LMFDB - Embedded newform 300.2.x.a.53.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(17,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 10, 13]))

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

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

chi := DirichletCharacter("300.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.x (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			53.2
Character	$\chi$	$=$	300.53
Dual form			300.2.x.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.58605 - 0.696021i) q^{3} +(-1.99640 + 1.00718i) q^{5} +(0.814380 - 0.814380i) q^{7} +(2.03111 + 2.20785i) q^{9} +O(q^{10})$	\(q+(-1.58605 - 0.696021i) q^{3} +(-1.99640 + 1.00718i) q^{5} +(0.814380 - 0.814380i) q^{7} +(2.03111 + 2.20785i) q^{9} +(3.46407 + 1.12554i) q^{11} +(-2.63271 + 5.16697i) q^{13} +(3.86740 - 0.207896i) q^{15} +(-0.902627 - 0.142962i) q^{17} +(4.29919 + 5.91733i) q^{19} +(-1.85847 + 0.724821i) q^{21} +(3.05909 + 6.00381i) q^{23} +(2.97120 - 4.02144i) q^{25} +(-1.68473 - 4.91545i) q^{27} +(-4.30536 - 3.12803i) q^{29} +(-1.78920 + 1.29993i) q^{31} +(-4.71078 - 4.19623i) q^{33} +(-0.805601 + 2.44605i) q^{35} +(2.74637 + 1.39935i) q^{37} +(7.77193 - 6.36266i) q^{39} +(2.66555 - 0.866089i) q^{41} +(-3.01283 - 3.01283i) q^{43} +(-6.27859 - 2.36206i) q^{45} +(-0.998165 - 6.30217i) q^{47} +5.67357i q^{49} +(1.33211 + 0.854993i) q^{51} +(-8.04180 + 1.27370i) q^{53} +(-8.04927 + 1.24189i) q^{55} +(-2.70014 - 12.3775i) q^{57} +(1.98388 + 6.10574i) q^{59} +(-4.21356 + 12.9680i) q^{61} +(3.45212 + 0.143935i) q^{63} +(0.0518720 - 12.9669i) q^{65} +(0.976557 - 6.16574i) q^{67} +(-0.673095 - 11.6515i) q^{69} +(5.88318 - 8.09750i) q^{71} +(-8.26387 + 4.21065i) q^{73} +(-7.51147 + 4.31019i) q^{75} +(3.73768 - 1.90445i) q^{77} +(4.29102 - 5.90609i) q^{79} +(-0.749199 + 8.96876i) q^{81} +(-0.190258 + 1.20124i) q^{83} +(1.94599 - 0.623695i) q^{85} +(4.65135 + 7.95784i) q^{87} +(3.41396 - 10.5071i) q^{89} +(2.06386 + 6.35190i) q^{91} +(3.74254 - 0.816433i) q^{93} +(-14.5427 - 7.48329i) q^{95} +(3.84712 - 0.609325i) q^{97} +(4.55086 + 9.93423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q - 2 * q^3 + 4 * q^7	$ 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) $ 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{20}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		0			0
$2$		0			0
$3$	−1.58605	−	0.696021i	−0.915706	−	0.401848i
$3$	−1.58605	−	0.696021i	−0.915706	−	0.401848i
$4$		0			0
$5$	−1.99640	+	1.00718i	−0.892815	+	0.450423i
$5$	−1.99640	+	1.00718i	−0.892815	+	0.450423i
$6$		0			0
$7$	0.814380	−	0.814380i	0.307807	−	0.307807i	−0.536252	−	0.844058i	$-0.680160\pi$
$7$	0.814380	−	0.814380i	0.307807	−	0.307807i	0.844058	+	0.536252i	$0.180160\pi$
$8$		0			0
$9$	2.03111	+	2.20785i	0.677036	+	0.735950i
$10$		0			0
$11$	3.46407	+	1.12554i	1.04446	+	0.339364i	0.780490	−	0.625168i	$-0.214970\pi$
$11$	3.46407	+	1.12554i	1.04446	+	0.339364i	0.263965	+	0.964532i	$0.414970\pi$
$12$		0			0
$13$	−2.63271	+	5.16697i	−0.730181	+	1.43306i	0.164510	+	0.986375i	$0.447396\pi$
$13$	−2.63271	+	5.16697i	−0.730181	+	1.43306i	−0.894691	+	0.446686i	$0.852604\pi$
$14$		0			0
$15$	3.86740	−	0.207896i	0.998558	−	0.0536785i
$16$		0			0
$17$	−0.902627	−	0.142962i	−0.218919	−	0.0346734i	0.0460112	−	0.998941i	$-0.485349\pi$
$17$	−0.902627	−	0.142962i	−0.218919	−	0.0346734i	−0.264930	+	0.964268i	$0.585349\pi$
$18$		0			0
$19$	4.29919	+	5.91733i	0.986302	+	1.35753i	0.933364	+	0.358930i	$0.116858\pi$
$19$	4.29919	+	5.91733i	0.986302	+	1.35753i	0.0529373	+	0.998598i	$0.483142\pi$
$20$		0			0
$21$	−1.85847	+	0.724821i	−0.405552	+	0.158169i
$22$		0			0
$23$	3.05909	+	6.00381i	0.637865	+	1.25188i	0.953039	+	0.302847i	$0.0979372\pi$
$23$	3.05909	+	6.00381i	0.637865	+	1.25188i	−0.315174	+	0.949034i	$0.602063\pi$
$24$		0			0
$25$	2.97120	−	4.02144i	0.594239	−	0.804289i
$26$		0			0
$27$	−1.68473	−	4.91545i	−0.324226	−	0.945980i
$28$		0			0
$29$	−4.30536	−	3.12803i	−0.799486	−	0.580861i	0.111277	−	0.993789i	$-0.464506\pi$
$29$	−4.30536	−	3.12803i	−0.799486	−	0.580861i	−0.910763	+	0.412929i	$0.864506\pi$
$30$		0			0
$31$	−1.78920	+	1.29993i	−0.321350	+	0.233475i	−0.736751	−	0.676164i	$-0.763641\pi$
$31$	−1.78920	+	1.29993i	−0.321350	+	0.233475i	0.415401	+	0.909638i	$0.363641\pi$
$32$		0			0
$33$	−4.71078	−	4.19623i	−0.820041	−	0.730470i
$34$		0			0
$35$	−0.805601	+	2.44605i	−0.136171	+	0.413458i
$36$		0			0
$37$	2.74637	+	1.39935i	0.451501	+	0.230051i	0.664927	−	0.746908i	$-0.268462\pi$
$37$	2.74637	+	1.39935i	0.451501	+	0.230051i	−0.213427	+	0.976959i	$0.568462\pi$
$38$		0			0
$39$	7.77193	−	6.36266i	1.24450	−	1.01884i
$40$		0			0
$41$	2.66555	−	0.866089i	0.416289	−	0.135260i	−0.0933813	−	0.995630i	$-0.529768\pi$
$41$	2.66555	−	0.866089i	0.416289	−	0.135260i	0.509670	+	0.860370i	$0.329768\pi$
$42$		0			0
$43$	−3.01283	−	3.01283i	−0.459453	−	0.459453i	0.439023	−	0.898476i	$-0.355325\pi$
$43$	−3.01283	−	3.01283i	−0.459453	−	0.459453i	−0.898476	+	0.439023i	$0.855325\pi$
$44$		0			0
$45$	−6.27859	−	2.36206i	−0.935957	−	0.352115i
$46$		0			0
$47$	−0.998165	−	6.30217i	−0.145597	−	0.919265i	−0.947022	−	0.321169i	$-0.895924\pi$
$47$	−0.998165	−	6.30217i	−0.145597	−	0.919265i	0.801424	−	0.598096i	$-0.204076\pi$
$48$		0			0
$49$			5.67357i			0.810510i
$50$		0			0
$51$	1.33211	+	0.854993i	0.186532	+	0.119723i
$52$		0			0
$53$	−8.04180	+	1.27370i	−1.10463	+	0.174956i	−0.682002	−	0.731350i	$-0.738891\pi$
$53$	−8.04180	+	1.27370i	−1.10463	+	0.174956i	−0.422623	+	0.906305i	$0.638891\pi$
$54$		0			0
$55$	−8.04927	+	1.24189i	−1.08536	+	0.167457i
$56$		0			0
$57$	−2.70014	−	12.3775i	−0.357643	−	1.63944i
$58$		0			0
$59$	1.98388	+	6.10574i	0.258279	+	0.794900i	0.993166	+	0.116711i	$0.0372350\pi$
$59$	1.98388	+	6.10574i	0.258279	+	0.794900i	−0.734887	+	0.678189i	$0.762765\pi$
$60$		0			0
$61$	−4.21356	+	12.9680i	−0.539492	+	1.66038i	0.194247	+	0.980953i	$0.437774\pi$
$61$	−4.21356	+	12.9680i	−0.539492	+	1.66038i	−0.733739	+	0.679432i	$0.762226\pi$
$62$		0			0
$63$	3.45212	+	0.143935i	0.434926	+	0.0181341i
$64$		0			0
$65$	0.0518720	−	12.9669i	0.00643393	−	1.60835i
$66$		0			0
$67$	0.976557	−	6.16574i	0.119305	−	0.753265i	−0.853406	−	0.521247i	$-0.825467\pi$
$67$	0.976557	−	6.16574i	0.119305	−	0.753265i	0.972712	−	0.232018i	$-0.0745328\pi$
$68$		0			0
$69$	−0.673095	−	11.6515i	−0.0810311	−	1.40268i
$70$		0			0
$71$	5.88318	−	8.09750i	0.698205	−	0.960996i	−0.301766	−	0.953382i	$-0.597576\pi$
$71$	5.88318	−	8.09750i	0.698205	−	0.960996i	0.999971	−	0.00761427i	$-0.00242372\pi$
$72$		0			0
$73$	−8.26387	+	4.21065i	−0.967212	+	0.492819i	−0.864906	−	0.501934i	$-0.832622\pi$
$73$	−8.26387	+	4.21065i	−0.967212	+	0.492819i	−0.102306	+	0.994753i	$0.532622\pi$
$74$		0			0
$75$	−7.51147	+	4.31019i	−0.867350	+	0.497698i
$76$		0			0
