766	+	44.5545i	0.522040	+	1.60668i	0.770095	+	0.637929i	$0.220209\pi$
$769$	14.4766	+	44.5545i	0.522040	+	1.60668i	−0.248055	+	0.968746i	$0.579791\pi$
$770$		0			0
$771$	4.66674	−	14.3627i	0.168068	−	0.517261i
$772$		0			0
$773$	11.0434	+	15.1999i	0.397202	+	0.546702i	0.960039	−	0.279866i	$-0.0902901\pi$
$773$	11.0434	+	15.1999i	0.397202	+	0.546702i	−0.562837	+	0.826568i	$0.690290\pi$
$774$		0			0
$775$	18.2423	+	23.2379i	0.655284	+	0.834731i
$776$		0			0
$777$	−2.89542	−	3.98520i	−0.103873	−	0.142968i
$778$		0			0
$779$	−15.0437	+	46.2999i	−0.538998	+	1.65887i
$780$		0			0
$781$	−4.54530	−	13.9890i	−0.162644	−	0.500566i
$782$		0			0
$783$	11.3427	−	3.68548i	0.405356	−	0.131708i
$784$		0			0
$785$	−32.8748	+	5.83599i	−1.17335	+	0.208295i
$786$		0			0
$787$	−5.62115	+	7.73685i	−0.200372	+	0.275789i	−0.897365	−	0.441290i	$-0.854521\pi$
$787$	−5.62115	+	7.73685i	−0.200372	+	0.275789i	0.696992	+	0.717079i	$0.254521\pi$
$788$		0			0
$789$	16.5451	−	12.0207i	0.589022	−	0.427950i
$790$		0			0
$791$	18.9369	+	13.7585i	0.673319	+	0.489195i
$792$		0			0
$793$		−	4.14122i		−	0.147059i
$794$		0			0
$795$	−0.451304	+	0.928037i	−0.0160061	+	0.0329141i
$796$		0			0
$797$	−0.960348	−	0.312036i	−0.0340173	−	0.0110529i	0.291959	−	0.956431i	$-0.405693\pi$
$797$	−0.960348	−	0.312036i	−0.0340173	−	0.0110529i	−0.325976	+	0.945378i	$0.605693\pi$
$798$		0			0
$799$	−13.7014			−0.484719
$800$		0			0
$801$	29.4353			1.04005
$802$		0			0
$803$	−16.2466	−	5.27884i	−0.573330	−	0.186286i
$804$		0			0
$805$	−9.94119	−	9.57786i	−0.350381	−	0.337575i
$806$		0			0
$807$		−	16.0071i		−	0.563476i
$808$		0			0
$809$	0.627224	+	0.455705i	0.0220520	+	0.0160217i	0.598757	−	0.800931i	$-0.295662\pi$
$809$	0.627224	+	0.455705i	0.0220520	+	0.0160217i	−0.576705	+	0.816953i	$0.695662\pi$
$810$		0			0
$811$	4.12534	−	2.99723i	0.144860	−	0.105247i	−0.512995	−	0.858392i	$-0.671464\pi$
$811$	4.12534	−	2.99723i	0.144860	−	0.105247i	0.657855	+	0.753145i	$0.271464\pi$
$812$		0			0
$813$	−13.9998	+	19.2691i	−0.490995	+	0.675797i
$814$		0			0
$815$	−35.1713	−	17.1038i	−1.23200	−	0.599119i
$816$		0			0
$817$	−48.2553	+	15.6791i	−1.68824	+	0.548543i
$818$		0			0
$819$	−5.74244	−	17.6734i	−0.200657	−	0.617559i
$820$		0			0
$821$	−0.899576	+	2.76861i	−0.0313954	+	0.0966252i	−0.965526	−	0.260305i	$-0.916177\pi$
$821$	−0.899576	+	2.76861i	−0.0313954	+	0.0966252i	0.934131	+	0.356931i	$0.116177\pi$
