LMFDB - Embedded newform 600.2.y.c.481.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,2,Mod(121,600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("600.121"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.y (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 16 x^{10} - 29 x^{9} + 106 x^{8} - 250 x^{7} + 815 x^{6} - 1250 x^{5} + 2650 x^{4} + \cdots + 15625 $ x^12 - 4x^11 + 16x^10 - 29x^9 + 106x^8 - 250x^7 + 815x^6 - 1250x^5 + 2650x^4 - 3625x^3 + 10000x^2 - 12500*x + 15625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			481.3
Root			$1.44033 + 1.71039i$ of defining polynomial
Character	$\chi$	$=$	600.481
Dual form			600.2.y.c.121.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 + 0.587785i) q^{3} +(1.44033 - 1.71039i) q^{5} -1.48253 q^{7} +(0.309017 - 0.951057i) q^{9} +(-1.39017 - 4.27851i) q^{11} +(-0.272140 + 0.837560i) q^{13} +(-0.159908 + 2.23034i) q^{15} +(1.74935 + 1.27098i) q^{17} +(-5.95275 - 4.32493i) q^{19} +(1.19939 - 0.871407i) q^{21} +(-0.583871 - 1.79697i) q^{23} +(-0.850891 - 4.92707i) q^{25} +(0.309017 + 0.951057i) q^{27} +(0.837809 - 0.608704i) q^{29} +(-0.627423 - 0.455850i) q^{31} +(3.63952 + 2.64427i) q^{33} +(-2.13533 + 2.53570i) q^{35} +(2.54448 - 7.83109i) q^{37} +(-0.272140 - 0.837560i) q^{39} +(0.979614 - 3.01494i) q^{41} +10.1241 q^{43} +(-1.18159 - 1.89838i) q^{45} +(0.905243 - 0.657698i) q^{47} -4.80212 q^{49} -2.16231 q^{51} +(-2.12173 + 1.54153i) q^{53} +(-9.32025 - 3.78473i) q^{55} +7.35800 q^{57} +(-2.16139 + 6.65209i) q^{59} +(-3.89586 - 11.9902i) q^{61} +(-0.458126 + 1.40997i) q^{63} +(1.04059 + 1.67183i) q^{65} +(-0.925752 - 0.672598i) q^{67} +(1.52859 + 1.11059i) q^{69} +(11.9658 - 8.69368i) q^{71} +(-1.22267 - 3.76298i) q^{73} +(3.58444 + 3.48594i) q^{75} +(2.06097 + 6.34301i) q^{77} +(-7.18238 + 5.21830i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(9.56139 + 6.94676i) q^{83} +(4.69351 - 1.16145i) q^{85} +(-0.320014 + 0.984903i) q^{87} +(4.77756 + 14.7038i) q^{89} +(0.403454 - 1.24170i) q^{91} +0.775537 q^{93} +(-15.9713 + 3.95222i) q^{95} +(-0.342398 + 0.248767i) q^{97} -4.49870 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} + 4 q^{5} - 8 q^{7} - 3 q^{9} - 4 q^{11} - 4 q^{13} - q^{15} + q^{17} - 5 q^{19} - 3 q^{21} - 21 q^{23} - 16 q^{25} - 3 q^{27} + 11 q^{29} - 19 q^{31} + 11 q^{33} + 10 q^{35} + 34 q^{37}+ \cdots - 14 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 + 4 * q^5 - 8 * q^7 - 3 * q^9 - 4 * q^11 - 4 * q^13 - q^15 + q^17 - 5 * q^19 - 3 * q^21 - 21 * q^23 - 16 * q^25 - 3 * q^27 + 11 * q^29 - 19 * q^31 + 11 * q^33 + 10 * q^35 + 34 * q^37 - 4 * q^39 - 20 * q^41 + 28 * q^43 + 4 * q^45 + 19 * q^47 + 12 * q^49 - 14 * q^51 + 8 * q^53 - q^55 - 10 * q^57 - 18 * q^59 + 10 * q^61 + 7 * q^63 + 34 * q^65 - 40 * q^67 + 24 * q^69 - 7 * q^71 + 8 * q^73 + 4 * q^75 - 11 * q^77 - 26 * q^79 - 3 * q^81 + 10 * q^83 + 41 * q^85 - 4 * q^87 + 9 * q^89 - q^91 + 6 * q^93 - 81 * q^95 - 12 * q^97 - 14 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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
$5$	1.44033	−	1.71039i	0.644136	−	0.764911i
$5$	1.44033	−	1.71039i	0.644136	−	0.764911i
$6$		0			0
$7$	−1.48253			−0.560342			−0.280171	−	0.959950i	$-0.590391\pi$
$7$	−1.48253			−0.560342			−0.280171	+	0.959950i	$0.590391\pi$
$8$		0			0
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	−1.39017	−	4.27851i	−0.419153	−	1.29002i	−0.908483	−	0.417922i	$-0.862759\pi$
$11$	−1.39017	−	4.27851i	−0.419153	−	1.29002i	0.489330	−	0.872099i	$-0.337241\pi$
$12$		0			0
$13$	−0.272140	+	0.837560i	−0.0754780	+	0.232297i	−0.981676	−	0.190555i	$-0.938971\pi$
$13$	−0.272140	+	0.837560i	−0.0754780	+	0.232297i	0.906199	+	0.422853i	$0.138971\pi$
$14$		0			0
$15$	−0.159908	+	2.23034i	−0.0412882	+	0.575872i
$16$		0			0
$17$	1.74935	+	1.27098i	0.424279	+	0.308257i	0.779357	−	0.626580i	$-0.215546\pi$
$17$	1.74935	+	1.27098i	0.424279	+	0.308257i	−0.355078	+	0.934837i	$0.615546\pi$
$18$		0			0
$19$	−5.95275	−	4.32493i	−1.36565	−	0.992206i	−0.998063	−	0.0622189i	$-0.980182\pi$
$19$	−5.95275	−	4.32493i	−1.36565	−	0.992206i	−0.367592	−	0.929987i	$-0.619818\pi$
$20$		0			0
$21$	1.19939	−	0.871407i	0.261728	−	0.190156i
$22$		0			0
$23$	−0.583871	−	1.79697i	−0.121746	−	0.374694i	0.871549	−	0.490309i	$-0.163116\pi$
$23$	−0.583871	−	1.79697i	−0.121746	−	0.374694i	−0.993294	+	0.115615i	$0.963116\pi$
$24$		0			0
$25$	−0.850891	−	4.92707i	−0.170178	−	0.985413i
$26$		0			0
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$		0			0
$29$	0.837809	−	0.608704i	0.155577	−	0.113033i	−0.507273	−	0.861785i	$-0.669347\pi$
$29$	0.837809	−	0.608704i	0.155577	−	0.113033i	0.662850	+	0.748752i	$0.269347\pi$
$30$		0			0
$31$	−0.627423	−	0.455850i	−0.112689	−	0.0818730i	0.530014	−	0.847989i	$-0.322187\pi$
$31$	−0.627423	−	0.455850i	−0.112689	−	0.0818730i	−0.642702	+	0.766116i	$0.722187\pi$
$32$		0			0
$33$	3.63952	+	2.64427i	0.633559	+	0.460308i
$34$		0			0
$35$	−2.13533	+	2.53570i	−0.360936	+	0.428612i
$36$		0			0
$37$	2.54448	−	7.83109i	0.418309	−	1.28742i	−0.490948	−	0.871189i	$-0.663349\pi$
$37$	2.54448	−	7.83109i	0.418309	−	1.28742i	0.909257	−	0.416235i	$-0.136651\pi$
$38$		0			0
$39$	−0.272140	−	0.837560i	−0.0435772	−	0.134117i
$40$		0			0
$41$	0.979614	−	3.01494i	0.152990	−	0.470855i	−0.844962	−	0.534827i	$-0.820377\pi$
$41$	0.979614	−	3.01494i	0.152990	−	0.470855i	0.997952	+	0.0639721i	$0.0203769\pi$
$42$		0			0
$43$	10.1241			1.54391			0.771957	−	0.635675i	$-0.219278\pi$
$43$	10.1241			1.54391			0.771957	+	0.635675i	$0.219278\pi$
$44$		0			0
$45$	−1.18159	−	1.89838i	−0.176142	−	0.282993i
$46$		0			0
$47$	0.905243	−	0.657698i	0.132043	−	0.0959351i	−0.519803	−	0.854286i	$-0.673995\pi$
$47$	0.905243	−	0.657698i	0.132043	−	0.0959351i	0.651846	+	0.758351i	$0.273995\pi$
$48$		0			0
$49$	−4.80212			−0.686017
$50$		0			0
$51$	−2.16231			−0.302784
$52$		0			0
$53$	−2.12173	+	1.54153i	−0.291442	+	0.211745i	−0.723893	−	0.689913i	$-0.757649\pi$
$53$	−2.12173	+	1.54153i	−0.291442	+	0.211745i	0.432451	+	0.901658i	$0.357649\pi$
$54$		0			0
$55$	−9.32025	−	3.78473i	−1.25674	−	0.510334i
$56$		0			0
$57$	7.35800			0.974591
$58$		0			0
$59$	−2.16139	+	6.65209i	−0.281390	+	0.866028i	0.706068	+	0.708144i	$0.250467\pi$
$59$	−2.16139	+	6.65209i	−0.281390	+	0.866028i	−0.987458	+	0.157884i	$0.949533\pi$
$60$		0			0
$61$	−3.89586	−	11.9902i	−0.498814	−	1.53519i	−0.810927	−	0.585148i	$-0.801037\pi$
$61$	−3.89586	−	11.9902i	−0.498814	−	1.53519i	0.312112	−	0.950045i	$-0.398963\pi$
$62$		0			0
$63$	−0.458126	+	1.40997i	−0.0577184	+	0.177639i
$64$		0			0
$65$	1.04059	+	1.67183i	0.129069	+	0.207365i
$66$		0			0
$67$	−0.925752	−	0.672598i	−0.113099	−	0.0821709i	0.529798	−	0.848124i	$-0.322268\pi$
