LMFDB - Embedded newform 300.2.m.a.181.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(61,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("300.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.m (of order $5$, degree $4$, 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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.2
Root			$-0.978148 - 0.207912i$ of defining polynomial
Character	$\chi$	$=$	300.181
Dual form			300.2.m.a.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{3} +(2.04275 + 0.909491i) q^{5} +0.747238 q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{3} +(2.04275 + 0.909491i) q^{5} +0.747238 q^{7} +(0.309017 - 0.951057i) q^{9} +(0.0646021 + 0.198825i) q^{11} +(-0.773659 + 2.38108i) q^{13} +(-2.18720 + 0.464905i) q^{15} +(5.51712 + 4.00842i) q^{17} +(-1.00739 - 0.731913i) q^{19} +(-0.604528 + 0.439216i) q^{21} +(1.00457 + 3.09174i) q^{23} +(3.34565 + 3.71572i) q^{25} +(0.309017 + 0.951057i) q^{27} +(4.19332 - 3.04662i) q^{29} +(-3.02547 - 2.19813i) q^{31} +(-0.169131 - 0.122881i) q^{33} +(1.52642 + 0.679606i) q^{35} +(0.607352 - 1.86924i) q^{37} +(-0.773659 - 2.38108i) q^{39} +(0.993096 - 3.05644i) q^{41} -12.7127 q^{43} +(1.49622 - 1.66172i) q^{45} +(5.24425 - 3.81017i) q^{47} -6.44163 q^{49} -6.81953 q^{51} +(-3.35177 + 2.43520i) q^{53} +(-0.0488635 + 0.464905i) q^{55} +1.24520 q^{57} +(3.61882 - 11.1376i) q^{59} +(-3.85634 - 11.8686i) q^{61} +(0.230909 - 0.710666i) q^{63} +(-3.74596 + 4.16031i) q^{65} +(-2.35995 - 1.71460i) q^{67} +(-2.62999 - 1.91080i) q^{69} +(-5.29912 + 3.85004i) q^{71} +(-0.778516 - 2.39603i) q^{73} +(-4.89074 - 1.03956i) q^{75} +(0.0482732 + 0.148570i) q^{77} +(8.28621 - 6.02028i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(4.59240 + 3.33658i) q^{83} +(7.62447 + 13.2060i) q^{85} +(-1.60171 + 4.92954i) q^{87} +(-0.284829 - 0.876615i) q^{89} +(-0.578108 + 1.77923i) q^{91} +3.73968 q^{93} +(-1.39218 - 2.41133i) q^{95} +(12.5757 - 9.13679i) q^{97} +0.209057 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 5 q^{5} - 8 q^{7} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 5 * q^5 - 8 * q^7 - 2 * q^9	$ 8 q - 2 q^{3} + 5 q^{5} - 8 q^{7} - 2 q^{9} - 2 q^{11} - 5 q^{15} + 7 q^{17} + 5 q^{19} - 3 q^{21} + 7 q^{23} + 5 q^{25} - 2 q^{27} + 27 q^{29} - 3 q^{31} + 3 q^{33} + 20 q^{35} - 9 q^{37} + 20 q^{41} - 68 q^{43} - 5 q^{45} - 7 q^{47} - 8 q^{49} - 8 q^{51} - 11 q^{53} + 5 q^{55} - 10 q^{57} + 2 q^{59} - 14 q^{61} + 7 q^{63} - 35 q^{65} + 28 q^{67} + 2 q^{69} - 15 q^{71} + 6 q^{73} + 5 q^{75} + 17 q^{77} + 24 q^{79} - 2 q^{81} + 2 q^{83} + 10 q^{85} - 23 q^{87} + 5 q^{91} - 18 q^{93} + 5 q^{95} + 34 q^{97} - 2 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 + 5 * q^5 - 8 * q^7 - 2 * q^9 - 2 * q^11 - 5 * q^15 + 7 * q^17 + 5 * q^19 - 3 * q^21 + 7 * q^23 + 5 * q^25 - 2 * q^27 + 27 * q^29 - 3 * q^31 + 3 * q^33 + 20 * q^35 - 9 * q^37 + 20 * q^41 - 68 * q^43 - 5 * q^45 - 7 * q^47 - 8 * q^49 - 8 * q^51 - 11 * q^53 + 5 * q^55 - 10 * q^57 + 2 * q^59 - 14 * q^61 + 7 * q^63 - 35 * q^65 + 28 * q^67 + 2 * q^69 - 15 * q^71 + 6 * q^73 + 5 * q^75 + 17 * q^77 + 24 * q^79 - 2 * q^81 + 2 * q^83 + 10 * q^85 - 23 * q^87 + 5 * q^91 - 18 * q^93 + 5 * q^95 + 34 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$		0			0
$5$	2.04275	+	0.909491i	0.913545	+	0.406737i
$5$	2.04275	+	0.909491i	0.913545	+	0.406737i
$6$		0			0
$7$	0.747238			0.282430			0.141215	−	0.989979i	$-0.454899\pi$
$7$	0.747238			0.282430			0.141215	+	0.989979i	$0.454899\pi$
$8$		0			0
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	0.0646021	+	0.198825i	0.0194783	+	0.0599480i	0.960323	−	0.278889i	$-0.0899663\pi$
$11$	0.0646021	+	0.198825i	0.0194783	+	0.0599480i	−0.940845	+	0.338837i	$0.889966\pi$
$12$		0			0
$13$	−0.773659	+	2.38108i	−0.214574	+	0.660392i	0.784609	+	0.619991i	$0.212864\pi$
$13$	−0.773659	+	2.38108i	−0.214574	+	0.660392i	−0.999184	+	0.0404014i	$0.987136\pi$
$14$		0			0
$15$	−2.18720	+	0.464905i	−0.564734	+	0.120038i
$16$		0			0
$17$	5.51712	+	4.00842i	1.33810	+	0.972185i	0.999512	+	0.0312497i	$0.00994869\pi$
$17$	5.51712	+	4.00842i	1.33810	+	0.972185i	0.338586	+	0.940935i	$0.390051\pi$
$18$		0			0
$19$	−1.00739	−	0.731913i	−0.231112	−	0.167912i	0.466203	−	0.884678i	$-0.345622\pi$
$19$	−1.00739	−	0.731913i	−0.231112	−	0.167912i	−0.697314	+	0.716766i	$0.745622\pi$
$20$		0			0
$21$	−0.604528	+	0.439216i	−0.131919	+	0.0958447i
$22$		0			0
$23$	1.00457	+	3.09174i	0.209467	+	0.644673i	0.999500	+	0.0316092i	$0.0100632\pi$
$23$	1.00457	+	3.09174i	0.209467	+	0.644673i	−0.790033	+	0.613064i	$0.789937\pi$
$24$		0			0
$25$	3.34565	+	3.71572i	0.669131	+	0.743145i
$26$		0			0
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$		0			0
$29$	4.19332	−	3.04662i	0.778680	−	0.565744i	−0.125903	−	0.992043i	$-0.540183\pi$
$29$	4.19332	−	3.04662i	0.778680	−	0.565744i	0.904582	+	0.426299i	$0.140183\pi$
$30$		0			0
$31$	−3.02547	−	2.19813i	−0.543390	−	0.394796i	0.281953	−	0.959428i	$-0.409018\pi$
$31$	−3.02547	−	2.19813i	−0.543390	−	0.394796i	−0.825342	+	0.564633i	$0.809018\pi$
$32$		0			0
$33$	−0.169131	−	0.122881i	−0.0294419	−	0.0213908i
$34$		0			0
$35$	1.52642	+	0.679606i	0.258012	+	0.114874i
$36$		0			0
$37$	0.607352	−	1.86924i	0.0998480	−	0.307301i	−0.888639	−	0.458608i	$-0.848348\pi$
$37$	0.607352	−	1.86924i	0.0998480	−	0.307301i	0.988487	+	0.151307i	$0.0483483\pi$
$38$		0			0
$39$	−0.773659	−	2.38108i	−0.123885	−	0.381278i
$40$		0			0
$41$	0.993096	−	3.05644i	0.155096	−	0.477335i	−0.843075	−	0.537796i	$-0.819257\pi$
$41$	0.993096	−	3.05644i	0.155096	−	0.477335i	0.998171	+	0.0604609i	$0.0192570\pi$
$42$		0			0
$43$	−12.7127			−1.93866			−0.969332	−	0.245755i	$-0.920964\pi$
$43$	−12.7127			−1.93866			−0.969332	+	0.245755i	$0.920964\pi$
$44$		0			0
$45$	1.49622	−	1.66172i	0.223044	−	0.247715i
$46$		0			0
$47$	5.24425	−	3.81017i	0.764952	−	0.555770i	−0.135473	−	0.990781i	$-0.543255\pi$
$47$	5.24425	−	3.81017i	0.764952	−	0.555770i	0.900425	+	0.435011i	$0.143255\pi$
$48$		0			0
$49$	−6.44163			−0.920234
$50$		0			0
$51$	−6.81953			−0.954926
$52$		0			0
$53$	−3.35177	+	2.43520i	−0.460401	+	0.334501i	−0.793688	−	0.608325i	$-0.791842\pi$
$53$	−3.35177	+	2.43520i	−0.460401	+	0.334501i	0.333288	+	0.942825i	$0.391842\pi$
$54$		0			0
$55$	−0.0488635	+	0.464905i	−0.00658875	+	0.0626877i
$56$		0			0
$57$	1.24520			0.164931
$58$		0			0
$59$	3.61882	−	11.1376i	0.471131	−	1.44999i	−0.379975	−	0.924997i	$-0.624067\pi$
$59$	3.61882	−	11.1376i	0.471131	−	1.44999i	0.851106	−	0.524995i	$-0.175933\pi$
$60$		0			0
$61$	−3.85634	−	11.8686i	−0.493753	−	1.51962i	−0.818891	−	0.573949i	$-0.805411\pi$
$61$	−3.85634	−	11.8686i	−0.493753	−	1.51962i	0.325138	−	0.945667i	$-0.394589\pi$
$62$		0			0
$63$	0.230909	−	0.710666i	0.0290918	−	0.0895355i
$64$		0			0
$65$	−3.74596	+	4.16031i	−0.464629	+	0.516023i
$66$		0			0
$67$	−2.35995	−	1.71460i	−0.288314	−	0.209472i	0.434222	−	0.900806i	$-0.357023\pi$