$822$		0			0
$823$	23.3797	+	32.1795i	0.814967	+	1.12171i	0.990538	+	0.137239i	$0.0438227\pi$
$823$	23.3797	+	32.1795i	0.814967	+	1.12171i	−0.175571	+	0.984467i	$0.556177\pi$
$824$		0			0
$825$	−12.7935	+	10.0432i	−0.445413	+	0.349660i
$826$		0			0
$827$	22.0301	+	30.3218i	0.766062	+	1.05439i	0.996686	+	0.0813507i	$0.0259234\pi$
$827$	22.0301	+	30.3218i	0.766062	+	1.05439i	−0.230624	+	0.973043i	$0.574077\pi$
$828$		0			0
$829$	−2.55874	+	7.87500i	−0.0888688	+	0.273510i	−0.985607	−	0.169051i	$-0.945930\pi$
$829$	−2.55874	+	7.87500i	−0.0888688	+	0.273510i	0.896739	+	0.442561i	$0.145930\pi$
$830$		0			0
$831$	−0.586054	−	1.80369i	−0.0203300	−	0.0625693i
$832$		0			0
$833$	20.6216	−	6.70035i	0.714495	−	0.232153i
$834$		0			0
$835$	−3.59684	−	6.74580i	−0.124474	−	0.233448i
$836$		0			0
$837$	−15.6223	+	21.5022i	−0.539985	+	0.743225i
$838$		0			0
$839$	−7.50765	+	5.45463i	−0.259193	+	0.188315i	−0.709791	−	0.704412i	$-0.751211\pi$
$839$	−7.50765	+	5.45463i	−0.259193	+	0.188315i	0.450598	+	0.892727i	$0.351211\pi$
$840$		0			0
$841$	17.7743	+	12.9138i	0.612908	+	0.445304i
$842$		0			0
$843$		−	21.9648i		−	0.756509i
$844$		0			0
$845$	−34.8256	+	18.5689i	−1.19804	+	0.638790i
$846$		0			0
$847$	4.96706	+	1.61389i	0.170670	+	0.0554541i
$848$		0			0
$849$	−10.5425			−0.361817
$850$		0			0
$851$	16.3297			0.559774
$852$		0			0
$853$	11.5495	+	3.75264i	0.395446	+	0.128488i	0.499988	−	0.866032i	$-0.333338\pi$
$853$	11.5495	+	3.75264i	0.395446	+	0.128488i	−0.104542	+	0.994520i	$0.533338\pi$
$854$		0			0
$855$	−34.6739	−	4.83214i	−1.18582	−	0.165256i
$856$		0			0
$857$			7.84578i			0.268007i	0.990981	+	0.134003i	$0.0427833\pi$
$857$			7.84578i			0.268007i	−0.990981	+	0.134003i	$0.957217\pi$
$858$		0			0
$859$	21.9597	+	15.9547i	0.749255	+	0.544366i	0.895596	−	0.444868i	$-0.146750\pi$
$859$	21.9597	+	15.9547i	0.749255	+	0.544366i	−0.146341	+	0.989234i	$0.546750\pi$
$860$		0			0
$861$	−7.20448	+	5.23436i	−0.245528	+	0.178386i
$862$		0			0
$863$	33.5350	−	46.1570i	1.14155	−	1.57120i	0.377539	−	0.925994i	$-0.376770\pi$
$863$	33.5350	−	46.1570i	1.14155	−	1.57120i	0.764006	−	0.645209i	$-0.223230\pi$
$864$		0			0
$865$	35.5973	−	36.9477i	1.21034	−	1.25626i
$866$		0			0
$867$	2.64436	−	0.859203i	0.0898070	−	0.0291801i
$868$		0			0
$869$	19.5790	+	60.2579i	0.664172	+	2.04411i
$870$		0			0
$871$	−22.7904	+	70.1417i	−0.772224	+	2.37666i
$872$		0			0