$67$	−0.925752	−	0.672598i	−0.113099	−	0.0821709i	−0.642897	+	0.765953i	$0.722268\pi$
$68$		0			0
$69$	1.52859	+	1.11059i	0.184021	+	0.133699i
$70$		0			0
$71$	11.9658	−	8.69368i	1.42008	−	1.03175i	0.428325	−	0.903625i	$-0.359104\pi$
$71$	11.9658	−	8.69368i	1.42008	−	1.03175i	0.991758	−	0.128125i	$-0.0408960\pi$
$72$		0			0
$73$	−1.22267	−	3.76298i	−0.143102	−	0.440423i	0.853660	−	0.520831i	$-0.174378\pi$
$73$	−1.22267	−	3.76298i	−0.143102	−	0.440423i	−0.996762	+	0.0804077i	$0.974378\pi$
$74$		0			0
$75$	3.58444	+	3.48594i	0.413896	+	0.402522i
$76$		0			0
$77$	2.06097	+	6.34301i	0.234869	+	0.722853i
$78$		0			0
$79$	−7.18238	+	5.21830i	−0.808080	+	0.587105i	−0.913273	−	0.407347i	$-0.866454\pi$
$79$	−7.18238	+	5.21830i	−0.808080	+	0.587105i	0.105193	+	0.994452i	$0.466454\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	9.56139	+	6.94676i	1.04950	+	0.762506i	0.972117	−	0.234496i	$-0.0753438\pi$
$83$	9.56139	+	6.94676i	1.04950	+	0.762506i	0.0773822	+	0.997001i	$0.475344\pi$
$84$		0			0
$85$	4.69351	−	1.16145i	0.509083	−	0.125977i
$86$		0			0
$87$	−0.320014	+	0.984903i	−0.0343091	+	0.105593i
$88$		0			0
$89$	4.77756	+	14.7038i	0.506421	+	1.55860i	0.798369	+	0.602169i	$0.205697\pi$
$89$	4.77756	+	14.7038i	0.506421	+	1.55860i	−0.291948	+	0.956434i	$0.594303\pi$
$90$		0			0
$91$	0.403454	−	1.24170i	0.0422935	−	0.130166i
$92$		0			0
$93$	0.775537			0.0804195
$94$		0			0
$95$	−15.9713	+	3.95222i	−1.63862	+	0.405489i
$96$		0			0
$97$	−0.342398	+	0.248767i	−0.0347652	+	0.0252584i	−0.605032	−	0.796201i	$-0.706840\pi$
$97$	−0.342398	+	0.248767i	−0.0347652	+	0.0252584i	0.570267	+	0.821459i	$0.306840\pi$
$98$		0			0
$99$	−4.49870			−0.452136
$100$		0			0
$101$	7.90054			0.786133			0.393067	−	0.919510i	$-0.371414\pi$
$101$	7.90054			0.786133			0.393067	+	0.919510i	$0.371414\pi$
$102$		0			0
$103$	−12.4492	+	9.04485i	−1.22665	+	0.891216i	−0.996635	−	0.0819702i	$-0.973879\pi$
$103$	−12.4492	+	9.04485i	−1.22665	+	0.891216i	−0.230019	+	0.973186i	$0.573879\pi$
$104$		0			0
$105$	0.237068	−	3.30654i	0.0231355	−	0.322685i
$106$		0			0
$107$	2.53157			0.244736			0.122368	−	0.992485i	$-0.460951\pi$
$107$	2.53157			0.244736			0.122368	+	0.992485i	$0.460951\pi$
$108$		0			0
$109$	−1.62719	+	5.00797i	−0.155856	+	0.479677i	−0.998247	−	0.0591912i	$-0.981148\pi$
$109$	−1.62719	+	5.00797i	−0.155856	+	0.479677i	0.842390	+	0.538868i	$0.181148\pi$
$110$		0			0
$111$	2.54448	+	7.83109i	0.241511	+	0.743295i
$112$		0			0
$113$	−4.01513	+	12.3573i	−0.377711	+	1.16248i	0.563920	+	0.825830i	$0.309293\pi$
$113$	−4.01513	+	12.3573i	−0.377711	+	1.16248i	−0.941631	+	0.336646i	$0.890707\pi$
$114$		0			0
$115$	−3.91449	−	1.58958i	−0.365028	−	0.148229i
$116$		0			0
$117$	0.712471	+	0.517640i	0.0658680	+	0.0478559i
$118$		0			0
$119$	−2.59345	−	1.88425i	−0.237741	−	0.172729i
$120$		0			0
$121$	−7.47392	+	5.43012i	−0.679447	+	0.493647i
$122$		0			0
$123$	0.979614	+	3.01494i	0.0883288	+	0.271848i
$124$		0			0
$125$	−9.65279	−	5.64125i	−0.863372	−	0.504569i
$126$		0			0
$127$	2.31067	+	7.11152i	0.205039	+	0.631045i	0.999712	+	0.0240071i	$0.00764243\pi$
$127$	2.31067	+	7.11152i	0.205039	+	0.631045i	−0.794673	+	0.607038i	$0.792358\pi$
$128$		0			0
$129$	−8.19058	+	5.95081i	−0.721141	+	0.523939i
$130$		0			0
$131$	2.97326	+	2.16020i	0.259775	+	0.188737i	0.710048	−	0.704154i	$-0.248673\pi$
$131$	2.97326	+	2.16020i	0.259775	+	0.188737i	−0.450273	+	0.892891i	$0.648673\pi$
$132$		0			0
$133$	8.82510	+	6.41181i	0.765233	+	0.555975i
$134$		0			0
$135$	2.07177	+	0.841296i	0.178309	+	0.0724072i
$136$		0			0
$137$	−6.12679	+	18.8563i	−0.523447	+	1.61100i	0.243919	+	0.969796i	$0.421567\pi$
$137$	−6.12679	+	18.8563i	−0.523447	+	1.61100i	−0.767366	+	0.641209i	$0.778433\pi$
$138$		0			0
$139$	−3.23064	−	9.94289i	−0.274019	−	0.843345i	−0.989477	−	0.144689i	$-0.953782\pi$
$139$	−3.23064	−	9.94289i	−0.274019	−	0.843345i	0.715458	−	0.698656i	$-0.246218\pi$
$140$		0			0
$141$	−0.345772	+	1.06418i	−0.0291193	+	0.0896199i
$142$		0			0
$143$	3.96183			0.331305
$144$		0			0
$145$	0.165599	−	2.30972i	0.0137523	−	0.191812i
$146$		0			0
$147$	3.88500	−	2.82261i	0.320429	−	0.232805i
$148$		0			0
$149$	−5.77618			−0.473203			−0.236601	−	0.971607i	$-0.576034\pi$
$149$	−5.77618			−0.473203			−0.236601	+	0.971607i	$0.576034\pi$
$150$		0			0
$151$	12.7506			1.03763			0.518813	−	0.854887i	$-0.326374\pi$
$151$	12.7506			1.03763			0.518813	+	0.854887i	$0.326374\pi$
$152$		0			0
$153$	1.74935	−	1.27098i	0.141426	−	0.102752i
$154$		0			0
$155$	−1.68338	+	0.416566i	−0.135212	+	0.0334594i
$156$		0			0
$157$	23.0376			1.83860			0.919302	−	0.393554i	$-0.128754\pi$
$157$	23.0376			1.83860			0.919302	+	0.393554i	$0.128754\pi$
$158$		0			0
$159$	0.810428	−	2.49424i	0.0642711	−	0.197806i
$160$		0			0
$161$	0.865604	+	2.66405i	0.0682191	+	0.209957i
$162$		0			0
$163$	−3.54966	+	10.9247i	−0.278031	+	0.855690i	0.710371	+	0.703827i	$0.248527\pi$
$163$	−3.54966	+	10.9247i	−0.278031	+	0.855690i	−0.988402	+	0.151863i	$0.951473\pi$
$164$		0			0
$165$	9.76486	−	2.41639i	0.760193	−	0.188116i
$166$		0			0
$167$	5.77853	+	4.19835i	0.447156	+	0.324878i	0.788472	−	0.615071i	$-0.210873\pi$
$167$	5.77853	+	4.19835i	0.447156	+	0.324878i	−0.341316	+	0.939949i	$0.610873\pi$
$168$		0			0
$169$	9.88977	+	7.18534i	0.760752	+	0.552719i
$170$		0			0
$171$	−5.95275	+	4.32493i	−0.455218	+	0.330735i
$172$		0			0
$173$	−4.97199	−	15.3022i	−0.378014	−	1.16341i	−0.941423	−	0.337228i	$-0.890511\pi$
$173$	−4.97199	−	15.3022i	−0.378014	−	1.16341i	0.563409	−	0.826178i	$-0.309489\pi$
$174$		0			0
$175$	1.26147	+	7.30450i	0.0953580	+	0.552168i
$176$		0			0
$177$	−2.16139	−	6.65209i	−0.162460	−	0.500002i
$178$		0			0
$179$	14.5291	−	10.5560i	1.08596	−	0.788994i	0.107246	−	0.994233i	$-0.465797\pi$
$179$	14.5291	−	10.5560i	1.08596	−	0.788994i	0.978712	+	0.205238i	$0.0657969\pi$
$180$		0			0
$181$	−11.2450	−	8.16994i	−0.835831	−	0.607267i	0.0853722	−	0.996349i	$-0.472792\pi$
$181$	−11.2450	−	8.16994i	−0.835831	−	0.607267i	−0.921203	+	0.389083i	$0.872792\pi$
$182$		0			0
$183$	10.1995	+	7.41037i	0.753969	+	0.547791i
$184$		0			0
$185$	−9.72936	−	15.6314i	−0.715317	−	1.14925i
$186$		0			0
$187$	3.00599	−	9.25149i	0.219820	−	0.676536i
$188$		0			0
$189$	−0.458126	−	1.40997i	−0.0333237	−	0.102560i
$190$		0			0
$191$	4.24569	−	13.0669i	0.307208	−	0.945488i	−0.671637	−	0.740881i	$-0.734408\pi$
$191$	4.24569	−	13.0669i	0.307208	−	0.945488i	0.978844	−	0.204607i	$-0.0655916\pi$
$192$		0			0
$193$	−13.0810			−0.941590			−0.470795	−	0.882243i	$-0.656033\pi$
$193$	−13.0810			−0.941590			−0.470795	+	0.882243i	$0.656033\pi$
$194$		0			0
$195$	−1.82453	−	0.740898i	−0.130657	−	0.0530568i
$196$		0			0
$197$	16.9105	−	12.2862i	1.20482	−	0.875354i	0.210071	−	0.977686i	$-0.432630\pi$