$77$	3.73768	−	1.90445i	0.425949	−	0.217032i
$78$		0			0
$79$	4.29102	−	5.90609i	0.482778	−	0.664487i	−0.496258	−	0.868175i	$-0.665293\pi$
$79$	4.29102	−	5.90609i	0.482778	−	0.664487i	0.979036	+	0.203689i	$0.0652930\pi$
$80$		0			0
$81$	−0.749199	+	8.96876i	−0.0832444	+	0.996529i
$82$		0			0
$83$	−0.190258	+	1.20124i	−0.0208835	+	0.131853i	−0.995927	−	0.0901590i	$-0.971262\pi$
$83$	−0.190258	+	1.20124i	−0.0208835	+	0.131853i	0.975044	+	0.222012i	$0.0712625\pi$
$84$		0			0
$85$	1.94599	−	0.623695i	0.211072	−	0.0676492i
$86$		0			0
$87$	4.65135	+	7.95784i	0.498677	+	0.853170i
$88$		0			0
$89$	3.41396	−	10.5071i	0.361879	−	1.11375i	−0.590034	−	0.807378i	$-0.700886\pi$
$89$	3.41396	−	10.5071i	0.361879	−	1.11375i	0.951913	−	0.306369i	$-0.0991143\pi$
$90$		0			0
$91$	2.06386	+	6.35190i	0.216351	+	0.665860i
$92$		0			0
$93$	3.74254	−	0.816433i	0.388084	−	0.0846602i
$94$		0			0
$95$	−14.5427	−	7.48329i	−1.49205	−	0.767769i
$96$		0			0
$97$	3.84712	−	0.609325i	0.390616	−	0.0618675i	0.0419626	−	0.999119i	$-0.486639\pi$
$97$	3.84712	−	0.609325i	0.390616	−	0.0618675i	0.348654	+	0.937252i	$0.386639\pi$
$98$		0			0
$99$	4.55086	+	9.93423i	0.457379	+	0.998428i
$100$		0			0
$101$			1.83199i			0.182290i	0.995838	+	0.0911450i	$0.0290527\pi$
$101$			1.83199i			0.182290i	−0.995838	+	0.0911450i	$0.970947\pi$
$102$		0			0
$103$	−1.59260	−	10.0553i	−0.156923	−	0.990775i	−0.932932	−	0.360053i	$-0.882759\pi$
$103$	−1.59260	−	10.0553i	−0.156923	−	0.990775i	0.776009	−	0.630722i	$-0.217241\pi$
$104$		0			0
$105$	2.98023	−	3.31884i	0.290840	−	0.323885i
$106$		0			0
$107$	12.7040	+	12.7040i	1.22814	+	1.22814i	0.964668	+	0.263470i	$0.0848669\pi$
$107$	12.7040	+	12.7040i	1.22814	+	1.22814i	0.263470	+	0.964668i	$0.415133\pi$
$108$		0			0
$109$	7.48884	−	2.43327i	0.717301	−	0.233065i	0.0724482	−	0.997372i	$-0.476919\pi$
$109$	7.48884	−	2.43327i	0.717301	−	0.233065i	0.644853	+	0.764307i	$0.276919\pi$
$110$		0			0
$111$	−3.38191	−	4.13097i	−0.320996	−	0.392094i
$112$		0			0
$113$	16.6927	+	8.50535i	1.57032	+	0.800116i	0.999776	−	0.0211535i	$-0.00673389\pi$
$113$	16.6927	+	8.50535i	1.57032	+	0.800116i	0.570540	+	0.821270i	$0.306734\pi$
$114$		0			0
$115$	−12.1541	−	8.90494i	−1.13337	−	0.830390i
$116$		0			0
$117$	−16.7552	+	4.68207i	−1.54902	+	0.432857i
$118$		0			0
$119$	−0.851507	+	0.618656i	−0.0780575	+	0.0567121i
$120$		0			0
$121$	1.83371	+	1.33227i	0.166701	+	0.121116i
$122$		0			0
$123$	−4.83051	−	0.481618i	−0.435552	−	0.0434261i
$124$		0			0
$125$	−1.88138	+	11.0209i	−0.168276	+	0.985740i
$126$		0			0
$127$	3.30459	+	6.48562i	0.293235	+	0.575505i	0.989879	−	0.141911i	$-0.0453246\pi$
$127$	3.30459	+	6.48562i	0.293235	+	0.575505i	−0.696645	+	0.717416i	$0.745325\pi$
$128$		0			0
$129$	2.68151	+	6.87550i	0.236094	+	0.605354i
$130$		0			0
$131$	−3.48009	−	4.78993i	−0.304057	−	0.418498i	0.629460	−	0.777033i	$-0.283276\pi$
$131$	−3.48009	−	4.78993i	−0.304057	−	0.418498i	−0.933516	+	0.358535i	$0.883276\pi$
$132$		0			0
$133$	8.32012	+	1.31778i	0.721446	+	0.114266i
$134$		0			0
$135$	8.31411	+	8.11638i	0.715565	+	0.698547i
$136$		0			0
$137$	−2.92241	+	5.73556i	−0.249679	+	0.490022i	−0.981497	−	0.191478i	$-0.938672\pi$
$137$	−2.92241	+	5.73556i	−0.249679	+	0.490022i	0.731818	+	0.681500i	$0.238672\pi$
$138$		0			0
$139$	−2.67670	−	0.869713i	−0.227035	−	0.0737681i	0.193290	−	0.981142i	$-0.438084\pi$
$139$	−2.67670	−	0.869713i	−0.227035	−	0.0737681i	−0.420325	+	0.907373i	$0.638084\pi$
$140$		0			0
$141$	−2.80330	+	10.6903i	−0.236081	+	0.900285i
$142$		0			0
$143$	−14.9355	+	14.9355i	−1.24897	+	1.24897i
$144$		0			0
$145$	11.7457	+	1.90853i	0.975426	+	0.158495i
$146$		0			0
$147$	3.94893	−	8.99857i	0.325702	−	0.742189i
$148$		0			0
$149$	−21.8247			−1.78795			−0.893974	−	0.448119i	$-0.852094\pi$
$149$	−21.8247			−1.78795			−0.893974	+	0.448119i	$0.852094\pi$
$150$		0			0
$151$	−7.79667			−0.634484			−0.317242	−	0.948345i	$-0.602757\pi$
$151$	−7.79667			−0.634484			−0.317242	+	0.948345i	$0.602757\pi$
$152$		0			0
$153$	−1.51770	−	2.28324i	−0.122698	−	0.184589i
$154$		0			0
$155$	2.26270	−	4.39722i	0.181744	−	0.353193i
$156$		0			0
$157$	10.3925	−	10.3925i	0.829410	−	0.829410i	−0.158025	−	0.987435i	$-0.550513\pi$
$157$	10.3925	−	10.3925i	0.829410	−	0.829410i	0.987435	+	0.158025i	$0.0505126\pi$
$158$		0			0
$159$	13.6412	+	3.57712i	1.08182	+	0.283684i
$160$		0			0
$161$	7.38065	+	2.39812i	0.581677	+	0.188998i
$162$		0			0
$163$	3.53766	−	6.94305i	0.277091	−	0.543822i	−0.709957	−	0.704245i	$-0.751286\pi$
$163$	3.53766	−	6.94305i	0.277091	−	0.543822i	0.987048	+	0.160423i	$0.0512859\pi$
$164$		0			0
$165$	13.6309	+	3.63276i	1.06117	+	0.282810i
$166$		0			0
$167$	−0.370295	−	0.0586489i	−0.0286543	−	0.00453839i	0.142091	−	0.989854i	$-0.454617\pi$
$167$	−0.370295	−	0.0586489i	−0.0286543	−	0.00453839i	−0.170745	+	0.985315i	$0.554617\pi$
$168$		0			0
$169$	−12.1253	−	16.6890i	−0.932714	−	1.28377i
$170$		0			0
$171$	−4.33245	+	21.5107i	−0.331311	+	1.64496i
$172$		0			0
$173$	5.57182	+	10.9353i	0.423618	+	0.831397i	0.999900	+	0.0141460i	$0.00450296\pi$
$173$	5.57182	+	10.9353i	0.423618	+	0.831397i	−0.576282	+	0.817251i	$0.695497\pi$
$174$		0			0
$175$	−0.855300	−	5.69466i	−0.0646546	−	0.430476i
$176$		0			0
$177$	1.10320	−	11.0648i	0.0829217	−	0.831684i
$178$		0			0
$179$	−4.46475	−	3.24383i	−0.333711	−	0.242455i	0.408293	−	0.912851i	$-0.366124\pi$
$179$	−4.46475	−	3.24383i	−0.333711	−	0.242455i	−0.742004	+	0.670396i	$0.766124\pi$
$180$		0			0
$181$	8.04985	−	5.84856i	0.598340	−	0.434720i	−0.246949	−	0.969028i	$-0.579428\pi$
$181$	8.04985	−	5.84856i	0.598340	−	0.434720i	0.845289	+	0.534309i	$0.179428\pi$
$182$		0			0
$183$	15.7089	−	17.6352i	1.16124	−	1.30363i
$184$		0			0
$185$	−6.89223	−	0.0275712i	−0.506727	−	0.00202708i
$186$		0			0
$187$	−2.96585	−	1.51118i	−0.216884	−	0.110508i
$188$		0			0
$189$	−5.37506	−	2.63104i	−0.390978	−	0.191380i
$190$		0			0
$191$	9.80442	−	3.18565i	0.709423	−	0.230505i	0.0679914	−	0.997686i	$-0.478341\pi$
$191$	9.80442	−	3.18565i	0.709423	−	0.230505i	0.641431	+	0.767181i	$0.278341\pi$
$192$		0			0
$193$	−0.238354	−	0.238354i	−0.0171571	−	0.0171571i	0.698476	−	0.715633i	$-0.253862\pi$
$193$	−0.238354	−	0.238354i	−0.0171571	−	0.0171571i	−0.715633	+	0.698476i	$0.753862\pi$
$194$		0			0
$195$	−9.10753	+	20.5301i	−0.652204	+	1.47019i
$196$		0			0
$197$	−0.296468	−	1.87183i	−0.0211225	−	0.133362i	0.974874	−	0.222759i	$-0.0715062\pi$
$197$	−0.296468	−	1.87183i	−0.0211225	−	0.133362i	−0.995996	+	0.0893965i	$0.971506\pi$
$198$		0			0
$199$			18.6398i			1.32134i	0.750676	+	0.660670i	$0.229728\pi$
$199$			18.6398i			1.32134i	−0.750676	+	0.660670i	$0.770272\pi$
$200$		0			0
$201$	−5.84035	+	9.09946i	−0.411947	+	0.641826i
$202$		0			0
$203$	−6.05361	+	0.958797i	−0.424880	+	0.0672944i
$204$		0			0