$873$	10.2941	+	14.1686i	0.348403	+	0.479536i
$874$		0			0
$875$	−14.2758	+	8.30845i	−0.482611	+	0.280877i
$876$		0			0
$877$	−7.23415	−	9.95696i	−0.244280	−	0.336223i	0.669218	−	0.743066i	$-0.266629\pi$
$877$	−7.23415	−	9.95696i	−0.244280	−	0.336223i	−0.913498	+	0.406844i	$0.866629\pi$
$878$		0			0
$879$	−4.21809	+	12.9819i	−0.142273	+	0.437870i
$880$		0			0
$881$	5.06645	+	15.5929i	0.170693	+	0.525340i	0.999411	−	0.0343277i	$-0.0109290\pi$
$881$	5.06645	+	15.5929i	0.170693	+	0.525340i	−0.828717	+	0.559667i	$0.810929\pi$
$882$		0			0
$883$	4.36478	−	1.41820i	0.146887	−	0.0477264i	−0.234651	−	0.972080i	$-0.575395\pi$
$883$	4.36478	−	1.41820i	0.146887	−	0.0477264i	0.381538	+	0.924353i	$0.375395\pi$
$884$		0			0
$885$	6.67501	−	6.92822i	0.224378	−	0.232890i
$886$		0			0
$887$	−30.1517	+	41.5003i	−1.01240	+	1.39344i	−0.0949948	+	0.995478i	$0.530283\pi$
$887$	−30.1517	+	41.5003i	−1.01240	+	1.39344i	−0.917401	+	0.397965i	$0.869717\pi$
$888$		0			0
$889$	2.09041	−	1.51877i	0.0701099	−	0.0509379i
$890$		0			0
$891$	9.18509	+	6.67336i	0.307712	+	0.223566i
$892$		0			0
$893$		−	20.9771i		−	0.701970i
$894$		0			0
$895$	−52.9462	−	7.37856i	−1.76980	−	0.246638i
$896$		0			0
$897$	−18.7729	−	6.09970i	−0.626810	−	0.203663i
$898$		0			0
$899$	15.6658			0.522484
$900$		0			0
$901$	−2.43452			−0.0811057
$902$		0			0
$903$	−8.82707	−	2.86809i	−0.293747	−	0.0954440i
$904$		0			0
$905$	20.9635	−	11.1777i	0.696851	−	0.371558i
$906$		0			0
$907$		−	2.86749i		−	0.0952136i	−0.998866	−	0.0476068i	$-0.984841\pi$
$907$		−	2.86749i		−	0.0952136i	0.998866	−	0.0476068i	$-0.0151594\pi$
$908$		0			0
$909$	−7.15676	−	5.19969i	−0.237375	−	0.172463i
$910$		0			0
$911$	−8.70682	+	6.32587i	−0.288470	+	0.209586i	−0.722603	−	0.691263i	$-0.757055\pi$
$911$	−8.70682	+	6.32587i	−0.288470	+	0.209586i	0.434134	+	0.900849i	$0.357055\pi$
$912$		0			0
$913$	4.04128	−	5.56235i	0.133747	−	0.184087i
$914$		0			0
$915$	−0.671459	−	1.25931i	−0.0221977	−	0.0416315i
$916$		0			0
$917$	−25.5552	+	8.30338i	−0.843906	+	0.274202i
$918$		0			0
$919$	−1.99879	−	6.15164i	−0.0659340	−	0.202924i	0.912662	−	0.408715i	$-0.134023\pi$
$919$	−1.99879	−	6.15164i	−0.0659340	−	0.202924i	−0.978596	+	0.205791i	$0.934023\pi$
$920$		0			0
$921$	6.82328	−	20.9999i	0.224835	−	0.691970i
$922$		0			0
$923$	−12.5547	−	17.2800i	−0.413243	−	0.568780i
$924$		0			0
$925$	5.34218	−	18.7946i	0.175650	−	0.617964i
$926$		0			0