$67$	−2.35995	−	1.71460i	−0.288314	−	0.209472i	−0.722535	+	0.691334i	$0.757023\pi$
$68$		0			0
$69$	−2.62999	−	1.91080i	−0.316614	−	0.230034i
$70$		0			0
$71$	−5.29912	+	3.85004i	−0.628890	+	0.456916i	−0.856016	−	0.516950i	$-0.827067\pi$
$71$	−5.29912	+	3.85004i	−0.628890	+	0.456916i	0.227125	+	0.973866i	$0.427067\pi$
$72$		0			0
$73$	−0.778516	−	2.39603i	−0.0911184	−	0.280434i	0.895104	−	0.445857i	$-0.147101\pi$
$73$	−0.778516	−	2.39603i	−0.0911184	−	0.280434i	−0.986223	+	0.165423i	$0.947101\pi$
$74$		0			0
$75$	−4.89074	−	1.03956i	−0.564734	−	0.120038i
$76$		0			0
$77$	0.0482732	+	0.148570i	0.00550124	+	0.0169311i
$78$		0			0
$79$	8.28621	−	6.02028i	0.932271	−	0.677335i	−0.0142765	−	0.999898i	$-0.504545\pi$
$79$	8.28621	−	6.02028i	0.932271	−	0.677335i	0.946548	+	0.322563i	$0.104545\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	4.59240	+	3.33658i	0.504082	+	0.366237i	0.810574	−	0.585636i	$-0.199155\pi$
$83$	4.59240	+	3.33658i	0.504082	+	0.366237i	−0.306492	+	0.951873i	$0.599155\pi$
$84$		0			0
$85$	7.62447	+	13.2060i	0.826990	+	1.43239i
$86$		0			0
$87$	−1.60171	+	4.92954i	−0.171721	+	0.528502i
$88$		0			0
$89$	−0.284829	−	0.876615i	−0.0301919	−	0.0929210i	0.934825	−	0.355109i	$-0.115556\pi$
$89$	−0.284829	−	0.876615i	−0.0301919	−	0.0929210i	−0.965017	+	0.262188i	$0.915556\pi$
$90$		0			0
$91$	−0.578108	+	1.77923i	−0.0606022	+	0.186514i
$92$		0			0
$93$	3.73968			0.387787
$94$		0			0
$95$	−1.39218	−	2.41133i	−0.142835	−	0.247397i
$96$		0			0
$97$	12.5757	−	9.13679i	1.27687	−	0.927700i	0.277416	−	0.960750i	$-0.410522\pi$
$97$	12.5757	−	9.13679i	1.27687	−	0.927700i	0.999454	+	0.0330496i	$0.0105219\pi$
$98$		0			0
$99$	0.209057			0.0210110
$100$		0			0
$101$	−11.0405			−1.09857			−0.549285	−	0.835635i	$-0.685100\pi$
$101$	−11.0405			−1.09857			−0.549285	+	0.835635i	$0.685100\pi$
$102$		0			0
$103$	−11.2326	+	8.16097i	−1.10678	+	0.804124i	−0.982154	−	0.188079i	$-0.939774\pi$
$103$	−11.2326	+	8.16097i	−1.10678	+	0.804124i	−0.124628	+	0.992203i	$0.539774\pi$
$104$		0			0
$105$	−1.63436	+	0.347395i	−0.159497	+	0.0339022i
$106$		0			0
$107$	1.02510			0.0991002			0.0495501	−	0.998772i	$-0.484221\pi$
$107$	1.02510			0.0991002			0.0495501	+	0.998772i	$0.484221\pi$
$108$		0			0
$109$	−2.07199	+	6.37694i	−0.198461	+	0.610800i	0.801458	+	0.598051i	$0.204058\pi$
$109$	−2.07199	+	6.37694i	−0.198461	+	0.610800i	−0.999919	+	0.0127488i	$0.995942\pi$
$110$		0			0
$111$	0.607352	+	1.86924i	0.0576473	+	0.177420i
$112$		0			0
$113$	2.57151	−	7.91428i	0.241907	−	0.744513i	−0.754223	−	0.656618i	$-0.771986\pi$
$113$	2.57151	−	7.91428i	0.241907	−	0.744513i	0.996130	−	0.0878944i	$-0.0280138\pi$
$114$		0			0
$115$	−0.759830	+	7.22930i	−0.0708546	+	0.674136i
$116$		0			0
$117$	2.02547	+	1.47159i	0.187254	+	0.136048i
$118$		0			0
$119$	4.12260	+	2.99525i	0.377918	+	0.274574i
$120$		0			0
$121$	8.86383	−	6.43995i	0.805803	−	0.585450i
$122$		0			0
$123$	0.993096	+	3.05644i	0.0895445	+	0.275590i
$124$		0			0
$125$	3.45492	+	10.6331i	0.309017	+	0.951057i
$126$		0			0
$127$	−4.49195	−	13.8248i	−0.398597	−	1.22675i	−0.926125	−	0.377217i	$-0.876881\pi$
$127$	−4.49195	−	13.8248i	−0.398597	−	1.22675i	0.527529	−	0.849537i	$-0.323119\pi$
$128$		0			0
$129$	10.2848	−	7.47232i	0.905523	−	0.657901i
$130$		0			0
$131$	−6.00611	−	4.36370i	−0.524757	−	0.381258i	0.293636	−	0.955917i	$-0.405135\pi$
$131$	−6.00611	−	4.36370i	−0.524757	−	0.381258i	−0.818393	+	0.574659i	$0.805135\pi$
$132$		0			0
$133$	−0.752762	−	0.546913i	−0.0652727	−	0.0474234i
$134$		0			0
$135$	−0.233733	+	2.22382i	−0.0201165	+	0.191396i
$136$		0			0
$137$	−2.26676	+	6.97636i	−0.193662	+	0.596030i	0.806328	+	0.591469i	$0.201452\pi$
$137$	−2.26676	+	6.97636i	−0.193662	+	0.596030i	−0.999990	+	0.00456114i	$0.998548\pi$
$138$		0			0
$139$	6.10219	+	18.7806i	0.517581	+	1.59295i	0.778536	+	0.627600i	$0.215963\pi$
$139$	6.10219	+	18.7806i	0.517581	+	1.59295i	−0.260954	+	0.965351i	$0.584037\pi$
$140$		0			0
$141$	−2.00313	+	6.16499i	−0.168694	+	0.519185i
$142$		0			0
$143$	−0.523398			−0.0437687
$144$		0			0
$145$	11.3368	−	2.40971i	0.941468	−	0.200115i
$146$		0			0
$147$	5.21139	−	3.78630i	0.429828	−	0.312289i
$148$		0			0
$149$	−21.7551			−1.78224			−0.891122	−	0.453763i	$-0.850081\pi$
$149$	−21.7551			−1.78224			−0.891122	+	0.453763i	$0.850081\pi$
$150$		0			0
$151$	10.1308			0.824432			0.412216	−	0.911086i	$-0.364755\pi$
$151$	10.1308			0.824432			0.412216	+	0.911086i	$0.364755\pi$
$152$		0			0
$153$	5.51712	−	4.00842i	0.446033	−	0.324062i
$154$		0			0
$155$	−4.18109	−	7.24186i	−0.335833	−	0.581680i
$156$		0			0
$157$	−9.99520			−0.797704			−0.398852	−	0.917015i	$-0.630591\pi$
$157$	−9.99520			−0.797704			−0.398852	+	0.917015i	$0.630591\pi$
$158$		0			0
$159$	1.28026	−	3.94024i	0.101531	−	0.312481i
$160$		0			0
$161$	0.750652	+	2.31027i	0.0591597	+	0.182075i
$162$		0			0
$163$	−0.792035	+	2.43763i	−0.0620369	+	0.190930i	−0.977272	−	0.211991i	$-0.932005\pi$
$163$	−0.792035	+	2.43763i	−0.0620369	+	0.190930i	0.915235	+	0.402921i	$0.132005\pi$
$164$		0			0
$165$	−0.233733	−	0.404837i	−0.0181961	−	0.0315165i
$166$		0			0
$167$	16.8690	+	12.2560i	1.30536	+	0.948401i	0.999993	−	0.00383355i	$-0.00122026\pi$
$167$	16.8690	+	12.2560i	1.30536	+	0.948401i	0.305369	+	0.952234i	$0.401220\pi$
$168$		0			0
$169$	5.44624	+	3.95692i	0.418941	+	0.304379i
$170$		0			0
$171$	−1.00739	+	0.731913i	−0.0770372	+	0.0559708i
$172$		0			0
$173$	0.635016	+	1.95438i	0.0482794	+	0.148589i	0.972290	−	0.233778i	$-0.0751090\pi$
$173$	0.635016	+	1.95438i	0.0482794	+	0.148589i	−0.924011	+	0.382367i	$0.875109\pi$
$174$		0			0
$175$	2.50000	+	2.77653i	0.188982	+	0.209886i
$176$		0			0
$177$	3.61882	+	11.1376i	0.272007	+	0.837153i
$178$		0			0
$179$	15.8247	−	11.4973i	1.18279	−	0.859349i	0.190309	−	0.981724i	$-0.439051\pi$
$179$	15.8247	−	11.4973i	1.18279	−	0.859349i	0.992484	+	0.122375i	$0.0390510\pi$
$180$		0			0
$181$	5.96251	+	4.33202i	0.443190	+	0.321996i	0.786901	−	0.617079i	$-0.211684\pi$
$181$	5.96251	+	4.33202i	0.443190	+	0.321996i	−0.343711	+	0.939075i	$0.611684\pi$
$182$		0			0
$183$	10.0960	+	7.33519i	0.746319	+	0.542233i
$184$		0			0
$185$	2.94072	−	3.26600i	0.216206	−	0.240121i
$186$		0			0
$187$	−0.440557	+	1.35589i	−0.0322167	+	0.0991528i
$188$		0			0
$189$	0.230909	+	0.710666i	0.0167962	+	0.0516933i
$190$		0			0
$191$	−0.693806	+	2.13532i	−0.0502021	+	0.154506i	−0.973015	−	0.230743i	$-0.925884\pi$
$191$	−0.693806	+	2.13532i	−0.0502021	+	0.154506i	0.922813	+	0.385249i	$0.125884\pi$
$192$		0			0
$193$	1.10589			0.0796035			0.0398018	−	0.999208i	$-0.487327\pi$
$193$	1.10589			0.0796035			0.0398018	+	0.999208i	$0.487327\pi$
$194$		0			0
$195$	0.585176	−	5.56758i	0.0419054	−	0.398703i
$196$		0			0
$197$	−16.6953	+	12.1299i	−1.18949	+	0.864217i	−0.993211	−	0.116331i	$-0.962887\pi$
$197$	−16.6953	+	12.1299i	−1.18949	+	0.864217i	−0.196282	+	0.980547i	$0.562887\pi$
$198$		0			0