$205$	−4.44919	+	4.41373i	−0.310745	+	0.308268i
$206$		0			0
$207$	−7.04216	+	18.9484i	−0.489464	+	1.31701i
$208$		0			0
$209$	8.23247	+	25.3369i	0.569452	+	1.75259i
$210$		0			0
$211$	7.77153	−	23.9183i	0.535014	−	1.64660i	−0.208604	−	0.978000i	$-0.566892\pi$
$211$	7.77153	−	23.9183i	0.535014	−	1.64660i	0.743618	−	0.668604i	$-0.233108\pi$
$212$		0			0
$213$	−14.9670	+	8.74822i	−1.02552	+	0.599418i
$214$		0			0
$215$	9.04926	+	2.98036i	0.617155	+	0.203259i
$216$		0			0
$217$	−0.398452	+	2.51573i	−0.0270487	+	0.170779i
$218$		0			0
$219$	16.0376	−	0.926472i	1.08372	−	0.0626052i
$220$		0			0
$221$	3.11503	−	4.28748i	0.209540	−	0.288407i
$222$		0			0
$223$	4.28530	−	2.18347i	0.286965	−	0.146216i	−0.304583	−	0.952486i	$-0.598517\pi$
$223$	4.28530	−	2.18347i	0.286965	−	0.146216i	0.591548	+	0.806270i	$0.298517\pi$
$224$		0			0
$225$	14.9136	−	1.60803i	0.994237	−	0.107202i
$226$		0			0
$227$	11.3411	−	5.77860i	0.752738	−	0.383539i	−0.0351307	−	0.999383i	$-0.511185\pi$
$227$	11.3411	−	5.77860i	0.752738	−	0.383539i	0.787868	+	0.615844i	$0.211185\pi$
$228$		0			0
$229$	0.0954879	−	0.131428i	0.00631002	−	0.00868500i	−0.805850	−	0.592119i	$-0.798291\pi$
$229$	0.0954879	−	0.131428i	0.00631002	−	0.00868500i	0.812160	+	0.583434i	$0.198291\pi$
$230$		0			0
$231$	−7.25369	+	0.419037i	−0.477258	+	0.0275706i
$232$		0			0
$233$	0.939042	−	5.92888i	0.0615187	−	0.388414i	−0.937648	−	0.347587i	$-0.887001\pi$
$233$	0.939042	−	5.92888i	0.0615187	−	0.388414i	0.999166	−	0.0408262i	$-0.0129990\pi$
$234$		0			0
$235$	8.34012	+	11.5763i	0.544049	+	0.755154i
$236$		0			0
$237$	−10.9165	+	6.38070i	−0.709105	+	0.414471i
$238$		0			0
$239$	3.44778	−	10.6112i	0.223019	−	0.686380i	−0.775468	−	0.631387i	$-0.782486\pi$
$239$	3.44778	−	10.6112i	0.223019	−	0.686380i	0.998487	−	0.0549938i	$-0.0175139\pi$
$240$		0			0
$241$	−8.68635	−	26.7338i	−0.559537	−	1.72208i	−0.683650	−	0.729810i	$-0.739609\pi$
$241$	−8.68635	−	26.7338i	−0.559537	−	1.72208i	0.124114	−	0.992268i	$-0.460391\pi$
$242$		0			0
$243$	7.43072	−	13.7034i	0.476681	−	0.879076i
$244$		0			0
$245$	−5.71428	−	11.3267i	−0.365072	−	0.723636i
$246$		0			0
$247$	−41.8932	+	6.63523i	−2.66560	+	0.422189i
$248$		0			0
$249$	1.13785	−	1.77280i	0.0721081	−	0.112347i
$250$		0			0
$251$		−	28.1347i		−	1.77585i	−0.459991	−	0.887924i	$-0.652147\pi$
$251$		−	28.1347i		−	1.77585i	0.459991	−	0.887924i	$-0.347853\pi$
$252$		0			0
$253$	3.83936	+	24.2407i	0.241378	+	1.52400i
$254$		0			0
$255$	−3.52054	−	0.365239i	−0.220465	−	0.0228722i
$256$		0			0
$257$	12.8233	+	12.8233i	0.799894	+	0.799894i	0.983079	−	0.183184i	$-0.0586405\pi$
$257$	12.8233	+	12.8233i	0.799894	+	0.799894i	−0.183184	+	0.983079i	$0.558641\pi$
$258$		0			0
$259$	3.37619	−	1.09699i	0.209786	−	0.0681637i
$260$		0			0
$261$	−1.83844	−	15.8590i	−0.113797	−	0.981645i
$262$		0			0
$263$	−18.6904	−	9.52321i	−1.15250	−	0.587226i	−0.229984	−	0.973194i	$-0.573868\pi$
$263$	−18.6904	−	9.52321i	−1.15250	−	0.587226i	−0.922512	+	0.385968i	$0.873868\pi$
$264$		0			0
$265$	14.7718	−	10.6423i	0.907423	−	0.653751i
$266$		0			0
$267$	−12.7279	+	14.2886i	−0.778932	+	0.874446i
$268$		0			0
$269$	−10.9550	+	7.95929i	−0.667940	+	0.485287i	−0.869335	−	0.494223i	$-0.835452\pi$
$269$	−10.9550	+	7.95929i	−0.667940	+	0.485287i	0.201395	+	0.979510i	$0.435452\pi$
$270$		0			0
$271$	1.95011	+	1.41684i	0.118461	+	0.0860669i	0.645438	−	0.763812i	$-0.276675\pi$
$271$	1.95011	+	1.41684i	0.118461	+	0.0860669i	−0.526977	+	0.849879i	$0.676675\pi$
$272$		0			0
$273$	1.14768	−	11.5109i	0.0694607	−	0.696673i
$274$		0			0
$275$	14.8187	−	10.5863i	0.893602	−	0.638380i
$276$		0			0
$277$	−4.61588	−	9.05917i	−0.277341	−	0.544313i	0.709753	−	0.704450i	$-0.248806\pi$
$277$	−4.61588	−	9.05917i	−0.277341	−	0.544313i	−0.987095	+	0.160137i	$0.948806\pi$
$278$		0			0
$279$	−6.50412	−	1.30999i	−0.389391	−	0.0784269i
$280$		0			0
$281$	3.75864	+	5.17333i	0.224222	+	0.308615i	0.906276	−	0.422687i	$-0.138913\pi$
$281$	3.75864	+	5.17333i	0.224222	+	0.308615i	−0.682054	+	0.731302i	$0.738913\pi$
$282$		0			0
$283$	−12.2845	−	1.94568i	−0.730239	−	0.115658i	−0.219766	−	0.975553i	$-0.570529\pi$
$283$	−12.2845	−	1.94568i	−0.730239	−	0.115658i	−0.510472	+	0.859894i	$0.670529\pi$
$284$		0			0
$285$	17.8569	+	21.9909i	1.05775	+	1.30263i
$286$		0			0
$287$	1.46544	−	2.87609i	0.0865024	−	0.169770i
$288$		0			0
$289$	−15.3737	−	4.99521i	−0.904333	−	0.293836i
$290$		0			0
$291$	−6.52583	−	1.71126i	−0.382551	−	0.100316i
$292$		0			0
$293$	20.0058	−	20.0058i	1.16875	−	1.16875i	0.186248	−	0.982503i	$-0.440367\pi$
$293$	20.0058	−	20.0058i	1.16875	−	1.16875i	0.982503	−	0.186248i	$-0.0596329\pi$
$294$		0			0
$295$	−10.1102	−	10.1914i	−0.588636	−	0.593364i
$296$		0			0
$297$	−0.303452	−	18.9237i	−0.0176081	−	1.09806i
$298$		0			0
$299$	−39.0752			−2.25978
$300$		0			0
$301$	−4.90718			−0.282845
$302$		0			0
$303$	1.27511	−	2.90563i	0.0732529	−	0.166924i
$304$		0			0
$305$	−4.64913	−	30.1331i	−0.266208	−	1.72542i
$306$		0			0
$307$	1.67900	−	1.67900i	0.0958255	−	0.0958255i	−0.657569	−	0.753394i	$-0.728415\pi$
$307$	1.67900	−	1.67900i	0.0958255	−	0.0958255i	0.753394	+	0.657569i	$0.228415\pi$
$308$		0			0
$309$	−4.47274	+	17.0566i	−0.254445	+	0.970318i
$310$		0			0
$311$	−16.6707	−	5.41664i	−0.945310	−	0.307150i	−0.204501	−	0.978866i	$-0.565557\pi$
$311$	−16.6707	−	5.41664i	−0.945310	−	0.307150i	−0.740808	+	0.671717i	$0.765557\pi$
$312$		0			0
$313$	7.60246	−	14.9207i	0.429716	−	0.843366i	−0.570047	−	0.821612i	$-0.693075\pi$
$313$	7.60246	−	14.9207i	0.429716	−	0.843366i	0.999763	−	0.0217538i	$-0.00692499\pi$
$314$		0			0
$315$	−7.03677	+	3.18954i	−0.396477	+	0.179710i
$316$		0			0
$317$	10.0629	+	1.59380i	0.565187	+	0.0895168i	0.432488	−	0.901640i	$-0.357636\pi$
$317$	10.0629	+	1.59380i	0.565187	+	0.0895168i	0.132699	+	0.991156i	$0.457636\pi$
$318$		0			0
$319$	−11.3933	−	15.6816i	−0.637904	−	0.878000i
$320$		0			0
$321$	−11.3069	−	28.9913i	−0.631088	−	1.61814i
$322$		0			0
$323$	−3.03461	−	5.95576i	−0.168850	−	0.331388i
$324$		0			0
$325$	12.9564	+	25.9394i	0.718692	+	1.43886i
$326$		0			0
$327$	−13.5713	−	1.35310i	−0.750494	−	0.0748268i
$328$		0			0
$329$	−5.94524	−	4.31947i	−0.327772	−	0.238140i
$330$		0			0
$331$	21.8809	−	15.8974i	1.20268	−	0.873801i	0.208138	−	0.978099i	$-0.433260\pi$
$331$	21.8809	−	15.8974i	1.20268	−	0.873801i	0.994546	+	0.104298i	$0.0332597\pi$
$332$		0			0
$333$	2.48863	+	8.90580i	0.136376	+	0.488035i
$334$		0			0
$335$	4.26038	+	13.2928i	0.232770	+	0.726264i
$336$		0			0
$337$	13.4244	+	6.84007i	0.731273	+	0.372602i	0.779640	−	0.626227i	$-0.215402\pi$
$337$	13.4244	+	6.84007i	0.731273	+	0.372602i	−0.0483675	+	0.998830i	$0.515402\pi$
$338$		0			0
$339$	−20.5555	−	25.1084i	−1.11642	−	1.36370i
$340$		0			0
$341$	−7.66104	+	2.48922i	−0.414869	+	0.134799i
$342$		0			0
$343$	10.3211	+	10.3211i	0.557287	+	0.557287i