$927$	10.8573	+	14.9437i	0.356599	+	0.490816i
$928$		0			0
$929$	−7.98426	+	24.5730i	−0.261955	+	0.806215i	0.730424	+	0.682994i	$0.239322\pi$
$929$	−7.98426	+	24.5730i	−0.261955	+	0.806215i	−0.992379	+	0.123221i	$0.960678\pi$
$930$		0			0
$931$	10.2584	+	31.5720i	0.336205	+	1.03473i
$932$		0			0
$933$	−9.52377	+	3.09446i	−0.311794	+	0.101308i
$934$		0			0
$935$	−34.5068	−	16.7807i	−1.12849	−	0.548786i
$936$		0			0
$937$	27.3971	−	37.7088i	0.895023	−	1.23189i	−0.0770057	−	0.997031i	$-0.524536\pi$
$937$	27.3971	−	37.7088i	0.895023	−	1.23189i	0.972029	−	0.234863i	$-0.0754640\pi$
$938$		0			0
$939$	−1.98585	+	1.44281i	−0.0648058	+	0.0470842i
$940$		0			0
$941$	−32.0618	−	23.2942i	−1.04518	−	0.759371i	−0.0738934	−	0.997266i	$-0.523542\pi$
$941$	−32.0618	−	23.2942i	−1.04518	−	0.759371i	−0.971291	+	0.237895i	$0.923542\pi$
$942$		0			0
$943$		−	29.5209i		−	0.961333i
$944$		0			0
$945$	−10.7013	−	10.3102i	−0.348114	−	0.335391i
$946$		0			0
$947$	−26.4207	−	8.58459i	−0.858556	−	0.278962i	−0.153531	−	0.988144i	$-0.549064\pi$
$947$	−26.4207	−	8.58459i	−0.858556	−	0.278962i	−0.705025	+	0.709182i	$0.749064\pi$
$948$		0			0
$949$	−24.8064			−0.805248
$950$		0			0
$951$	20.7241			0.672023
$952$		0			0
$953$	−45.5260	−	14.7923i	−1.47473	−	0.479169i	−0.542198	−	0.840251i	$-0.682408\pi$
$953$	−45.5260	−	14.7923i	−1.47473	−	0.479169i	−0.932534	+	0.361082i	$0.882408\pi$
$954$		0			0
$955$	5.25194	−	10.7998i	0.169949	−	0.349474i
$956$		0			0
$957$			8.62473i			0.278798i
$958$		0			0
$959$	−6.33734	−	4.60435i	−0.204643	−	0.148682i
$960$		0			0
$961$	−3.16433	+	2.29902i	−0.102075	+	0.0741620i
$962$		0			0
$963$	15.8123	−	21.7637i	0.509543	−	0.701326i
$964$		0			0
$965$	15.4963	−	2.75093i	0.498843	−	0.0885555i
$966$		0			0
$967$	14.4346	−	4.69008i	0.464185	−	0.150823i	−0.0675819	−	0.997714i	$-0.521528\pi$
$967$	14.4346	−	4.69008i	0.464185	−	0.150823i	0.531767	+	0.846891i	$0.321528\pi$
$968$		0			0
$969$	8.17791	+	25.1690i	0.262712	+	0.808546i
$970$		0			0
$971$	4.65266	−	14.3194i	0.149311	−	0.459532i	−0.848229	−	0.529629i	$-0.822331\pi$
$971$	4.65266	−	14.3194i	0.149311	−	0.459532i	0.997540	+	0.0700977i	$0.0223311\pi$
$972$		0			0
$973$	14.5622	+	20.0431i	0.466842	+	0.642553i
$974$		0			0
$975$	−13.1619	+	19.6112i	−0.421519	+	0.628061i
$976$		0			0
$977$	−31.9648	−	43.9957i	−1.02264	−	1.40755i	−0.910334	−	0.413874i	$-0.864175\pi$
$977$	−31.9648	−	43.9957i	−1.02264	−	1.40755i	−0.112309	−	0.993673i	$-0.535825\pi$