$199$	−12.3822			−0.877749			−0.438874	−	0.898548i	$-0.644623\pi$
$199$	−12.3822			−0.877749			−0.438874	+	0.898548i	$0.644623\pi$
$200$		0			0
$201$	2.91706			0.205753
$202$		0			0
$203$	3.13341	−	2.27655i	0.219922	−	0.159783i
$204$		0			0
$205$	4.80845	−	5.34032i	0.335837	−	0.372984i
$206$		0			0
$207$	3.25085			0.225950
$208$		0			0
$209$	0.0804429	−	0.247578i	0.00556435	−	0.0171253i
$210$		0			0
$211$	6.37422	+	19.6178i	0.438820	+	1.35055i	0.889121	+	0.457671i	$0.151316\pi$
$211$	6.37422	+	19.6178i	0.438820	+	1.35055i	−0.450302	+	0.892876i	$0.648684\pi$
$212$		0			0
$213$	2.02409	−	6.22949i	0.138688	−	0.426838i
$214$		0			0
$215$	−25.9688	−	11.5621i	−1.77106	−	0.788526i
$216$		0			0
$217$	−2.26074	−	1.64253i	−0.153469	−	0.111502i
$218$		0			0
$219$	2.03818	+	1.48083i	0.137728	+	0.100065i
$220$		0			0
$221$	−13.8127	+	10.0355i	−0.929145	+	0.675063i
$222$		0			0
$223$	−1.28385	−	3.95129i	−0.0859732	−	0.264598i	0.898823	−	0.438312i	$-0.144423\pi$
$223$	−1.28385	−	3.95129i	−0.0859732	−	0.264598i	−0.984796	+	0.173713i	$0.944423\pi$
$224$		0			0
$225$	4.56773	−	2.03368i	0.304515	−	0.135579i
$226$		0			0
$227$	−7.30175	−	22.4725i	−0.484634	−	1.49155i	−0.832510	−	0.554010i	$-0.813097\pi$
$227$	−7.30175	−	22.4725i	−0.484634	−	1.49155i	0.347876	−	0.937541i	$-0.386903\pi$
$228$		0			0
$229$	−14.7565	+	10.7212i	−0.975139	+	0.708480i	−0.956617	−	0.291348i	$-0.905896\pi$
$229$	−14.7565	+	10.7212i	−0.975139	+	0.708480i	−0.0185221	+	0.999828i	$0.505896\pi$
$230$		0			0
$231$	−0.126381	−	0.0918211i	−0.00831525	−	0.00604138i
$232$		0			0
$233$	−1.83438	−	1.33276i	−0.120174	−	0.0873117i	0.526075	−	0.850438i	$-0.323663\pi$
$233$	−1.83438	−	1.33276i	−0.120174	−	0.0873117i	−0.646249	+	0.763127i	$0.723663\pi$
$234$		0			0
$235$	14.1780	−	3.01363i	0.924871	−	0.196587i
$236$		0			0
$237$	−3.16505	+	9.74102i	−0.205592	+	0.632747i
$238$		0			0
$239$	5.28631	+	16.2696i	0.341943	+	1.05239i	0.963200	+	0.268786i	$0.0866223\pi$
$239$	5.28631	+	16.2696i	0.341943	+	1.05239i	−0.621257	+	0.783607i	$0.713378\pi$
$240$		0			0
$241$	8.71435	−	26.8200i	0.561341	−	1.72763i	−0.117240	−	0.993104i	$-0.537405\pi$
$241$	8.71435	−	26.8200i	0.561341	−	1.72763i	0.678581	−	0.734526i	$-0.262595\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−13.1586	−	5.85861i	−0.840675	−	0.374293i
$246$		0			0
$247$	2.52212	−	1.83243i	0.160479	−	0.116595i
$248$		0			0
$249$	−5.67652			−0.359735
$250$		0			0
$251$	23.9575			1.51219			0.756093	−	0.654464i	$-0.227106\pi$
$251$	23.9575			1.51219			0.756093	+	0.654464i	$0.227106\pi$
$252$		0			0
$253$	−0.549819	+	0.399467i	−0.0345668	+	0.0251142i
$254$		0			0
$255$	−13.9306	−	6.20230i	−0.872368	−	0.388403i
$256$		0			0
$257$	−28.5421			−1.78041			−0.890204	−	0.455561i	$-0.849439\pi$
$257$	−28.5421			−1.78041			−0.890204	+	0.455561i	$0.849439\pi$
$258$		0			0
$259$	0.453837	−	1.39677i	0.0282000	−	0.0867908i
$260$		0			0
$261$	−1.60171	−	4.92954i	−0.0991431	−	0.305131i
$262$		0			0
$263$	−1.09911	+	3.38270i	−0.0677738	+	0.208586i	−0.979208	−	0.202860i	$-0.934976\pi$
$263$	−1.09911	+	3.38270i	−0.0677738	+	0.208586i	0.911434	+	0.411447i	$0.134976\pi$
$264$		0			0
$265$	−9.06161	+	1.92611i	−0.556650	+	0.118320i
$266$		0			0
$267$	0.745693	+	0.541778i	0.0456357	+	0.0331563i
$268$		0			0
$269$	−23.6733	−	17.1997i	−1.44339	−	1.04868i	−0.987321	−	0.158736i	$-0.949258\pi$
$269$	−23.6733	−	17.1997i	−1.44339	−	1.04868i	−0.456066	−	0.889946i	$-0.650742\pi$
$270$		0			0
$271$	20.0784	−	14.5878i	1.21968	−	0.886147i	0.223603	−	0.974680i	$-0.428218\pi$
$271$	20.0784	−	14.5878i	1.21968	−	0.886147i	0.996073	+	0.0885338i	$0.0282181\pi$
$272$		0			0
$273$	−0.578108	−	1.77923i	−0.0349887	−	0.107684i
$274$		0			0
$275$	−0.522642	+	0.905243i	−0.0315165	+	0.0545882i
$276$		0			0
$277$	−5.38539	−	16.5745i	−0.323577	−	0.995867i	−0.972079	−	0.234654i	$-0.924604\pi$
$277$	−5.38539	−	16.5745i	−0.323577	−	0.995867i	0.648502	−	0.761213i	$-0.275396\pi$
$278$		0			0
$279$	−3.02547	+	2.19813i	−0.181130	+	0.131599i
$280$		0			0
$281$	−3.03664	−	2.20625i	−0.181151	−	0.131614i	0.493515	−	0.869738i	$-0.335712\pi$
$281$	−3.03664	−	2.20625i	−0.181151	−	0.131614i	−0.674665	+	0.738124i	$0.735712\pi$
$282$		0			0
$283$	−13.2464	−	9.62409i	−0.787418	−	0.572093i	0.119778	−	0.992801i	$-0.461782\pi$
$283$	−13.2464	−	9.62409i	−0.787418	−	0.572093i	−0.907196	+	0.420708i	$0.861782\pi$
$284$		0			0
$285$	2.54364	+	1.13250i	0.150672	+	0.0670836i
$286$		0			0
$287$	0.742080	−	2.28389i	0.0438036	−	0.134814i
$288$		0			0
$289$	9.11787	+	28.0619i	0.536345	+	1.65070i
$290$		0			0
$291$	−4.80349	+	14.7836i	−0.281586	+	0.866632i
$292$		0			0
$293$	8.70991			0.508838			0.254419	−	0.967094i	$-0.418116\pi$
$293$	8.70991			0.508838			0.254419	+	0.967094i	$0.418116\pi$
$294$		0			0
$295$	17.5219	−	19.4600i	1.02016	−	1.13301i
$296$		0			0
$297$	−0.169131	+	0.122881i	−0.00981395	+	0.00713025i
$298$		0			0
$299$	−8.13888			−0.470683
$300$		0			0
$301$	−9.49939			−0.547536
$302$		0			0
$303$	8.93194	−	6.48944i	0.513127	−	0.372808i
$304$		0			0
$305$	2.91684	−	27.7518i	0.167018	−	1.58907i
$306$		0			0
$307$	−17.7123			−1.01090			−0.505448	−	0.862857i	$-0.668673\pi$
$307$	−17.7123			−1.01090			−0.505448	+	0.862857i	$0.668673\pi$
$308$		0			0
$309$	4.29048	−	13.2047i	0.244077	−	0.751191i
$310$		0			0
$311$	6.26921	+	19.2946i	0.355494	+	1.09410i	0.955722	+	0.294270i	$0.0950763\pi$
$311$	6.26921	+	19.2946i	0.355494	+	1.09410i	−0.600228	+	0.799829i	$0.704924\pi$
$312$		0			0
$313$	6.41831	−	19.7535i	0.362785	−	1.11654i	−0.588572	−	0.808445i	$-0.700310\pi$
$313$	6.41831	−	19.7535i	0.362785	−	1.11654i	0.951357	−	0.308091i	$-0.0996902\pi$
$314$		0			0
$315$	1.11803	−	1.24170i	0.0629941	−	0.0699620i
$316$		0			0
$317$	13.5633	+	9.85429i	0.761789	+	0.553472i	0.899458	−	0.437006i	$-0.143961\pi$
$317$	13.5633	+	9.85429i	0.761789	+	0.553472i	−0.137670	+	0.990478i	$0.543961\pi$
$318$		0			0
$319$	0.876642	+	0.636918i	0.0490825	+	0.0356606i
$320$		0			0
$321$	−0.829324	+	0.602539i	−0.0462884	+	0.0336305i
$322$		0			0
$323$	−2.62408	−	8.07610i	−0.146008	−	0.449366i
$324$		0			0
$325$	−11.4358	+	5.09156i	−0.634345	+	0.282429i
$326$		0			0
$327$	−2.07199	−	6.37694i	−0.114582	−	0.352646i
$328$		0			0
$329$	3.91870	−	2.84711i	0.216045	−	0.156966i
$330$		0			0
$331$	21.2090	+	15.4092i	1.16575	+	0.846968i	0.990494	−	0.137555i	$-0.0439243\pi$
$331$	21.2090	+	15.4092i	1.16575	+	0.846968i	0.175257	+	0.984523i	$0.443924\pi$
$332$		0			0
$333$	−1.59007	−	1.15525i	−0.0871352	−	0.0633074i
$334$		0			0
$335$	−3.26137	−	5.64886i	−0.178188	−	0.308630i
$336$		0			0
$337$	−8.03519	+	24.7298i	−0.437705	+	1.34712i	0.452584	+	0.891722i	$0.350502\pi$
$337$	−8.03519	+	24.7298i	−0.437705	+	1.34712i	−0.890289	+	0.455395i	$0.849498\pi$
$338$		0			0
$339$	2.57151	+	7.91428i	0.139665	+	0.429845i
$340$		0			0
$341$	0.241591	−	0.743542i	0.0130829	−	0.0402651i
$342$		0			0
$343$	−10.0441			−0.542331
$344$		0			0
$345$	−3.63456	−	6.29525i	−0.195678	−	0.338925i