$344$		0			0
$345$	13.0789	+	22.5832i	0.704145	+	1.21584i
$346$		0			0
$347$	1.70896	+	10.7899i	0.0917415	+	0.579233i	0.990143	+	0.140059i	$0.0447291\pi$
$347$	1.70896	+	10.7899i	0.0917415	+	0.579233i	−0.898402	+	0.439175i	$0.855271\pi$
$348$		0			0
$349$		−	4.93794i		−	0.264322i	−0.991228	−	0.132161i	$-0.957808\pi$
$349$		−	4.93794i		−	0.264322i	0.991228	−	0.132161i	$-0.0421916\pi$
$350$		0			0
$351$	29.8334	+	4.23600i	1.59239	+	0.226101i
$352$		0			0
$353$	2.96257	−	0.469225i	0.157682	−	0.0249744i	−0.0770944	−	0.997024i	$-0.524564\pi$
$353$	2.96257	−	0.469225i	0.157682	−	0.0249744i	0.234776	+	0.972049i	$0.424564\pi$
$354$		0			0
$355$	−3.58955	+	22.0912i	−0.190513	+	1.17248i
$356$		0			0
$357$	1.78113	−	0.388552i	0.0942674	−	0.0205644i
$358$		0			0
$359$	9.84389	+	30.2964i	0.519540	+	1.59898i	0.774866	+	0.632126i	$0.217817\pi$
$359$	9.84389	+	30.2964i	0.519540	+	1.59898i	−0.255325	+	0.966855i	$0.582183\pi$
$360$		0			0
$361$	−10.6604	+	32.8093i	−0.561074	+	1.72681i
$362$		0			0
$363$	−1.98107	−	3.38935i	−0.103979	−	0.177895i
$364$		0			0
$365$	12.2571	−	16.7293i	0.641565	−	0.875651i
$366$		0			0
$367$	−4.72166	+	29.8114i	−0.246469	+	1.55614i	0.485152	+	0.874430i	$0.338764\pi$
$367$	−4.72166	+	29.8114i	−0.246469	+	1.55614i	−0.731621	+	0.681712i	$0.761236\pi$
$368$		0			0
$369$	7.32621	+	4.12601i	0.381387	+	0.214791i
$370$		0			0
$371$	−5.51180	+	7.58635i	−0.286159	+	0.393864i
$372$		0			0
$373$	17.7102	−	9.02378i	0.916998	−	0.467234i	0.0692297	−	0.997601i	$-0.477946\pi$
$373$	17.7102	−	9.02378i	0.916998	−	0.467234i	0.847768	+	0.530367i	$0.177946\pi$
$374$		0			0
$375$	10.6548	−	16.1702i	0.550209	−	0.835027i
$376$		0			0
$377$	27.4972	−	14.0105i	1.41618	−	0.721579i
$378$		0			0
$379$	−8.60609	+	11.8453i	−0.442065	+	0.608450i	−0.970669	−	0.240418i	$-0.922716\pi$
$379$	−8.60609	+	11.8453i	−0.442065	+	0.608450i	0.528604	+	0.848868i	$0.322716\pi$
$380$		0			0
$381$	−0.727111	−	12.5866i	−0.0372510	−	0.644830i
$382$		0			0
$383$	−4.01050	+	25.3213i	−0.204927	+	1.29386i	0.643868	+	0.765137i	$0.277329\pi$
$383$	−4.01050	+	25.3213i	−0.204927	+	1.29386i	−0.848795	+	0.528722i	$0.822671\pi$
$384$		0			0
$385$	−5.54379	+	7.56653i	−0.282538	+	0.385626i
$386$		0			0
$387$	0.532493	−	12.7713i	0.0270681	−	0.649200i
$388$		0			0
$389$	−3.42204	+	10.5320i	−0.173504	+	0.533991i	−0.999562	−	0.0295942i	$-0.990578\pi$
$389$	−3.42204	+	10.5320i	−0.173504	+	0.533991i	0.826058	+	0.563586i	$0.190578\pi$
$390$		0			0
$391$	−1.90291	−	5.85654i	−0.0962341	−	0.296178i
$392$		0			0
$393$	2.18570	+	10.0193i	0.110254	+	0.505406i
$394$		0			0
$395$	−2.61812	+	16.1127i	−0.131732	+	0.810718i
$396$		0			0
$397$	−34.8560	+	5.52065i	−1.74937	+	0.277074i	−0.947346	−	0.320212i	$-0.896246\pi$
$397$	−34.8560	+	5.52065i	−1.74937	+	0.277074i	−0.802029	+	0.597286i	$0.796246\pi$
$398$		0			0
$399$	−12.2789	−	7.88105i	−0.614715	−	0.394546i
$400$		0			0
$401$			28.2805i			1.41226i	0.708081	+	0.706131i	$0.249561\pi$
$401$			28.2805i			1.41226i	−0.708081	+	0.706131i	$0.750439\pi$
$402$		0			0
$403$	−2.00627	−	12.6671i	−0.0999395	−	0.630993i
$404$		0			0
$405$	−7.53742	−	18.6598i	−0.374537	−	0.927212i
$406$		0			0
$407$	7.93859	+	7.93859i	0.393501	+	0.393501i
$408$		0			0
$409$	15.1592	−	4.92552i	0.749574	−	0.243551i	0.0907761	−	0.995871i	$-0.471065\pi$
$409$	15.1592	−	4.92552i	0.749574	−	0.243551i	0.658798	+	0.752320i	$0.271065\pi$
$410$		0			0
$411$	8.62717	−	7.06282i	0.425547	−	0.348383i
$412$		0			0
$413$	6.58802	+	3.35676i	0.324175	+	0.165176i
$414$		0			0
$415$	−0.830029	−	2.58977i	−0.0407445	−	0.127127i
$416$		0			0
$417$	3.64004	+	3.24245i	0.178254	+	0.158784i
$418$		0			0
$419$	28.4906	−	20.6996i	1.39186	−	1.01124i	0.396197	−	0.918166i	$-0.370330\pi$
$419$	28.4906	−	20.6996i	1.39186	−	1.01124i	0.995659	−	0.0930769i	$-0.0296702\pi$
$420$		0			0
$421$	−1.21908	−	0.885714i	−0.0594143	−	0.0431670i	0.557682	−	0.830055i	$-0.311691\pi$
$421$	−1.21908	−	0.885714i	−0.0594143	−	0.0431670i	−0.617096	+	0.786888i	$0.711691\pi$
$422$		0			0
$423$	11.8869	−	15.0042i	0.577959	−	0.729528i
$424$		0			0
$425$	−3.25680	+	3.20510i	−0.157978	+	0.155470i
$426$		0			0
$427$	7.12945	+	13.9923i	0.345018	+	0.677137i
$428$		0			0
$429$	34.0839	−	13.2930i	1.64559	−	0.641794i
$430$		0			0
$431$	−3.75782	−	5.17220i	−0.181008	−	0.249136i	0.708865	−	0.705344i	$-0.249207\pi$
$431$	−3.75782	−	5.17220i	−0.181008	−	0.249136i	−0.889873	+	0.456208i	$0.849207\pi$
$432$		0			0
$433$	22.5721	+	3.57506i	1.08474	+	0.171807i	0.673110	−	0.739542i	$-0.264958\pi$
$433$	22.5721	+	3.57506i	1.08474	+	0.171807i	0.411634	+	0.911349i	$0.364958\pi$
$434$		0			0
$435$	−17.3009	−	11.2023i	−0.829513	−	0.537108i
$436$		0			0
$437$	−22.3749	+	43.9132i	−1.07034	+	2.10065i
$438$		0			0
$439$	−1.74365	−	0.566545i	−0.0832197	−	0.0270397i	0.267111	−	0.963666i	$-0.413931\pi$
$439$	−1.74365	−	0.566545i	−0.0832197	−	0.0270397i	−0.350331	+	0.936626i	$0.613931\pi$
$440$		0			0
$441$	−12.5264	+	11.5236i	−0.596495	+	0.548745i
$442$		0			0
$443$	−6.75410	+	6.75410i	−0.320897	+	0.320897i	−0.849111	−	0.528214i	$-0.822862\pi$
$443$	−6.75410	+	6.75410i	−0.320897	+	0.320897i	0.528214	+	0.849111i	$0.322862\pi$
$444$		0			0
$445$	3.76686	+	24.4147i	0.178566	+	1.15737i
$446$		0			0
$447$	34.6150	+	15.1905i	1.63724	+	0.718484i
$448$		0			0
$449$	−24.0642			−1.13566			−0.567830	−	0.823146i	$-0.692217\pi$
$449$	−24.0642			−1.13566			−0.567830	+	0.823146i	$0.692217\pi$
$450$		0			0
$451$	10.2085			0.480697
$452$		0			0
$453$	12.3659	+	5.42665i	0.581001	+	0.254966i
$454$		0			0
$455$	−10.5178	−	10.6022i	−0.493080	−	0.497041i
$456$		0			0
$457$	15.7146	−	15.7146i	0.735097	−	0.735097i	−0.236528	−	0.971625i	$-0.576010\pi$
$457$	15.7146	−	15.7146i	0.735097	−	0.735097i	0.971625	+	0.236528i	$0.0760095\pi$
$458$		0			0
$459$	0.817958	+	4.67768i	0.0381790	+	0.218335i
$460$		0			0
$461$	−8.27650	−	2.68920i	−0.385475	−	0.125248i	0.109867	−	0.993946i	$-0.464957\pi$
$461$	−8.27650	−	2.68920i	−0.385475	−	0.125248i	−0.495342	+	0.868698i	$0.664957\pi$
$462$		0			0
$463$	−6.79566	+	13.3372i	−0.315821	+	0.619834i	−0.993281	−	0.115726i	$-0.963081\pi$
$463$	−6.79566	+	13.3372i	−0.315821	+	0.619834i	0.677460	+	0.735560i	$0.263081\pi$
$464$		0			0
$465$	−6.64931	+	5.39932i	−0.308354	+	0.250388i
$466$		0			0
$467$	−32.4831	−	5.14481i	−1.50314	−	0.238074i	−0.650070	−	0.759874i	$-0.725261\pi$
$467$	−32.4831	−	5.14481i	−1.50314	−	0.238074i	−0.853067	+	0.521801i	$0.825261\pi$
$468$		0			0
$469$	−4.22596	−	5.81654i	−0.195137	−	0.268583i
$470$		0			0
$471$	−23.7164	+	9.24960i	−1.09279	+	0.426199i
$472$		0			0
$473$	−7.04558	−	13.8277i	−0.323956	−	0.635800i
$474$		0			0
$475$	36.5699	+	0.292588i	1.67794	+	0.0134249i
$476$		0			0
$477$	−19.1459	−	15.1681i	−0.876630	−	0.694498i
$478$		0			0