$978$		0			0
$979$	−15.2634	+	46.9761i	−0.487822	+	1.50136i
$980$		0			0
$981$	−8.61565	−	26.5163i	−0.275077	−	0.846599i
$982$		0			0
$983$	23.9980	−	7.79742i	0.765417	−	0.248699i	0.0998152	−	0.995006i	$-0.468175\pi$
$983$	23.9980	−	7.79742i	0.765417	−	0.248699i	0.665602	+	0.746307i	$0.268175\pi$
$984$		0			0
$985$	−2.50184	+	17.9524i	−0.0797151	+	0.572010i
$986$		0			0
$987$	2.25546	−	3.10437i	0.0717919	−	0.0988131i
$988$		0			0
$989$	24.8916	−	18.0848i	0.791507	−	0.575063i
$990$		0			0
$991$	17.4086	+	12.6481i	0.553001	+	0.401779i	0.828891	−	0.559410i	$-0.188972\pi$
$991$	17.4086	+	12.6481i	0.553001	+	0.401779i	−0.275890	+	0.961189i	$0.588972\pi$
$992$		0			0
$993$		−	11.0214i		−	0.349752i
$994$		0			0
$995$	8.16348	+	45.9858i	0.258800	+	1.45785i
$996$		0			0
$997$	−9.16907	−	2.97921i	−0.290387	−	0.0943526i	0.160201	−	0.987084i	$-0.448786\pi$
$997$	−9.16907	−	2.97921i	−0.290387	−	0.0943526i	−0.450588	+	0.892732i	$0.648786\pi$
$998$		0			0
$999$	17.5783			0.556153

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.y.d.289.6		32
4.3	odd	2		200.2.q.a.89.3	yes	32
20.3	even	4		1000.2.m.e.801.6		32
20.7	even	4		1000.2.m.d.801.3		32
20.19	odd	2		1000.2.q.c.449.6		32
25.3	odd	20		10000.2.a.br.1.5		16
25.9	even	10	inner	400.2.y.d.209.6		32
25.22	odd	20		10000.2.a.bq.1.12		16
100.3	even	20		5000.2.a.q.1.12		16
100.47	even	20		5000.2.a.r.1.5		16
100.59	odd	10		200.2.q.a.9.3	✓	32
100.63	even	20		1000.2.m.e.201.6		32
100.87	even	20		1000.2.m.d.201.3		32
100.91	odd	10		1000.2.q.c.49.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.q.a.9.3	✓	32	100.59	odd	10
200.2.q.a.89.3	yes	32	4.3	odd	2
400.2.y.d.209.6		32	25.9	even	10	inner
400.2.y.d.289.6		32	1.1	even	1	trivial
1000.2.m.d.201.3		32	100.87	even	20
1000.2.m.d.801.3		32	20.7	even	4
1000.2.m.e.201.6		32	100.63	even	20
1000.2.m.e.801.6		32	20.3	even	4
1000.2.q.c.49.6		32	100.91	odd	10
1000.2.q.c.449.6		32	20.19	odd	2
5000.2.a.q.1.12		16	100.3	even	20
5000.2.a.r.1.5		16	100.47	even	20
10000.2.a.bq.1.12		16	25.22	odd	20
10000.2.a.br.1.5		16	25.3	odd	20