$346$		0			0
$347$	−3.72256	+	2.70460i	−0.199838	+	0.145191i	−0.683204	−	0.730228i	$-0.739414\pi$
$347$	−3.72256	+	2.70460i	−0.199838	+	0.145191i	0.483366	+	0.875418i	$0.339414\pi$
$348$		0			0
$349$	−29.2108			−1.56362			−0.781810	−	0.623516i	$-0.785703\pi$
$349$	−29.2108			−1.56362			−0.781810	+	0.623516i	$0.785703\pi$
$350$		0			0
$351$	−2.50361			−0.133633
$352$		0			0
$353$	22.7505	−	16.5292i	1.21088	−	0.879759i	0.215574	−	0.976488i	$-0.430838\pi$
$353$	22.7505	−	16.5292i	1.21088	−	0.879759i	0.995311	+	0.0967283i	$0.0308378\pi$
$354$		0			0
$355$	−14.3264	+	3.04516i	−0.760364	+	0.161620i
$356$		0			0
$357$	−5.09582			−0.269699
$358$		0			0
$359$	−2.90570	+	8.94282i	−0.153357	+	0.471984i	−0.997991	−	0.0633604i	$-0.979818\pi$
$359$	−2.90570	+	8.94282i	−0.153357	+	0.471984i	0.844634	+	0.535345i	$0.179818\pi$
$360$		0			0
$361$	−5.39218	−	16.5954i	−0.283799	−	0.873444i
$362$		0			0
$363$	−3.38568	+	10.4201i	−0.177702	+	0.546911i
$364$		0			0
$365$	0.588850	−	5.60253i	0.0308218	−	0.293250i
$366$		0			0
$367$	−17.8033	−	12.9349i	−0.929326	−	0.675195i	0.0165016	−	0.999864i	$-0.494747\pi$
$367$	−17.8033	−	12.9349i	−0.929326	−	0.675195i	−0.945828	+	0.324669i	$0.894747\pi$
$368$		0			0
$369$	−2.59996	−	1.88898i	−0.135349	−	0.0983365i
$370$		0			0
$371$	−2.50457	+	1.81968i	−0.130031	+	0.0944728i
$372$		0			0
$373$	5.75384	+	17.7085i	0.297923	+	0.916911i	0.982224	+	0.187712i	$0.0601072\pi$
$373$	5.75384	+	17.7085i	0.297923	+	0.916911i	−0.684302	+	0.729199i	$0.739893\pi$
$374$		0			0
$375$	−9.04508	−	6.57164i	−0.467086	−	0.339358i
$376$		0			0
$377$	4.01005	+	12.3417i	0.206528	+	0.635628i
$378$		0			0
$379$	13.6515	−	9.91838i	0.701230	−	0.509473i	−0.179103	−	0.983830i	$-0.557320\pi$
$379$	13.6515	−	9.91838i	0.701230	−	0.509473i	0.880332	+	0.474357i	$0.157320\pi$
$380$		0			0
$381$	11.7601	+	8.54421i	0.602488	+	0.437733i
$382$		0			0
$383$	7.32847	+	5.32445i	0.374467	+	0.272066i	0.759061	−	0.651020i	$-0.225658\pi$
$383$	7.32847	+	5.32445i	0.374467	+	0.272066i	−0.384594	+	0.923086i	$0.625658\pi$
$384$		0			0
$385$	−0.0365126	+	0.347395i	−0.00186086	+	0.0177049i
$386$		0			0
$387$	−3.92843	+	12.0905i	−0.199693	+	0.614593i
$388$		0			0
$389$	10.2225	+	31.4616i	0.518301	+	1.59517i	0.777194	+	0.629261i	$0.216642\pi$
$389$	10.2225	+	31.4616i	0.518301	+	1.59517i	−0.258893	+	0.965906i	$0.583358\pi$
$390$		0			0
$391$	−6.85069	+	21.0843i	−0.346454	+	1.06628i
$392$		0			0
$393$	7.42396			0.374489
$394$		0			0
$395$	22.4020	−	4.76170i	1.12717	−	0.239587i
$396$		0			0
$397$	17.5773	−	12.7706i	0.882177	−	0.640939i	−0.0516494	−	0.998665i	$-0.516448\pi$
$397$	17.5773	−	12.7706i	0.882177	−	0.640939i	0.933827	+	0.357726i	$0.116448\pi$
$398$		0			0
$399$	0.930465			0.0465815
$400$		0			0
$401$	20.1663			1.00706			0.503529	−	0.863978i	$-0.332035\pi$
$401$	20.1663			1.00706			0.503529	+	0.863978i	$0.332035\pi$
$402$		0			0
$403$	7.57460	−	5.50327i	0.377318	−	0.274137i
$404$		0			0
$405$	−1.11803	−	1.93649i	−0.0555556	−	0.0962250i
$406$		0			0
$407$	0.410887			0.0203669
$408$		0			0
$409$	−4.34139	+	13.3614i	−0.214668	+	0.660679i	0.784509	+	0.620117i	$0.212915\pi$
$409$	−4.34139	+	13.3614i	−0.214668	+	0.660679i	−0.999177	+	0.0405623i	$0.987085\pi$
$410$		0			0
$411$	−2.26676	−	6.97636i	−0.111811	−	0.344118i
$412$		0			0
$413$	2.70412	−	8.32244i	0.133061	−	0.409520i
$414$		0			0
$415$	6.34655	+	10.9925i	0.311540	+	0.539602i
$416$		0			0
$417$	−15.9757	−	11.6071i	−0.782336	−	0.568400i
$418$		0			0
$419$	16.3919	+	11.9094i	0.800794	+	0.581811i	0.911147	−	0.412081i	$-0.135198\pi$
$419$	16.3919	+	11.9094i	0.800794	+	0.581811i	−0.110353	+	0.993892i	$0.535198\pi$
$420$		0			0
$421$	−3.54258	+	2.57384i	−0.172655	+	0.125441i	−0.670757	−	0.741677i	$-0.734031\pi$
$421$	−3.54258	+	2.57384i	−0.172655	+	0.125441i	0.498102	+	0.867119i	$0.334031\pi$
$422$		0			0
$423$	−2.00313	−	6.16499i	−0.0973953	−	0.299752i
$424$		0			0
$425$	3.56418	+	33.9109i	0.172888	+	1.64492i
$426$		0			0
$427$	−2.88160	−	8.86866i	−0.139450	−	0.429184i
$428$		0			0
$429$	0.423438	−	0.307645i	0.0204438	−	0.0148533i
$430$		0			0
$431$	−0.944967	−	0.686559i	−0.0455175	−	0.0330704i	0.564794	−	0.825232i	$-0.308956\pi$
$431$	−0.944967	−	0.686559i	−0.0455175	−	0.0330704i	−0.610311	+	0.792162i	$0.708956\pi$
$432$		0			0
$433$	−1.81940	−	1.32187i	−0.0874347	−	0.0635250i	0.543209	−	0.839597i	$-0.317209\pi$
$433$	−1.81940	−	1.32187i	−0.0874347	−	0.0635250i	−0.630644	+	0.776072i	$0.717209\pi$
$434$		0			0
$435$	−7.75525	+	8.61308i	−0.371836	+	0.412966i
$436$		0			0
$437$	1.25089	−	3.84985i	0.0598383	−	0.184163i
$438$		0			0
$439$	6.83477	+	21.0353i	0.326206	+	1.00396i	0.970893	+	0.239512i	$0.0769875\pi$
$439$	6.83477	+	21.0353i	0.326206	+	1.00396i	−0.644688	+	0.764446i	$0.723013\pi$
$440$		0			0
$441$	−1.99057	+	6.12636i	−0.0947893	+	0.291731i
$442$		0			0
$443$	28.1534			1.33761			0.668804	−	0.743439i	$-0.266807\pi$
$443$	28.1534			1.33761			0.668804	+	0.743439i	$0.266807\pi$
$444$		0			0
$445$	0.215438	−	2.04975i	0.0102127	−	0.0971677i
$446$		0			0
$447$	17.6002	−	12.7873i	0.832462	−	0.604819i
$448$		0			0
$449$	16.5924			0.783044			0.391522	−	0.920169i	$-0.371949\pi$
$449$	16.5924			0.783044			0.391522	+	0.920169i	$0.371949\pi$
$450$		0			0
$451$	0.671852			0.0316363
$452$		0			0
$453$	−8.19598	+	5.95473i	−0.385081	+	0.279777i
$454$		0			0
$455$	−2.79912	+	3.10874i	−0.131225	+	0.145740i
$456$		0			0
$457$	−11.1599			−0.522039			−0.261019	−	0.965334i	$-0.584059\pi$
$457$	−11.1599			−0.522039			−0.261019	+	0.965334i	$0.584059\pi$
$458$		0			0
$459$	−2.10735	+	6.48576i	−0.0983628	+	0.302729i
$460$		0			0
$461$	1.93631	+	5.95935i	0.0901830	+	0.277555i	0.985968	−	0.166932i	$-0.0533861\pi$
$461$	1.93631	+	5.95935i	0.0901830	+	0.277555i	−0.895785	+	0.444487i	$0.853386\pi$
$462$		0			0
$463$	−5.26243	+	16.1961i	−0.244566	+	0.752696i	0.751142	+	0.660141i	$0.229503\pi$
$463$	−5.26243	+	16.1961i	−0.244566	+	0.752696i	−0.995708	+	0.0925550i	$0.970497\pi$
$464$		0			0
$465$	7.63923	+	3.40121i	0.354261	+	0.157727i
$466$		0			0
$467$	15.1159	+	10.9823i	0.699481	+	0.508202i	0.879763	−	0.475413i	$-0.157701\pi$
$467$	15.1159	+	10.9823i	0.699481	+	0.508202i	−0.180282	+	0.983615i	$0.557701\pi$
$468$		0			0
$469$	−1.76344	−	1.28122i	−0.0814283	−	0.0591611i
$470$		0			0
$471$	8.08629	−	5.87503i	0.372597	−	0.270707i
$472$		0			0
$473$	−0.821266	−	2.52760i	−0.0377618	−	0.116219i
$474$		0			0
$475$	−0.650797	−	6.19192i	−0.0298606	−	0.284105i
$476$		0			0
$477$	1.28026	+	3.94024i	0.0586191	+	0.180411i
$478$		0			0
$479$	−2.38111	+	1.72998i	−0.108796	+	0.0790448i	−0.640853	−	0.767664i	$-0.721419\pi$
$479$	−2.38111	+	1.72998i	−0.108796	+	0.0790448i	0.532057	+	0.846708i	$0.321419\pi$
$480$		0			0
$481$	3.98092	+	2.89230i	0.181514	+	0.131878i
$482$		0			0
$483$	−1.96523	−	1.42782i	−0.0894212	−	0.0649683i
$484$		0			0
$485$	33.9989	−	7.22668i	1.54381	−	0.328147i
$486$		0			0