$197$	16.9105	−	12.2862i	1.20482	−	0.875354i	0.994750	+	0.102332i	$0.0326304\pi$
$198$		0			0
$199$	−15.8831			−1.12592			−0.562961	−	0.826484i	$-0.690338\pi$
$199$	−15.8831			−1.12592			−0.562961	+	0.826484i	$0.690338\pi$
$200$		0			0
$201$	1.14429			0.0807122
$202$		0			0
$203$	−1.24207	+	0.902419i	−0.0871764	+	0.0633374i
$204$		0			0
$205$	−3.74577	−	6.01804i	−0.261616	−	0.420318i
$206$		0			0
$207$	−1.88945			−0.131326
$208$		0			0
$209$	−10.2289	+	31.4813i	−0.707548	+	2.17761i
$210$		0			0
$211$	−5.81983	−	17.9116i	−0.400653	−	1.23308i	−0.924470	−	0.381254i	$-0.875492\pi$
$211$	−5.81983	−	17.9116i	−0.400653	−	1.23308i	0.523817	−	0.851831i	$-0.324508\pi$
$212$		0			0
$213$	−4.57054	+	14.0667i	−0.313168	+	0.963833i
$214$		0			0
$215$	14.5821	−	17.3162i	0.994490	−	1.18096i
$216$		0			0
$217$	0.930171	+	0.675808i	0.0631441	+	0.0458769i
$218$		0			0
$219$	3.20098	+	2.32565i	0.216302	+	0.157153i
$220$		0			0
$221$	−1.54059	+	1.11930i	−0.103631	+	0.0752923i
$222$		0			0
$223$	4.57032	+	14.0660i	0.306051	+	0.941929i	0.979283	+	0.202497i	$0.0649057\pi$
$223$	4.57032	+	14.0660i	0.306051	+	0.941929i	−0.673232	+	0.739432i	$0.735094\pi$
$224$		0			0
$225$	−4.94886	−	0.713301i	−0.329924	−	0.0475534i
$226$		0			0
$227$	−0.244241	−	0.751696i	−0.0162108	−	0.0498918i	0.942624	−	0.333857i	$-0.108350\pi$
$227$	−0.244241	−	0.751696i	−0.0162108	−	0.0498918i	−0.958835	+	0.283965i	$0.908350\pi$
$228$		0			0
$229$	12.9885	−	9.43670i	0.858305	−	0.623595i	−0.0691186	−	0.997608i	$-0.522019\pi$
$229$	12.9885	−	9.43670i	0.858305	−	0.623595i	0.927423	+	0.374014i	$0.122019\pi$
$230$		0			0
$231$	−5.39568	−	3.92019i	−0.355010	−	0.257930i
$232$		0			0
$233$	−4.40698	−	3.20186i	−0.288711	−	0.209761i	0.433997	−	0.900914i	$-0.357103\pi$
$233$	−4.40698	−	3.20186i	−0.288711	−	0.209761i	−0.722708	+	0.691154i	$0.757103\pi$
$234$		0			0
$235$	0.178928	−	2.49563i	0.0116720	−	0.162797i
$236$		0			0
$237$	2.74342	−	8.44339i	0.178205	−	0.548457i
$238$		0			0
$239$	0.0972307	+	0.299245i	0.00628933	+	0.0193566i	0.954152	−	0.299323i	$-0.0967607\pi$
$239$	0.0972307	+	0.299245i	0.00628933	+	0.0193566i	−0.947863	+	0.318679i	$0.896761\pi$
$240$		0			0
$241$	−7.26570	+	22.3615i	−0.468025	+	1.44043i	0.387113	+	0.922032i	$0.373472\pi$
$241$	−7.26570	+	22.3615i	−0.468025	+	1.44043i	−0.855138	+	0.518400i	$0.826528\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−6.91664	+	8.21351i	−0.441888	+	0.524742i
$246$		0			0
$247$	5.24236	−	3.80880i	0.333564	−	0.242348i
$248$		0			0
$249$	−11.8185			−0.748969
$250$		0			0
$251$	12.5486			0.792060			0.396030	−	0.918238i	$-0.370388\pi$
$251$	12.5486			0.792060			0.396030	+	0.918238i	$0.370388\pi$
$252$		0			0
$253$	−6.87668	+	4.99620i	−0.432333	+	0.314108i
$254$		0			0
$255$	−3.11445	+	3.69841i	−0.195034	+	0.231603i
$256$		0			0
$257$	−5.05447			−0.315289			−0.157645	−	0.987496i	$-0.550390\pi$
$257$	−5.05447			−0.315289			−0.157645	+	0.987496i	$0.550390\pi$
$258$		0			0
$259$	−3.77225	+	11.6098i	−0.234396	+	0.721398i
$260$		0			0
$261$	−0.320014	−	0.984903i	−0.0198084	−	0.0609640i
$262$		0			0
$263$	9.79440	−	30.1441i	0.603948	−	1.85876i	0.100084	−	0.994979i	$-0.468089\pi$
$263$	9.79440	−	30.1441i	0.603948	−	1.85876i	0.503864	−	0.863783i	$-0.331911\pi$
$264$		0			0
$265$	−0.419376	+	5.84930i	−0.0257621	+	0.359319i
$266$		0			0
$267$	−12.5078	−	9.08747i	−0.765466	−	0.556144i
$268$		0			0
$269$	16.3541	+	11.8819i	0.997127	+	0.724455i	0.961470	−	0.274909i	$-0.0886477\pi$
$269$	16.3541	+	11.8819i	0.997127	+	0.724455i	0.0356567	+	0.999364i	$0.488648\pi$
$270$		0			0
$271$	13.9304	−	10.1210i	0.846210	−	0.614807i	−0.0778885	−	0.996962i	$-0.524818\pi$
$271$	13.9304	−	10.1210i	0.846210	−	0.614807i	0.924098	+	0.382155i	$0.124818\pi$
$272$		0			0
$273$	0.403454	+	1.24170i	0.0244181	+	0.0751513i
$274$		0			0
$275$	−19.8976	+	10.4900i	−1.19987	+	0.632573i
$276$		0			0
$277$	−4.27133	−	13.1458i	−0.256640	−	0.789855i	−0.993502	−	0.113813i	$-0.963694\pi$
$277$	−4.27133	−	13.1458i	−0.256640	−	0.789855i	0.736863	−	0.676043i	$-0.236306\pi$
$278$		0			0
$279$	−0.627423	+	0.455850i	−0.0375628	+	0.0272910i
$280$		0			0
$281$	−16.2656	−	11.8176i	−0.970324	−	0.704981i	−0.0147984	−	0.999890i	$-0.504711\pi$
$281$	−16.2656	−	11.8176i	−0.970324	−	0.704981i	−0.955525	+	0.294909i	$0.904711\pi$
$282$		0			0
$283$	16.4921	+	11.9822i	0.980357	+	0.712271i	0.957788	−	0.287475i	$-0.0928157\pi$
$283$	16.4921	+	11.9822i	0.980357	+	0.712271i	0.0225683	+	0.999745i	$0.492816\pi$
$284$		0			0
$285$	10.5980	−	12.5851i	0.627769	−	0.745476i
$286$		0			0
$287$	−1.45230	+	4.46973i	−0.0857267	+	0.263840i
$288$		0			0
$289$	−3.80845	−	11.7212i	−0.224026	−	0.689482i
$290$		0			0
$291$	0.130784	−	0.402513i	0.00766672	−	0.0235957i
$292$		0			0
$293$	−14.2565			−0.832876			−0.416438	−	0.909164i	$-0.636722\pi$
$293$	−14.2565			−0.832876			−0.416438	+	0.909164i	$0.636722\pi$
$294$		0			0
$295$	8.26457	+	13.2780i	0.481182	+	0.773078i
$296$		0			0
$297$	3.63952	−	2.64427i	0.211186	−	0.153436i
$298$		0			0
$299$	1.66396			0.0962296
$300$		0			0
$301$	−15.0093			−0.865119
$302$		0			0
$303$	−6.39167	+	4.64382i	−0.367192	+	0.266781i
$304$		0			0
$305$	−26.1194	−	10.6065i	−1.49559	−	0.607324i
$306$		0			0
$307$	2.52045			0.143850			0.0719248	−	0.997410i	$-0.477086\pi$
$307$	2.52045			0.143850			0.0719248	+	0.997410i	$0.477086\pi$
$308$		0			0
$309$	4.75516	−	14.6349i	0.270512	−	0.832549i
$310$		0			0
$311$	−5.00165	−	15.3935i	−0.283617	−	0.872885i	−0.986810	−	0.161885i	$-0.948243\pi$
$311$	−5.00165	−	15.3935i	−0.283617	−	0.872885i	0.703192	−	0.711000i	$-0.251757\pi$
$312$		0			0
$313$	4.41204	−	13.5789i	0.249383	−	0.767522i	−0.745502	−	0.666504i	$-0.767790\pi$
$313$	4.41204	−	13.5789i	0.249383	−	0.767522i	0.994885	−	0.101018i	$-0.0322100\pi$
$314$		0			0
$315$	1.75174	+	2.81439i	0.0986995	+	0.158573i
$316$		0			0
$317$	22.6744	+	16.4739i	1.27352	+	0.925269i	0.999337	−	0.0364079i	$-0.0115915\pi$
$317$	22.6744	+	16.4739i	1.27352	+	0.925269i	0.274186	+	0.961677i	$0.411592\pi$
$318$		0			0
$319$	−3.76905	−	2.73837i	−0.211026	−	0.153319i
$320$		0			0
$321$	−2.04808	+	1.48802i	−0.114313	+	0.0830531i
$322$		0			0
$323$	−4.91656	−	15.1316i	−0.273564	−	0.841945i
$324$		0			0
$325$	4.35827	+	0.628178i	0.241754	+	0.0348450i
$326$		0			0
$327$	−1.62719	−	5.00797i	−0.0899838	−	0.276942i
$328$		0			0
$329$	−1.34205	+	0.975054i	−0.0739894	+	0.0537565i
$330$		0			0
$331$	16.9465	+	12.3124i	0.931466	+	0.676749i	0.946351	−	0.323140i	$-0.104738\pi$
$331$	16.9465	+	12.3124i	0.931466	+	0.676749i	−0.0148857	+	0.999889i	$0.504738\pi$
$332$		0			0
$333$	−6.66153	−	4.83988i	−0.365049	−	0.265224i
$334$		0			0
$335$	−2.48380	+	0.614636i	−0.135704	+	0.0335811i
$336$		0			0
$337$	6.30737	−	19.4121i	0.343584	−	1.05744i	−0.618753	−	0.785586i	$-0.712362\pi$