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.y (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.811472 + 0.263663i) q^{3} +(-0.390840 - 2.20165i) q^{5} +1.47738i q^{7} +(-1.83808 - 1.33545i) q^{9} +O(q^{10})\)	\(q+(0.811472 + 0.263663i) q^{3} +(-0.390840 - 2.20165i) q^{5} +1.47738i q^{7} +(-1.83808 - 1.33545i) q^{9} +(3.08437 - 2.24093i) q^{11} +(3.25413 - 4.47892i) q^{13} +(0.263337 - 1.88962i) q^{15} +(4.28068 - 1.39088i) q^{17} +(2.12946 + 6.55380i) q^{19} +(-0.389530 + 1.19885i) q^{21} +(-2.45619 - 3.38065i) q^{23} +(-4.69449 + 1.72098i) q^{25} +(-2.64400 - 3.63915i) q^{27} +(-0.819316 + 2.52160i) q^{29} +(-1.82585 - 5.61939i) q^{31} +(3.09373 - 1.00521i) q^{33} +(3.25266 - 0.577418i) q^{35} +(-2.29696 + 3.16150i) q^{37} +(3.82156 - 2.77653i) q^{39} +(5.71537 + 4.15246i) q^{41} +7.36296i q^{43} +(-2.22178 + 4.56875i) q^{45} +(-2.89510 - 0.940676i) q^{47} +4.81736 q^{49} +3.84037 q^{51} +(-0.514416 - 0.167144i) q^{53} +(-6.13922 - 5.91485i) q^{55} +5.87969i q^{57} +(4.07951 + 2.96394i) q^{59} +(0.605160 - 0.439675i) q^{61} +(1.97295 - 2.71554i) q^{63} +(-11.1328 - 5.41389i) q^{65} +(-12.6695 + 4.11658i) q^{67} +(-1.10177 - 3.39091i) q^{69} +(1.19221 - 3.66925i) q^{71} +(-2.63370 - 3.62497i) q^{73} +(-4.26321 + 0.158766i) q^{75} +(3.31069 + 4.55677i) q^{77} +(-5.13548 + 15.8054i) q^{79} +(0.920236 + 2.83219i) q^{81} +(1.71513 - 0.557280i) q^{83} +(-4.73528 - 8.88092i) q^{85} +(-1.32970 + 1.83018i) q^{87} +(-10.4814 + 7.61517i) q^{89} +(6.61705 + 4.80757i) q^{91} -5.04139i q^{93} +(13.5969 - 7.24980i) q^{95} +(-7.33111 - 2.38202i) q^{97} -8.66196 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{5} + 10 q^{9}+O(q^{10}) \) 32 * q + 2 * q^5 + 10 * q^9	\( 32 q + 2 q^{5} + 10 q^{9} - 6 q^{11} - 12 q^{15} + 6 q^{19} - 4 q^{21} + 30 q^{23} + 6 q^{25} - 2 q^{29} - 6 q^{31} - 8 q^{35} - 40 q^{37} + 12 q^{39} - 12 q^{45} + 20 q^{47} - 60 q^{49} + 60 q^{51} - 30 q^{53} + 28 q^{55} + 30 q^{59} + 14 q^{61} + 20 q^{63} - 26 q^{65} - 4 q^{69} - 12 q^{71} + 40 q^{73} - 16 q^{75} - 16 q^{79} - 52 q^{81} - 30 q^{83} + 60 q^{85} - 110 q^{87} + 24 q^{89} + 4 q^{91} - 68 q^{95} + 30 q^{97} - 92 q^{99}+O(q^{100}) \) 32 * q + 2 * q^5 + 10 * q^9 - 6 * q^11 - 12 * q^15 + 6 * q^19 - 4 * q^21 + 30 * q^23 + 6 * q^25 - 2 * q^29 - 6 * q^31 - 8 * q^35 - 40 * q^37 + 12 * q^39 - 12 * q^45 + 20 * q^47 - 60 * q^49 + 60 * q^51 - 30 * q^53 + 28 * q^55 + 30 * q^59 + 14 * q^61 + 20 * q^63 - 26 * q^65 - 4 * q^69 - 12 * q^71 + 40 * q^73 - 16 * q^75 - 16 * q^79 - 52 * q^81 - 30 * q^83 + 60 * q^85 - 110 * q^87 + 24 * q^89 + 4 * q^91 - 68 * q^95 + 30 * q^97 - 92 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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