$479$	22.4708	+	16.3260i	1.02672	+	0.745953i	0.967649	−	0.252301i	$-0.0811872\pi$
$479$	22.4708	+	16.3260i	1.02672	+	0.745953i	0.0590677	+	0.998254i	$0.481187\pi$
$480$		0			0
$481$	−14.4608	+	10.5064i	−0.659355	+	0.479049i
$482$		0			0
$483$	−10.0369	−	8.94062i	−0.456696	−	0.406812i
$484$		0			0
$485$	−7.06669	+	5.09118i	−0.320882	+	0.231179i
$486$		0			0
$487$	28.0023	+	14.2679i	1.26891	+	0.646540i	0.953207	−	0.302319i	$-0.0977607\pi$
$487$	28.0023	+	14.2679i	1.26891	+	0.646540i	0.315700	+	0.948859i	$0.397761\pi$
$488$		0			0
$489$	−10.4434	+	8.54973i	−0.472268	+	0.386632i
$490$		0			0
$491$	11.6547	−	3.78683i	0.525968	−	0.170897i	−0.0339840	−	0.999422i	$-0.510820\pi$
$491$	11.6547	−	3.78683i	0.525968	−	0.170897i	0.559952	+	0.828525i	$0.310820\pi$
$492$		0			0
$493$	3.43895	+	3.43895i	0.154883	+	0.154883i
$494$		0			0
$495$	−19.0908	−	15.2492i	−0.858069	−	0.685398i
$496$		0			0
$497$	−1.80330	−	11.3856i	−0.0808890	−	0.510713i
$498$		0			0
$499$			2.58376i			0.115665i	0.998326	+	0.0578324i	$0.0184189\pi$
$499$			2.58376i			0.115665i	−0.998326	+	0.0578324i	$0.981581\pi$
$500$		0			0
$501$	0.546485	+	0.350753i	0.0244151	+	0.0156705i
$502$		0			0
$503$	29.7370	−	4.70988i	1.32591	−	0.210003i	0.546995	−	0.837136i	$-0.315772\pi$
$503$	29.7370	−	4.70988i	1.32591	−	0.210003i	0.778913	+	0.627132i	$0.215772\pi$
$504$		0			0
$505$	−1.84514	−	3.65738i	−0.0821076	−	0.162751i
$506$		0			0
$507$	7.61539	+	34.9091i	0.338211	+	1.55037i
$508$		0			0
$509$	−10.5395	−	32.4372i	−0.467155	−	1.43776i	−0.856252	−	0.516559i	$-0.827213\pi$
$509$	−10.5395	−	32.4372i	−0.467155	−	1.43776i	0.389097	−	0.921197i	$-0.372787\pi$
$510$		0			0
$511$	−3.30086	+	10.1590i	−0.146021	+	0.449407i
$512$		0			0
$513$	21.8434	−	31.1016i	0.964409	−	1.37317i
$514$		0			0
$515$	13.3069	+	18.4703i	0.586371	+	0.813898i
$516$		0			0
$517$	3.63565	−	22.9546i	0.159896	−	1.00954i
$518$		0			0
$519$	−1.22597	−	21.2221i	−0.0538142	−	0.931545i
$520$		0			0
$521$	7.87830	−	10.8435i	0.345154	−	0.475064i	−0.600784	−	0.799412i	$-0.705145\pi$
$521$	7.87830	−	10.8435i	0.345154	−	0.475064i	0.945938	+	0.324347i	$0.105145\pi$
$522$		0			0
$523$	11.1465	−	5.67941i	0.487401	−	0.248343i	−0.192979	−	0.981203i	$-0.561815\pi$
$523$	11.1465	−	5.67941i	0.487401	−	0.248343i	0.680380	+	0.732860i	$0.261815\pi$
$524$		0			0
$525$	−2.60706	+	9.62733i	−0.113781	+	0.420171i
$526$		0			0
$527$	1.80082	−	0.917566i	0.0784451	−	0.0399698i
$528$		0			0
$529$	−13.1686	+	18.1251i	−0.572549	+	0.788046i
$530$		0			0
$531$	−9.45109	+	16.7815i	−0.410143	+	0.728256i
$532$		0			0
$533$	−2.54254	+	16.0530i	−0.110130	+	0.695332i
$534$		0			0
$535$	−38.1572	−	12.5670i	−1.64968	−	0.543319i
$536$		0			0
$537$	4.82354	+	8.25243i	0.208151	+	0.356119i
$538$		0			0
$539$	−6.38585	+	19.6536i	−0.275058	+	0.846541i
$540$		0			0
$541$	1.14874	+	3.53545i	0.0493881	+	0.152001i	0.972709	−	0.232028i	$-0.0745362\pi$
$541$	1.14874	+	3.53545i	0.0493881	+	0.152001i	−0.923321	+	0.384029i	$0.874536\pi$
$542$		0			0
$543$	−16.8382	+	3.67323i	−0.722595	+	0.157634i
$544$		0			0
$545$	−12.5000	+	12.4003i	−0.535439	+	0.531173i
$546$		0			0
$547$	−2.64836	+	0.419459i	−0.113236	+	0.0179348i	−0.212795	−	0.977097i	$-0.568257\pi$
$547$	−2.64836	+	0.419459i	−0.113236	+	0.0179348i	0.0995594	+	0.995032i	$0.468257\pi$
$548$		0			0
$549$	−37.1896	+	17.0365i	−1.58722	+	0.727101i
$550$		0			0
$551$		−	38.9242i		−	1.65823i
$552$		0			0
$553$	−1.31527	−	8.30432i	−0.0559312	−	0.353136i
$554$		0			0
$555$	10.9122	+	4.84087i	0.463199	+	0.205484i
$556$		0			0
$557$	−19.5853	−	19.5853i	−0.829857	−	0.829857i	0.157639	−	0.987497i	$-0.449612\pi$
$557$	−19.5853	−	19.5853i	−0.829857	−	0.829857i	−0.987497	+	0.157639i	$0.949612\pi$
$558$		0			0
$559$	23.4991	−	7.63533i	0.993908	−	0.322940i
$560$		0			0
$561$	3.65218	+	4.46110i	0.154195	+	0.188348i
$562$		0			0
$563$	−14.2772	−	7.27459i	−0.601712	−	0.306587i	0.126471	−	0.991970i	$-0.459635\pi$
$563$	−14.2772	−	7.27459i	−0.601712	−	0.306587i	−0.728183	+	0.685383i	$0.759635\pi$
$564$		0			0
$565$	−41.8916	−	0.167580i	−1.76239	−	0.00705015i
$566$		0			0
$567$	6.69385	+	7.91411i	0.281115	+	0.332361i
$568$		0			0
$569$	29.7086	−	21.5845i	1.24545	−	0.904871i	0.247499	−	0.968888i	$-0.420391\pi$
$569$	29.7086	−	21.5845i	1.24545	−	0.904871i	0.997949	+	0.0640170i	$0.0203912\pi$
$570$		0			0
$571$	34.0496	+	24.7385i	1.42493	+	1.03527i	0.990933	+	0.134358i	$0.0428971\pi$
$571$	34.0496	+	24.7385i	1.42493	+	1.03527i	0.433997	+	0.900914i	$0.357103\pi$
$572$		0			0
$573$	−17.7676	−	1.77149i	−0.742251	−	0.0740050i
$574$		0			0
$575$	33.2332	+	5.53652i	1.38592	+	0.230889i
$576$		0			0
$577$	19.4132	+	38.1006i	0.808182	+	1.58615i	0.810203	+	0.586149i	$0.199357\pi$
$577$	19.4132	+	38.1006i	0.808182	+	1.58615i	−0.00202117	+	0.999998i	$0.500643\pi$
$578$		0			0
$579$	0.212141	+	0.543940i	0.00881630	+	0.0226054i
$580$		0			0
$581$	0.823323	+	1.13321i	0.0341572	+	0.0470133i
$582$		0			0
$583$	−29.2909	−	4.63922i	−1.21311	−	0.192137i
$584$		0			0
$585$	28.7344	−	26.2227i	1.18802	−	1.08418i
$586$		0			0
$587$	0.114338	−	0.224402i	0.00471925	−	0.00926205i	−0.888635	−	0.458615i	$-0.848346\pi$
$587$	0.114338	−	0.224402i	0.00471925	−	0.00926205i	0.893354	+	0.449353i	$0.148346\pi$
$588$		0			0
$589$	−15.3842	−	4.99864i	−0.633897	−	0.205966i
$590$		0			0
$591$	−0.832618	+	3.17516i	−0.0342493	+	0.130609i
$592$		0			0
$593$	−14.4925	+	14.4925i	−0.595137	+	0.595137i	−0.939014	−	0.343878i	$-0.888259\pi$
$593$	−14.4925	+	14.4925i	−0.595137	+	0.595137i	0.343878	+	0.939014i	$0.388259\pi$
$594$		0			0
$595$	1.07685	−	2.09270i	0.0441466	−	0.0857923i
$596$		0			0
$597$	12.9737	−	29.5637i	0.530978	−	1.20996i
$598$		0			0
$599$	16.6754			0.681340			0.340670	−	0.940183i	$-0.389346\pi$
$599$	16.6754			0.681340			0.340670	+	0.940183i	$0.389346\pi$
$600$		0			0
$601$	−21.5251			−0.878028			−0.439014	−	0.898480i	$-0.644672\pi$
$601$	−21.5251			−0.878028			−0.439014	+	0.898480i	$0.644672\pi$
$602$		0			0
$603$	15.5965	−	10.3672i	0.635139	−	0.422184i
$604$		0			0
$605$	−5.00265	−	0.812870i	−0.203387	−	0.0330479i
$606$		0			0
$607$	7.49042	−	7.49042i	0.304027	−	0.304027i	−0.538560	−	0.842587i	$-0.681032\pi$
$607$	7.49042	−	7.49042i	0.304027	−	0.304027i	0.842587	+	0.538560i	$0.181032\pi$
$608$		0			0
$609$	10.2687	+	2.69274i	0.416107	+	0.109115i
$610$		0			0
$611$	35.1910	+	11.4343i	1.42368	+	0.462580i
$612$		0			0
$613$	−9.77730	+	19.1890i	−0.394902	+	0.775038i	−0.999773	−	0.0212848i	$-0.993224\pi$
$613$	−9.77730	+	19.1890i	−0.394902	+	0.775038i	0.604872	+	0.796323i	$0.293224\pi$
$614$		0			0
$615$	10.1287	−	3.90367i	0.408428	−	0.157411i
$616$		0			0
$617$	9.79635	+	1.55159i	0.394386	+	0.0624646i	0.350478	−	0.936571i	$-0.386019\pi$
$617$	9.79635	+	1.55159i	0.394386	+	0.0624646i	0.0439081	+	0.999036i	$0.486019\pi$
$618$		0			0