$337$	6.30737	−	19.4121i	0.343584	−	1.05744i	0.962337	−	0.271858i	$-0.0876382\pi$
$338$		0			0
$339$	−4.01513	−	12.3573i	−0.218072	−	0.671156i
$340$		0			0
$341$	−1.07813	+	3.31815i	−0.0583841	+	0.179688i
$342$		0			0
$343$	17.4969			0.944746
$344$		0			0
$345$	4.10123	−	1.01488i	0.220803	−	0.0546394i
$346$		0			0
$347$	−21.8918	+	15.9053i	−1.17521	+	0.853843i	−0.991624	−	0.129160i	$-0.958772\pi$
$347$	−21.8918	+	15.9053i	−1.17521	+	0.853843i	−0.183590	+	0.983003i	$0.558772\pi$
$348$		0			0
$349$	−0.747728			−0.0400249			−0.0200125	−	0.999800i	$-0.506371\pi$
$349$	−0.747728			−0.0400249			−0.0200125	+	0.999800i	$0.506371\pi$
$350$		0			0
$351$	−0.880663			−0.0470063
$352$		0			0
$353$	−0.983516	+	0.714566i	−0.0523473	+	0.0380325i	−0.613651	−	0.789577i	$-0.710300\pi$
$353$	−0.983516	+	0.714566i	−0.0523473	+	0.0380325i	0.561304	+	0.827610i	$0.310300\pi$
$354$		0			0
$355$	2.36514	−	32.9881i	0.125529	−	1.75082i
$356$		0			0
$357$	3.20568			0.169663
$358$		0			0
$359$	9.35888	−	28.8037i	0.493943	−	1.52020i	−0.324654	−	0.945833i	$-0.605248\pi$
$359$	9.35888	−	28.8037i	0.493943	−	1.52020i	0.818597	−	0.574368i	$-0.194752\pi$
$360$		0			0
$361$	10.8589	+	33.4203i	0.571522	+	1.75896i
$362$		0			0
$363$	2.85478	−	8.78612i	0.149837	−	0.461152i
$364$		0			0
$365$	−8.19722	−	3.32870i	−0.429062	−	0.174232i
$366$		0			0
$367$	1.87175	+	1.35991i	0.0977047	+	0.0709866i	0.635565	−	0.772047i	$-0.280767\pi$
$367$	1.87175	+	1.35991i	0.0977047	+	0.0709866i	−0.537860	+	0.843034i	$0.680767\pi$
$368$		0			0
$369$	−2.56466	−	1.86334i	−0.133511	−	0.0970014i
$370$		0			0
$371$	3.14552	−	2.28535i	0.163307	−	0.118649i
$372$		0			0
$373$	−8.08582	−	24.8856i	−0.418668	−	1.28853i	−0.908929	−	0.416952i	$-0.863098\pi$
$373$	−8.08582	−	24.8856i	−0.418668	−	1.28853i	0.490261	−	0.871576i	$-0.336902\pi$
$374$		0			0
$375$	11.1251	−	1.10990i	0.574498	−	0.0573150i
$376$		0			0
$377$	0.281825	+	0.867367i	0.0145147	+	0.0446717i
$378$		0			0
$379$	4.86638	−	3.53563i	0.249969	−	0.181613i	−0.455744	−	0.890111i	$-0.650627\pi$
$379$	4.86638	−	3.53563i	0.249969	−	0.181613i	0.705713	+	0.708498i	$0.250627\pi$
$380$		0			0
$381$	−6.04942	−	4.39516i	−0.309921	−	0.225171i
$382$		0			0
$383$	−0.166419	−	0.120910i	−0.00850360	−	0.00617823i	0.583525	−	0.812095i	$-0.301673\pi$
$383$	−0.166419	−	0.120910i	−0.00850360	−	0.00617823i	−0.592029	+	0.805917i	$0.701673\pi$
$384$		0			0
$385$	13.8175	+	5.61097i	0.704206	+	0.285961i
$386$		0			0
$387$	3.12852	−	9.62861i	0.159032	−	0.489450i
$388$		0			0
$389$	−8.94799	−	27.5391i	−0.453681	−	1.39629i	−0.872676	−	0.488299i	$-0.837618\pi$
$389$	−8.94799	−	27.5391i	−0.453681	−	1.39629i	0.418995	−	0.907988i	$-0.362382\pi$
$390$		0			0
$391$	1.26251	−	3.88561i	0.0638480	−	0.196504i
$392$		0			0
$393$	−3.67515			−0.185387
$394$		0			0
$395$	−1.41965	+	19.8008i	−0.0714304	+	0.996285i
$396$		0			0
$397$	−16.8148	+	12.2167i	−0.843913	+	0.613139i	−0.923461	−	0.383692i	$-0.874652\pi$
$397$	−16.8148	+	12.2167i	−0.843913	+	0.613139i	0.0795480	+	0.996831i	$0.474652\pi$
$398$		0			0
$399$	−10.9084			−0.546104
$400$		0			0
$401$	27.5525			1.37591			0.687953	−	0.725755i	$-0.258509\pi$
$401$	27.5525			1.37591			0.687953	+	0.725755i	$0.258509\pi$
$402$		0			0
$403$	0.552548	−	0.401450i	0.0275244	−	0.0199976i
$404$		0			0
$405$	−2.17060	+	0.537132i	−0.107858	+	0.0266903i
$406$		0			0
$407$	−37.0427			−1.83614
$408$		0			0
$409$	−12.4065	+	38.1833i	−0.613462	+	1.88804i	−0.191262	+	0.981539i	$0.561258\pi$
$409$	−12.4065	+	38.1833i	−0.613462	+	1.88804i	−0.422200	+	0.906503i	$0.638742\pi$
$410$		0			0
$411$	−6.12679	−	18.8563i	−0.302212	−	0.930114i
$412$		0			0
$413$	3.20432	−	9.86189i	0.157674	−	0.485272i
$414$		0			0
$415$	25.6533	−	6.34811i	1.25927	−	0.311617i
$416$		0			0
$417$	8.45792	+	6.14504i	0.414186	+	0.300924i
$418$		0			0
$419$	25.3057	+	18.3857i	1.23626	+	0.898198i	0.997344	−	0.0728408i	$-0.0232065\pi$
$419$	25.3057	+	18.3857i	1.23626	+	0.898198i	0.238920	+	0.971039i	$0.423206\pi$
$420$		0			0
$421$	−4.36995	+	3.17495i	−0.212978	+	0.154738i	−0.689160	−	0.724609i	$-0.742020\pi$
$421$	−4.36995	+	3.17495i	−0.212978	+	0.154738i	0.476182	+	0.879347i	$0.342020\pi$
$422$		0			0
$423$	−0.345772	−	1.06418i	−0.0168120	−	0.0517421i
$424$		0			0
$425$	4.77368	−	9.70062i	0.231557	−	0.470549i
$426$		0			0
$427$	5.77572	+	17.7758i	0.279507	+	0.860233i
$428$		0			0
$429$	−3.20519	+	2.32871i	−0.154748	+	0.112431i
$430$		0			0
$431$	20.1399	+	14.6325i	0.970106	+	0.704823i	0.955476	−	0.295070i	$-0.0953428\pi$
$431$	20.1399	+	14.6325i	0.970106	+	0.704823i	0.0146304	+	0.999893i	$0.495343\pi$
$432$		0			0
$433$	23.0438	+	16.7423i	1.10741	+	0.804582i	0.982254	−	0.187554i	$-0.0600561\pi$
$433$	23.0438	+	16.7423i	1.10741	+	0.804582i	0.125159	+	0.992137i	$0.460056\pi$
$434$		0			0
$435$	1.22365	+	1.96594i	0.0586693	+	0.0942595i
$436$		0			0
$437$	−4.29612	+	13.2221i	−0.205512	+	0.632499i
$438$		0			0
$439$	−5.79858	−	17.8462i	−0.276751	−	0.851752i	−0.988751	−	0.149572i	$-0.952210\pi$
$439$	−5.79858	−	17.8462i	−0.276751	−	0.851752i	0.712000	−	0.702180i	$-0.247790\pi$
$440$		0			0
$441$	−1.48394	+	4.56709i	−0.0706636	+	0.217480i
$442$		0			0
$443$	−6.04098			−0.287015			−0.143508	−	0.989649i	$-0.545838\pi$
$443$	−6.04098			−0.287015			−0.143508	+	0.989649i	$0.545838\pi$
$444$		0			0
$445$	32.0306	+	13.0069i	1.51840	+	0.616585i
$446$		0			0
$447$	4.67303	−	3.39515i	0.221027	−	0.160585i
$448$		0			0
$449$	10.9136			0.515043			0.257521	−	0.966273i	$-0.417094\pi$
$449$	10.9136			0.515043			0.257521	+	0.966273i	$0.417094\pi$
$450$		0			0
$451$	−14.2613			−0.671538
$452$		0			0
$453$	−10.3154	+	7.49460i	−0.484661	+	0.352127i
$454$		0			0
$455$	−1.54269	−	2.47853i	−0.0723226	−	0.116195i
$456$		0			0
$457$	−27.3312			−1.27850			−0.639249	−	0.769000i	$-0.720755\pi$
$457$	−27.3312			−1.27850			−0.639249	+	0.769000i	$0.720755\pi$
$458$		0			0
$459$	−0.668192	+	2.05648i	−0.0311885	+	0.0959884i
$460$		0			0
$461$	−2.54874	−	7.84422i	−0.118707	−	0.365342i	0.873995	−	0.485934i	$-0.161521\pi$
$461$	−2.54874	−	7.84422i	−0.118707	−	0.365342i	−0.992702	+	0.120592i	$0.961521\pi$
$462$		0			0
$463$	−10.9011	+	33.5501i	−0.506616	+	1.55920i	0.291421	+	0.956595i	$0.405872\pi$
$463$	−10.9011	+	33.5501i	−0.506616	+	1.55920i	−0.798037	+	0.602609i	$0.794128\pi$
$464$		0			0
$465$	1.11703	−	1.32647i	0.0518011	−	0.0615138i
$466$		0			0
$467$	−19.7375	−	14.3401i	−0.913341	−	0.663581i	0.0285164	−	0.999593i	$-0.490922\pi$
$467$	−19.7375	−	14.3401i	−0.913341	−	0.663581i	−0.941858	+	0.336012i	$0.890922\pi$
$468$		0			0
$469$	1.37245	+	0.997144i	0.0633739	+	0.0460438i
$470$		0			0
$471$	−18.6378	+	13.5412i	−0.858786	+	0.623945i
$472$		0			0
$473$	−14.0743	−	43.3162i	−0.647136	−	1.99168i