$487$	−4.33109	+	13.3297i	−0.196261	+	0.604028i	0.803699	+	0.595036i	$0.202862\pi$
$487$	−4.33109	+	13.3297i	−0.196261	+	0.604028i	−0.999960	+	0.00899199i	$0.997138\pi$
$488$		0			0
$489$	−0.792035	−	2.43763i	−0.0358170	−	0.110234i
$490$		0			0
$491$	2.76416	−	8.50720i	0.124745	−	0.383925i	−0.869110	−	0.494619i	$-0.835308\pi$
$491$	2.76416	−	8.50720i	0.124745	−	0.383925i	0.993854	+	0.110695i	$0.0353075\pi$
$492$		0			0
$493$	35.3472			1.59196
$494$		0			0
$495$	0.427051	+	0.190135i	0.0191945	+	0.00854595i
$496$		0			0
$497$	−3.95971	+	2.87690i	−0.177617	+	0.129046i
$498$		0			0
$499$	−2.39366			−0.107155			−0.0535774	−	0.998564i	$-0.517062\pi$
$499$	−2.39366			−0.107155			−0.0535774	+	0.998564i	$0.517062\pi$
$500$		0			0
$501$	−20.8512			−0.931564
$502$		0			0
$503$	−6.81519	+	4.95152i	−0.303874	+	0.220777i	−0.729264	−	0.684233i	$-0.760137\pi$
$503$	−6.81519	+	4.95152i	−0.303874	+	0.220777i	0.425389	+	0.905010i	$0.360137\pi$
$504$		0			0
$505$	−22.5530	−	10.0412i	−1.00359	−	0.446829i
$506$		0			0
$507$	−6.73192			−0.298975
$508$		0			0
$509$	9.98528	−	30.7315i	0.442590	−	1.36215i	−0.442516	−	0.896761i	$-0.645914\pi$
$509$	9.98528	−	30.7315i	0.442590	−	1.36215i	0.885106	−	0.465390i	$-0.154086\pi$
$510$		0			0
$511$	−0.581737	−	1.79040i	−0.0257345	−	0.0792027i
$512$		0			0
$513$	0.384789	−	1.18426i	0.0169889	−	0.0522864i
$514$		0			0
$515$	−30.3677	+	6.45486i	−1.33816	+	0.284435i
$516$		0			0
$517$	1.09635	+	0.796543i	0.0482173	+	0.0350319i
$518$		0			0
$519$	−1.66249	−	1.20787i	−0.0729754	−	0.0530197i
$520$		0			0
$521$	−2.88427	+	2.09554i	−0.126362	+	0.0918074i	−0.649171	−	0.760642i	$-0.724884\pi$
$521$	−2.88427	+	2.09554i	−0.126362	+	0.0918074i	0.522809	+	0.852450i	$0.324884\pi$
$522$		0			0
$523$	−10.0241	−	30.8511i	−0.438325	−	1.34903i	−0.889640	−	0.456662i	$-0.849045\pi$
$523$	−10.0241	−	30.8511i	−0.438325	−	1.34903i	0.451315	−	0.892365i	$-0.350955\pi$
$524$		0			0
$525$	−3.65455	−	0.776798i	−0.159497	−	0.0339022i
$526$		0			0
$527$	−7.88082	−	24.2547i	−0.343294	−	1.05655i
$528$		0			0
$529$	10.0577	−	7.30732i	0.437290	−	0.317710i
$530$		0			0
$531$	−9.47420	−	6.88341i	−0.411145	−	0.298715i
$532$		0			0
$533$	6.50929	+	4.72928i	0.281949	+	0.204848i
$534$		0			0
$535$	2.09402	+	0.932320i	0.0905326	+	0.0403077i
$536$		0			0
$537$	−6.04449	+	18.6030i	−0.260839	+	0.802781i
$538$		0			0
$539$	−0.416143	−	1.28076i	−0.0179246	−	0.0551661i
$540$		0			0
$541$	−3.40378	+	10.4757i	−0.146340	+	0.450388i	−0.997181	−	0.0750356i	$-0.976093\pi$
$541$	−3.40378	+	10.4757i	−0.146340	+	0.450388i	0.850841	+	0.525423i	$0.176093\pi$
$542$		0			0
$543$	−7.37007			−0.316280
$544$		0			0
$545$	−10.0323	+	11.1420i	−0.429738	+	0.477272i
$546$		0			0
$547$	4.31795	−	3.13718i	0.184622	−	0.134136i	−0.491635	−	0.870801i	$-0.663601\pi$
$547$	4.31795	−	3.13718i	0.184622	−	0.134136i	0.676258	+	0.736665i	$0.263601\pi$
$548$		0			0
$549$	−12.4794			−0.532606
$550$		0			0
$551$	−6.45418			−0.274957
$552$		0			0
$553$	6.19177	−	4.49859i	0.263301	−	0.191299i
$554$		0			0
$555$	−0.459386	+	4.37076i	−0.0194998	+	0.185529i
$556$		0			0
$557$	−0.0652731			−0.00276571			−0.00138286	−	0.999999i	$-0.500440\pi$
$557$	−0.0652731			−0.00276571			−0.00138286	+	0.999999i	$0.500440\pi$
$558$		0			0
$559$	9.83527	−	30.2699i	0.415988	−	1.28028i
$560$		0			0
$561$	−0.440557	−	1.35589i	−0.0186003	−	0.0572459i
$562$		0			0
$563$	−8.88197	+	27.3359i	−0.374330	+	1.15207i	0.569599	+	0.821923i	$0.307098\pi$
$563$	−8.88197	+	27.3359i	−0.374330	+	1.15207i	−0.943929	+	0.330147i	$0.892902\pi$
$564$		0			0
$565$	12.4509	−	13.8281i	0.523814	−	0.581754i
$566$		0			0
$567$	−0.604528	−	0.439216i	−0.0253878	−	0.0184453i
$568$		0			0
$569$	6.68501	+	4.85694i	0.280250	+	0.203614i	0.719026	−	0.694983i	$-0.244588\pi$
$569$	6.68501	+	4.85694i	0.280250	+	0.203614i	−0.438776	+	0.898596i	$0.644588\pi$
$570$		0			0
$571$	−9.49451	+	6.89817i	−0.397333	+	0.288679i	−0.768454	−	0.639905i	$-0.778974\pi$
$571$	−9.49451	+	6.89817i	−0.397333	+	0.288679i	0.371121	+	0.928585i	$0.378974\pi$
$572$		0			0
$573$	−0.693806	−	2.13532i	−0.0289842	−	0.0892041i
$574$		0			0
$575$	−8.12713	+	14.0766i	−0.338925	+	0.587035i
$576$		0			0
$577$	6.60944	+	20.3418i	0.275154	+	0.846838i	0.989178	+	0.146717i	$0.0468707\pi$
$577$	6.60944	+	20.3418i	0.275154	+	0.846838i	−0.714024	+	0.700121i	$0.753129\pi$
$578$		0			0
$579$	−0.894682	+	0.650024i	−0.0371817	+	0.0270141i
$580$		0			0
$581$	3.43162	+	2.49322i	0.142368	+	0.103436i
$582$		0			0
$583$	−0.700710	−	0.509096i	−0.0290204	−	0.0210846i
$584$		0			0
$585$	2.79912	+	4.84823i	0.115730	+	0.200449i
$586$		0			0
$587$	12.7412	−	39.2133i	0.525885	−	1.61851i	−0.236674	−	0.971589i	$-0.576057\pi$
$587$	12.7412	−	39.2133i	0.525885	−	1.61851i	0.762559	−	0.646918i	$-0.223943\pi$
$588$		0			0
$589$	1.43899	+	4.42876i	0.0592925	+	0.182484i
$590$		0			0
$591$	6.37705	−	19.6265i	0.262317	−	0.807328i
$592$		0			0
$593$	−23.2238			−0.953685			−0.476843	−	0.878989i	$-0.658219\pi$
$593$	−23.2238			−0.953685			−0.476843	+	0.878989i	$0.658219\pi$
$594$		0			0
$595$	5.69730	+	9.86801i	0.233566	+	0.404549i
$596$		0			0
$597$	10.0174	−	7.27806i	0.409984	−	0.297871i
$598$		0			0
$599$	−22.6226			−0.924335			−0.462168	−	0.886793i	$-0.652928\pi$
$599$	−22.6226			−0.924335			−0.462168	+	0.886793i	$0.652928\pi$
$600$		0			0
$601$	−12.9540			−0.528405			−0.264203	−	0.964467i	$-0.585109\pi$
$601$	−12.9540			−0.528405			−0.264203	+	0.964467i	$0.585109\pi$
$602$		0			0
$603$	−2.35995	+	1.71460i	−0.0961045	+	0.0698240i
$604$		0			0
$605$	23.9637	−	5.09363i	0.974261	−	0.207086i
$606$		0			0
$607$	4.54036			0.184288			0.0921439	−	0.995746i	$-0.470628\pi$
$607$	4.54036			0.184288			0.0921439	+	0.995746i	$0.470628\pi$
$608$		0			0
$609$	−1.19686	+	3.68354i	−0.0484990	+	0.149265i
$610$		0			0
$611$	5.01505	+	15.4347i	0.202887	+	0.624423i
$612$		0			0
$613$	−7.83471	+	24.1128i	−0.316441	+	0.973905i	0.658716	+	0.752391i	$0.271100\pi$
$613$	−7.83471	+	24.1128i	−0.316441	+	0.973905i	−0.975157	+	0.221514i	$0.928900\pi$
$614$		0			0
$615$	−0.751153	+	7.14675i	−0.0302894	+	0.288185i
$616$		0			0
$617$	36.5829	+	26.5790i	1.47277	+	1.07003i	0.979799	+	0.199986i	$0.0640896\pi$
$617$	36.5829	+	26.5790i	1.47277	+	1.07003i	0.492972	+	0.870045i	$0.335910\pi$
$618$		0			0
$619$	−25.3666	−	18.4299i	−1.01957	−	0.740762i	−0.0533766	−	0.998574i	$-0.516998\pi$
$619$	−25.3666	−	18.4299i	−1.01957	−	0.740762i	−0.966195	+	0.257812i	$0.916998\pi$
$620$		0			0
$621$	−2.62999	+	1.91080i	−0.105538	+	0.0766779i
$622$		0			0
$623$	−0.212835	−	0.655040i	−0.00852707	−	0.0262436i
$624$		0			0
$625$	−2.61321	+	24.8630i	−0.104528	+	0.994522i
$626$		0			0
$627$	0.0804429	+	0.247578i	0.00321258	+	0.00988730i
$628$		0			0
$629$	10.8435	−	7.87828i	0.432360	−	0.314128i
$630$		0			0
$631$	−25.8455	−	18.7779i	−1.02889	−	0.747535i	−0.0608071	−	0.998150i	$-0.519367\pi$
$631$	−25.8455	−	18.7779i	−1.02889	−	0.747535i	−0.968087	+	0.250614i	$0.919367\pi$