$619$	4.81151	+	6.62247i	0.193391	+	0.266180i	0.894690	−	0.446687i	$-0.147396\pi$
$619$	4.81151	+	6.62247i	0.193391	+	0.266180i	−0.701299	+	0.712867i	$0.747396\pi$
$620$		0			0
$621$	24.3577	−	25.1516i	0.977442	−	1.00930i
$622$		0			0
$623$	−5.77649	−	11.3370i	−0.231430	−	0.454208i
$624$		0			0
$625$	−7.34400	−	23.8970i	−0.293760	−	0.955879i
$626$		0			0
$627$	4.57794	−	45.9156i	0.182825	−	1.83369i
$628$		0			0
$629$	−2.27890	−	1.65572i	−0.0908656	−	0.0660177i
$630$		0			0
$631$	−0.620208	+	0.450607i	−0.0246901	+	0.0179384i	−0.600062	−	0.799954i	$-0.704857\pi$
$631$	−0.620208	+	0.450607i	−0.0246901	+	0.0179384i	0.575372	+	0.817892i	$0.304857\pi$
$632$		0			0
$633$	−28.9737	+	32.5265i	−1.15160	+	1.29281i
$634$		0			0
$635$	−13.1294	−	9.61956i	−0.521025	−	0.381741i
$636$		0			0
$637$	−29.3152	−	14.9368i	−1.16151	−	0.591819i
$638$		0			0
$639$	29.8274	−	3.45772i	1.17995	−	0.136785i
$640$		0			0
$641$	−16.9921	+	5.52105i	−0.671146	+	0.218068i	−0.624715	−	0.780853i	$-0.714785\pi$
$641$	−16.9921	+	5.52105i	−0.671146	+	0.218068i	−0.0464310	+	0.998922i	$0.514785\pi$
$642$		0			0
$643$	5.47671	+	5.47671i	0.215980	+	0.215980i	0.806802	−	0.590822i	$-0.201196\pi$
$643$	5.47671	+	5.47671i	0.215980	+	0.215980i	−0.590822	+	0.806802i	$0.701196\pi$
$644$		0			0
$645$	−12.2782	−	11.0255i	−0.483453	−	0.434128i
$646$		0			0
$647$	−5.84782	−	36.9217i	−0.229902	−	1.45154i	−0.784865	−	0.619667i	$-0.787268\pi$
$647$	−5.84782	−	36.9217i	−0.229902	−	1.45154i	0.554963	−	0.831875i	$-0.312732\pi$
$648$		0			0
$649$			23.3836i			0.917888i
$650$		0			0
$651$	2.38297	−	3.71274i	0.0933958	−	0.145514i
$652$		0			0
$653$	32.5406	−	5.15393i	1.27341	−	0.201689i	0.517115	−	0.855916i	$-0.327006\pi$
$653$	32.5406	−	5.15393i	1.27341	−	0.201689i	0.756298	+	0.654227i	$0.227006\pi$
$654$		0			0
$655$	11.7719	+	6.05753i	0.459967	+	0.236687i
$656$		0			0
$657$	−26.0813	−	9.69309i	−1.01753	−	0.378163i
$658$		0			0
$659$	−5.58239	−	17.1808i	−0.217459	−	0.669270i	−0.998970	−	0.0453785i	$-0.985551\pi$
$659$	−5.58239	−	17.1808i	−0.217459	−	0.669270i	0.781511	−	0.623892i	$-0.214449\pi$
$660$		0			0
$661$	5.43861	−	16.7383i	0.211537	−	0.651045i	−0.787844	−	0.615875i	$-0.788803\pi$
$661$	5.43861	−	16.7383i	0.211537	−	0.651045i	0.999381	−	0.0351703i	$-0.0111974\pi$
$662$		0			0
$663$	−7.92477	+	4.63202i	−0.307773	+	0.179893i
$664$		0			0
$665$	−17.9375	+	5.74902i	−0.695586	+	0.222937i
$666$		0			0
$667$	5.60959	−	35.4175i	0.217204	−	1.37137i
$668$		0			0
$669$	−8.31644	+	0.480431i	−0.321532	+	0.0185745i
$670$		0			0
$671$	−29.1921	+	40.1795i	−1.12695	+	1.55111i
$672$		0			0
$673$	−44.4567	+	22.6518i	−1.71368	+	0.873164i	−0.732327	+	0.680953i	$0.761566\pi$
$673$	−44.4567	+	22.6518i	−1.71368	+	0.873164i	−0.981354	+	0.192211i	$0.938434\pi$
$674$		0			0
$675$	−24.7729	−	7.82974i	−0.953508	−	0.301367i
$676$		0			0
$677$	13.4384	−	6.84718i	0.516478	−	0.263159i	−0.176266	−	0.984343i	$-0.556402\pi$
$677$	13.4384	−	6.84718i	0.516478	−	0.263159i	0.692744	+	0.721184i	$0.256402\pi$
$678$		0			0
$679$	2.63680	−	3.62924i	0.101191	−	0.139278i
$680$		0			0
$681$	−22.0096	+	1.27147i	−0.843411	+	0.0487228i
$682$		0			0
$683$	2.11149	−	13.3314i	0.0807939	−	0.510113i	−0.913791	−	0.406185i	$-0.866859\pi$
$683$	2.11149	−	13.3314i	0.0807939	−	0.510113i	0.994585	−	0.103928i	$-0.0331411\pi$
$684$		0			0
$685$	0.0575801	−	14.3938i	0.00220002	−	0.549960i
$686$		0			0
$687$	−0.242925	+	0.141989i	−0.00926818	+	0.00541724i
$688$		0			0
$689$	14.5905	−	44.9050i	0.555855	−	1.71075i
$690$		0			0
$691$	−1.08757	−	3.34720i	−0.0413731	−	0.127333i	0.928237	−	0.371991i	$-0.121325\pi$
$691$	−1.08757	−	3.34720i	−0.0413731	−	0.127333i	−0.969610	+	0.244657i	$0.921325\pi$
$692$		0			0
$693$	11.7964	+	4.38411i	0.448107	+	0.166539i
$694$		0			0
$695$	6.21971	−	0.959617i	0.235927	−	0.0364003i
$696$		0			0
$697$	−2.52981	+	0.400683i	−0.0958236	+	0.0151770i
$698$		0			0
$699$	−5.61599	+	8.74990i	−0.212416	+	0.330952i
$700$		0			0
$701$			40.9855i			1.54800i	0.633184	+	0.774001i	$0.281747\pi$
$701$			40.9855i			1.54800i	−0.633184	+	0.774001i	$0.718253\pi$
$702$		0			0
$703$	3.52678	+	22.2672i	0.133015	+	0.839825i
$704$		0			0
$705$	−5.17050	−	24.1655i	−0.194732	−	0.910125i
$706$		0			0
$707$	1.49194	+	1.49194i	0.0561101	+	0.0561101i
$708$		0			0
$709$	12.6101	−	4.09726i	0.473581	−	0.153876i	−0.0624957	−	0.998045i	$-0.519906\pi$
$709$	12.6101	−	4.09726i	0.473581	−	0.153876i	0.536076	+	0.844170i	$0.319906\pi$
$710$		0			0
$711$	21.7553	−	2.52197i	0.815887	−	0.0945811i
$712$		0			0
$713$	−13.2779	−	6.76542i	−0.497261	−	0.253367i
$714$		0			0
$715$	14.7745	−	44.8599i	0.552536	−	1.67766i
$716$		0			0
$717$	−12.8540	+	14.4301i	−0.480040	+	0.538903i
$718$		0			0
$719$	−18.6310	+	13.5362i	−0.694820	+	0.504816i	−0.878241	−	0.478218i	$-0.841283\pi$
$719$	−18.6310	+	13.5362i	−0.694820	+	0.504816i	0.183421	+	0.983034i	$0.441283\pi$
$720$		0			0
$721$	−9.48579	−	6.89183i	−0.353269	−	0.256665i
$722$		0			0
$723$	−4.83034	+	48.4471i	−0.179642	+	1.80177i
$724$		0			0
$725$	−25.3713	+	8.01979i	−0.942265	+	0.297847i
$726$		0			0
$727$	−10.3618	−	20.3362i	−0.384299	−	0.754229i	0.615116	−	0.788437i	$-0.289109\pi$
$727$	−10.3618	−	20.3362i	−0.384299	−	0.754229i	−0.999415	+	0.0342075i	$0.989109\pi$
$728$		0			0
$729$	−21.3234	+	16.5624i	−0.789755	+	0.613422i
$730$		0			0
$731$	2.28875	+	3.15019i	0.0846523	+	0.116514i
$732$		0			0
$733$	−13.2294	−	2.09532i	−0.488638	−	0.0773926i	−0.0927459	−	0.995690i	$-0.529564\pi$
$733$	−13.2294	−	2.09532i	−0.488638	−	0.0773926i	−0.395892	+	0.918297i	$0.629564\pi$
$734$		0			0
$735$	1.17951	+	21.9420i	0.0435070	+	0.809342i
$736$		0			0
$737$	10.3227	−	20.2594i	0.380240	−	0.746263i
$738$		0			0
$739$	15.0540	+	4.89134i	0.553770	+	0.179931i	0.572516	−	0.819894i	$-0.305967\pi$
$739$	15.0540	+	4.89134i	0.553770	+	0.179931i	−0.0187462	+	0.999824i	$0.505967\pi$
$740$		0			0
$741$	71.0629	+	18.6348i	2.61056	+	0.684565i
$742$		0			0
$743$	7.06750	−	7.06750i	0.259281	−	0.259281i	−0.565480	−	0.824762i	$-0.691309\pi$
$743$	7.06750	−	7.06750i	0.259281	−	0.259281i	0.824762	+	0.565480i	$0.191309\pi$
$744$		0			0
$745$	43.5707	−	21.9813i	1.59631	−	0.805332i
$746$		0			0
$747$	−3.03859	+	2.01979i	−0.111176	+	0.0739001i
$748$		0			0
$749$	20.6917			0.756058
$750$		0			0
$751$	−51.2590			−1.87047			−0.935234	−	0.354031i	$-0.884811\pi$
$751$	−51.2590			−1.87047			−0.935234	+	0.354031i	$0.884811\pi$
$752$		0			0
$753$	−19.5824	+	44.6231i	−0.713621	+	1.62615i
$754$		0			0
$755$	15.5652	−	7.85262i	0.566477	−	0.285786i
$756$		0			0
$757$	10.5818	−	10.5818i	0.384604	−	0.384604i	−0.488154	−	0.872758i	$-0.662330\pi$
$757$	10.5818	−	10.5818i	0.384604	−	0.384604i	0.872758	+	0.488154i	$0.162330\pi$
$758$		0			0
$759$	10.7827	−	41.1193i	0.391386	−	1.49254i
$760$		0			0
$761$	−36.8728	−	11.9807i	−1.33664	−	0.434300i	−0.448460	−	0.893803i	$-0.648027\pi$