$474$		0			0
$475$	−16.2441	+	33.0096i	−0.745328	+	1.51459i
$476$		0			0
$477$	0.810428	+	2.49424i	0.0371069	+	0.114203i
$478$		0			0
$479$	12.7478	−	9.26179i	0.582460	−	0.423182i	−0.257150	−	0.966371i	$-0.582783\pi$
$479$	12.7478	−	9.26179i	0.582460	−	0.423182i	0.839610	+	0.543189i	$0.182783\pi$
$480$		0			0
$481$	5.86656	+	4.26230i	0.267492	+	0.194344i
$482$		0			0
$483$	−2.26618	−	1.64648i	−0.103115	−	0.0749172i
$484$		0			0
$485$	−0.0676776	+	0.943942i	−0.00307308	+	0.0428622i
$486$		0			0
$487$	1.61751	−	4.97819i	0.0732964	−	0.225583i	−0.907696	−	0.419628i	$-0.862161\pi$
$487$	1.61751	−	4.97819i	0.0732964	−	0.225583i	0.980993	+	0.194045i	$0.0621606\pi$
$488$		0			0
$489$	−3.54966	−	10.9247i	−0.160521	−	0.494033i
$490$		0			0
$491$	0.630232	−	1.93965i	0.0284420	−	0.0875354i	−0.935828	−	0.352457i	$-0.885346\pi$
$491$	0.630232	−	1.93965i	0.0284420	−	0.0875354i	0.964270	+	0.264922i	$0.0853462\pi$
$492$		0			0
$493$	2.23927			0.100852
$494$		0			0
$495$	−6.47961	+	7.69454i	−0.291237	+	0.345844i
$496$		0			0
$497$	−17.7396	+	12.8886i	−0.795732	+	0.578133i
$498$		0			0
$499$	15.7841			0.706593			0.353296	−	0.935511i	$-0.385061\pi$
$499$	15.7841			0.706593			0.353296	+	0.935511i	$0.385061\pi$
$500$		0			0
$501$	−7.14265			−0.319110
$502$		0			0
$503$	−20.5972	+	14.9647i	−0.918382	+	0.667243i	−0.943121	−	0.332450i	$-0.892125\pi$
$503$	−20.5972	+	14.9647i	−0.918382	+	0.667243i	0.0247389	+	0.999694i	$0.492125\pi$
$504$		0			0
$505$	11.3794	−	13.5130i	0.506376	−	0.601322i
$506$		0			0
$507$	−12.2244			−0.542906
$508$		0			0
$509$	1.01483	−	3.12332i	0.0449814	−	0.138439i	−0.926044	−	0.377417i	$-0.876812\pi$
$509$	1.01483	−	3.12332i	0.0449814	−	0.138439i	0.971025	+	0.238978i	$0.0768124\pi$
$510$		0			0
$511$	1.81263	+	5.57871i	0.0801862	+	0.246788i
$512$		0			0
$513$	2.27375	−	6.99788i	0.100388	−	0.308964i
$514$		0			0
$515$	−2.46068	+	34.3206i	−0.108430	+	1.51235i
$516$		0			0
$517$	−4.07242	−	2.95878i	−0.179105	−	0.130127i
$518$		0			0
$519$	13.0168	+	9.45729i	0.571376	+	0.415129i
$520$		0			0
$521$	22.4906	−	16.3404i	0.985330	−	0.715884i	0.0264367	−	0.999650i	$-0.491584\pi$
$521$	22.4906	−	16.3404i	0.985330	−	0.715884i	0.958894	+	0.283766i	$0.0915840\pi$
$522$		0			0
$523$	−2.59595	−	7.98953i	−0.113513	−	0.349358i	0.878121	−	0.478439i	$-0.158797\pi$
$523$	−2.59595	−	7.98953i	−0.113513	−	0.349358i	−0.991634	+	0.129081i	$0.958797\pi$
$524$		0			0
$525$	−5.31403	−	5.16799i	−0.231923	−	0.225550i
$526$		0			0
$527$	−0.518208	−	1.59488i	−0.0225735	−	0.0694740i
$528$		0			0
$529$	15.7192	−	11.4207i	0.683443	−	0.496551i
$530$		0			0
$531$	5.65861	+	4.11122i	0.245563	+	0.178412i
$532$		0			0
$533$	2.25860	+	1.64097i	0.0978309	+	0.0710783i
$534$		0			0
$535$	3.64630	−	4.32998i	0.157643	−	0.187201i
$536$		0			0
$537$	−5.54963	+	17.0800i	−0.239484	+	0.737057i
$538$		0			0
$539$	6.67578	+	20.5459i	0.287546	+	0.884976i
$540$		0			0
$541$	−7.04394	+	21.6790i	−0.302843	+	0.932054i	0.677631	+	0.735402i	$0.263007\pi$
$541$	−7.04394	+	21.6790i	−0.302843	+	0.932054i	−0.980473	+	0.196651i	$0.936993\pi$
$542$		0			0
$543$	13.8995			0.596486
$544$		0			0
$545$	6.22191	+	9.99627i	0.266517	+	0.428193i
$546$		0			0
$547$	−8.88553	+	6.45571i	−0.379918	+	0.276026i	−0.761312	−	0.648386i	$-0.775444\pi$
$547$	−8.88553	+	6.45571i	−0.379918	+	0.276026i	0.381394	+	0.924413i	$0.375444\pi$
$548$		0			0
$549$	−12.6073			−0.538066
$550$		0			0
$551$	−7.61986			−0.324617
$552$		0			0
$553$	10.6481	−	7.73626i	0.452801	−	0.328979i
$554$		0			0
$555$	17.0591	+	6.92731i	0.724120	+	0.294048i
$556$		0			0
$557$	29.0988			1.23296			0.616478	−	0.787372i	$-0.288559\pi$
$557$	29.0988			1.23296			0.616478	+	0.787372i	$0.288559\pi$
$558$		0			0
$559$	−2.75517	+	8.47956i	−0.116531	+	0.358647i
$560$		0			0
$561$	3.00599	+	9.25149i	0.126913	+	0.390598i
$562$		0			0
$563$	7.60523	−	23.4065i	0.320522	−	0.986466i	−0.652899	−	0.757445i	$-0.726448\pi$
$563$	7.60523	−	23.4065i	0.320522	−	0.986466i	0.973422	−	0.229021i	$-0.0735524\pi$
$564$		0			0
$565$	15.3527	+	24.6660i	0.645894	+	1.03771i
$566$		0			0
$567$	1.19939	+	0.871407i	0.0503696	+	0.0365956i
$568$		0			0
$569$	13.8599	+	10.0698i	0.581036	+	0.422148i	0.839098	−	0.543981i	$-0.183084\pi$
$569$	13.8599	+	10.0698i	0.581036	+	0.422148i	−0.258061	+	0.966129i	$0.583084\pi$
$570$		0			0
$571$	−26.4769	+	19.2366i	−1.10802	+	0.805027i	−0.982351	−	0.187045i	$-0.940109\pi$
$571$	−26.4769	+	19.2366i	−1.10802	+	0.805027i	−0.125673	+	0.992072i	$0.540109\pi$
$572$		0			0
$573$	4.24569	+	13.0669i	0.177366	+	0.545878i
$574$		0			0
$575$	−8.35698	+	4.40580i	−0.348510	+	0.183734i
$576$		0			0
$577$	1.15526	+	3.55553i	0.0480941	+	0.148019i	0.972220	−	0.234071i	$-0.0752047\pi$
$577$	1.15526	+	3.55553i	0.0480941	+	0.148019i	−0.924125	+	0.382089i	$0.875205\pi$
$578$		0			0
$579$	10.5827	−	7.68881i	0.439804	−	0.319536i
$580$		0			0
$581$	−14.1750	−	10.2987i	−0.588079	−	0.427264i
$582$		0			0
$583$	9.54501	+	6.93486i	0.395314	+	0.287212i
$584$		0			0
$585$	1.91156	−	0.473032i	0.0790334	−	0.0195575i
$586$		0			0
$587$	−10.4591	+	32.1897i	−0.431692	+	1.32861i	0.464747	+	0.885443i	$0.346145\pi$
$587$	−10.4591	+	32.1897i	−0.431692	+	1.32861i	−0.896439	+	0.443167i	$0.853855\pi$
$588$		0			0
$589$	1.76338	+	5.42712i	0.0726587	+	0.223620i
$590$		0			0
$591$	−6.45923	+	19.8795i	−0.265697	+	0.817732i
$592$		0			0
$593$	42.8353			1.75904			0.879518	−	0.475866i	$-0.157865\pi$
$593$	42.8353			1.75904			0.879518	+	0.475866i	$0.157865\pi$
$594$		0			0
$595$	−6.95825	+	1.72188i	−0.285260	+	0.0705900i
$596$		0			0
$597$	12.8497	−	9.33584i	0.525902	−	0.382091i
$598$		0			0
$599$	−18.4653			−0.754473			−0.377236	−	0.926117i	$-0.623126\pi$
$599$	−18.4653			−0.754473			−0.377236	+	0.926117i	$0.623126\pi$
$600$		0			0
$601$	−21.0828			−0.859987			−0.429993	−	0.902832i	$-0.641484\pi$
$601$	−21.0828			−0.859987			−0.429993	+	0.902832i	$0.641484\pi$
$602$		0			0
$603$	−0.925752	+	0.672598i	−0.0376995	+	0.0273903i
$604$		0			0
$605$	−1.47728	+	20.6045i	−0.0600599	+	0.837693i
$606$		0			0
$607$	−9.93692			−0.403327			−0.201664	−	0.979455i	$-0.564635\pi$
$607$	−9.93692			−0.403327			−0.201664	+	0.979455i	$0.564635\pi$
$608$		0			0
$609$	0.474430	−	1.46014i	0.0192249	−	0.0591680i
$610$		0			0
$611$	0.304509	+	0.937181i	0.0123191	+	0.0379143i
$612$		0			0
$613$	3.93033	−	12.0963i	0.158744	−	0.488565i	−0.839777	−	0.542932i	$-0.817314\pi$
$613$	3.93033	−	12.0963i	0.158744	−	0.488565i	0.998521	+	0.0543671i	$0.0173141\pi$
$614$		0			0
$615$	6.56770	+	2.66699i	0.264835	+	0.107543i
$616$		0			0
$617$	−9.43322	−	6.85364i	−0.379767	−	0.275917i	0.381482	−	0.924376i	$-0.375414\pi$
$617$	−9.43322	−	6.85364i	−0.379767	−	0.275917i	−0.761250	+	0.648459i	$0.775414\pi$
$618$		0			0