$632$		0			0
$633$	−16.6879	−	12.1245i	−0.663286	−	0.481905i
$634$		0			0
$635$	3.39760	−	32.3260i	0.134830	−	1.28282i
$636$		0			0
$637$	4.98363	−	15.3380i	0.197459	−	0.607715i
$638$		0			0
$639$	2.02409	+	6.22949i	0.0800716	+	0.246435i
$640$		0			0
$641$	12.7727	−	39.3103i	0.504491	−	1.55267i	−0.297132	−	0.954836i	$-0.596030\pi$
$641$	12.7727	−	39.3103i	0.504491	−	1.55267i	0.801624	−	0.597829i	$-0.203970\pi$
$642$		0			0
$643$	−33.2313			−1.31052			−0.655258	−	0.755406i	$-0.727440\pi$
$643$	−33.2313			−1.31052			−0.655258	+	0.755406i	$0.727440\pi$
$644$		0			0
$645$	27.8052	−	5.91018i	1.09483	−	0.232713i
$646$		0			0
$647$	−27.2571	+	19.8034i	−1.07159	+	0.778553i	−0.976197	−	0.216887i	$-0.930410\pi$
$647$	−27.2571	+	19.8034i	−1.07159	+	0.778553i	−0.0953892	+	0.995440i	$0.530410\pi$
$648$		0			0
$649$	2.44822			0.0961009
$650$		0			0
$651$	2.79443			0.109522
$652$		0			0
$653$	−17.6754	+	12.8419i	−0.691692	+	0.502544i	−0.877216	−	0.480096i	$-0.840602\pi$
$653$	−17.6754	+	12.8419i	−0.691692	+	0.502544i	0.185524	+	0.982640i	$0.440602\pi$
$654$		0			0
$655$	−8.30025	−	14.3764i	−0.324317	−	0.561734i
$656$		0			0
$657$	−2.51933			−0.0982885
$658$		0			0
$659$	−3.48829	+	10.7359i	−0.135884	+	0.418209i	−0.995727	−	0.0923507i	$-0.970562\pi$
$659$	−3.48829	+	10.7359i	−0.135884	+	0.418209i	0.859842	+	0.510560i	$0.170562\pi$
$660$		0			0
$661$	−11.3014	−	34.7821i	−0.439573	−	1.35287i	−0.888327	−	0.459211i	$-0.848132\pi$
$661$	−11.3014	−	34.7821i	−0.439573	−	1.35287i	0.448754	−	0.893655i	$-0.351868\pi$
$662$		0			0
$663$	5.27599	−	16.2378i	0.204903	−	0.630625i
$664$		0			0
$665$	−1.04029	−	1.80184i	−0.0403408	−	0.0698722i
$666$		0			0
$667$	13.6319	+	9.90412i	0.527828	+	0.383489i
$668$		0			0
$669$	3.36117	+	2.44203i	0.129950	+	0.0944145i
$670$		0			0
$671$	2.11064	−	1.53347i	0.0814804	−	0.0591990i
$672$		0			0
$673$	2.37563	+	7.31143i	0.0915737	+	0.281835i	0.986346	−	0.164689i	$-0.0526619\pi$
$673$	2.37563	+	7.31143i	0.0915737	+	0.281835i	−0.894772	+	0.446523i	$0.852662\pi$
$674$		0			0
$675$	−2.50000	+	4.33013i	−0.0962250	+	0.166667i
$676$		0			0
$677$	−11.5253	−	35.4711i	−0.442952	−	1.36327i	−0.884714	−	0.466133i	$-0.845647\pi$
$677$	−11.5253	−	35.4711i	−0.442952	−	1.36327i	0.441763	−	0.897132i	$-0.354353\pi$
$678$		0			0
$679$	9.39705	−	6.82736i	0.360626	−	0.262010i
$680$		0			0
$681$	19.1162	+	13.8888i	0.732535	+	0.532218i
$682$		0			0
$683$	−29.5125	−	21.4421i	−1.12926	−	0.820458i	−0.143676	−	0.989625i	$-0.545892\pi$
$683$	−29.5125	−	21.4421i	−1.12926	−	0.820458i	−0.985587	+	0.169166i	$0.945892\pi$
$684$		0			0
$685$	−10.9753	+	12.1894i	−0.419346	+	0.465731i
$686$		0			0
$687$	5.63649	−	17.3473i	0.215046	−	0.661842i
$688$		0			0
$689$	−3.20528	−	9.86483i	−0.122111	−	0.375820i
$690$		0			0
$691$	−9.99734	+	30.7686i	−0.380317	+	1.17049i	0.559504	+	0.828827i	$0.310992\pi$
$691$	−9.99734	+	30.7686i	−0.380317	+	1.17049i	−0.939821	+	0.341667i	$0.889008\pi$
$692$		0			0
$693$	0.156215			0.00593413
$694$		0			0
$695$	−4.61555	+	43.9140i	−0.175078	+	1.66575i
$696$		0			0
$697$	17.7305	−	12.8820i	0.671591	−	0.487940i
$698$		0			0
$699$	2.26742			0.0857617
$700$		0			0
$701$	5.27498			0.199233			0.0996166	−	0.995026i	$-0.468238\pi$
$701$	5.27498			0.199233			0.0996166	+	0.995026i	$0.468238\pi$
$702$		0			0
$703$	−1.97996	+	1.43853i	−0.0746756	+	0.0542550i
$704$		0			0
$705$	−9.69888	+	10.7717i	−0.365281	+	0.405686i
$706$		0			0
$707$	−8.24988			−0.310268
$708$		0			0
$709$	9.03055	−	27.7932i	0.339149	−	1.04379i	−0.625493	−	0.780230i	$-0.715102\pi$
$709$	9.03055	−	27.7932i	0.339149	−	1.04379i	0.964642	−	0.263564i	$-0.0848981\pi$
$710$		0			0
$711$	−3.16505	−	9.74102i	−0.118699	−	0.365317i
$712$		0			0
$713$	3.75677	−	11.5621i	0.140692	−	0.433005i
$714$		0			0
$715$	−1.06917	−	0.476025i	−0.0399847	−	0.0178023i
$716$		0			0
$717$	−13.8397	−	10.0552i	−0.516855	−	0.375517i
$718$		0			0
$719$	−35.5675	−	25.8413i	−1.32644	−	0.963718i	−0.999828	−	0.0185605i	$-0.994092\pi$
$719$	−35.5675	−	25.8413i	−1.32644	−	0.963718i	−0.326616	−	0.945157i	$-0.605908\pi$
$720$		0			0
$721$	−8.39344	+	6.09819i	−0.312588	+	0.227108i
$722$		0			0
$723$	8.71435	+	26.8200i	0.324090	+	0.997447i
$724$		0			0
$725$	25.3498	+	5.38827i	0.941468	+	0.200115i
$726$		0			0
$727$	9.24768	+	28.4614i	0.342977	+	1.05558i	0.962658	+	0.270721i	$0.0872622\pi$
$727$	9.24768	+	28.4614i	0.342977	+	1.05558i	−0.619680	+	0.784854i	$0.712738\pi$
$728$		0			0
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	−70.1373	−	50.9577i	−2.59412	−	1.88474i
$732$		0			0
$733$	13.3702	+	9.71402i	0.493840	+	0.358795i	0.806659	−	0.591017i	$-0.201273\pi$
$733$	13.3702	+	9.71402i	0.493840	+	0.358795i	−0.312819	+	0.949813i	$0.601273\pi$
$734$		0			0
$735$	14.0892	−	2.99475i	0.519687	−	0.110463i
$736$		0			0
$737$	0.188448	−	0.579984i	0.00694158	−	0.0213640i
$738$		0			0
$739$	−15.7285	−	48.4073i	−0.578581	−	1.78069i	−0.623648	−	0.781706i	$-0.714350\pi$
$739$	−15.7285	−	48.4073i	−0.578581	−	1.78069i	0.0450666	−	0.998984i	$-0.485650\pi$
$740$		0			0
$741$	−0.963364	+	2.96493i	−0.0353901	+	0.108919i
$742$		0			0
$743$	−28.6937			−1.05267			−0.526336	−	0.850277i	$-0.676434\pi$
$743$	−28.6937			−1.05267			−0.526336	+	0.850277i	$0.676434\pi$
$744$		0			0
$745$	−44.4402	−	19.7860i	−1.62816	−	0.724904i
$746$		0			0
$747$	4.59240	−	3.33658i	0.168027	−	0.122079i
$748$		0			0
$749$	0.765995			0.0279888
$750$		0			0
$751$	−0.927935			−0.0338608			−0.0169304	−	0.999857i	$-0.505389\pi$
$751$	−0.927935			−0.0338608			−0.0169304	+	0.999857i	$0.505389\pi$
$752$		0			0
$753$	−19.3821	+	14.0819i	−0.706322	+	0.513173i
$754$		0			0
$755$	20.6947	+	9.21385i	0.753156	+	0.335327i
$756$		0			0
$757$	41.4243			1.50559			0.752796	−	0.658254i	$-0.228705\pi$
$757$	41.4243			1.50559			0.752796	+	0.658254i	$0.228705\pi$
$758$		0			0
$759$	0.210012	−	0.646350i	0.00762295	−	0.0234610i
$760$		0			0
$761$	1.17031	+	3.60185i	0.0424237	+	0.130567i	0.970025	−	0.243005i	$-0.0781330\pi$
$761$	1.17031	+	3.60185i	0.0424237	+	0.130567i	−0.927601	+	0.373572i	$0.878133\pi$
$762$		0			0
$763$	−1.54827	+	4.76509i	−0.0560513	+	0.172508i
$764$		0			0
$765$	14.9157	−	3.17043i	0.539279	−	0.114627i
$766$		0			0
$767$	23.7197	+	17.2334i	0.856470	+	0.622262i
$768$		0			0
$769$	1.06014	+	0.770234i	0.0382295	+	0.0277753i	0.606736	−	0.794903i	$-0.292479\pi$
$769$	1.06014	+	0.770234i	0.0382295	+	0.0277753i	−0.568506	+	0.822679i	$0.692479\pi$
$770$		0			0
$771$	23.0911	−	16.7766i	0.831604	−	0.604196i
$772$		0			0
$773$	9.00241	+	27.7066i	0.323794	+	0.996536i	0.971982	+	0.235055i	$0.0755272\pi$
$773$	9.00241	+	27.7066i	0.323794	+	0.996536i	−0.648188	+	0.761480i	$0.724473\pi$
$774$		0			0
$775$	−1.95452	−	18.5960i	−0.0702083	−	0.667987i
$776$		0			0
$777$	0.453837	+	1.39677i	0.0162813	+	0.0501087i
$778$		0			0
$779$	−3.23748	+	2.35217i	−0.115995	+	0.0842752i
$780$		0			0
$781$	−1.10782	−	0.804877i	−0.0396409	−	0.0288008i
$782$		0			0