$761$	−36.8728	−	11.9807i	−1.33664	−	0.434300i	−0.888176	+	0.459503i	$0.848027\pi$
$762$		0			0
$763$	4.11715	−	8.08037i	0.149051	−	0.292529i
$764$		0			0
$765$	5.32954	+	3.02966i	0.192690	+	0.109538i
$766$		0			0
$767$	−36.7712	−	5.82398i	−1.32773	−	0.210292i
$768$		0			0
$769$	30.1156	+	41.4506i	1.08600	+	1.49475i	0.852744	+	0.522329i	$0.174937\pi$
$769$	30.1156	+	41.4506i	1.08600	+	1.49475i	0.233252	+	0.972416i	$0.425063\pi$
$770$		0			0
$771$	−11.4131	−	29.2636i	−0.411032	−	1.05390i
$772$		0			0
$773$	−10.0630	−	19.7497i	−0.361940	−	0.710347i	0.636186	−	0.771535i	$-0.280511\pi$
$773$	−10.0630	−	19.7497i	−0.361940	−	0.710347i	−0.998126	+	0.0611885i	$0.980511\pi$
$774$		0			0
$775$	−0.0884689	+	11.0575i	−0.00317790	+	0.397198i
$776$		0			0
$777$	−6.11833	−	0.610019i	−0.219494	−	0.0218843i
$778$		0			0
$779$	16.5846	+	12.0494i	0.594206	+	0.431716i
$780$		0			0
$781$	29.4938	−	21.4285i	1.05537	−	0.766772i
$782$		0			0
$783$	−8.12232	+	26.4327i	−0.290268	+	0.944628i
$784$		0			0
$785$	−10.2805	+	31.2146i	−0.366925	+	1.11410i
$786$		0			0
$787$	7.51983	+	3.83155i	0.268053	+	0.136580i	0.582852	−	0.812579i	$-0.301937\pi$
$787$	7.51983	+	3.83155i	0.268053	+	0.136580i	−0.314798	+	0.949159i	$0.601937\pi$
$788$		0			0
$789$	23.0155	+	28.1132i	0.819373	+	1.00086i
$790$		0			0
$791$	20.5208	−	6.66761i	0.729635	−	0.237073i
$792$		0			0
$793$	−55.9124	−	55.9124i	−1.98551	−	1.98551i
$794$		0			0
$795$	−30.8360	+	6.59775i	−1.09364	+	0.233998i
$796$		0			0
$797$	3.19808	+	20.1919i	0.113282	+	0.715234i	0.977314	+	0.211797i	$0.0679315\pi$
$797$	3.19808	+	20.1919i	0.113282	+	0.715234i	−0.864032	+	0.503437i	$0.832069\pi$
$798$		0			0
$799$			5.83121i			0.206293i
$800$		0			0
$801$	30.1322	−	13.8035i	1.06467	−	0.487723i
$802$		0			0
$803$	−33.3658	+	5.28463i	−1.17746	+	0.186491i
$804$		0			0
$805$	−17.1500	+	2.64601i	−0.604459	+	0.0932598i
$806$		0			0
$807$	22.9151	−	4.99890i	0.806648	−	0.175970i
$808$		0			0
$809$	12.0010	+	36.9353i	0.421933	+	1.29857i	0.905901	+	0.423489i	$0.139195\pi$
$809$	12.0010	+	36.9353i	0.421933	+	1.29857i	−0.483969	+	0.875085i	$0.660805\pi$
$810$		0			0
$811$	−6.14194	+	18.9030i	−0.215673	+	0.663773i	0.783432	+	0.621477i	$0.213467\pi$
$811$	−6.14194	+	18.9030i	−0.215673	+	0.663773i	−0.999105	+	0.0422955i	$0.986533\pi$
$812$		0			0
$813$	−2.10683	−	3.60450i	−0.0738896	−	0.126415i
$814$		0			0
$815$	−0.0697022	+	17.4241i	−0.00244156	+	0.610340i
$816$		0			0
$817$	4.87518	−	30.7807i	0.170561	−	1.07688i
$818$		0			0
$819$	−9.83213	+	17.4581i	−0.343562	+	0.610035i
$820$		0			0
$821$	24.8586	−	34.2149i	0.867569	−	1.19411i	−0.112142	−	0.993692i	$-0.535771\pi$
$821$	24.8586	−	34.2149i	0.867569	−	1.19411i	0.979711	−	0.200415i	$-0.0642289\pi$
$822$		0			0
$823$	19.7004	−	10.0379i	0.686713	−	0.349898i	−0.0755710	−	0.997140i	$-0.524078\pi$
$823$	19.7004	−	10.0379i	0.686713	−	0.349898i	0.762284	+	0.647243i	$0.224078\pi$
$824$		0			0
$825$	−30.8715	+	6.47630i	−1.07481	+	0.225476i
$826$		0			0
$827$	−44.2895	+	22.5666i	−1.54010	+	0.784718i	−0.998437	−	0.0558808i	$-0.982203\pi$
$827$	−44.2895	+	22.5666i	−1.54010	+	0.784718i	−0.541658	+	0.840599i	$0.682203\pi$
$828$		0			0
$829$	19.2512	−	26.4971i	0.668624	−	0.920281i	−0.331105	−	0.943594i	$-0.607421\pi$
$829$	19.2512	−	26.4971i	0.668624	−	0.920281i	0.999728	+	0.0233127i	$0.00742133\pi$
$830$		0			0
$831$	1.01564	+	17.5811i	0.0352320	+	0.609880i
$832$		0			0
$833$	0.811106	−	5.12112i	0.0281032	−	0.177436i
$834$		0			0
$835$	0.798325	−	0.255865i	0.0276272	−	0.00885458i
$836$		0			0
$837$	9.40407	+	6.60471i	0.325052	+	0.228292i
$838$		0			0
$839$	0.975982	−	3.00376i	0.0336946	−	0.103701i	−0.932795	−	0.360408i	$-0.882637\pi$
$839$	0.975982	−	3.00376i	0.0336946	−	0.103701i	0.966489	+	0.256707i	$0.0826374\pi$
$840$		0			0
$841$	−0.209906	−	0.646024i	−0.00723813	−	0.0222767i
$842$		0			0
$843$	−2.36065	−	10.8213i	−0.0813050	−	0.372704i
$844$		0			0
$845$	41.0156	+	21.1056i	1.41098	+	0.726055i
$846$		0			0
$847$	2.57832	−	0.408365i	0.0885920	−	0.0140316i
$848$		0			0
$849$	18.1296	+	11.6362i	0.622207	+	0.399354i
$850$		0			0
$851$			20.7694i			0.711967i
$852$		0			0
$853$	−1.16933	−	7.38288i	−0.0400372	−	0.252785i	0.959549	−	0.281541i	$-0.0908455\pi$
$853$	−1.16933	−	7.38288i	−0.0400372	−	0.252785i	−0.999586	+	0.0287559i	$0.990845\pi$
$854$		0			0
$855$	−13.0158	−	47.3074i	−0.445130	−	1.61788i
$856$		0			0
$857$	−12.6960	−	12.6960i	−0.433687	−	0.433687i	0.456194	−	0.889880i	$-0.349212\pi$
$857$	−12.6960	−	12.6960i	−0.433687	−	0.433687i	−0.889880	+	0.456194i	$0.849212\pi$
$858$		0			0
$859$	−6.79763	+	2.20868i	−0.231932	+	0.0753593i	−0.422677	−	0.906280i	$-0.638910\pi$
$859$	−6.79763	+	2.20868i	−0.231932	+	0.0753593i	0.190745	+	0.981640i	$0.438910\pi$
$860$		0			0
$861$	−4.32609	+	3.54165i	−0.147433	+	0.120699i
$862$		0			0
$863$	1.56219	+	0.795974i	0.0531775	+	0.0270953i	0.480377	−	0.877062i	$-0.340500\pi$
$863$	1.56219	+	0.795974i	0.0531775	+	0.0270953i	−0.427200	+	0.904157i	$0.640500\pi$
$864$		0			0
$865$	−22.1374	−	16.2194i	−0.752693	−	0.551477i
$866$		0			0
$867$	20.9066	+	18.6230i	0.710026	+	0.632472i
$868$		0			0
$869$	21.5119	−	15.6293i	0.729742	−	0.530189i
$870$		0			0
$871$	29.2872	+	21.2784i	0.992359	+	0.720991i
$872$		0			0
$873$	9.15922	+	7.25627i	0.309993	+	0.245587i
$874$		0			0
$875$	7.44304	+	10.5074i	0.251621	+	0.355214i
$876$		0			0
$877$	15.1290	+	29.6923i	0.510869	+	1.00264i	0.992030	+	0.126004i	$0.0402153\pi$
$877$	15.1290	+	29.6923i	0.510869	+	1.00264i	−0.481161	+	0.876632i	$0.659785\pi$
$878$		0			0
$879$	−45.6547	+	17.8057i	−1.53989	+	0.600572i
$880$		0			0
$881$	26.0706	+	35.8831i	0.878341	+	1.20893i	0.976878	+	0.213799i	$0.0685838\pi$
$881$	26.0706	+	35.8831i	0.878341	+	1.20893i	−0.0985368	+	0.995133i	$0.531416\pi$
$882$		0			0
$883$	−1.25419	−	0.198645i	−0.0422070	−	0.00668493i	0.135295	−	0.990805i	$-0.456802\pi$
$883$	−1.25419	−	0.198645i	−0.0422070	−	0.00668493i	−0.177502	+	0.984120i	$0.556802\pi$
$884$		0			0
$885$	8.94180	+	23.2009i	0.300575	+	0.779890i
$886$		0			0
$887$	10.4643	−	20.5374i	0.351358	−	0.689579i	−0.645913	−	0.763411i	$-0.723523\pi$
$887$	10.4643	−	20.5374i	0.351358	−	0.689579i	0.997271	+	0.0738325i	$0.0235230\pi$
$888$		0			0
$889$	7.97294	+	2.59057i	0.267404	+	0.0868848i
$890$		0			0
$891$	−12.6900	+	30.2251i	−0.425131	+	1.01258i
$892$		0			0
$893$	33.0007	−	33.0007i	1.10433	−	1.10433i
$894$		0			0
$895$	12.1805	+	1.97918i	0.407149	+	0.0661568i
$896$		0			0
$897$	61.9753	+	27.1972i	2.06929	+	0.908088i
$898$		0			0
$899$	11.7694			0.392531
$900$		0			0
$901$	7.44084			0.247890
$902$		0			0
$903$	7.78304	+	3.41550i	0.259003	+	0.113661i
$904$		0			0
$905$	−10.1802	+	19.7836i	−0.338400	+	0.657631i
$906$		0			0
$907$	27.2663	−	27.2663i	0.905362	−	0.905362i	−0.0905313	−	0.995894i	$-0.528857\pi$