$619$	−32.5417	−	23.6429i	−1.30796	−	0.950289i	−0.307961	−	0.951399i	$-0.599647\pi$
$619$	−32.5417	−	23.6429i	−1.30796	−	0.950289i	−0.999999	+	0.00111028i	$0.999647\pi$
$620$		0			0
$621$	1.52859	−	1.11059i	0.0613404	−	0.0445664i
$622$		0			0
$623$	−7.08286	−	21.7988i	−0.283769	−	0.873351i
$624$		0			0
$625$	−23.5520	+	8.38480i	−0.942079	+	0.335392i
$626$		0			0
$627$	−10.2289	−	31.4813i	−0.408503	−	1.25724i
$628$		0			0
$629$	14.4043	−	10.4653i	0.574337	−	0.417281i
$630$		0			0
$631$	6.86496	+	4.98768i	0.273290	+	0.198557i	0.715985	−	0.698115i	$-0.245978\pi$
$631$	6.86496	+	4.98768i	0.273290	+	0.198557i	−0.442696	+	0.896672i	$0.645978\pi$
$632$		0			0
$633$	15.2365	+	11.0700i	0.605597	+	0.439992i
$634$		0			0
$635$	15.4916	+	6.29078i	0.614766	+	0.249642i
$636$		0			0
$637$	1.30685	−	4.02206i	0.0517792	−	0.159360i
$638$		0			0
$639$	−4.57054	−	14.0667i	−0.180808	−	0.556469i
$640$		0			0
$641$	−0.855102	+	2.63173i	−0.0337745	+	0.103947i	−0.966523	−	0.256582i	$-0.917404\pi$
$641$	−0.855102	+	2.63173i	−0.0337745	+	0.103947i	0.932748	+	0.360529i	$0.117404\pi$
$642$		0			0
$643$	11.4484			0.451481			0.225741	−	0.974187i	$-0.427520\pi$
$643$	11.4484			0.451481			0.225741	+	0.974187i	$0.427520\pi$
$644$		0			0
$645$	−1.61893	+	22.5803i	−0.0637454	+	0.889097i
$646$		0			0
$647$	−5.10076	+	3.70592i	−0.200532	+	0.145695i	−0.683519	−	0.729932i	$-0.739552\pi$
$647$	−5.10076	+	3.70592i	−0.200532	+	0.145695i	0.482988	+	0.875627i	$0.339552\pi$
$648$		0			0
$649$	31.4658			1.23514
$650$		0			0
$651$	−1.14975			−0.0450624
$652$		0			0
$653$	−33.5723	+	24.3917i	−1.31379	+	0.954521i	−0.313798	+	0.949490i	$0.601601\pi$
$653$	−33.5723	+	24.3917i	−1.31379	+	0.954521i	−0.999987	+	0.00503103i	$0.998399\pi$
$654$		0			0
$655$	7.97727	−	1.97404i	0.311698	−	0.0771321i
$656$		0			0
$657$	−3.95663			−0.154363
$658$		0			0
$659$	−6.03274	+	18.5669i	−0.235002	+	0.723262i	0.762119	+	0.647437i	$0.224159\pi$
$659$	−6.03274	+	18.5669i	−0.235002	+	0.723262i	−0.997121	+	0.0758253i	$0.975841\pi$
$660$		0			0
$661$	12.1498	+	37.3933i	0.472573	+	1.45443i	0.849204	+	0.528066i	$0.177083\pi$
$661$	12.1498	+	37.3933i	0.472573	+	1.45443i	−0.376631	+	0.926363i	$0.622917\pi$
$662$		0			0
$663$	0.588451	−	1.81107i	0.0228536	−	0.0703360i
$664$		0			0
$665$	23.6778	−	5.85926i	0.918185	−	0.227212i
$666$		0			0
$667$	−1.58299	−	1.15011i	−0.0612938	−	0.0445325i
$668$		0			0
$669$	−11.9653	−	8.69326i	−0.462603	−	0.336101i
$670$		0			0
$671$	−45.8845	+	33.3370i	−1.77135	+	1.28696i
$672$		0			0
$673$	−12.5016	−	38.4759i	−0.481901	−	1.48314i	−0.836420	−	0.548090i	$-0.815355\pi$
$673$	−12.5016	−	38.4759i	−0.481901	−	1.48314i	0.354519	−	0.935049i	$-0.384645\pi$
$674$		0			0
$675$	4.42298	−	2.33179i	0.170241	−	0.0897508i
$676$		0			0
$677$	−2.85057	−	8.77317i	−0.109556	−	0.337180i	0.881216	−	0.472713i	$-0.156725\pi$
$677$	−2.85057	−	8.77317i	−0.109556	−	0.337180i	−0.990773	+	0.135533i	$0.956725\pi$
$678$		0			0
$679$	0.507614	−	0.368803i	0.0194804	−	0.0141534i
$680$		0			0
$681$	0.639431	+	0.464574i	0.0245031	+	0.0178025i
$682$		0			0
$683$	−4.69474	−	3.41093i	−0.179639	−	0.130516i	0.494332	−	0.869273i	$-0.335413\pi$
$683$	−4.69474	−	3.41093i	−0.179639	−	0.130516i	−0.673971	+	0.738758i	$0.735413\pi$
$684$		0			0
$685$	23.4271	+	37.6386i	0.895104	+	1.43810i
$686$		0			0
$687$	−4.96117	+	15.2689i	−0.189280	+	0.582545i
$688$		0			0
$689$	−0.713714	−	2.19658i	−0.0271903	−	0.0836832i
$690$		0			0
$691$	8.59582	−	26.4552i	0.327000	−	1.00640i	−0.643529	−	0.765421i	$-0.722531\pi$
$691$	8.59582	−	26.4552i	0.327000	−	1.00640i	0.970530	−	0.240982i	$-0.0774694\pi$
$692$		0			0
$693$	6.66943			0.253351
$694$		0			0
$695$	−21.6594	−	8.79538i	−0.821589	−	0.333628i
$696$		0			0
$697$	5.54560	−	4.02912i	0.210055	−	0.152614i
$698$		0			0
$699$	5.44732			0.206037
$700$		0			0
$701$	4.01617			0.151689			0.0758444	−	0.997120i	$-0.475835\pi$
$701$	4.01617			0.151689			0.0758444	+	0.997120i	$0.475835\pi$
$702$		0			0
$703$	−49.0155	+	35.6119i	−1.84866	+	1.34313i
$704$		0			0
$705$	1.32214	+	2.12417i	0.0497945	+	0.0800010i
$706$		0			0
$707$	−11.7127			−0.440503
$708$		0			0
$709$	11.6653	−	35.9021i	0.438100	−	1.34833i	−0.451776	−	0.892131i	$-0.649209\pi$
$709$	11.6653	−	35.9021i	0.438100	−	1.34833i	0.889876	−	0.456202i	$-0.150791\pi$
$710$		0			0
$711$	2.74342	+	8.44339i	0.102886	+	0.316652i
$712$		0			0
$713$	−0.452814	+	1.39362i	−0.0169580	+	0.0521914i
$714$		0			0
$715$	5.70635	−	6.77629i	0.213406	−	0.253419i
$716$		0			0
$717$	−0.254553	−	0.184944i	−0.00950646	−	0.00690685i
$718$		0			0
$719$	40.7378	+	29.5977i	1.51926	+	1.10381i	0.961852	+	0.273571i	$0.0882048\pi$
$719$	40.7378	+	29.5977i	1.51926	+	1.10381i	0.557410	+	0.830237i	$0.311795\pi$
$720$		0			0
$721$	18.4562	−	13.4092i	0.687345	−	0.499386i
$722$		0			0
$723$	−7.26570	−	22.3615i	−0.270214	−	0.831634i
$724$		0			0
$725$	−3.71201	−	3.61000i	−0.137860	−	0.134072i
$726$		0			0
$727$	1.69289	+	5.21019i	0.0627859	+	0.193235i	0.977529	−	0.210801i	$-0.0676071\pi$
$727$	1.69289	+	5.21019i	0.0627859	+	0.193235i	−0.914743	+	0.404036i	$0.867607\pi$
$728$		0			0
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	17.7106	+	12.8675i	0.655051	+	0.475922i
$732$		0			0
$733$	−4.35856	−	3.16668i	−0.160987	−	0.116964i	0.504375	−	0.863485i	$-0.331723\pi$
$733$	−4.35856	−	3.16668i	−0.160987	−	0.116964i	−0.665362	+	0.746521i	$0.731723\pi$
$734$		0			0
$735$	0.767899	−	10.7104i	0.0283244	−	0.395058i
$736$		0			0
$737$	−1.59077	+	4.89587i	−0.0585966	+	0.180342i
$738$		0			0
$739$	−14.8673	−	45.7567i	−0.546901	−	1.68319i	−0.716427	−	0.697662i	$-0.754224\pi$
$739$	−14.8673	−	45.7567i	−0.546901	−	1.68319i	0.169526	−	0.985526i	$-0.445776\pi$
$740$		0			0
$741$	−2.00240	+	6.16277i	−0.0735602	+	0.226395i
$742$		0			0
$743$	6.21757			0.228101			0.114050	−	0.993475i	$-0.463618\pi$
$743$	6.21757			0.228101			0.114050	+	0.993475i	$0.463618\pi$
$744$		0			0
$745$	−8.31961	+	9.87953i	−0.304807	+	0.361958i
$746$		0			0
$747$	9.56139	−	6.94676i	0.349833	−	0.254169i
$748$		0			0
$749$	−3.75312			−0.137136
$750$		0			0
$751$	4.45733			0.162650			0.0813252	−	0.996688i	$-0.474085\pi$
$751$	4.45733			0.162650			0.0813252	+	0.996688i	$0.474085\pi$
$752$		0			0
$753$	−10.1520	+	7.37588i	−0.369960	+	0.268792i
$754$		0			0
$755$	18.3651	−	21.8085i	0.668373	−	0.793693i
$756$		0			0
$757$	13.2472			0.481478			0.240739	−	0.970590i	$-0.422610\pi$
$757$	13.2472			0.481478			0.240739	+	0.970590i	$0.422610\pi$
$758$		0			0
$759$	2.62666	−	8.08402i	0.0953417	−	0.293431i
$760$		0			0
$761$	11.7491	+	36.1600i	0.425905	+	1.31080i	0.902125	+	0.431475i	$0.142007\pi$
$761$	11.7491	+	36.1600i	0.425905	+	1.31080i	−0.476220	+	0.879326i	$0.657993\pi$
$762$		0			0
$763$	2.41235	−	7.42445i	0.0873329	−	0.268783i