$783$	4.19332	+	3.04662i	0.149857	+	0.108877i
$784$		0			0
$785$	−20.4177	−	9.09055i	−0.728739	−	0.324455i
$786$		0			0
$787$	−14.4050	+	44.3341i	−0.513484	+	1.58034i	0.272540	+	0.962145i	$0.412136\pi$
$787$	−14.4050	+	44.3341i	−0.513484	+	1.58034i	−0.786023	+	0.618197i	$0.787864\pi$
$788$		0			0
$789$	−1.09911	−	3.38270i	−0.0391292	−	0.120427i
$790$		0			0
$791$	1.92153	−	5.91385i	0.0683217	−	0.210272i
$792$		0			0
$793$	31.2435			1.10949
$794$		0			0
$795$	6.19886	−	6.88453i	0.219851	−	0.244169i
$796$		0			0
$797$	11.1308	−	8.08703i	0.394275	−	0.286457i	−0.372930	−	0.927859i	$-0.621647\pi$
$797$	11.1308	−	8.08703i	0.394275	−	0.286457i	0.767205	+	0.641402i	$0.221647\pi$
$798$		0			0
$799$	44.2059			1.56389
$800$		0			0
$801$	−0.921727			−0.0325676
$802$		0			0
$803$	0.426096	−	0.309577i	0.0150366	−	0.0109247i
$804$		0			0
$805$	−0.567774	+	5.40201i	−0.0200114	+	0.190396i
$806$		0			0
$807$	29.2618			1.03006
$808$		0			0
$809$	3.08886	−	9.50654i	0.108599	−	0.334232i	−0.881960	−	0.471325i	$-0.843776\pi$
$809$	3.08886	−	9.50654i	0.108599	−	0.334232i	0.990558	+	0.137093i	$0.0437759\pi$
$810$		0			0
$811$	5.72277	+	17.6129i	0.200954	+	0.618472i	0.999855	+	0.0170101i	$0.00541474\pi$
$811$	5.72277	+	17.6129i	0.200954	+	0.618472i	−0.798902	+	0.601462i	$0.794585\pi$
$812$		0			0
$813$	−7.66927	+	23.6036i	−0.268973	+	0.827814i
$814$		0			0
$815$	−3.83493	+	4.25912i	−0.134332	+	0.149191i
$816$		0			0
$817$	12.8066	+	9.30457i	0.448048	+	0.325526i
$818$		0			0
$819$	1.51351	+	1.09963i	0.0528862	+	0.0384240i
$820$		0			0
$821$	−22.9081	+	16.6437i	−0.799498	+	0.580869i	−0.910767	−	0.412921i	$-0.864509\pi$
$821$	−22.9081	+	16.6437i	−0.799498	+	0.580869i	0.111269	+	0.993790i	$0.464509\pi$
$822$		0			0
$823$	3.70366	+	11.3987i	0.129101	+	0.397333i	0.994626	−	0.103533i	$-0.0330148\pi$
$823$	3.70366	+	11.3987i	0.129101	+	0.397333i	−0.865525	+	0.500866i	$0.833015\pi$
$824$		0			0
$825$	−0.109262	−	1.03956i	−0.00380401	−	0.0361928i
$826$		0			0
$827$	4.13191	+	12.7167i	0.143681	+	0.442204i	0.996839	−	0.0794485i	$-0.0253159\pi$
$827$	4.13191	+	12.7167i	0.143681	+	0.442204i	−0.853158	+	0.521652i	$0.825316\pi$
$828$		0			0
$829$	13.3909	−	9.72909i	0.465087	−	0.337905i	−0.330437	−	0.943828i	$-0.607196\pi$
$829$	13.3909	−	9.72909i	0.465087	−	0.337905i	0.795523	+	0.605923i	$0.207196\pi$
$830$		0			0
$831$	14.0991	+	10.2436i	0.489094	+	0.355347i
$832$		0			0
$833$	−35.5393	−	25.8208i	−1.23136	−	0.894637i
$834$		0			0
$835$	23.3124	+	40.3782i	0.806758	+	1.39735i
$836$		0			0
$837$	1.15563	−	3.55665i	0.0399442	−	0.122936i
$838$		0			0
$839$	7.56589	+	23.2854i	0.261204	+	0.803902i	0.992544	+	0.121889i	$0.0388953\pi$
$839$	7.56589	+	23.2854i	0.261204	+	0.803902i	−0.731340	+	0.682013i	$0.761105\pi$
$840$		0			0
$841$	−0.659493	+	2.02971i	−0.0227411	+	0.0699900i
$842$		0			0
$843$	3.75349			0.129277
$844$		0			0
$845$	7.52652	+	13.0363i	0.258920	+	0.448463i
$846$		0			0
$847$	6.62339	−	4.81218i	0.227582	−	0.165348i
$848$		0			0
$849$	16.3735			0.561936
$850$		0			0
$851$	6.38933			0.219023
$852$		0			0
$853$	−15.4809	+	11.2475i	−0.530055	+	0.385108i	−0.820379	−	0.571821i	$-0.806237\pi$
$853$	−15.4809	+	11.2475i	−0.530055	+	0.385108i	0.290323	+	0.956929i	$0.406237\pi$
$854$		0			0
$855$	−2.72352	+	0.578902i	−0.0931423	+	0.0197980i
$856$		0			0
$857$	−7.43367			−0.253929			−0.126965	−	0.991907i	$-0.540523\pi$
$857$	−7.43367			−0.253929			−0.126965	+	0.991907i	$0.540523\pi$
$858$		0			0
$859$	12.7368	−	39.1999i	0.434575	−	1.33748i	−0.458947	−	0.888464i	$-0.651773\pi$
$859$	12.7368	−	39.1999i	0.434575	−	1.33748i	0.893522	−	0.449020i	$-0.148227\pi$
$860$		0			0
$861$	0.742080	+	2.28389i	0.0252900	+	0.0778346i
$862$		0			0
$863$	−11.7794	+	36.2532i	−0.400975	+	1.23407i	0.523234	+	0.852189i	$0.324725\pi$
$863$	−11.7794	+	36.2532i	−0.400975	+	1.23407i	−0.924210	+	0.381886i	$0.875275\pi$
$864$		0			0
$865$	−0.480310	+	4.56985i	−0.0163310	+	0.155380i
$866$		0			0
$867$	−23.8709	−	17.3432i	−0.810698	−	0.589007i
$868$		0			0
$869$	1.73229	+	1.25858i	0.0587639	+	0.0426945i
$870$		0			0
$871$	5.90840	−	4.29270i	0.200198	−	0.145453i
$872$		0			0
$873$	−4.80349	−	14.7836i	−0.162574	−	0.500350i
$874$		0			0
$875$	2.58164	+	7.94549i	0.0872755	+	0.268606i
$876$		0			0
$877$	8.96931	+	27.6047i	0.302872	+	0.932145i	0.980463	+	0.196705i	$0.0630242\pi$
$877$	8.96931	+	27.6047i	0.302872	+	0.932145i	−0.677591	+	0.735439i	$0.736976\pi$
$878$		0			0
$879$	−7.04647	+	5.11956i	−0.237671	+	0.172678i
$880$		0			0
$881$	27.8503	+	20.2344i	0.938300	+	0.681715i	0.948011	−	0.318238i	$-0.103091\pi$
$881$	27.8503	+	20.2344i	0.938300	+	0.681715i	−0.00971098	+	0.999953i	$0.503091\pi$
$882$		0			0
$883$	31.3921	+	22.8077i	1.05643	+	0.767539i	0.973424	−	0.229010i	$-0.0735490\pi$
$883$	31.3921	+	22.8077i	1.05643	+	0.767539i	0.0830028	+	0.996549i	$0.473549\pi$
$884$		0			0
$885$	−2.73719	+	26.0426i	−0.0920096	+	0.875413i
$886$		0			0
$887$	1.78288	−	5.48715i	0.0598634	−	0.184241i	−0.916653	−	0.399684i	$-0.869120\pi$
$887$	1.78288	−	5.48715i	0.0598634	−	0.184241i	0.976516	+	0.215444i	$0.0691198\pi$
$888$		0			0
$889$	−3.35656	−	10.3304i	−0.112575	−	0.346472i
$890$		0			0
$891$	0.0646021	−	0.198825i	0.00216425	−	0.00666089i
$892$		0			0
$893$	−8.07173			−0.270110
$894$		0			0
$895$	42.7826	−	9.09372i	1.43006	−	0.303970i
$896$		0			0
$897$	6.58449	−	4.78391i	0.219850	−	0.159730i
$898$		0			0
$899$	−19.3836			−0.646480
$900$		0			0
$901$	−28.2534			−0.941257
$902$		0			0
$903$	7.68517	−	5.58360i	0.255746	−	0.185811i
$904$		0			0
$905$	8.23999	+	14.2721i	0.273906	+	0.474420i
$906$		0			0
$907$	31.7260			1.05345			0.526723	−	0.850037i	$-0.323421\pi$
$907$	31.7260			1.05345			0.526723	+	0.850037i	$0.323421\pi$
$908$		0			0
$909$	−3.41170	+	10.5001i	−0.113159	+	0.348267i
$910$		0			0
$911$	−4.95450	−	15.2484i	−0.164150	−	0.505202i	0.834823	−	0.550519i	$-0.185570\pi$
$911$	−4.95450	−	15.2484i	−0.164150	−	0.505202i	−0.998973	+	0.0453174i	$0.985570\pi$
$912$		0			0
$913$	−0.366716	+	1.12863i	−0.0121365	+	0.0373523i
$914$		0			0
$915$	13.9524	+	24.1662i	0.461251	+	0.798909i
$916$		0			0
$917$	−4.48800	−	3.26072i	−0.148207	−	0.107679i
$918$		0			0
$919$	8.82328	+	6.41049i	0.291053	+	0.211462i	0.723724	−	0.690089i	$-0.242429\pi$
$919$	8.82328	+	6.41049i	0.291053	+	0.211462i	−0.432671	+	0.901552i	$0.642429\pi$
$920$		0			0
$921$	14.3296	−	10.4111i	0.472176	−	0.343056i
$922$		0			0
$923$	−5.06753	−	15.5962i	−0.166800	−	0.513357i
$924$		0			0
$925$	8.97756	−	3.99707i	0.295180	−	0.131423i
$926$		0			0
$927$	4.29048	+	13.2047i	0.140918	+	0.433700i
$928$		0			0
$929$	−18.3021	+	13.2973i	−0.600473	+	0.436269i	−0.846047	−	0.533108i	$-0.821024\pi$
$929$	−18.3021	+	13.2973i	−0.600473	+	0.436269i	0.245573	+	0.969378i	$0.421024\pi$
$930$		0			0
$931$	6.48925	+	4.71472i	0.212677	+	0.154519i
$932$		0			0
$933$	−16.4130	−	11.9247i	−0.537337	−	0.390398i
$934$		0			0
$935$	−2.13312	+	2.36907i	−0.0697605	+	0.0774768i