$907$	27.2663	−	27.2663i	0.905362	−	0.905362i	0.995894	+	0.0905313i	$0.0288565\pi$
$908$		0			0
$909$	−4.04476	+	3.72097i	−0.134156	+	0.123417i
$910$		0			0
$911$	30.7557	+	9.99312i	1.01898	+	0.331087i	0.770425	−	0.637531i	$-0.220044\pi$
$911$	30.7557	+	9.99312i	1.01898	+	0.331087i	0.248556	+	0.968618i	$0.420044\pi$
$912$		0			0
$913$	−2.01111	+	3.94703i	−0.0665581	+	0.130628i
$914$		0			0
$915$	−13.5995	+	51.0285i	−0.449587	+	1.68695i
$916$		0			0
$917$	−6.73493	−	1.06671i	−0.222407	−	0.0352258i
$918$		0			0
$919$	12.6727	+	17.4425i	0.418034	+	0.575375i	0.965155	−	0.261679i	$-0.0842762\pi$
$919$	12.6727	+	17.4425i	0.418034	+	0.575375i	−0.547121	+	0.837054i	$0.684276\pi$
$920$		0			0
$921$	−3.83159	+	1.49436i	−0.126255	+	0.0492407i
$922$		0			0
$923$	26.3509	+	51.7165i	0.867350	+	1.70227i
$924$		0			0
$925$	13.7874	−	6.88665i	0.453327	−	0.226432i
$926$		0			0
$927$	18.9658	−	23.9396i	0.622918	−	0.786278i
$928$		0			0
$929$	−4.52028	−	3.28417i	−0.148306	−	0.107750i	0.511158	−	0.859487i	$-0.329217\pi$
$929$	−4.52028	−	3.28417i	−0.148306	−	0.107750i	−0.659464	+	0.751736i	$0.729217\pi$
$930$		0			0
$931$	−33.5724	+	24.3918i	−1.10029	+	0.799408i
$932$		0			0
$933$	22.6705	+	20.1942i	0.742198	+	0.661130i
$934$		0			0
$935$	7.44303	+	0.0297746i	0.243413	+	0.000973733i
$936$		0			0
$937$	−22.6738	−	11.5529i	−0.740722	−	0.377417i	0.0425510	−	0.999094i	$-0.486451\pi$
$937$	−22.6738	−	11.5529i	−0.740722	−	0.377417i	−0.783273	+	0.621677i	$0.786451\pi$
$938$		0			0
$939$	−22.4430	+	18.3734i	−0.732399	+	0.599595i
$940$		0			0
$941$	−41.8477	+	13.5972i	−1.36420	+	0.443255i	−0.897442	−	0.441132i	$-0.854577\pi$
$941$	−41.8477	+	13.5972i	−1.36420	+	0.443255i	−0.466755	+	0.884387i	$0.654577\pi$
$942$		0			0
$943$	13.3540	+	13.3540i	0.434866	+	0.434866i
$944$		0			0
$945$	13.3807	−	0.161029i	0.435273	−	0.00523828i
$946$		0			0
$947$	−3.85915	−	24.3657i	−0.125405	−	0.791779i	−0.967578	−	0.252571i	$-0.918724\pi$
$947$	−3.85915	−	24.3657i	−0.125405	−	0.791779i	0.842173	−	0.539208i	$-0.181276\pi$
$948$		0			0
$949$		−	53.7846i		−	1.74592i
$950$		0			0
$951$	−14.8509	−	9.53182i	−0.481573	−	0.309090i
$952$		0			0
$953$	−39.1670	+	6.20345i	−1.26874	+	0.200949i	−0.754274	−	0.656559i	$-0.772011\pi$
$953$	−39.1670	+	6.20345i	−1.26874	+	0.200949i	−0.514470	+	0.857509i	$0.672011\pi$
$954$		0			0
$955$	−16.3650	+	16.2346i	−0.529559	+	0.525339i
$956$		0			0
$957$	7.15568	+	32.8018i	0.231310	+	1.06033i
$958$		0			0
$959$	2.29097	+	7.05088i	0.0739793	+	0.227685i
$960$		0			0
$961$	−8.06810	+	24.8311i	−0.260261	+	0.801002i
$962$		0			0
$963$	−2.24531	+	53.8515i	−0.0723543	+	1.73534i
$964$		0			0
$965$	0.715912	+	0.235784i	0.0230460	+	0.00759016i
$966$		0			0
$967$	5.37217	−	33.9186i	0.172757	−	1.09075i	−0.737087	−	0.675798i	$-0.763799\pi$
$967$	5.37217	−	33.9186i	0.172757	−	1.09075i	0.909844	−	0.414949i	$-0.136201\pi$
$968$		0			0
$969$	0.667708	+	11.5583i	0.0214499	+	0.371306i
$970$		0			0
$971$	−8.75446	+	12.0495i	−0.280944	+	0.386686i	−0.926046	−	0.377410i	$-0.876815\pi$
$971$	−8.75446	+	12.0495i	−0.280944	+	0.386686i	0.645102	+	0.764096i	$0.276815\pi$
$972$		0			0
$973$	−2.88813	+	1.47158i	−0.0925892	+	0.0471765i
$974$		0			0
$975$	−2.49516	−	50.1591i	−0.0799091	−	1.60638i
$976$		0			0
$977$	−40.7823	+	20.7796i	−1.30474	+	0.664799i	−0.961592	−	0.274482i	$-0.911494\pi$
$977$	−40.7823	+	20.7796i	−1.30474	+	0.664799i	−0.343149	+	0.939281i	$0.611494\pi$
$978$		0			0
$979$	23.6523	−	32.5546i	0.755932	−	1.04045i
$980$		0			0
$981$	20.5829	+	11.5920i	0.657163	+	0.370104i
$982$		0			0
$983$	2.55096	−	16.1062i	0.0813631	−	0.513706i	−0.913024	−	0.407905i	$-0.866259\pi$
$983$	2.55096	−	16.1062i	0.0813631	−	0.513706i	0.994387	−	0.105801i	$-0.0337407\pi$
$984$		0			0
$985$	2.47713	+	3.43831i	0.0789278	+	0.109554i
$986$		0			0
$987$	6.42301	+	10.9889i	0.204447	+	0.349781i
$988$		0			0
$989$	8.87194	−	27.3050i	0.282111	−	0.868250i
$990$		0			0
$991$	−6.55535	−	20.1753i	−0.208237	−	0.640889i	−0.999565	−	0.0294965i	$-0.990610\pi$
$991$	−6.55535	−	20.1753i	−0.208237	−	0.640889i	0.791327	−	0.611393i	$-0.209390\pi$
$992$		0			0
$993$	−45.7692	+	9.98451i	−1.45244	+	0.316849i
$994$		0			0
$995$	−18.7736	−	37.2124i	−0.595162	−	1.17971i
$996$		0			0
$997$	−30.9129	+	4.89612i	−0.979020	+	0.155062i	−0.625380	−	0.780320i	$-0.715056\pi$
$997$	−30.9129	+	4.89612i	−0.979020	+	0.155062i	−0.353640	+	0.935382i	$0.615056\pi$
$998$		0			0
$999$	2.25153	−	15.8572i	0.0712354	−	0.501699i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.x.a.53.2	yes	80
3.2	odd	2	inner	300.2.x.a.53.9	yes	80
25.17	odd	20	inner	300.2.x.a.17.9	yes	80
75.17	even	20	inner	300.2.x.a.17.2	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.x.a.17.2	✓	80	75.17	even	20	inner
300.2.x.a.17.9	yes	80	25.17	odd	20	inner
300.2.x.a.53.2	yes	80	1.1	even	1	trivial
300.2.x.a.53.9	yes	80	3.2	odd	2	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.x (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.58605 - 0.696021i) q^{3} +(-1.99640 + 1.00718i) q^{5} +(0.814380 - 0.814380i) q^{7} +(2.03111 + 2.20785i) q^{9} +O(q^{10})\)	\(q+(-1.58605 - 0.696021i) q^{3} +(-1.99640 + 1.00718i) q^{5} +(0.814380 - 0.814380i) q^{7} +(2.03111 + 2.20785i) q^{9} +(3.46407 + 1.12554i) q^{11} +(-2.63271 + 5.16697i) q^{13} +(3.86740 - 0.207896i) q^{15} +(-0.902627 - 0.142962i) q^{17} +(4.29919 + 5.91733i) q^{19} +(-1.85847 + 0.724821i) q^{21} +(3.05909 + 6.00381i) q^{23} +(2.97120 - 4.02144i) q^{25} +(-1.68473 - 4.91545i) q^{27} +(-4.30536 - 3.12803i) q^{29} +(-1.78920 + 1.29993i) q^{31} +(-4.71078 - 4.19623i) q^{33} +(-0.805601 + 2.44605i) q^{35} +(2.74637 + 1.39935i) q^{37} +(7.77193 - 6.36266i) q^{39} +(2.66555 - 0.866089i) q^{41} +(-3.01283 - 3.01283i) q^{43} +(-6.27859 - 2.36206i) q^{45} +(-0.998165 - 6.30217i) q^{47} +5.67357i q^{49} +(1.33211 + 0.854993i) q^{51} +(-8.04180 + 1.27370i) q^{53} +(-8.04927 + 1.24189i) q^{55} +(-2.70014 - 12.3775i) q^{57} +(1.98388 + 6.10574i) q^{59} +(-4.21356 + 12.9680i) q^{61} +(3.45212 + 0.143935i) q^{63} +(0.0518720 - 12.9669i) q^{65} +(0.976557 - 6.16574i) q^{67} +(-0.673095 - 11.6515i) q^{69} +(5.88318 - 8.09750i) q^{71} +(-8.26387 + 4.21065i) q^{73} +(-7.51147 + 4.31019i) q^{75} +(3.73768 - 1.90445i) q^{77} +(4.29102 - 5.90609i) q^{79} +(-0.749199 + 8.96876i) q^{81} +(-0.190258 + 1.20124i) q^{83} +(1.94599 - 0.623695i) q^{85} +(4.65135 + 7.95784i) q^{87} +(3.41396 - 10.5071i) q^{89} +(2.06386 + 6.35190i) q^{91} +(3.74254 - 0.816433i) q^{93} +(-14.5427 - 7.48329i) q^{95} +(3.84712 - 0.609325i) q^{97} +(4.55086 + 9.93423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q - 2 * q^3 + 4 * q^7	\( 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) \) 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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