$764$		0			0
$765$	0.345772	−	4.82270i	0.0125014	−	0.174365i
$766$		0			0
$767$	−4.98332	−	3.62060i	−0.179937	−	0.130732i
$768$		0			0
$769$	−0.598235	−	0.434643i	−0.0215729	−	0.0156736i	0.576947	−	0.816782i	$-0.304244\pi$
$769$	−0.598235	−	0.434643i	−0.0215729	−	0.0156736i	−0.598519	+	0.801108i	$0.704244\pi$
$770$		0			0
$771$	4.08915	−	2.97094i	0.147267	−	0.106996i
$772$		0			0
$773$	−11.3512	−	34.9355i	−0.408276	−	1.25654i	−0.918129	−	0.396282i	$-0.870300\pi$
$773$	−11.3512	−	34.9355i	−0.408276	−	1.25654i	0.509853	−	0.860262i	$-0.329700\pi$
$774$		0			0
$775$	−1.71213	+	3.47923i	−0.0615016	+	0.124978i
$776$		0			0
$777$	−3.77225	−	11.6098i	−0.135329	−	0.416499i
$778$		0			0
$779$	−18.8708	+	13.7104i	−0.676116	+	0.491227i
$780$		0			0
$781$	−53.8306	−	39.1102i	−1.92621	−	1.39947i
$782$		0			0
$783$	0.837809	+	0.608704i	0.0299408	+	0.0217533i
$784$		0			0
$785$	33.1818	−	39.4034i	1.18431	−	1.40637i
$786$		0			0
$787$	1.05666	−	3.25207i	0.0376659	−	0.115924i	−0.930456	−	0.366405i	$-0.880589\pi$
$787$	1.05666	−	3.25207i	0.0376659	−	0.115924i	0.968122	+	0.250481i	$0.0805886\pi$
$788$		0			0
$789$	9.79440	+	30.1441i	0.348690	+	1.07316i
$790$		0			0
$791$	5.95253	−	18.3200i	0.211647	−	0.651384i
$792$		0			0
$793$	11.1028			0.394271
$794$		0			0
$795$	−3.09885	−	4.97868i	−0.109905	−	0.176576i
$796$		0			0
$797$	−19.4316	+	14.1179i	−0.688301	+	0.500080i	−0.876101	−	0.482127i	$-0.839864\pi$
$797$	−19.4316	+	14.1179i	−0.688301	+	0.500080i	0.187800	+	0.982207i	$0.439864\pi$
$798$		0			0
$799$	2.41950			0.0855959
$800$		0			0
$801$	15.4605			0.546271
$802$		0			0
$803$	−14.4002	+	10.4624i	−0.508173	+	0.369210i
$804$		0			0
$805$	5.80334	+	2.35660i	0.204541	+	0.0830591i
$806$		0			0
$807$	−20.2148			−0.711594
$808$		0			0
$809$	13.7576	−	42.3415i	0.483691	−	1.48865i	−0.350177	−	0.936683i	$-0.613879\pi$
$809$	13.7576	−	42.3415i	0.483691	−	1.48865i	0.833868	−	0.551964i	$-0.186121\pi$
$810$		0			0
$811$	−1.29829	−	3.99572i	−0.0455890	−	0.140309i	0.925671	−	0.378329i	$-0.123501\pi$
$811$	−1.29829	−	3.99572i	−0.0455890	−	0.140309i	−0.971260	+	0.238021i	$0.923501\pi$
$812$		0			0
$813$	−5.32093	+	16.3761i	−0.186613	+	0.574336i
$814$		0			0
$815$	13.5729	+	21.8065i	0.475438	+	0.763849i
$816$		0			0
$817$	−60.2663	−	43.7861i	−2.10845	−	1.53188i
$818$		0			0
$819$	−1.05626	−	0.767415i	−0.0369086	−	0.0268157i
$820$		0			0
$821$	25.2939	−	18.3771i	0.882765	−	0.641366i	−0.0512167	−	0.998688i	$-0.516310\pi$
$821$	25.2939	−	18.3771i	0.882765	−	0.641366i	0.933981	+	0.357321i	$0.116310\pi$
$822$		0			0
$823$	−16.6677	−	51.2980i	−0.581000	−	1.78814i	−0.614771	−	0.788706i	$-0.710752\pi$
$823$	−16.6677	−	51.2980i	−0.581000	−	1.78814i	0.0337706	−	0.999430i	$-0.489248\pi$
$824$		0			0
$825$	9.93164	−	20.1822i	0.345775	−	0.702652i
$826$		0			0
$827$	6.73640	+	20.7325i	0.234248	+	0.720940i	0.997220	+	0.0745092i	$0.0237390\pi$
$827$	6.73640	+	20.7325i	0.234248	+	0.720940i	−0.762973	+	0.646431i	$0.776261\pi$
$828$		0			0
$829$	35.9342	−	26.1077i	1.24805	−	0.906758i	0.249938	−	0.968262i	$-0.419590\pi$
$829$	35.9342	−	26.1077i	1.24805	−	0.906758i	0.998107	+	0.0615038i	$0.0195896\pi$
$830$		0			0
$831$	11.1825	+	8.12456i	0.387917	+	0.281838i
$832$		0			0
$833$	−8.40058	−	6.10338i	−0.291063	−	0.211469i
$834$		0			0
$835$	15.5038	−	3.83655i	0.536532	−	0.132769i
$836$		0			0
$837$	0.239654	−	0.737580i	0.00828366	−	0.0254945i
$838$		0			0
$839$	−3.44012	−	10.5876i	−0.118766	−	0.365524i	0.873948	−	0.486020i	$-0.161552\pi$
$839$	−3.44012	−	10.5876i	−0.118766	−	0.365524i	−0.992714	+	0.120496i	$0.961552\pi$
$840$		0			0
$841$	−8.63009	+	26.5607i	−0.297589	+	0.915886i
$842$		0			0
$843$	20.1054			0.692466
$844$		0			0
$845$	26.5343	−	6.56613i	0.912808	−	0.225882i
$846$		0			0
$847$	11.0803	−	8.05029i	0.380723	−	0.276611i
$848$		0			0
$849$	−20.3854			−0.699626
$850$		0			0
$851$	−15.5579			−0.533318
$852$		0			0
$853$	−20.9221	+	15.2008i	−0.716358	+	0.520464i	−0.885218	−	0.465176i	$-0.845991\pi$
$853$	−20.9221	+	15.2008i	−0.716358	+	0.520464i	0.168861	+	0.985640i	$0.445991\pi$
$854$		0			0
$855$	−1.17661	+	16.4109i	−0.0402391	+	0.561240i
$856$		0			0
$857$	−20.6374			−0.704961			−0.352481	−	0.935819i	$-0.614662\pi$
$857$	−20.6374			−0.704961			−0.352481	+	0.935819i	$0.614662\pi$
$858$		0			0
$859$	−11.1207	+	34.2261i	−0.379435	+	1.16778i	0.561003	+	0.827814i	$0.310416\pi$
$859$	−11.1207	+	34.2261i	−0.379435	+	1.16778i	−0.940438	+	0.339966i	$0.889584\pi$
$860$		0			0
$861$	−1.45230	−	4.46973i	−0.0494943	−	0.152328i
$862$		0			0
$863$	10.1995	−	31.3910i	0.347196	−	1.06856i	−0.613201	−	0.789927i	$-0.710118\pi$
$863$	10.1995	−	31.3910i	0.347196	−	1.06856i	0.960397	−	0.278634i	$-0.0898815\pi$
$864$		0			0
$865$	−33.3341	−	13.5362i	−1.13339	−	0.460245i
$866$		0			0
$867$	9.97065	+	7.24410i	0.338621	+	0.246023i
$868$		0			0
$869$	32.3113	+	23.4756i	1.09609	+	0.796354i
$870$		0			0
$871$	0.815275	−	0.592332i	0.0276245	−	0.0200704i
$872$		0			0
$873$	0.130784	+	0.402513i	0.00442638	+	0.0136230i
$874$		0			0
$875$	14.3105	+	8.36329i	0.483783	+	0.282731i
$876$		0			0
$877$	0.124205	+	0.382265i	0.00419412	+	0.0129082i	0.953132	−	0.302556i	$-0.0978399\pi$
$877$	0.124205	+	0.382265i	0.00419412	+	0.0129082i	−0.948938	+	0.315464i	$0.897840\pi$
$878$		0			0
$879$	11.5338	−	8.37978i	0.389025	−	0.282643i
$880$		0			0
$881$	22.5308	+	16.3696i	0.759081	+	0.551505i	0.898628	−	0.438711i	$-0.144565\pi$
$881$	22.5308	+	16.3696i	0.759081	+	0.551505i	−0.139547	+	0.990215i	$0.544565\pi$
$882$		0			0
$883$	−40.7739	−	29.6240i	−1.37215	−	0.996926i	−0.997566	−	0.0697337i	$-0.977785\pi$
$883$	−40.7739	−	29.6240i	−1.37215	−	0.996926i	−0.374585	−	0.927192i	$-0.622215\pi$
$884$		0			0
$885$	−14.4908	−	5.88438i	−0.487103	−	0.197801i
$886$		0			0
$887$	0.115485	−	0.355427i	0.00387761	−	0.0119341i	−0.949099	−	0.314978i	$-0.898003\pi$
$887$	0.115485	−	0.355427i	0.00387761	−	0.0119341i	0.952977	+	0.303044i	$0.0980029\pi$
$888$		0			0
$889$	−3.42563	−	10.5430i	−0.114892	−	0.353601i
$890$		0			0
$891$	−1.39017	+	4.27851i	−0.0465726	+	0.143336i
$892$		0			0
$893$	−8.23318			−0.275513
$894$		0			0
$895$	2.87179	−	40.0547i	0.0959935	−	1.33888i
$896$		0			0
$897$	−1.34618	+	0.978054i	−0.0449475	+	0.0326563i
$898$		0			0
$899$	−0.803138			−0.0267861
$900$		0			0
$901$	−5.67088			−0.188924
$902$		0			0
$903$	12.1427	−	8.82222i	0.404085	−	0.293585i
$904$		0			0
$905$	−30.1703	+	7.46588i	−1.00289	+	0.248174i
$906$		0			0
$907$	42.2714			1.40360			0.701800	−	0.712374i	$-0.252380\pi$
$907$	42.2714			1.40360			0.701800	+	0.712374i	$0.252380\pi$
$908$		0			0
$909$	2.44140	−	7.51386i	0.0809762	−	0.249219i
$910$		0			0
$911$	3.93498	+	12.1106i	0.130372	+	0.401243i	0.994841	−	0.101442i	$-0.0323457\pi$