$936$		0			0
$937$	−1.59323	+	4.90347i	−0.0520487	+	0.160189i	−0.973702	−	0.227824i	$-0.926839\pi$
$937$	−1.59323	+	4.90347i	−0.0520487	+	0.160189i	0.921654	+	0.388014i	$0.126839\pi$
$938$		0			0
$939$	6.41831	+	19.7535i	0.209454	+	0.644632i
$940$		0			0
$941$	3.84942	−	11.8473i	0.125488	−	0.386211i	−0.868502	−	0.495686i	$-0.834917\pi$
$941$	3.84942	−	11.8473i	0.125488	−	0.386211i	0.993990	+	0.109475i	$0.0349168\pi$
$942$		0			0
$943$	10.4474			0.340213
$944$		0			0
$945$	−0.174654	+	1.66172i	−0.00568150	+	0.0540558i
$946$		0			0
$947$	−13.4795	+	9.79345i	−0.438026	+	0.318244i	−0.784850	−	0.619686i	$-0.787260\pi$
$947$	−13.4795	+	9.79345i	−0.438026	+	0.318244i	0.346824	+	0.937930i	$0.387260\pi$
$948$		0			0
$949$	6.30743			0.204748
$950$		0			0
$951$	−16.7651			−0.543646
$952$		0			0
$953$	−41.9537	+	30.4812i	−1.35901	+	0.987382i	−0.360508	+	0.932756i	$0.617396\pi$
$953$	−41.9537	+	30.4812i	−1.35901	+	0.987382i	−0.998507	+	0.0546255i	$0.982604\pi$
$954$		0			0
$955$	−3.35932	+	3.73091i	−0.108705	+	0.120729i
$956$		0			0
$957$	−1.08359			−0.0350275
$958$		0			0
$959$	−1.69381	+	5.21300i	−0.0546959	+	0.168337i
$960$		0			0
$961$	−5.25786	−	16.1820i	−0.169608	−	0.522001i
$962$		0			0
$963$	0.316774	−	0.974929i	0.0102079	−	0.0314166i
$964$		0			0
$965$	2.25905	+	1.00579i	0.0727214	+	0.0323777i
$966$		0			0
$967$	−10.3327	−	7.50713i	−0.332277	−	0.241413i	0.409119	−	0.912481i	$-0.365836\pi$
$967$	−10.3327	−	7.50713i	−0.332277	−	0.241413i	−0.741396	+	0.671068i	$0.765836\pi$
$968$		0			0
$969$	6.86994	+	4.99131i	0.220694	+	0.160344i
$970$		0			0
$971$	12.5679	−	9.13110i	0.403323	−	0.293031i	−0.367570	−	0.929996i	$-0.619810\pi$
$971$	12.5679	−	9.13110i	0.403323	−	0.293031i	0.770893	+	0.636965i	$0.219810\pi$
$972$		0			0
$973$	4.55979	+	14.0336i	0.146180	+	0.449896i
$974$		0			0
$975$	6.25903	−	10.8410i	0.200449	−	0.347189i
$976$		0			0
$977$	−10.2613	−	31.5811i	−0.328288	−	1.01037i	−0.969934	−	0.243367i	$-0.921748\pi$
$977$	−10.2613	−	31.5811i	−0.328288	−	1.01037i	0.641646	−	0.767001i	$-0.278252\pi$
$978$		0			0
$979$	0.155892	−	0.113262i	0.00498234	−	0.00361988i
$980$		0			0
$981$	5.42455	+	3.94117i	0.173193	+	0.125832i
$982$		0			0
$983$	39.7183	+	28.8570i	1.26682	+	0.920395i	0.999071	−	0.0430944i	$-0.0137216\pi$
$983$	39.7183	+	28.8570i	1.26682	+	0.920395i	0.267745	+	0.963490i	$0.413722\pi$
$984$		0			0
$985$	−45.1364	+	9.59403i	−1.43816	+	0.305691i
$986$		0			0
$987$	−1.49681	+	4.60671i	−0.0476440	+	0.146633i
$988$		0			0
$989$	−12.7707	−	39.3043i	−0.406086	−	1.24980i
$990$		0			0
$991$	−7.91583	+	24.3624i	−0.251455	+	0.773898i	0.743053	+	0.669233i	$0.233377\pi$
$991$	−7.91583	+	24.3624i	−0.251455	+	0.773898i	−0.994508	+	0.104665i	$0.966623\pi$
$992$		0			0
$993$	−26.2157			−0.831932
$994$		0			0
$995$	−25.2937	−	11.2615i	−0.801863	−	0.357013i
$996$		0			0
$997$	8.76157	−	6.36565i	0.277482	−	0.201602i	−0.440337	−	0.897833i	$-0.645141\pi$
$997$	8.76157	−	6.36565i	0.277482	−	0.201602i	0.717818	+	0.696231i	$0.245141\pi$
$998$		0			0
$999$	1.96543			0.0621835

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.m.a.181.2	yes	8
3.2	odd	2		900.2.n.a.181.1		8
5.2	odd	4		1500.2.o.a.349.4		16
5.3	odd	4		1500.2.o.a.349.1		16
5.4	even	2		1500.2.m.b.901.1		8
25.2	odd	20		7500.2.d.d.1249.4		8
25.3	odd	20		1500.2.o.a.649.3		16
25.4	even	10		1500.2.m.b.601.1		8
25.11	even	5		7500.2.a.g.1.4		4
25.14	even	10		7500.2.a.d.1.1		4
25.21	even	5	inner	300.2.m.a.121.2	✓	8
25.22	odd	20		1500.2.o.a.649.2		16
25.23	odd	20		7500.2.d.d.1249.5		8
75.71	odd	10		900.2.n.a.721.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.m.a.121.2	✓	8	25.21	even	5	inner
300.2.m.a.181.2	yes	8	1.1	even	1	trivial
900.2.n.a.181.1		8	3.2	odd	2
900.2.n.a.721.1		8	75.71	odd	10
1500.2.m.b.601.1		8	25.4	even	10
1500.2.m.b.901.1		8	5.4	even	2
1500.2.o.a.349.1		16	5.3	odd	4
1500.2.o.a.349.4		16	5.2	odd	4
1500.2.o.a.649.2		16	25.22	odd	20
1500.2.o.a.649.3		16	25.3	odd	20
7500.2.a.d.1.1		4	25.14	even	10
7500.2.a.g.1.4		4	25.11	even	5
7500.2.d.d.1249.4		8	25.2	odd	20
7500.2.d.d.1249.5		8	25.23	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{3} +(2.04275 + 0.909491i) q^{5} +0.747238 q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{3} +(2.04275 + 0.909491i) q^{5} +0.747238 q^{7} +(0.309017 - 0.951057i) q^{9} +(0.0646021 + 0.198825i) q^{11} +(-0.773659 + 2.38108i) q^{13} +(-2.18720 + 0.464905i) q^{15} +(5.51712 + 4.00842i) q^{17} +(-1.00739 - 0.731913i) q^{19} +(-0.604528 + 0.439216i) q^{21} +(1.00457 + 3.09174i) q^{23} +(3.34565 + 3.71572i) q^{25} +(0.309017 + 0.951057i) q^{27} +(4.19332 - 3.04662i) q^{29} +(-3.02547 - 2.19813i) q^{31} +(-0.169131 - 0.122881i) q^{33} +(1.52642 + 0.679606i) q^{35} +(0.607352 - 1.86924i) q^{37} +(-0.773659 - 2.38108i) q^{39} +(0.993096 - 3.05644i) q^{41} -12.7127 q^{43} +(1.49622 - 1.66172i) q^{45} +(5.24425 - 3.81017i) q^{47} -6.44163 q^{49} -6.81953 q^{51} +(-3.35177 + 2.43520i) q^{53} +(-0.0488635 + 0.464905i) q^{55} +1.24520 q^{57} +(3.61882 - 11.1376i) q^{59} +(-3.85634 - 11.8686i) q^{61} +(0.230909 - 0.710666i) q^{63} +(-3.74596 + 4.16031i) q^{65} +(-2.35995 - 1.71460i) q^{67} +(-2.62999 - 1.91080i) q^{69} +(-5.29912 + 3.85004i) q^{71} +(-0.778516 - 2.39603i) q^{73} +(-4.89074 - 1.03956i) q^{75} +(0.0482732 + 0.148570i) q^{77} +(8.28621 - 6.02028i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(4.59240 + 3.33658i) q^{83} +(7.62447 + 13.2060i) q^{85} +(-1.60171 + 4.92954i) q^{87} +(-0.284829 - 0.876615i) q^{89} +(-0.578108 + 1.77923i) q^{91} +3.73968 q^{93} +(-1.39218 - 2.41133i) q^{95} +(12.5757 - 9.13679i) q^{97} +0.209057 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 5 q^{5} - 8 q^{7} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 5 * q^5 - 8 * q^7 - 2 * q^9	\( 8 q - 2 q^{3} + 5 q^{5} - 8 q^{7} - 2 q^{9} - 2 q^{11} - 5 q^{15} + 7 q^{17} + 5 q^{19} - 3 q^{21} + 7 q^{23} + 5 q^{25} - 2 q^{27} + 27 q^{29} - 3 q^{31} + 3 q^{33} + 20 q^{35} - 9 q^{37} + 20 q^{41} - 68 q^{43} - 5 q^{45} - 7 q^{47} - 8 q^{49} - 8 q^{51} - 11 q^{53} + 5 q^{55} - 10 q^{57} + 2 q^{59} - 14 q^{61} + 7 q^{63} - 35 q^{65} + 28 q^{67} + 2 q^{69} - 15 q^{71} + 6 q^{73} + 5 q^{75} + 17 q^{77} + 24 q^{79} - 2 q^{81} + 2 q^{83} + 10 q^{85} - 23 q^{87} + 5 q^{91} - 18 q^{93} + 5 q^{95} + 34 q^{97} - 2 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 5 * q^5 - 8 * q^7 - 2 * q^9 - 2 * q^11 - 5 * q^15 + 7 * q^17 + 5 * q^19 - 3 * q^21 + 7 * q^23 + 5 * q^25 - 2 * q^27 + 27 * q^29 - 3 * q^31 + 3 * q^33 + 20 * q^35 - 9 * q^37 + 20 * q^41 - 68 * q^43 - 5 * q^45 - 7 * q^47 - 8 * q^49 - 8 * q^51 - 11 * q^53 + 5 * q^55 - 10 * q^57 + 2 * q^59 - 14 * q^61 + 7 * q^63 - 35 * q^65 + 28 * q^67 + 2 * q^69 - 15 * q^71 + 6 * q^73 + 5 * q^75 + 17 * q^77 + 24 * q^79 - 2 * q^81 + 2 * q^83 + 10 * q^85 - 23 * q^87 + 5 * q^91 - 18 * q^93 + 5 * q^95 + 34 * q^97 - 2 * q^99

Introduction

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