$911$	3.93498	+	12.1106i	0.130372	+	0.401243i	−0.864470	+	0.502685i	$0.832346\pi$
$912$		0			0
$913$	16.4298	−	50.5658i	0.543748	−	1.67348i
$914$		0			0
$915$	27.3653	−	6.77177i	0.904670	−	0.223868i
$916$		0			0
$917$	−4.40793	−	3.20255i	−0.145563	−	0.105757i
$918$		0			0
$919$	−13.0136	−	9.45495i	−0.429280	−	0.311890i	0.352081	−	0.935970i	$-0.385474\pi$
$919$	−13.0136	−	9.45495i	−0.429280	−	0.311890i	−0.781361	+	0.624079i	$0.785474\pi$
$920$		0			0
$921$	−2.03908	+	1.48148i	−0.0671901	+	0.0488165i
$922$		0			0
$923$	4.02510	+	12.3880i	0.132488	+	0.407756i
$924$		0			0
$925$	−40.7494	−	5.87340i	−1.33983	−	0.193116i
$926$		0			0
$927$	4.75516	+	14.6349i	0.156180	+	0.480673i
$928$		0			0
$929$	−10.8693	+	7.89700i	−0.356610	+	0.259092i	−0.751637	−	0.659577i	$-0.770735\pi$
$929$	−10.8693	+	7.89700i	−0.356610	+	0.259092i	0.395027	+	0.918670i	$0.370735\pi$
$930$		0			0
$931$	28.5858	+	20.7688i	0.936862	+	0.680670i
$932$		0			0
$933$	13.0945	+	9.51370i	0.428694	+	0.311465i
$934$		0			0
$935$	−11.4941	−	18.4666i	−0.375896	−	0.603924i
$936$		0			0
$937$	−0.963115	+	2.96416i	−0.0314636	+	0.0968350i	−0.965555	−	0.260199i	$-0.916212\pi$
$937$	−0.963115	+	2.96416i	−0.0314636	+	0.0968350i	0.934091	+	0.357034i	$0.116212\pi$
$938$		0			0
$939$	4.41204	+	13.5789i	0.143981	+	0.443129i
$940$		0			0
$941$	1.64738	−	5.07011i	0.0537030	−	0.165281i	−0.920608	−	0.390489i	$-0.872306\pi$
$941$	1.64738	−	5.07011i	0.0537030	−	0.165281i	0.974311	+	0.225208i	$0.0723061\pi$
$942$		0			0
$943$	−5.98973			−0.195052
$944$		0			0
$945$	−3.07145	−	1.24724i	−0.0999142	−	0.0405728i
$946$		0			0
$947$	39.3236	−	28.5702i	1.27784	−	0.928408i	0.278358	−	0.960477i	$-0.410210\pi$
$947$	39.3236	−	28.5702i	1.27784	−	0.928408i	0.999486	+	0.0320693i	$0.0102097\pi$
$948$		0			0
$949$	3.48446			0.113110
$950$		0			0
$951$	−28.0271			−0.908842
$952$		0			0
$953$	18.6879	−	13.5775i	0.605360	−	0.439820i	−0.242417	−	0.970172i	$-0.577940\pi$
$953$	18.6879	−	13.5775i	0.605360	−	0.439820i	0.847777	+	0.530352i	$0.177940\pi$
$954$		0			0
$955$	−16.2343	−	26.0825i	−0.525331	−	0.844009i
$956$		0			0
$957$	4.65880			0.150598
$958$		0			0
$959$	9.08312	−	27.9550i	0.293309	−	0.902713i
$960$		0			0
$961$	−9.39367	−	28.9107i	−0.303021	−	0.932604i
$962$		0			0
$963$	0.782298	−	2.40767i	0.0252092	−	0.0775859i
$964$		0			0
$965$	−18.8410	+	22.3736i	−0.606512	+	0.720233i
$966$		0			0
$967$	7.36595	+	5.35168i	0.236873	+	0.172098i	0.699889	−	0.714252i	$-0.253233\pi$
$967$	7.36595	+	5.35168i	0.236873	+	0.172098i	−0.463016	+	0.886350i	$0.653233\pi$
$968$		0			0
$969$	12.8717	+	9.35185i	0.413499	+	0.300425i
$970$		0			0
$971$	−19.4911	+	14.1611i	−0.625498	+	0.454451i	−0.854838	−	0.518896i	$-0.826343\pi$
$971$	−19.4911	+	14.1611i	−0.625498	+	0.454451i	0.229340	+	0.973346i	$0.426343\pi$
$972$		0			0
$973$	4.78950	+	14.7406i	0.153544	+	0.472561i
$974$		0			0
$975$	−3.89515	+	2.05352i	−0.124745	+	0.0657654i
$976$		0			0
$977$	−9.27681	−	28.5511i	−0.296791	−	0.913430i	−0.982614	−	0.185661i	$-0.940557\pi$
$977$	−9.27681	−	28.5511i	−0.296791	−	0.913430i	0.685822	−	0.727769i	$-0.259443\pi$
$978$		0			0
$979$	56.2689	−	40.8818i	1.79836	−	1.30659i
$980$		0			0
$981$	4.26004	+	3.09510i	0.136012	+	0.0988189i
$982$		0			0
$983$	8.80770	+	6.39917i	0.280922	+	0.204102i	0.719319	−	0.694679i	$-0.244454\pi$
$983$	8.80770	+	6.39917i	0.280922	+	0.204102i	−0.438397	+	0.898781i	$0.644454\pi$
$984$		0			0
$985$	3.34249	−	46.6197i	0.106500	−	1.48543i
$986$		0			0
$987$	0.512616	−	1.57767i	0.0163167	−	0.0502178i
$988$		0			0
$989$	−5.91118	−	18.1927i	−0.187965	−	0.578495i
$990$		0			0
$991$	6.88482	−	21.1893i	0.218704	−	0.673101i	−0.780166	−	0.625572i	$-0.784866\pi$
$991$	6.88482	−	21.1893i	0.218704	−	0.673101i	0.998870	−	0.0475284i	$-0.0151345\pi$
$992$		0			0
$993$	−20.9471			−0.664735
$994$		0			0
$995$	−22.8769	+	27.1663i	−0.725246	+	0.861230i
$996$		0			0
$997$	−30.0870	+	21.8595i	−0.952865	+	0.692297i	−0.951483	−	0.307702i	$-0.900440\pi$
$997$	−30.0870	+	21.8595i	−0.952865	+	0.692297i	−0.00138214	+	0.999999i	$0.500440\pi$
$998$		0			0
$999$	8.23410			0.260515

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.y.c.481.3	yes	12
25.21	even	5	inner	600.2.y.c.121.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.y.c.121.3	✓	12	25.21	even	5	inner
600.2.y.c.481.3	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.y (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{3} +(1.44033 - 1.71039i) q^{5} -1.48253 q^{7} +(0.309017 - 0.951057i) q^{9} +(-1.39017 - 4.27851i) q^{11} +(-0.272140 + 0.837560i) q^{13} +(-0.159908 + 2.23034i) q^{15} +(1.74935 + 1.27098i) q^{17} +(-5.95275 - 4.32493i) q^{19} +(1.19939 - 0.871407i) q^{21} +(-0.583871 - 1.79697i) q^{23} +(-0.850891 - 4.92707i) q^{25} +(0.309017 + 0.951057i) q^{27} +(0.837809 - 0.608704i) q^{29} +(-0.627423 - 0.455850i) q^{31} +(3.63952 + 2.64427i) q^{33} +(-2.13533 + 2.53570i) q^{35} +(2.54448 - 7.83109i) q^{37} +(-0.272140 - 0.837560i) q^{39} +(0.979614 - 3.01494i) q^{41} +10.1241 q^{43} +(-1.18159 - 1.89838i) q^{45} +(0.905243 - 0.657698i) q^{47} -4.80212 q^{49} -2.16231 q^{51} +(-2.12173 + 1.54153i) q^{53} +(-9.32025 - 3.78473i) q^{55} +7.35800 q^{57} +(-2.16139 + 6.65209i) q^{59} +(-3.89586 - 11.9902i) q^{61} +(-0.458126 + 1.40997i) q^{63} +(1.04059 + 1.67183i) q^{65} +(-0.925752 - 0.672598i) q^{67} +(1.52859 + 1.11059i) q^{69} +(11.9658 - 8.69368i) q^{71} +(-1.22267 - 3.76298i) q^{73} +(3.58444 + 3.48594i) q^{75} +(2.06097 + 6.34301i) q^{77} +(-7.18238 + 5.21830i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(9.56139 + 6.94676i) q^{83} +(4.69351 - 1.16145i) q^{85} +(-0.320014 + 0.984903i) q^{87} +(4.77756 + 14.7038i) q^{89} +(0.403454 - 1.24170i) q^{91} +0.775537 q^{93} +(-15.9713 + 3.95222i) q^{95} +(-0.342398 + 0.248767i) q^{97} -4.49870 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} + 4 q^{5} - 8 q^{7} - 3 q^{9} - 4 q^{11} - 4 q^{13} - q^{15} + q^{17} - 5 q^{19} - 3 q^{21} - 21 q^{23} - 16 q^{25} - 3 q^{27} + 11 q^{29} - 19 q^{31} + 11 q^{33} + 10 q^{35} + 34 q^{37}+ \cdots - 14 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 + 4 * q^5 - 8 * q^7 - 3 * q^9 - 4 * q^11 - 4 * q^13 - q^15 + q^17 - 5 * q^19 - 3 * q^21 - 21 * q^23 - 16 * q^25 - 3 * q^27 + 11 * q^29 - 19 * q^31 + 11 * q^33 + 10 * q^35 + 34 * q^37 - 4 * q^39 - 20 * q^41 + 28 * q^43 + 4 * q^45 + 19 * q^47 + 12 * q^49 - 14 * q^51 + 8 * q^53 - q^55 - 10 * q^57 - 18 * q^59 + 10 * q^61 + 7 * q^63 + 34 * q^65 - 40 * q^67 + 24 * q^69 - 7 * q^71 + 8 * q^73 + 4 * q^75 - 11 * q^77 - 26 * q^79 - 3 * q^81 + 10 * q^83 + 41 * q^85 - 4 * q^87 + 9 * q^89 - q^91 + 6 * q^93 - 81 * q^95 - 12 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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